Subgroups — C₄×C₅×#10597245 #27130866

Order 12100.

108 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, direct product factor, Hall
3	C₄×#10597245	C₅	1	5	yes	maximal, direct product factor
4	C₄×C₅×C₁₁²	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic
6	C₂×#10597245	C₂×C₅	1	5	yes	—
7	C₄×C₅×C₁₁⋊C₅	—	11	2	no	maximal
8	C₅×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented
9	#10597245	C₄×C₅	1	5	yes	direct product factor
10	C₂×C₅×C₁₁⋊C₅	—	11	2	no	—
11	C₄×C₁₁²	C₅²	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₁⋊C₅	—	11	2	no	—
13	C₂×C₁₁²	C₂×C₅²	1	1	yes	characteristic
14	C₄×C₅×C₁₁	—	5	2	no	—
15	C₄×C₅×C₁₁	C₁₁⋊C₅	1	2	yes	complemented
16	C₄×C₁₁⋊C₅	—	11	10	no	—
17	C₁₁²	C₄×C₅²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅×C₁₁	—	5	2	no	—
19	C₂×C₅×C₁₁	C₂×C₁₁⋊C₅	1	2	yes	—
20	C₂×C₁₁⋊C₅	—	11	10	no	—
21	C₄×C₅²	—	121	1	no	Hall
22	C₅×C₁₁	—	5	2	no	—
23	C₅×C₁₁	C₄×C₁₁⋊C₅	1	2	yes	complemented
24	C₁₁⋊C₅	—	11	10	no	—
25	C₂×C₅²	—	121	1	no	—
26	C₄×C₁₁	—	5	2	no	—
27	C₄×C₁₁	C₅×C₁₁⋊C₅	1	2	yes	complemented
28	C₅²	—	121	1	no	Sylow
29	C₂×C₁₁	—	5	2	no	—
30	C₂×C₁₁	C₂×C₅×C₁₁⋊C₅	1	2	yes	—
31	C₄×C₅	—	121	5	no	—
32	C₄×C₅	#10597245	1	1	yes	characteristic, direct product factor
33	C₁₁	—	5	2	no	—
34	C₁₁	C₄×C₅×C₁₁⋊C₅	1	2	yes	complemented
35	C₂×C₅	—	121	5	no	—
36	C₂×C₅	C₂×#10597245	1	1	yes	characteristic
37	C₅	—	121	5	no	—
38	C₅	C₄×#10597245	1	1	yes	characteristic, direct product factor
39	C₄	C₅×#10597245	1	1	yes	characteristic, direct product factor, Sylow
40	C₂	C₂×C₅×#10597245	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅	#10597245
commutator, hypocenter	C₁₁²	C₄×C₅²
Frattini	C₂	C₂×C₅×#10597245
Fitting	C₄×C₅×C₁₁²	C₅
socle	C₂×C₅×C₁₁²	C₂×C₅
prime radical	C₂×C₅×#10597245	C₂
cosocle	C₂×C₁₁²	C₂×C₅²
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#10597245	C₄	direct (N × H)
3. C₄×#10597245	C₅	direct (N × H)
4. C₄×C₅×C₁₁²	C₅	semidirect
8. C₅×C₁₁²	C₄×C₅	semidirect
9. #10597245	C₄×C₅	direct (N × H)
11. C₄×C₁₁²	C₅²	semidirect
15. C₄×C₅×C₁₁	C₁₁⋊C₅	semidirect
17. C₁₁²	C₄×C₅²	semidirect
23. C₅×C₁₁	C₄×C₁₁⋊C₅	semidirect
27. C₄×C₁₁	C₅×C₁₁⋊C₅	semidirect
32. C₄×C₅	#10597245	direct (N × H)
34. C₁₁	C₄×C₅×C₁₁⋊C₅	semidirect
38. C₅	C₄×#10597245	direct (N × H)
39. C₄	C₅×#10597245	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
C₄×#10597245	5
C₄×C₅×C₁₁²	5
C₄×C₅×C₁₁⋊C₅	11

Subgroups — C4×C5×#10597245 #27130866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#10597245 #27130866