Subgroups — C₂×C₁₁×C₂⁴⋊C₅ #13183468

Order 1760.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂⁴⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂⁵×C₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂⁴×C₁₁	—	5	3	no	—
4	C₂⁴×C₁₁	—	5	3	no	—
5	C₂⁴×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
6	C₂×C₂⁴⋊C₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₁₁	—	16	1	no	maximal
8	C₂³×C₁₁	—	5	3	no	—
9	C₂³×C₁₁	—	5	6	no	—
10	C₂³×C₁₁	—	5	6	no	—
11	C₂³×C₁₁	—	5	12	no	—
12	C₂³×C₁₁	—	5	3	no	—
13	C₂³×C₁₁	—	5	1	no	—
14	C₂⁴⋊C₅	C₂×C₁₁	1	1	yes	characteristic, direct product factor
15	C₅×C₁₁	—	16	1	no	Hall
16	C₂²×C₁₁	—	5	6	no	—
17	C₂²×C₁₁	—	5	6	no	—
18	C₂²×C₁₁	—	5	1	no	—
19	C₂²×C₁₁	—	5	3	no	—
20	C₂²×C₁₁	—	5	12	no	—
21	C₂²×C₁₁	—	5	3	no	—
22	C₂⁵	C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₁	—	5	3	no	—
24	C₂×C₁₁	—	5	3	no	—
25	C₂×C₁₁	C₂⁴⋊C₅	1	1	yes	characteristic, direct product factor
26	C₂⁴	—	5	3	no	—
27	C₂⁴	—	5	3	no	—
28	C₂⁴	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
29	C₁₁	C₂×C₂⁴⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₅	—	16	1	no	—
31	C₂³	—	5	3	no	—
32	C₂³	—	5	6	no	—
33	C₂³	—	5	6	no	—
34	C₂³	—	5	12	no	—
35	C₂³	—	5	3	no	—
36	C₂³	—	5	1	no	—
37	C₅	—	16	1	no	Sylow
38	C₂²	—	5	6	no	—
39	C₂²	—	5	6	no	—
40	C₂²	—	5	1	no	—
41	C₂²	—	5	3	no	—
42	C₂²	—	5	12	no	—
43	C₂²	—	5	3	no	—
44	C₂	—	5	3	no	—
45	C₂	—	5	3	no	—
46	C₂	C₁₁×C₂⁴⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	C₂⁴⋊C₅
commutator, cosocle, hypocenter	C₂⁴	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₁	C₅
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₂⁴⋊C₅	C₂	direct (N × H)
2. C₂⁵×C₁₁	C₅	semidirect
5. C₂⁴×C₁₁	C₂×C₅	semidirect
6. C₂×C₂⁴⋊C₅	C₁₁	direct (N × H)
14. C₂⁴⋊C₅	C₂×C₁₁	direct (N × H)
22. C₂⁵	C₅×C₁₁	semidirect
25. C₂×C₁₁	C₂⁴⋊C₅	direct (N × H)
28. C₂⁴	C₂×C₅×C₁₁	semidirect
29. C₁₁	C₂×C₂⁴⋊C₅	direct (N × H)
46. C₂	C₁₁×C₂⁴⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₂⁴⋊C₅	2
C₂⁵×C₁₁	5
C₂×C₂⁴⋊C₅	11
C₂×C₅×C₁₁	16

Subgroups — C2×C11×C24⋊C5 #13183468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₂⁴⋊C₅ #13183468