Subgroups — C₅×#34260 #11956980

Order 1280.

2462 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#520	C₂	1	1	yes	maximal, characteristic
2	C₅×#2356	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2353	C₂	1	2	yes	maximal, complemented
5	C₅×#2352	C₂	1	2	yes	maximal, complemented
6	C₅×#2349	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2345	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2344	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2343	C₂	1	2	yes	maximal, complemented
11	C₅×#2343	C₂	1	2	yes	maximal, complemented
12	C₅×#2339	C₂	1	1	yes	maximal, characteristic
13	C₅×#2339	C₂	1	1	yes	maximal, characteristic
14	C₅×#2320	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2318	C₂	1	2	yes	maximal, complemented
16	C₅×#2314	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#2313	C₂	1	2	yes	maximal, complemented
18	C₅×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2290	C₂	1	2	yes	maximal, complemented
21	C₂×C₅×#387	C₂	1	2	yes	maximal, complemented
22	C₅×#2275	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
25	C₅×#520	C₄	1	16	yes	complemented
26	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
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	2	yes	—
35	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
36	C₂×C₅×#117	C₂²	1	2	yes	—
37	C₂×C₅×#117	C₂²	1	1	yes	characteristic
38	C₂×C₅×#117	C₂²	1	2	yes	—
39	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₅	C₂²	1	2	yes	—
43	C₅×#391	C₂²	1	1	yes	characteristic
44	C₅×#391	C₂²	1	1	yes	characteristic
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#391	C₂²	1	1	yes	characteristic
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#389	C₂²	1	1	yes	characteristic
49	C₅×#389	C₂²	1	1	yes	characteristic
50	C₅×#389	C₂²	1	1	yes	characteristic
51	C₅×#388	C₂²	1	1	yes	characteristic
52	C₅×#388	C₂²	1	2	yes	—
53	C₅×#388	C₂²	1	1	yes	characteristic
54	C₅×#388	C₂²	1	1	yes	characteristic
55	C₅×#388	C₂²	1	1	yes	characteristic
56	C₅×#388	C₂²	1	2	yes	—
57	C₅×#387	C₂²	1	1	yes	characteristic
58	C₅×#387	C₂²	1	2	yes	—
59	C₅×#387	C₂²	1	2	yes	—
60	C₅×#387	C₂²	1	2	yes	—
61	C₅×#387	C₂²	1	2	yes	—
62	C₅×#387	C₂²	1	2	yes	—
63	C₅×#387	C₂²	1	2	yes	—
64	C₅×#387	C₂²	1	2	yes	—
65	C₅×#387	C₂²	1	2	yes	—
66	C₅×#387	C₂²	1	2	yes	—
67	C₅×#387	C₂²	1	1	yes	characteristic
68	C₅×#387	C₂²	1	1	yes	characteristic
69	C₅×#387	C₂²	1	1	yes	characteristic
70	C₅×#387	C₂²	1	2	yes	—
71	C₅×#387	C₂²	1	2	yes	—
72	C₅×#387	C₂²	1	2	yes	—
73	C₅×#387	C₂²	1	2	yes	—
74	C₅×#387	C₂²	1	2	yes	—
75	C₅×#386	C₂²	1	2	yes	—
76	C₅×#386	C₂²	1	2	yes	—
77	C₅×#386	C₂²	1	2	yes	—
78	C₅×#386	C₂²	1	2	yes	—
79	C₅×#385	C₂²	1	2	yes	—
80	C₅×#385	C₂²	1	2	yes	—
81	C₅×#385	C₂²	1	2	yes	—
82	C₅×#385	C₂²	1	2	yes	—
83	C₅×#384	C₂²	1	1	yes	characteristic
84	C₅×#383	C₂²	1	2	yes	—
85	C₅×#383	C₂²	1	2	yes	—
86	C₅×#382	C₂²	1	1	yes	characteristic
87	C₅×#382	C₂²	1	2	yes	—
88	C₅×#382	C₂²	1	2	yes	—
89	C₅×#381	C₂²	1	2	yes	—
90	C₅×#381	C₂²	1	2	yes	—
91	C₅×#381	C₂²	1	2	yes	—
92	C₅×#380	C₂²	1	2	yes	—
93	C₅×#380	C₂²	1	2	yes	—
94	C₅×#380	C₂²	1	1	yes	characteristic
95	C₅×#380	C₂²	1	1	yes	characteristic
96	C₅×#380	C₂²	1	2	yes	—
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	2	yes	—
104	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
105	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
110	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₅×#376	C₂²	1	1	yes	characteristic
117	C₅×#376	C₂²	1	2	yes	—
118	C₅×#376	C₂²	1	2	yes	—
119	C₂×C₅×#95	C₂²	1	2	yes	—
120	C₂×C₅×#95	C₂²	1	2	yes	—
121	C₂×C₅×#95	C₂²	1	2	yes	—
122	C₂×C₅×#95	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	1	yes	characteristic
124	#34260	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂×C₅×#41	—	2	4	no	—
126	C₂×C₅×#41	—	2	4	no	—
127	C₂×C₅×#41	C₂×C₄	1	8	yes	—
128	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₅×D₄	C₂³	1	2	yes	—
130	C₂²×C₅×D₄	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	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅	C₂³	1	2	yes	—
136	C₂³×C₄×C₅	C₂³	1	2	yes	—
137	C₂³×C₄×C₅	C₂³	1	2	yes	—
138	C₂³×C₄×C₅	C₂³	1	2	yes	—
139	C₂³×C₄×C₅	C₂³	1	2	yes	—
140	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
141	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
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	—	2	4	no	—
146	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
147	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
148	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
149	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
150	C₅×#117	—	4	4	no	—
151	C₅×#117	C₂×C₄	1	8	yes	complemented
152	C₅×#117	C₂×C₄	1	16	yes	complemented
153	C₂×C₅×C₄⋊C₄	—	4	4	no	—
154	C₂×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
155	C₂×C₅×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
156	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
183	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅	—	4	4	no	—
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	2	yes	—
199	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅	C₂³	1	2	yes	—
202	C₂×C₄²×C₅	C₂³	1	2	yes	—
203	C₂×C₄²×C₅	C₂³	1	2	yes	—
204	C₂×C₄²×C₅	C₂³	1	2	yes	—
205	C₂×C₄²×C₅	C₂³	1	2	yes	—
206	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅	C₂³	1	2	yes	—
208	C₂×C₄²×C₅	C₂³	1	2	yes	—
209	C₂×C₄²×C₅	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	2	yes	—
215	C₅×#95	C₂³	1	2	yes	—
216	C₅×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
227	C₅×#95	C₂³	1	1	yes	characteristic
228	C₅×#95	C₂³	1	1	yes	characteristic
229	C₅×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
239	C₅×#95	C₂³	1	1	yes	characteristic
240	C₅×#95	C₂³	1	1	yes	characteristic
241	C₅×#95	C₂³	1	2	yes	—
242	C₅×#95	C₂³	1	2	yes	—
243	C₅×#95	C₂³	1	1	yes	characteristic
244	C₂×#520	C₂×C₅	1	1	yes	characteristic
245	#2356	C₂×C₅	1	1	yes	characteristic, complemented
246	#2355	C₂×C₅	1	1	yes	characteristic, complemented
247	#2353	C₂×C₅	1	2	yes	complemented
248	#2352	C₂×C₅	1	2	yes	complemented
249	#2349	C₂×C₅	1	1	yes	characteristic, complemented
250	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
251	#2345	C₂×C₅	1	1	yes	characteristic, complemented
252	#2344	C₂×C₅	1	1	yes	characteristic, complemented
253	#2343	C₂×C₅	1	2	yes	complemented
254	#2343	C₂×C₅	1	2	yes	complemented
255	#2339	C₂×C₅	1	1	yes	characteristic
256	#2339	C₂×C₅	1	1	yes	characteristic
257	#2320	C₂×C₅	1	1	yes	characteristic, complemented
258	#2318	C₂×C₅	1	2	yes	complemented
259	#2314	C₂×C₅	1	1	yes	characteristic, complemented
260	#2313	C₂×C₅	1	2	yes	complemented
261	#2298	C₂×C₅	1	1	yes	characteristic, complemented
262	#2295	C₂×C₅	1	1	yes	characteristic, complemented
263	#2290	C₂×C₅	1	2	yes	complemented
264	C₂×#387	C₂×C₅	1	2	yes	complemented
265	#2275	C₂×C₅	1	1	yes	characteristic, complemented
266	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
267	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₅	C₂⁴	1	2	yes	—
269	C₅×#41	—	2	32	no	—
270	C₂×C₅×Q₈	—	2	2	no	—
271	C₂×C₅×Q₈	—	2	2	no	—
272	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
273	C₂×C₅×D₄	—	2	4	no	—
274	C₂×C₅×D₄	—	2	4	no	—
275	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
276	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
277	C₂×C₅×D₄	#41	1	4	yes	—
278	C₂×C₅×D₄	#41	1	4	yes	—
279	C₂²×C₄×C₅	—	2	4	no	—
280	C₂²×C₄×C₅	—	2	4	no	—
281	C₂²×C₄×C₅	—	2	2	no	—
282	C₂²×C₄×C₅	—	2	2	no	—
283	C₂²×C₄×C₅	—	2	4	no	—
284	C₂²×C₄×C₅	—	2	4	no	—
285	C₂²×C₄×C₅	—	2	4	no	—
286	C₂²×C₄×C₅	—	2	4	no	—
287	C₂²×C₄×C₅	—	2	4	no	—
288	C₂²×C₄×C₅	—	2	4	no	—
289	C₂²×C₄×C₅	—	4	2	no	—
290	C₂²×C₄×C₅	—	4	2	no	—
291	C₂²×C₄×C₅	—	4	2	no	—
292	C₂²×C₄×C₅	—	4	2	no	—
293	C₂²×C₄×C₅	—	4	2	no	—
294	C₂²×C₄×C₅	—	4	2	no	—
295	C₂²×C₄×C₅	—	4	2	no	—
296	C₂²×C₄×C₅	—	4	2	no	—
297	C₂²×C₄×C₅	—	4	2	no	—
298	C₂²×C₄×C₅	—	4	2	no	—
299	C₂²×C₄×C₅	—	4	2	no	—
300	C₂²×C₄×C₅	—	4	2	no	—
301	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
302	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
303	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
304	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
305	C₂²×C₄×C₅	C₂²×C₄	1	8	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	2	yes	—
311	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
327	C₅×C₄⋊C₄	—	2	2	no	—
328	C₅×C₄⋊C₄	—	2	2	no	—
329	C₅×C₄⋊C₄	—	2	2	no	—
330	C₅×C₄⋊C₄	—	2	2	no	—
331	C₅×C₄⋊C₄	—	2	2	no	—
332	C₅×C₄⋊C₄	—	2	4	no	—
333	C₅×C₄⋊C₄	—	2	2	no	—
334	C₅×C₄⋊C₄	—	4	2	no	—
335	C₅×C₄⋊C₄	—	4	2	no	—
336	C₅×C₄⋊C₄	—	4	1	no	—
337	C₅×C₄⋊C₄	—	4	2	no	—
338	C₅×C₄⋊C₄	—	4	1	no	—
339	C₅×C₄⋊C₄	—	4	2	no	—
340	C₅×C₄⋊C₄	—	4	2	no	—
341	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
342	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
343	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
344	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
345	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
346	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
347	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
348	C₅×C₂²⋊C₄	—	2	4	no	—
349	C₅×C₂²⋊C₄	—	2	4	no	—
350	C₅×C₂²⋊C₄	—	2	4	no	—
351	C₅×C₂²⋊C₄	—	2	4	no	—
352	C₅×C₂²⋊C₄	—	2	2	no	—
353	C₅×C₂²⋊C₄	—	2	2	no	—
354	C₅×C₂²⋊C₄	—	4	1	no	—
355	C₅×C₂²⋊C₄	—	4	1	no	—
356	C₅×C₂²⋊C₄	—	4	2	no	—
357	C₅×C₂²⋊C₄	—	4	2	no	—
358	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
359	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
360	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
361	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
362	C₄²×C₅	—	2	2	no	—
363	C₄²×C₅	—	2	2	no	—
364	C₄²×C₅	—	2	2	no	—
365	C₄²×C₅	—	2	2	no	—
366	C₄²×C₅	—	2	2	no	—
367	C₄²×C₅	—	2	4	no	—
368	C₄²×C₅	—	2	2	no	—
369	C₄²×C₅	—	4	2	no	—
370	C₄²×C₅	—	4	2	no	—
371	C₄²×C₅	—	4	1	no	—
372	C₄²×C₅	—	4	2	no	—
373	C₄²×C₅	—	4	2	no	—
374	C₄²×C₅	—	4	1	no	—
375	C₄²×C₅	—	4	2	no	—
376	C₄²×C₅	C₂²×C₄	1	4	yes	—
377	C₄²×C₅	C₂²×C₄	1	4	yes	—
378	C₄²×C₅	C₂²×C₄	1	8	yes	—
379	C₄²×C₅	C₂²×C₄	1	8	yes	—
380	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
381	#520	C₄×C₅	1	16	yes	complemented
382	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
383	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
388	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
389	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
390	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
391	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
392	C₂×#117	C₂²×C₅	1	2	yes	—
393	C₂×#117	C₂²×C₅	1	1	yes	characteristic
394	C₂×#117	C₂²×C₅	1	2	yes	—
395	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
396	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
397	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
398	C₂²×C₄²	C₂²×C₅	1	2	yes	—
399	#391	C₂²×C₅	1	1	yes	characteristic
400	#391	C₂²×C₅	1	1	yes	characteristic
401	#391	C₂²×C₅	1	1	yes	characteristic
402	#391	C₂²×C₅	1	1	yes	characteristic
403	#389	C₂²×C₅	1	1	yes	characteristic
404	#389	C₂²×C₅	1	1	yes	characteristic
405	#389	C₂²×C₅	1	1	yes	characteristic
406	#389	C₂²×C₅	1	1	yes	characteristic
407	#388	C₂²×C₅	1	2	yes	—
408	#388	C₂²×C₅	1	2	yes	—
409	#388	C₂²×C₅	1	1	yes	characteristic
410	#388	C₂²×C₅	1	1	yes	characteristic
411	#388	C₂²×C₅	1	1	yes	characteristic
412	#388	C₂²×C₅	1	1	yes	characteristic
413	#387	C₂²×C₅	1	1	yes	characteristic
414	#387	C₂²×C₅	1	2	yes	—
415	#387	C₂²×C₅	1	2	yes	—
416	#387	C₂²×C₅	1	2	yes	—
417	#387	C₂²×C₅	1	2	yes	—
418	#387	C₂²×C₅	1	2	yes	—
419	#387	C₂²×C₅	1	2	yes	—
420	#387	C₂²×C₅	1	2	yes	—
421	#387	C₂²×C₅	1	2	yes	—
422	#387	C₂²×C₅	1	2	yes	—
423	#387	C₂²×C₅	1	1	yes	characteristic
424	#387	C₂²×C₅	1	1	yes	characteristic
425	#387	C₂²×C₅	1	2	yes	—
426	#387	C₂²×C₅	1	2	yes	—
427	#387	C₂²×C₅	1	2	yes	—
428	#387	C₂²×C₅	1	2	yes	—
429	#387	C₂²×C₅	1	1	yes	characteristic
430	#387	C₂²×C₅	1	2	yes	—
431	#386	C₂²×C₅	1	2	yes	—
432	#386	C₂²×C₅	1	2	yes	—
433	#386	C₂²×C₅	1	2	yes	—
434	#386	C₂²×C₅	1	2	yes	—
435	#385	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	#384	C₂²×C₅	1	1	yes	characteristic
440	#383	C₂²×C₅	1	2	yes	—
441	#383	C₂²×C₅	1	2	yes	—
442	#382	C₂²×C₅	1	1	yes	characteristic
443	#382	C₂²×C₅	1	2	yes	—
444	#382	C₂²×C₅	1	2	yes	—
445	#381	C₂²×C₅	1	2	yes	—
446	#381	C₂²×C₅	1	2	yes	—
447	#381	C₂²×C₅	1	2	yes	—
448	#380	C₂²×C₅	1	2	yes	—
449	#380	C₂²×C₅	1	2	yes	—
450	#380	C₂²×C₅	1	1	yes	characteristic
451	#380	C₂²×C₅	1	1	yes	characteristic
452	#380	C₂²×C₅	1	2	yes	—
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	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
460	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
463	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
465	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
466	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
467	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
472	#376	C₂²×C₅	1	1	yes	characteristic
473	#376	C₂²×C₅	1	2	yes	—
474	#376	C₂²×C₅	1	2	yes	—
475	C₂×#95	C₂²×C₅	1	2	yes	—
476	C₂×#95	C₂²×C₅	1	2	yes	—
477	C₂×#95	C₂²×C₅	1	2	yes	—
478	C₂×#95	C₂²×C₅	1	2	yes	—
479	C₄³	C₂²×C₅	1	1	yes	characteristic
480	C₂³×C₅	—	2	2	no	—
481	C₂³×C₅	—	2	2	no	—
482	C₂³×C₅	—	2	2	no	—
483	C₂³×C₅	—	2	2	no	—
484	C₂³×C₅	—	2	1	no	—
485	C₂³×C₅	—	2	1	no	—
486	C₂³×C₅	—	2	1	no	—
487	C₂³×C₅	—	2	1	no	—
488	C₂³×C₅	—	2	1	no	—
489	C₂³×C₅	—	2	1	no	—
490	C₂³×C₅	C₂³×C₄	1	2	yes	—
491	C₂³×C₅	C₂³×C₄	1	4	yes	—
492	C₂³×C₅	C₂×#41	1	4	yes	—
493	C₂³×C₅	C₂×#41	1	4	yes	—
494	C₂³×C₅	C₂⁵	1	1	yes	characteristic
495	C₅×Q₈	—	2	8	no	—
496	C₅×D₄	—	2	16	no	—
497	C₅×D₄	#117	1	16	yes	complemented
498	C₂×C₄×C₅	—	2	16	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	2	no	—
504	C₂×C₄×C₅	—	2	2	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	2	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	2	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	2	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	1	no	—
518	C₂×C₄×C₅	—	2	2	no	—
519	C₂×C₄×C₅	—	2	8	no	—
520	C₂×C₄×C₅	—	2	1	no	—
521	C₂×C₄×C₅	—	2	1	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	1	no	—
525	C₂×C₄×C₅	—	2	1	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	2	no	—
530	C₂×C₄×C₅	—	2	2	no	—
531	C₂×C₄×C₅	—	2	1	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	1	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	—	2	1	no	—
538	C₂×C₄×C₅	—	2	2	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	—	2	1	no	—
544	C₂×C₄×C₅	—	2	2	no	—
545	C₂×C₄×C₅	—	2	2	no	—
546	C₂×C₄×C₅	—	2	2	no	—
547	C₂×C₄×C₅	—	2	1	no	—
548	C₂×C₄×C₅	—	2	1	no	—
549	C₂×C₄×C₅	—	2	1	no	—
550	C₂×C₄×C₅	—	4	8	no	—
551	C₂×C₄×C₅	—	4	8	no	—
552	C₂×C₄×C₅	—	4	8	no	—
553	C₂×C₄×C₅	—	4	8	no	—
554	C₂×C₄×C₅	—	4	8	no	—
555	C₂×C₄×C₅	—	8	4	no	—
556	C₂×C₄×C₅	—	8	4	no	—
557	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
558	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
559	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
560	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
561	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
562	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
563	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
564	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
565	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
566	C₂×C₄×C₅	C₂×#41	1	2	yes	—
567	C₂×C₄×C₅	C₂×#41	1	2	yes	—
568	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
569	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
570	C₂×#41	—	2	4	no	—
571	C₂×#41	—	2	4	no	—
572	C₂×#41	C₂×C₄×C₅	1	8	yes	—
573	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₅	1	2	yes	—
575	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₅	1	2	yes	—
577	C₂³×C₄	C₂³×C₅	1	2	yes	—
578	C₂³×C₄	C₂³×C₅	1	2	yes	—
579	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₅	1	2	yes	—
581	C₂³×C₄	C₂³×C₅	1	2	yes	—
582	C₂³×C₄	C₂³×C₅	1	2	yes	—
583	C₂³×C₄	C₂³×C₅	1	2	yes	—
584	C₂³×C₄	C₂³×C₅	1	2	yes	—
585	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
586	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
587	C₄×D₄	—	2	4	no	—
588	C₄×D₄	—	2	4	no	—
589	C₄×D₄	—	2	4	no	—
590	C₄×D₄	—	2	4	no	—
591	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
592	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
593	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
594	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
595	#117	—	4	4	no	—
596	#117	C₂×C₄×C₅	1	8	yes	complemented
597	#117	C₂×C₄×C₅	1	16	yes	complemented
598	C₂×C₄⋊C₄	—	4	4	no	—
599	C₂×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
600	C₂×C₄⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
601	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
636	C₂×C₄²	—	4	4	no	—
637	C₂×C₄²	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
644	C₂×C₄²	C₂³×C₅	1	2	yes	—
645	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₅	1	2	yes	—
648	C₂×C₄²	C₂³×C₅	1	2	yes	—
649	C₂×C₄²	C₂³×C₅	1	2	yes	—
650	C₂×C₄²	C₂³×C₅	1	2	yes	—
651	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₅	1	2	yes	—
653	C₂×C₄²	C₂³×C₅	1	2	yes	—
654	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
655	#95	C₂³×C₅	1	1	yes	characteristic
656	#95	C₂³×C₅	1	1	yes	characteristic
657	#95	C₂³×C₅	1	1	yes	characteristic
658	#95	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
672	#95	C₂³×C₅	1	1	yes	characteristic
673	#95	C₂³×C₅	1	1	yes	characteristic
674	#95	C₂³×C₅	1	1	yes	characteristic
675	#95	C₂³×C₅	1	2	yes	—
676	#95	C₂³×C₅	1	2	yes	—
677	#95	C₂³×C₅	1	2	yes	—
678	#95	C₂³×C₅	1	2	yes	—
679	#95	C₂³×C₅	1	2	yes	—
680	#95	C₂³×C₅	1	2	yes	—
681	#95	C₂³×C₅	1	2	yes	—
682	#95	C₂³×C₅	1	2	yes	—
683	#95	C₂³×C₅	1	1	yes	characteristic
684	#95	C₂³×C₅	1	1	yes	characteristic
685	#95	C₂³×C₅	1	1	yes	characteristic
686	#95	C₂³×C₅	1	2	yes	—
687	#95	C₂³×C₅	1	2	yes	—
688	#95	C₂³×C₅	1	1	yes	characteristic
689	C₂²×C₅	—	2	4	no	—
690	C₂²×C₅	—	2	4	no	—
691	C₂²×C₅	—	2	4	no	—
692	C₂²×C₅	—	2	4	no	—
693	C₂²×C₅	—	2	4	no	—
694	C₂²×C₅	—	2	4	no	—
695	C₂²×C₅	—	2	2	no	—
696	C₂²×C₅	—	2	2	no	—
697	C₂²×C₅	—	2	2	no	—
698	C₂²×C₅	—	4	1	no	—
699	C₂²×C₅	—	4	1	no	—
700	C₂²×C₅	—	4	1	no	—
701	C₂²×C₅	—	4	1	no	—
702	C₂²×C₅	C₂×#117	1	8	yes	—
703	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
704	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
705	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
706	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
708	C₂²×C₅	#585	1	1	yes	characteristic
709	C₂²×C₅	#585	1	1	yes	characteristic
710	C₄×C₅	—	2	2	no	—
711	C₄×C₅	—	2	4	no	—
712	C₄×C₅	—	2	2	no	—
713	C₄×C₅	—	2	4	no	—
714	C₄×C₅	—	2	2	no	—
715	C₄×C₅	—	2	4	no	—
716	C₄×C₅	—	2	2	no	—
717	C₄×C₅	—	2	2	no	—
718	C₄×C₅	—	2	2	no	—
719	C₄×C₅	—	2	2	no	—
720	C₄×C₅	—	4	2	no	—
721	C₄×C₅	—	4	2	no	—
722	C₄×C₅	—	4	1	no	—
723	C₄×C₅	—	4	1	no	—
724	C₄×C₅	—	4	1	no	—
725	C₄×C₅	—	4	1	no	—
726	C₄×C₅	—	4	2	no	—
727	C₄×C₅	—	4	1	no	—
728	C₄×C₅	—	4	2	no	—
729	C₄×C₅	—	4	1	no	—
730	C₄×C₅	C₂×#117	1	4	yes	—
731	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
732	C₂⁴	C₂⁴×C₅	1	2	yes	—
733	#41	—	2	32	no	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
740	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
741	C₂×D₄	C₅×#41	1	4	yes	—
742	C₂×D₄	C₅×#41	1	4	yes	—
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	—	2	4	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	—	4	2	no	—
762	C₂²×C₄	—	4	2	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	—	4	2	no	—
765	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
766	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
767	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
768	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
769	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
770	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	1	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	—	4	1	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
806	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
807	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
808	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
809	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
810	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
811	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	1	no	—
820	C₂²⋊C₄	—	4	1	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	4	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	4	2	no	—
834	C₄²	—	4	2	no	—
835	C₄²	—	4	2	no	—
836	C₄²	—	4	1	no	—
837	C₄²	—	4	2	no	—
838	C₄²	—	4	2	no	—
839	C₄²	—	4	1	no	—
840	C₄²	C₂²×C₄×C₅	1	4	yes	—
841	C₄²	C₂²×C₄×C₅	1	4	yes	—
842	C₄²	C₂²×C₄×C₅	1	8	yes	—
843	C₄²	C₂²×C₄×C₅	1	8	yes	—
844	C₂×C₅	—	2	8	no	—
845	C₂×C₅	—	4	2	no	—
846	C₂×C₅	C₂²×#117	1	1	yes	characteristic
847	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
848	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
849	C₂×C₅	#3513	1	1	yes	characteristic
850	C₂×C₅	#3515	1	1	yes	characteristic
851	C₂×C₅	#3520	1	1	yes	characteristic
852	C₂×C₅	#3521	1	1	yes	characteristic
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	C₂³×C₄×C₅	1	2	yes	—
864	C₂³	C₂³×C₄×C₅	1	4	yes	—
865	C₂³	C₂×C₅×#41	1	4	yes	—
866	C₂³	C₂×C₅×#41	1	4	yes	—
867	C₂³	C₂⁵×C₅	1	1	yes	characteristic
868	Q₈	—	2	8	no	—
869	D₄	—	2	16	no	—
870	D₄	C₅×#117	1	16	yes	complemented
871	C₂×C₄	—	2	16	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	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	8	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	4	8	no	—
924	C₂×C₄	—	4	8	no	—
925	C₂×C₄	—	4	8	no	—
926	C₂×C₄	—	4	8	no	—
927	C₂×C₄	—	4	8	no	—
928	C₂×C₄	—	8	4	no	—
929	C₂×C₄	—	8	4	no	—
930	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
931	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
932	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
933	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
934	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
935	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
936	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
937	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
938	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
939	C₂×C₄	C₂×C₅×#41	1	2	yes	—
940	C₂×C₄	C₂×C₅×#41	1	2	yes	—
941	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
942	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
943	C₅	#34260	1	1	yes	characteristic, direct product factor, Sylow
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	2	4	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	4	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	C₂×C₅×#117	1	8	yes	—
958	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
959	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
960	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
961	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
963	C₂²	C₅×#585	1	1	yes	characteristic
964	C₂²	C₅×#585	1	1	yes	characteristic
965	C₄	—	2	2	no	—
966	C₄	—	2	4	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	4	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	4	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	1	no	—
985	C₄	C₂×C₅×#117	1	4	yes	—
986	C₂	—	2	8	no	—
987	C₂	—	4	2	no	—
988	C₂	C₂²×C₅×#117	1	1	yes	characteristic
989	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
990	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
991	C₂	C₅×#3513	1	1	yes	characteristic
992	C₂	C₅×#3515	1	1	yes	characteristic
993	C₂	C₅×#3520	1	1	yes	characteristic
994	C₂	C₅×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2356	C₂	semidirect
3. C₅×#2355	C₂	semidirect
4. C₅×#2353	C₂	semidirect
5. C₅×#2352	C₂	semidirect
6. C₅×#2349	C₂	semidirect
7. C₅×D₄×C₄⋊C₄	C₂	semidirect
8. C₅×#2345	C₂	semidirect
9. C₅×#2344	C₂	semidirect
10. C₅×#2343	C₂	semidirect
11. C₅×#2343	C₂	semidirect
14. C₅×#2320	C₂	semidirect
15. C₅×#2318	C₂	semidirect
16. C₅×#2314	C₂	semidirect
17. C₅×#2313	C₂	semidirect
18. C₅×#2298	C₂	semidirect
19. C₅×#2295	C₂	semidirect
20. C₅×#2290	C₂	semidirect
21. C₂×C₅×#387	C₂	semidirect
22. C₅×#2275	C₂	semidirect
23. C₄²×C₅×D₄	C₂	semidirect
25. C₅×#520	C₄	semidirect
124. #34260	C₅	direct (N × H)
140. C₄×C₅×Q₈	C₂×C₄	semidirect
141. C₄×C₅×Q₈	C₂×C₄	semidirect
148. C₄×C₅×D₄	C₂×C₄	semidirect
149. C₄×C₅×D₄	C₂×C₄	semidirect
151. C₅×#117	C₂×C₄	semidirect
152. C₅×#117	C₂×C₄	semidirect
154. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
155. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
245. #2356	C₂×C₅	semidirect
246. #2355	C₂×C₅	semidirect
247. #2353	C₂×C₅	semidirect
248. #2352	C₂×C₅	semidirect
249. #2349	C₂×C₅	semidirect
250. D₄×C₄⋊C₄	C₂×C₅	semidirect
251. #2345	C₂×C₅	semidirect
252. #2344	C₂×C₅	semidirect
253. #2343	C₂×C₅	semidirect
254. #2343	C₂×C₅	semidirect
257. #2320	C₂×C₅	semidirect
258. #2318	C₂×C₅	semidirect
259. #2314	C₂×C₅	semidirect
260. #2313	C₂×C₅	semidirect
261. #2298	C₂×C₅	semidirect
262. #2295	C₂×C₅	semidirect
263. #2290	C₂×C₅	semidirect
264. C₂×#387	C₂×C₅	semidirect
265. #2275	C₂×C₅	semidirect
266. C₄²×D₄	C₂×C₅	semidirect
381. #520	C₄×C₅	semidirect
497. C₅×D₄	#117	semidirect
585. C₄×Q₈	C₂×C₄×C₅	semidirect
586. C₄×Q₈	C₂×C₄×C₅	semidirect
593. C₄×D₄	C₂×C₄×C₅	semidirect
594. C₄×D₄	C₂×C₄×C₅	semidirect
596. #117	C₂×C₄×C₅	semidirect
597. #117	C₂×C₄×C₅	semidirect
599. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
600. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
870. D₄	C₅×#117	semidirect
943. C₅	#34260	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#520	2
C₅×#2356	2
C₅×#2355	2
C₅×#2353	2
C₅×#2352	2
C₅×#2349	2
C₅×D₄×C₄⋊C₄	2
C₅×#2345	2
C₅×#2344	2
C₅×#2343	2
C₅×#2339	2
C₅×#2320	2
C₅×#2318	2
C₅×#2314	2
C₅×#2313	2
C₅×#2298	2
C₅×#2295	2
C₅×#2290	2
C₂×C₅×#387	2
C₅×#2275	2
C₄²×C₅×D₄	2
#34260	5

Subgroups — C5×#34260 #11956980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34260 #11956980