Subgroups — #14522644

Order 2000.

640 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅³	C₂	1	1	yes	maximal, characteristic
2	#11758733	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅³	C₄	1	1	yes	characteristic
4	C₄×C₅³	C₄	1	1	yes	characteristic
5	C₄×C₅³	C₂²	1	1	yes	characteristic
6	#87804	—	5	31	no	maximal
7	C₂×C₅³	—	2	1	no	—
8	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₅²	D₅	1	31	yes	—
10	#6029	—	5	62	no	—
11	C₅³	M₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₅²	Dic₅	1	31	yes	—
13	C₄×C₅²	Dic₅	1	31	yes	—
14	C₄×C₅²	C₂×D₅	1	31	yes	—
15	#681	—	25	31	no	—
16	C₂×C₅²	—	2	31	no	—
17	C₂×C₅²	C₂×Dic₅	1	31	yes	—
18	C₂×C₄×C₅	C₅⋊D₅	1	31	yes	—
19	#168	—	25	62	no	—
20	C₅²	#681	1	31	yes	complemented
21	C₂²×C₅	#1039	1	31	yes	—
22	C₄×C₅	#1039	1	31	yes	—
23	C₄×C₅	C₂×C₅⋊D₅	1	31	yes	—
24	M₁₆	—	125	1	no	Sylow
25	C₂×C₅	—	2	31	no	—
26	C₂×C₅	C₂×#1039	1	31	yes	—
27	C₂×C₄	C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
28	C₈	—	125	2	no	—
29	C₅	#87804	1	31	yes	complemented
30	C₂²	#92553	1	1	yes	characteristic
31	C₄	#92553	1	1	yes	characteristic
32	C₄	C₂×C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#92553	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.