Subgroups — C₄²×#1035 #13098674

Order 1600.

387 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#1035	C₂	1	6	yes	maximal
2	C₄²×D₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×#1035	C₂²	1	4	yes	—
4	C₂×C₄×D₂₅	C₂²	1	3	yes	—
5	C₄×#1035	C₄	1	24	yes	direct product factor
6	C₄²×C₂₅	C₄	1	1	yes	characteristic, complemented
7	C₄×Dic₂₅	C₄	1	3	yes	complemented
8	C₄²×AGL(1,𝔽₅)	—	5	1	no	maximal
9	C₂²×D₂₅	C₂³	1	1	yes	characteristic
10	C₂×#1035	C₂×C₄	1	24	yes	—
11	C₂×C₄×C₂₅	C₂×C₄	1	3	yes	—
12	C₂×Dic₂₅	C₂×C₄	1	3	yes	—
13	C₄×D₂₅	C₂×C₄	1	12	yes	—
14	C₂×C₄×AGL(1,𝔽₅)	—	5	6	no	—
15	C₄²×D₅	—	5	1	no	—
16	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
17	C₂×D₂₅	C₂²×C₄	1	6	yes	—
18	#1035	C₄²	1	16	yes	direct product factor
19	C₄×C₂₅	C₄²	1	6	yes	complemented
20	Dic₂₅	C₄²	1	6	yes	complemented
21	C₂²×AGL(1,𝔽₅)	—	5	4	no	—
22	C₂×C₄×D₅	—	5	3	no	—
23	C₄×AGL(1,𝔽₅)	—	5	24	no	—
24	C₄²×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₄×Dic₅	—	5	3	no	—
26	C₄³	—	25	1	no	Sylow
27	C₂×C₂₅	C₂×C₄²	1	3	yes	—
28	D₂₅	C₂×C₄²	1	4	yes	—
29	C₂²×D₅	—	5	1	no	—
30	C₂×AGL(1,𝔽₅)	—	5	24	no	—
31	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	3	yes	—
32	C₂×Dic₅	—	5	3	no	—
33	C₄×D₅	—	5	12	no	—
34	C₂×C₄²	—	25	6	no	—
35	C₂×C₄²	—	25	1	no	—
36	C₂₅	C₄³	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
38	C₂×D₅	—	5	6	no	—
39	AGL(1,𝔽₅)	—	5	16	no	—
40	C₄×C₅	C₄×AGL(1,𝔽₅)	1	6	yes	—
41	Dic₅	—	5	6	no	—
42	C₂²×C₄	—	25	4	no	—
43	C₂²×C₄	—	25	3	no	—
44	C₄²	—	25	24	no	—
45	C₄²	—	25	3	no	—
46	C₄²	#1035	1	1	yes	characteristic, direct product factor
47	C₂×C₅	C₂×C₄×AGL(1,𝔽₅)	1	3	yes	—
48	D₅	—	5	4	no	—
49	C₂³	—	25	1	no	—
50	C₂×C₄	—	25	24	no	—
51	C₂×C₄	—	25	3	no	—
52	C₂×C₄	—	25	12	no	—
53	C₂×C₄	C₂×#1035	1	3	yes	—
54	C₅	C₄²×AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₂²	—	25	6	no	—
56	C₂²	C₂²×#1035	1	1	yes	characteristic
57	C₄	—	25	16	no	—
58	C₄	—	25	6	no	—
59	C₄	C₄×#1035	1	6	yes	direct product factor
60	C₂	—	25	4	no	—
61	C₂	C₂×C₄×#1035	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₄²	#1035
commutator, hypocenter	C₂₅	C₄³
Frattini, socle	C₂²×C₅	C₂²×AGL(1,𝔽₅)
Fitting	C₄²×C₂₅	C₄
prime radical, cosocle	C₂²×D₂₅	C₂³
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
5. C₄×#1035	C₄	direct (N × H)
6. C₄²×C₂₅	C₄	semidirect
7. C₄×Dic₂₅	C₄	semidirect
18. #1035	C₄²	direct (N × H)
19. C₄×C₂₅	C₄²	semidirect
20. Dic₂₅	C₄²	semidirect
36. C₂₅	C₄³	semidirect
46. C₄²	#1035	direct (N × H)
59. C₄	C₄×#1035	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×C₄×#1035	2
C₄²×D₂₅	2
C₄²×AGL(1,𝔽₅)	5

Subgroups — C42×#1035 #13098674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#1035 #13098674