Subgroups — C₂²×C₄×D₅₅ #13183441

Order 1760.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₅₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Dic₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₅₅	C₂	1	12	yes	maximal, direct product factor
5	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×D₅₅	C₄	1	8	yes	direct product factor
7	C₂²×D₅₅	C₂²	1	6	yes	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	6	yes	complemented
9	C₂×Dic₅₅	C₂²	1	6	yes	complemented
10	C₄×D₅₅	C₂²	1	16	yes	direct product factor
11	C₂²×C₄×D₁₁	—	5	1	no	maximal, Hall
12	C₂²×C₅×C₁₁	C₂×C₄	1	4	yes	complemented
13	C₂²×C₅×C₁₁	C₂³	1	3	yes	—
14	C₂×D₅₅	C₂×C₄	1	24	yes	direct product factor
15	C₂×D₅₅	C₂³	1	4	yes	—
16	C₄×C₅×C₁₁	C₂³	1	4	yes	complemented
17	Dic₅₅	C₂³	1	4	yes	complemented
18	C₂³×D₁₁	—	5	1	no	—
19	C₂²×C₄×C₁₁	D₅	1	1	yes	characteristic, complemented
20	C₂²×Dic₁₁	—	5	1	no	—
21	C₂×C₄×D₁₁	—	5	12	no	—
22	C₂²×C₄×D₅	—	11	1	no	maximal, Hall
23	C₂×C₅×C₁₁	C₂²×C₄	1	6	yes	complemented
24	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
25	D₅₅	C₂²×C₄	1	8	yes	direct product factor
26	C₂³×C₁₁	C₂×D₅	1	1	yes	characteristic
27	C₂²×D₁₁	—	5	8	no	—
28	C₂²×D₁₁	—	5	6	no	—
29	C₂×C₄×C₁₁	C₂×D₅	1	6	yes	complemented
30	C₂×Dic₁₁	—	5	6	no	—
31	C₄×D₁₁	—	5	16	no	—
32	C₂³×D₅	—	11	1	no	—
33	C₂²×C₄×C₅	D₁₁	1	1	yes	characteristic, complemented
34	C₂²×Dic₅	—	11	1	no	—
35	C₂×C₄×D₅	—	11	12	no	—
36	C₅×C₁₁	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₁₁	C₄×D₅	1	4	yes	complemented
38	C₂²×C₁₁	C₂²×D₅	1	3	yes	—
39	C₂×D₁₁	—	5	24	no	—
40	C₂×D₁₁	—	5	4	no	—
41	C₄×C₁₁	C₂²×D₅	1	4	yes	complemented
42	Dic₁₁	—	5	4	no	—
43	C₂³×C₅	C₂×D₁₁	1	1	yes	characteristic
44	C₂²×D₅	—	11	6	no	—
45	C₂²×D₅	—	11	8	no	—
46	C₂×C₄×C₅	C₂×D₁₁	1	6	yes	complemented
47	C₂×Dic₅	—	11	6	no	—
48	C₄×D₅	—	11	16	no	—
49	C₂³×C₄	—	55	1	no	Sylow
50	C₂×C₁₁	C₂×C₄×D₅	1	6	yes	complemented
51	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
52	D₁₁	—	5	8	no	—
53	C₂²×C₅	C₄×D₁₁	1	4	yes	complemented
54	C₂²×C₅	C₂²×D₁₁	1	3	yes	—
55	C₂×D₅	—	11	24	no	—
56	C₂×D₅	—	11	4	no	—
57	C₄×C₅	C₂²×D₁₁	1	4	yes	complemented
58	Dic₅	—	11	4	no	—
59	C₂⁴	—	55	1	no	—
60	C₂²×C₄	—	55	1	no	—
61	C₂²×C₄	—	55	12	no	—
62	C₂²×C₄	D₅₅	1	1	yes	characteristic, direct product factor
63	C₁₁	C₂²×C₄×D₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	C₂×C₄×D₁₁	1	6	yes	complemented
65	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
66	D₅	—	11	8	no	—
67	C₂³	—	55	8	no	—
68	C₂³	—	55	6	no	—
69	C₂³	C₂×D₅₅	1	1	yes	characteristic
70	C₂×C₄	—	55	6	no	—
71	C₂×C₄	—	55	16	no	—
72	C₂×C₄	C₂×D₅₅	1	6	yes	direct product factor
73	C₅	C₂²×C₄×D₁₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	55	24	no	—
75	C₂²	—	55	4	no	—
76	C₂²	C₄×D₅₅	1	4	yes	direct product factor
77	C₂²	C₂²×D₅₅	1	3	yes	—
78	C₄	—	55	4	no	—
79	C₄	C₂²×D₅₅	1	4	yes	direct product factor
80	C₂	—	55	8	no	—
81	C₂	C₂×C₄×D₅₅	1	6	yes	direct product factor
82	C₂	C₂³×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₅₅
commutator, hypocenter	C₅×C₁₁	C₂³×C₄
Frattini	C₂	C₂³×D₅₅
Fitting	C₂²×C₄×C₅×C₁₁	C₂
socle	C₂³×C₅×C₁₁	C₂²
prime radical	C₂³×D₅₅	C₂
cosocle	C₂×C₅×C₁₁	C₂⁴
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₅×C₁₁	C₂	semidirect
3. C₂²×Dic₅₅	C₂	semidirect
4. C₂×C₄×D₅₅	C₂	direct (N × H)
6. C₂²×D₅₅	C₄	direct (N × H)
8. C₂×C₄×C₅×C₁₁	C₂²	semidirect
9. C₂×Dic₅₅	C₂²	semidirect
10. C₄×D₅₅	C₂²	direct (N × H)
12. C₂²×C₅×C₁₁	C₂×C₄	semidirect
14. C₂×D₅₅	C₂×C₄	direct (N × H)
16. C₄×C₅×C₁₁	C₂³	semidirect
17. Dic₅₅	C₂³	semidirect
19. C₂²×C₄×C₁₁	D₅	semidirect
23. C₂×C₅×C₁₁	C₂²×C₄	semidirect
25. D₅₅	C₂²×C₄	direct (N × H)
29. C₂×C₄×C₁₁	C₂×D₅	semidirect
33. C₂²×C₄×C₅	D₁₁	semidirect
36. C₅×C₁₁	C₂³×C₄	semidirect
37. C₂²×C₁₁	C₄×D₅	semidirect
41. C₄×C₁₁	C₂²×D₅	semidirect
46. C₂×C₄×C₅	C₂×D₁₁	semidirect
50. C₂×C₁₁	C₂×C₄×D₅	semidirect
53. C₂²×C₅	C₄×D₁₁	semidirect
57. C₄×C₅	C₂²×D₁₁	semidirect
62. C₂²×C₄	D₅₅	direct (N × H)
63. C₁₁	C₂²×C₄×D₅	semidirect
64. C₂×C₅	C₂×C₄×D₁₁	semidirect
72. C₂×C₄	C₂×D₅₅	direct (N × H)
73. C₅	C₂²×C₄×D₁₁	semidirect
76. C₂²	C₄×D₅₅	direct (N × H)
79. C₄	C₂²×D₅₅	direct (N × H)
81. C₂	C₂×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
C₂³×D₅₅	2
C₂²×C₄×C₅×C₁₁	2
C₂²×Dic₅₅	2
C₂×C₄×D₅₅	2
C₂²×C₄×D₁₁	5
C₂²×C₄×D₅	11

Subgroups — C22×C4×D55 #13183441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×D₅₅ #13183441