Subgroups — #14522136

Order 2000.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#6953	C₂	1	1	yes	maximal, characteristic
2	#6045⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	#6029⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#6953	—	2	1	no	—
5	C₄×H(3,𝔽₅)	C₂²	1	1	yes	characteristic
6	#1039⋊C₅	—	2	1	no	—
7	#87773	—	5	1	no	maximal
8	#87772	—	5	1	no	maximal
9	C₂×H(3,𝔽₅)	D₄	1	1	yes	characteristic
10	#6953	—	4	1	no	—
11	#6045	D₅	1	1	yes	characteristic, complemented
12	C₅×D₂₀	—	5	1	no	—
13	C₅×D₂₀	—	5	1	no	—
14	C₅×D₂₀	—	10	2	no	—
15	C₅×Dic₁₀	—	5	1	no	—
16	#6029	D₅	1	1	yes	characteristic, complemented
17	C₅×#168	—	5	1	no	—
18	H(3,𝔽₅)	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×D₅	—	10	4	no	—
20	C₂×C₅×D₅	—	10	1	no	—
21	C₂×C₅×D₅	—	10	1	no	—
22	C₄×C₅²	—	2	2	no	—
23	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
24	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
25	#1039	—	2	1	no	—
26	C₅×Dic₅	—	10	1	no	—
27	#688	—	25	1	no	—
28	#687	—	25	1	no	—
29	#677	—	25	1	no	—
30	C₂×C₅²	—	2	2	no	—
31	C₂×C₅²	D₂₀	1	1	yes	characteristic
32	C₂×C₅²	C₂²⋊D₅	1	1	yes	characteristic
33	C₅×D₅	—	20	4	no	—
34	C₅×D₅	—	20	1	no	—
35	C₅×D₅	—	20	1	no	—
36	C₅×Q₈	—	25	1	no	—
37	C₅×D₄	—	25	1	no	—
38	D₂₀	—	5	1	no	—
39	D₂₀	—	5	1	no	—
40	D₂₀	—	10	2	no	—
41	Dic₁₀	—	5	1	no	—
42	Dic₁₀	—	25	1	no	—
43	C₅×C₈	—	25	1	no	—
44	#168	—	5	1	no	—
45	#168	—	25	1	no	—
46	C₅²	—	2	2	no	—
47	C₅²	#677	1	1	yes	characteristic, complemented
48	C₅²	#688	1	1	yes	characteristic, complemented
49	C₂²×C₅	—	50	1	no	—
50	C₂×D₅	—	10	1	no	—
51	C₂×D₅	—	10	1	no	—
52	C₂×D₅	—	10	4	no	—
53	C₄×C₅	—	5	1	no	—
54	C₄×C₅	—	5	1	no	—
55	C₄×C₅	—	10	2	no	—
56	C₄×C₅	—	50	1	no	—
57	C₄×C₅	D₅²	1	1	yes	characteristic
58	Dic₅	—	10	1	no	—
59	Dic₅	—	50	1	no	—
60	SD₁₆	—	125	1	no	Sylow
61	C₂×C₅	—	5	1	no	—
62	C₂×C₅	—	5	1	no	—
63	C₂×C₅	—	10	2	no	—
64	C₂×C₅	—	100	1	no	—
65	C₂×C₅	#6038	1	1	yes	characteristic
66	D₅	—	20	1	no	—
67	D₅	—	20	1	no	—
68	D₅	—	20	4	no	—
69	Q₈	—	25	1	no	—
70	D₄	—	25	1	no	—
71	C₈	—	25	1	no	—
72	C₅	—	5	1	no	—
73	C₅	—	5	1	no	—
74	C₅	—	10	2	no	—
75	C₅	#87774	1	1	yes	characteristic
76	C₂²	—	50	1	no	—
77	C₄	—	50	1	no	—
78	C₄	((C₅⋊D₅)⋊C₅)⋊C₂	1	1	yes	characteristic
79	C₂	—	100	1	no	—
80	C₂	#11758661	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11758661
commutator, Fitting, cosocle	C₄×H(3,𝔽₅)	C₂²
Frattini	C₄×C₅	D₅²
socle	C₂×C₅	#6038
prime radical	C₄⋊#6953	C₂
hypercenter	C₄	((C₅⋊D₅)⋊C₅)⋊C₂
hypocenter	H(3,𝔽₅)	SD₁₆
LCS	G ▷ C₄×H(3,𝔽₅) ▷ C₂×H(3,𝔽₅) ▷ H(3,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. #6045⋊C₅	C₂	semidirect
3. #6029⋊C₅	C₂	semidirect
11. #6045	D₅	semidirect
16. #6029	D₅	semidirect
18. H(3,𝔽₅)	SD₁₆	semidirect
47. C₅²	#677	semidirect
48. C₅²	#688	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#6953	2
#6045⋊C₅	2
#6029⋊C₅	2
#87773	5
#87772	5