Subgroups — C₃×C₆₇×Dic₃₉ #44535683

Order 31356.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×Dic₃₉	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×Dic₁₃×C₆₇	—	3	1	no	maximal
4	C₃²×C₁₃×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₆₇	—	2	1	no	—
6	C₂×C₃×C₁₃×C₆₇	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
8	Dic₁₃×C₆₇	—	3	1	no	Hall
9	C₃×C₁₃×C₆₇	—	2	1	no	—
10	C₃×C₁₃×C₆₇	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₁₃×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×Dic₃×C₆₇	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₆₇	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²×C₆₇	D₁₃	1	1	yes	characteristic
15	C₁₃×C₆₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄×C₆₇	—	39	1	no	—
17	Dic₃×C₆₇	—	13	1	no	—
18	C₃²×C₆₇	Dic₁₃	1	1	yes	characteristic, complemented, Hall
19	C₃×Dic₃₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₃×C₆₇	—	2	1	no	—
21	C₂×C₃×C₆₇	C₃×D₁₃	1	1	yes	characteristic
22	C₂×C₃×C₆₇	D₃₉	1	1	yes	characteristic
23	C₄×C₆₇	—	39	1	no	Hall
24	C₂×C₃²×C₁₃	C₂×C₆₇	1	1	yes	characteristic
25	C₃×C₆₇	—	2	1	no	—
26	C₃×C₆₇	C₃×Dic₁₃	1	1	yes	characteristic, complemented
27	C₃×C₆₇	Dic₃₉	1	1	yes	characteristic, direct product factor
28	Dic₃₉	C₃×C₆₇	1	1	yes	characteristic, direct product factor
29	C₃×Dic₁₃	—	3	1	no	—
30	C₂×C₆₇	C₃×D₃₉	1	1	yes	characteristic
31	C₃²×C₁₃	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×C₁₃	—	2	1	no	—
33	C₂×C₃×C₁₃	D₃×C₆₇	1	1	yes	characteristic
34	C₂×C₃×C₁₃	C₂×C₃×C₆₇	1	1	yes	characteristic
35	C₆₇	C₃×Dic₃₉	1	1	yes	characteristic, direct product factor, Sylow
36	Dic₁₃	—	3	1	no	Hall
37	C₃×C₁₃	—	2	1	no	—
38	C₃×C₁₃	Dic₃×C₆₇	1	1	yes	characteristic, complemented
39	C₃×C₁₃	C₃×C₄×C₆₇	1	1	yes	characteristic, complemented
40	C₃×Dic₃	—	13	1	no	Hall
41	C₂×C₁₃	C₃×D₃×C₆₇	1	1	yes	characteristic
42	C₂×C₃²	D₁₃×C₆₇	1	1	yes	characteristic
43	C₁₃	C₃×Dic₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	39	1	no	—
45	Dic₃	—	13	1	no	—
46	C₃²	Dic₁₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₃×D₁₃×C₆₇	1	1	yes	characteristic
49	C₂×C₃	C₆₇×D₃₉	1	1	yes	characteristic
50	C₄	—	39	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×Dic₁₃×C₆₇	1	1	yes	characteristic, complemented
53	C₃	C₆₇×Dic₃₉	1	1	yes	characteristic, direct product factor
54	C₂	C₃×C₆₇×D₃₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₆₇	D₃₉
commutator, hypocenter	C₃×C₁₃	C₃×C₄×C₆₇
Frattini	C₂	C₃×C₆₇×D₃₉
Fitting, socle, prime radical	C₂×C₃²×C₁₃×C₆₇	C₂
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₆₇
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₃×C₆₇

Complements

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

N	H ≅ G/N	type
2. C₆₇×Dic₃₉	C₃	direct (N × H)
4. C₃²×C₁₃×C₆₇	C₄	semidirect
10. C₃×C₁₃×C₆₇	Dic₃	semidirect
11. C₃×C₁₃×C₆₇	C₃×C₄	semidirect
15. C₁₃×C₆₇	C₃×Dic₃	semidirect
18. C₃²×C₆₇	Dic₁₃	semidirect
19. C₃×Dic₃₉	C₆₇	direct (N × H)
26. C₃×C₆₇	C₃×Dic₁₃	semidirect
27. C₃×C₆₇	Dic₃₉	direct (N × H)
28. Dic₃₉	C₃×C₆₇	direct (N × H)
31. C₃²×C₁₃	C₄×C₆₇	semidirect
35. C₆₇	C₃×Dic₃₉	direct (N × H)
38. C₃×C₁₃	Dic₃×C₆₇	semidirect
39. C₃×C₁₃	C₃×C₄×C₆₇	semidirect
43. C₁₃	C₃×Dic₃×C₆₇	semidirect
46. C₃²	Dic₁₃×C₆₇	semidirect
52. C₃	C₃×Dic₁₃×C₆₇	semidirect
53. C₃	C₆₇×Dic₃₉	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×C₃²×C₁₃×C₆₇	2
C₆₇×Dic₃₉	3
C₃×Dic₁₃×C₆₇	3
C₃×Dic₃×C₆₇	13
C₃×Dic₃₉	67

Subgroups — C3×C67×Dic39 #44535683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₆₇×Dic₃₉ #44535683