Subgroups — C₅²×C₁₁×D₄₉ #41003956

Order 26950.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₁×C₄₉	C₂	semidirect
2. C₅×C₁₁×D₄₉	C₅	direct (N × H)
4. C₅×C₁₁×C₄₉	C₂×C₅	semidirect
5. C₅²×D₄₉	C₁₁	direct (N × H)
7. C₅²×C₄₉	C₂×C₁₁	semidirect
8. C₁₁×D₄₉	C₅²	direct (N × H)
11. C₁₁×C₄₉	C₂×C₅²	semidirect
12. C₅×D₄₉	C₅×C₁₁	direct (N × H)
15. C₅²×C₁₁	D₄₉	direct (N × H)
16. C₅×C₄₉	C₂×C₅×C₁₁	semidirect
20. D₄₉	C₅²×C₁₁	direct (N × H)
23. C₅×C₁₁	C₅×D₄₉	direct (N × H)
25. C₄₉	C₂×C₅²×C₁₁	semidirect
27. C₅²	C₁₁×D₄₉	direct (N × H)
30. C₁₁	C₅²×D₄₉	direct (N × H)
33. C₅	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
C₅²×C₁₁×C₄₉	2
C₅×C₁₁×D₄₉	5
C₅²×C₁₁×D₇	7
C₅²×D₄₉	11

Subgroups — C52×C11×D49 #41003956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₁₁×D₄₉ #41003956