Subgroups — C₄³×C₅×C₁₁ #72183178

Order 3520.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅×C₁₁	C₂	1	7	yes	maximal
2	C₂²×C₄×C₅×C₁₁	C₂²	1	7	yes	—
3	C₄²×C₅×C₁₁	C₄	1	28	yes	direct product factor
4	C₄³×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₅×C₁₁	C₂³	1	1	yes	characteristic
6	C₂×C₄×C₅×C₁₁	C₂×C₄	1	42	yes	—
7	C₂×C₄²×C₁₁	C₂×C₅	1	7	yes	—
8	C₄³×C₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅×C₁₁	C₂²×C₄	1	7	yes	—
10	C₄×C₅×C₁₁	C₄²	1	28	yes	direct product factor
11	C₂²×C₄×C₁₁	C₂²×C₅	1	7	yes	—
12	C₄²×C₁₁	C₄×C₅	1	28	yes	direct product factor
13	C₂×C₄²×C₅	C₂×C₁₁	1	7	yes	—
14	C₂×C₅×C₁₁	C₂×C₄²	1	7	yes	—
15	C₂³×C₁₁	C₂³×C₅	1	1	yes	characteristic
16	C₂×C₄×C₁₁	C₂×C₄×C₅	1	42	yes	—
17	C₂²×C₄×C₅	C₂²×C₁₁	1	7	yes	—
18	C₄²×C₅	C₄×C₁₁	1	28	yes	direct product factor
19	C₄³	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₅×C₁₁	C₄³	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₁₁	C₂²×C₄×C₅	1	7	yes	—
22	C₄×C₁₁	C₄²×C₅	1	28	yes	direct product factor
23	C₂³×C₅	C₂³×C₁₁	1	1	yes	characteristic
24	C₂×C₄×C₅	C₂×C₄×C₁₁	1	42	yes	—
25	C₂×C₄²	C₂×C₅×C₁₁	1	7	yes	—
26	C₂×C₁₁	C₂×C₄²×C₅	1	7	yes	—
27	C₂²×C₅	C₂²×C₄×C₁₁	1	7	yes	—
28	C₄×C₅	C₄²×C₁₁	1	28	yes	direct product factor
29	C₂²×C₄	C₂²×C₅×C₁₁	1	7	yes	—
30	C₄²	C₄×C₅×C₁₁	1	28	yes	direct product factor
31	C₁₁	C₄³×C₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₅	C₂×C₄²×C₁₁	1	7	yes	—
33	C₂³	C₂³×C₅×C₁₁	1	1	yes	characteristic
34	C₂×C₄	C₂×C₄×C₅×C₁₁	1	42	yes	—
35	C₅	C₄³×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₂²×C₄×C₅×C₁₁	1	7	yes	—
37	C₄	C₄²×C₅×C₁₁	1	28	yes	direct product factor
38	C₂	C₂×C₄²×C₅×C₁₁	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂³×C₅×C₁₁
socle, prime radical	C₂³×C₅×C₁₁	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄²×C₅×C₁₁	C₄	direct (N × H)
4. C₄³×C₁₁	C₅	direct (N × H)
8. C₄³×C₅	C₁₁	direct (N × H)
10. C₄×C₅×C₁₁	C₄²	direct (N × H)
12. C₄²×C₁₁	C₄×C₅	direct (N × H)
18. C₄²×C₅	C₄×C₁₁	direct (N × H)
19. C₄³	C₅×C₁₁	direct (N × H)
20. C₅×C₁₁	C₄³	direct (N × H)
22. C₄×C₁₁	C₄²×C₅	direct (N × H)
28. C₄×C₅	C₄²×C₁₁	direct (N × H)
30. C₄²	C₄×C₅×C₁₁	direct (N × H)
31. C₁₁	C₄³×C₅	direct (N × H)
35. C₅	C₄³×C₁₁	direct (N × H)
37. C₄	C₄²×C₅×C₁₁	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×C₄²×C₅×C₁₁	2
C₄³×C₁₁	5
C₄³×C₅	11

Subgroups — C43×C5×C11 #72183178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×C₅×C₁₁ #72183178