Subgroups — C₅×#22599 #11945319

Order 1280.

988 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#431	C₂	1	2	yes	maximal
2	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#1939	C₂	1	2	yes	maximal, complemented
4	C₅×#1916	C₂	1	4	yes	maximal, complemented
5	C₅×#1817	C₂	1	2	yes	maximal
6	C₅×#1797	C₂	1	1	yes	maximal, characteristic
7	C₅×C₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
10	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
11	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₅	C₂²	1	2	yes	—
13	C₅×#431	—	2	8	no	—
14	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
16	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×C₈	C₂²	1	4	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
22	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	—
23	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
24	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×#95	C₄	1	2	yes	—
28	C₅×#336	C₂²	1	4	yes	—
29	C₅×#336	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	4	yes	—
31	C₅×#336	C₂²	1	2	yes	—
32	#22599	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₅×C₈	C₂³	1	2	yes	—
39	C₂²×C₅×C₈	C₂³	1	4	yes	—
40	C₂²×C₅×C₈	C₂³	1	2	yes	—
41	C₂×C₅×C₄⋊C₄	—	2	4	no	—
42	C₂×C₅×C₄⋊C₄	C₈	1	8	yes	complemented
43	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
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×C₄²×C₅	—	2	4	no	—
50	C₂×C₄²×C₅	—	2	4	no	—
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	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₅	C₂³	1	2	yes	—
57	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂³	1	2	yes	—
59	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₅×C₄⋊C₈	—	2	8	no	—
61	C₅×C₄⋊C₈	—	2	4	no	—
62	C₅×C₂²⋊C₈	—	2	4	no	—
63	C₅×C₂²⋊C₈	—	2	2	no	—
64	C₅×C₂²⋊C₈	D₄	1	4	yes	—
65	C₄×C₅×C₈	—	2	8	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	C₂×#431	C₂×C₅	1	2	yes	—
72	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
73	#1939	C₂×C₅	1	2	yes	complemented
74	#1916	C₂×C₅	1	4	yes	complemented
75	#1817	C₂×C₅	1	2	yes	—
76	#1797	C₂×C₅	1	1	yes	characteristic
77	C₈×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
78	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
79	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	—	2	4	no	—
81	C₂²×C₄×C₅	—	2	4	no	—
82	C₂²×C₄×C₅	—	2	2	no	—
83	C₂²×C₄×C₅	—	2	2	no	—
84	C₂²×C₄×C₅	—	2	2	no	—
85	C₂²×C₄×C₅	—	2	2	no	—
86	C₂²×C₄×C₅	—	2	4	no	—
87	C₂²×C₄×C₅	—	2	2	no	—
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	4	no	—
90	C₂²×C₄×C₅	—	4	1	no	—
91	C₂²×C₄×C₅	—	4	2	no	—
92	C₂²×C₄×C₅	C₂×C₈	1	8	yes	—
93	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₅	#41	1	2	yes	—
105	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₂×C₅×C₈	—	2	2	no	—
107	C₂×C₅×C₈	—	2	2	no	—
108	C₂×C₅×C₈	—	2	4	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	4	no	—
112	C₂×C₅×C₈	—	2	4	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
115	C₅×C₄⋊C₄	—	2	4	no	—
116	C₅×C₄⋊C₄	—	2	2	no	—
117	C₅×C₄⋊C₄	C₂×C₈	1	8	yes	—
118	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
119	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
120	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
121	C₄²×C₅	—	2	2	no	—
122	C₄²×C₅	—	2	2	no	—
123	C₄²×C₅	—	2	4	no	—
124	C₄²×C₅	—	2	4	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×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
132	C₂²×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
133	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
134	C₂²×C₄²	C₂²×C₅	1	2	yes	—
135	#431	—	2	8	no	—
136	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
137	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
138	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
139	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₄×C₈	C₂²×C₅	1	4	yes	—
142	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
143	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
144	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
145	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
146	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
147	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
149	C₂×#95	C₄×C₅	1	2	yes	—
150	#336	C₂²×C₅	1	2	yes	—
151	#336	C₂²×C₅	1	4	yes	—
152	#336	C₂²×C₅	1	4	yes	—
153	#336	C₂²×C₅	1	2	yes	—
154	C₂³×C₅	—	2	1	no	—
155	C₂³×C₅	—	2	1	no	—
156	C₂³×C₅	—	2	1	no	—
157	C₂³×C₅	—	2	1	no	—
158	C₂³×C₅	C₄×D₄	1	2	yes	—
159	C₂³×C₅	C₂²×C₈	1	2	yes	—
160	C₂³×C₅	#131	1	2	yes	—
161	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₅	—	2	1	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	—	2	2	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	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	1	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	16	no	—
175	C₂×C₄×C₅	—	2	4	no	—
176	C₂×C₄×C₅	—	2	4	no	—
177	C₂×C₄×C₅	—	2	8	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	1	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	4	4	no	—
185	C₂×C₄×C₅	—	4	8	no	—
186	C₂×C₄×C₅	#117	1	2	yes	—
187	C₂×C₄×C₅	#117	1	2	yes	—
188	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
190	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
191	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
192	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
193	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
194	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×#41	1	2	yes	—
197	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
199	C₅×C₈	—	2	4	no	—
200	C₅×C₈	—	4	4	no	—
201	C₅×C₈	—	4	2	no	—
202	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
203	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
206	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₅	1	2	yes	—
208	C₂²×C₈	C₂³×C₅	1	4	yes	—
209	C₂²×C₈	C₂³×C₅	1	2	yes	—
210	C₂×C₄⋊C₄	—	2	4	no	—
211	C₂×C₄⋊C₄	C₅×C₈	1	8	yes	complemented
212	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
214	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
215	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂×C₄²	—	2	4	no	—
219	C₂×C₄²	—	2	4	no	—
220	C₂×C₄²	—	2	4	no	—
221	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
224	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
225	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₅	1	2	yes	—
227	C₂×C₄²	C₂³×C₅	1	2	yes	—
228	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
229	C₄⋊C₈	—	2	8	no	—
230	C₄⋊C₈	—	2	4	no	—
231	C₂²⋊C₈	—	2	4	no	—
232	C₂²⋊C₈	—	2	2	no	—
233	C₂²⋊C₈	C₅×D₄	1	4	yes	—
234	C₄×C₈	—	2	8	no	—
235	C₄×C₈	—	2	4	no	—
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	C₂²×C₅	—	2	2	no	—
241	C₂²×C₅	—	2	2	no	—
242	C₂²×C₅	—	2	2	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	C₈×D₄	1	4	yes	—
247	C₂²×C₅	C₂×#117	1	1	yes	characteristic
248	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
249	C₂²×C₅	#519	1	1	yes	characteristic
250	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
251	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
252	C₂²×C₅	C₂×#131	1	1	yes	characteristic
253	C₂²×C₅	#568	1	1	yes	characteristic
254	C₄×C₅	—	2	2	no	—
255	C₄×C₅	—	2	2	no	—
256	C₄×C₅	—	2	2	no	—
257	C₄×C₅	—	2	4	no	—
258	C₄×C₅	—	2	4	no	—
259	C₄×C₅	—	2	4	no	—
260	C₄×C₅	—	4	1	no	—
261	C₄×C₅	—	4	2	no	—
262	C₄×C₅	#431	1	4	yes	complemented
263	C₄×C₅	#547	1	2	yes	—
264	C₄×C₅	#552	1	2	yes	—
265	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
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	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	C₂×C₅×C₈	1	8	yes	—
279	C₂²×C₄	C₂×C₅×C₈	1	4	yes	—
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	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
290	C₂²×C₄	C₅×#41	1	2	yes	—
291	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	C₂×C₅×C₈	1	8	yes	—
304	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
305	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
306	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	4	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	C₅×#41	1	4	yes	—
317	C₂×C₅	—	2	4	no	—
318	C₂×C₅	#2344	1	1	yes	characteristic
319	C₂×C₅	C₂×#431	1	1	yes	characteristic
320	C₂×C₅	#2924	1	1	yes	characteristic
321	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
322	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
323	C₂×C₅	#2982	1	1	yes	characteristic
324	C₂×C₅	#2984	1	1	yes	characteristic
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	C₄×C₅×D₄	1	2	yes	—
330	C₂³	C₂²×C₅×C₈	1	2	yes	—
331	C₂³	C₅×#131	1	2	yes	—
332	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
333	C₂×C₄	—	2	16	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	1	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	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	C₅×#117	1	2	yes	—
358	C₂×C₄	C₅×#117	1	2	yes	—
359	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
360	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
361	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
362	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
363	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
364	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
365	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
366	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
367	C₂×C₄	C₂×C₅×#41	1	2	yes	—
368	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
369	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
370	C₈	—	2	4	no	—
371	C₈	—	4	4	no	—
372	C₈	—	4	2	no	—
373	C₅	#22599	1	1	yes	characteristic, direct product factor, Sylow
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	C₅×C₈×D₄	1	4	yes	—
381	C₂²	C₂×C₅×#117	1	1	yes	characteristic
382	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
383	C₂²	C₅×#519	1	1	yes	characteristic
384	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
385	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
386	C₂²	C₂×C₅×#131	1	1	yes	characteristic
387	C₂²	C₅×#568	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	2	4	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	2	no	—
396	C₄	C₅×#431	1	4	yes	complemented
397	C₄	C₅×#547	1	2	yes	—
398	C₄	C₅×#552	1	2	yes	—
399	C₂	—	2	4	no	—
400	C₂	C₅×#2344	1	1	yes	characteristic
401	C₂	C₂×C₅×#431	1	1	yes	characteristic
402	C₂	C₅×#2924	1	1	yes	characteristic
403	C₂	C₂×C₅×C₈×D₄	1	1	yes	characteristic
404	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
405	C₂	C₅×#2982	1	1	yes	characteristic
406	C₂	C₅×#2984	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
3. C₅×#1939	C₂	semidirect
4. C₅×#1916	C₂	semidirect
7. C₅×C₈×C₄⋊C₄	C₂	semidirect
32. #22599	C₅	direct (N × H)
42. C₂×C₅×C₄⋊C₄	C₈	semidirect
73. #1939	C₂×C₅	semidirect
74. #1916	C₂×C₅	semidirect
77. C₈×C₄⋊C₄	C₂×C₅	semidirect
211. C₂×C₄⋊C₄	C₅×C₈	semidirect
262. C₄×C₅	#431	semidirect
373. C₅	#22599	direct (N × H)
396. C₄	C₅×#431	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#431	2
C₂×C₄×C₅×C₄⋊C₄	2
C₅×#1939	2
C₅×#1916	2
C₅×#1817	2
C₅×#1797	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×C₂²⋊C₈	2
#22599	5

Subgroups — C5×#22599 #11945319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22599 #11945319