Subgroups — C₂×D₃×C₁₃×C₆₇⋊C₃ #44535762

Order 31356.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₆₇⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×C₆₇⋊C₃	—	3	1	no	maximal
5	C₃×C₁₃×C₆₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₃×C₆₇	C₂×C₃	1	2	yes	complemented
7	C₂×C₁₃×C₆₇⋊C₃	—	2	1	no	—
8	C₂×C₁₃×C₆₇⋊C₃	—	3	2	no	—
9	C₂×C₁₃×C₆₇⋊C₃	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×C₁₃×C₆₇	—	3	1	no	Hall
12	C₃×C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₁₃×C₆₇⋊C₃	—	2	1	no	—
14	C₁₃×C₆₇⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₂×D₃×C₆₇⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₁₃×C₆₇	—	3	2	no	—
17	C₂×C₁₃×C₆₇	C₃×D₃	1	1	yes	characteristic, complemented
18	C₂×C₃×C₆₇⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
19	D₃×C₆₇⋊C₃	C₂×C₁₃	1	2	yes	direct product factor
20	C₁₃×C₆₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃×C₆₇	C₃×C₁₃	1	1	yes	characteristic, complemented
22	C₂²×C₆₇⋊C₃	—	3	1	no	—
23	C₃×C₆₇⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×D₃×C₁₃	—	67	1	no	maximal, Hall
25	C₂×C₃×C₆₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
26	D₃×C₆₇	C₂×C₃×C₁₃	1	2	yes	complemented
27	C₂×C₆₇⋊C₃	—	2	1	no	—
28	C₂×C₆₇⋊C₃	—	3	2	no	—
29	C₂×C₆₇⋊C₃	D₃×C₁₃	1	1	yes	characteristic, direct product factor
30	C₂²×C₆₇	—	3	1	no	Hall
31	C₂×C₃²×C₁₃	—	67	1	no	—
32	C₃×D₃×C₁₃	—	67	2	no	—
33	C₃×C₆₇	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
34	C₆₇⋊C₃	—	2	1	no	—
35	C₆₇⋊C₃	C₂×D₃×C₁₃	1	1	yes	characteristic, direct product factor
36	C₂²×C₃×C₁₃	—	201	1	no	—
37	C₂×D₃×C₁₃	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
38	C₂×C₆₇	—	3	2	no	—
39	C₂×C₆₇	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented
40	C₃²×C₁₃	—	67	1	no	Hall
41	C₂×C₃×C₁₃	—	67	1	no	—
42	C₂×C₃×C₁₃	—	134	1	no	—
43	C₂×C₃×C₁₃	—	201	2	no	—
44	C₂×C₃×C₁₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented
45	D₃×C₁₃	C₂×C₆₇⋊C₃	1	2	yes	direct product factor
46	C₆₇	C₂×C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₁₃	—	3	1	no	Hall
48	C₃×C₁₃	—	67	1	no	—
49	C₃×C₁₃	—	134	1	no	—
50	C₃×C₁₃	C₂²×C₆₇⋊C₃	1	1	yes	characteristic, complemented
51	C₂×C₃×D₃	—	67	1	no	Hall
52	C₂×C₁₃	—	3	2	no	—
53	C₂×C₁₃	D₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
54	C₂×C₃²	—	67	1	no	—
55	C₃×D₃	—	67	2	no	—
56	C₁₃	C₂×D₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₃	—	201	1	no	—
58	C₂×D₃	C₁₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
59	C₃²	—	67	1	no	Sylow
60	C₂×C₃	—	67	1	no	—
61	C₂×C₃	—	134	1	no	—
62	C₂×C₃	—	201	2	no	—
63	C₂×C₃	C₂×C₁₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented
64	D₃	C₂×C₁₃×C₆₇⋊C₃	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	67	1	no	—
67	C₃	—	134	1	no	—
68	C₃	C₂²×C₁₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	D₃×C₁₃×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₃×C₆₇⋊C₃	C₂	semidirect
2. D₃×C₁₃×C₆₇⋊C₃	C₂	direct (N × H)
3. C₂×D₃×C₁₃×C₆₇	C₃	semidirect
5. C₃×C₁₃×C₆₇⋊C₃	C₂²	semidirect
6. D₃×C₁₃×C₆₇	C₂×C₃	semidirect
9. C₂×C₁₃×C₆₇⋊C₃	D₃	direct (N × H)
10. C₂×C₃×C₁₃×C₆₇	C₂×C₃	semidirect
12. C₃×C₁₃×C₆₇	C₂²×C₃	semidirect
14. C₁₃×C₆₇⋊C₃	C₂×D₃	direct (N × H)
15. C₂×D₃×C₆₇⋊C₃	C₁₃	direct (N × H)
17. C₂×C₁₃×C₆₇	C₃×D₃	semidirect
18. C₂×C₃×C₆₇⋊C₃	C₂×C₁₃	semidirect
19. D₃×C₆₇⋊C₃	C₂×C₁₃	direct (N × H)
20. C₁₃×C₆₇	C₂×C₃×D₃	semidirect
21. C₂×D₃×C₆₇	C₃×C₁₃	semidirect
23. C₃×C₆₇⋊C₃	C₂²×C₁₃	semidirect
25. C₂×C₃×C₆₇	C₂×C₃×C₁₃	semidirect
26. D₃×C₆₇	C₂×C₃×C₁₃	semidirect
29. C₂×C₆₇⋊C₃	D₃×C₁₃	direct (N × H)
33. C₃×C₆₇	C₂²×C₃×C₁₃	semidirect
35. C₆₇⋊C₃	C₂×D₃×C₁₃	direct (N × H)
37. C₂×D₃×C₁₃	C₆₇⋊C₃	direct (N × H)
39. C₂×C₆₇	C₃×D₃×C₁₃	semidirect
44. C₂×C₃×C₁₃	C₂×C₆₇⋊C₃	semidirect
45. D₃×C₁₃	C₂×C₆₇⋊C₃	direct (N × H)
46. C₆₇	C₂×C₃×D₃×C₁₃	semidirect
50. C₃×C₁₃	C₂²×C₆₇⋊C₃	semidirect
53. C₂×C₁₃	D₃×C₆₇⋊C₃	direct (N × H)
56. C₁₃	C₂×D₃×C₆₇⋊C₃	direct (N × H)
58. C₂×D₃	C₁₃×C₆₇⋊C₃	direct (N × H)
63. C₂×C₃	C₂×C₁₃×C₆₇⋊C₃	semidirect
64. D₃	C₂×C₁₃×C₆₇⋊C₃	direct (N × H)
68. C₃	C₂²×C₁₃×C₆₇⋊C₃	semidirect
70. C₂	D₃×C₁₃×C₆₇⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₃×C₆₇⋊C₃	2
D₃×C₁₃×C₆₇⋊C₃	2
C₂×D₃×C₁₃×C₆₇	3
C₂²×C₁₃×C₆₇⋊C₃	3
C₂×D₃×C₆₇⋊C₃	13
C₂×C₃×D₃×C₁₃	67

Subgroups — C2×D3×C13×C67⋊C3 #44535762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₁₃×C₆₇⋊C₃ #44535762