Subgroups — D₁₁₂₀ #72210121

Order 2240.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₆₀	C₂	1	2	yes	maximal, complemented
2	C₅×C₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₈₀	—	2	2	no	—
4	C₅×C₇×C₁₆	C₂²	1	1	yes	characteristic
5	D₂₂₄	—	5	1	no	maximal, Hall
6	D₁₆₀	—	7	1	no	maximal, Hall
7	D₁₄₀	—	4	2	no	—
8	C₅×C₇×C₈	D₄	1	1	yes	characteristic
9	D₁₁₂	—	5	2	no	—
10	C₇×C₃₂	D₅	1	1	yes	characteristic, complemented
11	D₈₀	—	7	2	no	—
12	C₅×C₃₂	D₇	1	1	yes	characteristic, complemented
13	C₂×D₃₅	—	8	2	no	—
14	C₄×C₅×C₇	D₈	1	1	yes	characteristic
15	D₅₆	—	10	2	no	—
16	C₇×C₁₆	C₂×D₅	1	1	yes	characteristic
17	D₄₀	—	14	2	no	—
18	C₅×C₁₆	C₂×D₇	1	1	yes	characteristic
19	C₂×C₅×C₇	D₁₆	1	1	yes	characteristic
20	D₃₅	—	16	2	no	—
21	D₃₂	—	35	1	no	Sylow
22	D₂₈	—	20	2	no	—
23	C₇×C₈	D₂₀	1	1	yes	characteristic
24	D₂₀	—	28	2	no	—
25	C₅×C₈	D₂₈	1	1	yes	characteristic
26	C₅×C₇	D₃₂	1	1	yes	characteristic, complemented, Hall
27	D₁₆	—	35	2	no	—
28	C₃₂	D₃₅	1	1	yes	characteristic, complemented
29	C₂×D₇	—	40	2	no	—
30	C₄×C₇	D₄₀	1	1	yes	characteristic
31	C₂×D₅	—	56	2	no	—
32	C₄×C₅	D₅₆	1	1	yes	characteristic
33	D₈	—	70	2	no	—
34	C₁₆	C₂×D₃₅	1	1	yes	characteristic
35	C₂×C₇	D₈₀	1	1	yes	characteristic
36	D₇	—	80	2	no	—
37	C₂×C₅	D₁₁₂	1	1	yes	characteristic
38	D₅	—	112	2	no	—
39	D₄	—	140	2	no	—
40	C₈	D₁₄₀	1	1	yes	characteristic
41	C₇	D₁₆₀	1	1	yes	characteristic, complemented, Sylow
42	C₅	D₂₂₄	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	280	2	no	—
44	C₄	D₂₈₀	1	1	yes	characteristic
45	C₂	—	560	2	no	—
46	C₂	D₅₆₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₅₆₀
commutator, cosocle	C₅×C₇×C₁₆	C₂²
Frattini	C₁₆	C₂×D₃₅
Fitting	C₅×C₇×C₃₂	C₂
socle	C₂×C₅×C₇	D₁₆
hypercenter	C₃₂	D₃₅
hypocenter	C₅×C₇	D₃₂
LCS	G ▷ C₅×C₇×C₁₆ ▷ C₅×C₇×C₈ ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
1. D₅₆₀	C₂	semidirect
2. C₅×C₇×C₃₂	C₂	semidirect
10. C₇×C₃₂	D₅	semidirect
12. C₅×C₃₂	D₇	semidirect
26. C₅×C₇	D₃₂	semidirect
28. C₃₂	D₃₅	semidirect
41. C₇	D₁₆₀	semidirect
42. C₅	D₂₂₄	semidirect

Maximal subgroups

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

subgroup	index
D₅₆₀	2
C₅×C₇×C₃₂	2
D₂₂₄	5
D₁₆₀	7

Subgroups — D1120 #72210121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁₂₀ #72210121