Subgroups — C₂×C₃×D₅×C₂₃² #44540769

Order 31740.

520 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₃²	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃×C₂₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₂₃²	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₂₃²

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×C₂₃²	C₂	direct (N × H)
2. C₂×C₃×C₅×C₂₃²	C₂	semidirect
3. C₂×D₅×C₂₃²	C₃	direct (N × H)
4. C₃×C₅×C₂₃²	C₂²	semidirect
6. D₅×C₂₃²	C₂×C₃	direct (N × H)
7. C₂×C₅×C₂₃²	C₂×C₃	semidirect
9. C₂×C₃×C₂₃²	D₅	direct (N × H)
10. C₅×C₂₃²	C₂²×C₃	semidirect
12. C₃×C₂₃²	C₂×D₅	direct (N × H)
13. C₂×C₃×D₅×C₂₃	C₂₃	direct (N × H)
15. C₂×C₂₃²	C₃×D₅	direct (N × H)
16. C₂×C₃×C₅×C₂₃	C₂×C₂₃	semidirect
17. C₃×D₅×C₂₃	C₂×C₂₃	direct (N × H)
18. C₂₃²	C₂×C₃×D₅	direct (N × H)
19. C₂×D₅×C₂₃	C₃×C₂₃	direct (N × H)
20. C₃×C₅×C₂₃	C₂²×C₂₃	semidirect
22. C₂×C₅×C₂₃	C₂×C₃×C₂₃	semidirect
23. D₅×C₂₃	C₂×C₃×C₂₃	direct (N × H)
25. C₂×C₃×C₂₃	D₅×C₂₃	direct (N × H)
26. C₅×C₂₃	C₂²×C₃×C₂₃	semidirect
28. C₃×C₂₃	C₂×D₅×C₂₃	direct (N × H)
29. C₂×C₃×D₅	C₂₃²	direct (N × H)
31. C₂×C₂₃	C₃×D₅×C₂₃	direct (N × H)
32. C₂×C₃×C₅	C₂×C₂₃²	semidirect
33. C₃×D₅	C₂×C₂₃²	direct (N × H)
34. C₂₃	C₂×C₃×D₅×C₂₃	direct (N × H)
35. C₂×D₅	C₃×C₂₃²	direct (N × H)
36. C₃×C₅	C₂²×C₂₃²	semidirect
38. C₂×C₅	C₂×C₃×C₂₃²	semidirect
39. D₅	C₂×C₃×C₂₃²	direct (N × H)
41. C₂×C₃	D₅×C₂₃²	direct (N × H)
42. C₅	C₂²×C₃×C₂₃²	semidirect
44. C₃	C₂×D₅×C₂₃²	direct (N × H)
46. C₂	C₃×D₅×C₂₃²	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×D₅×C₂₃²	2
C₂×C₃×C₅×C₂₃²	2
C₂×D₅×C₂₃²	3
C₂²×C₃×C₂₃²	5
C₂×C₃×D₅×C₂₃	23

Subgroups — C2×C3×D5×C232 #44540769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₅×C₂₃² #44540769