Subgroups — C₇×D₄×D₁₃ #13089886

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	C₇×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
4	C₇×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₇×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×C₁₃	C₂²	1	2	yes	complemented
7	C₂×C₇×D₁₃	—	2	4	no	—
8	C₂×C₇×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₇×D₁₃	C₂²	1	2	yes	complemented
10	C₄×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented
11	C₇×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
12	D₄×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₇×C₁₃	—	2	2	no	—
14	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
15	C₇×D₁₃	—	2	2	no	—
16	C₇×D₁₃	D₄	1	2	yes	direct product factor
17	C₂×C₇×D₄	—	13	1	no	maximal, Hall
18	C₂²×D₁₃	C₂×C₇	1	2	yes	complemented
19	D₄×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
20	C₂²⋊D₁₃	C₂×C₇	1	2	yes	complemented
21	D₅₂	C₂×C₇	1	1	yes	characteristic, complemented
22	C₄×D₁₃	C₂×C₇	1	1	yes	characteristic, complemented
23	C₇×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
24	C₂³×C₇	—	13	2	no	—
25	C₇×D₄	—	13	2	no	—
26	C₇×D₄	—	13	1	no	—
27	C₇×D₄	D₁₃	1	1	yes	characteristic, direct product factor
28	C₂×C₄×C₇	—	13	1	no	—
29	C₂²×C₁₃	C₂²×C₇	1	2	yes	complemented
30	C₂×D₁₃	—	2	4	no	—
31	C₂×D₁₃	C₂²×C₇	1	1	yes	characteristic
32	C₂×D₁₃	C₂²×C₇	1	2	yes	complemented
33	C₄×C₁₃	C₂²×C₇	1	1	yes	characteristic, complemented
34	Dic₁₃	C₂²×C₇	1	1	yes	characteristic, complemented
35	C₂²×C₇	—	13	1	no	—
36	C₂²×C₇	—	13	2	no	—
37	C₂²×C₇	—	26	4	no	—
38	C₂²×C₇	C₂×D₁₃	1	2	yes	complemented
39	C₄×C₇	—	13	1	no	—
40	C₄×C₇	C₂×D₁₃	1	1	yes	characteristic, complemented
41	C₂×C₁₃	—	2	2	no	—
42	C₂×C₁₃	C₂³×C₇	1	1	yes	characteristic
43	D₁₃	—	2	2	no	—
44	D₁₃	C₇×D₄	1	2	yes	direct product factor
45	C₂×D₄	—	13	1	no	Sylow
46	C₂×C₇	—	2	2	no	—
47	C₂×C₇	—	13	2	no	—
48	C₂×C₇	—	26	2	no	—
49	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
50	C₁₃	C₂×C₇×D₄	1	1	yes	characteristic, complemented, Sylow
51	C₂³	—	13	2	no	—
52	D₄	—	13	2	no	—
53	D₄	—	13	1	no	—
54	D₄	C₇×D₁₃	1	1	yes	characteristic, direct product factor
55	C₂×C₄	—	13	1	no	—
56	C₇	D₄×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²	—	13	1	no	—
58	C₂²	—	13	2	no	—
59	C₂²	—	26	4	no	—
60	C₂²	C₂×C₇×D₁₃	1	2	yes	complemented
61	C₄	—	13	1	no	—
62	C₄	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented
63	C₂	—	2	2	no	—
64	C₂	—	13	2	no	—
65	C₂	—	26	2	no	—
66	C₂	C₂²×C₇×D₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×D₁₃	C₂	semidirect
2. C₇×D₄×C₁₃	C₂	semidirect
3. C₇×C₂²⋊D₁₃	C₂	semidirect
4. C₇×D₅₂	C₂	semidirect
5. C₄×C₇×D₁₃	C₂	semidirect
6. C₂²×C₇×C₁₃	C₂²	semidirect
9. C₂×C₇×D₁₃	C₂²	semidirect
10. C₄×C₇×C₁₃	C₂²	semidirect
11. C₇×Dic₁₃	C₂²	semidirect
12. D₄×D₁₃	C₇	direct (N × H)
16. C₇×D₁₃	D₄	direct (N × H)
18. C₂²×D₁₃	C₂×C₇	semidirect
19. D₄×C₁₃	C₂×C₇	semidirect
20. C₂²⋊D₁₃	C₂×C₇	semidirect
21. D₅₂	C₂×C₇	semidirect
22. C₄×D₁₃	C₂×C₇	semidirect
23. C₇×C₁₃	C₂×D₄	semidirect
27. C₇×D₄	D₁₃	direct (N × H)
29. C₂²×C₁₃	C₂²×C₇	semidirect
32. C₂×D₁₃	C₂²×C₇	semidirect
33. C₄×C₁₃	C₂²×C₇	semidirect
34. Dic₁₃	C₂²×C₇	semidirect
38. C₂²×C₇	C₂×D₁₃	semidirect
40. C₄×C₇	C₂×D₁₃	semidirect
44. D₁₃	C₇×D₄	direct (N × H)
50. C₁₃	C₂×C₇×D₄	semidirect
54. D₄	C₇×D₁₃	direct (N × H)
56. C₇	D₄×D₁₃	direct (N × H)
60. C₂²	C₂×C₇×D₁₃	semidirect
62. C₄	C₂×C₇×D₁₃	semidirect

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

Subgroups — C7×D4×D13 #13089886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₄×D₁₃ #13089886