Subgroups — C₅×C₁₁×Dic₄₉ #24924694

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	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×Dic₇	—	7	1	no	maximal
5	C₂×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic
6	C₅×Dic₄₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₇×C₁₁	D₇	1	1	yes	characteristic
8	C₁₁×C₄₉	C₄×C₅	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	—	7	1	no	—
12	C₅×C₄₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₄×C₅×C₁₁	—	49	1	no	Hall
14	Dic₄₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic
16	C₅×Dic₇	—	7	1	no	—
17	C₂×C₅×C₁₁	D₄₉	1	1	yes	characteristic
18	C₂×C₄₉	C₂×C₅×C₁₁	1	1	yes	characteristic
19	C₇×C₁₁	C₅×Dic₇	1	1	yes	characteristic
20	C₂×C₅×C₇	C₁₁×D₇	1	1	yes	characteristic
21	C₅×C₁₁	Dic₄₉	1	1	yes	characteristic, direct product factor, Hall
22	C₄₉	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₁₁	—	49	1	no	Hall
24	C₅×C₇	C₁₁×Dic₇	1	1	yes	characteristic
25	Dic₇	—	7	1	no	—
26	C₂×C₁₁	C₅×D₄₉	1	1	yes	characteristic
27	C₄×C₅	—	49	1	no	Hall
28	C₂×C₇	C₅×C₁₁×D₇	1	1	yes	characteristic
29	C₁₁	C₅×Dic₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₅	C₁₁×D₄₉	1	1	yes	characteristic
31	C₇	C₅×C₁₁×Dic₇	1	1	yes	characteristic
32	C₅	C₁₁×Dic₄₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₄	—	49	1	no	Sylow
34	C₂	C₅×C₁₁×D₄₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁	D₄₉
commutator, hypocenter	C₄₉	C₄×C₅×C₁₁
Frattini	C₂×C₇	C₅×C₁₁×D₇
Fitting	C₂×C₅×C₁₁×C₄₉	C₂
socle, prime radical	C₂×C₅×C₇×C₁₁	D₇
cosocle	C₂×C₄₉	C₂×C₅×C₁₁
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₅×C₁₁

Complements

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

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

Subgroups — C5×C11×Dic49 #24924694

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₁₁×Dic₄₉ #24924694