Subgroups — C₄×#92562 #14522811

Order 2000.

960 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	C₄	1	4	yes	direct product factor
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)	C₂×C₄	1	2	yes	—
10	C₂×#1043	—	5	62	no	—
11	C₄×C₅⋊D₅	—	5	31	no	—
12	C₅³	C₄²	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₅⋊D₅	—	5	31	no	—
14	#1043	—	5	124	no	—
15	C₄×C₅²	AGL(1,𝔽₅)	1	31	yes	complemented
16	#1039	—	5	31	no	—
17	C₄×AGL(1,𝔽₅)	—	25	31	no	—
18	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	31	yes	—
19	C₅⋊D₅	—	5	62	no	—
20	C₂×AGL(1,𝔽₅)	—	25	62	no	—
21	C₄×D₅	—	25	31	no	—
22	C₅²	C₄×AGL(1,𝔽₅)	1	31	yes	complemented
23	C₂×D₅	—	25	31	no	—
24	AGL(1,𝔽₅)	—	25	124	no	—
25	C₄×C₅	#1043	1	31	yes	complemented
26	Dic₅	—	25	31	no	—
27	C₄²	—	125	1	no	Sylow
28	C₂×C₅	C₂×#1043	1	31	yes	—
29	D₅	—	25	62	no	—
30	C₂×C₄	—	125	2	no	—
31	C₂×C₄	—	125	1	no	—
32	C₅	C₄×#1043	1	31	yes	complemented
33	C₂²	—	125	1	no	—
34	C₄	—	125	4	no	—
35	C₄	—	125	1	no	—
36	C₄	#92562	1	1	yes	characteristic, direct product factor
37	C₂	—	125	2	no	—
38	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.