Subgroups — #87809

Order 400.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	#6029	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅²	—	2	1	no	—
5	C₂×C₅⋊D₅	—	2	1	no	—
6	C₄×C₅²	C₂²	1	1	yes	characteristic
7	#686	—	5	6	no	maximal
8	C₂×C₅²	—	4	1	no	—
9	C₂×C₅²	D₄	1	1	yes	characteristic
10	C₅⋊D₅	—	4	1	no	—
11	C₅×D₄	D₅	1	6	yes	complemented
12	D₂₀	—	5	6	no	—
13	#168	—	5	6	no	—
14	C₅²	D₈	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₅	—	2	6	no	—
16	C₂×D₅	—	10	6	no	—
17	C₄×C₅	C₂×D₅	1	6	yes	—
18	D₈	—	25	1	no	Sylow
19	C₂×C₅	—	4	6	no	—
20	C₂×C₅	C₂²⋊D₅	1	6	yes	—
21	D₅	—	20	6	no	—
22	D₄	—	25	1	no	—
23	D₄	C₅⋊D₅	1	1	yes	characteristic, complemented
24	C₈	—	25	1	no	—
25	C₅	#686	1	6	yes	complemented
26	C₂²	—	2	1	no	—
27	C₂²	—	50	1	no	—
28	C₄	C₂×C₅⋊D₅	1	1	yes	characteristic
29	C₂	—	4	1	no	—
30	C₂	—	100	1	no	—
31	C₂	C₂²⋊(C₅⋊D₅)	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.