Subgroups — C₆₇×(C₃⋊D₃)⋊D₁₃ #44535801

Order 31356.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₆₇×D₃₉	C₂	1	2	yes	maximal, complemented
2	C₁₃×C₃⋊D₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×D₁₃×C₆₇	—	3	2	no	maximal
4	C₃²×C₁₃×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₆₇×D₃₉	D₃	1	2	yes	complemented
6	D₃×C₁₃×C₆₇	—	3	2	no	—
7	D₃×C₁₃×C₆₇	—	6	1	no	—
8	C₃×D₁₃×C₆₇	—	3	2	no	—
9	C₂×D₁₃×C₆₇	—	9	1	no	Hall
10	C₃×C₁₃×C₆₇	—	2	1	no	—
11	C₃×C₁₃×C₆₇	C₂×D₃	1	2	yes	complemented
12	D₃²×C₆₇	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₆₇	—	9	1	no	—
14	D₁₃×C₆₇	—	3	2	no	—
15	C₃⋊D₃×C₆₇	D₁₃	1	1	yes	characteristic, complemented
16	C₃×D₃×C₆₇	—	13	2	no	—
17	C₁₃×C₆₇	D₃²	1	1	yes	characteristic, complemented, Hall
18	C₂×D₃×C₆₇	—	39	2	no	—
19	C₃²×C₆₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
20	(C₃⋊D₃)⋊D₁₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₆₇	—	39	2	no	—
22	D₃×C₆₇	—	3	2	no	—
23	D₃×C₆₇	—	6	1	no	—
24	D₃×C₆₇	—	13	2	no	—
25	C₂²×C₆₇	—	117	1	no	Hall
26	C₁₃×C₃⋊D₃	C₂×C₆₇	1	1	yes	characteristic, complemented
27	C₃×D₃₉	C₂×C₆₇	1	2	yes	complemented
28	C₃×C₆₇	—	2	1	no	—
29	C₃×C₆₇	D₃×D₁₃	1	2	yes	complemented
30	D₃×D₁₃	—	3	2	no	—
31	C₂×C₆₇	—	9	1	no	—
32	C₂×C₆₇	—	39	2	no	—
33	C₃²×C₁₃	C₂²×C₆₇	1	1	yes	characteristic, complemented, Hall
34	D₃₉	D₃×C₆₇	1	2	yes	complemented
35	C₃×D₁₃	—	3	2	no	—
36	D₃×C₁₃	—	3	2	no	—
37	D₃×C₁₃	—	6	1	no	—
38	C₆₇	(C₃⋊D₃)⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₁₃	—	9	1	no	Hall
40	C₃×C₁₃	—	2	1	no	—
41	C₃×C₁₃	C₂×D₃×C₆₇	1	2	yes	complemented
42	D₃²	—	13	1	no	Hall
43	C₂×C₁₃	—	9	1	no	—
44	D₁₃	—	3	2	no	—
45	C₃⋊D₃	D₁₃×C₆₇	1	1	yes	characteristic, complemented
46	C₃×D₃	—	13	2	no	—
47	C₁₃	D₃²×C₆₇	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₃	—	39	2	no	—
49	C₃²	C₂×D₁₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	39	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	13	2	no	—
54	C₂²	—	117	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₁₃×C₆₇	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	39	2	no	—

	subgroup	G/H
center, hypercenter	C₆₇	(C₃⋊D₃)⋊D₁₃
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₆₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₆₇	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₆₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₆₇×D₃₉	C₂	semidirect
2. C₁₃×C₃⋊D₃×C₆₇	C₂	semidirect
4. C₃²×C₁₃×C₆₇	C₂²	semidirect
5. C₆₇×D₃₉	D₃	semidirect
11. C₃×C₁₃×C₆₇	C₂×D₃	semidirect
15. C₃⋊D₃×C₆₇	D₁₃	semidirect
17. C₁₃×C₆₇	D₃²	semidirect
19. C₃²×C₆₇	C₂×D₁₃	semidirect
20. (C₃⋊D₃)⋊D₁₃	C₆₇	direct (N × H)
26. C₁₃×C₃⋊D₃	C₂×C₆₇	semidirect
27. C₃×D₃₉	C₂×C₆₇	semidirect
29. C₃×C₆₇	D₃×D₁₃	semidirect
33. C₃²×C₁₃	C₂²×C₆₇	semidirect
34. D₃₉	D₃×C₆₇	semidirect
38. C₆₇	(C₃⋊D₃)⋊D₁₃	direct (N × H)
41. C₃×C₁₃	C₂×D₃×C₆₇	semidirect
45. C₃⋊D₃	D₁₃×C₆₇	semidirect
47. C₁₃	D₃²×C₆₇	semidirect
49. C₃²	C₂×D₁₃×C₆₇	semidirect
56. C₃	D₃×D₁₃×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₆₇×D₃₉	2
C₁₃×C₃⋊D₃×C₆₇	2
D₃×D₁₃×C₆₇	3
D₃²×C₆₇	13
(C₃⋊D₃)⋊D₁₃	67

Subgroups — C67×(C3⋊D3)⋊D13 #44535801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×(C₃⋊D₃)⋊D₁₃ #44535801