Subgroups — C₄×C₅×#10597243 #27130865

Order 12100.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#10597243	C₂	1	1	yes	maximal, characteristic
2	C₅×#10597243	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×#10597243	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×#10597243	C₂×C₅	1	5	yes	—
7	C₄×C₅×C₁₁⋊C₅	—	11	12	no	maximal
8	C₅×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented
9	#10597243	C₄×C₅	1	5	yes	direct product factor
10	C₂×C₅×C₁₁⋊C₅	—	11	12	no	—
11	C₄×C₁₁²	C₅²	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₁⋊C₅	—	11	12	no	—
13	C₂×C₁₁²	C₂×C₅²	1	1	yes	characteristic
14	C₄×C₅×C₁₁	C₁₁⋊C₅	1	12	yes	complemented
15	C₄×C₁₁⋊C₅	—	11	60	no	—
16	C₁₁²	C₄×C₅²	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₅×C₁₁	C₂×C₁₁⋊C₅	1	12	yes	—
18	C₂×C₁₁⋊C₅	—	11	60	no	—
19	C₄×C₅²	—	121	1	no	Hall
20	C₅×C₁₁	C₄×C₁₁⋊C₅	1	12	yes	complemented
21	C₁₁⋊C₅	—	11	60	no	—
22	C₂×C₅²	—	121	1	no	—
23	C₄×C₁₁	C₅×C₁₁⋊C₅	1	12	yes	complemented
24	C₅²	—	121	1	no	Sylow
25	C₂×C₁₁	C₂×C₅×C₁₁⋊C₅	1	12	yes	—
26	C₄×C₅	—	121	5	no	—
27	C₄×C₅	#10597243	1	1	yes	characteristic, direct product factor
28	C₁₁	C₄×C₅×C₁₁⋊C₅	1	12	yes	complemented
29	C₂×C₅	—	121	5	no	—
30	C₂×C₅	C₂×#10597243	1	1	yes	characteristic
31	C₅	—	121	5	no	—
32	C₅	C₄×#10597243	1	1	yes	characteristic, direct product factor
33	C₄	C₅×#10597243	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅×#10597243	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅	#10597243
commutator, hypocenter	C₁₁²	C₄×C₅²
Frattini	C₂	C₂×C₅×#10597243
Fitting	C₄×C₅×C₁₁²	C₅
socle	C₂×C₅×C₁₁²	C₂×C₅
prime radical	C₂×C₅×#10597243	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×#10597243	C₄	direct (N × H)
3. C₄×#10597243	C₅	direct (N × H)
4. C₄×C₅×C₁₁²	C₅	semidirect
8. C₅×C₁₁²	C₄×C₅	semidirect
9. #10597243	C₄×C₅	direct (N × H)
11. C₄×C₁₁²	C₅²	semidirect
14. C₄×C₅×C₁₁	C₁₁⋊C₅	semidirect
16. C₁₁²	C₄×C₅²	semidirect
20. C₅×C₁₁	C₄×C₁₁⋊C₅	semidirect
23. C₄×C₁₁	C₅×C₁₁⋊C₅	semidirect
27. C₄×C₅	#10597243	direct (N × H)
28. C₁₁	C₄×C₅×C₁₁⋊C₅	semidirect
32. C₅	C₄×#10597243	direct (N × H)
33. C₄	C₅×#10597243	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×#10597243	2
C₄×#10597243	5
C₄×C₅×C₁₁²	5
C₄×C₅×C₁₁⋊C₅	11

Subgroups — C4×C5×#10597243 #27130865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#10597243 #27130865