Subgroups — #6053⋊D₅ #14522952

Order 2000.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758788	C₂	1	1	yes	maximal, characteristic
2	#11758780	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#6053	C₂	1	1	yes	maximal, characteristic, complemented
4	#92566	C₄	1	1	yes	characteristic
5	#92560	C₄	1	1	yes	characteristic
6	C₅×#1043	C₂²	1	1	yes	characteristic
7	#6053⋊C₂	—	5	1	no	maximal
8	C₅×C₅⋊D₅	—	2	1	no	—
9	C₅×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
10	D₅⋊AGL(1,𝔽₅)	—	5	1	no	—
11	D₅×AGL(1,𝔽₅)	—	10	1	no	—
12	#6053	—	5	1	no	—
13	#6053	D₅	1	1	yes	characteristic, complemented
14	C₅³	M₁₆	1	1	yes	characteristic, complemented, Sylow
15	D₅²	—	5	1	no	—
16	D₅²	—	10	1	no	—
17	#1044	—	5	1	no	—
18	#1043	C₂×D₅	1	1	yes	characteristic
19	#1042	—	10	1	no	—
20	C₅×AGL(1,𝔽₅)	—	10	1	no	—
21	C₅×AGL(1,𝔽₅)	—	20	1	no	—
22	#676	—	25	1	no	maximal
23	C₅⋊D₅	—	2	1	no	—
24	C₅⋊D₅	C₄×D₅	1	1	yes	characteristic
25	C₅×D₅	—	10	1	no	—
26	C₅×D₅	—	10	1	no	—
27	C₅×D₅	—	10	1	no	—
28	C₅×D₅	—	20	1	no	—
29	C₅×D₅	—	40	1	no	—
30	C₂×AGL(1,𝔽₅)	—	50	1	no	—
31	C₄×D₅	—	25	1	no	—
32	C₅×C₈	—	25	1	no	—
33	#168	—	25	1	no	—
34	C₅²	—	2	1	no	—
35	C₅²	—	4	1	no	—
36	C₅²	—	8	1	no	—
37	C₅²	—	16	1	no	—
38	C₅²	#676	1	1	yes	characteristic, complemented
39	C₂×D₅	—	25	1	no	—
40	C₂×D₅	—	50	1	no	—
41	AGL(1,𝔽₅)	—	10	1	no	—
42	AGL(1,𝔽₅)	—	20	1	no	—
43	AGL(1,𝔽₅)	—	50	1	no	—
44	C₄×C₅	—	25	1	no	—
45	Dic₅	—	25	1	no	—
46	M₁₆	—	125	1	no	Sylow
47	C₂×C₅	—	25	1	no	—
48	C₂×C₅	—	50	1	no	—
49	D₅	—	10	1	no	—
50	D₅	—	10	1	no	—
51	D₅	—	10	1	no	—
52	D₅	—	20	1	no	—
53	D₅	—	40	1	no	—
54	C₂×C₄	—	125	1	no	—
55	C₈	—	25	1	no	—
56	C₈	—	125	1	no	—
57	C₅	—	2	1	no	—
58	C₅	—	4	1	no	—
59	C₅	—	8	1	no	—
60	C₅	—	16	1	no	—
61	C₅	#6053⋊C₂	1	1	yes	characteristic, complemented
62	C₂²	—	125	1	no	—
63	C₄	—	25	1	no	—
64	C₄	—	125	1	no	—
65	C₂	—	25	1	no	—
66	C₂	—	50	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator	C₅×C₅⋊D₅	C₂×C₄
Fitting, socle, hypocenter	C₅³	M₁₆
prime radical	#92566	C₄
cosocle	C₅×#1043	C₂²
LCS	G ▷ C₅×C₅⋊D₅ ▷ C₅³
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #11758780	C₂	semidirect
3. C₅×#6053	C₂	semidirect
13. #6053	D₅	semidirect
14. C₅³	M₁₆	semidirect
38. C₅²	#676	semidirect
61. C₅	#6053⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
#11758788	2
#11758780	2
C₅×#6053	2
#6053⋊C₂	5
#676	25

Subgroups — #6053⋊D5 #14522952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #6053⋊D₅ #14522952