Subgroups — D₁₃⋊C₃×D₂₀₁ #44535727

Order 31356.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₃×D₂₀₁	C₂	semidirect
2. C₃⋊((C₁₃⋊C₃)⋊D₆₇)	C₂	semidirect
3. C₃×C₆₇×D₁₃⋊C₃	C₂	semidirect
4. D₁₃×D₂₀₁	C₃	semidirect
6. C₃×C₁₃⋊C₃×C₆₇	C₂²	semidirect
9. C₆₇×D₁₃⋊C₃	D₃	semidirect
11. D₂₆₁₃	C₂×C₃	semidirect
12. C₁₃×D₂₀₁	C₂×C₃	semidirect
13. C₃×D₁₃×C₆₇	C₂×C₃	semidirect
15. C₃×C₁₃×C₆₇	C₂²×C₃	semidirect
17. C₁₃⋊C₃×C₆₇	C₂×D₃	semidirect
21. D₁₃×C₆₇	C₃×D₃	semidirect
25. C₁₃×C₆₇	C₂×C₃×D₃	semidirect
34. D₂₀₁	D₁₃⋊C₃	direct (N × H)
40. C₃×D₁₃⋊C₃	D₆₇	semidirect
43. C₃×C₆₇	C₂×D₁₃⋊C₃	semidirect
49. C₃×C₁₃⋊C₃	C₂×D₆₇	semidirect
51. C₃×D₁₃	C₃×D₆₇	semidirect
56. D₁₃⋊C₃	D₂₀₁	direct (N × H)
57. C₆₇	D₃×D₁₃⋊C₃	semidirect
59. C₃×C₁₃	C₂×C₃×D₆₇	semidirect
61. C₁₃⋊C₃	C₂×D₂₀₁	semidirect
65. D₁₃	C₃×D₂₀₁	semidirect
69. C₁₃	C₂×C₃×D₂₀₁	semidirect
83. C₃	D₁₃⋊C₃×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊C₃×D₂₀₁	2
C₃⋊((C₁₃⋊C₃)⋊D₆₇)	2
C₃×C₆₇×D₁₃⋊C₃	2
D₁₃×D₂₀₁	3
D₁₃⋊C₃×D₆₇	3
C₂×C₃×D₂₀₁	13
D₃×D₁₃⋊C₃	67

Subgroups — D13⋊C3×D201 #44535727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊C₃×D₂₀₁ #44535727