Subgroups — C₂⁴×#1035 #13103251

Order 1600.

2043 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×#1035	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₂₅	C₄	1	1	yes	characteristic, complemented
4	C₂³×D₂₅	C₄	1	15	yes	complemented
5	C₂³×D₂₅	C₂²	1	15	yes	—
6	C₂²×#1035	C₂²	1	140	yes	direct product factor
7	C₂⁴×AGL(1,𝔽₅)	—	5	1	no	maximal
8	C₂³×C₂₅	C₂×C₄	1	15	yes	complemented
9	C₂²×D₂₅	C₂×C₄	1	105	yes	complemented
10	C₂²×D₂₅	C₂³	1	35	yes	—
11	C₂×#1035	C₂³	1	120	yes	direct product factor
12	C₂⁴×D₅	—	5	1	no	—
13	C₂³×AGL(1,𝔽₅)	—	5	30	no	—
14	C₂²×C₂₅	C₂²×C₄	1	35	yes	complemented
15	C₂×D₂₅	C₂²×C₄	1	105	yes	complemented
16	C₂×D₂₅	C₂⁴	1	15	yes	—
17	#1035	C₂⁴	1	16	yes	direct product factor
18	C₂⁴×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
19	C₂³×D₅	—	5	15	no	—
20	C₂³×D₅	—	5	15	no	—
21	C₂²×AGL(1,𝔽₅)	—	5	140	no	—
22	C₂⁴×C₄	—	25	1	no	Sylow
23	C₂×C₂₅	C₂³×C₄	1	15	yes	complemented
24	D₂₅	C₂³×C₄	1	15	yes	complemented
25	D₂₅	C₂⁵	1	1	yes	characteristic
26	C₂³×C₅	C₂×AGL(1,𝔽₅)	1	15	yes	—
27	C₂²×D₅	—	5	105	no	—
28	C₂²×D₅	—	5	35	no	—
29	C₂×AGL(1,𝔽₅)	—	5	120	no	—
30	C₂⁵	—	25	1	no	—
31	C₂³×C₄	—	25	30	no	—
32	C₂₅	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	35	yes	—
34	C₂×D₅	—	5	105	no	—
35	C₂×D₅	—	5	15	no	—
36	AGL(1,𝔽₅)	—	5	16	no	—
37	C₂⁴	—	25	15	no	—
38	C₂⁴	—	25	15	no	—
39	C₂⁴	#1035	1	1	yes	characteristic, direct product factor
40	C₂²×C₄	—	25	140	no	—
41	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	15	yes	—
42	D₅	—	5	1	no	—
43	D₅	—	5	15	no	—
44	C₂³	—	25	35	no	—
45	C₂³	—	25	105	no	—
46	C₂³	C₂×#1035	1	15	yes	direct product factor
47	C₂×C₄	—	25	120	no	—
48	C₅	C₂⁴×AGL(1,𝔽₅)	1	1	yes	characteristic
49	C₂²	—	25	15	no	—
50	C₂²	—	25	105	no	—
51	C₂²	C₂²×#1035	1	35	yes	direct product factor
52	C₄	—	25	16	no	—
53	C₂	—	25	1	no	—
54	C₂	—	25	15	no	—
55	C₂	C₂³×#1035	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴	#1035
commutator, hypocenter	C₂₅	C₂⁴×C₄
Frattini	C₅	C₂⁴×AGL(1,𝔽₅)
Fitting	C₂⁴×C₂₅	C₄
socle	C₂⁴×C₅	AGL(1,𝔽₅)
prime radical	C₂⁴×D₂₅	C₂
cosocle	D₂₅	C₂⁵
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
2. C₂³×#1035	C₂	direct (N × H)
3. C₂⁴×C₂₅	C₄	semidirect
4. C₂³×D₂₅	C₄	semidirect
6. C₂²×#1035	C₂²	direct (N × H)
8. C₂³×C₂₅	C₂×C₄	semidirect
9. C₂²×D₂₅	C₂×C₄	semidirect
11. C₂×#1035	C₂³	direct (N × H)
14. C₂²×C₂₅	C₂²×C₄	semidirect
15. C₂×D₂₅	C₂²×C₄	semidirect
17. #1035	C₂⁴	direct (N × H)
23. C₂×C₂₅	C₂³×C₄	semidirect
24. D₂₅	C₂³×C₄	semidirect
32. C₂₅	C₂⁴×C₄	semidirect
39. C₂⁴	#1035	direct (N × H)
46. C₂³	C₂×#1035	direct (N × H)
51. C₂²	C₂²×#1035	direct (N × H)
55. C₂	C₂³×#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
C₂⁴×D₂₅	2
C₂³×#1035	2
C₂⁴×AGL(1,𝔽₅)	5

Subgroups — C24×#1035 #13103251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#1035 #13103251