Subgroups — #87739

Order 400.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₅	C₂	1	1	yes	maximal, characteristic
2	#6016	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₅	C₄	1	1	yes	characteristic
4	Dic₂₅	C₄	1	1	yes	characteristic
5	Dic₂₅	C₂²	1	1	yes	characteristic
6	#704	—	5	1	no	maximal
7	C₂×C₂₅	—	2	1	no	—
8	C₂×C₂₅	C₂×C₄	1	1	yes	characteristic
9	C₂×Dic₅	—	5	1	no	—
10	#170	—	5	2	no	—
11	C₂₅	M₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
13	Dic₅	—	5	1	no	—
14	Dic₅	—	5	1	no	—
15	M₁₆	—	25	1	no	Sylow
16	C₂×C₅	—	2	1	no	—
17	C₂×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
18	C₂×C₄	—	25	1	no	—
19	C₈	—	25	2	no	—
20	C₅	#704	1	1	yes	characteristic
21	C₂²	#1035	1	1	yes	characteristic
22	C₄	—	25	1	no	—
23	C₄	—	25	1	no	—
24	C₂	—	2	1	no	—
25	C₂	C₂×#1035	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #6016	C₂	semidirect
11. C₂₅	M₁₆	semidirect

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