Subgroups — D₂₈₈₆₀ #72292467

Order 57720.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₆₂₀	—	3	1	no	maximal, Hall
2	D₅₇₇₂	—	5	1	no	maximal, Hall
3	D₂₂₂₀	—	13	1	no	maximal, Hall
4	D₁₉₂₄	—	15	1	no	Hall
5	C₂×D₇₂₁₅	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×C₅×C₁₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	D₇₂₁₅	—	2	2	no	—
8	C₂×C₃×C₅×C₁₃×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×D₂₄₀₅	—	3	2	no	—
10	C₄×C₅×C₁₃×C₃₇	D₃	1	1	yes	characteristic, complemented
11	C₃×C₅×C₁₃×C₃₇	D₄	1	1	yes	characteristic, complemented, Hall
12	C₂×D₁₄₄₃	—	5	2	no	—
13	C₃×C₄×C₁₃×C₃₇	D₅	1	1	yes	characteristic, complemented
14	D₂₄₀₅	—	6	2	no	—
15	C₂×C₅×C₁₃×C₃₇	C₂×D₃	1	1	yes	characteristic
16	D₁₄₄₃	—	10	2	no	—
17	C₂×C₃×C₁₃×C₃₇	C₂×D₅	1	1	yes	characteristic
18	C₅×C₁₃×C₃₇	D₁₂	1	1	yes	characteristic, complemented, Hall
19	C₂×D₅₅₅	—	13	2	no	—
20	C₃×C₄×C₅×C₃₇	D₁₃	1	1	yes	characteristic, complemented
21	C₂×D₄₈₁	—	15	2	no	—
22	C₄×C₁₃×C₃₇	D₁₅	1	1	yes	characteristic, complemented
23	D₇₈₀	—	37	1	no	maximal, Hall
24	D₇₄₀	—	39	1	no	Hall
25	C₃×C₁₃×C₃₇	D₂₀	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅×C₃₇	C₂×D₁₃	1	1	yes	characteristic
27	D₅₅₅	—	26	2	no	—
28	C₂×C₁₃×C₃₇	C₂×D₁₅	1	1	yes	characteristic
29	D₄₈₁	—	30	2	no	—
30	D₄₄₄	—	65	1	no	Hall
31	C₂×D₁₉₅	—	37	2	no	—
32	C₃×C₄×C₅×C₁₃	D₃₇	1	1	yes	characteristic, complemented
33	C₂×D₁₈₅	—	39	2	no	—
34	C₄×C₅×C₃₇	D₃₉	1	1	yes	characteristic, complemented
35	C₃×C₅×C₃₇	D₅₂	1	1	yes	characteristic, complemented, Hall
36	D₂₆₀	—	111	1	no	Hall
37	C₁₃×C₃₇	D₆₀	1	1	yes	characteristic, complemented, Hall
38	C₂×D₁₁₁	—	65	2	no	—
39	C₃×C₄×C₃₇	D₆₅	1	1	yes	characteristic, complemented
40	C₂×C₃×C₅×C₁₃	C₂×D₃₇	1	1	yes	characteristic
41	D₁₉₅	—	74	2	no	—
42	C₂×C₅×C₃₇	C₂×D₃₉	1	1	yes	characteristic
43	D₁₈₅	—	78	2	no	—
44	D₁₅₆	—	185	1	no	Hall
45	D₁₄₈	—	195	1	no	Hall
46	C₂×D₆₅	—	111	2	no	—
47	C₄×C₅×C₁₃	D₁₁₁	1	1	yes	characteristic, complemented
48	C₂×C₃×C₃₇	C₂×D₆₅	1	1	yes	characteristic
49	D₁₁₁	—	130	2	no	—
50	C₃×C₅×C₁₃	D₁₄₈	1	1	yes	characteristic, complemented, Hall
51	C₅×C₃₇	D₁₅₆	1	1	yes	characteristic, complemented, Hall
52	C₂×D₃₉	—	185	2	no	—
53	C₃×C₄×C₁₃	D₁₈₅	1	1	yes	characteristic, complemented
54	C₂×D₃₇	—	195	2	no	—
55	C₄×C₃₇	D₁₉₅	1	1	yes	characteristic, complemented
56	C₂×C₅×C₁₃	C₂×D₁₁₁	1	1	yes	characteristic
57	D₆₅	—	222	2	no	—
58	D₆₀	—	481	1	no	Hall
59	C₃×C₃₇	D₂₆₀	1	1	yes	characteristic, complemented, Hall
60	D₅₂	—	555	1	no	Hall
61	C₂×C₃×C₁₃	C₂×D₁₈₅	1	1	yes	characteristic
62	D₃₉	—	370	2	no	—
63	C₂×C₃₇	C₂×D₁₉₅	1	1	yes	characteristic
64	D₃₇	—	390	2	no	—
65	C₅×C₁₃	D₄₄₄	1	1	yes	characteristic, complemented, Hall
66	C₂×D₁₅	—	481	2	no	—
67	C₃×C₄×C₅	D₄₈₁	1	1	yes	characteristic, complemented
68	C₂×D₁₃	—	555	2	no	—
69	C₄×C₁₃	D₅₅₅	1	1	yes	characteristic, complemented
70	D₂₀	—	1443	1	no	Hall
71	C₃×C₁₃	D₇₄₀	1	1	yes	characteristic, complemented, Hall
72	C₃₇	D₇₈₀	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃×C₅	C₂×D₄₈₁	1	1	yes	characteristic
74	D₁₅	—	962	2	no	—
75	C₂×C₁₃	C₂×D₅₅₅	1	1	yes	characteristic
76	D₁₃	—	1110	2	no	—
77	D₁₂	—	2405	1	no	Hall
78	C₂×D₅	—	1443	2	no	—
79	C₄×C₅	D₁₄₄₃	1	1	yes	characteristic, complemented
80	C₃×C₅	D₁₉₂₄	1	1	yes	characteristic, complemented, Hall
81	C₁₃	D₂₂₂₀	1	1	yes	characteristic, complemented, Sylow
82	C₂×D₃	—	2405	2	no	—
83	C₃×C₄	D₂₄₀₅	1	1	yes	characteristic, complemented
84	C₂×C₅	C₂×D₁₄₄₃	1	1	yes	characteristic
85	D₅	—	2886	2	no	—
86	D₄	—	7215	1	no	Sylow
87	C₂×C₃	C₂×D₂₄₀₅	1	1	yes	characteristic
88	D₃	—	4810	2	no	—
89	C₅	D₅₇₇₂	1	1	yes	characteristic, complemented, Sylow
90	C₂²	—	7215	2	no	—
91	C₄	D₇₂₁₅	1	1	yes	characteristic, complemented
92	C₃	D₉₆₂₀	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	14430	2	no	—
94	C₂	C₂×D₇₂₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₇₂₁₅
commutator, socle, cosocle	C₂×C₃×C₅×C₁₃×C₃₇	C₂²
Fitting	C₃×C₄×C₅×C₁₃×C₃₇	C₂
hypercenter	C₄	D₇₂₁₅
hypocenter	C₃×C₅×C₁₃×C₃₇	D₄
LCS	G ▷ C₂×C₃×C₅×C₁₃×C₃₇ ▷ C₃×C₅×C₁₃×C₃₇
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
5. C₂×D₇₂₁₅	C₂	semidirect
6. C₃×C₄×C₅×C₁₃×C₃₇	C₂	semidirect
10. C₄×C₅×C₁₃×C₃₇	D₃	semidirect
11. C₃×C₅×C₁₃×C₃₇	D₄	semidirect
13. C₃×C₄×C₁₃×C₃₇	D₅	semidirect
18. C₅×C₁₃×C₃₇	D₁₂	semidirect
20. C₃×C₄×C₅×C₃₇	D₁₃	semidirect
22. C₄×C₁₃×C₃₇	D₁₅	semidirect
25. C₃×C₁₃×C₃₇	D₂₀	semidirect
32. C₃×C₄×C₅×C₁₃	D₃₇	semidirect
34. C₄×C₅×C₃₇	D₃₉	semidirect
35. C₃×C₅×C₃₇	D₅₂	semidirect
37. C₁₃×C₃₇	D₆₀	semidirect
39. C₃×C₄×C₃₇	D₆₅	semidirect
47. C₄×C₅×C₁₃	D₁₁₁	semidirect
50. C₃×C₅×C₁₃	D₁₄₈	semidirect
51. C₅×C₃₇	D₁₅₆	semidirect
53. C₃×C₄×C₁₃	D₁₈₅	semidirect
55. C₄×C₃₇	D₁₉₅	semidirect
59. C₃×C₃₇	D₂₆₀	semidirect
65. C₅×C₁₃	D₄₄₄	semidirect
67. C₃×C₄×C₅	D₄₈₁	semidirect
69. C₄×C₁₃	D₅₅₅	semidirect
71. C₃×C₁₃	D₇₄₀	semidirect
72. C₃₇	D₇₈₀	semidirect
79. C₄×C₅	D₁₄₄₃	semidirect
80. C₃×C₅	D₁₉₂₄	semidirect
81. C₁₃	D₂₂₂₀	semidirect
83. C₃×C₄	D₂₄₀₅	semidirect
89. C₅	D₅₇₇₂	semidirect
91. C₄	D₇₂₁₅	semidirect
92. C₃	D₉₆₂₀	semidirect

Maximal subgroups

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

subgroup	index
D₉₆₂₀	3
D₅₇₇₂	5
D₂₂₂₀	13
C₂×D₇₂₁₅	2
C₃×C₄×C₅×C₁₃×C₃₇	2
D₇₈₀	37

Subgroups — D28860 #72292467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₈₈₆₀ #72292467