Subgroups — Dic₃₇₀₅ #28414734

Order 14820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₂₃₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₇₄₁	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₃×C₁₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₁₉	D₅	1	1	yes	characteristic
7	C₅×C₁₃×C₁₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₂₈₅	—	13	1	no	maximal, Hall
9	Dic₂₄₇	—	15	1	no	Hall
10	Dic₁₉₅	—	19	1	no	maximal, Hall
11	C₃×C₁₃×C₁₉	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₁₉	D₁₃	1	1	yes	characteristic
13	C₂×C₁₃×C₁₉	D₁₅	1	1	yes	characteristic
14	C₂×C₃×C₅×C₁₃	D₁₉	1	1	yes	characteristic
15	Dic₉₅	—	39	1	no	Hall
16	C₃×C₅×C₁₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
17	Dic₆₅	—	57	1	no	Hall
18	C₁₃×C₁₉	Dic₁₅	1	1	yes	characteristic, complemented, Hall
19	Dic₅₇	—	65	1	no	Hall
20	C₃×C₅×C₁₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₁₉	D₃₉	1	1	yes	characteristic
22	Dic₃₉	—	95	1	no	Hall
23	C₂×C₅×C₁₃	D₅₇	1	1	yes	characteristic
24	C₂×C₃×C₁₉	D₆₅	1	1	yes	characteristic
25	C₅×C₁₉	Dic₃₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₃	D₉₅	1	1	yes	characteristic
27	Dic₁₉	—	195	1	no	Hall
28	C₅×C₁₃	Dic₅₇	1	1	yes	characteristic, complemented, Hall
29	Dic₁₅	—	247	1	no	Hall
30	C₃×C₁₉	Dic₆₅	1	1	yes	characteristic, complemented, Hall
31	Dic₁₃	—	285	1	no	Hall
32	C₃×C₁₃	Dic₉₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₉	D₁₉₅	1	1	yes	characteristic
34	C₂×C₃×C₅	D₂₄₇	1	1	yes	characteristic
35	C₂×C₁₃	D₂₈₅	1	1	yes	characteristic
36	Dic₅	—	741	1	no	Hall
37	C₁₉	Dic₁₉₅	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	Dic₂₄₇	1	1	yes	characteristic, complemented, Hall
39	C₁₃	Dic₂₈₅	1	1	yes	characteristic, complemented, Sylow
40	Dic₃	—	1235	1	no	Hall
41	C₂×C₅	D₇₄₁	1	1	yes	characteristic
42	C₂×C₃	D₁₂₃₅	1	1	yes	characteristic
43	C₅	Dic₇₄₁	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	3705	1	no	Sylow
45	C₃	Dic₁₂₃₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	D₃₇₀₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₇₀₅
commutator, hypocenter	C₃×C₅×C₁₃×C₁₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₅×C₁₃×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₃×C₁₉	C₄	semidirect
7. C₅×C₁₃×C₁₉	Dic₃	semidirect
11. C₃×C₁₃×C₁₉	Dic₅	semidirect
16. C₃×C₅×C₁₉	Dic₁₃	semidirect
18. C₁₃×C₁₉	Dic₁₅	semidirect
20. C₃×C₅×C₁₃	Dic₁₉	semidirect
25. C₅×C₁₉	Dic₃₉	semidirect
28. C₅×C₁₃	Dic₅₇	semidirect
30. C₃×C₁₉	Dic₆₅	semidirect
32. C₃×C₁₃	Dic₉₅	semidirect
37. C₁₉	Dic₁₉₅	semidirect
38. C₃×C₅	Dic₂₄₇	semidirect
39. C₁₃	Dic₂₈₅	semidirect
43. C₅	Dic₇₄₁	semidirect
45. C₃	Dic₁₂₃₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₁₃×C₁₉	2
Dic₁₂₃₅	3
Dic₇₄₁	5
Dic₂₈₅	13
Dic₁₉₅	19

Subgroups — Dic3705 #28414734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃₇₀₅ #28414734