Subgroups — Dic₆₄₀ #72210509

Order 2560.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

N	H ≅ G/N	type
29. C₅	Q₅₁₂	semidirect

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