Subgroups — C₂×C₃⋊D₁₃₁₁ #30628649

Order 15732.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₃₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃₁₁	—	3	4	no	maximal
4	C₃²×C₁₉×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃₁₁	—	3	8	no	—
6	C₂×C₃×C₁₉×C₂₃	D₃	1	4	yes	complemented
7	C₂×D₄₃₇	—	9	1	no	Hall
8	C₃×C₁₉×C₂₃	C₂×D₃	1	4	yes	complemented
9	C₂×C₁₉×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented
10	D₄₃₇	—	9	2	no	—
11	C₂×C₃⋊D₆₉	—	19	1	no	maximal, Hall
12	C₂×C₃⋊D₅₇	—	23	1	no	maximal, Hall
13	C₁₉×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃²×C₂₃	D₁₉	1	1	yes	characteristic, complemented
15	C₃⋊D₆₉	—	19	2	no	—
16	C₂×C₃²×C₁₉	D₂₃	1	1	yes	characteristic, complemented
17	C₃⋊D₅₇	—	23	2	no	—
18	C₂×D₆₉	—	57	4	no	—
19	C₂×D₅₇	—	69	4	no	—
20	C₃²×C₂₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₁₉	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₂₃	D₅₇	1	4	yes	complemented
23	D₆₉	—	57	8	no	—
24	C₂×C₃×C₁₉	D₆₉	1	4	yes	complemented
25	D₅₇	—	69	8	no	—
26	C₂×D₂₃	—	171	1	no	Hall
27	C₂×D₁₉	—	207	1	no	Hall
28	C₃×C₂₃	C₂×D₅₇	1	4	yes	complemented
29	C₃×C₁₉	C₂×D₆₉	1	4	yes	complemented
30	C₂×C₂₃	C₃⋊D₅₇	1	1	yes	characteristic, complemented
31	D₂₃	—	171	2	no	—
32	C₂×C₁₉	C₃⋊D₆₉	1	1	yes	characteristic, complemented
33	D₁₉	—	207	2	no	—
34	C₂×C₃⋊D₃	—	437	1	no	Hall
35	C₂₃	C₂×C₃⋊D₅₇	1	1	yes	characteristic, complemented, Sylow
36	C₁₉	C₂×C₃⋊D₆₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²	D₄₃₇	1	1	yes	characteristic, complemented
38	C₃⋊D₃	—	437	2	no	—
39	C₂×D₃	—	1311	4	no	—
40	C₃²	C₂×D₄₃₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₁₃₁₁	1	4	yes	complemented
42	D₃	—	1311	8	no	—
43	C₂²	—	3933	1	no	Sylow
44	C₃	C₂×D₁₃₁₁	1	4	yes	complemented
45	C₂	—	3933	2	no	—
46	C₂	C₃⋊D₁₃₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₁₃₁₁
commutator, cosocle, hypocenter	C₃²×C₁₉×C₂₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₂₃	C₂
LCS	G ▷ C₃²×C₁₉×C₂₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₃₁₁	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
9. C₂×C₁₉×C₂₃	C₃⋊D₃	semidirect
13. C₁₉×C₂₃	C₂×C₃⋊D₃	semidirect
14. C₂×C₃²×C₂₃	D₁₉	semidirect
16. C₂×C₃²×C₁₉	D₂₃	semidirect
20. C₃²×C₂₃	C₂×D₁₉	semidirect
21. C₃²×C₁₉	C₂×D₂₃	semidirect
22. C₂×C₃×C₂₃	D₅₇	semidirect
24. C₂×C₃×C₁₉	D₆₉	semidirect
28. C₃×C₂₃	C₂×D₅₇	semidirect
29. C₃×C₁₉	C₂×D₆₉	semidirect
30. C₂×C₂₃	C₃⋊D₅₇	semidirect
32. C₂×C₁₉	C₃⋊D₆₉	semidirect
35. C₂₃	C₂×C₃⋊D₅₇	semidirect
36. C₁₉	C₂×C₃⋊D₆₉	semidirect
37. C₂×C₃²	D₄₃₇	semidirect
40. C₃²	C₂×D₄₃₇	semidirect
41. C₂×C₃	D₁₃₁₁	semidirect
44. C₃	C₂×D₁₃₁₁	semidirect
46. C₂	C₃⋊D₁₃₁₁	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⋊D₁₃₁₁	2
C₂×C₃²×C₁₉×C₂₃	2
C₂×D₁₃₁₁	3
C₂×C₃⋊D₆₉	19
C₂×C₃⋊D₅₇	23

Subgroups — C2×C3⋊D1311 #30628649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₁₃₁₁ #30628649