Subgroups — C₂×C₃×D₂₆₀₃ #44530348

Order 31236.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₆₀₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₉×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₆₀₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₉×C₁₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₁₃₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₂₆₀₃	C₂×C₃	1	2	yes	direct product factor
7	C₁₉×C₁₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₁₃₇	—	19	1	no	maximal, Hall
9	C₂×C₃×C₁₃₇	D₁₉	1	1	yes	characteristic, complemented
10	C₃×D₁₃₇	—	19	2	no	—
11	C₂×D₁₃₇	—	19	1	no	Hall
12	C₃×C₁₃₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₃₇	C₃×D₁₉	1	1	yes	characteristic, complemented
14	D₁₃₇	—	19	2	no	—
15	C₂×C₃×D₁₉	—	137	1	no	maximal, Hall
16	C₁₃₇	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₁₉	D₁₃₇	1	1	yes	characteristic, complemented
18	C₃×D₁₉	—	137	2	no	—
19	C₂×D₁₉	—	137	1	no	Hall
20	C₃×C₁₉	C₂×D₁₃₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₉	C₃×D₁₃₇	1	1	yes	characteristic, complemented
22	D₁₉	—	137	2	no	—
23	C₁₉	C₂×C₃×D₁₃₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2603	1	no	Hall
25	C₂×C₃	—	2603	2	no	—
26	C₂×C₃	D₂₆₀₃	1	1	yes	characteristic, direct product factor
27	C₂²	—	2603	1	no	Sylow
28	C₃	C₂×D₂₆₀₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	2603	2	no	—
30	C₂	C₃×D₂₆₀₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₆₀₃
commutator, cosocle, hypocenter	C₁₉×C₁₃₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₁₃₇	C₂
LCS	G ▷ C₁₉×C₁₃₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₆₀₃	C₂	direct (N × H)
2. C₂×C₃×C₁₉×C₁₃₇	C₂	semidirect
3. C₂×D₂₆₀₃	C₃	direct (N × H)
4. C₃×C₁₉×C₁₃₇	C₂²	semidirect
5. C₂×C₁₉×C₁₃₇	C₂×C₃	semidirect
6. D₂₆₀₃	C₂×C₃	direct (N × H)
7. C₁₉×C₁₃₇	C₂²×C₃	semidirect
9. C₂×C₃×C₁₃₇	D₁₉	semidirect
12. C₃×C₁₃₇	C₂×D₁₉	semidirect
13. C₂×C₁₃₇	C₃×D₁₉	semidirect
16. C₁₃₇	C₂×C₃×D₁₉	semidirect
17. C₂×C₃×C₁₉	D₁₃₇	semidirect
20. C₃×C₁₉	C₂×D₁₃₇	semidirect
21. C₂×C₁₉	C₃×D₁₃₇	semidirect
23. C₁₉	C₂×C₃×D₁₃₇	semidirect
26. C₂×C₃	D₂₆₀₃	direct (N × H)
28. C₃	C₂×D₂₆₀₃	direct (N × H)
30. C₂	C₃×D₂₆₀₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₂₆₀₃	2
C₂×C₃×C₁₉×C₁₃₇	2
C₂×D₂₆₀₃	3
C₂×C₃×D₁₃₇	19
C₂×C₃×D₁₉	137

Subgroups — C2×C3×D2603 #44530348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₂₆₀₃ #44530348