Subgroups — C₈×#6032 #13100162

Order 1600.

159 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6032	C₂	1	2	yes	maximal
2	C₅×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×#6032	C₄	1	4	yes	—
4	C₂×C₅²×C₈	C₄	1	1	yes	characteristic
5	C₄×C₅×Dic₅	C₂²	1	1	yes	characteristic
6	C₂×C₅×#168	C₄	1	1	yes	characteristic
7	C₈×#170	—	5	1	no	maximal
8	C₈×#168	—	5	1	no	maximal
9	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₂×C₅×Dic₅	C₂×C₄	1	2	yes	—
11	#6032	C₈	1	8	yes	direct product factor
12	C₅²×C₈	C₈	1	2	yes	complemented
13	C₅×#168	C₈	1	2	yes	complemented
14	C₄×#170	—	5	2	no	—
15	C₄×C₅×C₈	—	5	1	no	—
16	C₈×Dic₅	D₅	1	1	yes	characteristic
17	C₄×#168	—	5	2	no	—
18	C₂²×C₅²	C₄²	1	1	yes	characteristic
19	C₄×C₅²	C₂×C₈	1	1	yes	characteristic
20	C₄×C₅²	C₂×C₈	1	1	yes	characteristic
21	C₅×Dic₅	C₂×C₈	1	4	yes	—
22	C₂×#170	—	5	4	no	—
23	C₂×C₅×C₈	—	4	1	no	—
24	C₂×C₅×C₈	—	5	1	no	—
25	C₂×C₅×C₈	Dic₅	1	1	yes	characteristic
26	C₂×C₅×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₄²×C₅	—	5	1	no	—
28	C₄×Dic₅	C₂×D₅	1	1	yes	characteristic
29	C₂×#168	—	5	4	no	—
30	C₂×#168	Dic₅	1	1	yes	characteristic
31	C₈²	—	25	1	no	Sylow
32	C₂×C₅²	C₄×C₈	1	1	yes	characteristic
33	C₂×C₅²	C₄×C₈	1	2	yes	—
34	C₂×C₄×C₅	—	4	1	no	—
35	C₂×C₄×C₅	—	5	2	no	—
36	C₂×C₄×C₅	C₂×Dic₅	1	1	yes	characteristic
37	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
38	C₂×Dic₅	C₄×D₅	1	2	yes	—
39	#170	—	5	8	no	—
40	C₅×C₈	—	4	2	no	—
41	C₅×C₈	—	5	2	no	—
42	C₅×C₈	#168	1	2	yes	complemented
43	C₅×C₈	#170	1	2	yes	complemented
44	#168	—	5	8	no	—
45	#168	#168	1	2	yes	complemented
46	C₄×C₈	—	5	1	no	—
47	C₄×C₈	—	25	2	no	—
48	C₅²	C₈²	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₅	—	4	1	no	—
50	C₂²×C₅	C₄×Dic₅	1	1	yes	characteristic
51	C₂²×C₅	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
52	C₄×C₅	—	4	1	no	—
53	C₄×C₅	—	4	1	no	—
54	C₄×C₅	—	5	4	no	—
55	C₄×C₅	C₂×#168	1	1	yes	characteristic
56	C₄×C₅	C₂×#168	1	1	yes	characteristic
57	C₄×C₅	D₅⋊C₈	1	1	yes	characteristic
58	C₄×C₅	C₂×#170	1	1	yes	characteristic
59	Dic₅	C₈×D₅	1	4	yes	—
60	C₂×C₈	—	5	1	no	—
61	C₂×C₈	—	25	4	no	—
62	C₂×C₈	#1042	1	1	yes	characteristic
63	C₄²	—	5	1	no	—
64	C₂×C₅	—	4	2	no	—
65	C₂×C₅	—	4	1	no	—
66	C₂×C₅	C₄×#168	1	1	yes	characteristic
67	C₂×C₅	C₈×Dic₅	1	2	yes	—
68	C₂×C₅	C₈×AGL(1,𝔽₅)	1	2	yes	—
69	C₂×C₅	C₄×#170	1	1	yes	characteristic
70	C₂×C₄	—	5	2	no	—
71	C₂×C₄	C₂×#1042	1	1	yes	characteristic
72	C₈	—	5	2	no	—
73	C₈	—	25	8	no	—
74	C₈	#6032	1	2	yes	direct product factor
75	C₅	—	4	1	no	—
76	C₅	C₈×#168	1	1	yes	characteristic, complemented
77	C₅	C₈×#170	1	1	yes	characteristic, complemented
78	C₂²	C₄×#1042	1	1	yes	characteristic
79	C₄	—	5	4	no	—
80	C₄	D₅⋊#168	1	1	yes	characteristic
81	C₄	C₂×#6032	1	1	yes	characteristic
82	C₂	C₈×#1042	1	2	yes	—
83	C₂	C₄×#6032	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	#1042
commutator, hypocenter	C₅²	C₈²
Frattini	C₂×C₄	C₂×#1042
Fitting	C₂×C₅²×C₈	C₄
socle, prime radical	C₂²×C₅²	C₄²
cosocle	C₄×C₅×Dic₅	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
11. #6032	C₈	direct (N × H)
12. C₅²×C₈	C₈	semidirect
13. C₅×#168	C₈	semidirect
42. C₅×C₈	#168	semidirect
43. C₅×C₈	#170	semidirect
45. #168	#168	semidirect
48. C₅²	C₈²	semidirect
74. C₈	#6032	direct (N × H)
76. C₅	C₈×#168	semidirect
77. C₅	C₈×#170	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6032	2
C₅×C₈×Dic₅	2
C₈×#170	5
C₈×#168	5

Subgroups — C8×#6032 #13100162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#6032 #13100162