Subgroups — C₂×C₉×D₁₃×C₆₇ #44535639

Order 31356.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₁₃×C₆₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic
4	C₉×C₁₃×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₁₃×C₆₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
7	C₂×D₁₃×C₆₇	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic
9	C₂²×C₉×C₆₇	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₆₇	C₂×C₉	1	1	yes	characteristic, complemented
11	D₁₃×C₆₇	C₂×C₉	1	2	yes	direct product factor
12	C₂×C₉×C₆₇	—	13	2	no	—
13	C₂×C₉×C₆₇	D₁₃	1	1	yes	characteristic, direct product factor
14	C₁₃×C₆₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₃×C₆₇	—	13	1	no	—
16	C₉×C₆₇	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₉×D₁₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₃×C₆₇	—	13	2	no	—
19	C₂×C₃×C₆₇	C₃×D₁₃	1	1	yes	characteristic
20	C₂²×C₆₇	—	13	1	no	Hall
21	C₂×C₉×C₁₃	C₂×C₆₇	1	1	yes	characteristic, complemented
22	C₉×D₁₃	C₂×C₆₇	1	2	yes	direct product factor
23	C₃×C₆₇	C₂×C₃×D₁₃	1	1	yes	characteristic
24	C₂×C₃×D₁₃	C₃×C₆₇	1	1	yes	characteristic
25	C₂×C₆₇	—	13	2	no	—
26	C₂×C₆₇	C₉×D₁₃	1	1	yes	characteristic, direct product factor
27	C₉×C₁₃	C₂²×C₆₇	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₃	C₂×C₃×C₆₇	1	1	yes	characteristic
29	C₃×D₁₃	C₂×C₃×C₆₇	1	2	yes	—
30	C₆₇	C₂×C₉×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×D₁₃	C₉×C₆₇	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₃	C₂²×C₃×C₆₇	1	1	yes	characteristic
33	C₂²×C₉	—	13	1	no	Hall
34	C₂×C₁₃	C₂×C₉×C₆₇	1	1	yes	characteristic, complemented
35	D₁₃	C₂×C₉×C₆₇	1	2	yes	direct product factor
36	C₂×C₉	—	13	2	no	—
37	C₂×C₉	D₁₃×C₆₇	1	1	yes	characteristic, direct product factor
38	C₁₃	C₂²×C₉×C₆₇	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	13	1	no	—
40	C₉	C₂×D₁₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	13	2	no	—
42	C₂×C₃	C₃×D₁₃×C₆₇	1	1	yes	characteristic
43	C₂²	—	13	1	no	Sylow
44	C₃	C₂×C₃×D₁₃×C₆₇	1	1	yes	characteristic
45	C₂	—	13	2	no	—
46	C₂	C₉×D₁₃×C₆₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉×C₆₇	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₉×C₆₇
Frattini	C₃	C₂×C₃×D₁₃×C₆₇
Fitting	C₂×C₉×C₁₃×C₆₇	C₂
socle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
prime radical	C₂×C₃×D₁₃×C₆₇	C₃
cosocle	C₃×C₁₃	C₂²×C₃×C₆₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₉×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₉×D₁₃×C₆₇	C₂	direct (N × H)
2. C₂×C₉×C₁₃×C₆₇	C₂	semidirect
4. C₉×C₁₃×C₆₇	C₂²	semidirect
7. C₂×D₁₃×C₆₇	C₉	direct (N × H)
10. C₂×C₁₃×C₆₇	C₂×C₉	semidirect
11. D₁₃×C₆₇	C₂×C₉	direct (N × H)
13. C₂×C₉×C₆₇	D₁₃	direct (N × H)
14. C₁₃×C₆₇	C₂²×C₉	semidirect
16. C₉×C₆₇	C₂×D₁₃	direct (N × H)
17. C₂×C₉×D₁₃	C₆₇	direct (N × H)
21. C₂×C₉×C₁₃	C₂×C₆₇	semidirect
22. C₉×D₁₃	C₂×C₆₇	direct (N × H)
26. C₂×C₆₇	C₉×D₁₃	direct (N × H)
27. C₉×C₁₃	C₂²×C₆₇	semidirect
30. C₆₇	C₂×C₉×D₁₃	direct (N × H)
31. C₂×D₁₃	C₉×C₆₇	direct (N × H)
34. C₂×C₁₃	C₂×C₉×C₆₇	semidirect
35. D₁₃	C₂×C₉×C₆₇	direct (N × H)
37. C₂×C₉	D₁₃×C₆₇	direct (N × H)
38. C₁₃	C₂²×C₉×C₆₇	semidirect
40. C₉	C₂×D₁₃×C₆₇	direct (N × H)
46. C₂	C₉×D₁₃×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
C₉×D₁₃×C₆₇	2
C₂×C₉×C₁₃×C₆₇	2
C₂×C₃×D₁₃×C₆₇	3
C₂²×C₉×C₆₇	13
C₂×C₉×D₁₃	67

Subgroups — C2×C9×D13×C67 #44535639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₁₃×C₆₇ #44535639