Subgroups — #10618717

Order 640.

1052 conjugacy classes of subgroups.

The subgroup lattice has 970 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	#66042	C₂	1	1	yes	maximal, characteristic, complemented
3	#66042	C₂	1	1	yes	maximal, characteristic, complemented
4	#66041	C₂	1	1	yes	maximal, characteristic, complemented
5	#66040	C₂	1	1	yes	maximal, characteristic, complemented
6	#66014	C₂	1	1	yes	maximal, characteristic, complemented
7	#66013	C₂	1	1	yes	maximal, characteristic, complemented
8	#65994	C₂	1	1	yes	maximal, characteristic, complemented
9	#65994	C₂	1	1	yes	maximal, characteristic, complemented
10	#65993	C₂	1	1	yes	maximal, characteristic, complemented
11	#65992	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
13	#65984	C₂	1	1	yes	maximal, characteristic, complemented
14	#65976	C₂	1	1	yes	maximal, characteristic, complemented
15	#65973	C₂	1	1	yes	maximal, characteristic, complemented
16	#65972	C₂	1	1	yes	maximal, characteristic, complemented
17	#65968	C₂	1	1	yes	maximal, characteristic, complemented
18	#65923	C₂	1	1	yes	maximal, characteristic
19	#65921	C₂	1	1	yes	maximal, characteristic, complemented
20	#65891	C₂	1	1	yes	maximal, characteristic, complemented
21	#65890	C₂	1	1	yes	maximal, characteristic, complemented
22	#65879	C₂	1	1	yes	maximal, characteristic, complemented
23	#65875	C₂	1	1	yes	maximal, characteristic, complemented
24	#65865	C₂	1	1	yes	maximal, characteristic, complemented
25	#65863	C₂	1	1	yes	maximal, characteristic, complemented
26	#65862	C₂	1	1	yes	maximal, characteristic, complemented
27	D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
28	#65829	C₂	1	1	yes	maximal, characteristic, complemented
29	#65829	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#4029	C₂	1	1	yes	maximal, characteristic, complemented
31	#65820	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₅	C₂²	1	1	yes	characteristic
33	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
34	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
35	C₅×#126	C₂²	1	1	yes	characteristic, complemented
36	C₅×#126	C₂²	1	1	yes	characteristic, complemented
37	C₅×#124	C₂²	1	1	yes	characteristic, complemented
38	C₅×#123	C₂²	1	1	yes	characteristic
39	C₅×#123	C₂²	1	1	yes	characteristic, complemented
40	C₅×#123	C₂²	1	1	yes	characteristic, complemented
41	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₅×#120	C₂²	1	1	yes	characteristic
44	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
45	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
46	C₅×#117	C₂²	1	1	yes	characteristic, complemented
47	C₅×#117	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	#4099	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
53	#4092	C₂²	1	1	yes	characteristic, complemented
54	#4092	C₂²	1	1	yes	characteristic, complemented
55	#4092	C₂²	1	1	yes	characteristic, complemented
56	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
57	#4084	C₂²	1	1	yes	characteristic
58	#4084	C₂²	1	1	yes	characteristic
59	#4083	C₂²	1	1	yes	characteristic
60	#4083	C₂²	1	1	yes	characteristic
61	#4082	C₂²	1	1	yes	characteristic, complemented
62	#4081	C₂²	1	1	yes	characteristic
63	#4081	C₂²	1	1	yes	characteristic
64	#4081	C₂²	1	1	yes	characteristic, complemented
65	#4081	C₂²	1	1	yes	characteristic, complemented
66	D₄×Dic₅	C₂²	1	1	yes	characteristic
67	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
68	#4075	C₂²	1	1	yes	characteristic
69	#4075	C₂²	1	1	yes	characteristic, complemented
70	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
74	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
77	C₂×#685	C₂²	1	1	yes	characteristic
78	C₂×#685	C₂²	1	1	yes	characteristic, complemented
79	#4072	C₂²	1	1	yes	characteristic, complemented
80	#4072	C₂²	1	1	yes	characteristic, complemented
81	#4072	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
83	#4070	C₂²	1	1	yes	characteristic, complemented
84	#4070	C₂²	1	1	yes	characteristic, complemented
85	#4070	C₂²	1	1	yes	characteristic, complemented
86	C₂×#683	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	#4043	C₂²	1	1	yes	characteristic, complemented
91	#4043	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	#4042	C₂²	1	1	yes	characteristic, complemented
97	#4040	C₂²	1	1	yes	characteristic, complemented
98	#4040	C₂²	1	1	yes	characteristic, complemented
99	#4039	C₂²	1	1	yes	characteristic, complemented
100	#4038	C₂²	1	1	yes	characteristic, complemented
101	#4038	C₂²	1	1	yes	characteristic, complemented
102	#4038	C₂²	1	1	yes	characteristic, complemented
103	#4038	C₂²	1	1	yes	characteristic, complemented
104	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	#4036	C₂²	1	1	yes	characteristic, complemented
109	#4036	C₂²	1	1	yes	characteristic, complemented
110	#4036	C₂²	1	1	yes	characteristic, complemented
111	#4036	C₂²	1	1	yes	characteristic, complemented
112	#4035	C₂²	1	1	yes	characteristic, complemented
113	#4035	C₂²	1	1	yes	characteristic, complemented
114	#4035	C₂²	1	1	yes	characteristic, complemented
115	#4035	C₂²	1	1	yes	characteristic, complemented
116	#4035	C₂²	1	1	yes	characteristic, complemented
117	#4035	C₂²	1	1	yes	characteristic, complemented
118	#4033	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	#4031	C₂²	1	1	yes	characteristic, complemented
123	#4031	C₂²	1	1	yes	characteristic, complemented
124	#4030	C₂²	1	1	yes	characteristic
125	#4030	C₂²	1	1	yes	characteristic
126	#4029	C₂²	1	1	yes	characteristic
127	#4029	C₂²	1	1	yes	characteristic
128	#4029	C₂²	1	1	yes	characteristic
129	#4029	C₂²	1	1	yes	characteristic
130	#4029	C₂²	1	1	yes	characteristic
131	#4029	C₂²	1	1	yes	characteristic
132	#4029	C₂²	1	1	yes	characteristic, complemented
133	#4029	C₂²	1	1	yes	characteristic, complemented
134	#4029	C₂²	1	1	yes	characteristic, complemented
135	#4029	C₂²	1	1	yes	characteristic, complemented
136	#4029	C₂²	1	1	yes	characteristic, complemented
137	#4029	C₂²	1	1	yes	characteristic, complemented
138	#4029	C₂²	1	1	yes	characteristic, complemented
139	#4029	C₂²	1	1	yes	characteristic, complemented
140	#4027	C₂²	1	1	yes	characteristic
141	#4027	C₂²	1	1	yes	characteristic
142	#4027	C₂²	1	1	yes	characteristic
143	#4027	C₂²	1	1	yes	characteristic, complemented
144	#4027	C₂²	1	1	yes	characteristic, complemented
145	#4027	C₂²	1	1	yes	characteristic, complemented
146	#4027	C₂²	1	1	yes	characteristic, complemented
147	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
148	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
149	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
150	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	#4025	C₂²	1	1	yes	characteristic, complemented
154	#4025	C₂²	1	1	yes	characteristic, complemented
155	#4025	C₂²	1	1	yes	characteristic, complemented
156	#4025	C₂²	1	1	yes	characteristic, complemented
157	#4025	C₂²	1	1	yes	characteristic, complemented
158	#4025	C₂²	1	1	yes	characteristic, complemented
159	#4025	C₂²	1	1	yes	characteristic, complemented
160	#4025	C₂²	1	1	yes	characteristic, complemented
161	#4025	C₂²	1	1	yes	characteristic, complemented
162	#4025	C₂²	1	1	yes	characteristic, complemented
163	#4024	C₂²	1	1	yes	characteristic, complemented
164	#4024	C₂²	1	1	yes	characteristic, complemented
165	#4024	C₂²	1	1	yes	characteristic, complemented
166	#4024	C₂²	1	1	yes	characteristic, complemented
167	#4024	C₂²	1	1	yes	characteristic, complemented
168	#4023	C₂²	1	1	yes	characteristic, complemented
169	#4023	C₂²	1	1	yes	characteristic, complemented
170	#4023	C₂²	1	1	yes	characteristic, complemented
171	#4023	C₂²	1	1	yes	characteristic, complemented
172	#4023	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, complemented
176	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
177	#4018	C₂²	1	1	yes	characteristic, complemented
178	#4018	C₂²	1	1	yes	characteristic, complemented
179	#4018	C₂²	1	1	yes	characteristic, complemented
180	#4018	C₂²	1	1	yes	characteristic, complemented
181	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
182	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
183	#4016	C₂²	1	1	yes	characteristic, complemented
184	#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	#3491	—	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	C₂×C₅×Q₈	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	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₅	—	2	4	no	—
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	C₂²×Dic₅	C₂³	1	1	yes	characteristic
210	C₂²×Dic₅	C₂³	1	1	yes	characteristic
211	C₂²×Dic₅	C₂³	1	1	yes	characteristic
212	C₂²×Dic₅	C₂³	1	1	yes	characteristic
213	C₂²×Dic₅	C₂³	1	1	yes	characteristic
214	C₂²×Dic₅	C₂³	1	1	yes	characteristic
215	D₄×D₅	—	2	4	no	—
216	C₂×D₂₀	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₅	—	2	4	no	—
218	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
231	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
232	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
233	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
234	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
253	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₄²×C₅	C₂³	1	1	yes	characteristic
257	C₄²×C₅	C₂³	1	1	yes	characteristic
258	C₄²×C₅	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
275	#685	C₂³	1	1	yes	characteristic
276	#685	C₂³	1	1	yes	characteristic
277	#685	C₂³	1	1	yes	characteristic
278	#685	C₂³	1	1	yes	characteristic
279	#685	C₂³	1	1	yes	characteristic
280	#685	C₂³	1	1	yes	characteristic
281	#685	C₂³	1	1	yes	characteristic
282	#685	C₂³	1	1	yes	characteristic
283	#685	C₂³	1	1	yes	characteristic
284	#685	C₂³	1	1	yes	characteristic
285	#685	C₂³	1	1	yes	characteristic
286	#685	C₂³	1	1	yes	characteristic
287	#685	C₂³	1	1	yes	characteristic
288	#685	C₂³	1	1	yes	characteristic
289	#685	C₂³	1	1	yes	characteristic
290	#685	C₂³	1	1	yes	characteristic
291	#685	C₂³	1	1	yes	characteristic
292	#685	C₂³	1	1	yes	characteristic
293	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
295	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
296	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
307	#683	C₂³	1	1	yes	characteristic
308	#683	C₂³	1	1	yes	characteristic
309	#683	C₂³	1	1	yes	characteristic
310	#683	C₂³	1	1	yes	characteristic
311	#683	C₂³	1	1	yes	characteristic
312	#683	C₂³	1	1	yes	characteristic
313	#683	C₂³	1	1	yes	characteristic
314	#683	C₂³	1	1	yes	characteristic
315	#683	C₂³	1	1	yes	characteristic
316	#683	C₂³	1	1	yes	characteristic
317	#683	C₂³	1	1	yes	characteristic
318	#683	C₂³	1	1	yes	characteristic
319	#683	C₂³	1	1	yes	characteristic
320	#683	C₂³	1	1	yes	characteristic
321	#683	C₂³	1	1	yes	characteristic
322	#683	C₂³	1	1	yes	characteristic
323	#683	C₂³	1	1	yes	characteristic
324	#683	C₂³	1	1	yes	characteristic
325	#683	C₂³	1	1	yes	characteristic
326	#683	C₂³	1	1	yes	characteristic
327	#683	C₂³	1	1	yes	characteristic
328	#683	C₂³	1	1	yes	characteristic
329	#683	C₂³	1	1	yes	characteristic
330	#683	C₂³	1	1	yes	characteristic
331	#683	C₂³	1	1	yes	characteristic
332	#683	C₂³	1	1	yes	characteristic
333	C₄×Dic₅	C₂³	1	1	yes	characteristic
334	C₄×Dic₅	C₂³	1	1	yes	characteristic
335	C₄×Dic₅	C₂³	1	1	yes	characteristic
336	C₄×Dic₅	C₂³	1	1	yes	characteristic
337	C₄×Dic₅	C₂³	1	1	yes	characteristic
338	C₄×Dic₅	C₂³	1	1	yes	characteristic
339	C₄×Dic₅	C₂³	1	1	yes	characteristic
340	C₄×Dic₅	C₂³	1	1	yes	characteristic
341	C₄×Dic₅	C₂³	1	1	yes	characteristic
342	C₄×Dic₅	C₂³	1	1	yes	characteristic
343	C₄×Dic₅	C₂³	1	1	yes	characteristic
344	C₄×Dic₅	C₂³	1	1	yes	characteristic
345	C₄×Dic₅	C₂³	1	1	yes	characteristic
346	#552	—	5	1	no	—
347	#552	—	5	1	no	—
348	#552	—	5	1	no	—
349	#552	—	5	1	no	—
350	#552	—	5	1	no	—
351	#552	—	5	1	no	—
352	#552	—	5	1	no	—
353	#552	—	5	1	no	—
354	#551	—	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	#551	D₅	1	1	yes	characteristic, complemented
362	#543	—	5	1	no	—
363	#539	—	5	1	no	—
364	#539	—	5	1	no	—
365	#539	—	5	1	no	—
366	#539	—	5	1	no	—
367	#534	—	5	1	no	—
368	#529	—	5	1	no	—
369	#529	—	5	1	no	—
370	#529	—	5	1	no	—
371	#529	—	5	1	no	—
372	C₂×#123	—	5	1	no	—
373	C₂×#123	—	5	1	no	—
374	#518	—	5	1	no	—
375	#518	—	5	1	no	—
376	C₂×#117	—	5	1	no	—
377	C₂³×C₅	—	2	2	no	—
378	C₂³×C₅	—	4	1	no	—
379	C₂³×C₅	—	4	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	—	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	#41	1	4	yes	—
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	C₅×Q₈	—	4	1	no	—
394	C₅×D₄	—	2	2	no	—
395	C₅×D₄	—	4	1	no	—
396	C₅×D₄	—	4	1	no	—
397	C₂×C₄×C₅	—	2	2	no	—
398	C₂×C₄×C₅	—	4	1	no	—
399	C₂×C₄×C₅	—	4	1	no	—
400	C₂×C₄×C₅	—	4	1	no	—
401	C₂×C₄×C₅	—	4	1	no	—
402	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
405	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
406	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
407	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
413	C₂²⋊D₅	—	2	2	no	—
414	C₂²⋊D₅	—	2	2	no	—
415	C₂²⋊D₅	—	2	2	no	—
416	C₂²⋊D₅	—	2	2	no	—
417	C₂²⋊D₅	—	2	2	no	—
418	C₂²⋊D₅	—	2	2	no	—
419	C₂²⋊D₅	—	4	1	no	—
420	C₂²⋊D₅	—	4	1	no	—
421	C₂×Dic₅	—	2	2	no	—
422	C₂×Dic₅	—	2	2	no	—
423	C₂×Dic₅	—	4	1	no	—
424	C₂×Dic₅	—	4	1	no	—
425	C₂×Dic₅	—	4	1	no	—
426	C₂×Dic₅	—	4	1	no	—
427	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
433	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
434	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
435	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
436	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
437	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
440	D₂₀	—	2	2	no	—
441	C₄×D₅	—	2	2	no	—
442	C₄×D₅	—	2	2	no	—
443	C₄×D₅	—	2	2	no	—
444	C₄×D₅	—	2	2	no	—
445	C₄×D₅	—	2	2	no	—
446	C₄×D₅	—	4	1	no	—
447	C₄×D₅	—	4	1	no	—
448	C₄×D₅	—	4	1	no	—
449	C₄×D₅	—	4	1	no	—
450	C₄×D₅	—	4	1	no	—
451	C₄×D₅	—	4	1	no	—
452	C₄×D₅	—	4	1	no	—
453	C₄×D₅	—	4	1	no	—
454	Dic₁₀	—	4	1	no	—
455	Dic₁₀	—	4	1	no	—
456	Dic₁₀	—	4	1	no	—
457	C₂²×D₄	—	5	1	no	—
458	C₂²×D₄	—	5	1	no	—
459	C₂³×C₄	—	5	1	no	—
460	#126	—	5	1	no	—
461	#126	—	5	1	no	—
462	#126	—	5	1	no	—
463	#126	—	5	1	no	—
464	#126	—	5	1	no	—
465	#126	—	5	1	no	—
466	#126	—	5	1	no	—
467	#126	—	5	1	no	—
468	#126	—	5	1	no	—
469	#126	—	5	1	no	—
470	#126	—	5	1	no	—
471	#126	—	5	1	no	—
472	#126	—	5	1	no	—
473	#126	—	5	1	no	—
474	#126	C₂×D₅	1	1	yes	characteristic, complemented
475	#126	C₂×D₅	1	1	yes	characteristic, complemented
476	#125	—	5	1	no	—
477	#125	—	5	1	no	—
478	#125	—	5	1	no	—
479	#125	—	5	1	no	—
480	#125	—	5	1	no	—
481	#125	—	5	1	no	—
482	#125	—	5	1	no	—
483	#125	—	5	1	no	—
484	#125	—	5	1	no	—
485	#125	—	5	1	no	—
486	#125	—	5	1	no	—
487	#125	—	5	1	no	—
488	#124	—	5	1	no	—
489	#124	—	5	1	no	—
490	#124	—	5	1	no	—
491	#124	C₂×D₅	1	1	yes	characteristic, complemented
492	#123	—	5	1	no	—
493	#123	—	5	1	no	—
494	#123	—	5	1	no	—
495	#123	—	5	1	no	—
496	#123	—	5	1	no	—
497	#123	—	5	1	no	—
498	#123	—	5	1	no	—
499	#123	—	5	1	no	—
500	#123	—	5	1	no	—
501	#123	—	5	1	no	—
502	#123	—	5	1	no	—
503	#123	—	5	1	no	—
504	#123	—	5	1	no	—
505	#123	—	5	1	no	—
506	#123	—	5	1	no	—
507	#123	—	5	1	no	—
508	#123	—	5	1	no	—
509	#123	—	5	1	no	—
510	#123	—	5	1	no	—
511	#123	—	5	1	no	—
512	#123	—	5	1	no	—
513	#123	—	5	1	no	—
514	#123	—	5	1	no	—
515	#123	—	5	1	no	—
516	#123	—	5	1	no	—
517	#123	C₂×D₅	1	1	yes	characteristic
518	#123	C₂×D₅	1	1	yes	characteristic, complemented
519	#123	C₂×D₅	1	1	yes	characteristic, complemented
520	C₂²⋊Q₈	—	5	1	no	—
521	C₂²⋊Q₈	—	5	1	no	—
522	C₂²⋊Q₈	—	5	1	no	—
523	C₂²⋊Q₈	—	5	1	no	—
524	C₂²⋊Q₈	—	5	1	no	—
525	C₂²⋊Q₈	—	5	1	no	—
526	C₂²⋊Q₈	—	5	1	no	—
527	C₂²⋊Q₈	—	5	1	no	—
528	C₂²⋊Q₈	—	5	1	no	—
529	C₂²⋊Q₈	—	5	1	no	—
530	C₂²⋊Q₈	—	5	1	no	—
531	C₂²⋊Q₈	—	5	1	no	—
532	C₂²⋊Q₈	—	5	1	no	—
533	C₂²⋊Q₈	—	5	1	no	—
534	C₂²⋊Q₈	—	5	1	no	—
535	C₂²⋊Q₈	—	5	1	no	—
536	C₂²⋊Q₈	—	5	1	no	—
537	C₂²⋊Q₈	—	5	1	no	—
538	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
539	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
540	#121	—	5	1	no	—
541	#121	—	5	1	no	—
542	#121	—	5	1	no	—
543	#121	—	5	1	no	—
544	#120	—	5	1	no	—
545	#120	—	5	1	no	—
546	#120	—	5	1	no	—
547	#120	C₂×D₅	1	1	yes	characteristic
548	C₄×Q₈	—	5	1	no	—
549	C₄×Q₈	—	5	1	no	—
550	C₄×Q₈	—	5	1	no	—
551	C₄×Q₈	—	5	1	no	—
552	C₄×D₄	—	5	1	no	—
553	C₄×D₄	—	5	1	no	—
554	C₄×D₄	—	5	1	no	—
555	C₄×D₄	—	5	1	no	—
556	C₄×D₄	—	5	1	no	—
557	C₄×D₄	—	5	1	no	—
558	C₄×D₄	—	5	1	no	—
559	C₄×D₄	—	5	1	no	—
560	C₄×D₄	—	5	1	no	—
561	C₄×D₄	—	5	1	no	—
562	C₄×D₄	—	5	1	no	—
563	C₄×D₄	—	5	1	no	—
564	C₄×D₄	—	5	1	no	—
565	C₄×D₄	—	5	1	no	—
566	C₄×D₄	—	5	1	no	—
567	C₄×D₄	—	5	1	no	—
568	C₄×D₄	—	5	1	no	—
569	C₄×D₄	—	5	1	no	—
570	C₄×D₄	C₂×D₅	1	1	yes	characteristic
571	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
572	#117	—	5	1	no	—
573	#117	—	5	1	no	—
574	#117	—	5	1	no	—
575	#117	—	5	1	no	—
576	#117	—	5	1	no	—
577	#117	—	5	1	no	—
578	#117	—	5	1	no	—
579	#117	—	5	1	no	—
580	#117	—	5	1	no	—
581	#117	—	5	1	no	—
582	#117	—	5	1	no	—
583	#117	—	5	1	no	—
584	#117	—	5	1	no	—
585	#117	—	5	1	no	—
586	#117	—	5	1	no	—
587	#117	—	5	1	no	—
588	#117	—	5	1	no	—
589	#117	—	5	1	no	—
590	#117	C₂×D₅	1	1	yes	characteristic, complemented
591	#117	C₂×D₅	1	1	yes	characteristic, complemented
592	C₂×C₄⋊C₄	—	5	1	no	—
593	C₂×C₄⋊C₄	—	5	1	no	—
594	C₂×C₄⋊C₄	—	5	1	no	—
595	C₂×C₄⋊C₄	—	5	1	no	—
596	C₂×C₄⋊C₄	—	5	1	no	—
597	C₂×C₄⋊C₄	—	5	1	no	—
598	C₂×C₂²⋊C₄	—	5	1	no	—
599	C₂×C₂²⋊C₄	—	5	1	no	—
600	C₂×C₂²⋊C₄	—	5	1	no	—
601	C₂×C₂²⋊C₄	—	5	1	no	—
602	C₂×C₂²⋊C₄	—	5	1	no	—
603	C₂×C₂²⋊C₄	—	5	1	no	—
604	C₂×C₂²⋊C₄	—	5	1	no	—
605	C₂×C₂²⋊C₄	—	5	1	no	—
606	C₂×C₂²⋊C₄	—	5	1	no	—
607	C₂×C₂²⋊C₄	—	5	1	no	—
608	C₂×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
609	C₂×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
610	C₂×C₄²	—	5	1	no	—
611	C₂×C₄²	—	5	1	no	—
612	C₂²×C₅	—	2	1	no	—
613	C₂²×C₅	—	2	1	no	—
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	2	1	no	—
617	C₂²×C₅	—	2	1	no	—
618	C₂²×C₅	—	2	1	no	—
619	C₂²×C₅	—	2	1	no	—
620	C₂²×C₅	—	2	1	no	—
621	C₂²×C₅	—	2	1	no	—
622	C₂²×C₅	—	2	1	no	—
623	C₂²×C₅	—	8	2	no	—
624	C₂²×C₅	C₂×#41	1	2	yes	—
625	C₂²×C₅	C₂⁵	1	1	yes	characteristic
626	C₂×D₅	—	2	1	no	—
627	C₂×D₅	—	2	1	no	—
628	C₂×D₅	—	2	1	no	—
629	C₂×D₅	—	2	1	no	—
630	C₂×D₅	—	2	1	no	—
631	C₂×D₅	—	2	1	no	—
632	C₂×D₅	—	2	1	no	—
633	C₂×D₅	—	4	4	no	—
634	C₂×D₅	—	8	2	no	—
635	C₂×D₅	C₂×#41	1	2	yes	—
636	C₂×D₅	C₂×#41	1	2	yes	—
637	C₄×C₅	—	2	1	no	—
638	C₄×C₅	—	2	1	no	—
639	C₄×C₅	—	2	1	no	—
640	C₄×C₅	—	2	1	no	—
641	C₄×C₅	—	2	1	no	—
642	C₄×C₅	—	2	1	no	—
643	C₄×C₅	—	2	1	no	—
644	C₄×C₅	—	2	1	no	—
645	C₄×C₅	—	2	1	no	—
646	C₄×C₅	—	2	1	no	—
647	C₄×C₅	—	2	1	no	—
648	Dic₅	—	2	1	no	—
649	Dic₅	—	2	1	no	—
650	Dic₅	—	2	1	no	—
651	Dic₅	—	2	1	no	—
652	Dic₅	—	2	1	no	—
653	Dic₅	—	2	1	no	—
654	Dic₅	—	2	1	no	—
655	Dic₅	—	2	1	no	—
656	Dic₅	—	2	1	no	—
657	Dic₅	—	2	1	no	—
658	Dic₅	—	2	1	no	—
659	Dic₅	—	2	1	no	—
660	Dic₅	—	2	1	no	—
661	C₂⁴	—	5	1	no	—
662	C₂⁴	—	5	1	no	—
663	C₂⁴	C₂²×D₅	1	1	yes	characteristic
664	C₂×Q₈	—	5	1	no	—
665	C₂×Q₈	—	5	1	no	—
666	C₂×Q₈	—	5	1	no	—
667	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
668	C₂×D₄	—	5	1	no	—
669	C₂×D₄	—	5	1	no	—
670	C₂×D₄	—	5	1	no	—
671	C₂×D₄	—	5	1	no	—
672	C₂×D₄	—	5	1	no	—
673	C₂×D₄	—	5	1	no	—
674	C₂×D₄	—	5	1	no	—
675	C₂×D₄	—	5	1	no	—
676	C₂×D₄	—	5	1	no	—
677	C₂×D₄	—	10	4	no	—
678	C₂×D₄	—	10	4	no	—
679	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
680	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
681	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
682	C₂²×C₄	—	5	1	no	—
683	C₂²×C₄	—	5	1	no	—
684	C₂²×C₄	—	5	1	no	—
685	C₂²×C₄	—	5	1	no	—
686	C₂²×C₄	—	5	1	no	—
687	C₂²×C₄	—	5	1	no	—
688	C₂²×C₄	—	5	1	no	—
689	C₂²×C₄	—	5	1	no	—
690	C₂²×C₄	—	5	1	no	—
691	C₂²×C₄	—	5	1	no	—
692	C₂²×C₄	—	5	1	no	—
693	C₂²×C₄	—	5	1	no	—
694	C₂²×C₄	—	5	1	no	—
695	C₂²×C₄	—	5	1	no	—
696	C₂²×C₄	—	5	1	no	—
697	C₂²×C₄	—	5	1	no	—
698	C₂²×C₄	—	5	1	no	—
699	C₂²×C₄	—	5	1	no	—
700	C₂²×C₄	—	5	1	no	—
701	C₂²×C₄	—	10	4	no	—
702	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
703	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
705	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
706	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
707	C₄⋊C₄	—	5	1	no	—
708	C₄⋊C₄	—	5	1	no	—
709	C₄⋊C₄	—	5	1	no	—
710	C₄⋊C₄	—	5	1	no	—
711	C₄⋊C₄	—	5	1	no	—
712	C₄⋊C₄	—	5	1	no	—
713	C₄⋊C₄	—	5	1	no	—
714	C₄⋊C₄	—	5	1	no	—
715	C₄⋊C₄	—	5	1	no	—
716	C₄⋊C₄	—	5	1	no	—
717	C₄⋊C₄	—	5	1	no	—
718	C₄⋊C₄	—	5	1	no	—
719	C₄⋊C₄	—	5	1	no	—
720	C₄⋊C₄	—	5	1	no	—
721	C₄⋊C₄	—	5	1	no	—
722	C₄⋊C₄	—	5	1	no	—
723	C₄⋊C₄	—	5	1	no	—
724	C₄⋊C₄	—	5	1	no	—
725	C₄⋊C₄	—	5	1	no	—
726	C₄⋊C₄	—	5	1	no	—
727	C₄⋊C₄	—	5	1	no	—
728	C₄⋊C₄	—	5	1	no	—
729	C₄⋊C₄	—	5	1	no	—
730	C₄⋊C₄	—	5	1	no	—
731	C₄⋊C₄	—	5	1	no	—
732	C₄⋊C₄	—	5	1	no	—
733	C₄⋊C₄	—	5	1	no	—
734	C₄⋊C₄	—	5	1	no	—
735	C₄⋊C₄	—	5	1	no	—
736	C₄⋊C₄	—	5	1	no	—
737	C₄⋊C₄	—	5	1	no	—
738	C₄⋊C₄	—	5	1	no	—
739	C₄⋊C₄	—	5	1	no	—
740	C₄⋊C₄	—	5	1	no	—
741	C₄⋊C₄	—	5	1	no	—
742	C₄⋊C₄	—	5	1	no	—
743	C₄⋊C₄	—	5	1	no	—
744	C₄⋊C₄	—	5	1	no	—
745	C₄⋊C₄	—	5	1	no	—
746	C₄⋊C₄	—	5	1	no	—
747	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
748	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
751	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
752	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
754	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
755	C₂²⋊C₄	—	5	1	no	—
756	C₂²⋊C₄	—	5	1	no	—
757	C₂²⋊C₄	—	5	1	no	—
758	C₂²⋊C₄	—	5	1	no	—
759	C₂²⋊C₄	—	5	1	no	—
760	C₂²⋊C₄	—	5	1	no	—
761	C₂²⋊C₄	—	5	1	no	—
762	C₂²⋊C₄	—	5	1	no	—
763	C₂²⋊C₄	—	5	1	no	—
764	C₂²⋊C₄	—	5	1	no	—
765	C₂²⋊C₄	—	5	1	no	—
766	C₂²⋊C₄	—	5	1	no	—
767	C₂²⋊C₄	—	5	1	no	—
768	C₂²⋊C₄	—	5	1	no	—
769	C₂²⋊C₄	—	5	1	no	—
770	C₂²⋊C₄	—	5	1	no	—
771	C₂²⋊C₄	—	5	1	no	—
772	C₂²⋊C₄	—	5	1	no	—
773	C₂²⋊C₄	—	5	1	no	—
774	C₂²⋊C₄	—	5	1	no	—
775	C₂²⋊C₄	—	5	1	no	—
776	C₂²⋊C₄	—	5	1	no	—
777	C₂²⋊C₄	—	5	1	no	—
778	C₂²⋊C₄	—	5	1	no	—
779	C₂²⋊C₄	—	5	1	no	—
780	C₂²⋊C₄	—	5	1	no	—
781	C₂²⋊C₄	—	5	1	no	—
782	C₂²⋊C₄	—	5	1	no	—
783	C₂²⋊C₄	—	5	1	no	—
784	C₂²⋊C₄	—	5	1	no	—
785	C₂²⋊C₄	—	5	1	no	—
786	C₂²⋊C₄	—	5	1	no	—
787	C₂²⋊C₄	—	5	1	no	—
788	C₂²⋊C₄	—	5	1	no	—
789	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
790	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
791	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
792	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
803	C₄²	—	5	1	no	—
804	C₄²	—	5	1	no	—
805	C₄²	—	5	1	no	—
806	C₄²	—	5	1	no	—
807	C₄²	—	5	1	no	—
808	C₄²	—	5	1	no	—
809	C₄²	—	5	1	no	—
810	C₄²	—	5	1	no	—
811	C₄²	—	5	1	no	—
812	C₄²	—	5	1	no	—
813	C₄²	—	5	1	no	—
814	C₄²	—	5	1	no	—
815	C₄²	—	5	1	no	—
816	C₄²	C₂²×D₅	1	1	yes	characteristic
817	C₄²	C₂²×D₅	1	1	yes	characteristic
818	C₄²	C₂²×D₅	1	1	yes	characteristic
819	C₂×C₅	—	2	2	no	—
820	C₂×C₅	—	4	1	no	—
821	C₂×C₅	—	4	1	no	—
822	C₂×C₅	—	4	1	no	—
823	C₂×C₅	C₂²×#41	1	1	yes	characteristic
824	C₂×C₅	#585	1	1	yes	characteristic
825	C₂×C₅	#585	1	1	yes	characteristic
826	D₅	—	2	2	no	—
827	D₅	—	2	2	no	—
828	D₅	—	4	1	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	1	no	—
832	C₂³	—	5	1	no	—
833	C₂³	—	5	1	no	—
834	C₂³	—	5	4	no	—
835	C₂³	—	5	1	no	—
836	C₂³	—	10	2	no	—
837	C₂³	—	20	1	no	—
838	C₂³	—	20	1	no	—
839	C₂³	—	20	1	no	—
840	C₂³	—	20	1	no	—
841	C₂³	C₂³×D₅	1	1	yes	characteristic
842	C₂³	C₂³×D₅	1	1	yes	characteristic
843	C₂³	C₂³×D₅	1	1	yes	characteristic
844	C₂³	C₂³×D₅	1	1	yes	characteristic
845	Q₈	—	4	1	no	—
846	Q₈	—	20	1	no	—
847	Q₈	—	20	1	no	—
848	Q₈	—	20	1	no	—
849	D₄	—	2	2	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	10	2	no	—
853	D₄	—	10	2	no	—
854	D₄	—	10	2	no	—
855	D₄	—	10	2	no	—
856	D₄	—	10	2	no	—
857	D₄	—	10	2	no	—
858	D₄	—	10	2	no	—
859	D₄	—	20	1	no	—
860	D₄	—	20	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	5	1	no	—
867	C₂×C₄	—	5	1	no	—
868	C₂×C₄	—	5	1	no	—
869	C₂×C₄	—	5	1	no	—
870	C₂×C₄	—	5	1	no	—
871	C₂×C₄	—	5	1	no	—
872	C₂×C₄	—	5	1	no	—
873	C₂×C₄	—	5	1	no	—
874	C₂×C₄	—	5	1	no	—
875	C₂×C₄	—	5	1	no	—
876	C₂×C₄	—	5	1	no	—
877	C₂×C₄	—	5	1	no	—
878	C₂×C₄	—	5	1	no	—
879	C₂×C₄	—	10	2	no	—
880	C₂×C₄	—	10	2	no	—
881	C₂×C₄	—	10	2	no	—
882	C₂×C₄	—	10	2	no	—
883	C₂×C₄	—	10	2	no	—
884	C₂×C₄	—	10	2	no	—
885	C₂×C₄	—	10	2	no	—
886	C₂×C₄	—	20	1	no	—
887	C₂×C₄	—	20	1	no	—
888	C₂×C₄	—	20	1	no	—
889	C₂×C₄	—	20	1	no	—
890	C₂×C₄	—	20	1	no	—
891	C₂×C₄	—	20	1	no	—
892	C₂×C₄	—	20	1	no	—
893	C₂×C₄	—	20	1	no	—
894	C₂×C₄	—	20	1	no	—
895	C₂×C₄	—	20	1	no	—
896	C₂×C₄	—	20	1	no	—
897	C₂×C₄	—	20	1	no	—
898	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
899	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
908	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
909	C₅	#3491	1	1	yes	characteristic, complemented, Sylow
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	5	2	no	—
922	C₂²	—	5	2	no	—
923	C₂²	—	8	2	no	—
924	C₂²	—	10	1	no	—
925	C₂²	—	10	1	no	—
926	C₂²	—	10	1	no	—
927	C₂²	—	10	1	no	—
928	C₂²	—	10	1	no	—
929	C₂²	—	10	1	no	—
930	C₂²	—	10	1	no	—
931	C₂²	—	20	4	no	—
932	C₂²	—	40	2	no	—
933	C₂²	D₅×#41	1	2	yes	—
934	C₂²	C₂⁴×D₅	1	1	yes	characteristic
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	1	no	—
945	C₄	—	2	1	no	—
946	C₄	—	10	1	no	—
947	C₄	—	10	1	no	—
948	C₄	—	10	1	no	—
949	C₄	—	10	1	no	—
950	C₄	—	10	1	no	—
951	C₄	—	10	1	no	—
952	C₄	—	10	1	no	—
953	C₄	—	10	1	no	—
954	C₄	—	10	1	no	—
955	C₄	—	10	1	no	—
956	C₄	—	10	1	no	—
957	C₄	—	10	1	no	—
958	C₄	—	10	1	no	—
959	C₂	—	2	2	no	—
960	C₂	—	4	1	no	—
961	C₂	—	4	1	no	—
962	C₂	—	4	1	no	—
963	C₂	—	10	2	no	—
964	C₂	—	10	2	no	—
965	C₂	—	20	1	no	—
966	C₂	C₂×D₅×#41	1	1	yes	characteristic
967	C₂	#66283	1	1	yes	characteristic
968	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#551	C₂
prime radical	#65923	C₂
hypercenter	#551	D₅
hypocenter	C₅	#3491
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. #66042	C₂	semidirect
3. #66042	C₂	semidirect
4. #66041	C₂	semidirect
5. #66040	C₂	semidirect
6. #66014	C₂	semidirect
7. #66013	C₂	semidirect
8. #65994	C₂	semidirect
9. #65994	C₂	semidirect
10. #65993	C₂	semidirect
11. #65992	C₂	semidirect
12. D₅×#123	C₂	semidirect
13. #65984	C₂	semidirect
14. #65976	C₂	semidirect
15. #65973	C₂	semidirect
16. #65972	C₂	semidirect
17. #65968	C₂	semidirect
19. #65921	C₂	semidirect
20. #65891	C₂	semidirect
21. #65890	C₂	semidirect
22. #65879	C₂	semidirect
23. #65875	C₂	semidirect
24. #65865	C₂	semidirect
25. #65863	C₂	semidirect
26. #65862	C₂	semidirect
27. D₅×#117	C₂	semidirect
28. #65829	C₂	semidirect
29. #65829	C₂	semidirect
30. C₂×#4029	C₂	semidirect
31. #65820	C₂	semidirect
35. C₅×#126	C₂²	semidirect
36. C₅×#126	C₂²	semidirect
37. C₅×#124	C₂²	semidirect
39. C₅×#123	C₂²	semidirect
40. C₅×#123	C₂²	semidirect
41. C₅×C₂²⋊Q₈	C₂²	semidirect
42. C₅×C₂²⋊Q₈	C₂²	semidirect
45. C₄×C₅×D₄	C₂²	semidirect
46. C₅×#117	C₂²	semidirect
47. C₅×#117	C₂²	semidirect
48. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
49. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
51. C₂×C₂²⋊Dic₅	C₂²	semidirect
52. C₂×C₂²⋊Dic₅	C₂²	semidirect
53. #4092	C₂²	semidirect
54. #4092	C₂²	semidirect
55. #4092	C₂²	semidirect
56. Q₈×Dic₅	C₂²	semidirect
61. #4082	C₂²	semidirect
64. #4081	C₂²	semidirect
65. #4081	C₂²	semidirect
67. D₄×Dic₅	C₂²	semidirect
69. #4075	C₂²	semidirect
73. C₄×C₂²⋊D₅	C₂²	semidirect
74. C₄×C₂²⋊D₅	C₂²	semidirect
75. C₄×C₂²⋊D₅	C₂²	semidirect
76. C₄×C₂²⋊D₅	C₂²	semidirect
78. C₂×#685	C₂²	semidirect
79. #4072	C₂²	semidirect
80. #4072	C₂²	semidirect
81. #4072	C₂²	semidirect
82. C₂×C₄⋊Dic₅	C₂²	semidirect
83. #4070	C₂²	semidirect
84. #4070	C₂²	semidirect
85. #4070	C₂²	semidirect
86. C₂×#683	C₂²	semidirect
87. #4044	C₂²	semidirect
88. #4044	C₂²	semidirect
89. #4044	C₂²	semidirect
90. #4043	C₂²	semidirect
91. #4043	C₂²	semidirect
92. #4042	C₂²	semidirect
93. #4042	C₂²	semidirect
94. #4042	C₂²	semidirect
95. #4042	C₂²	semidirect
96. #4042	C₂²	semidirect
97. #4040	C₂²	semidirect
98. #4040	C₂²	semidirect
99. #4039	C₂²	semidirect
100. #4038	C₂²	semidirect
101. #4038	C₂²	semidirect
102. #4038	C₂²	semidirect
103. #4038	C₂²	semidirect
104. D₅×C₄⋊C₄	C₂²	semidirect
105. D₅×C₄⋊C₄	C₂²	semidirect
106. D₅×C₄⋊C₄	C₂²	semidirect
107. D₅×C₄⋊C₄	C₂²	semidirect
108. #4036	C₂²	semidirect
109. #4036	C₂²	semidirect
110. #4036	C₂²	semidirect
111. #4036	C₂²	semidirect
112. #4035	C₂²	semidirect
113. #4035	C₂²	semidirect
114. #4035	C₂²	semidirect
115. #4035	C₂²	semidirect
116. #4035	C₂²	semidirect
117. #4035	C₂²	semidirect
118. #4033	C₂²	semidirect
121. #4032	C₂²	semidirect
122. #4031	C₂²	semidirect
123. #4031	C₂²	semidirect
132. #4029	C₂²	semidirect
133. #4029	C₂²	semidirect
134. #4029	C₂²	semidirect
135. #4029	C₂²	semidirect
136. #4029	C₂²	semidirect
137. #4029	C₂²	semidirect
138. #4029	C₂²	semidirect
139. #4029	C₂²	semidirect
143. #4027	C₂²	semidirect
144. #4027	C₂²	semidirect
145. #4027	C₂²	semidirect
146. #4027	C₂²	semidirect
150. D₅×C₂²⋊C₄	C₂²	semidirect
151. D₅×C₂²⋊C₄	C₂²	semidirect
152. D₅×C₂²⋊C₄	C₂²	semidirect
153. #4025	C₂²	semidirect
154. #4025	C₂²	semidirect
155. #4025	C₂²	semidirect
156. #4025	C₂²	semidirect
157. #4025	C₂²	semidirect
158. #4025	C₂²	semidirect
159. #4025	C₂²	semidirect
160. #4025	C₂²	semidirect
161. #4025	C₂²	semidirect
162. #4025	C₂²	semidirect
163. #4024	C₂²	semidirect
164. #4024	C₂²	semidirect
165. #4024	C₂²	semidirect
166. #4024	C₂²	semidirect
167. #4024	C₂²	semidirect
168. #4023	C₂²	semidirect
169. #4023	C₂²	semidirect
170. #4023	C₂²	semidirect
171. #4023	C₂²	semidirect
172. #4023	C₂²	semidirect
173. #4023	C₂²	semidirect
174. #4023	C₂²	semidirect
175. #4022	C₂²	semidirect
176. C₄×D₂₀	C₂²	semidirect
177. #4018	C₂²	semidirect
178. #4018	C₂²	semidirect
179. #4018	C₂²	semidirect
180. #4018	C₂²	semidirect
181. C₄²×D₅	C₂²	semidirect
182. C₄²×D₅	C₂²	semidirect
183. #4016	C₂²	semidirect
184. #4016	C₂²	semidirect
185. C₄×Dic₁₀	C₂²	semidirect
186. C₄×Dic₁₀	C₂²	semidirect
361. #551	D₅	semidirect
474. #126	C₂×D₅	semidirect
475. #126	C₂×D₅	semidirect
491. #124	C₂×D₅	semidirect
518. #123	C₂×D₅	semidirect
519. #123	C₂×D₅	semidirect
538. C₂²⋊Q₈	C₂×D₅	semidirect
539. C₂²⋊Q₈	C₂×D₅	semidirect
571. C₄×D₄	C₂×D₅	semidirect
590. #117	C₂×D₅	semidirect
591. #117	C₂×D₅	semidirect
608. C₂×C₂²⋊C₄	C₂×D₅	semidirect
609. C₂×C₂²⋊C₄	C₂×D₅	semidirect
909. C₅	#3491	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
#66042	2
#66041	2
#66040	2
#66014	2
#66013	2
#65994	2
#65993	2
#65992	2
D₅×#123	2
#65984	2
#65976	2
#65973	2
#65972	2
#65968	2
#65923	2
#65921	2
#65891	2
#65890	2
#65879	2
#65875	2
#65865	2
#65863	2
#65862	2
D₅×#117	2
#65829	2
C₂×#4029	2
#65820	2
#3491	5