Subgroups — #13100356

Order 1600.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#87765	C₂	1	2	yes	maximal
2	C₈×#1039	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅²×C₈	C₄	1	1	yes	characteristic
4	C₄×#1039	C₄	1	1	yes	characteristic
5	C₂×#6029	C₂²	1	1	yes	characteristic
6	#87765	C₄	1	4	yes	complemented
7	#64886	—	5	2	no	maximal
8	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic
9	C₂×#1039	C₈	1	2	yes	—
10	C₅²×C₈	C₈	1	2	yes	—
11	#6029	C₂×C₄	1	2	yes	—
12	C₂×#674	—	5	4	no	—
13	C₈×Dic₅	—	5	2	no	—
14	C₈×Dic₅	—	10	2	no	—
15	C₂²×C₅²	C₂×C₈	1	1	yes	characteristic
16	C₄×C₅²	C₄²	1	1	yes	characteristic
17	C₄×C₅²	C₂×C₈	1	1	yes	characteristic
18	#1039	—	2	2	no	—
19	C₂×C₅×C₈	—	2	2	no	—
20	C₂×C₅×C₈	AGL(1,𝔽₅)	1	2	yes	—
21	C₄×Dic₅	—	5	2	no	—
22	C₄×Dic₅	—	10	2	no	—
23	C₂×#168	—	5	2	no	—
24	C₂×#168	—	10	2	no	—
25	#674	—	5	8	no	—
26	#346	—	25	1	no	Sylow
27	C₂×C₅²	C₄×C₈	1	1	yes	characteristic
28	C₂×C₅²	M₃₂	1	2	yes	—
29	C₂×C₄×C₅	—	2	2	no	—
30	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	2	yes	—
31	C₂×Dic₅	—	5	4	no	—
32	C₂×Dic₅	—	10	4	no	—
33	C₅×C₈	—	2	4	no	—
34	C₅×C₈	#170	1	4	yes	—
35	#168	—	5	4	no	—
36	#168	—	10	4	no	—
37	C₂×C₁₆	—	25	2	no	—
38	C₄×C₈	—	25	1	no	—
39	C₅²	#346	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₅	—	2	2	no	—
41	C₂²×C₅	D₅⋊C₈	1	2	yes	—
42	C₄×C₅	—	2	2	no	—
43	C₄×C₅	—	2	2	no	—
44	C₄×C₅	C₄×AGL(1,𝔽₅)	1	2	yes	—
45	C₄×C₅	C₂×#170	1	2	yes	—
46	Dic₅	—	10	8	no	—
47	Dic₅	—	10	4	no	—
48	C₂×C₈	—	25	1	no	—
49	C₂×C₈	#1044	1	1	yes	characteristic
50	C₄²	—	25	1	no	—
51	C₁₆	—	25	4	no	—
52	C₂×C₅	—	2	4	no	—
53	C₂×C₅	—	2	2	no	—
54	C₂×C₅	#3990	1	4	yes	—
55	C₂×C₅	C₄×#170	1	2	yes	—
56	C₂×C₄	—	25	2	no	—
57	C₂×C₄	C₂×#1044	1	1	yes	characteristic
58	C₈	—	25	2	no	—
59	C₈	#6034	1	2	yes	—
60	C₅	—	2	2	no	—
61	C₅	#64886	1	2	yes	complemented
62	C₂²	#87862	1	1	yes	characteristic
63	C₄	—	50	2	no	—
64	C₄	C₄×#1044	1	1	yes	characteristic
65	C₄	C₂×#6034	1	1	yes	characteristic
66	C₂	#11716883	1	2	yes	—
67	C₂	C₄×#6034	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#1044
commutator	C₂×C₅²	C₄×C₈
Fitting	C₂×C₅²×C₈	C₄
socle, prime radical	C₂²×C₅²	C₂×C₈
cosocle	C₂×#6029	C₂²
hypercenter	C₂×C₈	#1044
hypocenter	C₅²	#346
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. #87765	C₄	semidirect
39. C₅²	#346	semidirect
61. C₅	#64886	semidirect

Maximal subgroups

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

subgroup	index
C₂×#87765	2
C₈×#1039	2
#64886	5