Subgroups — C₅×C₁₁²×#261 #44538232

Order 31460.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁²×#261	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁²×D₁₃	C₂×C₅	1	1	yes	characteristic
5	C₅×C₁₁×#261	C₁₁	1	12	yes	maximal, direct product factor
6	C₄×C₅×C₁₁²	—	13	1	no	maximal, Hall
7	C₁₁²×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₁×D₁₃	C₂×C₁₁	1	12	yes	—
9	C₂×C₅×C₁₁²	—	13	1	no	—
10	C₅×C₁₁×C₁₃	C₄×C₁₁	1	12	yes	complemented
11	C₅×C₁₁²	#261	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁×#261	C₅×C₁₁	1	12	yes	direct product factor
13	C₄×C₁₁²	—	13	1	no	Hall
14	C₁₁×D₁₃	C₂×C₅×C₁₁	1	12	yes	—
15	C₅×#261	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₁²	—	13	1	no	—
17	C₄×C₅×C₁₁	—	13	12	no	—
18	C₁₁×C₁₃	C₄×C₅×C₁₁	1	12	yes	complemented
19	C₅×D₁₃	C₂×C₁₁²	1	1	yes	characteristic
20	C₁₁²	C₅×#261	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₅×C₁₁	—	13	12	no	—
22	C₅×C₁₃	C₄×C₁₁²	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₁	C₁₁×#261	1	12	yes	direct product factor
24	#261	C₅×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
25	C₄×C₁₁	—	13	12	no	—
26	D₁₃	C₂×C₅×C₁₁²	1	1	yes	characteristic
27	C₂×C₁₁	—	13	12	no	—
28	C₄×C₅	—	13	1	no	Hall
29	C₁₃	C₄×C₅×C₁₁²	1	1	yes	characteristic, complemented, Sylow
30	C₁₁	C₅×C₁₁×#261	1	12	yes	direct product factor
31	C₂×C₅	—	13	1	no	—
32	C₅	C₁₁²×#261	1	1	yes	characteristic, direct product factor, Sylow
33	C₄	—	13	1	no	Sylow
34	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁²	#261
commutator, hypocenter	C₁₃	C₄×C₅×C₁₁²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₁₃	C₄
prime radical	C₅×C₁₁²×D₁₃	C₂
cosocle	D₁₃	C₂×C₅×C₁₁²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₁₁²

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁²×C₁₃	C₄	semidirect
3. C₁₁²×#261	C₅	direct (N × H)
5. C₅×C₁₁×#261	C₁₁	direct (N × H)
7. C₁₁²×C₁₃	C₄×C₅	semidirect
10. C₅×C₁₁×C₁₃	C₄×C₁₁	semidirect
11. C₅×C₁₁²	#261	direct (N × H)
12. C₁₁×#261	C₅×C₁₁	direct (N × H)
15. C₅×#261	C₁₁²	direct (N × H)
18. C₁₁×C₁₃	C₄×C₅×C₁₁	semidirect
20. C₁₁²	C₅×#261	direct (N × H)
22. C₅×C₁₃	C₄×C₁₁²	semidirect
23. C₅×C₁₁	C₁₁×#261	direct (N × H)
24. #261	C₅×C₁₁²	direct (N × H)
29. C₁₃	C₄×C₅×C₁₁²	semidirect
30. C₁₁	C₅×C₁₁×#261	direct (N × H)
32. C₅	C₁₁²×#261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁²×D₁₃	2
C₁₁²×#261	5
C₅×C₁₁×#261	11
C₄×C₅×C₁₁²	13

Subgroups — C5×C112×#261 #44538232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁²×#261 #44538232