Subgroups — #14522639

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	C₅³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758733	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊(C₅⋊D₅)	C₄	1	1	yes	characteristic
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	#92553	C₄	1	1	yes	characteristic
7	#87799	—	5	31	no	maximal
8	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
9	C₅⋊(C₅⋊D₅)	—	2	1	no	—
10	C₄×C₅⋊D₅	—	5	31	no	—
11	C₅²×C₈	D₅	1	31	yes	complemented
12	#6029	—	5	31	no	—
13	C₅³	M₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅⋊D₅	—	5	31	no	—
15	C₄×C₅²	C₂×D₅	1	31	yes	—
16	#1039	—	5	31	no	—
17	#676	—	25	31	no	—
18	C₂×C₅²	C₄×D₅	1	31	yes	—
19	C₅⋊D₅	—	10	31	no	—
20	C₄×D₅	—	25	31	no	—
21	C₅×C₈	C₅⋊D₅	1	31	yes	complemented
22	#168	—	25	31	no	—
23	C₅²	#676	1	31	yes	complemented
24	C₂×D₅	—	25	31	no	—
25	C₄×C₅	C₂×C₅⋊D₅	1	31	yes	—
26	Dic₅	—	25	31	no	—
27	M₁₆	—	125	1	no	Sylow
28	C₂×C₅	C₄×C₅⋊D₅	1	31	yes	—
29	D₅	—	50	31	no	—
30	C₂×C₄	—	125	1	no	—
31	C₈	—	125	1	no	—
32	C₈	C₅⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented
33	C₅	#87799	1	31	yes	complemented
34	C₂²	—	125	1	no	—
35	C₄	—	125	1	no	—
36	C₄	C₂×C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
37	C₂	—	250	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.