Subgroups — C₅×C₁₁×#89204 #37564685

Order 24255.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₁	C₃	1	1	yes	maximal, characteristic
2	C₁₁×#89204	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₁×C₇⋊C₉	—	7	8	no	maximal
4	C₅×C₇²×C₁₁	C₉	1	1	yes	characteristic, complemented, Hall
5	C₅×#89204	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇²×C₁₁	C₃×C₅	1	1	yes	characteristic
7	C₃×C₅×C₇×C₁₁	ΓL(1,𝔽₈)	1	8	yes	—
8	C₃×C₅×C₇²	C₃×C₁₁	1	1	yes	characteristic
9	C₁₁×C₇⋊C₉	—	7	8	no	—
10	C₇²×C₁₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
11	C₅×C₉×C₁₁	—	49	1	no	Hall
12	#89204	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₇×C₁₁	C₇⋊C₉	1	8	yes	complemented
14	C₅×C₇⋊C₉	—	7	8	no	—
15	C₅×C₇²	C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×C₁₁	C₅×ΓL(1,𝔽₈)	1	8	yes	—
17	C₃×C₅×C₁₁	#3861	1	1	yes	characteristic
18	C₃×C₇²	C₃×C₅×C₁₁	1	1	yes	characteristic
19	C₃×C₅×C₇	C₁₁×ΓL(1,𝔽₈)	1	8	yes	—
20	C₉×C₁₁	—	49	1	no	Hall
21	C₇×C₁₁	C₅×C₇⋊C₉	1	8	yes	complemented
22	C₇⋊C₉	—	7	8	no	—
23	C₅×C₁₁	#89204	1	1	yes	characteristic, direct product factor, Hall
24	C₇²	C₅×C₉×C₁₁	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₉	—	49	1	no	Hall
26	C₅×C₇	C₁₁×C₇⋊C₉	1	8	yes	complemented
27	C₃×C₁₁	C₅×#3861	1	1	yes	characteristic
28	C₃×C₇	C₅×C₁₁×ΓL(1,𝔽₈)	1	8	yes	—
29	C₃×C₅	C₁₁×#3861	1	1	yes	characteristic
30	C₁₁	C₅×#89204	1	1	yes	characteristic, direct product factor, Sylow
31	C₉	—	49	1	no	Sylow
32	C₇	C₅×C₁₁×C₇⋊C₉	1	8	yes	complemented
33	C₅	C₁₁×#89204	1	1	yes	characteristic, direct product factor, Sylow
34	C₃	C₅×C₁₁×#3861	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₁	#3861
commutator, hypocenter	C₇²	C₅×C₉×C₁₁
Frattini	C₃	C₅×C₁₁×#3861
Fitting, socle, prime radical	C₃×C₅×C₇²×C₁₁	C₃
cosocle	C₃×C₇²	C₃×C₅×C₁₁
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×#89204	C₅	direct (N × H)
4. C₅×C₇²×C₁₁	C₉	semidirect
5. C₅×#89204	C₁₁	direct (N × H)
10. C₇²×C₁₁	C₅×C₉	semidirect
12. #89204	C₅×C₁₁	direct (N × H)
13. C₅×C₇×C₁₁	C₇⋊C₉	semidirect
15. C₅×C₇²	C₉×C₁₁	semidirect
21. C₇×C₁₁	C₅×C₇⋊C₉	semidirect
23. C₅×C₁₁	#89204	direct (N × H)
24. C₇²	C₅×C₉×C₁₁	semidirect
26. C₅×C₇	C₁₁×C₇⋊C₉	semidirect
30. C₁₁	C₅×#89204	direct (N × H)
32. C₇	C₅×C₁₁×C₇⋊C₉	semidirect
33. C₅	C₁₁×#89204	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×C₇²×C₁₁	3
C₁₁×#89204	5
C₅×C₁₁×C₇⋊C₉	7
C₅×#89204	11

Subgroups — C5×C11×#89204 #37564685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×#89204 #37564685