Subgroups — #10618317

Order 640.

1152 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	#66042	C₂	1	1	yes	maximal, characteristic, complemented
3	#66041	C₂	1	1	yes	maximal, characteristic, complemented
4	#66040	C₂	1	1	yes	maximal, characteristic, complemented
5	#66039	C₂	1	1	yes	maximal, characteristic, complemented
6	#66015	C₂	1	1	yes	maximal, characteristic, complemented
7	#66014	C₂	1	1	yes	maximal, characteristic, complemented
8	#66013	C₂	1	1	yes	maximal, characteristic, complemented
9	#66012	C₂	1	1	yes	maximal, characteristic, complemented
10	#65996	C₂	1	1	yes	maximal, characteristic, complemented
11	#65995	C₂	1	1	yes	maximal, characteristic, complemented
12	#65989	C₂	1	1	yes	maximal, characteristic, complemented
13	D₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
14	#65971	C₂	1	1	yes	maximal, characteristic, complemented
15	#65969	C₂	1	1	yes	maximal, characteristic, complemented
16	#65952	C₂	1	1	yes	maximal, characteristic, complemented
17	#65949	C₂	1	1	yes	maximal, characteristic, complemented
18	#65946	C₂	1	1	yes	maximal, characteristic, complemented
19	#65944	C₂	1	1	yes	maximal, characteristic, complemented
20	#65940	C₂	1	1	yes	maximal, characteristic, complemented
21	#65935	C₂	1	1	yes	maximal, characteristic, complemented
22	#65925	C₂	1	1	yes	maximal, characteristic, complemented
23	#65925	C₂	1	1	yes	maximal, characteristic, complemented
24	#65924	C₂	1	1	yes	maximal, characteristic, complemented
25	#65921	C₂	1	1	yes	maximal, characteristic, complemented
26	#65898	C₂	1	1	yes	maximal, characteristic, complemented
27	#65881	C₂	1	1	yes	maximal, characteristic, complemented
28	#65880	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#4029	C₂	1	1	yes	maximal, characteristic, complemented
31	#65820	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₅	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊D₅	C₂²	1	1	yes	characteristic
34	C₂×#711	C₂²	1	1	yes	characteristic
35	C₂×#711	C₂²	1	1	yes	characteristic, complemented
36	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
37	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
38	C₂×#709	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
41	C₅×#126	C₂²	1	1	yes	characteristic, complemented
42	C₅×#126	C₂²	1	1	yes	characteristic, complemented
43	C₅×#124	C₂²	1	1	yes	characteristic, complemented
44	C₅×#124	C₂²	1	1	yes	characteristic, complemented
45	C₅×#123	C₂²	1	1	yes	characteristic, complemented
46	C₅×#123	C₂²	1	1	yes	characteristic, complemented
47	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₅×#121	C₂²	1	1	yes	characteristic, complemented
49	C₅×#121	C₂²	1	1	yes	characteristic, complemented
50	C₅×#121	C₂²	1	1	yes	characteristic, complemented
51	C₅×#120	C₂²	1	1	yes	characteristic
52	C₅×#120	C₂²	1	1	yes	characteristic, complemented
53	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
54	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
58	#4093	C₂²	1	1	yes	characteristic, complemented
59	#4092	C₂²	1	1	yes	characteristic, complemented
60	#4092	C₂²	1	1	yes	characteristic, complemented
61	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
62	#4086	C₂²	1	1	yes	characteristic
63	#4085	C₂²	1	1	yes	characteristic
64	#4085	C₂²	1	1	yes	characteristic
65	#4085	C₂²	1	1	yes	characteristic, complemented
66	#4085	C₂²	1	1	yes	characteristic, complemented
67	#4085	C₂²	1	1	yes	characteristic, complemented
68	#4085	C₂²	1	1	yes	characteristic, complemented
69	#4085	C₂²	1	1	yes	characteristic, complemented
70	#4084	C₂²	1	1	yes	characteristic
71	#4084	C₂²	1	1	yes	characteristic, complemented
72	#4084	C₂²	1	1	yes	characteristic, complemented
73	#4083	C₂²	1	1	yes	characteristic
74	#4083	C₂²	1	1	yes	characteristic, complemented
75	#4083	C₂²	1	1	yes	characteristic, complemented
76	#4083	C₂²	1	1	yes	characteristic, complemented
77	#4082	C₂²	1	1	yes	characteristic, complemented
78	#4081	C₂²	1	1	yes	characteristic, complemented
79	#4081	C₂²	1	1	yes	characteristic, complemented
80	#4081	C₂²	1	1	yes	characteristic, complemented
81	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
85	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
86	#4075	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
94	C₂×#685	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
96	#4070	C₂²	1	1	yes	characteristic, complemented
97	C₂×#683	C₂²	1	1	yes	characteristic, complemented
98	C₂×#683	C₂²	1	1	yes	characteristic, complemented
99	#4044	C₂²	1	1	yes	characteristic, complemented
100	#4044	C₂²	1	1	yes	characteristic, complemented
101	#4043	C₂²	1	1	yes	characteristic, complemented
102	#4043	C₂²	1	1	yes	characteristic, complemented
103	#4042	C₂²	1	1	yes	characteristic, complemented
104	#4042	C₂²	1	1	yes	characteristic, complemented
105	#4042	C₂²	1	1	yes	characteristic, complemented
106	#4040	C₂²	1	1	yes	characteristic, complemented
107	#4040	C₂²	1	1	yes	characteristic, complemented
108	#4040	C₂²	1	1	yes	characteristic, complemented
109	#4040	C₂²	1	1	yes	characteristic, complemented
110	#4039	C₂²	1	1	yes	characteristic, complemented
111	#4039	C₂²	1	1	yes	characteristic, complemented
112	#4038	C₂²	1	1	yes	characteristic, complemented
113	#4038	C₂²	1	1	yes	characteristic, complemented
114	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	#4036	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	#4034	C₂²	1	1	yes	characteristic, complemented
122	#4033	C₂²	1	1	yes	characteristic, complemented
123	#4032	C₂²	1	1	yes	characteristic, complemented
124	#4032	C₂²	1	1	yes	characteristic, complemented
125	#4032	C₂²	1	1	yes	characteristic, complemented
126	#4032	C₂²	1	1	yes	characteristic, complemented
127	#4031	C₂²	1	1	yes	characteristic, complemented
128	#4031	C₂²	1	1	yes	characteristic, complemented
129	#4031	C₂²	1	1	yes	characteristic, complemented
130	#4030	C₂²	1	1	yes	characteristic
131	#4030	C₂²	1	1	yes	characteristic
132	#4030	C₂²	1	1	yes	characteristic, complemented
133	#4030	C₂²	1	1	yes	characteristic, complemented
134	#4029	C₂²	1	1	yes	characteristic
135	#4029	C₂²	1	1	yes	characteristic
136	#4029	C₂²	1	1	yes	characteristic
137	#4029	C₂²	1	1	yes	characteristic, complemented
138	#4029	C₂²	1	1	yes	characteristic, complemented
139	#4029	C₂²	1	1	yes	characteristic, complemented
140	#4029	C₂²	1	1	yes	characteristic, complemented
141	#4029	C₂²	1	1	yes	characteristic, complemented
142	#4029	C₂²	1	1	yes	characteristic, complemented
143	#4029	C₂²	1	1	yes	characteristic, complemented
144	#4029	C₂²	1	1	yes	characteristic, complemented
145	#4029	C₂²	1	1	yes	characteristic, complemented
146	#4028	C₂²	1	1	yes	characteristic
147	#4028	C₂²	1	1	yes	characteristic
148	#4027	C₂²	1	1	yes	characteristic
149	#4027	C₂²	1	1	yes	characteristic
150	#4027	C₂²	1	1	yes	characteristic
151	#4027	C₂²	1	1	yes	characteristic, complemented
152	#4027	C₂²	1	1	yes	characteristic, complemented
153	#4027	C₂²	1	1	yes	characteristic, complemented
154	#4027	C₂²	1	1	yes	characteristic, complemented
155	#4027	C₂²	1	1	yes	characteristic, complemented
156	#4027	C₂²	1	1	yes	characteristic, complemented
157	#4027	C₂²	1	1	yes	characteristic, complemented
158	#4027	C₂²	1	1	yes	characteristic, complemented
159	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
161	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
162	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	#4025	C₂²	1	1	yes	characteristic, complemented
166	#4025	C₂²	1	1	yes	characteristic, complemented
167	#4025	C₂²	1	1	yes	characteristic, complemented
168	#4025	C₂²	1	1	yes	characteristic, complemented
169	#4025	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	#4024	C₂²	1	1	yes	characteristic, complemented
174	#4023	C₂²	1	1	yes	characteristic, complemented
175	#4023	C₂²	1	1	yes	characteristic, complemented
176	#4023	C₂²	1	1	yes	characteristic, complemented
177	#4023	C₂²	1	1	yes	characteristic, complemented
178	#4023	C₂²	1	1	yes	characteristic, complemented
179	#4022	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
182	#4018	C₂²	1	1	yes	characteristic, complemented
183	#4018	C₂²	1	1	yes	characteristic, complemented
184	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
185	#4016	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
187	#3513	—	5	1	no	maximal, Sylow
188	C₂⁴×C₅	C₂³	1	1	yes	characteristic
189	C₂³×D₅	C₂³	1	1	yes	characteristic
190	C₂³×D₅	C₂³	1	1	yes	characteristic
191	C₂³×D₅	C₂³	1	1	yes	characteristic
192	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
193	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
194	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
195	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
196	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
197	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
198	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
199	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₅	—	2	4	no	—
205	C₂×C₂²⋊D₅	—	4	2	no	—
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	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
220	C₂²×Dic₅	C₂³	1	1	yes	characteristic
221	C₂²×Dic₅	C₂³	1	1	yes	characteristic
222	C₂²×Dic₅	C₂³	1	1	yes	characteristic
223	C₂²×Dic₅	C₂³	1	1	yes	characteristic
224	C₂²×Dic₅	C₂³	1	1	yes	characteristic
225	C₂²×Dic₅	C₂³	1	1	yes	characteristic
226	C₂²×Dic₅	C₂³	1	1	yes	characteristic
227	C₂²×Dic₅	C₂³	1	1	yes	characteristic
228	C₂²×Dic₅	C₂³	1	1	yes	characteristic
229	#711	—	2	4	no	—
230	#711	—	4	2	no	—
231	D₄×D₅	—	2	4	no	—
232	D₄×D₅	—	4	2	no	—
233	#709	—	4	2	no	—
234	C₂×D₂₀	C₂³	1	1	yes	characteristic
235	C₂×D₂₀	C₂³	1	1	yes	characteristic
236	C₂×D₂₀	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₅	—	4	2	no	—
238	C₂×C₄×D₅	—	4	2	no	—
239	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
253	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
254	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
255	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
256	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₄²×C₅	C₂³	1	1	yes	characteristic
277	C₄²×C₅	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
289	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
290	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
291	C₂²⋊Dic₅	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	#685	C₂³	1	1	yes	characteristic
299	#685	C₂³	1	1	yes	characteristic
300	#685	C₂³	1	1	yes	characteristic
301	#685	C₂³	1	1	yes	characteristic
302	#685	C₂³	1	1	yes	characteristic
303	#685	C₂³	1	1	yes	characteristic
304	#685	C₂³	1	1	yes	characteristic
305	#685	C₂³	1	1	yes	characteristic
306	#685	C₂³	1	1	yes	characteristic
307	#685	C₂³	1	1	yes	characteristic
308	#685	C₂³	1	1	yes	characteristic
309	#685	C₂³	1	1	yes	characteristic
310	#685	C₂³	1	1	yes	characteristic
311	#685	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
315	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
316	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₅	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	#683	C₂³	1	1	yes	characteristic
335	#683	C₂³	1	1	yes	characteristic
336	#683	C₂³	1	1	yes	characteristic
337	#683	C₂³	1	1	yes	characteristic
338	#683	C₂³	1	1	yes	characteristic
339	#683	C₂³	1	1	yes	characteristic
340	#683	C₂³	1	1	yes	characteristic
341	#683	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	C₄×Dic₅	C₂³	1	1	yes	characteristic
347	C₄×Dic₅	C₂³	1	1	yes	characteristic
348	C₄×Dic₅	C₂³	1	1	yes	characteristic
349	C₄×Dic₅	C₂³	1	1	yes	characteristic
350	C₄×Dic₅	C₂³	1	1	yes	characteristic
351	C₄×Dic₅	C₂³	1	1	yes	characteristic
352	#559	—	5	1	no	—
353	#554	—	5	1	no	—
354	#553	—	5	1	no	—
355	#553	—	5	1	no	—
356	#553	—	5	1	no	—
357	#552	—	5	1	no	—
358	#551	—	5	1	no	—
359	#551	—	5	1	no	—
360	#551	—	5	1	no	—
361	#551	—	5	1	no	—
362	#547	—	5	1	no	—
363	#546	—	5	1	no	—
364	#546	—	5	1	no	—
365	#546	—	5	1	no	—
366	#546	—	5	1	no	—
367	D₄²	—	5	1	no	—
368	#542	—	5	1	no	—
369	#540	—	5	1	no	—
370	#539	—	5	1	no	—
371	#539	—	5	1	no	—
372	#538	—	5	1	no	—
373	#538	D₅	1	1	yes	characteristic, complemented
374	#529	—	5	1	no	—
375	#529	—	5	1	no	—
376	#525	—	5	1	no	—
377	#525	—	5	1	no	—
378	C₂×#123	—	5	1	no	—
379	C₂×#123	—	5	1	no	—
380	#520	—	5	1	no	—
381	#518	—	5	1	no	—
382	C₂×C₄×D₄	—	5	1	no	—
383	C₂³×C₅	—	2	2	no	—
384	C₂³×C₅	—	4	1	no	—
385	C₂³×C₅	—	4	1	no	—
386	C₂³×C₅	C₂⁴	1	1	yes	characteristic
387	C₂³×C₅	C₂⁴	1	1	yes	characteristic
388	C₂³×C₅	C₂⁴	1	1	yes	characteristic
389	C₂³×C₅	C₂⁴	1	1	yes	characteristic
390	C₂³×C₅	C₂⁴	1	1	yes	characteristic
391	C₂²×D₅	—	2	2	no	—
392	C₂²×D₅	—	2	2	no	—
393	C₂²×D₅	—	2	2	no	—
394	C₂²×D₅	—	2	2	no	—
395	C₂²×D₅	—	2	2	no	—
396	C₂²×D₅	—	4	1	no	—
397	C₂²×D₅	—	4	1	no	—
398	C₂²×D₅	—	4	1	no	—
399	C₂²×D₅	—	4	1	no	—
400	C₂²×D₅	C₂⁴	1	1	yes	characteristic
401	C₂²×D₅	C₂⁴	1	1	yes	characteristic
402	C₂²×D₅	C₂⁴	1	1	yes	characteristic
403	C₂²×D₅	C₂⁴	1	1	yes	characteristic
404	C₅×Q₈	—	4	1	no	—
405	C₅×D₄	—	2	2	no	—
406	C₅×D₄	—	2	2	no	—
407	C₅×D₄	—	4	1	no	—
408	C₅×D₄	—	4	1	no	—
409	C₅×D₄	—	4	1	no	—
410	C₅×D₄	—	4	1	no	—
411	C₅×D₄	—	4	1	no	—
412	C₂×C₄×C₅	—	4	1	no	—
413	C₂×C₄×C₅	—	4	1	no	—
414	C₂×C₄×C₅	—	4	1	no	—
415	C₂×C₄×C₅	—	4	1	no	—
416	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
418	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
419	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
420	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
421	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
423	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
424	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
425	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
426	C₂²⋊D₅	—	2	2	no	—
427	C₂²⋊D₅	—	2	2	no	—
428	C₂²⋊D₅	—	2	2	no	—
429	C₂²⋊D₅	—	2	2	no	—
430	C₂²⋊D₅	—	2	2	no	—
431	C₂²⋊D₅	—	2	2	no	—
432	C₂²⋊D₅	—	2	2	no	—
433	C₂²⋊D₅	—	2	2	no	—
434	C₂²⋊D₅	—	4	1	no	—
435	C₂²⋊D₅	—	4	1	no	—
436	C₂²⋊D₅	—	4	1	no	—
437	C₂²⋊D₅	—	4	1	no	—
438	C₂²⋊D₅	—	4	1	no	—
439	C₂²⋊D₅	#41	1	4	yes	complemented
440	C₂×Dic₅	—	2	2	no	—
441	C₂×Dic₅	—	2	2	no	—
442	C₂×Dic₅	—	2	2	no	—
443	C₂×Dic₅	—	4	1	no	—
444	C₂×Dic₅	—	4	1	no	—
445	C₂×Dic₅	—	4	1	no	—
446	C₂×Dic₅	—	4	1	no	—
447	C₂×Dic₅	—	4	1	no	—
448	C₂×Dic₅	—	4	1	no	—
449	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
450	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
451	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
452	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
453	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
454	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
455	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
456	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
457	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
458	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
459	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
460	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
461	D₂₀	—	2	2	no	—
462	D₂₀	—	2	2	no	—
463	D₂₀	—	4	1	no	—
464	C₄×D₅	—	2	2	no	—
465	C₄×D₅	—	2	2	no	—
466	C₄×D₅	—	2	2	no	—
467	C₄×D₅	—	2	2	no	—
468	C₄×D₅	—	2	2	no	—
469	C₄×D₅	—	4	1	no	—
470	C₄×D₅	—	4	1	no	—
471	C₄×D₅	—	4	1	no	—
472	C₄×D₅	—	4	1	no	—
473	C₄×D₅	—	4	1	no	—
474	C₄×D₅	—	4	1	no	—
475	C₄×D₅	—	4	1	no	—
476	C₄×D₅	—	4	1	no	—
477	C₄×D₅	—	4	1	no	—
478	Dic₁₀	—	2	2	no	—
479	Dic₁₀	—	4	1	no	—
480	Dic₁₀	—	4	1	no	—
481	C₂×#41	—	5	1	no	—
482	C₂×#41	—	5	1	no	—
483	C₂×#41	—	5	1	no	—
484	C₂²×D₄	—	5	1	no	—
485	C₂²×D₄	—	5	1	no	—
486	C₂²×D₄	—	5	1	no	—
487	C₂²×D₄	—	5	1	no	—
488	C₂³×C₄	—	5	1	no	—
489	C₂³×C₄	—	5	1	no	—
490	C₄⋊Q₈	—	5	1	no	—
491	#127	—	5	1	no	—
492	#126	—	5	1	no	—
493	#126	—	5	1	no	—
494	#126	—	5	1	no	—
495	#126	—	5	1	no	—
496	#126	—	5	1	no	—
497	#126	—	5	1	no	—
498	#126	—	5	1	no	—
499	#126	—	5	1	no	—
500	#126	C₂×D₅	1	1	yes	characteristic, complemented
501	#126	C₂×D₅	1	1	yes	characteristic, complemented
502	#125	—	5	1	no	—
503	#125	—	5	1	no	—
504	#125	—	5	1	no	—
505	#125	—	5	1	no	—
506	#125	—	5	1	no	—
507	#124	—	5	1	no	—
508	#124	—	5	1	no	—
509	#124	—	5	1	no	—
510	#124	—	5	1	no	—
511	#124	—	5	1	no	—
512	#124	C₂×D₅	1	1	yes	characteristic, complemented
513	#124	C₂×D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
521	#123	—	5	1	no	—
522	#123	—	5	1	no	—
523	#123	—	5	1	no	—
524	#123	—	5	1	no	—
525	#123	—	5	1	no	—
526	#123	—	5	1	no	—
527	#123	—	5	1	no	—
528	#123	—	5	1	no	—
529	#123	—	5	1	no	—
530	#123	—	5	1	no	—
531	#123	—	5	1	no	—
532	#123	—	5	1	no	—
533	#123	—	5	1	no	—
534	#123	—	5	1	no	—
535	#123	—	5	1	no	—
536	#123	—	5	1	no	—
537	#123	—	5	1	no	—
538	#123	C₂×D₅	1	1	yes	characteristic, complemented
539	#123	C₂×D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
546	C₂²⋊Q₈	—	5	1	no	—
547	C₂²⋊Q₈	—	5	1	no	—
548	C₂²⋊Q₈	—	5	1	no	—
549	C₂²⋊Q₈	—	5	1	no	—
550	C₂²⋊Q₈	—	5	1	no	—
551	C₂²⋊Q₈	—	5	1	no	—
552	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
553	#121	—	5	1	no	—
554	#121	—	5	1	no	—
555	#121	—	5	1	no	—
556	#121	—	5	1	no	—
557	#121	—	5	1	no	—
558	#121	—	5	1	no	—
559	#121	—	5	1	no	—
560	#121	—	5	1	no	—
561	#121	—	5	1	no	—
562	#121	—	5	1	no	—
563	#121	—	5	1	no	—
564	#121	—	5	1	no	—
565	#121	—	5	1	no	—
566	#121	—	5	1	no	—
567	#121	C₂×D₅	1	1	yes	characteristic, complemented
568	#121	C₂×D₅	1	1	yes	characteristic, complemented
569	#121	C₂×D₅	1	1	yes	characteristic, complemented
570	#120	—	5	1	no	—
571	#120	—	5	1	no	—
572	#120	—	5	1	no	—
573	#120	—	5	1	no	—
574	#120	—	5	1	no	—
575	#120	—	5	1	no	—
576	#120	C₂×D₅	1	1	yes	characteristic
577	#120	C₂×D₅	1	1	yes	characteristic, complemented
578	C₄×Q₈	—	5	1	no	—
579	C₄×Q₈	—	5	1	no	—
580	C₄×Q₈	—	5	1	no	—
581	C₄×D₄	—	5	1	no	—
582	C₄×D₄	—	5	1	no	—
583	C₄×D₄	—	5	1	no	—
584	C₄×D₄	—	5	1	no	—
585	C₄×D₄	—	5	1	no	—
586	C₄×D₄	—	5	1	no	—
587	C₄×D₄	—	5	1	no	—
588	C₄×D₄	—	5	1	no	—
589	C₄×D₄	—	5	1	no	—
590	C₄×D₄	—	5	1	no	—
591	C₄×D₄	—	5	1	no	—
592	C₄×D₄	—	5	1	no	—
593	C₄×D₄	—	5	1	no	—
594	C₄×D₄	—	5	1	no	—
595	C₄×D₄	—	5	1	no	—
596	C₄×D₄	—	5	1	no	—
597	C₄×D₄	—	5	1	no	—
598	C₄×D₄	—	5	1	no	—
599	C₄×D₄	—	5	1	no	—
600	C₄×D₄	—	5	1	no	—
601	C₄×D₄	—	5	1	no	—
602	C₄×D₄	—	5	1	no	—
603	C₄×D₄	—	5	1	no	—
604	C₄×D₄	—	5	1	no	—
605	C₄×D₄	—	5	1	no	—
606	C₄×D₄	—	5	1	no	—
607	C₄×D₄	—	5	1	no	—
608	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
609	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
610	#117	—	5	1	no	—
611	#117	—	5	1	no	—
612	#117	—	5	1	no	—
613	#117	—	5	1	no	—
614	#117	—	5	1	no	—
615	#117	—	5	1	no	—
616	#117	—	5	1	no	—
617	#117	—	5	1	no	—
618	#117	—	5	1	no	—
619	C₂×C₄⋊C₄	—	5	1	no	—
620	C₂×C₄⋊C₄	—	5	1	no	—
621	C₂×C₄⋊C₄	—	5	1	no	—
622	C₂×C₄⋊C₄	—	5	1	no	—
623	C₂×C₄⋊C₄	—	5	1	no	—
624	C₂×C₄⋊C₄	—	5	1	no	—
625	C₂×C₂²⋊C₄	—	5	1	no	—
626	C₂×C₂²⋊C₄	—	5	1	no	—
627	C₂×C₂²⋊C₄	—	5	1	no	—
628	C₂×C₂²⋊C₄	—	5	1	no	—
629	C₂×C₂²⋊C₄	—	5	1	no	—
630	C₂×C₂²⋊C₄	—	5	1	no	—
631	C₂×C₂²⋊C₄	—	5	1	no	—
632	C₂×C₂²⋊C₄	—	5	1	no	—
633	C₂×C₂²⋊C₄	—	5	1	no	—
634	C₂×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
635	C₂×C₄²	—	5	1	no	—
636	C₂²×C₅	—	2	1	no	—
637	C₂²×C₅	—	2	1	no	—
638	C₂²×C₅	—	2	1	no	—
639	C₂²×C₅	—	2	1	no	—
640	C₂²×C₅	—	2	1	no	—
641	C₂²×C₅	—	2	1	no	—
642	C₂²×C₅	—	2	1	no	—
643	C₂²×C₅	—	2	1	no	—
644	C₂²×C₅	—	2	1	no	—
645	C₂²×C₅	—	2	1	no	—
646	C₂²×C₅	—	2	1	no	—
647	C₂²×C₅	—	2	1	no	—
648	C₂²×C₅	—	2	1	no	—
649	C₂²×C₅	—	2	1	no	—
650	C₂²×C₅	—	8	2	no	—
651	C₂²×C₅	C₂×#41	1	2	yes	—
652	C₂²×C₅	C₂⁵	1	1	yes	characteristic
653	C₂×D₅	—	2	1	no	—
654	C₂×D₅	—	2	1	no	—
655	C₂×D₅	—	2	1	no	—
656	C₂×D₅	—	2	1	no	—
657	C₂×D₅	—	2	1	no	—
658	C₂×D₅	—	2	1	no	—
659	C₂×D₅	—	2	1	no	—
660	C₂×D₅	—	2	1	no	—
661	C₂×D₅	—	2	1	no	—
662	C₂×D₅	—	2	1	no	—
663	C₂×D₅	—	4	4	no	—
664	C₂×D₅	—	4	4	no	—
665	C₂×D₅	—	8	2	no	—
666	C₂×D₅	C₂×#41	1	2	yes	—
667	C₂×D₅	H(5,𝔽₂)	1	2	yes	—
668	C₄×C₅	—	2	1	no	—
669	C₄×C₅	—	2	1	no	—
670	C₄×C₅	—	2	1	no	—
671	C₄×C₅	—	2	1	no	—
672	C₄×C₅	—	2	1	no	—
673	C₄×C₅	—	2	1	no	—
674	C₄×C₅	—	2	1	no	—
675	C₄×C₅	—	2	1	no	—
676	C₄×C₅	—	2	1	no	—
677	C₄×C₅	—	2	1	no	—
678	Dic₅	—	2	1	no	—
679	Dic₅	—	2	1	no	—
680	Dic₅	—	2	1	no	—
681	Dic₅	—	2	1	no	—
682	Dic₅	—	2	1	no	—
683	Dic₅	—	2	1	no	—
684	Dic₅	—	2	1	no	—
685	Dic₅	—	2	1	no	—
686	Dic₅	—	2	1	no	—
687	Dic₅	—	2	1	no	—
688	Dic₅	—	2	1	no	—
689	Dic₅	C₂×#41	1	2	yes	—
690	C₂⁴	—	5	1	no	—
691	C₂⁴	—	5	1	no	—
692	C₂⁴	—	5	1	no	—
693	C₂⁴	C₂²×D₅	1	1	yes	characteristic
694	#41	—	10	4	no	—
695	#41	—	20	2	no	—
696	#41	—	20	2	no	—
697	C₂×Q₈	—	5	1	no	—
698	C₂×Q₈	—	5	1	no	—
699	C₂×Q₈	—	5	1	no	—
700	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
701	C₂×D₄	—	5	1	no	—
702	C₂×D₄	—	5	1	no	—
703	C₂×D₄	—	5	1	no	—
704	C₂×D₄	—	5	1	no	—
705	C₂×D₄	—	5	1	no	—
706	C₂×D₄	—	5	1	no	—
707	C₂×D₄	—	5	1	no	—
708	C₂×D₄	—	5	1	no	—
709	C₂×D₄	—	5	1	no	—
710	C₂×D₄	—	5	1	no	—
711	C₂×D₄	—	5	1	no	—
712	C₂×D₄	—	5	1	no	—
713	C₂×D₄	—	5	1	no	—
714	C₂×D₄	—	5	1	no	—
715	C₂×D₄	—	5	1	no	—
716	C₂×D₄	—	5	1	no	—
717	C₂×D₄	—	5	1	no	—
718	C₂×D₄	—	10	4	no	—
719	C₂×D₄	—	10	4	no	—
720	C₂×D₄	—	20	2	no	—
721	C₂×D₄	—	20	2	no	—
722	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
723	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
724	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
725	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
726	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
727	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
728	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
729	C₂²×C₄	—	5	1	no	—
730	C₂²×C₄	—	5	1	no	—
731	C₂²×C₄	—	5	1	no	—
732	C₂²×C₄	—	5	1	no	—
733	C₂²×C₄	—	5	1	no	—
734	C₂²×C₄	—	5	1	no	—
735	C₂²×C₄	—	5	1	no	—
736	C₂²×C₄	—	5	1	no	—
737	C₂²×C₄	—	5	1	no	—
738	C₂²×C₄	—	5	1	no	—
739	C₂²×C₄	—	5	1	no	—
740	C₂²×C₄	—	5	1	no	—
741	C₂²×C₄	—	5	1	no	—
742	C₂²×C₄	—	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	—	20	2	no	—
753	C₂²×C₄	—	20	2	no	—
754	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
758	C₄⋊C₄	—	5	1	no	—
759	C₄⋊C₄	—	5	1	no	—
760	C₄⋊C₄	—	5	1	no	—
761	C₄⋊C₄	—	5	1	no	—
762	C₄⋊C₄	—	5	1	no	—
763	C₄⋊C₄	—	5	1	no	—
764	C₄⋊C₄	—	5	1	no	—
765	C₄⋊C₄	—	5	1	no	—
766	C₄⋊C₄	—	5	1	no	—
767	C₄⋊C₄	—	5	1	no	—
768	C₄⋊C₄	—	5	1	no	—
769	C₄⋊C₄	—	5	1	no	—
770	C₄⋊C₄	—	5	1	no	—
771	C₄⋊C₄	—	5	1	no	—
772	C₄⋊C₄	—	5	1	no	—
773	C₄⋊C₄	—	5	1	no	—
774	C₄⋊C₄	—	5	1	no	—
775	C₄⋊C₄	—	5	1	no	—
776	C₄⋊C₄	—	5	1	no	—
777	C₄⋊C₄	—	5	1	no	—
778	C₄⋊C₄	—	5	1	no	—
779	C₄⋊C₄	—	5	1	no	—
780	C₄⋊C₄	—	5	1	no	—
781	C₄⋊C₄	—	5	1	no	—
782	C₄⋊C₄	—	5	1	no	—
783	C₄⋊C₄	—	5	1	no	—
784	C₄⋊C₄	—	5	1	no	—
785	C₄⋊C₄	—	5	1	no	—
786	C₄⋊C₄	—	5	1	no	—
787	C₄⋊C₄	—	5	1	no	—
788	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
794	C₂²⋊C₄	—	5	1	no	—
795	C₂²⋊C₄	—	5	1	no	—
796	C₂²⋊C₄	—	5	1	no	—
797	C₂²⋊C₄	—	5	1	no	—
798	C₂²⋊C₄	—	5	1	no	—
799	C₂²⋊C₄	—	5	1	no	—
800	C₂²⋊C₄	—	5	1	no	—
801	C₂²⋊C₄	—	5	1	no	—
802	C₂²⋊C₄	—	5	1	no	—
803	C₂²⋊C₄	—	5	1	no	—
804	C₂²⋊C₄	—	5	1	no	—
805	C₂²⋊C₄	—	5	1	no	—
806	C₂²⋊C₄	—	5	1	no	—
807	C₂²⋊C₄	—	5	1	no	—
808	C₂²⋊C₄	—	5	1	no	—
809	C₂²⋊C₄	—	5	1	no	—
810	C₂²⋊C₄	—	5	1	no	—
811	C₂²⋊C₄	—	5	1	no	—
812	C₂²⋊C₄	—	5	1	no	—
813	C₂²⋊C₄	—	5	1	no	—
814	C₂²⋊C₄	—	5	1	no	—
815	C₂²⋊C₄	—	5	1	no	—
816	C₂²⋊C₄	—	5	1	no	—
817	C₂²⋊C₄	—	5	1	no	—
818	C₂²⋊C₄	—	5	1	no	—
819	C₂²⋊C₄	—	5	1	no	—
820	C₂²⋊C₄	—	5	1	no	—
821	C₂²⋊C₄	—	5	1	no	—
822	C₂²⋊C₄	—	5	1	no	—
823	C₂²⋊C₄	—	5	1	no	—
824	C₂²⋊C₄	—	5	1	no	—
825	C₂²⋊C₄	—	5	1	no	—
826	C₂²⋊C₄	—	5	1	no	—
827	C₂²⋊C₄	—	5	1	no	—
828	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
829	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
830	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
832	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
834	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
842	C₄²	—	5	1	no	—
843	C₄²	—	5	1	no	—
844	C₄²	—	5	1	no	—
845	C₄²	—	5	1	no	—
846	C₄²	—	5	1	no	—
847	C₄²	—	5	1	no	—
848	C₄²	—	5	1	no	—
849	C₄²	—	5	1	no	—
850	C₄²	—	5	1	no	—
851	C₄²	—	5	1	no	—
852	C₄²	C₂²×D₅	1	1	yes	characteristic
853	C₄²	C₂²×D₅	1	1	yes	characteristic
854	C₂×C₅	—	2	2	no	—
855	C₂×C₅	—	4	1	no	—
856	C₂×C₅	—	4	1	no	—
857	C₂×C₅	—	4	1	no	—
858	C₂×C₅	—	4	1	no	—
859	C₂×C₅	C₂²×#41	1	1	yes	characteristic
860	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
861	C₂×C₅	#585	1	1	yes	characteristic
862	D₅	—	2	2	no	—
863	D₅	—	2	2	no	—
864	D₅	—	4	1	no	—
865	D₅	—	4	1	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	4	1	no	—
868	C₂³	—	4	1	no	—
869	C₂³	—	5	1	no	—
870	C₂³	—	5	1	no	—
871	C₂³	—	5	1	no	—
872	C₂³	—	5	1	no	—
873	C₂³	—	10	2	no	—
874	C₂³	—	10	2	no	—
875	C₂³	—	10	2	no	—
876	C₂³	—	10	2	no	—
877	C₂³	—	10	2	no	—
878	C₂³	—	20	1	no	—
879	C₂³	—	20	1	no	—
880	C₂³	—	20	1	no	—
881	C₂³	—	20	1	no	—
882	C₂³	C₂³×D₅	1	1	yes	characteristic
883	C₂³	C₂³×D₅	1	1	yes	characteristic
884	C₂³	C₂³×D₅	1	1	yes	characteristic
885	C₂³	C₂³×D₅	1	1	yes	characteristic
886	C₂³	C₂³×D₅	1	1	yes	characteristic
887	Q₈	—	4	1	no	—
888	Q₈	—	10	2	no	—
889	Q₈	—	20	1	no	—
890	Q₈	—	20	1	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	4	1	no	—
894	D₄	—	4	1	no	—
895	D₄	—	4	1	no	—
896	D₄	—	4	1	no	—
897	D₄	—	4	1	no	—
898	D₄	—	5	4	no	—
899	D₄	—	10	2	no	—
900	D₄	—	10	2	no	—
901	D₄	—	10	2	no	—
902	D₄	—	10	2	no	—
903	D₄	—	10	2	no	—
904	D₄	—	10	2	no	—
905	D₄	—	10	2	no	—
906	D₄	—	10	2	no	—
907	D₄	—	10	2	no	—
908	D₄	—	10	2	no	—
909	D₄	—	20	1	no	—
910	D₄	—	20	1	no	—
911	D₄	—	20	1	no	—
912	D₄	—	20	1	no	—
913	D₄	—	20	1	no	—
914	D₄	—	20	1	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	5	1	no	—
920	C₂×C₄	—	5	1	no	—
921	C₂×C₄	—	5	1	no	—
922	C₂×C₄	—	5	1	no	—
923	C₂×C₄	—	5	1	no	—
924	C₂×C₄	—	5	1	no	—
925	C₂×C₄	—	5	1	no	—
926	C₂×C₄	—	5	1	no	—
927	C₂×C₄	—	5	1	no	—
928	C₂×C₄	—	5	1	no	—
929	C₂×C₄	—	5	1	no	—
930	C₂×C₄	—	5	1	no	—
931	C₂×C₄	—	10	2	no	—
932	C₂×C₄	—	10	2	no	—
933	C₂×C₄	—	10	2	no	—
934	C₂×C₄	—	10	2	no	—
935	C₂×C₄	—	10	2	no	—
936	C₂×C₄	—	10	2	no	—
937	C₂×C₄	—	10	2	no	—
938	C₂×C₄	—	10	2	no	—
939	C₂×C₄	—	20	1	no	—
940	C₂×C₄	—	20	1	no	—
941	C₂×C₄	—	20	1	no	—
942	C₂×C₄	—	20	1	no	—
943	C₂×C₄	—	20	1	no	—
944	C₂×C₄	—	20	1	no	—
945	C₂×C₄	—	20	1	no	—
946	C₂×C₄	—	20	1	no	—
947	C₂×C₄	—	20	1	no	—
948	C₂×C₄	—	20	1	no	—
949	C₂×C₄	—	20	1	no	—
950	C₂×C₄	—	20	1	no	—
951	C₂×C₄	—	20	1	no	—
952	C₂×C₄	—	20	1	no	—
953	C₂×C₄	—	20	1	no	—
954	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
955	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
964	C₅	#3513	1	1	yes	characteristic, complemented, Sylow
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	5	2	no	—
980	C₂²	—	5	2	no	—
981	C₂²	—	8	2	no	—
982	C₂²	—	10	1	no	—
983	C₂²	—	10	1	no	—
984	C₂²	—	10	1	no	—
985	C₂²	—	10	1	no	—
986	C₂²	—	10	1	no	—
987	C₂²	—	10	1	no	—
988	C₂²	—	10	1	no	—
989	C₂²	—	10	1	no	—
990	C₂²	—	10	1	no	—
991	C₂²	—	10	1	no	—
992	C₂²	—	20	4	no	—
993	C₂²	—	20	4	no	—
994	C₂²	—	40	2	no	—
995	C₂²	D₅×#41	1	2	yes	—
996	C₂²	C₂⁴×D₅	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	5	2	no	—
1008	C₄	—	10	1	no	—
1009	C₄	—	10	1	no	—
1010	C₄	—	10	1	no	—
1011	C₄	—	10	1	no	—
1012	C₄	—	10	1	no	—
1013	C₄	—	10	1	no	—
1014	C₄	—	10	1	no	—
1015	C₄	—	10	1	no	—
1016	C₄	—	10	1	no	—
1017	C₄	—	10	1	no	—
1018	C₄	—	10	1	no	—
1019	C₂	—	2	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	4	1	no	—
1024	C₂	—	10	2	no	—
1025	C₂	—	10	2	no	—
1026	C₂	—	20	1	no	—
1027	C₂	—	20	1	no	—
1028	C₂	C₂×D₅×#41	1	1	yes	characteristic
1029	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic
1030	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#538	C₂
hypercenter	#538	D₅
hypocenter	C₅	#3513
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. C₅×#538	C₂	semidirect
2. #66042	C₂	semidirect
3. #66041	C₂	semidirect
4. #66040	C₂	semidirect
5. #66039	C₂	semidirect
6. #66015	C₂	semidirect
7. #66014	C₂	semidirect
8. #66013	C₂	semidirect
9. #66012	C₂	semidirect
10. #65996	C₂	semidirect
11. #65995	C₂	semidirect
12. #65989	C₂	semidirect
13. D₅×#123	C₂	semidirect
14. #65971	C₂	semidirect
15. #65969	C₂	semidirect
16. #65952	C₂	semidirect
17. #65949	C₂	semidirect
18. #65946	C₂	semidirect
19. #65944	C₂	semidirect
20. #65940	C₂	semidirect
21. #65935	C₂	semidirect
22. #65925	C₂	semidirect
23. #65925	C₂	semidirect
24. #65924	C₂	semidirect
25. #65921	C₂	semidirect
26. #65898	C₂	semidirect
27. #65881	C₂	semidirect
28. #65880	C₂	semidirect
29. C₄×D₄×D₅	C₂	semidirect
30. C₂×#4029	C₂	semidirect
31. #65820	C₂	semidirect
35. C₂×#711	C₂²	semidirect
38. C₂×#709	C₂²	semidirect
39. C₂²×C₄×D₅	C₂²	semidirect
40. C₂²×C₄×D₅	C₂²	semidirect
41. C₅×#126	C₂²	semidirect
42. C₅×#126	C₂²	semidirect
43. C₅×#124	C₂²	semidirect
44. C₅×#124	C₂²	semidirect
45. C₅×#123	C₂²	semidirect
46. C₅×#123	C₂²	semidirect
47. C₅×C₂²⋊Q₈	C₂²	semidirect
48. C₅×#121	C₂²	semidirect
49. C₅×#121	C₂²	semidirect
50. C₅×#121	C₂²	semidirect
52. C₅×#120	C₂²	semidirect
53. C₄×C₅×D₄	C₂²	semidirect
54. C₄×C₅×D₄	C₂²	semidirect
55. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
56. C₂×C₂²⋊Dic₅	C₂²	semidirect
57. C₂×C₂²⋊Dic₅	C₂²	semidirect
58. #4093	C₂²	semidirect
59. #4092	C₂²	semidirect
60. #4092	C₂²	semidirect
61. Q₈×Dic₅	C₂²	semidirect
65. #4085	C₂²	semidirect
66. #4085	C₂²	semidirect
67. #4085	C₂²	semidirect
68. #4085	C₂²	semidirect
69. #4085	C₂²	semidirect
71. #4084	C₂²	semidirect
72. #4084	C₂²	semidirect
74. #4083	C₂²	semidirect
75. #4083	C₂²	semidirect
76. #4083	C₂²	semidirect
77. #4082	C₂²	semidirect
78. #4081	C₂²	semidirect
79. #4081	C₂²	semidirect
80. #4081	C₂²	semidirect
81. D₄×Dic₅	C₂²	semidirect
82. D₄×Dic₅	C₂²	semidirect
83. D₄×Dic₅	C₂²	semidirect
84. D₄×Dic₅	C₂²	semidirect
85. D₄×Dic₅	C₂²	semidirect
86. #4075	C₂²	semidirect
89. C₄×C₂²⋊D₅	C₂²	semidirect
90. C₄×C₂²⋊D₅	C₂²	semidirect
91. C₄×C₂²⋊D₅	C₂²	semidirect
92. C₄×C₂²⋊D₅	C₂²	semidirect
93. C₄×C₂²⋊D₅	C₂²	semidirect
94. C₂×#685	C₂²	semidirect
95. C₂×C₄⋊Dic₅	C₂²	semidirect
96. #4070	C₂²	semidirect
97. C₂×#683	C₂²	semidirect
98. C₂×#683	C₂²	semidirect
99. #4044	C₂²	semidirect
100. #4044	C₂²	semidirect
101. #4043	C₂²	semidirect
102. #4043	C₂²	semidirect
103. #4042	C₂²	semidirect
104. #4042	C₂²	semidirect
105. #4042	C₂²	semidirect
106. #4040	C₂²	semidirect
107. #4040	C₂²	semidirect
108. #4040	C₂²	semidirect
109. #4040	C₂²	semidirect
110. #4039	C₂²	semidirect
111. #4039	C₂²	semidirect
112. #4038	C₂²	semidirect
113. #4038	C₂²	semidirect
114. D₅×C₄⋊C₄	C₂²	semidirect
115. D₅×C₄⋊C₄	C₂²	semidirect
116. D₅×C₄⋊C₄	C₂²	semidirect
117. #4036	C₂²	semidirect
118. #4035	C₂²	semidirect
119. #4035	C₂²	semidirect
120. #4035	C₂²	semidirect
121. #4034	C₂²	semidirect
122. #4033	C₂²	semidirect
123. #4032	C₂²	semidirect
124. #4032	C₂²	semidirect
125. #4032	C₂²	semidirect
126. #4032	C₂²	semidirect
127. #4031	C₂²	semidirect
128. #4031	C₂²	semidirect
129. #4031	C₂²	semidirect
132. #4030	C₂²	semidirect
133. #4030	C₂²	semidirect
137. #4029	C₂²	semidirect
138. #4029	C₂²	semidirect
139. #4029	C₂²	semidirect
140. #4029	C₂²	semidirect
141. #4029	C₂²	semidirect
142. #4029	C₂²	semidirect
143. #4029	C₂²	semidirect
144. #4029	C₂²	semidirect
145. #4029	C₂²	semidirect
151. #4027	C₂²	semidirect
152. #4027	C₂²	semidirect
153. #4027	C₂²	semidirect
154. #4027	C₂²	semidirect
155. #4027	C₂²	semidirect
156. #4027	C₂²	semidirect
157. #4027	C₂²	semidirect
158. #4027	C₂²	semidirect
159. D₅×C₂²⋊C₄	C₂²	semidirect
160. D₅×C₂²⋊C₄	C₂²	semidirect
161. D₅×C₂²⋊C₄	C₂²	semidirect
162. D₅×C₂²⋊C₄	C₂²	semidirect
163. D₅×C₂²⋊C₄	C₂²	semidirect
164. D₅×C₂²⋊C₄	C₂²	semidirect
165. #4025	C₂²	semidirect
166. #4025	C₂²	semidirect
167. #4025	C₂²	semidirect
168. #4025	C₂²	semidirect
169. #4025	C₂²	semidirect
170. #4024	C₂²	semidirect
171. #4024	C₂²	semidirect
172. #4024	C₂²	semidirect
173. #4024	C₂²	semidirect
174. #4023	C₂²	semidirect
175. #4023	C₂²	semidirect
176. #4023	C₂²	semidirect
177. #4023	C₂²	semidirect
178. #4023	C₂²	semidirect
179. #4022	C₂²	semidirect
180. C₄×D₂₀	C₂²	semidirect
181. C₄×D₂₀	C₂²	semidirect
182. #4018	C₂²	semidirect
183. #4018	C₂²	semidirect
184. C₄²×D₅	C₂²	semidirect
185. #4016	C₂²	semidirect
186. C₄×Dic₁₀	C₂²	semidirect
373. #538	D₅	semidirect
439. C₂²⋊D₅	#41	semidirect
500. #126	C₂×D₅	semidirect
501. #126	C₂×D₅	semidirect
512. #124	C₂×D₅	semidirect
513. #124	C₂×D₅	semidirect
538. #123	C₂×D₅	semidirect
539. #123	C₂×D₅	semidirect
552. C₂²⋊Q₈	C₂×D₅	semidirect
567. #121	C₂×D₅	semidirect
568. #121	C₂×D₅	semidirect
569. #121	C₂×D₅	semidirect
577. #120	C₂×D₅	semidirect
608. C₄×D₄	C₂×D₅	semidirect
609. C₄×D₄	C₂×D₅	semidirect
634. C₂×C₂²⋊C₄	C₂×D₅	semidirect
964. C₅	#3513	semidirect

Maximal subgroups

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

subgroup	index
C₅×#538	2
#66042	2
#66041	2
#66040	2
#66039	2
#66015	2
#66014	2
#66013	2
#66012	2
#65996	2
#65995	2
#65989	2
D₅×#123	2
#65971	2
#65969	2
#65952	2
#65949	2
#65946	2
#65944	2
#65940	2
#65935	2
#65925	2
#65924	2
#65921	2
#65898	2
#65881	2
#65880	2
C₄×D₄×D₅	2
C₂×#4029	2
#65820	2
#3513	5