Subgroups — Dic₁₀₇₄₀ #72274792

Order 42960.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₃₇₀	C₂	1	2	yes	maximal
2	Dic₃₅₈₀	—	3	1	no	maximal, Hall
3	Dic₂₁₄₈	—	5	1	no	maximal, Hall
4	Dic₁₇₉₀	—	3	2	no	—
5	Dic₁₀₇₄	—	5	2	no	—
6	C₃×C₅×C₈×C₁₇₉	C₂	1	1	yes	maximal, characteristic
7	C₅×C₈×C₁₇₉	D₃	1	1	yes	characteristic
8	C₃×C₈×C₁₇₉	D₅	1	1	yes	characteristic
9	Dic₂₆₈₅	—	2	2	no	—
10	C₃×C₄×C₅×C₁₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₁₇₉	D₄	1	1	yes	characteristic
12	Dic₈₉₅	—	6	2	no	—
13	C₄×C₅×C₁₇₉	C₂×D₃	1	1	yes	characteristic
14	Dic₇₁₆	—	15	1	no	Hall
15	C₃×C₅×C₁₇₉	Q₁₆	1	1	yes	characteristic, complemented, Hall
16	Dic₅₃₇	—	10	2	no	—
17	C₃×C₄×C₁₇₉	C₂×D₅	1	1	yes	characteristic
18	C₂×C₅×C₁₇₉	D₁₂	1	1	yes	characteristic
19	Dic₃₅₈	—	15	2	no	—
20	C₈×C₁₇₉	D₁₅	1	1	yes	characteristic
21	C₂×C₃×C₁₇₉	D₂₀	1	1	yes	characteristic
22	C₅×C₁₇₉	Dic₁₂	1	1	yes	characteristic, complemented, Hall
23	C₄×C₁₇₉	C₂×D₁₅	1	1	yes	characteristic
24	Dic₁₇₉	—	30	2	no	—
25	C₃×C₁₇₉	Dic₂₀	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₇₉	D₆₀	1	1	yes	characteristic
27	Dic₆₀	—	179	1	no	maximal, Hall
28	C₁₇₉	Dic₆₀	1	1	yes	characteristic, complemented, Sylow
29	Dic₃₀	—	179	2	no	—
30	C₃×C₅×C₈	D₁₇₉	1	1	yes	characteristic
31	Dic₂₀	—	537	1	no	Hall
32	C₃×C₄×C₅	C₂×D₁₇₉	1	1	yes	characteristic
33	Dic₁₅	—	358	2	no	—
34	Dic₁₂	—	895	1	no	Hall
35	Dic₁₀	—	537	2	no	—
36	C₅×C₈	D₅₃₇	1	1	yes	characteristic
37	C₂×C₃×C₅	D₇₁₆	1	1	yes	characteristic
38	Dic₆	—	895	2	no	—
39	C₃×C₈	D₈₉₅	1	1	yes	characteristic
40	C₄×C₅	C₂×D₅₃₇	1	1	yes	characteristic
41	Dic₅	—	1074	2	no	—
42	Q₁₆	—	2685	1	no	Sylow
43	C₃×C₅	Dic₇₁₆	1	1	yes	characteristic, complemented, Hall
44	C₃×C₄	C₂×D₈₉₅	1	1	yes	characteristic
45	Dic₃	—	1790	2	no	—
46	C₂×C₅	D₂₁₄₈	1	1	yes	characteristic
47	Q₈	—	2685	2	no	—
48	C₈	D₂₆₈₅	1	1	yes	characteristic
49	C₂×C₃	D₃₅₈₀	1	1	yes	characteristic
50	C₅	Dic₂₁₄₈	1	1	yes	characteristic, complemented, Sylow
51	C₄	—	5370	2	no	—
52	C₄	C₂×D₂₆₈₅	1	1	yes	characteristic
53	C₃	Dic₃₅₈₀	1	1	yes	characteristic, complemented, Sylow
54	C₂	D₁₀₇₄₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₀₇₄₀
commutator, cosocle	C₃×C₄×C₅×C₁₇₉	C₂²
Frattini	C₄	C₂×D₂₆₈₅
Fitting	C₃×C₅×C₈×C₁₇₉	C₂
socle, prime radical	C₂×C₃×C₅×C₁₇₉	D₄
hypercenter	C₈	D₂₆₈₅
hypocenter	C₃×C₅×C₁₇₉	Q₁₆
LCS	G ▷ C₃×C₄×C₅×C₁₇₉ ▷ C₂×C₃×C₅×C₁₇₉ ▷ C₃×C₅×C₁₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
15. C₃×C₅×C₁₇₉	Q₁₆	semidirect
22. C₅×C₁₇₉	Dic₁₂	semidirect
25. C₃×C₁₇₉	Dic₂₀	semidirect
28. C₁₇₉	Dic₆₀	semidirect
43. C₃×C₅	Dic₇₁₆	semidirect
50. C₅	Dic₂₁₄₈	semidirect
53. C₃	Dic₃₅₈₀	semidirect

Maximal subgroups

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

subgroup	index
Dic₅₃₇₀	2
Dic₃₅₈₀	3
Dic₂₁₄₈	5
C₃×C₅×C₈×C₁₇₉	2
Dic₆₀	179

Subgroups — Dic10740 #72274792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₀₇₄₀ #72274792