Subgroups — D₂₉₉₆₀ #72295310

Order 59920.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₄₉₈₀	C₂	1	2	yes	maximal, complemented
2	D₅₉₉₂	—	5	1	no	maximal, Hall
3	D₄₂₈₀	—	7	1	no	maximal, Hall
4	D₂₁₄₀	—	7	2	no	—
5	D₂₉₉₆	—	5	2	no	—
6	C₅×C₇×C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×C₈×C₁₀₇	D₅	1	1	yes	characteristic, complemented
8	C₅×C₈×C₁₀₇	D₇	1	1	yes	characteristic, complemented
9	C₂×D₃₇₄₅	—	2	2	no	—
10	C₄×C₅×C₇×C₁₀₇	C₂²	1	1	yes	characteristic
11	D₃₇₄₅	—	4	2	no	—
12	C₂×C₅×C₇×C₁₀₇	D₄	1	1	yes	characteristic
13	C₅×C₇×C₁₀₇	D₈	1	1	yes	characteristic, complemented, Hall
14	C₂×D₇₄₉	—	10	2	no	—
15	C₄×C₇×C₁₀₇	C₂×D₅	1	1	yes	characteristic
16	C₂×D₅₃₅	—	14	2	no	—
17	C₄×C₅×C₁₀₇	C₂×D₇	1	1	yes	characteristic
18	D₈₅₆	—	35	1	no	Hall
19	C₂×C₇×C₁₀₇	D₂₀	1	1	yes	characteristic
20	D₇₄₉	—	20	2	no	—
21	C₂×C₅×C₁₀₇	D₂₈	1	1	yes	characteristic
22	D₅₃₅	—	28	2	no	—
23	D₄₂₈	—	35	2	no	—
24	C₈×C₁₀₇	D₃₅	1	1	yes	characteristic, complemented
25	C₇×C₁₀₇	D₄₀	1	1	yes	characteristic, complemented, Hall
26	D₂₈₀	—	107	1	no	maximal, Hall
27	C₅×C₁₀₇	D₅₆	1	1	yes	characteristic, complemented, Hall
28	C₂×D₁₀₇	—	70	2	no	—
29	C₄×C₁₀₇	C₂×D₃₅	1	1	yes	characteristic
30	D₁₄₀	—	107	2	no	—
31	C₅×C₇×C₈	D₁₀₇	1	1	yes	characteristic, complemented
32	C₂×C₁₀₇	D₁₄₀	1	1	yes	characteristic
33	D₁₀₇	—	140	2	no	—
34	C₂×D₃₅	—	214	2	no	—
35	C₄×C₅×C₇	C₂×D₁₀₇	1	1	yes	characteristic
36	D₅₆	—	535	1	no	Hall
37	C₁₀₇	D₂₈₀	1	1	yes	characteristic, complemented, Sylow
38	D₄₀	—	749	1	no	Hall
39	C₂×C₅×C₇	D₄₂₈	1	1	yes	characteristic
40	D₃₅	—	428	2	no	—
41	D₂₈	—	535	2	no	—
42	C₇×C₈	D₅₃₅	1	1	yes	characteristic, complemented
43	D₂₀	—	749	2	no	—
44	C₅×C₈	D₇₄₉	1	1	yes	characteristic, complemented
45	C₅×C₇	D₈₅₆	1	1	yes	characteristic, complemented, Hall
46	C₂×D₇	—	1070	2	no	—
47	C₄×C₇	C₂×D₅₃₅	1	1	yes	characteristic
48	C₂×D₅	—	1498	2	no	—
49	C₄×C₅	C₂×D₇₄₉	1	1	yes	characteristic
50	D₈	—	3745	1	no	Sylow
51	C₂×C₇	D₂₁₄₀	1	1	yes	characteristic
52	D₇	—	2140	2	no	—
53	C₂×C₅	D₂₉₉₆	1	1	yes	characteristic
54	D₅	—	2996	2	no	—
55	D₄	—	3745	2	no	—
56	C₈	D₃₇₄₅	1	1	yes	characteristic, complemented
57	C₇	D₄₂₈₀	1	1	yes	characteristic, complemented, Sylow
58	C₅	D₅₉₉₂	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	7490	2	no	—
60	C₄	C₂×D₃₇₄₅	1	1	yes	characteristic
61	C₂	—	14980	2	no	—
62	C₂	D₁₄₉₈₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₄₉₈₀
commutator, cosocle	C₄×C₅×C₇×C₁₀₇	C₂²
Frattini	C₄	C₂×D₃₇₄₅
Fitting	C₅×C₇×C₈×C₁₀₇	C₂
socle	C₂×C₅×C₇×C₁₀₇	D₄
hypercenter	C₈	D₃₇₄₅
hypocenter	C₅×C₇×C₁₀₇	D₈
LCS	G ▷ C₄×C₅×C₇×C₁₀₇ ▷ C₂×C₅×C₇×C₁₀₇ ▷ C₅×C₇×C₁₀₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. D₁₄₉₈₀	C₂	semidirect
6. C₅×C₇×C₈×C₁₀₇	C₂	semidirect
7. C₇×C₈×C₁₀₇	D₅	semidirect
8. C₅×C₈×C₁₀₇	D₇	semidirect
13. C₅×C₇×C₁₀₇	D₈	semidirect
24. C₈×C₁₀₇	D₃₅	semidirect
25. C₇×C₁₀₇	D₄₀	semidirect
27. C₅×C₁₀₇	D₅₆	semidirect
31. C₅×C₇×C₈	D₁₀₇	semidirect
37. C₁₀₇	D₂₈₀	semidirect
42. C₇×C₈	D₅₃₅	semidirect
44. C₅×C₈	D₇₄₉	semidirect
45. C₅×C₇	D₈₅₆	semidirect
56. C₈	D₃₇₄₅	semidirect
57. C₇	D₄₂₈₀	semidirect
58. C₅	D₅₉₉₂	semidirect

Maximal subgroups

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

subgroup	index
D₁₄₉₈₀	2
D₅₉₉₂	5
D₄₂₈₀	7
C₅×C₇×C₈×C₁₀₇	2
D₂₈₀	107

Subgroups — D29960 #72295310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉₉₆₀ #72295310