Subgroups — Dic₁₂₈₀ #72211862

Order 5120.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₄₀	C₂	1	2	yes	maximal
2	Q₁₀₂₄	—	5	1	no	maximal, Sylow
3	C₅×C₅₁₂	C₂	1	1	yes	maximal, characteristic
4	Dic₃₂₀	—	2	2	no	—
5	C₅×C₂₅₆	C₂²	1	1	yes	characteristic
6	Dic₁₆₀	—	4	2	no	—
7	C₅×C₁₂₈	D₄	1	1	yes	characteristic
8	Q₅₁₂	—	5	2	no	—
9	C₅₁₂	D₅	1	1	yes	characteristic
10	Dic₈₀	—	8	2	no	—
11	C₅×C₆₄	D₈	1	1	yes	characteristic
12	Q₂₅₆	—	10	2	no	—
13	C₂₅₆	C₂×D₅	1	1	yes	characteristic
14	Dic₄₀	—	16	2	no	—
15	C₅×C₃₂	D₁₆	1	1	yes	characteristic
16	Q₁₂₈	—	20	2	no	—
17	C₁₂₈	D₂₀	1	1	yes	characteristic
18	Dic₂₀	—	32	2	no	—
19	C₅×C₁₆	D₃₂	1	1	yes	characteristic
20	Q₆₄	—	40	2	no	—
21	C₆₄	D₄₀	1	1	yes	characteristic
22	Dic₁₀	—	64	2	no	—
23	C₅×C₈	D₆₄	1	1	yes	characteristic
24	Q₃₂	—	80	2	no	—
25	C₃₂	D₈₀	1	1	yes	characteristic
26	C₄×C₅	D₁₂₈	1	1	yes	characteristic
27	Dic₅	—	128	2	no	—
28	Q₁₆	—	160	2	no	—
29	C₁₆	D₁₆₀	1	1	yes	characteristic
30	C₂×C₅	D₂₅₆	1	1	yes	characteristic
31	Q₈	—	320	2	no	—
32	C₈	D₃₂₀	1	1	yes	characteristic
33	C₅	Q₁₀₂₄	1	1	yes	characteristic, complemented, Sylow
34	C₄	—	640	2	no	—
35	C₄	D₆₄₀	1	1	yes	characteristic
36	C₂	D₁₂₈₀	1	1	yes	characteristic

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

N	H ≅ G/N	type
33. C₅	Q₁₀₂₄	semidirect

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