Subgroups — #14522810

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	#11758742	C₂	1	2	yes	maximal, complemented
3	C₂×C₅⋊(C₅⋊D₅)	C₄	1	1	yes	characteristic
4	C₄×C₅³	C₄	1	1	yes	characteristic
5	#92553	C₂²	1	1	yes	characteristic
6	#87856	—	5	31	no	maximal
7	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
8	C₅⋊(C₅⋊D₅)	—	2	1	no	—
9	C₄×C₅⋊D₅	—	5	31	no	—
10	#6033	—	5	62	no	—
11	C₅³	M₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅⋊D₅	—	5	31	no	—
13	C₄×C₅²	AGL(1,𝔽₅)	1	31	yes	—
14	#1039	—	5	31	no	—
15	#700	—	25	31	no	—
16	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	31	yes	—
17	C₅⋊D₅	—	10	31	no	—
18	C₄×D₅	—	25	31	no	—
19	#170	—	25	62	no	—
20	C₅²	#700	1	31	yes	complemented
21	C₂×D₅	—	25	31	no	—
22	C₄×C₅	#1043	1	31	yes	—
23	Dic₅	—	25	31	no	—
24	M₁₆	—	125	1	no	Sylow
25	C₂×C₅	C₂×#1043	1	31	yes	—
26	D₅	—	50	31	no	—
27	C₂×C₄	—	125	1	no	—
28	C₈	—	125	2	no	—
29	C₅	#87856	1	31	yes	complemented
30	C₂²	—	125	1	no	—
31	C₄	—	125	1	no	—
32	C₄	#92562	1	1	yes	characteristic
33	C₂	—	250	1	no	—
34	C₂	C₂×#92562	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.