Subgroups — C₃×C₅×#3541 #14276575

Order 1920.

2064 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#563	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#562	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#554	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#553	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#548	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
15	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, 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×#537	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#3541	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, complemented
28	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
34	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#126	C₂²	1	2	yes	—
36	C₃×C₅×#126	C₂²	1	2	yes	—
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	2	yes	complemented
41	C₃×C₅×#126	C₂²	1	2	yes	complemented
42	C₃×C₅×#125	C₂²	1	2	yes	complemented
43	C₃×C₅×#125	C₂²	1	2	yes	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	2	yes	—
48	C₃×C₅×#124	C₂²	1	2	yes	—
49	C₃×C₅×#124	C₂²	1	2	yes	—
50	C₃×C₅×#124	C₂²	1	2	yes	—
51	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#124	C₂²	1	2	yes	complemented
53	C₃×C₅×#123	C₂²	1	1	yes	characteristic
54	C₃×C₅×#123	C₂²	1	1	yes	characteristic
55	C₃×C₅×#123	C₂²	1	2	yes	—
56	C₃×C₅×#123	C₂²	1	2	yes	—
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	2	yes	complemented
61	C₃×C₅×#123	C₂²	1	2	yes	complemented
62	C₃×C₅×#123	C₂²	1	2	yes	complemented
63	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
64	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
65	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
66	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
67	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
68	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
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
72	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
73	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
74	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
75	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
77	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
78	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
79	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
80	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
81	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
82	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
83	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
84	C₃×C₅×#121	C₂²	1	1	yes	characteristic
85	C₃×C₅×#121	C₂²	1	1	yes	characteristic
86	C₃×C₅×#121	C₂²	1	1	yes	characteristic
87	C₃×C₅×#121	C₂²	1	1	yes	characteristic
88	C₃×C₅×#121	C₂²	1	2	yes	—
89	C₃×C₅×#121	C₂²	1	2	yes	—
90	C₃×C₅×#121	C₂²	1	2	yes	—
91	C₃×C₅×#121	C₂²	1	2	yes	—
92	C₃×C₅×#121	C₂²	1	2	yes	—
93	C₃×C₅×#121	C₂²	1	2	yes	—
94	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
95	C₃×C₅×#121	C₂²	1	2	yes	complemented
96	C₃×C₅×#120	C₂²	1	1	yes	characteristic
97	C₃×C₅×#120	C₂²	1	2	yes	—
98	C₃×C₅×#120	C₂²	1	1	yes	characteristic
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	2	yes	complemented
103	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
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	1	yes	characteristic
108	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
109	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
110	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
111	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
112	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
113	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
114	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
115	C₃×C₅×#117	C₂²	1	1	yes	characteristic
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	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
121	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
123	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
124	C₃×#3541	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
125	C₅×#563	C₂×C₃	1	2	yes	complemented
126	C₅×#562	C₂×C₃	1	2	yes	complemented
127	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
128	C₅×#554	C₂×C₃	1	1	yes	characteristic, complemented
129	C₅×#554	C₂×C₃	1	2	yes	complemented
130	C₅×#553	C₂×C₃	1	1	yes	characteristic, complemented
131	C₅×#553	C₂×C₃	1	2	yes	complemented
132	C₅×#552	C₂×C₃	1	1	yes	characteristic, complemented
133	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
134	C₅×#548	C₂×C₃	1	1	yes	characteristic, complemented
135	C₅×#548	C₂×C₃	1	1	yes	characteristic, complemented
136	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
137	C₅×#542	C₂×C₃	1	1	yes	characteristic, complemented
138	C₅×#542	C₂×C₃	1	2	yes	complemented
139	C₅×#541	C₂×C₃	1	1	yes	characteristic, 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×#537	C₂×C₃	1	1	yes	characteristic, complemented
144	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
145	C₅×#525	C₂×C₃	1	1	yes	characteristic, complemented
146	C₅×#525	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
149	C₃×C₅×#41	—	4	2	no	—
150	C₃×C₅×#41	—	4	2	no	—
151	C₃×C₅×#41	—	4	2	no	—
152	C₂×C₃×C₅×Q₈	—	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	2	yes	—
158	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
159	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
160	C₂×C₃×C₅×Q₈	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	2	yes	—
164	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
167	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
169	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
171	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
173	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
174	C₂²×C₃×C₄×C₅	—	4	2	no	—
175	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
176	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
177	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
181	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	1	yes	characteristic
188	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
189	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
190	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
197	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
206	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
211	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
212	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
213	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
214	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
215	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
216	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
217	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
218	C₃×C₅×C₄⋊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	2	yes	—
225	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
227	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
240	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
246	C₃×C₄²×C₅	C₂³	1	2	yes	—
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	2	yes	—
251	C₃×C₄²×C₅	C₂³	1	2	yes	—
252	C₃×C₄²×C₅	C₂³	1	2	yes	—
253	C₃×#563	C₂×C₅	1	2	yes	complemented
254	C₃×#562	C₂×C₅	1	2	yes	complemented
255	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
256	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
257	C₃×#554	C₂×C₅	1	2	yes	complemented
258	C₃×#553	C₂×C₅	1	1	yes	characteristic, complemented
259	C₃×#553	C₂×C₅	1	2	yes	complemented
260	C₃×#552	C₂×C₅	1	1	yes	characteristic, complemented
261	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
262	C₃×#548	C₂×C₅	1	1	yes	characteristic, complemented
263	C₃×#548	C₂×C₅	1	1	yes	characteristic, complemented
264	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
265	C₃×#542	C₂×C₅	1	1	yes	characteristic, complemented
266	C₃×#542	C₂×C₅	1	2	yes	complemented
267	C₃×#541	C₂×C₅	1	1	yes	characteristic, 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×#537	C₂×C₅	1	1	yes	characteristic, complemented
272	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
273	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
274	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
275	C₂×C₃×C₂²⋊Q₈	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, complemented
279	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
280	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
281	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
282	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
283	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
284	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
285	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₅×#126	C₂²×C₃	1	2	yes	—
287	C₅×#126	C₂²×C₃	1	2	yes	—
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	2	yes	complemented
292	C₅×#126	C₂²×C₃	1	2	yes	complemented
293	C₅×#125	C₂²×C₃	1	2	yes	complemented
294	C₅×#125	C₂²×C₃	1	2	yes	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	2	yes	—
299	C₅×#124	C₂²×C₃	1	2	yes	—
300	C₅×#124	C₂²×C₃	1	2	yes	—
301	C₅×#124	C₂²×C₃	1	2	yes	—
302	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
303	C₅×#124	C₂²×C₃	1	2	yes	complemented
304	C₅×#123	C₂²×C₃	1	1	yes	characteristic
305	C₅×#123	C₂²×C₃	1	1	yes	characteristic
306	C₅×#123	C₂²×C₃	1	2	yes	—
307	C₅×#123	C₂²×C₃	1	2	yes	—
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	2	yes	complemented
312	C₅×#123	C₂²×C₃	1	2	yes	complemented
313	C₅×#123	C₂²×C₃	1	2	yes	complemented
314	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
315	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
316	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
317	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
318	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
319	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
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
323	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
324	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
325	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
326	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
328	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
329	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
330	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
331	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
332	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
333	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
334	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
335	C₅×#121	C₂²×C₃	1	1	yes	characteristic
336	C₅×#121	C₂²×C₃	1	1	yes	characteristic
337	C₅×#121	C₂²×C₃	1	1	yes	characteristic
338	C₅×#121	C₂²×C₃	1	1	yes	characteristic
339	C₅×#121	C₂²×C₃	1	2	yes	—
340	C₅×#121	C₂²×C₃	1	2	yes	—
341	C₅×#121	C₂²×C₃	1	2	yes	—
342	C₅×#121	C₂²×C₃	1	2	yes	—
343	C₅×#121	C₂²×C₃	1	2	yes	—
344	C₅×#121	C₂²×C₃	1	2	yes	—
345	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
346	C₅×#121	C₂²×C₃	1	2	yes	complemented
347	C₅×#120	C₂²×C₃	1	1	yes	characteristic
348	C₅×#120	C₂²×C₃	1	2	yes	—
349	C₅×#120	C₂²×C₃	1	1	yes	characteristic
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	2	yes	complemented
354	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
359	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
360	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
361	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
362	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
363	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
364	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
365	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
366	C₅×#117	C₂²×C₃	1	1	yes	characteristic
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	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
371	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
372	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
373	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
374	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
375	#3541	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³×C₃×C₅	—	2	2	no	—
377	C₂³×C₃×C₅	—	4	1	no	—
378	C₂³×C₃×C₅	—	4	1	no	—
379	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
380	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
381	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
382	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
383	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
384	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
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	2	no	—
390	C₃×C₅×Q₈	—	4	2	no	—
391	C₃×C₅×Q₈	—	4	1	no	—
392	C₃×C₅×D₄	—	2	2	no	—
393	C₃×C₅×D₄	—	2	2	no	—
394	C₃×C₅×D₄	—	2	4	no	—
395	C₃×C₅×D₄	—	2	2	no	—
396	C₃×C₅×D₄	—	4	1	no	—
397	C₃×C₅×D₄	—	4	2	no	—
398	C₃×C₅×D₄	—	4	2	no	—
399	C₃×C₅×D₄	—	4	1	no	—
400	C₃×C₅×D₄	—	4	1	no	—
401	C₃×C₅×D₄	—	4	1	no	—
402	C₃×C₅×D₄	—	4	1	no	—
403	C₃×C₅×D₄	—	4	2	no	—
404	C₃×C₅×D₄	—	4	2	no	—
405	C₂×C₃×C₄×C₅	—	2	2	no	—
406	C₂×C₃×C₄×C₅	—	2	2	no	—
407	C₂×C₃×C₄×C₅	—	2	2	no	—
408	C₂×C₃×C₄×C₅	—	2	2	no	—
409	C₂×C₃×C₄×C₅	—	2	2	no	—
410	C₂×C₃×C₄×C₅	—	4	1	no	—
411	C₂×C₃×C₄×C₅	—	4	1	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	2	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	C₂⁴	1	2	yes	—
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	2	yes	—
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	2	yes	—
429	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
430	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
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	1	yes	characteristic
434	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
435	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
436	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
437	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
438	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
439	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
440	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
441	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
442	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
443	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
444	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
445	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
446	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
447	C₃×#126	C₂²×C₅	1	2	yes	—
448	C₃×#126	C₂²×C₅	1	2	yes	—
449	C₃×#126	C₂²×C₅	1	2	yes	—
450	C₃×#126	C₂²×C₅	1	2	yes	—
451	C₃×#126	C₂²×C₅	1	2	yes	complemented
452	C₃×#126	C₂²×C₅	1	2	yes	complemented
453	C₃×#126	C₂²×C₅	1	2	yes	complemented
454	C₃×#125	C₂²×C₅	1	2	yes	complemented
455	C₃×#125	C₂²×C₅	1	2	yes	complemented
456	C₃×#125	C₂²×C₅	1	2	yes	complemented
457	C₃×#125	C₂²×C₅	1	2	yes	complemented
458	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
459	C₃×#124	C₂²×C₅	1	2	yes	—
460	C₃×#124	C₂²×C₅	1	2	yes	—
461	C₃×#124	C₂²×C₅	1	2	yes	—
462	C₃×#124	C₂²×C₅	1	2	yes	—
463	C₃×#124	C₂²×C₅	1	2	yes	complemented
464	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
465	C₃×#123	C₂²×C₅	1	2	yes	—
466	C₃×#123	C₂²×C₅	1	2	yes	—
467	C₃×#123	C₂²×C₅	1	2	yes	—
468	C₃×#123	C₂²×C₅	1	1	yes	characteristic
469	C₃×#123	C₂²×C₅	1	1	yes	characteristic
470	C₃×#123	C₂²×C₅	1	2	yes	—
471	C₃×#123	C₂²×C₅	1	2	yes	—
472	C₃×#123	C₂²×C₅	1	2	yes	complemented
473	C₃×#123	C₂²×C₅	1	2	yes	complemented
474	C₃×#123	C₂²×C₅	1	2	yes	complemented
475	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
476	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
477	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
478	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
479	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
480	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
481	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
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
485	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
486	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
487	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
488	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
489	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
490	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
491	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
492	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
493	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
494	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
495	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
496	C₃×#121	C₂²×C₅	1	1	yes	characteristic
497	C₃×#121	C₂²×C₅	1	2	yes	—
498	C₃×#121	C₂²×C₅	1	2	yes	—
499	C₃×#121	C₂²×C₅	1	1	yes	characteristic
500	C₃×#121	C₂²×C₅	1	1	yes	characteristic
501	C₃×#121	C₂²×C₅	1	1	yes	characteristic
502	C₃×#121	C₂²×C₅	1	2	yes	—
503	C₃×#121	C₂²×C₅	1	2	yes	—
504	C₃×#121	C₂²×C₅	1	2	yes	—
505	C₃×#121	C₂²×C₅	1	2	yes	—
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	1	yes	characteristic
509	C₃×#120	C₂²×C₅	1	2	yes	—
510	C₃×#120	C₂²×C₅	1	1	yes	characteristic
511	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
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	2	yes	complemented
515	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
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	—
521	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
522	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
523	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
524	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
525	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
526	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
527	C₃×#117	C₂²×C₅	1	1	yes	characteristic
528	C₃×#117	C₂²×C₅	1	1	yes	characteristic
529	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
530	C₃×#117	C₂²×C₅	1	2	yes	complemented
531	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
532	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
533	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
534	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
535	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
536	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
537	C₅×#41	—	4	2	no	—
538	C₅×#41	—	4	2	no	—
539	C₅×#41	—	4	2	no	—
540	C₂×C₅×Q₈	—	4	2	no	—
541	C₂×C₅×Q₈	—	4	2	no	—
542	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
546	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
547	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
556	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
557	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
559	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
561	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
562	C₂²×C₄×C₅	—	4	2	no	—
563	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
564	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
565	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
566	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
567	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
568	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
569	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
570	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
571	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
576	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
577	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
578	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
580	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
581	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
589	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
590	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
602	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
603	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
604	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
605	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
606	C₅×C₄⋊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	1	yes	characteristic
612	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
613	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
614	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
615	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
616	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
617	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
618	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
619	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
620	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
621	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
622	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
623	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
628	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
629	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
630	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
631	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
632	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
633	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
634	C₄²×C₅	C₂³×C₃	1	2	yes	—
635	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
636	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
637	C₄²×C₅	C₂³×C₃	1	2	yes	—
638	C₄²×C₅	C₂³×C₃	1	2	yes	—
639	C₄²×C₅	C₂³×C₃	1	2	yes	—
640	C₄²×C₅	C₂³×C₃	1	2	yes	—
641	#563	C₂×C₃×C₅	1	2	yes	complemented
642	#562	C₂×C₃×C₅	1	2	yes	complemented
643	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
644	#554	C₂×C₃×C₅	1	1	yes	characteristic, complemented
645	#554	C₂×C₃×C₅	1	2	yes	complemented
646	#553	C₂×C₃×C₅	1	1	yes	characteristic, complemented
647	#553	C₂×C₃×C₅	1	2	yes	complemented
648	#552	C₂×C₃×C₅	1	1	yes	characteristic, complemented
649	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
650	#548	C₂×C₃×C₅	1	1	yes	characteristic, complemented
651	#548	C₂×C₃×C₅	1	1	yes	characteristic, complemented
652	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
653	#542	C₂×C₃×C₅	1	1	yes	characteristic, complemented
654	#542	C₂×C₃×C₅	1	2	yes	complemented
655	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
656	#539	C₂×C₃×C₅	1	2	yes	complemented
657	#538	C₂×C₃×C₅	1	2	yes	complemented
658	#538	C₂×C₃×C₅	1	2	yes	complemented
659	#537	C₂×C₃×C₅	1	1	yes	characteristic, complemented
660	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
661	#525	C₂×C₃×C₅	1	1	yes	characteristic, complemented
662	#525	C₂×C₃×C₅	1	1	yes	characteristic, complemented
663	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
664	C₂²×C₃×C₅	—	2	1	no	—
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	1	no	—
669	C₂²×C₃×C₅	—	2	1	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	1	no	—
675	C₂²×C₃×C₅	—	2	1	no	—
676	C₂²×C₃×C₅	—	2	1	no	—
677	C₂²×C₃×C₅	—	2	2	no	—
678	C₂²×C₃×C₅	—	2	1	no	—
679	C₂²×C₃×C₅	—	2	1	no	—
680	C₂²×C₃×C₅	—	2	1	no	—
681	C₂²×C₃×C₅	—	4	4	no	—
682	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
683	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
684	C₃×C₄×C₅	—	2	1	no	—
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	1	no	—
689	C₃×C₄×C₅	—	2	2	no	—
690	C₃×C₄×C₅	—	2	2	no	—
691	C₃×C₄×C₅	—	2	2	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	2	no	—
696	C₃×C₄×C₅	—	2	1	no	—
697	C₃×C₄×C₅	—	2	2	no	—
698	C₃×C₄×C₅	—	2	2	no	—
699	C₃×C₄×C₅	—	2	1	no	—
700	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
701	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
702	C₃×#41	—	4	2	no	—
703	C₃×#41	—	4	2	no	—
704	C₃×#41	—	4	2	no	—
705	C₂×C₃×Q₈	—	4	2	no	—
706	C₂×C₃×Q₈	—	4	2	no	—
707	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
711	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
712	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
713	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
721	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
722	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
723	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
724	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
725	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
726	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
727	C₂²×C₃×C₄	—	4	2	no	—
728	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
729	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
730	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
731	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
732	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
733	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
734	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
735	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
736	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
741	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
742	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
743	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
744	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
745	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
746	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
754	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
755	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
767	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
768	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
769	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
770	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
771	C₃×C₄⋊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	1	yes	characteristic
777	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
778	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
779	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
780	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
781	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
782	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
783	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
784	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
785	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
786	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
787	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
788	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
793	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
794	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
795	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
796	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
797	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
798	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
799	C₃×C₄²	C₂³×C₅	1	2	yes	—
800	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
801	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
802	C₃×C₄²	C₂³×C₅	1	2	yes	—
803	C₃×C₄²	C₂³×C₅	1	2	yes	—
804	C₃×C₄²	C₂³×C₅	1	2	yes	—
805	C₃×C₄²	C₂³×C₅	1	2	yes	—
806	C₂³×C₅	—	2	2	no	—
807	C₂³×C₅	—	4	1	no	—
808	C₂³×C₅	—	4	1	no	—
809	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
810	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
811	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
812	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
813	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
814	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
815	C₅×Q₈	—	2	2	no	—
816	C₅×Q₈	—	2	2	no	—
817	C₅×Q₈	—	2	2	no	—
818	C₅×Q₈	—	4	2	no	—
819	C₅×Q₈	—	4	2	no	—
820	C₅×Q₈	—	4	2	no	—
821	C₅×Q₈	—	4	1	no	—
822	C₅×D₄	—	2	2	no	—
823	C₅×D₄	—	2	2	no	—
824	C₅×D₄	—	2	4	no	—
825	C₅×D₄	—	2	2	no	—
826	C₅×D₄	—	4	1	no	—
827	C₅×D₄	—	4	2	no	—
828	C₅×D₄	—	4	2	no	—
829	C₅×D₄	—	4	1	no	—
830	C₅×D₄	—	4	1	no	—
831	C₅×D₄	—	4	1	no	—
832	C₅×D₄	—	4	1	no	—
833	C₅×D₄	—	4	2	no	—
834	C₅×D₄	—	4	2	no	—
835	C₂×C₄×C₅	—	2	2	no	—
836	C₂×C₄×C₅	—	2	2	no	—
837	C₂×C₄×C₅	—	2	2	no	—
838	C₂×C₄×C₅	—	2	2	no	—
839	C₂×C₄×C₅	—	2	2	no	—
840	C₂×C₄×C₅	—	4	1	no	—
841	C₂×C₄×C₅	—	4	1	no	—
842	C₂×C₄×C₅	—	4	1	no	—
843	C₂×C₄×C₅	—	4	2	no	—
844	C₂×C₄×C₅	—	4	2	no	—
845	C₂×C₄×C₅	—	4	2	no	—
846	C₂×C₄×C₅	—	4	2	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	C₂⁴×C₃	1	2	yes	—
851	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	2	yes	—
861	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
862	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
863	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
864	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
865	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
866	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
867	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
868	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
869	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
870	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
871	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
872	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
873	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
874	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
875	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
876	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
877	#126	C₂²×C₃×C₅	1	2	yes	—
878	#126	C₂²×C₃×C₅	1	2	yes	—
879	#126	C₂²×C₃×C₅	1	2	yes	—
880	#126	C₂²×C₃×C₅	1	2	yes	—
881	#126	C₂²×C₃×C₅	1	2	yes	complemented
882	#126	C₂²×C₃×C₅	1	2	yes	complemented
883	#126	C₂²×C₃×C₅	1	2	yes	complemented
884	#125	C₂²×C₃×C₅	1	2	yes	complemented
885	#125	C₂²×C₃×C₅	1	2	yes	complemented
886	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
887	#125	C₂²×C₃×C₅	1	2	yes	complemented
888	#125	C₂²×C₃×C₅	1	2	yes	complemented
889	#124	C₂²×C₃×C₅	1	2	yes	—
890	#124	C₂²×C₃×C₅	1	2	yes	—
891	#124	C₂²×C₃×C₅	1	2	yes	—
892	#124	C₂²×C₃×C₅	1	2	yes	—
893	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
894	#124	C₂²×C₃×C₅	1	2	yes	complemented
895	#123	C₂²×C₃×C₅	1	1	yes	characteristic
896	#123	C₂²×C₃×C₅	1	1	yes	characteristic
897	#123	C₂²×C₃×C₅	1	2	yes	—
898	#123	C₂²×C₃×C₅	1	2	yes	—
899	#123	C₂²×C₃×C₅	1	2	yes	—
900	#123	C₂²×C₃×C₅	1	2	yes	—
901	#123	C₂²×C₃×C₅	1	2	yes	—
902	#123	C₂²×C₃×C₅	1	2	yes	complemented
903	#123	C₂²×C₃×C₅	1	2	yes	complemented
904	#123	C₂²×C₃×C₅	1	2	yes	complemented
905	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
906	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
907	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
908	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
909	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
910	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
911	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
912	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
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	2	yes	—
916	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
917	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
918	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
919	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
920	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
921	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
922	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
923	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
924	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
925	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
926	#121	C₂²×C₃×C₅	1	1	yes	characteristic
927	#121	C₂²×C₃×C₅	1	1	yes	characteristic
928	#121	C₂²×C₃×C₅	1	1	yes	characteristic
929	#121	C₂²×C₃×C₅	1	1	yes	characteristic
930	#121	C₂²×C₃×C₅	1	2	yes	—
931	#121	C₂²×C₃×C₅	1	2	yes	—
932	#121	C₂²×C₃×C₅	1	2	yes	—
933	#121	C₂²×C₃×C₅	1	2	yes	—
934	#121	C₂²×C₃×C₅	1	2	yes	—
935	#121	C₂²×C₃×C₅	1	2	yes	—
936	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
937	#121	C₂²×C₃×C₅	1	2	yes	complemented
938	#120	C₂²×C₃×C₅	1	1	yes	characteristic
939	#120	C₂²×C₃×C₅	1	2	yes	—
940	#120	C₂²×C₃×C₅	1	1	yes	characteristic
941	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
942	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
943	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
944	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
945	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
946	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
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	2	yes	—
951	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
952	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
953	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
954	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
955	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
956	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
957	#117	C₂²×C₃×C₅	1	1	yes	characteristic
958	#117	C₂²×C₃×C₅	1	1	yes	characteristic
959	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
960	#117	C₂²×C₃×C₅	1	2	yes	complemented
961	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
963	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
964	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
965	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
966	C₂×C₃×C₅	—	2	2	no	—
967	C₂×C₃×C₅	—	4	1	no	—
968	C₂×C₃×C₅	—	4	1	no	—
969	C₂×C₃×C₅	—	4	2	no	—
970	C₂×C₃×C₅	—	4	1	no	—
971	C₂×C₃×C₅	—	4	1	no	—
972	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
973	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
974	C₂×C₃×C₅	#585	1	1	yes	characteristic
975	C₂³×C₃	—	2	2	no	—
976	C₂³×C₃	—	4	1	no	—
977	C₂³×C₃	—	4	1	no	—
978	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
979	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
980	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
981	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
982	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
983	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
984	C₃×Q₈	—	2	2	no	—
985	C₃×Q₈	—	2	2	no	—
986	C₃×Q₈	—	2	2	no	—
987	C₃×Q₈	—	4	2	no	—
988	C₃×Q₈	—	4	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	4	no	—
994	C₃×D₄	—	2	2	no	—
995	C₃×D₄	—	4	1	no	—
996	C₃×D₄	—	4	2	no	—
997	C₃×D₄	—	4	2	no	—
998	C₃×D₄	—	4	1	no	—
999	C₃×D₄	—	4	1	no	—
1000	C₃×D₄	—	4	1	no	—
1001	C₃×D₄	—	4	1	no	—
1002	C₃×D₄	—	4	2	no	—
1003	C₃×D₄	—	4	2	no	—
1004	C₂×C₃×C₄	—	2	2	no	—
1005	C₂×C₃×C₄	—	2	2	no	—
1006	C₂×C₃×C₄	—	2	2	no	—
1007	C₂×C₃×C₄	—	2	2	no	—
1008	C₂×C₃×C₄	—	2	2	no	—
1009	C₂×C₃×C₄	—	4	1	no	—
1010	C₂×C₃×C₄	—	4	1	no	—
1011	C₂×C₃×C₄	—	4	1	no	—
1012	C₂×C₃×C₄	—	4	2	no	—
1013	C₂×C₃×C₄	—	4	2	no	—
1014	C₂×C₃×C₄	—	4	2	no	—
1015	C₂×C₃×C₄	—	4	2	no	—
1016	C₂×C₃×C₄	—	4	2	no	—
1017	C₂×C₃×C₄	—	4	2	no	—
1018	C₂×C₃×C₄	—	4	2	no	—
1019	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1020	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1021	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1022	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1023	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
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	2	yes	—
1027	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1028	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1029	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1030	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1031	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1032	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1033	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1034	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1035	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1036	C₂²×C₅	—	2	1	no	—
1037	C₂²×C₅	—	2	1	no	—
1038	C₂²×C₅	—	2	1	no	—
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	1	no	—
1044	C₂²×C₅	—	2	1	no	—
1045	C₂²×C₅	—	2	2	no	—
1046	C₂²×C₅	—	2	1	no	—
1047	C₂²×C₅	—	2	1	no	—
1048	C₂²×C₅	—	2	1	no	—
1049	C₂²×C₅	—	2	2	no	—
1050	C₂²×C₅	—	2	1	no	—
1051	C₂²×C₅	—	2	1	no	—
1052	C₂²×C₅	—	2	1	no	—
1053	C₂²×C₅	—	4	4	no	—
1054	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
1055	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
1056	C₄×C₅	—	2	1	no	—
1057	C₄×C₅	—	2	1	no	—
1058	C₄×C₅	—	2	1	no	—
1059	C₄×C₅	—	2	1	no	—
1060	C₄×C₅	—	2	1	no	—
1061	C₄×C₅	—	2	2	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	1	no	—
1067	C₄×C₅	—	2	2	no	—
1068	C₄×C₅	—	2	1	no	—
1069	C₄×C₅	—	2	2	no	—
1070	C₄×C₅	—	2	2	no	—
1071	C₄×C₅	—	2	1	no	—
1072	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
1073	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
1074	#41	—	4	2	no	—
1075	#41	—	4	2	no	—
1076	#41	—	4	2	no	—
1077	C₂×Q₈	—	4	2	no	—
1078	C₂×Q₈	—	4	2	no	—
1079	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1080	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1081	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1082	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
1083	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
1084	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1085	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
1086	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1087	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1088	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
1095	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1096	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1097	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1098	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1099	C₂²×C₄	—	4	2	no	—
1100	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1101	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1102	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1103	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1104	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1105	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1106	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1107	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1108	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1109	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1110	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1111	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1112	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1113	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1114	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1115	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1116	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1117	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1118	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1119	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
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	1	yes	characteristic
1123	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1124	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1125	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
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	1	yes	characteristic
1130	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
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	2	yes	—
1134	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1135	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
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	2	yes	—
1141	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1142	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1143	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1144	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
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	1	yes	characteristic
1149	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1150	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1151	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1152	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1153	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1154	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1155	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
1165	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
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	2	yes	—
1170	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1171	C₄²	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	2	yes	—
1175	C₄²	C₂³×C₃×C₅	1	2	yes	—
1176	C₄²	C₂³×C₃×C₅	1	2	yes	—
1177	C₄²	C₂³×C₃×C₅	1	2	yes	—
1178	C₃×C₅	#3541	1	1	yes	characteristic, direct product factor, Hall
1179	C₂²×C₃	—	2	1	no	—
1180	C₂²×C₃	—	2	1	no	—
1181	C₂²×C₃	—	2	1	no	—
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	1	no	—
1187	C₂²×C₃	—	2	1	no	—
1188	C₂²×C₃	—	2	2	no	—
1189	C₂²×C₃	—	2	1	no	—
1190	C₂²×C₃	—	2	1	no	—
1191	C₂²×C₃	—	2	1	no	—
1192	C₂²×C₃	—	2	2	no	—
1193	C₂²×C₃	—	2	1	no	—
1194	C₂²×C₃	—	2	1	no	—
1195	C₂²×C₃	—	2	1	no	—
1196	C₂²×C₃	—	4	4	no	—
1197	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
1198	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1199	C₃×C₄	—	2	1	no	—
1200	C₃×C₄	—	2	1	no	—
1201	C₃×C₄	—	2	1	no	—
1202	C₃×C₄	—	2	1	no	—
1203	C₃×C₄	—	2	1	no	—
1204	C₃×C₄	—	2	2	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	1	no	—
1210	C₃×C₄	—	2	2	no	—
1211	C₃×C₄	—	2	1	no	—
1212	C₃×C₄	—	2	2	no	—
1213	C₃×C₄	—	2	2	no	—
1214	C₃×C₄	—	2	1	no	—
1215	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1216	C₂×C₅	—	2	2	no	—
1217	C₂×C₅	—	4	1	no	—
1218	C₂×C₅	—	4	1	no	—
1219	C₂×C₅	—	4	1	no	—
1220	C₂×C₅	—	4	1	no	—
1221	C₂×C₅	—	4	2	no	—
1222	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1223	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1224	C₂×C₅	C₃×#585	1	1	yes	characteristic
1225	C₂³	—	2	2	no	—
1226	C₂³	—	4	1	no	—
1227	C₂³	—	4	1	no	—
1228	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1229	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1230	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1231	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1232	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1233	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1234	Q₈	—	2	2	no	—
1235	Q₈	—	2	2	no	—
1236	Q₈	—	2	2	no	—
1237	Q₈	—	4	2	no	—
1238	Q₈	—	4	2	no	—
1239	Q₈	—	4	1	no	—
1240	Q₈	—	4	2	no	—
1241	D₄	—	2	2	no	—
1242	D₄	—	2	2	no	—
1243	D₄	—	2	4	no	—
1244	D₄	—	2	2	no	—
1245	D₄	—	4	1	no	—
1246	D₄	—	4	1	no	—
1247	D₄	—	4	1	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	1	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	2	no	—
1256	C₂×C₄	—	2	2	no	—
1257	C₂×C₄	—	2	2	no	—
1258	C₂×C₄	—	2	2	no	—
1259	C₂×C₄	—	4	1	no	—
1260	C₂×C₄	—	4	1	no	—
1261	C₂×C₄	—	4	1	no	—
1262	C₂×C₄	—	4	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	C₂⁴×C₃×C₅	1	2	yes	—
1270	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1271	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1272	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1273	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
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	2	yes	—
1277	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
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	2	yes	—
1281	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1282	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1283	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1284	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1285	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1286	C₂×C₃	—	2	2	no	—
1287	C₂×C₃	—	4	1	no	—
1288	C₂×C₃	—	4	1	no	—
1289	C₂×C₃	—	4	1	no	—
1290	C₂×C₃	—	4	1	no	—
1291	C₂×C₃	—	4	2	no	—
1292	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1293	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1294	C₂×C₃	C₅×#585	1	1	yes	characteristic
1295	C₅	C₃×#3541	1	1	yes	characteristic, direct product factor, Sylow
1296	C₂²	—	2	1	no	—
1297	C₂²	—	2	1	no	—
1298	C₂²	—	2	1	no	—
1299	C₂²	—	2	1	no	—
1300	C₂²	—	2	1	no	—
1301	C₂²	—	2	1	no	—
1302	C₂²	—	2	2	no	—
1303	C₂²	—	2	1	no	—
1304	C₂²	—	2	1	no	—
1305	C₂²	—	2	2	no	—
1306	C₂²	—	2	1	no	—
1307	C₂²	—	2	1	no	—
1308	C₂²	—	2	1	no	—
1309	C₂²	—	2	2	no	—
1310	C₂²	—	2	1	no	—
1311	C₂²	—	2	1	no	—
1312	C₂²	—	2	1	no	—
1313	C₂²	—	4	4	no	—
1314	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
1315	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
1316	C₄	—	2	1	no	—
1317	C₄	—	2	1	no	—
1318	C₄	—	2	1	no	—
1319	C₄	—	2	1	no	—
1320	C₄	—	2	1	no	—
1321	C₄	—	2	2	no	—
1322	C₄	—	2	2	no	—
1323	C₄	—	2	2	no	—
1324	C₄	—	2	2	no	—
1325	C₄	—	2	1	no	—
1326	C₄	—	2	1	no	—
1327	C₄	—	2	2	no	—
1328	C₄	—	2	1	no	—
1329	C₄	—	2	2	no	—
1330	C₄	—	2	2	no	—
1331	C₄	—	2	1	no	—
1332	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
1333	C₃	C₅×#3541	1	1	yes	characteristic, direct product factor, Sylow
1334	C₂	—	2	2	no	—
1335	C₂	—	4	1	no	—
1336	C₂	—	4	1	no	—
1337	C₂	—	4	1	no	—
1338	C₂	—	4	1	no	—
1339	C₂	—	4	2	no	—
1340	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1341	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1342	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×#563	C₂	semidirect
2. C₃×C₅×#562	C₂	semidirect
3. C₃×C₅×#556	C₂	semidirect
4. C₃×C₅×#554	C₂	semidirect
5. C₃×C₅×#554	C₂	semidirect
6. C₃×C₅×#553	C₂	semidirect
7. C₃×C₅×#553	C₂	semidirect
8. C₃×C₅×#552	C₂	semidirect
9. C₃×C₅×D₄×Q₈	C₂	semidirect
10. C₃×C₅×#548	C₂	semidirect
11. C₃×C₅×#548	C₂	semidirect
12. C₃×C₅×#547	C₂	semidirect
13. C₃×C₅×#542	C₂	semidirect
14. C₃×C₅×#542	C₂	semidirect
15. C₃×C₅×#541	C₂	semidirect
16. C₃×C₅×#539	C₂	semidirect
17. C₃×C₅×#538	C₂	semidirect
18. C₃×C₅×#538	C₂	semidirect
19. C₃×C₅×#537	C₂	semidirect
20. C₃×C₅×#536	C₂	semidirect
21. C₃×C₅×#525	C₂	semidirect
22. C₃×C₅×#525	C₂	semidirect
23. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
24. C₅×#3541	C₃	direct (N × H)
27. 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
33. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
34. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
39. C₃×C₅×#126	C₂²	semidirect
40. C₃×C₅×#126	C₂²	semidirect
41. C₃×C₅×#126	C₂²	semidirect
42. C₃×C₅×#125	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
51. C₃×C₅×#124	C₂²	semidirect
52. C₃×C₅×#124	C₂²	semidirect
60. C₃×C₅×#123	C₂²	semidirect
61. C₃×C₅×#123	C₂²	semidirect
62. C₃×C₅×#123	C₂²	semidirect
75. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
76. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
77. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
78. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
79. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
80. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
81. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
82. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
83. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
94. C₃×C₅×#121	C₂²	semidirect
95. 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
113. C₃×C₄×C₅×D₄	C₂²	semidirect
114. C₃×C₄×C₅×D₄	C₂²	semidirect
117. C₃×C₅×#117	C₂²	semidirect
118. C₃×C₅×#117	C₂²	semidirect
121. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
122. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
124. C₃×#3541	C₅	direct (N × H)
125. C₅×#563	C₂×C₃	semidirect
126. C₅×#562	C₂×C₃	semidirect
127. C₅×#556	C₂×C₃	semidirect
128. C₅×#554	C₂×C₃	semidirect
129. C₅×#554	C₂×C₃	semidirect
130. C₅×#553	C₂×C₃	semidirect
131. C₅×#553	C₂×C₃	semidirect
132. C₅×#552	C₂×C₃	semidirect
133. C₅×D₄×Q₈	C₂×C₃	semidirect
134. C₅×#548	C₂×C₃	semidirect
135. C₅×#548	C₂×C₃	semidirect
136. C₅×#547	C₂×C₃	semidirect
137. C₅×#542	C₂×C₃	semidirect
138. C₅×#542	C₂×C₃	semidirect
139. C₅×#541	C₂×C₃	semidirect
140. C₅×#539	C₂×C₃	semidirect
141. C₅×#538	C₂×C₃	semidirect
142. C₅×#538	C₂×C₃	semidirect
143. C₅×#537	C₂×C₃	semidirect
144. C₅×#536	C₂×C₃	semidirect
145. C₅×#525	C₂×C₃	semidirect
146. C₅×#525	C₂×C₃	semidirect
147. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
253. C₃×#563	C₂×C₅	semidirect
254. C₃×#562	C₂×C₅	semidirect
255. C₃×#556	C₂×C₅	semidirect
256. C₃×#554	C₂×C₅	semidirect
257. C₃×#554	C₂×C₅	semidirect
258. C₃×#553	C₂×C₅	semidirect
259. C₃×#553	C₂×C₅	semidirect
260. C₃×#552	C₂×C₅	semidirect
261. C₃×D₄×Q₈	C₂×C₅	semidirect
262. C₃×#548	C₂×C₅	semidirect
263. C₃×#548	C₂×C₅	semidirect
264. C₃×#547	C₂×C₅	semidirect
265. C₃×#542	C₂×C₅	semidirect
266. C₃×#542	C₂×C₅	semidirect
267. C₃×#541	C₂×C₅	semidirect
268. C₃×#539	C₂×C₅	semidirect
269. C₃×#538	C₂×C₅	semidirect
270. C₃×#538	C₂×C₅	semidirect
271. C₃×#537	C₂×C₅	semidirect
272. C₃×#536	C₂×C₅	semidirect
273. C₃×#525	C₂×C₅	semidirect
274. C₃×#525	C₂×C₅	semidirect
275. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
278. 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
284. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
285. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
290. C₅×#126	C₂²×C₃	semidirect
291. C₅×#126	C₂²×C₃	semidirect
292. C₅×#126	C₂²×C₃	semidirect
293. C₅×#125	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
302. C₅×#124	C₂²×C₃	semidirect
303. C₅×#124	C₂²×C₃	semidirect
311. C₅×#123	C₂²×C₃	semidirect
312. C₅×#123	C₂²×C₃	semidirect
313. C₅×#123	C₂²×C₃	semidirect
326. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
327. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
328. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
329. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
330. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
331. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
332. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
333. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
334. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
345. C₅×#121	C₂²×C₃	semidirect
346. 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
364. C₄×C₅×D₄	C₂²×C₃	semidirect
365. C₄×C₅×D₄	C₂²×C₃	semidirect
368. C₅×#117	C₂²×C₃	semidirect
369. C₅×#117	C₂²×C₃	semidirect
372. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
373. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
375. #3541	C₃×C₅	direct (N × H)
439. C₂×C₃×#41	C₂²×C₅	semidirect
441. C₂²×C₃×Q₈	C₂²×C₅	semidirect
443. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
444. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
445. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
446. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
451. C₃×#126	C₂²×C₅	semidirect
452. C₃×#126	C₂²×C₅	semidirect
453. C₃×#126	C₂²×C₅	semidirect
454. C₃×#125	C₂²×C₅	semidirect
455. C₃×#125	C₂²×C₅	semidirect
456. C₃×#125	C₂²×C₅	semidirect
457. C₃×#125	C₂²×C₅	semidirect
458. C₃×#125	C₂²×C₅	semidirect
463. C₃×#124	C₂²×C₅	semidirect
464. C₃×#124	C₂²×C₅	semidirect
472. C₃×#123	C₂²×C₅	semidirect
473. C₃×#123	C₂²×C₅	semidirect
474. C₃×#123	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
491. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
492. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
493. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
494. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
495. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
506. C₃×#121	C₂²×C₅	semidirect
507. C₃×#121	C₂²×C₅	semidirect
511. C₃×C₄×Q₈	C₂²×C₅	semidirect
512. C₃×C₄×Q₈	C₂²×C₅	semidirect
513. C₃×C₄×Q₈	C₂²×C₅	semidirect
514. C₃×C₄×Q₈	C₂²×C₅	semidirect
525. C₃×C₄×D₄	C₂²×C₅	semidirect
526. C₃×C₄×D₄	C₂²×C₅	semidirect
529. C₃×#117	C₂²×C₅	semidirect
530. C₃×#117	C₂²×C₅	semidirect
533. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
534. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
641. #563	C₂×C₃×C₅	semidirect
642. #562	C₂×C₃×C₅	semidirect
643. #556	C₂×C₃×C₅	semidirect
644. #554	C₂×C₃×C₅	semidirect
645. #554	C₂×C₃×C₅	semidirect
646. #553	C₂×C₃×C₅	semidirect
647. #553	C₂×C₃×C₅	semidirect
648. #552	C₂×C₃×C₅	semidirect
649. D₄×Q₈	C₂×C₃×C₅	semidirect
650. #548	C₂×C₃×C₅	semidirect
651. #548	C₂×C₃×C₅	semidirect
652. #547	C₂×C₃×C₅	semidirect
653. #542	C₂×C₃×C₅	semidirect
654. #542	C₂×C₃×C₅	semidirect
655. #541	C₂×C₃×C₅	semidirect
656. #539	C₂×C₃×C₅	semidirect
657. #538	C₂×C₃×C₅	semidirect
658. #538	C₂×C₃×C₅	semidirect
659. #537	C₂×C₃×C₅	semidirect
660. #536	C₂×C₃×C₅	semidirect
661. #525	C₂×C₃×C₅	semidirect
662. #525	C₂×C₃×C₅	semidirect
663. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
869. C₂×#41	C₂²×C₃×C₅	semidirect
871. C₂²×Q₈	C₂²×C₃×C₅	semidirect
873. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
874. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
875. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
876. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
881. #126	C₂²×C₃×C₅	semidirect
882. #126	C₂²×C₃×C₅	semidirect
883. #126	C₂²×C₃×C₅	semidirect
884. #125	C₂²×C₃×C₅	semidirect
885. #125	C₂²×C₃×C₅	semidirect
886. #125	C₂²×C₃×C₅	semidirect
887. #125	C₂²×C₃×C₅	semidirect
888. #125	C₂²×C₃×C₅	semidirect
893. #124	C₂²×C₃×C₅	semidirect
894. #124	C₂²×C₃×C₅	semidirect
902. #123	C₂²×C₃×C₅	semidirect
903. #123	C₂²×C₃×C₅	semidirect
904. #123	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
922. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
923. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
924. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
925. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
936. #121	C₂²×C₃×C₅	semidirect
937. #121	C₂²×C₃×C₅	semidirect
941. C₄×Q₈	C₂²×C₃×C₅	semidirect
942. C₄×Q₈	C₂²×C₃×C₅	semidirect
943. C₄×Q₈	C₂²×C₃×C₅	semidirect
944. C₄×Q₈	C₂²×C₃×C₅	semidirect
955. C₄×D₄	C₂²×C₃×C₅	semidirect
956. C₄×D₄	C₂²×C₃×C₅	semidirect
959. #117	C₂²×C₃×C₅	semidirect
960. #117	C₂²×C₃×C₅	semidirect
963. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
964. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
1178. C₃×C₅	#3541	direct (N × H)
1295. C₅	C₃×#3541	direct (N × H)
1333. C₃	C₅×#3541	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×#563	2
C₃×C₅×#562	2
C₃×C₅×#556	2
C₃×C₅×#554	2
C₃×C₅×#553	2
C₃×C₅×#552	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#548	2
C₃×C₅×#547	2
C₃×C₅×#542	2
C₃×C₅×#541	2
C₃×C₅×#539	2
C₃×C₅×#538	2
C₃×C₅×#537	2
C₃×C₅×#536	2
C₃×C₅×#525	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₅×#3541	3
C₃×#3541	5

Subgroups — C3×C5×#3541 #14276575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3541 #14276575