Subgroups — #10618069

Order 640.

1042 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#66040	C₂	1	1	yes	maximal, characteristic, complemented
3	#66040	C₂	1	1	yes	maximal, characteristic, complemented
4	#66040	C₂	1	1	yes	maximal, characteristic, complemented
5	D₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
6	#66030	C₂	1	1	yes	maximal, characteristic, complemented
7	#66026	C₂	1	1	yes	maximal, characteristic, complemented
8	#66012	C₂	1	1	yes	maximal, characteristic, complemented
9	#66003	C₂	1	1	yes	maximal, characteristic, complemented
10	#65992	C₂	1	1	yes	maximal, characteristic, complemented
11	#65989	C₂	1	1	yes	maximal, characteristic, complemented
12	#65988	C₂	1	1	yes	maximal, characteristic, complemented
13	#65984	C₂	1	1	yes	maximal, characteristic, complemented
14	#65971	C₂	1	1	yes	maximal, characteristic, complemented
15	#65970	C₂	1	1	yes	maximal, characteristic, complemented
16	#65944	C₂	1	1	yes	maximal, characteristic, complemented
17	#65935	C₂	1	1	yes	maximal, characteristic, complemented
18	#65915	C₂	1	1	yes	maximal, characteristic, complemented
19	#65902	C₂	1	1	yes	maximal, characteristic, complemented
20	#65898	C₂	1	1	yes	maximal, characteristic, complemented
21	#65894	C₂	1	1	yes	maximal, characteristic, complemented
22	#65890	C₂	1	1	yes	maximal, characteristic, complemented
23	#65880	C₂	1	1	yes	maximal, characteristic, complemented
24	#65879	C₂	1	1	yes	maximal, characteristic, complemented
25	#65874	C₂	1	1	yes	maximal, characteristic, complemented
26	#65867	C₂	1	1	yes	maximal, characteristic, complemented
27	#65865	C₂	1	1	yes	maximal, characteristic, complemented
28	#65864	C₂	1	1	yes	maximal, characteristic, complemented
29	#65861	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#4022	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#711	C₂²	1	1	yes	characteristic
33	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
34	C₂×#709	C₂²	1	1	yes	characteristic
35	C₅×#126	C₂²	1	1	yes	characteristic, complemented
36	C₅×#126	C₂²	1	1	yes	characteristic, complemented
37	C₅×#125	C₂²	1	1	yes	characteristic, complemented
38	C₅×#124	C₂²	1	1	yes	characteristic, complemented
39	C₅×#123	C₂²	1	1	yes	characteristic
40	C₅×#123	C₂²	1	1	yes	characteristic, complemented
41	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₅×#121	C₂²	1	1	yes	characteristic
43	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
45	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
46	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
47	C₅×#117	C₂²	1	1	yes	characteristic, complemented
48	C₅×#117	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
50	#4093	C₂²	1	1	yes	characteristic
51	#4092	C₂²	1	1	yes	characteristic, complemented
52	#4092	C₂²	1	1	yes	characteristic, complemented
53	#4090	C₂²	1	1	yes	characteristic, complemented
54	#4085	C₂²	1	1	yes	characteristic
55	#4085	C₂²	1	1	yes	characteristic
56	#4085	C₂²	1	1	yes	characteristic, complemented
57	#4085	C₂²	1	1	yes	characteristic, complemented
58	#4083	C₂²	1	1	yes	characteristic
59	#4083	C₂²	1	1	yes	characteristic
60	#4081	C₂²	1	1	yes	characteristic
61	#4081	C₂²	1	1	yes	characteristic, complemented
62	D₄×Dic₅	C₂²	1	1	yes	characteristic
63	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
64	#4076	C₂²	1	1	yes	characteristic, complemented
65	#4075	C₂²	1	1	yes	characteristic
66	#4075	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
73	C₂×#685	C₂²	1	1	yes	characteristic
74	C₂×#685	C₂²	1	1	yes	characteristic
75	C₂×#685	C₂²	1	1	yes	characteristic
76	C₂×#685	C₂²	1	1	yes	characteristic
77	#4072	C₂²	1	1	yes	characteristic, complemented
78	#4070	C₂²	1	1	yes	characteristic, complemented
79	C₂×#683	C₂²	1	1	yes	characteristic, complemented
80	C₂×#683	C₂²	1	1	yes	characteristic, complemented
81	C₂×#683	C₂²	1	1	yes	characteristic, complemented
82	C₂×#683	C₂²	1	1	yes	characteristic, complemented
83	#4044	C₂²	1	1	yes	characteristic
84	#4044	C₂²	1	1	yes	characteristic
85	#4044	C₂²	1	1	yes	characteristic
86	#4044	C₂²	1	1	yes	characteristic
87	#4044	C₂²	1	1	yes	characteristic
88	#4044	C₂²	1	1	yes	characteristic, complemented
89	#4043	C₂²	1	1	yes	characteristic, complemented
90	#4042	C₂²	1	1	yes	characteristic
91	#4042	C₂²	1	1	yes	characteristic
92	#4042	C₂²	1	1	yes	characteristic, complemented
93	#4042	C₂²	1	1	yes	characteristic, complemented
94	#4042	C₂²	1	1	yes	characteristic, complemented
95	#4042	C₂²	1	1	yes	characteristic, complemented
96	#4041	C₂²	1	1	yes	characteristic
97	#4040	C₂²	1	1	yes	characteristic
98	#4040	C₂²	1	1	yes	characteristic
99	#4040	C₂²	1	1	yes	characteristic
100	#4040	C₂²	1	1	yes	characteristic, complemented
101	#4040	C₂²	1	1	yes	characteristic, complemented
102	#4040	C₂²	1	1	yes	characteristic, complemented
103	#4039	C₂²	1	1	yes	characteristic
104	#4039	C₂²	1	1	yes	characteristic
105	#4039	C₂²	1	1	yes	characteristic, complemented
106	#4038	C₂²	1	1	yes	characteristic
107	#4038	C₂²	1	1	yes	characteristic, complemented
108	#4038	C₂²	1	1	yes	characteristic, complemented
109	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
110	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	#4036	C₂²	1	1	yes	characteristic, complemented
113	#4035	C₂²	1	1	yes	characteristic, complemented
114	#4035	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	#4034	C₂²	1	1	yes	characteristic, complemented
120	#4033	C₂²	1	1	yes	characteristic, complemented
121	#4033	C₂²	1	1	yes	characteristic, complemented
122	#4033	C₂²	1	1	yes	characteristic, complemented
123	#4032	C₂²	1	1	yes	characteristic
124	#4032	C₂²	1	1	yes	characteristic, complemented
125	#4031	C₂²	1	1	yes	characteristic
126	#4031	C₂²	1	1	yes	characteristic
127	#4031	C₂²	1	1	yes	characteristic
128	#4031	C₂²	1	1	yes	characteristic, complemented
129	#4030	C₂²	1	1	yes	characteristic
130	#4030	C₂²	1	1	yes	characteristic
131	#4030	C₂²	1	1	yes	characteristic
132	#4030	C₂²	1	1	yes	characteristic, complemented
133	#4029	C₂²	1	1	yes	characteristic, complemented
134	#4029	C₂²	1	1	yes	characteristic, complemented
135	#4029	C₂²	1	1	yes	characteristic, complemented
136	#4029	C₂²	1	1	yes	characteristic, complemented
137	#4028	C₂²	1	1	yes	characteristic
138	#4028	C₂²	1	1	yes	characteristic
139	#4027	C₂²	1	1	yes	characteristic
140	#4027	C₂²	1	1	yes	characteristic
141	#4027	C₂²	1	1	yes	characteristic
142	#4027	C₂²	1	1	yes	characteristic
143	#4027	C₂²	1	1	yes	characteristic, complemented
144	#4027	C₂²	1	1	yes	characteristic, complemented
145	#4027	C₂²	1	1	yes	characteristic, complemented
146	#4027	C₂²	1	1	yes	characteristic, complemented
147	D₅×C₂²⋊C₄	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	#4025	C₂²	1	1	yes	characteristic, complemented
152	#4025	C₂²	1	1	yes	characteristic, complemented
153	#4025	C₂²	1	1	yes	characteristic, complemented
154	#4025	C₂²	1	1	yes	characteristic, complemented
155	#4024	C₂²	1	1	yes	characteristic, complemented
156	#4024	C₂²	1	1	yes	characteristic, complemented
157	#4024	C₂²	1	1	yes	characteristic, complemented
158	#4024	C₂²	1	1	yes	characteristic, complemented
159	#4023	C₂²	1	1	yes	characteristic, complemented
160	#4023	C₂²	1	1	yes	characteristic, complemented
161	#4023	C₂²	1	1	yes	characteristic, complemented
162	#4023	C₂²	1	1	yes	characteristic, complemented
163	#4022	C₂²	1	1	yes	characteristic
164	#4022	C₂²	1	1	yes	characteristic
165	#4022	C₂²	1	1	yes	characteristic
166	#4022	C₂²	1	1	yes	characteristic
167	#4022	C₂²	1	1	yes	characteristic, complemented
168	#4022	C₂²	1	1	yes	characteristic, complemented
169	#4022	C₂²	1	1	yes	characteristic, complemented
170	#4022	C₂²	1	1	yes	characteristic, complemented
171	#4022	C₂²	1	1	yes	characteristic, complemented
172	#4022	C₂²	1	1	yes	characteristic, complemented
173	#4021	C₂²	1	1	yes	characteristic
174	C₄×D₂₀	C₂²	1	1	yes	characteristic
175	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
176	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
177	#4018	C₂²	1	1	yes	characteristic
178	#4018	C₂²	1	1	yes	characteristic, complemented
179	#4018	C₂²	1	1	yes	characteristic, complemented
180	#4018	C₂²	1	1	yes	characteristic, complemented
181	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
182	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
183	#4016	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	#3521	—	5	1	no	maximal, Sylow
188	C₂³×D₅	C₂³	1	1	yes	characteristic
189	C₂³×D₅	C₂³	1	1	yes	characteristic
190	C₂×C₅×Q₈	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	C₂²×C₄×C₅	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	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₅	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	C₂²×Dic₅	C₂³	1	1	yes	characteristic
208	C₂²×Dic₅	C₂³	1	1	yes	characteristic
209	C₂²×Dic₅	C₂³	1	1	yes	characteristic
210	C₂²×Dic₅	C₂³	1	1	yes	characteristic
211	C₂²×Dic₅	C₂³	1	1	yes	characteristic
212	C₂²×Dic₅	C₂³	1	1	yes	characteristic
213	#711	—	2	4	no	—
214	D₄×D₅	—	2	4	no	—
215	#709	—	2	4	no	—
216	C₂×D₂₀	C₂³	1	1	yes	characteristic
217	C₂×D₂₀	C₂³	1	1	yes	characteristic
218	C₂×D₂₀	C₂³	1	1	yes	characteristic
219	C₂×D₂₀	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×C₄×D₅	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
232	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
233	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
234	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
235	C₂×Dic₁₀	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₅×C₄⋊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	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
253	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₄²×C₅	C₂³	1	1	yes	characteristic
257	C₄²×C₅	C₂³	1	1	yes	characteristic
258	C₄²×C₅	C₂³	1	1	yes	characteristic
259	C₄²×C₅	C₂³	1	1	yes	characteristic
260	C₄²×C₅	C₂³	1	1	yes	characteristic
261	C₄²×C₅	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	#685	C₂³	1	1	yes	characteristic
293	#685	C₂³	1	1	yes	characteristic
294	#685	C₂³	1	1	yes	characteristic
295	#685	C₂³	1	1	yes	characteristic
296	#685	C₂³	1	1	yes	characteristic
297	#685	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	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₅	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	#683	C₂³	1	1	yes	characteristic
331	#683	C₂³	1	1	yes	characteristic
332	#683	C₂³	1	1	yes	characteristic
333	#683	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	C₄×Dic₅	C₂³	1	1	yes	characteristic
344	C₄×Dic₅	C₂³	1	1	yes	characteristic
345	C₄×Dic₅	C₂³	1	1	yes	characteristic
346	#556	—	5	1	no	—
347	#556	—	5	1	no	—
348	#554	—	5	1	no	—
349	#553	—	5	1	no	—
350	#553	—	5	1	no	—
351	#553	—	5	1	no	—
352	#552	—	5	1	no	—
353	#552	—	5	1	no	—
354	#552	—	5	1	no	—
355	#551	—	5	1	no	—
356	#551	—	5	1	no	—
357	#551	—	5	1	no	—
358	#551	—	5	1	no	—
359	#547	—	5	1	no	—
360	#546	—	5	1	no	—
361	#546	—	5	1	no	—
362	#542	—	5	1	no	—
363	#541	—	5	1	no	—
364	#539	—	5	1	no	—
365	#539	—	5	1	no	—
366	#538	—	5	1	no	—
367	#538	—	5	1	no	—
368	#529	—	5	1	no	—
369	#529	—	5	1	no	—
370	#529	—	5	1	no	—
371	#529	D₅	1	1	yes	characteristic, complemented
372	C₂×#126	—	5	1	no	—
373	C₂×#126	—	5	1	no	—
374	#520	—	5	1	no	—
375	#518	—	5	1	no	—
376	C₄×#41	—	5	1	no	—
377	C₂³×C₅	C₂⁴	1	1	yes	characteristic
378	C₂³×C₅	C₂⁴	1	1	yes	characteristic
379	C₂³×C₅	C₂⁴	1	1	yes	characteristic
380	C₂²×D₅	—	2	2	no	—
381	C₂²×D₅	—	2	2	no	—
382	C₂²×D₅	—	4	1	no	—
383	C₂²×D₅	—	4	1	no	—
384	C₂²×D₅	—	4	1	no	—
385	C₂²×D₅	—	4	1	no	—
386	C₂²×D₅	C₂⁴	1	1	yes	characteristic
387	C₂²×D₅	C₂⁴	1	1	yes	characteristic
388	C₂²×D₅	C₂⁴	1	1	yes	characteristic
389	C₂²×D₅	C₂⁴	1	1	yes	characteristic
390	C₅×Q₈	—	4	1	no	—
391	C₅×D₄	—	2	2	no	—
392	C₅×D₄	—	2	2	no	—
393	C₅×D₄	—	4	1	no	—
394	C₂×C₄×C₅	—	2	2	no	—
395	C₂×C₄×C₅	—	4	1	no	—
396	C₂×C₄×C₅	—	4	1	no	—
397	C₂×C₄×C₅	—	4	1	no	—
398	C₂×C₄×C₅	—	4	1	no	—
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	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
411	C₂²⋊D₅	—	2	2	no	—
412	C₂²⋊D₅	—	2	2	no	—
413	C₂²⋊D₅	—	2	2	no	—
414	C₂²⋊D₅	—	4	1	no	—
415	C₂²⋊D₅	—	4	1	no	—
416	C₂²⋊D₅	—	4	1	no	—
417	C₂²⋊D₅	—	4	1	no	—
418	C₂²⋊D₅	#41	1	4	yes	—
419	C₂×Dic₅	—	2	2	no	—
420	C₂×Dic₅	—	2	2	no	—
421	C₂×Dic₅	—	4	1	no	—
422	C₂×Dic₅	—	4	1	no	—
423	C₂×Dic₅	—	4	1	no	—
424	C₂×Dic₅	—	4	1	no	—
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	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
436	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
437	D₂₀	—	2	2	no	—
438	D₂₀	—	2	2	no	—
439	D₂₀	—	4	1	no	—
440	D₂₀	—	4	1	no	—
441	C₄×D₅	—	2	2	no	—
442	C₄×D₅	—	2	2	no	—
443	C₄×D₅	—	2	2	no	—
444	C₄×D₅	—	2	2	no	—
445	C₄×D₅	—	4	1	no	—
446	C₄×D₅	—	4	1	no	—
447	C₄×D₅	—	4	1	no	—
448	C₄×D₅	—	4	1	no	—
449	C₄×D₅	—	4	1	no	—
450	C₄×D₅	—	4	1	no	—
451	C₄×D₅	—	4	1	no	—
452	C₄×D₅	—	4	1	no	—
453	Dic₁₀	—	2	2	no	—
454	Dic₁₀	—	2	2	no	—
455	Dic₁₀	—	4	1	no	—
456	Dic₁₀	—	4	1	no	—
457	C₂×#41	—	5	1	no	—
458	C₂×#41	—	5	1	no	—
459	C₂²×D₄	—	5	1	no	—
460	C₄⋊Q₈	—	5	1	no	—
461	C₄⋊Q₈	—	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	—	5	1	no	—
473	#126	—	5	1	no	—
474	#126	—	5	1	no	—
475	#126	—	5	1	no	—
476	#126	—	5	1	no	—
477	#126	—	5	1	no	—
478	#126	—	5	1	no	—
479	#126	—	5	1	no	—
480	#126	—	5	1	no	—
481	#126	—	5	1	no	—
482	#126	C₂×D₅	1	1	yes	characteristic, complemented
483	#126	C₂×D₅	1	1	yes	characteristic, complemented
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	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	C₂×D₅	1	1	yes	characteristic, complemented
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	C₂×D₅	1	1	yes	characteristic
517	#123	C₂×D₅	1	1	yes	characteristic, complemented
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	C₂×D₅	1	1	yes	characteristic, complemented
533	#121	—	5	1	no	—
534	#121	—	5	1	no	—
535	#121	—	5	1	no	—
536	#121	—	5	1	no	—
537	#121	—	5	1	no	—
538	#121	—	5	1	no	—
539	#121	—	5	1	no	—
540	#121	—	5	1	no	—
541	#121	—	5	1	no	—
542	#121	—	5	1	no	—
543	#121	C₂×D₅	1	1	yes	characteristic
544	#120	—	5	1	no	—
545	#120	—	5	1	no	—
546	#120	—	5	1	no	—
547	#120	—	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	C₂×D₅	1	1	yes	characteristic, complemented
555	C₄×D₄	—	5	1	no	—
556	C₄×D₄	—	5	1	no	—
557	C₄×D₄	—	5	1	no	—
558	C₄×D₄	—	5	1	no	—
559	C₄×D₄	—	5	1	no	—
560	C₄×D₄	—	5	1	no	—
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	—	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	C₂×D₅	1	1	yes	characteristic
578	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
579	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
580	#117	—	5	1	no	—
581	#117	—	5	1	no	—
582	#117	—	5	1	no	—
583	#117	—	5	1	no	—
584	#117	—	5	1	no	—
585	#117	—	5	1	no	—
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	C₂×D₅	1	1	yes	characteristic, complemented
593	#117	C₂×D₅	1	1	yes	characteristic, complemented
594	C₂×C₄⋊C₄	—	5	1	no	—
595	C₂×C₄⋊C₄	—	5	1	no	—
596	C₂×C₄⋊C₄	—	5	1	no	—
597	C₂×C₄⋊C₄	—	5	1	no	—
598	C₂×C₄⋊C₄	—	5	1	no	—
599	C₂×C₄⋊C₄	—	5	1	no	—
600	C₂×C₄⋊C₄	—	5	1	no	—
601	C₂×C₂²⋊C₄	—	5	1	no	—
602	C₂×C₂²⋊C₄	—	5	1	no	—
603	C₂×C₂²⋊C₄	—	5	1	no	—
604	C₂×C₂²⋊C₄	—	5	1	no	—
605	C₂×C₂²⋊C₄	—	5	1	no	—
606	C₂×C₂²⋊C₄	—	5	1	no	—
607	C₂×C₂²⋊C₄	—	5	1	no	—
608	C₂×C₂²⋊C₄	—	5	1	no	—
609	C₂×C₄²	—	5	1	no	—
610	C₂×C₄²	—	5	1	no	—
611	C₂×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
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	—	2	1	no	—
618	C₂²×C₅	—	2	1	no	—
619	C₂²×C₅	—	2	1	no	—
620	C₂²×C₅	C₂×#41	1	2	yes	—
621	C₂²×C₅	C₂⁵	1	1	yes	characteristic
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	—	2	1	no	—
628	C₂×D₅	—	2	1	no	—
629	C₂×D₅	—	2	1	no	—
630	C₂×D₅	—	2	1	no	—
631	C₂×D₅	—	2	1	no	—
632	C₂×D₅	—	2	1	no	—
633	C₂×D₅	—	8	2	no	—
634	C₂×D₅	—	8	2	no	—
635	C₂×D₅	C₂×#41	1	2	yes	—
636	C₄×C₅	—	2	1	no	—
637	C₄×C₅	—	2	1	no	—
638	C₄×C₅	—	2	1	no	—
639	C₄×C₅	—	2	1	no	—
640	C₄×C₅	—	2	1	no	—
641	C₄×C₅	—	2	1	no	—
642	C₄×C₅	—	2	1	no	—
643	C₄×C₅	—	2	1	no	—
644	C₄×C₅	—	2	1	no	—
645	C₄×C₅	—	2	1	no	—
646	C₄×C₅	—	2	1	no	—
647	C₄×C₅	—	2	1	no	—
648	Dic₅	—	2	1	no	—
649	Dic₅	—	2	1	no	—
650	Dic₅	—	2	1	no	—
651	Dic₅	—	2	1	no	—
652	Dic₅	—	2	1	no	—
653	Dic₅	—	2	1	no	—
654	Dic₅	—	2	1	no	—
655	Dic₅	—	2	1	no	—
656	Dic₅	—	2	1	no	—
657	Dic₅	—	2	1	no	—
658	Dic₅	—	2	1	no	—
659	Dic₅	C₂×#41	1	2	yes	—
660	C₂⁴	—	5	1	no	—
661	C₂⁴	—	5	1	no	—
662	#41	—	10	4	no	—
663	#41	—	10	4	no	—
664	C₂×Q₈	—	5	1	no	—
665	C₂×Q₈	—	5	1	no	—
666	C₂×Q₈	—	5	1	no	—
667	C₂×Q₈	—	5	1	no	—
668	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
669	C₂×D₄	—	5	1	no	—
670	C₂×D₄	—	5	1	no	—
671	C₂×D₄	—	5	1	no	—
672	C₂×D₄	—	5	1	no	—
673	C₂×D₄	—	5	1	no	—
674	C₂×D₄	—	5	1	no	—
675	C₂×D₄	—	5	1	no	—
676	C₂×D₄	—	5	1	no	—
677	C₂×D₄	—	5	1	no	—
678	C₂×D₄	—	5	1	no	—
679	C₂×D₄	—	5	1	no	—
680	C₂×D₄	—	5	1	no	—
681	C₂×D₄	—	10	4	no	—
682	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
683	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
684	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
690	C₂²×C₄	—	5	1	no	—
691	C₂²×C₄	—	5	1	no	—
692	C₂²×C₄	—	5	1	no	—
693	C₂²×C₄	—	5	1	no	—
694	C₂²×C₄	—	5	1	no	—
695	C₂²×C₄	—	5	1	no	—
696	C₂²×C₄	—	5	1	no	—
697	C₂²×C₄	—	5	1	no	—
698	C₂²×C₄	—	5	1	no	—
699	C₂²×C₄	—	5	1	no	—
700	C₂²×C₄	—	5	1	no	—
701	C₂²×C₄	—	5	1	no	—
702	C₂²×C₄	—	5	1	no	—
703	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
705	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
706	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
707	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
734	C₄⋊C₄	—	5	1	no	—
735	C₄⋊C₄	—	5	1	no	—
736	C₄⋊C₄	—	5	1	no	—
737	C₄⋊C₄	—	5	1	no	—
738	C₄⋊C₄	—	5	1	no	—
739	C₄⋊C₄	—	5	1	no	—
740	C₄⋊C₄	—	5	1	no	—
741	C₄⋊C₄	—	5	1	no	—
742	C₄⋊C₄	—	5	1	no	—
743	C₄⋊C₄	—	5	1	no	—
744	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
746	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
747	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
748	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
751	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
752	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
782	C₂²⋊C₄	—	5	1	no	—
783	C₂²⋊C₄	—	5	1	no	—
784	C₂²⋊C₄	—	5	1	no	—
785	C₂²⋊C₄	—	5	1	no	—
786	C₂²⋊C₄	—	5	1	no	—
787	C₂²⋊C₄	—	5	1	no	—
788	C₂²⋊C₄	—	5	1	no	—
789	C₂²⋊C₄	—	5	1	no	—
790	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
791	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
792	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
800	C₄²	—	5	1	no	—
801	C₄²	—	5	1	no	—
802	C₄²	—	5	1	no	—
803	C₄²	—	5	1	no	—
804	C₄²	—	5	1	no	—
805	C₄²	—	5	1	no	—
806	C₄²	—	5	1	no	—
807	C₄²	—	5	1	no	—
808	C₄²	—	5	1	no	—
809	C₄²	—	5	1	no	—
810	C₄²	—	5	1	no	—
811	C₄²	—	5	1	no	—
812	C₄²	C₂²×D₅	1	1	yes	characteristic
813	C₄²	C₂²×D₅	1	1	yes	characteristic
814	C₄²	C₂²×D₅	1	1	yes	characteristic
815	C₄²	C₂²×D₅	1	1	yes	characteristic
816	C₄²	C₂²×D₅	1	1	yes	characteristic
817	C₄²	C₂²×D₅	1	1	yes	characteristic
818	C₂×C₅	—	2	2	no	—
819	C₂×C₅	—	4	1	no	—
820	C₂×C₅	—	4	1	no	—
821	C₂×C₅	C₂²×#41	1	1	yes	characteristic
822	C₂×C₅	#585	1	1	yes	characteristic
823	C₂×C₅	#585	1	1	yes	characteristic
824	D₅	—	2	2	no	—
825	D₅	—	4	1	no	—
826	D₅	—	4	1	no	—
827	D₅	—	4	1	no	—
828	C₂³	—	5	1	no	—
829	C₂³	—	5	1	no	—
830	C₂³	—	5	1	no	—
831	C₂³	—	5	1	no	—
832	C₂³	—	10	2	no	—
833	C₂³	—	10	2	no	—
834	C₂³	—	20	1	no	—
835	C₂³	—	20	1	no	—
836	C₂³	—	20	1	no	—
837	C₂³	—	20	1	no	—
838	C₂³	C₂³×D₅	1	1	yes	characteristic
839	C₂³	C₂³×D₅	1	1	yes	characteristic
840	C₂³	C₂³×D₅	1	1	yes	characteristic
841	Q₈	—	4	1	no	—
842	Q₈	—	10	2	no	—
843	Q₈	—	10	2	no	—
844	Q₈	—	20	1	no	—
845	Q₈	—	20	1	no	—
846	D₄	—	2	2	no	—
847	D₄	—	2	2	no	—
848	D₄	—	4	1	no	—
849	D₄	—	5	4	no	—
850	D₄	—	10	2	no	—
851	D₄	—	10	2	no	—
852	D₄	—	10	2	no	—
853	D₄	—	10	2	no	—
854	D₄	—	10	2	no	—
855	D₄	—	20	1	no	—
856	D₄	—	20	1	no	—
857	D₄	—	20	1	no	—
858	D₄	—	20	1	no	—
859	D₄	—	20	1	no	—
860	D₄	—	20	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	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	—	5	1	no	—
871	C₂×C₄	—	5	1	no	—
872	C₂×C₄	—	5	1	no	—
873	C₂×C₄	—	5	1	no	—
874	C₂×C₄	—	5	1	no	—
875	C₂×C₄	—	5	1	no	—
876	C₂×C₄	—	5	1	no	—
877	C₂×C₄	—	5	1	no	—
878	C₂×C₄	—	10	2	no	—
879	C₂×C₄	—	10	2	no	—
880	C₂×C₄	—	10	2	no	—
881	C₂×C₄	—	10	2	no	—
882	C₂×C₄	—	10	2	no	—
883	C₂×C₄	—	10	2	no	—
884	C₂×C₄	—	20	1	no	—
885	C₂×C₄	—	20	1	no	—
886	C₂×C₄	—	20	1	no	—
887	C₂×C₄	—	20	1	no	—
888	C₂×C₄	—	20	1	no	—
889	C₂×C₄	—	20	1	no	—
890	C₂×C₄	—	20	1	no	—
891	C₂×C₄	—	20	1	no	—
892	C₂×C₄	—	20	1	no	—
893	C₂×C₄	—	20	1	no	—
894	C₂×C₄	—	20	1	no	—
895	C₂×C₄	—	20	1	no	—
896	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
897	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
898	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
899	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
908	C₅	#3521	1	1	yes	characteristic, complemented, Sylow
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	5	2	no	—
918	C₂²	—	10	1	no	—
919	C₂²	—	10	1	no	—
920	C₂²	—	10	1	no	—
921	C₂²	—	10	1	no	—
922	C₂²	—	10	1	no	—
923	C₂²	—	10	1	no	—
924	C₂²	—	10	1	no	—
925	C₂²	—	10	1	no	—
926	C₂²	—	10	1	no	—
927	C₂²	—	10	1	no	—
928	C₂²	—	10	1	no	—
929	C₂²	—	40	2	no	—
930	C₂²	—	40	2	no	—
931	C₂²	D₅×#41	1	2	yes	—
932	C₂²	C₂⁴×D₅	1	1	yes	characteristic
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	1	no	—
945	C₄	—	5	2	no	—
946	C₄	—	10	1	no	—
947	C₄	—	10	1	no	—
948	C₄	—	10	1	no	—
949	C₄	—	10	1	no	—
950	C₄	—	10	1	no	—
951	C₄	—	10	1	no	—
952	C₄	—	10	1	no	—
953	C₄	—	10	1	no	—
954	C₄	—	10	1	no	—
955	C₄	—	10	1	no	—
956	C₄	—	10	1	no	—
957	C₂	—	2	2	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	10	2	no	—
961	C₂	—	20	1	no	—
962	C₂	—	20	1	no	—
963	C₂	—	20	1	no	—
964	C₂	C₂×D₅×#41	1	1	yes	characteristic
965	C₂	#66283	1	1	yes	characteristic
966	C₂	#66283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#529	C₂
hypercenter	#529	D₅
hypocenter	C₅	#3521
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₅×#529	C₂	semidirect
2. #66040	C₂	semidirect
3. #66040	C₂	semidirect
4. #66040	C₂	semidirect
5. D₅×#126	C₂	semidirect
6. #66030	C₂	semidirect
7. #66026	C₂	semidirect
8. #66012	C₂	semidirect
9. #66003	C₂	semidirect
10. #65992	C₂	semidirect
11. #65989	C₂	semidirect
12. #65988	C₂	semidirect
13. #65984	C₂	semidirect
14. #65971	C₂	semidirect
15. #65970	C₂	semidirect
16. #65944	C₂	semidirect
17. #65935	C₂	semidirect
18. #65915	C₂	semidirect
19. #65902	C₂	semidirect
20. #65898	C₂	semidirect
21. #65894	C₂	semidirect
22. #65890	C₂	semidirect
23. #65880	C₂	semidirect
24. #65879	C₂	semidirect
25. #65874	C₂	semidirect
26. #65867	C₂	semidirect
27. #65865	C₂	semidirect
28. #65864	C₂	semidirect
29. #65861	C₂	semidirect
30. C₂×#4022	C₂	semidirect
31. C₄×#709	C₂	semidirect
35. C₅×#126	C₂²	semidirect
36. C₅×#126	C₂²	semidirect
37. C₅×#125	C₂²	semidirect
38. C₅×#124	C₂²	semidirect
40. C₅×#123	C₂²	semidirect
41. C₅×C₂²⋊Q₈	C₂²	semidirect
43. C₄×C₅×Q₈	C₂²	semidirect
45. C₄×C₅×D₄	C₂²	semidirect
46. C₄×C₅×D₄	C₂²	semidirect
47. C₅×#117	C₂²	semidirect
48. C₅×#117	C₂²	semidirect
49. C₂×C₄²×C₅	C₂²	semidirect
51. #4092	C₂²	semidirect
52. #4092	C₂²	semidirect
53. #4090	C₂²	semidirect
56. #4085	C₂²	semidirect
57. #4085	C₂²	semidirect
61. #4081	C₂²	semidirect
63. D₄×Dic₅	C₂²	semidirect
64. #4076	C₂²	semidirect
66. #4075	C₂²	semidirect
70. C₄×C₂²⋊D₅	C₂²	semidirect
71. C₄×C₂²⋊D₅	C₂²	semidirect
72. C₄×C₂²⋊D₅	C₂²	semidirect
77. #4072	C₂²	semidirect
78. #4070	C₂²	semidirect
79. C₂×#683	C₂²	semidirect
80. C₂×#683	C₂²	semidirect
81. C₂×#683	C₂²	semidirect
82. C₂×#683	C₂²	semidirect
88. #4044	C₂²	semidirect
89. #4043	C₂²	semidirect
92. #4042	C₂²	semidirect
93. #4042	C₂²	semidirect
94. #4042	C₂²	semidirect
95. #4042	C₂²	semidirect
100. #4040	C₂²	semidirect
101. #4040	C₂²	semidirect
102. #4040	C₂²	semidirect
105. #4039	C₂²	semidirect
107. #4038	C₂²	semidirect
108. #4038	C₂²	semidirect
109. D₅×C₄⋊C₄	C₂²	semidirect
110. D₅×C₄⋊C₄	C₂²	semidirect
111. D₅×C₄⋊C₄	C₂²	semidirect
112. #4036	C₂²	semidirect
113. #4035	C₂²	semidirect
114. #4035	C₂²	semidirect
115. #4035	C₂²	semidirect
116. #4035	C₂²	semidirect
117. #4035	C₂²	semidirect
118. #4035	C₂²	semidirect
119. #4034	C₂²	semidirect
120. #4033	C₂²	semidirect
121. #4033	C₂²	semidirect
122. #4033	C₂²	semidirect
124. #4032	C₂²	semidirect
128. #4031	C₂²	semidirect
132. #4030	C₂²	semidirect
133. #4029	C₂²	semidirect
134. #4029	C₂²	semidirect
135. #4029	C₂²	semidirect
136. #4029	C₂²	semidirect
143. #4027	C₂²	semidirect
144. #4027	C₂²	semidirect
145. #4027	C₂²	semidirect
146. #4027	C₂²	semidirect
151. #4025	C₂²	semidirect
152. #4025	C₂²	semidirect
153. #4025	C₂²	semidirect
154. #4025	C₂²	semidirect
155. #4024	C₂²	semidirect
156. #4024	C₂²	semidirect
157. #4024	C₂²	semidirect
158. #4024	C₂²	semidirect
159. #4023	C₂²	semidirect
160. #4023	C₂²	semidirect
161. #4023	C₂²	semidirect
162. #4023	C₂²	semidirect
167. #4022	C₂²	semidirect
168. #4022	C₂²	semidirect
169. #4022	C₂²	semidirect
170. #4022	C₂²	semidirect
171. #4022	C₂²	semidirect
172. #4022	C₂²	semidirect
175. C₄×D₂₀	C₂²	semidirect
176. C₄×D₂₀	C₂²	semidirect
178. #4018	C₂²	semidirect
179. #4018	C₂²	semidirect
180. #4018	C₂²	semidirect
181. C₄²×D₅	C₂²	semidirect
182. C₄²×D₅	C₂²	semidirect
183. #4016	C₂²	semidirect
184. C₄×Dic₁₀	C₂²	semidirect
185. C₄×Dic₁₀	C₂²	semidirect
186. C₄×Dic₁₀	C₂²	semidirect
371. #529	D₅	semidirect
482. #126	C₂×D₅	semidirect
483. #126	C₂×D₅	semidirect
492. #125	C₂×D₅	semidirect
499. #124	C₂×D₅	semidirect
517. #123	C₂×D₅	semidirect
532. C₂²⋊Q₈	C₂×D₅	semidirect
554. C₄×Q₈	C₂×D₅	semidirect
578. C₄×D₄	C₂×D₅	semidirect
579. C₄×D₄	C₂×D₅	semidirect
592. #117	C₂×D₅	semidirect
593. #117	C₂×D₅	semidirect
611. C₂×C₄²	C₂×D₅	semidirect
908. C₅	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₅×#529	2
#66040	2
D₅×#126	2
#66030	2
#66026	2
#66012	2
#66003	2
#65992	2
#65989	2
#65988	2
#65984	2
#65971	2
#65970	2
#65944	2
#65935	2
#65915	2
#65902	2
#65898	2
#65894	2
#65890	2
#65880	2
#65879	2
#65874	2
#65867	2
#65865	2
#65864	2
#65861	2
C₂×#4022	2
C₄×#709	2
#3521	5