Subgroups — #87802

Order 400.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6045	C₂	1	2	yes	maximal
2	C₅²×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅²	C₂²	1	1	yes	characteristic
4	#1039	—	2	2	no	—
5	Dic₂₀	—	5	6	no	maximal
6	C₂×C₅²	D₄	1	1	yes	characteristic
7	Dic₁₀	—	5	12	no	—
8	C₅×C₈	D₅	1	6	yes	—
9	C₅²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
10	C₄×C₅	C₂×D₅	1	6	yes	—
11	Dic₅	—	10	12	no	—
12	Q₁₆	—	25	1	no	Sylow
13	C₂×C₅	D₂₀	1	6	yes	—
14	Q₈	—	25	2	no	—
15	C₈	C₅⋊D₅	1	1	yes	characteristic
16	C₅	Dic₂₀	1	6	yes	complemented
17	C₄	—	50	2	no	—
18	C₄	C₂×C₅⋊D₅	1	1	yes	characteristic
19	C₂	C₄⋊(C₅⋊D₅)	1	1	yes	characteristic

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

N	H ≅ G/N	type
9. C₅²	Q₁₆	semidirect
16. C₅	Dic₂₀	semidirect

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