Subgroups — C₂×C₁₁⋊C₅×D₄₉ #24924703

Order 10780.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁⋊C₅×D₄₉	C₂	1	2	yes	maximal, direct product factor
3	C₄₉×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₄₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×D₇×C₁₁⋊C₅	—	7	1	no	maximal
6	C₂×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented
7	C₁₁×D₄₉	C₂×C₅	1	2	yes	complemented
8	C₂×C₅×D₄₉	—	11	1	no	maximal, Hall
9	C₂×C₇×C₁₁⋊C₅	D₇	1	1	yes	characteristic
10	D₇×C₁₁⋊C₅	—	7	2	no	—
11	C₁₁×C₄₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₄₉	—	11	1	no	—
13	C₅×D₄₉	—	11	2	no	—
14	C₇×C₁₁⋊C₅	C₂×D₇	1	1	yes	characteristic
15	C₂×C₁₁×D₇	—	7	1	no	—
16	C₅×C₄₉	—	11	1	no	Hall
17	C₂²×C₁₁⋊C₅	—	49	1	no	Hall
18	C₂×D₄₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic
20	C₁₁×D₇	—	7	2	no	—
21	C₂×C₅×D₇	—	77	1	no	—
22	C₂×C₁₁⋊C₅	—	49	2	no	—
23	C₂×C₁₁⋊C₅	D₄₉	1	1	yes	characteristic, direct product factor
24	C₂×C₄₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
25	D₄₉	C₂×C₁₁⋊C₅	1	2	yes	direct product factor
26	C₇×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic
27	C₂×C₅×C₇	—	11	1	no	—
28	C₅×D₇	—	77	2	no	—
29	C₁₁⋊C₅	C₂×D₄₉	1	1	yes	characteristic, direct product factor, Hall
30	C₄₉	C₂²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₁₁	—	49	1	no	Hall
32	C₅×C₇	—	11	1	no	—
33	C₂×D₇	—	7	1	no	—
34	C₂×C₁₁	—	49	2	no	—
35	C₂×C₁₁	C₅×D₄₉	1	1	yes	characteristic, complemented
36	C₂²×C₅	—	539	1	no	Hall
37	C₂×C₇	D₇×C₁₁⋊C₅	1	1	yes	characteristic
38	D₇	—	7	2	no	—
39	C₁₁	C₂×C₅×D₄₉	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	—	11	1	no	—
41	C₂×C₅	—	539	2	no	—
42	C₇	C₂×D₇×C₁₁⋊C₅	1	1	yes	characteristic
43	C₅	—	11	1	no	Sylow
44	C₂²	—	49	1	no	Sylow
45	C₂	—	49	2	no	—
46	C₂	C₁₁⋊C₅×D₄₉	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₉×C₁₁⋊C₅	C₂	semidirect
2. C₁₁⋊C₅×D₄₉	C₂	direct (N × H)
3. C₄₉×C₁₁⋊C₅	C₂²	semidirect
4. C₂×C₁₁×D₄₉	C₅	semidirect
6. C₂×C₁₁×C₄₉	C₂×C₅	semidirect
7. C₁₁×D₄₉	C₂×C₅	semidirect
11. C₁₁×C₄₉	C₂²×C₅	semidirect
18. C₂×D₄₉	C₁₁⋊C₅	direct (N × H)
23. C₂×C₁₁⋊C₅	D₄₉	direct (N × H)
24. C₂×C₄₉	C₂×C₁₁⋊C₅	semidirect
25. D₄₉	C₂×C₁₁⋊C₅	direct (N × H)
29. C₁₁⋊C₅	C₂×D₄₉	direct (N × H)
30. C₄₉	C₂²×C₁₁⋊C₅	semidirect
35. C₂×C₁₁	C₅×D₄₉	semidirect
39. C₁₁	C₂×C₅×D₄₉	semidirect
46. C₂	C₁₁⋊C₅×D₄₉	direct (N × H)

Subgroups — C2×C11⋊C5×D49 #24924703

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₁⋊C₅×D₄₉ #24924703