Subgroups — C₁₁×Dic₂₄₅ #24924698

Order 10780.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×Dic₄₉	—	5	1	no	maximal, Hall
4	C₁₁×Dic₃₅	—	7	1	no	maximal
5	C₂×C₁₁×C₄₉	D₅	1	1	yes	characteristic
6	Dic₂₄₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₇×C₁₁	D₇	1	1	yes	characteristic
8	C₁₁×C₄₉	Dic₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₄₉	C₂×C₁₁	1	1	yes	characteristic
10	C₅×C₇×C₁₁	Dic₇	1	1	yes	characteristic
11	C₁₁×Dic₇	—	35	1	no	—
12	C₅×C₄₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×Dic₅	—	49	1	no	Hall
14	Dic₄₉	—	5	1	no	Hall
15	C₂×C₇×C₁₁	D₃₅	1	1	yes	characteristic
16	Dic₃₅	—	7	1	no	—
17	C₂×C₅×C₁₁	D₄₉	1	1	yes	characteristic
18	C₂×C₄₉	D₅×C₁₁	1	1	yes	characteristic
19	C₇×C₁₁	Dic₃₅	1	1	yes	characteristic
20	C₂×C₅×C₇	C₁₁×D₇	1	1	yes	characteristic
21	C₅×C₁₁	Dic₄₉	1	1	yes	characteristic, complemented, Hall
22	C₄₉	C₁₁×Dic₅	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₁₁	—	245	1	no	Hall
24	C₅×C₇	C₁₁×Dic₇	1	1	yes	characteristic
25	Dic₇	—	35	1	no	—
26	C₂×C₁₁	D₂₄₅	1	1	yes	characteristic
27	Dic₅	—	49	1	no	Hall
28	C₂×C₇	C₁₁×D₃₅	1	1	yes	characteristic
29	C₁₁	Dic₂₄₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₅	C₁₁×D₄₉	1	1	yes	characteristic
31	C₇	C₁₁×Dic₃₅	1	1	yes	characteristic
32	C₅	C₁₁×Dic₄₉	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	245	1	no	Sylow
34	C₂	C₁₁×D₂₄₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₂₄₅
commutator, hypocenter	C₅×C₄₉	C₄×C₁₁
Frattini	C₂×C₇	C₁₁×D₃₅
Fitting	C₂×C₅×C₁₁×C₄₉	C₂
socle, prime radical	C₂×C₅×C₇×C₁₁	D₇
cosocle	C₂×C₅×C₄₉	C₂×C₁₁
LCS	G ▷ C₅×C₄₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁×C₄₉	C₄	semidirect
6. Dic₂₄₅	C₁₁	direct (N × H)
8. C₁₁×C₄₉	Dic₅	semidirect
12. C₅×C₄₉	C₄×C₁₁	semidirect
21. C₅×C₁₁	Dic₄₉	semidirect
22. C₄₉	C₁₁×Dic₅	semidirect
29. C₁₁	Dic₂₄₅	direct (N × H)
32. C₅	C₁₁×Dic₄₉	semidirect

Subgroups — C11×Dic245 #24924698

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×Dic₂₄₅ #24924698