Subgroups — D₅×C₁₁×D₄₉ #24924713

Order 10780.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₂₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×D₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×D₄₉	—	5	1	no	maximal, Hall
6	D₅×C₁₁×D₇	—	7	1	no	maximal
7	C₂×C₁₁×C₄₉	—	5	1	no	—
8	C₁₁×D₄₉	—	5	1	no	—
9	C₁₁×D₄₉	D₅	1	1	yes	characteristic, direct product factor
10	D₅×D₄₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₁×D₃₅	—	7	1	no	—
12	C₇×D₅×C₁₁	D₇	1	1	yes	characteristic
13	C₅×C₁₁×D₇	—	7	1	no	—
14	C₁₁×C₄₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	D₂₄₅	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₅×D₄₉	C₂×C₁₁	1	1	yes	characteristic, complemented
17	D₅×C₄₉	C₂×C₁₁	1	1	yes	characteristic, complemented
18	C₅×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic
19	C₂×C₁₁×D₇	—	35	1	no	—
20	C₅×C₄₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×D₅×C₁₁	—	49	1	no	Hall
22	C₂×D₄₉	—	5	1	no	Hall
23	C₂×C₇×C₁₁	—	5	1	no	—
24	C₁₁×D₇	—	7	1	no	—
25	C₁₁×D₇	—	35	1	no	—
26	D₅×D₇	—	7	1	no	—
27	C₂×C₅×C₁₁	—	49	1	no	—
28	D₅×C₁₁	—	49	1	no	—
29	D₅×C₁₁	D₄₉	1	1	yes	characteristic, direct product factor
30	C₂×C₄₉	—	5	1	no	—
31	D₄₉	—	5	1	no	—
32	D₄₉	D₅×C₁₁	1	1	yes	characteristic, direct product factor
33	C₇×C₁₁	D₅×D₇	1	1	yes	characteristic
34	D₃₅	—	7	1	no	—
35	C₅×D₇	—	7	1	no	—
36	C₇×D₅	C₁₁×D₇	1	1	yes	characteristic
37	C₅×C₁₁	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
38	C₄₉	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₁₁	—	245	1	no	Hall
40	C₅×C₇	C₂×C₁₁×D₇	1	1	yes	characteristic
41	C₂×D₇	—	35	1	no	—
42	C₂×C₁₁	—	5	1	no	—
43	C₂×C₁₁	—	49	1	no	—
44	C₂×C₁₁	—	245	1	no	—
45	C₂×D₅	—	49	1	no	Hall
46	C₂×C₇	—	5	1	no	—
47	D₇	—	7	1	no	—
48	D₇	—	35	1	no	—
49	C₁₁	D₅×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₅	—	49	1	no	—
51	D₅	—	49	1	no	—
52	D₅	C₁₁×D₄₉	1	1	yes	characteristic, direct product factor
53	C₇	D₅×C₁₁×D₇	1	1	yes	characteristic
54	C₅	C₂×C₁₁×D₄₉	1	1	yes	characteristic, complemented, Sylow
55	C₂²	—	245	1	no	Sylow
56	C₂	—	5	1	no	—
57	C₂	—	49	1	no	—
58	C₂	—	245	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₅×D₄₉
commutator, cosocle, hypocenter	C₅×C₄₉	C₂²×C₁₁
Frattini	C₇	D₅×C₁₁×D₇
Fitting	C₅×C₁₁×C₄₉	C₂²
socle	C₅×C₇×C₁₁	C₂×D₇
LCS	G ▷ C₅×C₄₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₂₄₅	C₂	semidirect
2. D₅×C₁₁×C₄₉	C₂	semidirect
3. C₅×C₁₁×D₄₉	C₂	semidirect
4. C₅×C₁₁×C₄₉	C₂²	semidirect
9. C₁₁×D₄₉	D₅	direct (N × H)
10. D₅×D₄₉	C₁₁	direct (N × H)
14. C₁₁×C₄₉	C₂×D₅	semidirect
15. D₂₄₅	C₂×C₁₁	semidirect
16. C₅×D₄₉	C₂×C₁₁	semidirect
17. D₅×C₄₉	C₂×C₁₁	semidirect
20. C₅×C₄₉	C₂²×C₁₁	semidirect
29. D₅×C₁₁	D₄₉	direct (N × H)
32. D₄₉	D₅×C₁₁	direct (N × H)
37. C₅×C₁₁	C₂×D₄₉	semidirect
38. C₄₉	C₂×D₅×C₁₁	semidirect
49. C₁₁	D₅×D₄₉	direct (N × H)
52. D₅	C₁₁×D₄₉	direct (N × H)
54. C₅	C₂×C₁₁×D₄₉	semidirect

Subgroups — D5×C11×D49 #24924713

Conjugacy classes of subgroups

Complements

Subgroups — D₅×C₁₁×D₄₉ #24924713