Subgroups — C₂×C₁₃×C₃⋊D₃×C₆₇ #44535828

Order 31356.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₆₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₃×C₆₇	—	3	4	no	maximal
4	C₃²×C₁₃×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₁₃×C₆₇	—	3	8	no	—
6	C₂×C₃×C₁₃×C₆₇	D₃	1	4	yes	complemented
7	C₂²×C₁₃×C₆₇	—	9	1	no	Hall
8	C₃×C₁₃×C₆₇	C₂×D₃	1	4	yes	complemented
9	C₂×C₃⋊D₃×C₆₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₆₇	—	9	2	no	—
11	C₂×C₁₃×C₆₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
12	C₂×C₃²×C₆₇	C₂×C₁₃	1	1	yes	characteristic, complemented
13	C₃⋊D₃×C₆₇	C₂×C₁₃	1	2	yes	direct product factor
14	C₁₃×C₆₇	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂×D₃×C₆₇	—	3	4	no	—
16	C₃²×C₆₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₃×C₃⋊D₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₃×C₆₇	D₃×C₁₃	1	4	yes	complemented
19	D₃×C₆₇	—	3	8	no	—
20	C₂²×C₆₇	—	9	1	no	Hall
21	C₂×C₃²×C₁₃	C₂×C₆₇	1	1	yes	characteristic, complemented
22	C₁₃×C₃⋊D₃	C₂×C₆₇	1	2	yes	direct product factor
23	C₃×C₆₇	C₂×D₃×C₁₃	1	4	yes	complemented
24	C₂×D₃×C₁₃	—	3	4	no	—
25	C₂×C₆₇	—	9	2	no	—
26	C₂×C₆₇	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
27	C₃²×C₁₃	C₂²×C₆₇	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₃	D₃×C₆₇	1	4	yes	complemented
29	D₃×C₁₃	—	3	8	no	—
30	C₆₇	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²×C₁₃	—	9	1	no	Hall
32	C₃×C₁₃	C₂×D₃×C₆₇	1	4	yes	complemented
33	C₂×C₃⋊D₃	C₁₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₃	—	9	2	no	—
35	C₂×C₁₃	C₃⋊D₃×C₆₇	1	1	yes	characteristic, direct product factor
36	C₂×C₃²	C₂×C₁₃×C₆₇	1	1	yes	characteristic, complemented
37	C₃⋊D₃	C₂×C₁₃×C₆₇	1	2	yes	direct product factor
38	C₁₃	C₂×C₃⋊D₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₃	—	3	4	no	—
40	C₃²	C₂²×C₁₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃×C₁₃×C₆₇	1	4	yes	complemented
42	D₃	—	3	8	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₁₃×C₆₇	1	4	yes	complemented
45	C₂	—	9	2	no	—
46	C₂	C₁₃×C₃⋊D₃×C₆₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₆₇	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₃×C₆₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₆₇	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₃×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₃×C₆₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₆₇	C₂	semidirect
4. C₃²×C₁₃×C₆₇	C₂²	semidirect
6. C₂×C₃×C₁₃×C₆₇	D₃	semidirect
8. C₃×C₁₃×C₆₇	C₂×D₃	semidirect
9. C₂×C₃⋊D₃×C₆₇	C₁₃	direct (N × H)
11. C₂×C₁₃×C₆₇	C₃⋊D₃	direct (N × H)
12. C₂×C₃²×C₆₇	C₂×C₁₃	semidirect
13. C₃⋊D₃×C₆₇	C₂×C₁₃	direct (N × H)
14. C₁₃×C₆₇	C₂×C₃⋊D₃	direct (N × H)
16. C₃²×C₆₇	C₂²×C₁₃	semidirect
17. C₂×C₁₃×C₃⋊D₃	C₆₇	direct (N × H)
18. C₂×C₃×C₆₇	D₃×C₁₃	semidirect
21. C₂×C₃²×C₁₃	C₂×C₆₇	semidirect
22. C₁₃×C₃⋊D₃	C₂×C₆₇	direct (N × H)
23. C₃×C₆₇	C₂×D₃×C₁₃	semidirect
26. C₂×C₆₇	C₁₃×C₃⋊D₃	direct (N × H)
27. C₃²×C₁₃	C₂²×C₆₇	semidirect
28. C₂×C₃×C₁₃	D₃×C₆₇	semidirect
30. C₆₇	C₂×C₁₃×C₃⋊D₃	direct (N × H)
32. C₃×C₁₃	C₂×D₃×C₆₇	semidirect
33. C₂×C₃⋊D₃	C₁₃×C₆₇	direct (N × H)
35. C₂×C₁₃	C₃⋊D₃×C₆₇	direct (N × H)
36. C₂×C₃²	C₂×C₁₃×C₆₇	semidirect
37. C₃⋊D₃	C₂×C₁₃×C₆₇	direct (N × H)
38. C₁₃	C₂×C₃⋊D₃×C₆₇	direct (N × H)
40. C₃²	C₂²×C₁₃×C₆₇	semidirect
41. C₂×C₃	D₃×C₁₃×C₆₇	semidirect
44. C₃	C₂×D₃×C₁₃×C₆₇	semidirect
46. C₂	C₁₃×C₃⋊D₃×C₆₇	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×C₃⋊D₃×C₆₇	2
C₂×C₃²×C₁₃×C₆₇	2
C₂×D₃×C₁₃×C₆₇	3
C₂×C₃⋊D₃×C₆₇	13
C₂×C₁₃×C₃⋊D₃	67

Subgroups — C2×C13×C3⋊D3×C67 #44535828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₃⋊D₃×C₆₇ #44535828