Subgroups — C₅×#22632 #11945352

Order 1280.

828 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₅×#1939	C₂	1	2	yes	maximal, complemented
3	C₅×#1923	C₂	1	4	yes	maximal
4	C₅×#1831	C₂	1	2	yes	maximal, complemented
5	C₅×#1797	C₂	1	1	yes	maximal, characteristic
6	C₅×C₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₅×#1744	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#117	C₄	1	1	yes	characteristic
10	C₂×C₅×#117	C₄	1	1	yes	characteristic
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	4	yes	—
14	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₄×C₅×C₈	C₂²	1	4	yes	—
17	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
18	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
19	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
23	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₅×#376	C₄	1	2	yes	—
25	C₄³×C₅	C₂²	1	2	yes	—
26	C₅×#336	C₂²	1	4	yes	—
27	C₅×#336	C₂²	1	2	yes	—
28	C₅×#336	C₂²	1	1	yes	characteristic
29	C₅×#336	C₂²	1	4	yes	—
30	C₅×#336	C₂²	1	1	yes	characteristic
31	#22632	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×C₈	C₂³	1	2	yes	—
36	C₂²×C₅×C₈	C₂³	1	4	yes	—
37	C₂²×C₅×C₈	C₂³	1	2	yes	—
38	C₅×#117	—	2	4	no	—
39	C₅×#117	C₈	1	8	yes	complemented
40	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
41	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₅	—	2	4	no	—
47	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₅	C₂³	1	2	yes	—
55	C₂×C₄²×C₅	C₂³	1	2	yes	—
56	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₅×C₄⋊C₈	—	2	4	no	—
58	C₅×C₄⋊C₈	—	4	4	no	—
59	C₅×C₂²⋊C₈	—	2	4	no	—
60	C₅×C₂²⋊C₈	—	4	2	no	—
61	C₄×C₅×C₈	—	2	8	no	—
62	C₄×C₅×C₈	—	2	4	no	—
63	C₅×#95	C₂×C₄	1	2	yes	—
64	C₅×#95	C₂×C₄	1	2	yes	—
65	C₅×#95	C₂×C₄	1	2	yes	—
66	C₅×#95	C₂×C₄	1	2	yes	—
67	C₄×#117	C₂×C₅	1	1	yes	characteristic
68	#1939	C₂×C₅	1	2	yes	complemented
69	#1923	C₂×C₅	1	4	yes	—
70	#1831	C₂×C₅	1	2	yes	complemented
71	#1797	C₂×C₅	1	1	yes	characteristic
72	C₈×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
73	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
74	#1744	C₂×C₅	1	2	yes	complemented
75	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅	—	2	2	no	—
77	C₂²×C₄×C₅	—	2	2	no	—
78	C₂²×C₄×C₅	—	2	2	no	—
79	C₂²×C₄×C₅	—	2	2	no	—
80	C₂²×C₄×C₅	—	2	2	no	—
81	C₂²×C₄×C₅	—	2	2	no	—
82	C₂²×C₄×C₅	—	2	1	no	—
83	C₂²×C₄×C₅	—	2	1	no	—
84	C₂²×C₄×C₅	—	4	1	no	—
85	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
86	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₂×C₅×C₈	—	2	2	no	—
97	C₂×C₅×C₈	—	2	2	no	—
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	—	2	4	no	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	4	no	—
102	C₂×C₅×C₈	—	2	4	no	—
103	C₂×C₅×C₈	—	2	2	no	—
104	C₂×C₅×C₈	#41	1	4	yes	—
105	C₅×C₄⋊C₄	—	2	2	no	—
106	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
107	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
108	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
109	C₅×C₂²⋊C₄	—	2	4	no	—
110	C₅×C₂²⋊C₄	C₂×C₈	1	8	yes	—
111	C₄²×C₅	—	2	2	no	—
112	C₄²×C₅	—	2	2	no	—
113	C₄²×C₅	—	2	4	no	—
114	C₄²×C₅	—	2	4	no	—
115	C₄²×C₅	—	2	2	no	—
116	C₄²×C₅	—	2	4	no	—
117	C₄²×C₅	—	2	2	no	—
118	C₄²×C₅	—	2	2	no	—
119	C₄²×C₅	—	4	2	no	—
120	C₄²×C₅	C₂×C₈	1	8	yes	—
121	C₄²×C₅	#41	1	4	yes	—
122	C₂×#117	C₄×C₅	1	1	yes	characteristic
123	C₂×#117	C₄×C₅	1	1	yes	characteristic
124	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
126	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
127	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
128	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
129	C₂×C₄×C₈	C₂²×C₅	1	4	yes	—
130	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
131	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
132	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
133	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
134	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
135	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
136	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
137	#376	C₄×C₅	1	2	yes	—
138	C₄³	C₂²×C₅	1	2	yes	—
139	#336	C₂²×C₅	1	2	yes	—
140	#336	C₂²×C₅	1	1	yes	characteristic
141	#336	C₂²×C₅	1	4	yes	—
142	#336	C₂²×C₅	1	4	yes	—
143	#336	C₂²×C₅	1	1	yes	characteristic
144	C₂³×C₅	—	2	1	no	—
145	C₂³×C₅	—	2	1	no	—
146	C₂³×C₅	—	2	1	no	—
147	C₂³×C₅	—	2	1	no	—
148	C₂³×C₅	—	2	1	no	—
149	C₂³×C₅	—	2	1	no	—
150	C₂³×C₅	C₂²×C₈	1	2	yes	—
151	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₅	—	2	1	no	—
153	C₂×C₄×C₅	—	2	1	no	—
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	1	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	1	no	—
160	C₂×C₄×C₅	—	2	1	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	2	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	8	no	—
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	2	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	4	4	no	—
172	C₂×C₄×C₅	—	4	2	no	—
173	C₂×C₄×C₅	—	4	2	no	—
174	C₂×C₄×C₅	#117	1	2	yes	—
175	C₂×C₄×C₅	#117	1	2	yes	—
176	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
177	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
178	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
179	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
180	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
181	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₅	#131	1	2	yes	—
183	C₂×C₄×C₅	C₂×#41	1	2	yes	—
184	C₂×C₄×C₅	C₂×#41	1	2	yes	—
185	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
187	C₅×C₈	—	2	4	no	—
188	C₅×C₈	—	4	2	no	—
189	C₅×C₈	—	4	4	no	—
190	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
192	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
193	C₂²×C₈	C₂³×C₅	1	2	yes	—
194	C₂²×C₈	C₂³×C₅	1	4	yes	—
195	C₂²×C₈	C₂³×C₅	1	2	yes	—
196	#117	—	2	4	no	—
197	#117	C₅×C₈	1	8	yes	complemented
198	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
199	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
202	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
203	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
204	C₂×C₄²	—	2	4	no	—
205	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
208	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
210	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
211	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
212	C₂×C₄²	C₂³×C₅	1	2	yes	—
213	C₂×C₄²	C₂³×C₅	1	2	yes	—
214	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
215	C₄⋊C₈	—	2	4	no	—
216	C₄⋊C₈	—	4	4	no	—
217	C₂²⋊C₈	—	2	4	no	—
218	C₂²⋊C₈	—	4	2	no	—
219	C₄×C₈	—	2	8	no	—
220	C₄×C₈	—	2	4	no	—
221	#95	C₂×C₄×C₅	1	2	yes	—
222	#95	C₂×C₄×C₅	1	2	yes	—
223	#95	C₂×C₄×C₅	1	2	yes	—
224	#95	C₂×C₄×C₅	1	2	yes	—
225	C₂²×C₅	—	2	2	no	—
226	C₂²×C₅	—	2	2	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	4	1	no	—
229	C₂²×C₅	—	4	1	no	—
230	C₂²×C₅	—	4	1	no	—
231	C₂²×C₅	—	4	1	no	—
232	C₂²×C₅	C₂×#117	1	1	yes	characteristic
233	C₂²×C₅	C₄×#41	1	1	yes	characteristic
234	C₂²×C₅	#520	1	1	yes	characteristic
235	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
236	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
237	C₂²×C₅	C₂×#131	1	1	yes	characteristic
238	C₂²×C₅	#568	1	1	yes	characteristic
239	C₄×C₅	—	2	2	no	—
240	C₄×C₅	—	2	2	no	—
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	—	2	4	no	—
243	C₄×C₅	—	2	4	no	—
244	C₄×C₅	—	2	4	no	—
245	C₄×C₅	—	4	1	no	—
246	C₄×C₅	—	4	2	no	—
247	C₄×C₅	#431	1	4	yes	—
248	C₄×C₅	#552	1	2	yes	—
249	C₄×C₅	#555	1	2	yes	—
250	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	4	1	no	—
260	C₂²×C₄	C₂×C₅×C₈	1	4	yes	—
261	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
266	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
270	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	C₅×#41	1	4	yes	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
282	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
283	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
284	C₂²⋊C₄	—	2	4	no	—
285	C₂²⋊C₄	C₂×C₅×C₈	1	8	yes	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	4	no	—
289	C₄²	—	2	4	no	—
290	C₄²	—	2	4	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	4	2	no	—
295	C₄²	C₂×C₅×C₈	1	8	yes	—
296	C₄²	C₅×#41	1	4	yes	—
297	C₂×C₅	—	4	2	no	—
298	C₂×C₅	#2346	1	1	yes	characteristic
299	C₂×C₅	C₂×#431	1	1	yes	characteristic
300	C₂×C₅	#2924	1	1	yes	characteristic
301	C₂×C₅	C₈×#41	1	1	yes	characteristic
302	C₂×C₅	#2970	1	1	yes	characteristic
303	C₂×C₅	#2988	1	1	yes	characteristic
304	C₂×C₅	#2991	1	1	yes	characteristic
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	C₂²×C₅×C₈	1	2	yes	—
312	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	C₅×#117	1	2	yes	—
336	C₂×C₄	C₅×#117	1	2	yes	—
337	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
338	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
339	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
340	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
341	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
342	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
343	C₂×C₄	C₅×#131	1	2	yes	—
344	C₂×C₄	C₂×C₅×#41	1	2	yes	—
345	C₂×C₄	C₂×C₅×#41	1	2	yes	—
346	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
348	C₈	—	2	4	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	4	no	—
351	C₅	#22632	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	C₂×C₅×#117	1	1	yes	characteristic
360	C₂²	C₄×C₅×#41	1	1	yes	characteristic
361	C₂²	C₅×#520	1	1	yes	characteristic
362	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
363	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
364	C₂²	C₂×C₅×#131	1	1	yes	characteristic
365	C₂²	C₅×#568	1	1	yes	characteristic
366	C₄	—	2	4	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	2	4	no	—
371	C₄	—	2	4	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	1	no	—
374	C₄	C₅×#431	1	4	yes	—
375	C₄	C₅×#552	1	2	yes	—
376	C₄	C₅×#555	1	2	yes	—
377	C₂	—	4	2	no	—
378	C₂	C₅×#2346	1	1	yes	characteristic
379	C₂	C₂×C₅×#431	1	1	yes	characteristic
380	C₂	C₅×#2924	1	1	yes	characteristic
381	C₂	C₅×C₈×#41	1	1	yes	characteristic
382	C₂	C₅×#2970	1	1	yes	characteristic
383	C₂	C₅×#2988	1	1	yes	characteristic
384	C₂	C₅×#2991	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂² ▷ 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×#1939	C₂	semidirect
4. C₅×#1831	C₂	semidirect
6. C₅×C₈×C₄⋊C₄	C₂	semidirect
8. C₅×#1744	C₂	semidirect
31. #22632	C₅	direct (N × H)
39. C₅×#117	C₈	semidirect
68. #1939	C₂×C₅	semidirect
70. #1831	C₂×C₅	semidirect
72. C₈×C₄⋊C₄	C₂×C₅	semidirect
74. #1744	C₂×C₅	semidirect
197. #117	C₅×C₈	semidirect
351. C₅	#22632	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×#117	2
C₅×#1939	2
C₅×#1923	2
C₅×#1831	2
C₅×#1797	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×C₂²⋊C₈	2
C₅×#1744	2
#22632	5

Subgroups — C5×#22632 #11945352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22632 #11945352