Subgroups — C₂×C₁₃×#13089649 #49176136

Order 37518.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#13089649	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×#13089649	C₁₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₁₃×C₃₇⋊C₃	—	13	1	no	maximal
6	#13089649	C₂×C₁₃	1	1	yes	characteristic, direct product factor
7	C₁₃×C₃₇⋊C₃	—	13	1	no	—
8	C₂×C₁₃×C₁₃⋊C₃	—	37	1	no	maximal, Hall
9	C₂×C₁₃×C₃₇	—	3	4	no	—
10	C₂×C₁₃×C₃₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented
11	C₂×C₁₃×C₃₇	C₃×C₁₃	1	1	yes	characteristic, complemented
12	C₁₃×C₁₃⋊C₃	—	37	1	no	Hall
13	C₁₃×C₃₇	—	3	4	no	—
14	C₁₃×C₃₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₃₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
16	C₂×C₁₃²	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃₇⋊C₃	—	13	1	no	Hall
18	C₁₃²	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₃₇⋊C₃	—	13	1	no	Hall
20	C₂×C₃×C₁₃	—	481	1	no	—
21	C₂×C₁₃⋊C₃	—	37	1	no	—
22	C₂×C₃₇	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₃	—	481	1	no	—
24	C₁₃⋊C₃	—	37	1	no	—
25	C₃₇	C₂×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₃	—	3	4	no	—
27	C₂×C₁₃	C₁₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented
28	C₂×C₁₃	#13089649	1	1	yes	characteristic, direct product factor
29	C₁₃	—	3	4	no	—
30	C₁₃	C₂×C₁₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented
31	C₁₃	C₂×#13089649	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	481	1	no	Hall
33	C₃	—	481	1	no	Sylow
34	C₂	C₁₃×#13089649	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₃	#13089649
commutator, cosocle, hypocenter	C₁₃×C₃₇	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²×C₃₇	C₃
LCS	G ▷ C₁₃×C₃₇
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×#13089649	C₂	direct (N × H)
2. C₂×C₁₃²×C₃₇	C₃	semidirect
3. C₁₃²×C₃₇	C₂×C₃	semidirect
4. C₂×#13089649	C₁₃	direct (N × H)
6. #13089649	C₂×C₁₃	direct (N × H)
10. C₂×C₁₃×C₃₇	C₁₃⋊C₃	semidirect
11. C₂×C₁₃×C₃₇	C₃×C₁₃	semidirect
14. C₁₃×C₃₇	C₂×C₁₃⋊C₃	semidirect
15. C₁₃×C₃₇	C₂×C₃×C₁₃	semidirect
16. C₂×C₁₃²	C₃₇⋊C₃	semidirect
18. C₁₃²	C₂×C₃₇⋊C₃	semidirect
22. C₂×C₃₇	C₁₃×C₁₃⋊C₃	semidirect
25. C₃₇	C₂×C₁₃×C₁₃⋊C₃	semidirect
27. C₂×C₁₃	C₁₃×C₃₇⋊C₃	semidirect
28. C₂×C₁₃	#13089649	direct (N × H)
30. C₁₃	C₂×C₁₃×C₃₇⋊C₃	semidirect
31. C₁₃	C₂×#13089649	direct (N × H)
34. C₂	C₁₃×#13089649	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#13089649	2
C₂×C₁₃²×C₃₇	3
C₂×#13089649	13
C₂×C₁₃×C₃₇⋊C₃	13
C₂×C₁₃×C₁₃⋊C₃	37

Subgroups — C2×C13×#13089649 #49176136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#13089649 #49176136