Subgroups — #87724⋊C₅ #14522210

Order 2000.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×5₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊(D₂₅⋊C₅)	C₂	1	1	yes	maximal, characteristic
3	#6014⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₅⋊C₅	—	2	1	no	—
5	C₄×5₋¹⁺²	—	2	1	no	—
6	C₄×5₋¹⁺²	C₂²	1	1	yes	characteristic
7	C₅×#688	—	5	1	no	maximal
8	#87724	C₅	1	1	yes	maximal, characteristic, complemented
9	C₂×5₋¹⁺²	D₄	1	1	yes	characteristic
10	D₂₅⋊C₅	—	4	1	no	—
11	C₅²×Q₈	D₅	1	1	yes	characteristic
12	C₅×D₂₀	—	5	1	no	—
13	C₅×#168	—	5	1	no	—
14	Q₈×C₂₅	—	2	2	no	—
15	Q₈×C₂₅	C₂×C₅	1	1	yes	characteristic, complemented
16	D₁₀₀	C₂×C₅	1	1	yes	characteristic
17	#6014	C₂×C₅	1	1	yes	characteristic, complemented
18	5₋¹⁺²	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×D₅	—	10	1	no	—
20	C₄×C₅²	—	2	1	no	—
21	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
22	C₂×D₂₅	—	2	1	no	—
23	C₄×C₂₅	—	2	4	no	—
24	C₄×C₂₅	—	2	1	no	—
25	C₄×C₂₅	—	2	2	no	—
26	C₄×C₂₅	C₂²×C₅	1	1	yes	characteristic
27	C₅×SD₁₆	—	25	1	no	—
28	#688	—	5	1	no	—
29	C₂×C₅²	C₂²⋊D₅	1	1	yes	characteristic
30	C₅×D₅	—	20	1	no	—
31	C₂×C₂₅	—	2	2	no	—
32	C₂×C₂₅	C₅×D₄	1	1	yes	characteristic
33	D₂₅	—	4	1	no	—
34	C₅×Q₈	—	5	1	no	—
35	C₅×Q₈	C₅×D₅	1	1	yes	characteristic
36	C₅×D₄	—	25	1	no	—
37	D₂₀	—	5	1	no	—
38	C₅×C₈	—	25	1	no	—
39	#168	—	5	1	no	—
40	C₅²	#688	1	1	yes	characteristic
41	C₂₅	—	2	2	no	—
42	C₂₅	C₅×SD₁₆	1	1	yes	characteristic, complemented
43	C₂²×C₅	—	50	1	no	—
44	C₂×D₅	—	10	1	no	—
45	C₄×C₅	—	2	1	no	—
46	C₄×C₅	—	5	1	no	—
47	C₄×C₅	—	10	1	no	—
48	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
49	SD₁₆	—	25	1	no	Sylow
50	C₂×C₅	—	5	1	no	—
51	C₂×C₅	—	100	1	no	—
52	C₂×C₅	C₅×C₂²⋊D₅	1	1	yes	characteristic
53	D₅	—	20	1	no	—
54	Q₈	D₂₅⋊C₅	1	1	yes	characteristic, complemented
55	D₄	—	25	1	no	—
56	C₈	—	25	1	no	—
57	C₅	—	5	1	no	—
58	C₅	C₅×#688	1	1	yes	characteristic
59	C₂²	—	50	1	no	—
60	C₄	—	2	1	no	—
61	C₄	C₂×D₂₅⋊C₅	1	1	yes	characteristic
62	C₂	—	100	1	no	—
63	C₂	C₂²⋊(D₂₅⋊C₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊(D₂₅⋊C₅)
commutator, cosocle	C₄×C₂₅	C₂²×C₅
Frattini	C₄×C₅	C₂×C₅×D₅
Fitting	Q₈×5₋¹⁺²	C₂
socle	C₂×C₅	C₅×C₂²⋊D₅
prime radical	C₄⋊(D₂₅⋊C₅)	C₂
hypercenter	Q₈	D₂₅⋊C₅
hypocenter	C₂₅	C₅×SD₁₆
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. Q₈×5₋¹⁺²	C₂	semidirect
3. #6014⋊C₅	C₂	semidirect
8. #87724	C₅	semidirect
15. Q₈×C₂₅	C₂×C₅	semidirect
17. #6014	C₂×C₅	semidirect
18. 5₋¹⁺²	SD₁₆	semidirect
42. C₂₅	C₅×SD₁₆	semidirect
54. Q₈	D₂₅⋊C₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₈×5₋¹⁺²	2
C₄⋊(D₂₅⋊C₅)	2
#6014⋊C₅	2
C₅×#688	5
#87724	5

Subgroups — #87724⋊C5 #14522210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #87724⋊C₅ #14522210