Subgroups — C₃²×C₅×D₁₁₅ #23780392

Order 10350.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₁₁₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₁₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₃²×C₅×D₂₃	—	5	1	no	maximal
5	C₃×C₅²×C₂₃	C₂×C₃	1	4	yes	complemented
6	C₅×D₁₁₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₂₃	—	2	2	no	—
8	C₃²×C₅×C₂₃	D₅	1	1	yes	characteristic, complemented
9	C₃²×C₅×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×D₁₁₅	C₃×C₅	1	4	yes	direct product factor
11	C₃×C₅×D₂₃	—	5	4	no	—
12	C₅²×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₅×D₅	—	23	1	no	maximal, Hall
14	C₃²×D₂₃	—	5	1	no	Hall
15	C₃×C₅×C₂₃	—	2	8	no	—
16	C₃×C₅×C₂₃	C₃×D₅	1	4	yes	complemented
17	C₃×C₅×C₂₃	C₂×C₃×C₅	1	4	yes	complemented
18	D₁₁₅	C₃²×C₅	1	1	yes	characteristic, direct product factor
19	C₅×D₂₃	—	5	1	no	—
20	C₃²×C₅²	D₂₃	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₂₃	C₅×D₅	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅×D₅	—	23	4	no	—
23	C₃×D₂₃	—	5	4	no	—
24	C₅×C₂₃	—	2	2	no	—
25	C₅×C₂₃	C₃²×D₅	1	1	yes	characteristic, complemented
26	C₅×C₂₃	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
27	C₂×C₃²×C₅	—	115	1	no	—
28	C₃²×D₅	—	23	1	no	—
29	C₃×C₅²	C₃×D₂₃	1	4	yes	complemented
30	C₃×C₂₃	C₃×C₅×D₅	1	4	yes	complemented
31	C₅×D₅	—	23	1	no	Hall
32	D₂₃	—	5	1	no	Hall
33	C₃²×C₅	—	2	2	no	—
34	C₃²×C₅	C₅×D₂₃	1	1	yes	characteristic, complemented
35	C₃²×C₅	D₁₁₅	1	1	yes	characteristic, direct product factor
36	C₂×C₃×C₅	—	115	4	no	—
37	C₃×D₅	—	23	4	no	—
38	C₅²	C₃²×D₂₃	1	1	yes	characteristic, complemented, Sylow
39	C₂₃	C₃²×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃²	—	115	1	no	Hall
41	C₃×C₅	—	2	8	no	—
42	C₃×C₅	C₃×C₅×D₂₃	1	4	yes	complemented
43	C₃×C₅	C₃×D₁₁₅	1	4	yes	direct product factor
44	C₂×C₅	—	115	1	no	—
45	D₅	—	23	1	no	—
46	C₃²	C₅×D₁₁₅	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	115	4	no	—
48	C₅	—	2	2	no	—
49	C₅	C₃²×C₅×D₂₃	1	1	yes	characteristic, complemented
50	C₅	C₃²×D₁₁₅	1	1	yes	characteristic, direct product factor
51	C₃	C₃×C₅×D₁₁₅	1	4	yes	direct product factor
52	C₂	—	115	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₅	D₁₁₅
commutator, cosocle, hypocenter	C₅×C₂₃	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₃	C₂
LCS	G ▷ C₅×C₂₃
UCS	C₁ ◁ C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₂₃	C₂	semidirect
2. C₃×C₅×D₁₁₅	C₃	direct (N × H)
3. C₃²×D₁₁₅	C₅	direct (N × H)
5. C₃×C₅²×C₂₃	C₂×C₃	semidirect
6. C₅×D₁₁₅	C₃²	direct (N × H)
8. C₃²×C₅×C₂₃	D₅	semidirect
9. C₃²×C₅×C₂₃	C₂×C₅	semidirect
10. C₃×D₁₁₅	C₃×C₅	direct (N × H)
12. C₅²×C₂₃	C₂×C₃²	semidirect
16. C₃×C₅×C₂₃	C₃×D₅	semidirect
17. C₃×C₅×C₂₃	C₂×C₃×C₅	semidirect
18. D₁₁₅	C₃²×C₅	direct (N × H)
20. C₃²×C₅²	D₂₃	semidirect
21. C₃²×C₂₃	C₅×D₅	semidirect
25. C₅×C₂₃	C₃²×D₅	semidirect
26. C₅×C₂₃	C₂×C₃²×C₅	semidirect
29. C₃×C₅²	C₃×D₂₃	semidirect
30. C₃×C₂₃	C₃×C₅×D₅	semidirect
34. C₃²×C₅	C₅×D₂₃	semidirect
35. C₃²×C₅	D₁₁₅	direct (N × H)
38. C₅²	C₃²×D₂₃	semidirect
39. C₂₃	C₃²×C₅×D₅	semidirect
42. C₃×C₅	C₃×C₅×D₂₃	semidirect
43. C₃×C₅	C₃×D₁₁₅	direct (N × H)
46. C₃²	C₅×D₁₁₅	direct (N × H)
49. C₅	C₃²×C₅×D₂₃	semidirect
50. C₅	C₃²×D₁₁₅	direct (N × H)
51. C₃	C₃×C₅×D₁₁₅	direct (N × H)

Subgroups — C32×C5×D115 #23780392

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₅×D₁₁₅ #23780392