Subgroups — C₂³×D₁₀₀ #13099684

Order 1600.

2043 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₂₅	C₂	1	2	yes	maximal, complemented
2	C₂³×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₀₀	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₂₅	C₂²	1	1	yes	characteristic
5	C₂³×D₂₅	—	2	16	no	—
6	C₂³×D₂₅	C₂²	1	28	yes	complemented
7	C₂²×C₄×C₂₅	C₂²	1	14	yes	complemented
8	C₂×D₁₀₀	C₂²	1	112	yes	direct product factor
9	C₂³×D₂₀	—	5	1	no	maximal
10	C₂³×C₂₅	D₄	1	8	yes	complemented
11	C₂³×C₂₅	C₂³	1	7	yes	—
12	C₂²×D₂₅	—	2	112	no	—
13	C₂²×D₂₅	C₂³	1	56	yes	complemented
14	C₂×C₄×C₂₅	C₂³	1	28	yes	complemented
15	D₁₀₀	C₂³	1	64	yes	direct product factor
16	C₂⁴×D₅	—	5	2	no	—
17	C₂³×C₄×C₅	D₅	1	1	yes	characteristic
18	C₂²×D₂₀	—	5	28	no	—
19	C₂²×C₂₅	C₂×D₄	1	28	yes	complemented
20	C₂²×C₂₅	C₂⁴	1	7	yes	—
21	C₂×D₂₅	—	2	112	no	—
22	C₂×D₂₅	C₂⁴	1	16	yes	complemented
23	C₄×C₂₅	C₂⁴	1	8	yes	complemented
24	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic
25	C₂³×D₅	—	5	28	no	—
26	C₂³×D₅	—	10	16	no	—
27	C₂²×C₄×C₅	C₂×D₅	1	14	yes	—
28	C₂×D₂₀	—	5	112	no	—
29	C₂³×D₄	—	25	1	no	Sylow
30	C₂×C₂₅	C₂²×D₄	1	14	yes	complemented
31	C₂×C₂₅	C₂⁵	1	1	yes	characteristic
32	D₂₅	—	2	16	no	—
33	C₂³×C₅	D₂₀	1	8	yes	—
34	C₂³×C₅	C₂²×D₅	1	7	yes	—
35	C₂²×D₅	—	5	56	no	—
36	C₂²×D₅	—	10	112	no	—
37	C₂×C₄×C₅	C₂²×D₅	1	28	yes	—
38	D₂₀	—	5	64	no	—
39	C₂⁵	—	25	2	no	—
40	C₂²×D₄	—	25	28	no	—
41	C₂³×C₄	D₂₅	1	1	yes	characteristic, complemented
42	C₂₅	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₅	C₂×D₂₀	1	28	yes	—
44	C₂²×C₅	C₂³×D₅	1	7	yes	—
45	C₂×D₅	—	5	16	no	—
46	C₂×D₅	—	10	112	no	—
47	C₄×C₅	C₂³×D₅	1	8	yes	—
48	C₂⁴	—	25	28	no	—
49	C₂⁴	—	50	16	no	—
50	C₂⁴	C₂×D₂₅	1	1	yes	characteristic
51	C₂×D₄	—	25	112	no	—
52	C₂²×C₄	C₂×D₂₅	1	14	yes	complemented
53	C₂×C₅	C₂²×D₂₀	1	14	yes	—
54	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
55	D₅	—	10	16	no	—
56	C₂³	—	25	56	no	—
57	C₂³	—	50	112	no	—
58	C₂³	D₁₀₀	1	8	yes	direct product factor
59	C₂³	C₂²×D₂₅	1	7	yes	—
60	D₄	—	25	64	no	—
61	C₂×C₄	C₂²×D₂₅	1	28	yes	complemented
62	C₅	C₂³×D₂₀	1	1	yes	characteristic
63	C₂²	—	25	16	no	—
64	C₂²	—	50	112	no	—
65	C₂²	C₂×D₁₀₀	1	28	yes	direct product factor
66	C₂²	C₂³×D₂₅	1	7	yes	—
67	C₄	C₂³×D₂₅	1	8	yes	complemented
68	C₂	—	50	16	no	—
69	C₂	C₂²×D₁₀₀	1	14	yes	direct product factor
70	C₂	C₂⁴×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₂₅
commutator, cosocle	C₂×C₂₅	C₂⁵
Frattini	C₂×C₅	C₂⁴×D₅
Fitting	C₂³×C₄×C₂₅	C₂
socle	C₂⁴×C₅	C₂×D₅
hypercenter	C₂³×C₄	D₂₅
hypocenter	C₂₅	C₂³×D₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₂₅	C₂	semidirect
2. C₂³×C₄×C₂₅	C₂	semidirect
3. C₂²×D₁₀₀	C₂	direct (N × H)
6. C₂³×D₂₅	C₂²	semidirect
7. C₂²×C₄×C₂₅	C₂²	semidirect
8. C₂×D₁₀₀	C₂²	direct (N × H)
10. C₂³×C₂₅	D₄	semidirect
13. C₂²×D₂₅	C₂³	semidirect
14. C₂×C₄×C₂₅	C₂³	semidirect
15. D₁₀₀	C₂³	direct (N × H)
19. C₂²×C₂₅	C₂×D₄	semidirect
22. C₂×D₂₅	C₂⁴	semidirect
23. C₄×C₂₅	C₂⁴	semidirect
30. C₂×C₂₅	C₂²×D₄	semidirect
41. C₂³×C₄	D₂₅	semidirect
42. C₂₅	C₂³×D₄	semidirect
52. C₂²×C₄	C₂×D₂₅	semidirect
58. C₂³	D₁₀₀	direct (N × H)
61. C₂×C₄	C₂²×D₂₅	semidirect
65. C₂²	C₂×D₁₀₀	direct (N × H)
67. C₄	C₂³×D₂₅	semidirect
69. C₂	C₂²×D₁₀₀	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×C₄×C₂₅	2
C₂²×D₁₀₀	2
C₂³×D₂₀	5

Subgroups — C23×D100 #13099684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₁₀₀ #13099684