Subgroups — C₄⋊#92562 #14522812

Order 2000.

832 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92562	C₂	1	2	yes	maximal
2	C₄×C₅⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅⋊(C₅⋊D₅)	C₂²	1	1	yes	characteristic
4	#92562	—	2	2	no	—
5	C₄×C₅³	C₄	1	1	yes	characteristic, complemented
6	#92553	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#1043	—	5	31	no	maximal
8	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
9	C₅⋊(C₅⋊D₅)	D₄	1	1	yes	characteristic
10	C₅⋊(C₅⋊D₅)	Q₈	1	1	yes	characteristic
11	C₂×#1043	—	5	62	no	—
12	C₄×C₅⋊D₅	—	5	31	no	—
13	C₅³	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅⋊D₅	—	5	31	no	—
15	#1043	—	10	62	no	—
16	C₄×C₅²	AGL(1,𝔽₅)	1	31	yes	complemented
17	#1039	—	5	31	no	—
18	C₄⋊AGL(1,𝔽₅)	—	25	31	no	—
19	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	31	yes	—
20	C₅⋊D₅	—	5	31	no	—
21	C₅⋊D₅	—	5	31	no	—
22	C₂×AGL(1,𝔽₅)	—	25	62	no	—
23	C₄×D₅	—	25	31	no	—
24	C₅²	C₄⋊AGL(1,𝔽₅)	1	31	yes	complemented
25	C₂×D₅	—	25	31	no	—
26	AGL(1,𝔽₅)	—	50	62	no	—
27	C₄×C₅	#1043	1	31	yes	complemented
28	Dic₅	—	25	31	no	—
29	C₄⋊C₄	—	125	1	no	Sylow
30	C₂×C₅	C₂×#1043	1	31	yes	—
31	D₅	—	25	31	no	—
32	D₅	—	25	31	no	—
33	C₂×C₄	—	125	1	no	—
34	C₂×C₄	—	125	2	no	—
35	C₅	C₄⋊#1043	1	31	yes	complemented
36	C₂²	—	125	1	no	—
37	C₄	—	125	1	no	—
38	C₄	—	250	2	no	—
39	C₄	#92562	1	1	yes	characteristic, complemented
40	C₂	—	125	1	no	—
41	C₂	—	125	1	no	—
42	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.