Subgroups — C₁₃×#1157 #13089895

Order 1456.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
3	C₁₃×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×D₇	C₂	1	2	yes	maximal, complemented
5	C₁₃×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×D₇	C₂²	1	2	yes	—
8	C₄×C₇×C₁₃	C₂²	1	1	yes	characteristic
9	C₄×C₇×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×Dic₇	C₂²	1	2	yes	—
11	C₁₃×#41	—	7	1	no	maximal, Hall
12	C₂×C₇×C₁₃	—	2	1	no	—
13	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
14	C₁₃×D₇	—	2	2	no	—
15	#1157	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	Q₈×C₁₃	—	7	1	no	—
17	D₄×C₁₃	—	7	2	no	—
18	D₄×C₁₃	—	7	1	no	—
19	C₂×C₄×C₁₃	—	7	2	no	—
20	C₂×C₄×C₁₃	D₇	1	1	yes	characteristic, complemented
21	C₇×C₁₃	#41	1	1	yes	characteristic, complemented, Hall
22	C₂×C₄×C₇	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₂²⋊D₇	C₂×C₁₃	1	2	yes	complemented
24	D₂₈	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₄×D₇	C₂×C₁₃	1	2	yes	complemented
26	Dic₁₄	C₂×C₁₃	1	1	yes	characteristic, complemented
27	C₂²×C₁₃	—	7	2	no	—
28	C₂²×C₁₃	C₂×D₇	1	1	yes	characteristic
29	C₄×C₁₃	—	7	2	no	—
30	C₄×C₁₃	C₂×D₇	1	1	yes	characteristic
31	C₄×C₁₃	C₂×D₇	1	1	yes	characteristic
32	C₂²×C₇	C₂²×C₁₃	1	1	yes	characteristic
33	C₂×D₇	C₂²×C₁₃	1	2	yes	—
34	C₄×C₇	C₂²×C₁₃	1	1	yes	characteristic
35	C₄×C₇	C₂²×C₁₃	1	1	yes	characteristic
36	Dic₇	C₂²×C₁₃	1	2	yes	—
37	C₂×C₁₃	—	2	1	no	—
38	C₂×C₁₃	—	14	2	no	—
39	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
40	#41	—	7	1	no	Sylow
41	C₂×C₇	—	2	1	no	—
42	C₂×C₇	C₂³×C₁₃	1	1	yes	characteristic
43	D₇	—	2	2	no	—
44	C₁₃	#1157	1	1	yes	characteristic, direct product factor, Sylow
45	Q₈	—	7	1	no	—
46	D₄	—	7	2	no	—
47	D₄	—	7	1	no	—
48	C₂×C₄	—	7	2	no	—
49	C₂×C₄	C₁₃×D₇	1	1	yes	characteristic, complemented
50	C₇	C₁₃×#41	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	7	2	no	—
52	C₂²	C₂×C₁₃×D₇	1	1	yes	characteristic
53	C₄	—	7	2	no	—
54	C₄	C₂×C₁₃×D₇	1	1	yes	characteristic
55	C₄	C₂×C₁₃×D₇	1	1	yes	characteristic
56	C₂	—	2	1	no	—
57	C₂	—	14	2	no	—
58	C₂	C₂²×C₁₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	C₂×D₇
commutator, cosocle	C₂×C₇	C₂³×C₁₃
Frattini	C₂	C₂²×C₁₃×D₇
Fitting	C₂×C₄×C₇×C₁₃	C₂
socle	C₂×C₇×C₁₃	C₂³
hypercenter	C₂×C₄×C₁₃	D₇
hypocenter	C₇	C₁₃×#41
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₇×C₁₃	C₂	semidirect
2. C₁₃×C₂²⋊D₇	C₂	semidirect
3. C₁₃×D₂₈	C₂	semidirect
4. C₄×C₁₃×D₇	C₂	semidirect
5. C₁₃×Dic₁₄	C₂	semidirect
15. #1157	C₁₃	direct (N × H)
20. C₂×C₄×C₁₃	D₇	semidirect
21. C₇×C₁₃	#41	semidirect
22. C₂×C₄×C₇	C₂×C₁₃	semidirect
23. C₂²⋊D₇	C₂×C₁₃	semidirect
24. D₂₈	C₂×C₁₃	semidirect
25. C₄×D₇	C₂×C₁₃	semidirect
26. Dic₁₄	C₂×C₁₃	semidirect
44. C₁₃	#1157	direct (N × H)
49. C₂×C₄	C₁₃×D₇	semidirect
50. C₇	C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₇×C₁₃	2
C₁₃×C₂²⋊D₇	2
C₁₃×D₂₈	2
C₄×C₁₃×D₇	2
C₁₃×Dic₁₄	2
C₁₃×#41	7
#1157	13

Subgroups — C13×#1157 #13089895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1157 #13089895