Subgroups — C₅×#22635 #11945355

Order 1280.

680 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2283	C₂	1	1	yes	maximal, characteristic
2	C₅×#1940	C₂	1	2	yes	maximal, complemented
3	C₅×#1924	C₂	1	2	yes	maximal
4	C₅×#1923	C₂	1	2	yes	maximal
5	C₅×#1832	C₂	1	2	yes	maximal, complemented
6	C₅×#1797	C₂	1	1	yes	maximal, characteristic
7	C₅×#1771	C₂	1	2	yes	maximal, complemented
8	C₅×#1749	C₂	1	1	yes	maximal, characteristic
9	C₅×#1746	C₂	1	2	yes	maximal, complemented
10	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#97	C₂²	1	2	yes	—
18	C₂×C₅×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
20	C₅×#383	C₄	1	2	yes	—
21	C₅×#382	C₄	1	1	yes	characteristic
22	C₅×#382	C₄	1	1	yes	characteristic
23	C₅×#381	C₄	1	2	yes	—
24	C₅×#380	C₄	1	1	yes	characteristic
25	C₅×#380	C₄	1	1	yes	characteristic
26	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₅×#376	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	2	yes	—
31	C₅×#336	C₂²	1	2	yes	—
32	C₅×#336	C₂²	1	2	yes	—
33	C₅×#336	C₂²	1	1	yes	characteristic
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	1	yes	characteristic
37	#22635	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×C₈	C₂³	1	2	yes	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₅	—	2	4	no	—
52	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₅	C₂³	1	2	yes	—
56	C₂×C₄²×C₅	C₂³	1	2	yes	—
57	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₅×C₄⋊C₈	—	2	4	no	—
59	C₅×C₄⋊C₈	—	4	2	no	—
60	C₅×C₄⋊C₈	—	4	2	no	—
61	C₅×C₂²⋊C₈	—	2	4	no	—
62	C₅×C₂²⋊C₈	—	4	1	no	—
63	C₅×C₂²⋊C₈	—	4	1	no	—
64	C₅×#97	—	2	4	no	—
65	C₅×#97	—	2	4	no	—
66	C₄×C₅×C₈	—	2	4	no	—
67	C₅×#95	C₂×C₄	1	2	yes	—
68	C₅×#95	C₂×C₄	1	2	yes	—
69	C₅×#95	C₂×C₄	1	2	yes	—
70	C₅×#95	C₂×C₄	1	2	yes	—
71	C₅×#95	C₂×C₄	1	2	yes	—
72	C₅×#95	C₂×C₄	1	2	yes	—
73	C₅×#95	C₂×C₄	1	2	yes	—
74	C₅×#95	C₂×C₄	1	2	yes	—
75	#2283	C₂×C₅	1	1	yes	characteristic
76	#1940	C₂×C₅	1	2	yes	complemented
77	#1924	C₂×C₅	1	2	yes	—
78	#1923	C₂×C₅	1	2	yes	—
79	#1832	C₂×C₅	1	2	yes	complemented
80	#1797	C₂×C₅	1	1	yes	characteristic
81	#1771	C₂×C₅	1	2	yes	complemented
82	#1749	C₂×C₅	1	1	yes	characteristic
83	#1746	C₂×C₅	1	2	yes	complemented
84	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	—	2	2	no	—
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	—	2	2	no	—
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	2	1	no	—
91	C₂²×C₄×C₅	—	2	1	no	—
92	C₂²×C₄×C₅	—	4	1	no	—
93	C₂²×C₄×C₅	—	4	1	no	—
94	C₂²×C₄×C₅	—	4	1	no	—
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
105	C₂×C₅×C₈	—	2	2	no	—
106	C₂×C₅×C₈	—	2	2	no	—
107	C₂×C₅×C₈	—	2	2	no	—
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	#41	1	4	yes	—
117	C₅×C₄⋊C₄	—	4	1	no	—
118	C₅×C₄⋊C₄	—	4	1	no	—
119	C₅×C₄⋊C₄	—	4	1	no	—
120	C₅×C₄⋊C₄	—	4	1	no	—
121	C₅×C₂²⋊C₄	—	2	4	no	—
122	C₅×C₂²⋊C₄	—	4	2	no	—
123	C₄²×C₅	—	2	2	no	—
124	C₄²×C₅	—	2	2	no	—
125	C₄²×C₅	—	2	2	no	—
126	C₄²×C₅	—	2	2	no	—
127	C₄²×C₅	—	2	2	no	—
128	C₄²×C₅	—	2	2	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₄²×C₅	#41	1	4	yes	—
131	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
133	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
134	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
135	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
136	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
138	C₂×#97	C₂²×C₅	1	2	yes	—
139	C₂×#97	C₂²×C₅	1	2	yes	—
140	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
141	#383	C₄×C₅	1	2	yes	—
142	#382	C₄×C₅	1	1	yes	characteristic
143	#382	C₄×C₅	1	1	yes	characteristic
144	#381	C₄×C₅	1	2	yes	—
145	#380	C₄×C₅	1	1	yes	characteristic
146	#380	C₄×C₅	1	1	yes	characteristic
147	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
149	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
150	#376	C₂²×C₅	1	2	yes	—
151	#336	C₂²×C₅	1	2	yes	—
152	#336	C₂²×C₅	1	1	yes	characteristic
153	#336	C₂²×C₅	1	2	yes	—
154	#336	C₂²×C₅	1	2	yes	—
155	#336	C₂²×C₅	1	2	yes	—
156	#336	C₂²×C₅	1	2	yes	—
157	#336	C₂²×C₅	1	1	yes	characteristic
158	C₂³×C₅	—	2	1	no	—
159	C₂³×C₅	—	2	1	no	—
160	C₂³×C₅	—	2	1	no	—
161	C₂³×C₅	—	2	1	no	—
162	C₂³×C₅	—	2	1	no	—
163	C₂³×C₅	—	2	1	no	—
164	C₂³×C₅	#131	1	2	yes	—
165	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	2	1	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	1	no	—
172	C₂×C₄×C₅	—	2	1	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	4	4	no	—
192	C₂×C₄×C₅	—	4	4	no	—
193	C₂×C₄×C₅	—	4	2	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	#117	1	2	yes	—
196	C₂×C₄×C₅	#117	1	2	yes	—
197	C₂×C₄×C₅	C₂×#41	1	2	yes	—
198	C₂×C₄×C₅	C₂×#41	1	2	yes	—
199	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
201	C₅×C₈	—	2	4	no	—
202	C₅×C₈	—	4	2	no	—
203	C₅×C₈	—	4	2	no	—
204	C₅×C₈	—	4	2	no	—
205	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₅	1	2	yes	—
209	C₂²×C₈	C₂³×C₅	1	2	yes	—
210	C₂²×C₈	C₂³×C₅	1	2	yes	—
211	C₂²×C₈	C₂³×C₅	1	2	yes	—
212	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
217	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
218	C₂×C₄²	—	2	4	no	—
219	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₅	1	2	yes	—
223	C₂×C₄²	C₂³×C₅	1	2	yes	—
224	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
225	C₄⋊C₈	—	2	4	no	—
226	C₄⋊C₈	—	4	2	no	—
227	C₄⋊C₈	—	4	2	no	—
228	C₂²⋊C₈	—	2	4	no	—
229	C₂²⋊C₈	—	4	1	no	—
230	C₂²⋊C₈	—	4	1	no	—
231	#97	—	2	4	no	—
232	#97	—	2	4	no	—
233	C₄×C₈	—	2	4	no	—
234	#95	C₂×C₄×C₅	1	2	yes	—
235	#95	C₂×C₄×C₅	1	2	yes	—
236	#95	C₂×C₄×C₅	1	2	yes	—
237	#95	C₂×C₄×C₅	1	2	yes	—
238	#95	C₂×C₄×C₅	1	2	yes	—
239	#95	C₂×C₄×C₅	1	2	yes	—
240	#95	C₂×C₄×C₅	1	2	yes	—
241	#95	C₂×C₄×C₅	1	2	yes	—
242	C₂²×C₅	—	2	2	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	4	1	no	—
246	C₂²×C₅	—	4	1	no	—
247	C₂²×C₅	—	4	1	no	—
248	C₂²×C₅	—	4	1	no	—
249	C₂²×C₅	C₂×#117	1	1	yes	characteristic
250	C₂²×C₅	C₄×#41	1	1	yes	characteristic
251	C₂²×C₅	#520	1	1	yes	characteristic
252	C₂²×C₅	C₂×#131	1	1	yes	characteristic
253	C₂²×C₅	#568	1	1	yes	characteristic
254	C₂²×C₅	#568	1	1	yes	characteristic
255	C₂²×C₅	#568	1	1	yes	characteristic
256	C₄×C₅	—	2	2	no	—
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	—	4	1	no	—
259	C₄×C₅	—	4	1	no	—
260	C₄×C₅	—	4	1	no	—
261	C₄×C₅	—	4	2	no	—
262	C₄×C₅	—	4	2	no	—
263	C₄×C₅	—	4	2	no	—
264	C₄×C₅	—	4	2	no	—
265	C₄×C₅	#552	1	2	yes	—
266	C₄×C₅	#555	1	2	yes	—
267	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	C₅×#41	1	4	yes	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	4	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₅×#41	1	4	yes	—
314	C₂×C₅	—	4	2	no	—
315	C₂×C₅	#2346	1	1	yes	characteristic
316	C₂×C₅	#2921	1	1	yes	characteristic
317	C₂×C₅	#2924	1	1	yes	characteristic
318	C₂×C₅	#2967	1	1	yes	characteristic
319	C₂×C₅	#2968	1	1	yes	characteristic
320	C₂×C₅	#2992	1	1	yes	characteristic
321	C₂×C₅	#2995	1	1	yes	characteristic
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	C₅×#131	1	2	yes	—
329	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₅×#117	1	2	yes	—
360	C₂×C₄	C₅×#117	1	2	yes	—
361	C₂×C₄	C₂×C₅×#41	1	2	yes	—
362	C₂×C₄	C₂×C₅×#41	1	2	yes	—
363	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
365	C₈	—	2	4	no	—
366	C₈	—	4	2	no	—
367	C₈	—	4	2	no	—
368	C₈	—	4	2	no	—
369	C₅	#22635	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	C₂×C₅×#117	1	1	yes	characteristic
378	C₂²	C₄×C₅×#41	1	1	yes	characteristic
379	C₂²	C₅×#520	1	1	yes	characteristic
380	C₂²	C₂×C₅×#131	1	1	yes	characteristic
381	C₂²	C₅×#568	1	1	yes	characteristic
382	C₂²	C₅×#568	1	1	yes	characteristic
383	C₂²	C₅×#568	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	C₅×#552	1	2	yes	—
394	C₄	C₅×#555	1	2	yes	—
395	C₂	—	4	2	no	—
396	C₂	C₅×#2346	1	1	yes	characteristic
397	C₂	C₅×#2921	1	1	yes	characteristic
398	C₂	C₅×#2924	1	1	yes	characteristic
399	C₂	C₅×#2967	1	1	yes	characteristic
400	C₂	C₅×#2968	1	1	yes	characteristic
401	C₂	C₅×#2992	1	1	yes	characteristic
402	C₂	C₅×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#1940	C₂	semidirect
5. C₅×#1832	C₂	semidirect
7. C₅×#1771	C₂	semidirect
9. C₅×#1746	C₂	semidirect
37. #22635	C₅	direct (N × H)
76. #1940	C₂×C₅	semidirect
79. #1832	C₂×C₅	semidirect
81. #1771	C₂×C₅	semidirect
83. #1746	C₂×C₅	semidirect
369. C₅	#22635	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2283	2
C₅×#1940	2
C₅×#1924	2
C₅×#1923	2
C₅×#1832	2
C₅×#1797	2
C₅×#1771	2
C₅×#1749	2
C₅×#1746	2
#22635	5

Subgroups — C5×#22635 #11945355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22635 #11945355