Subgroups — Q₁₆×D₅₅ #13183216

Order 1760.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₅₅	C₂	1	2	yes	maximal
2	C₅×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#11724936	C₂	1	2	yes	maximal, complemented
4	Dic₂₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₅₅	C₂	1	1	yes	maximal, characteristic
6	C₅×Q₈×C₁₁	C₂²	1	2	yes	—
7	C₄×D₅₅	—	2	2	no	—
8	C₄×D₅₅	C₂²	1	1	yes	characteristic
9	Dic₁₁₀	—	2	2	no	—
10	Dic₁₁₀	C₂²	1	2	yes	—
11	C₅×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁⋊#168	C₂²	1	1	yes	characteristic
13	Q₁₆×D₁₁	—	5	1	no	maximal, Hall
14	C₂×D₅₅	D₄	1	1	yes	characteristic
15	C₄×C₅×C₁₁	—	2	2	no	—
16	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
17	Dic₅₅	—	2	2	no	—
18	Dic₅₅	D₄	1	1	yes	characteristic
19	Q₈×D₁₁	—	5	2	no	—
20	C₁₁×Q₁₆	D₅	1	1	yes	characteristic, complemented
21	#4326	—	5	2	no	—
22	Dic₄₄	—	5	1	no	—
23	C₈×D₁₁	—	5	1	no	—
24	D₅×Q₁₆	—	11	1	no	maximal, Hall
25	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
26	D₅₅	Q₁₆	1	2	yes	direct product factor
27	Q₈×C₁₁	C₂×D₅	1	2	yes	—
28	C₄×D₁₁	—	5	1	no	—
29	C₄×D₁₁	—	10	2	no	—
30	Dic₂₂	—	5	2	no	—
31	Dic₂₂	—	10	2	no	—
32	C₈×C₁₁	C₂×D₅	1	1	yes	characteristic
33	C₁₁⋊C₈	—	5	1	no	—
34	Q₈×D₅	—	11	2	no	—
35	C₅×Q₁₆	D₁₁	1	1	yes	characteristic, complemented
36	#689	—	11	2	no	—
37	Dic₂₀	—	11	1	no	—
38	C₈×D₅	—	11	1	no	—
39	C₅×C₁₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
40	C₂×D₁₁	—	5	1	no	—
41	C₄×C₁₁	—	2	2	no	—
42	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
43	Dic₁₁	—	5	1	no	—
44	Dic₁₁	—	10	2	no	—
45	C₅×Q₈	C₂×D₁₁	1	2	yes	—
46	C₄×D₅	—	11	1	no	—
47	C₄×D₅	—	22	2	no	—
48	Dic₁₀	—	11	2	no	—
49	Dic₁₀	—	22	2	no	—
50	C₅×C₈	C₂×D₁₁	1	1	yes	characteristic
51	#168	—	11	1	no	—
52	C₂×Q₁₆	—	55	1	no	Sylow
53	C₂×C₁₁	D₄×D₅	1	1	yes	characteristic
54	D₁₁	—	5	2	no	—
55	C₂×D₅	—	11	1	no	—
56	C₄×C₅	—	2	2	no	—
57	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
58	Dic₅	—	11	1	no	—
59	Dic₅	—	22	2	no	—
60	C₂×Q₈	—	55	2	no	—
61	Q₁₆	—	55	2	no	—
62	Q₁₆	—	55	1	no	—
63	Q₁₆	D₅₅	1	1	yes	characteristic, direct product factor
64	C₂×C₈	—	55	1	no	—
65	C₁₁	D₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₅	D₄×D₁₁	1	1	yes	characteristic
67	D₅	—	11	2	no	—
68	Q₈	—	55	2	no	—
69	Q₈	—	110	2	no	—
70	Q₈	C₂×D₅₅	1	2	yes	—
71	C₂×C₄	—	55	1	no	—
72	C₂×C₄	—	110	2	no	—
73	C₈	—	55	1	no	—
74	C₈	C₂×D₅₅	1	1	yes	characteristic
75	C₅	Q₁₆×D₁₁	1	1	yes	characteristic, complemented, Sylow
76	C₂²	—	55	1	no	—
77	C₄	—	2	2	no	—
78	C₄	—	55	1	no	—
79	C₄	—	110	2	no	—
80	C₄	C₂²×D₅₅	1	1	yes	characteristic
81	C₂	—	55	2	no	—
82	C₂	D₄×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₅₅
commutator, cosocle	C₄×C₅×C₁₁	C₂³
Frattini	C₄	C₂²×D₅₅
Fitting	C₅×C₁₁×Q₁₆	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
prime radical	C₂×D₅₅	D₄
hypercenter	Q₁₆	D₅₅
hypocenter	C₅×C₁₁	C₂×Q₁₆
LCS	G ▷ C₄×C₅×C₁₁ ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁×Q₁₆	C₂	semidirect
3. #11724936	C₂	semidirect
4. Dic₂₂₀	C₂	semidirect
20. C₁₁×Q₁₆	D₅	semidirect
26. D₅₅	Q₁₆	direct (N × H)
35. C₅×Q₁₆	D₁₁	semidirect
39. C₅×C₁₁	C₂×Q₁₆	semidirect
63. Q₁₆	D₅₅	direct (N × H)
65. C₁₁	D₅×Q₁₆	semidirect
75. C₅	Q₁₆×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₅₅	2
C₅×C₁₁×Q₁₆	2
#11724936	2
Dic₂₂₀	2
C₈×D₅₅	2
Q₁₆×D₁₁	5
D₅×Q₁₆	11

Subgroups — Q16×D55 #13183216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×D₅₅ #13183216