Subgroups — #10618803

Order 640.

1050 conjugacy classes of subgroups.

The subgroup lattice has 1014 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	#66043	C₂	1	1	yes	maximal, characteristic, complemented
3	#66040	C₂	1	1	yes	maximal, characteristic, complemented
4	#66038	C₂	1	1	yes	maximal, characteristic, complemented
5	#66036	C₂	1	1	yes	maximal, characteristic, complemented
6	#66034	C₂	1	1	yes	maximal, characteristic, complemented
7	#66030	C₂	1	1	yes	maximal, characteristic, complemented
8	#66000	C₂	1	1	yes	maximal, characteristic, complemented
9	#65994	C₂	1	1	yes	maximal, characteristic, complemented
10	#65988	C₂	1	1	yes	maximal, characteristic, complemented
11	#65982	C₂	1	1	yes	maximal, characteristic, complemented
12	#65955	C₂	1	1	yes	maximal, characteristic, complemented
13	#65954	C₂	1	1	yes	maximal, characteristic, complemented
14	#65949	C₂	1	1	yes	maximal, characteristic, complemented
15	#65949	C₂	1	1	yes	maximal, characteristic, complemented
16	#65947	C₂	1	1	yes	maximal, characteristic, complemented
17	#65944	C₂	1	1	yes	maximal, characteristic, complemented
18	#65941	C₂	1	1	yes	maximal, characteristic, complemented
19	#65933	C₂	1	1	yes	maximal, characteristic, complemented
20	#65896	C₂	1	1	yes	maximal, characteristic, complemented
21	#65894	C₂	1	1	yes	maximal, characteristic, complemented
22	#65894	C₂	1	1	yes	maximal, characteristic, complemented
23	#65893	C₂	1	1	yes	maximal, characteristic, complemented
24	#65890	C₂	1	1	yes	maximal, characteristic, complemented
25	#65886	C₂	1	1	yes	maximal, characteristic, complemented
26	#65886	C₂	1	1	yes	maximal, characteristic, complemented
27	#65882	C₂	1	1	yes	maximal, characteristic, complemented
28	#65862	C₂	1	1	yes	maximal, characteristic, complemented
29	#65861	C₂	1	1	yes	maximal, characteristic, complemented
30	#65849	C₂	1	1	yes	maximal, characteristic, complemented
31	#65841	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	C₂×#709	C₂²	1	1	yes	characteristic
36	C₂×#709	C₂²	1	1	yes	characteristic, complemented
37	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
38	C₅×#126	C₂²	1	1	yes	characteristic, complemented
39	C₅×#126	C₂²	1	1	yes	characteristic, complemented
40	C₅×#125	C₂²	1	1	yes	characteristic, complemented
41	C₅×#123	C₂²	1	1	yes	characteristic
42	C₅×#123	C₂²	1	1	yes	characteristic, complemented
43	C₅×#121	C₂²	1	1	yes	characteristic
44	C₅×#121	C₂²	1	1	yes	characteristic
45	C₅×#121	C₂²	1	1	yes	characteristic, complemented
46	C₅×#121	C₂²	1	1	yes	characteristic, complemented
47	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
49	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
51	C₅×#117	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	#4086	C₂²	1	1	yes	characteristic
54	#4086	C₂²	1	1	yes	characteristic
55	#4086	C₂²	1	1	yes	characteristic, complemented
56	#4086	C₂²	1	1	yes	characteristic, complemented
57	#4085	C₂²	1	1	yes	characteristic
58	#4085	C₂²	1	1	yes	characteristic
59	#4085	C₂²	1	1	yes	characteristic
60	#4085	C₂²	1	1	yes	characteristic, complemented
61	#4085	C₂²	1	1	yes	characteristic, complemented
62	#4085	C₂²	1	1	yes	characteristic, complemented
63	#4085	C₂²	1	1	yes	characteristic, complemented
64	#4084	C₂²	1	1	yes	characteristic
65	#4084	C₂²	1	1	yes	characteristic, complemented
66	#4084	C₂²	1	1	yes	characteristic, complemented
67	#4083	C₂²	1	1	yes	characteristic
68	#4083	C₂²	1	1	yes	characteristic
69	#4083	C₂²	1	1	yes	characteristic
70	#4083	C₂²	1	1	yes	characteristic
71	#4082	C₂²	1	1	yes	characteristic, complemented
72	#4081	C₂²	1	1	yes	characteristic
73	#4081	C₂²	1	1	yes	characteristic, complemented
74	#4081	C₂²	1	1	yes	characteristic, complemented
75	#4076	C₂²	1	1	yes	characteristic
76	#4076	C₂²	1	1	yes	characteristic
77	#4076	C₂²	1	1	yes	characteristic
78	#4076	C₂²	1	1	yes	characteristic, complemented
79	#4075	C₂²	1	1	yes	characteristic
80	#4075	C₂²	1	1	yes	characteristic, complemented
81	#4075	C₂²	1	1	yes	characteristic, complemented
82	#4075	C₂²	1	1	yes	characteristic, complemented
83	#4075	C₂²	1	1	yes	characteristic, complemented
84	#4075	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
91	C₂×#685	C₂²	1	1	yes	characteristic
92	C₂×#685	C₂²	1	1	yes	characteristic
93	#4070	C₂²	1	1	yes	characteristic, complemented
94	#4070	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, complemented
99	#4044	C₂²	1	1	yes	characteristic, complemented
100	#4044	C₂²	1	1	yes	characteristic, complemented
101	#4042	C₂²	1	1	yes	characteristic
102	#4042	C₂²	1	1	yes	characteristic
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	#4042	C₂²	1	1	yes	characteristic, complemented
107	#4042	C₂²	1	1	yes	characteristic, complemented
108	#4042	C₂²	1	1	yes	characteristic, complemented
109	#4042	C₂²	1	1	yes	characteristic, complemented
110	#4041	C₂²	1	1	yes	characteristic
111	#4041	C₂²	1	1	yes	characteristic
112	#4041	C₂²	1	1	yes	characteristic
113	#4041	C₂²	1	1	yes	characteristic, complemented
114	#4041	C₂²	1	1	yes	characteristic, complemented
115	#4040	C₂²	1	1	yes	characteristic
116	#4040	C₂²	1	1	yes	characteristic
117	#4040	C₂²	1	1	yes	characteristic
118	#4040	C₂²	1	1	yes	characteristic
119	#4040	C₂²	1	1	yes	characteristic, complemented
120	#4040	C₂²	1	1	yes	characteristic, complemented
121	#4040	C₂²	1	1	yes	characteristic, complemented
122	#4039	C₂²	1	1	yes	characteristic
123	#4039	C₂²	1	1	yes	characteristic, complemented
124	#4038	C₂²	1	1	yes	characteristic
125	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
126	#4036	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	#4035	C₂²	1	1	yes	characteristic, complemented
131	#4034	C₂²	1	1	yes	characteristic, complemented
132	#4034	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, complemented
136	#4031	C₂²	1	1	yes	characteristic
137	#4031	C₂²	1	1	yes	characteristic
138	#4031	C₂²	1	1	yes	characteristic
139	#4031	C₂²	1	1	yes	characteristic
140	#4031	C₂²	1	1	yes	characteristic
141	#4031	C₂²	1	1	yes	characteristic
142	#4031	C₂²	1	1	yes	characteristic, complemented
143	#4031	C₂²	1	1	yes	characteristic, complemented
144	#4030	C₂²	1	1	yes	characteristic
145	#4030	C₂²	1	1	yes	characteristic
146	#4030	C₂²	1	1	yes	characteristic
147	#4030	C₂²	1	1	yes	characteristic, complemented
148	#4030	C₂²	1	1	yes	characteristic, complemented
149	#4030	C₂²	1	1	yes	characteristic, complemented
150	#4030	C₂²	1	1	yes	characteristic, complemented
151	#4029	C₂²	1	1	yes	characteristic, complemented
152	#4029	C₂²	1	1	yes	characteristic, complemented
153	#4029	C₂²	1	1	yes	characteristic, complemented
154	#4029	C₂²	1	1	yes	characteristic, complemented
155	#4029	C₂²	1	1	yes	characteristic, complemented
156	#4028	C₂²	1	1	yes	characteristic
157	#4028	C₂²	1	1	yes	characteristic
158	#4028	C₂²	1	1	yes	characteristic
159	#4028	C₂²	1	1	yes	characteristic
160	#4027	C₂²	1	1	yes	characteristic
161	#4027	C₂²	1	1	yes	characteristic
162	#4027	C₂²	1	1	yes	characteristic, complemented
163	#4027	C₂²	1	1	yes	characteristic, complemented
164	#4027	C₂²	1	1	yes	characteristic, complemented
165	#4027	C₂²	1	1	yes	characteristic, complemented
166	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
167	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	#4023	C₂²	1	1	yes	characteristic, complemented
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	#4021	C₂²	1	1	yes	characteristic, complemented
179	#4021	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	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
187	#3562	—	5	1	no	maximal, Sylow
188	C₂³×D₅	C₂³	1	1	yes	characteristic
189	C₂³×D₅	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	C₂×C₅×D₄	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	C₂²×C₄×C₅	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	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	C₂²×Dic₅	C₂³	1	1	yes	characteristic
219	C₂²×Dic₅	C₂³	1	1	yes	characteristic
220	C₂²×Dic₅	C₂³	1	1	yes	characteristic
221	C₂²×Dic₅	C₂³	1	1	yes	characteristic
222	#711	—	4	2	no	—
223	D₄×D₅	—	4	2	no	—
224	#709	—	4	2	no	—
225	#709	—	4	2	no	—
226	#709	—	4	2	no	—
227	C₂×D₂₀	C₂³	1	1	yes	characteristic
228	C₂×D₂₀	C₂³	1	1	yes	characteristic
229	C₂×D₂₀	C₂³	1	1	yes	characteristic
230	C₂×D₂₀	C₂³	1	1	yes	characteristic
231	C₂×D₂₀	C₂³	1	1	yes	characteristic
232	C₂×D₂₀	C₂³	1	1	yes	characteristic
233	C₂×D₂₀	C₂³	1	1	yes	characteristic
234	C₂×D₂₀	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
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×Dic₁₀	—	4	2	no	—
247	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
248	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
249	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
250	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
251	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
252	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
253	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₅×C₄⋊C₄	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×C₄⋊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	C₄²×C₅	C₂³	1	1	yes	characteristic
274	C₄²×C₅	C₂³	1	1	yes	characteristic
275	C₄²×C₅	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₅	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	#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	#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	#685	C₂³	1	1	yes	characteristic
313	#685	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	#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	#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	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	C₄×Dic₅	C₂³	1	1	yes	characteristic
347	C₄×Dic₅	C₂³	1	1	yes	characteristic
348	C₄×Dic₅	C₂³	1	1	yes	characteristic
349	#562	—	5	1	no	—
350	#562	—	5	1	no	—
351	#560	—	5	1	no	—
352	#560	—	5	1	no	—
353	#559	—	5	1	no	—
354	#556	—	5	1	no	—
355	#553	—	5	1	no	—
356	#553	D₅	1	1	yes	characteristic, complemented
357	#551	—	5	1	no	—
358	#551	—	5	1	no	—
359	#550	—	5	1	no	—
360	#548	—	5	1	no	—
361	#548	—	5	1	no	—
362	#547	—	5	1	no	—
363	#546	—	5	1	no	—
364	#546	—	5	1	no	—
365	#541	—	5	1	no	—
366	#540	—	5	1	no	—
367	#540	—	5	1	no	—
368	#540	—	5	1	no	—
369	#539	—	5	1	no	—
370	#539	—	5	1	no	—
371	#538	—	5	1	no	—
372	#538	—	5	1	no	—
373	#538	—	5	1	no	—
374	#538	—	5	1	no	—
375	#536	—	5	1	no	—
376	#535	—	5	1	no	—
377	#532	—	5	1	no	—
378	#529	—	5	1	no	—
379	#529	—	5	1	no	—
380	C₂³×C₅	C₂⁴	1	1	yes	characteristic
381	C₂³×C₅	C₂⁴	1	1	yes	characteristic
382	C₂³×C₅	C₂⁴	1	1	yes	characteristic
383	C₂³×C₅	C₂⁴	1	1	yes	characteristic
384	C₂²×D₅	—	4	1	no	—
385	C₂²×D₅	—	4	1	no	—
386	C₂²×D₅	—	4	1	no	—
387	C₂²×D₅	—	4	1	no	—
388	C₂²×D₅	—	4	1	no	—
389	C₂²×D₅	—	4	1	no	—
390	C₂²×D₅	C₂⁴	1	1	yes	characteristic
391	C₂²×D₅	C₂⁴	1	1	yes	characteristic
392	C₂²×D₅	C₂⁴	1	1	yes	characteristic
393	C₂²×D₅	C₂⁴	1	1	yes	characteristic
394	C₂²×D₅	C₂⁴	1	1	yes	characteristic
395	C₅×D₄	—	4	1	no	—
396	C₅×D₄	—	4	1	no	—
397	C₅×D₄	—	4	1	no	—
398	C₅×D₄	—	4	1	no	—
399	C₅×D₄	—	4	1	no	—
400	C₅×D₄	—	4	1	no	—
401	C₂×C₄×C₅	—	4	1	no	—
402	C₂×C₄×C₅	—	4	1	no	—
403	C₂×C₄×C₅	—	4	1	no	—
404	C₂×C₄×C₅	—	4	1	no	—
405	C₂×C₄×C₅	—	4	1	no	—
406	C₂×C₄×C₅	—	4	1	no	—
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	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
418	C₂²⋊D₅	—	2	2	no	—
419	C₂²⋊D₅	—	2	2	no	—
420	C₂²⋊D₅	—	2	2	no	—
421	C₂²⋊D₅	—	4	1	no	—
422	C₂²⋊D₅	—	4	1	no	—
423	C₂²⋊D₅	—	4	1	no	—
424	C₂²⋊D₅	—	4	1	no	—
425	C₂²⋊D₅	—	4	1	no	—
426	C₂²⋊D₅	—	4	1	no	—
427	C₂²⋊D₅	—	4	1	no	—
428	C₂²⋊D₅	—	4	1	no	—
429	C₂²⋊D₅	—	4	1	no	—
430	C₂²⋊D₅	—	4	1	no	—
431	C₂²⋊D₅	—	4	1	no	—
432	C₂²⋊D₅	—	4	1	no	—
433	C₂²⋊D₅	—	4	1	no	—
434	C₂×Dic₅	—	2	2	no	—
435	C₂×Dic₅	—	4	1	no	—
436	C₂×Dic₅	—	4	1	no	—
437	C₂×Dic₅	—	4	1	no	—
438	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
440	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
441	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
442	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
443	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
444	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
445	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
446	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
447	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
448	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
449	D₂₀	—	4	1	no	—
450	D₂₀	—	4	1	no	—
451	D₂₀	—	4	1	no	—
452	D₂₀	—	4	1	no	—
453	D₂₀	—	4	1	no	—
454	D₂₀	—	4	1	no	—
455	D₂₀	—	4	1	no	—
456	D₂₀	—	4	1	no	—
457	C₄×D₅	—	2	2	no	—
458	C₄×D₅	—	2	2	no	—
459	C₄×D₅	—	4	1	no	—
460	C₄×D₅	—	4	1	no	—
461	C₄×D₅	—	4	1	no	—
462	C₄×D₅	—	4	1	no	—
463	C₄×D₅	—	4	1	no	—
464	C₄×D₅	—	4	1	no	—
465	C₄×D₅	—	4	1	no	—
466	C₄×D₅	—	4	1	no	—
467	C₄×D₅	—	4	1	no	—
468	Dic₁₀	—	2	2	no	—
469	Dic₁₀	—	2	2	no	—
470	Dic₁₀	—	2	2	no	—
471	Dic₁₀	—	4	1	no	—
472	Dic₁₀	—	4	1	no	—
473	Dic₁₀	—	4	1	no	—
474	C₂×#41	—	5	1	no	—
475	C₂×#41	—	5	1	no	—
476	C₂×#41	—	5	1	no	—
477	C₂×#41	—	5	1	no	—
478	C₂²×Q₈	—	5	1	no	—
479	C₂²×D₄	—	5	1	no	—
480	C₄⋊Q₈	—	5	1	no	—
481	C₄⋊Q₈	—	5	1	no	—
482	#127	—	5	1	no	—
483	#127	—	5	1	no	—
484	#127	—	5	1	no	—
485	#127	—	5	1	no	—
486	#126	—	5	1	no	—
487	#126	—	5	1	no	—
488	#126	—	5	1	no	—
489	#126	—	5	1	no	—
490	#126	—	5	1	no	—
491	#126	—	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	C₂×D₅	1	1	yes	characteristic, complemented
497	#126	C₂×D₅	1	1	yes	characteristic, complemented
498	#125	—	5	1	no	—
499	#125	—	5	1	no	—
500	#125	—	5	1	no	—
501	#125	—	5	1	no	—
502	#125	—	5	1	no	—
503	#125	C₂×D₅	1	1	yes	characteristic, complemented
504	#124	—	5	1	no	—
505	#124	—	5	1	no	—
506	#124	—	5	1	no	—
507	#124	—	5	1	no	—
508	#124	—	5	1	no	—
509	#124	—	5	1	no	—
510	#124	—	5	1	no	—
511	#124	—	5	1	no	—
512	#124	—	5	1	no	—
513	#124	—	5	1	no	—
514	#124	—	5	1	no	—
515	#124	—	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
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	—	5	1	no	—
553	C₂²⋊Q₈	—	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	—	5	1	no	—
568	#121	—	5	1	no	—
569	#121	—	5	1	no	—
570	#121	—	5	1	no	—
571	#121	—	5	1	no	—
572	#121	—	5	1	no	—
573	#121	—	5	1	no	—
574	#121	—	5	1	no	—
575	#121	—	5	1	no	—
576	#121	—	5	1	no	—
577	#121	—	5	1	no	—
578	#121	—	5	1	no	—
579	#121	—	5	1	no	—
580	#121	C₂×D₅	1	1	yes	characteristic
581	#121	C₂×D₅	1	1	yes	characteristic
582	#121	C₂×D₅	1	1	yes	characteristic, complemented
583	#121	C₂×D₅	1	1	yes	characteristic, complemented
584	#120	—	5	1	no	—
585	#120	—	5	1	no	—
586	#120	—	5	1	no	—
587	#120	—	5	1	no	—
588	#120	—	5	1	no	—
589	#120	—	5	1	no	—
590	#120	—	5	1	no	—
591	#120	—	5	1	no	—
592	C₄×Q₈	—	5	1	no	—
593	C₄×Q₈	—	5	1	no	—
594	C₄×Q₈	—	5	1	no	—
595	C₄×Q₈	—	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	—	5	1	no	—
609	C₄×D₄	—	5	1	no	—
610	C₄×D₄	—	5	1	no	—
611	C₄×D₄	—	5	1	no	—
612	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
613	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
614	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
615	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
616	#117	—	5	1	no	—
617	#117	—	5	1	no	—
618	#117	—	5	1	no	—
619	#117	—	5	1	no	—
620	#117	—	5	1	no	—
621	#117	C₂×D₅	1	1	yes	characteristic, complemented
622	C₂×C₄⋊C₄	—	5	1	no	—
623	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
624	C₂×C₂²⋊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×C₄²	—	5	1	no	—
629	C₂²×C₅	—	2	1	no	—
630	C₂²×C₅	—	2	1	no	—
631	C₂²×C₅	—	2	1	no	—
632	C₂²×C₅	—	2	1	no	—
633	C₂²×C₅	—	2	1	no	—
634	C₂²×C₅	—	2	1	no	—
635	C₂²×C₅	—	2	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	C₂⁵	1	1	yes	characteristic
642	C₂×D₅	—	2	1	no	—
643	C₂×D₅	—	2	1	no	—
644	C₂×D₅	—	2	1	no	—
645	C₂×D₅	—	2	1	no	—
646	C₂×D₅	—	2	1	no	—
647	C₂×D₅	—	2	1	no	—
648	C₂×D₅	—	2	1	no	—
649	C₂×D₅	—	2	1	no	—
650	C₂×D₅	—	2	1	no	—
651	C₂×D₅	—	2	1	no	—
652	C₂×D₅	—	2	1	no	—
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	—	8	2	no	—
658	C₂×D₅	—	8	2	no	—
659	C₄×C₅	—	2	1	no	—
660	C₄×C₅	—	2	1	no	—
661	C₄×C₅	—	2	1	no	—
662	C₄×C₅	—	2	1	no	—
663	C₄×C₅	—	2	1	no	—
664	C₄×C₅	—	2	1	no	—
665	C₄×C₅	—	2	1	no	—
666	C₄×C₅	—	2	1	no	—
667	C₄×C₅	—	2	1	no	—
668	C₄×C₅	—	2	1	no	—
669	C₄×C₅	—	2	1	no	—
670	Dic₅	—	2	1	no	—
671	Dic₅	—	2	1	no	—
672	Dic₅	—	2	1	no	—
673	Dic₅	—	2	1	no	—
674	Dic₅	—	2	1	no	—
675	Dic₅	—	2	1	no	—
676	Dic₅	—	2	1	no	—
677	Dic₅	—	2	1	no	—
678	Dic₅	—	2	1	no	—
679	Dic₅	—	2	1	no	—
680	Dic₅	H(5,𝔽₂)	1	2	yes	—
681	C₂⁴	—	5	1	no	—
682	C₂⁴	—	5	1	no	—
683	#41	—	20	2	no	—
684	#41	—	20	2	no	—
685	#41	—	20	2	no	—
686	#41	—	20	2	no	—
687	C₂×Q₈	—	5	1	no	—
688	C₂×Q₈	—	5	1	no	—
689	C₂×Q₈	—	5	1	no	—
690	C₂×Q₈	—	5	1	no	—
691	C₂×Q₈	—	5	1	no	—
692	C₂×Q₈	—	5	1	no	—
693	C₂×Q₈	—	20	2	no	—
694	C₂×D₄	—	5	1	no	—
695	C₂×D₄	—	5	1	no	—
696	C₂×D₄	—	5	1	no	—
697	C₂×D₄	—	5	1	no	—
698	C₂×D₄	—	5	1	no	—
699	C₂×D₄	—	5	1	no	—
700	C₂×D₄	—	5	1	no	—
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	—	20	2	no	—
719	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
720	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
721	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
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	C₂²×C₄	—	5	1	no	—
726	C₂²×C₄	—	5	1	no	—
727	C₂²×C₄	—	5	1	no	—
728	C₂²×C₄	—	5	1	no	—
729	C₂²×C₄	—	5	1	no	—
730	C₂²×C₄	—	5	1	no	—
731	C₂²×C₄	—	5	1	no	—
732	C₂²×C₄	—	5	1	no	—
733	C₂²×C₄	—	5	1	no	—
734	C₂²×C₄	—	5	1	no	—
735	C₂²×C₄	—	5	1	no	—
736	C₂²×C₄	—	5	1	no	—
737	C₂²×C₄	—	5	1	no	—
738	C₂²×C₄	—	5	1	no	—
739	C₂²×C₄	—	5	1	no	—
740	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
741	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
742	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
743	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
744	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
745	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
746	C₄⋊C₄	—	5	1	no	—
747	C₄⋊C₄	—	5	1	no	—
748	C₄⋊C₄	—	5	1	no	—
749	C₄⋊C₄	—	5	1	no	—
750	C₄⋊C₄	—	5	1	no	—
751	C₄⋊C₄	—	5	1	no	—
752	C₄⋊C₄	—	5	1	no	—
753	C₄⋊C₄	—	5	1	no	—
754	C₄⋊C₄	—	5	1	no	—
755	C₄⋊C₄	—	5	1	no	—
756	C₄⋊C₄	—	5	1	no	—
757	C₄⋊C₄	—	5	1	no	—
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	C₂²×D₅	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
791	C₂²⋊C₄	—	5	1	no	—
792	C₂²⋊C₄	—	5	1	no	—
793	C₂²⋊C₄	—	5	1	no	—
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	C₂²×D₅	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
829	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
830	C₄²	—	5	1	no	—
831	C₄²	—	5	1	no	—
832	C₄²	—	5	1	no	—
833	C₄²	—	5	1	no	—
834	C₄²	—	5	1	no	—
835	C₄²	—	5	1	no	—
836	C₄²	—	5	1	no	—
837	C₄²	—	5	1	no	—
838	C₄²	—	5	1	no	—
839	C₄²	C₂²×D₅	1	1	yes	characteristic
840	C₄²	C₂²×D₅	1	1	yes	characteristic
841	C₄²	C₂²×D₅	1	1	yes	characteristic
842	C₂×C₅	—	4	1	no	—
843	C₂×C₅	—	4	1	no	—
844	C₂×C₅	—	4	1	no	—
845	C₂×C₅	—	4	1	no	—
846	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
847	C₂×C₅	#585	1	1	yes	characteristic
848	C₂×C₅	#585	1	1	yes	characteristic
849	D₅	—	4	1	no	—
850	D₅	—	4	1	no	—
851	D₅	—	4	1	no	—
852	D₅	—	4	1	no	—
853	D₅	—	4	1	no	—
854	C₂³	—	5	1	no	—
855	C₂³	—	5	1	no	—
856	C₂³	—	5	1	no	—
857	C₂³	—	5	1	no	—
858	C₂³	—	5	1	no	—
859	C₂³	—	20	1	no	—
860	C₂³	—	20	1	no	—
861	C₂³	—	20	1	no	—
862	C₂³	—	20	1	no	—
863	C₂³	—	20	1	no	—
864	C₂³	—	20	1	no	—
865	C₂³	C₂³×D₅	1	1	yes	characteristic
866	C₂³	C₂³×D₅	1	1	yes	characteristic
867	C₂³	C₂³×D₅	1	1	yes	characteristic
868	C₂³	C₂³×D₅	1	1	yes	characteristic
869	Q₈	—	10	2	no	—
870	Q₈	—	10	2	no	—
871	Q₈	—	10	2	no	—
872	Q₈	—	20	1	no	—
873	Q₈	—	20	1	no	—
874	Q₈	—	20	1	no	—
875	D₄	—	4	1	no	—
876	D₄	—	4	1	no	—
877	D₄	—	4	1	no	—
878	D₄	—	4	1	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	1	no	—
881	D₄	—	10	2	no	—
882	D₄	—	10	2	no	—
883	D₄	—	10	2	no	—
884	D₄	—	20	1	no	—
885	D₄	—	20	1	no	—
886	D₄	—	20	1	no	—
887	D₄	—	20	1	no	—
888	D₄	—	20	1	no	—
889	D₄	—	20	1	no	—
890	D₄	—	20	1	no	—
891	D₄	—	20	1	no	—
892	D₄	—	20	1	no	—
893	D₄	—	20	1	no	—
894	D₄	—	20	1	no	—
895	D₄	—	20	1	no	—
896	D₄	—	20	1	no	—
897	D₄	—	20	1	no	—
898	D₄	—	20	1	no	—
899	D₄	—	20	1	no	—
900	D₄	—	20	1	no	—
901	D₄	—	20	1	no	—
902	D₄	—	20	1	no	—
903	D₄	—	20	1	no	—
904	D₄	—	20	1	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	5	1	no	—
912	C₂×C₄	—	5	1	no	—
913	C₂×C₄	—	5	1	no	—
914	C₂×C₄	—	5	1	no	—
915	C₂×C₄	—	5	1	no	—
916	C₂×C₄	—	5	1	no	—
917	C₂×C₄	—	5	1	no	—
918	C₂×C₄	—	5	1	no	—
919	C₂×C₄	—	5	1	no	—
920	C₂×C₄	—	5	1	no	—
921	C₂×C₄	—	5	1	no	—
922	C₂×C₄	—	10	2	no	—
923	C₂×C₄	—	10	2	no	—
924	C₂×C₄	—	10	2	no	—
925	C₂×C₄	—	20	1	no	—
926	C₂×C₄	—	20	1	no	—
927	C₂×C₄	—	20	1	no	—
928	C₂×C₄	—	20	1	no	—
929	C₂×C₄	—	20	1	no	—
930	C₂×C₄	—	20	1	no	—
931	C₂×C₄	—	20	1	no	—
932	C₂×C₄	—	20	1	no	—
933	C₂×C₄	—	20	1	no	—
934	C₂×C₄	—	20	1	no	—
935	C₂×C₄	—	20	1	no	—
936	C₂×C₄	—	20	1	no	—
937	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
938	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
939	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
948	C₅	#3562	1	1	yes	characteristic, complemented, Sylow
949	C₂²	—	2	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	10	1	no	—
962	C₂²	—	10	1	no	—
963	C₂²	—	10	1	no	—
964	C₂²	—	10	1	no	—
965	C₂²	—	10	1	no	—
966	C₂²	—	10	1	no	—
967	C₂²	—	10	1	no	—
968	C₂²	—	10	1	no	—
969	C₂²	—	10	1	no	—
970	C₂²	—	10	1	no	—
971	C₂²	—	10	1	no	—
972	C₂²	—	10	1	no	—
973	C₂²	—	10	1	no	—
974	C₂²	—	10	1	no	—
975	C₂²	—	10	1	no	—
976	C₂²	—	40	2	no	—
977	C₂²	—	40	2	no	—
978	C₂²	C₂⁴×D₅	1	1	yes	characteristic
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	5	2	no	—
991	C₄	—	10	1	no	—
992	C₄	—	10	1	no	—
993	C₄	—	10	1	no	—
994	C₄	—	10	1	no	—
995	C₄	—	10	1	no	—
996	C₄	—	10	1	no	—
997	C₄	—	10	1	no	—
998	C₄	—	10	1	no	—
999	C₄	—	10	1	no	—
1000	C₄	—	10	1	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	4	1	no	—
1003	C₂	—	4	1	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	20	1	no	—
1006	C₂	—	20	1	no	—
1007	C₂	—	20	1	no	—
1008	C₂	—	20	1	no	—
1009	C₂	—	20	1	no	—
1010	C₂	#66283	1	1	yes	characteristic
1011	C₂	#66283	1	1	yes	characteristic
1012	C₂	D₅×H(5,𝔽₂)	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	#3562
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. #66043	C₂	semidirect
3. #66040	C₂	semidirect
4. #66038	C₂	semidirect
5. #66036	C₂	semidirect
6. #66034	C₂	semidirect
7. #66030	C₂	semidirect
8. #66000	C₂	semidirect
9. #65994	C₂	semidirect
10. #65988	C₂	semidirect
11. #65982	C₂	semidirect
12. #65955	C₂	semidirect
13. #65954	C₂	semidirect
14. #65949	C₂	semidirect
15. #65949	C₂	semidirect
16. #65947	C₂	semidirect
17. #65944	C₂	semidirect
18. #65941	C₂	semidirect
19. #65933	C₂	semidirect
20. #65896	C₂	semidirect
21. #65894	C₂	semidirect
22. #65894	C₂	semidirect
23. #65893	C₂	semidirect
24. #65890	C₂	semidirect
25. #65886	C₂	semidirect
26. #65886	C₂	semidirect
27. #65882	C₂	semidirect
28. #65862	C₂	semidirect
29. #65861	C₂	semidirect
30. #65849	C₂	semidirect
31. #65841	C₂	semidirect
36. C₂×#709	C₂²	semidirect
37. C₂²×Dic₁₀	C₂²	semidirect
38. C₅×#126	C₂²	semidirect
39. C₅×#126	C₂²	semidirect
40. C₅×#125	C₂²	semidirect
42. C₅×#123	C₂²	semidirect
45. C₅×#121	C₂²	semidirect
46. C₅×#121	C₂²	semidirect
47. C₄×C₅×D₄	C₂²	semidirect
48. C₄×C₅×D₄	C₂²	semidirect
49. C₄×C₅×D₄	C₂²	semidirect
50. C₄×C₅×D₄	C₂²	semidirect
51. C₅×#117	C₂²	semidirect
52. C₂×C₅×C₄⋊C₄	C₂²	semidirect
55. #4086	C₂²	semidirect
56. #4086	C₂²	semidirect
60. #4085	C₂²	semidirect
61. #4085	C₂²	semidirect
62. #4085	C₂²	semidirect
63. #4085	C₂²	semidirect
65. #4084	C₂²	semidirect
66. #4084	C₂²	semidirect
71. #4082	C₂²	semidirect
73. #4081	C₂²	semidirect
74. #4081	C₂²	semidirect
78. #4076	C₂²	semidirect
80. #4075	C₂²	semidirect
81. #4075	C₂²	semidirect
82. #4075	C₂²	semidirect
83. #4075	C₂²	semidirect
84. #4075	C₂²	semidirect
86. C₄×C₂²⋊D₅	C₂²	semidirect
87. C₄×C₂²⋊D₅	C₂²	semidirect
88. C₄×C₂²⋊D₅	C₂²	semidirect
89. C₄×C₂²⋊D₅	C₂²	semidirect
90. C₄×C₂²⋊D₅	C₂²	semidirect
93. #4070	C₂²	semidirect
94. #4070	C₂²	semidirect
98. #4044	C₂²	semidirect
99. #4044	C₂²	semidirect
100. #4044	C₂²	semidirect
103. #4042	C₂²	semidirect
104. #4042	C₂²	semidirect
105. #4042	C₂²	semidirect
106. #4042	C₂²	semidirect
107. #4042	C₂²	semidirect
108. #4042	C₂²	semidirect
109. #4042	C₂²	semidirect
113. #4041	C₂²	semidirect
114. #4041	C₂²	semidirect
119. #4040	C₂²	semidirect
120. #4040	C₂²	semidirect
121. #4040	C₂²	semidirect
123. #4039	C₂²	semidirect
125. D₅×C₄⋊C₄	C₂²	semidirect
126. #4036	C₂²	semidirect
127. #4035	C₂²	semidirect
128. #4035	C₂²	semidirect
129. #4035	C₂²	semidirect
130. #4035	C₂²	semidirect
131. #4034	C₂²	semidirect
132. #4034	C₂²	semidirect
133. #4033	C₂²	semidirect
134. #4033	C₂²	semidirect
135. #4032	C₂²	semidirect
142. #4031	C₂²	semidirect
143. #4031	C₂²	semidirect
147. #4030	C₂²	semidirect
148. #4030	C₂²	semidirect
149. #4030	C₂²	semidirect
150. #4030	C₂²	semidirect
151. #4029	C₂²	semidirect
152. #4029	C₂²	semidirect
153. #4029	C₂²	semidirect
154. #4029	C₂²	semidirect
155. #4029	C₂²	semidirect
162. #4027	C₂²	semidirect
163. #4027	C₂²	semidirect
164. #4027	C₂²	semidirect
165. #4027	C₂²	semidirect
168. #4025	C₂²	semidirect
169. #4025	C₂²	semidirect
170. #4024	C₂²	semidirect
171. #4024	C₂²	semidirect
172. #4024	C₂²	semidirect
173. #4023	C₂²	semidirect
174. #4023	C₂²	semidirect
178. #4021	C₂²	semidirect
179. #4021	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. C₄×Dic₁₀	C₂²	semidirect
186. C₄×Dic₁₀	C₂²	semidirect
356. #553	D₅	semidirect
496. #126	C₂×D₅	semidirect
497. #126	C₂×D₅	semidirect
503. #125	C₂×D₅	semidirect
539. #123	C₂×D₅	semidirect
582. #121	C₂×D₅	semidirect
583. #121	C₂×D₅	semidirect
612. C₄×D₄	C₂×D₅	semidirect
613. C₄×D₄	C₂×D₅	semidirect
614. C₄×D₄	C₂×D₅	semidirect
615. C₄×D₄	C₂×D₅	semidirect
621. #117	C₂×D₅	semidirect
623. C₂×C₄⋊C₄	C₂×D₅	semidirect
948. C₅	#3562	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
#66043	2
#66040	2
#66038	2
#66036	2
#66034	2
#66030	2
#66000	2
#65994	2
#65988	2
#65982	2
#65955	2
#65954	2
#65949	2
#65947	2
#65944	2
#65941	2
#65933	2
#65896	2
#65894	2
#65893	2
#65890	2
#65886	2
#65882	2
#65862	2
#65861	2
#65849	2
#65841	2
#3562	5