Subgroups — #10617957

Order 640.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	#66167	C₂	1	1	yes	maximal, characteristic, complemented
3	#66159	C₂	1	1	yes	maximal, characteristic, complemented
4	#66125	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#4070	C₂	1	1	yes	maximal, characteristic, complemented
6	#65996	C₂	1	2	yes	maximal, complemented
7	#65994	C₂	1	2	yes	maximal, complemented
8	#65980	C₂	1	2	yes	maximal, complemented
9	#65970	C₂	1	2	yes	maximal, complemented
10	#65955	C₂	1	2	yes	maximal, complemented
11	#65935	C₂	1	2	yes	maximal, complemented
12	#65927	C₂	1	2	yes	maximal, complemented
13	#65927	C₂	1	2	yes	maximal, complemented
14	#65899	C₂	1	1	yes	maximal, characteristic, complemented
15	#65886	C₂	1	1	yes	maximal, characteristic, complemented
16	#65886	C₂	1	1	yes	maximal, characteristic, complemented
17	#65885	C₂	1	1	yes	maximal, characteristic, complemented
18	#65877	C₂	1	1	yes	maximal, characteristic, complemented
19	#65876	C₂	1	1	yes	maximal, characteristic, complemented
20	#65875	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
22	#65868	C₂	1	1	yes	maximal, characteristic, complemented
23	#65852	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₅	C₂²	1	1	yes	characteristic
26	C₂×#709	C₂²	1	1	yes	characteristic
27	C₂×#709	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic
29	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
30	C₅×#123	C₂²	1	1	yes	characteristic
31	C₅×#123	C₂²	1	1	yes	characteristic
32	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₅×#121	C₂²	1	1	yes	characteristic
35	C₅×#121	C₂²	1	1	yes	characteristic
36	C₅×#120	C₂²	1	1	yes	characteristic
37	C₅×#120	C₂²	1	1	yes	characteristic
38	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
42	C₅×#117	C₂²	1	1	yes	characteristic
43	#4099	C₂²	1	2	yes	—
44	C₂×C₂²⋊Dic₅	C₂²	1	2	yes	—
45	#4092	C₂²	1	2	yes	complemented
46	#4090	C₂²	1	2	yes	complemented
47	#4085	C₂²	1	2	yes	—
48	#4085	C₂²	1	2	yes	—
49	#4085	C₂²	1	2	yes	—
50	#4085	C₂²	1	2	yes	—
51	#4085	C₂²	1	2	yes	complemented
52	#4084	C₂²	1	2	yes	—
53	#4084	C₂²	1	2	yes	—
54	#4082	C₂²	1	2	yes	—
55	#4082	C₂²	1	2	yes	—
56	#4081	C₂²	1	2	yes	—
57	#4081	C₂²	1	2	yes	—
58	#4081	C₂²	1	2	yes	complemented
59	D₄×Dic₅	C₂²	1	2	yes	—
60	D₄×Dic₅	C₂²	1	2	yes	—
61	#4076	C₂²	1	1	yes	characteristic
62	#4076	C₂²	1	1	yes	characteristic
63	#4076	C₂²	1	1	yes	characteristic, complemented
64	#4075	C₂²	1	2	yes	—
65	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
66	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
67	#4072	C₂²	1	1	yes	characteristic
68	#4072	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
70	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
71	#4070	C₂²	1	1	yes	characteristic
72	#4070	C₂²	1	1	yes	characteristic
73	#4070	C₂²	1	1	yes	characteristic
74	#4070	C₂²	1	1	yes	characteristic
75	#4070	C₂²	1	1	yes	characteristic
76	#4070	C₂²	1	2	yes	—
77	#4070	C₂²	1	2	yes	—
78	#4070	C₂²	1	1	yes	characteristic
79	#4070	C₂²	1	1	yes	characteristic, complemented
80	#4070	C₂²	1	1	yes	characteristic, complemented
81	#4070	C₂²	1	1	yes	characteristic, complemented
82	C₂×#683	C₂²	1	2	yes	—
83	#4044	C₂²	1	2	yes	complemented
84	#4044	C₂²	1	2	yes	complemented
85	#4042	C₂²	1	2	yes	complemented
86	#4042	C₂²	1	2	yes	complemented
87	#4042	C₂²	1	2	yes	complemented
88	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
89	#4036	C₂²	1	2	yes	complemented
90	#4035	C₂²	1	2	yes	complemented
91	#4035	C₂²	1	2	yes	complemented
92	#4035	C₂²	1	2	yes	complemented
93	#4034	C₂²	1	2	yes	complemented
94	#4033	C₂²	1	2	yes	complemented
95	#4031	C₂²	1	2	yes	—
96	#4031	C₂²	1	2	yes	—
97	#4031	C₂²	1	2	yes	complemented
98	#4029	C₂²	1	2	yes	—
99	#4029	C₂²	1	2	yes	—
100	#4029	C₂²	1	2	yes	complemented
101	#4029	C₂²	1	2	yes	complemented
102	#4027	C₂²	1	2	yes	—
103	#4027	C₂²	1	2	yes	—
104	#4027	C₂²	1	2	yes	complemented
105	#4025	C₂²	1	2	yes	—
106	#4025	C₂²	1	2	yes	—
107	#4025	C₂²	1	2	yes	—
108	#4025	C₂²	1	2	yes	—
109	#4025	C₂²	1	2	yes	complemented
110	#4024	C₂²	1	2	yes	—
111	#4024	C₂²	1	2	yes	—
112	#4024	C₂²	1	2	yes	complemented
113	#4024	C₂²	1	2	yes	complemented
114	#4023	C₂²	1	2	yes	complemented
115	#4021	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
117	#4016	C₂²	1	1	yes	characteristic, complemented
118	#4015	C₂²	1	1	yes	characteristic, complemented
119	#4015	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3541	—	5	1	no	maximal, Sylow
124	C₂⁴×C₅	C₂³	1	1	yes	characteristic
125	C₅×#41	—	4	2	no	—
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
131	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
132	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
133	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₅	—	4	2	no	—
135	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
148	C₂²×Dic₅	C₂³	1	2	yes	—
149	C₂²×Dic₅	C₂³	1	2	yes	—
150	C₂²×Dic₅	C₂³	1	2	yes	—
151	C₂²×Dic₅	C₂³	1	2	yes	—
152	#709	—	4	2	no	—
153	#709	—	4	2	no	—
154	C₂×D₂₀	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₅	C₂³	1	2	yes	—
156	C₂×C₄×D₅	C₂³	1	2	yes	—
157	C₂×C₄×D₅	C₂³	1	2	yes	—
158	C₂×Dic₁₀	—	4	2	no	—
159	C₂×Dic₁₀	—	4	2	no	—
160	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
161	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
162	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
163	C₂×Dic₁₀	C₂³	1	2	yes	—
164	C₂×Dic₁₀	C₂³	1	2	yes	—
165	C₂×Dic₁₀	C₂³	1	2	yes	—
166	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₄²×C₅	C₂³	1	1	yes	characteristic
183	C₄²×C₅	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₅	C₂³	1	2	yes	—
185	C₂²⋊Dic₅	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	2	yes	—
187	C₂²⋊Dic₅	C₂³	1	2	yes	—
188	C₂²⋊Dic₅	C₂³	1	2	yes	—
189	C₂²⋊Dic₅	C₂³	1	2	yes	—
190	C₂²⋊Dic₅	C₂³	1	2	yes	—
191	C₂²⋊Dic₅	C₂³	1	2	yes	—
192	C₂²⋊Dic₅	C₂³	1	2	yes	—
193	C₂²⋊Dic₅	C₂³	1	2	yes	—
194	C₂²⋊Dic₅	C₂³	1	2	yes	—
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	2	yes	—
197	#685	C₂³	1	2	yes	—
198	#685	C₂³	1	2	yes	—
199	#685	C₂³	1	2	yes	—
200	#685	C₂³	1	2	yes	—
201	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₅	C₂³	1	2	yes	—
206	C₄⋊Dic₅	C₂³	1	2	yes	—
207	C₄⋊Dic₅	C₂³	1	2	yes	—
208	C₄⋊Dic₅	C₂³	1	2	yes	—
209	C₄⋊Dic₅	C₂³	1	2	yes	—
210	#683	C₂³	1	2	yes	—
211	#683	C₂³	1	2	yes	—
212	#683	C₂³	1	2	yes	—
213	#683	C₂³	1	2	yes	—
214	#683	C₂³	1	2	yes	—
215	#683	C₂³	1	2	yes	—
216	#683	C₂³	1	2	yes	—
217	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	2	yes	—
220	#683	C₂³	1	2	yes	—
221	#683	C₂³	1	2	yes	—
222	#683	C₂³	1	2	yes	—
223	#683	C₂³	1	2	yes	—
224	C₄×Dic₅	C₂³	1	2	yes	—
225	C₄×Dic₅	C₂³	1	2	yes	—
226	C₄×Dic₅	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	2	yes	—
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#563	—	5	2	no	—
230	#562	—	5	2	no	—
231	#556	—	5	1	no	—
232	#554	—	5	2	no	—
233	#554	—	5	1	no	—
234	#553	—	5	2	no	—
235	#553	—	5	1	no	—
236	#552	—	5	1	no	—
237	D₄×Q₈	—	5	1	no	—
238	#548	—	5	1	no	—
239	#548	—	5	1	no	—
240	#547	—	5	1	no	—
241	#542	—	5	2	no	—
242	#542	—	5	1	no	—
243	#541	—	5	1	no	—
244	#539	—	5	2	no	—
245	#538	—	5	2	no	—
246	#538	—	5	2	no	—
247	#537	—	5	1	no	—
248	#536	—	5	1	no	—
249	#525	—	5	1	no	—
250	#525	D₅	1	1	yes	characteristic, complemented
251	C₂×C₂²⋊Q₈	—	5	1	no	—
252	C₂³×C₅	—	2	2	no	—
253	C₂³×C₅	—	4	1	no	—
254	C₂³×C₅	—	4	1	no	—
255	C₂³×C₅	C₂⁴	1	1	yes	characteristic
256	C₂³×C₅	C₂⁴	1	1	yes	characteristic
257	C₂³×C₅	C₂⁴	1	1	yes	characteristic
258	C₂³×C₅	C₂⁴	1	1	yes	characteristic
259	C₂³×C₅	C₂⁴	1	1	yes	characteristic
260	C₂²×D₅	C₂⁴	1	2	yes	—
261	C₅×Q₈	—	4	1	no	—
262	C₅×D₄	—	2	2	no	—
263	C₅×D₄	—	2	2	no	—
264	C₅×D₄	—	4	1	no	—
265	C₅×D₄	—	4	1	no	—
266	C₅×D₄	—	4	1	no	—
267	C₅×D₄	—	4	1	no	—
268	C₅×D₄	—	4	1	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	4	1	no	—
275	C₂×C₄×C₅	—	4	1	no	—
276	C₂×C₄×C₅	—	4	1	no	—
277	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂²⋊D₅	—	2	4	no	—
288	C₂²⋊D₅	—	4	2	no	—
289	C₂²⋊D₅	—	4	2	no	—
290	C₂²⋊D₅	—	4	2	no	—
291	C₂²⋊D₅	—	4	2	no	—
292	C₂×Dic₅	—	4	2	no	—
293	C₂×Dic₅	—	4	2	no	—
294	C₂×Dic₅	—	4	2	no	—
295	C₂×Dic₅	—	4	2	no	—
296	C₂×Dic₅	C₂⁴	1	2	yes	—
297	C₂×Dic₅	C₂⁴	1	2	yes	—
298	C₂×Dic₅	C₂⁴	1	2	yes	—
299	C₂×Dic₅	C₂⁴	1	2	yes	—
300	C₂×Dic₅	C₂⁴	1	2	yes	—
301	C₂×Dic₅	C₂⁴	1	2	yes	—
302	C₂×Dic₅	C₂⁴	1	2	yes	—
303	D₂₀	—	2	2	no	—
304	C₄×D₅	—	4	2	no	—
305	C₄×D₅	—	4	2	no	—
306	C₄×D₅	—	4	2	no	—
307	Dic₁₀	—	2	2	no	—
308	Dic₁₀	—	2	2	no	—
309	Dic₁₀	—	2	2	no	—
310	Dic₁₀	—	4	2	no	—
311	Dic₁₀	—	4	2	no	—
312	Dic₁₀	—	4	2	no	—
313	C₂×#41	—	5	1	no	—
314	C₂×#41	—	5	1	no	—
315	C₂×#41	C₂×D₅	1	1	yes	characteristic
316	C₂²×Q₈	—	5	1	no	—
317	C₂²×Q₈	—	5	1	no	—
318	C₂³×C₄	C₂×D₅	1	1	yes	characteristic
319	C₄⋊Q₈	—	5	2	no	—
320	C₄⋊Q₈	—	5	2	no	—
321	C₄⋊Q₈	—	5	1	no	—
322	C₄⋊Q₈	—	5	1	no	—
323	#126	—	5	2	no	—
324	#126	—	5	2	no	—
325	#126	—	5	2	no	—
326	#126	—	5	2	no	—
327	#126	—	5	2	no	—
328	#126	—	5	2	no	—
329	#126	—	5	2	no	—
330	#125	—	5	2	no	—
331	#125	—	5	2	no	—
332	#125	—	5	2	no	—
333	#125	—	5	2	no	—
334	#125	—	5	1	no	—
335	#124	—	5	2	no	—
336	#124	—	5	2	no	—
337	#124	—	5	2	no	—
338	#124	—	5	2	no	—
339	#124	—	5	2	no	—
340	#124	—	5	1	no	—
341	#123	—	5	2	no	—
342	#123	—	5	2	no	—
343	#123	—	5	2	no	—
344	#123	—	5	2	no	—
345	#123	—	5	2	no	—
346	#123	—	5	2	no	—
347	#123	—	5	2	no	—
348	#123	—	5	2	no	—
349	#123	C₂×D₅	1	1	yes	characteristic
350	#123	C₂×D₅	1	1	yes	characteristic
351	C₂²⋊Q₈	—	5	2	no	—
352	C₂²⋊Q₈	—	5	1	no	—
353	C₂²⋊Q₈	—	5	1	no	—
354	C₂²⋊Q₈	—	5	2	no	—
355	C₂²⋊Q₈	—	5	1	no	—
356	C₂²⋊Q₈	—	5	1	no	—
357	C₂²⋊Q₈	—	5	2	no	—
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	5	1	no	—
360	C₂²⋊Q₈	—	5	1	no	—
361	C₂²⋊Q₈	—	5	1	no	—
362	C₂²⋊Q₈	—	5	1	no	—
363	C₂²⋊Q₈	—	5	2	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	—	5	2	no	—
366	C₂²⋊Q₈	—	5	2	no	—
367	C₂²⋊Q₈	—	5	2	no	—
368	C₂²⋊Q₈	—	5	2	no	—
369	C₂²⋊Q₈	—	5	2	no	—
370	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
371	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
372	#121	—	5	2	no	—
373	#121	—	5	2	no	—
374	#121	—	5	2	no	—
375	#121	—	5	2	no	—
376	#121	—	5	2	no	—
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	1	no	—
380	#121	—	5	1	no	—
381	#121	—	5	1	no	—
382	#121	C₂×D₅	1	1	yes	characteristic
383	#121	C₂×D₅	1	1	yes	characteristic
384	#120	—	5	2	no	—
385	#120	C₂×D₅	1	1	yes	characteristic
386	#120	C₂×D₅	1	1	yes	characteristic
387	C₄×Q₈	—	5	2	no	—
388	C₄×Q₈	—	5	1	no	—
389	C₄×Q₈	—	5	1	no	—
390	C₄×Q₈	—	5	1	no	—
391	C₄×D₄	—	5	2	no	—
392	C₄×D₄	—	5	2	no	—
393	C₄×D₄	—	5	2	no	—
394	C₄×D₄	—	5	2	no	—
395	C₄×D₄	—	5	2	no	—
396	C₄×D₄	—	5	2	no	—
397	C₄×D₄	—	5	2	no	—
398	C₄×D₄	—	5	1	no	—
399	C₄×D₄	C₂×D₅	1	1	yes	characteristic
400	C₄×D₄	C₂×D₅	1	1	yes	characteristic
401	C₄×D₄	C₂×D₅	1	1	yes	characteristic
402	C₄×D₄	C₂×D₅	1	1	yes	characteristic
403	#117	—	5	1	no	—
404	#117	—	5	1	no	—
405	#117	—	5	2	no	—
406	#117	C₂×D₅	1	1	yes	characteristic
407	C₂×C₄⋊C₄	—	5	2	no	—
408	C₂×C₄⋊C₄	—	5	1	no	—
409	C₂×C₄⋊C₄	—	5	1	no	—
410	C₂×C₄⋊C₄	—	5	2	no	—
411	C₂×C₂²⋊C₄	—	5	2	no	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	2	1	no	—
423	C₂²×C₅	—	2	1	no	—
424	C₂²×C₅	—	2	1	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	4	4	no	—
427	C₂²×C₅	2₋¹⁺⁴	1	2	yes	—
428	C₂²×C₅	C₂⁵	1	1	yes	characteristic
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	2	2	no	—
431	C₂×D₅	—	2	2	no	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	2	1	no	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	1	no	—
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
442	Dic₅	—	2	2	no	—
443	Dic₅	—	2	2	no	—
444	Dic₅	—	2	2	no	—
445	Dic₅	—	2	2	no	—
446	Dic₅	—	2	2	no	—
447	Dic₅	—	2	2	no	—
448	Dic₅	—	2	2	no	—
449	C₂⁴	C₂²×D₅	1	1	yes	characteristic
450	#41	—	4	2	no	—
451	#41	—	20	2	no	—
452	#41	—	20	2	no	—
453	C₂×Q₈	—	5	1	no	—
454	C₂×Q₈	—	5	1	no	—
455	C₂×Q₈	—	5	1	no	—
456	C₂×Q₈	—	5	2	no	—
457	C₂×Q₈	—	5	2	no	—
458	C₂×Q₈	—	5	2	no	—
459	C₂×Q₈	—	20	2	no	—
460	C₂×Q₈	—	20	2	no	—
461	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
462	C₂×D₄	—	5	2	no	—
463	C₂×D₄	—	5	2	no	—
464	C₂×D₄	—	5	2	no	—
465	C₂×D₄	—	5	2	no	—
466	C₂×D₄	—	5	2	no	—
467	C₂×D₄	—	5	1	no	—
468	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
469	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
470	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
471	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
472	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
473	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
474	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	5	2	no	—
477	C₂²×C₄	—	5	2	no	—
478	C₂²×C₄	—	5	2	no	—
479	C₂²×C₄	—	5	2	no	—
480	C₂²×C₄	—	5	2	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	—	5	2	no	—
483	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
484	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
485	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
491	C₄⋊C₄	—	5	1	no	—
492	C₄⋊C₄	—	5	2	no	—
493	C₄⋊C₄	—	5	2	no	—
494	C₄⋊C₄	—	5	1	no	—
495	C₄⋊C₄	—	5	1	no	—
496	C₄⋊C₄	—	5	2	no	—
497	C₄⋊C₄	—	5	2	no	—
498	C₄⋊C₄	—	5	2	no	—
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	—	5	2	no	—
501	C₄⋊C₄	—	5	2	no	—
502	C₄⋊C₄	—	5	1	no	—
503	C₄⋊C₄	—	5	2	no	—
504	C₄⋊C₄	—	5	2	no	—
505	C₄⋊C₄	—	5	2	no	—
506	C₄⋊C₄	—	5	2	no	—
507	C₄⋊C₄	—	5	2	no	—
508	C₄⋊C₄	—	5	2	no	—
509	C₄⋊C₄	—	5	2	no	—
510	C₄⋊C₄	—	5	2	no	—
511	C₄⋊C₄	—	5	2	no	—
512	C₄⋊C₄	—	5	2	no	—
513	C₄⋊C₄	—	5	2	no	—
514	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
520	C₂²⋊C₄	—	5	2	no	—
521	C₂²⋊C₄	—	5	2	no	—
522	C₂²⋊C₄	—	5	2	no	—
523	C₂²⋊C₄	—	5	2	no	—
524	C₂²⋊C₄	—	5	2	no	—
525	C₂²⋊C₄	—	5	2	no	—
526	C₂²⋊C₄	—	5	2	no	—
527	C₂²⋊C₄	—	5	2	no	—
528	C₂²⋊C₄	—	5	2	no	—
529	C₂²⋊C₄	—	5	2	no	—
530	C₂²⋊C₄	—	5	2	no	—
531	C₂²⋊C₄	—	5	2	no	—
532	C₂²⋊C₄	—	5	2	no	—
533	C₂²⋊C₄	—	5	2	no	—
534	C₂²⋊C₄	—	5	2	no	—
535	C₂²⋊C₄	—	5	2	no	—
536	C₂²⋊C₄	—	5	2	no	—
537	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
538	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
539	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
540	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
541	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
542	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
544	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
547	C₄²	—	5	2	no	—
548	C₄²	—	5	2	no	—
549	C₄²	—	5	2	no	—
550	C₄²	—	5	2	no	—
551	C₄²	—	5	2	no	—
552	C₄²	C₂²×D₅	1	1	yes	characteristic
553	C₄²	C₂²×D₅	1	1	yes	characteristic
554	C₂×C₅	—	2	2	no	—
555	C₂×C₅	—	4	1	no	—
556	C₂×C₅	—	4	1	no	—
557	C₂×C₅	—	4	1	no	—
558	C₂×C₅	—	4	1	no	—
559	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	C₂×C₅	#585	1	1	yes	characteristic
562	D₅	—	4	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	5	2	no	—
567	C₂³	C₂³×D₅	1	1	yes	characteristic
568	C₂³	C₂³×D₅	1	1	yes	characteristic
569	C₂³	C₂³×D₅	1	1	yes	characteristic
570	C₂³	C₂³×D₅	1	1	yes	characteristic
571	C₂³	C₂³×D₅	1	1	yes	characteristic
572	Q₈	—	4	1	no	—
573	Q₈	—	10	2	no	—
574	Q₈	—	10	2	no	—
575	Q₈	—	10	2	no	—
576	Q₈	—	20	2	no	—
577	Q₈	—	20	2	no	—
578	Q₈	—	20	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	10	4	no	—
587	D₄	—	10	2	no	—
588	D₄	—	20	2	no	—
589	D₄	—	20	2	no	—
590	D₄	—	20	2	no	—
591	D₄	—	20	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	5	2	no	—
601	C₂×C₄	—	5	2	no	—
602	C₂×C₄	—	5	2	no	—
603	C₂×C₄	—	5	2	no	—
604	C₂×C₄	—	5	2	no	—
605	C₂×C₄	—	5	2	no	—
606	C₂×C₄	—	5	2	no	—
607	C₂×C₄	—	20	2	no	—
608	C₂×C₄	—	20	2	no	—
609	C₂×C₄	—	20	2	no	—
610	C₂×C₄	—	20	2	no	—
611	C₂×C₄	—	20	2	no	—
612	C₂×C₄	—	20	2	no	—
613	C₂×C₄	—	20	2	no	—
614	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
624	C₅	#3541	1	1	yes	characteristic, complemented, Sylow
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	10	2	no	—
641	C₂²	—	10	2	no	—
642	C₂²	—	10	2	no	—
643	C₂²	#4150	1	2	yes	—
644	C₂²	C₂⁴×D₅	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	10	2	no	—
655	C₄	—	10	2	no	—
656	C₄	—	10	2	no	—
657	C₄	—	10	2	no	—
658	C₄	—	10	2	no	—
659	C₄	—	10	2	no	—
660	C₄	—	10	2	no	—
661	C₄	#4144	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	1	no	—
667	C₂	—	20	2	no	—
668	C₂	C₂×#4144	1	1	yes	characteristic
669	C₂	C₂×#4150	1	1	yes	characteristic
670	C₂	#66283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#525	C₂
hypercenter	#525	D₅
hypocenter	C₅	#3541
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₅×#525	C₂	semidirect
2. #66167	C₂	semidirect
3. #66159	C₂	semidirect
4. #66125	C₂	semidirect
5. C₂×#4070	C₂	semidirect
6. #65996	C₂	semidirect
7. #65994	C₂	semidirect
8. #65980	C₂	semidirect
9. #65970	C₂	semidirect
10. #65955	C₂	semidirect
11. #65935	C₂	semidirect
12. #65927	C₂	semidirect
13. #65927	C₂	semidirect
14. #65899	C₂	semidirect
15. #65886	C₂	semidirect
16. #65886	C₂	semidirect
17. #65885	C₂	semidirect
18. #65877	C₂	semidirect
19. #65876	C₂	semidirect
20. #65875	C₂	semidirect
21. D₄×Dic₁₀	C₂	semidirect
22. #65868	C₂	semidirect
23. #65852	C₂	semidirect
27. C₂×#709	C₂²	semidirect
29. C₂²×Dic₁₀	C₂²	semidirect
45. #4092	C₂²	semidirect
46. #4090	C₂²	semidirect
51. #4085	C₂²	semidirect
58. #4081	C₂²	semidirect
63. #4076	C₂²	semidirect
68. #4072	C₂²	semidirect
70. C₂×C₄⋊Dic₅	C₂²	semidirect
79. #4070	C₂²	semidirect
80. #4070	C₂²	semidirect
81. #4070	C₂²	semidirect
83. #4044	C₂²	semidirect
84. #4044	C₂²	semidirect
85. #4042	C₂²	semidirect
86. #4042	C₂²	semidirect
87. #4042	C₂²	semidirect
88. D₅×C₄⋊C₄	C₂²	semidirect
89. #4036	C₂²	semidirect
90. #4035	C₂²	semidirect
91. #4035	C₂²	semidirect
92. #4035	C₂²	semidirect
93. #4034	C₂²	semidirect
94. #4033	C₂²	semidirect
97. #4031	C₂²	semidirect
100. #4029	C₂²	semidirect
101. #4029	C₂²	semidirect
104. #4027	C₂²	semidirect
109. #4025	C₂²	semidirect
112. #4024	C₂²	semidirect
113. #4024	C₂²	semidirect
114. #4023	C₂²	semidirect
115. #4021	C₂²	semidirect
116. C₄×D₂₀	C₂²	semidirect
117. #4016	C₂²	semidirect
118. #4015	C₂²	semidirect
119. #4015	C₂²	semidirect
120. C₄×Dic₁₀	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
250. #525	D₅	semidirect
624. C₅	#3541	semidirect

Maximal subgroups

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

subgroup	index
C₅×#525	2
#66167	2
#66159	2
#66125	2
C₂×#4070	2
#65996	2
#65994	2
#65980	2
#65970	2
#65955	2
#65935	2
#65927	2
#65899	2
#65886	2
#65885	2
#65877	2
#65876	2
#65875	2
D₄×Dic₁₀	2
#65868	2
#65852	2
#3541	5