Subgroups — D₁₁×C₂₅×C₄₉ #41003939

Order 26950.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₅×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₁×C₄₉	C₅	1	1	yes	maximal, characteristic
3	C₇×D₁₁×C₂₅	C₇	1	1	yes	maximal, characteristic
4	C₅×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic
5	C₂×C₂₅×C₄₉	—	11	1	no	maximal, Hall
6	C₇×C₁₁×C₂₅	C₂×C₇	1	1	yes	characteristic
7	C₂₅×C₄₉	D₁₁	1	1	yes	characteristic, direct product factor, Hall
8	D₁₁×C₄₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₇×D₁₁	C₅×C₇	1	1	yes	characteristic
10	D₁₁×C₂₅	C₄₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×C₄₉	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₄₉	—	11	1	no	—
13	C₅×C₇×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic
14	C₂×C₇×C₂₅	—	11	1	no	—
15	C₁₁×C₂₅	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
16	C₅×C₄₉	C₅×D₁₁	1	1	yes	characteristic
17	C₇×C₂₅	C₇×D₁₁	1	1	yes	characteristic
18	C₇×D₁₁	C₇×C₂₅	1	1	yes	characteristic
19	C₅×D₁₁	C₅×C₄₉	1	1	yes	characteristic
20	C₂×C₄₉	—	11	1	no	Hall
21	C₇×C₁₁	C₂×C₇×C₂₅	1	1	yes	characteristic
22	C₂×C₅×C₇	—	11	1	no	—
23	C₅×C₁₁	C₂×C₅×C₄₉	1	1	yes	characteristic
24	C₂×C₂₅	—	11	1	no	Hall
25	C₄₉	D₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₅×C₇	C₅×C₇×D₁₁	1	1	yes	characteristic
27	C₂₅	D₁₁×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
28	D₁₁	C₂₅×C₄₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇	—	11	1	no	—
30	C₁₁	C₂×C₂₅×C₄₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	11	1	no	—
32	C₇	C₇×D₁₁×C₂₅	1	1	yes	characteristic
33	C₅	C₅×D₁₁×C₄₉	1	1	yes	characteristic
34	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₅×C₄₉	D₁₁
commutator, hypocenter	C₁₁	C₂×C₂₅×C₄₉
Frattini	C₅×C₇	C₅×C₇×D₁₁
Fitting	C₁₁×C₂₅×C₄₉	C₂
socle, cosocle	C₅×C₇×C₁₁	C₂×C₅×C₇
prime radical	C₅×C₇×D₁₁	C₅×C₇
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂₅×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₂₅×C₄₉	C₂	semidirect
7. C₂₅×C₄₉	D₁₁	direct (N × H)
8. D₁₁×C₄₉	C₂₅	direct (N × H)
10. D₁₁×C₂₅	C₄₉	direct (N × H)
11. C₁₁×C₄₉	C₂×C₂₅	semidirect
15. C₁₁×C₂₅	C₂×C₄₉	semidirect
25. C₄₉	D₁₁×C₂₅	direct (N × H)
27. C₂₅	D₁₁×C₄₉	direct (N × H)
28. D₁₁	C₂₅×C₄₉	direct (N × H)
30. C₁₁	C₂×C₂₅×C₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₂₅×C₄₉	2
C₅×D₁₁×C₄₉	5
C₇×D₁₁×C₂₅	7
C₂×C₂₅×C₄₉	11

Subgroups — D11×C25×C49 #41003939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×C₂₅×C₄₉ #41003939