Subgroups — C₅×D₂₃×C₁₃⋊C₉ #41002091

Order 26910.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₃×D₂₃	C₃	1	1	yes	maximal, characteristic
3	D₂₃×C₁₃⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₃×D₂₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₂₃×C₁₃⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₉×D₂₃	—	13	1	no	maximal, Hall
8	C₃×C₁₃×D₂₃	C₃×C₅	1	1	yes	characteristic
9	C₅×C₁₃×C₂₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₁₃⋊C₉	—	23	1	no	maximal, Hall
11	C₅×C₉×C₂₃	—	13	1	no	Hall
12	C₃×C₁₃×C₂₃	C₂×C₃×C₅	1	1	yes	characteristic
13	C₃×C₅×D₂₃	C₁₃⋊C₃	1	1	yes	characteristic
14	C₁₃×D₂₃	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₃⋊C₉	D₂₃	1	1	yes	characteristic, direct product factor, Hall
16	C₉×D₂₃	—	13	1	no	Hall
17	C₂×C₃×C₅×C₁₃	—	23	1	no	—
18	C₃×C₅×C₂₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
19	C₁₃×C₂₃	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₃⋊C₉	—	23	1	no	Hall
21	C₅×D₂₃	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
22	C₉×C₂₃	—	13	1	no	Hall
23	C₃×C₅×C₁₃	C₃×D₂₃	1	1	yes	characteristic
24	C₃×D₂₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic
25	C₂×C₅×C₁₃	—	23	1	no	Hall
26	C₁₃⋊C₉	C₅×D₂₃	1	1	yes	characteristic, direct product factor, Hall
27	C₅×C₂₃	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×C₉	—	299	1	no	Hall
29	C₂×C₃×C₁₃	—	23	1	no	—
30	C₃×C₂₃	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic
31	C₅×C₁₃	C₉×D₂₃	1	1	yes	characteristic, complemented, Hall
32	D₂₃	C₅×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
33	C₅×C₉	—	13	1	no	Hall
34	C₃×C₁₃	C₃×C₅×D₂₃	1	1	yes	characteristic
35	C₂×C₃×C₅	—	23	1	no	—
36	C₂×C₁₃	—	23	1	no	Hall
37	C₂₃	C₂×C₅×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₉	—	299	1	no	Hall
39	C₃×C₅	C₁₃⋊C₃×D₂₃	1	1	yes	characteristic
40	C₁₃	C₅×C₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	23	1	no	Hall
42	C₉	—	13	1	no	Sylow
43	C₂×C₃	—	23	1	no	—
44	C₅	D₂₃×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×C₁₃⋊C₃×D₂₃	1	1	yes	characteristic
46	C₂	—	23	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	C₁₃⋊C₃×D₂₃
commutator, hypocenter	C₁₃×C₂₃	C₂×C₅×C₉
Frattini	C₃	C₅×C₁₃⋊C₃×D₂₃
Fitting, socle	C₃×C₅×C₁₃×C₂₃	C₂×C₃
prime radical	C₃×C₅×C₁₃×D₂₃	C₃
cosocle	C₃×C₁₃×C₂₃	C₂×C₃×C₅
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₃×C₁₃⋊C₉	C₂	semidirect
3. D₂₃×C₁₃⋊C₉	C₅	direct (N × H)
5. C₅×C₁₃×D₂₃	C₉	semidirect
6. C₂₃×C₁₃⋊C₉	C₂×C₅	semidirect
9. C₅×C₁₃×C₂₃	C₂×C₉	semidirect
14. C₁₃×D₂₃	C₅×C₉	semidirect
15. C₅×C₁₃⋊C₉	D₂₃	direct (N × H)
19. C₁₃×C₂₃	C₂×C₅×C₉	semidirect
21. C₅×D₂₃	C₁₃⋊C₉	direct (N × H)
26. C₁₃⋊C₉	C₅×D₂₃	direct (N × H)
27. C₅×C₂₃	C₂×C₁₃⋊C₉	semidirect
31. C₅×C₁₃	C₉×D₂₃	semidirect
32. D₂₃	C₅×C₁₃⋊C₉	direct (N × H)
37. C₂₃	C₂×C₅×C₁₃⋊C₉	semidirect
40. C₁₃	C₅×C₉×D₂₃	semidirect
44. C₅	D₂₃×C₁₃⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₂₃×C₁₃⋊C₉	2
C₃×C₅×C₁₃×D₂₃	3
D₂₃×C₁₃⋊C₉	5
C₅×C₉×D₂₃	13
C₂×C₅×C₁₃⋊C₉	23

Subgroups — C5×D23×C13⋊C9 #41002091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₂₃×C₁₃⋊C₉ #41002091