Subgroups — C₅×Dic₁₁×C₄₉ #24924693

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	Dic₁₁×C₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×Dic₁₁	C₇	1	1	yes	maximal, characteristic
5	C₂×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic
6	C₄×C₅×C₄₉	—	11	1	no	maximal, Hall
7	C₂×C₅×C₇×C₁₁	C₂×C₇	1	1	yes	characteristic
8	C₁₁×C₄₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₄₉	D₁₁	1	1	yes	characteristic
10	C₅×C₇×C₁₁	C₄×C₇	1	1	yes	characteristic
11	C₇×Dic₁₁	C₅×C₇	1	1	yes	characteristic
12	C₅×C₄₉	Dic₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅×Dic₁₁	C₄₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₄₉	—	11	1	no	Hall
15	C₂×C₇×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic
16	C₄×C₅×C₇	—	11	1	no	—
17	C₂×C₅×C₁₁	C₂×C₄₉	1	1	yes	characteristic
18	C₂×C₄₉	C₅×D₁₁	1	1	yes	characteristic
19	C₇×C₁₁	C₄×C₅×C₇	1	1	yes	characteristic
20	C₂×C₅×C₇	C₇×D₁₁	1	1	yes	characteristic
21	C₅×C₁₁	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
22	C₄₉	C₅×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
23	Dic₁₁	C₅×C₄₉	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₇	C₇×Dic₁₁	1	1	yes	characteristic
25	C₄×C₇	—	11	1	no	—
26	C₂×C₁₁	C₂×C₅×C₄₉	1	1	yes	characteristic
27	C₄×C₅	—	11	1	no	Hall
28	C₂×C₇	C₅×C₇×D₁₁	1	1	yes	characteristic
29	C₁₁	C₄×C₅×C₄₉	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₅	D₁₁×C₄₉	1	1	yes	characteristic
31	C₇	C₅×C₇×Dic₁₁	1	1	yes	characteristic
32	C₅	Dic₁₁×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₄	—	11	1	no	Sylow
34	C₂	C₅×D₁₁×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₄₉	D₁₁
commutator, hypocenter	C₁₁	C₄×C₅×C₄₉
Frattini	C₂×C₇	C₅×C₇×D₁₁
Fitting	C₂×C₅×C₁₁×C₄₉	C₂
socle, prime radical	C₂×C₅×C₇×C₁₁	C₂×C₇
cosocle	C₂×C₇×C₁₁	C₂×C₅×C₇
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅×C₄₉

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁×C₄₉	C₄	semidirect
3. Dic₁₁×C₄₉	C₅	direct (N × H)
8. C₁₁×C₄₉	C₄×C₅	semidirect
12. C₅×C₄₉	Dic₁₁	direct (N × H)
13. C₅×Dic₁₁	C₄₉	direct (N × H)
21. C₅×C₁₁	C₄×C₄₉	semidirect
22. C₄₉	C₅×Dic₁₁	direct (N × H)
23. Dic₁₁	C₅×C₄₉	direct (N × H)
29. C₁₁	C₄×C₅×C₄₉	semidirect
32. C₅	Dic₁₁×C₄₉	direct (N × H)

Subgroups — C5×Dic11×C49 #24924693

Conjugacy classes of subgroups

Complements

Subgroups — C₅×Dic₁₁×C₄₉ #24924693