Subgroups — C₃⋊D₅₁₁₅ #44501889

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₁₁₅	—	3	4	no	maximal
3	C₃⋊D₁₀₂₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₃₁	D₃	1	4	yes	complemented
5	D₁₇₀₅	—	9	1	no	Hall
6	C₃²×C₁₁×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃⋊D₄₆₅	—	11	1	no	maximal, Hall
8	D₁₀₂₃	—	15	4	no	—
9	C₅×C₁₁×C₃₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₅×C₃₁	D₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁×C₃₁	D₁₅	1	4	yes	complemented
12	C₃⋊D₁₆₅	—	31	1	no	maximal, Hall
13	D₄₆₅	—	33	4	no	—
14	D₃₄₁	—	45	1	no	Hall
15	C₃⋊D₉₃	—	55	1	no	Hall
16	C₃²×C₅×C₁₁	D₃₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₃₁	D₃₃	1	4	yes	complemented
18	C₁₁×C₃₁	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
19	D₁₆₅	—	93	4	no	—
20	D₁₅₅	—	99	1	no	Hall
21	C₃²×C₃₁	D₅₅	1	1	yes	characteristic, complemented, Hall
22	C₃⋊D₃₃	—	155	1	no	Hall
23	D₉₃	—	165	4	no	—
24	C₃×C₅×C₁₁	D₉₃	1	4	yes	complemented
25	C₅×C₃₁	C₃⋊D₃₃	1	1	yes	characteristic, complemented, Hall
26	D₅₅	—	279	1	no	Hall
27	C₃²×C₁₁	D₁₅₅	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	D₁₆₅	1	4	yes	complemented
29	C₃⋊D₁₅	—	341	1	no	Hall
30	D₃₃	—	465	4	no	—
31	D₃₁	—	495	1	no	Hall
32	C₅×C₁₁	C₃⋊D₉₃	1	1	yes	characteristic, complemented, Hall
33	C₃²×C₅	D₃₄₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₁	D₄₆₅	1	4	yes	complemented
35	C₃₁	C₃⋊D₁₆₅	1	1	yes	characteristic, complemented, Sylow
36	D₁₅	—	1023	4	no	—
37	D₁₁	—	1395	1	no	Hall
38	C₃⋊D₃	—	1705	1	no	Hall
39	C₃×C₅	D₁₀₂₃	1	4	yes	complemented
40	C₁₁	C₃⋊D₄₆₅	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	3069	1	no	Hall
42	C₃²	D₁₇₀₅	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	5115	4	no	—
44	C₅	C₃⋊D₁₀₂₃	1	1	yes	characteristic, complemented, Sylow
45	C₃	D₅₁₁₅	1	4	yes	complemented
46	C₂	—	15345	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₁₁×C₃₁	C₂
LCS	G ▷ C₃²×C₅×C₁₁×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₁×C₃₁	C₂	semidirect
4. C₃×C₅×C₁₁×C₃₁	D₃	semidirect
6. C₃²×C₁₁×C₃₁	D₅	semidirect
9. C₅×C₁₁×C₃₁	C₃⋊D₃	semidirect
10. C₃²×C₅×C₃₁	D₁₁	semidirect
11. C₃×C₁₁×C₃₁	D₁₅	semidirect
16. C₃²×C₅×C₁₁	D₃₁	semidirect
17. C₃×C₅×C₃₁	D₃₃	semidirect
18. C₁₁×C₃₁	C₃⋊D₁₅	semidirect
21. C₃²×C₃₁	D₅₅	semidirect
24. C₃×C₅×C₁₁	D₉₃	semidirect
25. C₅×C₃₁	C₃⋊D₃₃	semidirect
27. C₃²×C₁₁	D₁₅₅	semidirect
28. C₃×C₃₁	D₁₆₅	semidirect
32. C₅×C₁₁	C₃⋊D₉₃	semidirect
33. C₃²×C₅	D₃₄₁	semidirect
34. C₃×C₁₁	D₄₆₅	semidirect
35. C₃₁	C₃⋊D₁₆₅	semidirect
39. C₃×C₅	D₁₀₂₃	semidirect
40. C₁₁	C₃⋊D₄₆₅	semidirect
42. C₃²	D₁₇₀₅	semidirect
44. C₅	C₃⋊D₁₀₂₃	semidirect
45. C₃	D₅₁₁₅	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₁×C₃₁	2
D₅₁₁₅	3
C₃⋊D₁₀₂₃	5
C₃⋊D₄₆₅	11
C₃⋊D₁₆₅	31

Subgroups — C3⋊D5115 #44501889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₅₁₁₅ #44501889