Subgroups — C₁₃×C₇⋊#4380 #30655760

Order 16380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₇×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×C₇⋊#157	—	5	1	no	maximal, Hall
4	C₇×C₁₃×D₁₅	—	6	2	no	—
5	C₁₃×#4380	—	7	1	no	maximal, Hall
6	C₁₃×C₇⋊AGL(1,𝔽₅)	—	9	1	no	maximal, Hall
7	C₇×C₁₃×C₃⋊D₃	—	5	1	no	—
8	C₃×C₅×C₇×C₁₃	—	2	2	no	—
9	C₇⋊#4380	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₃×C₃⋊D₁₅	D₇	1	1	yes	characteristic
11	C₇×D₅×C₁₃	—	9	1	no	—
12	C₃²×C₇×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
13	C₇×C₃⋊D₁₅	C₂×C₁₃	1	1	yes	characteristic
14	C₃²×C₅×C₁₃	Dic₇	1	1	yes	characteristic, complemented, Hall
15	D₃×C₇×C₁₃	—	30	2	no	—
16	C₁₃×#157	—	35	1	no	Hall
17	C₅×C₇×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
18	C₁₃×D₁₅	—	6	2	no	—
19	C₁₃×Dic₇	—	45	1	no	Hall
20	C₃²×C₅×C₇	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₇×C₁₃	—	2	2	no	—
22	C₁₃×AGL(1,𝔽₅)	—	63	1	no	Hall
23	C₇⋊#157	—	5	1	no	Hall
24	C₁₃×C₃⋊D₃	—	5	1	no	—
25	C₇×D₁₅	—	6	2	no	—
26	C₃×C₅×C₁₃	—	2	2	no	—
27	C₂×C₇×C₁₃	—	45	1	no	—
28	#4380	—	7	1	no	Hall
29	C₇⋊AGL(1,𝔽₅)	—	9	1	no	Hall
30	D₅×C₁₃	—	9	1	no	—
31	C₇×C₃⋊D₃	—	5	1	no	—
32	C₃²×C₁₃	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅×C₇	—	2	2	no	—
34	C₇×C₁₃	#4380	1	1	yes	characteristic, complemented, Hall
35	C₃⋊D₁₅	C₁₃×D₇	1	1	yes	characteristic
36	D₃×C₁₃	—	30	2	no	—
37	C₇×D₅	—	9	1	no	—
38	C₅×C₁₃	C₇⋊#157	1	1	yes	characteristic, complemented, Hall
39	C₃²×C₇	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
40	C₄×C₁₃	—	315	1	no	Hall
41	C₃²×C₅	C₁₃×Dic₇	1	1	yes	characteristic, complemented, Hall
42	D₃×C₇	—	30	2	no	—
43	C₃×C₁₃	—	2	2	no	—
44	#157	—	35	1	no	Hall
45	C₅×C₇	C₁₃×#157	1	1	yes	characteristic, complemented, Hall
46	D₁₅	—	6	2	no	—
47	Dic₇	—	45	1	no	Hall
48	C₂×C₁₃	—	45	1	no	—
49	C₃×C₇	—	2	2	no	—
50	AGL(1,𝔽₅)	—	63	1	no	Hall
51	C₃⋊D₃	—	5	1	no	—
52	C₃×C₅	—	2	2	no	—
53	C₂×C₇	—	45	1	no	—
54	C₁₃	C₇⋊#4380	1	1	yes	characteristic, direct product factor, Sylow
55	D₅	—	9	1	no	—
56	C₃²	C₁₃×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
57	C₇	C₁₃×#4380	1	1	yes	characteristic, complemented, Sylow
58	D₃	—	30	2	no	—
59	C₅	C₁₃×C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	315	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₇⋊#4380
commutator, hypocenter	C₃²×C₅×C₇	C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₃	C₄
prime radical	C₇×C₁₃×C₃⋊D₁₅	C₂
cosocle	C₇×C₃⋊D₁₅	C₂×C₁₃
LCS	G ▷ C₃²×C₅×C₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₇×C₁₃	C₄	semidirect
9. C₇⋊#4380	C₁₃	direct (N × H)
12. C₃²×C₇×C₁₃	AGL(1,𝔽₅)	semidirect
14. C₃²×C₅×C₁₃	Dic₇	semidirect
17. C₅×C₇×C₁₃	#157	semidirect
20. C₃²×C₅×C₇	C₄×C₁₃	semidirect
32. C₃²×C₁₃	C₇⋊AGL(1,𝔽₅)	semidirect
34. C₇×C₁₃	#4380	semidirect
38. C₅×C₁₃	C₇⋊#157	semidirect
39. C₃²×C₇	C₁₃×AGL(1,𝔽₅)	semidirect
41. C₃²×C₅	C₁₃×Dic₇	semidirect
45. C₅×C₇	C₁₃×#157	semidirect
54. C₁₃	C₇⋊#4380	direct (N × H)
56. C₃²	C₁₃×C₇⋊AGL(1,𝔽₅)	semidirect
57. C₇	C₁₃×#4380	semidirect
59. C₅	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
C₇×C₁₃×C₃⋊D₁₅	2
C₁₃×C₇⋊#157	5
C₁₃×#4380	7
C₁₃×C₇⋊AGL(1,𝔽₅)	9
C₇⋊#4380	13

Subgroups — C13×C7⋊#4380 #30655760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₇⋊#4380 #30655760