Subgroups — C₂×C₁₃×D₂₈ #13089894

Order 1456.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×D₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₂₈	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₁₃×D₇	—	2	4	no	—
6	C₂×C₁₃×D₇	C₂²	1	4	yes	complemented
7	C₄×C₇×C₁₃	C₂²	1	2	yes	complemented
8	C₂×D₄×C₁₃	—	7	1	no	maximal, Hall
9	C₂×C₇×C₁₃	D₄	1	2	yes	complemented
10	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
11	C₁₃×D₇	—	2	4	no	—
12	C₂×D₂₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₁₃	—	7	2	no	—
14	D₄×C₁₃	—	7	4	no	—
15	C₂×C₄×C₁₃	D₇	1	1	yes	characteristic, complemented
16	C₇×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
17	C₂²×D₇	C₂×C₁₃	1	2	yes	complemented
18	C₂×C₄×C₇	C₂×C₁₃	1	1	yes	characteristic, complemented
19	D₂₈	C₂×C₁₃	1	4	yes	direct product factor
20	C₂²×C₁₃	—	7	4	no	—
21	C₂²×C₁₃	—	14	4	no	—
22	C₂²×C₁₃	C₂×D₇	1	1	yes	characteristic
23	C₄×C₁₃	C₂×D₇	1	2	yes	complemented
24	C₂²×C₇	C₂²×C₁₃	1	1	yes	characteristic
25	C₂×D₇	—	2	4	no	—
26	C₂×D₇	C₂²×C₁₃	1	4	yes	complemented
27	C₄×C₇	C₂²×C₁₃	1	2	yes	complemented
28	C₂×C₁₃	—	14	4	no	—
29	C₂×C₁₃	D₂₈	1	2	yes	direct product factor
30	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
31	C₂×D₄	—	7	1	no	Sylow
32	C₂×C₇	D₄×C₁₃	1	2	yes	complemented
33	C₂×C₇	C₂³×C₁₃	1	1	yes	characteristic
34	D₇	—	2	4	no	—
35	C₁₃	C₂×D₂₈	1	1	yes	characteristic, direct product factor, Sylow
36	C₂³	—	7	2	no	—
37	D₄	—	7	4	no	—
38	C₂×C₄	C₁₃×D₇	1	1	yes	characteristic, complemented
39	C₇	C₂×D₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	7	4	no	—
41	C₂²	—	14	4	no	—
42	C₂²	C₂×C₁₃×D₇	1	1	yes	characteristic
43	C₄	C₂×C₁₃×D₇	1	2	yes	complemented
44	C₂	—	14	4	no	—
45	C₂	C₁₃×D₂₈	1	2	yes	direct product factor
46	C₂	C₂²×C₁₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	C₂×D₇
commutator, cosocle	C₂×C₇	C₂³×C₁₃
Frattini	C₂	C₂²×C₁₃×D₇
Fitting	C₂×C₄×C₇×C₁₃	C₂
socle	C₂²×C₇×C₁₃	C₂²
hypercenter	C₂×C₄×C₁₃	D₇
hypocenter	C₇	C₂×D₄×C₁₃
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×D₇	C₂	semidirect
2. C₂×C₄×C₇×C₁₃	C₂	semidirect
3. C₁₃×D₂₈	C₂	direct (N × H)
6. C₂×C₁₃×D₇	C₂²	semidirect
7. C₄×C₇×C₁₃	C₂²	semidirect
9. C₂×C₇×C₁₃	D₄	semidirect
12. C₂×D₂₈	C₁₃	direct (N × H)
15. C₂×C₄×C₁₃	D₇	semidirect
16. C₇×C₁₃	C₂×D₄	semidirect
17. C₂²×D₇	C₂×C₁₃	semidirect
18. C₂×C₄×C₇	C₂×C₁₃	semidirect
19. D₂₈	C₂×C₁₃	direct (N × H)
23. C₄×C₁₃	C₂×D₇	semidirect
26. C₂×D₇	C₂²×C₁₃	semidirect
27. C₄×C₇	C₂²×C₁₃	semidirect
29. C₂×C₁₃	D₂₈	direct (N × H)
32. C₂×C₇	D₄×C₁₃	semidirect
35. C₁₃	C₂×D₂₈	direct (N × H)
38. C₂×C₄	C₁₃×D₇	semidirect
39. C₇	C₂×D₄×C₁₃	semidirect
43. C₄	C₂×C₁₃×D₇	semidirect
45. C₂	C₁₃×D₂₈	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×C₁₃×D₇	2
C₂×C₄×C₇×C₁₃	2
C₁₃×D₂₈	2
C₂×D₄×C₁₃	7
C₂×D₂₈	13

Subgroups — C2×C13×D28 #13089894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₂₈ #13089894