Subgroups — C₂×C₇×D₅₂ #13089884

Order 1456.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₁₃	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₅₂	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₇×D₁₃	—	2	4	no	—
6	C₂×C₇×D₁₃	C₂²	1	4	yes	complemented
7	C₄×C₇×C₁₃	C₂²	1	2	yes	complemented
8	C₂×D₅₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₇×C₁₃	D₄	1	2	yes	complemented
10	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
11	C₇×D₁₃	—	2	4	no	—
12	C₂×C₇×D₄	—	13	1	no	maximal, Hall
13	C₂²×D₁₃	C₂×C₇	1	2	yes	complemented
14	C₂×C₄×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
15	D₅₂	C₂×C₇	1	4	yes	direct product factor
16	C₇×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
17	C₂³×C₇	—	13	2	no	—
18	C₇×D₄	—	13	4	no	—
19	C₂×C₄×C₇	D₁₃	1	1	yes	characteristic, complemented
20	C₂²×C₁₃	C₂²×C₇	1	1	yes	characteristic
21	C₂×D₁₃	—	2	4	no	—
22	C₂×D₁₃	C₂²×C₇	1	4	yes	complemented
23	C₄×C₁₃	C₂²×C₇	1	2	yes	complemented
24	C₂²×C₇	—	13	4	no	—
25	C₂²×C₇	—	26	4	no	—
26	C₂²×C₇	C₂×D₁₃	1	1	yes	characteristic
27	C₄×C₇	C₂×D₁₃	1	2	yes	complemented
28	C₂×C₁₃	C₇×D₄	1	2	yes	complemented
29	C₂×C₁₃	C₂³×C₇	1	1	yes	characteristic
30	D₁₃	—	2	4	no	—
31	C₂×D₄	—	13	1	no	Sylow
32	C₂×C₇	—	26	4	no	—
33	C₂×C₇	D₅₂	1	2	yes	direct product factor
34	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
35	C₁₃	C₂×C₇×D₄	1	1	yes	characteristic, complemented, Sylow
36	C₂³	—	13	2	no	—
37	D₄	—	13	4	no	—
38	C₂×C₄	C₇×D₁₃	1	1	yes	characteristic, complemented
39	C₇	C₂×D₅₂	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²	—	13	4	no	—
41	C₂²	—	26	4	no	—
42	C₂²	C₂×C₇×D₁₃	1	1	yes	characteristic
43	C₄	C₂×C₇×D₁₃	1	2	yes	complemented
44	C₂	—	26	4	no	—
45	C₂	C₇×D₅₂	1	2	yes	direct product factor
46	C₂	C₂²×C₇×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₇	C₂×D₁₃
commutator, cosocle	C₂×C₁₃	C₂³×C₇
Frattini	C₂	C₂²×C₇×D₁₃
Fitting	C₂×C₄×C₇×C₁₃	C₂
socle	C₂²×C₇×C₁₃	C₂²
hypercenter	C₂×C₄×C₇	D₁₃
hypocenter	C₁₃	C₂×C₇×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×D₁₃	C₂	semidirect
2. C₂×C₄×C₇×C₁₃	C₂	semidirect
3. C₇×D₅₂	C₂	direct (N × H)
6. C₂×C₇×D₁₃	C₂²	semidirect
7. C₄×C₇×C₁₃	C₂²	semidirect
8. C₂×D₅₂	C₇	direct (N × H)
9. C₂×C₇×C₁₃	D₄	semidirect
13. C₂²×D₁₃	C₂×C₇	semidirect
14. C₂×C₄×C₁₃	C₂×C₇	semidirect
15. D₅₂	C₂×C₇	direct (N × H)
16. C₇×C₁₃	C₂×D₄	semidirect
19. C₂×C₄×C₇	D₁₃	semidirect
22. C₂×D₁₃	C₂²×C₇	semidirect
23. C₄×C₁₃	C₂²×C₇	semidirect
27. C₄×C₇	C₂×D₁₃	semidirect
28. C₂×C₁₃	C₇×D₄	semidirect
33. C₂×C₇	D₅₂	direct (N × H)
35. C₁₃	C₂×C₇×D₄	semidirect
38. C₂×C₄	C₇×D₁₃	semidirect
39. C₇	C₂×D₅₂	direct (N × H)
43. C₄	C₂×C₇×D₁₃	semidirect
45. C₂	C₇×D₅₂	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×D₁₃	2
C₂×C₄×C₇×C₁₃	2
C₇×D₅₂	2
C₂×D₅₂	7
C₂×C₇×D₄	13

Subgroups — C2×C7×D52 #13089884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₅₂ #13089884