Subgroups — C₂×D₅₀₀₈ #34094573

Order 20032.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₅₀₄	C₂	1	2	yes	maximal, complemented
2	D₅₀₀₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₂₅₂	—	2	2	no	—
5	D₂₅₀₄	—	2	2	no	—
6	D₂₅₀₄	C₂²	1	4	yes	complemented
7	C₂×C₈×C₃₁₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₃₁₃	C₂²	1	2	yes	complemented
9	C₂²×D₃₁₃	—	4	2	no	—
10	D₁₂₅₂	—	2	4	no	—
11	D₁₂₅₂	—	4	2	no	—
12	C₂×C₄×C₃₁₃	D₄	1	1	yes	characteristic
13	C₈×C₃₁₃	D₄	1	1	yes	characteristic
14	C₈×C₃₁₃	C₂³	1	1	yes	characteristic
15	C₂²×C₃₁₃	D₈	1	1	yes	characteristic
16	C₂×D₃₁₃	—	4	4	no	—
17	C₂×D₃₁₃	—	8	4	no	—
18	C₄×C₃₁₃	D₈	1	1	yes	characteristic
19	C₄×C₃₁₃	C₂×D₄	1	1	yes	characteristic
20	C₂×C₃₁₃	D₁₆	1	2	yes	complemented
21	C₂×C₃₁₃	C₂×D₈	1	1	yes	characteristic
22	D₃₁₃	—	8	4	no	—
23	C₃₁₃	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₆	—	313	1	no	maximal, Sylow
25	C₂×D₈	—	313	2	no	—
26	D₁₆	—	313	4	no	—
27	C₂×C₁₆	D₃₁₃	1	1	yes	characteristic, complemented
28	C₂×D₄	—	626	2	no	—
29	D₈	—	313	4	no	—
30	D₈	—	626	2	no	—
31	C₂×C₈	C₂×D₃₁₃	1	1	yes	characteristic
32	C₁₆	C₂×D₃₁₃	1	2	yes	complemented
33	C₂³	—	1252	2	no	—
34	D₄	—	626	4	no	—
35	D₄	—	1252	2	no	—
36	C₂×C₄	D₁₂₅₂	1	1	yes	characteristic
37	C₈	D₁₂₅₂	1	1	yes	characteristic
38	C₈	C₂²×D₃₁₃	1	1	yes	characteristic
39	C₂²	—	2504	4	no	—
40	C₂²	—	1252	4	no	—
41	C₂²	D₂₅₀₄	1	1	yes	characteristic
42	C₄	D₂₅₀₄	1	1	yes	characteristic
43	C₄	C₂×D₁₂₅₂	1	1	yes	characteristic
44	C₂	—	2504	4	no	—
45	C₂	D₅₀₀₈	1	2	yes	direct product factor
46	C₂	C₂×D₂₅₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₅₀₄
commutator, cosocle	C₈×C₃₁₃	C₂³
Frattini	C₈	C₂²×D₃₁₃
Fitting	C₂×C₁₆×C₃₁₃	C₂
socle	C₂²×C₃₁₃	D₈
hypercenter	C₂×C₁₆	D₃₁₃
hypocenter	C₃₁₃	C₂×D₁₆
LCS	G ▷ C₈×C₃₁₃ ▷ C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₅₀₄	C₂	semidirect
2. D₅₀₀₈	C₂	direct (N × H)
3. C₂×C₁₆×C₃₁₃	C₂	semidirect
6. D₂₅₀₄	C₂²	semidirect
8. C₁₆×C₃₁₃	C₂²	semidirect
20. C₂×C₃₁₃	D₁₆	semidirect
23. C₃₁₃	C₂×D₁₆	semidirect
27. C₂×C₁₆	D₃₁₃	semidirect
32. C₁₆	C₂×D₃₁₃	semidirect
45. C₂	D₅₀₀₈	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×D₂₅₀₄	2
D₅₀₀₈	2
C₂×C₁₆×C₃₁₃	2
C₂×D₁₆	313

Subgroups — C2×D5008 #34094573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅₀₀₈ #34094573