Subgroups — Dic₂₅₆₀ #72212813

Order 10240.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₂₈₀	C₂	1	2	yes	maximal
2	Dic₆₄₀	—	2	2	no	—
3	Q₂₀₄₈	—	5	1	no	maximal, Sylow
4	Q₁₀₂₄	—	5	2	no	—
5	C₅×C₁₀₂₄	C₂	1	1	yes	maximal, characteristic
6	C₅×C₅₁₂	C₂²	1	1	yes	characteristic
7	C₁₀₂₄	D₅	1	1	yes	characteristic
8	Dic₃₂₀	—	4	2	no	—
9	C₅×C₂₅₆	D₄	1	1	yes	characteristic
10	Dic₁₆₀	—	8	2	no	—
11	C₅×C₁₂₈	D₈	1	1	yes	characteristic
12	Q₅₁₂	—	10	2	no	—
13	C₅₁₂	C₂×D₅	1	1	yes	characteristic
14	Dic₈₀	—	16	2	no	—
15	C₅×C₆₄	D₁₆	1	1	yes	characteristic
16	Q₂₅₆	—	20	2	no	—
17	C₂₅₆	D₂₀	1	1	yes	characteristic
18	Dic₄₀	—	32	2	no	—
19	C₅×C₃₂	D₃₂	1	1	yes	characteristic
20	Q₁₂₈	—	40	2	no	—
21	C₁₂₈	D₄₀	1	1	yes	characteristic
22	Dic₂₀	—	64	2	no	—
23	C₅×C₁₆	D₆₄	1	1	yes	characteristic
24	Q₆₄	—	80	2	no	—
25	C₆₄	D₈₀	1	1	yes	characteristic
26	Dic₁₀	—	128	2	no	—
27	C₅×C₈	D₁₂₈	1	1	yes	characteristic
28	Q₃₂	—	160	2	no	—
29	C₃₂	D₁₆₀	1	1	yes	characteristic
30	C₄×C₅	D₂₅₆	1	1	yes	characteristic
31	Dic₅	—	256	2	no	—
32	Q₁₆	—	320	2	no	—
33	C₁₆	D₃₂₀	1	1	yes	characteristic
34	C₂×C₅	D₅₁₂	1	1	yes	characteristic
35	Q₈	—	640	2	no	—
36	C₈	D₆₄₀	1	1	yes	characteristic
37	C₅	Q₂₀₄₈	1	1	yes	characteristic, complemented, Sylow
38	C₄	—	1280	2	no	—
39	C₄	D₁₂₈₀	1	1	yes	characteristic
40	C₂	D₂₅₆₀	1	1	yes	characteristic

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

N	H ≅ G/N	type
37. C₅	Q₂₀₄₈	semidirect

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