Subgroups — C₁₃⋊C₃×C₅⋊(C₇⋊D₇) #34062173

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₅⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₇⋊D₇	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃⋊C₃×D₃₅	—	7	8	no	maximal
6	C₇²×C₁₃⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅⋊(C₇⋊D₇)	—	13	1	no	maximal, Hall
8	C₅×C₇×C₁₃⋊C₃	D₇	1	8	yes	complemented
9	C₁₃×C₇⋊D₇	—	5	1	no	Hall
10	C₁₃×D₃₅	—	7	8	no	—
11	C₃×C₅×C₇²	—	13	1	no	Hall
12	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
13	D₇×C₁₃⋊C₃	—	35	8	no	—
14	C₅⋊(C₇⋊D₇)	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₇×C₁₃	C₃×D₇	1	8	yes	complemented
16	D₅×C₁₃⋊C₃	—	49	1	no	Hall
17	C₃×C₇⋊D₇	—	65	1	no	Hall
18	C₇×C₁₃⋊C₃	D₃₅	1	8	yes	complemented
19	C₅×C₇²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₃×D₃₅	—	91	8	no	—
21	C₅×C₁₃⋊C₃	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
22	C₁₃×D₇	—	35	8	no	—
23	C₃×C₇²	—	13	1	no	Hall
24	D₅×C₁₃	—	49	1	no	Hall
25	C₃×C₅×C₇	—	13	8	no	—
26	C₇⋊D₇	—	5	1	no	Hall
27	C₇×C₁₃	C₃×D₃₅	1	8	yes	complemented
28	C₂×C₁₃⋊C₃	—	245	1	no	Hall
29	D₃₅	—	7	8	no	—
30	C₅×C₁₃	C₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
31	C₇²	D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₇	—	455	8	no	—
33	C₁₃⋊C₃	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Hall
34	C₅×C₇	D₇×C₁₃⋊C₃	1	8	yes	complemented
35	C₃×D₅	—	637	1	no	Hall
36	C₂×C₁₃	—	245	1	no	Hall
37	C₃×C₇	—	13	8	no	—
38	C₃×C₅	—	13	1	no	Hall
39	D₇	—	35	8	no	—
40	C₁₃	C₃×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	49	1	no	Hall
42	C₇	C₁₃⋊C₃×D₃₅	1	8	yes	complemented
43	C₂×C₃	—	3185	1	no	Hall
44	C₅	C₁₃⋊C₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	245	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₇²×C₁₃⋊C₃	C₂	semidirect
2. C₁₃×C₅⋊(C₇⋊D₇)	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
6. C₇²×C₁₃⋊C₃	D₅	semidirect
8. C₅×C₇×C₁₃⋊C₃	D₇	semidirect
12. C₇²×C₁₃	C₃×D₅	semidirect
14. C₅⋊(C₇⋊D₇)	C₁₃⋊C₃	direct (N × H)
15. C₅×C₇×C₁₃	C₃×D₇	semidirect
18. C₇×C₁₃⋊C₃	D₃₅	semidirect
19. C₅×C₇²	C₂×C₁₃⋊C₃	semidirect
21. C₅×C₁₃⋊C₃	C₇⋊D₇	semidirect
27. C₇×C₁₃	C₃×D₃₅	semidirect
30. C₅×C₁₃	C₃×C₇⋊D₇	semidirect
31. C₇²	D₅×C₁₃⋊C₃	semidirect
33. C₁₃⋊C₃	C₅⋊(C₇⋊D₇)	direct (N × H)
34. C₅×C₇	D₇×C₁₃⋊C₃	semidirect
40. C₁₃	C₃×C₅⋊(C₇⋊D₇)	semidirect
42. C₇	C₁₃⋊C₃×D₃₅	semidirect
44. C₅	C₁₃⋊C₃×C₇⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇²×C₁₃⋊C₃	2
C₁₃×C₅⋊(C₇⋊D₇)	3
C₁₃⋊C₃×C₇⋊D₇	5
C₁₃⋊C₃×D₃₅	7
C₃×C₅⋊(C₇⋊D₇)	13

Subgroups — C13⋊C3×C5⋊(C7⋊D7) #34062173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×C₅⋊(C₇⋊D₇) #34062173