Subgroups — C₂×C₇×C₂²⋊D₁₃ #13089891

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×C₇×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂²⋊D₁₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇×Dic₁₃	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×C₇×D₁₃	—	2	2	no	—
9	C₂×C₇×D₁₃	C₂²	1	2	yes	complemented
10	C₇×Dic₁₃	C₂²	1	2	yes	complemented
11	C₂×C₂²⋊D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, 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	C₇×D₁₃	—	2	2	no	—
16	C₂×C₇×D₄	—	13	1	no	maximal, Hall
17	C₂³×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂²×D₁₃	C₂×C₇	1	1	yes	characteristic, complemented
19	C₂²⋊D₁₃	C₂×C₇	1	4	yes	direct product factor
20	C₂×Dic₁₃	C₂×C₇	1	1	yes	characteristic, complemented
21	C₇×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
22	C₂³×C₇	—	13	1	no	—
23	C₂³×C₇	D₁₃	1	1	yes	characteristic, complemented
24	C₇×D₄	—	13	4	no	—
25	C₂×C₄×C₇	—	13	1	no	—
26	C₂²×C₁₃	—	2	2	no	—
27	C₂²×C₁₃	C₂²×C₇	1	1	yes	characteristic
28	C₂²×C₁₃	C₂²×C₇	1	2	yes	complemented
29	C₂×D₁₃	—	2	2	no	—
30	C₂×D₁₃	C₂²×C₇	1	2	yes	complemented
31	Dic₁₃	C₂²×C₇	1	2	yes	complemented
32	C₂²×C₇	—	2	2	no	—
33	C₂²×C₇	—	13	2	no	—
34	C₂²×C₇	—	26	2	no	—
35	C₂²×C₇	C₂×D₁₃	1	1	yes	characteristic
36	C₂²×C₇	C₂×D₁₃	1	2	yes	complemented
37	C₄×C₇	—	13	2	no	—
38	C₂×C₁₃	—	2	2	no	—
39	C₂×C₁₃	C₇×D₄	1	2	yes	complemented
40	C₂×C₁₃	C₂³×C₇	1	1	yes	characteristic
41	D₁₃	—	2	2	no	—
42	C₂×D₄	—	13	1	no	Sylow
43	C₂×C₇	—	2	2	no	—
44	C₂×C₇	—	26	2	no	—
45	C₂×C₇	C₂²⋊D₁₃	1	2	yes	direct product factor
46	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
47	C₁₃	C₂×C₇×D₄	1	1	yes	characteristic, complemented, Sylow
48	C₂³	—	13	1	no	—
49	C₂³	C₇×D₁₃	1	1	yes	characteristic, complemented
50	D₄	—	13	4	no	—
51	C₂×C₄	—	13	1	no	—
52	C₇	C₂×C₂²⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²	—	2	2	no	—
54	C₂²	—	13	2	no	—
55	C₂²	—	26	2	no	—
56	C₂²	C₂×C₇×D₁₃	1	1	yes	characteristic
57	C₂²	C₂×C₇×D₁₃	1	2	yes	complemented
58	C₄	—	13	2	no	—
59	C₂	—	2	2	no	—
60	C₂	—	26	2	no	—
61	C₂	C₇×C₂²⋊D₁₃	1	2	yes	direct product factor
62	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	C₂³×C₇×C₁₃	C₂
socle	C₂²×C₇×C₁₃	C₂²
hypercenter	C₂³×C₇	D₁₃
hypocenter	C₁₃	C₂×C₇×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₇ ◁ C₂³×C₇

Complements

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

N	H ≅ G/N	type
1. C₂³×C₇×C₁₃	C₂	semidirect
2. C₂²×C₇×D₁₃	C₂	semidirect
3. C₇×C₂²⋊D₁₃	C₂	direct (N × H)
4. C₂×C₇×Dic₁₃	C₂	semidirect
7. C₂²×C₇×C₁₃	C₂²	semidirect
9. C₂×C₇×D₁₃	C₂²	semidirect
10. C₇×Dic₁₃	C₂²	semidirect
11. C₂×C₂²⋊D₁₃	C₇	direct (N × H)
13. C₂×C₇×C₁₃	D₄	semidirect
17. C₂³×C₁₃	C₂×C₇	semidirect
18. C₂²×D₁₃	C₂×C₇	semidirect
19. C₂²⋊D₁₃	C₂×C₇	direct (N × H)
20. C₂×Dic₁₃	C₂×C₇	semidirect
21. C₇×C₁₃	C₂×D₄	semidirect
23. C₂³×C₇	D₁₃	semidirect
28. C₂²×C₁₃	C₂²×C₇	semidirect
30. C₂×D₁₃	C₂²×C₇	semidirect
31. Dic₁₃	C₂²×C₇	semidirect
36. C₂²×C₇	C₂×D₁₃	semidirect
39. C₂×C₁₃	C₇×D₄	semidirect
45. C₂×C₇	C₂²⋊D₁₃	direct (N × H)
47. C₁₃	C₂×C₇×D₄	semidirect
49. C₂³	C₇×D₁₃	semidirect
52. C₇	C₂×C₂²⋊D₁₃	direct (N × H)
57. C₂²	C₂×C₇×D₁₃	semidirect
61. C₂	C₇×C₂²⋊D₁₃	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×C₇×D₁₃	2
C₇×C₂²⋊D₁₃	2
C₂×C₇×Dic₁₃	2
C₂×C₂²⋊D₁₃	7
C₂×C₇×D₄	13

Subgroups — C2×C7×C22⋊D13 #13089891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₂²⋊D₁₃ #13089891