Subgroups — C₅×#14559049 #27130848

Order 12100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#10597245	C₂	1	1	yes	maximal, characteristic
2	C₅×#10597245	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×C₁₁×Dic₁₁	—	5	1	no	maximal
4	#14559049	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₅×C₁₁²	D₅	1	1	yes	characteristic
6	C₂×#10597245	—	2	2	no	—
7	C₂×#10597245	C₂×C₅	1	1	yes	characteristic
8	C₅×C₁₁²	Dic₅	1	1	yes	characteristic, complemented
9	#10597245	—	2	2	no	—
10	#10597245	C₄×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₁₁⋊C₅	—	22	1	no	—
12	C₁₁×Dic₁₁	—	5	1	no	Hall
13	C₅×C₁₁⋊C₅	—	22	1	no	—
14	C₂×C₁₁²	C₅×D₅	1	1	yes	characteristic
15	C₄×C₅×C₁₁	—	55	1	no	—
16	C₅×Dic₁₁	—	5	1	no	—
17	C₁₁²	C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅×C₁₁	—	2	1	no	—
19	C₂×C₅×C₁₁	—	5	1	no	—
20	C₂×C₅×C₁₁	—	5	1	no	—
21	C₂×C₁₁⋊C₅	—	22	1	no	—
22	C₂×C₁₁⋊C₅	—	22	4	no	—
23	C₅×Dic₅	—	121	1	no	maximal, Hall
24	C₅×C₁₁	—	2	1	no	—
25	C₅×C₁₁	—	5	1	no	—
26	C₅×C₁₁	—	5	1	no	—
27	C₁₁⋊C₅	—	22	1	no	—
28	C₁₁⋊C₅	—	22	4	no	—
29	C₂×C₅²	—	121	1	no	—
30	C₄×C₁₁	—	55	1	no	—
31	Dic₁₁	—	5	1	no	—
32	C₅²	—	121	1	no	Sylow
33	C₂×C₁₁	—	2	1	no	—
34	C₂×C₁₁	—	5	1	no	—
35	C₂×C₁₁	—	5	1	no	—
36	C₄×C₅	—	55	1	no	—
37	Dic₅	—	121	1	no	—
38	C₁₁	—	2	1	no	—
39	C₁₁	—	5	1	no	—
40	C₁₁	—	5	1	no	—
41	C₂×C₅	—	121	1	no	—
42	C₂×C₅	—	242	2	no	—
43	C₂×C₅	#11925890	1	1	yes	characteristic
44	C₅	—	121	1	no	—
45	C₅	—	242	2	no	—
46	C₅	#14559049	1	1	yes	characteristic, direct product factor
47	C₄	—	55	1	no	Sylow
48	C₂	C₅×#11925890	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	#11925890
commutator, hypocenter	#10597245	C₄×C₅
Frattini	C₂	C₅×#11925890
Fitting, socle	C₂×C₅×C₁₁²	D₅
prime radical	C₂×C₅×#10597245	C₂
cosocle	C₂×#10597245	C₂×C₅
LCS	G ▷ #10597245
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#10597245	C₄	semidirect
4. #14559049	C₅	direct (N × H)
8. C₅×C₁₁²	Dic₅	semidirect
10. #10597245	C₄×C₅	semidirect
17. C₁₁²	C₅×Dic₅	semidirect
46. C₅	#14559049	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#10597245	2
C₅×C₁₁×Dic₁₁	5
#14559049	5
C₅×Dic₅	121

Subgroups — C5×#14559049 #27130848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#14559049 #27130848