Subgroups — #10618771

Order 640.

936 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#66039	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
4	#66036	C₂	1	1	yes	maximal, characteristic, complemented
5	#66035	C₂	1	1	yes	maximal, characteristic, complemented
6	#66033	C₂	1	1	yes	maximal, characteristic, complemented
7	#66030	C₂	1	1	yes	maximal, characteristic, complemented
8	#66030	C₂	1	1	yes	maximal, characteristic, complemented
9	#66027	C₂	1	1	yes	maximal, characteristic, complemented
10	#66024	C₂	1	1	yes	maximal, characteristic, complemented
11	#66023	C₂	1	1	yes	maximal, characteristic, complemented
12	#65994	C₂	1	1	yes	maximal, characteristic, complemented
13	#65993	C₂	1	1	yes	maximal, characteristic, complemented
14	#65991	C₂	1	1	yes	maximal, characteristic
15	#65985	C₂	1	1	yes	maximal, characteristic, complemented
16	#65980	C₂	1	1	yes	maximal, characteristic, complemented
17	#65980	C₂	1	1	yes	maximal, characteristic, complemented
18	#65972	C₂	1	1	yes	maximal, characteristic, complemented
19	#65968	C₂	1	1	yes	maximal, characteristic, complemented
20	#65915	C₂	1	1	yes	maximal, characteristic, complemented
21	#65912	C₂	1	1	yes	maximal, characteristic, complemented
22	#65895	C₂	1	1	yes	maximal, characteristic, complemented
23	#65890	C₂	1	1	yes	maximal, characteristic, complemented
24	#65868	C₂	1	1	yes	maximal, characteristic, complemented
25	#65867	C₂	1	1	yes	maximal, characteristic, complemented
26	#65863	C₂	1	1	yes	maximal, characteristic, complemented
27	#65862	C₂	1	1	yes	maximal, characteristic, complemented
28	#65861	C₂	1	1	yes	maximal, characteristic, complemented
29	#65852	C₂	1	1	yes	maximal, characteristic, complemented
30	#65849	C₂	1	1	yes	maximal, characteristic, complemented
31	#65845	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅×#126	C₂²	1	1	yes	characteristic
33	C₅×#126	C₂²	1	1	yes	characteristic
34	C₅×#125	C₂²	1	1	yes	characteristic, complemented
35	C₅×#125	C₂²	1	1	yes	characteristic, complemented
36	C₅×#125	C₂²	1	1	yes	characteristic, complemented
37	C₅×#123	C₂²	1	1	yes	characteristic
38	C₅×#123	C₂²	1	1	yes	characteristic
39	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
43	C₅×#117	C₂²	1	1	yes	characteristic
44	C₅×#117	C₂²	1	1	yes	characteristic, complemented
45	C₅×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	#4092	C₂²	1	1	yes	characteristic
48	#4092	C₂²	1	1	yes	characteristic
49	#4092	C₂²	1	1	yes	characteristic, complemented
50	#4090	C₂²	1	1	yes	characteristic, complemented
51	#4084	C₂²	1	1	yes	characteristic
52	#4083	C₂²	1	1	yes	characteristic
53	#4082	C₂²	1	1	yes	characteristic
54	#4081	C₂²	1	1	yes	characteristic
55	#4076	C₂²	1	1	yes	characteristic
56	#4075	C₂²	1	1	yes	characteristic
57	#4075	C₂²	1	1	yes	characteristic
58	#4075	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
64	C₂×#685	C₂²	1	1	yes	characteristic
65	#4070	C₂²	1	1	yes	characteristic
66	#4070	C₂²	1	1	yes	characteristic
67	#4070	C₂²	1	1	yes	characteristic, complemented
68	#4070	C₂²	1	1	yes	characteristic, complemented
69	#4070	C₂²	1	1	yes	characteristic, complemented
70	#4070	C₂²	1	1	yes	characteristic, complemented
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, complemented
78	#4044	C₂²	1	1	yes	characteristic, complemented
79	#4044	C₂²	1	1	yes	characteristic, complemented
80	#4044	C₂²	1	1	yes	characteristic, complemented
81	#4043	C₂²	1	1	yes	characteristic
82	#4043	C₂²	1	1	yes	characteristic
83	#4043	C₂²	1	1	yes	characteristic
84	#4043	C₂²	1	1	yes	characteristic
85	#4043	C₂²	1	1	yes	characteristic, complemented
86	#4042	C₂²	1	1	yes	characteristic
87	#4042	C₂²	1	1	yes	characteristic
88	#4042	C₂²	1	1	yes	characteristic
89	#4042	C₂²	1	1	yes	characteristic
90	#4042	C₂²	1	1	yes	characteristic
91	#4042	C₂²	1	1	yes	characteristic
92	#4042	C₂²	1	1	yes	characteristic
93	#4042	C₂²	1	1	yes	characteristic
94	#4042	C₂²	1	1	yes	characteristic
95	#4042	C₂²	1	1	yes	characteristic, complemented
96	#4042	C₂²	1	1	yes	characteristic, complemented
97	#4042	C₂²	1	1	yes	characteristic, complemented
98	#4040	C₂²	1	1	yes	characteristic
99	#4040	C₂²	1	1	yes	characteristic
100	#4040	C₂²	1	1	yes	characteristic
101	#4040	C₂²	1	1	yes	characteristic
102	#4040	C₂²	1	1	yes	characteristic
103	#4039	C₂²	1	1	yes	characteristic
104	#4039	C₂²	1	1	yes	characteristic
105	#4038	C₂²	1	1	yes	characteristic
106	#4038	C₂²	1	1	yes	characteristic
107	#4038	C₂²	1	1	yes	characteristic
108	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	#4036	C₂²	1	1	yes	characteristic, complemented
113	#4036	C₂²	1	1	yes	characteristic, complemented
114	#4036	C₂²	1	1	yes	characteristic, complemented
115	#4035	C₂²	1	1	yes	characteristic, complemented
116	#4035	C₂²	1	1	yes	characteristic, complemented
117	#4035	C₂²	1	1	yes	characteristic, complemented
118	#4035	C₂²	1	1	yes	characteristic, complemented
119	#4035	C₂²	1	1	yes	characteristic, complemented
120	#4035	C₂²	1	1	yes	characteristic, complemented
121	#4035	C₂²	1	1	yes	characteristic, complemented
122	#4035	C₂²	1	1	yes	characteristic, complemented
123	#4035	C₂²	1	1	yes	characteristic, complemented
124	#4035	C₂²	1	1	yes	characteristic, complemented
125	#4035	C₂²	1	1	yes	characteristic, complemented
126	#4034	C₂²	1	1	yes	characteristic, complemented
127	#4034	C₂²	1	1	yes	characteristic, complemented
128	#4034	C₂²	1	1	yes	characteristic, complemented
129	#4034	C₂²	1	1	yes	characteristic, complemented
130	#4034	C₂²	1	1	yes	characteristic, complemented
131	#4034	C₂²	1	1	yes	characteristic, complemented
132	#4033	C₂²	1	1	yes	characteristic, complemented
133	#4033	C₂²	1	1	yes	characteristic, complemented
134	#4033	C₂²	1	1	yes	characteristic, complemented
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, complemented
140	#4030	C₂²	1	1	yes	characteristic
141	#4029	C₂²	1	1	yes	characteristic
142	#4029	C₂²	1	1	yes	characteristic
143	#4029	C₂²	1	1	yes	characteristic
144	#4029	C₂²	1	1	yes	characteristic
145	#4029	C₂²	1	1	yes	characteristic, complemented
146	#4028	C₂²	1	1	yes	characteristic
147	#4027	C₂²	1	1	yes	characteristic
148	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
149	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
150	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
151	D₅×C₂²⋊C₄	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	#4025	C₂²	1	1	yes	characteristic
159	#4025	C₂²	1	1	yes	characteristic, complemented
160	#4025	C₂²	1	1	yes	characteristic, complemented
161	#4025	C₂²	1	1	yes	characteristic, complemented
162	#4025	C₂²	1	1	yes	characteristic, complemented
163	#4024	C₂²	1	1	yes	characteristic
164	#4024	C₂²	1	1	yes	characteristic
165	#4024	C₂²	1	1	yes	characteristic
166	#4023	C₂²	1	1	yes	characteristic
167	#4022	C₂²	1	1	yes	characteristic
168	#4022	C₂²	1	1	yes	characteristic
169	#4022	C₂²	1	1	yes	characteristic
170	#4021	C₂²	1	1	yes	characteristic
171	C₄×D₂₀	C₂²	1	1	yes	characteristic
172	C₄×D₂₀	C₂²	1	1	yes	characteristic
173	#4018	C₂²	1	1	yes	characteristic
174	#4018	C₂²	1	1	yes	characteristic
175	#4018	C₂²	1	1	yes	characteristic
176	#4018	C₂²	1	1	yes	characteristic, complemented
177	#4018	C₂²	1	1	yes	characteristic, complemented
178	C₄²×D₅	C₂²	1	1	yes	characteristic
179	#4016	C₂²	1	1	yes	characteristic, complemented
180	#4016	C₂²	1	1	yes	characteristic, complemented
181	#4015	C₂²	1	1	yes	characteristic, complemented
182	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
183	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
187	#3564	—	5	1	no	maximal, Sylow
188	C₂³×D₅	C₂³	1	1	yes	characteristic
189	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
190	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
199	C₂²×Dic₅	C₂³	1	1	yes	characteristic
200	C₂×D₂₀	C₂³	1	1	yes	characteristic
201	C₂×D₂₀	C₂³	1	1	yes	characteristic
202	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
203	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
204	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
205	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
206	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
207	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
208	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
209	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
210	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
213	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
214	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
215	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
216	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
217	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
218	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
219	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
220	C₂×Dic₁₀	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₅×C₄⋊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	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₄²×C₅	C₂³	1	1	yes	characteristic
246	C₄²×C₅	C₂³	1	1	yes	characteristic
247	C₄²×C₅	C₂³	1	1	yes	characteristic
248	C₄²×C₅	C₂³	1	1	yes	characteristic
249	C₄²×C₅	C₂³	1	1	yes	characteristic
250	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
251	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
252	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
253	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
254	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
255	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
256	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
257	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
260	#685	C₂³	1	1	yes	characteristic
261	#685	C₂³	1	1	yes	characteristic
262	#685	C₂³	1	1	yes	characteristic
263	#685	C₂³	1	1	yes	characteristic
264	#685	C₂³	1	1	yes	characteristic
265	#685	C₂³	1	1	yes	characteristic
266	#685	C₂³	1	1	yes	characteristic
267	#685	C₂³	1	1	yes	characteristic
268	#685	C₂³	1	1	yes	characteristic
269	#685	C₂³	1	1	yes	characteristic
270	#685	C₂³	1	1	yes	characteristic
271	#685	C₂³	1	1	yes	characteristic
272	#685	C₂³	1	1	yes	characteristic
273	#685	C₂³	1	1	yes	characteristic
274	#685	C₂³	1	1	yes	characteristic
275	#685	C₂³	1	1	yes	characteristic
276	#685	C₂³	1	1	yes	characteristic
277	#685	C₂³	1	1	yes	characteristic
278	#685	C₂³	1	1	yes	characteristic
279	#685	C₂³	1	1	yes	characteristic
280	#685	C₂³	1	1	yes	characteristic
281	#685	C₂³	1	1	yes	characteristic
282	#685	C₂³	1	1	yes	characteristic
283	#685	C₂³	1	1	yes	characteristic
284	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
285	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
286	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
287	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
288	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
289	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
290	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
291	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
292	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
293	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
295	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
296	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₅	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	#683	C₂³	1	1	yes	characteristic
321	#683	C₂³	1	1	yes	characteristic
322	#683	C₂³	1	1	yes	characteristic
323	#683	C₂³	1	1	yes	characteristic
324	#683	C₂³	1	1	yes	characteristic
325	#683	C₂³	1	1	yes	characteristic
326	#683	C₂³	1	1	yes	characteristic
327	#683	C₂³	1	1	yes	characteristic
328	#683	C₂³	1	1	yes	characteristic
329	#683	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	—	5	1	no	—
347	#556	—	5	1	no	—
348	#556	—	5	1	no	—
349	#554	—	5	1	no	—
350	#554	—	5	1	no	—
351	#552	—	5	1	no	—
352	#552	—	5	1	no	—
353	#552	—	5	1	no	—
354	#552	D₅	1	1	yes	characteristic, complemented
355	#551	—	5	1	no	—
356	#551	—	5	1	no	—
357	#551	—	5	1	no	—
358	#551	—	5	1	no	—
359	#544	—	5	1	no	—
360	#543	—	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	#539	—	5	1	no	—
368	#539	—	5	1	no	—
369	#539	—	5	1	no	—
370	#538	—	5	1	no	—
371	#533	—	5	1	no	—
372	#529	—	5	1	no	—
373	C₂×#126	—	5	1	no	—
374	C₂³×C₅	C₂⁴	1	1	yes	characteristic
375	C₂³×C₅	C₂⁴	1	1	yes	characteristic
376	C₂²×D₅	—	2	2	no	—
377	C₂²×D₅	—	4	1	no	—
378	C₂²×D₅	—	4	1	no	—
379	C₂²×D₅	C₂⁴	1	1	yes	characteristic
380	C₂²×D₅	C₂⁴	1	1	yes	characteristic
381	C₂²×D₅	C₂⁴	1	1	yes	characteristic
382	C₅×Q₈	—	4	1	no	—
383	C₅×D₄	—	4	1	no	—
384	C₂×C₄×C₅	—	4	1	no	—
385	C₂×C₄×C₅	—	4	1	no	—
386	C₂×C₄×C₅	—	4	1	no	—
387	C₂×C₄×C₅	—	4	1	no	—
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	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
398	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
399	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
401	C₂²⋊D₅	—	2	2	no	—
402	C₂²⋊D₅	—	4	1	no	—
403	C₂²⋊D₅	—	4	1	no	—
404	C₂²⋊D₅	—	4	1	no	—
405	C₂×Dic₅	—	4	1	no	—
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	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
419	D₂₀	—	2	2	no	—
420	D₂₀	—	4	1	no	—
421	C₄×D₅	—	2	2	no	—
422	C₄×D₅	—	2	2	no	—
423	C₄×D₅	—	4	1	no	—
424	C₄×D₅	—	4	1	no	—
425	C₄×D₅	—	4	1	no	—
426	C₄×D₅	—	4	1	no	—
427	C₄×D₅	—	4	1	no	—
428	C₄×D₅	—	4	1	no	—
429	C₄×D₅	—	4	1	no	—
430	C₄×D₅	—	4	1	no	—
431	C₄×D₅	—	4	1	no	—
432	Dic₁₀	—	4	1	no	—
433	Dic₁₀	—	4	1	no	—
434	Dic₁₀	—	4	1	no	—
435	Dic₁₀	—	4	1	no	—
436	Dic₁₀	—	4	1	no	—
437	Dic₁₀	—	4	1	no	—
438	Dic₁₀	—	4	1	no	—
439	Dic₁₀	—	4	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	—	5	1	no	—
447	C₄⋊Q₈	—	5	1	no	—
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	—	5	1	no	—
471	#126	—	5	1	no	—
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	C₂×D₅	1	1	yes	characteristic, complemented
491	#125	C₂×D₅	1	1	yes	characteristic, complemented
492	#125	C₂×D₅	1	1	yes	characteristic, complemented
493	#124	—	5	1	no	—
494	#124	—	5	1	no	—
495	#124	—	5	1	no	—
496	#124	—	5	1	no	—
497	#124	—	5	1	no	—
498	#124	—	5	1	no	—
499	#124	—	5	1	no	—
500	#123	—	5	1	no	—
501	#123	—	5	1	no	—
502	#123	—	5	1	no	—
503	#123	—	5	1	no	—
504	#123	—	5	1	no	—
505	#123	—	5	1	no	—
506	#123	—	5	1	no	—
507	#123	—	5	1	no	—
508	#123	—	5	1	no	—
509	#123	—	5	1	no	—
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	—	5	1	no	—
538	C₂²⋊Q₈	—	5	1	no	—
539	C₂²⋊Q₈	—	5	1	no	—
540	C₂²⋊Q₈	—	5	1	no	—
541	C₂²⋊Q₈	—	5	1	no	—
542	C₂²⋊Q₈	—	5	1	no	—
543	C₂²⋊Q₈	—	5	1	no	—
544	C₂²⋊Q₈	—	5	1	no	—
545	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
546	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
547	#121	—	5	1	no	—
548	#121	—	5	1	no	—
549	#121	—	5	1	no	—
550	#120	—	5	1	no	—
551	#120	—	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	C₂×D₅	1	1	yes	characteristic, complemented
561	C₄×D₄	—	5	1	no	—
562	C₄×D₄	—	5	1	no	—
563	C₄×D₄	—	5	1	no	—
564	C₄×D₄	—	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	C₄×D₄	—	5	1	no	—
571	C₄×D₄	C₂×D₅	1	1	yes	characteristic
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	C₂×D₅	1	1	yes	characteristic
582	#117	C₂×D₅	1	1	yes	characteristic, complemented
583	#117	C₂×D₅	1	1	yes	characteristic, complemented
584	C₂×C₄⋊C₄	—	5	1	no	—
585	C₂×C₄⋊C₄	—	5	1	no	—
586	C₂×C₄⋊C₄	—	5	1	no	—
587	C₂×C₄⋊C₄	—	5	1	no	—
588	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
589	C₂×C₂²⋊C₄	—	5	1	no	—
590	C₂×C₂²⋊C₄	—	5	1	no	—
591	C₂×C₂²⋊C₄	—	5	1	no	—
592	C₂×C₂²⋊C₄	—	5	1	no	—
593	C₂×C₂²⋊C₄	—	5	1	no	—
594	C₂×C₄²	—	5	1	no	—
595	C₂²×C₅	—	2	1	no	—
596	C₂²×C₅	—	2	1	no	—
597	C₂²×C₅	—	2	1	no	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	2	1	no	—
600	C₂²×C₅	—	2	1	no	—
601	C₂²×C₅	C₂⁵	1	1	yes	characteristic
602	C₂×D₅	—	2	1	no	—
603	C₂×D₅	—	2	1	no	—
604	C₂×D₅	—	2	1	no	—
605	C₂×D₅	—	2	1	no	—
606	C₂×D₅	—	2	1	no	—
607	C₂×D₅	—	2	1	no	—
608	C₂×D₅	—	2	1	no	—
609	C₂×D₅	—	2	1	no	—
610	C₂×D₅	—	8	2	no	—
611	C₂×D₅	2₋¹⁺⁴	1	2	yes	—
612	C₄×C₅	—	2	1	no	—
613	C₄×C₅	—	2	1	no	—
614	C₄×C₅	—	2	1	no	—
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	2	1	no	—
617	C₄×C₅	—	2	1	no	—
618	C₄×C₅	—	2	1	no	—
619	C₄×C₅	—	2	1	no	—
620	C₄×C₅	—	2	1	no	—
621	C₄×C₅	—	2	1	no	—
622	C₄×C₅	—	2	1	no	—
623	C₄×C₅	—	2	1	no	—
624	C₄×C₅	—	2	1	no	—
625	Dic₅	—	2	1	no	—
626	Dic₅	—	2	1	no	—
627	Dic₅	—	2	1	no	—
628	Dic₅	—	2	1	no	—
629	Dic₅	—	2	1	no	—
630	Dic₅	—	2	1	no	—
631	Dic₅	—	2	1	no	—
632	Dic₅	—	2	1	no	—
633	Dic₅	—	2	1	no	—
634	Dic₅	—	2	1	no	—
635	Dic₅	—	2	1	no	—
636	Dic₅	—	2	1	no	—
637	Dic₅	—	2	1	no	—
638	C₂⁴	—	5	1	no	—
639	C₂×Q₈	—	5	1	no	—
640	C₂×Q₈	—	5	1	no	—
641	C₂×Q₈	—	5	1	no	—
642	C₂×Q₈	—	5	1	no	—
643	C₂×Q₈	—	5	1	no	—
644	C₂×Q₈	—	5	1	no	—
645	C₂×Q₈	—	5	1	no	—
646	C₂×Q₈	—	5	1	no	—
647	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
648	C₂×D₄	—	5	1	no	—
649	C₂×D₄	—	5	1	no	—
650	C₂×D₄	—	5	1	no	—
651	C₂×D₄	—	5	1	no	—
652	C₂×D₄	—	5	1	no	—
653	C₂×D₄	—	5	1	no	—
654	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
655	C₂²×C₄	—	5	1	no	—
656	C₂²×C₄	—	5	1	no	—
657	C₂²×C₄	—	5	1	no	—
658	C₂²×C₄	—	5	1	no	—
659	C₂²×C₄	—	5	1	no	—
660	C₂²×C₄	—	5	1	no	—
661	C₂²×C₄	—	5	1	no	—
662	C₂²×C₄	—	5	1	no	—
663	C₂²×C₄	—	5	1	no	—
664	C₂²×C₄	—	5	1	no	—
665	C₂²×C₄	—	5	1	no	—
666	C₂²×C₄	—	5	1	no	—
667	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
668	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
669	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
670	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
707	C₄⋊C₄	—	5	1	no	—
708	C₄⋊C₄	—	5	1	no	—
709	C₄⋊C₄	—	5	1	no	—
710	C₄⋊C₄	—	5	1	no	—
711	C₄⋊C₄	—	5	1	no	—
712	C₄⋊C₄	—	5	1	no	—
713	C₄⋊C₄	—	5	1	no	—
714	C₄⋊C₄	—	5	1	no	—
715	C₄⋊C₄	—	5	1	no	—
716	C₄⋊C₄	—	5	1	no	—
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	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
723	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
724	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
725	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
731	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
732	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
743	C₂²⋊C₄	—	5	1	no	—
744	C₂²⋊C₄	—	5	1	no	—
745	C₂²⋊C₄	—	5	1	no	—
746	C₂²⋊C₄	—	5	1	no	—
747	C₂²⋊C₄	—	5	1	no	—
748	C₂²⋊C₄	—	5	1	no	—
749	C₂²⋊C₄	—	5	1	no	—
750	C₂²⋊C₄	—	5	1	no	—
751	C₂²⋊C₄	—	5	1	no	—
752	C₂²⋊C₄	—	5	1	no	—
753	C₂²⋊C₄	—	5	1	no	—
754	C₂²⋊C₄	—	5	1	no	—
755	C₂²⋊C₄	—	5	1	no	—
756	C₂²⋊C₄	—	5	1	no	—
757	C₂²⋊C₄	—	5	1	no	—
758	C₂²⋊C₄	—	5	1	no	—
759	C₂²⋊C₄	—	5	1	no	—
760	C₂²⋊C₄	—	5	1	no	—
761	C₂²⋊C₄	—	5	1	no	—
762	C₂²⋊C₄	—	5	1	no	—
763	C₂²⋊C₄	—	5	1	no	—
764	C₂²⋊C₄	—	5	1	no	—
765	C₂²⋊C₄	—	5	1	no	—
766	C₂²⋊C₄	—	5	1	no	—
767	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
768	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
769	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
770	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
771	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
772	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
773	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
774	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
775	C₄²	—	5	1	no	—
776	C₄²	—	5	1	no	—
777	C₄²	—	5	1	no	—
778	C₄²	—	5	1	no	—
779	C₄²	—	5	1	no	—
780	C₄²	—	5	1	no	—
781	C₄²	—	5	1	no	—
782	C₄²	—	5	1	no	—
783	C₄²	—	5	1	no	—
784	C₄²	—	5	1	no	—
785	C₄²	—	5	1	no	—
786	C₄²	—	5	1	no	—
787	C₄²	—	5	1	no	—
788	C₄²	C₂²×D₅	1	1	yes	characteristic
789	C₄²	C₂²×D₅	1	1	yes	characteristic
790	C₄²	C₂²×D₅	1	1	yes	characteristic
791	C₄²	C₂²×D₅	1	1	yes	characteristic
792	C₄²	C₂²×D₅	1	1	yes	characteristic
793	C₂×C₅	—	4	1	no	—
794	C₂×C₅	—	4	1	no	—
795	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
796	C₂×C₅	#585	1	1	yes	characteristic
797	C₂×C₅	#585	1	1	yes	characteristic
798	D₅	—	2	2	no	—
799	D₅	—	4	1	no	—
800	D₅	—	4	1	no	—
801	C₂³	—	5	1	no	—
802	C₂³	—	5	1	no	—
803	C₂³	—	5	1	no	—
804	C₂³	—	10	2	no	—
805	C₂³	—	20	1	no	—
806	C₂³	—	20	1	no	—
807	C₂³	C₂³×D₅	1	1	yes	characteristic
808	C₂³	C₂³×D₅	1	1	yes	characteristic
809	Q₈	—	4	1	no	—
810	Q₈	—	20	1	no	—
811	Q₈	—	20	1	no	—
812	Q₈	—	20	1	no	—
813	Q₈	—	20	1	no	—
814	Q₈	—	20	1	no	—
815	Q₈	—	20	1	no	—
816	Q₈	—	20	1	no	—
817	Q₈	—	20	1	no	—
818	D₄	—	4	1	no	—
819	D₄	—	10	2	no	—
820	D₄	—	10	2	no	—
821	D₄	—	20	1	no	—
822	D₄	—	20	1	no	—
823	D₄	—	20	1	no	—
824	D₄	—	20	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	5	1	no	—
830	C₂×C₄	—	5	1	no	—
831	C₂×C₄	—	5	1	no	—
832	C₂×C₄	—	5	1	no	—
833	C₂×C₄	—	5	1	no	—
834	C₂×C₄	—	5	1	no	—
835	C₂×C₄	—	5	1	no	—
836	C₂×C₄	—	5	1	no	—
837	C₂×C₄	—	5	1	no	—
838	C₂×C₄	—	5	1	no	—
839	C₂×C₄	—	5	1	no	—
840	C₂×C₄	—	5	1	no	—
841	C₂×C₄	—	5	1	no	—
842	C₂×C₄	—	10	2	no	—
843	C₂×C₄	—	10	2	no	—
844	C₂×C₄	—	20	1	no	—
845	C₂×C₄	—	20	1	no	—
846	C₂×C₄	—	20	1	no	—
847	C₂×C₄	—	20	1	no	—
848	C₂×C₄	—	20	1	no	—
849	C₂×C₄	—	20	1	no	—
850	C₂×C₄	—	20	1	no	—
851	C₂×C₄	—	20	1	no	—
852	C₂×C₄	—	20	1	no	—
853	C₂×C₄	—	20	1	no	—
854	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
855	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
857	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
858	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
859	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
860	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
861	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
862	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
863	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
864	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
865	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
866	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
867	C₅	#3564	1	1	yes	characteristic, complemented, Sylow
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	5	2	no	—
875	C₂²	—	10	1	no	—
876	C₂²	—	10	1	no	—
877	C₂²	—	10	1	no	—
878	C₂²	—	10	1	no	—
879	C₂²	—	10	1	no	—
880	C₂²	—	10	1	no	—
881	C₂²	—	10	1	no	—
882	C₂²	—	10	1	no	—
883	C₂²	—	40	2	no	—
884	C₂²	C₂⁴×D₅	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	10	1	no	—
899	C₄	—	10	1	no	—
900	C₄	—	10	1	no	—
901	C₄	—	10	1	no	—
902	C₄	—	10	1	no	—
903	C₄	—	10	1	no	—
904	C₄	—	10	1	no	—
905	C₄	—	10	1	no	—
906	C₄	—	10	1	no	—
907	C₄	—	10	1	no	—
908	C₄	—	10	1	no	—
909	C₄	—	10	1	no	—
910	C₄	—	10	1	no	—
911	C₂	—	4	1	no	—
912	C₂	—	4	1	no	—
913	C₂	—	10	2	no	—
914	C₂	—	20	1	no	—
915	C₂	—	20	1	no	—
916	C₂	#66283	1	1	yes	characteristic
917	C₂	#66283	1	1	yes	characteristic
918	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×#552	C₂
prime radical	#65991	C₂
hypercenter	#552	D₅
hypocenter	C₅	#3564
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₅×#552	C₂	semidirect
2. #66039	C₂	semidirect
3. D₅×#126	C₂	semidirect
4. #66036	C₂	semidirect
5. #66035	C₂	semidirect
6. #66033	C₂	semidirect
7. #66030	C₂	semidirect
8. #66030	C₂	semidirect
9. #66027	C₂	semidirect
10. #66024	C₂	semidirect
11. #66023	C₂	semidirect
12. #65994	C₂	semidirect
13. #65993	C₂	semidirect
15. #65985	C₂	semidirect
16. #65980	C₂	semidirect
17. #65980	C₂	semidirect
18. #65972	C₂	semidirect
19. #65968	C₂	semidirect
20. #65915	C₂	semidirect
21. #65912	C₂	semidirect
22. #65895	C₂	semidirect
23. #65890	C₂	semidirect
24. #65868	C₂	semidirect
25. #65867	C₂	semidirect
26. #65863	C₂	semidirect
27. #65862	C₂	semidirect
28. #65861	C₂	semidirect
29. #65852	C₂	semidirect
30. #65849	C₂	semidirect
31. #65845	C₂	semidirect
34. C₅×#125	C₂²	semidirect
35. C₅×#125	C₂²	semidirect
36. C₅×#125	C₂²	semidirect
40. C₅×C₂²⋊Q₈	C₂²	semidirect
41. C₄×C₅×Q₈	C₂²	semidirect
44. C₅×#117	C₂²	semidirect
45. C₅×#117	C₂²	semidirect
46. C₂×C₅×C₄⋊C₄	C₂²	semidirect
49. #4092	C₂²	semidirect
50. #4090	C₂²	semidirect
58. #4075	C₂²	semidirect
63. C₄×C₂²⋊D₅	C₂²	semidirect
67. #4070	C₂²	semidirect
68. #4070	C₂²	semidirect
69. #4070	C₂²	semidirect
70. #4070	C₂²	semidirect
77. #4044	C₂²	semidirect
78. #4044	C₂²	semidirect
79. #4044	C₂²	semidirect
80. #4044	C₂²	semidirect
85. #4043	C₂²	semidirect
95. #4042	C₂²	semidirect
96. #4042	C₂²	semidirect
97. #4042	C₂²	semidirect
111. D₅×C₄⋊C₄	C₂²	semidirect
112. #4036	C₂²	semidirect
113. #4036	C₂²	semidirect
114. #4036	C₂²	semidirect
115. #4035	C₂²	semidirect
116. #4035	C₂²	semidirect
117. #4035	C₂²	semidirect
118. #4035	C₂²	semidirect
119. #4035	C₂²	semidirect
120. #4035	C₂²	semidirect
121. #4035	C₂²	semidirect
122. #4035	C₂²	semidirect
123. #4035	C₂²	semidirect
124. #4035	C₂²	semidirect
125. #4035	C₂²	semidirect
126. #4034	C₂²	semidirect
127. #4034	C₂²	semidirect
128. #4034	C₂²	semidirect
129. #4034	C₂²	semidirect
130. #4034	C₂²	semidirect
131. #4034	C₂²	semidirect
132. #4033	C₂²	semidirect
133. #4033	C₂²	semidirect
134. #4033	C₂²	semidirect
139. #4031	C₂²	semidirect
145. #4029	C₂²	semidirect
159. #4025	C₂²	semidirect
160. #4025	C₂²	semidirect
161. #4025	C₂²	semidirect
162. #4025	C₂²	semidirect
176. #4018	C₂²	semidirect
177. #4018	C₂²	semidirect
179. #4016	C₂²	semidirect
180. #4016	C₂²	semidirect
181. #4015	C₂²	semidirect
182. C₄×Dic₁₀	C₂²	semidirect
183. C₄×Dic₁₀	C₂²	semidirect
184. C₄×Dic₁₀	C₂²	semidirect
185. C₄×Dic₁₀	C₂²	semidirect
186. C₄×Dic₁₀	C₂²	semidirect
354. #552	D₅	semidirect
490. #125	C₂×D₅	semidirect
491. #125	C₂×D₅	semidirect
492. #125	C₂×D₅	semidirect
546. C₂²⋊Q₈	C₂×D₅	semidirect
560. C₄×Q₈	C₂×D₅	semidirect
582. #117	C₂×D₅	semidirect
583. #117	C₂×D₅	semidirect
588. C₂×C₄⋊C₄	C₂×D₅	semidirect
867. C₅	#3564	semidirect

Maximal subgroups

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

subgroup	index
C₅×#552	2
#66039	2
D₅×#126	2
#66036	2
#66035	2
#66033	2
#66030	2
#66027	2
#66024	2
#66023	2
#65994	2
#65993	2
#65991	2
#65985	2
#65980	2
#65972	2
#65968	2
#65915	2
#65912	2
#65895	2
#65890	2
#65868	2
#65867	2
#65863	2
#65862	2
#65861	2
#65852	2
#65849	2
#65845	2
#3564	5