Subgroups — D₅×C₁₁×Q₁₆ #13183130

Order 1760.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₁₁	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₅×C₁₁×Q₁₆	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
prime radical	C₂×D₅×C₁₁	D₄
hypercenter	C₁₁×Q₁₆	D₅
hypocenter	C₅	C₂×C₁₁×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₁₁×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁×Q₁₆	C₂	semidirect
3. C₁₁×#689	C₂	semidirect
4. C₁₁×Dic₂₀	C₂	semidirect
22. C₁₁×Q₁₆	D₅	direct (N × H)
24. D₅×Q₁₆	C₁₁	direct (N × H)
26. D₅×C₁₁	Q₁₆	direct (N × H)
35. C₅×Q₁₆	C₂×C₁₁	semidirect
36. #689	C₂×C₁₁	semidirect
37. Dic₂₀	C₂×C₁₁	semidirect
39. C₅×C₁₁	C₂×Q₁₆	semidirect
63. Q₁₆	D₅×C₁₁	direct (N × H)
65. C₁₁	D₅×Q₁₆	direct (N × H)
67. D₅	C₁₁×Q₁₆	direct (N × H)
75. C₅	C₂×C₁₁×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₅×C₁₁	2
C₅×C₁₁×Q₁₆	2
C₁₁×#689	2
C₁₁×Dic₂₀	2
C₈×D₅×C₁₁	2
C₂×C₁₁×Q₁₆	5
D₅×Q₁₆	11

Subgroups — D5×C11×Q16 #13183130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₁×Q₁₆ #13183130