Subgroups — C₅×#34969 #11957689

Order 1280.

1962 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2530	C₂	1	2	yes	maximal, complemented
2	C₅×#2527	C₂	1	2	yes	maximal, complemented
3	C₅×#2511	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2492	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2477	C₂	1	2	yes	maximal, complemented
8	C₅×#2470	C₂	1	2	yes	maximal, complemented
9	C₅×#2452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2427	C₂	1	1	yes	maximal, characteristic
12	C₅×#2422	C₂	1	1	yes	maximal, characteristic
13	C₅×#2401	C₂	1	2	yes	maximal, complemented
14	C₅×#2398	C₂	1	2	yes	maximal, complemented
15	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₅×#123	C₂	1	2	yes	maximal, complemented
20	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic
21	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×#124	C₂²	1	1	yes	characteristic
26	C₂×C₅×#123	C₂²	1	2	yes	—
27	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
32	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
36	C₂×C₅×#117	C₂²	1	1	yes	characteristic
37	C₂×C₅×#117	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₅	C₂²	1	2	yes	—
40	C₅×#401	C₂²	1	2	yes	—
41	C₅×#400	C₂²	1	2	yes	—
42	C₅×#400	C₂²	1	2	yes	—
43	C₅×#400	C₂²	1	2	yes	—
44	C₅×#400	C₂²	1	2	yes	—
45	C₅×#400	C₂²	1	2	yes	—
46	C₅×#397	C₂²	1	2	yes	—
47	C₅×#397	C₂²	1	2	yes	—
48	C₅×#397	C₂²	1	2	yes	—
49	C₅×#397	C₂²	1	2	yes	—
50	C₅×#397	C₂²	1	2	yes	—
51	C₅×#396	C₂²	1	2	yes	—
52	C₅×#394	C₂²	1	2	yes	—
53	C₅×#394	C₂²	1	2	yes	—
54	C₅×#393	C₂²	1	2	yes	—
55	C₅×#393	C₂²	1	2	yes	—
56	C₅×#391	C₂²	1	2	yes	—
57	C₅×#391	C₂²	1	1	yes	characteristic
58	C₅×#391	C₂²	1	2	yes	—
59	C₅×#391	C₂²	1	1	yes	characteristic
60	C₅×#391	C₂²	1	1	yes	characteristic
61	C₅×#391	C₂²	1	1	yes	characteristic
62	C₅×#390	C₂²	1	1	yes	characteristic
63	C₅×#390	C₂²	1	1	yes	characteristic
64	C₅×#389	C₂²	1	2	yes	—
65	C₅×#389	C₂²	1	2	yes	—
66	C₅×#389	C₂²	1	1	yes	characteristic
67	C₅×#389	C₂²	1	1	yes	characteristic
68	C₅×#389	C₂²	1	1	yes	characteristic
69	C₅×#389	C₂²	1	1	yes	characteristic
70	C₅×#389	C₂²	1	1	yes	characteristic
71	C₅×#389	C₂²	1	1	yes	characteristic
72	C₅×#388	C₂²	1	2	yes	—
73	C₅×#388	C₂²	1	2	yes	—
74	C₅×#388	C₂²	1	2	yes	—
75	C₅×#388	C₂²	1	2	yes	—
76	C₅×#388	C₂²	1	2	yes	—
77	C₅×#387	C₂²	1	2	yes	—
78	C₅×#387	C₂²	1	2	yes	—
79	C₅×#387	C₂²	1	2	yes	—
80	C₅×#387	C₂²	1	2	yes	—
81	C₅×#387	C₂²	1	2	yes	—
82	C₅×#387	C₂²	1	2	yes	—
83	C₅×#387	C₂²	1	2	yes	—
84	C₅×#386	C₂²	1	2	yes	—
85	C₅×#386	C₂²	1	2	yes	—
86	C₅×#385	C₂²	1	2	yes	—
87	C₅×#385	C₂²	1	2	yes	—
88	C₅×#385	C₂²	1	2	yes	—
89	C₅×#385	C₂²	1	2	yes	—
90	C₅×#384	C₂²	1	1	yes	characteristic
91	C₅×#382	C₂²	1	1	yes	characteristic
92	C₅×#381	C₂²	1	2	yes	—
93	C₅×#380	C₂²	1	1	yes	characteristic
94	C₅×#380	C₂²	1	1	yes	characteristic
95	C₅×#380	C₂²	1	2	yes	—
96	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
105	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
106	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
108	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
109	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₅×#376	C₂²	1	1	yes	characteristic
119	C₅×#376	C₂²	1	1	yes	characteristic
120	C₅×#376	C₂²	1	2	yes	—
121	C₄³×C₅	C₂²	1	1	yes	characteristic
122	C₄³×C₅	C₂²	1	1	yes	characteristic
123	#34969	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₅×Q₈	C₂³	1	2	yes	—
126	C₂²×C₅×D₄	C₂³	1	2	yes	—
127	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅	C₂³	1	2	yes	—
132	C₂³×C₄×C₅	C₂³	1	2	yes	—
133	C₂³×C₄×C₅	C₂³	1	2	yes	—
134	C₅×C₄⋊Q₈	—	2	4	no	—
135	C₅×#124	—	2	4	no	—
136	C₅×#123	—	2	8	no	—
137	C₅×C₂²⋊Q₈	—	2	8	no	—
138	C₅×C₂²⋊Q₈	—	2	4	no	—
139	C₅×#121	—	2	4	no	—
140	C₄×C₅×Q₈	—	2	4	no	—
141	C₄×C₅×Q₈	—	4	4	no	—
142	C₄×C₅×D₄	—	2	4	no	—
143	C₄×C₅×D₄	—	2	4	no	—
144	C₄×C₅×D₄	—	2	4	no	—
145	C₄×C₅×D₄	—	4	4	no	—
146	C₅×#117	—	2	4	no	—
147	C₅×#117	—	2	4	no	—
148	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₅	—	2	4	no	—
187	C₂×C₄²×C₅	—	4	4	no	—
188	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅	C₂³	1	2	yes	—
203	C₂×C₄²×C₅	C₂³	1	2	yes	—
204	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₅	C₂³	1	2	yes	—
206	C₂×C₄²×C₅	C₂³	1	2	yes	—
207	C₂×C₄²×C₅	C₂³	1	2	yes	—
208	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
209	C₅×#95	C₂³	1	1	yes	characteristic
210	C₅×#95	C₂³	1	1	yes	characteristic
211	C₅×#95	C₂³	1	1	yes	characteristic
212	C₅×#95	C₂³	1	1	yes	characteristic
213	C₅×#95	C₂³	1	1	yes	characteristic
214	C₅×#95	C₂³	1	1	yes	characteristic
215	C₅×#95	C₂³	1	1	yes	characteristic
216	C₅×#95	C₂³	1	1	yes	characteristic
217	C₅×#95	C₂³	1	2	yes	—
218	C₅×#95	C₂³	1	2	yes	—
219	C₅×#95	C₂³	1	2	yes	—
220	C₅×#95	C₂³	1	2	yes	—
221	C₅×#95	C₂³	1	2	yes	—
222	C₅×#95	C₂³	1	2	yes	—
223	C₅×#95	C₂³	1	2	yes	—
224	C₅×#95	C₂³	1	2	yes	—
225	C₅×#95	C₂³	1	2	yes	—
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	2	yes	—
228	C₅×#95	C₂³	1	2	yes	—
229	C₅×#95	C₂³	1	2	yes	—
230	C₅×#95	C₂³	1	2	yes	—
231	C₅×#95	C₂³	1	2	yes	—
232	C₅×#95	C₂³	1	2	yes	—
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	2	yes	—
235	C₅×#95	C₂³	1	2	yes	—
236	C₅×#95	C₂³	1	2	yes	—
237	C₅×#95	C₂³	1	2	yes	—
238	C₅×#95	C₂³	1	2	yes	—
239	#2530	C₂×C₅	1	2	yes	complemented
240	#2527	C₂×C₅	1	2	yes	complemented
241	#2511	C₂×C₅	1	1	yes	characteristic, complemented
242	#2509	C₂×C₅	1	1	yes	characteristic, complemented
243	#2494	C₂×C₅	1	1	yes	characteristic, complemented
244	#2492	C₂×C₅	1	1	yes	characteristic, complemented
245	#2477	C₂×C₅	1	2	yes	complemented
246	#2470	C₂×C₅	1	2	yes	complemented
247	#2452	C₂×C₅	1	1	yes	characteristic, complemented
248	#2447	C₂×C₅	1	1	yes	characteristic, complemented
249	#2427	C₂×C₅	1	1	yes	characteristic
250	#2422	C₂×C₅	1	1	yes	characteristic
251	#2401	C₂×C₅	1	2	yes	complemented
252	#2398	C₂×C₅	1	2	yes	complemented
253	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
254	C₄×#124	C₂×C₅	1	1	yes	characteristic, complemented
255	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
256	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
257	C₄×#123	C₂×C₅	1	2	yes	complemented
258	C₄×#121	C₂×C₅	1	1	yes	characteristic
259	#2295	C₂×C₅	1	1	yes	characteristic, complemented
260	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
261	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
262	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₅	C₂⁴	1	2	yes	—
264	C₂×C₅×Q₈	—	2	2	no	—
265	C₂×C₅×Q₈	—	2	4	no	—
266	C₂×C₅×Q₈	—	2	2	no	—
267	C₂×C₅×Q₈	—	2	2	no	—
268	C₂×C₅×Q₈	—	2	4	no	—
269	C₂×C₅×Q₈	—	4	2	no	—
270	C₂×C₅×D₄	—	2	4	no	—
271	C₂×C₅×D₄	—	2	4	no	—
272	C₂×C₅×D₄	—	2	2	no	—
273	C₂×C₅×D₄	—	2	2	no	—
274	C₂×C₅×D₄	—	4	2	no	—
275	C₂×C₅×D₄	#41	1	4	yes	—
276	C₂²×C₄×C₅	—	2	2	no	—
277	C₂²×C₄×C₅	—	2	2	no	—
278	C₂²×C₄×C₅	—	2	2	no	—
279	C₂²×C₄×C₅	—	2	4	no	—
280	C₂²×C₄×C₅	—	2	2	no	—
281	C₂²×C₄×C₅	—	2	2	no	—
282	C₂²×C₄×C₅	—	2	4	no	—
283	C₂²×C₄×C₅	—	2	4	no	—
284	C₂²×C₄×C₅	—	2	2	no	—
285	C₂²×C₄×C₅	—	2	4	no	—
286	C₂²×C₄×C₅	—	2	2	no	—
287	C₂²×C₄×C₅	—	2	4	no	—
288	C₂²×C₄×C₅	—	2	4	no	—
289	C₂²×C₄×C₅	—	2	2	no	—
290	C₂²×C₄×C₅	—	2	2	no	—
291	C₂²×C₄×C₅	—	2	4	no	—
292	C₂²×C₄×C₅	—	4	2	no	—
293	C₂²×C₄×C₅	—	4	2	no	—
294	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
315	C₅×C₄⋊C₄	—	2	2	no	—
316	C₅×C₄⋊C₄	—	2	2	no	—
317	C₅×C₄⋊C₄	—	2	2	no	—
318	C₅×C₄⋊C₄	—	2	2	no	—
319	C₅×C₄⋊C₄	—	2	2	no	—
320	C₅×C₄⋊C₄	—	2	2	no	—
321	C₅×C₄⋊C₄	—	2	4	no	—
322	C₅×C₄⋊C₄	—	2	2	no	—
323	C₅×C₄⋊C₄	—	2	4	no	—
324	C₅×C₄⋊C₄	—	2	4	no	—
325	C₅×C₄⋊C₄	—	2	4	no	—
326	C₅×C₄⋊C₄	—	2	4	no	—
327	C₅×C₄⋊C₄	—	2	4	no	—
328	C₅×C₄⋊C₄	—	2	4	no	—
329	C₅×C₄⋊C₄	—	2	2	no	—
330	C₅×C₄⋊C₄	—	4	2	no	—
331	C₅×C₄⋊C₄	—	4	2	no	—
332	C₅×C₄⋊C₄	—	4	2	no	—
333	C₅×C₄⋊C₄	—	4	2	no	—
334	C₅×C₄⋊C₄	#41	1	4	yes	—
335	C₅×C₄⋊C₄	#41	1	4	yes	—
336	C₅×C₂²⋊C₄	—	2	2	no	—
337	C₅×C₂²⋊C₄	—	2	4	no	—
338	C₅×C₂²⋊C₄	—	2	4	no	—
339	C₅×C₂²⋊C₄	—	2	4	no	—
340	C₅×C₂²⋊C₄	—	2	4	no	—
341	C₅×C₂²⋊C₄	—	2	4	no	—
342	C₅×C₂²⋊C₄	—	2	2	no	—
343	C₅×C₂²⋊C₄	—	2	2	no	—
344	C₅×C₂²⋊C₄	—	2	4	no	—
345	C₅×C₂²⋊C₄	—	2	4	no	—
346	C₅×C₂²⋊C₄	—	2	4	no	—
347	C₅×C₂²⋊C₄	—	2	4	no	—
348	C₅×C₂²⋊C₄	—	2	4	no	—
349	C₅×C₂²⋊C₄	—	2	4	no	—
350	C₅×C₂²⋊C₄	—	4	2	no	—
351	C₅×C₂²⋊C₄	—	4	2	no	—
352	C₅×C₂²⋊C₄	#41	1	4	yes	—
353	C₄²×C₅	—	2	2	no	—
354	C₄²×C₅	—	2	2	no	—
355	C₄²×C₅	—	2	2	no	—
356	C₄²×C₅	—	2	2	no	—
357	C₄²×C₅	—	2	2	no	—
358	C₄²×C₅	—	2	2	no	—
359	C₄²×C₅	—	2	2	no	—
360	C₄²×C₅	—	2	2	no	—
361	C₄²×C₅	—	2	2	no	—
362	C₄²×C₅	—	2	4	no	—
363	C₄²×C₅	—	2	2	no	—
364	C₄²×C₅	—	2	2	no	—
365	C₄²×C₅	—	2	2	no	—
366	C₄²×C₅	—	2	4	no	—
367	C₄²×C₅	—	2	4	no	—
368	C₄²×C₅	—	2	2	no	—
369	C₄²×C₅	—	2	2	no	—
370	C₄²×C₅	—	2	2	no	—
371	C₄²×C₅	—	4	2	no	—
372	C₄²×C₅	—	4	2	no	—
373	C₄²×C₅	#41	1	4	yes	—
374	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
375	C₂×#124	C₂²×C₅	1	1	yes	characteristic
376	C₂×#123	C₂²×C₅	1	2	yes	—
377	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
378	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
379	C₂×#121	C₂²×C₅	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
382	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
386	C₂×#117	C₂²×C₅	1	1	yes	characteristic
387	C₂×#117	C₂²×C₅	1	1	yes	characteristic
388	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
389	C₂²×C₄²	C₂²×C₅	1	2	yes	—
390	#401	C₂²×C₅	1	2	yes	—
391	#400	C₂²×C₅	1	2	yes	—
392	#400	C₂²×C₅	1	2	yes	—
393	#400	C₂²×C₅	1	2	yes	—
394	#400	C₂²×C₅	1	2	yes	—
395	#400	C₂²×C₅	1	2	yes	—
396	#397	C₂²×C₅	1	2	yes	—
397	#397	C₂²×C₅	1	2	yes	—
398	#397	C₂²×C₅	1	2	yes	—
399	#397	C₂²×C₅	1	2	yes	—
400	#397	C₂²×C₅	1	2	yes	—
401	#396	C₂²×C₅	1	2	yes	—
402	#394	C₂²×C₅	1	2	yes	—
403	#394	C₂²×C₅	1	2	yes	—
404	#393	C₂²×C₅	1	2	yes	—
405	#393	C₂²×C₅	1	2	yes	—
406	#391	C₂²×C₅	1	2	yes	—
407	#391	C₂²×C₅	1	1	yes	characteristic
408	#391	C₂²×C₅	1	1	yes	characteristic
409	#391	C₂²×C₅	1	1	yes	characteristic
410	#391	C₂²×C₅	1	1	yes	characteristic
411	#391	C₂²×C₅	1	2	yes	—
412	#390	C₂²×C₅	1	1	yes	characteristic
413	#390	C₂²×C₅	1	1	yes	characteristic
414	#389	C₂²×C₅	1	1	yes	characteristic
415	#389	C₂²×C₅	1	1	yes	characteristic
416	#389	C₂²×C₅	1	2	yes	—
417	#389	C₂²×C₅	1	1	yes	characteristic
418	#389	C₂²×C₅	1	1	yes	characteristic
419	#389	C₂²×C₅	1	1	yes	characteristic
420	#389	C₂²×C₅	1	2	yes	—
421	#389	C₂²×C₅	1	1	yes	characteristic
422	#388	C₂²×C₅	1	2	yes	—
423	#388	C₂²×C₅	1	2	yes	—
424	#388	C₂²×C₅	1	2	yes	—
425	#388	C₂²×C₅	1	2	yes	—
426	#388	C₂²×C₅	1	2	yes	—
427	#387	C₂²×C₅	1	2	yes	—
428	#387	C₂²×C₅	1	2	yes	—
429	#387	C₂²×C₅	1	2	yes	—
430	#387	C₂²×C₅	1	2	yes	—
431	#387	C₂²×C₅	1	2	yes	—
432	#387	C₂²×C₅	1	2	yes	—
433	#387	C₂²×C₅	1	2	yes	—
434	#386	C₂²×C₅	1	2	yes	—
435	#386	C₂²×C₅	1	2	yes	—
436	#385	C₂²×C₅	1	2	yes	—
437	#385	C₂²×C₅	1	2	yes	—
438	#385	C₂²×C₅	1	2	yes	—
439	#385	C₂²×C₅	1	2	yes	—
440	#384	C₂²×C₅	1	1	yes	characteristic
441	#382	C₂²×C₅	1	1	yes	characteristic
442	#381	C₂²×C₅	1	2	yes	—
443	#380	C₂²×C₅	1	1	yes	characteristic
444	#380	C₂²×C₅	1	2	yes	—
445	#380	C₂²×C₅	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
451	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
458	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
460	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
462	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
464	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
465	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
467	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
468	#376	C₂²×C₅	1	2	yes	—
469	#376	C₂²×C₅	1	1	yes	characteristic
470	#376	C₂²×C₅	1	1	yes	characteristic
471	C₄³	C₂²×C₅	1	1	yes	characteristic
472	C₄³	C₂²×C₅	1	1	yes	characteristic
473	C₂³×C₅	—	2	1	no	—
474	C₂³×C₅	—	2	1	no	—
475	C₂³×C₅	—	2	2	no	—
476	C₂³×C₅	—	2	2	no	—
477	C₂³×C₅	—	2	2	no	—
478	C₂³×C₅	—	2	2	no	—
479	C₂³×C₅	—	2	1	no	—
480	C₂³×C₅	—	2	1	no	—
481	C₂³×C₅	—	2	1	no	—
482	C₂³×C₅	—	2	2	no	—
483	C₂³×C₅	—	2	1	no	—
484	C₂³×C₅	—	2	2	no	—
485	C₂³×C₅	C₂×#41	1	4	yes	—
486	C₂³×C₅	C₂×#41	1	2	yes	—
487	C₂³×C₅	C₂⁵	1	1	yes	characteristic
488	C₅×Q₈	—	4	8	no	—
489	C₅×Q₈	—	4	4	no	—
490	C₅×D₄	—	2	8	no	—
491	C₅×D₄	—	4	8	no	—
492	C₂×C₄×C₅	—	2	8	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	1	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	2	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	2	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	1	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	1	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	2	no	—
518	C₂×C₄×C₅	—	2	2	no	—
519	C₂×C₄×C₅	—	2	2	no	—
520	C₂×C₄×C₅	—	2	1	no	—
521	C₂×C₄×C₅	—	2	2	no	—
522	C₂×C₄×C₅	—	2	2	no	—
523	C₂×C₄×C₅	—	2	2	no	—
524	C₂×C₄×C₅	—	2	2	no	—
525	C₂×C₄×C₅	—	2	2	no	—
526	C₂×C₄×C₅	—	2	2	no	—
527	C₂×C₄×C₅	—	2	2	no	—
528	C₂×C₄×C₅	—	2	2	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	2	no	—
531	C₂×C₄×C₅	—	2	2	no	—
532	C₂×C₄×C₅	—	2	2	no	—
533	C₂×C₄×C₅	—	2	2	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	2	2	no	—
536	C₂×C₄×C₅	—	2	2	no	—
537	C₂×C₄×C₅	—	2	1	no	—
538	C₂×C₄×C₅	—	2	1	no	—
539	C₂×C₄×C₅	—	2	1	no	—
540	C₂×C₄×C₅	—	2	1	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	2	no	—
543	C₂×C₄×C₅	—	4	8	no	—
544	C₂×C₄×C₅	—	4	8	no	—
545	C₂×C₄×C₅	—	4	4	no	—
546	C₂×C₄×C₅	—	4	4	no	—
547	C₂×C₄×C₅	—	4	8	no	—
548	C₂×C₄×C₅	C₂×#41	1	2	yes	—
549	C₂×C₄×C₅	C₂×#41	1	2	yes	—
550	C₂×C₄×C₅	C₂×#41	1	2	yes	—
551	C₂×C₄×C₅	C₂×#41	1	2	yes	—
552	C₂×C₄×C₅	C₂×#41	1	2	yes	—
553	C₂×C₄×C₅	C₂×#41	1	2	yes	—
554	C₂×C₄×C₅	C₂×#41	1	4	yes	—
555	C₂×C₄×C₅	C₂×#41	1	2	yes	—
556	C₂×C₄×C₅	C₂×#41	1	2	yes	—
557	C₂×C₄×C₅	C₂×#41	1	2	yes	—
558	C₂×C₄×C₅	C₂×#41	1	2	yes	—
559	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
560	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
561	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₅	1	2	yes	—
563	C₂²×D₄	C₂³×C₅	1	2	yes	—
564	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₅	1	2	yes	—
568	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
569	C₂³×C₄	C₂³×C₅	1	2	yes	—
570	C₂³×C₄	C₂³×C₅	1	2	yes	—
571	C₄⋊Q₈	—	2	4	no	—
572	#124	—	2	4	no	—
573	#123	—	2	8	no	—
574	C₂²⋊Q₈	—	2	8	no	—
575	C₂²⋊Q₈	—	2	4	no	—
576	#121	—	2	4	no	—
577	C₄×Q₈	—	2	4	no	—
578	C₄×Q₈	—	4	4	no	—
579	C₄×D₄	—	2	4	no	—
580	C₄×D₄	—	2	4	no	—
581	C₄×D₄	—	2	4	no	—
582	C₄×D₄	—	4	4	no	—
583	#117	—	2	4	no	—
584	#117	—	2	4	no	—
585	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
623	C₂×C₄²	—	2	4	no	—
624	C₂×C₄²	—	4	4	no	—
625	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₅	1	2	yes	—
630	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₅	1	2	yes	—
634	C₂×C₄²	C₂³×C₅	1	2	yes	—
635	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₅	1	2	yes	—
644	C₂×C₄²	C₂³×C₅	1	2	yes	—
645	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
646	#95	C₂³×C₅	1	1	yes	characteristic
647	#95	C₂³×C₅	1	1	yes	characteristic
648	#95	C₂³×C₅	1	1	yes	characteristic
649	#95	C₂³×C₅	1	1	yes	characteristic
650	#95	C₂³×C₅	1	1	yes	characteristic
651	#95	C₂³×C₅	1	1	yes	characteristic
652	#95	C₂³×C₅	1	1	yes	characteristic
653	#95	C₂³×C₅	1	1	yes	characteristic
654	#95	C₂³×C₅	1	2	yes	—
655	#95	C₂³×C₅	1	2	yes	—
656	#95	C₂³×C₅	1	2	yes	—
657	#95	C₂³×C₅	1	2	yes	—
658	#95	C₂³×C₅	1	2	yes	—
659	#95	C₂³×C₅	1	2	yes	—
660	#95	C₂³×C₅	1	2	yes	—
661	#95	C₂³×C₅	1	2	yes	—
662	#95	C₂³×C₅	1	2	yes	—
663	#95	C₂³×C₅	1	2	yes	—
664	#95	C₂³×C₅	1	2	yes	—
665	#95	C₂³×C₅	1	2	yes	—
666	#95	C₂³×C₅	1	2	yes	—
667	#95	C₂³×C₅	1	2	yes	—
668	#95	C₂³×C₅	1	2	yes	—
669	#95	C₂³×C₅	1	2	yes	—
670	#95	C₂³×C₅	1	2	yes	—
671	#95	C₂³×C₅	1	2	yes	—
672	#95	C₂³×C₅	1	2	yes	—
673	#95	C₂³×C₅	1	2	yes	—
674	#95	C₂³×C₅	1	2	yes	—
675	#95	C₂³×C₅	1	2	yes	—
676	C₂²×C₅	—	2	4	no	—
677	C₂²×C₅	—	2	2	no	—
678	C₂²×C₅	—	2	4	no	—
679	C₂²×C₅	—	2	2	no	—
680	C₂²×C₅	—	2	2	no	—
681	C₂²×C₅	—	2	4	no	—
682	C₂²×C₅	—	4	1	no	—
683	C₂²×C₅	—	4	2	no	—
684	C₂²×C₅	—	4	2	no	—
685	C₂²×C₅	—	4	1	no	—
686	C₂²×C₅	—	4	2	no	—
687	C₂²×C₅	—	4	1	no	—
688	C₂²×C₅	—	4	2	no	—
689	C₂²×C₅	—	4	1	no	—
690	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
691	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
692	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
693	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
694	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
695	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
697	C₄×C₅	—	2	2	no	—
698	C₄×C₅	—	2	2	no	—
699	C₄×C₅	—	2	2	no	—
700	C₄×C₅	—	2	2	no	—
701	C₄×C₅	—	2	4	no	—
702	C₄×C₅	—	2	2	no	—
703	C₄×C₅	—	2	2	no	—
704	C₄×C₅	—	4	1	no	—
705	C₄×C₅	—	4	2	no	—
706	C₄×C₅	—	4	2	no	—
707	C₄×C₅	—	4	1	no	—
708	C₄×C₅	—	4	2	no	—
709	C₄×C₅	—	4	1	no	—
710	C₄×C₅	—	4	2	no	—
711	C₄×C₅	—	4	2	no	—
712	C₄×C₅	—	4	2	no	—
713	C₄×C₅	—	4	1	no	—
714	C₄×C₅	—	4	1	no	—
715	C₄×C₅	—	4	1	no	—
716	C₄×C₅	#529	1	4	yes	—
717	C₄×C₅	#542	1	4	yes	—
718	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
719	C₂⁴	C₂⁴×C₅	1	2	yes	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	4	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	4	no	—
725	C₂×Q₈	—	4	2	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	C₅×#41	1	4	yes	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	C₅×#41	1	4	yes	—
791	C₄⋊C₄	C₅×#41	1	4	yes	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	C₅×#41	1	4	yes	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	4	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	4	no	—
823	C₄²	—	2	4	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	4	2	no	—
828	C₄²	—	4	2	no	—
829	C₄²	C₅×#41	1	4	yes	—
830	C₂×C₅	—	4	4	no	—
831	C₂×C₅	—	4	2	no	—
832	C₂×C₅	C₂×#529	1	1	yes	characteristic
833	C₂×C₅	#3444	1	1	yes	characteristic
834	C₂×C₅	C₂×#542	1	1	yes	characteristic
835	C₂×C₅	#3481	1	1	yes	characteristic
836	C₂×C₅	#3481	1	1	yes	characteristic
837	C₂×C₅	#3482	1	1	yes	characteristic
838	C₂×C₅	#3482	1	1	yes	characteristic
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	2	no	—
851	C₂³	C₂×C₅×#41	1	4	yes	—
852	C₂³	C₂×C₅×#41	1	2	yes	—
853	C₂³	C₂⁵×C₅	1	1	yes	characteristic
854	Q₈	—	4	8	no	—
855	Q₈	—	4	4	no	—
856	D₄	—	2	8	no	—
857	D₄	—	4	8	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	4	8	no	—
910	C₂×C₄	—	4	8	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	8	no	—
914	C₂×C₄	C₂×C₅×#41	1	2	yes	—
915	C₂×C₄	C₂×C₅×#41	1	2	yes	—
916	C₂×C₄	C₂×C₅×#41	1	2	yes	—
917	C₂×C₄	C₂×C₅×#41	1	2	yes	—
918	C₂×C₄	C₂×C₅×#41	1	2	yes	—
919	C₂×C₄	C₂×C₅×#41	1	2	yes	—
920	C₂×C₄	C₂×C₅×#41	1	4	yes	—
921	C₂×C₄	C₂×C₅×#41	1	2	yes	—
922	C₂×C₄	C₂×C₅×#41	1	2	yes	—
923	C₂×C₄	C₂×C₅×#41	1	2	yes	—
924	C₂×C₄	C₂×C₅×#41	1	2	yes	—
925	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
926	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
927	C₅	#34969	1	1	yes	characteristic, direct product factor, Sylow
928	C₂²	—	2	4	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	1	no	—
942	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
943	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
944	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
945	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
946	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
947	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
948	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	4	1	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	C₅×#529	1	4	yes	—
969	C₄	C₅×#542	1	4	yes	—
970	C₂	—	4	4	no	—
971	C₂	—	4	2	no	—
972	C₂	C₂×C₅×#529	1	1	yes	characteristic
973	C₂	C₅×#3444	1	1	yes	characteristic
974	C₂	C₂×C₅×#542	1	1	yes	characteristic
975	C₂	C₅×#3481	1	1	yes	characteristic
976	C₂	C₅×#3481	1	1	yes	characteristic
977	C₂	C₅×#3482	1	1	yes	characteristic
978	C₂	C₅×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂×C₅×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2530	C₂	semidirect
2. C₅×#2527	C₂	semidirect
3. C₅×#2511	C₂	semidirect
4. C₅×#2509	C₂	semidirect
5. C₅×#2494	C₂	semidirect
6. C₅×#2492	C₂	semidirect
7. C₅×#2477	C₂	semidirect
8. C₅×#2470	C₂	semidirect
9. C₅×#2452	C₂	semidirect
10. C₅×#2447	C₂	semidirect
13. C₅×#2401	C₂	semidirect
14. C₅×#2398	C₂	semidirect
15. C₄×C₅×C₄⋊Q₈	C₂	semidirect
16. C₄×C₅×#124	C₂	semidirect
17. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
19. C₄×C₅×#123	C₂	semidirect
21. C₅×#2295	C₂	semidirect
22. C₄²×C₅×D₄	C₂	semidirect
23. C₄×C₅×#117	C₂	semidirect
123. #34969	C₅	direct (N × H)
239. #2530	C₂×C₅	semidirect
240. #2527	C₂×C₅	semidirect
241. #2511	C₂×C₅	semidirect
242. #2509	C₂×C₅	semidirect
243. #2494	C₂×C₅	semidirect
244. #2492	C₂×C₅	semidirect
245. #2477	C₂×C₅	semidirect
246. #2470	C₂×C₅	semidirect
247. #2452	C₂×C₅	semidirect
248. #2447	C₂×C₅	semidirect
251. #2401	C₂×C₅	semidirect
252. #2398	C₂×C₅	semidirect
253. C₄×C₄⋊Q₈	C₂×C₅	semidirect
254. C₄×#124	C₂×C₅	semidirect
255. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
256. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
257. C₄×#123	C₂×C₅	semidirect
259. #2295	C₂×C₅	semidirect
260. C₄²×D₄	C₂×C₅	semidirect
261. C₄×#117	C₂×C₅	semidirect
927. C₅	#34969	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2530	2
C₅×#2527	2
C₅×#2511	2
C₅×#2509	2
C₅×#2494	2
C₅×#2492	2
C₅×#2477	2
C₅×#2470	2
C₅×#2452	2
C₅×#2447	2
C₅×#2427	2
C₅×#2422	2
C₅×#2401	2
C₅×#2398	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#124	2
C₄×C₅×C₂²⋊Q₈	2
C₄×C₅×#123	2
C₄×C₅×#121	2
C₅×#2295	2
C₄²×C₅×D₄	2
C₄×C₅×#117	2
#34969	5

Subgroups — C5×#34969 #11957689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34969 #11957689