Subgroups — C₂×C₃⋊D₃×C₁₉×C₂₃ #30628652

Order 15732.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₉×C₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₉×C₂₃	—	3	4	no	maximal
4	C₃²×C₁₉×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₁₉×C₂₃	—	3	8	no	—
6	C₂×C₃×C₁₉×C₂₃	D₃	1	4	yes	complemented
7	C₂²×C₁₉×C₂₃	—	9	1	no	Hall
8	C₃×C₁₉×C₂₃	C₂×D₃	1	4	yes	complemented
9	C₂×C₁₉×C₂₃	—	9	2	no	—
10	C₂×C₁₉×C₂₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃⋊D₃×C₂₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃⋊D₃×C₁₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₉×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃²×C₂₃	C₂×C₁₉	1	1	yes	characteristic, complemented
15	C₃⋊D₃×C₂₃	C₂×C₁₉	1	2	yes	direct product factor
16	C₂×C₃²×C₁₉	C₂×C₂₃	1	1	yes	characteristic, complemented
17	C₃⋊D₃×C₁₉	C₂×C₂₃	1	2	yes	direct product factor
18	C₂×D₃×C₂₃	—	3	4	no	—
19	C₂×D₃×C₁₉	—	3	4	no	—
20	C₃²×C₂₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₁₉	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₂₃	D₃×C₁₉	1	4	yes	complemented
23	D₃×C₂₃	—	3	8	no	—
24	C₂×C₃×C₁₉	D₃×C₂₃	1	4	yes	complemented
25	D₃×C₁₉	—	3	8	no	—
26	C₂²×C₂₃	—	9	1	no	Hall
27	C₂²×C₁₉	—	9	1	no	Hall
28	C₃×C₂₃	C₂×D₃×C₁₉	1	4	yes	complemented
29	C₃×C₁₉	C₂×D₃×C₂₃	1	4	yes	complemented
30	C₂×C₂₃	—	9	2	no	—
31	C₂×C₂₃	C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor
32	C₂×C₁₉	—	9	2	no	—
33	C₂×C₁₉	C₃⋊D₃×C₂₃	1	1	yes	characteristic, direct product factor
34	C₂×C₃⋊D₃	C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
35	C₂₃	C₂×C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₉	C₂×C₃⋊D₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃²	C₂×C₁₉×C₂₃	1	1	yes	characteristic, complemented
38	C₃⋊D₃	C₂×C₁₉×C₂₃	1	2	yes	direct product factor
39	C₂×D₃	—	3	4	no	—
40	C₃²	C₂²×C₁₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃×C₁₉×C₂₃	1	4	yes	complemented
42	D₃	—	3	8	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₁₉×C₂₃	1	4	yes	complemented
45	C₂	—	9	2	no	—
46	C₂	C₃⋊D₃×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₉×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₉×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃×C₁₉×C₂₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₉×C₂₃	C₂	semidirect
4. C₃²×C₁₉×C₂₃	C₂²	semidirect
6. C₂×C₃×C₁₉×C₂₃	D₃	semidirect
8. C₃×C₁₉×C₂₃	C₂×D₃	semidirect
10. C₂×C₁₉×C₂₃	C₃⋊D₃	direct (N × H)
11. C₂×C₃⋊D₃×C₂₃	C₁₉	direct (N × H)
12. C₂×C₃⋊D₃×C₁₉	C₂₃	direct (N × H)
13. C₁₉×C₂₃	C₂×C₃⋊D₃	direct (N × H)
14. C₂×C₃²×C₂₃	C₂×C₁₉	semidirect
15. C₃⋊D₃×C₂₃	C₂×C₁₉	direct (N × H)
16. C₂×C₃²×C₁₉	C₂×C₂₃	semidirect
17. C₃⋊D₃×C₁₉	C₂×C₂₃	direct (N × H)
20. C₃²×C₂₃	C₂²×C₁₉	semidirect
21. C₃²×C₁₉	C₂²×C₂₃	semidirect
22. C₂×C₃×C₂₃	D₃×C₁₉	semidirect
24. C₂×C₃×C₁₉	D₃×C₂₃	semidirect
28. C₃×C₂₃	C₂×D₃×C₁₉	semidirect
29. C₃×C₁₉	C₂×D₃×C₂₃	semidirect
31. C₂×C₂₃	C₃⋊D₃×C₁₉	direct (N × H)
33. C₂×C₁₉	C₃⋊D₃×C₂₃	direct (N × H)
34. C₂×C₃⋊D₃	C₁₉×C₂₃	direct (N × H)
35. C₂₃	C₂×C₃⋊D₃×C₁₉	direct (N × H)
36. C₁₉	C₂×C₃⋊D₃×C₂₃	direct (N × H)
37. C₂×C₃²	C₂×C₁₉×C₂₃	semidirect
38. C₃⋊D₃	C₂×C₁₉×C₂₃	direct (N × H)
40. C₃²	C₂²×C₁₉×C₂₃	semidirect
41. C₂×C₃	D₃×C₁₉×C₂₃	semidirect
44. C₃	C₂×D₃×C₁₉×C₂₃	semidirect
46. C₂	C₃⋊D₃×C₁₉×C₂₃	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⋊D₃×C₁₉×C₂₃	2
C₂×C₃²×C₁₉×C₂₃	2
C₂×D₃×C₁₉×C₂₃	3
C₂×C₃⋊D₃×C₂₃	19
C₂×C₃⋊D₃×C₁₉	23

Subgroups — C2×C3⋊D3×C19×C23 #30628652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₃×C₁₉×C₂₃ #30628652