Subgroups — C₁₁⋊#15668133 #44535503

Order 31350.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊D₁₀₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#15668133	—	11	1	no	maximal, Hall
5	D₁₀₄₅	—	15	2	no	—
6	C₁₁⋊((C₅⋊D₅)⋊C₃)	—	19	1	no	maximal, Hall
7	C₁₉⋊(C₅²⋊C₃)	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁⋊(D₁₉⋊C₃)	—	25	1	no	maximal, Hall
9	C₅×C₁₁×C₁₉	—	3	2	no	—
10	C₅⋊D₉₅	—	11	1	no	Hall
11	C₁₁×C₅²⋊C₃	—	19	1	no	Hall
12	C₁₁×C₁₉⋊C₃	—	25	1	no	Hall
13	C₅⋊D₅₅	—	19	1	no	Hall
14	C₅²×C₁₉	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
15	D₂₀₉	—	25	1	no	Hall
16	C₅²×C₁₁	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₁₁×C₁₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Hall
18	D₉₅	—	165	2	no	—
19	(C₅⋊D₅)⋊C₃	—	209	1	no	Hall
20	D₁₉⋊C₃	—	275	1	no	Hall
21	D₅₅	—	285	2	no	—
22	C₅×C₁₉	—	3	2	no	—
23	C₅²⋊C₃	—	19	1	no	Hall
24	C₃×D₁₁	—	475	1	no	Hall
25	C₁₉⋊C₃	—	25	1	no	Hall
26	C₅×C₁₁	—	3	2	no	—
27	C₅⋊D₅	—	209	1	no	Hall
28	D₁₉	—	275	1	no	Hall
29	C₃×C₁₁	—	475	1	no	Hall
30	C₅²	C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
31	D₁₁	—	475	1	no	Hall
32	C₁₉	C₁₁⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, complemented, Sylow
33	C₁₁	#15668133	1	1	yes	characteristic, complemented, Sylow
34	D₅	—	3135	2	no	—
35	C₂×C₃	—	5225	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	475	1	no	Sylow
38	C₂	—	5225	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₁×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉⋊(C₅²⋊C₃)	C₂	semidirect
2. C₅⋊D₁₀₄₅	C₃	semidirect
3. C₅²×C₁₁×C₁₉	C₂×C₃	semidirect
7. C₁₉⋊(C₅²⋊C₃)	D₁₁	semidirect
14. C₅²×C₁₉	C₃×D₁₁	semidirect
16. C₅²×C₁₁	D₁₉⋊C₃	semidirect
17. C₁₁×C₁₉	(C₅⋊D₅)⋊C₃	semidirect
30. C₅²	C₁₁⋊(D₁₉⋊C₃)	semidirect
32. C₁₉	C₁₁⋊((C₅⋊D₅)⋊C₃)	semidirect
33. C₁₁	#15668133	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉⋊(C₅²⋊C₃)	2
C₅⋊D₁₀₄₅	3
#15668133	11
C₁₁⋊((C₅⋊D₅)⋊C₃)	19
C₁₁⋊(D₁₉⋊C₃)	25

Subgroups — C11⋊#15668133 #44535503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊#15668133 #44535503