Subgroups — C₂₃×C₃⋊D₁₉₅ #41002136

Order 26910.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×D₁₉₅	—	3	4	no	maximal
3	C₂₃×C₃⋊D₃₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₂₃	D₃	1	4	yes	complemented
5	C₂₃×D₆₅	—	9	1	no	Hall
6	C₃²×C₁₃×C₂₃	D₅	1	1	yes	characteristic, complemented, Hall
7	C₂₃×C₃⋊D₁₅	—	13	1	no	maximal, Hall
8	C₂₃×D₃₉	—	15	4	no	—
9	C₅×C₁₃×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃⋊D₁₉₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₅×C₂₃	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₂₃	D₁₅	1	4	yes	complemented
13	C₂₃×D₁₅	—	39	4	no	—
14	C₂₃×D₁₃	—	45	1	no	Hall
15	C₃²×C₅×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
16	C₃⋊D₃×C₂₃	—	65	1	no	Hall
17	D₁₉₅	—	3	4	no	—
18	C₃×C₅×C₂₃	D₃₉	1	4	yes	complemented
19	C₁₃×C₂₃	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
20	C₃⋊D₃₉	—	5	1	no	Hall
21	D₅×C₂₃	—	117	1	no	Hall
22	C₃²×C₂₃	D₆₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	D₃×C₂₃	1	4	yes	complemented
24	D₃×C₂₃	—	195	4	no	—
25	D₆₅	—	9	1	no	Hall
26	C₃²×C₁₃	D₅×C₂₃	1	1	yes	characteristic, complemented, Hall
27	C₅×C₂₃	C₃⋊D₃₉	1	1	yes	characteristic, complemented, Hall
28	C₃⋊D₁₅	—	13	1	no	Hall
29	D₃₉	—	15	4	no	—
30	C₃×C₂₃	D₁₉₅	1	4	yes	complemented
31	C₅×C₁₃	C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented, Hall
32	C₂×C₂₃	—	585	1	no	Hall
33	C₃²×C₅	C₂₃×D₁₃	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₃	C₂₃×D₁₅	1	4	yes	complemented
35	D₁₅	—	39	4	no	—
36	D₁₃	—	45	1	no	Hall
37	C₂₃	C₃⋊D₁₉₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₃⋊D₃	—	65	1	no	Hall
39	C₃×C₅	C₂₃×D₃₉	1	4	yes	complemented
40	C₁₃	C₂₃×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	117	1	no	Hall
42	C₃²	C₂₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	195	4	no	—
44	C₅	C₂₃×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₂₃×D₁₉₅	1	4	yes	complemented
46	C₂	—	585	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	C₃⋊D₁₉₅
commutator, cosocle, hypocenter	C₃²×C₅×C₁₃	C₂×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃×C₂₃	C₂
LCS	G ▷ C₃²×C₅×C₁₃
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃×C₂₃	C₂	semidirect
4. C₃×C₅×C₁₃×C₂₃	D₃	semidirect
6. C₃²×C₁₃×C₂₃	D₅	semidirect
9. C₅×C₁₃×C₂₃	C₃⋊D₃	semidirect
10. C₃⋊D₁₉₅	C₂₃	direct (N × H)
11. C₃²×C₅×C₂₃	D₁₃	semidirect
12. C₃×C₁₃×C₂₃	D₁₅	semidirect
15. C₃²×C₅×C₁₃	C₂×C₂₃	semidirect
18. C₃×C₅×C₂₃	D₃₉	semidirect
19. C₁₃×C₂₃	C₃⋊D₁₅	semidirect
22. C₃²×C₂₃	D₆₅	semidirect
23. C₃×C₅×C₁₃	D₃×C₂₃	semidirect
26. C₃²×C₁₃	D₅×C₂₃	semidirect
27. C₅×C₂₃	C₃⋊D₃₉	semidirect
30. C₃×C₂₃	D₁₉₅	semidirect
31. C₅×C₁₃	C₃⋊D₃×C₂₃	semidirect
33. C₃²×C₅	C₂₃×D₁₃	semidirect
34. C₃×C₁₃	C₂₃×D₁₅	semidirect
37. C₂₃	C₃⋊D₁₉₅	direct (N × H)
39. C₃×C₅	C₂₃×D₃₉	semidirect
40. C₁₃	C₂₃×C₃⋊D₁₅	semidirect
42. C₃²	C₂₃×D₆₅	semidirect
44. C₅	C₂₃×C₃⋊D₃₉	semidirect
45. C₃	C₂₃×D₁₉₅	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×C₂₃	2
C₂₃×D₁₉₅	3
C₂₃×C₃⋊D₃₉	5
C₂₃×C₃⋊D₁₅	13
C₃⋊D₁₉₅	23

Subgroups — C23×C3⋊D195 #41002136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×C₃⋊D₁₉₅ #41002136