Subgroups — C₂³×Dic₅₅ #13183453

Order 1760.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₅₅	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₅×C₁₁	C₄	1	8	yes	complemented
4	C₂³×C₅×C₁₁	C₂²	1	7	yes	—
5	C₂×Dic₅₅	C₂²	1	28	yes	direct product factor
6	C₂³×Dic₁₁	—	5	1	no	maximal, Hall
7	C₂²×C₅×C₁₁	C₂×C₄	1	28	yes	complemented
8	C₂²×C₅×C₁₁	C₂³	1	7	yes	—
9	Dic₅₅	C₂³	1	8	yes	direct product factor
10	C₂⁴×C₁₁	D₅	1	1	yes	characteristic
11	C₂²×Dic₁₁	—	5	14	no	—
12	C₂³×Dic₅	—	11	1	no	maximal, Hall
13	C₂×C₅×C₁₁	C₂²×C₄	1	14	yes	complemented
14	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
15	C₂³×C₁₁	Dic₅	1	8	yes	complemented
16	C₂³×C₁₁	C₂×D₅	1	7	yes	—
17	C₂×Dic₁₁	—	5	28	no	—
18	C₂⁴×C₅	D₁₁	1	1	yes	characteristic
19	C₂²×Dic₅	—	11	14	no	—
20	C₅×C₁₁	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₁₁	C₂×Dic₅	1	28	yes	complemented
22	C₂²×C₁₁	C₂²×D₅	1	7	yes	—
23	Dic₁₁	—	5	8	no	—
24	C₂³×C₅	Dic₁₁	1	8	yes	complemented
25	C₂³×C₅	C₂×D₁₁	1	7	yes	—
26	C₂×Dic₅	—	11	28	no	—
27	C₂³×C₄	—	55	1	no	Sylow
28	C₂×C₁₁	C₂²×Dic₅	1	14	yes	complemented
29	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
30	C₂²×C₅	C₂×Dic₁₁	1	28	yes	complemented
31	C₂²×C₅	C₂²×D₁₁	1	7	yes	—
32	Dic₅	—	11	8	no	—
33	C₂⁴	D₅₅	1	1	yes	characteristic
34	C₂²×C₄	—	55	14	no	—
35	C₁₁	C₂³×Dic₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₅	C₂²×Dic₁₁	1	14	yes	complemented
37	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
38	C₂³	Dic₅₅	1	8	yes	direct product factor
39	C₂³	C₂×D₅₅	1	7	yes	—
40	C₂×C₄	—	55	28	no	—
41	C₅	C₂³×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
42	C₂²	C₂×Dic₅₅	1	28	yes	direct product factor
43	C₂²	C₂²×D₅₅	1	7	yes	—
44	C₄	—	55	8	no	—
45	C₂	C₂²×Dic₅₅	1	14	yes	direct product factor
46	C₂	C₂³×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴	D₅₅
commutator, hypocenter	C₅×C₁₁	C₂³×C₄
Frattini	C₂	C₂³×D₅₅
Fitting, socle, prime radical	C₂⁴×C₅×C₁₁	C₂
cosocle	C₂×C₅×C₁₁	C₂⁴
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₅₅	C₂	direct (N × H)
3. C₂³×C₅×C₁₁	C₄	semidirect
5. C₂×Dic₅₅	C₂²	direct (N × H)
7. C₂²×C₅×C₁₁	C₂×C₄	semidirect
9. Dic₅₅	C₂³	direct (N × H)
13. C₂×C₅×C₁₁	C₂²×C₄	semidirect
15. C₂³×C₁₁	Dic₅	semidirect
20. C₅×C₁₁	C₂³×C₄	semidirect
21. C₂²×C₁₁	C₂×Dic₅	semidirect
24. C₂³×C₅	Dic₁₁	semidirect
28. C₂×C₁₁	C₂²×Dic₅	semidirect
30. C₂²×C₅	C₂×Dic₁₁	semidirect
35. C₁₁	C₂³×Dic₅	semidirect
36. C₂×C₅	C₂²×Dic₁₁	semidirect
38. C₂³	Dic₅₅	direct (N × H)
41. C₅	C₂³×Dic₁₁	semidirect
42. C₂²	C₂×Dic₅₅	direct (N × H)
45. C₂	C₂²×Dic₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×C₁₁	2
C₂²×Dic₅₅	2
C₂³×Dic₁₁	5
C₂³×Dic₅	11

Subgroups — C23×Dic55 #13183453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₅₅ #13183453