Subgroups — #10618806

Order 640.

954 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#66046	C₂	1	1	yes	maximal, characteristic, complemented
3	#66044	C₂	1	1	yes	maximal, characteristic, complemented
4	#66039	C₂	1	1	yes	maximal, characteristic, complemented
5	#66035	C₂	1	1	yes	maximal, characteristic, complemented
6	#66030	C₂	1	1	yes	maximal, characteristic, complemented
7	#66027	C₂	1	1	yes	maximal, characteristic, complemented
8	#65998	C₂	1	1	yes	maximal, characteristic, complemented
9	#65994	C₂	1	1	yes	maximal, characteristic, complemented
10	#65992	C₂	1	1	yes	maximal, characteristic, complemented
11	#65983	C₂	1	1	yes	maximal, characteristic, complemented
12	#65955	C₂	1	1	yes	maximal, characteristic, complemented
13	#65955	C₂	1	1	yes	maximal, characteristic, complemented
14	#65954	C₂	1	1	yes	maximal, characteristic, complemented
15	#65953	C₂	1	1	yes	maximal, characteristic, complemented
16	#65950	C₂	1	1	yes	maximal, characteristic, complemented
17	#65947	C₂	1	1	yes	maximal, characteristic, complemented
18	#65947	C₂	1	1	yes	maximal, characteristic, complemented
19	#65936	C₂	1	1	yes	maximal, characteristic, complemented
20	#65895	C₂	1	1	yes	maximal, characteristic, complemented
21	#65894	C₂	1	1	yes	maximal, characteristic, complemented
22	#65892	C₂	1	1	yes	maximal, characteristic, complemented
23	#65890	C₂	1	1	yes	maximal, characteristic, complemented
24	#65876	C₂	1	1	yes	maximal, characteristic, complemented
25	#65874	C₂	1	1	yes	maximal, characteristic, complemented
26	#65872	C₂	1	1	yes	maximal, characteristic, complemented
27	#65872	C₂	1	1	yes	maximal, characteristic, complemented
28	#65868	C₂	1	1	yes	maximal, characteristic, complemented
29	#65865	C₂	1	1	yes	maximal, characteristic, complemented
30	#65849	C₂	1	1	yes	maximal, characteristic, complemented
31	#65847	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅×#126	C₂²	1	1	yes	characteristic
33	C₅×#126	C₂²	1	1	yes	characteristic, complemented
34	C₅×#125	C₂²	1	1	yes	characteristic, complemented
35	C₅×#123	C₂²	1	1	yes	characteristic
36	C₅×#123	C₂²	1	1	yes	characteristic, complemented
37	C₅×#121	C₂²	1	1	yes	characteristic
38	C₅×#121	C₂²	1	1	yes	characteristic
39	C₅×#121	C₂²	1	1	yes	characteristic
40	C₅×#121	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
42	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
43	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₅×D₄	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	#4086	C₂²	1	1	yes	characteristic
48	#4085	C₂²	1	1	yes	characteristic
49	#4085	C₂²	1	1	yes	characteristic
50	#4085	C₂²	1	1	yes	characteristic
51	#4085	C₂²	1	1	yes	characteristic
52	#4085	C₂²	1	1	yes	characteristic
53	#4085	C₂²	1	1	yes	characteristic, complemented
54	#4084	C₂²	1	1	yes	characteristic
55	#4084	C₂²	1	1	yes	characteristic
56	#4084	C₂²	1	1	yes	characteristic
57	#4084	C₂²	1	1	yes	characteristic, complemented
58	#4083	C₂²	1	1	yes	characteristic
59	#4083	C₂²	1	1	yes	characteristic
60	#4083	C₂²	1	1	yes	characteristic
61	#4082	C₂²	1	1	yes	characteristic
62	#4082	C₂²	1	1	yes	characteristic
63	#4082	C₂²	1	1	yes	characteristic, complemented
64	#4081	C₂²	1	1	yes	characteristic
65	#4081	C₂²	1	1	yes	characteristic
66	#4081	C₂²	1	1	yes	characteristic
67	#4081	C₂²	1	1	yes	characteristic, complemented
68	#4081	C₂²	1	1	yes	characteristic, complemented
69	D₄×Dic₅	C₂²	1	1	yes	characteristic
70	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
71	#4076	C₂²	1	1	yes	characteristic
72	#4076	C₂²	1	1	yes	characteristic
73	#4075	C₂²	1	1	yes	characteristic
74	#4075	C₂²	1	1	yes	characteristic
75	#4075	C₂²	1	1	yes	characteristic
76	#4075	C₂²	1	1	yes	characteristic
77	#4075	C₂²	1	1	yes	characteristic
78	#4075	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
85	C₂×#685	C₂²	1	1	yes	characteristic
86	#4072	C₂²	1	1	yes	characteristic
87	#4072	C₂²	1	1	yes	characteristic, complemented
88	#4072	C₂²	1	1	yes	characteristic, complemented
89	#4070	C₂²	1	1	yes	characteristic
90	#4070	C₂²	1	1	yes	characteristic, complemented
91	#4070	C₂²	1	1	yes	characteristic, complemented
92	#4070	C₂²	1	1	yes	characteristic, complemented
93	C₂×#683	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
95	#4044	C₂²	1	1	yes	characteristic
96	#4044	C₂²	1	1	yes	characteristic
97	#4044	C₂²	1	1	yes	characteristic
98	#4044	C₂²	1	1	yes	characteristic
99	#4044	C₂²	1	1	yes	characteristic
100	#4044	C₂²	1	1	yes	characteristic
101	#4044	C₂²	1	1	yes	characteristic
102	#4044	C₂²	1	1	yes	characteristic, complemented
103	#4043	C₂²	1	1	yes	characteristic
104	#4043	C₂²	1	1	yes	characteristic
105	#4042	C₂²	1	1	yes	characteristic
106	#4042	C₂²	1	1	yes	characteristic
107	#4042	C₂²	1	1	yes	characteristic
108	#4042	C₂²	1	1	yes	characteristic
109	#4042	C₂²	1	1	yes	characteristic, complemented
110	#4042	C₂²	1	1	yes	characteristic, complemented
111	#4040	C₂²	1	1	yes	characteristic
112	#4040	C₂²	1	1	yes	characteristic
113	#4040	C₂²	1	1	yes	characteristic
114	#4040	C₂²	1	1	yes	characteristic
115	#4039	C₂²	1	1	yes	characteristic
116	#4038	C₂²	1	1	yes	characteristic
117	#4038	C₂²	1	1	yes	characteristic
118	#4038	C₂²	1	1	yes	characteristic, complemented
119	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	#4036	C₂²	1	1	yes	characteristic, complemented
121	#4036	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	#4035	C₂²	1	1	yes	characteristic, complemented
127	#4035	C₂²	1	1	yes	characteristic, complemented
128	#4035	C₂²	1	1	yes	characteristic, complemented
129	#4035	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	#4032	C₂²	1	1	yes	characteristic
136	#4032	C₂²	1	1	yes	characteristic
137	#4032	C₂²	1	1	yes	characteristic, complemented
138	#4031	C₂²	1	1	yes	characteristic
139	#4031	C₂²	1	1	yes	characteristic
140	#4031	C₂²	1	1	yes	characteristic
141	#4031	C₂²	1	1	yes	characteristic
142	#4031	C₂²	1	1	yes	characteristic
143	#4031	C₂²	1	1	yes	characteristic
144	#4031	C₂²	1	1	yes	characteristic, complemented
145	#4031	C₂²	1	1	yes	characteristic, complemented
146	#4030	C₂²	1	1	yes	characteristic
147	#4030	C₂²	1	1	yes	characteristic
148	#4029	C₂²	1	1	yes	characteristic
149	#4029	C₂²	1	1	yes	characteristic
150	#4029	C₂²	1	1	yes	characteristic
151	#4029	C₂²	1	1	yes	characteristic, complemented
152	#4028	C₂²	1	1	yes	characteristic
153	#4027	C₂²	1	1	yes	characteristic
154	#4027	C₂²	1	1	yes	characteristic
155	#4027	C₂²	1	1	yes	characteristic
156	#4027	C₂²	1	1	yes	characteristic, complemented
157	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
158	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
159	#4025	C₂²	1	1	yes	characteristic
160	#4025	C₂²	1	1	yes	characteristic
161	#4025	C₂²	1	1	yes	characteristic
162	#4025	C₂²	1	1	yes	characteristic
163	#4025	C₂²	1	1	yes	characteristic, complemented
164	#4025	C₂²	1	1	yes	characteristic, complemented
165	#4025	C₂²	1	1	yes	characteristic, complemented
166	#4025	C₂²	1	1	yes	characteristic, complemented
167	#4024	C₂²	1	1	yes	characteristic
168	#4024	C₂²	1	1	yes	characteristic
169	#4024	C₂²	1	1	yes	characteristic, complemented
170	#4024	C₂²	1	1	yes	characteristic, complemented
171	#4024	C₂²	1	1	yes	characteristic, complemented
172	#4024	C₂²	1	1	yes	characteristic, complemented
173	#4023	C₂²	1	1	yes	characteristic
174	#4023	C₂²	1	1	yes	characteristic, complemented
175	#4022	C₂²	1	1	yes	characteristic
176	#4022	C₂²	1	1	yes	characteristic
177	#4021	C₂²	1	1	yes	characteristic
178	C₄×D₂₀	C₂²	1	1	yes	characteristic
179	#4018	C₂²	1	1	yes	characteristic
180	#4018	C₂²	1	1	yes	characteristic
181	#4018	C₂²	1	1	yes	characteristic, complemented
182	#4016	C₂²	1	1	yes	characteristic, complemented
183	#4015	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	#3566	—	5	1	no	maximal, Sylow
188	C₂³×D₅	C₂³	1	1	yes	characteristic
189	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
190	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
191	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
192	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
193	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
194	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
211	C₂²×Dic₅	C₂³	1	1	yes	characteristic
212	C₂²×Dic₅	C₂³	1	1	yes	characteristic
213	C₂²×Dic₅	C₂³	1	1	yes	characteristic
214	C₂²×Dic₅	C₂³	1	1	yes	characteristic
215	C₂²×Dic₅	C₂³	1	1	yes	characteristic
216	C₂×D₂₀	C₂³	1	1	yes	characteristic
217	C₂×D₂₀	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
225	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
226	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
227	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
228	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
229	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
230	C₂×Dic₁₀	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₅×C₄⋊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	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₄²×C₅	C₂³	1	1	yes	characteristic
252	C₄²×C₅	C₂³	1	1	yes	characteristic
253	C₄²×C₅	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	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₅	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	#685	C₂³	1	1	yes	characteristic
285	#685	C₂³	1	1	yes	characteristic
286	#685	C₂³	1	1	yes	characteristic
287	#685	C₂³	1	1	yes	characteristic
288	#685	C₂³	1	1	yes	characteristic
289	#685	C₂³	1	1	yes	characteristic
290	#685	C₂³	1	1	yes	characteristic
291	#685	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	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₅	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	#562	—	5	1	no	—
345	#562	—	5	1	no	—
346	#560	—	5	1	no	—
347	#559	—	5	1	no	—
348	#556	—	5	1	no	—
349	#555	—	5	1	no	—
350	#553	—	5	1	no	—
351	#553	—	5	1	no	—
352	#553	D₅	1	1	yes	characteristic, complemented
353	#552	—	5	1	no	—
354	#552	—	5	1	no	—
355	#552	—	5	1	no	—
356	#551	—	5	1	no	—
357	#551	—	5	1	no	—
358	#551	—	5	1	no	—
359	#542	—	5	1	no	—
360	#542	—	5	1	no	—
361	#542	—	5	1	no	—
362	#541	—	5	1	no	—
363	#541	—	5	1	no	—
364	#540	—	5	1	no	—
365	#539	—	5	1	no	—
366	#539	—	5	1	no	—
367	#539	—	5	1	no	—
368	#538	—	5	1	no	—
369	#538	—	5	1	no	—
370	#538	—	5	1	no	—
371	#529	—	5	1	no	—
372	#529	—	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	C₂³×C₅	C₂⁴	1	1	yes	characteristic
377	C₂³×C₅	C₂⁴	1	1	yes	characteristic
378	C₂²×D₅	—	4	1	no	—
379	C₂²×D₅	—	4	1	no	—
380	C₂²×D₅	—	4	1	no	—
381	C₂²×D₅	C₂⁴	1	1	yes	characteristic
382	C₂²×D₅	C₂⁴	1	1	yes	characteristic
383	C₂²×D₅	C₂⁴	1	1	yes	characteristic
384	C₅×D₄	—	4	1	no	—
385	C₅×D₄	—	4	1	no	—
386	C₅×D₄	—	4	1	no	—
387	C₅×D₄	—	4	1	no	—
388	C₅×D₄	—	4	1	no	—
389	C₅×D₄	—	4	1	no	—
390	C₂×C₄×C₅	—	4	1	no	—
391	C₂×C₄×C₅	—	4	1	no	—
392	C₂×C₄×C₅	—	4	1	no	—
393	C₂×C₄×C₅	—	4	1	no	—
394	C₂×C₄×C₅	—	4	1	no	—
395	C₂×C₄×C₅	—	4	1	no	—
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	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
405	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
406	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
407	C₂²⋊D₅	—	4	1	no	—
408	C₂²⋊D₅	—	4	1	no	—
409	C₂²⋊D₅	—	4	1	no	—
410	C₂²⋊D₅	—	4	1	no	—
411	C₂²⋊D₅	—	4	1	no	—
412	C₂²⋊D₅	—	4	1	no	—
413	C₂²⋊D₅	—	4	1	no	—
414	C₂²⋊D₅	—	4	1	no	—
415	C₂²⋊D₅	—	4	1	no	—
416	C₂²⋊D₅	—	4	1	no	—
417	C₂×Dic₅	—	4	1	no	—
418	C₂×Dic₅	—	4	1	no	—
419	C₂×Dic₅	—	4	1	no	—
420	C₂×Dic₅	—	4	1	no	—
421	C₂×Dic₅	—	4	1	no	—
422	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
424	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
425	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
426	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
427	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
433	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
434	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
435	D₂₀	—	4	1	no	—
436	D₂₀	—	4	1	no	—
437	C₄×D₅	—	4	1	no	—
438	C₄×D₅	—	4	1	no	—
439	C₄×D₅	—	4	1	no	—
440	C₄×D₅	—	4	1	no	—
441	C₄×D₅	—	4	1	no	—
442	C₄×D₅	—	4	1	no	—
443	C₄×D₅	—	4	1	no	—
444	Dic₁₀	—	4	1	no	—
445	Dic₁₀	—	4	1	no	—
446	Dic₁₀	—	4	1	no	—
447	Dic₁₀	—	4	1	no	—
448	Dic₁₀	—	4	1	no	—
449	Dic₁₀	—	4	1	no	—
450	C₄⋊Q₈	—	5	1	no	—
451	C₄⋊Q₈	—	5	1	no	—
452	C₄⋊Q₈	—	5	1	no	—
453	#127	—	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, complemented
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	C₂×D₅	1	1	yes	characteristic, complemented
486	#124	—	5	1	no	—
487	#124	—	5	1	no	—
488	#124	—	5	1	no	—
489	#124	—	5	1	no	—
490	#124	—	5	1	no	—
491	#124	—	5	1	no	—
492	#124	—	5	1	no	—
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	#123	—	5	1	no	—
499	#123	—	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	—	5	1	no	—
515	#123	—	5	1	no	—
516	#123	—	5	1	no	—
517	#123	—	5	1	no	—
518	#123	—	5	1	no	—
519	#123	—	5	1	no	—
520	#123	C₂×D₅	1	1	yes	characteristic
521	#123	C₂×D₅	1	1	yes	characteristic, complemented
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	#121	—	5	1	no	—
541	#121	—	5	1	no	—
542	#121	—	5	1	no	—
543	#121	—	5	1	no	—
544	#121	—	5	1	no	—
545	#121	—	5	1	no	—
546	#121	—	5	1	no	—
547	#121	—	5	1	no	—
548	#121	—	5	1	no	—
549	#121	—	5	1	no	—
550	#121	—	5	1	no	—
551	#121	—	5	1	no	—
552	#121	—	5	1	no	—
553	#121	—	5	1	no	—
554	#121	C₂×D₅	1	1	yes	characteristic
555	#121	C₂×D₅	1	1	yes	characteristic
556	#121	C₂×D₅	1	1	yes	characteristic
557	#121	C₂×D₅	1	1	yes	characteristic, complemented
558	#120	—	5	1	no	—
559	#120	—	5	1	no	—
560	#120	—	5	1	no	—
561	#120	—	5	1	no	—
562	C₄×Q₈	—	5	1	no	—
563	C₄×Q₈	—	5	1	no	—
564	C₄×Q₈	—	5	1	no	—
565	C₄×Q₈	—	5	1	no	—
566	C₄×Q₈	—	5	1	no	—
567	C₄×Q₈	—	5	1	no	—
568	C₄×D₄	—	5	1	no	—
569	C₄×D₄	—	5	1	no	—
570	C₄×D₄	—	5	1	no	—
571	C₄×D₄	—	5	1	no	—
572	C₄×D₄	—	5	1	no	—
573	C₄×D₄	—	5	1	no	—
574	C₄×D₄	—	5	1	no	—
575	C₄×D₄	—	5	1	no	—
576	C₄×D₄	—	5	1	no	—
577	C₄×D₄	—	5	1	no	—
578	C₄×D₄	—	5	1	no	—
579	C₄×D₄	—	5	1	no	—
580	C₄×D₄	—	5	1	no	—
581	C₄×D₄	—	5	1	no	—
582	C₄×D₄	C₂×D₅	1	1	yes	characteristic
583	C₄×D₄	C₂×D₅	1	1	yes	characteristic
584	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
585	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
586	#117	—	5	1	no	—
587	#117	—	5	1	no	—
588	#117	—	5	1	no	—
589	#117	—	5	1	no	—
590	#117	—	5	1	no	—
591	#117	—	5	1	no	—
592	#117	—	5	1	no	—
593	#117	—	5	1	no	—
594	#117	—	5	1	no	—
595	#117	—	5	1	no	—
596	#117	—	5	1	no	—
597	#117	C₂×D₅	1	1	yes	characteristic, complemented
598	C₂×C₄⋊C₄	—	5	1	no	—
599	C₂×C₄⋊C₄	—	5	1	no	—
600	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
601	C₂×C₂²⋊C₄	—	5	1	no	—
602	C₂×C₂²⋊C₄	—	5	1	no	—
603	C₂×C₂²⋊C₄	—	5	1	no	—
604	C₂×C₄²	—	5	1	no	—
605	C₂²×C₅	—	2	1	no	—
606	C₂²×C₅	—	2	1	no	—
607	C₂²×C₅	—	2	1	no	—
608	C₂²×C₅	—	2	1	no	—
609	C₂²×C₅	—	2	1	no	—
610	C₂²×C₅	—	2	1	no	—
611	C₂²×C₅	—	2	1	no	—
612	C₂²×C₅	—	2	1	no	—
613	C₂²×C₅	—	2	1	no	—
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	2	1	no	—
617	C₂²×C₅	C₂⁵	1	1	yes	characteristic
618	C₂×D₅	—	2	1	no	—
619	C₂×D₅	—	2	1	no	—
620	C₂×D₅	—	2	1	no	—
621	C₂×D₅	—	2	1	no	—
622	C₂×D₅	—	2	1	no	—
623	C₂×D₅	—	2	1	no	—
624	C₂×D₅	—	2	1	no	—
625	C₂×D₅	—	2	1	no	—
626	C₂×D₅	—	2	1	no	—
627	C₂×D₅	—	8	2	no	—
628	C₄×C₅	—	2	1	no	—
629	C₄×C₅	—	2	1	no	—
630	C₄×C₅	—	2	1	no	—
631	C₄×C₅	—	2	1	no	—
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	2	1	no	—
634	C₄×C₅	—	2	1	no	—
635	C₄×C₅	—	2	1	no	—
636	C₄×C₅	—	2	1	no	—
637	C₄×C₅	—	2	1	no	—
638	C₄×C₅	—	2	1	no	—
639	Dic₅	—	2	1	no	—
640	Dic₅	—	2	1	no	—
641	Dic₅	—	2	1	no	—
642	Dic₅	—	2	1	no	—
643	Dic₅	—	2	1	no	—
644	Dic₅	—	2	1	no	—
645	Dic₅	—	2	1	no	—
646	Dic₅	—	2	1	no	—
647	Dic₅	—	2	1	no	—
648	Dic₅	—	2	1	no	—
649	Dic₅	—	2	1	no	—
650	Dic₅	—	2	1	no	—
651	Dic₅	—	2	1	no	—
652	C₂⁴	—	5	1	no	—
653	C₂×Q₈	—	5	1	no	—
654	C₂×Q₈	—	5	1	no	—
655	C₂×Q₈	—	5	1	no	—
656	C₂×Q₈	—	5	1	no	—
657	C₂×Q₈	—	5	1	no	—
658	C₂×Q₈	—	5	1	no	—
659	C₂×D₄	—	5	1	no	—
660	C₂×D₄	—	5	1	no	—
661	C₂×D₄	—	5	1	no	—
662	C₂×D₄	—	5	1	no	—
663	C₂×D₄	—	5	1	no	—
664	C₂×D₄	—	5	1	no	—
665	C₂×D₄	—	5	1	no	—
666	C₂×D₄	—	5	1	no	—
667	C₂×D₄	—	5	1	no	—
668	C₂×D₄	—	5	1	no	—
669	C₂×D₄	—	5	1	no	—
670	C₂×D₄	—	5	1	no	—
671	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
672	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
673	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
674	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
675	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
676	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
677	C₂²×C₄	—	5	1	no	—
678	C₂²×C₄	—	5	1	no	—
679	C₂²×C₄	—	5	1	no	—
680	C₂²×C₄	—	5	1	no	—
681	C₂²×C₄	—	5	1	no	—
682	C₂²×C₄	—	5	1	no	—
683	C₂²×C₄	—	5	1	no	—
684	C₂²×C₄	—	5	1	no	—
685	C₂²×C₄	—	5	1	no	—
686	C₂²×C₄	—	5	1	no	—
687	C₂²×C₄	—	5	1	no	—
688	C₂²×C₄	—	5	1	no	—
689	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
690	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
691	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
692	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
693	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
694	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
718	C₄⋊C₄	—	5	1	no	—
719	C₄⋊C₄	—	5	1	no	—
720	C₄⋊C₄	—	5	1	no	—
721	C₄⋊C₄	—	5	1	no	—
722	C₄⋊C₄	—	5	1	no	—
723	C₄⋊C₄	—	5	1	no	—
724	C₄⋊C₄	—	5	1	no	—
725	C₄⋊C₄	—	5	1	no	—
726	C₄⋊C₄	—	5	1	no	—
727	C₄⋊C₄	—	5	1	no	—
728	C₄⋊C₄	—	5	1	no	—
729	C₄⋊C₄	—	5	1	no	—
730	C₄⋊C₄	—	5	1	no	—
731	C₄⋊C₄	—	5	1	no	—
732	C₄⋊C₄	—	5	1	no	—
733	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
734	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
768	C₂²⋊C₄	—	5	1	no	—
769	C₂²⋊C₄	—	5	1	no	—
770	C₂²⋊C₄	—	5	1	no	—
771	C₂²⋊C₄	—	5	1	no	—
772	C₂²⋊C₄	—	5	1	no	—
773	C₂²⋊C₄	—	5	1	no	—
774	C₂²⋊C₄	—	5	1	no	—
775	C₂²⋊C₄	—	5	1	no	—
776	C₂²⋊C₄	—	5	1	no	—
777	C₂²⋊C₄	—	5	1	no	—
778	C₂²⋊C₄	—	5	1	no	—
779	C₂²⋊C₄	—	5	1	no	—
780	C₂²⋊C₄	—	5	1	no	—
781	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
782	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
784	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
785	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
786	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
787	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
788	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
789	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
790	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
791	C₄²	—	5	1	no	—
792	C₄²	—	5	1	no	—
793	C₄²	—	5	1	no	—
794	C₄²	—	5	1	no	—
795	C₄²	—	5	1	no	—
796	C₄²	—	5	1	no	—
797	C₄²	—	5	1	no	—
798	C₄²	—	5	1	no	—
799	C₄²	—	5	1	no	—
800	C₄²	—	5	1	no	—
801	C₄²	—	5	1	no	—
802	C₄²	—	5	1	no	—
803	C₄²	—	5	1	no	—
804	C₄²	C₂²×D₅	1	1	yes	characteristic
805	C₄²	C₂²×D₅	1	1	yes	characteristic
806	C₄²	C₂²×D₅	1	1	yes	characteristic
807	C₂×C₅	—	4	1	no	—
808	C₂×C₅	—	4	1	no	—
809	C₂×C₅	—	4	1	no	—
810	C₂×C₅	—	4	1	no	—
811	C₂×C₅	#585	1	1	yes	characteristic
812	C₂×C₅	#585	1	1	yes	characteristic
813	C₂×C₅	#585	1	1	yes	characteristic
814	D₅	—	4	1	no	—
815	D₅	—	4	1	no	—
816	D₅	—	4	1	no	—
817	C₂³	—	5	1	no	—
818	C₂³	—	5	1	no	—
819	C₂³	—	5	1	no	—
820	C₂³	—	20	1	no	—
821	C₂³	—	20	1	no	—
822	C₂³	—	20	1	no	—
823	C₂³	C₂³×D₅	1	1	yes	characteristic
824	C₂³	C₂³×D₅	1	1	yes	characteristic
825	C₂³	C₂³×D₅	1	1	yes	characteristic
826	C₂³	C₂³×D₅	1	1	yes	characteristic
827	Q₈	—	20	1	no	—
828	Q₈	—	20	1	no	—
829	Q₈	—	20	1	no	—
830	Q₈	—	20	1	no	—
831	Q₈	—	20	1	no	—
832	Q₈	—	20	1	no	—
833	D₄	—	4	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	20	1	no	—
840	D₄	—	20	1	no	—
841	D₄	—	20	1	no	—
842	D₄	—	20	1	no	—
843	D₄	—	20	1	no	—
844	D₄	—	20	1	no	—
845	D₄	—	20	1	no	—
846	D₄	—	20	1	no	—
847	D₄	—	20	1	no	—
848	D₄	—	20	1	no	—
849	D₄	—	20	1	no	—
850	D₄	—	20	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	5	1	no	—
858	C₂×C₄	—	5	1	no	—
859	C₂×C₄	—	5	1	no	—
860	C₂×C₄	—	5	1	no	—
861	C₂×C₄	—	5	1	no	—
862	C₂×C₄	—	5	1	no	—
863	C₂×C₄	—	5	1	no	—
864	C₂×C₄	—	5	1	no	—
865	C₂×C₄	—	5	1	no	—
866	C₂×C₄	—	5	1	no	—
867	C₂×C₄	—	5	1	no	—
868	C₂×C₄	—	5	1	no	—
869	C₂×C₄	—	5	1	no	—
870	C₂×C₄	—	20	1	no	—
871	C₂×C₄	—	20	1	no	—
872	C₂×C₄	—	20	1	no	—
873	C₂×C₄	—	20	1	no	—
874	C₂×C₄	—	20	1	no	—
875	C₂×C₄	—	20	1	no	—
876	C₂×C₄	—	20	1	no	—
877	C₂×C₄	—	20	1	no	—
878	C₂×C₄	—	20	1	no	—
879	C₂×C₄	—	20	1	no	—
880	C₂×C₄	—	20	1	no	—
881	C₂×C₄	—	20	1	no	—
882	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
883	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
884	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
885	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
893	C₅	#3566	1	1	yes	characteristic, complemented, Sylow
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	10	1	no	—
907	C₂²	—	10	1	no	—
908	C₂²	—	10	1	no	—
909	C₂²	—	10	1	no	—
910	C₂²	—	10	1	no	—
911	C₂²	—	10	1	no	—
912	C₂²	—	10	1	no	—
913	C₂²	—	10	1	no	—
914	C₂²	—	10	1	no	—
915	C₂²	—	40	2	no	—
916	C₂²	C₂⁴×D₅	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	10	1	no	—
929	C₄	—	10	1	no	—
930	C₄	—	10	1	no	—
931	C₄	—	10	1	no	—
932	C₄	—	10	1	no	—
933	C₄	—	10	1	no	—
934	C₄	—	10	1	no	—
935	C₄	—	10	1	no	—
936	C₄	—	10	1	no	—
937	C₄	—	10	1	no	—
938	C₄	—	10	1	no	—
939	C₄	—	10	1	no	—
940	C₄	—	10	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	1	no	—
943	C₂	—	4	1	no	—
944	C₂	—	4	1	no	—
945	C₂	—	20	1	no	—
946	C₂	—	20	1	no	—
947	C₂	—	20	1	no	—
948	C₂	#66283	1	1	yes	characteristic
949	C₂	#66283	1	1	yes	characteristic
950	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#553	C₂
hypercenter	#553	D₅
hypocenter	C₅	#3566
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₅×#553	C₂	semidirect
2. #66046	C₂	semidirect
3. #66044	C₂	semidirect
4. #66039	C₂	semidirect
5. #66035	C₂	semidirect
6. #66030	C₂	semidirect
7. #66027	C₂	semidirect
8. #65998	C₂	semidirect
9. #65994	C₂	semidirect
10. #65992	C₂	semidirect
11. #65983	C₂	semidirect
12. #65955	C₂	semidirect
13. #65955	C₂	semidirect
14. #65954	C₂	semidirect
15. #65953	C₂	semidirect
16. #65950	C₂	semidirect
17. #65947	C₂	semidirect
18. #65947	C₂	semidirect
19. #65936	C₂	semidirect
20. #65895	C₂	semidirect
21. #65894	C₂	semidirect
22. #65892	C₂	semidirect
23. #65890	C₂	semidirect
24. #65876	C₂	semidirect
25. #65874	C₂	semidirect
26. #65872	C₂	semidirect
27. #65872	C₂	semidirect
28. #65868	C₂	semidirect
29. #65865	C₂	semidirect
30. #65849	C₂	semidirect
31. #65847	C₂	semidirect
33. C₅×#126	C₂²	semidirect
34. C₅×#125	C₂²	semidirect
36. C₅×#123	C₂²	semidirect
40. C₅×#121	C₂²	semidirect
43. C₄×C₅×D₄	C₂²	semidirect
44. C₄×C₅×D₄	C₂²	semidirect
45. C₅×#117	C₂²	semidirect
46. C₂×C₅×C₄⋊C₄	C₂²	semidirect
53. #4085	C₂²	semidirect
57. #4084	C₂²	semidirect
63. #4082	C₂²	semidirect
67. #4081	C₂²	semidirect
68. #4081	C₂²	semidirect
70. D₄×Dic₅	C₂²	semidirect
78. #4075	C₂²	semidirect
83. C₄×C₂²⋊D₅	C₂²	semidirect
84. C₄×C₂²⋊D₅	C₂²	semidirect
87. #4072	C₂²	semidirect
88. #4072	C₂²	semidirect
90. #4070	C₂²	semidirect
91. #4070	C₂²	semidirect
92. #4070	C₂²	semidirect
93. C₂×#683	C₂²	semidirect
94. C₂×C₄×Dic₅	C₂²	semidirect
102. #4044	C₂²	semidirect
109. #4042	C₂²	semidirect
110. #4042	C₂²	semidirect
118. #4038	C₂²	semidirect
119. D₅×C₄⋊C₄	C₂²	semidirect
120. #4036	C₂²	semidirect
121. #4036	C₂²	semidirect
122. #4035	C₂²	semidirect
123. #4035	C₂²	semidirect
124. #4035	C₂²	semidirect
125. #4035	C₂²	semidirect
126. #4035	C₂²	semidirect
127. #4035	C₂²	semidirect
128. #4035	C₂²	semidirect
129. #4035	C₂²	semidirect
130. #4034	C₂²	semidirect
131. #4034	C₂²	semidirect
132. #4033	C₂²	semidirect
133. #4033	C₂²	semidirect
134. #4033	C₂²	semidirect
137. #4032	C₂²	semidirect
144. #4031	C₂²	semidirect
145. #4031	C₂²	semidirect
151. #4029	C₂²	semidirect
156. #4027	C₂²	semidirect
163. #4025	C₂²	semidirect
164. #4025	C₂²	semidirect
165. #4025	C₂²	semidirect
166. #4025	C₂²	semidirect
169. #4024	C₂²	semidirect
170. #4024	C₂²	semidirect
171. #4024	C₂²	semidirect
172. #4024	C₂²	semidirect
174. #4023	C₂²	semidirect
181. #4018	C₂²	semidirect
182. #4016	C₂²	semidirect
183. #4015	C₂²	semidirect
184. C₄×Dic₁₀	C₂²	semidirect
185. C₄×Dic₁₀	C₂²	semidirect
186. C₄×Dic₁₀	C₂²	semidirect
352. #553	D₅	semidirect
473. #126	C₂×D₅	semidirect
485. #125	C₂×D₅	semidirect
521. #123	C₂×D₅	semidirect
557. #121	C₂×D₅	semidirect
584. C₄×D₄	C₂×D₅	semidirect
585. C₄×D₄	C₂×D₅	semidirect
597. #117	C₂×D₅	semidirect
600. C₂×C₄⋊C₄	C₂×D₅	semidirect
893. C₅	#3566	semidirect

Maximal subgroups

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

subgroup	index
C₅×#553	2
#66046	2
#66044	2
#66039	2
#66035	2
#66030	2
#66027	2
#65998	2
#65994	2
#65992	2
#65983	2
#65955	2
#65954	2
#65953	2
#65950	2
#65947	2
#65936	2
#65895	2
#65894	2
#65892	2
#65890	2
#65876	2
#65874	2
#65872	2
#65868	2
#65865	2
#65849	2
#65847	2
#3566	5