Subgroups — Dic₆₇₀₅ #41001222

Order 26820.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₂₃₅	—	3	1	no	maximal
3	C₅×C₉×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₃₄₁	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₄₉	D₃	1	1	yes	characteristic
6	Dic₇₄₅	—	9	1	no	Hall
7	C₂×C₉×C₁₄₉	D₅	1	1	yes	characteristic
8	C₃×C₅×C₁₄₉	Dic₃	1	1	yes	characteristic
9	Dic₄₄₇	—	15	1	no	—
10	C₂×C₅×C₁₄₉	D₉	1	1	yes	characteristic
11	C₉×C₁₄₉	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₄₉	D₁₅	1	1	yes	characteristic
13	C₅×C₁₄₉	Dic₉	1	1	yes	characteristic, complemented, Hall
14	Dic₁₄₉	—	45	1	no	Hall
15	C₃×C₁₄₉	Dic₁₅	1	1	yes	characteristic
16	C₂×C₁₄₉	D₄₅	1	1	yes	characteristic
17	Dic₄₅	—	149	1	no	maximal, Hall
18	C₁₄₉	Dic₄₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅×C₉	D₁₄₉	1	1	yes	characteristic
20	Dic₁₅	—	447	1	no	—
21	C₅×C₉	Dic₁₄₉	1	1	yes	characteristic, complemented, Hall
22	Dic₉	—	745	1	no	Hall
23	C₂×C₃×C₅	D₄₄₇	1	1	yes	characteristic
24	Dic₅	—	1341	1	no	Hall
25	C₂×C₉	D₇₄₅	1	1	yes	characteristic
26	C₃×C₅	Dic₄₄₇	1	1	yes	characteristic
27	Dic₃	—	2235	1	no	—
28	C₂×C₅	D₁₃₄₁	1	1	yes	characteristic
29	C₉	Dic₇₄₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	D₂₂₃₅	1	1	yes	characteristic
31	C₅	Dic₁₃₄₁	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	6705	1	no	Sylow
33	C₃	Dic₂₂₃₅	1	1	yes	characteristic
34	C₂	D₆₇₀₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₆₇₀₅
commutator, hypocenter	C₅×C₉×C₁₄₉	C₄
Frattini	C₂×C₃	D₂₂₃₅
Fitting, cosocle	C₂×C₅×C₉×C₁₄₉	C₂
socle, prime radical	C₂×C₃×C₅×C₁₄₉	D₃
LCS	G ▷ C₅×C₉×C₁₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₄₉	C₄	semidirect
11. C₉×C₁₄₉	Dic₅	semidirect
13. C₅×C₁₄₉	Dic₉	semidirect
18. C₁₄₉	Dic₄₅	semidirect
21. C₅×C₉	Dic₁₄₉	semidirect
29. C₉	Dic₇₄₅	semidirect
31. C₅	Dic₁₃₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₉×C₁₄₉	2
Dic₂₂₃₅	3
Dic₁₃₄₁	5
Dic₄₅	149

Subgroups — Dic6705 #41001222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₆₇₀₅ #41001222