Subgroups — #10617934

Order 640.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 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	#66164	C₂	1	1	yes	maximal, characteristic, complemented
4	#66125	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#4076	C₂	1	1	yes	maximal, characteristic, complemented
6	#65997	C₂	1	2	yes	maximal, complemented
7	#65991	C₂	1	2	yes	maximal, complemented
8	#65981	C₂	1	2	yes	maximal, complemented
9	#65971	C₂	1	2	yes	maximal, complemented
10	#65954	C₂	1	2	yes	maximal, complemented
11	#65944	C₂	1	2	yes	maximal, complemented
12	#65926	C₂	1	2	yes	maximal, complemented
13	#65923	C₂	1	2	yes	maximal, complemented
14	#65899	C₂	1	1	yes	maximal, characteristic, complemented
15	#65897	C₂	1	1	yes	maximal, characteristic, complemented
16	#65889	C₂	1	1	yes	maximal, characteristic, complemented
17	#65887	C₂	1	1	yes	maximal, characteristic, complemented
18	#65884	C₂	1	1	yes	maximal, characteristic, complemented
19	#65884	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
21	#65875	C₂	1	1	yes	maximal, characteristic, complemented
22	#65869	C₂	1	1	yes	maximal, characteristic, complemented
23	#65868	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
27	C₂×#711	C₂²	1	2	yes	complemented
28	C₂×D₄×D₅	C₂²	1	2	yes	—
29	C₂×#709	C₂²	1	1	yes	characteristic, complemented
30	C₂×#709	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₂₀	C₂²	1	1	yes	characteristic
32	C₂²×D₂₀	C₂²	1	1	yes	characteristic, complemented
33	C₅×#123	C₂²	1	1	yes	characteristic, complemented
34	C₅×#123	C₂²	1	1	yes	characteristic, complemented
35	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₅×#121	C₂²	1	1	yes	characteristic
38	C₅×#121	C₂²	1	1	yes	characteristic, complemented
39	C₅×#120	C₂²	1	1	yes	characteristic
40	C₅×#120	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
42	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
45	C₅×#117	C₂²	1	1	yes	characteristic, complemented
46	#4099	C₂²	1	2	yes	complemented
47	#4093	C₂²	1	2	yes	complemented
48	#4092	C₂²	1	2	yes	complemented
49	#4086	C₂²	1	2	yes	complemented
50	#4086	C₂²	1	2	yes	complemented
51	#4085	C₂²	1	2	yes	complemented
52	#4085	C₂²	1	2	yes	complemented
53	#4085	C₂²	1	2	yes	complemented
54	#4084	C₂²	1	2	yes	complemented
55	#4084	C₂²	1	2	yes	complemented
56	#4083	C₂²	1	2	yes	complemented
57	#4083	C₂²	1	2	yes	complemented
58	#4083	C₂²	1	2	yes	complemented
59	#4083	C₂²	1	2	yes	complemented
60	#4081	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
64	#4076	C₂²	1	1	yes	characteristic, complemented
65	#4076	C₂²	1	1	yes	characteristic, complemented
66	#4076	C₂²	1	2	yes	complemented
67	#4076	C₂²	1	2	yes	complemented
68	#4076	C₂²	1	1	yes	characteristic, complemented
69	#4076	C₂²	1	1	yes	characteristic, complemented
70	#4076	C₂²	1	1	yes	characteristic, complemented
71	#4076	C₂²	1	1	yes	characteristic, complemented
72	#4075	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
75	C₂×#685	C₂²	1	2	yes	complemented
76	#4072	C₂²	1	1	yes	characteristic, complemented
77	#4072	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
80	#4070	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	2	yes	complemented
84	#4044	C₂²	1	2	yes	complemented
85	#4043	C₂²	1	2	yes	complemented
86	#4042	C₂²	1	2	yes	complemented
87	#4041	C₂²	1	2	yes	complemented
88	#4040	C₂²	1	2	yes	complemented
89	#4040	C₂²	1	2	yes	complemented
90	#4040	C₂²	1	2	yes	complemented
91	#4040	C₂²	1	2	yes	complemented
92	#4039	C₂²	1	2	yes	complemented
93	#4038	C₂²	1	2	yes	complemented
94	#4035	C₂²	1	2	yes	complemented
95	#4032	C₂²	1	2	yes	complemented
96	#4032	C₂²	1	2	yes	complemented
97	#4031	C₂²	1	2	yes	complemented
98	#4031	C₂²	1	2	yes	complemented
99	#4031	C₂²	1	2	yes	complemented
100	#4030	C₂²	1	2	yes	complemented
101	#4030	C₂²	1	2	yes	complemented
102	#4030	C₂²	1	2	yes	complemented
103	#4030	C₂²	1	2	yes	complemented
104	#4030	C₂²	1	2	yes	complemented
105	#4030	C₂²	1	2	yes	complemented
106	#4029	C₂²	1	2	yes	complemented
107	#4029	C₂²	1	2	yes	complemented
108	#4028	C₂²	1	2	yes	—
109	#4028	C₂²	1	2	yes	complemented
110	#4027	C₂²	1	2	yes	complemented
111	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	#4025	C₂²	1	2	yes	complemented
114	#4023	C₂²	1	2	yes	complemented
115	#4021	C₂²	1	1	yes	characteristic, complemented
116	#4020	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
120	#4016	C₂²	1	1	yes	characteristic, complemented
121	#4015	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3542	—	5	1	no	maximal, Sylow
124	C₂⁴×C₅	C₂³	1	1	yes	characteristic
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₂³×D₅	C₂³	1	2	yes	—
127	C₅×#41	—	4	2	no	—
128	C₂×C₅×Q₈	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	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
135	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₅	—	4	2	no	—
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	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₅	—	4	4	no	—
146	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
157	C₂²×Dic₅	C₂³	1	2	yes	—
158	C₂²×Dic₅	C₂³	1	2	yes	—
159	#711	—	4	4	no	—
160	D₄×D₅	—	4	4	no	—
161	#709	—	4	2	no	—
162	#709	—	4	2	no	—
163	C₂×D₂₀	—	4	2	no	—
164	C₂×D₂₀	—	4	2	no	—
165	C₂×D₂₀	C₂³	1	1	yes	characteristic
166	C₂×D₂₀	C₂³	1	1	yes	characteristic
167	C₂×D₂₀	C₂³	1	1	yes	characteristic
168	C₂×D₂₀	C₂³	1	2	yes	—
169	C₂×D₂₀	C₂³	1	2	yes	—
170	C₂×D₂₀	C₂³	1	2	yes	—
171	C₂×D₂₀	C₂³	1	2	yes	—
172	C₂×C₄×D₅	C₂³	1	2	yes	—
173	C₂×C₄×D₅	C₂³	1	2	yes	—
174	C₂×C₄×D₅	C₂³	1	2	yes	—
175	C₂×C₄×D₅	C₂³	1	2	yes	—
176	C₂×C₄×D₅	C₂³	1	2	yes	—
177	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
178	C₂×Dic₁₀	C₂³	1	2	yes	—
179	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₂²⋊Dic₅	C₂³	1	2	yes	—
198	C₂²⋊Dic₅	C₂³	1	2	yes	—
199	C₂²⋊Dic₅	C₂³	1	2	yes	—
200	C₂²⋊Dic₅	C₂³	1	2	yes	—
201	C₂²⋊Dic₅	C₂³	1	2	yes	—
202	#685	C₂³	1	2	yes	—
203	#685	C₂³	1	2	yes	—
204	#685	C₂³	1	2	yes	—
205	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	2	yes	—
207	#685	C₂³	1	2	yes	—
208	#685	C₂³	1	2	yes	—
209	#685	C₂³	1	2	yes	—
210	#685	C₂³	1	2	yes	—
211	#685	C₂³	1	2	yes	—
212	#685	C₂³	1	2	yes	—
213	#685	C₂³	1	2	yes	—
214	#685	C₂³	1	2	yes	—
215	#685	C₂³	1	2	yes	—
216	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₅	C₂³	1	2	yes	—
219	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₅	C₂³	1	2	yes	—
222	C₄⋊Dic₅	C₂³	1	2	yes	—
223	#683	C₂³	1	2	yes	—
224	#683	C₂³	1	2	yes	—
225	#683	C₂³	1	2	yes	—
226	#683	C₂³	1	2	yes	—
227	#683	C₂³	1	2	yes	—
228	#683	C₂³	1	2	yes	—
229	C₄×Dic₅	C₂³	1	2	yes	—
230	C₄×Dic₅	C₂³	1	2	yes	—
231	C₄×Dic₅	C₂³	1	2	yes	—
232	#562	—	5	2	no	—
233	#560	—	5	2	no	—
234	#555	—	5	1	no	—
235	#553	—	5	1	no	—
236	#552	—	5	1	no	—
237	#551	—	5	2	no	—
238	#550	—	5	1	no	—
239	#547	—	5	1	no	—
240	#546	—	5	2	no	—
241	#546	—	5	1	no	—
242	#546	—	5	1	no	—
243	D₄²	—	5	1	no	—
244	#542	—	5	1	no	—
245	#540	—	5	2	no	—
246	#540	—	5	1	no	—
247	#538	—	5	2	no	—
248	#537	—	5	1	no	—
249	#535	—	5	1	no	—
250	#535	—	5	2	no	—
251	#534	—	5	2	no	—
252	#525	—	5	1	no	—
253	#525	D₅	1	1	yes	characteristic, complemented
254	C₂×#121	—	5	1	no	—
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	4	1	no	—
257	C₂³×C₅	—	4	1	no	—
258	C₂³×C₅	C₂⁴	1	1	yes	characteristic
259	C₂³×C₅	C₂⁴	1	1	yes	characteristic
260	C₂³×C₅	C₂⁴	1	1	yes	characteristic
261	C₂³×C₅	C₂⁴	1	1	yes	characteristic
262	C₂³×C₅	C₂⁴	1	1	yes	characteristic
263	C₂²×D₅	—	2	4	no	—
264	C₂²×D₅	—	4	2	no	—
265	C₂²×D₅	—	4	2	no	—
266	C₂²×D₅	—	4	2	no	—
267	C₂²×D₅	—	4	2	no	—
268	C₂²×D₅	—	4	2	no	—
269	C₂²×D₅	C₂⁴	1	2	yes	—
270	C₂²×D₅	C₂⁴	1	2	yes	—
271	C₂²×D₅	C₂⁴	1	2	yes	—
272	C₅×Q₈	—	4	1	no	—
273	C₅×D₄	—	2	2	no	—
274	C₅×D₄	—	2	2	no	—
275	C₅×D₄	—	4	1	no	—
276	C₅×D₄	—	4	1	no	—
277	C₅×D₄	—	4	1	no	—
278	C₅×D₄	—	4	1	no	—
279	C₅×D₄	—	4	1	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	4	1	no	—
286	C₂×C₄×C₅	—	4	1	no	—
287	C₂×C₄×C₅	—	4	1	no	—
288	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²⋊D₅	—	2	4	no	—
299	C₂²⋊D₅	—	4	2	no	—
300	C₂²⋊D₅	—	4	2	no	—
301	C₂²⋊D₅	—	4	2	no	—
302	C₂²⋊D₅	—	4	2	no	—
303	C₂²⋊D₅	—	4	2	no	—
304	C₂²⋊D₅	—	4	2	no	—
305	C₂²⋊D₅	—	4	2	no	—
306	C₂²⋊D₅	—	4	2	no	—
307	C₂²⋊D₅	—	4	2	no	—
308	C₂²⋊D₅	—	4	2	no	—
309	C₂×Dic₅	—	2	4	no	—
310	C₂×Dic₅	—	4	2	no	—
311	C₂×Dic₅	C₂⁴	1	2	yes	—
312	C₂×Dic₅	C₂⁴	1	2	yes	—
313	C₂×Dic₅	C₂⁴	1	2	yes	—
314	C₂×Dic₅	C₂⁴	1	2	yes	—
315	C₂×Dic₅	C₂⁴	1	2	yes	—
316	D₂₀	—	2	2	no	—
317	D₂₀	—	2	2	no	—
318	D₂₀	—	2	2	no	—
319	D₂₀	—	4	2	no	—
320	D₂₀	—	4	2	no	—
321	D₂₀	—	4	2	no	—
322	D₂₀	—	4	2	no	—
323	C₄×D₅	—	4	2	no	—
324	C₄×D₅	—	4	2	no	—
325	C₄×D₅	—	4	2	no	—
326	C₄×D₅	—	4	2	no	—
327	C₄×D₅	—	4	2	no	—
328	Dic₁₀	—	2	2	no	—
329	Dic₁₀	—	4	2	no	—
330	C₂×#41	—	5	2	no	—
331	C₂×#41	—	5	1	no	—
332	C₂×#41	—	5	1	no	—
333	C₂×#41	C₂×D₅	1	1	yes	characteristic, complemented
334	C₂²×D₄	—	5	2	no	—
335	C₂²×D₄	—	5	2	no	—
336	C₂²×D₄	—	5	1	no	—
337	C₂²×D₄	—	5	1	no	—
338	C₂³×C₄	C₂×D₅	1	1	yes	characteristic, complemented
339	C₄⋊Q₈	—	5	1	no	—
340	#127	—	5	2	no	—
341	#127	—	5	2	no	—
342	#127	—	5	1	no	—
343	#126	—	5	2	no	—
344	#126	—	5	2	no	—
345	#126	—	5	2	no	—
346	#125	—	5	2	no	—
347	#125	—	5	1	no	—
348	#124	—	5	2	no	—
349	#124	—	5	2	no	—
350	#124	—	5	2	no	—
351	#124	—	5	2	no	—
352	#124	—	5	1	no	—
353	#123	—	5	2	no	—
354	#123	—	5	2	no	—
355	#123	—	5	2	no	—
356	#123	—	5	2	no	—
357	#123	—	5	2	no	—
358	#123	—	5	2	no	—
359	#123	—	5	2	no	—
360	#123	—	5	2	no	—
361	#123	—	5	2	no	—
362	#123	—	5	2	no	—
363	#123	C₂×D₅	1	1	yes	characteristic, complemented
364	#123	C₂×D₅	1	1	yes	characteristic, complemented
365	C₂²⋊Q₈	—	5	2	no	—
366	C₂²⋊Q₈	—	5	1	no	—
367	C₂²⋊Q₈	—	5	1	no	—
368	C₂²⋊Q₈	—	5	1	no	—
369	C₂²⋊Q₈	—	5	2	no	—
370	C₂²⋊Q₈	—	5	2	no	—
371	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
372	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
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	1	no	—
379	#121	—	5	1	no	—
380	#121	—	5	2	no	—
381	#121	—	5	1	no	—
382	#121	—	5	1	no	—
383	#121	—	5	2	no	—
384	#121	—	5	1	no	—
385	#121	—	5	1	no	—
386	#121	—	5	1	no	—
387	#121	—	5	1	no	—
388	#121	—	5	1	no	—
389	#121	—	5	2	no	—
390	#121	—	5	2	no	—
391	#121	—	5	2	no	—
392	#121	—	5	2	no	—
393	#121	—	5	2	no	—
394	#121	—	5	2	no	—
395	#121	—	5	2	no	—
396	#121	C₂×D₅	1	1	yes	characteristic
397	#121	C₂×D₅	1	1	yes	characteristic, complemented
398	#120	—	5	2	no	—
399	#120	—	5	2	no	—
400	#120	—	5	2	no	—
401	#120	—	5	2	no	—
402	#120	—	5	2	no	—
403	#120	—	5	2	no	—
404	#120	—	5	2	no	—
405	#120	C₂×D₅	1	1	yes	characteristic
406	#120	C₂×D₅	1	1	yes	characteristic, complemented
407	C₄×Q₈	—	5	1	no	—
408	C₄×D₄	—	5	2	no	—
409	C₄×D₄	—	5	2	no	—
410	C₄×D₄	—	5	2	no	—
411	C₄×D₄	—	5	2	no	—
412	C₄×D₄	—	5	1	no	—
413	C₄×D₄	—	5	1	no	—
414	C₄×D₄	—	5	1	no	—
415	C₄×D₄	C₂×D₅	1	1	yes	characteristic
416	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
417	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
418	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
419	#117	—	5	1	no	—
420	#117	—	5	1	no	—
421	#117	—	5	2	no	—
422	#117	—	5	2	no	—
423	#117	C₂×D₅	1	1	yes	characteristic, complemented
424	C₂×C₄⋊C₄	—	5	1	no	—
425	C₂×C₄⋊C₄	—	5	1	no	—
426	C₂×C₂²⋊C₄	—	5	2	no	—
427	C₂×C₂²⋊C₄	—	5	2	no	—
428	C₂×C₂²⋊C₄	—	5	2	no	—
429	C₂²×C₅	—	2	1	no	—
430	C₂²×C₅	—	2	1	no	—
431	C₂²×C₅	—	2	1	no	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	1	no	—
435	C₂²×C₅	—	2	1	no	—
436	C₂²×C₅	—	2	1	no	—
437	C₂²×C₅	—	2	1	no	—
438	C₂²×C₅	—	2	1	no	—
439	C₂²×C₅	—	2	1	no	—
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	2	1	no	—
443	C₂²×C₅	—	4	4	no	—
444	C₂²×C₅	H(5,𝔽₂)	1	2	yes	—
445	C₂²×C₅	C₂⁵	1	1	yes	characteristic
446	C₂×D₅	—	2	2	no	—
447	C₂×D₅	—	2	2	no	—
448	C₂×D₅	—	2	2	no	—
449	C₂×D₅	—	2	2	no	—
450	C₂×D₅	—	2	2	no	—
451	C₂×D₅	—	2	2	no	—
452	C₂×D₅	—	2	2	no	—
453	C₂×D₅	—	2	2	no	—
454	C₂×D₅	—	2	2	no	—
455	C₂×D₅	—	8	4	no	—
456	C₂×D₅	—	8	4	no	—
457	C₄×C₅	—	2	1	no	—
458	C₄×C₅	—	2	1	no	—
459	C₄×C₅	—	2	1	no	—
460	C₄×C₅	—	2	1	no	—
461	C₄×C₅	—	2	1	no	—
462	C₄×C₅	—	2	1	no	—
463	C₄×C₅	—	2	1	no	—
464	C₄×C₅	—	2	1	no	—
465	C₄×C₅	—	2	1	no	—
466	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
467	Dic₅	—	2	2	no	—
468	Dic₅	—	2	2	no	—
469	Dic₅	—	2	2	no	—
470	Dic₅	—	2	2	no	—
471	Dic₅	—	2	2	no	—
472	C₂⁴	—	5	2	no	—
473	C₂⁴	—	5	2	no	—
474	C₂⁴	C₂²×D₅	1	1	yes	characteristic
475	#41	—	4	2	no	—
476	#41	—	20	2	no	—
477	#41	—	20	2	no	—
478	#41	—	20	4	no	—
479	C₂×Q₈	—	5	1	no	—
480	C₂×Q₈	—	5	2	no	—
481	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
482	C₂×D₄	—	5	2	no	—
483	C₂×D₄	—	5	2	no	—
484	C₂×D₄	—	5	2	no	—
485	C₂×D₄	—	5	2	no	—
486	C₂×D₄	—	5	2	no	—
487	C₂×D₄	—	5	2	no	—
488	C₂×D₄	—	5	2	no	—
489	C₂×D₄	—	5	2	no	—
490	C₂×D₄	—	5	2	no	—
491	C₂×D₄	—	5	2	no	—
492	C₂×D₄	—	5	2	no	—
493	C₂×D₄	—	5	1	no	—
494	C₂×D₄	—	5	1	no	—
495	C₂×D₄	—	5	1	no	—
496	C₂×D₄	—	5	2	no	—
497	C₂×D₄	—	5	2	no	—
498	C₂×D₄	—	5	2	no	—
499	C₂×D₄	—	5	2	no	—
500	C₂×D₄	—	20	2	no	—
501	C₂×D₄	—	20	2	no	—
502	C₂×D₄	—	20	4	no	—
503	C₂×D₄	—	20	4	no	—
504	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
505	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
506	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
507	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
509	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
510	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	5	2	no	—
513	C₂²×C₄	—	5	2	no	—
514	C₂²×C₄	—	5	2	no	—
515	C₂²×C₄	—	5	2	no	—
516	C₂²×C₄	—	5	2	no	—
517	C₂²×C₄	—	5	2	no	—
518	C₂²×C₄	—	5	2	no	—
519	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
520	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
521	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
522	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
527	C₄⋊C₄	—	5	1	no	—
528	C₄⋊C₄	—	5	1	no	—
529	C₄⋊C₄	—	5	1	no	—
530	C₄⋊C₄	—	5	2	no	—
531	C₄⋊C₄	—	5	2	no	—
532	C₄⋊C₄	—	5	1	no	—
533	C₄⋊C₄	—	5	2	no	—
534	C₄⋊C₄	—	5	2	no	—
535	C₄⋊C₄	—	5	2	no	—
536	C₄⋊C₄	—	5	2	no	—
537	C₄⋊C₄	—	5	2	no	—
538	C₄⋊C₄	—	5	2	no	—
539	C₄⋊C₄	—	5	2	no	—
540	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
546	C₂²⋊C₄	—	5	2	no	—
547	C₂²⋊C₄	—	5	2	no	—
548	C₂²⋊C₄	—	5	2	no	—
549	C₂²⋊C₄	—	5	2	no	—
550	C₂²⋊C₄	—	5	2	no	—
551	C₂²⋊C₄	—	5	2	no	—
552	C₂²⋊C₄	—	5	2	no	—
553	C₂²⋊C₄	—	5	2	no	—
554	C₂²⋊C₄	—	5	2	no	—
555	C₂²⋊C₄	—	5	2	no	—
556	C₂²⋊C₄	—	5	2	no	—
557	C₂²⋊C₄	—	5	2	no	—
558	C₂²⋊C₄	—	5	2	no	—
559	C₂²⋊C₄	—	5	2	no	—
560	C₂²⋊C₄	—	5	2	no	—
561	C₂²⋊C₄	—	5	2	no	—
562	C₂²⋊C₄	—	5	2	no	—
563	C₂²⋊C₄	—	5	2	no	—
564	C₂²⋊C₄	—	5	2	no	—
565	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
566	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
567	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
568	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
569	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
570	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
572	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
573	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
575	C₄²	—	5	2	no	—
576	C₄²	—	5	2	no	—
577	C₄²	—	5	2	no	—
578	C₄²	C₂²×D₅	1	1	yes	characteristic
579	C₄²	C₂²×D₅	1	1	yes	characteristic
580	C₂×C₅	—	2	2	no	—
581	C₂×C₅	—	4	1	no	—
582	C₂×C₅	—	4	1	no	—
583	C₂×C₅	—	4	1	no	—
584	C₂×C₅	—	4	1	no	—
585	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂×C₅	#585	1	1	yes	characteristic
588	D₅	—	4	2	no	—
589	D₅	—	4	2	no	—
590	D₅	—	4	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	5	2	no	—
595	C₂³	—	5	2	no	—
596	C₂³	—	5	2	no	—
597	C₂³	—	10	4	no	—
598	C₂³	—	20	2	no	—
599	C₂³	—	20	2	no	—
600	C₂³	—	20	2	no	—
601	C₂³	—	20	2	no	—
602	C₂³	—	20	2	no	—
603	C₂³	C₂³×D₅	1	1	yes	characteristic
604	C₂³	C₂³×D₅	1	1	yes	characteristic
605	C₂³	C₂³×D₅	1	1	yes	characteristic
606	C₂³	C₂³×D₅	1	1	yes	characteristic
607	C₂³	C₂³×D₅	1	1	yes	characteristic
608	Q₈	—	4	1	no	—
609	Q₈	—	10	2	no	—
610	Q₈	—	20	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	1	no	—
616	D₄	—	4	1	no	—
617	D₄	—	4	1	no	—
618	D₄	—	10	4	no	—
619	D₄	—	10	2	no	—
620	D₄	—	10	2	no	—
621	D₄	—	10	2	no	—
622	D₄	—	20	2	no	—
623	D₄	—	20	2	no	—
624	D₄	—	20	2	no	—
625	D₄	—	20	2	no	—
626	D₄	—	20	2	no	—
627	D₄	—	20	2	no	—
628	D₄	—	20	2	no	—
629	D₄	—	20	2	no	—
630	D₄	—	20	2	no	—
631	D₄	—	20	2	no	—
632	D₄	—	20	2	no	—
633	D₄	—	20	2	no	—
634	D₄	—	20	2	no	—
635	D₄	—	20	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	5	2	no	—
645	C₂×C₄	—	5	2	no	—
646	C₂×C₄	—	5	2	no	—
647	C₂×C₄	—	5	2	no	—
648	C₂×C₄	—	5	2	no	—
649	C₂×C₄	—	10	4	no	—
650	C₂×C₄	—	20	2	no	—
651	C₂×C₄	—	20	2	no	—
652	C₂×C₄	—	20	2	no	—
653	C₂×C₄	—	20	2	no	—
654	C₂×C₄	—	20	2	no	—
655	C₂×C₄	—	20	2	no	—
656	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
657	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
658	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
659	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
660	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
666	C₅	#3542	1	1	yes	characteristic, complemented, Sylow
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	10	2	no	—
683	C₂²	—	10	2	no	—
684	C₂²	—	10	2	no	—
685	C₂²	—	10	2	no	—
686	C₂²	—	10	2	no	—
687	C₂²	—	10	2	no	—
688	C₂²	—	10	2	no	—
689	C₂²	—	10	2	no	—
690	C₂²	—	10	2	no	—
691	C₂²	—	40	4	no	—
692	C₂²	—	40	4	no	—
693	C₂²	#4149	1	2	yes	—
694	C₂²	C₂⁴×D₅	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	10	2	no	—
705	C₄	—	10	2	no	—
706	C₄	—	10	2	no	—
707	C₄	—	10	2	no	—
708	C₄	—	10	2	no	—
709	C₄	#4144	1	2	yes	—
710	C₂	—	2	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	1	no	—
714	C₂	—	4	1	no	—
715	C₂	—	20	2	no	—
716	C₂	—	20	2	no	—
717	C₂	—	20	2	no	—
718	C₂	C₂×#4144	1	1	yes	characteristic
719	C₂	C₂×#4149	1	1	yes	characteristic
720	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	#3542
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. #66164	C₂	semidirect
4. #66125	C₂	semidirect
5. C₂×#4076	C₂	semidirect
6. #65997	C₂	semidirect
7. #65991	C₂	semidirect
8. #65981	C₂	semidirect
9. #65971	C₂	semidirect
10. #65954	C₂	semidirect
11. #65944	C₂	semidirect
12. #65926	C₂	semidirect
13. #65923	C₂	semidirect
14. #65899	C₂	semidirect
15. #65897	C₂	semidirect
16. #65889	C₂	semidirect
17. #65887	C₂	semidirect
18. #65884	C₂	semidirect
19. #65884	C₂	semidirect
20. D₄×D₂₀	C₂	semidirect
21. #65875	C₂	semidirect
22. #65869	C₂	semidirect
23. #65868	C₂	semidirect
24. C₂×C₅×#41	C₂²	semidirect
25. C₂³×C₄×C₅	C₂²	semidirect
26. C₂²×C₂²⋊D₅	C₂²	semidirect
27. C₂×#711	C₂²	semidirect
29. C₂×#709	C₂²	semidirect
30. C₂×#709	C₂²	semidirect
32. C₂²×D₂₀	C₂²	semidirect
33. C₅×#123	C₂²	semidirect
34. C₅×#123	C₂²	semidirect
35. C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₅×#121	C₂²	semidirect
40. C₅×#120	C₂²	semidirect
42. C₄×C₅×D₄	C₂²	semidirect
43. C₄×C₅×D₄	C₂²	semidirect
44. C₄×C₅×D₄	C₂²	semidirect
45. C₅×#117	C₂²	semidirect
46. #4099	C₂²	semidirect
47. #4093	C₂²	semidirect
48. #4092	C₂²	semidirect
49. #4086	C₂²	semidirect
50. #4086	C₂²	semidirect
51. #4085	C₂²	semidirect
52. #4085	C₂²	semidirect
53. #4085	C₂²	semidirect
54. #4084	C₂²	semidirect
55. #4084	C₂²	semidirect
56. #4083	C₂²	semidirect
57. #4083	C₂²	semidirect
58. #4083	C₂²	semidirect
59. #4083	C₂²	semidirect
64. #4076	C₂²	semidirect
65. #4076	C₂²	semidirect
66. #4076	C₂²	semidirect
67. #4076	C₂²	semidirect
68. #4076	C₂²	semidirect
69. #4076	C₂²	semidirect
70. #4076	C₂²	semidirect
71. #4076	C₂²	semidirect
72. #4075	C₂²	semidirect
73. C₄×C₂²⋊D₅	C₂²	semidirect
74. C₄×C₂²⋊D₅	C₂²	semidirect
75. C₂×#685	C₂²	semidirect
76. #4072	C₂²	semidirect
77. #4072	C₂²	semidirect
78. C₂×C₄⋊Dic₅	C₂²	semidirect
79. C₂×C₄⋊Dic₅	C₂²	semidirect
80. #4070	C₂²	semidirect
81. #4070	C₂²	semidirect
82. #4070	C₂²	semidirect
83. #4044	C₂²	semidirect
84. #4044	C₂²	semidirect
85. #4043	C₂²	semidirect
86. #4042	C₂²	semidirect
87. #4041	C₂²	semidirect
88. #4040	C₂²	semidirect
89. #4040	C₂²	semidirect
90. #4040	C₂²	semidirect
91. #4040	C₂²	semidirect
92. #4039	C₂²	semidirect
93. #4038	C₂²	semidirect
94. #4035	C₂²	semidirect
95. #4032	C₂²	semidirect
96. #4032	C₂²	semidirect
97. #4031	C₂²	semidirect
98. #4031	C₂²	semidirect
99. #4031	C₂²	semidirect
100. #4030	C₂²	semidirect
101. #4030	C₂²	semidirect
102. #4030	C₂²	semidirect
103. #4030	C₂²	semidirect
104. #4030	C₂²	semidirect
105. #4030	C₂²	semidirect
106. #4029	C₂²	semidirect
107. #4029	C₂²	semidirect
109. #4028	C₂²	semidirect
110. #4027	C₂²	semidirect
111. D₅×C₂²⋊C₄	C₂²	semidirect
112. D₅×C₂²⋊C₄	C₂²	semidirect
113. #4025	C₂²	semidirect
114. #4023	C₂²	semidirect
115. #4021	C₂²	semidirect
116. #4020	C₂²	semidirect
117. C₄×D₂₀	C₂²	semidirect
118. C₄×D₂₀	C₂²	semidirect
119. C₄×D₂₀	C₂²	semidirect
120. #4016	C₂²	semidirect
121. #4015	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
253. #525	D₅	semidirect
333. C₂×#41	C₂×D₅	semidirect
338. C₂³×C₄	C₂×D₅	semidirect
363. #123	C₂×D₅	semidirect
364. #123	C₂×D₅	semidirect
371. C₂²⋊Q₈	C₂×D₅	semidirect
372. C₂²⋊Q₈	C₂×D₅	semidirect
397. #121	C₂×D₅	semidirect
406. #120	C₂×D₅	semidirect
416. C₄×D₄	C₂×D₅	semidirect
417. C₄×D₄	C₂×D₅	semidirect
418. C₄×D₄	C₂×D₅	semidirect
423. #117	C₂×D₅	semidirect
666. C₅	#3542	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
#66164	2
#66125	2
C₂×#4076	2
#65997	2
#65991	2
#65981	2
#65971	2
#65954	2
#65944	2
#65926	2
#65923	2
#65899	2
#65897	2
#65889	2
#65887	2
#65884	2
D₄×D₂₀	2
#65875	2
#65869	2
#65868	2
#3542	5