Subgroups — D₈₁₆₀ #72213188

Order 16320.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₀₈₀	C₂	1	2	yes	maximal, complemented
2	D₂₀₄₀	—	2	2	no	—
3	D₂₇₂₀	—	3	1	no	maximal, Hall
4	D₁₆₃₂	—	5	1	no	maximal, Hall
5	D₁₃₆₀	—	3	2	no	—
6	D₁₀₂₀	—	4	2	no	—
7	C₃×C₅×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
9	C₅×C₁₇×C₃₂	D₃	1	1	yes	characteristic, complemented
10	C₃×C₅×C₈×C₁₇	D₄	1	1	yes	characteristic
11	D₈₁₆	—	5	2	no	—
12	C₃×C₁₇×C₃₂	D₅	1	1	yes	characteristic, complemented
13	D₆₈₀	—	6	2	no	—
14	C₅×C₁₆×C₁₇	C₂×D₃	1	1	yes	characteristic
15	D₅₄₄	—	15	1	no	Hall
16	C₂×D₂₅₅	—	8	2	no	—
17	C₃×C₄×C₅×C₁₇	D₈	1	1	yes	characteristic
18	D₄₈₀	—	17	1	no	maximal, Hall
19	D₄₀₈	—	10	2	no	—
20	C₃×C₁₆×C₁₇	C₂×D₅	1	1	yes	characteristic
21	D₃₄₀	—	12	2	no	—
22	C₅×C₈×C₁₇	D₁₂	1	1	yes	characteristic
23	D₂₇₂	—	15	2	no	—
24	C₁₇×C₃₂	D₁₅	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×C₁₇	D₁₆	1	1	yes	characteristic
26	D₂₅₅	—	16	2	no	—
27	D₂₄₀	—	17	2	no	—
28	C₃×C₅×C₃₂	D₁₇	1	1	yes	characteristic, complemented
29	D₂₀₄	—	20	2	no	—
30	C₃×C₈×C₁₇	D₂₀	1	1	yes	characteristic
31	C₂×D₈₅	—	24	2	no	—
32	C₄×C₅×C₁₇	D₂₄	1	1	yes	characteristic
33	D₁₆₀	—	51	1	no	Hall
34	D₁₃₆	—	30	2	no	—
35	C₁₆×C₁₇	C₂×D₁₅	1	1	yes	characteristic
36	C₃×C₅×C₁₇	D₃₂	1	1	yes	characteristic, complemented, Hall
37	D₁₂₀	—	34	2	no	—
38	C₃×C₅×C₁₆	C₂×D₁₇	1	1	yes	characteristic
39	C₂×D₅₁	—	40	2	no	—
40	C₃×C₄×C₁₇	D₄₀	1	1	yes	characteristic
41	D₉₆	—	85	1	no	Hall
42	C₂×C₅×C₁₇	D₄₈	1	1	yes	characteristic
43	D₈₅	—	48	2	no	—
44	D₈₀	—	51	2	no	—
45	C₅×C₃₂	D₅₁	1	1	yes	characteristic, complemented
46	D₆₈	—	60	2	no	—
47	C₈×C₁₇	D₆₀	1	1	yes	characteristic
48	D₆₀	—	68	2	no	—
49	C₃×C₅×C₈	D₆₈	1	1	yes	characteristic
50	C₂×C₃×C₁₇	D₈₀	1	1	yes	characteristic
51	D₅₁	—	80	2	no	—
52	D₄₈	—	85	2	no	—
53	C₃×C₃₂	D₈₅	1	1	yes	characteristic, complemented
54	C₅×C₁₇	D₉₆	1	1	yes	characteristic, complemented, Hall
55	D₄₀	—	102	2	no	—
56	C₅×C₁₆	C₂×D₅₁	1	1	yes	characteristic
57	C₂×D₁₇	—	120	2	no	—
58	C₄×C₁₇	D₁₂₀	1	1	yes	characteristic
59	D₃₂	—	255	1	no	Sylow
60	C₂×D₁₅	—	136	2	no	—
61	C₃×C₄×C₅	D₁₃₆	1	1	yes	characteristic
62	C₃×C₁₇	D₁₆₀	1	1	yes	characteristic, complemented, Hall
63	D₂₄	—	170	2	no	—
64	C₃×C₁₆	C₂×D₈₅	1	1	yes	characteristic
65	D₂₀	—	204	2	no	—
66	C₅×C₈	D₂₀₄	1	1	yes	characteristic
67	C₂×C₁₇	D₂₄₀	1	1	yes	characteristic
68	D₁₇	—	240	2	no	—
69	D₁₆	—	255	2	no	—
70	C₃₂	D₂₅₅	1	1	yes	characteristic, complemented
71	C₂×C₃×C₅	D₂₇₂	1	1	yes	characteristic
72	D₁₅	—	272	2	no	—
73	D₁₂	—	340	2	no	—
74	C₃×C₈	D₃₄₀	1	1	yes	characteristic
75	C₂×D₅	—	408	2	no	—
76	C₄×C₅	D₄₀₈	1	1	yes	characteristic
77	C₁₇	D₄₈₀	1	1	yes	characteristic, complemented, Sylow
78	D₈	—	510	2	no	—
79	C₁₆	C₂×D₂₅₅	1	1	yes	characteristic
80	C₃×C₅	D₅₄₄	1	1	yes	characteristic, complemented, Hall
81	C₂×D₃	—	680	2	no	—
82	C₃×C₄	D₆₈₀	1	1	yes	characteristic
83	C₂×C₅	D₈₁₆	1	1	yes	characteristic
84	D₅	—	816	2	no	—
85	D₄	—	1020	2	no	—
86	C₈	D₁₀₂₀	1	1	yes	characteristic
87	C₂×C₃	D₁₃₆₀	1	1	yes	characteristic
88	D₃	—	1360	2	no	—
89	C₅	D₁₆₃₂	1	1	yes	characteristic, complemented, Sylow
90	C₂²	—	2040	2	no	—
91	C₄	D₂₀₄₀	1	1	yes	characteristic
92	C₃	D₂₇₂₀	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	4080	2	no	—
94	C₂	D₄₀₈₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄₀₈₀
commutator, cosocle	C₃×C₅×C₁₆×C₁₇	C₂²
Frattini	C₁₆	C₂×D₂₅₅
Fitting	C₃×C₅×C₁₇×C₃₂	C₂
socle	C₂×C₃×C₅×C₁₇	D₁₆
hypercenter	C₃₂	D₂₅₅
hypocenter	C₃×C₅×C₁₇	D₃₂
LCS	G ▷ C₃×C₅×C₁₆×C₁₇ ▷ C₃×C₅×C₈×C₁₇ ▷ C₃×C₄×C₅×C₁₇ ▷ C₂×C₃×C₅×C₁₇ ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
1. D₄₀₈₀	C₂	semidirect
7. C₃×C₅×C₁₇×C₃₂	C₂	semidirect
9. C₅×C₁₇×C₃₂	D₃	semidirect
12. C₃×C₁₇×C₃₂	D₅	semidirect
24. C₁₇×C₃₂	D₁₅	semidirect
28. C₃×C₅×C₃₂	D₁₇	semidirect
36. C₃×C₅×C₁₇	D₃₂	semidirect
45. C₅×C₃₂	D₅₁	semidirect
53. C₃×C₃₂	D₈₅	semidirect
54. C₅×C₁₇	D₉₆	semidirect
62. C₃×C₁₇	D₁₆₀	semidirect
70. C₃₂	D₂₅₅	semidirect
77. C₁₇	D₄₈₀	semidirect
80. C₃×C₅	D₅₄₄	semidirect
89. C₅	D₁₆₃₂	semidirect
92. C₃	D₂₇₂₀	semidirect

Maximal subgroups

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

subgroup	index
D₄₀₈₀	2
D₂₇₂₀	3
D₁₆₃₂	5
C₃×C₅×C₁₇×C₃₂	2
D₄₈₀	17

Subgroups — D8160 #72213188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈₁₆₀ #72213188