Subgroups — C₉⋊((C₁₁⋊C₅)⋊D₃₁) #44501700

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₁×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊((C₁₁⋊C₅)⋊D₃₁)	—	3	1	no	maximal
3	D₃₀₆₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₃₁×C₁₁⋊C₅	D₃	1	1	yes	characteristic
5	(C₁₁⋊C₅)⋊D₃₁	—	9	1	no	Hall
6	C₉×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₂₇₉	—	11	1	no	maximal, Hall
8	D₁₀₂₃	—	3	1	no	—
9	C₃₁×C₁₁⋊C₅	D₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₉×C₃₁	—	11	1	no	Hall
11	C₃×C₁₁×C₃₁	C₅×D₃	1	1	yes	characteristic
12	C₉⋊AGL(1,𝔽₁₁)	—	31	1	no	maximal, Hall
13	C₅×D₉₃	—	33	1	no	—
14	D₃₄₁	—	9	1	no	Hall
15	D₂₇₉	—	11	1	no	Hall
16	C₉×C₁₁⋊C₅	D₃₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₃₁	—	11	1	no	—
18	C₁₁×C₃₁	C₅×D₉	1	1	yes	characteristic, complemented, Hall
19	C₃⋊AGL(1,𝔽₁₁)	—	93	1	no	—
20	C₅×D₃₁	—	99	1	no	Hall
21	C₉×C₃₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
22	D₉₉	—	31	1	no	Hall
23	D₉₃	—	33	1	no	—
24	C₃×C₁₁⋊C₅	D₉₃	1	1	yes	characteristic
25	C₅×C₃₁	—	11	1	no	Hall
26	AGL(1,𝔽₁₁)	—	279	1	no	Hall
27	C₉×C₁₁	C₅×D₃₁	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
29	C₅×D₉	—	341	1	no	Hall
30	D₃₃	—	93	1	no	—
31	D₃₁	—	99	1	no	Hall
32	C₁₁⋊C₅	D₂₇₉	1	1	yes	characteristic, complemented, Hall
33	C₅×C₉	—	11	1	no	Hall
34	C₃×C₁₁	C₅×D₉₃	1	1	yes	characteristic
35	C₃₁	C₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
36	C₅×D₃	—	1023	1	no	—
37	D₁₁	—	279	1	no	Hall
38	D₉	—	341	1	no	Hall
39	C₃×C₅	—	11	1	no	—
40	C₁₁	C₅×D₂₇₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	3069	1	no	Hall
42	C₉	(C₁₁⋊C₅)⋊D₃₁	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	1023	1	no	—
44	C₅	—	11	1	no	Sylow
45	C₃	C₃⋊((C₁₁⋊C₅)⋊D₃₁)	1	1	yes	characteristic
46	C₂	—	3069	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁×C₃₁	C₂×C₅
Frattini	C₃	C₃⋊((C₁₁⋊C₅)⋊D₃₁)
socle	C₃×C₁₁×C₃₁	C₅×D₃
LCS	G ▷ C₉×C₁₁×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₉×C₃₁×C₁₁⋊C₅	C₂	semidirect
3. D₃₀₆₉	C₅	semidirect
6. C₉×C₁₁×C₃₁	C₂×C₅	semidirect
9. C₃₁×C₁₁⋊C₅	D₉	semidirect
16. C₉×C₁₁⋊C₅	D₃₁	semidirect
18. C₁₁×C₃₁	C₅×D₉	semidirect
21. C₉×C₃₁	AGL(1,𝔽₁₁)	semidirect
27. C₉×C₁₁	C₅×D₃₁	semidirect
32. C₁₁⋊C₅	D₂₇₉	semidirect
35. C₃₁	C₉⋊AGL(1,𝔽₁₁)	semidirect
40. C₁₁	C₅×D₂₇₉	semidirect
42. C₉	(C₁₁⋊C₅)⋊D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₃₁×C₁₁⋊C₅	2
C₃⋊((C₁₁⋊C₅)⋊D₃₁)	3
D₃₀₆₉	5
C₅×D₂₇₉	11
C₉⋊AGL(1,𝔽₁₁)	31

Subgroups — C9⋊((C11⋊C5)⋊D31) #44501700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊((C₁₁⋊C₅)⋊D₃₁) #44501700