Subgroups — #87812⋊C₅ #14522207

Order 2000.

87 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×H(3,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	#6045⋊C₅	C₂	1	1	yes	maximal, characteristic
3	#6029⋊C₅	C₂	1	1	yes	maximal, characteristic
4	C₄×H(3,𝔽₅)	—	2	1	no	—
5	C₄×H(3,𝔽₅)	C₂²	1	1	yes	characteristic
6	#1039⋊C₅	—	2	1	no	—
7	#87812	C₅	1	1	yes	maximal, characteristic, complemented
8	C₅×#689	—	5	1	no	maximal
9	C₂×H(3,𝔽₅)	D₄	1	1	yes	characteristic
10	C₅²×Q₈	—	2	2	no	—
11	C₅²×Q₈	D₅	1	1	yes	characteristic
12	C₅²×Q₈	C₂×C₅	1	1	yes	characteristic
13	#6045	C₂×C₅	1	1	yes	characteristic
14	C₅×Dic₁₀	—	5	1	no	—
15	#6029	C₂×C₅	1	1	yes	characteristic
16	C₅×#168	—	5	1	no	—
17	H(3,𝔽₅)	Q₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅²	—	2	4	no	—
19	C₄×C₅²	—	2	2	no	—
20	C₄×C₅²	—	2	1	no	—
21	C₄×C₅²	—	2	1	no	—
22	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
23	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
24	#1039	—	2	1	no	—
25	C₅×Dic₅	—	10	1	no	—
26	C₅×Q₁₆	—	25	1	no	—
27	#689	—	5	1	no	—
28	#689	—	25	1	no	—
29	C₂×C₅²	—	2	2	no	—
30	C₂×C₅²	C₂²⋊D₅	1	1	yes	characteristic
31	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
32	C₅×Q₈	—	5	1	no	—
33	C₅×Q₈	—	5	1	no	—
34	C₅×Q₈	—	10	2	no	—
35	C₅×Q₈	—	25	1	no	—
36	C₅×Q₈	C₅×D₅	1	1	yes	characteristic
37	Dic₁₀	—	5	1	no	—
38	Dic₁₀	—	25	1	no	—
39	C₅×C₈	—	25	1	no	—
40	#168	—	5	1	no	—
41	#168	—	25	1	no	—
42	C₅²	—	2	2	no	—
43	C₅²	#689	1	1	yes	characteristic, complemented
44	C₅²	C₅×Q₁₆	1	1	yes	characteristic, complemented
45	C₄×C₅	—	2	1	no	—
46	C₄×C₅	—	5	1	no	—
47	C₄×C₅	—	5	1	no	—
48	C₄×C₅	—	10	1	no	—
49	C₄×C₅	—	10	1	no	—
50	C₄×C₅	—	10	4	no	—
51	C₄×C₅	—	10	2	no	—
52	C₄×C₅	—	50	1	no	—
53	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
54	Dic₅	—	10	1	no	—
55	Dic₅	—	50	1	no	—
56	Q₁₆	—	25	1	no	Sylow
57	C₂×C₅	—	5	1	no	—
58	C₂×C₅	—	5	1	no	—
59	C₂×C₅	—	10	2	no	—
60	C₂×C₅	C₅×C₂²⋊D₅	1	1	yes	characteristic
61	Q₈	—	25	1	no	—
62	Q₈	(C₅⋊D₅)⋊C₅	1	1	yes	characteristic
63	C₈	—	25	1	no	—
64	C₅	—	5	1	no	—
65	C₅	—	5	1	no	—
66	C₅	—	10	2	no	—
67	C₅	C₅×#689	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	50	1	no	—
70	C₄	C₂×(C₅⋊D₅)⋊C₅	1	1	yes	characteristic
71	C₂	C₂²⋊((C₅⋊D₅)⋊C₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊((C₅⋊D₅)⋊C₅)
commutator, cosocle	C₄×C₅²	C₂²×C₅
Frattini	C₄×C₅	C₂×C₅×D₅
Fitting	Q₈×H(3,𝔽₅)	C₂
socle	C₂×C₅	C₅×C₂²⋊D₅
prime radical	C₂×H(3,𝔽₅)	D₄
hypercenter	Q₈	(C₅⋊D₅)⋊C₅
hypocenter	C₅²	C₅×Q₁₆
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

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

N	H ≅ G/N	type
7. #87812	C₅	semidirect
17. H(3,𝔽₅)	Q₁₆	semidirect
43. C₅²	#689	semidirect
44. C₅²	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×H(3,𝔽₅)	2
#6045⋊C₅	2
#6029⋊C₅	2
#87812	5
C₅×#689	5

Subgroups — #87812⋊C5 #14522207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #87812⋊C₅ #14522207