Subgroups — C₃×C₁₁×C₅⋊D₅₅ #31827714

Order 18150.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₅⋊D₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×D₅₅	—	5	6	no	maximal
4	C₅²×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁²	D₅	1	6	yes	complemented
6	C₃×C₅⋊D₅₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor
7	C₃×C₁₁×C₅⋊D₅	—	11	1	no	maximal
8	C₁₁×D₅₅	—	5	6	no	—
9	C₃×C₅²×C₁₁	—	2	5	no	—
10	C₃×C₅²×C₁₁	D₁₁	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
12	C₃×C₁₁×D₁₁	—	25	1	no	Hall
13	C₅×C₁₁²	C₃×D₅	1	6	yes	complemented
14	C₅⋊D₅₅	C₃×C₁₁	1	1	yes	characteristic, direct product factor
15	C₁₁×C₅⋊D₅	—	11	1	no	—
16	C₃×C₁₁²	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
17	C₃×D₅₅	—	5	6	no	—
18	C₃×D₅×C₁₁	—	55	6	no	—
19	C₅²×C₁₁	—	2	5	no	—
20	C₅²×C₁₁	C₃×D₁₁	1	1	yes	characteristic, complemented
21	C₅²×C₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
22	C₁₁×D₁₁	—	25	1	no	Hall
23	C₃×C₅×C₁₁	—	2	30	no	—
24	C₃×C₅×C₁₁	D₅×C₁₁	1	6	yes	complemented
25	C₃×C₅×C₁₁	D₅₅	1	6	yes	complemented
26	C₃×C₅⋊D₅	—	11	1	no	Hall
27	C₁₁²	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
28	D₅₅	—	5	6	no	—
29	D₅×C₁₁	—	55	6	no	—
30	C₃×C₅²	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×C₁₁	—	275	1	no	—
32	C₃×D₁₁	—	25	1	no	—
33	C₅×C₁₁	—	2	30	no	—
34	C₅×C₁₁	C₃×D₅×C₁₁	1	6	yes	complemented
35	C₅×C₁₁	C₃×D₅₅	1	6	yes	complemented
36	C₅⋊D₅	—	11	1	no	Hall
37	C₃×C₁₁	—	2	5	no	—
38	C₃×C₁₁	C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented
39	C₃×C₁₁	C₅⋊D₅₅	1	1	yes	characteristic, direct product factor
40	C₃×D₅	—	55	6	no	—
41	C₅²	C₃×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₁₁	—	275	1	no	—
43	D₁₁	—	25	1	no	—
44	C₃×C₅	C₁₁×D₅₅	1	6	yes	complemented
45	C₁₁	—	2	5	no	—
46	C₁₁	C₃×C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented
47	C₁₁	C₃×C₅⋊D₅₅	1	1	yes	characteristic, direct product factor
48	D₅	—	55	6	no	—
49	C₂×C₃	—	275	1	no	Hall
50	C₅	C₃×C₁₁×D₅₅	1	6	yes	complemented
51	C₃	C₁₁×C₅⋊D₅₅	1	1	yes	characteristic, direct product factor, Sylow
52	C₂	—	275	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁	C₅⋊D₅₅
commutator, cosocle, hypocenter	C₅²×C₁₁	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₂
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁²	C₂	semidirect
2. C₁₁×C₅⋊D₅₅	C₃	direct (N × H)
4. C₅²×C₁₁²	C₂×C₃	semidirect
5. C₃×C₅×C₁₁²	D₅	semidirect
6. C₃×C₅⋊D₅₅	C₁₁	direct (N × H)
10. C₃×C₅²×C₁₁	D₁₁	semidirect
11. C₃×C₅²×C₁₁	C₂×C₁₁	semidirect
13. C₅×C₁₁²	C₃×D₅	semidirect
14. C₅⋊D₅₅	C₃×C₁₁	direct (N × H)
16. C₃×C₁₁²	C₅⋊D₅	semidirect
20. C₅²×C₁₁	C₃×D₁₁	semidirect
21. C₅²×C₁₁	C₂×C₃×C₁₁	semidirect
24. C₃×C₅×C₁₁	D₅×C₁₁	semidirect
25. C₃×C₅×C₁₁	D₅₅	semidirect
27. C₁₁²	C₃×C₅⋊D₅	semidirect
30. C₃×C₅²	C₁₁×D₁₁	semidirect
34. C₅×C₁₁	C₃×D₅×C₁₁	semidirect
35. C₅×C₁₁	C₃×D₅₅	semidirect
38. C₃×C₁₁	C₁₁×C₅⋊D₅	semidirect
39. C₃×C₁₁	C₅⋊D₅₅	direct (N × H)
41. C₅²	C₃×C₁₁×D₁₁	semidirect
44. C₃×C₅	C₁₁×D₅₅	semidirect
46. C₁₁	C₃×C₁₁×C₅⋊D₅	semidirect
47. C₁₁	C₃×C₅⋊D₅₅	direct (N × H)
50. C₅	C₃×C₁₁×D₅₅	semidirect
51. C₃	C₁₁×C₅⋊D₅₅	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×C₅²×C₁₁²	2
C₁₁×C₅⋊D₅₅	3
C₃×C₁₁×D₅₅	5
C₃×C₅⋊D₅₅	11
C₃×C₁₁×C₅⋊D₅	11

Subgroups — C3×C11×C5⋊D55 #31827714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×C₅⋊D₅₅ #31827714