Subgroups — C₅×#22628 #11945348

Order 1280.

724 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2285	C₂	1	1	yes	maximal, characteristic
2	C₅×#1940	C₂	1	2	yes	maximal, complemented
3	C₅×#1917	C₂	1	2	yes	maximal, complemented
4	C₅×#1916	C₂	1	2	yes	maximal, complemented
5	C₅×#1798	C₂	1	2	yes	maximal
6	C₅×#1797	C₂	1	1	yes	maximal, characteristic
7	C₅×#1771	C₂	1	2	yes	maximal, complemented
8	C₅×#1750	C₂	1	2	yes	maximal
9	C₅×#1749	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×#117	C₂²	1	2	yes	—
11	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#97	C₂²	1	2	yes	—
19	C₂×C₅×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₅×#384	C₄	1	1	yes	characteristic
22	C₅×#384	C₄	1	1	yes	characteristic
23	C₅×#382	C₄	1	2	yes	—
24	C₅×#380	C₄	1	2	yes	—
25	C₅×#380	C₄	1	1	yes	characteristic
26	C₅×#380	C₄	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₅×#336	C₂²	1	2	yes	—
31	C₅×#336	C₂²	1	2	yes	—
32	C₅×#336	C₂²	1	1	yes	characteristic
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	2	yes	—
37	#22628	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	C₅×#117	—	4	2	no	—
46	C₅×#117	—	4	2	no	—
47	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₅	—	2	4	no	—
58	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂³	1	2	yes	—
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	2	yes	—
63	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊C₈	—	2	4	no	—
65	C₅×C₄⋊C₈	—	4	2	no	—
66	C₅×C₄⋊C₈	—	4	2	no	—
67	C₅×C₂²⋊C₈	—	2	4	no	—
68	C₅×C₂²⋊C₈	—	2	2	no	—
69	C₅×C₂²⋊C₈	Q₈	1	4	yes	—
70	C₅×#97	—	2	4	no	—
71	C₅×#97	—	4	2	no	—
72	C₄×C₅×C₈	—	4	2	no	—
73	C₅×#95	C₂×C₄	1	2	yes	—
74	C₅×#95	C₂×C₄	1	2	yes	—
75	C₅×#95	C₂×C₄	1	2	yes	—
76	C₅×#95	C₂×C₄	1	2	yes	—
77	#2285	C₂×C₅	1	1	yes	characteristic
78	#1940	C₂×C₅	1	2	yes	complemented
79	#1917	C₂×C₅	1	2	yes	complemented
80	#1916	C₂×C₅	1	2	yes	complemented
81	#1798	C₂×C₅	1	2	yes	—
82	#1797	C₂×C₅	1	1	yes	characteristic
83	#1771	C₂×C₅	1	2	yes	complemented
84	#1750	C₂×C₅	1	2	yes	—
85	#1749	C₂×C₅	1	1	yes	characteristic
86	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
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	2	no	—
91	C₂²×C₄×C₅	—	2	2	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	2	yes	—
97	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₅	#41	1	2	yes	—
106	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
119	C₅×C₄⋊C₄	—	2	4	no	—
120	C₅×C₄⋊C₄	—	4	1	no	—
121	C₅×C₄⋊C₄	—	4	1	no	—
122	C₅×C₄⋊C₄	—	4	1	no	—
123	C₅×C₄⋊C₄	—	4	1	no	—
124	C₅×C₄⋊C₄	—	4	2	no	—
125	C₅×C₄⋊C₄	—	4	2	no	—
126	C₅×C₄⋊C₄	—	4	2	no	—
127	C₅×C₂²⋊C₄	—	4	2	no	—
128	C₅×C₂²⋊C₄	—	4	2	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₄²×C₅	—	2	2	no	—
131	C₄²×C₅	—	2	2	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	—	2	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	#41	1	4	yes	—
137	C₂×#117	C₂²×C₅	1	2	yes	—
138	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
140	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
141	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
142	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
143	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×#97	C₂²×C₅	1	2	yes	—
146	C₂×#97	C₂²×C₅	1	2	yes	—
147	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
148	#384	C₄×C₅	1	1	yes	characteristic
149	#384	C₄×C₅	1	1	yes	characteristic
150	#382	C₄×C₅	1	2	yes	—
151	#380	C₄×C₅	1	2	yes	—
152	#380	C₄×C₅	1	1	yes	characteristic
153	#380	C₄×C₅	1	1	yes	characteristic
154	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
155	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
156	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	#336	C₂²×C₅	1	1	yes	characteristic
158	#336	C₂²×C₅	1	1	yes	characteristic
159	#336	C₂²×C₅	1	2	yes	—
160	#336	C₂²×C₅	1	2	yes	—
161	#336	C₂²×C₅	1	2	yes	—
162	#336	C₂²×C₅	1	2	yes	—
163	#336	C₂²×C₅	1	2	yes	—
164	C₂³×C₅	—	2	1	no	—
165	C₂³×C₅	—	2	1	no	—
166	C₂³×C₅	—	2	1	no	—
167	C₂³×C₅	—	2	1	no	—
168	C₂³×C₅	—	2	1	no	—
169	C₂³×C₅	—	2	1	no	—
170	C₂³×C₅	C₄×Q₈	1	2	yes	—
171	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₅	—	2	1	no	—
173	C₂×C₄×C₅	—	2	1	no	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	4	no	—
181	C₂×C₄×C₅	—	2	4	no	—
182	C₂×C₄×C₅	—	2	1	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	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	4	4	no	—
198	C₂×C₄×C₅	—	4	4	no	—
199	C₂×C₄×C₅	#117	1	2	yes	—
200	C₂×C₄×C₅	#117	1	2	yes	—
201	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
202	C₂×C₄×C₅	#131	1	2	yes	—
203	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#41	1	2	yes	—
206	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
207	C₅×C₈	—	2	4	no	—
208	C₅×C₈	—	4	2	no	—
209	C₅×C₈	—	4	2	no	—
210	C₅×C₈	—	4	2	no	—
211	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₅	1	2	yes	—
215	C₂²×C₈	C₂³×C₅	1	2	yes	—
216	C₂²×C₈	C₂³×C₅	1	2	yes	—
217	C₂²×C₈	C₂³×C₅	1	2	yes	—
218	#117	—	4	2	no	—
219	#117	—	4	2	no	—
220	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
222	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
230	C₂×C₄²	—	2	4	no	—
231	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₅	1	2	yes	—
234	C₂×C₄²	C₂³×C₅	1	2	yes	—
235	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
237	C₄⋊C₈	—	2	4	no	—
238	C₄⋊C₈	—	4	2	no	—
239	C₄⋊C₈	—	4	2	no	—
240	C₂²⋊C₈	—	2	4	no	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	C₅×Q₈	1	4	yes	—
243	#97	—	2	4	no	—
244	#97	—	4	2	no	—
245	C₄×C₈	—	4	2	no	—
246	#95	C₂×C₄×C₅	1	2	yes	—
247	#95	C₂×C₄×C₅	1	2	yes	—
248	#95	C₂×C₄×C₅	1	2	yes	—
249	#95	C₂×C₄×C₅	1	2	yes	—
250	C₂²×C₅	—	2	2	no	—
251	C₂²×C₅	—	2	2	no	—
252	C₂²×C₅	—	2	2	no	—
253	C₂²×C₅	—	4	1	no	—
254	C₂²×C₅	—	4	1	no	—
255	C₂²×C₅	—	4	1	no	—
256	C₂²×C₅	—	4	1	no	—
257	C₂²×C₅	C₂×#117	1	1	yes	characteristic
258	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
259	C₂²×C₅	#518	1	1	yes	characteristic
260	C₂²×C₅	C₂×#131	1	1	yes	characteristic
261	C₂²×C₅	#568	1	1	yes	characteristic
262	C₂²×C₅	#568	1	1	yes	characteristic
263	C₂²×C₅	#568	1	1	yes	characteristic
264	C₄×C₅	—	2	2	no	—
265	C₄×C₅	—	2	2	no	—
266	C₄×C₅	—	2	2	no	—
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	—	4	1	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	—	4	2	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	—	4	2	no	—
273	C₄×C₅	#553	1	2	yes	—
274	C₄×C₅	#554	1	2	yes	—
275	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
294	C₂²×C₄	C₅×#41	1	2	yes	—
295	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	C₅×#41	1	4	yes	—
326	C₂×C₅	—	4	2	no	—
327	C₂×C₅	#2345	1	1	yes	characteristic
328	C₂×C₅	#2921	1	1	yes	characteristic
329	C₂×C₅	#2924	1	1	yes	characteristic
330	C₂×C₅	#2961	1	1	yes	characteristic
331	C₂×C₅	#2962	1	1	yes	characteristic
332	C₂×C₅	#2980	1	1	yes	characteristic
333	C₂×C₅	#2981	1	1	yes	characteristic
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	C₄×C₅×Q₈	1	2	yes	—
341	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	C₅×#117	1	2	yes	—
370	C₂×C₄	C₅×#117	1	2	yes	—
371	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
372	C₂×C₄	C₅×#131	1	2	yes	—
373	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
375	C₂×C₄	C₂×C₅×#41	1	2	yes	—
376	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
377	C₈	—	2	4	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₅	#22628	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	C₂×C₅×#117	1	1	yes	characteristic
390	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
391	C₂²	C₅×#518	1	1	yes	characteristic
392	C₂²	C₂×C₅×#131	1	1	yes	characteristic
393	C₂²	C₅×#568	1	1	yes	characteristic
394	C₂²	C₅×#568	1	1	yes	characteristic
395	C₂²	C₅×#568	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	C₅×#553	1	2	yes	—
406	C₄	C₅×#554	1	2	yes	—
407	C₂	—	4	2	no	—
408	C₂	C₅×#2345	1	1	yes	characteristic
409	C₂	C₅×#2921	1	1	yes	characteristic
410	C₂	C₅×#2924	1	1	yes	characteristic
411	C₂	C₅×#2961	1	1	yes	characteristic
412	C₂	C₅×#2962	1	1	yes	characteristic
413	C₂	C₅×#2980	1	1	yes	characteristic
414	C₂	C₅×#2981	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
3. C₅×#1917	C₂	semidirect
4. C₅×#1916	C₂	semidirect
7. C₅×#1771	C₂	semidirect
37. #22628	C₅	direct (N × H)
78. #1940	C₂×C₅	semidirect
79. #1917	C₂×C₅	semidirect
80. #1916	C₂×C₅	semidirect
83. #1771	C₂×C₅	semidirect
381. C₅	#22628	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×#2285	2
C₅×#1940	2
C₅×#1917	2
C₅×#1916	2
C₅×#1798	2
C₅×#1797	2
C₅×#1771	2
C₅×#1750	2
C₅×#1749	2
#22628	5

Subgroups — C5×#22628 #11945348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22628 #11945348