Subgroups — #87723⋊C₅ #14522209

Order 2000.

66 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
2	5₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	#6014⋊C₅	C₂	1	1	yes	maximal, characteristic
4	C₄×5₋¹⁺²	—	2	1	no	—
5	C₄×5₋¹⁺²	C₂²	1	1	yes	characteristic
6	Dic₂₅⋊C₅	—	2	1	no	—
7	C₅×#689	—	5	1	no	maximal
8	#87723	C₅	1	1	yes	maximal, characteristic, complemented
9	C₂×5₋¹⁺²	D₄	1	1	yes	characteristic
10	C₅²×Q₈	D₅	1	1	yes	characteristic
11	C₅×Dic₁₀	—	5	1	no	—
12	C₅×#168	—	5	1	no	—
13	Q₈×C₂₅	—	2	2	no	—
14	Q₈×C₂₅	C₂×C₅	1	1	yes	characteristic
15	Dic₅₀	C₂×C₅	1	1	yes	characteristic
16	#6014	C₂×C₅	1	1	yes	characteristic
17	5₋¹⁺²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅²	—	2	1	no	—
19	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
20	C₅×Dic₅	—	10	1	no	—
21	C₄×C₂₅	—	2	4	no	—
22	C₄×C₂₅	—	2	1	no	—
23	C₄×C₂₅	—	2	2	no	—
24	C₄×C₂₅	C₂²×C₅	1	1	yes	characteristic
25	Dic₂₅	—	2	1	no	—
26	C₅×Q₁₆	—	25	1	no	—
27	#689	—	5	1	no	—
28	C₂×C₅²	C₂²⋊D₅	1	1	yes	characteristic
29	C₂×C₂₅	—	2	2	no	—
30	C₂×C₂₅	C₅×D₄	1	1	yes	characteristic
31	C₅×Q₈	—	5	1	no	—
32	C₅×Q₈	—	25	1	no	—
33	C₅×Q₈	C₅×D₅	1	1	yes	characteristic
34	Dic₁₀	—	5	1	no	—
35	C₅×C₈	—	25	1	no	—
36	#168	—	5	1	no	—
37	C₅²	#689	1	1	yes	characteristic
38	C₂₅	—	2	2	no	—
39	C₂₅	C₅×Q₁₆	1	1	yes	characteristic, complemented
40	C₄×C₅	—	2	1	no	—
41	C₄×C₅	—	5	1	no	—
42	C₄×C₅	—	10	1	no	—
43	C₄×C₅	—	50	1	no	—
44	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
45	Dic₅	—	10	1	no	—
46	Q₁₆	—	25	1	no	Sylow
47	C₂×C₅	—	5	1	no	—
48	C₂×C₅	C₅×C₂²⋊D₅	1	1	yes	characteristic
49	Q₈	—	25	1	no	—
50	Q₈	D₂₅⋊C₅	1	1	yes	characteristic
51	C₈	—	25	1	no	—
52	C₅	—	5	1	no	—
53	C₅	C₅×#689	1	1	yes	characteristic
54	C₄	—	2	1	no	—
55	C₄	—	50	1	no	—
56	C₄	C₂×D₂₅⋊C₅	1	1	yes	characteristic
57	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	C₂×C₅²	C₂²⋊D₅
hypercenter	Q₈	D₂₅⋊C₅
hypocenter	C₂₅	C₅×Q₁₆
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
8. #87723	C₅	semidirect
17. 5₋¹⁺²	Q₁₆	semidirect
39. C₂₅	C₅×Q₁₆	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
5₋¹⁺²⋊Q₈	2
#6014⋊C₅	2
C₅×#689	5
#87723	5

Subgroups — #87723⋊C5 #14522209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #87723⋊C₅ #14522209