Subgroups — C₄×#92534 #14522345

Order 2000.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92534	C₂	1	2	yes	maximal
2	C₄×C₅×D₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×D₂₅	C₂²	1	1	yes	characteristic
4	#92534	C₄	1	4	yes	direct product factor
5	C₄×C₅×C₂₅	C₄	1	1	yes	characteristic, complemented
6	C₅×Dic₂₅	C₄	1	1	yes	characteristic, complemented
7	C₄×#1042	—	5	1	no	maximal
8	C₄×#1035	—	5	1	no	maximal
9	C₂×C₅×C₂₅	C₂×C₄	1	1	yes	characteristic
10	C₅×D₂₅	C₂×C₄	1	2	yes	—
11	C₂×#1042	—	5	2	no	—
12	C₄×C₅×D₅	—	5	1	no	—
13	C₂×#1035	—	5	2	no	—
14	C₄×D₂₅	D₅	1	1	yes	characteristic
15	C₅×C₂₅	C₄²	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅×D₅	—	5	1	no	—
17	#1042	—	5	4	no	—
18	C₄×C₅²	AGL(1,𝔽₅)	1	1	yes	characteristic
19	C₅×Dic₅	—	5	1	no	—
20	C₂×D₂₅	C₂×D₅	1	1	yes	characteristic
21	#1035	—	5	4	no	—
22	C₄×C₂₅	—	4	1	no	—
23	C₄×C₂₅	Dic₅	1	1	yes	characteristic, complemented
24	Dic₂₅	Dic₅	1	1	yes	characteristic, complemented
25	C₄×AGL(1,𝔽₅)	—	25	1	no	—
26	C₄×Dic₅	—	25	1	no	—
27	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₅×D₅	—	5	2	no	—
29	C₂×C₂₅	—	4	1	no	—
30	C₂×C₂₅	C₂×Dic₅	1	1	yes	characteristic
31	D₂₅	C₄×D₅	1	2	yes	—
32	C₂×AGL(1,𝔽₅)	—	25	2	no	—
33	C₂×C₄×C₅	—	25	1	no	—
34	C₂×Dic₅	—	25	2	no	—
35	C₄×D₅	—	5	1	no	—
36	C₅²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₂₅	—	4	1	no	—
38	C₂₅	C₄×Dic₅	1	1	yes	characteristic, complemented
39	C₂²×C₅	—	25	1	no	—
40	C₂×D₅	—	5	1	no	—
41	AGL(1,𝔽₅)	—	25	4	no	—
42	C₄×C₅	—	4	1	no	—
43	C₄×C₅	—	25	1	no	—
44	C₄×C₅	#1035	1	1	yes	characteristic, complemented
45	C₄×C₅	#1042	1	1	yes	characteristic
46	Dic₅	—	5	1	no	—
47	Dic₅	—	25	4	no	—
48	C₄²	—	125	1	no	Sylow
49	C₂×C₅	—	4	1	no	—
50	C₂×C₅	—	25	2	no	—
51	C₂×C₅	C₂×#1035	1	1	yes	characteristic
52	C₂×C₅	C₂×#1042	1	1	yes	characteristic
53	D₅	—	5	2	no	—
54	C₂×C₄	—	25	1	no	—
55	C₂×C₄	—	125	2	no	—
56	C₅	—	4	1	no	—
57	C₅	C₄×#1035	1	1	yes	characteristic, complemented
58	C₅	C₄×#1042	1	1	yes	characteristic
59	C₂²	—	25	1	no	—
60	C₄	—	25	1	no	—
61	C₄	—	125	4	no	—
62	C₄	#92534	1	1	yes	characteristic, direct product factor
63	C₂	—	25	2	no	—
64	C₂	C₂×#92534	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#92534
commutator, hypocenter	C₅×C₂₅	C₄²
Frattini	C₂×C₅	C₂×#1042
Fitting	C₄×C₅×C₂₅	C₄
socle	C₂×C₅²	C₂×AGL(1,𝔽₅)
prime radical, cosocle	C₂×C₅×D₂₅	C₂²
LCS	G ▷ C₅×C₂₅
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
4. #92534	C₄	direct (N × H)
5. C₄×C₅×C₂₅	C₄	semidirect
6. C₅×Dic₂₅	C₄	semidirect
15. C₅×C₂₅	C₄²	semidirect
23. C₄×C₂₅	Dic₅	semidirect
24. Dic₂₅	Dic₅	semidirect
38. C₂₅	C₄×Dic₅	semidirect
44. C₄×C₅	#1035	semidirect
57. C₅	C₄×#1035	semidirect
62. C₄	#92534	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#92534	2
C₄×C₅×D₂₅	2
C₄×#1042	5
C₄×#1035	5

Subgroups — C4×#92534 #14522345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#92534 #14522345