Subgroups — C₅×#33490 #11956210

Order 1280.

574 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2929	C₂	1	1	yes	maximal, characteristic
2	C₅×#2169	C₂	1	2	yes	maximal, complemented
3	C₅×#2168	C₂	1	2	yes	maximal, complemented
4	C₅×#2168	C₂	1	2	yes	maximal, complemented
5	C₅×D₄×C₁₆	C₂	1	2	yes	maximal, complemented
6	C₅×#2164	C₂	1	2	yes	maximal, complemented
7	C₅×#2113	C₂	1	2	yes	maximal, complemented
8	C₅×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#131	C₂²	1	1	yes	characteristic
11	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×#525	C₄	1	1	yes	characteristic
13	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
14	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
15	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
16	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
19	C₅×#435	C₄	1	2	yes	—
20	C₅×#435	C₄	1	2	yes	—
21	C₅×C₈×D₄	C₂²	1	2	yes	—
22	C₅×C₈×D₄	C₂²	1	2	yes	—
23	C₅×#424	C₄	1	1	yes	characteristic
24	C₅×#408	C₄	1	1	yes	characteristic
25	C₅×#407	C₄	1	1	yes	characteristic
26	C₅×#405	C₂²	1	1	yes	characteristic
27	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
28	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
29	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
30	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
31	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
33	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
34	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
35	C₅×#346	C₂²	1	2	yes	complemented
36	C₄×C₅×C₁₆	C₂²	1	2	yes	complemented
37	#33490	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₅×#131	—	4	1	no	—
41	C₅×#131	—	4	1	no	—
42	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
43	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
44	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
45	C₂²×C₅×C₈	—	4	1	no	—
46	C₂²×C₅×C₈	—	4	1	no	—
47	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₅×#123	C₈	1	2	yes	—
55	C₅×C₂²⋊Q₈	C₈	1	1	yes	characteristic
56	C₅×C₂²⋊Q₈	C₈	1	1	yes	characteristic
57	C₅×#121	C₈	1	1	yes	characteristic
58	C₅×#121	C₈	1	1	yes	characteristic
59	C₅×#120	C₈	1	2	yes	—
60	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
61	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
62	C₅×#117	C₂×C₄	1	1	yes	characteristic
63	C₅×M₃₂	—	4	1	no	—
64	C₅×M₃₂	—	4	1	no	—
65	C₅×M₃₂	—	4	2	no	—
66	C₂×C₅×C₁₆	—	4	1	no	—
67	C₂×C₅×C₁₆	—	4	1	no	—
68	C₂×C₅×C₁₆	—	4	2	no	—
69	C₂×C₅×C₁₆	C₂³	1	2	yes	—
70	C₂×C₅×C₁₆	C₂³	1	2	yes	—
71	C₂×C₅×C₁₆	C₂³	1	2	yes	—
72	C₂×C₅×C₁₆	C₂³	1	2	yes	—
73	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
74	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
75	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
76	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
77	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
78	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
79	C₅×#97	C₂×C₄	1	2	yes	—
80	C₄×C₅×C₈	C₂³	1	2	yes	—
81	#2929	C₂×C₅	1	1	yes	characteristic
82	#2169	C₂×C₅	1	2	yes	complemented
83	#2168	C₂×C₅	1	2	yes	complemented
84	#2168	C₂×C₅	1	2	yes	complemented
85	D₄×C₁₆	C₂×C₅	1	2	yes	complemented
86	#2164	C₂×C₅	1	2	yes	complemented
87	#2113	C₂×C₅	1	2	yes	complemented
88	#2112	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
91	C₅×#41	—	4	1	no	—
92	C₅×#41	—	4	1	no	—
93	C₂×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
94	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
95	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
96	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
97	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
98	C₂²×C₄×C₅	—	4	1	no	—
99	C₂²×C₄×C₅	—	4	1	no	—
100	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₅×M₁₆	—	4	1	no	—
108	C₅×M₁₆	—	4	2	no	—
109	C₅×M₁₆	—	4	1	no	—
110	C₂×C₅×C₈	—	2	1	no	—
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	—	2	1	no	—
113	C₂×C₅×C₈	—	2	1	no	—
114	C₂×C₅×C₈	—	2	1	no	—
115	C₂×C₅×C₈	—	2	1	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	4	1	no	—
119	C₂×C₅×C₈	—	4	1	no	—
120	C₂×C₅×C₈	—	4	1	no	—
121	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
125	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
127	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
128	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
129	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
130	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
131	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
132	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
133	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
134	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
135	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
136	C₄²×C₅	C₂²×C₄	1	2	yes	—
137	C₅×C₁₆	—	2	2	no	—
138	C₅×C₁₆	—	2	2	no	—
139	C₅×C₁₆	—	2	2	no	—
140	C₅×C₁₆	—	2	2	no	—
141	C₂×#131	C₂²×C₅	1	1	yes	characteristic
142	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
143	#525	C₄×C₅	1	1	yes	characteristic
144	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
145	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
146	C₂×M₃₂	C₂²×C₅	1	2	yes	complemented
147	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
148	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
149	C₂²×C₁₆	C₂²×C₅	1	2	yes	complemented
150	#435	C₄×C₅	1	2	yes	—
151	#435	C₄×C₅	1	2	yes	—
152	C₈×D₄	C₂²×C₅	1	2	yes	—
153	C₈×D₄	C₂²×C₅	1	2	yes	—
154	#424	C₄×C₅	1	1	yes	characteristic
155	#408	C₄×C₅	1	1	yes	characteristic
156	#407	C₄×C₅	1	1	yes	characteristic
157	#405	C₂²×C₅	1	1	yes	characteristic
158	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
159	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
160	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
161	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
162	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
163	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
164	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
165	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
166	#346	C₂²×C₅	1	2	yes	complemented
167	C₄×C₁₆	C₂²×C₅	1	2	yes	complemented
168	C₂³×C₅	—	2	2	no	—
169	C₂³×C₅	—	4	1	no	—
170	C₂³×C₅	—	4	1	no	—
171	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
172	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
173	C₂³×C₅	C₂²×C₈	1	2	yes	—
174	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
175	C₅×Q₈	—	4	1	no	—
176	C₅×D₄	—	2	4	no	—
177	C₅×D₄	—	4	2	no	—
178	C₅×D₄	—	4	1	no	—
179	C₅×D₄	—	4	2	no	—
180	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
185	C₂×C₄×C₅	—	2	1	no	—
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	4	1	no	—
189	C₂×C₄×C₅	—	4	1	no	—
190	C₂×C₄×C₅	—	4	1	no	—
191	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
192	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
193	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
196	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
198	C₅×C₈	—	2	1	no	—
199	C₅×C₈	—	2	1	no	—
200	C₅×C₈	—	2	1	no	—
201	C₅×C₈	—	2	2	no	—
202	C₅×C₈	—	2	2	no	—
203	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
204	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
207	#131	—	4	1	no	—
208	#131	—	4	1	no	—
209	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
211	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂²×C₈	—	4	1	no	—
213	C₂²×C₈	—	4	1	no	—
214	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
220	C₂²×C₈	C₂³×C₅	1	2	yes	—
221	#123	C₅×C₈	1	2	yes	—
222	C₂²⋊Q₈	C₅×C₈	1	1	yes	characteristic
223	C₂²⋊Q₈	C₅×C₈	1	1	yes	characteristic
224	#121	C₅×C₈	1	1	yes	characteristic
225	#121	C₅×C₈	1	1	yes	characteristic
226	#120	C₅×C₈	1	2	yes	—
227	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
228	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
229	#117	C₂×C₄×C₅	1	1	yes	characteristic
230	M₃₂	—	4	1	no	—
231	M₃₂	—	4	1	no	—
232	M₃₂	—	4	2	no	—
233	C₂×C₁₆	—	4	1	no	—
234	C₂×C₁₆	—	4	1	no	—
235	C₂×C₁₆	—	4	2	no	—
236	C₂×C₁₆	C₂³×C₅	1	2	yes	—
237	C₂×C₁₆	C₂³×C₅	1	2	yes	—
238	C₂×C₁₆	C₂³×C₅	1	2	yes	—
239	C₂×C₁₆	C₂³×C₅	1	2	yes	—
240	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
241	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
242	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
243	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
244	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
245	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
246	#97	C₂×C₄×C₅	1	2	yes	—
247	C₄×C₈	C₂³×C₅	1	2	yes	—
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	2	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	2	1	no	—
253	C₂²×C₅	—	2	1	no	—
254	C₂²×C₅	—	2	2	no	—
255	C₂²×C₅	—	2	1	no	—
256	C₂²×C₅	—	2	1	no	—
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	2	2	no	—
259	C₂²×C₅	—	4	4	no	—
260	C₂²×C₅	#504	1	2	yes	—
261	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
262	C₄×C₅	—	2	2	no	—
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	2	1	no	—
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	#518	1	1	yes	characteristic
269	C₄×C₅	#568	1	1	yes	characteristic
270	C₂⁴	C₂×C₅×C₈	1	1	yes	characteristic
271	#41	—	4	1	no	—
272	#41	—	4	1	no	—
273	C₂×Q₈	C₂×C₅×C₈	1	1	yes	characteristic
274	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
275	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
276	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
277	C₂×D₄	C₂×C₅×C₈	1	1	yes	characteristic
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	1	yes	characteristic
287	M₁₆	—	4	2	no	—
288	M₁₆	—	4	1	no	—
289	M₁₆	—	4	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
302	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
304	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
305	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
306	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
307	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
308	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
309	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
310	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
311	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
312	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
313	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
314	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
315	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
316	C₄²	C₂²×C₄×C₅	1	2	yes	—
317	C₁₆	—	2	2	no	—
318	C₁₆	—	2	2	no	—
319	C₁₆	—	2	2	no	—
320	C₁₆	—	2	2	no	—
321	C₂×C₅	—	2	2	no	—
322	C₂×C₅	—	4	2	no	—
323	C₂×C₅	—	4	1	no	—
324	C₂×C₅	—	4	1	no	—
325	C₂×C₅	#2972	1	1	yes	characteristic
326	C₂×C₅	C₂×#504	1	1	yes	characteristic
327	C₂×C₅	#3407	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
332	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
333	C₂³	C₂²×C₅×C₈	1	2	yes	—
334	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
335	Q₈	—	4	1	no	—
336	D₄	—	2	4	no	—
337	D₄	—	4	1	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
352	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
353	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
356	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
357	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	2	no	—
362	C₈	—	2	2	no	—
363	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
364	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
365	C₅	#33490	1	1	yes	characteristic, direct product factor, Sylow
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	4	no	—
378	C₂²	C₅×#504	1	2	yes	—
379	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	C₅×#518	1	1	yes	characteristic
387	C₄	C₅×#568	1	1	yes	characteristic
388	C₂	—	2	2	no	—
389	C₂	—	4	1	no	—
390	C₂	—	4	1	no	—
391	C₂	—	4	2	no	—
392	C₂	C₅×#2972	1	1	yes	characteristic
393	C₂	C₂×C₅×#504	1	1	yes	characteristic
394	C₂	C₅×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂³×C₈
prime radical	C₅×#525	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2169	C₂	semidirect
3. C₅×#2168	C₂	semidirect
4. C₅×#2168	C₂	semidirect
5. C₅×D₄×C₁₆	C₂	semidirect
6. C₅×#2164	C₂	semidirect
7. C₅×#2113	C₂	semidirect
8. C₅×#2112	C₂	semidirect
9. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
15. C₂×C₅×M₃₂	C₂²	semidirect
18. C₂²×C₅×C₁₆	C₂²	semidirect
27. C₅×C₄⋊C₁₆	C₂²	semidirect
28. C₅×C₄⋊C₁₆	C₂²	semidirect
33. C₅×C₂²⋊C₁₆	C₂²	semidirect
34. C₅×C₂²⋊C₁₆	C₂²	semidirect
35. C₅×#346	C₂²	semidirect
36. C₄×C₅×C₁₆	C₂²	semidirect
37. #33490	C₅	direct (N × H)
82. #2169	C₂×C₅	semidirect
83. #2168	C₂×C₅	semidirect
84. #2168	C₂×C₅	semidirect
85. D₄×C₁₆	C₂×C₅	semidirect
86. #2164	C₂×C₅	semidirect
87. #2113	C₂×C₅	semidirect
88. #2112	C₂×C₅	semidirect
89. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
146. C₂×M₃₂	C₂²×C₅	semidirect
149. C₂²×C₁₆	C₂²×C₅	semidirect
158. C₄⋊C₁₆	C₂²×C₅	semidirect
159. C₄⋊C₁₆	C₂²×C₅	semidirect
164. C₂²⋊C₁₆	C₂²×C₅	semidirect
165. C₂²⋊C₁₆	C₂²×C₅	semidirect
166. #346	C₂²×C₅	semidirect
167. C₄×C₁₆	C₂²×C₅	semidirect
365. C₅	#33490	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×#2929	2
C₅×#2169	2
C₅×#2168	2
C₅×D₄×C₁₆	2
C₅×#2164	2
C₅×#2113	2
C₅×#2112	2
C₂×C₅×C₂²⋊C₁₆	2
#33490	5

Subgroups — C5×#33490 #11956210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33490 #11956210