Subgroups — C₂×C₁₃×C₃⋊D₁₂₃ #34063005

Order 19188.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₁₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₁₂₃	—	3	4	no	maximal
4	C₃²×C₁₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₁₂₃	—	3	8	no	—
6	C₂×C₃×C₁₃×C₄₁	D₃	1	4	yes	complemented
7	C₂×C₁₃×D₄₁	—	9	1	no	Hall
8	C₃×C₁₃×C₄₁	C₂×D₃	1	4	yes	complemented
9	C₂×C₃⋊D₁₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₄₁	C₃⋊D₃	1	1	yes	characteristic, complemented
11	C₁₃×D₄₁	—	9	2	no	—
12	C₂×C₃²×C₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented
13	C₃⋊D₁₂₃	C₂×C₁₃	1	2	yes	direct product factor
14	C₁₃×C₄₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₂₃	—	3	4	no	—
16	C₂×C₁₃×C₃⋊D₃	—	41	1	no	maximal, Hall
17	C₃²×C₄₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₄₁	D₃×C₁₃	1	4	yes	complemented
19	D₁₂₃	—	3	8	no	—
20	C₂×C₃²×C₁₃	D₄₁	1	1	yes	characteristic, complemented
21	C₁₃×C₃⋊D₃	—	41	2	no	—
22	C₂×D₄₁	—	9	1	no	Hall
23	C₂×D₃×C₁₃	—	123	4	no	—
24	C₃×C₄₁	C₂×D₃×C₁₃	1	4	yes	complemented
25	C₃²×C₁₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₄₁	C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented
27	D₄₁	—	9	2	no	—
28	C₂×C₃×C₁₃	D₁₂₃	1	4	yes	complemented
29	D₃×C₁₃	—	123	8	no	—
30	C₂²×C₁₃	—	369	1	no	Hall
31	C₄₁	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
32	C₃×C₁₃	C₂×D₁₂₃	1	4	yes	complemented
33	C₂×C₃⋊D₃	—	41	1	no	Hall
34	C₂×C₁₃	—	369	2	no	—
35	C₂×C₁₃	C₃⋊D₁₂₃	1	1	yes	characteristic, direct product factor
36	C₂×C₃²	C₁₃×D₄₁	1	1	yes	characteristic, complemented
37	C₃⋊D₃	—	41	2	no	—
38	C₁₃	C₂×C₃⋊D₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₃	—	123	4	no	—
40	C₃²	C₂×C₁₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₁₃×D₁₂₃	1	4	yes	complemented
42	D₃	—	123	8	no	—
43	C₂²	—	369	1	no	Sylow
44	C₃	C₂×C₁₃×D₁₂₃	1	4	yes	complemented
45	C₂	—	369	2	no	—
46	C₂	C₁₃×C₃⋊D₁₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊D₁₂₃
commutator, cosocle, hypocenter	C₃²×C₄₁	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₄₁	C₂
LCS	G ▷ C₃²×C₄₁
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₁₂₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₄₁	C₂	semidirect
4. C₃²×C₁₃×C₄₁	C₂²	semidirect
6. C₂×C₃×C₁₃×C₄₁	D₃	semidirect
8. C₃×C₁₃×C₄₁	C₂×D₃	semidirect
9. C₂×C₃⋊D₁₂₃	C₁₃	direct (N × H)
10. C₂×C₁₃×C₄₁	C₃⋊D₃	semidirect
12. C₂×C₃²×C₄₁	C₂×C₁₃	semidirect
13. C₃⋊D₁₂₃	C₂×C₁₃	direct (N × H)
14. C₁₃×C₄₁	C₂×C₃⋊D₃	semidirect
17. C₃²×C₄₁	C₂²×C₁₃	semidirect
18. C₂×C₃×C₄₁	D₃×C₁₃	semidirect
20. C₂×C₃²×C₁₃	D₄₁	semidirect
24. C₃×C₄₁	C₂×D₃×C₁₃	semidirect
25. C₃²×C₁₃	C₂×D₄₁	semidirect
26. C₂×C₄₁	C₁₃×C₃⋊D₃	semidirect
28. C₂×C₃×C₁₃	D₁₂₃	semidirect
31. C₄₁	C₂×C₁₃×C₃⋊D₃	semidirect
32. C₃×C₁₃	C₂×D₁₂₃	semidirect
35. C₂×C₁₃	C₃⋊D₁₂₃	direct (N × H)
36. C₂×C₃²	C₁₃×D₄₁	semidirect
38. C₁₃	C₂×C₃⋊D₁₂₃	direct (N × H)
40. C₃²	C₂×C₁₃×D₄₁	semidirect
41. C₂×C₃	C₁₃×D₁₂₃	semidirect
44. C₃	C₂×C₁₃×D₁₂₃	semidirect
46. C₂	C₁₃×C₃⋊D₁₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₃⋊D₁₂₃	2
C₂×C₃²×C₁₃×C₄₁	2
C₂×C₁₃×D₁₂₃	3
C₂×C₃⋊D₁₂₃	13
C₂×C₁₃×C₃⋊D₃	41

Subgroups — C2×C13×C3⋊D123 #34063005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₃⋊D₁₂₃ #34063005