Subgroups — C₅×#11925896⋊C₂ #27130885

Order 12100.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#11925896	C₂	1	2	yes	maximal, complemented
2	C₅×#11925893	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#10597245	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₅×D₁₁²	C₅	1	1	yes	maximal, characteristic, complemented
5	#11925896⋊C₂	C₅	1	5	yes	maximal, direct product factor
6	C₅×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₅×C₁₁×D₁₁	C₂×C₅	1	2	yes	complemented
8	#11925896	C₂×C₅	1	10	yes	complemented
9	#11925893	C₂×C₅	1	5	yes	complemented
10	C₂×C₅×AGL(1,𝔽₁₁)	—	11	2	no	maximal
11	C₅×C₁₁²	C₂²×C₅	1	1	yes	characteristic, complemented
12	#10597245	C₂²×C₅	1	5	yes	complemented
13	C₂×C₅×C₁₁⋊C₅	—	11	2	no	—
14	C₅×AGL(1,𝔽₁₁)	—	11	2	no	—
15	C₅×AGL(1,𝔽₁₁)	—	11	2	no	—
16	D₁₁²	C₅²	1	1	yes	characteristic, complemented, Hall
17	C₅×C₁₁⋊C₅	—	11	2	no	—
18	C₁₁⋊D₁₁	C₂×C₅²	1	1	yes	characteristic, complemented
19	C₁₁×D₁₁	C₂×C₅²	1	2	yes	complemented
20	C₂×C₅×D₁₁	—	11	2	no	—
21	C₂×AGL(1,𝔽₁₁)	—	11	10	no	—
22	C₁₁²	C₂²×C₅²	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₅×C₁₁	—	11	2	no	—
24	C₅×D₁₁	—	11	2	no	—
25	C₅×D₁₁	—	110	1	no	—
26	C₅×D₁₁	AGL(1,𝔽₁₁)	1	2	yes	complemented
27	C₂×C₁₁⋊C₅	—	11	10	no	—
28	AGL(1,𝔽₁₁)	—	11	10	no	—
29	AGL(1,𝔽₁₁)	—	11	10	no	—
30	C₂²×C₅²	—	121	1	no	Hall
31	C₅×C₁₁	—	10	1	no	—
32	C₅×C₁₁	C₂×AGL(1,𝔽₁₁)	1	2	yes	complemented
33	C₁₁⋊C₅	—	11	10	no	—
34	C₂×C₅²	—	121	2	no	—
35	C₂×C₅²	—	121	1	no	—
36	C₂×D₁₁	—	11	2	no	—
37	C₅²	—	121	1	no	Sylow
38	C₂×C₁₁	—	11	2	no	—
39	D₁₁	—	11	2	no	—
40	D₁₁	—	110	1	no	—
41	D₁₁	C₅×AGL(1,𝔽₁₁)	1	2	yes	complemented
42	C₂²×C₅	—	121	1	no	—
43	C₂²×C₅	—	121	5	no	—
44	C₁₁	—	10	1	no	—
45	C₁₁	C₂×C₅×AGL(1,𝔽₁₁)	1	2	yes	complemented
46	C₂×C₅	—	11	2	no	—
47	C₂×C₅	—	121	10	no	—
48	C₂×C₅	—	121	5	no	—
49	C₂×C₅	—	121	1	no	—
50	C₅	—	121	5	no	—
51	C₅	#11925896⋊C₂	1	1	yes	characteristic, direct product factor
52	C₂²	—	121	1	no	Sylow
53	C₂	—	11	2	no	—
54	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#11925896⋊C₂
commutator, cosocle, hypocenter	C₁₁²	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²	C₂²×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#11925896	C₂	semidirect
2. C₅×#11925893	C₂	semidirect
3. C₅×#10597245	C₂²	semidirect
4. C₅×D₁₁²	C₅	semidirect
5. #11925896⋊C₂	C₅	direct (N × H)
6. C₅×C₁₁⋊D₁₁	C₂×C₅	semidirect
7. C₅×C₁₁×D₁₁	C₂×C₅	semidirect
8. #11925896	C₂×C₅	semidirect
9. #11925893	C₂×C₅	semidirect
11. C₅×C₁₁²	C₂²×C₅	semidirect
12. #10597245	C₂²×C₅	semidirect
16. D₁₁²	C₅²	semidirect
18. C₁₁⋊D₁₁	C₂×C₅²	semidirect
19. C₁₁×D₁₁	C₂×C₅²	semidirect
22. C₁₁²	C₂²×C₅²	semidirect
26. C₅×D₁₁	AGL(1,𝔽₁₁)	semidirect
32. C₅×C₁₁	C₂×AGL(1,𝔽₁₁)	semidirect
41. D₁₁	C₅×AGL(1,𝔽₁₁)	semidirect
45. C₁₁	C₂×C₅×AGL(1,𝔽₁₁)	semidirect
51. C₅	#11925896⋊C₂	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×#11925896	2
C₅×#11925893	2
C₅×D₁₁²	5
#11925896⋊C₂	5
C₂×C₅×AGL(1,𝔽₁₁)	11

Subgroups — C5×#11925896⋊C2 #27130885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11925896⋊C₂ #27130885