Subgroups — C₂×C₉×#13133721 #44501637

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#13133721	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×#13133721	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×#13133721	C₂×C₃	1	1	yes	characteristic
5	C₂×#13133721	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₉×ΓL(1,𝔽₃₂)	—	11	1	no	maximal, Hall
8	C₂×C₃×C₁₁×C₃₁	C₃×C₅	1	1	yes	characteristic
9	#13133721	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₉×ΓL(1,𝔽₃₂)	—	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×ΓL(1,𝔽₃₂)	—	11	1	no	—
14	C₂×C₁₁×C₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₉×C₃₁	C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
16	C₉×C₁₁⋊C₅	—	31	1	no	Hall
17	C₃×ΓL(1,𝔽₃₂)	—	11	1	no	—
18	C₁₁×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₁₁⋊C₅	—	31	1	no	—
20	C₂×ΓL(1,𝔽₃₂)	—	11	1	no	Hall
21	C₉×C₃₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₉×C₁₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₃₁	C₃×C₁₁⋊C₅	1	1	yes	characteristic
24	C₃×C₁₁⋊C₅	—	31	1	no	—
25	ΓL(1,𝔽₃₂)	—	11	1	no	Hall
26	C₂×C₁₁⋊C₅	—	31	1	no	Hall
27	C₉×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic
29	C₂×C₅×C₉	—	341	1	no	Hall
30	C₂×C₃×C₁₁	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
31	C₂×C₃₁	C₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
32	C₁₁⋊C₅	—	31	1	no	Hall
33	C₅×C₉	—	341	1	no	Hall
34	C₃×C₁₁	C₂×C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
35	C₃₁	C₂×C₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	—	341	1	no	—
37	C₂×C₁₁	C₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
38	C₂×C₉	#13133721	1	1	yes	characteristic, direct product factor, Hall
39	C₃×C₅	—	341	1	no	—
40	C₁₁	C₂×C₉×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	341	1	no	Hall
42	C₉	C₂×#13133721	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₃×#13133721	1	1	yes	characteristic
44	C₅	—	341	1	no	Sylow
45	C₃	C₂×C₃×#13133721	1	1	yes	characteristic
46	C₂	C₉×#13133721	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₉	#13133721
commutator, hypocenter	C₁₁×C₃₁	C₂×C₅×C₉
Frattini	C₃	C₂×C₃×#13133721
Fitting	C₂×C₉×C₁₁×C₃₁	C₅
socle	C₂×C₃×C₁₁×C₃₁	C₃×C₅
prime radical	C₂×C₃×#13133721	C₃
cosocle	C₃×C₁₁×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×#13133721	C₂	direct (N × H)
3. C₂×C₉×C₁₁×C₃₁	C₅	semidirect
5. C₂×#13133721	C₉	direct (N × H)
6. C₉×C₁₁×C₃₁	C₂×C₅	semidirect
9. #13133721	C₂×C₉	direct (N × H)
14. C₂×C₁₁×C₃₁	C₅×C₉	semidirect
15. C₂×C₉×C₃₁	C₁₁⋊C₅	semidirect
18. C₁₁×C₃₁	C₂×C₅×C₉	semidirect
21. C₉×C₃₁	C₂×C₁₁⋊C₅	semidirect
22. C₂×C₉×C₁₁	ΓL(1,𝔽₃₂)	semidirect
27. C₉×C₁₁	C₂×ΓL(1,𝔽₃₂)	semidirect
31. C₂×C₃₁	C₉×C₁₁⋊C₅	semidirect
35. C₃₁	C₂×C₉×C₁₁⋊C₅	semidirect
37. C₂×C₁₁	C₉×ΓL(1,𝔽₃₂)	semidirect
38. C₂×C₉	#13133721	direct (N × H)
40. C₁₁	C₂×C₉×ΓL(1,𝔽₃₂)	semidirect
42. C₉	C₂×#13133721	direct (N × H)
46. C₂	C₉×#13133721	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#13133721	2
C₂×C₃×#13133721	3
C₂×C₉×C₁₁×C₃₁	5
C₂×C₉×ΓL(1,𝔽₃₂)	11
C₂×C₉×C₁₁⋊C₅	31

Subgroups — C2×C9×#13133721 #44501637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#13133721 #44501637