Subgroups — #87707

Order 400.

15 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₅	C₄	1	1	yes	characteristic
3	#672	—	5	1	no	maximal
4	C₂×C₂₅	C₈	1	1	yes	characteristic
5	C₅×C₈	D₅	1	1	yes	characteristic
6	C₂₅	C₁₆	1	1	yes	characteristic, complemented, Sylow
7	C₄×C₅	Dic₅	1	1	yes	characteristic
8	C₁₆	—	25	1	no	Sylow
9	C₂×C₅	#168	1	1	yes	characteristic
10	C₈	D₂₅	1	1	yes	characteristic
11	C₅	#672	1	1	yes	characteristic
12	C₄	Dic₂₅	1	1	yes	characteristic
13	C₂	#6014	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. C₂₅	C₁₆	semidirect

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

subgroup	index
C₈×C₂₅	2
#672	5