Subgroups — D₂₈₄₄₀ #72292003

Order 56880.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₄₂₂₀	C₂	1	2	yes	maximal, complemented
2	D₉₄₈₀	—	3	1	no	maximal
3	D₅₆₈₈	—	5	1	no	maximal, Hall
4	D₄₇₄₀	—	3	2	no	—
5	D₃₁₆₀	—	9	1	no	Hall
6	D₁₈₉₆	—	15	1	no	—
7	D₂₈₄₄	—	5	2	no	—
8	D₁₅₈₀	—	9	2	no	—
9	C₅×C₈×C₉×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×C₈×C₇₉	D₃	1	1	yes	characteristic
11	C₈×C₉×C₇₉	D₅	1	1	yes	characteristic, complemented
12	C₅×C₈×C₇₉	D₉	1	1	yes	characteristic, complemented
13	C₂×D₃₅₅₅	—	2	2	no	—
14	C₄×C₅×C₉×C₇₉	C₂²	1	1	yes	characteristic
15	D₃₅₅₅	—	4	2	no	—
16	C₂×C₅×C₉×C₇₉	D₄	1	1	yes	characteristic
17	C₂×D₁₁₈₅	—	6	2	no	—
18	C₃×C₄×C₅×C₇₉	C₂×D₃	1	1	yes	characteristic
19	C₅×C₉×C₇₉	D₈	1	1	yes	characteristic, complemented, Hall
20	C₂×D₇₁₁	—	10	2	no	—
21	C₄×C₉×C₇₉	C₂×D₅	1	1	yes	characteristic
22	D₁₁₈₅	—	12	2	no	—
23	C₂×C₃×C₅×C₇₉	D₁₂	1	1	yes	characteristic
24	D₉₄₈	—	15	2	no	—
25	C₃×C₈×C₇₉	D₁₅	1	1	yes	characteristic
26	C₂×D₃₉₅	—	18	2	no	—
27	C₄×C₅×C₇₉	C₂×D₉	1	1	yes	characteristic
28	C₂×C₉×C₇₉	D₂₀	1	1	yes	characteristic
29	D₇₁₁	—	20	2	no	—
30	D₆₃₂	—	45	1	no	Hall
31	C₃×C₅×C₇₉	D₂₄	1	1	yes	characteristic
32	C₂×D₂₃₇	—	30	2	no	—
33	C₃×C₄×C₇₉	C₂×D₁₅	1	1	yes	characteristic
34	C₂×C₅×C₇₉	D₃₆	1	1	yes	characteristic
35	D₃₉₅	—	36	2	no	—
36	D₃₆₀	—	79	1	no	maximal, Hall
37	C₉×C₇₉	D₄₀	1	1	yes	characteristic, complemented, Hall
38	D₃₁₆	—	45	2	no	—
39	C₈×C₇₉	D₄₅	1	1	yes	characteristic, complemented
40	C₂×C₃×C₇₉	D₆₀	1	1	yes	characteristic
41	D₂₃₇	—	60	2	no	—
42	C₅×C₇₉	D₇₂	1	1	yes	characteristic, complemented, Hall
43	D₁₈₀	—	79	2	no	—
44	C₅×C₈×C₉	D₇₉	1	1	yes	characteristic, complemented
45	C₂×D₇₉	—	90	2	no	—
46	C₄×C₇₉	C₂×D₄₅	1	1	yes	characteristic
47	D₁₂₀	—	237	1	no	—
48	C₃×C₇₉	D₁₂₀	1	1	yes	characteristic
49	C₂×D₄₅	—	158	2	no	—
50	C₄×C₅×C₉	C₂×D₇₉	1	1	yes	characteristic
51	C₂×C₇₉	D₁₈₀	1	1	yes	characteristic
52	D₇₉	—	180	2	no	—
53	D₇₂	—	395	1	no	Hall
54	D₆₀	—	237	2	no	—
55	C₃×C₅×C₈	D₂₃₇	1	1	yes	characteristic
56	C₂×C₅×C₉	D₃₁₆	1	1	yes	characteristic
57	D₄₅	—	316	2	no	—
58	D₄₀	—	711	1	no	Hall
59	C₇₉	D₃₆₀	1	1	yes	characteristic, complemented, Sylow
60	D₃₆	—	395	2	no	—
61	C₈×C₉	D₃₉₅	1	1	yes	characteristic, complemented
62	C₂×D₁₅	—	474	2	no	—
63	C₃×C₄×C₅	C₂×D₂₃₇	1	1	yes	characteristic
64	D₂₄	—	1185	1	no	—
65	C₅×C₉	D₆₃₂	1	1	yes	characteristic, complemented, Hall
66	D₂₀	—	711	2	no	—
67	C₅×C₈	D₇₁₁	1	1	yes	characteristic, complemented
68	C₂×D₉	—	790	2	no	—
69	C₄×C₉	C₂×D₃₉₅	1	1	yes	characteristic
70	C₂×C₃×C₅	D₉₄₈	1	1	yes	characteristic
71	D₁₅	—	948	2	no	—
72	D₁₂	—	1185	2	no	—
73	C₃×C₈	D₁₁₈₅	1	1	yes	characteristic
74	C₂×D₅	—	1422	2	no	—
75	C₄×C₅	C₂×D₇₁₁	1	1	yes	characteristic
76	C₂×C₉	D₁₅₈₀	1	1	yes	characteristic
77	D₉	—	1580	2	no	—
78	D₈	—	3555	1	no	Sylow
79	C₃×C₅	D₁₈₉₆	1	1	yes	characteristic
80	C₂×D₃	—	2370	2	no	—
81	C₃×C₄	C₂×D₁₁₈₅	1	1	yes	characteristic
82	C₂×C₅	D₂₈₄₄	1	1	yes	characteristic
83	D₅	—	2844	2	no	—
84	C₉	D₃₁₆₀	1	1	yes	characteristic, complemented, Sylow
85	D₄	—	3555	2	no	—
86	C₈	D₃₅₅₅	1	1	yes	characteristic, complemented
87	C₂×C₃	D₄₇₄₀	1	1	yes	characteristic
88	D₃	—	4740	2	no	—
89	C₅	D₅₆₈₈	1	1	yes	characteristic, complemented, Sylow
90	C₂²	—	7110	2	no	—
91	C₄	C₂×D₃₅₅₅	1	1	yes	characteristic
92	C₃	D₉₄₈₀	1	1	yes	characteristic
93	C₂	—	14220	2	no	—
94	C₂	D₁₄₂₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₄₂₂₀
commutator, cosocle	C₄×C₅×C₉×C₇₉	C₂²
Frattini	C₃×C₄	C₂×D₁₁₈₅
Fitting	C₅×C₈×C₉×C₇₉	C₂
socle	C₂×C₃×C₅×C₇₉	D₁₂
hypercenter	C₈	D₃₅₅₅
hypocenter	C₅×C₉×C₇₉	D₈
LCS	G ▷ C₄×C₅×C₉×C₇₉ ▷ C₂×C₅×C₉×C₇₉ ▷ C₅×C₉×C₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. D₁₄₂₂₀	C₂	semidirect
9. C₅×C₈×C₉×C₇₉	C₂	semidirect
11. C₈×C₉×C₇₉	D₅	semidirect
12. C₅×C₈×C₇₉	D₉	semidirect
19. C₅×C₉×C₇₉	D₈	semidirect
37. C₉×C₇₉	D₄₀	semidirect
39. C₈×C₇₉	D₄₅	semidirect
42. C₅×C₇₉	D₇₂	semidirect
44. C₅×C₈×C₉	D₇₉	semidirect
59. C₇₉	D₃₆₀	semidirect
61. C₈×C₉	D₃₉₅	semidirect
65. C₅×C₉	D₆₃₂	semidirect
67. C₅×C₈	D₇₁₁	semidirect
84. C₉	D₃₁₆₀	semidirect
86. C₈	D₃₅₅₅	semidirect
89. C₅	D₅₆₈₈	semidirect

Maximal subgroups

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

subgroup	index
D₁₄₂₂₀	2
D₉₄₈₀	3
D₅₆₈₈	5
C₅×C₈×C₉×C₇₉	2
D₃₆₀	79

Subgroups — D28440 #72292003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₈₄₄₀ #72292003