Subgroups — D₄×C₁₃×D₇ #13089896

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	C₇×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
4	C₁₃×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×C₁₃	C₂²	1	2	yes	complemented
7	C₂×C₁₃×D₇	—	2	4	no	—
8	C₂×C₁₃×D₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×D₇	C₂²	1	2	yes	complemented
10	C₄×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented
11	C₁₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
12	C₂×D₄×C₁₃	—	7	1	no	maximal, Hall
13	C₂×C₇×C₁₃	—	2	2	no	—
14	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
15	C₁₃×D₇	—	2	2	no	—
16	C₁₃×D₇	D₄	1	2	yes	direct product factor
17	D₄×D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂³×C₁₃	—	7	2	no	—
19	D₄×C₁₃	—	7	2	no	—
20	D₄×C₁₃	—	7	1	no	—
21	D₄×C₁₃	D₇	1	1	yes	characteristic, direct product factor
22	C₂×C₄×C₁₃	—	7	1	no	—
23	C₇×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
24	C₂²×D₇	C₂×C₁₃	1	2	yes	complemented
25	C₇×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
26	C₂²⋊D₇	C₂×C₁₃	1	2	yes	complemented
27	D₂₈	C₂×C₁₃	1	1	yes	characteristic, complemented
28	C₄×D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
29	C₂²×C₁₃	—	7	1	no	—
30	C₂²×C₁₃	—	7	2	no	—
31	C₂²×C₁₃	—	14	4	no	—
32	C₂²×C₁₃	C₂×D₇	1	2	yes	complemented
33	C₄×C₁₃	—	7	1	no	—
34	C₄×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented
35	C₂²×C₇	C₂²×C₁₃	1	2	yes	complemented
36	C₂×D₇	—	2	4	no	—
37	C₂×D₇	C₂²×C₁₃	1	1	yes	characteristic
38	C₂×D₇	C₂²×C₁₃	1	2	yes	complemented
39	C₄×C₇	C₂²×C₁₃	1	1	yes	characteristic, complemented
40	Dic₇	C₂²×C₁₃	1	1	yes	characteristic, complemented
41	C₂×C₁₃	—	2	2	no	—
42	C₂×C₁₃	—	7	2	no	—
43	C₂×C₁₃	—	14	2	no	—
44	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
45	C₂×D₄	—	7	1	no	Sylow
46	C₂×C₇	—	2	2	no	—
47	C₂×C₇	C₂³×C₁₃	1	1	yes	characteristic
48	D₇	—	2	2	no	—
49	D₇	D₄×C₁₃	1	2	yes	direct product factor
50	C₁₃	D₄×D₇	1	1	yes	characteristic, direct product factor, Sylow
51	C₂³	—	7	2	no	—
52	D₄	—	7	2	no	—
53	D₄	—	7	1	no	—
54	D₄	C₁₃×D₇	1	1	yes	characteristic, direct product factor
55	C₂×C₄	—	7	1	no	—
56	C₇	C₂×D₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
57	C₂²	—	7	1	no	—
58	C₂²	—	7	2	no	—
59	C₂²	—	14	4	no	—
60	C₂²	C₂×C₁₃×D₇	1	2	yes	complemented
61	C₄	—	7	1	no	—
62	C₄	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented
63	C₂	—	2	2	no	—
64	C₂	—	7	2	no	—
65	C₂	—	14	2	no	—
66	C₂	C₂²×C₁₃×D₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×D₇	C₂	semidirect
2. C₇×D₄×C₁₃	C₂	semidirect
3. C₁₃×C₂²⋊D₇	C₂	semidirect
4. C₁₃×D₂₈	C₂	semidirect
5. C₄×C₁₃×D₇	C₂	semidirect
6. C₂²×C₇×C₁₃	C₂²	semidirect
9. C₂×C₁₃×D₇	C₂²	semidirect
10. C₄×C₇×C₁₃	C₂²	semidirect
11. C₁₃×Dic₇	C₂²	semidirect
16. C₁₃×D₇	D₄	direct (N × H)
17. D₄×D₇	C₁₃	direct (N × H)
21. D₄×C₁₃	D₇	direct (N × H)
23. C₇×C₁₃	C₂×D₄	semidirect
24. C₂²×D₇	C₂×C₁₃	semidirect
25. C₇×D₄	C₂×C₁₃	semidirect
26. C₂²⋊D₇	C₂×C₁₃	semidirect
27. D₂₈	C₂×C₁₃	semidirect
28. C₄×D₇	C₂×C₁₃	semidirect
32. C₂²×C₁₃	C₂×D₇	semidirect
34. C₄×C₁₃	C₂×D₇	semidirect
35. C₂²×C₇	C₂²×C₁₃	semidirect
38. C₂×D₇	C₂²×C₁₃	semidirect
39. C₄×C₇	C₂²×C₁₃	semidirect
40. Dic₇	C₂²×C₁₃	semidirect
49. D₇	D₄×C₁₃	direct (N × H)
50. C₁₃	D₄×D₇	direct (N × H)
54. D₄	C₁₃×D₇	direct (N × H)
56. C₇	C₂×D₄×C₁₃	semidirect
60. C₂²	C₂×C₁₃×D₇	semidirect
62. C₄	C₂×C₁₃×D₇	semidirect

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
C₇×D₄×C₁₃	2
C₁₃×C₂²⋊D₇	2
C₁₃×D₂₈	2
C₄×C₁₃×D₇	2
C₂×D₄×C₁₃	7
D₄×D₇	13

Subgroups — D4×C13×D7 #13089896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₃×D₇ #13089896