Subgroups — C₅×C₁₁×C₄₉⋊C₉ #37564673

Order 24255.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₄₉	C₃	1	1	yes	maximal, characteristic
2	C₁₁×C₄₉⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₁×C₇⋊C₉	—	7	1	no	maximal
4	C₅×C₁₁×C₄₉	C₉	1	1	yes	characteristic, complemented, Hall
5	C₅×C₄₉⋊C₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₁×C₄₉	C₃×C₅	1	1	yes	characteristic
7	C₃×C₅×C₇×C₁₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
8	C₃×C₅×C₄₉	C₃×C₁₁	1	1	yes	characteristic
9	C₁₁×C₇⋊C₉	—	7	1	no	—
10	C₁₁×C₄₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
11	C₅×C₉×C₁₁	—	49	1	no	Hall
12	C₄₉⋊C₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₇×C₁₁	C₇⋊C₉	1	1	yes	characteristic
14	C₅×C₇⋊C₉	—	7	1	no	—
15	C₅×C₄₉	C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×C₁₁	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₃×C₅×C₁₁	C₄₉⋊C₃	1	1	yes	characteristic
18	C₃×C₄₉	C₃×C₅×C₁₁	1	1	yes	characteristic
19	C₃×C₅×C₇	C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic
20	C₉×C₁₁	—	49	1	no	Hall
21	C₇×C₁₁	C₅×C₇⋊C₉	1	1	yes	characteristic
22	C₇⋊C₉	—	7	1	no	—
23	C₅×C₁₁	C₄₉⋊C₉	1	1	yes	characteristic, direct product factor, Hall
24	C₄₉	C₅×C₉×C₁₁	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₉	—	49	1	no	Hall
26	C₅×C₇	C₁₁×C₇⋊C₉	1	1	yes	characteristic
27	C₃×C₁₁	C₅×C₄₉⋊C₃	1	1	yes	characteristic
28	C₃×C₇	C₅×C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₃×C₅	C₁₁×C₄₉⋊C₃	1	1	yes	characteristic
30	C₁₁	C₅×C₄₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₉	—	49	1	no	Sylow
32	C₇	C₅×C₁₁×C₇⋊C₉	1	1	yes	characteristic
33	C₅	C₁₁×C₄₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₃	C₅×C₁₁×C₄₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₁	C₄₉⋊C₃
commutator, hypocenter	C₄₉	C₅×C₉×C₁₁
Frattini	C₃×C₇	C₅×C₁₁×ΓL(1,𝔽₈)
Fitting	C₃×C₅×C₁₁×C₄₉	C₃
socle, prime radical	C₃×C₅×C₇×C₁₁	ΓL(1,𝔽₈)
cosocle	C₃×C₄₉	C₃×C₅×C₁₁
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₄₉⋊C₉	C₅	direct (N × H)
4. C₅×C₁₁×C₄₉	C₉	semidirect
5. C₅×C₄₉⋊C₉	C₁₁	direct (N × H)
10. C₁₁×C₄₉	C₅×C₉	semidirect
12. C₄₉⋊C₉	C₅×C₁₁	direct (N × H)
15. C₅×C₄₉	C₉×C₁₁	semidirect
23. C₅×C₁₁	C₄₉⋊C₉	direct (N × H)
24. C₄₉	C₅×C₉×C₁₁	semidirect
30. C₁₁	C₅×C₄₉⋊C₉	direct (N × H)
33. C₅	C₁₁×C₄₉⋊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
C₃×C₅×C₁₁×C₄₉	3
C₁₁×C₄₉⋊C₉	5
C₅×C₁₁×C₇⋊C₉	7
C₅×C₄₉⋊C₉	11

Subgroups — C5×C11×C49⋊C9 #37564673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×C₄₉⋊C₉ #37564673