Subgroups — #10618696

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×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#66044	C₂	1	1	yes	maximal, characteristic, complemented
3	#66043	C₂	1	1	yes	maximal, characteristic, complemented
4	#66043	C₂	1	1	yes	maximal, characteristic, complemented
5	#66041	C₂	1	1	yes	maximal, characteristic, complemented
6	#66015	C₂	1	1	yes	maximal, characteristic, complemented
7	#66012	C₂	1	1	yes	maximal, characteristic, complemented
8	#65999	C₂	1	1	yes	maximal, characteristic, complemented
9	#65997	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	D₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
14	#65978	C₂	1	1	yes	maximal, characteristic, complemented
15	#65971	C₂	1	1	yes	maximal, characteristic, complemented
16	#65969	C₂	1	1	yes	maximal, characteristic, complemented
17	#65958	C₂	1	1	yes	maximal, characteristic, complemented
18	#65924	C₂	1	1	yes	maximal, characteristic, complemented
19	#65920	C₂	1	1	yes	maximal, characteristic, complemented
20	#65899	C₂	1	1	yes	maximal, characteristic, complemented
21	#65888	C₂	1	1	yes	maximal, characteristic, complemented
22	#65879	C₂	1	1	yes	maximal, characteristic, complemented
23	#65872	C₂	1	1	yes	maximal, characteristic, complemented
24	#65865	C₂	1	1	yes	maximal, characteristic, complemented
25	#65861	C₂	1	1	yes	maximal, characteristic, complemented
26	#65858	C₂	1	1	yes	maximal, characteristic, complemented
27	#65857	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂×#4032	C₂	1	1	yes	maximal, characteristic, complemented
29	#65824	C₂	1	1	yes	maximal, characteristic, complemented
30	#65824	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#4027	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	C₂³×Dic₅	C₂²	1	1	yes	characteristic, complemented
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
39	C₂×#709	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×#123	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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₅×#120	C₂²	1	1	yes	characteristic
50	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₅×#117	C₂²	1	1	yes	characteristic, complemented
53	C₅×#117	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	#4099	C₂²	1	1	yes	characteristic, complemented
57	#4093	C₂²	1	1	yes	characteristic, complemented
58	#4093	C₂²	1	1	yes	characteristic, complemented
59	#4092	C₂²	1	1	yes	characteristic, complemented
60	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
61	#4086	C₂²	1	1	yes	characteristic
62	#4085	C₂²	1	1	yes	characteristic
63	#4085	C₂²	1	1	yes	characteristic
64	#4085	C₂²	1	1	yes	characteristic, complemented
65	#4085	C₂²	1	1	yes	characteristic, complemented
66	#4083	C₂²	1	1	yes	characteristic
67	#4081	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
69	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
70	#4076	C₂²	1	1	yes	characteristic
71	#4076	C₂²	1	1	yes	characteristic, complemented
72	#4076	C₂²	1	1	yes	characteristic, complemented
73	#4075	C₂²	1	1	yes	characteristic
74	#4075	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
78	C₂×#685	C₂²	1	1	yes	characteristic, complemented
79	C₂×#685	C₂²	1	1	yes	characteristic, complemented
80	C₂×#685	C₂²	1	1	yes	characteristic, complemented
81	C₂×#685	C₂²	1	1	yes	characteristic, complemented
82	#4072	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
85	C₂×#683	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
87	#4044	C₂²	1	1	yes	characteristic, complemented
88	#4044	C₂²	1	1	yes	characteristic, complemented
89	#4044	C₂²	1	1	yes	characteristic, complemented
90	#4044	C₂²	1	1	yes	characteristic, complemented
91	#4044	C₂²	1	1	yes	characteristic, complemented
92	#4044	C₂²	1	1	yes	characteristic, complemented
93	#4043	C₂²	1	1	yes	characteristic, complemented
94	#4043	C₂²	1	1	yes	characteristic, complemented
95	#4043	C₂²	1	1	yes	characteristic, complemented
96	#4042	C₂²	1	1	yes	characteristic, complemented
97	#4042	C₂²	1	1	yes	characteristic, complemented
98	#4041	C₂²	1	1	yes	characteristic, complemented
99	#4041	C₂²	1	1	yes	characteristic, complemented
100	#4041	C₂²	1	1	yes	characteristic, complemented
101	#4040	C₂²	1	1	yes	characteristic, complemented
102	#4040	C₂²	1	1	yes	characteristic, complemented
103	#4040	C₂²	1	1	yes	characteristic, complemented
104	#4040	C₂²	1	1	yes	characteristic, complemented
105	#4040	C₂²	1	1	yes	characteristic, complemented
106	#4039	C₂²	1	1	yes	characteristic, complemented
107	#4039	C₂²	1	1	yes	characteristic, complemented
108	#4038	C₂²	1	1	yes	characteristic, complemented
109	#4038	C₂²	1	1	yes	characteristic, complemented
110	#4038	C₂²	1	1	yes	characteristic, complemented
111	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	#4036	C₂²	1	1	yes	characteristic, complemented
115	#4035	C₂²	1	1	yes	characteristic, complemented
116	#4035	C₂²	1	1	yes	characteristic, complemented
117	#4035	C₂²	1	1	yes	characteristic, complemented
118	#4034	C₂²	1	1	yes	characteristic, complemented
119	#4032	C₂²	1	1	yes	characteristic
120	#4032	C₂²	1	1	yes	characteristic
121	#4032	C₂²	1	1	yes	characteristic, complemented
122	#4032	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	#4032	C₂²	1	1	yes	characteristic, complemented
128	#4032	C₂²	1	1	yes	characteristic, complemented
129	#4031	C₂²	1	1	yes	characteristic, complemented
130	#4031	C₂²	1	1	yes	characteristic, complemented
131	#4031	C₂²	1	1	yes	characteristic, complemented
132	#4030	C₂²	1	1	yes	characteristic
133	#4030	C₂²	1	1	yes	characteristic
134	#4030	C₂²	1	1	yes	characteristic, complemented
135	#4030	C₂²	1	1	yes	characteristic, complemented
136	#4030	C₂²	1	1	yes	characteristic, complemented
137	#4030	C₂²	1	1	yes	characteristic, complemented
138	#4030	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	#4028	C₂²	1	1	yes	characteristic
145	#4028	C₂²	1	1	yes	characteristic
146	#4028	C₂²	1	1	yes	characteristic, complemented
147	#4028	C₂²	1	1	yes	characteristic, complemented
148	#4028	C₂²	1	1	yes	characteristic, complemented
149	#4027	C₂²	1	1	yes	characteristic
150	#4027	C₂²	1	1	yes	characteristic
151	#4027	C₂²	1	1	yes	characteristic
152	#4027	C₂²	1	1	yes	characteristic
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	#4027	C₂²	1	1	yes	characteristic, complemented
160	#4027	C₂²	1	1	yes	characteristic, complemented
161	#4027	C₂²	1	1	yes	characteristic, complemented
162	#4027	C₂²	1	1	yes	characteristic, complemented
163	#4027	C₂²	1	1	yes	characteristic, complemented
164	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	#4025	C₂²	1	1	yes	characteristic, complemented
169	#4024	C₂²	1	1	yes	characteristic, complemented
170	#4024	C₂²	1	1	yes	characteristic, complemented
171	#4024	C₂²	1	1	yes	characteristic, complemented
172	#4024	C₂²	1	1	yes	characteristic, complemented
173	#4024	C₂²	1	1	yes	characteristic, complemented
174	#4023	C₂²	1	1	yes	characteristic, complemented
175	#4022	C₂²	1	1	yes	characteristic, complemented
176	#4021	C₂²	1	1	yes	characteristic, complemented
177	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₂₀	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	#4016	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	#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	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₅	—	2	4	no	—
202	C₂×C₂²⋊D₅	—	4	2	no	—
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	C₂²×Dic₅	—	4	2	no	—
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	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	#711	—	4	2	no	—
228	D₄×D₅	—	2	4	no	—
229	D₄×D₅	—	4	2	no	—
230	#709	—	2	4	no	—
231	#709	—	4	2	no	—
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×D₂₀	C₂³	1	1	yes	characteristic
236	C₂×D₂₀	C₂³	1	1	yes	characteristic
237	C₂×D₂₀	C₂³	1	1	yes	characteristic
238	C₂×D₂₀	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₅	—	4	2	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₅×C₄⋊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	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₄²×C₅	C₂³	1	1	yes	characteristic
279	C₄²×C₅	C₂³	1	1	yes	characteristic
280	C₄²×C₅	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	#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	#685	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	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
324	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
325	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
326	C₄⋊Dic₅	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	#683	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	D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
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	—	2	2	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	C₂²×D₅	—	2	2	no	—
391	C₂²×D₅	—	2	2	no	—
392	C₂²×D₅	—	2	2	no	—
393	C₂²×D₅	—	2	2	no	—
394	C₂²×D₅	—	4	1	no	—
395	C₂²×D₅	—	4	1	no	—
396	C₂²×D₅	—	4	1	no	—
397	C₂²×D₅	—	4	1	no	—
398	C₂²×D₅	—	4	1	no	—
399	C₂²×D₅	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×C₅	—	2	2	no	—
409	C₂×C₄×C₅	—	2	2	no	—
410	C₂×C₄×C₅	—	4	1	no	—
411	C₂×C₄×C₅	—	4	1	no	—
412	C₂×C₄×C₅	—	4	1	no	—
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	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	C₂²⋊D₅	—	2	2	no	—
425	C₂²⋊D₅	—	2	2	no	—
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	—	4	1	no	—
433	C₂²⋊D₅	—	4	1	no	—
434	C₂²⋊D₅	—	4	1	no	—
435	C₂²⋊D₅	—	4	1	no	—
436	C₂²⋊D₅	—	4	1	no	—
437	C₂²⋊D₅	#41	1	4	yes	complemented
438	C₂×Dic₅	—	2	2	no	—
439	C₂×Dic₅	—	2	2	no	—
440	C₂×Dic₅	—	2	2	no	—
441	C₂×Dic₅	—	4	1	no	—
442	C₂×Dic₅	—	4	1	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	C₂⁴	1	1	yes	characteristic
448	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
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	D₂₀	—	2	2	no	—
459	D₂₀	—	2	2	no	—
460	D₂₀	—	4	1	no	—
461	D₂₀	—	4	1	no	—
462	D₂₀	—	4	1	no	—
463	D₂₀	—	4	1	no	—
464	D₂₀	—	4	1	no	—
465	C₄×D₅	—	2	2	no	—
466	C₄×D₅	—	2	2	no	—
467	C₄×D₅	—	2	2	no	—
468	C₄×D₅	—	4	1	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	—	5	1	no	—
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	C₂×D₅	1	1	yes	characteristic, complemented
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	C₂×D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
568	#121	—	5	1	no	—
569	#121	—	5	1	no	—
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	—	5	1	no	—
577	#120	C₂×D₅	1	1	yes	characteristic
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	C₂×D₅	1	1	yes	characteristic, complemented
618	#117	C₂×D₅	1	1	yes	characteristic, complemented
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	C₂×D₅	1	1	yes	characteristic, complemented
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	—	4	4	no	—
647	C₂²×C₅	C₂×#41	1	2	yes	—
648	C₂²×C₅	H(5,𝔽₂)	1	2	yes	—
649	C₂²×C₅	C₂⁵	1	1	yes	characteristic
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	—	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	—	2	1	no	—
664	C₂×D₅	—	4	4	no	—
665	C₂×D₅	—	8	2	no	—
666	C₂×D₅	—	8	2	no	—
667	C₂×D₅	C₂×#41	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	C₄×C₅	—	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	—	5	1	no	—
719	C₂×D₄	—	5	1	no	—
720	C₂×D₄	—	5	1	no	—
721	C₂×D₄	—	5	1	no	—
722	C₂×D₄	—	10	4	no	—
723	C₂×D₄	—	10	4	no	—
724	C₂×D₄	—	20	2	no	—
725	C₂×D₄	—	20	2	no	—
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	—	20	2	no	—
752	C₂²×C₄	—	20	2	no	—
753	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
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	C₂²×D₅	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	C₂²×D₅	1	1	yes	characteristic
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	—	2	2	no	—
856	C₂×C₅	—	4	1	no	—
857	C₂×C₅	—	4	1	no	—
858	C₂×C₅	C₂²×#41	1	1	yes	characteristic
859	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
860	C₂×C₅	#585	1	1	yes	characteristic
861	D₅	—	2	2	no	—
862	D₅	—	4	1	no	—
863	D₅	—	4	1	no	—
864	D₅	—	4	1	no	—
865	D₅	—	4	1	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	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	—	5	1	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	—	20	1	no	—
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	—	5	4	no	—
895	D₄	—	10	2	no	—
896	D₄	—	10	2	no	—
897	D₄	—	10	2	no	—
898	D₄	—	10	2	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	—	20	1	no	—
906	D₄	—	20	1	no	—
907	D₄	—	20	1	no	—
908	D₄	—	20	1	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	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	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	—	20	1	no	—
938	C₂×C₄	—	20	1	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	C₂³×D₅	1	1	yes	characteristic
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	—	4	4	no	—
976	C₂²	—	5	2	no	—
977	C₂²	—	10	1	no	—
978	C₂²	—	10	1	no	—
979	C₂²	—	10	1	no	—
980	C₂²	—	10	1	no	—
981	C₂²	—	10	1	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	—	20	4	no	—
992	C₂²	—	40	2	no	—
993	C₂²	—	40	2	no	—
994	C₂²	D₅×#41	1	2	yes	—
995	C₂²	#4149	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	—	2	1	no	—
1008	C₄	—	5	2	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	—	2	2	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	10	2	no	—
1024	C₂	—	20	1	no	—
1025	C₂	—	20	1	no	—
1026	C₂	—	20	1	no	—
1027	C₂	—	20	1	no	—
1028	C₂	C₂×D₅×#41	1	1	yes	characteristic
1029	C₂	C₂×#4149	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×#551	C₂
hypercenter	#551	D₅
hypocenter	C₅	#3513
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. C₅×#551	C₂	semidirect
2. #66044	C₂	semidirect
3. #66043	C₂	semidirect
4. #66043	C₂	semidirect
5. #66041	C₂	semidirect
6. #66015	C₂	semidirect
7. #66012	C₂	semidirect
8. #65999	C₂	semidirect
9. #65997	C₂	semidirect
10. #65992	C₂	semidirect
11. #65989	C₂	semidirect
12. #65988	C₂	semidirect
13. D₅×#123	C₂	semidirect
14. #65978	C₂	semidirect
15. #65971	C₂	semidirect
16. #65969	C₂	semidirect
17. #65958	C₂	semidirect
18. #65924	C₂	semidirect
19. #65920	C₂	semidirect
20. #65899	C₂	semidirect
21. #65888	C₂	semidirect
22. #65879	C₂	semidirect
23. #65872	C₂	semidirect
24. #65865	C₂	semidirect
25. #65861	C₂	semidirect
26. #65858	C₂	semidirect
27. #65857	C₂	semidirect
28. C₂×#4032	C₂	semidirect
29. #65824	C₂	semidirect
30. #65824	C₂	semidirect
31. C₂×#4027	C₂	semidirect
34. C₂³×Dic₅	C₂²	semidirect
35. C₂×#711	C₂²	semidirect
39. C₂×#709	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×#123	C₂²	semidirect
45. C₅×#123	C₂²	semidirect
46. C₅×#123	C₂²	semidirect
47. C₅×C₂²⋊Q₈	C₂²	semidirect
48. C₅×C₂²⋊Q₈	C₂²	semidirect
50. C₄×C₅×D₄	C₂²	semidirect
51. C₄×C₅×D₄	C₂²	semidirect
52. C₅×#117	C₂²	semidirect
53. C₅×#117	C₂²	semidirect
54. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
55. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
56. #4099	C₂²	semidirect
57. #4093	C₂²	semidirect
58. #4093	C₂²	semidirect
59. #4092	C₂²	semidirect
60. Q₈×Dic₅	C₂²	semidirect
64. #4085	C₂²	semidirect
65. #4085	C₂²	semidirect
67. #4081	C₂²	semidirect
68. D₄×Dic₅	C₂²	semidirect
69. D₄×Dic₅	C₂²	semidirect
71. #4076	C₂²	semidirect
72. #4076	C₂²	semidirect
74. #4075	C₂²	semidirect
76. C₄×C₂²⋊D₅	C₂²	semidirect
77. C₄×C₂²⋊D₅	C₂²	semidirect
78. C₂×#685	C₂²	semidirect
79. C₂×#685	C₂²	semidirect
80. C₂×#685	C₂²	semidirect
81. C₂×#685	C₂²	semidirect
82. #4072	C₂²	semidirect
83. C₂×C₄⋊Dic₅	C₂²	semidirect
84. C₂×C₄⋊Dic₅	C₂²	semidirect
85. C₂×#683	C₂²	semidirect
86. C₂×C₄×Dic₅	C₂²	semidirect
87. #4044	C₂²	semidirect
88. #4044	C₂²	semidirect
89. #4044	C₂²	semidirect
90. #4044	C₂²	semidirect
91. #4044	C₂²	semidirect
92. #4044	C₂²	semidirect
93. #4043	C₂²	semidirect
94. #4043	C₂²	semidirect
95. #4043	C₂²	semidirect
96. #4042	C₂²	semidirect
97. #4042	C₂²	semidirect
98. #4041	C₂²	semidirect
99. #4041	C₂²	semidirect
100. #4041	C₂²	semidirect
101. #4040	C₂²	semidirect
102. #4040	C₂²	semidirect
103. #4040	C₂²	semidirect
104. #4040	C₂²	semidirect
105. #4040	C₂²	semidirect
106. #4039	C₂²	semidirect
107. #4039	C₂²	semidirect
108. #4038	C₂²	semidirect
109. #4038	C₂²	semidirect
110. #4038	C₂²	semidirect
111. D₅×C₄⋊C₄	C₂²	semidirect
112. D₅×C₄⋊C₄	C₂²	semidirect
113. D₅×C₄⋊C₄	C₂²	semidirect
114. #4036	C₂²	semidirect
115. #4035	C₂²	semidirect
116. #4035	C₂²	semidirect
117. #4035	C₂²	semidirect
118. #4034	C₂²	semidirect
121. #4032	C₂²	semidirect
122. #4032	C₂²	semidirect
123. #4032	C₂²	semidirect
124. #4032	C₂²	semidirect
125. #4032	C₂²	semidirect
126. #4032	C₂²	semidirect
127. #4032	C₂²	semidirect
128. #4032	C₂²	semidirect
129. #4031	C₂²	semidirect
130. #4031	C₂²	semidirect
131. #4031	C₂²	semidirect
134. #4030	C₂²	semidirect
135. #4030	C₂²	semidirect
136. #4030	C₂²	semidirect
137. #4030	C₂²	semidirect
138. #4030	C₂²	semidirect
139. #4029	C₂²	semidirect
140. #4029	C₂²	semidirect
141. #4029	C₂²	semidirect
142. #4029	C₂²	semidirect
143. #4029	C₂²	semidirect
146. #4028	C₂²	semidirect
147. #4028	C₂²	semidirect
148. #4028	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. #4027	C₂²	semidirect
160. #4027	C₂²	semidirect
161. #4027	C₂²	semidirect
162. #4027	C₂²	semidirect
163. #4027	C₂²	semidirect
164. D₅×C₂²⋊C₄	C₂²	semidirect
165. D₅×C₂²⋊C₄	C₂²	semidirect
166. D₅×C₂²⋊C₄	C₂²	semidirect
167. D₅×C₂²⋊C₄	C₂²	semidirect
168. #4025	C₂²	semidirect
169. #4024	C₂²	semidirect
170. #4024	C₂²	semidirect
171. #4024	C₂²	semidirect
172. #4024	C₂²	semidirect
173. #4024	C₂²	semidirect
174. #4023	C₂²	semidirect
175. #4022	C₂²	semidirect
176. #4021	C₂²	semidirect
177. C₄×D₂₀	C₂²	semidirect
178. C₄×D₂₀	C₂²	semidirect
179. C₄×D₂₀	C₂²	semidirect
180. C₄×D₂₀	C₂²	semidirect
181. C₄×D₂₀	C₂²	semidirect
182. #4018	C₂²	semidirect
183. #4018	C₂²	semidirect
184. #4016	C₂²	semidirect
185. C₄×Dic₁₀	C₂²	semidirect
186. C₄×Dic₁₀	C₂²	semidirect
361. #551	D₅	semidirect
437. C₂²⋊D₅	#41	semidirect
500. #126	C₂×D₅	semidirect
501. #126	C₂×D₅	semidirect
513. #124	C₂×D₅	semidirect
537. #123	C₂×D₅	semidirect
538. #123	C₂×D₅	semidirect
539. #123	C₂×D₅	semidirect
551. C₂²⋊Q₈	C₂×D₅	semidirect
552. C₂²⋊Q₈	C₂×D₅	semidirect
608. C₄×D₄	C₂×D₅	semidirect
609. C₄×D₄	C₂×D₅	semidirect
617. #117	C₂×D₅	semidirect
618. #117	C₂×D₅	semidirect
633. C₂×C₂²⋊C₄	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×#551	2
#66044	2
#66043	2
#66041	2
#66015	2
#66012	2
#65999	2
#65997	2
#65992	2
#65989	2
#65988	2
D₅×#123	2
#65978	2
#65971	2
#65969	2
#65958	2
#65924	2
#65920	2
#65899	2
#65888	2
#65879	2
#65872	2
#65865	2
#65861	2
#65858	2
#65857	2
C₂×#4032	2
#65824	2
C₂×#4027	2
#3513	5