Subgroups — C₅×#672 #87755

Order 400.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅²	C₄	1	1	yes	characteristic
3	C₅×C₁₆	—	5	1	no	maximal
4	#672	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₅²	C₈	1	1	yes	characteristic
6	C₅×C₈	—	2	2	no	—
7	C₅×C₈	D₅	1	1	yes	characteristic
8	C₅×C₈	C₂×C₅	1	1	yes	characteristic
9	C₅²	C₁₆	1	1	yes	characteristic, complemented, Sylow
10	C₄×C₅	—	2	2	no	—
11	C₄×C₅	Dic₅	1	1	yes	characteristic
12	C₄×C₅	C₄×C₅	1	1	yes	characteristic
13	C₁₆	—	5	1	no	Sylow
14	C₂×C₅	—	2	2	no	—
15	C₂×C₅	#168	1	1	yes	characteristic
16	C₂×C₅	C₅×C₈	1	1	yes	characteristic
17	C₈	C₅×D₅	1	1	yes	characteristic
18	C₅	—	2	2	no	—
19	C₅	#672	1	1	yes	characteristic, direct product factor
20	C₅	C₅×C₁₆	1	1	yes	characteristic, complemented
21	C₄	C₅×Dic₅	1	1	yes	characteristic
22	C₂	C₅×#168	1	1	yes	characteristic

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

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