Subgroups — #3932

Order 160.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₀	C₂	1	1	yes	maximal, characteristic
3	C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₀	—	2	1	no	—
5	Dic₁₀	—	2	1	no	—
6	C₅×C₈	C₂²	1	1	yes	characteristic
7	SD₃₂	—	5	1	no	maximal, Sylow
8	C₂×D₅	—	4	1	no	—
9	C₄×C₅	D₄	1	1	yes	characteristic
10	Dic₅	—	4	1	no	—
11	Q₁₆	—	5	1	no	—
12	D₈	—	5	1	no	—
13	C₁₆	D₅	1	1	yes	characteristic, complemented
14	C₂×C₅	D₈	1	1	yes	characteristic
15	D₅	—	8	1	no	—
16	Q₈	—	10	1	no	—
17	D₄	—	10	1	no	—
18	C₈	C₂×D₅	1	1	yes	characteristic
19	C₅	SD₃₂	1	1	yes	characteristic, complemented, Sylow
20	C₂²	—	20	1	no	—
21	C₄	—	20	1	no	—
22	C₄	D₂₀	1	1	yes	characteristic
23	C₂	—	40	1	no	—
24	C₂	D₄₀	1	1	yes	characteristic

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

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