Subgroups — C₂×C₁₃×C₂²⋊D₇ #13089901

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	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₂²⋊D₇	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₇×C₁₃	—	2	2	no	—
6	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₇×C₁₃	C₂²	1	2	yes	complemented
8	C₂×C₁₃×D₇	—	2	2	no	—
9	C₂×C₁₃×D₇	C₂²	1	2	yes	complemented
10	C₁₃×Dic₇	C₂²	1	2	yes	complemented
11	C₂×D₄×C₁₃	—	7	1	no	maximal, Hall
12	C₂×C₇×C₁₃	—	2	2	no	—
13	C₂×C₇×C₁₃	D₄	1	2	yes	complemented
14	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
15	C₁₃×D₇	—	2	2	no	—
16	C₂×C₂²⋊D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₁₃	—	7	1	no	—
18	C₂³×C₁₃	D₇	1	1	yes	characteristic, complemented
19	D₄×C₁₃	—	7	4	no	—
20	C₂×C₄×C₁₃	—	7	1	no	—
21	C₇×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
22	C₂³×C₇	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₂²×D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₂²⋊D₇	C₂×C₁₃	1	4	yes	direct product factor
25	C₂×Dic₇	C₂×C₁₃	1	1	yes	characteristic, complemented
26	C₂²×C₁₃	—	2	2	no	—
27	C₂²×C₁₃	—	7	2	no	—
28	C₂²×C₁₃	—	14	2	no	—
29	C₂²×C₁₃	C₂×D₇	1	1	yes	characteristic
30	C₂²×C₁₃	C₂×D₇	1	2	yes	complemented
31	C₄×C₁₃	—	7	2	no	—
32	C₂²×C₇	—	2	2	no	—
33	C₂²×C₇	C₂²×C₁₃	1	1	yes	characteristic
34	C₂²×C₇	C₂²×C₁₃	1	2	yes	complemented
35	C₂×D₇	—	2	2	no	—
36	C₂×D₇	C₂²×C₁₃	1	2	yes	complemented
37	Dic₇	C₂²×C₁₃	1	2	yes	complemented
38	C₂×C₁₃	—	2	2	no	—
39	C₂×C₁₃	—	14	2	no	—
40	C₂×C₁₃	C₂²⋊D₇	1	2	yes	direct product factor
41	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
42	C₂×D₄	—	7	1	no	Sylow
43	C₂×C₇	—	2	2	no	—
44	C₂×C₇	D₄×C₁₃	1	2	yes	complemented
45	C₂×C₇	C₂³×C₁₃	1	1	yes	characteristic
46	D₇	—	2	2	no	—
47	C₁₃	C₂×C₂²⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
48	C₂³	—	7	1	no	—
49	C₂³	C₁₃×D₇	1	1	yes	characteristic, complemented
50	D₄	—	7	4	no	—
51	C₂×C₄	—	7	1	no	—
52	C₇	C₂×D₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	2	2	no	—
54	C₂²	—	7	2	no	—
55	C₂²	—	14	2	no	—
56	C₂²	C₂×C₁₃×D₇	1	1	yes	characteristic
57	C₂²	C₂×C₁₃×D₇	1	2	yes	complemented
58	C₄	—	7	2	no	—
59	C₂	—	2	2	no	—
60	C₂	—	14	2	no	—
61	C₂	C₁₃×C₂²⋊D₇	1	2	yes	direct product factor
62	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	C₂³×C₇×C₁₃	C₂
socle	C₂²×C₇×C₁₃	C₂²
hypercenter	C₂³×C₁₃	D₇
hypocenter	C₇	C₂×D₄×C₁₃
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂³×C₇×C₁₃	C₂	semidirect
2. C₂²×C₁₃×D₇	C₂	semidirect
3. C₁₃×C₂²⋊D₇	C₂	direct (N × H)
4. C₂×C₁₃×Dic₇	C₂	semidirect
7. C₂²×C₇×C₁₃	C₂²	semidirect
9. C₂×C₁₃×D₇	C₂²	semidirect
10. C₁₃×Dic₇	C₂²	semidirect
13. C₂×C₇×C₁₃	D₄	semidirect
16. C₂×C₂²⋊D₇	C₁₃	direct (N × H)
18. C₂³×C₁₃	D₇	semidirect
21. C₇×C₁₃	C₂×D₄	semidirect
22. C₂³×C₇	C₂×C₁₃	semidirect
23. C₂²×D₇	C₂×C₁₃	semidirect
24. C₂²⋊D₇	C₂×C₁₃	direct (N × H)
25. C₂×Dic₇	C₂×C₁₃	semidirect
30. C₂²×C₁₃	C₂×D₇	semidirect
34. C₂²×C₇	C₂²×C₁₃	semidirect
36. C₂×D₇	C₂²×C₁₃	semidirect
37. Dic₇	C₂²×C₁₃	semidirect
40. C₂×C₁₃	C₂²⋊D₇	direct (N × H)
44. C₂×C₇	D₄×C₁₃	semidirect
47. C₁₃	C₂×C₂²⋊D₇	direct (N × H)
49. C₂³	C₁₃×D₇	semidirect
52. C₇	C₂×D₄×C₁₃	semidirect
57. C₂²	C₂×C₁₃×D₇	semidirect
61. C₂	C₁₃×C₂²⋊D₇	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
C₂²×C₁₃×D₇	2
C₁₃×C₂²⋊D₇	2
C₂×C₁₃×Dic₇	2
C₂×D₄×C₁₃	7
C₂×C₂²⋊D₇	13

Subgroups — C2×C13×C22⋊D7 #13089901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₂²⋊D₇ #13089901