Subgroups — C₁₃×C₁₉×C₃⋊D₁₅ #36372736

Order 22230.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₁₉×D₁₅	—	3	4	no	maximal
3	C₁₃×C₃⋊D₃×C₁₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₁₉	D₃	1	4	yes	complemented
5	D₅×C₁₃×C₁₉	—	9	1	no	Hall
6	C₃²×C₁₃×C₁₉	D₅	1	1	yes	characteristic, complemented, Hall
7	C₁₉×C₃⋊D₁₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	D₃×C₁₃×C₁₉	—	15	4	no	—
9	C₅×C₁₃×C₁₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₁₃×C₃⋊D₁₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₅×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₁₉	D₁₅	1	4	yes	complemented
13	C₃²×C₅×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₁₉×D₁₅	—	3	4	no	—
15	C₂×C₁₃×C₁₉	—	45	1	no	Hall
16	C₁₃×D₁₅	—	3	4	no	—
17	C₃⋊D₃×C₁₉	—	5	1	no	Hall
18	C₃×C₅×C₁₉	D₃×C₁₃	1	4	yes	complemented
19	C₁₃×C₁₉	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Hall
20	C₁₃×C₃⋊D₃	—	5	1	no	Hall
21	C₃×C₅×C₁₃	D₃×C₁₉	1	4	yes	complemented
22	D₅×C₁₉	—	9	1	no	Hall
23	C₃²×C₁₉	D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
24	D₅×C₁₃	—	9	1	no	Hall
25	C₃²×C₁₃	D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
26	D₃×C₁₉	—	15	4	no	—
27	C₅×C₁₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
28	C₃⋊D₁₅	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	D₃×C₁₃	—	15	4	no	—
30	C₅×C₁₃	C₃⋊D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₉	C₁₃×D₁₅	1	4	yes	complemented
32	C₃²×C₅	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Hall
33	C₃×C₁₃	C₁₉×D₁₅	1	4	yes	complemented
34	C₂×C₁₉	—	45	1	no	Hall
35	D₁₅	—	3	4	no	—
36	C₂×C₁₃	—	45	1	no	Hall
37	C₁₉	C₁₃×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₃⋊D₃	—	5	1	no	Hall
39	C₃×C₅	D₃×C₁₃×C₁₉	1	4	yes	complemented
40	C₁₃	C₁₉×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
41	D₅	—	9	1	no	Hall
42	C₃²	D₅×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	15	4	no	—
44	C₅	C₁₃×C₃⋊D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₁₃×C₁₉×D₁₅	1	4	yes	complemented
46	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃×C₁₉	C₂	semidirect
4. C₃×C₅×C₁₃×C₁₉	D₃	semidirect
6. C₃²×C₁₃×C₁₉	D₅	semidirect
7. C₁₉×C₃⋊D₁₅	C₁₃	direct (N × H)
9. C₅×C₁₃×C₁₉	C₃⋊D₃	semidirect
10. C₁₃×C₃⋊D₁₅	C₁₉	direct (N × H)
11. C₃²×C₅×C₁₉	C₂×C₁₃	semidirect
12. C₃×C₁₃×C₁₉	D₁₅	semidirect
13. C₃²×C₅×C₁₃	C₂×C₁₉	semidirect
18. C₃×C₅×C₁₉	D₃×C₁₃	semidirect
19. C₁₃×C₁₉	C₃⋊D₁₅	direct (N × H)
21. C₃×C₅×C₁₃	D₃×C₁₉	semidirect
23. C₃²×C₁₉	D₅×C₁₃	semidirect
25. C₃²×C₁₃	D₅×C₁₉	semidirect
27. C₅×C₁₉	C₁₃×C₃⋊D₃	semidirect
28. C₃⋊D₁₅	C₁₃×C₁₉	direct (N × H)
30. C₅×C₁₃	C₃⋊D₃×C₁₉	semidirect
31. C₃×C₁₉	C₁₃×D₁₅	semidirect
32. C₃²×C₅	C₂×C₁₃×C₁₉	semidirect
33. C₃×C₁₃	C₁₉×D₁₅	semidirect
37. C₁₉	C₁₃×C₃⋊D₁₅	direct (N × H)
39. C₃×C₅	D₃×C₁₃×C₁₉	semidirect
40. C₁₃	C₁₉×C₃⋊D₁₅	direct (N × H)
42. C₃²	D₅×C₁₃×C₁₉	semidirect
44. C₅	C₁₃×C₃⋊D₃×C₁₉	semidirect
45. C₃	C₁₃×C₁₉×D₁₅	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₃×C₁₉	2
C₁₃×C₁₉×D₁₅	3
C₁₃×C₃⋊D₃×C₁₉	5
C₁₉×C₃⋊D₁₅	13
C₁₃×C₃⋊D₁₅	19

Subgroups — C13×C19×C3⋊D15 #36372736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₁₉×C₃⋊D₁₅ #36372736