Subgroups — #10619022

Order 640.

910 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#563	C₂	1	1	yes	maximal, characteristic, complemented
2	#66065	C₂	1	1	yes	maximal, characteristic, complemented
3	#66063	C₂	1	1	yes	maximal, characteristic, complemented
4	#66056	C₂	1	1	yes	maximal, characteristic, complemented
5	#66055	C₂	1	1	yes	maximal, characteristic, complemented
6	#66042	C₂	1	1	yes	maximal, characteristic, complemented
7	#66036	C₂	1	1	yes	maximal, characteristic, complemented
8	#66036	C₂	1	1	yes	maximal, characteristic, complemented
9	#66036	C₂	1	1	yes	maximal, characteristic, complemented
10	#66035	C₂	1	1	yes	maximal, characteristic, complemented
11	#66035	C₂	1	1	yes	maximal, characteristic, complemented
12	#66035	C₂	1	1	yes	maximal, characteristic, complemented
13	#66035	C₂	1	1	yes	maximal, characteristic, complemented
14	#66030	C₂	1	1	yes	maximal, characteristic, complemented
15	#66030	C₂	1	1	yes	maximal, characteristic, complemented
16	#66019	C₂	1	1	yes	maximal, characteristic, complemented
17	#66019	C₂	1	1	yes	maximal, characteristic, complemented
18	#66005	C₂	1	1	yes	maximal, characteristic, complemented
19	#66003	C₂	1	1	yes	maximal, characteristic
20	#65996	C₂	1	1	yes	maximal, characteristic
21	#65985	C₂	1	1	yes	maximal, characteristic, complemented
22	#65984	C₂	1	1	yes	maximal, characteristic, complemented
23	#65983	C₂	1	1	yes	maximal, characteristic
24	#65980	C₂	1	1	yes	maximal, characteristic, complemented
25	#65980	C₂	1	1	yes	maximal, characteristic, complemented
26	#65975	C₂	1	1	yes	maximal, characteristic, complemented
27	#65970	C₂	1	1	yes	maximal, characteristic, complemented
28	#65959	C₂	1	1	yes	maximal, characteristic, complemented
29	#65957	C₂	1	1	yes	maximal, characteristic, complemented
30	#65956	C₂	1	1	yes	maximal, characteristic, complemented
31	#65956	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₅×#126	C₂²	1	1	yes	characteristic
35	C₅×#126	C₂²	1	1	yes	characteristic
36	C₅×#126	C₂²	1	1	yes	characteristic
37	C₅×#126	C₂²	1	1	yes	characteristic
38	C₅×#125	C₂²	1	1	yes	characteristic
39	C₅×#125	C₂²	1	1	yes	characteristic
40	C₅×#124	C₂²	1	1	yes	characteristic
41	C₅×#123	C₂²	1	1	yes	characteristic
42	C₅×#123	C₂²	1	1	yes	characteristic
43	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	#4092	C₂²	1	1	yes	characteristic
48	#4092	C₂²	1	1	yes	characteristic
49	#4092	C₂²	1	1	yes	characteristic
50	Q₈×Dic₅	C₂²	1	1	yes	characteristic
51	Q₈×Dic₅	C₂²	1	1	yes	characteristic
52	Q₈×Dic₅	C₂²	1	1	yes	characteristic
53	#4090	C₂²	1	1	yes	characteristic
54	#4090	C₂²	1	1	yes	characteristic
55	#4090	C₂²	1	1	yes	characteristic
56	#4090	C₂²	1	1	yes	characteristic
57	#4090	C₂²	1	1	yes	characteristic
58	#4090	C₂²	1	1	yes	characteristic
59	#4085	C₂²	1	1	yes	characteristic
60	#4082	C₂²	1	1	yes	characteristic
61	#4081	C₂²	1	1	yes	characteristic
62	D₄×Dic₅	C₂²	1	1	yes	characteristic
63	#4075	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
65	#4072	C₂²	1	1	yes	characteristic
66	#4070	C₂²	1	1	yes	characteristic
67	#4070	C₂²	1	1	yes	characteristic
68	#4070	C₂²	1	1	yes	characteristic
69	C₂×#683	C₂²	1	1	yes	characteristic
70	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic
71	#4044	C₂²	1	1	yes	characteristic
72	#4044	C₂²	1	1	yes	characteristic
73	#4044	C₂²	1	1	yes	characteristic
74	#4044	C₂²	1	1	yes	characteristic
75	#4044	C₂²	1	1	yes	characteristic
76	#4044	C₂²	1	1	yes	characteristic
77	#4044	C₂²	1	1	yes	characteristic
78	#4044	C₂²	1	1	yes	characteristic
79	#4042	C₂²	1	1	yes	characteristic
80	#4042	C₂²	1	1	yes	characteristic
81	#4042	C₂²	1	1	yes	characteristic
82	#4042	C₂²	1	1	yes	characteristic
83	#4042	C₂²	1	1	yes	characteristic
84	#4038	C₂²	1	1	yes	characteristic
85	#4038	C₂²	1	1	yes	characteristic
86	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
87	#4036	C₂²	1	1	yes	characteristic
88	#4036	C₂²	1	1	yes	characteristic
89	#4036	C₂²	1	1	yes	characteristic
90	#4036	C₂²	1	1	yes	characteristic
91	#4036	C₂²	1	1	yes	characteristic
92	#4036	C₂²	1	1	yes	characteristic
93	#4035	C₂²	1	1	yes	characteristic
94	#4035	C₂²	1	1	yes	characteristic
95	#4035	C₂²	1	1	yes	characteristic
96	#4035	C₂²	1	1	yes	characteristic
97	#4035	C₂²	1	1	yes	characteristic
98	#4035	C₂²	1	1	yes	characteristic
99	#4035	C₂²	1	1	yes	characteristic
100	#4035	C₂²	1	1	yes	characteristic
101	#4035	C₂²	1	1	yes	characteristic
102	#4035	C₂²	1	1	yes	characteristic
103	#4035	C₂²	1	1	yes	characteristic
104	#4035	C₂²	1	1	yes	characteristic
105	#4035	C₂²	1	1	yes	characteristic
106	#4035	C₂²	1	1	yes	characteristic
107	#4035	C₂²	1	1	yes	characteristic
108	#4035	C₂²	1	1	yes	characteristic
109	#4035	C₂²	1	1	yes	characteristic
110	#4035	C₂²	1	1	yes	characteristic
111	#4035	C₂²	1	1	yes	characteristic
112	#4034	C₂²	1	1	yes	characteristic
113	#4034	C₂²	1	1	yes	characteristic
114	#4034	C₂²	1	1	yes	characteristic
115	#4034	C₂²	1	1	yes	characteristic
116	#4034	C₂²	1	1	yes	characteristic
117	#4034	C₂²	1	1	yes	characteristic
118	#4034	C₂²	1	1	yes	characteristic
119	#4034	C₂²	1	1	yes	characteristic
120	#4034	C₂²	1	1	yes	characteristic
121	#4034	C₂²	1	1	yes	characteristic
122	#4033	C₂²	1	1	yes	characteristic
123	#4033	C₂²	1	1	yes	characteristic
124	#4033	C₂²	1	1	yes	characteristic
125	#4033	C₂²	1	1	yes	characteristic
126	#4033	C₂²	1	1	yes	characteristic
127	#4033	C₂²	1	1	yes	characteristic
128	#4033	C₂²	1	1	yes	characteristic
129	#4033	C₂²	1	1	yes	characteristic
130	#4033	C₂²	1	1	yes	characteristic
131	#4033	C₂²	1	1	yes	characteristic
132	#4033	C₂²	1	1	yes	characteristic
133	#4033	C₂²	1	1	yes	characteristic
134	#4033	C₂²	1	1	yes	characteristic
135	#4031	C₂²	1	1	yes	characteristic
136	#4031	C₂²	1	1	yes	characteristic
137	#4031	C₂²	1	1	yes	characteristic
138	#4031	C₂²	1	1	yes	characteristic
139	#4031	C₂²	1	1	yes	characteristic
140	#4029	C₂²	1	1	yes	characteristic
141	#4029	C₂²	1	1	yes	characteristic
142	#4027	C₂²	1	1	yes	characteristic
143	#4027	C₂²	1	1	yes	characteristic
144	#4027	C₂²	1	1	yes	characteristic
145	#4025	C₂²	1	1	yes	characteristic
146	#4025	C₂²	1	1	yes	characteristic
147	#4025	C₂²	1	1	yes	characteristic
148	#4025	C₂²	1	1	yes	characteristic
149	#4025	C₂²	1	1	yes	characteristic
150	#4025	C₂²	1	1	yes	characteristic
151	#4025	C₂²	1	1	yes	characteristic
152	#4025	C₂²	1	1	yes	characteristic
153	#4025	C₂²	1	1	yes	characteristic
154	#4025	C₂²	1	1	yes	characteristic
155	#4025	C₂²	1	1	yes	characteristic
156	#4025	C₂²	1	1	yes	characteristic
157	#4025	C₂²	1	1	yes	characteristic
158	#4024	C₂²	1	1	yes	characteristic
159	#4024	C₂²	1	1	yes	characteristic
160	#4024	C₂²	1	1	yes	characteristic
161	#4024	C₂²	1	1	yes	characteristic
162	#4024	C₂²	1	1	yes	characteristic
163	#4024	C₂²	1	1	yes	characteristic
164	#4024	C₂²	1	1	yes	characteristic
165	#4024	C₂²	1	1	yes	characteristic
166	#4024	C₂²	1	1	yes	characteristic
167	#4024	C₂²	1	1	yes	characteristic
168	#4023	C₂²	1	1	yes	characteristic
169	#4023	C₂²	1	1	yes	characteristic
170	#4023	C₂²	1	1	yes	characteristic
171	#4023	C₂²	1	1	yes	characteristic
172	#4023	C₂²	1	1	yes	characteristic
173	#4023	C₂²	1	1	yes	characteristic
174	#4023	C₂²	1	1	yes	characteristic
175	#4022	C₂²	1	1	yes	characteristic
176	#4018	C₂²	1	1	yes	characteristic
177	#4018	C₂²	1	1	yes	characteristic
178	#4016	C₂²	1	1	yes	characteristic
179	#4016	C₂²	1	1	yes	characteristic
180	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
181	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
182	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
183	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
184	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
185	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
186	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
187	#3555	—	5	1	no	maximal, Sylow
188	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
189	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
190	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
191	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
196	C₂²×Dic₅	C₂³	1	1	yes	characteristic
197	C₂²×Dic₅	C₂³	1	1	yes	characteristic
198	C₂²×Dic₅	C₂³	1	1	yes	characteristic
199	C₂²×Dic₅	C₂³	1	1	yes	characteristic
200	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
201	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
202	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
203	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
204	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
205	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
206	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
207	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
208	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
209	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
210	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
211	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
212	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
219	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
221	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
231	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
232	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₄²×C₅	C₂³	1	1	yes	characteristic
240	C₄²×C₅	C₂³	1	1	yes	characteristic
241	C₄²×C₅	C₂³	1	1	yes	characteristic
242	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
243	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
244	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
245	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
246	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
247	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
248	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
249	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
250	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
251	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
252	#685	C₂³	1	1	yes	characteristic
253	#685	C₂³	1	1	yes	characteristic
254	#685	C₂³	1	1	yes	characteristic
255	#685	C₂³	1	1	yes	characteristic
256	#685	C₂³	1	1	yes	characteristic
257	#685	C₂³	1	1	yes	characteristic
258	#685	C₂³	1	1	yes	characteristic
259	#685	C₂³	1	1	yes	characteristic
260	#685	C₂³	1	1	yes	characteristic
261	#685	C₂³	1	1	yes	characteristic
262	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
263	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
264	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
265	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
266	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
267	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
268	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
269	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
270	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
271	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
272	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
273	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
274	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
275	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
276	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
277	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
278	#683	C₂³	1	1	yes	characteristic
279	#683	C₂³	1	1	yes	characteristic
280	#683	C₂³	1	1	yes	characteristic
281	#683	C₂³	1	1	yes	characteristic
282	#683	C₂³	1	1	yes	characteristic
283	#683	C₂³	1	1	yes	characteristic
284	#683	C₂³	1	1	yes	characteristic
285	#683	C₂³	1	1	yes	characteristic
286	#683	C₂³	1	1	yes	characteristic
287	#683	C₂³	1	1	yes	characteristic
288	#683	C₂³	1	1	yes	characteristic
289	#683	C₂³	1	1	yes	characteristic
290	#683	C₂³	1	1	yes	characteristic
291	#683	C₂³	1	1	yes	characteristic
292	#683	C₂³	1	1	yes	characteristic
293	#683	C₂³	1	1	yes	characteristic
294	#683	C₂³	1	1	yes	characteristic
295	#683	C₂³	1	1	yes	characteristic
296	#683	C₂³	1	1	yes	characteristic
297	#683	C₂³	1	1	yes	characteristic
298	#683	C₂³	1	1	yes	characteristic
299	#683	C₂³	1	1	yes	characteristic
300	#683	C₂³	1	1	yes	characteristic
301	#683	C₂³	1	1	yes	characteristic
302	#683	C₂³	1	1	yes	characteristic
303	#683	C₂³	1	1	yes	characteristic
304	#683	C₂³	1	1	yes	characteristic
305	#683	C₂³	1	1	yes	characteristic
306	#683	C₂³	1	1	yes	characteristic
307	#683	C₂³	1	1	yes	characteristic
308	#683	C₂³	1	1	yes	characteristic
309	#683	C₂³	1	1	yes	characteristic
310	#683	C₂³	1	1	yes	characteristic
311	#683	C₂³	1	1	yes	characteristic
312	#683	C₂³	1	1	yes	characteristic
313	#683	C₂³	1	1	yes	characteristic
314	#683	C₂³	1	1	yes	characteristic
315	#683	C₂³	1	1	yes	characteristic
316	#683	C₂³	1	1	yes	characteristic
317	#683	C₂³	1	1	yes	characteristic
318	#683	C₂³	1	1	yes	characteristic
319	#683	C₂³	1	1	yes	characteristic
320	C₄×Dic₅	C₂³	1	1	yes	characteristic
321	C₄×Dic₅	C₂³	1	1	yes	characteristic
322	C₄×Dic₅	C₂³	1	1	yes	characteristic
323	C₄×Dic₅	C₂³	1	1	yes	characteristic
324	C₄×Dic₅	C₂³	1	1	yes	characteristic
325	C₄×Dic₅	C₂³	1	1	yes	characteristic
326	C₄×Dic₅	C₂³	1	1	yes	characteristic
327	C₄×Dic₅	C₂³	1	1	yes	characteristic
328	C₄×Dic₅	C₂³	1	1	yes	characteristic
329	C₄×Dic₅	C₂³	1	1	yes	characteristic
330	C₄×Dic₅	C₂³	1	1	yes	characteristic
331	C₄×Dic₅	C₂³	1	1	yes	characteristic
332	C₄×Dic₅	C₂³	1	1	yes	characteristic
333	C₄×Dic₅	C₂³	1	1	yes	characteristic
334	C₄×Dic₅	C₂³	1	1	yes	characteristic
335	C₄×Dic₅	C₂³	1	1	yes	characteristic
336	C₄×Dic₅	C₂³	1	1	yes	characteristic
337	C₄×Dic₅	C₂³	1	1	yes	characteristic
338	C₄×Dic₅	C₂³	1	1	yes	characteristic
339	C₄×Dic₅	C₂³	1	1	yes	characteristic
340	C₄×Dic₅	C₂³	1	1	yes	characteristic
341	C₄×Dic₅	C₂³	1	1	yes	characteristic
342	C₄×Dic₅	C₂³	1	1	yes	characteristic
343	#563	—	5	1	no	—
344	#563	—	5	1	no	—
345	#563	—	5	1	no	—
346	#563	D₅	1	1	yes	characteristic, complemented
347	Q₈²	—	5	1	no	—
348	#557	—	5	1	no	—
349	#557	—	5	1	no	—
350	#557	—	5	1	no	—
351	#556	—	5	1	no	—
352	#556	—	5	1	no	—
353	#556	—	5	1	no	—
354	#556	—	5	1	no	—
355	#556	—	5	1	no	—
356	#554	—	5	1	no	—
357	#552	—	5	1	no	—
358	#552	—	5	1	no	—
359	#544	—	5	1	no	—
360	#544	—	5	1	no	—
361	#542	—	5	1	no	—
362	#542	—	5	1	no	—
363	#541	—	5	1	no	—
364	#541	—	5	1	no	—
365	#541	—	5	1	no	—
366	#541	—	5	1	no	—
367	#541	—	5	1	no	—
368	#541	—	5	1	no	—
369	#541	—	5	1	no	—
370	#541	—	5	1	no	—
371	#533	—	5	1	no	—
372	#533	—	5	1	no	—
373	#529	—	5	1	no	—
374	C₂³×C₅	C₂⁴	1	1	yes	characteristic
375	C₂³×C₅	C₂⁴	1	1	yes	characteristic
376	C₂²×D₅	C₂⁴	1	1	yes	characteristic
377	C₅×Q₈	—	4	1	no	—
378	C₅×Q₈	—	4	1	no	—
379	C₅×Q₈	—	4	1	no	—
380	C₅×D₄	—	4	1	no	—
381	C₂×C₄×C₅	—	4	1	no	—
382	C₂×C₄×C₅	—	4	1	no	—
383	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
384	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
396	C₂²⋊D₅	—	2	2	no	—
397	C₂²⋊D₅	—	4	1	no	—
398	C₂×Dic₅	—	2	2	no	—
399	C₂×Dic₅	—	2	2	no	—
400	C₂×Dic₅	—	2	2	no	—
401	C₂×Dic₅	—	4	1	no	—
402	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
417	C₄×D₅	—	2	2	no	—
418	C₄×D₅	—	4	1	no	—
419	C₄×D₅	—	4	1	no	—
420	Dic₁₀	—	2	2	no	—
421	Dic₁₀	—	2	2	no	—
422	Dic₁₀	—	2	2	no	—
423	Dic₁₀	—	2	2	no	—
424	Dic₁₀	—	2	2	no	—
425	Dic₁₀	—	4	1	no	—
426	Dic₁₀	—	4	1	no	—
427	Dic₁₀	—	4	1	no	—
428	Dic₁₀	—	4	1	no	—
429	Dic₁₀	—	4	1	no	—
430	C₄⋊Q₈	—	5	1	no	—
431	C₄⋊Q₈	—	5	1	no	—
432	C₄⋊Q₈	—	5	1	no	—
433	C₄⋊Q₈	—	5	1	no	—
434	C₄⋊Q₈	—	5	1	no	—
435	C₄⋊Q₈	—	5	1	no	—
436	C₄⋊Q₈	—	5	1	no	—
437	C₄⋊Q₈	—	5	1	no	—
438	C₄⋊Q₈	—	5	1	no	—
439	C₄⋊Q₈	—	5	1	no	—
440	C₄⋊Q₈	—	5	1	no	—
441	C₄⋊Q₈	—	5	1	no	—
442	C₄⋊Q₈	—	5	1	no	—
443	C₄⋊Q₈	—	5	1	no	—
444	C₄⋊Q₈	—	5	1	no	—
445	C₄⋊Q₈	—	5	1	no	—
446	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
447	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
448	#126	—	5	1	no	—
449	#126	—	5	1	no	—
450	#126	—	5	1	no	—
451	#126	—	5	1	no	—
452	#126	—	5	1	no	—
453	#126	—	5	1	no	—
454	#126	—	5	1	no	—
455	#126	—	5	1	no	—
456	#126	—	5	1	no	—
457	#126	—	5	1	no	—
458	#126	—	5	1	no	—
459	#126	—	5	1	no	—
460	#126	—	5	1	no	—
461	#126	—	5	1	no	—
462	#126	—	5	1	no	—
463	#126	—	5	1	no	—
464	#126	—	5	1	no	—
465	#126	—	5	1	no	—
466	#126	—	5	1	no	—
467	#126	—	5	1	no	—
468	#126	—	5	1	no	—
469	#126	—	5	1	no	—
470	#126	C₂×D₅	1	1	yes	characteristic
471	#126	C₂×D₅	1	1	yes	characteristic
472	#126	C₂×D₅	1	1	yes	characteristic
473	#126	C₂×D₅	1	1	yes	characteristic
474	#125	—	5	1	no	—
475	#125	—	5	1	no	—
476	#125	—	5	1	no	—
477	#125	—	5	1	no	—
478	#125	—	5	1	no	—
479	#125	—	5	1	no	—
480	#125	—	5	1	no	—
481	#125	—	5	1	no	—
482	#125	—	5	1	no	—
483	#125	—	5	1	no	—
484	#125	—	5	1	no	—
485	#125	—	5	1	no	—
486	#125	—	5	1	no	—
487	#125	—	5	1	no	—
488	#125	—	5	1	no	—
489	#125	—	5	1	no	—
490	#125	—	5	1	no	—
491	#125	—	5	1	no	—
492	#125	—	5	1	no	—
493	#125	—	5	1	no	—
494	#125	—	5	1	no	—
495	#125	—	5	1	no	—
496	#125	—	5	1	no	—
497	#125	—	5	1	no	—
498	#125	—	5	1	no	—
499	#125	—	5	1	no	—
500	#125	—	5	1	no	—
501	#125	C₂×D₅	1	1	yes	characteristic
502	#125	C₂×D₅	1	1	yes	characteristic
503	#124	—	5	1	no	—
504	#124	—	5	1	no	—
505	#124	—	5	1	no	—
506	#124	—	5	1	no	—
507	#124	—	5	1	no	—
508	#124	—	5	1	no	—
509	#124	C₂×D₅	1	1	yes	characteristic
510	#123	—	5	1	no	—
511	#123	—	5	1	no	—
512	#123	—	5	1	no	—
513	#123	—	5	1	no	—
514	#123	C₂×D₅	1	1	yes	characteristic
515	#123	C₂×D₅	1	1	yes	characteristic
516	C₂²⋊Q₈	—	5	1	no	—
517	C₂²⋊Q₈	—	5	1	no	—
518	C₂²⋊Q₈	—	5	1	no	—
519	C₂²⋊Q₈	—	5	1	no	—
520	C₂²⋊Q₈	—	5	1	no	—
521	C₂²⋊Q₈	—	5	1	no	—
522	C₂²⋊Q₈	—	5	1	no	—
523	C₂²⋊Q₈	—	5	1	no	—
524	C₂²⋊Q₈	—	5	1	no	—
525	C₂²⋊Q₈	—	5	1	no	—
526	C₂²⋊Q₈	—	5	1	no	—
527	C₂²⋊Q₈	—	5	1	no	—
528	C₂²⋊Q₈	—	5	1	no	—
529	C₂²⋊Q₈	—	5	1	no	—
530	C₂²⋊Q₈	—	5	1	no	—
531	C₂²⋊Q₈	—	5	1	no	—
532	C₂²⋊Q₈	—	5	1	no	—
533	C₂²⋊Q₈	—	5	1	no	—
534	C₂²⋊Q₈	—	5	1	no	—
535	C₂²⋊Q₈	—	5	1	no	—
536	C₂²⋊Q₈	—	5	1	no	—
537	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
538	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
539	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
540	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
541	#121	—	5	1	no	—
542	C₄×Q₈	—	5	1	no	—
543	C₄×Q₈	—	5	1	no	—
544	C₄×Q₈	—	5	1	no	—
545	C₄×Q₈	—	5	1	no	—
546	C₄×Q₈	—	5	1	no	—
547	C₄×Q₈	—	5	1	no	—
548	C₄×Q₈	—	5	1	no	—
549	C₄×Q₈	—	5	1	no	—
550	C₄×Q₈	—	5	1	no	—
551	C₄×Q₈	—	5	1	no	—
552	C₄×Q₈	—	5	1	no	—
553	C₄×Q₈	—	5	1	no	—
554	C₄×Q₈	—	5	1	no	—
555	C₄×Q₈	—	5	1	no	—
556	C₄×Q₈	—	5	1	no	—
557	C₄×Q₈	—	5	1	no	—
558	C₄×Q₈	—	5	1	no	—
559	C₄×Q₈	—	5	1	no	—
560	C₄×Q₈	—	5	1	no	—
561	C₄×Q₈	—	5	1	no	—
562	C₄×Q₈	—	5	1	no	—
563	C₄×Q₈	—	5	1	no	—
564	C₄×Q₈	—	5	1	no	—
565	C₄×D₄	—	5	1	no	—
566	C₄×D₄	—	5	1	no	—
567	C₄×D₄	—	5	1	no	—
568	C₄×D₄	—	5	1	no	—
569	C₄×D₄	—	5	1	no	—
570	#117	—	5	1	no	—
571	#117	—	5	1	no	—
572	#117	—	5	1	no	—
573	#117	—	5	1	no	—
574	#117	—	5	1	no	—
575	#117	—	5	1	no	—
576	#117	—	5	1	no	—
577	#117	—	5	1	no	—
578	#117	—	5	1	no	—
579	#117	—	5	1	no	—
580	#117	—	5	1	no	—
581	#117	—	5	1	no	—
582	C₂×C₄⋊C₄	—	5	1	no	—
583	C₂×C₄⋊C₄	—	5	1	no	—
584	C₂×C₄²	—	5	1	no	—
585	C₂²×C₅	—	2	1	no	—
586	C₂²×C₅	—	2	1	no	—
587	C₂²×C₅	—	2	1	no	—
588	C₂²×C₅	—	2	1	no	—
589	C₂²×C₅	—	2	1	no	—
590	C₂²×C₅	—	2	1	no	—
591	C₂²×C₅	C₂⁵	1	1	yes	characteristic
592	C₂×D₅	—	2	1	no	—
593	C₂×D₅	—	2	1	no	—
594	C₂×D₅	—	2	1	no	—
595	C₄×C₅	—	2	1	no	—
596	C₄×C₅	—	2	1	no	—
597	C₄×C₅	—	2	1	no	—
598	C₄×C₅	—	2	1	no	—
599	C₄×C₅	—	2	1	no	—
600	C₄×C₅	—	2	1	no	—
601	C₄×C₅	—	2	1	no	—
602	C₄×C₅	—	2	1	no	—
603	C₄×C₅	—	2	1	no	—
604	C₄×C₅	—	2	1	no	—
605	C₄×C₅	—	2	1	no	—
606	C₄×C₅	—	2	1	no	—
607	C₄×C₅	—	2	1	no	—
608	Dic₅	—	2	1	no	—
609	Dic₅	—	2	1	no	—
610	Dic₅	—	2	1	no	—
611	Dic₅	—	2	1	no	—
612	Dic₅	—	2	1	no	—
613	Dic₅	—	2	1	no	—
614	Dic₅	—	2	1	no	—
615	Dic₅	—	2	1	no	—
616	Dic₅	—	2	1	no	—
617	Dic₅	—	2	1	no	—
618	Dic₅	—	2	1	no	—
619	Dic₅	—	2	1	no	—
620	Dic₅	—	2	1	no	—
621	Dic₅	2₋¹⁺⁴	1	2	yes	—
622	Dic₅	2₋¹⁺⁴	1	2	yes	—
623	C₂×Q₈	—	5	1	no	—
624	C₂×Q₈	—	5	1	no	—
625	C₂×Q₈	—	5	1	no	—
626	C₂×Q₈	—	5	1	no	—
627	C₂×Q₈	—	5	1	no	—
628	C₂×Q₈	—	5	1	no	—
629	C₂×Q₈	—	5	1	no	—
630	C₂×Q₈	—	5	1	no	—
631	C₂×Q₈	—	5	1	no	—
632	C₂×Q₈	—	5	1	no	—
633	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
634	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
635	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
636	C₂×D₄	—	5	1	no	—
637	C₂×D₄	—	5	1	no	—
638	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
639	C₂²×C₄	—	5	1	no	—
640	C₂²×C₄	—	5	1	no	—
641	C₂²×C₄	—	5	1	no	—
642	C₂²×C₄	—	5	1	no	—
643	C₂²×C₄	—	5	1	no	—
644	C₂²×C₄	—	5	1	no	—
645	C₂²×C₄	—	5	1	no	—
646	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
647	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
648	C₄⋊C₄	—	5	1	no	—
649	C₄⋊C₄	—	5	1	no	—
650	C₄⋊C₄	—	5	1	no	—
651	C₄⋊C₄	—	5	1	no	—
652	C₄⋊C₄	—	5	1	no	—
653	C₄⋊C₄	—	5	1	no	—
654	C₄⋊C₄	—	5	1	no	—
655	C₄⋊C₄	—	5	1	no	—
656	C₄⋊C₄	—	5	1	no	—
657	C₄⋊C₄	—	5	1	no	—
658	C₄⋊C₄	—	5	1	no	—
659	C₄⋊C₄	—	5	1	no	—
660	C₄⋊C₄	—	5	1	no	—
661	C₄⋊C₄	—	5	1	no	—
662	C₄⋊C₄	—	5	1	no	—
663	C₄⋊C₄	—	5	1	no	—
664	C₄⋊C₄	—	5	1	no	—
665	C₄⋊C₄	—	5	1	no	—
666	C₄⋊C₄	—	5	1	no	—
667	C₄⋊C₄	—	5	1	no	—
668	C₄⋊C₄	—	5	1	no	—
669	C₄⋊C₄	—	5	1	no	—
670	C₄⋊C₄	—	5	1	no	—
671	C₄⋊C₄	—	5	1	no	—
672	C₄⋊C₄	—	5	1	no	—
673	C₄⋊C₄	—	5	1	no	—
674	C₄⋊C₄	—	5	1	no	—
675	C₄⋊C₄	—	5	1	no	—
676	C₄⋊C₄	—	5	1	no	—
677	C₄⋊C₄	—	5	1	no	—
678	C₄⋊C₄	—	5	1	no	—
679	C₄⋊C₄	—	5	1	no	—
680	C₄⋊C₄	—	5	1	no	—
681	C₄⋊C₄	—	5	1	no	—
682	C₄⋊C₄	—	5	1	no	—
683	C₄⋊C₄	—	5	1	no	—
684	C₄⋊C₄	—	5	1	no	—
685	C₄⋊C₄	—	5	1	no	—
686	C₄⋊C₄	—	5	1	no	—
687	C₄⋊C₄	—	5	1	no	—
688	C₄⋊C₄	—	5	1	no	—
689	C₄⋊C₄	—	5	1	no	—
690	C₄⋊C₄	—	5	1	no	—
691	C₄⋊C₄	—	5	1	no	—
692	C₄⋊C₄	—	5	1	no	—
693	C₄⋊C₄	—	5	1	no	—
694	C₄⋊C₄	—	5	1	no	—
695	C₄⋊C₄	—	5	1	no	—
696	C₄⋊C₄	—	5	1	no	—
697	C₄⋊C₄	—	5	1	no	—
698	C₄⋊C₄	—	5	1	no	—
699	C₄⋊C₄	—	5	1	no	—
700	C₄⋊C₄	—	5	1	no	—
701	C₄⋊C₄	—	5	1	no	—
702	C₄⋊C₄	—	5	1	no	—
703	C₄⋊C₄	—	5	1	no	—
704	C₄⋊C₄	—	5	1	no	—
705	C₄⋊C₄	—	5	1	no	—
706	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
707	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
708	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
709	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
710	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
711	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
712	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
713	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
714	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
715	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
716	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
717	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
718	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
719	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
720	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
721	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
722	C₂²⋊C₄	—	5	1	no	—
723	C₂²⋊C₄	—	5	1	no	—
724	C₂²⋊C₄	—	5	1	no	—
725	C₂²⋊C₄	—	5	1	no	—
726	C₂²⋊C₄	—	5	1	no	—
727	C₂²⋊C₄	—	5	1	no	—
728	C₂²⋊C₄	—	5	1	no	—
729	C₂²⋊C₄	—	5	1	no	—
730	C₂²⋊C₄	—	5	1	no	—
731	C₂²⋊C₄	—	5	1	no	—
732	C₂²⋊C₄	—	5	1	no	—
733	C₂²⋊C₄	—	5	1	no	—
734	C₂²⋊C₄	—	5	1	no	—
735	C₂²⋊C₄	—	5	1	no	—
736	C₂²⋊C₄	—	5	1	no	—
737	C₂²⋊C₄	—	5	1	no	—
738	C₂²⋊C₄	—	5	1	no	—
739	C₂²⋊C₄	—	5	1	no	—
740	C₂²⋊C₄	—	5	1	no	—
741	C₂²⋊C₄	—	5	1	no	—
742	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
743	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
744	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
745	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
746	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
747	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
748	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
749	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
750	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
751	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
752	C₄²	—	5	1	no	—
753	C₄²	—	5	1	no	—
754	C₄²	—	5	1	no	—
755	C₄²	—	5	1	no	—
756	C₄²	—	5	1	no	—
757	C₄²	—	5	1	no	—
758	C₄²	—	5	1	no	—
759	C₄²	—	5	1	no	—
760	C₄²	—	5	1	no	—
761	C₄²	—	5	1	no	—
762	C₄²	—	5	1	no	—
763	C₄²	—	5	1	no	—
764	C₄²	—	5	1	no	—
765	C₄²	—	5	1	no	—
766	C₄²	—	5	1	no	—
767	C₄²	—	5	1	no	—
768	C₄²	—	5	1	no	—
769	C₄²	—	5	1	no	—
770	C₄²	—	5	1	no	—
771	C₄²	—	5	1	no	—
772	C₄²	—	5	1	no	—
773	C₄²	—	5	1	no	—
774	C₄²	—	5	1	no	—
775	C₄²	C₂²×D₅	1	1	yes	characteristic
776	C₄²	C₂²×D₅	1	1	yes	characteristic
777	C₄²	C₂²×D₅	1	1	yes	characteristic
778	C₂×C₅	—	4	1	no	—
779	C₂×C₅	—	4	1	no	—
780	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
781	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
782	C₂×C₅	#585	1	1	yes	characteristic
783	D₅	—	4	1	no	—
784	C₂³	—	5	1	no	—
785	C₂³	C₂³×D₅	1	1	yes	characteristic
786	C₂³	C₂³×D₅	1	1	yes	characteristic
787	Q₈	—	4	1	no	—
788	Q₈	—	4	1	no	—
789	Q₈	—	4	1	no	—
790	Q₈	—	10	2	no	—
791	Q₈	—	10	2	no	—
792	Q₈	—	10	2	no	—
793	Q₈	—	10	2	no	—
794	Q₈	—	10	2	no	—
795	Q₈	—	20	1	no	—
796	Q₈	—	20	1	no	—
797	Q₈	—	20	1	no	—
798	Q₈	—	20	1	no	—
799	Q₈	—	20	1	no	—
800	D₄	—	4	1	no	—
801	D₄	—	10	2	no	—
802	D₄	—	20	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	5	1	no	—
806	C₂×C₄	—	5	1	no	—
807	C₂×C₄	—	5	1	no	—
808	C₂×C₄	—	5	1	no	—
809	C₂×C₄	—	5	1	no	—
810	C₂×C₄	—	5	1	no	—
811	C₂×C₄	—	5	1	no	—
812	C₂×C₄	—	5	1	no	—
813	C₂×C₄	—	5	1	no	—
814	C₂×C₄	—	5	1	no	—
815	C₂×C₄	—	5	1	no	—
816	C₂×C₄	—	5	1	no	—
817	C₂×C₄	—	5	1	no	—
818	C₂×C₄	—	5	1	no	—
819	C₂×C₄	—	5	1	no	—
820	C₂×C₄	—	10	2	no	—
821	C₂×C₄	—	10	2	no	—
822	C₂×C₄	—	10	2	no	—
823	C₂×C₄	—	10	2	no	—
824	C₂×C₄	—	20	1	no	—
825	C₂×C₄	—	20	1	no	—
826	C₂×C₄	—	20	1	no	—
827	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
828	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
829	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
830	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
831	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
832	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
833	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
834	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
835	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
836	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
837	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
838	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
839	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
840	C₅	#3555	1	1	yes	characteristic, complemented, Sylow
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	10	1	no	—
848	C₂²	—	10	1	no	—
849	C₂²	—	10	1	no	—
850	C₂²	C₂⁴×D₅	1	1	yes	characteristic
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	1	no	—
864	C₄	—	5	2	no	—
865	C₄	—	5	2	no	—
866	C₄	—	10	1	no	—
867	C₄	—	10	1	no	—
868	C₄	—	10	1	no	—
869	C₄	—	10	1	no	—
870	C₄	—	10	1	no	—
871	C₄	—	10	1	no	—
872	C₄	—	10	1	no	—
873	C₄	—	10	1	no	—
874	C₄	—	10	1	no	—
875	C₄	—	10	1	no	—
876	C₄	—	10	1	no	—
877	C₄	—	10	1	no	—
878	C₄	—	10	1	no	—
879	C₂	—	4	1	no	—
880	C₂	—	4	1	no	—
881	C₂	—	20	1	no	—
882	C₂	#66285	1	1	yes	characteristic
883	C₂	D₅×2₋¹⁺⁴	1	1	yes	characteristic
884	C₂	D₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#563	C₂
prime radical	#4085	C₂²
hypercenter	#563	D₅
hypocenter	C₅	#3555
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. C₅×#563	C₂	semidirect
2. #66065	C₂	semidirect
3. #66063	C₂	semidirect
4. #66056	C₂	semidirect
5. #66055	C₂	semidirect
6. #66042	C₂	semidirect
7. #66036	C₂	semidirect
8. #66036	C₂	semidirect
9. #66036	C₂	semidirect
10. #66035	C₂	semidirect
11. #66035	C₂	semidirect
12. #66035	C₂	semidirect
13. #66035	C₂	semidirect
14. #66030	C₂	semidirect
15. #66030	C₂	semidirect
16. #66019	C₂	semidirect
17. #66019	C₂	semidirect
18. #66005	C₂	semidirect
21. #65985	C₂	semidirect
22. #65984	C₂	semidirect
24. #65980	C₂	semidirect
25. #65980	C₂	semidirect
26. #65975	C₂	semidirect
27. #65970	C₂	semidirect
28. #65959	C₂	semidirect
29. #65957	C₂	semidirect
30. #65956	C₂	semidirect
31. #65956	C₂	semidirect
346. #563	D₅	semidirect
840. C₅	#3555	semidirect

Maximal subgroups

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

subgroup	index
C₅×#563	2
#66065	2
#66063	2
#66056	2
#66055	2
#66042	2
#66036	2
#66035	2
#66030	2
#66019	2
#66005	2
#66003	2
#65996	2
#65985	2
#65984	2
#65983	2
#65980	2
#65975	2
#65970	2
#65959	2
#65957	2
#65956	2
#3555	5