Subgroups — D₃₉⋊D₂₀₁ #44535802

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	1	yes	maximal, characteristic, complemented
2	C₃×D₂₆₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₃⋊D₂₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉⋊D₆₇	—	3	1	no	maximal
5	D₁₃×D₂₀₁	—	3	1	no	maximal
6	C₃²×C₁₃×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₆₁₃	D₃	1	1	yes	characteristic, complemented
8	C₆₇×D₃₉	D₃	1	1	yes	characteristic, complemented
9	C₁₃×D₂₀₁	—	3	1	no	—
10	C₁₃×D₂₀₁	—	3	1	no	—
11	C₁₃×D₂₀₁	—	6	1	no	—
12	C₃×D₈₇₁	—	3	1	no	—
13	C₃×D₁₃×C₆₇	—	3	1	no	—
14	D₁₃×D₆₇	—	9	1	no	Hall
15	C₃×C₁₃×C₆₇	—	2	1	no	—
16	C₃×C₁₃×C₆₇	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₆₇	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃×D₂₀₁	—	13	1	no	maximal, Hall
19	D₈₇₁	—	3	1	no	—
20	C₁₃×D₆₇	—	9	1	no	—
21	D₁₃×C₆₇	—	3	1	no	—
22	C₃⋊D₂₀₁	D₁₃	1	1	yes	characteristic, complemented
23	C₃×D₂₀₁	—	13	1	no	—
24	C₃×D₃×C₆₇	—	13	1	no	—
25	C₁₃×C₆₇	D₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×D₂₀₁	—	39	1	no	—
27	D₃×D₆₇	—	39	1	no	—
28	C₃²×C₆₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	(C₃⋊D₃)⋊D₁₃	—	67	1	no	maximal, Hall
30	C₂×C₃×C₆₇	—	39	1	no	—
31	D₂₀₁	—	3	1	no	—
32	D₂₀₁	—	3	1	no	—
33	D₂₀₁	—	6	1	no	—
34	D₂₀₁	—	13	1	no	—
35	C₃×D₆₇	—	39	1	no	—
36	D₃×C₆₇	—	13	1	no	—
37	C₂×D₆₇	—	117	1	no	Hall
38	C₁₃×C₃⋊D₃	—	67	1	no	—
39	C₃×D₃₉	—	67	1	no	—
40	C₃×D₃₉	D₆₇	1	1	yes	characteristic, complemented
41	C₃×C₆₇	—	2	1	no	—
42	C₃×C₆₇	D₃×D₁₃	1	1	yes	characteristic, complemented
43	C₃×C₆₇	D₃×D₁₃	1	1	yes	characteristic, complemented
44	D₃×D₁₃	—	201	1	no	—
45	D₃×D₁₃	—	201	1	no	—
46	C₂×C₆₇	—	39	1	no	—
47	D₆₇	—	9	1	no	—
48	D₆₇	—	39	1	no	—
49	C₃²×C₁₃	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
50	D₃₉	—	67	1	no	—
51	D₃₉	D₂₀₁	1	1	yes	characteristic, complemented
52	C₃×D₁₃	—	3	1	no	—
53	C₃×D₁₃	—	201	1	no	—
54	D₃×C₁₃	—	402	1	no	—
55	D₃×C₁₃	—	201	1	no	—
56	D₃×C₁₃	—	201	1	no	—
57	C₆₇	(C₃⋊D₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₁₃	—	603	1	no	Hall
59	C₃×C₁₃	—	2	1	no	—
60	C₃×C₁₃	D₃×D₆₇	1	1	yes	characteristic, complemented
61	C₃×C₁₃	C₂×D₂₀₁	1	1	yes	characteristic, complemented
62	D₃²	—	871	1	no	Hall
63	C₂×C₁₃	—	603	1	no	—
64	D₁₃	—	3	1	no	—
65	D₁₃	—	201	1	no	—
66	C₃⋊D₃	—	67	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	—	871	1	no	—
69	C₁₃	D₃×D₂₀₁	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₃	—	2613	1	no	—
71	C₂×D₃	—	2613	1	no	—
72	C₃²	D₁₃×D₆₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	39	1	no	—
74	C₂×C₃	—	2613	1	no	—
75	D₃	—	13	1	no	—
76	D₃	—	871	1	no	—
77	D₃	—	402	1	no	—
78	D₃	—	201	1	no	—
79	D₃	—	201	1	no	—
80	C₂²	—	7839	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₃×D₂₀₁	1	1	yes	characteristic, complemented
83	C₃	D₃₉⋊D₆₇	1	1	yes	characteristic, complemented
84	C₂	—	39	1	no	—
85	C₂	—	2613	1	no	—
86	C₂	—	603	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₆₇×D₃₉	C₂	semidirect
2. C₃×D₂₆₁₃	C₂	semidirect
3. C₁₃×C₃⋊D₂₀₁	C₂	semidirect
6. C₃²×C₁₃×C₆₇	C₂²	semidirect
7. D₂₆₁₃	D₃	semidirect
8. C₆₇×D₃₉	D₃	semidirect
16. C₃×C₁₃×C₆₇	C₂×D₃	semidirect
17. C₃×C₁₃×C₆₇	C₂×D₃	semidirect
22. C₃⋊D₂₀₁	D₁₃	semidirect
25. C₁₃×C₆₇	D₃²	semidirect
28. C₃²×C₆₇	C₂×D₁₃	semidirect
40. C₃×D₃₉	D₆₇	semidirect
42. C₃×C₆₇	D₃×D₁₃	semidirect
43. C₃×C₆₇	D₃×D₁₃	semidirect
49. C₃²×C₁₃	C₂×D₆₇	semidirect
51. D₃₉	D₂₀₁	semidirect
57. C₆₇	(C₃⋊D₃)⋊D₁₃	semidirect
60. C₃×C₁₃	D₃×D₆₇	semidirect
61. C₃×C₁₃	C₂×D₂₀₁	semidirect
69. C₁₃	D₃×D₂₀₁	semidirect
72. C₃²	D₁₃×D₆₇	semidirect
82. C₃	D₁₃×D₂₀₁	semidirect
83. C₃	D₃₉⋊D₆₇	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
C₃×D₂₆₁₃	2
C₁₃×C₃⋊D₂₀₁	2
D₃₉⋊D₆₇	3
D₁₃×D₂₀₁	3
D₃×D₂₀₁	13
(C₃⋊D₃)⋊D₁₃	67

Subgroups — D39⋊D201 #44535802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₉⋊D₂₀₁ #44535802