Subgroups — #14522640

Order 2000.

640 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₅⋊(C₅⋊D₅))	C₂	1	1	yes	maximal, characteristic
2	#11758769	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊(C₅⋊D₅)	—	2	1	no	—
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	#92553	—	2	1	no	—
7	#87800	—	5	31	no	maximal
8	C₂×C₅³	D₄	1	1	yes	characteristic
9	C₅⋊(C₅⋊D₅)	—	4	1	no	—
10	C₄⋊(C₅⋊D₅)	—	5	31	no	—
11	#6045	—	5	31	no	—
12	C₅²×C₈	D₅	1	31	yes	complemented
13	C₅³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅⋊D₅	—	10	31	no	—
15	C₄×C₅²	C₂×D₅	1	31	yes	—
16	#1039	—	10	31	no	—
17	#677	—	25	31	no	—
18	C₂×C₅²	D₂₀	1	31	yes	—
19	C₅⋊D₅	—	20	31	no	—
20	D₂₀	—	25	31	no	—
21	Dic₁₀	—	25	31	no	—
22	C₅×C₈	C₅⋊D₅	1	31	yes	complemented
23	C₅²	#677	1	31	yes	complemented
24	C₂×D₅	—	50	31	no	—
25	C₄×C₅	C₂×C₅⋊D₅	1	31	yes	—
26	Dic₅	—	50	31	no	—
27	SD₁₆	—	125	1	no	Sylow
28	C₂×C₅	C₄⋊(C₅⋊D₅)	1	31	yes	—
29	D₅	—	100	31	no	—
30	Q₈	—	125	1	no	—
31	D₄	—	125	1	no	—
32	C₈	C₅⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented
33	C₅	#87800	1	31	yes	complemented
34	C₂²	—	250	1	no	—
35	C₄	—	250	1	no	—
36	C₄	C₂×C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
37	C₂	—	500	1	no	—
38	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.