Subgroups — #87716

Order 400.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	#6014	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₅	C₄	1	1	yes	characteristic
4	C₄×C₂₅	C₄	1	1	yes	characteristic
5	C₄×C₂₅	C₂²	1	1	yes	characteristic
6	#681	—	5	1	no	maximal
7	C₂×C₂₅	—	2	1	no	—
8	C₂×C₂₅	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₅	D₅	1	1	yes	characteristic
10	#168	—	5	2	no	—
11	C₂₅	M₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₅	Dic₅	1	1	yes	characteristic
13	C₄×C₅	Dic₅	1	1	yes	characteristic
14	C₄×C₅	C₂×D₅	1	1	yes	characteristic
15	M₁₆	—	25	1	no	Sylow
16	C₂×C₅	—	2	1	no	—
17	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
18	C₂×C₄	D₂₅	1	1	yes	characteristic
19	C₈	—	25	2	no	—
20	C₅	#681	1	1	yes	characteristic
21	C₂²	Dic₂₅	1	1	yes	characteristic
22	C₄	Dic₂₅	1	1	yes	characteristic
23	C₄	C₂×D₂₅	1	1	yes	characteristic
24	C₂	—	2	1	no	—
25	C₂	C₂×Dic₂₅	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #6014	C₂	semidirect
11. C₂₅	M₁₆	semidirect

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