Subgroups — C₃×C₇²×D₅×C₁₃ #34062202

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃×C₇²×C₁₃	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₇²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₇²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇²×C₁₃	C₂	semidirect
2. C₇²×D₅×C₁₃	C₃	direct (N × H)
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
5. C₃×C₇×D₅×C₁₃	C₇	direct (N × H)
6. C₃×C₇²×C₁₃	D₅	direct (N × H)
7. C₃×C₇²×D₅	C₁₃	direct (N × H)
8. C₃×C₅×C₇×C₁₃	C₂×C₇	semidirect
10. C₇×D₅×C₁₃	C₃×C₇	direct (N × H)
11. C₃×C₅×C₇²	C₂×C₁₃	semidirect
12. C₇²×C₁₃	C₃×D₅	direct (N × H)
14. C₇²×D₅	C₃×C₁₃	direct (N × H)
15. C₅×C₇×C₁₃	C₂×C₃×C₇	semidirect
16. C₃×D₅×C₁₃	C₇²	direct (N × H)
18. C₃×C₇×C₁₃	C₇×D₅	direct (N × H)
19. C₅×C₇²	C₂×C₃×C₁₃	semidirect
20. C₃×C₇×D₅	C₇×C₁₃	direct (N × H)
21. C₃×C₅×C₁₃	C₂×C₇²	semidirect
23. C₃×C₇²	D₅×C₁₃	direct (N × H)
24. D₅×C₁₃	C₃×C₇²	direct (N × H)
25. C₃×C₅×C₇	C₂×C₇×C₁₃	semidirect
27. C₇×C₁₃	C₃×C₇×D₅	direct (N × H)
29. C₇×D₅	C₃×C₇×C₁₃	direct (N × H)
30. C₅×C₁₃	C₂×C₃×C₇²	semidirect
31. C₇²	C₃×D₅×C₁₃	direct (N × H)
33. C₃×C₁₃	C₇²×D₅	direct (N × H)
34. C₅×C₇	C₂×C₃×C₇×C₁₃	semidirect
35. C₃×D₅	C₇²×C₁₃	direct (N × H)
37. C₃×C₇	C₇×D₅×C₁₃	direct (N × H)
38. C₃×C₅	C₂×C₇²×C₁₃	semidirect
40. C₁₃	C₃×C₇²×D₅	direct (N × H)
41. D₅	C₃×C₇²×C₁₃	direct (N × H)
42. C₇	C₃×C₇×D₅×C₁₃	direct (N × H)
44. C₅	C₂×C₃×C₇²×C₁₃	semidirect
45. C₃	C₇²×D₅×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇²×C₁₃	2
C₇²×D₅×C₁₃	3
C₂×C₃×C₇²×C₁₃	5
C₃×C₇×D₅×C₁₃	7
C₃×C₇²×D₅	13

Subgroups — C3×C72×D5×C13 #34062202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇²×D₅×C₁₃ #34062202