Subgroups — C₃×C₂₃×C₅⋊(D₁₃⋊C₃) #41002102

Order 26910.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×C₅⋊(D₁₃⋊C₃)	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₂₃×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂₃×D₁₃⋊C₃	—	5	1	no	maximal, Hall
5	C₅×C₂₃×C₁₃⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂₃×D₆₅	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₂₃×C₁₃⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
9	C₃²×D₅×C₂₃	—	13	1	no	maximal, Hall
10	C₃×C₂₃×D₁₃	—	5	1	no	—
11	C₂₃×D₁₃⋊C₃	—	5	3	no	—
12	C₅×C₁₃×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅⋊(D₁₃⋊C₃)	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃²×C₅×C₂₃	—	13	1	no	Hall
15	C₃×C₁₃×C₂₃	C₃×D₅	1	1	yes	characteristic, complemented
16	C₂₃×C₁₃⋊C₃	C₃×D₅	1	3	yes	complemented
17	C₃×D₅×C₂₃	—	13	3	no	—
18	C₃×D₅×C₂₃	—	13	1	no	—
19	C₂₃×D₁₃	—	5	1	no	Hall
20	C₃×C₅×C₁₃⋊C₃	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃²×C₂₃	—	65	1	no	Hall
22	C₃×D₆₅	C₃×C₂₃	1	1	yes	characteristic, complemented
23	C₅⋊(D₁₃⋊C₃)	C₃×C₂₃	1	3	yes	direct product factor
24	C₃×C₅×C₂₃	—	13	3	no	—
25	C₃×C₅×C₂₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₁₃×C₂₃	C₃²×D₅	1	1	yes	characteristic, complemented, Hall
27	C₃×D₁₃⋊C₃	—	5	1	no	Hall
28	D₅×C₂₃	—	13	1	no	Hall
29	C₃²×C₂₃	—	13	1	no	Hall
30	C₃×C₅×C₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
31	C₅×C₁₃⋊C₃	C₂×C₃×C₂₃	1	3	yes	complemented
32	C₂×C₃×C₂₃	—	65	3	no	—
33	C₂×C₃×C₂₃	—	65	1	no	—
34	D₆₅	C₃²×C₂₃	1	1	yes	characteristic, complemented, Hall
35	C₃×C₁₃⋊C₃	D₅×C₂₃	1	1	yes	characteristic, complemented, Hall
36	C₅×C₂₃	C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
37	C₃²×D₅	—	13	1	no	Hall
38	C₃×D₁₃	—	5	1	no	—
39	D₁₃⋊C₃	—	5	3	no	—
40	C₃×C₂₃	—	13	3	no	—
41	C₃×C₂₃	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
42	C₅×C₁₃	C₂×C₃²×C₂₃	1	1	yes	characteristic, complemented, Hall
43	C₂×C₂₃	—	65	1	no	Hall
44	C₃²×C₅	—	13	1	no	Hall
45	C₃×C₁₃	C₃×D₅×C₂₃	1	1	yes	characteristic, complemented
46	C₁₃⋊C₃	C₃×D₅×C₂₃	1	3	yes	complemented
47	C₃×D₅	—	13	3	no	—
48	C₃×D₅	—	13	1	no	—
49	D₁₃	—	5	1	no	Hall
50	C₂₃	C₃×C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃²	—	65	1	no	Hall
52	C₃×C₅	—	13	3	no	—
53	C₃×C₅	C₂₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented
54	C₁₃	C₃²×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
55	D₅	—	13	1	no	Hall
56	C₃²	—	13	1	no	Sylow
57	C₂×C₃	—	65	3	no	—
58	C₂×C₃	—	65	1	no	—
59	C₅	C₃×C₂₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₃	—	13	3	no	—
61	C₃	C₂₃×C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
62	C₂	—	65	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	C₅⋊(D₁₃⋊C₃)
commutator, cosocle, hypocenter	C₅×C₁₃	C₂×C₃²×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₂₃	C₂×C₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₃×C₁₃⋊C₃	C₂	semidirect
2. C₂₃×C₅⋊(D₁₃⋊C₃)	C₃	direct (N × H)
3. C₃×C₂₃×D₆₅	C₃	semidirect
5. C₅×C₂₃×C₁₃⋊C₃	C₂×C₃	semidirect
6. C₃×C₅×C₁₃×C₂₃	C₂×C₃	semidirect
7. C₂₃×D₆₅	C₃²	semidirect
8. C₃×C₂₃×C₁₃⋊C₃	D₅	semidirect
12. C₅×C₁₃×C₂₃	C₂×C₃²	semidirect
13. C₃×C₅⋊(D₁₃⋊C₃)	C₂₃	direct (N × H)
15. C₃×C₁₃×C₂₃	C₃×D₅	semidirect
16. C₂₃×C₁₃⋊C₃	C₃×D₅	semidirect
20. C₃×C₅×C₁₃⋊C₃	C₂×C₂₃	semidirect
22. C₃×D₆₅	C₃×C₂₃	semidirect
23. C₅⋊(D₁₃⋊C₃)	C₃×C₂₃	direct (N × H)
25. C₃×C₅×C₂₃	D₁₃⋊C₃	semidirect
26. C₁₃×C₂₃	C₃²×D₅	semidirect
30. C₃×C₅×C₁₃	C₂×C₃×C₂₃	semidirect
31. C₅×C₁₃⋊C₃	C₂×C₃×C₂₃	semidirect
34. D₆₅	C₃²×C₂₃	semidirect
35. C₃×C₁₃⋊C₃	D₅×C₂₃	semidirect
36. C₅×C₂₃	C₃×D₁₃⋊C₃	semidirect
41. C₃×C₂₃	C₅⋊(D₁₃⋊C₃)	direct (N × H)
42. C₅×C₁₃	C₂×C₃²×C₂₃	semidirect
45. C₃×C₁₃	C₃×D₅×C₂₃	semidirect
46. C₁₃⋊C₃	C₃×D₅×C₂₃	semidirect
50. C₂₃	C₃×C₅⋊(D₁₃⋊C₃)	direct (N × H)
53. C₃×C₅	C₂₃×D₁₃⋊C₃	semidirect
54. C₁₃	C₃²×D₅×C₂₃	semidirect
59. C₅	C₃×C₂₃×D₁₃⋊C₃	semidirect
61. C₃	C₂₃×C₅⋊(D₁₃⋊C₃)	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×C₂₃×C₁₃⋊C₃	2
C₂₃×C₅⋊(D₁₃⋊C₃)	3
C₃×C₂₃×D₆₅	3
C₃×C₂₃×D₁₃⋊C₃	5
C₃²×D₅×C₂₃	13
C₃×C₅⋊(D₁₃⋊C₃)	23

Subgroups — C3×C23×C5⋊(D13⋊C3) #41002102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₃×C₅⋊(D₁₃⋊C₃) #41002102