Subgroups — C₅×#11925890⋊C₂ #27130888

Order 12100.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#11925890	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	—	5	1	no	maximal
5	#11925890⋊C₂	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₅×C₁₁⋊D₁₁	D₅	1	1	yes	characteristic, complemented
7	C₅×C₁₁×D₁₁	—	5	2	no	—
8	#11925893	—	2	2	no	—
9	#11925893	C₂×C₅	1	1	yes	characteristic, complemented
10	#11925890	C₂×C₅	1	2	yes	complemented
11	C₅×C₁₁²	C₂×D₅	1	1	yes	characteristic, complemented
12	#10597245	—	2	2	no	—
13	#10597245	C₂²×C₅	1	1	yes	characteristic, complemented
14	C₅×AGL(1,𝔽₁₁)	—	22	1	no	—
15	D₁₁²	—	5	1	no	Hall
16	C₅×C₁₁⋊C₅	—	22	1	no	—
17	C₁₁⋊D₁₁	C₅×D₅	1	1	yes	characteristic, complemented
18	C₁₁×D₁₁	—	5	2	no	—
19	C₂×C₅×D₁₁	—	55	2	no	—
20	C₁₁²	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₅×C₁₁	—	55	2	no	—
22	C₅×D₁₁	—	5	2	no	—
23	C₅×D₁₁	—	22	1	no	—
24	C₅×D₁₁	—	55	2	no	—
25	AGL(1,𝔽₁₁)	—	22	1	no	—
26	AGL(1,𝔽₁₁)	—	22	4	no	—
27	C₂×C₅×D₅	—	121	1	no	maximal, Hall
28	C₅×C₁₁	—	2	1	no	—
29	C₅×C₁₁	—	5	2	no	—
30	C₁₁⋊C₅	—	22	1	no	—
31	C₁₁⋊C₅	—	22	4	no	—
32	C₂×C₅²	—	121	1	no	—
33	C₅×D₅	—	121	2	no	—
34	C₂×D₁₁	—	55	2	no	—
35	C₅²	—	121	1	no	Sylow
36	C₂×C₁₁	—	55	2	no	—
37	D₁₁	—	5	2	no	—
38	D₁₁	—	22	1	no	—
39	D₁₁	—	55	2	no	—
40	C₂²×C₅	—	605	1	no	—
41	C₂×D₅	—	121	1	no	—
42	C₁₁	—	2	1	no	—
43	C₁₁	—	5	2	no	—
44	C₂×C₅	—	55	2	no	—
45	C₂×C₅	—	121	1	no	—
46	C₂×C₅	—	121	1	no	—
47	C₂×C₅	—	242	2	no	—
48	D₅	—	121	2	no	—
49	C₅	—	121	1	no	—
50	C₅	—	242	2	no	—
51	C₅	#11925890⋊C₂	1	1	yes	characteristic, direct product factor
52	C₂²	—	605	1	no	Sylow
53	C₂	—	55	2	no	—
54	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#11925890⋊C₂
commutator, cosocle, hypocenter	#10597245	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²	C₂×D₅
LCS	G ▷ #10597245
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#11925890	C₂	semidirect
2. C₅×#11925893	C₂	semidirect
3. C₅×#10597245	C₂²	semidirect
5. #11925890⋊C₂	C₅	direct (N × H)
6. C₅×C₁₁⋊D₁₁	D₅	semidirect
9. #11925893	C₂×C₅	semidirect
10. #11925890	C₂×C₅	semidirect
11. C₅×C₁₁²	C₂×D₅	semidirect
13. #10597245	C₂²×C₅	semidirect
17. C₁₁⋊D₁₁	C₅×D₅	semidirect
20. C₁₁²	C₂×C₅×D₅	semidirect
51. C₅	#11925890⋊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×#11925890	2
C₅×#11925893	2
C₅×D₁₁²	5
#11925890⋊C₂	5
C₂×C₅×D₅	121

Subgroups — C5×#11925890⋊C2 #27130888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11925890⋊C₂ #27130888