Subgroups — C₂²×C₃×#10625202 #22580386

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#10625202	C₂	1	3	yes	maximal, direct product factor
2	C₂²×#10625202	C₃	1	3	yes	maximal, direct product factor
3	C₂²×C₃×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#10625202	C₂²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	3	yes	complemented
6	C₂×#10625202	C₂×C₃	1	9	yes	direct product factor
7	C₂²×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
9	#10625202	C₂²×C₃	1	3	yes	direct product factor
10	C₂²×C₃×C₁₉⋊C₃	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₁₉	C₂×C₃²	1	3	yes	complemented
12	C₂²×C₃×C₁₃⋊C₃	—	19	1	no	maximal, Hall
13	C₂×C₃×C₁₉⋊C₃	—	13	3	no	—
14	C₁₃×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₃⋊C₃	—	19	3	no	—
16	C₂²×C₃×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
17	C₂²×C₁₉⋊C₃	—	13	3	no	—
18	C₃×C₁₉⋊C₃	—	13	1	no	Hall
19	C₂²×C₃×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented
20	C₂²×C₁₃⋊C₃	—	19	3	no	—
21	C₃×C₁₃⋊C₃	—	19	1	no	Hall
22	C₂×C₃×C₁₉	C₂×C₁₃⋊C₃	1	3	yes	complemented
23	C₂×C₁₉⋊C₃	—	13	9	no	—
24	C₂×C₃×C₁₃	C₂×C₁₉⋊C₃	1	3	yes	complemented
25	C₂×C₁₃⋊C₃	—	19	9	no	—
26	C₂²×C₁₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₃×C₁₉	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
28	C₁₉⋊C₃	—	13	3	no	—
29	C₂²×C₁₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₃×C₁₃	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
31	C₁₃⋊C₃	—	19	3	no	—
32	C₂×C₁₉	C₂×C₃×C₁₃⋊C₃	1	3	yes	complemented
33	C₂²×C₃²	—	247	1	no	Hall
34	C₂×C₁₃	C₂×C₃×C₁₉⋊C₃	1	3	yes	complemented
35	C₁₉	C₂²×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	—	247	3	no	—
37	C₁₃	C₂²×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₃	—	247	3	no	—
39	C₂²×C₃	#10625202	1	1	yes	characteristic, direct product factor
40	C₃²	—	247	1	no	Sylow
41	C₂×C₃	—	247	9	no	—
42	C₂×C₃	C₂×#10625202	1	3	yes	direct product factor
43	C₂²	C₃×#10625202	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	247	3	no	—
45	C₃	C₂²×#10625202	1	1	yes	characteristic, direct product factor
46	C₂	C₂×C₃×#10625202	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	#10625202
commutator, hypocenter	C₁₃×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃×C₁₉	C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#10625202	C₂	direct (N × H)
2. C₂²×#10625202	C₃	direct (N × H)
3. C₂²×C₃×C₁₃×C₁₉	C₃	semidirect
4. C₃×#10625202	C₂²	direct (N × H)
5. C₂×C₃×C₁₃×C₁₉	C₂×C₃	semidirect
6. C₂×#10625202	C₂×C₃	direct (N × H)
7. C₂²×C₁₃×C₁₉	C₃²	semidirect
8. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
9. #10625202	C₂²×C₃	direct (N × H)
11. C₂×C₁₃×C₁₉	C₂×C₃²	semidirect
14. C₁₃×C₁₉	C₂²×C₃²	semidirect
16. C₂²×C₃×C₁₉	C₁₃⋊C₃	semidirect
19. C₂²×C₃×C₁₃	C₁₉⋊C₃	semidirect
22. C₂×C₃×C₁₉	C₂×C₁₃⋊C₃	semidirect
24. C₂×C₃×C₁₃	C₂×C₁₉⋊C₃	semidirect
26. C₂²×C₁₉	C₃×C₁₃⋊C₃	semidirect
27. C₃×C₁₉	C₂²×C₁₃⋊C₃	semidirect
29. C₂²×C₁₃	C₃×C₁₉⋊C₃	semidirect
30. C₃×C₁₃	C₂²×C₁₉⋊C₃	semidirect
32. C₂×C₁₉	C₂×C₃×C₁₃⋊C₃	semidirect
34. C₂×C₁₃	C₂×C₃×C₁₉⋊C₃	semidirect
35. C₁₉	C₂²×C₃×C₁₃⋊C₃	semidirect
37. C₁₃	C₂²×C₃×C₁₉⋊C₃	semidirect
39. C₂²×C₃	#10625202	direct (N × H)
42. C₂×C₃	C₂×#10625202	direct (N × H)
43. C₂²	C₃×#10625202	direct (N × H)
45. C₃	C₂²×#10625202	direct (N × H)
46. C₂	C₂×C₃×#10625202	direct (N × H)

Subgroups — C22×C3×#10625202 #22580386

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₃×#10625202 #22580386