Subgroups — D₃×D₂₂₄₅ #41002273

Order 26940.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₇₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₄₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₂₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₂₄₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₄₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₄₄₉	—	5	1	no	maximal, Hall
7	C₂×C₅×C₄₄₉	—	3	1	no	—
8	D₂₂₄₅	—	3	1	no	—
9	D₂₂₄₅	D₃	1	1	yes	characteristic, direct product factor
10	D₁₃₄₇	—	5	1	no	—
11	C₃×D₄₄₉	—	5	1	no	—
12	D₃×C₄₄₉	D₅	1	1	yes	characteristic, complemented
13	C₅×C₄₄₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₄₄₉	—	15	1	no	Hall
15	C₃×C₄₄₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₄₄₉	—	3	1	no	—
17	D₄₄₉	—	5	1	no	—
18	D₄₄₉	—	15	1	no	—
19	C₄₄₉	D₃×D₅	1	1	yes	characteristic, complemented, Sylow
20	D₃×D₅	—	449	1	no	maximal, Hall
21	D₁₅	—	449	1	no	—
22	C₃×D₅	—	449	1	no	—
23	C₅×D₃	D₄₄₉	1	1	yes	characteristic, complemented
24	C₂×D₅	—	1347	1	no	Hall
25	C₃×C₅	C₂×D₄₄₉	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃	—	2245	1	no	Hall
27	C₂×C₅	—	3	1	no	—
28	D₅	—	1347	1	no	—
29	D₅	—	449	1	no	—
30	C₂×C₃	—	2245	1	no	—
31	D₃	—	2245	1	no	—
32	D₃	D₂₂₄₅	1	1	yes	characteristic, direct product factor
33	C₅	D₃×D₄₄₉	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	6735	1	no	Sylow
35	C₃	C₂×D₂₂₄₅	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	6735	1	no	—
38	C₂	—	2245	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₄₄₉	C₂²
LCS	G ▷ C₃×C₅×C₄₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₇₃₅	C₂	semidirect
2. C₅×D₃×C₄₄₉	C₂	semidirect
3. C₃×D₂₂₄₅	C₂	semidirect
5. C₃×C₅×C₄₄₉	C₂²	semidirect
9. D₂₂₄₅	D₃	direct (N × H)
12. D₃×C₄₄₉	D₅	semidirect
13. C₅×C₄₄₉	C₂×D₃	semidirect
15. C₃×C₄₄₉	C₂×D₅	semidirect
19. C₄₄₉	D₃×D₅	semidirect
23. C₅×D₃	D₄₄₉	semidirect
25. C₃×C₅	C₂×D₄₄₉	semidirect
32. D₃	D₂₂₄₅	direct (N × H)
33. C₅	D₃×D₄₄₉	semidirect
35. C₃	C₂×D₂₂₄₅	semidirect

Maximal subgroups

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

subgroup	index
D₆₇₃₅	2
C₅×D₃×C₄₄₉	2
C₃×D₂₂₄₅	2
C₂×D₂₂₄₅	3
D₃×D₄₄₉	5
D₃×D₅	449

Subgroups — D3×D2245 #41002273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₂₄₅ #41002273