Subgroups — C₂×D₅₀₅₆ #34209312

Order 20224.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₅₂₈	C₂	1	2	yes	maximal, complemented
2	D₅₀₅₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₂₆₄	—	2	2	no	—
5	D₂₅₂₈	—	2	2	no	—
6	D₂₅₂₈	C₂²	1	4	yes	complemented
7	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
8	C₆₄×C₇₉	C₂²	1	2	yes	complemented
9	C₂×D₆₃₂	—	4	2	no	—
10	D₁₂₆₄	—	2	4	no	—
11	D₁₂₆₄	—	4	2	no	—
12	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
13	C₃₂×C₇₉	D₄	1	1	yes	characteristic
14	C₃₂×C₇₉	C₂³	1	1	yes	characteristic
15	C₂×D₃₁₆	—	8	2	no	—
16	D₆₃₂	—	4	4	no	—
17	D₆₃₂	—	8	2	no	—
18	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
19	C₁₆×C₇₉	D₈	1	1	yes	characteristic
20	C₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
21	C₂²×D₇₉	—	16	2	no	—
22	C₂×C₄×C₇₉	D₁₆	1	1	yes	characteristic
23	D₃₁₆	—	8	4	no	—
24	D₃₁₆	—	16	2	no	—
25	C₈×C₇₉	D₁₆	1	1	yes	characteristic
26	C₈×C₇₉	C₂×D₈	1	1	yes	characteristic
27	C₂²×C₇₉	D₃₂	1	1	yes	characteristic
28	C₂×D₇₉	—	16	4	no	—
29	C₂×D₇₉	—	32	4	no	—
30	C₄×C₇₉	D₃₂	1	1	yes	characteristic
31	C₄×C₇₉	C₂×D₁₆	1	1	yes	characteristic
32	C₂×D₆₄	—	79	1	no	maximal, Sylow
33	C₂×C₇₉	D₆₄	1	2	yes	complemented
34	C₂×C₇₉	C₂×D₃₂	1	1	yes	characteristic
35	D₇₉	—	32	4	no	—
36	C₂×D₃₂	—	79	2	no	—
37	D₆₄	—	79	4	no	—
38	C₂×C₆₄	D₇₉	1	1	yes	characteristic, complemented
39	C₇₉	C₂×D₆₄	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₁₆	—	158	2	no	—
41	D₃₂	—	79	4	no	—
42	D₃₂	—	158	2	no	—
43	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
44	C₆₄	C₂×D₇₉	1	2	yes	complemented
45	C₂×D₈	—	316	2	no	—
46	D₁₆	—	316	2	no	—
47	D₁₆	—	158	4	no	—
48	C₂×C₁₆	D₃₁₆	1	1	yes	characteristic
49	C₃₂	D₃₁₆	1	1	yes	characteristic
50	C₃₂	C₂²×D₇₉	1	1	yes	characteristic
51	C₂×D₄	—	632	2	no	—
52	D₈	—	316	4	no	—
53	D₈	—	632	2	no	—
54	C₂×C₈	D₆₃₂	1	1	yes	characteristic
55	C₁₆	D₆₃₂	1	1	yes	characteristic
56	C₁₆	C₂×D₃₁₆	1	1	yes	characteristic
57	C₂³	—	1264	2	no	—
58	D₄	—	632	4	no	—
59	D₄	—	1264	2	no	—
60	C₂×C₄	D₁₂₆₄	1	1	yes	characteristic
61	C₈	D₁₂₆₄	1	1	yes	characteristic
62	C₈	C₂×D₆₃₂	1	1	yes	characteristic
63	C₂²	—	2528	4	no	—
64	C₂²	—	1264	4	no	—
65	C₂²	D₂₅₂₈	1	1	yes	characteristic
66	C₄	D₂₅₂₈	1	1	yes	characteristic
67	C₄	C₂×D₁₂₆₄	1	1	yes	characteristic
68	C₂	—	2528	4	no	—
69	C₂	D₅₀₅₆	1	2	yes	direct product factor
70	C₂	C₂×D₂₅₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₅₂₈
commutator, cosocle	C₃₂×C₇₉	C₂³
Frattini	C₃₂	C₂²×D₇₉
Fitting	C₂×C₆₄×C₇₉	C₂
socle	C₂²×C₇₉	D₃₂
hypercenter	C₂×C₆₄	D₇₉
hypocenter	C₇₉	C₂×D₆₄
LCS	G ▷ C₃₂×C₇₉ ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₅₂₈	C₂	semidirect
2. D₅₀₅₆	C₂	direct (N × H)
3. C₂×C₆₄×C₇₉	C₂	semidirect
6. D₂₅₂₈	C₂²	semidirect
8. C₆₄×C₇₉	C₂²	semidirect
33. C₂×C₇₉	D₆₄	semidirect
38. C₂×C₆₄	D₇₉	semidirect
39. C₇₉	C₂×D₆₄	semidirect
44. C₆₄	C₂×D₇₉	semidirect
69. C₂	D₅₀₅₆	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×D₂₅₂₈	2
D₅₀₅₆	2
C₂×C₆₄×C₇₉	2
C₂×D₆₄	79

Subgroups — C2×D5056 #34209312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅₀₅₆ #34209312