Subgroups — #14522652

Order 2000.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×Q₈	C₂	1	1	yes	maximal, characteristic
2	#11758769	C₂	1	1	yes	maximal, characteristic
3	#11758733	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅³	—	2	1	no	—
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	#92553	—	2	1	no	—
7	#87812	—	5	31	no	maximal
8	C₂×C₅³	D₄	1	1	yes	characteristic
9	C₅²×Q₈	D₅	1	31	yes	—
10	#6045	—	5	31	no	—
11	#6029	—	5	31	no	—
12	C₅³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
13	C₄×C₅²	—	2	31	no	—
14	C₄×C₅²	C₂×D₅	1	31	yes	—
15	#1039	—	10	31	no	—
16	#689	—	25	31	no	—
17	C₂×C₅²	C₂²⋊D₅	1	31	yes	—
18	C₅×Q₈	C₅⋊D₅	1	31	yes	—
19	Dic₁₀	—	25	31	no	—
20	#168	—	25	31	no	—
21	C₅²	#689	1	31	yes	complemented
22	C₄×C₅	—	2	31	no	—
23	C₄×C₅	C₂×C₅⋊D₅	1	31	yes	—
24	Dic₅	—	50	31	no	—
25	Q₁₆	—	125	1	no	Sylow
26	C₂×C₅	C₂²⋊(C₅⋊D₅)	1	31	yes	—
27	Q₈	—	125	1	no	—
28	Q₈	C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
29	C₈	—	125	1	no	—
30	C₅	#87812	1	31	yes	complemented
31	C₄	—	2	1	no	—
32	C₄	—	250	1	no	—
33	C₄	C₂×C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
34	C₂	C₂²⋊(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.