Subgroups — C₄×C₅×C₁₁×C₄₉ #24924688

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, direct product factor, Hall
3	C₄×C₁₁×C₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₅×C₇×C₁₁	C₇	1	1	yes	maximal, characteristic
5	C₂×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic
6	C₄×C₅×C₄₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₇×C₁₁	C₂×C₇	1	1	yes	characteristic
8	C₁₁×C₄₉	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₄₉	C₂×C₁₁	1	1	yes	characteristic
10	C₅×C₇×C₁₁	C₄×C₇	1	1	yes	characteristic
11	C₄×C₇×C₁₁	C₅×C₇	1	1	yes	characteristic
12	C₅×C₄₉	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₅×C₁₁	C₄₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₄₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₇×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic
16	C₄×C₅×C₇	C₇×C₁₁	1	1	yes	characteristic
17	C₂×C₅×C₁₁	C₂×C₄₉	1	1	yes	characteristic
18	C₂×C₄₉	C₂×C₅×C₁₁	1	1	yes	characteristic
19	C₇×C₁₁	C₄×C₅×C₇	1	1	yes	characteristic
20	C₂×C₅×C₇	C₂×C₇×C₁₁	1	1	yes	characteristic
21	C₅×C₁₁	C₄×C₄₉	1	1	yes	characteristic, direct product factor, Hall
22	C₄₉	C₄×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
23	C₄×C₁₁	C₅×C₄₉	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₇	C₄×C₇×C₁₁	1	1	yes	characteristic
25	C₄×C₇	C₅×C₇×C₁₁	1	1	yes	characteristic
26	C₂×C₁₁	C₂×C₅×C₄₉	1	1	yes	characteristic
27	C₄×C₅	C₁₁×C₄₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₇	C₂×C₅×C₇×C₁₁	1	1	yes	characteristic
29	C₁₁	C₄×C₅×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₅	C₂×C₁₁×C₄₉	1	1	yes	characteristic
31	C₇	C₄×C₅×C₇×C₁₁	1	1	yes	characteristic
32	C₅	C₄×C₁₁×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₄	C₅×C₁₁×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅×C₁₁×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₇	C₂×C₅×C₇×C₁₁
socle, prime radical	C₂×C₅×C₇×C₁₁	C₂×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

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

Subgroups — C4×C5×C11×C49 #24924688

Conjugacy classes of subgroups

Complements

Subgroups — C₄×C₅×C₁₁×C₄₉ #24924688