Subgroups — C₃×C₅×C₁₁×D₄₉ #30633461

Order 16170.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×D₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×D₇	—	7	1	no	maximal
6	C₃×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×D₄₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×C₇×C₁₁	D₇	1	1	yes	characteristic
9	C₁₁×D₄₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₁₁×D₇	—	7	1	no	—
11	C₃×C₅×C₄₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₄₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	C₅×D₄₉	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₁×D₇	—	7	1	no	—
15	C₅×C₇×C₁₁	C₃×D₇	1	1	yes	characteristic
16	C₂×C₃×C₅×C₁₁	—	49	1	no	Hall
17	C₃×D₄₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₄₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic
20	C₃×C₅×D₇	—	7	1	no	—
21	C₃×C₅×C₁₁	D₄₉	1	1	yes	characteristic, direct product factor, Hall
22	C₁₁×D₇	—	7	1	no	—
23	C₃×C₄₉	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₁₁	—	49	1	no	Hall
25	C₃×C₅×C₇	C₁₁×D₇	1	1	yes	characteristic
26	D₄₉	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
27	C₇×C₁₁	C₃×C₅×D₇	1	1	yes	characteristic
28	C₅×D₇	—	7	1	no	—
29	C₂×C₃×C₁₁	—	49	1	no	Hall
30	C₅×C₁₁	C₃×D₄₉	1	1	yes	characteristic, direct product factor, Hall
31	C₄₉	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₇	—	7	1	no	—
33	C₅×C₇	C₃×C₁₁×D₇	1	1	yes	characteristic
34	C₃×C₁₁	C₅×D₄₉	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₃×C₅	—	49	1	no	Hall
36	C₂×C₁₁	—	49	1	no	Hall
37	C₃×C₇	C₅×C₁₁×D₇	1	1	yes	characteristic
38	C₃×C₅	C₁₁×D₄₉	1	1	yes	characteristic, direct product factor, Hall
39	D₇	—	7	1	no	—
40	C₁₁	C₃×C₅×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	49	1	no	Hall
42	C₇	C₃×C₅×C₁₁×D₇	1	1	yes	characteristic
43	C₂×C₃	—	49	1	no	Hall
44	C₅	C₃×C₁₁×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×C₁₁×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₁	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂×C₃×C₅×C₁₁
Frattini	C₇	C₃×C₅×C₁₁×D₇
Fitting	C₃×C₅×C₁₁×C₄₉	C₂
socle	C₃×C₅×C₇×C₁₁	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₄₉	C₂	semidirect
2. C₅×C₁₁×D₄₉	C₃	direct (N × H)
3. C₃×C₁₁×D₄₉	C₅	direct (N × H)
4. C₅×C₁₁×C₄₉	C₂×C₃	semidirect
6. C₃×C₁₁×C₄₉	C₂×C₅	semidirect
7. C₃×C₅×D₄₉	C₁₁	direct (N × H)
9. C₁₁×D₄₉	C₃×C₅	direct (N × H)
11. C₃×C₅×C₄₉	C₂×C₁₁	semidirect
12. C₁₁×C₄₉	C₂×C₃×C₅	semidirect
13. C₅×D₄₉	C₃×C₁₁	direct (N × H)
17. C₃×D₄₉	C₅×C₁₁	direct (N × H)
18. C₅×C₄₉	C₂×C₃×C₁₁	semidirect
21. C₃×C₅×C₁₁	D₄₉	direct (N × H)
23. C₃×C₄₉	C₂×C₅×C₁₁	semidirect
26. D₄₉	C₃×C₅×C₁₁	direct (N × H)
30. C₅×C₁₁	C₃×D₄₉	direct (N × H)
31. C₄₉	C₂×C₃×C₅×C₁₁	semidirect
34. C₃×C₁₁	C₅×D₄₉	direct (N × H)
38. C₃×C₅	C₁₁×D₄₉	direct (N × H)
40. C₁₁	C₃×C₅×D₄₉	direct (N × H)
44. C₅	C₃×C₁₁×D₄₉	direct (N × H)
45. C₃	C₅×C₁₁×D₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₁×C₄₉	2
C₅×C₁₁×D₄₉	3
C₃×C₁₁×D₄₉	5
C₃×C₅×C₁₁×D₇	7
C₃×C₅×D₄₉	11

Subgroups — C3×C5×C11×D49 #30633461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₁×D₄₉ #30633461