Subgroups — #14522641

Order 2000.

704 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₅⋊(C₅⋊D₅))	C₂	1	2	yes	maximal, complemented
2	C₅³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅⋊(C₅⋊D₅)	—	2	2	no	—
4	C₄×C₅³	C₂²	1	1	yes	characteristic
5	#87801	—	5	31	no	maximal
6	C₂×C₅³	D₄	1	1	yes	characteristic
7	C₅⋊(C₅⋊D₅)	—	4	2	no	—
8	C₄⋊(C₅⋊D₅)	—	5	62	no	—
9	C₅²×C₈	D₅	1	31	yes	complemented
10	C₅³	D₈	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₅⋊D₅	—	10	62	no	—
12	C₄×C₅²	C₂×D₅	1	31	yes	—
13	D₄₀	—	25	31	no	—
14	C₂×C₅²	D₂₀	1	31	yes	—
15	C₅⋊D₅	—	20	62	no	—
16	D₂₀	—	25	62	no	—
17	C₅×C₈	C₅⋊D₅	1	31	yes	complemented
18	C₅²	D₄₀	1	31	yes	complemented
19	C₂×D₅	—	50	62	no	—
20	C₄×C₅	C₂×C₅⋊D₅	1	31	yes	—
21	D₈	—	125	1	no	Sylow
22	C₂×C₅	C₄⋊(C₅⋊D₅)	1	31	yes	—
23	D₅	—	100	62	no	—
24	D₄	—	125	2	no	—
25	C₈	C₅⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented
26	C₅	#87801	1	31	yes	complemented
27	C₂²	—	250	2	no	—
28	C₄	C₂×C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
29	C₂	—	500	2	no	—
30	C₂	C₄⋊(C₅⋊(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.