Subgroups — C₂×C₃×C₇×D₃₀₇ #38788674

Order 25788.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₃₀₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₃₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₃₀₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₃₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₃₀₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₃₀₇	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₃×D₃₀₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₃₀₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₃₀₇	C₂×C₇	1	1	yes	characteristic, complemented
10	C₃×D₃₀₇	C₂×C₇	1	2	yes	direct product factor
11	C₂×D₃₀₇	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₃₀₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃₀₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
14	D₃₀₇	C₂×C₃×C₇	1	2	yes	direct product factor
15	C₃₀₇	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₃×C₇	—	307	1	no	maximal, Hall
17	C₂×C₃×C₇	—	307	2	no	—
18	C₂×C₃×C₇	D₃₀₇	1	1	yes	characteristic, direct product factor
19	C₂²×C₇	—	307	1	no	Hall
20	C₃×C₇	C₂×D₃₀₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇	—	307	2	no	—
22	C₂×C₇	C₃×D₃₀₇	1	1	yes	characteristic, direct product factor
23	C₂²×C₃	—	307	1	no	Hall
24	C₇	C₂×C₃×D₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	—	307	2	no	—
26	C₂×C₃	C₇×D₃₀₇	1	1	yes	characteristic, direct product factor
27	C₂²	—	307	1	no	Sylow
28	C₃	C₂×C₇×D₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	307	2	no	—
30	C₂	C₃×C₇×D₃₀₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₃₀₇
commutator, cosocle, hypocenter	C₃₀₇	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₃₀₇	C₂
LCS	G ▷ C₃₀₇
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₃₀₇	C₂	direct (N × H)
2. C₂×C₃×C₇×C₃₀₇	C₂	semidirect
3. C₂×C₇×D₃₀₇	C₃	direct (N × H)
4. C₃×C₇×C₃₀₇	C₂²	semidirect
5. C₂×C₇×C₃₀₇	C₂×C₃	semidirect
6. C₇×D₃₀₇	C₂×C₃	direct (N × H)
7. C₂×C₃×D₃₀₇	C₇	direct (N × H)
8. C₇×C₃₀₇	C₂²×C₃	semidirect
9. C₂×C₃×C₃₀₇	C₂×C₇	semidirect
10. C₃×D₃₀₇	C₂×C₇	direct (N × H)
11. C₂×D₃₀₇	C₃×C₇	direct (N × H)
12. C₃×C₃₀₇	C₂²×C₇	semidirect
13. C₂×C₃₀₇	C₂×C₃×C₇	semidirect
14. D₃₀₇	C₂×C₃×C₇	direct (N × H)
15. C₃₀₇	C₂²×C₃×C₇	semidirect
18. C₂×C₃×C₇	D₃₀₇	direct (N × H)
20. C₃×C₇	C₂×D₃₀₇	direct (N × H)
22. C₂×C₇	C₃×D₃₀₇	direct (N × H)
24. C₇	C₂×C₃×D₃₀₇	direct (N × H)
26. C₂×C₃	C₇×D₃₀₇	direct (N × H)
28. C₃	C₂×C₇×D₃₀₇	direct (N × H)
30. C₂	C₃×C₇×D₃₀₇	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×C₇×D₃₀₇	2
C₂×C₃×C₇×C₃₀₇	2
C₂×C₇×D₃₀₇	3
C₂×C₃×D₃₀₇	7
C₂²×C₃×C₇	307

Subgroups — C2×C3×C7×D307 #38788674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×D₃₀₇ #38788674