Subgroups — #87775

Order 400.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₁₀	C₂	1	2	yes	maximal
2	#6029	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅²	C₂²	1	1	yes	characteristic
4	C₅×Dic₅	—	2	2	no	—
5	#689	—	5	2	no	maximal
6	C₂×C₅²	D₄	1	1	yes	characteristic
7	C₅×Q₈	—	5	2	no	—
8	Dic₁₀	D₅	1	2	yes	—
9	#168	—	5	2	no	—
10	#168	—	10	2	no	—
11	C₅²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₄×C₅	—	2	2	no	—
13	C₄×C₅	—	10	2	no	—
14	C₄×C₅	C₂×D₅	1	2	yes	—
15	Dic₅	—	2	2	no	—
16	Q₁₆	—	25	1	no	Sylow
17	C₂×C₅	—	2	2	no	—
18	C₂×C₅	C₂²⋊D₅	1	2	yes	—
19	Q₈	—	5	2	no	—
20	C₈	—	25	1	no	—
21	C₅	—	2	2	no	—
22	C₅	#689	1	2	yes	complemented
23	C₄	—	10	2	no	—
24	C₄	D₅²	1	1	yes	characteristic
25	C₂	#6037	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₅²	Q₁₆	semidirect
22. C₅	#689	semidirect

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