Subgroups — C₄⋊#92537 #14522367

Order 2000.

195 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92537	C₂	1	2	yes	maximal
2	C₄×#6953	C₂	1	1	yes	maximal, characteristic
3	C₂×#6953	C₂²	1	1	yes	characteristic
4	#92537	—	2	2	no	—
5	C₄×H(3,𝔽₅)	C₄	1	1	yes	characteristic, complemented
6	#92525	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#1042	—	5	6	no	maximal
8	C₂×H(3,𝔽₅)	C₂×C₄	1	1	yes	characteristic
9	#6953	D₄	1	1	yes	characteristic
10	#6953	Q₈	1	1	yes	characteristic
11	C₂×#1042	—	5	12	no	—
12	C₄×C₅×D₅	—	5	6	no	—
13	H(3,𝔽₅)	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅×D₅	—	5	6	no	—
15	#1042	—	10	12	no	—
16	C₄×C₅²	AGL(1,𝔽₅)	1	6	yes	complemented
17	C₅×Dic₅	—	5	6	no	—
18	C₄⋊AGL(1,𝔽₅)	—	25	6	no	—
19	C₄⋊Dic₅	—	25	1	no	—
20	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	6	yes	—
21	C₅×D₅	—	5	6	no	—
22	C₅×D₅	—	5	6	no	—
23	C₂×AGL(1,𝔽₅)	—	25	12	no	—
24	C₂×C₄×C₅	—	25	1	no	—
25	C₂×Dic₅	—	25	2	no	—
26	C₄×D₅	—	5	6	no	—
27	C₅²	C₄⋊AGL(1,𝔽₅)	1	6	yes	complemented
28	C₂²×C₅	—	25	1	no	—
29	C₂×D₅	—	5	6	no	—
30	AGL(1,𝔽₅)	—	50	12	no	—
31	C₄×C₅	—	5	6	no	—
32	C₄×C₅	—	25	1	no	—
33	C₄×C₅	#1043	1	1	yes	characteristic
34	Dic₅	—	5	6	no	—
35	Dic₅	—	50	2	no	—
36	C₄⋊C₄	—	125	1	no	Sylow
37	C₂×C₅	—	5	6	no	—
38	C₂×C₅	—	25	1	no	—
39	C₂×C₅	—	25	1	no	—
40	C₂×C₅	C₂×#1043	1	1	yes	characteristic
41	D₅	—	5	6	no	—
42	D₅	—	5	6	no	—
43	C₂×C₄	—	25	1	no	—
44	C₂×C₄	—	125	2	no	—
45	C₅	—	5	6	no	—
46	C₅	C₄⋊#1043	1	1	yes	characteristic
47	C₂²	—	25	1	no	—
48	C₄	—	25	1	no	—
49	C₄	—	250	2	no	—
50	C₄	#92537	1	1	yes	characteristic, complemented
51	C₂	—	25	1	no	—
52	C₂	—	25	1	no	—
53	C₂	C₂×#92537	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#92537
commutator	C₂×H(3,𝔽₅)	C₂×C₄
Frattini, socle	C₂×C₅	C₂×#1043
Fitting	C₄×H(3,𝔽₅)	C₄
prime radical, cosocle	C₂×#6953	C₂²
hypercenter	C₄	#92537
hypocenter	H(3,𝔽₅)	C₄⋊C₄
LCS	G ▷ 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
5. C₄×H(3,𝔽₅)	C₄	semidirect
6. #92525	C₄	semidirect
13. H(3,𝔽₅)	C₄⋊C₄	semidirect
16. C₄×C₅²	AGL(1,𝔽₅)	semidirect
27. C₅²	C₄⋊AGL(1,𝔽₅)	semidirect
50. C₄	#92537	semidirect

Maximal subgroups

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

subgroup	index
C₂×#92537	2
C₄×#6953	2
C₄⋊#1042	5

Subgroups — C4⋊#92537 #14522367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#92537 #14522367