Subgroups — C₂×C₃×#19104947 #44535754

Order 31356.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#14579732	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#19104947	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#19104947	C₃	1	3	yes	maximal, direct product factor
5	C₃×#14579732	C₂²	1	1	yes	characteristic, complemented, Hall
6	#19104947	C₂×C₃	1	6	yes	direct product factor
7	C₃×D₁₃×C₆₇	C₂×C₃	1	2	yes	complemented
8	C₂×#14579732	C₂×C₃	1	3	yes	complemented
9	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×D₁₃×C₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented
12	#14579732	C₂²×C₃	1	3	yes	complemented
13	C₂²×C₃×C₆₇⋊C₃	—	13	1	no	maximal, Hall
14	C₂×C₁₃×C₆₇	C₂×C₃²	1	1	yes	characteristic, complemented
15	D₁₃×C₆₇	C₂×C₃²	1	2	yes	complemented
16	C₂×C₃×C₆₇⋊C₃	—	13	2	no	—
17	C₂×C₃×C₆₇⋊C₃	—	13	1	no	—
18	C₁₃×C₆₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃×C₆₇	—	13	1	no	—
20	C₂²×C₆₇⋊C₃	—	13	3	no	—
21	C₃×C₆₇⋊C₃	—	13	1	no	Hall
22	C₂×C₃×D₁₃⋊C₃	—	67	1	no	maximal, Hall
23	C₂×C₃×C₆₇	—	13	2	no	—
24	C₂×C₃×C₆₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
25	C₂×C₆₇⋊C₃	—	13	6	no	—
26	C₂×C₆₇⋊C₃	—	13	3	no	—
27	C₂²×C₆₇	—	13	1	no	Hall
28	C₂×C₃×C₁₃⋊C₃	—	67	1	no	—
29	C₃×D₁₃⋊C₃	—	67	2	no	—
30	C₃×C₆₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₆₇⋊C₃	—	13	3	no	—
32	C₂×C₃×D₁₃	C₆₇⋊C₃	1	1	yes	characteristic, complemented
33	C₂×D₁₃⋊C₃	—	67	3	no	—
34	C₂×C₆₇	—	13	2	no	—
35	C₂×C₆₇	C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented
36	C₃×C₁₃⋊C₃	—	67	1	no	Hall
37	C₂×C₃×C₁₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented
38	C₃×D₁₃	C₂×C₆₇⋊C₃	1	2	yes	complemented
39	C₂×C₁₃⋊C₃	—	67	3	no	—
40	D₁₃⋊C₃	—	67	6	no	—
41	C₆₇	C₂×C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×D₁₃	C₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
43	C₃×C₁₃	C₂²×C₆₇⋊C₃	1	1	yes	characteristic, complemented
44	C₁₃⋊C₃	—	67	3	no	—
45	C₂²×C₃²	—	871	1	no	Hall
46	C₂×C₁₃	C₂×C₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented
47	D₁₃	C₂×C₃×C₆₇⋊C₃	1	2	yes	complemented
48	C₂×C₃²	—	871	2	no	—
49	C₂×C₃²	—	871	1	no	—
50	C₁₃	C₂²×C₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₃	—	13	1	no	—
52	C₂²×C₃	—	871	3	no	—
53	C₃²	—	871	1	no	Sylow
54	C₂×C₃	—	13	2	no	—
55	C₂×C₃	—	871	6	no	—
56	C₂×C₃	—	871	3	no	—
57	C₂×C₃	#19104947	1	1	yes	characteristic, direct product factor
58	C₂²	—	13	1	no	Sylow
59	C₃	—	871	3	no	—
60	C₃	C₂×#19104947	1	1	yes	characteristic, direct product factor
61	C₂	—	13	2	no	—
62	C₂	C₃×#19104947	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#19104947
commutator, cosocle, hypocenter	C₁₃×C₆₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#14579732	C₂	semidirect
2. C₃×#19104947	C₂	direct (N × H)
3. C₂×C₃×D₁₃×C₆₇	C₃	semidirect
4. C₂×#19104947	C₃	direct (N × H)
5. C₃×#14579732	C₂²	semidirect
6. #19104947	C₂×C₃	direct (N × H)
7. C₃×D₁₃×C₆₇	C₂×C₃	semidirect
8. C₂×#14579732	C₂×C₃	semidirect
9. C₂×C₃×C₁₃×C₆₇	C₂×C₃	semidirect
10. C₂×D₁₃×C₆₇	C₃²	semidirect
11. C₃×C₁₃×C₆₇	C₂²×C₃	semidirect
12. #14579732	C₂²×C₃	semidirect
14. C₂×C₁₃×C₆₇	C₂×C₃²	semidirect
15. D₁₃×C₆₇	C₂×C₃²	semidirect
18. C₁₃×C₆₇	C₂²×C₃²	semidirect
24. C₂×C₃×C₆₇	D₁₃⋊C₃	semidirect
30. C₃×C₆₇	C₂×D₁₃⋊C₃	semidirect
32. C₂×C₃×D₁₃	C₆₇⋊C₃	semidirect
35. C₂×C₆₇	C₃×D₁₃⋊C₃	semidirect
37. C₂×C₃×C₁₃	C₂×C₆₇⋊C₃	semidirect
38. C₃×D₁₃	C₂×C₆₇⋊C₃	semidirect
41. C₆₇	C₂×C₃×D₁₃⋊C₃	semidirect
42. C₂×D₁₃	C₃×C₆₇⋊C₃	semidirect
43. C₃×C₁₃	C₂²×C₆₇⋊C₃	semidirect
46. C₂×C₁₃	C₂×C₃×C₆₇⋊C₃	semidirect
47. D₁₃	C₂×C₃×C₆₇⋊C₃	semidirect
50. C₁₃	C₂²×C₃×C₆₇⋊C₃	semidirect
57. C₂×C₃	#19104947	direct (N × H)
60. C₃	C₂×#19104947	direct (N × H)
62. C₂	C₃×#19104947	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×#14579732	2
C₃×#19104947	2
C₂×C₃×D₁₃×C₆₇	3
C₂×#19104947	3
C₂²×C₃×C₆₇⋊C₃	13
C₂×C₃×D₁₃⋊C₃	67

Subgroups — C2×C3×#19104947 #44535754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#19104947 #44535754