Subgroups — C₃×C₅×#3560 #14276594

Order 1920.

2112 conjugacy classes of subgroups.

The subgroup lattice has 1180 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×#560	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#547	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#539	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#538	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
14	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
15	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₅×#534	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#3560	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
22	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
23	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
24	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#126	C₂²	1	2	yes	complemented
28	C₃×C₅×#126	C₂²	1	2	yes	complemented
29	C₃×C₅×#126	C₂²	1	2	yes	complemented
30	C₃×C₅×#126	C₂²	1	2	yes	complemented
31	C₃×C₅×#126	C₂²	1	2	yes	complemented
32	C₃×C₅×#126	C₂²	1	2	yes	complemented
33	C₃×C₅×#126	C₂²	1	2	yes	complemented
34	C₃×C₅×#126	C₂²	1	2	yes	complemented
35	C₃×C₅×#126	C₂²	1	2	yes	complemented
36	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₅×#125	C₂²	1	2	yes	complemented
38	C₃×C₅×#125	C₂²	1	2	yes	complemented
39	C₃×C₅×#124	C₂²	1	2	yes	—
40	C₃×C₅×#124	C₂²	1	2	yes	—
41	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×#124	C₂²	1	2	yes	complemented
43	C₃×C₅×#124	C₂²	1	2	yes	complemented
44	C₃×C₅×#123	C₂²	1	2	yes	—
45	C₃×C₅×#123	C₂²	1	2	yes	—
46	C₃×C₅×#123	C₂²	1	2	yes	—
47	C₃×C₅×#123	C₂²	1	2	yes	—
48	C₃×C₅×#123	C₂²	1	2	yes	complemented
49	C₃×C₅×#123	C₂²	1	2	yes	complemented
50	C₃×C₅×#123	C₂²	1	2	yes	complemented
51	C₃×C₅×#123	C₂²	1	2	yes	complemented
52	C₃×C₅×#123	C₂²	1	2	yes	complemented
53	C₃×C₅×#123	C₂²	1	2	yes	complemented
54	C₃×C₅×#123	C₂²	1	2	yes	complemented
55	C₃×C₅×#123	C₂²	1	2	yes	complemented
56	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
58	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
59	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₃×C₅×#121	C₂²	1	1	yes	characteristic
65	C₃×C₅×#121	C₂²	1	1	yes	characteristic
66	C₃×C₅×#121	C₂²	1	2	yes	—
67	C₃×C₅×#121	C₂²	1	2	yes	—
68	C₃×C₅×#121	C₂²	1	2	yes	—
69	C₃×C₅×#121	C₂²	1	2	yes	—
70	C₃×C₅×#121	C₂²	1	2	yes	—
71	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
72	C₃×C₅×#121	C₂²	1	2	yes	complemented
73	C₃×C₅×#121	C₂²	1	2	yes	complemented
74	C₃×C₅×#121	C₂²	1	2	yes	complemented
75	C₃×C₅×#121	C₂²	1	2	yes	complemented
76	C₃×C₅×#121	C₂²	1	2	yes	complemented
77	C₃×C₅×#121	C₂²	1	2	yes	complemented
78	C₃×C₅×#121	C₂²	1	2	yes	complemented
79	C₃×C₅×#120	C₂²	1	2	yes	—
80	C₃×C₅×#120	C₂²	1	2	yes	—
81	C₃×C₅×#120	C₂²	1	2	yes	—
82	C₃×C₅×#120	C₂²	1	2	yes	complemented
83	C₃×C₅×#120	C₂²	1	2	yes	complemented
84	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
86	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
87	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
88	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
89	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
90	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
91	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
92	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
93	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
94	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
95	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
96	C₃×C₅×#117	C₂²	1	2	yes	complemented
97	C₃×C₅×#117	C₂²	1	2	yes	complemented
98	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
102	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
108	C₃×#3560	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
109	C₅×#563	C₂×C₃	1	2	yes	complemented
110	C₅×#560	C₂×C₃	1	2	yes	complemented
111	C₅×#553	C₂×C₃	1	2	yes	complemented
112	C₅×#553	C₂×C₃	1	2	yes	complemented
113	C₅×#551	C₂×C₃	1	2	yes	complemented
114	C₅×#547	C₂×C₃	1	2	yes	complemented
115	C₅×#546	C₂×C₃	1	2	yes	complemented
116	C₅×#546	C₂×C₃	1	2	yes	complemented
117	C₅×#542	C₂×C₃	1	2	yes	complemented
118	C₅×#539	C₂×C₃	1	2	yes	complemented
119	C₅×#539	C₂×C₃	1	1	yes	characteristic, complemented
120	C₅×#538	C₂×C₃	1	1	yes	characteristic, complemented
121	C₅×#538	C₂×C₃	1	2	yes	complemented
122	C₅×#538	C₂×C₃	1	2	yes	complemented
123	C₅×#537	C₂×C₃	1	1	yes	characteristic, complemented
124	C₅×#534	C₂×C₃	1	1	yes	characteristic, complemented
125	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
126	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
129	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
130	C₃×C₅×#41	—	4	4	no	—
131	C₃×C₅×#41	—	4	4	no	—
132	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
134	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
135	C₂×C₃×C₅×D₄	—	4	4	no	—
136	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
137	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
138	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
139	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
140	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
141	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
142	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
143	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
144	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
145	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
146	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
147	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
148	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
149	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
150	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
151	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
158	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
159	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
160	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
161	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
162	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
163	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
164	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
165	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
178	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
181	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
182	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
183	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
186	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
212	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
213	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
214	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
215	C₃×C₄²×C₅	C₂³	1	2	yes	—
216	C₃×C₄²×C₅	C₂³	1	2	yes	—
217	C₃×C₄²×C₅	C₂³	1	2	yes	—
218	C₃×#563	C₂×C₅	1	2	yes	complemented
219	C₃×#560	C₂×C₅	1	2	yes	complemented
220	C₃×#553	C₂×C₅	1	2	yes	complemented
221	C₃×#553	C₂×C₅	1	2	yes	complemented
222	C₃×#551	C₂×C₅	1	2	yes	complemented
223	C₃×#547	C₂×C₅	1	2	yes	complemented
224	C₃×#546	C₂×C₅	1	2	yes	complemented
225	C₃×#546	C₂×C₅	1	2	yes	complemented
226	C₃×#542	C₂×C₅	1	2	yes	complemented
227	C₃×#539	C₂×C₅	1	2	yes	complemented
228	C₃×#539	C₂×C₅	1	1	yes	characteristic, complemented
229	C₃×#538	C₂×C₅	1	1	yes	characteristic, complemented
230	C₃×#538	C₂×C₅	1	2	yes	complemented
231	C₃×#538	C₂×C₅	1	2	yes	complemented
232	C₃×#537	C₂×C₅	1	1	yes	characteristic, complemented
233	C₃×#534	C₂×C₅	1	1	yes	characteristic, complemented
234	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
235	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
236	C₂×C₃×#126	C₂×C₅	1	1	yes	characteristic, complemented
237	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
238	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
239	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
240	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
241	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
242	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
243	C₅×#126	C₂²×C₃	1	2	yes	complemented
244	C₅×#126	C₂²×C₃	1	2	yes	complemented
245	C₅×#126	C₂²×C₃	1	2	yes	complemented
246	C₅×#126	C₂²×C₃	1	2	yes	complemented
247	C₅×#126	C₂²×C₃	1	2	yes	complemented
248	C₅×#126	C₂²×C₃	1	2	yes	complemented
249	C₅×#126	C₂²×C₃	1	2	yes	complemented
250	C₅×#126	C₂²×C₃	1	2	yes	complemented
251	C₅×#126	C₂²×C₃	1	2	yes	complemented
252	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
253	C₅×#125	C₂²×C₃	1	2	yes	complemented
254	C₅×#125	C₂²×C₃	1	2	yes	complemented
255	C₅×#124	C₂²×C₃	1	2	yes	—
256	C₅×#124	C₂²×C₃	1	2	yes	—
257	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
258	C₅×#124	C₂²×C₃	1	2	yes	complemented
259	C₅×#124	C₂²×C₃	1	2	yes	complemented
260	C₅×#123	C₂²×C₃	1	2	yes	—
261	C₅×#123	C₂²×C₃	1	2	yes	—
262	C₅×#123	C₂²×C₃	1	2	yes	—
263	C₅×#123	C₂²×C₃	1	2	yes	—
264	C₅×#123	C₂²×C₃	1	2	yes	complemented
265	C₅×#123	C₂²×C₃	1	2	yes	complemented
266	C₅×#123	C₂²×C₃	1	2	yes	complemented
267	C₅×#123	C₂²×C₃	1	2	yes	complemented
268	C₅×#123	C₂²×C₃	1	2	yes	complemented
269	C₅×#123	C₂²×C₃	1	2	yes	complemented
270	C₅×#123	C₂²×C₃	1	2	yes	complemented
271	C₅×#123	C₂²×C₃	1	2	yes	complemented
272	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
273	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
274	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
275	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
276	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
277	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
278	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
279	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
280	C₅×#121	C₂²×C₃	1	1	yes	characteristic
281	C₅×#121	C₂²×C₃	1	1	yes	characteristic
282	C₅×#121	C₂²×C₃	1	2	yes	—
283	C₅×#121	C₂²×C₃	1	2	yes	—
284	C₅×#121	C₂²×C₃	1	2	yes	—
285	C₅×#121	C₂²×C₃	1	2	yes	—
286	C₅×#121	C₂²×C₃	1	2	yes	—
287	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
288	C₅×#121	C₂²×C₃	1	2	yes	complemented
289	C₅×#121	C₂²×C₃	1	2	yes	complemented
290	C₅×#121	C₂²×C₃	1	2	yes	complemented
291	C₅×#121	C₂²×C₃	1	2	yes	complemented
292	C₅×#121	C₂²×C₃	1	2	yes	complemented
293	C₅×#121	C₂²×C₃	1	2	yes	complemented
294	C₅×#121	C₂²×C₃	1	2	yes	complemented
295	C₅×#120	C₂²×C₃	1	2	yes	—
296	C₅×#120	C₂²×C₃	1	2	yes	—
297	C₅×#120	C₂²×C₃	1	2	yes	—
298	C₅×#120	C₂²×C₃	1	2	yes	complemented
299	C₅×#120	C₂²×C₃	1	2	yes	complemented
300	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
301	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
302	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
303	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
304	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
306	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
307	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
308	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
309	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
310	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
311	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
312	C₅×#117	C₂²×C₃	1	2	yes	complemented
313	C₅×#117	C₂²×C₃	1	2	yes	complemented
314	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
316	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
317	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
318	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
319	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
320	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
321	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
322	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
323	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
324	#3560	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
325	C₂³×C₃×C₅	—	2	2	no	—
326	C₂³×C₃×C₅	—	4	2	no	—
327	C₂³×C₃×C₅	—	4	1	no	—
328	C₂³×C₃×C₅	—	4	1	no	—
329	C₂³×C₃×C₅	—	4	2	no	—
330	C₂³×C₃×C₅	—	4	2	no	—
331	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
332	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
333	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
334	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
335	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
336	C₃×C₅×Q₈	—	4	1	no	—
337	C₃×C₅×Q₈	—	4	2	no	—
338	C₃×C₅×Q₈	—	4	2	no	—
339	C₃×C₅×D₄	—	2	4	no	—
340	C₃×C₅×D₄	—	2	4	no	—
341	C₃×C₅×D₄	—	2	4	no	—
342	C₃×C₅×D₄	—	4	2	no	—
343	C₃×C₅×D₄	—	4	2	no	—
344	C₃×C₅×D₄	—	4	2	no	—
345	C₃×C₅×D₄	—	4	2	no	—
346	C₃×C₅×D₄	—	4	2	no	—
347	C₃×C₅×D₄	—	4	2	no	—
348	C₃×C₅×D₄	—	4	1	no	—
349	C₃×C₅×D₄	—	4	1	no	—
350	C₃×C₅×D₄	—	4	2	no	—
351	C₃×C₅×D₄	—	4	1	no	—
352	C₃×C₅×D₄	—	4	2	no	—
353	C₃×C₅×D₄	—	4	2	no	—
354	C₂×C₃×C₄×C₅	—	2	2	no	—
355	C₂×C₃×C₄×C₅	—	2	2	no	—
356	C₂×C₃×C₄×C₅	—	4	2	no	—
357	C₂×C₃×C₄×C₅	—	4	1	no	—
358	C₂×C₃×C₄×C₅	—	4	1	no	—
359	C₂×C₃×C₄×C₅	—	4	1	no	—
360	C₂×C₃×C₄×C₅	—	4	2	no	—
361	C₂×C₃×C₄×C₅	—	4	2	no	—
362	C₂×C₃×C₄×C₅	—	4	1	no	—
363	C₂×C₃×C₄×C₅	—	4	2	no	—
364	C₂×C₃×C₄×C₅	—	4	2	no	—
365	C₂×C₃×C₄×C₅	—	4	2	no	—
366	C₂×C₃×C₄×C₅	—	4	2	no	—
367	C₂×C₃×C₄×C₅	—	4	2	no	—
368	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
369	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
371	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
372	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
374	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
376	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
378	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
379	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
380	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
381	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
382	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
383	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
384	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
385	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
386	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
387	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
388	C₃×#126	C₂²×C₅	1	2	yes	complemented
389	C₃×#126	C₂²×C₅	1	2	yes	complemented
390	C₃×#126	C₂²×C₅	1	2	yes	complemented
391	C₃×#126	C₂²×C₅	1	2	yes	complemented
392	C₃×#126	C₂²×C₅	1	2	yes	complemented
393	C₃×#126	C₂²×C₅	1	2	yes	complemented
394	C₃×#126	C₂²×C₅	1	2	yes	complemented
395	C₃×#126	C₂²×C₅	1	2	yes	complemented
396	C₃×#126	C₂²×C₅	1	2	yes	complemented
397	C₃×#125	C₂²×C₅	1	2	yes	complemented
398	C₃×#125	C₂²×C₅	1	2	yes	complemented
399	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
400	C₃×#124	C₂²×C₅	1	2	yes	—
401	C₃×#124	C₂²×C₅	1	2	yes	—
402	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
403	C₃×#124	C₂²×C₅	1	2	yes	complemented
404	C₃×#124	C₂²×C₅	1	2	yes	complemented
405	C₃×#123	C₂²×C₅	1	2	yes	—
406	C₃×#123	C₂²×C₅	1	2	yes	—
407	C₃×#123	C₂²×C₅	1	2	yes	—
408	C₃×#123	C₂²×C₅	1	2	yes	—
409	C₃×#123	C₂²×C₅	1	2	yes	complemented
410	C₃×#123	C₂²×C₅	1	2	yes	complemented
411	C₃×#123	C₂²×C₅	1	2	yes	complemented
412	C₃×#123	C₂²×C₅	1	2	yes	complemented
413	C₃×#123	C₂²×C₅	1	2	yes	complemented
414	C₃×#123	C₂²×C₅	1	2	yes	complemented
415	C₃×#123	C₂²×C₅	1	2	yes	complemented
416	C₃×#123	C₂²×C₅	1	2	yes	complemented
417	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
418	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
419	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
420	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
421	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
422	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
423	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
424	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
425	C₃×#121	C₂²×C₅	1	2	yes	—
426	C₃×#121	C₂²×C₅	1	2	yes	—
427	C₃×#121	C₂²×C₅	1	1	yes	characteristic
428	C₃×#121	C₂²×C₅	1	1	yes	characteristic
429	C₃×#121	C₂²×C₅	1	2	yes	—
430	C₃×#121	C₂²×C₅	1	2	yes	—
431	C₃×#121	C₂²×C₅	1	2	yes	—
432	C₃×#121	C₂²×C₅	1	2	yes	complemented
433	C₃×#121	C₂²×C₅	1	2	yes	complemented
434	C₃×#121	C₂²×C₅	1	2	yes	complemented
435	C₃×#121	C₂²×C₅	1	2	yes	complemented
436	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
437	C₃×#121	C₂²×C₅	1	2	yes	complemented
438	C₃×#121	C₂²×C₅	1	2	yes	complemented
439	C₃×#121	C₂²×C₅	1	2	yes	complemented
440	C₃×#120	C₂²×C₅	1	2	yes	—
441	C₃×#120	C₂²×C₅	1	2	yes	—
442	C₃×#120	C₂²×C₅	1	2	yes	—
443	C₃×#120	C₂²×C₅	1	2	yes	complemented
444	C₃×#120	C₂²×C₅	1	2	yes	complemented
445	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
446	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
447	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
448	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
449	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
450	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
451	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
452	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
453	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
454	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
455	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
456	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
457	C₃×#117	C₂²×C₅	1	2	yes	complemented
458	C₃×#117	C₂²×C₅	1	2	yes	complemented
459	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
460	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
461	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
462	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
463	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
464	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
465	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
466	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
467	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
468	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
469	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
470	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
471	C₅×#41	—	4	4	no	—
472	C₅×#41	—	4	4	no	—
473	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
474	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
475	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
476	C₂×C₅×D₄	—	4	4	no	—
477	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
478	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
479	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
480	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
481	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
482	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
483	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
484	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
485	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
486	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
487	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
488	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
489	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
490	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
491	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
492	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
493	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
494	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
495	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
496	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
497	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
498	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
499	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
500	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
501	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
502	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
503	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
504	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
505	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
506	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
507	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
508	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
509	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
510	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
511	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
512	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
514	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
516	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
517	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
518	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
519	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
520	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
521	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
522	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
523	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
524	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
525	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
526	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
527	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
528	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
529	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
530	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
531	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
532	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
533	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
534	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
536	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
537	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
538	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
539	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
540	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
541	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
542	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
544	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
545	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
546	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
547	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
548	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
549	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
550	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
551	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
552	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
553	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
554	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
555	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
556	C₄²×C₅	C₂³×C₃	1	2	yes	—
557	C₄²×C₅	C₂³×C₃	1	2	yes	—
558	C₄²×C₅	C₂³×C₃	1	2	yes	—
559	#563	C₂×C₃×C₅	1	2	yes	complemented
560	#560	C₂×C₃×C₅	1	2	yes	complemented
561	#553	C₂×C₃×C₅	1	2	yes	complemented
562	#553	C₂×C₃×C₅	1	2	yes	complemented
563	#551	C₂×C₃×C₅	1	2	yes	complemented
564	#547	C₂×C₃×C₅	1	2	yes	complemented
565	#546	C₂×C₃×C₅	1	2	yes	complemented
566	#546	C₂×C₃×C₅	1	2	yes	complemented
567	#542	C₂×C₃×C₅	1	2	yes	complemented
568	#539	C₂×C₃×C₅	1	2	yes	complemented
569	#539	C₂×C₃×C₅	1	1	yes	characteristic, complemented
570	#538	C₂×C₃×C₅	1	1	yes	characteristic, complemented
571	#538	C₂×C₃×C₅	1	2	yes	complemented
572	#538	C₂×C₃×C₅	1	2	yes	complemented
573	#537	C₂×C₃×C₅	1	1	yes	characteristic, complemented
574	#534	C₂×C₃×C₅	1	1	yes	characteristic, complemented
575	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
576	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
577	C₂×#126	C₂×C₃×C₅	1	1	yes	characteristic, complemented
578	C₂²×C₃×C₅	—	2	1	no	—
579	C₂²×C₃×C₅	—	2	1	no	—
580	C₂²×C₃×C₅	—	2	2	no	—
581	C₂²×C₃×C₅	—	2	2	no	—
582	C₂²×C₃×C₅	—	2	2	no	—
583	C₂²×C₃×C₅	—	2	2	no	—
584	C₂²×C₃×C₅	—	2	2	no	—
585	C₂²×C₃×C₅	—	2	2	no	—
586	C₂²×C₃×C₅	—	2	2	no	—
587	C₂²×C₃×C₅	—	2	2	no	—
588	C₂²×C₃×C₅	—	2	2	no	—
589	C₂²×C₃×C₅	—	2	2	no	—
590	C₂²×C₃×C₅	—	2	2	no	—
591	C₂²×C₃×C₅	—	2	2	no	—
592	C₂²×C₃×C₅	—	8	2	no	—
593	C₂²×C₃×C₅	—	8	4	no	—
594	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
595	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
596	C₃×C₄×C₅	—	2	1	no	—
597	C₃×C₄×C₅	—	2	2	no	—
598	C₃×C₄×C₅	—	2	1	no	—
599	C₃×C₄×C₅	—	2	2	no	—
600	C₃×C₄×C₅	—	2	2	no	—
601	C₃×C₄×C₅	—	2	2	no	—
602	C₃×C₄×C₅	—	2	1	no	—
603	C₃×C₄×C₅	—	2	2	no	—
604	C₃×C₄×C₅	—	2	2	no	—
605	C₃×C₄×C₅	—	2	2	no	—
606	C₃×C₄×C₅	—	2	1	no	—
607	C₃×C₄×C₅	—	2	1	no	—
608	C₃×C₄×C₅	—	2	2	no	—
609	C₃×C₄×C₅	—	2	1	no	—
610	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
611	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
612	C₃×#41	—	4	4	no	—
613	C₃×#41	—	4	4	no	—
614	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
615	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
616	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
617	C₂×C₃×D₄	—	4	4	no	—
618	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
619	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
620	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
621	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
622	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
623	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
624	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
625	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
626	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
627	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
628	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
629	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
630	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
631	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
632	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
633	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
634	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
635	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
636	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
637	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
638	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
639	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
640	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
641	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
642	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
643	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
644	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
645	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
646	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
647	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
648	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
649	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
650	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
651	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
652	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
653	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
654	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
655	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
656	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
657	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
658	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
659	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
660	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
661	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
662	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
663	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
664	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
665	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
666	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
667	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
668	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
669	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
670	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
671	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
672	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
673	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
674	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
675	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
676	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
677	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
678	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
679	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
680	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
681	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
682	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
683	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
684	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
685	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
686	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
687	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
688	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
689	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
690	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
691	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
692	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
693	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
694	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
695	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
696	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
697	C₃×C₄²	C₂³×C₅	1	2	yes	—
698	C₃×C₄²	C₂³×C₅	1	2	yes	—
699	C₃×C₄²	C₂³×C₅	1	2	yes	—
700	C₂³×C₅	—	2	2	no	—
701	C₂³×C₅	—	4	2	no	—
702	C₂³×C₅	—	4	1	no	—
703	C₂³×C₅	—	4	1	no	—
704	C₂³×C₅	—	4	2	no	—
705	C₂³×C₅	—	4	2	no	—
706	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
707	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
708	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
709	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
710	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
711	C₅×Q₈	—	4	1	no	—
712	C₅×Q₈	—	4	2	no	—
713	C₅×Q₈	—	4	2	no	—
714	C₅×D₄	—	2	4	no	—
715	C₅×D₄	—	2	4	no	—
716	C₅×D₄	—	2	4	no	—
717	C₅×D₄	—	4	2	no	—
718	C₅×D₄	—	4	2	no	—
719	C₅×D₄	—	4	2	no	—
720	C₅×D₄	—	4	2	no	—
721	C₅×D₄	—	4	2	no	—
722	C₅×D₄	—	4	2	no	—
723	C₅×D₄	—	4	1	no	—
724	C₅×D₄	—	4	1	no	—
725	C₅×D₄	—	4	2	no	—
726	C₅×D₄	—	4	1	no	—
727	C₅×D₄	—	4	2	no	—
728	C₅×D₄	—	4	2	no	—
729	C₂×C₄×C₅	—	2	2	no	—
730	C₂×C₄×C₅	—	2	2	no	—
731	C₂×C₄×C₅	—	4	2	no	—
732	C₂×C₄×C₅	—	4	1	no	—
733	C₂×C₄×C₅	—	4	1	no	—
734	C₂×C₄×C₅	—	4	1	no	—
735	C₂×C₄×C₅	—	4	2	no	—
736	C₂×C₄×C₅	—	4	2	no	—
737	C₂×C₄×C₅	—	4	1	no	—
738	C₂×C₄×C₅	—	4	2	no	—
739	C₂×C₄×C₅	—	4	2	no	—
740	C₂×C₄×C₅	—	4	2	no	—
741	C₂×C₄×C₅	—	4	2	no	—
742	C₂×C₄×C₅	—	4	2	no	—
743	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
744	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
745	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
746	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
747	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
748	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
749	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
750	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
751	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
752	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
753	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
754	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
755	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
756	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
757	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
758	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
759	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
760	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
761	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
762	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
763	#126	C₂²×C₃×C₅	1	2	yes	complemented
764	#126	C₂²×C₃×C₅	1	2	yes	complemented
765	#126	C₂²×C₃×C₅	1	2	yes	complemented
766	#126	C₂²×C₃×C₅	1	2	yes	complemented
767	#126	C₂²×C₃×C₅	1	2	yes	complemented
768	#126	C₂²×C₃×C₅	1	2	yes	complemented
769	#126	C₂²×C₃×C₅	1	2	yes	complemented
770	#126	C₂²×C₃×C₅	1	2	yes	complemented
771	#126	C₂²×C₃×C₅	1	2	yes	complemented
772	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
773	#125	C₂²×C₃×C₅	1	2	yes	complemented
774	#125	C₂²×C₃×C₅	1	2	yes	complemented
775	#124	C₂²×C₃×C₅	1	2	yes	—
776	#124	C₂²×C₃×C₅	1	2	yes	—
777	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
778	#124	C₂²×C₃×C₅	1	2	yes	complemented
779	#124	C₂²×C₃×C₅	1	2	yes	complemented
780	#123	C₂²×C₃×C₅	1	2	yes	—
781	#123	C₂²×C₃×C₅	1	2	yes	—
782	#123	C₂²×C₃×C₅	1	2	yes	—
783	#123	C₂²×C₃×C₅	1	2	yes	—
784	#123	C₂²×C₃×C₅	1	2	yes	complemented
785	#123	C₂²×C₃×C₅	1	2	yes	complemented
786	#123	C₂²×C₃×C₅	1	2	yes	complemented
787	#123	C₂²×C₃×C₅	1	2	yes	complemented
788	#123	C₂²×C₃×C₅	1	2	yes	complemented
789	#123	C₂²×C₃×C₅	1	2	yes	complemented
790	#123	C₂²×C₃×C₅	1	2	yes	complemented
791	#123	C₂²×C₃×C₅	1	2	yes	complemented
792	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
793	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
794	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
795	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
796	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
797	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
798	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
799	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
800	#121	C₂²×C₃×C₅	1	1	yes	characteristic
801	#121	C₂²×C₃×C₅	1	1	yes	characteristic
802	#121	C₂²×C₃×C₅	1	2	yes	—
803	#121	C₂²×C₃×C₅	1	2	yes	—
804	#121	C₂²×C₃×C₅	1	2	yes	—
805	#121	C₂²×C₃×C₅	1	2	yes	—
806	#121	C₂²×C₃×C₅	1	2	yes	—
807	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
808	#121	C₂²×C₃×C₅	1	2	yes	complemented
809	#121	C₂²×C₃×C₅	1	2	yes	complemented
810	#121	C₂²×C₃×C₅	1	2	yes	complemented
811	#121	C₂²×C₃×C₅	1	2	yes	complemented
812	#121	C₂²×C₃×C₅	1	2	yes	complemented
813	#121	C₂²×C₃×C₅	1	2	yes	complemented
814	#121	C₂²×C₃×C₅	1	2	yes	complemented
815	#120	C₂²×C₃×C₅	1	2	yes	—
816	#120	C₂²×C₃×C₅	1	2	yes	—
817	#120	C₂²×C₃×C₅	1	2	yes	—
818	#120	C₂²×C₃×C₅	1	2	yes	complemented
819	#120	C₂²×C₃×C₅	1	2	yes	complemented
820	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
821	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
822	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
823	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
824	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
825	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
826	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
827	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
828	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
829	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
830	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
831	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
832	#117	C₂²×C₃×C₅	1	2	yes	complemented
833	#117	C₂²×C₃×C₅	1	2	yes	complemented
834	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
835	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
836	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
837	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
838	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
839	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
840	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
841	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
842	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
843	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
844	C₂×C₃×C₅	—	2	2	no	—
845	C₂×C₃×C₅	—	4	2	no	—
846	C₂×C₃×C₅	—	4	2	no	—
847	C₂×C₃×C₅	—	4	2	no	—
848	C₂×C₃×C₅	—	4	2	no	—
849	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
850	C₂×C₃×C₅	#585	1	1	yes	characteristic
851	C₂×C₃×C₅	#585	1	1	yes	characteristic
852	C₂³×C₃	—	2	2	no	—
853	C₂³×C₃	—	4	2	no	—
854	C₂³×C₃	—	4	1	no	—
855	C₂³×C₃	—	4	1	no	—
856	C₂³×C₃	—	4	2	no	—
857	C₂³×C₃	—	4	2	no	—
858	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
859	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
860	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
861	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
862	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
863	C₃×Q₈	—	4	1	no	—
864	C₃×Q₈	—	4	2	no	—
865	C₃×Q₈	—	4	2	no	—
866	C₃×D₄	—	2	4	no	—
867	C₃×D₄	—	2	4	no	—
868	C₃×D₄	—	2	4	no	—
869	C₃×D₄	—	4	2	no	—
870	C₃×D₄	—	4	2	no	—
871	C₃×D₄	—	4	2	no	—
872	C₃×D₄	—	4	2	no	—
873	C₃×D₄	—	4	2	no	—
874	C₃×D₄	—	4	2	no	—
875	C₃×D₄	—	4	1	no	—
876	C₃×D₄	—	4	1	no	—
877	C₃×D₄	—	4	2	no	—
878	C₃×D₄	—	4	1	no	—
879	C₃×D₄	—	4	2	no	—
880	C₃×D₄	—	4	2	no	—
881	C₂×C₃×C₄	—	2	2	no	—
882	C₂×C₃×C₄	—	2	2	no	—
883	C₂×C₃×C₄	—	4	2	no	—
884	C₂×C₃×C₄	—	4	1	no	—
885	C₂×C₃×C₄	—	4	1	no	—
886	C₂×C₃×C₄	—	4	1	no	—
887	C₂×C₃×C₄	—	4	2	no	—
888	C₂×C₃×C₄	—	4	2	no	—
889	C₂×C₃×C₄	—	4	1	no	—
890	C₂×C₃×C₄	—	4	2	no	—
891	C₂×C₃×C₄	—	4	2	no	—
892	C₂×C₃×C₄	—	4	2	no	—
893	C₂×C₃×C₄	—	4	2	no	—
894	C₂×C₃×C₄	—	4	2	no	—
895	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
896	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
897	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
898	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
899	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
900	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
901	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
902	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
903	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
904	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
905	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
906	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
907	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
908	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
909	C₂²×C₅	—	2	1	no	—
910	C₂²×C₅	—	2	1	no	—
911	C₂²×C₅	—	2	2	no	—
912	C₂²×C₅	—	2	2	no	—
913	C₂²×C₅	—	2	2	no	—
914	C₂²×C₅	—	2	2	no	—
915	C₂²×C₅	—	2	2	no	—
916	C₂²×C₅	—	2	2	no	—
917	C₂²×C₅	—	2	2	no	—
918	C₂²×C₅	—	2	2	no	—
919	C₂²×C₅	—	2	2	no	—
920	C₂²×C₅	—	2	2	no	—
921	C₂²×C₅	—	2	2	no	—
922	C₂²×C₅	—	2	2	no	—
923	C₂²×C₅	—	8	2	no	—
924	C₂²×C₅	—	8	4	no	—
925	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
926	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
927	C₄×C₅	—	2	1	no	—
928	C₄×C₅	—	2	2	no	—
929	C₄×C₅	—	2	1	no	—
930	C₄×C₅	—	2	2	no	—
931	C₄×C₅	—	2	2	no	—
932	C₄×C₅	—	2	2	no	—
933	C₄×C₅	—	2	1	no	—
934	C₄×C₅	—	2	2	no	—
935	C₄×C₅	—	2	2	no	—
936	C₄×C₅	—	2	2	no	—
937	C₄×C₅	—	2	1	no	—
938	C₄×C₅	—	2	1	no	—
939	C₄×C₅	—	2	2	no	—
940	C₄×C₅	—	2	1	no	—
941	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
942	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
943	#41	—	4	4	no	—
944	#41	—	4	4	no	—
945	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
946	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
947	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
948	C₂×D₄	—	4	4	no	—
949	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
950	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
951	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
952	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
953	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
954	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
955	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
956	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
957	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
958	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
959	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
960	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
961	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
962	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
963	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
964	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
965	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
966	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
967	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
968	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
969	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
970	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
971	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
972	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
973	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
974	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
975	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
976	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
977	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
978	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
979	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
980	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
981	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
982	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
983	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
984	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
985	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
986	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
987	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
988	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
989	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
990	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
991	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
992	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
993	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
994	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
995	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
996	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
997	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
998	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
999	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1000	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1001	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1002	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1003	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1004	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1005	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1006	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1007	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1008	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1009	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1010	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1011	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1012	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1013	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1014	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1015	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1016	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1017	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1018	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1019	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1020	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1021	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1022	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1023	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1024	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1025	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1026	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1027	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1028	C₄²	C₂³×C₃×C₅	1	2	yes	—
1029	C₄²	C₂³×C₃×C₅	1	2	yes	—
1030	C₄²	C₂³×C₃×C₅	1	2	yes	—
1031	C₃×C₅	#3560	1	1	yes	characteristic, direct product factor, Hall
1032	C₂²×C₃	—	2	1	no	—
1033	C₂²×C₃	—	2	1	no	—
1034	C₂²×C₃	—	2	2	no	—
1035	C₂²×C₃	—	2	2	no	—
1036	C₂²×C₃	—	2	2	no	—
1037	C₂²×C₃	—	2	2	no	—
1038	C₂²×C₃	—	2	2	no	—
1039	C₂²×C₃	—	2	2	no	—
1040	C₂²×C₃	—	2	2	no	—
1041	C₂²×C₃	—	2	2	no	—
1042	C₂²×C₃	—	2	2	no	—
1043	C₂²×C₃	—	2	2	no	—
1044	C₂²×C₃	—	2	2	no	—
1045	C₂²×C₃	—	2	2	no	—
1046	C₂²×C₃	—	8	2	no	—
1047	C₂²×C₃	—	8	4	no	—
1048	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
1049	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1050	C₃×C₄	—	2	1	no	—
1051	C₃×C₄	—	2	2	no	—
1052	C₃×C₄	—	2	1	no	—
1053	C₃×C₄	—	2	2	no	—
1054	C₃×C₄	—	2	2	no	—
1055	C₃×C₄	—	2	2	no	—
1056	C₃×C₄	—	2	1	no	—
1057	C₃×C₄	—	2	2	no	—
1058	C₃×C₄	—	2	2	no	—
1059	C₃×C₄	—	2	2	no	—
1060	C₃×C₄	—	2	1	no	—
1061	C₃×C₄	—	2	1	no	—
1062	C₃×C₄	—	2	2	no	—
1063	C₃×C₄	—	2	1	no	—
1064	C₂×C₅	—	2	2	no	—
1065	C₂×C₅	—	4	2	no	—
1066	C₂×C₅	—	4	2	no	—
1067	C₂×C₅	—	4	2	no	—
1068	C₂×C₅	—	4	2	no	—
1069	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1070	C₂×C₅	C₃×#585	1	1	yes	characteristic
1071	C₂×C₅	C₃×#585	1	1	yes	characteristic
1072	C₂³	—	2	2	no	—
1073	C₂³	—	4	2	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	—	4	2	no	—
1077	C₂³	—	4	2	no	—
1078	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1079	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1080	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1081	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1082	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1083	Q₈	—	4	2	no	—
1084	Q₈	—	4	2	no	—
1085	Q₈	—	4	1	no	—
1086	D₄	—	2	4	no	—
1087	D₄	—	2	4	no	—
1088	D₄	—	2	4	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	1	no	—
1098	D₄	—	4	1	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	4	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1116	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1117	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1118	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1119	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1120	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1121	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1122	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1123	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1124	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1125	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1126	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1127	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1128	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1129	C₂×C₃	—	2	2	no	—
1130	C₂×C₃	—	4	2	no	—
1131	C₂×C₃	—	4	2	no	—
1132	C₂×C₃	—	4	2	no	—
1133	C₂×C₃	—	4	2	no	—
1134	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1135	C₂×C₃	C₅×#585	1	1	yes	characteristic
1136	C₂×C₃	C₅×#585	1	1	yes	characteristic
1137	C₅	C₃×#3560	1	1	yes	characteristic, direct product factor, Sylow
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	8	2	no	—
1153	C₂²	—	8	4	no	—
1154	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
1155	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	1	no	—
1167	C₄	—	2	1	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	2	1	no	—
1170	C₃	C₅×#3560	1	1	yes	characteristic, direct product factor, Sylow
1171	C₂	—	2	2	no	—
1172	C₂	—	4	2	no	—
1173	C₂	—	4	2	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	2	no	—
1176	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1177	C₂	C₃×C₅×#585	1	1	yes	characteristic
1178	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×#560	C₂	semidirect
3. C₃×C₅×#553	C₂	semidirect
4. C₃×C₅×#553	C₂	semidirect
5. C₃×C₅×#551	C₂	semidirect
6. C₃×C₅×#547	C₂	semidirect
7. C₃×C₅×#546	C₂	semidirect
8. C₃×C₅×#546	C₂	semidirect
9. C₃×C₅×#542	C₂	semidirect
10. C₃×C₅×#539	C₂	semidirect
11. C₃×C₅×#539	C₂	semidirect
12. C₃×C₅×#538	C₂	semidirect
13. C₃×C₅×#538	C₂	semidirect
14. C₃×C₅×#538	C₂	semidirect
15. C₃×C₅×#537	C₂	semidirect
16. C₃×C₅×#534	C₂	semidirect
17. C₃×C₅×#532	C₂	semidirect
18. C₃×C₅×#529	C₂	semidirect
19. C₂×C₃×C₅×#126	C₂	semidirect
20. C₅×#3560	C₃	direct (N × H)
21. C₂×C₃×C₅×#41	C₂²	semidirect
22. C₂×C₃×C₅×#41	C₂²	semidirect
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
26. C₃×C₅×#127	C₂²	semidirect
27. C₃×C₅×#126	C₂²	semidirect
28. C₃×C₅×#126	C₂²	semidirect
29. C₃×C₅×#126	C₂²	semidirect
30. C₃×C₅×#126	C₂²	semidirect
31. C₃×C₅×#126	C₂²	semidirect
32. C₃×C₅×#126	C₂²	semidirect
33. C₃×C₅×#126	C₂²	semidirect
34. C₃×C₅×#126	C₂²	semidirect
35. C₃×C₅×#126	C₂²	semidirect
36. C₃×C₅×#125	C₂²	semidirect
37. C₃×C₅×#125	C₂²	semidirect
38. C₃×C₅×#125	C₂²	semidirect
41. C₃×C₅×#124	C₂²	semidirect
42. C₃×C₅×#124	C₂²	semidirect
43. C₃×C₅×#124	C₂²	semidirect
48. C₃×C₅×#123	C₂²	semidirect
49. C₃×C₅×#123	C₂²	semidirect
50. C₃×C₅×#123	C₂²	semidirect
51. C₃×C₅×#123	C₂²	semidirect
52. C₃×C₅×#123	C₂²	semidirect
53. C₃×C₅×#123	C₂²	semidirect
54. C₃×C₅×#123	C₂²	semidirect
55. C₃×C₅×#123	C₂²	semidirect
56. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
57. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
58. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
59. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
60. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
61. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
62. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
63. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
71. C₃×C₅×#121	C₂²	semidirect
72. C₃×C₅×#121	C₂²	semidirect
73. C₃×C₅×#121	C₂²	semidirect
74. C₃×C₅×#121	C₂²	semidirect
75. C₃×C₅×#121	C₂²	semidirect
76. C₃×C₅×#121	C₂²	semidirect
77. C₃×C₅×#121	C₂²	semidirect
78. C₃×C₅×#121	C₂²	semidirect
82. C₃×C₅×#120	C₂²	semidirect
83. C₃×C₅×#120	C₂²	semidirect
84. C₃×C₄×C₅×Q₈	C₂²	semidirect
85. C₃×C₄×C₅×D₄	C₂²	semidirect
86. C₃×C₄×C₅×D₄	C₂²	semidirect
87. C₃×C₄×C₅×D₄	C₂²	semidirect
88. C₃×C₄×C₅×D₄	C₂²	semidirect
89. C₃×C₄×C₅×D₄	C₂²	semidirect
90. C₃×C₄×C₅×D₄	C₂²	semidirect
91. C₃×C₄×C₅×D₄	C₂²	semidirect
92. C₃×C₄×C₅×D₄	C₂²	semidirect
93. C₃×C₄×C₅×D₄	C₂²	semidirect
94. C₃×C₄×C₅×D₄	C₂²	semidirect
95. C₃×C₄×C₅×D₄	C₂²	semidirect
96. C₃×C₅×#117	C₂²	semidirect
97. C₃×C₅×#117	C₂²	semidirect
98. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
99. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
100. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
101. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
105. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
106. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
107. C₂×C₃×C₄²×C₅	C₂²	semidirect
108. C₃×#3560	C₅	direct (N × H)
109. C₅×#563	C₂×C₃	semidirect
110. C₅×#560	C₂×C₃	semidirect
111. C₅×#553	C₂×C₃	semidirect
112. C₅×#553	C₂×C₃	semidirect
113. C₅×#551	C₂×C₃	semidirect
114. C₅×#547	C₂×C₃	semidirect
115. C₅×#546	C₂×C₃	semidirect
116. C₅×#546	C₂×C₃	semidirect
117. C₅×#542	C₂×C₃	semidirect
118. C₅×#539	C₂×C₃	semidirect
119. C₅×#539	C₂×C₃	semidirect
120. C₅×#538	C₂×C₃	semidirect
121. C₅×#538	C₂×C₃	semidirect
122. C₅×#538	C₂×C₃	semidirect
123. C₅×#537	C₂×C₃	semidirect
124. C₅×#534	C₂×C₃	semidirect
125. C₅×#532	C₂×C₃	semidirect
126. C₅×#529	C₂×C₃	semidirect
127. C₂×C₅×#126	C₂×C₃	semidirect
218. C₃×#563	C₂×C₅	semidirect
219. C₃×#560	C₂×C₅	semidirect
220. C₃×#553	C₂×C₅	semidirect
221. C₃×#553	C₂×C₅	semidirect
222. C₃×#551	C₂×C₅	semidirect
223. C₃×#547	C₂×C₅	semidirect
224. C₃×#546	C₂×C₅	semidirect
225. C₃×#546	C₂×C₅	semidirect
226. C₃×#542	C₂×C₅	semidirect
227. C₃×#539	C₂×C₅	semidirect
228. C₃×#539	C₂×C₅	semidirect
229. C₃×#538	C₂×C₅	semidirect
230. C₃×#538	C₂×C₅	semidirect
231. C₃×#538	C₂×C₅	semidirect
232. C₃×#537	C₂×C₅	semidirect
233. C₃×#534	C₂×C₅	semidirect
234. C₃×#532	C₂×C₅	semidirect
235. C₃×#529	C₂×C₅	semidirect
236. C₂×C₃×#126	C₂×C₅	semidirect
237. C₂×C₅×#41	C₂²×C₃	semidirect
238. C₂×C₅×#41	C₂²×C₃	semidirect
240. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
241. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
242. C₅×#127	C₂²×C₃	semidirect
243. C₅×#126	C₂²×C₃	semidirect
244. C₅×#126	C₂²×C₃	semidirect
245. C₅×#126	C₂²×C₃	semidirect
246. C₅×#126	C₂²×C₃	semidirect
247. C₅×#126	C₂²×C₃	semidirect
248. C₅×#126	C₂²×C₃	semidirect
249. C₅×#126	C₂²×C₃	semidirect
250. C₅×#126	C₂²×C₃	semidirect
251. C₅×#126	C₂²×C₃	semidirect
252. C₅×#125	C₂²×C₃	semidirect
253. C₅×#125	C₂²×C₃	semidirect
254. C₅×#125	C₂²×C₃	semidirect
257. C₅×#124	C₂²×C₃	semidirect
258. C₅×#124	C₂²×C₃	semidirect
259. C₅×#124	C₂²×C₃	semidirect
264. C₅×#123	C₂²×C₃	semidirect
265. C₅×#123	C₂²×C₃	semidirect
266. C₅×#123	C₂²×C₃	semidirect
267. C₅×#123	C₂²×C₃	semidirect
268. C₅×#123	C₂²×C₃	semidirect
269. C₅×#123	C₂²×C₃	semidirect
270. C₅×#123	C₂²×C₃	semidirect
271. C₅×#123	C₂²×C₃	semidirect
272. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
273. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
274. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
275. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
276. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
277. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
278. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
279. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
287. C₅×#121	C₂²×C₃	semidirect
288. C₅×#121	C₂²×C₃	semidirect
289. C₅×#121	C₂²×C₃	semidirect
290. C₅×#121	C₂²×C₃	semidirect
291. C₅×#121	C₂²×C₃	semidirect
292. C₅×#121	C₂²×C₃	semidirect
293. C₅×#121	C₂²×C₃	semidirect
294. C₅×#121	C₂²×C₃	semidirect
298. C₅×#120	C₂²×C₃	semidirect
299. C₅×#120	C₂²×C₃	semidirect
300. C₄×C₅×Q₈	C₂²×C₃	semidirect
301. C₄×C₅×D₄	C₂²×C₃	semidirect
302. C₄×C₅×D₄	C₂²×C₃	semidirect
303. C₄×C₅×D₄	C₂²×C₃	semidirect
304. C₄×C₅×D₄	C₂²×C₃	semidirect
305. C₄×C₅×D₄	C₂²×C₃	semidirect
306. C₄×C₅×D₄	C₂²×C₃	semidirect
307. C₄×C₅×D₄	C₂²×C₃	semidirect
308. C₄×C₅×D₄	C₂²×C₃	semidirect
309. C₄×C₅×D₄	C₂²×C₃	semidirect
310. C₄×C₅×D₄	C₂²×C₃	semidirect
311. C₄×C₅×D₄	C₂²×C₃	semidirect
312. C₅×#117	C₂²×C₃	semidirect
313. C₅×#117	C₂²×C₃	semidirect
314. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
315. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
316. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
317. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
321. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
322. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
323. C₂×C₄²×C₅	C₂²×C₃	semidirect
324. #3560	C₃×C₅	direct (N × H)
382. C₂×C₃×#41	C₂²×C₅	semidirect
383. C₂×C₃×#41	C₂²×C₅	semidirect
385. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
386. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
387. C₃×#127	C₂²×C₅	semidirect
388. C₃×#126	C₂²×C₅	semidirect
389. C₃×#126	C₂²×C₅	semidirect
390. C₃×#126	C₂²×C₅	semidirect
391. C₃×#126	C₂²×C₅	semidirect
392. C₃×#126	C₂²×C₅	semidirect
393. C₃×#126	C₂²×C₅	semidirect
394. C₃×#126	C₂²×C₅	semidirect
395. C₃×#126	C₂²×C₅	semidirect
396. C₃×#126	C₂²×C₅	semidirect
397. C₃×#125	C₂²×C₅	semidirect
398. C₃×#125	C₂²×C₅	semidirect
399. C₃×#125	C₂²×C₅	semidirect
402. C₃×#124	C₂²×C₅	semidirect
403. C₃×#124	C₂²×C₅	semidirect
404. C₃×#124	C₂²×C₅	semidirect
409. C₃×#123	C₂²×C₅	semidirect
410. C₃×#123	C₂²×C₅	semidirect
411. C₃×#123	C₂²×C₅	semidirect
412. C₃×#123	C₂²×C₅	semidirect
413. C₃×#123	C₂²×C₅	semidirect
414. C₃×#123	C₂²×C₅	semidirect
415. C₃×#123	C₂²×C₅	semidirect
416. C₃×#123	C₂²×C₅	semidirect
417. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
418. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
419. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
420. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
421. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
422. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
423. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
424. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
432. C₃×#121	C₂²×C₅	semidirect
433. C₃×#121	C₂²×C₅	semidirect
434. C₃×#121	C₂²×C₅	semidirect
435. C₃×#121	C₂²×C₅	semidirect
436. C₃×#121	C₂²×C₅	semidirect
437. C₃×#121	C₂²×C₅	semidirect
438. C₃×#121	C₂²×C₅	semidirect
439. C₃×#121	C₂²×C₅	semidirect
443. C₃×#120	C₂²×C₅	semidirect
444. C₃×#120	C₂²×C₅	semidirect
445. C₃×C₄×Q₈	C₂²×C₅	semidirect
446. C₃×C₄×D₄	C₂²×C₅	semidirect
447. C₃×C₄×D₄	C₂²×C₅	semidirect
448. C₃×C₄×D₄	C₂²×C₅	semidirect
449. C₃×C₄×D₄	C₂²×C₅	semidirect
450. C₃×C₄×D₄	C₂²×C₅	semidirect
451. C₃×C₄×D₄	C₂²×C₅	semidirect
452. C₃×C₄×D₄	C₂²×C₅	semidirect
453. C₃×C₄×D₄	C₂²×C₅	semidirect
454. C₃×C₄×D₄	C₂²×C₅	semidirect
455. C₃×C₄×D₄	C₂²×C₅	semidirect
456. C₃×C₄×D₄	C₂²×C₅	semidirect
457. C₃×#117	C₂²×C₅	semidirect
458. C₃×#117	C₂²×C₅	semidirect
459. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
460. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
461. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
462. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
466. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
467. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
468. C₂×C₃×C₄²	C₂²×C₅	semidirect
559. #563	C₂×C₃×C₅	semidirect
560. #560	C₂×C₃×C₅	semidirect
561. #553	C₂×C₃×C₅	semidirect
562. #553	C₂×C₃×C₅	semidirect
563. #551	C₂×C₃×C₅	semidirect
564. #547	C₂×C₃×C₅	semidirect
565. #546	C₂×C₃×C₅	semidirect
566. #546	C₂×C₃×C₅	semidirect
567. #542	C₂×C₃×C₅	semidirect
568. #539	C₂×C₃×C₅	semidirect
569. #539	C₂×C₃×C₅	semidirect
570. #538	C₂×C₃×C₅	semidirect
571. #538	C₂×C₃×C₅	semidirect
572. #538	C₂×C₃×C₅	semidirect
573. #537	C₂×C₃×C₅	semidirect
574. #534	C₂×C₃×C₅	semidirect
575. #532	C₂×C₃×C₅	semidirect
576. #529	C₂×C₃×C₅	semidirect
577. C₂×#126	C₂×C₃×C₅	semidirect
757. C₂×#41	C₂²×C₃×C₅	semidirect
758. C₂×#41	C₂²×C₃×C₅	semidirect
760. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
761. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
762. #127	C₂²×C₃×C₅	semidirect
763. #126	C₂²×C₃×C₅	semidirect
764. #126	C₂²×C₃×C₅	semidirect
765. #126	C₂²×C₃×C₅	semidirect
766. #126	C₂²×C₃×C₅	semidirect
767. #126	C₂²×C₃×C₅	semidirect
768. #126	C₂²×C₃×C₅	semidirect
769. #126	C₂²×C₃×C₅	semidirect
770. #126	C₂²×C₃×C₅	semidirect
771. #126	C₂²×C₃×C₅	semidirect
772. #125	C₂²×C₃×C₅	semidirect
773. #125	C₂²×C₃×C₅	semidirect
774. #125	C₂²×C₃×C₅	semidirect
777. #124	C₂²×C₃×C₅	semidirect
778. #124	C₂²×C₃×C₅	semidirect
779. #124	C₂²×C₃×C₅	semidirect
784. #123	C₂²×C₃×C₅	semidirect
785. #123	C₂²×C₃×C₅	semidirect
786. #123	C₂²×C₃×C₅	semidirect
787. #123	C₂²×C₃×C₅	semidirect
788. #123	C₂²×C₃×C₅	semidirect
789. #123	C₂²×C₃×C₅	semidirect
790. #123	C₂²×C₃×C₅	semidirect
791. #123	C₂²×C₃×C₅	semidirect
792. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
793. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
794. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
795. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
796. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
797. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
798. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
799. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
807. #121	C₂²×C₃×C₅	semidirect
808. #121	C₂²×C₃×C₅	semidirect
809. #121	C₂²×C₃×C₅	semidirect
810. #121	C₂²×C₃×C₅	semidirect
811. #121	C₂²×C₃×C₅	semidirect
812. #121	C₂²×C₃×C₅	semidirect
813. #121	C₂²×C₃×C₅	semidirect
814. #121	C₂²×C₃×C₅	semidirect
818. #120	C₂²×C₃×C₅	semidirect
819. #120	C₂²×C₃×C₅	semidirect
820. C₄×Q₈	C₂²×C₃×C₅	semidirect
821. C₄×D₄	C₂²×C₃×C₅	semidirect
822. C₄×D₄	C₂²×C₃×C₅	semidirect
823. C₄×D₄	C₂²×C₃×C₅	semidirect
824. C₄×D₄	C₂²×C₃×C₅	semidirect
825. C₄×D₄	C₂²×C₃×C₅	semidirect
826. C₄×D₄	C₂²×C₃×C₅	semidirect
827. C₄×D₄	C₂²×C₃×C₅	semidirect
828. C₄×D₄	C₂²×C₃×C₅	semidirect
829. C₄×D₄	C₂²×C₃×C₅	semidirect
830. C₄×D₄	C₂²×C₃×C₅	semidirect
831. C₄×D₄	C₂²×C₃×C₅	semidirect
832. #117	C₂²×C₃×C₅	semidirect
833. #117	C₂²×C₃×C₅	semidirect
834. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
835. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
836. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
837. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
841. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
842. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
843. C₂×C₄²	C₂²×C₃×C₅	semidirect
1031. C₃×C₅	#3560	direct (N × H)
1137. C₅	C₃×#3560	direct (N × H)
1170. C₃	C₅×#3560	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×#560	2
C₃×C₅×#553	2
C₃×C₅×#551	2
C₃×C₅×#547	2
C₃×C₅×#546	2
C₃×C₅×#542	2
C₃×C₅×#539	2
C₃×C₅×#538	2
C₃×C₅×#537	2
C₃×C₅×#534	2
C₃×C₅×#532	2
C₃×C₅×#529	2
C₂×C₃×C₅×#126	2
C₅×#3560	3
C₃×#3560	5

Subgroups — C3×C5×#3560 #14276594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3560 #14276594