Subgroups — C₅×C₁₁⋊C₅×D₄₉ #41003949

Order 26950.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₄₉	C₅	1	1	yes	maximal, characteristic, complemented
3	C₁₁⋊C₅×D₄₉	C₅	1	5	yes	maximal, direct product factor
4	C₅×D₇×C₁₁⋊C₅	—	7	1	no	maximal
5	C₄₉×C₁₁⋊C₅	C₂×C₅	1	5	yes	complemented
6	C₅×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented
7	C₅²×D₄₉	—	11	1	no	maximal, Hall
8	C₅×C₇×C₁₁⋊C₅	D₇	1	1	yes	characteristic
9	C₅²×C₄₉	—	11	1	no	Hall
10	C₁₁×D₄₉	C₅²	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₁×D₇	—	7	1	no	—
12	D₇×C₁₁⋊C₅	—	7	5	no	—
13	C₂×C₅×C₁₁⋊C₅	—	49	1	no	Hall
14	C₁₁×C₄₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
15	C₅×D₄₉	—	11	5	no	—
16	C₅×D₄₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
17	C₅×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic
18	C₇×C₁₁⋊C₅	C₅×D₇	1	5	yes	—
19	C₅²×D₇	—	77	1	no	—
20	C₅×C₁₁⋊C₅	D₄₉	1	1	yes	characteristic, direct product factor, Hall
21	C₅×C₄₉	—	11	5	no	—
22	C₅×C₄₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
23	C₅²×C₇	—	11	1	no	—
24	C₁₁×D₇	—	7	1	no	—
25	C₂×C₅×C₁₁	—	49	1	no	—
26	C₂×C₁₁⋊C₅	—	49	5	no	—
27	D₄₉	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₁₁	C₅²×D₇	1	1	yes	characteristic
29	C₅×D₇	—	7	1	no	—
30	C₅×D₇	—	77	5	no	—
31	C₅×C₁₁	C₅×D₄₉	1	1	yes	characteristic, complemented
32	C₁₁⋊C₅	C₅×D₄₉	1	5	yes	direct product factor
33	C₂×C₅²	—	539	1	no	Hall
34	C₄₉	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
35	C₅×C₇	—	11	5	no	—
36	C₅×C₇	D₇×C₁₁⋊C₅	1	1	yes	characteristic
37	C₅²	—	11	1	no	Sylow
38	C₂×C₁₁	—	49	1	no	Hall
39	D₇	—	7	1	no	—
40	C₁₁	C₅²×D₄₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	539	5	no	—
42	C₂×C₅	—	49	1	no	—
43	C₇	C₅×D₇×C₁₁⋊C₅	1	1	yes	characteristic
44	C₅	—	11	5	no	—
45	C₅	C₁₁⋊C₅×D₄₉	1	1	yes	characteristic, direct product factor
46	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊C₅×D₄₉
commutator, cosocle, hypocenter	C₁₁×C₄₉	C₂×C₅²
Frattini	C₇	C₅×D₇×C₁₁⋊C₅
Fitting	C₅×C₁₁×C₄₉	C₂×C₅
socle	C₅×C₇×C₁₁	C₅×D₇
LCS	G ▷ C₁₁×C₄₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₄₉×C₁₁⋊C₅	C₂	semidirect
2. C₅×C₁₁×D₄₉	C₅	semidirect
3. C₁₁⋊C₅×D₄₉	C₅	direct (N × H)
5. C₄₉×C₁₁⋊C₅	C₂×C₅	semidirect
6. C₅×C₁₁×C₄₉	C₂×C₅	semidirect
10. C₁₁×D₄₉	C₅²	semidirect
14. C₁₁×C₄₉	C₂×C₅²	semidirect
16. C₅×D₄₉	C₁₁⋊C₅	direct (N × H)
20. C₅×C₁₁⋊C₅	D₄₉	direct (N × H)
22. C₅×C₄₉	C₂×C₁₁⋊C₅	semidirect
27. D₄₉	C₅×C₁₁⋊C₅	direct (N × H)
31. C₅×C₁₁	C₅×D₄₉	semidirect
32. C₁₁⋊C₅	C₅×D₄₉	direct (N × H)
34. C₄₉	C₂×C₅×C₁₁⋊C₅	semidirect
40. C₁₁	C₅²×D₄₉	semidirect
45. C₅	C₁₁⋊C₅×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
C₅×C₄₉×C₁₁⋊C₅	2
C₅×C₁₁×D₄₉	5
C₁₁⋊C₅×D₄₉	5
C₅×D₇×C₁₁⋊C₅	7
C₅²×D₄₉	11

Subgroups — C5×C11⋊C5×D49 #41003949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁⋊C₅×D₄₉ #41003949