Subgroups — C₅×#20431 #11943151

Order 1280.

1146 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	2	yes	maximal
4	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
5	C₅×#1768	C₂	1	4	yes	maximal, complemented
6	C₅×#1767	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₅×#1729	C₂	1	2	yes	maximal
9	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
10	C₂³×C₅×C₈	C₂²	1	2	yes	—
11	C₂×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₅×#423	C₄	1	8	yes	complemented
15	C₂×C₅×C₄⋊C₈	C₄	1	8	yes	complemented
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₅×#405	—	2	8	no	—
22	C₂×C₅×#97	C₂²	1	4	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	4	yes	—
24	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	—
25	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	—
26	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
27	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
28	C₅×#376	C₂²	1	2	yes	—
29	C₄³×C₅	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	4	yes	—
31	C₅×#336	C₂²	1	4	yes	—
32	#20431	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	1	yes	characteristic
35	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₅×M₁₆	—	2	4	no	—
37	C₂×C₅×M₁₆	—	2	4	no	—
38	C₂×C₅×M₁₆	C₂×C₄	1	8	yes	—
39	C₂²×C₅×C₈	—	2	4	no	—
40	C₂²×C₅×C₈	—	2	4	no	—
41	C₂²×C₅×C₈	C₂×C₄	1	8	yes	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	4	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₅×#117	—	2	2	no	—
46	C₅×#117	—	2	2	no	—
47	C₅×#117	D₄	1	4	yes	—
48	C₅×#117	Q₈	1	4	yes	—
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₅	C₂³	1	2	yes	—
60	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	2	yes	—
63	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
64	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
65	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	—
66	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	—
67	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	—
68	C₅×#97	—	2	8	no	—
69	C₄×C₅×C₈	—	2	8	no	—
70	C₅×#95	C₂×C₄	1	4	yes	—
71	C₅×#95	C₂×C₄	1	4	yes	—
72	C₂×#423	C₂×C₅	1	1	yes	characteristic
73	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
74	C₂×#405	C₂×C₅	1	2	yes	—
75	C₄×#117	C₂×C₅	1	1	yes	characteristic
76	#1768	C₂×C₅	1	4	yes	complemented
77	#1767	C₂×C₅	1	2	yes	complemented
78	C₄×C₄⋊C₈	C₂×C₅	1	2	yes	complemented
79	#1729	C₂×C₅	1	2	yes	—
80	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	—	2	4	no	—
82	C₂²×C₄×C₅	—	4	2	no	—
83	C₂²×C₄×C₅	C₄²	1	4	yes	—
84	C₂²×C₄×C₅	C₄²	1	4	yes	—
85	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
90	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₅	#41	1	2	yes	—
97	C₂²×C₄×C₅	#41	1	2	yes	—
98	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
99	C₅×M₁₆	—	2	16	no	—
100	C₂×C₅×C₈	—	2	16	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	2	4	no	—
104	C₂×C₅×C₈	—	2	2	no	—
105	C₂×C₅×C₈	—	2	2	no	—
106	C₂×C₅×C₈	—	2	4	no	—
107	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
108	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
109	C₂×C₅×C₈	C₂²×C₄	1	8	yes	—
110	C₅×C₄⋊C₄	—	2	4	no	—
111	C₅×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
112	C₅×C₂²⋊C₄	—	2	4	no	—
113	C₅×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
114	C₄²×C₅	—	2	8	no	—
115	C₄²×C₅	—	2	2	no	—
116	C₄²×C₅	—	2	2	no	—
117	C₄²×C₅	—	4	4	no	—
118	C₄²×C₅	C₄²	1	4	yes	—
119	C₄²×C₅	C₄²	1	4	yes	—
120	C₄²×C₅	C₂²×C₄	1	2	yes	—
121	C₄²×C₅	C₂²×C₄	1	2	yes	—
122	C₄²×C₅	C₂²×C₄	1	2	yes	—
123	C₄²×C₅	C₂²×C₄	1	2	yes	—
124	C₄²×C₅	C₂×D₄	1	4	yes	—
125	C₄²×C₅	C₂×Q₈	1	4	yes	—
126	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
127	C₂³×C₈	C₂²×C₅	1	2	yes	—
128	C₂×#117	C₂²×C₅	1	1	yes	characteristic
129	C₂×#117	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
131	#423	C₄×C₅	1	8	yes	complemented
132	C₂×C₄⋊C₈	C₄×C₅	1	8	yes	complemented
133	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
136	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
137	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
138	#405	—	2	8	no	—
139	C₂×#97	C₂²×C₅	1	4	yes	—
140	C₂×C₄×C₈	C₂²×C₅	1	4	yes	—
141	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
142	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
143	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
144	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
145	#376	C₂²×C₅	1	2	yes	—
146	C₄³	C₂²×C₅	1	2	yes	—
147	#336	C₂²×C₅	1	4	yes	—
148	#336	C₂²×C₅	1	4	yes	—
149	C₂³×C₅	—	2	2	no	—
150	C₂³×C₅	—	2	2	no	—
151	C₂³×C₅	C₂×C₄²	1	2	yes	—
152	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
153	C₂³×C₅	#117	1	2	yes	—
154	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₅	—	2	4	no	—
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	2	no	—
158	C₂×C₄×C₅	—	2	4	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	8	no	—
161	C₂×C₄×C₅	—	2	4	no	—
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	2	4	no	—
164	C₂×C₄×C₅	—	4	4	no	—
165	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
166	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
167	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
168	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
169	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
170	C₂×C₄×C₅	C₂×C₄⋊C₄	1	8	yes	—
171	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₅	#117	1	2	yes	—
173	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
174	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
175	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
176	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
177	C₂×C₄×C₅	#131	1	4	yes	—
178	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
184	C₅×C₈	—	2	4	no	—
185	C₅×C₈	—	2	4	no	—
186	C₅×C₈	—	2	8	no	—
187	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
188	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
189	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
190	C₂×M₁₆	—	2	4	no	—
191	C₂×M₁₆	—	2	4	no	—
192	C₂×M₁₆	C₂×C₄×C₅	1	8	yes	—
193	C₂²×C₈	—	2	4	no	—
194	C₂²×C₈	—	2	4	no	—
195	C₂²×C₈	C₂×C₄×C₅	1	8	yes	—
196	C₂²×C₈	C₂³×C₅	1	2	yes	—
197	C₂²×C₈	C₂³×C₅	1	2	yes	—
198	C₂²×C₈	C₂³×C₅	1	4	yes	—
199	#117	—	2	2	no	—
200	#117	—	2	2	no	—
201	#117	C₅×D₄	1	4	yes	—
202	#117	C₅×Q₈	1	4	yes	—
203	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
204	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
208	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
209	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
212	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
213	C₂×C₄²	C₂³×C₅	1	2	yes	—
214	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
215	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
216	C₂×C₄²	C₂³×C₅	1	2	yes	—
217	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
218	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
219	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	—
220	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	—
221	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	—
222	#97	—	2	8	no	—
223	C₄×C₈	—	2	8	no	—
224	#95	C₂×C₄×C₅	1	4	yes	—
225	#95	C₂×C₄×C₅	1	4	yes	—
226	C₂²×C₅	—	2	2	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	2	4	no	—
229	C₂²×C₅	—	2	4	no	—
230	C₂²×C₅	C₄×C₄⋊C₄	1	4	yes	—
231	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
232	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
233	C₂²×C₅	C₂×#117	1	1	yes	characteristic
234	C₂²×C₅	C₂×#131	1	2	yes	—
235	C₂²×C₅	#568	1	2	yes	—
236	C₄×C₅	—	2	2	no	—
237	C₄×C₅	—	2	2	no	—
238	C₄×C₅	—	2	2	no	—
239	C₄×C₅	—	2	8	no	—
240	C₄×C₅	—	4	4	no	—
241	C₄×C₅	C₄×C₄⋊C₄	1	4	yes	—
242	C₄×C₅	#405	1	4	yes	complemented
243	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
245	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
246	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
247	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	C₄²×C₅	1	4	yes	—
251	C₂²×C₄	C₄²×C₅	1	4	yes	—
252	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
253	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
257	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
259	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
261	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
262	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
263	C₂²×C₄	C₅×#41	1	2	yes	—
264	C₂²×C₄	C₅×#41	1	2	yes	—
265	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
266	M₁₆	—	2	16	no	—
267	C₂×C₈	—	2	16	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
275	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
276	C₂×C₈	C₂²×C₄×C₅	1	8	yes	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	C₅×C₄⋊C₄	1	8	yes	—
279	C₂²⋊C₄	—	2	4	no	—
280	C₂²⋊C₄	C₅×C₄⋊C₄	1	8	yes	—
281	C₄²	—	2	8	no	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	2	no	—
284	C₄²	—	4	4	no	—
285	C₄²	C₄²×C₅	1	4	yes	—
286	C₄²	C₄²×C₅	1	4	yes	—
287	C₄²	C₂²×C₄×C₅	1	2	yes	—
288	C₄²	C₂²×C₄×C₅	1	2	yes	—
289	C₄²	C₂²×C₄×C₅	1	2	yes	—
290	C₄²	C₂²×C₄×C₅	1	2	yes	—
291	C₄²	C₂×C₅×D₄	1	4	yes	—
292	C₄²	C₂×C₅×Q₈	1	4	yes	—
293	C₂×C₅	—	2	4	no	—
294	C₂×C₅	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
295	C₂×C₅	C₂×#405	1	1	yes	characteristic
296	C₂×C₅	#2873	1	1	yes	characteristic
297	C₂×C₅	#2906	1	2	yes	—
298	C₂×C₅	#2925	1	2	yes	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	C₂×C₄²×C₅	1	2	yes	—
302	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
303	C₂³	C₅×#117	1	2	yes	—
304	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
316	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
317	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
318	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
319	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
320	C₂×C₄	C₂×C₅×C₄⋊C₄	1	8	yes	—
321	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
322	C₂×C₄	C₅×#117	1	2	yes	—
323	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
324	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
325	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
326	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
327	C₂×C₄	C₅×#131	1	4	yes	—
328	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
329	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
330	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
331	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
332	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
333	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
334	C₈	—	2	4	no	—
335	C₈	—	2	4	no	—
336	C₈	—	2	8	no	—
337	C₅	#20431	1	1	yes	characteristic, direct product factor, Sylow
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	C₄×C₅×C₄⋊C₄	1	4	yes	—
343	C₂²	C₂²×C₄²×C₅	1	1	yes	characteristic
344	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
345	C₂²	C₂×C₅×#117	1	1	yes	characteristic
346	C₂²	C₂×C₅×#131	1	2	yes	—
347	C₂²	C₅×#568	1	2	yes	—
348	C₄	—	2	2	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	8	no	—
352	C₄	—	4	4	no	—
353	C₄	C₄×C₅×C₄⋊C₄	1	4	yes	—
354	C₄	C₅×#405	1	4	yes	complemented
355	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
356	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
357	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
358	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
359	C₂	—	2	4	no	—
360	C₂	C₂×C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
361	C₂	C₂×C₅×#405	1	1	yes	characteristic
362	C₂	C₅×#2873	1	1	yes	characteristic
363	C₂	C₅×#2906	1	2	yes	—
364	C₂	C₅×#2925	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂²×C₄²×C₅
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
5. C₅×#1768	C₂	semidirect
6. C₅×#1767	C₂	semidirect
7. C₄×C₅×C₄⋊C₈	C₂	semidirect
14. C₅×#423	C₄	semidirect
15. C₂×C₅×C₄⋊C₈	C₄	semidirect
32. #20431	C₅	direct (N × H)
76. #1768	C₂×C₅	semidirect
77. #1767	C₂×C₅	semidirect
78. C₄×C₄⋊C₈	C₂×C₅	semidirect
131. #423	C₄×C₅	semidirect
132. C₂×C₄⋊C₈	C₄×C₅	semidirect
242. C₄×C₅	#405	semidirect
337. C₅	#20431	direct (N × H)
354. C₄	C₅×#405	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#423	2
C₂²×C₅×C₄⋊C₈	2
C₂×C₅×#405	2
C₄×C₅×#117	2
C₅×#1768	2
C₅×#1767	2
C₄×C₅×C₄⋊C₈	2
C₅×#1729	2
#20431	5

Subgroups — C5×#20431 #11943151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20431 #11943151