Subgroups — C₃×C₅×#3562 #14276596

Order 1920.

2100 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#562	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#560	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#540	C₂	1	2	yes	maximal, complemented
16	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
17	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
18	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
19	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#3562	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#127	C₂²	1	1	yes	characteristic
34	C₃×C₅×#127	C₂²	1	1	yes	characteristic
35	C₃×C₅×#127	C₂²	1	2	yes	complemented
36	C₃×C₅×#126	C₂²	1	1	yes	characteristic
37	C₃×C₅×#126	C₂²	1	2	yes	—
38	C₃×C₅×#126	C₂²	1	2	yes	—
39	C₃×C₅×#126	C₂²	1	2	yes	complemented
40	C₃×C₅×#126	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₅×#126	C₂²	1	2	yes	complemented
42	C₃×C₅×#126	C₂²	1	2	yes	complemented
43	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#125	C₂²	1	2	yes	complemented
46	C₃×C₅×#125	C₂²	1	2	yes	complemented
47	C₃×C₅×#124	C₂²	1	1	yes	characteristic
48	C₃×C₅×#124	C₂²	1	1	yes	characteristic
49	C₃×C₅×#124	C₂²	1	1	yes	characteristic
50	C₃×C₅×#124	C₂²	1	1	yes	characteristic
51	C₃×C₅×#124	C₂²	1	1	yes	characteristic
52	C₃×C₅×#124	C₂²	1	2	yes	—
53	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×#124	C₂²	1	2	yes	complemented
55	C₃×C₅×#124	C₂²	1	2	yes	complemented
56	C₃×C₅×#123	C₂²	1	1	yes	characteristic
57	C₃×C₅×#123	C₂²	1	2	yes	—
58	C₃×C₅×#123	C₂²	1	2	yes	—
59	C₃×C₅×#123	C₂²	1	2	yes	—
60	C₃×C₅×#123	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₅×#123	C₂²	1	2	yes	complemented
62	C₃×C₅×#123	C₂²	1	2	yes	complemented
63	C₃×C₅×#123	C₂²	1	2	yes	complemented
64	C₃×C₅×#123	C₂²	1	2	yes	complemented
65	C₃×C₅×#123	C₂²	1	2	yes	complemented
66	C₃×C₅×#123	C₂²	1	2	yes	complemented
67	C₃×C₅×#123	C₂²	1	2	yes	complemented
68	C₃×C₅×#123	C₂²	1	2	yes	complemented
69	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
70	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
71	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
72	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
73	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
74	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₃×C₅×#121	C₂²	1	1	yes	characteristic
79	C₃×C₅×#121	C₂²	1	1	yes	characteristic
80	C₃×C₅×#121	C₂²	1	2	yes	—
81	C₃×C₅×#121	C₂²	1	2	yes	—
82	C₃×C₅×#121	C₂²	1	2	yes	—
83	C₃×C₅×#121	C₂²	1	2	yes	—
84	C₃×C₅×#121	C₂²	1	1	yes	characteristic
85	C₃×C₅×#121	C₂²	1	2	yes	—
86	C₃×C₅×#121	C₂²	1	2	yes	—
87	C₃×C₅×#121	C₂²	1	2	yes	complemented
88	C₃×C₅×#121	C₂²	1	2	yes	complemented
89	C₃×C₅×#121	C₂²	1	2	yes	complemented
90	C₃×C₅×#121	C₂²	1	2	yes	complemented
91	C₃×C₅×#121	C₂²	1	2	yes	complemented
92	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
93	C₃×C₅×#121	C₂²	1	2	yes	complemented
94	C₃×C₅×#121	C₂²	1	2	yes	complemented
95	C₃×C₅×#120	C₂²	1	2	yes	—
96	C₃×C₅×#120	C₂²	1	2	yes	—
97	C₃×C₅×#120	C₂²	1	2	yes	—
98	C₃×C₅×#120	C₂²	1	2	yes	—
99	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
100	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
101	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
102	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
103	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
108	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
109	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
110	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
111	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
112	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
113	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
114	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
115	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
116	C₃×C₅×#117	C₂²	1	1	yes	characteristic
117	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
118	C₃×C₅×#117	C₂²	1	2	yes	complemented
119	C₃×C₅×#117	C₂²	1	2	yes	complemented
120	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
121	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
124	C₃×#3562	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
125	C₅×#562	C₂×C₃	1	2	yes	complemented
126	C₅×#560	C₂×C₃	1	2	yes	complemented
127	C₅×#559	C₂×C₃	1	1	yes	characteristic, complemented
128	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
129	C₅×#553	C₂×C₃	1	2	yes	complemented
130	C₅×#551	C₂×C₃	1	2	yes	complemented
131	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
132	C₅×#548	C₂×C₃	1	1	yes	characteristic, complemented
133	C₅×#548	C₂×C₃	1	1	yes	characteristic, complemented
134	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
135	C₅×#546	C₂×C₃	1	1	yes	characteristic, complemented
136	C₅×#546	C₂×C₃	1	1	yes	characteristic, complemented
137	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
138	C₅×#540	C₂×C₃	1	1	yes	characteristic, complemented
139	C₅×#540	C₂×C₃	1	2	yes	complemented
140	C₅×#539	C₂×C₃	1	2	yes	complemented
141	C₅×#538	C₂×C₃	1	2	yes	complemented
142	C₅×#538	C₂×C₃	1	2	yes	complemented
143	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
144	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
145	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
146	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
147	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
149	C₃×C₅×#41	—	4	2	no	—
150	C₃×C₅×#41	—	4	2	no	—
151	C₃×C₅×#41	—	4	2	no	—
152	C₃×C₅×#41	—	4	2	no	—
153	C₂×C₃×C₅×Q₈	—	4	2	no	—
154	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
159	C₂×C₃×C₅×D₄	—	4	2	no	—
160	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
166	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
167	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
168	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
169	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
170	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
171	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
172	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
174	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
175	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
176	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
177	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
178	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
179	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
180	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
181	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
182	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
183	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
184	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
185	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
186	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
187	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
188	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
189	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
190	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
191	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
199	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
202	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
208	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
209	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
210	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
211	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
212	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
214	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
215	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
245	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
246	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
247	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
248	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
249	C₃×C₄²×C₅	C₂³	1	2	yes	—
250	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
251	C₃×C₄²×C₅	C₂³	1	2	yes	—
252	C₃×C₄²×C₅	C₂³	1	2	yes	—
253	C₃×#562	C₂×C₅	1	2	yes	complemented
254	C₃×#560	C₂×C₅	1	2	yes	complemented
255	C₃×#559	C₂×C₅	1	1	yes	characteristic, complemented
256	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
257	C₃×#553	C₂×C₅	1	2	yes	complemented
258	C₃×#551	C₂×C₅	1	2	yes	complemented
259	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
260	C₃×#548	C₂×C₅	1	1	yes	characteristic, complemented
261	C₃×#548	C₂×C₅	1	1	yes	characteristic, complemented
262	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
263	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
264	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
265	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
266	C₃×#540	C₂×C₅	1	1	yes	characteristic, complemented
267	C₃×#540	C₂×C₅	1	2	yes	complemented
268	C₃×#539	C₂×C₅	1	2	yes	complemented
269	C₃×#538	C₂×C₅	1	2	yes	complemented
270	C₃×#538	C₂×C₅	1	2	yes	complemented
271	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
272	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
273	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
274	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
275	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
276	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
277	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
278	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
279	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
280	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
281	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
282	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
283	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
284	C₅×#127	C₂²×C₃	1	1	yes	characteristic
285	C₅×#127	C₂²×C₃	1	1	yes	characteristic
286	C₅×#127	C₂²×C₃	1	2	yes	complemented
287	C₅×#126	C₂²×C₃	1	1	yes	characteristic
288	C₅×#126	C₂²×C₃	1	2	yes	—
289	C₅×#126	C₂²×C₃	1	2	yes	—
290	C₅×#126	C₂²×C₃	1	2	yes	complemented
291	C₅×#126	C₂²×C₃	1	1	yes	characteristic, complemented
292	C₅×#126	C₂²×C₃	1	2	yes	complemented
293	C₅×#126	C₂²×C₃	1	2	yes	complemented
294	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
295	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₅×#125	C₂²×C₃	1	2	yes	complemented
297	C₅×#125	C₂²×C₃	1	2	yes	complemented
298	C₅×#124	C₂²×C₃	1	1	yes	characteristic
299	C₅×#124	C₂²×C₃	1	1	yes	characteristic
300	C₅×#124	C₂²×C₃	1	1	yes	characteristic
301	C₅×#124	C₂²×C₃	1	1	yes	characteristic
302	C₅×#124	C₂²×C₃	1	1	yes	characteristic
303	C₅×#124	C₂²×C₃	1	2	yes	—
304	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₅×#124	C₂²×C₃	1	2	yes	complemented
306	C₅×#124	C₂²×C₃	1	2	yes	complemented
307	C₅×#123	C₂²×C₃	1	1	yes	characteristic
308	C₅×#123	C₂²×C₃	1	2	yes	—
309	C₅×#123	C₂²×C₃	1	2	yes	—
310	C₅×#123	C₂²×C₃	1	2	yes	—
311	C₅×#123	C₂²×C₃	1	1	yes	characteristic, complemented
312	C₅×#123	C₂²×C₃	1	2	yes	complemented
313	C₅×#123	C₂²×C₃	1	2	yes	complemented
314	C₅×#123	C₂²×C₃	1	2	yes	complemented
315	C₅×#123	C₂²×C₃	1	2	yes	complemented
316	C₅×#123	C₂²×C₃	1	2	yes	complemented
317	C₅×#123	C₂²×C₃	1	2	yes	complemented
318	C₅×#123	C₂²×C₃	1	2	yes	complemented
319	C₅×#123	C₂²×C₃	1	2	yes	complemented
320	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
321	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
322	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
323	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
324	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
325	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
326	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
327	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
328	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
329	C₅×#121	C₂²×C₃	1	1	yes	characteristic
330	C₅×#121	C₂²×C₃	1	1	yes	characteristic
331	C₅×#121	C₂²×C₃	1	2	yes	—
332	C₅×#121	C₂²×C₃	1	2	yes	—
333	C₅×#121	C₂²×C₃	1	2	yes	—
334	C₅×#121	C₂²×C₃	1	2	yes	—
335	C₅×#121	C₂²×C₃	1	1	yes	characteristic
336	C₅×#121	C₂²×C₃	1	2	yes	—
337	C₅×#121	C₂²×C₃	1	2	yes	—
338	C₅×#121	C₂²×C₃	1	2	yes	complemented
339	C₅×#121	C₂²×C₃	1	2	yes	complemented
340	C₅×#121	C₂²×C₃	1	2	yes	complemented
341	C₅×#121	C₂²×C₃	1	2	yes	complemented
342	C₅×#121	C₂²×C₃	1	2	yes	complemented
343	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
344	C₅×#121	C₂²×C₃	1	2	yes	complemented
345	C₅×#121	C₂²×C₃	1	2	yes	complemented
346	C₅×#120	C₂²×C₃	1	2	yes	—
347	C₅×#120	C₂²×C₃	1	2	yes	—
348	C₅×#120	C₂²×C₃	1	2	yes	—
349	C₅×#120	C₂²×C₃	1	2	yes	—
350	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
351	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
352	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
353	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
354	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
356	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
357	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
358	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
359	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
360	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
361	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
362	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
363	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
364	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
365	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
366	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
367	C₅×#117	C₂²×C₃	1	1	yes	characteristic
368	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
369	C₅×#117	C₂²×C₃	1	2	yes	complemented
370	C₅×#117	C₂²×C₃	1	2	yes	complemented
371	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
372	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
373	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
374	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
375	#3562	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³×C₃×C₅	—	4	2	no	—
377	C₂³×C₃×C₅	—	4	2	no	—
378	C₂³×C₃×C₅	—	4	2	no	—
379	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
380	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
381	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
382	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
383	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
384	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
385	C₃×C₅×Q₈	—	2	2	no	—
386	C₃×C₅×Q₈	—	2	2	no	—
387	C₃×C₅×Q₈	—	2	2	no	—
388	C₃×C₅×Q₈	—	4	2	no	—
389	C₃×C₅×Q₈	—	4	1	no	—
390	C₃×C₅×D₄	—	2	2	no	—
391	C₃×C₅×D₄	—	2	2	no	—
392	C₃×C₅×D₄	—	2	2	no	—
393	C₃×C₅×D₄	—	4	2	no	—
394	C₃×C₅×D₄	—	4	1	no	—
395	C₃×C₅×D₄	—	4	2	no	—
396	C₃×C₅×D₄	—	4	2	no	—
397	C₃×C₅×D₄	—	4	2	no	—
398	C₃×C₅×D₄	—	4	2	no	—
399	C₃×C₅×D₄	—	4	2	no	—
400	C₃×C₅×D₄	—	4	1	no	—
401	C₃×C₅×D₄	—	4	2	no	—
402	C₃×C₅×D₄	—	4	1	no	—
403	C₃×C₅×D₄	—	4	2	no	—
404	C₃×C₅×D₄	—	4	2	no	—
405	C₃×C₅×D₄	—	4	2	no	—
406	C₃×C₅×D₄	—	4	2	no	—
407	C₃×C₅×D₄	—	4	2	no	—
408	C₂×C₃×C₄×C₅	—	2	2	no	—
409	C₂×C₃×C₄×C₅	—	2	2	no	—
410	C₂×C₃×C₄×C₅	—	2	2	no	—
411	C₂×C₃×C₄×C₅	—	4	2	no	—
412	C₂×C₃×C₄×C₅	—	4	1	no	—
413	C₂×C₃×C₄×C₅	—	4	2	no	—
414	C₂×C₃×C₄×C₅	—	4	2	no	—
415	C₂×C₃×C₄×C₅	—	4	1	no	—
416	C₂×C₃×C₄×C₅	—	4	2	no	—
417	C₂×C₃×C₄×C₅	—	4	2	no	—
418	C₂×C₃×C₄×C₅	—	4	2	no	—
419	C₂×C₃×C₄×C₅	—	4	2	no	—
420	C₂×C₃×C₄×C₅	—	4	2	no	—
421	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
422	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
423	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
424	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
425	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
426	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
427	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
428	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
429	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
430	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
431	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
432	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
433	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
434	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
435	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
436	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
437	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
438	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
439	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
440	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
441	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
442	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
443	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
444	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
445	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
446	C₃×#127	C₂²×C₅	1	1	yes	characteristic
447	C₃×#127	C₂²×C₅	1	1	yes	characteristic
448	C₃×#127	C₂²×C₅	1	2	yes	complemented
449	C₃×#126	C₂²×C₅	1	2	yes	—
450	C₃×#126	C₂²×C₅	1	1	yes	characteristic
451	C₃×#126	C₂²×C₅	1	2	yes	—
452	C₃×#126	C₂²×C₅	1	2	yes	complemented
453	C₃×#126	C₂²×C₅	1	2	yes	complemented
454	C₃×#126	C₂²×C₅	1	1	yes	characteristic, complemented
455	C₃×#126	C₂²×C₅	1	2	yes	complemented
456	C₃×#125	C₂²×C₅	1	2	yes	complemented
457	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
458	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
459	C₃×#125	C₂²×C₅	1	2	yes	complemented
460	C₃×#124	C₂²×C₅	1	1	yes	characteristic
461	C₃×#124	C₂²×C₅	1	1	yes	characteristic
462	C₃×#124	C₂²×C₅	1	1	yes	characteristic
463	C₃×#124	C₂²×C₅	1	1	yes	characteristic
464	C₃×#124	C₂²×C₅	1	1	yes	characteristic
465	C₃×#124	C₂²×C₅	1	2	yes	—
466	C₃×#124	C₂²×C₅	1	2	yes	complemented
467	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
468	C₃×#124	C₂²×C₅	1	2	yes	complemented
469	C₃×#123	C₂²×C₅	1	2	yes	—
470	C₃×#123	C₂²×C₅	1	1	yes	characteristic
471	C₃×#123	C₂²×C₅	1	2	yes	—
472	C₃×#123	C₂²×C₅	1	2	yes	—
473	C₃×#123	C₂²×C₅	1	2	yes	complemented
474	C₃×#123	C₂²×C₅	1	2	yes	complemented
475	C₃×#123	C₂²×C₅	1	2	yes	complemented
476	C₃×#123	C₂²×C₅	1	2	yes	complemented
477	C₃×#123	C₂²×C₅	1	2	yes	complemented
478	C₃×#123	C₂²×C₅	1	2	yes	complemented
479	C₃×#123	C₂²×C₅	1	1	yes	characteristic, complemented
480	C₃×#123	C₂²×C₅	1	2	yes	complemented
481	C₃×#123	C₂²×C₅	1	2	yes	complemented
482	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
483	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
484	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
485	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
486	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
487	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
488	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
489	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
490	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
491	C₃×#121	C₂²×C₅	1	1	yes	characteristic
492	C₃×#121	C₂²×C₅	1	2	yes	—
493	C₃×#121	C₂²×C₅	1	2	yes	—
494	C₃×#121	C₂²×C₅	1	2	yes	—
495	C₃×#121	C₂²×C₅	1	2	yes	—
496	C₃×#121	C₂²×C₅	1	1	yes	characteristic
497	C₃×#121	C₂²×C₅	1	2	yes	—
498	C₃×#121	C₂²×C₅	1	1	yes	characteristic
499	C₃×#121	C₂²×C₅	1	2	yes	—
500	C₃×#121	C₂²×C₅	1	2	yes	complemented
501	C₃×#121	C₂²×C₅	1	2	yes	complemented
502	C₃×#121	C₂²×C₅	1	2	yes	complemented
503	C₃×#121	C₂²×C₅	1	2	yes	complemented
504	C₃×#121	C₂²×C₅	1	2	yes	complemented
505	C₃×#121	C₂²×C₅	1	2	yes	complemented
506	C₃×#121	C₂²×C₅	1	2	yes	complemented
507	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
508	C₃×#120	C₂²×C₅	1	2	yes	—
509	C₃×#120	C₂²×C₅	1	2	yes	—
510	C₃×#120	C₂²×C₅	1	2	yes	—
511	C₃×#120	C₂²×C₅	1	2	yes	—
512	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
513	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
514	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
515	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
516	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
517	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
518	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
519	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
520	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
521	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
522	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
523	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
524	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
525	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
526	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
527	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
528	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
529	C₃×#117	C₂²×C₅	1	1	yes	characteristic
530	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
531	C₃×#117	C₂²×C₅	1	2	yes	complemented
532	C₃×#117	C₂²×C₅	1	2	yes	complemented
533	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
534	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
535	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
536	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
537	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
538	C₅×#41	—	4	2	no	—
539	C₅×#41	—	4	2	no	—
540	C₅×#41	—	4	2	no	—
541	C₅×#41	—	4	2	no	—
542	C₂×C₅×Q₈	—	4	2	no	—
543	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
548	C₂×C₅×D₄	—	4	2	no	—
549	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
555	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
556	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
557	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
558	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
559	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
560	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
561	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
563	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
564	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
565	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
566	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
567	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
568	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
569	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
570	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
571	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
572	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
573	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
574	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
575	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
576	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
577	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
578	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
579	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
580	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
581	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
582	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
583	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
584	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
585	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
586	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
587	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
588	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
589	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
590	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
591	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
592	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
593	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
594	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
595	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
596	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
597	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
598	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
599	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
600	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
601	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
602	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
603	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
604	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
605	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
606	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
607	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
608	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
609	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
610	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
611	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
612	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
613	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
614	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
615	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
616	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
617	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
618	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
619	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
620	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
621	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
622	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
623	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
624	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
625	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
626	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
627	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
628	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
629	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
630	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
631	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
632	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
633	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
634	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
635	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
636	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
637	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
638	C₄²×C₅	C₂³×C₃	1	2	yes	—
639	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
640	C₄²×C₅	C₂³×C₃	1	2	yes	—
641	C₄²×C₅	C₂³×C₃	1	2	yes	—
642	#562	C₂×C₃×C₅	1	2	yes	complemented
643	#560	C₂×C₃×C₅	1	2	yes	complemented
644	#559	C₂×C₃×C₅	1	1	yes	characteristic, complemented
645	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
646	#553	C₂×C₃×C₅	1	2	yes	complemented
647	#551	C₂×C₃×C₅	1	2	yes	complemented
648	#550	C₂×C₃×C₅	1	1	yes	characteristic, complemented
649	#548	C₂×C₃×C₅	1	1	yes	characteristic, complemented
650	#548	C₂×C₃×C₅	1	1	yes	characteristic, complemented
651	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
652	#546	C₂×C₃×C₅	1	1	yes	characteristic, complemented
653	#546	C₂×C₃×C₅	1	1	yes	characteristic, complemented
654	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
655	#540	C₂×C₃×C₅	1	1	yes	characteristic, complemented
656	#540	C₂×C₃×C₅	1	2	yes	complemented
657	#539	C₂×C₃×C₅	1	2	yes	complemented
658	#538	C₂×C₃×C₅	1	2	yes	complemented
659	#538	C₂×C₃×C₅	1	2	yes	complemented
660	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
661	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
662	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
663	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
664	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
665	C₂²×C₃×C₅	—	2	1	no	—
666	C₂²×C₃×C₅	—	2	1	no	—
667	C₂²×C₃×C₅	—	2	1	no	—
668	C₂²×C₃×C₅	—	2	2	no	—
669	C₂²×C₃×C₅	—	2	2	no	—
670	C₂²×C₃×C₅	—	2	2	no	—
671	C₂²×C₃×C₅	—	2	1	no	—
672	C₂²×C₃×C₅	—	2	1	no	—
673	C₂²×C₃×C₅	—	2	2	no	—
674	C₂²×C₃×C₅	—	2	2	no	—
675	C₂²×C₃×C₅	—	2	2	no	—
676	C₂²×C₃×C₅	—	2	1	no	—
677	C₂²×C₃×C₅	—	2	1	no	—
678	C₂²×C₃×C₅	—	2	2	no	—
679	C₂²×C₃×C₅	—	2	2	no	—
680	C₂²×C₃×C₅	—	2	2	no	—
681	C₂²×C₃×C₅	—	2	1	no	—
682	C₂²×C₃×C₅	—	2	1	no	—
683	C₂²×C₃×C₅	—	8	4	no	—
684	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
685	C₃×C₄×C₅	—	2	1	no	—
686	C₃×C₄×C₅	—	2	1	no	—
687	C₃×C₄×C₅	—	2	1	no	—
688	C₃×C₄×C₅	—	2	2	no	—
689	C₃×C₄×C₅	—	2	2	no	—
690	C₃×C₄×C₅	—	2	2	no	—
691	C₃×C₄×C₅	—	2	1	no	—
692	C₃×C₄×C₅	—	2	2	no	—
693	C₃×C₄×C₅	—	2	1	no	—
694	C₃×C₄×C₅	—	2	1	no	—
695	C₃×C₄×C₅	—	2	1	no	—
696	C₃×C₄×C₅	—	2	2	no	—
697	C₃×C₄×C₅	—	2	1	no	—
698	C₃×C₄×C₅	—	2	1	no	—
699	C₃×C₄×C₅	—	2	1	no	—
700	C₃×C₄×C₅	—	2	1	no	—
701	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
702	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
703	C₃×#41	—	4	2	no	—
704	C₃×#41	—	4	2	no	—
705	C₃×#41	—	4	2	no	—
706	C₃×#41	—	4	2	no	—
707	C₂×C₃×Q₈	—	4	2	no	—
708	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
709	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
710	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
711	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
712	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
713	C₂×C₃×D₄	—	4	2	no	—
714	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
715	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
716	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
717	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
718	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
719	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
720	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
721	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
722	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
723	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
724	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
725	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
726	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
727	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
728	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
729	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
730	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
731	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
732	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
733	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
734	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
735	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
736	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
737	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
738	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
739	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
740	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
741	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
742	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
743	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
744	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
745	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
746	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
747	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
748	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
749	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
750	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
751	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
752	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
753	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
754	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
755	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
756	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
757	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
758	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
759	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
760	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
761	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
762	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
763	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
764	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
765	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
766	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
767	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
768	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
769	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
770	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
771	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
772	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
773	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
774	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
775	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
776	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
777	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
778	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
779	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
780	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
781	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
782	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
783	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
784	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
785	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
786	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
787	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
788	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
789	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
790	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
791	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
792	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
793	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
794	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
795	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
796	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
797	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
798	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
799	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
800	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
801	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
802	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
803	C₃×C₄²	C₂³×C₅	1	2	yes	—
804	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
805	C₃×C₄²	C₂³×C₅	1	2	yes	—
806	C₃×C₄²	C₂³×C₅	1	2	yes	—
807	C₂³×C₅	—	4	2	no	—
808	C₂³×C₅	—	4	2	no	—
809	C₂³×C₅	—	4	2	no	—
810	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
811	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
812	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
813	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
814	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
815	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
816	C₅×Q₈	—	2	2	no	—
817	C₅×Q₈	—	2	2	no	—
818	C₅×Q₈	—	2	2	no	—
819	C₅×Q₈	—	4	2	no	—
820	C₅×Q₈	—	4	1	no	—
821	C₅×D₄	—	2	2	no	—
822	C₅×D₄	—	2	2	no	—
823	C₅×D₄	—	2	2	no	—
824	C₅×D₄	—	4	2	no	—
825	C₅×D₄	—	4	1	no	—
826	C₅×D₄	—	4	2	no	—
827	C₅×D₄	—	4	2	no	—
828	C₅×D₄	—	4	2	no	—
829	C₅×D₄	—	4	2	no	—
830	C₅×D₄	—	4	2	no	—
831	C₅×D₄	—	4	1	no	—
832	C₅×D₄	—	4	2	no	—
833	C₅×D₄	—	4	1	no	—
834	C₅×D₄	—	4	2	no	—
835	C₅×D₄	—	4	2	no	—
836	C₅×D₄	—	4	2	no	—
837	C₅×D₄	—	4	2	no	—
838	C₅×D₄	—	4	2	no	—
839	C₂×C₄×C₅	—	2	2	no	—
840	C₂×C₄×C₅	—	2	2	no	—
841	C₂×C₄×C₅	—	2	2	no	—
842	C₂×C₄×C₅	—	4	2	no	—
843	C₂×C₄×C₅	—	4	1	no	—
844	C₂×C₄×C₅	—	4	2	no	—
845	C₂×C₄×C₅	—	4	2	no	—
846	C₂×C₄×C₅	—	4	1	no	—
847	C₂×C₄×C₅	—	4	2	no	—
848	C₂×C₄×C₅	—	4	2	no	—
849	C₂×C₄×C₅	—	4	2	no	—
850	C₂×C₄×C₅	—	4	2	no	—
851	C₂×C₄×C₅	—	4	2	no	—
852	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
853	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
854	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
855	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
856	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
857	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
858	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
859	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
860	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
861	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
862	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
863	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
864	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
865	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
866	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
867	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
868	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
869	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
870	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
871	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
872	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
873	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
874	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
875	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
876	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
877	#127	C₂²×C₃×C₅	1	1	yes	characteristic
878	#127	C₂²×C₃×C₅	1	1	yes	characteristic
879	#127	C₂²×C₃×C₅	1	2	yes	complemented
880	#126	C₂²×C₃×C₅	1	1	yes	characteristic
881	#126	C₂²×C₃×C₅	1	2	yes	—
882	#126	C₂²×C₃×C₅	1	2	yes	—
883	#126	C₂²×C₃×C₅	1	2	yes	complemented
884	#126	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
885	#126	C₂²×C₃×C₅	1	2	yes	complemented
886	#126	C₂²×C₃×C₅	1	2	yes	complemented
887	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
888	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
889	#125	C₂²×C₃×C₅	1	2	yes	complemented
890	#125	C₂²×C₃×C₅	1	2	yes	complemented
891	#124	C₂²×C₃×C₅	1	1	yes	characteristic
892	#124	C₂²×C₃×C₅	1	1	yes	characteristic
893	#124	C₂²×C₃×C₅	1	1	yes	characteristic
894	#124	C₂²×C₃×C₅	1	1	yes	characteristic
895	#124	C₂²×C₃×C₅	1	1	yes	characteristic
896	#124	C₂²×C₃×C₅	1	2	yes	—
897	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
898	#124	C₂²×C₃×C₅	1	2	yes	complemented
899	#124	C₂²×C₃×C₅	1	2	yes	complemented
900	#123	C₂²×C₃×C₅	1	1	yes	characteristic
901	#123	C₂²×C₃×C₅	1	2	yes	—
902	#123	C₂²×C₃×C₅	1	2	yes	—
903	#123	C₂²×C₃×C₅	1	2	yes	—
904	#123	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
905	#123	C₂²×C₃×C₅	1	2	yes	complemented
906	#123	C₂²×C₃×C₅	1	2	yes	complemented
907	#123	C₂²×C₃×C₅	1	2	yes	complemented
908	#123	C₂²×C₃×C₅	1	2	yes	complemented
909	#123	C₂²×C₃×C₅	1	2	yes	complemented
910	#123	C₂²×C₃×C₅	1	2	yes	complemented
911	#123	C₂²×C₃×C₅	1	2	yes	complemented
912	#123	C₂²×C₃×C₅	1	2	yes	complemented
913	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
914	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
915	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
916	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
917	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
918	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
919	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
920	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
921	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
922	#121	C₂²×C₃×C₅	1	1	yes	characteristic
923	#121	C₂²×C₃×C₅	1	1	yes	characteristic
924	#121	C₂²×C₃×C₅	1	2	yes	—
925	#121	C₂²×C₃×C₅	1	2	yes	—
926	#121	C₂²×C₃×C₅	1	2	yes	—
927	#121	C₂²×C₃×C₅	1	2	yes	—
928	#121	C₂²×C₃×C₅	1	1	yes	characteristic
929	#121	C₂²×C₃×C₅	1	2	yes	—
930	#121	C₂²×C₃×C₅	1	2	yes	—
931	#121	C₂²×C₃×C₅	1	2	yes	complemented
932	#121	C₂²×C₃×C₅	1	2	yes	complemented
933	#121	C₂²×C₃×C₅	1	2	yes	complemented
934	#121	C₂²×C₃×C₅	1	2	yes	complemented
935	#121	C₂²×C₃×C₅	1	2	yes	complemented
936	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
937	#121	C₂²×C₃×C₅	1	2	yes	complemented
938	#121	C₂²×C₃×C₅	1	2	yes	complemented
939	#120	C₂²×C₃×C₅	1	2	yes	—
940	#120	C₂²×C₃×C₅	1	2	yes	—
941	#120	C₂²×C₃×C₅	1	2	yes	—
942	#120	C₂²×C₃×C₅	1	2	yes	—
943	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
944	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
945	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
946	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
947	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
948	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
949	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
950	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
951	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
952	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
953	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
954	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
955	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
956	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
957	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
958	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
959	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
960	#117	C₂²×C₃×C₅	1	1	yes	characteristic
961	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
962	#117	C₂²×C₃×C₅	1	2	yes	complemented
963	#117	C₂²×C₃×C₅	1	2	yes	complemented
964	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
965	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
966	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
967	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
968	C₂×C₃×C₅	—	4	1	no	—
969	C₂×C₃×C₅	—	4	1	no	—
970	C₂×C₃×C₅	—	4	2	no	—
971	C₂×C₃×C₅	—	4	2	no	—
972	C₂×C₃×C₅	—	4	2	no	—
973	C₂×C₃×C₅	—	4	1	no	—
974	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
975	C₂×C₃×C₅	#585	1	1	yes	characteristic
976	C₂×C₃×C₅	#585	1	1	yes	characteristic
977	C₂³×C₃	—	4	2	no	—
978	C₂³×C₃	—	4	2	no	—
979	C₂³×C₃	—	4	2	no	—
980	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
981	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
982	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
983	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
984	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
985	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
986	C₃×Q₈	—	2	2	no	—
987	C₃×Q₈	—	2	2	no	—
988	C₃×Q₈	—	2	2	no	—
989	C₃×Q₈	—	4	2	no	—
990	C₃×Q₈	—	4	1	no	—
991	C₃×D₄	—	2	2	no	—
992	C₃×D₄	—	2	2	no	—
993	C₃×D₄	—	2	2	no	—
994	C₃×D₄	—	4	2	no	—
995	C₃×D₄	—	4	1	no	—
996	C₃×D₄	—	4	2	no	—
997	C₃×D₄	—	4	2	no	—
998	C₃×D₄	—	4	2	no	—
999	C₃×D₄	—	4	2	no	—
1000	C₃×D₄	—	4	2	no	—
1001	C₃×D₄	—	4	1	no	—
1002	C₃×D₄	—	4	2	no	—
1003	C₃×D₄	—	4	1	no	—
1004	C₃×D₄	—	4	2	no	—
1005	C₃×D₄	—	4	2	no	—
1006	C₃×D₄	—	4	2	no	—
1007	C₃×D₄	—	4	2	no	—
1008	C₃×D₄	—	4	2	no	—
1009	C₂×C₃×C₄	—	2	2	no	—
1010	C₂×C₃×C₄	—	2	2	no	—
1011	C₂×C₃×C₄	—	2	2	no	—
1012	C₂×C₃×C₄	—	4	2	no	—
1013	C₂×C₃×C₄	—	4	1	no	—
1014	C₂×C₃×C₄	—	4	2	no	—
1015	C₂×C₃×C₄	—	4	2	no	—
1016	C₂×C₃×C₄	—	4	1	no	—
1017	C₂×C₃×C₄	—	4	2	no	—
1018	C₂×C₃×C₄	—	4	2	no	—
1019	C₂×C₃×C₄	—	4	2	no	—
1020	C₂×C₃×C₄	—	4	2	no	—
1021	C₂×C₃×C₄	—	4	2	no	—
1022	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1023	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1024	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1025	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1026	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1027	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1028	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1029	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1030	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1031	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1032	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1033	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1034	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1035	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1036	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1037	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1038	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1039	C₂²×C₅	—	2	1	no	—
1040	C₂²×C₅	—	2	1	no	—
1041	C₂²×C₅	—	2	1	no	—
1042	C₂²×C₅	—	2	2	no	—
1043	C₂²×C₅	—	2	2	no	—
1044	C₂²×C₅	—	2	2	no	—
1045	C₂²×C₅	—	2	1	no	—
1046	C₂²×C₅	—	2	1	no	—
1047	C₂²×C₅	—	2	2	no	—
1048	C₂²×C₅	—	2	2	no	—
1049	C₂²×C₅	—	2	2	no	—
1050	C₂²×C₅	—	2	1	no	—
1051	C₂²×C₅	—	2	1	no	—
1052	C₂²×C₅	—	2	2	no	—
1053	C₂²×C₅	—	2	2	no	—
1054	C₂²×C₅	—	2	2	no	—
1055	C₂²×C₅	—	2	1	no	—
1056	C₂²×C₅	—	2	1	no	—
1057	C₂²×C₅	—	8	4	no	—
1058	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
1059	C₄×C₅	—	2	1	no	—
1060	C₄×C₅	—	2	1	no	—
1061	C₄×C₅	—	2	1	no	—
1062	C₄×C₅	—	2	2	no	—
1063	C₄×C₅	—	2	2	no	—
1064	C₄×C₅	—	2	2	no	—
1065	C₄×C₅	—	2	1	no	—
1066	C₄×C₅	—	2	2	no	—
1067	C₄×C₅	—	2	1	no	—
1068	C₄×C₅	—	2	1	no	—
1069	C₄×C₅	—	2	1	no	—
1070	C₄×C₅	—	2	2	no	—
1071	C₄×C₅	—	2	1	no	—
1072	C₄×C₅	—	2	1	no	—
1073	C₄×C₅	—	2	1	no	—
1074	C₄×C₅	—	2	1	no	—
1075	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
1076	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
1077	#41	—	4	2	no	—
1078	#41	—	4	2	no	—
1079	#41	—	4	2	no	—
1080	#41	—	4	2	no	—
1081	C₂×Q₈	—	4	2	no	—
1082	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1083	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1084	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1085	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1086	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
1087	C₂×D₄	—	4	2	no	—
1088	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1089	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1090	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1091	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1092	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1093	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1094	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1095	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1096	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1097	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1098	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1099	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1100	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1101	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1102	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1103	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1104	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1105	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1106	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1107	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1108	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1109	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1110	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1111	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1112	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1113	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1114	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1115	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1116	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1117	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1118	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1119	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1120	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1121	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1122	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1123	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1124	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1125	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1126	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1127	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1128	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1129	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1130	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1131	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1132	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1133	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1134	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1135	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1136	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1137	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1138	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1139	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1140	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1141	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1142	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1143	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1144	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1145	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1146	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1147	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1148	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1149	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1150	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1151	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1152	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1153	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1154	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1155	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1156	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1157	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1158	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1159	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1160	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1161	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1162	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1163	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1164	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1165	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1166	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1167	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1168	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1169	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1170	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1171	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1172	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1173	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1174	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1175	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1176	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1177	C₄²	C₂³×C₃×C₅	1	2	yes	—
1178	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1179	C₄²	C₂³×C₃×C₅	1	2	yes	—
1180	C₄²	C₂³×C₃×C₅	1	2	yes	—
1181	C₃×C₅	#3562	1	1	yes	characteristic, direct product factor, Hall
1182	C₂²×C₃	—	2	1	no	—
1183	C₂²×C₃	—	2	1	no	—
1184	C₂²×C₃	—	2	1	no	—
1185	C₂²×C₃	—	2	2	no	—
1186	C₂²×C₃	—	2	2	no	—
1187	C₂²×C₃	—	2	2	no	—
1188	C₂²×C₃	—	2	1	no	—
1189	C₂²×C₃	—	2	1	no	—
1190	C₂²×C₃	—	2	2	no	—
1191	C₂²×C₃	—	2	2	no	—
1192	C₂²×C₃	—	2	2	no	—
1193	C₂²×C₃	—	2	1	no	—
1194	C₂²×C₃	—	2	1	no	—
1195	C₂²×C₃	—	2	2	no	—
1196	C₂²×C₃	—	2	2	no	—
1197	C₂²×C₃	—	2	2	no	—
1198	C₂²×C₃	—	2	1	no	—
1199	C₂²×C₃	—	2	1	no	—
1200	C₂²×C₃	—	8	4	no	—
1201	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1202	C₃×C₄	—	2	1	no	—
1203	C₃×C₄	—	2	1	no	—
1204	C₃×C₄	—	2	1	no	—
1205	C₃×C₄	—	2	2	no	—
1206	C₃×C₄	—	2	2	no	—
1207	C₃×C₄	—	2	2	no	—
1208	C₃×C₄	—	2	1	no	—
1209	C₃×C₄	—	2	2	no	—
1210	C₃×C₄	—	2	1	no	—
1211	C₃×C₄	—	2	1	no	—
1212	C₃×C₄	—	2	1	no	—
1213	C₃×C₄	—	2	2	no	—
1214	C₃×C₄	—	2	1	no	—
1215	C₃×C₄	—	2	1	no	—
1216	C₃×C₄	—	2	1	no	—
1217	C₃×C₄	—	2	1	no	—
1218	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1219	C₂×C₅	—	4	1	no	—
1220	C₂×C₅	—	4	2	no	—
1221	C₂×C₅	—	4	2	no	—
1222	C₂×C₅	—	4	1	no	—
1223	C₂×C₅	—	4	1	no	—
1224	C₂×C₅	—	4	2	no	—
1225	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1226	C₂×C₅	C₃×#585	1	1	yes	characteristic
1227	C₂×C₅	C₃×#585	1	1	yes	characteristic
1228	C₂³	—	4	2	no	—
1229	C₂³	—	4	2	no	—
1230	C₂³	—	4	2	no	—
1231	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1232	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1233	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1234	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1235	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1236	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1237	Q₈	—	2	2	no	—
1238	Q₈	—	2	2	no	—
1239	Q₈	—	2	2	no	—
1240	Q₈	—	4	2	no	—
1241	Q₈	—	4	1	no	—
1242	D₄	—	2	2	no	—
1243	D₄	—	2	2	no	—
1244	D₄	—	2	2	no	—
1245	D₄	—	4	2	no	—
1246	D₄	—	4	2	no	—
1247	D₄	—	4	2	no	—
1248	D₄	—	4	2	no	—
1249	D₄	—	4	2	no	—
1250	D₄	—	4	1	no	—
1251	D₄	—	4	2	no	—
1252	D₄	—	4	2	no	—
1253	D₄	—	4	2	no	—
1254	D₄	—	4	2	no	—
1255	D₄	—	4	2	no	—
1256	D₄	—	4	1	no	—
1257	D₄	—	4	2	no	—
1258	D₄	—	4	1	no	—
1259	D₄	—	4	2	no	—
1260	C₂×C₄	—	2	2	no	—
1261	C₂×C₄	—	2	2	no	—
1262	C₂×C₄	—	2	2	no	—
1263	C₂×C₄	—	4	2	no	—
1264	C₂×C₄	—	4	2	no	—
1265	C₂×C₄	—	4	2	no	—
1266	C₂×C₄	—	4	2	no	—
1267	C₂×C₄	—	4	2	no	—
1268	C₂×C₄	—	4	2	no	—
1269	C₂×C₄	—	4	1	no	—
1270	C₂×C₄	—	4	2	no	—
1271	C₂×C₄	—	4	2	no	—
1272	C₂×C₄	—	4	1	no	—
1273	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1274	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1275	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1276	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1277	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1278	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1279	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1280	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1281	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1282	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1283	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1284	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1285	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1286	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1287	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1288	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1289	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1290	C₂×C₃	—	4	1	no	—
1291	C₂×C₃	—	4	2	no	—
1292	C₂×C₃	—	4	2	no	—
1293	C₂×C₃	—	4	1	no	—
1294	C₂×C₃	—	4	1	no	—
1295	C₂×C₃	—	4	2	no	—
1296	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1297	C₂×C₃	C₅×#585	1	1	yes	characteristic
1298	C₂×C₃	C₅×#585	1	1	yes	characteristic
1299	C₅	C₃×#3562	1	1	yes	characteristic, direct product factor, Sylow
1300	C₂²	—	2	1	no	—
1301	C₂²	—	2	1	no	—
1302	C₂²	—	2	1	no	—
1303	C₂²	—	2	2	no	—
1304	C₂²	—	2	2	no	—
1305	C₂²	—	2	2	no	—
1306	C₂²	—	2	1	no	—
1307	C₂²	—	2	1	no	—
1308	C₂²	—	2	2	no	—
1309	C₂²	—	2	2	no	—
1310	C₂²	—	2	2	no	—
1311	C₂²	—	2	1	no	—
1312	C₂²	—	2	1	no	—
1313	C₂²	—	2	2	no	—
1314	C₂²	—	2	2	no	—
1315	C₂²	—	2	2	no	—
1316	C₂²	—	2	1	no	—
1317	C₂²	—	2	1	no	—
1318	C₂²	—	8	4	no	—
1319	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
1320	C₄	—	2	1	no	—
1321	C₄	—	2	1	no	—
1322	C₄	—	2	1	no	—
1323	C₄	—	2	2	no	—
1324	C₄	—	2	2	no	—
1325	C₄	—	2	2	no	—
1326	C₄	—	2	1	no	—
1327	C₄	—	2	2	no	—
1328	C₄	—	2	1	no	—
1329	C₄	—	2	1	no	—
1330	C₄	—	2	1	no	—
1331	C₄	—	2	2	no	—
1332	C₄	—	2	1	no	—
1333	C₄	—	2	1	no	—
1334	C₄	—	2	1	no	—
1335	C₄	—	2	1	no	—
1336	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
1337	C₃	C₅×#3562	1	1	yes	characteristic, direct product factor, Sylow
1338	C₂	—	4	1	no	—
1339	C₂	—	4	2	no	—
1340	C₂	—	4	2	no	—
1341	C₂	—	4	1	no	—
1342	C₂	—	4	1	no	—
1343	C₂	—	4	2	no	—
1344	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1345	C₂	C₃×C₅×#585	1	1	yes	characteristic
1346	C₂	C₃×C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×#562	C₂	semidirect
2. C₃×C₅×#560	C₂	semidirect
3. C₃×C₅×#559	C₂	semidirect
4. C₃×C₅×#556	C₂	semidirect
5. C₃×C₅×#553	C₂	semidirect
6. C₃×C₅×#551	C₂	semidirect
7. C₃×C₅×#550	C₂	semidirect
8. C₃×C₅×#548	C₂	semidirect
9. C₃×C₅×#548	C₂	semidirect
10. C₃×C₅×#547	C₂	semidirect
11. C₃×C₅×#546	C₂	semidirect
12. C₃×C₅×#546	C₂	semidirect
13. C₃×C₅×#541	C₂	semidirect
14. C₃×C₅×#540	C₂	semidirect
15. C₃×C₅×#540	C₂	semidirect
16. C₃×C₅×#539	C₂	semidirect
17. C₃×C₅×#538	C₂	semidirect
18. C₃×C₅×#538	C₂	semidirect
19. C₃×C₅×#536	C₂	semidirect
20. C₃×C₅×#535	C₂	semidirect
21. C₃×C₅×#532	C₂	semidirect
22. C₃×C₅×#529	C₂	semidirect
23. C₃×C₅×#529	C₂	semidirect
24. C₅×#3562	C₃	direct (N × H)
28. C₂×C₃×C₅×#41	C₂²	semidirect
29. C₂²×C₃×C₅×Q₈	C₂²	semidirect
31. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
32. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
35. C₃×C₅×#127	C₂²	semidirect
39. C₃×C₅×#126	C₂²	semidirect
40. C₃×C₅×#126	C₂²	semidirect
41. C₃×C₅×#126	C₂²	semidirect
42. C₃×C₅×#126	C₂²	semidirect
43. C₃×C₅×#125	C₂²	semidirect
44. C₃×C₅×#125	C₂²	semidirect
45. C₃×C₅×#125	C₂²	semidirect
46. C₃×C₅×#125	C₂²	semidirect
53. C₃×C₅×#124	C₂²	semidirect
54. C₃×C₅×#124	C₂²	semidirect
55. C₃×C₅×#124	C₂²	semidirect
60. C₃×C₅×#123	C₂²	semidirect
61. C₃×C₅×#123	C₂²	semidirect
62. C₃×C₅×#123	C₂²	semidirect
63. C₃×C₅×#123	C₂²	semidirect
64. C₃×C₅×#123	C₂²	semidirect
65. C₃×C₅×#123	C₂²	semidirect
66. C₃×C₅×#123	C₂²	semidirect
67. C₃×C₅×#123	C₂²	semidirect
68. C₃×C₅×#123	C₂²	semidirect
71. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
72. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
73. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
74. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
75. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
76. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
77. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
87. C₃×C₅×#121	C₂²	semidirect
88. C₃×C₅×#121	C₂²	semidirect
89. C₃×C₅×#121	C₂²	semidirect
90. C₃×C₅×#121	C₂²	semidirect
91. C₃×C₅×#121	C₂²	semidirect
92. C₃×C₅×#121	C₂²	semidirect
93. C₃×C₅×#121	C₂²	semidirect
94. C₃×C₅×#121	C₂²	semidirect
99. C₃×C₄×C₅×Q₈	C₂²	semidirect
100. C₃×C₄×C₅×Q₈	C₂²	semidirect
101. C₃×C₄×C₅×Q₈	C₂²	semidirect
102. C₃×C₄×C₅×Q₈	C₂²	semidirect
107. C₃×C₄×C₅×D₄	C₂²	semidirect
108. C₃×C₄×C₅×D₄	C₂²	semidirect
109. C₃×C₄×C₅×D₄	C₂²	semidirect
110. C₃×C₄×C₅×D₄	C₂²	semidirect
111. C₃×C₄×C₅×D₄	C₂²	semidirect
112. C₃×C₄×C₅×D₄	C₂²	semidirect
113. C₃×C₄×C₅×D₄	C₂²	semidirect
114. C₃×C₄×C₅×D₄	C₂²	semidirect
115. C₃×C₄×C₅×D₄	C₂²	semidirect
117. C₃×C₅×#117	C₂²	semidirect
118. C₃×C₅×#117	C₂²	semidirect
119. C₃×C₅×#117	C₂²	semidirect
120. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
123. C₂×C₃×C₄²×C₅	C₂²	semidirect
124. C₃×#3562	C₅	direct (N × H)
125. C₅×#562	C₂×C₃	semidirect
126. C₅×#560	C₂×C₃	semidirect
127. C₅×#559	C₂×C₃	semidirect
128. C₅×#556	C₂×C₃	semidirect
129. C₅×#553	C₂×C₃	semidirect
130. C₅×#551	C₂×C₃	semidirect
131. C₅×#550	C₂×C₃	semidirect
132. C₅×#548	C₂×C₃	semidirect
133. C₅×#548	C₂×C₃	semidirect
134. C₅×#547	C₂×C₃	semidirect
135. C₅×#546	C₂×C₃	semidirect
136. C₅×#546	C₂×C₃	semidirect
137. C₅×#541	C₂×C₃	semidirect
138. C₅×#540	C₂×C₃	semidirect
139. C₅×#540	C₂×C₃	semidirect
140. C₅×#539	C₂×C₃	semidirect
141. C₅×#538	C₂×C₃	semidirect
142. C₅×#538	C₂×C₃	semidirect
143. C₅×#536	C₂×C₃	semidirect
144. C₅×#535	C₂×C₃	semidirect
145. C₅×#532	C₂×C₃	semidirect
146. C₅×#529	C₂×C₃	semidirect
147. C₅×#529	C₂×C₃	semidirect
253. C₃×#562	C₂×C₅	semidirect
254. C₃×#560	C₂×C₅	semidirect
255. C₃×#559	C₂×C₅	semidirect
256. C₃×#556	C₂×C₅	semidirect
257. C₃×#553	C₂×C₅	semidirect
258. C₃×#551	C₂×C₅	semidirect
259. C₃×#550	C₂×C₅	semidirect
260. C₃×#548	C₂×C₅	semidirect
261. C₃×#548	C₂×C₅	semidirect
262. C₃×#547	C₂×C₅	semidirect
263. C₃×#546	C₂×C₅	semidirect
264. C₃×#546	C₂×C₅	semidirect
265. C₃×#541	C₂×C₅	semidirect
266. C₃×#540	C₂×C₅	semidirect
267. C₃×#540	C₂×C₅	semidirect
268. C₃×#539	C₂×C₅	semidirect
269. C₃×#538	C₂×C₅	semidirect
270. C₃×#538	C₂×C₅	semidirect
271. C₃×#536	C₂×C₅	semidirect
272. C₃×#535	C₂×C₅	semidirect
273. C₃×#532	C₂×C₅	semidirect
274. C₃×#529	C₂×C₅	semidirect
275. C₃×#529	C₂×C₅	semidirect
279. C₂×C₅×#41	C₂²×C₃	semidirect
280. C₂²×C₅×Q₈	C₂²×C₃	semidirect
282. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
283. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
286. C₅×#127	C₂²×C₃	semidirect
290. C₅×#126	C₂²×C₃	semidirect
291. C₅×#126	C₂²×C₃	semidirect
292. C₅×#126	C₂²×C₃	semidirect
293. C₅×#126	C₂²×C₃	semidirect
294. C₅×#125	C₂²×C₃	semidirect
295. C₅×#125	C₂²×C₃	semidirect
296. C₅×#125	C₂²×C₃	semidirect
297. C₅×#125	C₂²×C₃	semidirect
304. C₅×#124	C₂²×C₃	semidirect
305. C₅×#124	C₂²×C₃	semidirect
306. C₅×#124	C₂²×C₃	semidirect
311. C₅×#123	C₂²×C₃	semidirect
312. C₅×#123	C₂²×C₃	semidirect
313. C₅×#123	C₂²×C₃	semidirect
314. C₅×#123	C₂²×C₃	semidirect
315. C₅×#123	C₂²×C₃	semidirect
316. C₅×#123	C₂²×C₃	semidirect
317. C₅×#123	C₂²×C₃	semidirect
318. C₅×#123	C₂²×C₃	semidirect
319. C₅×#123	C₂²×C₃	semidirect
322. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
323. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
324. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
325. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
326. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
327. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
328. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
338. C₅×#121	C₂²×C₃	semidirect
339. C₅×#121	C₂²×C₃	semidirect
340. C₅×#121	C₂²×C₃	semidirect
341. C₅×#121	C₂²×C₃	semidirect
342. C₅×#121	C₂²×C₃	semidirect
343. C₅×#121	C₂²×C₃	semidirect
344. C₅×#121	C₂²×C₃	semidirect
345. C₅×#121	C₂²×C₃	semidirect
350. C₄×C₅×Q₈	C₂²×C₃	semidirect
351. C₄×C₅×Q₈	C₂²×C₃	semidirect
352. C₄×C₅×Q₈	C₂²×C₃	semidirect
353. C₄×C₅×Q₈	C₂²×C₃	semidirect
358. C₄×C₅×D₄	C₂²×C₃	semidirect
359. C₄×C₅×D₄	C₂²×C₃	semidirect
360. C₄×C₅×D₄	C₂²×C₃	semidirect
361. C₄×C₅×D₄	C₂²×C₃	semidirect
362. C₄×C₅×D₄	C₂²×C₃	semidirect
363. C₄×C₅×D₄	C₂²×C₃	semidirect
364. C₄×C₅×D₄	C₂²×C₃	semidirect
365. C₄×C₅×D₄	C₂²×C₃	semidirect
366. C₄×C₅×D₄	C₂²×C₃	semidirect
368. C₅×#117	C₂²×C₃	semidirect
369. C₅×#117	C₂²×C₃	semidirect
370. C₅×#117	C₂²×C₃	semidirect
371. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
374. C₂×C₄²×C₅	C₂²×C₃	semidirect
375. #3562	C₃×C₅	direct (N × H)
441. C₂×C₃×#41	C₂²×C₅	semidirect
442. C₂²×C₃×Q₈	C₂²×C₅	semidirect
444. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
445. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
448. C₃×#127	C₂²×C₅	semidirect
452. C₃×#126	C₂²×C₅	semidirect
453. C₃×#126	C₂²×C₅	semidirect
454. C₃×#126	C₂²×C₅	semidirect
455. C₃×#126	C₂²×C₅	semidirect
456. C₃×#125	C₂²×C₅	semidirect
457. C₃×#125	C₂²×C₅	semidirect
458. C₃×#125	C₂²×C₅	semidirect
459. C₃×#125	C₂²×C₅	semidirect
466. C₃×#124	C₂²×C₅	semidirect
467. C₃×#124	C₂²×C₅	semidirect
468. C₃×#124	C₂²×C₅	semidirect
473. C₃×#123	C₂²×C₅	semidirect
474. C₃×#123	C₂²×C₅	semidirect
475. C₃×#123	C₂²×C₅	semidirect
476. C₃×#123	C₂²×C₅	semidirect
477. C₃×#123	C₂²×C₅	semidirect
478. C₃×#123	C₂²×C₅	semidirect
479. C₃×#123	C₂²×C₅	semidirect
480. C₃×#123	C₂²×C₅	semidirect
481. C₃×#123	C₂²×C₅	semidirect
484. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
485. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
486. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
487. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
488. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
489. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
490. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
500. C₃×#121	C₂²×C₅	semidirect
501. C₃×#121	C₂²×C₅	semidirect
502. C₃×#121	C₂²×C₅	semidirect
503. C₃×#121	C₂²×C₅	semidirect
504. C₃×#121	C₂²×C₅	semidirect
505. C₃×#121	C₂²×C₅	semidirect
506. C₃×#121	C₂²×C₅	semidirect
507. C₃×#121	C₂²×C₅	semidirect
512. C₃×C₄×Q₈	C₂²×C₅	semidirect
513. C₃×C₄×Q₈	C₂²×C₅	semidirect
514. C₃×C₄×Q₈	C₂²×C₅	semidirect
515. C₃×C₄×Q₈	C₂²×C₅	semidirect
520. C₃×C₄×D₄	C₂²×C₅	semidirect
521. C₃×C₄×D₄	C₂²×C₅	semidirect
522. C₃×C₄×D₄	C₂²×C₅	semidirect
523. C₃×C₄×D₄	C₂²×C₅	semidirect
524. C₃×C₄×D₄	C₂²×C₅	semidirect
525. C₃×C₄×D₄	C₂²×C₅	semidirect
526. C₃×C₄×D₄	C₂²×C₅	semidirect
527. C₃×C₄×D₄	C₂²×C₅	semidirect
528. C₃×C₄×D₄	C₂²×C₅	semidirect
530. C₃×#117	C₂²×C₅	semidirect
531. C₃×#117	C₂²×C₅	semidirect
532. C₃×#117	C₂²×C₅	semidirect
533. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
536. C₂×C₃×C₄²	C₂²×C₅	semidirect
642. #562	C₂×C₃×C₅	semidirect
643. #560	C₂×C₃×C₅	semidirect
644. #559	C₂×C₃×C₅	semidirect
645. #556	C₂×C₃×C₅	semidirect
646. #553	C₂×C₃×C₅	semidirect
647. #551	C₂×C₃×C₅	semidirect
648. #550	C₂×C₃×C₅	semidirect
649. #548	C₂×C₃×C₅	semidirect
650. #548	C₂×C₃×C₅	semidirect
651. #547	C₂×C₃×C₅	semidirect
652. #546	C₂×C₃×C₅	semidirect
653. #546	C₂×C₃×C₅	semidirect
654. #541	C₂×C₃×C₅	semidirect
655. #540	C₂×C₃×C₅	semidirect
656. #540	C₂×C₃×C₅	semidirect
657. #539	C₂×C₃×C₅	semidirect
658. #538	C₂×C₃×C₅	semidirect
659. #538	C₂×C₃×C₅	semidirect
660. #536	C₂×C₃×C₅	semidirect
661. #535	C₂×C₃×C₅	semidirect
662. #532	C₂×C₃×C₅	semidirect
663. #529	C₂×C₃×C₅	semidirect
664. #529	C₂×C₃×C₅	semidirect
872. C₂×#41	C₂²×C₃×C₅	semidirect
873. C₂²×Q₈	C₂²×C₃×C₅	semidirect
875. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
876. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
879. #127	C₂²×C₃×C₅	semidirect
883. #126	C₂²×C₃×C₅	semidirect
884. #126	C₂²×C₃×C₅	semidirect
885. #126	C₂²×C₃×C₅	semidirect
886. #126	C₂²×C₃×C₅	semidirect
887. #125	C₂²×C₃×C₅	semidirect
888. #125	C₂²×C₃×C₅	semidirect
889. #125	C₂²×C₃×C₅	semidirect
890. #125	C₂²×C₃×C₅	semidirect
897. #124	C₂²×C₃×C₅	semidirect
898. #124	C₂²×C₃×C₅	semidirect
899. #124	C₂²×C₃×C₅	semidirect
904. #123	C₂²×C₃×C₅	semidirect
905. #123	C₂²×C₃×C₅	semidirect
906. #123	C₂²×C₃×C₅	semidirect
907. #123	C₂²×C₃×C₅	semidirect
908. #123	C₂²×C₃×C₅	semidirect
909. #123	C₂²×C₃×C₅	semidirect
910. #123	C₂²×C₃×C₅	semidirect
911. #123	C₂²×C₃×C₅	semidirect
912. #123	C₂²×C₃×C₅	semidirect
915. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
916. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
917. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
918. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
919. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
920. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
921. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
931. #121	C₂²×C₃×C₅	semidirect
932. #121	C₂²×C₃×C₅	semidirect
933. #121	C₂²×C₃×C₅	semidirect
934. #121	C₂²×C₃×C₅	semidirect
935. #121	C₂²×C₃×C₅	semidirect
936. #121	C₂²×C₃×C₅	semidirect
937. #121	C₂²×C₃×C₅	semidirect
938. #121	C₂²×C₃×C₅	semidirect
943. C₄×Q₈	C₂²×C₃×C₅	semidirect
944. C₄×Q₈	C₂²×C₃×C₅	semidirect
945. C₄×Q₈	C₂²×C₃×C₅	semidirect
946. C₄×Q₈	C₂²×C₃×C₅	semidirect
951. C₄×D₄	C₂²×C₃×C₅	semidirect
952. C₄×D₄	C₂²×C₃×C₅	semidirect
953. C₄×D₄	C₂²×C₃×C₅	semidirect
954. C₄×D₄	C₂²×C₃×C₅	semidirect
955. C₄×D₄	C₂²×C₃×C₅	semidirect
956. C₄×D₄	C₂²×C₃×C₅	semidirect
957. C₄×D₄	C₂²×C₃×C₅	semidirect
958. C₄×D₄	C₂²×C₃×C₅	semidirect
959. C₄×D₄	C₂²×C₃×C₅	semidirect
961. #117	C₂²×C₃×C₅	semidirect
962. #117	C₂²×C₃×C₅	semidirect
963. #117	C₂²×C₃×C₅	semidirect
964. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
967. C₂×C₄²	C₂²×C₃×C₅	semidirect
1181. C₃×C₅	#3562	direct (N × H)
1299. C₅	C₃×#3562	direct (N × H)
1337. C₃	C₅×#3562	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#562	2
C₃×C₅×#560	2
C₃×C₅×#559	2
C₃×C₅×#556	2
C₃×C₅×#553	2
C₃×C₅×#551	2
C₃×C₅×#550	2
C₃×C₅×#548	2
C₃×C₅×#547	2
C₃×C₅×#546	2
C₃×C₅×#541	2
C₃×C₅×#540	2
C₃×C₅×#539	2
C₃×C₅×#538	2
C₃×C₅×#536	2
C₃×C₅×#535	2
C₃×C₅×#532	2
C₃×C₅×#529	2
C₅×#3562	3
C₃×#3562	5

Subgroups — C3×C5×#3562 #14276596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3562 #14276596