Subgroups — C₂×C₁₁⋊C₅×C₃₁⋊C₉ #44501643

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×C₃₁⋊C₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₃₁×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₃₁⋊C₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₃₁×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic
5	C₂×C₃₁×C₁₁⋊C₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₁×C₃₁⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₃₁⋊C₉	—	11	1	no	maximal, Hall
8	C₂×C₃×C₁₁×C₃₁	C₃×C₅	1	1	yes	characteristic
9	C₃₁×C₁₁⋊C₅	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₃₁⋊C₉	—	11	1	no	Hall
11	C₃×C₁₁×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
12	C₂×C₉×C₁₁⋊C₅	—	31	1	no	maximal, Hall
13	C₂×C₃×C₅×C₃₁	—	11	1	no	—
14	C₂×C₁₁×C₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃₁⋊C₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
16	C₉×C₁₁⋊C₅	—	31	1	no	Hall
17	C₃×C₅×C₃₁	—	11	1	no	—
18	C₁₁×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₁₁⋊C₅	C₃₁⋊C₃	1	1	yes	characteristic
20	C₂×C₅×C₃₁	—	11	1	no	Hall
21	C₃₁⋊C₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₉×C₁₁	—	31	1	no	Hall
23	C₂×C₃×C₃₁	C₃×C₁₁⋊C₅	1	1	yes	characteristic
24	C₃×C₁₁⋊C₅	C₂×C₃₁⋊C₃	1	1	yes	characteristic
25	C₅×C₃₁	—	11	1	no	Hall
26	C₂×C₁₁⋊C₅	C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Hall
27	C₉×C₁₁	—	31	1	no	Hall
28	C₃×C₃₁	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic
29	C₂×C₅×C₉	—	341	1	no	Hall
30	C₂×C₃×C₁₁	C₅×C₃₁⋊C₃	1	1	yes	characteristic
31	C₂×C₃₁	C₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
32	C₁₁⋊C₅	C₂×C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Hall
33	C₅×C₉	—	341	1	no	Hall
34	C₃×C₁₁	C₂×C₅×C₃₁⋊C₃	1	1	yes	characteristic
35	C₃₁	C₂×C₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	—	11	1	no	—
37	C₂×C₁₁	C₅×C₃₁⋊C₉	1	1	yes	characteristic, complemented, Hall
38	C₂×C₉	—	31	1	no	Hall
39	C₃×C₅	—	11	1	no	—
40	C₁₁	C₂×C₅×C₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	11	1	no	Hall
42	C₉	—	31	1	no	Sylow
43	C₂×C₃	C₁₁⋊C₅×C₃₁⋊C₃	1	1	yes	characteristic
44	C₅	—	11	1	no	Sylow
45	C₃	C₂×C₁₁⋊C₅×C₃₁⋊C₃	1	1	yes	characteristic
46	C₂	C₁₁⋊C₅×C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₁⋊C₅×C₃₁⋊C₃
commutator, hypocenter	C₁₁×C₃₁	C₂×C₅×C₉
Frattini	C₃	C₂×C₁₁⋊C₅×C₃₁⋊C₃
Fitting, socle	C₂×C₃×C₁₁×C₃₁	C₃×C₅
prime radical	C₂×C₃×C₃₁×C₁₁⋊C₅	C₃
cosocle	C₃×C₁₁×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊C₅×C₃₁⋊C₉	C₂	direct (N × H)
3. C₂×C₁₁×C₃₁⋊C₉	C₅	semidirect
5. C₂×C₃₁×C₁₁⋊C₅	C₉	semidirect
6. C₁₁×C₃₁⋊C₉	C₂×C₅	semidirect
9. C₃₁×C₁₁⋊C₅	C₂×C₉	semidirect
14. C₂×C₁₁×C₃₁	C₅×C₉	semidirect
15. C₂×C₃₁⋊C₉	C₁₁⋊C₅	direct (N × H)
18. C₁₁×C₃₁	C₂×C₅×C₉	semidirect
21. C₃₁⋊C₉	C₂×C₁₁⋊C₅	direct (N × H)
26. C₂×C₁₁⋊C₅	C₃₁⋊C₉	direct (N × H)
31. C₂×C₃₁	C₉×C₁₁⋊C₅	semidirect
32. C₁₁⋊C₅	C₂×C₃₁⋊C₉	direct (N × H)
35. C₃₁	C₂×C₉×C₁₁⋊C₅	semidirect
37. C₂×C₁₁	C₅×C₃₁⋊C₉	semidirect
40. C₁₁	C₂×C₅×C₃₁⋊C₉	semidirect
46. C₂	C₁₁⋊C₅×C₃₁⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁⋊C₅×C₃₁⋊C₉	2
C₂×C₃×C₃₁×C₁₁⋊C₅	3
C₂×C₁₁×C₃₁⋊C₉	5
C₂×C₅×C₃₁⋊C₉	11
C₂×C₉×C₁₁⋊C₅	31

Subgroups — C2×C11⋊C5×C31⋊C9 #44501643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁⋊C₅×C₃₁⋊C₉ #44501643