Subgroups — #87770

Order 400.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₂₀	C₂	1	2	yes	maximal, complemented
2	#6029	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₅	—	2	2	no	—
4	C₄×C₅²	C₂²	1	1	yes	characteristic
5	#686	—	5	2	no	maximal
6	C₂×C₅²	D₄	1	1	yes	characteristic
7	C₅×D₅	—	4	2	no	—
8	C₅×D₄	—	5	2	no	—
9	D₂₀	D₅	1	2	yes	complemented
10	#168	—	5	2	no	—
11	#168	—	10	2	no	—
12	C₅²	D₈	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₅	—	10	2	no	—
14	C₂×D₅	—	2	2	no	—
15	C₄×C₅	—	2	2	no	—
16	C₄×C₅	C₂×D₅	1	2	yes	—
17	D₈	—	25	1	no	Sylow
18	C₂×C₅	—	2	2	no	—
19	C₂×C₅	—	20	2	no	—
20	C₂×C₅	C₂²⋊D₅	1	2	yes	—
21	D₅	—	4	2	no	—
22	D₄	—	5	2	no	—
23	C₈	—	25	1	no	—
24	C₅	—	2	2	no	—
25	C₅	#686	1	2	yes	complemented
26	C₂²	—	10	2	no	—
27	C₄	D₅²	1	1	yes	characteristic
28	C₂	—	20	2	no	—
29	C₂	#6037	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.