Subgroups — C₂×C₁₃⋊C₃×C₃₇⋊C₃ #22575889

Order 8658.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×#13089649	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#13089650	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	#13089650	C₂×C₃	1	1	yes	characteristic, complemented
7	#13089649	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃₇×C₁₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₁₃×C₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₃₇⋊C₃	—	13	1	no	maximal, Hall
12	C₁₃×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃×C₃₇⋊C₃	—	13	1	no	Hall
14	C₂×C₃×C₁₃⋊C₃	—	37	1	no	maximal, Hall
15	C₂×C₃×C₃₇	—	13	1	no	—
16	C₂×C₃₇⋊C₃	—	13	1	no	—
17	C₂×C₃₇⋊C₃	—	13	1	no	—
18	C₂×C₃₇⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
19	C₃×C₁₃⋊C₃	—	37	1	no	Hall
20	C₃×C₃₇	—	13	1	no	—
21	C₃₇⋊C₃	—	13	1	no	—
22	C₃₇⋊C₃	—	13	1	no	—
23	C₃₇⋊C₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
24	C₂×C₃×C₁₃	—	37	1	no	—
25	C₂×C₁₃⋊C₃	—	37	1	no	—
26	C₂×C₁₃⋊C₃	—	37	1	no	—
27	C₂×C₁₃⋊C₃	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
28	C₂×C₃₇	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₃	—	37	1	no	—
30	C₁₃⋊C₃	—	37	1	no	—
31	C₁₃⋊C₃	—	37	1	no	—
32	C₁₃⋊C₃	C₂×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
33	C₃₇	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₁₃	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃²	—	481	1	no	Hall
36	C₁₃	C₂×C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
37	C₃²	—	481	1	no	Sylow
38	C₂×C₃	—	13	1	no	—
39	C₂×C₃	—	37	1	no	—
40	C₂×C₃	—	481	1	no	—
41	C₂×C₃	—	481	1	no	—
42	C₃	—	13	1	no	—
43	C₃	—	37	1	no	—
44	C₃	—	481	1	no	—
45	C₃	—	481	1	no	—
46	C₂	C₁₃⋊C₃×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₁₃⋊C₃×C₃₇⋊C₃
commutator, hypocenter	C₁₃×C₃₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₃₇	C₃²
LCS	G ▷ C₁₃×C₃₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₃×C₃₇⋊C₃	C₂	direct (N × H)
2. C₂×#13089649	C₃	semidirect
3. C₂×#13089650	C₃	semidirect
4. C₂×C₃₇×C₁₃⋊C₃	C₃	semidirect
5. C₂×C₁₃×C₃₇⋊C₃	C₃	semidirect
6. #13089650	C₂×C₃	semidirect
7. #13089649	C₂×C₃	semidirect
8. C₁₃×C₃₇⋊C₃	C₂×C₃	semidirect
9. C₃₇×C₁₃⋊C₃	C₂×C₃	semidirect
10. C₂×C₁₃×C₃₇	C₃²	semidirect
12. C₁₃×C₃₇	C₂×C₃²	semidirect
18. C₂×C₃₇⋊C₃	C₁₃⋊C₃	direct (N × H)
23. C₃₇⋊C₃	C₂×C₁₃⋊C₃	direct (N × H)
27. C₂×C₁₃⋊C₃	C₃₇⋊C₃	direct (N × H)
28. C₂×C₃₇	C₃×C₁₃⋊C₃	semidirect
32. C₁₃⋊C₃	C₂×C₃₇⋊C₃	direct (N × H)
33. C₃₇	C₂×C₃×C₁₃⋊C₃	semidirect
34. C₂×C₁₃	C₃×C₃₇⋊C₃	semidirect
36. C₁₃	C₂×C₃×C₃₇⋊C₃	semidirect
46. C₂	C₁₃⋊C₃×C₃₇⋊C₃	direct (N × H)

Subgroups — C2×C13⋊C3×C37⋊C3 #22575889

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₃⋊C₃×C₃₇⋊C₃ #22575889