Subgroups — #14522642

Order 2000.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758769	C₂	1	2	yes	maximal
2	C₅³×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅³	C₂²	1	1	yes	characteristic
4	#92553	—	2	2	no	—
5	#87802	—	5	31	no	maximal
6	C₂×C₅³	D₄	1	1	yes	characteristic
7	#6045	—	5	62	no	—
8	C₅²×C₈	D₅	1	31	yes	—
9	C₅³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
10	C₄×C₅²	C₂×D₅	1	31	yes	—
11	#1039	—	10	62	no	—
12	Dic₂₀	—	25	31	no	—
13	C₂×C₅²	D₂₀	1	31	yes	—
14	Dic₁₀	—	25	62	no	—
15	C₅×C₈	C₅⋊D₅	1	31	yes	—
16	C₅²	Dic₂₀	1	31	yes	complemented
17	C₄×C₅	C₂×C₅⋊D₅	1	31	yes	—
18	Dic₅	—	50	62	no	—
19	Q₁₆	—	125	1	no	Sylow
20	C₂×C₅	C₄⋊(C₅⋊D₅)	1	31	yes	—
21	Q₈	—	125	2	no	—
22	C₈	C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
23	C₅	#87802	1	31	yes	complemented
24	C₄	—	250	2	no	—
25	C₄	C₂×C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
26	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.