Subgroups — D₇×D₅₂ #13089867

Order 1456.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇×D₁₃	C₂	1	2	yes	maximal, complemented
2	D₃₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#10624411	C₂	1	2	yes	maximal, complemented
6	C₂×D₉₁	C₂²	1	2	yes	complemented
7	C₂×C₁₃×D₇	C₂²	1	1	yes	characteristic
8	C₂×C₇×D₁₃	C₂²	1	2	yes	complemented
9	D₇×D₁₃	—	2	4	no	—
10	C₄×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented
11	C₁₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
12	C₂×D₅₂	—	7	1	no	maximal, Hall
13	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
14	D₉₁	—	2	2	no	—
15	C₇×D₁₃	—	2	2	no	—
16	C₁₃×D₇	D₄	1	2	yes	complemented
17	D₄×D₇	—	13	1	no	maximal, Hall
18	C₂²×D₁₃	—	7	2	no	—
19	C₂×C₄×C₁₃	—	7	1	no	—
20	D₅₂	—	7	2	no	—
21	D₅₂	—	7	1	no	—
22	D₅₂	D₇	1	1	yes	characteristic, direct product factor
23	C₇×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
24	C₂²×D₇	—	13	2	no	—
25	C₇×D₄	—	13	1	no	—
26	C₂²⋊D₇	—	13	2	no	—
27	D₂₈	—	13	1	no	—
28	C₄×D₇	D₁₃	1	1	yes	characteristic, complemented
29	C₂²×C₁₃	—	7	1	no	—
30	C₂×D₁₃	—	7	2	no	—
31	C₂×D₁₃	—	14	4	no	—
32	C₂×D₁₃	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	—	13	2	no	—
36	C₂×D₇	—	13	2	no	—
37	C₂×D₇	—	26	4	no	—
38	C₂×D₇	C₂×D₁₃	1	1	yes	characteristic
39	C₄×C₇	C₂×D₁₃	1	1	yes	characteristic, complemented
40	Dic₇	C₂×D₁₃	1	1	yes	characteristic, complemented
41	C₂×C₁₃	—	7	2	no	—
42	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
43	D₁₃	—	2	2	no	—
44	D₁₃	—	14	2	no	—
45	C₂×D₄	—	91	1	no	Sylow
46	C₂×C₇	—	26	2	no	—
47	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
48	D₇	—	26	2	no	—
49	D₇	D₅₂	1	2	yes	direct product factor
50	C₁₃	D₄×D₇	1	1	yes	characteristic, complemented, Sylow
51	C₂³	—	91	2	no	—
52	D₄	—	13	1	no	—
53	D₄	—	91	2	no	—
54	D₄	—	91	1	no	—
55	C₂×C₄	—	7	1	no	—
56	C₇	C₂×D₅₂	1	1	yes	characteristic, complemented, Sylow
57	C₂²	—	7	1	no	—
58	C₂²	—	13	2	no	—
59	C₂²	—	91	2	no	—
60	C₂²	—	182	4	no	—
61	C₄	—	7	1	no	—
62	C₄	D₇×D₁₃	1	1	yes	characteristic, complemented
63	C₂	—	7	2	no	—
64	C₂	—	26	2	no	—
65	C₂	—	182	2	no	—
66	C₂	C₂×D₇×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₇×D₁₃
commutator, socle, cosocle	C₂×C₇×C₁₃	C₂³
Fitting	C₄×C₇×C₁₃	C₂²
hypercenter	C₄	D₇×D₁₃
hypocenter	C₇×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₇×C₁₃ ▷ C₇×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₇×D₁₃	C₂	semidirect
2. D₃₆₄	C₂	semidirect
3. C₄×C₁₃×D₇	C₂	semidirect
4. C₇×D₅₂	C₂	semidirect
5. #10624411	C₂	semidirect
6. C₂×D₉₁	C₂²	semidirect
8. C₂×C₇×D₁₃	C₂²	semidirect
10. C₄×C₇×C₁₃	C₂²	semidirect
11. C₁₃×Dic₇	C₂²	semidirect
16. C₁₃×D₇	D₄	semidirect
22. D₅₂	D₇	direct (N × H)
23. C₇×C₁₃	C₂×D₄	semidirect
28. C₄×D₇	D₁₃	semidirect
32. C₂×D₁₃	C₂×D₇	semidirect
34. C₄×C₁₃	C₂×D₇	semidirect
39. C₄×C₇	C₂×D₁₃	semidirect
40. Dic₇	C₂×D₁₃	semidirect
49. D₇	D₅₂	direct (N × H)
50. C₁₃	D₄×D₇	semidirect
56. C₇	C₂×D₅₂	semidirect
62. C₄	D₇×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₇×D₁₃	2
D₃₆₄	2
C₄×C₁₃×D₇	2
C₇×D₅₂	2
#10624411	2
C₂×D₅₂	7
D₄×D₇	13

Subgroups — D7×D52 #13089867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₅₂ #13089867