Subgroups — C₈×D₁₀₅ #13132353

Order 1680.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₀₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₇⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₃₅	—	3	1	no	maximal, Hall
5	C₂×D₁₀₅	C₄	1	1	yes	characteristic
6	C₃×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
7	Dic₁₀₅	C₄	1	1	yes	characteristic
8	C₈×D₂₁	—	5	1	no	maximal, Hall
9	C₄×D₃₅	—	3	1	no	—
10	C₅×C₇×C₈	D₃	1	1	yes	characteristic, complemented
11	C₇⋊#168	—	3	1	no	—
12	C₈×D₁₅	—	7	1	no	maximal, Hall
13	C₂×C₃×C₅×C₇	C₂×C₄	1	1	yes	characteristic
14	D₁₀₅	C₈	1	2	yes	direct product factor
15	C₄×D₂₁	—	5	1	no	—
16	C₃×C₇×C₈	D₅	1	1	yes	characteristic, complemented
17	C₃⋊(C₇⋊C₈)	—	5	1	no	—
18	C₂×D₃₅	—	3	1	no	—
19	C₄×C₅×C₇	C₂×D₃	1	1	yes	characteristic
20	Dic₃₅	—	3	1	no	—
21	C₄×D₁₅	—	7	1	no	—
22	C₃×C₅×C₈	D₇	1	1	yes	characteristic, complemented
23	C₃⋊#168	—	7	1	no	—
24	C₈×D₇	—	15	1	no	Hall
25	C₃×C₅×C₇	C₂×C₈	1	1	yes	characteristic, complemented, Hall
26	C₂×D₂₁	—	5	1	no	—
27	C₃×C₄×C₇	C₂×D₅	1	1	yes	characteristic
28	Dic₂₁	—	5	1	no	—
29	C₈×D₅	—	21	1	no	Hall
30	C₂×C₅×C₇	C₄×D₃	1	1	yes	characteristic
31	D₃₅	—	3	2	no	—
32	C₂×D₁₅	—	7	1	no	—
33	C₃×C₄×C₅	C₂×D₇	1	1	yes	characteristic
34	Dic₁₅	—	7	1	no	—
35	C₄×D₇	—	15	1	no	—
36	C₇×C₈	D₁₅	1	1	yes	characteristic, complemented
37	C₇⋊C₈	—	15	1	no	—
38	D₃×C₈	—	35	1	no	Hall
39	C₂×C₃×C₇	C₄×D₅	1	1	yes	characteristic
40	D₂₁	—	5	2	no	—
41	C₄×D₅	—	21	1	no	—
42	C₅×C₈	D₂₁	1	1	yes	characteristic, complemented
43	#168	—	21	1	no	—
44	C₅×C₇	D₃×C₈	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×C₅	C₄×D₇	1	1	yes	characteristic
46	D₁₅	—	7	2	no	—
47	C₂×D₇	—	15	1	no	—
48	C₄×C₇	C₂×D₁₅	1	1	yes	characteristic
49	Dic₇	—	15	1	no	—
50	C₄×D₃	—	35	1	no	—
51	C₃×C₈	D₃₅	1	1	yes	characteristic, complemented
52	C₃⋊C₈	—	35	1	no	—
53	C₃×C₇	C₈×D₅	1	1	yes	characteristic, complemented, Hall
54	C₂×D₅	—	21	1	no	—
55	C₄×C₅	C₂×D₂₁	1	1	yes	characteristic
56	Dic₅	—	21	1	no	—
57	C₂×C₈	—	105	1	no	Sylow
58	C₃×C₅	C₈×D₇	1	1	yes	characteristic, complemented, Hall
59	C₂×C₇	C₄×D₁₅	1	1	yes	characteristic
60	D₇	—	15	2	no	—
61	C₂×D₃	—	35	1	no	—
62	C₃×C₄	C₂×D₃₅	1	1	yes	characteristic
63	Dic₃	—	35	1	no	—
64	C₂×C₅	C₄×D₂₁	1	1	yes	characteristic
65	D₅	—	21	2	no	—
66	C₂×C₄	—	105	1	no	—
67	C₈	—	105	1	no	—
68	C₈	D₁₀₅	1	1	yes	characteristic, direct product factor
69	C₇	C₈×D₁₅	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	C₄×D₃₅	1	1	yes	characteristic
71	D₃	—	35	2	no	—
72	C₅	C₈×D₂₁	1	1	yes	characteristic, complemented, Sylow
73	C₂²	—	105	1	no	—
74	C₄	—	105	1	no	—
75	C₄	C₂×D₁₀₅	1	1	yes	characteristic
76	C₃	C₈×D₃₅	1	1	yes	characteristic, complemented, Sylow
77	C₂	—	105	2	no	—
78	C₂	C₄×D₁₀₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	D₁₀₅
commutator, hypocenter	C₃×C₅×C₇	C₂×C₈
Frattini	C₄	C₂×D₁₀₅
Fitting	C₃×C₅×C₇×C₈	C₂
socle	C₂×C₃×C₅×C₇	C₂×C₄
prime radical	C₂×D₁₀₅	C₄
cosocle	C₃×C₄×C₅×C₇	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₇×C₈	C₂	semidirect
3. C₃⋊(C₇⋊#168)	C₂	semidirect
10. C₅×C₇×C₈	D₃	semidirect
14. D₁₀₅	C₈	direct (N × H)
16. C₃×C₇×C₈	D₅	semidirect
22. C₃×C₅×C₈	D₇	semidirect
25. C₃×C₅×C₇	C₂×C₈	semidirect
36. C₇×C₈	D₁₅	semidirect
42. C₅×C₈	D₂₁	semidirect
44. C₅×C₇	D₃×C₈	semidirect
51. C₃×C₈	D₃₅	semidirect
53. C₃×C₇	C₈×D₅	semidirect
58. C₃×C₅	C₈×D₇	semidirect
68. C₈	D₁₀₅	direct (N × H)
69. C₇	C₈×D₁₅	semidirect
72. C₅	C₈×D₂₁	semidirect
76. C₃	C₈×D₃₅	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₀₅	2
C₃×C₅×C₇×C₈	2
C₃⋊(C₇⋊#168)	2
C₈×D₃₅	3
C₈×D₂₁	5
C₈×D₁₅	7

Subgroups — C8×D105 #13132353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×D₁₀₅ #13132353