Subgroups — #10618466

Order 640.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#66067	C₂	1	1	yes	maximal, characteristic, complemented
3	#66058	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	#66039	C₂	1	1	yes	maximal, characteristic, complemented
7	#66038	C₂	1	1	yes	maximal, characteristic, complemented
8	#66017	C₂	1	1	yes	maximal, characteristic, complemented
9	#66013	C₂	1	1	yes	maximal, characteristic, complemented
10	#66012	C₂	1	1	yes	maximal, characteristic, complemented
11	#66010	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
13	#66004	C₂	1	1	yes	maximal, characteristic, complemented
14	#66001	C₂	1	1	yes	maximal, characteristic, complemented
15	#65996	C₂	1	1	yes	maximal, characteristic, complemented
16	#65988	C₂	1	1	yes	maximal, characteristic, complemented
17	#65987	C₂	1	1	yes	maximal, characteristic, complemented
18	#65981	C₂	1	1	yes	maximal, characteristic, complemented
19	#65980	C₂	1	1	yes	maximal, characteristic, complemented
20	#65978	C₂	1	1	yes	maximal, characteristic, complemented
21	#65971	C₂	1	1	yes	maximal, characteristic, complemented
22	#65964	C₂	1	1	yes	maximal, characteristic, complemented
23	#65962	C₂	1	1	yes	maximal, characteristic, complemented
24	#65947	C₂	1	1	yes	maximal, characteristic, complemented
25	#65939	C₂	1	1	yes	maximal, characteristic, complemented
26	#65916	C₂	1	1	yes	maximal, characteristic, complemented
27	#65914	C₂	1	1	yes	maximal, characteristic, complemented
28	#65890	C₂	1	1	yes	maximal, characteristic, complemented
29	#65884	C₂	1	1	yes	maximal, characteristic, complemented
30	#65866	C₂	1	1	yes	maximal, characteristic, complemented
31	#65861	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#713	C₂²	1	1	yes	characteristic
33	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
36	C₂×#709	C₂²	1	1	yes	characteristic
37	C₂²×D₂₀	C₂²	1	1	yes	characteristic, complemented
38	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₅×#126	C₂²	1	1	yes	characteristic, complemented
40	C₅×#126	C₂²	1	1	yes	characteristic, complemented
41	C₅×#124	C₂²	1	1	yes	characteristic, complemented
42	C₅×#124	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×C₂²⋊Q₈	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×#121	C₂²	1	1	yes	characteristic
50	C₄×C₅×Q₈	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	#4093	C₂²	1	1	yes	characteristic, complemented
54	#4093	C₂²	1	1	yes	characteristic, complemented
55	#4093	C₂²	1	1	yes	characteristic, complemented
56	#4093	C₂²	1	1	yes	characteristic, complemented
57	#4093	C₂²	1	1	yes	characteristic, complemented
58	#4092	C₂²	1	1	yes	characteristic, complemented
59	#4092	C₂²	1	1	yes	characteristic, complemented
60	#4092	C₂²	1	1	yes	characteristic, complemented
61	#4092	C₂²	1	1	yes	characteristic, complemented
62	#4090	C₂²	1	1	yes	characteristic, complemented
63	#4085	C₂²	1	1	yes	characteristic
64	#4085	C₂²	1	1	yes	characteristic, complemented
65	#4085	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, complemented
70	#4083	C₂²	1	1	yes	characteristic, complemented
71	#4082	C₂²	1	1	yes	characteristic, complemented
72	#4081	C₂²	1	1	yes	characteristic, complemented
73	#4076	C₂²	1	1	yes	characteristic, complemented
74	#4076	C₂²	1	1	yes	characteristic, complemented
75	#4075	C₂²	1	1	yes	characteristic
76	#4075	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₅	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	#4070	C₂²	1	1	yes	characteristic, complemented
82	#4070	C₂²	1	1	yes	characteristic, complemented
83	#4044	C₂²	1	1	yes	characteristic, complemented
84	#4044	C₂²	1	1	yes	characteristic, complemented
85	#4044	C₂²	1	1	yes	characteristic, complemented
86	#4044	C₂²	1	1	yes	characteristic, complemented
87	#4044	C₂²	1	1	yes	characteristic, complemented
88	#4043	C₂²	1	1	yes	characteristic, complemented
89	#4043	C₂²	1	1	yes	characteristic, complemented
90	#4042	C₂²	1	1	yes	characteristic, complemented
91	#4042	C₂²	1	1	yes	characteristic, complemented
92	#4042	C₂²	1	1	yes	characteristic, complemented
93	#4042	C₂²	1	1	yes	characteristic, complemented
94	#4042	C₂²	1	1	yes	characteristic, complemented
95	#4042	C₂²	1	1	yes	characteristic, complemented
96	#4041	C₂²	1	1	yes	characteristic
97	#4041	C₂²	1	1	yes	characteristic
98	#4041	C₂²	1	1	yes	characteristic
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	#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	#4040	C₂²	1	1	yes	characteristic, complemented
111	#4040	C₂²	1	1	yes	characteristic, complemented
112	#4040	C₂²	1	1	yes	characteristic, complemented
113	#4039	C₂²	1	1	yes	characteristic, complemented
114	#4039	C₂²	1	1	yes	characteristic, complemented
115	#4039	C₂²	1	1	yes	characteristic, complemented
116	#4038	C₂²	1	1	yes	characteristic, complemented
117	#4038	C₂²	1	1	yes	characteristic, complemented
118	#4036	C₂²	1	1	yes	characteristic, complemented
119	#4035	C₂²	1	1	yes	characteristic, complemented
120	#4034	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	#4031	C₂²	1	1	yes	characteristic
125	#4031	C₂²	1	1	yes	characteristic
126	#4031	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	#4031	C₂²	1	1	yes	characteristic, complemented
131	#4031	C₂²	1	1	yes	characteristic, complemented
132	#4031	C₂²	1	1	yes	characteristic, complemented
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
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	#4028	C₂²	1	1	yes	characteristic
146	#4028	C₂²	1	1	yes	characteristic
147	#4028	C₂²	1	1	yes	characteristic
148	#4028	C₂²	1	1	yes	characteristic
149	#4028	C₂²	1	1	yes	characteristic, complemented
150	#4028	C₂²	1	1	yes	characteristic, complemented
151	#4028	C₂²	1	1	yes	characteristic, complemented
152	#4028	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	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	D₅×C₂²⋊C₄	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	#4024	C₂²	1	1	yes	characteristic, complemented
169	#4023	C₂²	1	1	yes	characteristic, complemented
170	#4023	C₂²	1	1	yes	characteristic, complemented
171	#4022	C₂²	1	1	yes	characteristic, complemented
172	#4022	C₂²	1	1	yes	characteristic, complemented
173	#4021	C₂²	1	1	yes	characteristic, complemented
174	#4021	C₂²	1	1	yes	characteristic, complemented
175	#4021	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	#4018	C₂²	1	1	yes	characteristic, complemented
182	#4018	C₂²	1	1	yes	characteristic, complemented
183	#4018	C₂²	1	1	yes	characteristic, complemented
184	#4018	C₂²	1	1	yes	characteristic, complemented
185	#4018	C₂²	1	1	yes	characteristic, complemented
186	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
187	#3545	—	5	1	no	maximal, Sylow
188	C₂³×D₅	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×Q₈	C₂³	1	1	yes	characteristic
194	C₂×C₅×Q₈	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	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
211	C₂²×Dic₅	C₂³	1	1	yes	characteristic
212	C₂²×Dic₅	C₂³	1	1	yes	characteristic
213	#713	—	4	2	no	—
214	Q₈×D₅	—	4	2	no	—
215	D₄×D₅	—	4	2	no	—
216	D₄×D₅	—	4	2	no	—
217	#709	—	4	2	no	—
218	C₂×D₂₀	—	4	2	no	—
219	C₂×D₂₀	C₂³	1	1	yes	characteristic
220	C₂×D₂₀	C₂³	1	1	yes	characteristic
221	C₂×D₂₀	C₂³	1	1	yes	characteristic
222	C₂×D₂₀	C₂³	1	1	yes	characteristic
223	C₂×D₂₀	C₂³	1	1	yes	characteristic
224	C₂×D₂₀	C₂³	1	1	yes	characteristic
225	C₂×D₂₀	C₂³	1	1	yes	characteristic
226	C₂×D₂₀	C₂³	1	1	yes	characteristic
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×C₄×D₅	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₅	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×Dic₁₀	C₂³	1	1	yes	characteristic
245	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
246	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
247	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
248	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
249	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₅×C₄⋊C₄	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₅×C₂²⋊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	C₄²×C₅	C₂³	1	1	yes	characteristic
272	C₄²×C₅	C₂³	1	1	yes	characteristic
273	C₄²×C₅	C₂³	1	1	yes	characteristic
274	C₄²×C₅	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₅	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	#685	C₂³	1	1	yes	characteristic
284	#685	C₂³	1	1	yes	characteristic
285	#685	C₂³	1	1	yes	characteristic
286	#685	C₂³	1	1	yes	characteristic
287	#685	C₂³	1	1	yes	characteristic
288	#685	C₂³	1	1	yes	characteristic
289	#685	C₂³	1	1	yes	characteristic
290	#685	C₂³	1	1	yes	characteristic
291	#685	C₂³	1	1	yes	characteristic
292	#685	C₂³	1	1	yes	characteristic
293	#685	C₂³	1	1	yes	characteristic
294	#685	C₂³	1	1	yes	characteristic
295	#685	C₂³	1	1	yes	characteristic
296	#685	C₂³	1	1	yes	characteristic
297	#685	C₂³	1	1	yes	characteristic
298	#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	#685	C₂³	1	1	yes	characteristic
316	#685	C₂³	1	1	yes	characteristic
317	#685	C₂³	1	1	yes	characteristic
318	#685	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	#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	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	#563	—	5	1	no	—
350	#562	—	5	1	no	—
351	#562	—	5	1	no	—
352	H(3,𝔽₄)	—	5	1	no	—
353	#555	—	5	1	no	—
354	#555	—	5	1	no	—
355	#551	—	5	1	no	—
356	#551	—	5	1	no	—
357	#551	—	5	1	no	—
358	#551	—	5	1	no	—
359	#551	—	5	1	no	—
360	#551	—	5	1	no	—
361	#546	—	5	1	no	—
362	#546	—	5	1	no	—
363	#546	—	5	1	no	—
364	#546	—	5	1	no	—
365	#542	—	5	1	no	—
366	#542	—	5	1	no	—
367	#542	—	5	1	no	—
368	#542	D₅	1	1	yes	characteristic, complemented
369	#538	—	5	1	no	—
370	#538	—	5	1	no	—
371	#538	—	5	1	no	—
372	#538	—	5	1	no	—
373	#536	—	5	1	no	—
374	#536	—	5	1	no	—
375	#534	—	5	1	no	—
376	#534	—	5	1	no	—
377	#529	—	5	1	no	—
378	#529	—	5	1	no	—
379	C₂×#124	—	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	C₂²×D₅	—	2	2	no	—
384	C₂²×D₅	—	2	2	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	—	4	1	no	—
391	C₂²×D₅	—	4	1	no	—
392	C₂²×D₅	—	4	1	no	—
393	C₂²×D₅	—	4	1	no	—
394	C₂²×D₅	—	4	1	no	—
395	C₂²×D₅	C₂⁴	1	1	yes	characteristic
396	C₂²×D₅	C₂⁴	1	1	yes	characteristic
397	C₂²×D₅	C₂⁴	1	1	yes	characteristic
398	C₂²×D₅	C₂⁴	1	1	yes	characteristic
399	C₂²×D₅	C₂⁴	1	1	yes	characteristic
400	C₂²×D₅	C₂⁴	1	1	yes	characteristic
401	C₅×Q₈	—	4	1	no	—
402	C₅×Q₈	—	4	1	no	—
403	C₅×Q₈	—	4	1	no	—
404	C₅×D₄	—	4	1	no	—
405	C₅×D₄	—	4	1	no	—
406	C₅×D₄	—	4	1	no	—
407	C₂×C₄×C₅	—	4	1	no	—
408	C₂×C₄×C₅	—	4	1	no	—
409	C₂×C₄×C₅	—	4	1	no	—
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	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	C₂²⋊D₅	—	2	2	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	C₂×Dic₅	—	4	1	no	—
433	C₂×Dic₅	—	4	1	no	—
434	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
435	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
436	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
437	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
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	D₂₀	—	2	2	no	—
445	D₂₀	—	2	2	no	—
446	D₂₀	—	2	2	no	—
447	D₂₀	—	4	1	no	—
448	D₂₀	—	4	1	no	—
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	C₄×D₅	—	2	2	no	—
456	C₄×D₅	—	2	2	no	—
457	C₄×D₅	—	2	2	no	—
458	C₄×D₅	—	4	1	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	C₄×D₅	—	4	1	no	—
469	Dic₁₀	—	4	1	no	—
470	Dic₁₀	—	4	1	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	C₂²×Q₈	—	5	1	no	—
477	C₂²×D₄	—	5	1	no	—
478	C₂²×D₄	—	5	1	no	—
479	C₂²×D₄	—	5	1	no	—
480	C₄⋊Q₈	—	5	1	no	—
481	C₄⋊Q₈	—	5	1	no	—
482	C₄⋊Q₈	—	5	1	no	—
483	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
484	#126	—	5	1	no	—
485	#126	—	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	C₂×D₅	1	1	yes	characteristic, complemented
495	#126	C₂×D₅	1	1	yes	characteristic, complemented
496	#125	—	5	1	no	—
497	#125	—	5	1	no	—
498	#124	—	5	1	no	—
499	#124	—	5	1	no	—
500	#124	—	5	1	no	—
501	#124	—	5	1	no	—
502	#124	—	5	1	no	—
503	#124	—	5	1	no	—
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	#124	—	5	1	no	—
517	#124	C₂×D₅	1	1	yes	characteristic, complemented
518	#124	C₂×D₅	1	1	yes	characteristic, complemented
519	#124	C₂×D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
539	#123	—	5	1	no	—
540	#123	—	5	1	no	—
541	#123	—	5	1	no	—
542	#123	C₂×D₅	1	1	yes	characteristic, complemented
543	#123	C₂×D₅	1	1	yes	characteristic, complemented
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	C₂²⋊Q₈	—	5	1	no	—
555	C₂²⋊Q₈	—	5	1	no	—
556	C₂²⋊Q₈	—	5	1	no	—
557	C₂²⋊Q₈	—	5	1	no	—
558	C₂²⋊Q₈	—	5	1	no	—
559	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
560	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
561	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
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	C₂×D₅	1	1	yes	characteristic
580	#120	—	5	1	no	—
581	#120	—	5	1	no	—
582	#120	—	5	1	no	—
583	#120	—	5	1	no	—
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	C₂×D₅	1	1	yes	characteristic, complemented
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	C₂×D₅	1	1	yes	characteristic, complemented
608	#117	—	5	1	no	—
609	#117	—	5	1	no	—
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	C₂×C₂²⋊C₄	—	5	1	no	—
619	C₂×C₂²⋊C₄	—	5	1	no	—
620	C₂×C₂²⋊C₄	—	5	1	no	—
621	C₂×C₂²⋊C₄	—	5	1	no	—
622	C₂×C₂²⋊C₄	—	5	1	no	—
623	C₂×C₂²⋊C₄	—	5	1	no	—
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	C₂⁵	1	1	yes	characteristic
639	C₂×D₅	—	2	1	no	—
640	C₂×D₅	—	2	1	no	—
641	C₂×D₅	—	2	1	no	—
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	—	8	2	no	—
657	C₂×D₅	—	8	2	no	—
658	C₂×D₅	—	8	2	no	—
659	C₂×D₅	—	8	2	no	—
660	C₂×D₅	H(5,𝔽₂)	1	2	yes	—
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	C₄×C₅	—	2	1	no	—
671	C₄×C₅	—	2	1	no	—
672	C₄×C₅	—	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	—	2	1	no	—
681	Dic₅	—	2	1	no	—
682	Dic₅	—	2	1	no	—
683	C₂⁴	—	5	1	no	—
684	C₂⁴	—	5	1	no	—
685	C₂⁴	—	5	1	no	—
686	C₂⁴	—	5	1	no	—
687	#41	—	20	2	no	—
688	#41	—	20	2	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	—	5	1	no	—
694	C₂×Q₈	—	20	2	no	—
695	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
696	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
697	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
719	C₂×D₄	—	20	2	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	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	—	5	1	no	—
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	C₄⋊C₄	—	5	1	no	—
745	C₄⋊C₄	—	5	1	no	—
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	C₂²×D₅	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	C₂²⋊C₄	—	5	1	no	—
777	C₂²⋊C₄	—	5	1	no	—
778	C₂²⋊C₄	—	5	1	no	—
779	C₂²⋊C₄	—	5	1	no	—
780	C₂²⋊C₄	—	5	1	no	—
781	C₂²⋊C₄	—	5	1	no	—
782	C₂²⋊C₄	—	5	1	no	—
783	C₂²⋊C₄	—	5	1	no	—
784	C₂²⋊C₄	—	5	1	no	—
785	C₂²⋊C₄	—	5	1	no	—
786	C₂²⋊C₄	—	5	1	no	—
787	C₂²⋊C₄	—	5	1	no	—
788	C₂²⋊C₄	—	5	1	no	—
789	C₂²⋊C₄	—	5	1	no	—
790	C₂²⋊C₄	—	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	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	1	no	—
840	C₄²	C₂²×D₅	1	1	yes	characteristic
841	C₄²	C₂²×D₅	1	1	yes	characteristic
842	C₄²	C₂²×D₅	1	1	yes	characteristic
843	C₄²	C₂²×D₅	1	1	yes	characteristic
844	C₂×C₅	—	4	1	no	—
845	C₂×C₅	—	4	1	no	—
846	C₂×C₅	—	4	1	no	—
847	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
848	C₂×C₅	#585	1	1	yes	characteristic
849	C₂×C₅	#585	1	1	yes	characteristic
850	D₅	—	2	2	no	—
851	D₅	—	4	1	no	—
852	D₅	—	4	1	no	—
853	D₅	—	4	1	no	—
854	D₅	—	4	1	no	—
855	D₅	—	4	1	no	—
856	C₂³	—	5	1	no	—
857	C₂³	—	5	1	no	—
858	C₂³	—	5	1	no	—
859	C₂³	—	5	1	no	—
860	C₂³	—	5	1	no	—
861	C₂³	—	5	1	no	—
862	C₂³	—	10	2	no	—
863	C₂³	—	10	2	no	—
864	C₂³	—	20	1	no	—
865	C₂³	—	20	1	no	—
866	C₂³	—	20	1	no	—
867	C₂³	—	20	1	no	—
868	C₂³	—	20	1	no	—
869	C₂³	—	20	1	no	—
870	C₂³	—	20	1	no	—
871	C₂³	—	20	1	no	—
872	C₂³	—	20	1	no	—
873	C₂³	—	20	1	no	—
874	C₂³	C₂³×D₅	1	1	yes	characteristic
875	C₂³	C₂³×D₅	1	1	yes	characteristic
876	C₂³	C₂³×D₅	1	1	yes	characteristic
877	Q₈	—	4	1	no	—
878	Q₈	—	4	1	no	—
879	Q₈	—	4	1	no	—
880	Q₈	—	20	1	no	—
881	Q₈	—	20	1	no	—
882	Q₈	—	20	1	no	—
883	Q₈	—	20	1	no	—
884	Q₈	—	20	1	no	—
885	D₄	—	4	1	no	—
886	D₄	—	4	1	no	—
887	D₄	—	4	1	no	—
888	D₄	—	10	2	no	—
889	D₄	—	10	2	no	—
890	D₄	—	10	2	no	—
891	D₄	—	10	2	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	D₄	—	20	1	no	—
906	D₄	—	20	1	no	—
907	D₄	—	20	1	no	—
908	D₄	—	20	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	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	—	20	1	no	—
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	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
950	C₅	#3545	1	1	yes	characteristic, complemented, Sylow
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	—	5	2	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	—	10	1	no	—
977	C₂²	—	10	1	no	—
978	C₂²	—	40	2	no	—
979	C₂²	—	40	2	no	—
980	C₂²	—	40	2	no	—
981	C₂²	—	40	2	no	—
982	C₂²	C₂⁴×D₅	1	1	yes	characteristic
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	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	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	C₄	—	10	1	no	—
1002	C₄	—	10	1	no	—
1003	C₄	—	10	1	no	—
1004	C₄	—	10	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	4	1	no	—
1008	C₂	—	10	2	no	—
1009	C₂	—	20	1	no	—
1010	C₂	—	20	1	no	—
1011	C₂	—	20	1	no	—
1012	C₂	—	20	1	no	—
1013	C₂	—	20	1	no	—
1014	C₂	#66283	1	1	yes	characteristic
1015	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic
1016	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#542	C₂
hypercenter	#542	D₅
hypocenter	C₅	#3545
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₅×#542	C₂	semidirect
2. #66067	C₂	semidirect
3. #66058	C₂	semidirect
4. #66040	C₂	semidirect
5. #66039	C₂	semidirect
6. #66039	C₂	semidirect
7. #66038	C₂	semidirect
8. #66017	C₂	semidirect
9. #66013	C₂	semidirect
10. #66012	C₂	semidirect
11. #66010	C₂	semidirect
12. D₅×#124	C₂	semidirect
13. #66004	C₂	semidirect
14. #66001	C₂	semidirect
15. #65996	C₂	semidirect
16. #65988	C₂	semidirect
17. #65987	C₂	semidirect
18. #65981	C₂	semidirect
19. #65980	C₂	semidirect
20. #65978	C₂	semidirect
21. #65971	C₂	semidirect
22. #65964	C₂	semidirect
23. #65962	C₂	semidirect
24. #65947	C₂	semidirect
25. #65939	C₂	semidirect
26. #65916	C₂	semidirect
27. #65914	C₂	semidirect
28. #65890	C₂	semidirect
29. #65884	C₂	semidirect
30. #65866	C₂	semidirect
31. #65861	C₂	semidirect
33. C₂×Q₈×D₅	C₂²	semidirect
35. C₂×D₄×D₅	C₂²	semidirect
37. C₂²×D₂₀	C₂²	semidirect
38. C₅×C₄⋊Q₈	C₂²	semidirect
39. C₅×#126	C₂²	semidirect
40. C₅×#126	C₂²	semidirect
41. C₅×#124	C₂²	semidirect
42. C₅×#124	C₂²	semidirect
43. C₅×#124	C₂²	semidirect
44. C₅×#123	C₂²	semidirect
45. C₅×#123	C₂²	semidirect
46. C₅×C₂²⋊Q₈	C₂²	semidirect
47. C₅×C₂²⋊Q₈	C₂²	semidirect
48. C₅×C₂²⋊Q₈	C₂²	semidirect
50. C₄×C₅×Q₈	C₂²	semidirect
51. C₄×C₅×D₄	C₂²	semidirect
52. C₅×#117	C₂²	semidirect
53. #4093	C₂²	semidirect
54. #4093	C₂²	semidirect
55. #4093	C₂²	semidirect
56. #4093	C₂²	semidirect
57. #4093	C₂²	semidirect
58. #4092	C₂²	semidirect
59. #4092	C₂²	semidirect
60. #4092	C₂²	semidirect
61. #4092	C₂²	semidirect
62. #4090	C₂²	semidirect
64. #4085	C₂²	semidirect
65. #4085	C₂²	semidirect
66. #4084	C₂²	semidirect
69. #4083	C₂²	semidirect
70. #4083	C₂²	semidirect
71. #4082	C₂²	semidirect
72. #4081	C₂²	semidirect
73. #4076	C₂²	semidirect
74. #4076	C₂²	semidirect
76. #4075	C₂²	semidirect
77. C₄×C₂²⋊D₅	C₂²	semidirect
78. C₄×C₂²⋊D₅	C₂²	semidirect
79. C₂×#685	C₂²	semidirect
80. C₂×#685	C₂²	semidirect
81. #4070	C₂²	semidirect
82. #4070	C₂²	semidirect
83. #4044	C₂²	semidirect
84. #4044	C₂²	semidirect
85. #4044	C₂²	semidirect
86. #4044	C₂²	semidirect
87. #4044	C₂²	semidirect
88. #4043	C₂²	semidirect
89. #4043	C₂²	semidirect
90. #4042	C₂²	semidirect
91. #4042	C₂²	semidirect
92. #4042	C₂²	semidirect
93. #4042	C₂²	semidirect
94. #4042	C₂²	semidirect
95. #4042	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. #4040	C₂²	semidirect
107. #4040	C₂²	semidirect
108. #4040	C₂²	semidirect
109. #4040	C₂²	semidirect
110. #4040	C₂²	semidirect
111. #4040	C₂²	semidirect
112. #4040	C₂²	semidirect
113. #4039	C₂²	semidirect
114. #4039	C₂²	semidirect
115. #4039	C₂²	semidirect
116. #4038	C₂²	semidirect
117. #4038	C₂²	semidirect
118. #4036	C₂²	semidirect
119. #4035	C₂²	semidirect
120. #4034	C₂²	semidirect
121. #4034	C₂²	semidirect
122. #4033	C₂²	semidirect
123. #4032	C₂²	semidirect
126. #4031	C₂²	semidirect
127. #4031	C₂²	semidirect
128. #4031	C₂²	semidirect
129. #4031	C₂²	semidirect
130. #4031	C₂²	semidirect
131. #4031	C₂²	semidirect
132. #4031	C₂²	semidirect
134. #4030	C₂²	semidirect
135. #4030	C₂²	semidirect
136. #4030	C₂²	semidirect
137. #4030	C₂²	semidirect
138. #4030	C₂²	semidirect
140. #4029	C₂²	semidirect
141. #4029	C₂²	semidirect
142. #4029	C₂²	semidirect
143. #4029	C₂²	semidirect
144. #4029	C₂²	semidirect
149. #4028	C₂²	semidirect
150. #4028	C₂²	semidirect
151. #4028	C₂²	semidirect
152. #4028	C₂²	semidirect
153. #4027	C₂²	semidirect
154. #4027	C₂²	semidirect
155. #4027	C₂²	semidirect
156. #4027	C₂²	semidirect
157. D₅×C₂²⋊C₄	C₂²	semidirect
158. D₅×C₂²⋊C₄	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. #4024	C₂²	semidirect
169. #4023	C₂²	semidirect
170. #4023	C₂²	semidirect
171. #4022	C₂²	semidirect
172. #4022	C₂²	semidirect
173. #4021	C₂²	semidirect
174. #4021	C₂²	semidirect
175. #4021	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. #4018	C₂²	semidirect
182. #4018	C₂²	semidirect
183. #4018	C₂²	semidirect
184. #4018	C₂²	semidirect
185. #4018	C₂²	semidirect
186. C₄²×D₅	C₂²	semidirect
368. #542	D₅	semidirect
483. C₄⋊Q₈	C₂×D₅	semidirect
494. #126	C₂×D₅	semidirect
495. #126	C₂×D₅	semidirect
517. #124	C₂×D₅	semidirect
518. #124	C₂×D₅	semidirect
519. #124	C₂×D₅	semidirect
542. #123	C₂×D₅	semidirect
543. #123	C₂×D₅	semidirect
559. C₂²⋊Q₈	C₂×D₅	semidirect
560. C₂²⋊Q₈	C₂×D₅	semidirect
561. C₂²⋊Q₈	C₂×D₅	semidirect
593. C₄×Q₈	C₂×D₅	semidirect
607. C₄×D₄	C₂×D₅	semidirect
617. #117	C₂×D₅	semidirect
950. C₅	#3545	semidirect

Maximal subgroups

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

subgroup	index
C₅×#542	2
#66067	2
#66058	2
#66040	2
#66039	2
#66038	2
#66017	2
#66013	2
#66012	2
#66010	2
D₅×#124	2
#66004	2
#66001	2
#65996	2
#65988	2
#65987	2
#65981	2
#65980	2
#65978	2
#65971	2
#65964	2
#65962	2
#65947	2
#65939	2
#65916	2
#65914	2
#65890	2
#65884	2
#65866	2
#65861	2
#3545	5