Subgroups — C₄²×D₅₅ #13183170

Order 1760.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅₅	C₂	1	3	yes	maximal
2	C₄²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₅₅	C₂	1	3	yes	maximal, complemented
4	C₂²×D₅₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
6	C₂×Dic₅₅	C₂²	1	3	yes	—
7	C₄×D₅₅	C₄	1	12	yes	direct product factor
8	C₄²×D₁₁	—	5	1	no	maximal, Hall
9	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
10	C₂×D₅₅	C₂×C₄	1	6	yes	—
11	C₄×C₅×C₁₁	C₂×C₄	1	6	yes	complemented
12	Dic₅₅	C₂×C₄	1	6	yes	complemented
13	C₂×C₄×D₁₁	—	5	3	no	—
14	C₄²×C₁₁	D₅	1	1	yes	characteristic, complemented
15	C₄×Dic₁₁	—	5	3	no	—
16	C₄²×D₅	—	11	1	no	maximal, Hall
17	C₂×C₅×C₁₁	C₂²×C₄	1	3	yes	—
18	D₅₅	C₄²	1	4	yes	direct product factor
19	C₂²×D₁₁	—	5	1	no	—
20	C₂×C₄×C₁₁	C₂×D₅	1	3	yes	—
21	C₂×Dic₁₁	—	5	3	no	—
22	C₄×D₁₁	—	5	12	no	—
23	C₂×C₄×D₅	—	11	3	no	—
24	C₄²×C₅	D₁₁	1	1	yes	characteristic, complemented
25	C₄×Dic₅	—	11	3	no	—
26	C₅×C₁₁	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
28	C₂×D₁₁	—	5	6	no	—
29	C₄×C₁₁	C₄×D₅	1	6	yes	complemented
30	Dic₁₁	—	5	6	no	—
31	C₂²×D₅	—	11	1	no	—
32	C₂×C₄×C₅	C₂×D₁₁	1	3	yes	—
33	C₂×Dic₅	—	11	3	no	—
34	C₄×D₅	—	11	12	no	—
35	C₂×C₄²	—	55	1	no	Sylow
36	C₂×C₁₁	C₂×C₄×D₅	1	3	yes	—
37	D₁₁	—	5	4	no	—
38	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
39	C₂×D₅	—	11	6	no	—
40	C₄×C₅	C₄×D₁₁	1	6	yes	complemented
41	Dic₅	—	11	6	no	—
42	C₂²×C₄	—	55	3	no	—
43	C₄²	—	55	3	no	—
44	C₄²	D₅₅	1	1	yes	characteristic, direct product factor
45	C₁₁	C₄²×D₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₅	C₂×C₄×D₁₁	1	3	yes	—
47	D₅	—	11	4	no	—
48	C₂³	—	55	1	no	—
49	C₂×C₄	—	55	3	no	—
50	C₂×C₄	—	55	12	no	—
51	C₂×C₄	C₂×D₅₅	1	3	yes	—
52	C₅	C₄²×D₁₁	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	55	6	no	—
54	C₂²	C₂²×D₅₅	1	1	yes	characteristic
55	C₄	—	55	6	no	—
56	C₄	C₄×D₅₅	1	6	yes	direct product factor
57	C₂	—	55	4	no	—
58	C₂	C₂×C₄×D₅₅	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₄²	D₅₅
commutator, hypocenter	C₅×C₁₁	C₂×C₄²
Frattini	C₂²	C₂²×D₅₅
Fitting	C₄²×C₅×C₁₁	C₂
socle, cosocle	C₂²×C₅×C₁₁	C₂³
prime radical	C₂²×D₅₅	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄²×C₅×C₁₁	C₂	semidirect
3. C₄×Dic₅₅	C₂	semidirect
7. C₄×D₅₅	C₄	direct (N × H)
11. C₄×C₅×C₁₁	C₂×C₄	semidirect
12. Dic₅₅	C₂×C₄	semidirect
14. C₄²×C₁₁	D₅	semidirect
18. D₅₅	C₄²	direct (N × H)
24. C₄²×C₅	D₁₁	semidirect
26. C₅×C₁₁	C₂×C₄²	semidirect
29. C₄×C₁₁	C₄×D₅	semidirect
40. C₄×C₅	C₄×D₁₁	semidirect
44. C₄²	D₅₅	direct (N × H)
45. C₁₁	C₄²×D₅	semidirect
52. C₅	C₄²×D₁₁	semidirect
56. C₄	C₄×D₅₅	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×C₄×D₅₅	2
C₄²×C₅×C₁₁	2
C₄×Dic₅₅	2
C₄²×D₁₁	5
C₄²×D₅	11

Subgroups — C42×D55 #13183170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×D₅₅ #13183170