Subgroups — C₃×D₅×C₂₃⋊D₂₃ #44540739

Order 31740.

520 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃⋊D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅×C₂₃²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅⋊(C₂₃⋊D₂₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₂₃⋊D₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₂₃²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₂₃⋊D₂₃	—	5	1	no	maximal, Hall
7	C₅⋊(C₂₃⋊D₂₃)	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₂₃²	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₂₃⋊D₂₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₂₃⋊D₂₃	—	5	1	no	—
11	C₃×C₂₃⋊D₂₃	D₅	1	1	yes	characteristic, direct product factor
12	C₂×C₃×C₂₃²	—	5	1	no	—
13	C₅×C₂₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₂₃⋊D₂₃	—	5	1	no	Hall
15	C₃×C₂₃²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₃×D₅×D₂₃	—	23	24	no	maximal
17	C₂×C₂₃²	—	5	1	no	—
18	C₂₃⋊D₂₃	—	5	1	no	—
19	C₂₃⋊D₂₃	C₃×D₅	1	1	yes	characteristic, direct product factor
20	C₃×D₁₁₅	—	23	24	no	—
21	C₃×D₅×C₂₃	D₂₃	1	24	yes	complemented
22	C₃×C₅×D₂₃	—	23	24	no	—
23	C₂₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
24	D₅×D₂₃	—	23	24	no	—
25	C₃×C₅×C₂₃	C₂×D₂₃	1	24	yes	complemented
26	C₂×C₃×D₂₃	—	115	24	no	—
27	D₁₁₅	—	23	24	no	—
28	C₅×D₂₃	—	23	24	no	—
29	D₅×C₂₃	C₃×D₂₃	1	24	yes	complemented
30	C₂×C₃×C₂₃	—	5	24	no	—
31	C₃×D₂₃	—	23	24	no	—
32	C₃×D₂₃	—	115	24	no	—
33	C₅×C₂₃	C₂×C₃×D₂₃	1	24	yes	complemented
34	C₂×D₂₃	—	115	24	no	—
35	C₃×C₂₃	D₅×D₂₃	1	24	yes	complemented
36	C₂×C₃×D₅	—	529	1	no	Hall
37	C₂×C₂₃	—	5	24	no	—
38	D₂₃	—	23	24	no	—
39	D₂₃	—	115	24	no	—
40	C₂×C₃×C₅	—	529	1	no	—
41	C₃×D₅	—	529	1	no	—
42	C₃×D₅	C₂₃⋊D₂₃	1	1	yes	characteristic, direct product factor
43	C₂₃	C₃×D₅×D₂₃	1	24	yes	complemented
44	C₂×D₅	—	529	1	no	Hall
45	C₃×C₅	C₂×C₂₃⋊D₂₃	1	1	yes	characteristic, complemented, Hall
46	C₂²×C₃	—	2645	1	no	Hall
47	C₂×C₅	—	529	1	no	—
48	D₅	—	529	1	no	—
49	D₅	C₃×C₂₃⋊D₂₃	1	1	yes	characteristic, direct product factor
50	C₂×C₃	—	5	1	no	—
51	C₂×C₃	—	529	1	no	—
52	C₂×C₃	—	2645	1	no	—
53	C₅	C₂×C₃×C₂₃⋊D₂₃	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	2645	1	no	Sylow
55	C₃	D₅×C₂₃⋊D₂₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	5	1	no	—
57	C₂	—	529	1	no	—
58	C₂	—	2645	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×C₂₃⋊D₂₃
commutator, cosocle, hypocenter	C₅×C₂₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₃²	C₂²
LCS	G ▷ C₅×C₂₃²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₃⋊D₂₃	C₂	semidirect
2. C₃×D₅×C₂₃²	C₂	semidirect
3. C₃×C₅⋊(C₂₃⋊D₂₃)	C₂	semidirect
4. D₅×C₂₃⋊D₂₃	C₃	direct (N × H)
5. C₃×C₅×C₂₃²	C₂²	semidirect
7. C₅⋊(C₂₃⋊D₂₃)	C₂×C₃	semidirect
8. D₅×C₂₃²	C₂×C₃	semidirect
9. C₅×C₂₃⋊D₂₃	C₂×C₃	semidirect
11. C₃×C₂₃⋊D₂₃	D₅	direct (N × H)
13. C₅×C₂₃²	C₂²×C₃	semidirect
15. C₃×C₂₃²	C₂×D₅	semidirect
19. C₂₃⋊D₂₃	C₃×D₅	direct (N × H)
21. C₃×D₅×C₂₃	D₂₃	semidirect
23. C₂₃²	C₂×C₃×D₅	semidirect
25. C₃×C₅×C₂₃	C₂×D₂₃	semidirect
29. D₅×C₂₃	C₃×D₂₃	semidirect
33. C₅×C₂₃	C₂×C₃×D₂₃	semidirect
35. C₃×C₂₃	D₅×D₂₃	semidirect
42. C₃×D₅	C₂₃⋊D₂₃	direct (N × H)
43. C₂₃	C₃×D₅×D₂₃	semidirect
45. C₃×C₅	C₂×C₂₃⋊D₂₃	semidirect
49. D₅	C₃×C₂₃⋊D₂₃	direct (N × H)
53. C₅	C₂×C₃×C₂₃⋊D₂₃	semidirect
55. C₃	D₅×C₂₃⋊D₂₃	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⋊D₂₃	2
C₃×D₅×C₂₃²	2
C₃×C₅⋊(C₂₃⋊D₂₃)	2
D₅×C₂₃⋊D₂₃	3
C₂×C₃×C₂₃⋊D₂₃	5
C₃×D₅×D₂₃	23

Subgroups — C3×D5×C23⋊D23 #44540739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×C₂₃⋊D₂₃ #44540739