Subgroups — C₂×C₇×D₄×C₁₃ #13089913

Order 1456.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂²×C₇×C₁₃	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₇×C₁₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₇×C₁₃	C₂	semidirect
2. C₇×D₄×C₁₃	C₂	direct (N × H)
3. C₂×C₄×C₇×C₁₃	C₂	semidirect
6. C₂²×C₇×C₁₃	C₂²	semidirect
7. C₄×C₇×C₁₃	C₂²	semidirect
8. C₂×D₄×C₁₃	C₇	direct (N × H)
10. C₂×C₇×C₁₃	D₄	direct (N × H)
12. C₂×C₇×D₄	C₁₃	direct (N × H)
13. C₂³×C₁₃	C₂×C₇	semidirect
14. D₄×C₁₃	C₂×C₇	direct (N × H)
15. C₂×C₄×C₁₃	C₂×C₇	semidirect
16. C₇×C₁₃	C₂×D₄	direct (N × H)
17. C₂³×C₇	C₂×C₁₃	semidirect
18. C₇×D₄	C₂×C₁₃	direct (N × H)
19. C₂×C₄×C₇	C₂×C₁₃	semidirect
22. C₂²×C₁₃	C₂²×C₇	semidirect
23. C₄×C₁₃	C₂²×C₇	semidirect
26. C₂²×C₇	C₂²×C₁₃	semidirect
27. C₄×C₇	C₂²×C₁₃	semidirect
29. C₂×C₁₃	C₇×D₄	direct (N × H)
31. C₂×D₄	C₇×C₁₃	direct (N × H)
33. C₂×C₇	D₄×C₁₃	direct (N × H)
35. C₁₃	C₂×C₇×D₄	direct (N × H)
36. C₂³	C₂×C₇×C₁₃	semidirect
37. D₄	C₂×C₇×C₁₃	direct (N × H)
38. C₂×C₄	C₂×C₇×C₁₃	semidirect
39. C₇	C₂×D₄×C₁₃	direct (N × H)
42. C₂²	C₂²×C₇×C₁₃	semidirect
43. C₄	C₂²×C₇×C₁₃	semidirect
45. C₂	C₇×D₄×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₇×C₁₃	2
C₇×D₄×C₁₃	2
C₂×C₄×C₇×C₁₃	2
C₂×D₄×C₁₃	7
C₂×C₇×D₄	13

Subgroups — C2×C7×D4×C13 #13089913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₄×C₁₃ #13089913