Subgroups — C₁₃×C₇⋊(C₇⋊#157) #37525564

Order 22932.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇²×C₁₃	—	6	2	no	—
4	C₁₃×C₇⋊#157	—	7	8	no	maximal
5	C₁₃×C₇⋊Dic₇	—	9	1	no	maximal, Hall
6	C₃×C₇²×C₁₃	—	2	2	no	—
7	C₇⋊(C₇⋊#157)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₃×C₃⋊D₃	D₇	1	8	yes	—
9	C₂×C₇²×C₁₃	—	9	1	no	—
10	C₇²×C₃⋊D₃	C₂×C₁₃	1	1	yes	characteristic
11	C₃²×C₇×C₁₃	Dic₇	1	8	yes	complemented
12	C₇²×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
13	D₃×C₇×C₁₃	—	6	16	no	—
14	C₁₃×#157	—	49	1	no	Hall
15	C₃²×C₇²	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₁₃×Dic₇	—	63	8	no	—
17	D₃×C₇²	—	6	2	no	—
18	C₃×C₇×C₁₃	—	2	16	no	—
19	C₇⋊#157	—	7	8	no	—
20	C₁₃×C₃⋊D₃	C₇⋊D₇	1	1	yes	characteristic
21	C₇⋊Dic₇	—	9	1	no	Hall
22	C₂×C₇×C₁₃	—	9	8	no	—
23	C₃×C₇²	—	2	2	no	—
24	C₇×C₃⋊D₃	C₁₃×D₇	1	8	yes	—
25	C₃²×C₁₃	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇²	—	9	1	no	—
27	C₇×C₁₃	C₇⋊#157	1	8	yes	complemented
28	D₃×C₁₃	—	6	2	no	—
29	C₃²×C₇	C₁₃×Dic₇	1	8	yes	complemented
30	C₄×C₁₃	—	441	1	no	Hall
31	C₇²	C₁₃×#157	1	1	yes	characteristic, complemented, Sylow
32	D₃×C₇	—	6	16	no	—
33	C₃×C₁₃	—	2	2	no	—
34	#157	—	49	1	no	Hall
35	Dic₇	—	63	8	no	—
36	C₂×C₁₃	—	9	1	no	—
37	C₃×C₇	—	2	16	no	—
38	C₃⋊D₃	C₁₃×C₇⋊D₇	1	1	yes	characteristic
39	C₂×C₇	—	9	8	no	—
40	C₁₃	C₇⋊(C₇⋊#157)	1	1	yes	characteristic, direct product factor, Sylow
41	C₃²	C₁₃×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₁₃×C₇⋊#157	1	8	yes	complemented
43	D₃	—	6	2	no	—
44	C₄	—	441	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₇⋊(C₇⋊#157)
commutator, hypocenter	C₃²×C₇²	C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₄
prime radical	C₇²×C₁₃×C₃⋊D₃	C₂
cosocle	C₇²×C₃⋊D₃	C₂×C₁₃
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇²×C₁₃	C₄	semidirect
7. C₇⋊(C₇⋊#157)	C₁₃	direct (N × H)
11. C₃²×C₇×C₁₃	Dic₇	semidirect
12. C₇²×C₁₃	#157	semidirect
15. C₃²×C₇²	C₄×C₁₃	semidirect
25. C₃²×C₁₃	C₇⋊Dic₇	semidirect
27. C₇×C₁₃	C₇⋊#157	semidirect
29. C₃²×C₇	C₁₃×Dic₇	semidirect
31. C₇²	C₁₃×#157	semidirect
40. C₁₃	C₇⋊(C₇⋊#157)	direct (N × H)
41. C₃²	C₁₃×C₇⋊Dic₇	semidirect
42. C₇	C₁₃×C₇⋊#157	semidirect

Maximal subgroups

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

subgroup	index
C₇²×C₁₃×C₃⋊D₃	2
C₁₃×C₇⋊#157	7
C₁₃×C₇⋊Dic₇	9
C₇⋊(C₇⋊#157)	13

Subgroups — C13×C7⋊(C7⋊#157) #37525564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₇⋊(C₇⋊#157) #37525564