Subgroups — C₃×D₁₃×D₁₆₁ #38737411

Order 25116.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₀₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₁₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₀₉₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₁₆₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₂₃×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₁₃×D₂₃	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₁₆₁	—	13	1	no	maximal, Hall
12	C₃×D₂₉₉	—	7	1	no	—
13	C₃×C₂₃×D₁₃	D₇	1	1	yes	characteristic, complemented
14	C₃×C₁₃×D₂₃	—	7	1	no	—
15	D₁₃×D₂₃	—	7	1	no	Hall
16	C₃×D₇×D₁₃	—	23	1	no	maximal, Hall
17	C₂×C₃×C₇×C₂₃	—	13	1	no	—
18	C₃×D₁₆₁	—	13	1	no	—
19	C₃×D₁₆₁	D₁₃	1	1	yes	characteristic, direct product factor
20	C₃×C₁₃×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₂×D₁₆₁	—	13	1	no	Hall
22	D₂₉₉	—	7	1	no	—
23	C₁₃×D₂₃	—	7	1	no	—
24	C₂₃×D₁₃	C₃×D₇	1	1	yes	characteristic, complemented
25	C₃×D₉₁	—	23	1	no	—
26	C₃×C₁₃×D₇	—	23	1	no	—
27	C₃×C₇×D₁₃	D₂₃	1	1	yes	characteristic, complemented
28	C₃×C₇×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	D₇×D₁₃	—	23	1	no	Hall
30	C₂×C₇×C₂₃	—	13	1	no	—
31	D₁₆₁	—	13	1	no	—
32	D₁₆₁	C₃×D₁₃	1	1	yes	characteristic, direct product factor
33	C₁₃×C₂₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×D₂₃	—	91	1	no	Hall
35	C₃×C₇×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
36	D₉₁	—	23	1	no	—
37	C₇×D₁₃	C₃×D₂₃	1	1	yes	characteristic, complemented
38	C₁₃×D₇	—	23	1	no	—
39	C₇×C₂₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×D₁₃	—	161	1	no	Hall
41	C₂×C₃×C₂₃	—	13	1	no	—
42	C₃×D₂₃	—	7	1	no	—
43	C₃×D₂₃	—	91	1	no	—
44	C₂×D₂₃	—	91	1	no	Hall
45	C₇×C₁₃	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×D₇	—	299	1	no	Hall
47	C₂×C₃×C₁₃	—	161	1	no	—
48	C₃×D₁₃	—	161	1	no	—
49	C₃×D₁₃	D₁₆₁	1	1	yes	characteristic, direct product factor
50	C₃×C₂₃	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	161	1	no	Hall
52	C₂×C₂₃	—	13	1	no	—
53	D₂₃	—	7	1	no	—
54	D₂₃	—	91	1	no	—
55	C₂×C₃×C₇	—	13	1	no	—
56	C₃×D₇	—	23	1	no	—
57	C₃×D₇	—	299	1	no	—
58	C₃×C₁₃	C₂×D₁₆₁	1	1	yes	characteristic, complemented, Hall
59	C₂×D₇	—	299	1	no	Hall
60	C₂×C₁₃	—	161	1	no	—
61	D₁₃	—	161	1	no	—
62	D₁₃	C₃×D₁₆₁	1	1	yes	characteristic, direct product factor
63	C₂₃	C₃×D₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₇	D₁₃×D₂₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	13	1	no	—
66	D₇	—	23	1	no	—
67	D₇	—	299	1	no	—
68	C₁₃	C₂×C₃×D₁₆₁	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₃	—	2093	1	no	Hall
70	C₇	C₃×D₁₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	13	1	no	—
72	C₂×C₃	—	2093	1	no	—
73	C₂×C₃	—	161	1	no	—
74	C₂²	—	2093	1	no	Sylow
75	C₃	D₁₃×D₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	13	1	no	—
77	C₂	—	2093	1	no	—
78	C₂	—	161	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₃×D₁₆₁
commutator, cosocle, hypocenter	C₇×C₁₃×C₂₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₂₃	C₂²
LCS	G ▷ C₇×C₁₃×C₂₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₀₉₃	C₂	semidirect
2. C₃×C₁₃×D₁₆₁	C₂	semidirect
3. C₃×C₇×C₂₃×D₁₃	C₂	semidirect
4. D₁₃×D₁₆₁	C₃	direct (N × H)
5. C₃×C₇×C₁₃×C₂₃	C₂²	semidirect
6. D₂₀₉₃	C₂×C₃	semidirect
7. C₁₃×D₁₆₁	C₂×C₃	semidirect
8. C₇×C₂₃×D₁₃	C₂×C₃	semidirect
10. C₇×C₁₃×C₂₃	C₂²×C₃	semidirect
13. C₃×C₂₃×D₁₃	D₇	semidirect
19. C₃×D₁₆₁	D₁₃	direct (N × H)
20. C₃×C₁₃×C₂₃	C₂×D₇	semidirect
24. C₂₃×D₁₃	C₃×D₇	semidirect
27. C₃×C₇×D₁₃	D₂₃	semidirect
28. C₃×C₇×C₂₃	C₂×D₁₃	semidirect
32. D₁₆₁	C₃×D₁₃	direct (N × H)
33. C₁₃×C₂₃	C₂×C₃×D₇	semidirect
35. C₃×C₇×C₁₃	C₂×D₂₃	semidirect
37. C₇×D₁₃	C₃×D₂₃	semidirect
39. C₇×C₂₃	C₂×C₃×D₁₃	semidirect
45. C₇×C₁₃	C₂×C₃×D₂₃	semidirect
49. C₃×D₁₃	D₁₆₁	direct (N × H)
50. C₃×C₂₃	D₇×D₁₃	semidirect
58. C₃×C₁₃	C₂×D₁₆₁	semidirect
62. D₁₃	C₃×D₁₆₁	direct (N × H)
63. C₂₃	C₃×D₇×D₁₃	semidirect
64. C₃×C₇	D₁₃×D₂₃	semidirect
68. C₁₃	C₂×C₃×D₁₆₁	semidirect
70. C₇	C₃×D₁₃×D₂₃	semidirect
75. C₃	D₁₃×D₁₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₂₀₉₃	2
C₃×C₁₃×D₁₆₁	2
C₃×C₇×C₂₃×D₁₃	2
D₁₃×D₁₆₁	3
C₃×D₁₃×D₂₃	7
C₂×C₃×D₁₆₁	13
C₃×D₇×D₁₃	23

Subgroups — C3×D13×D161 #38737411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₃×D₁₆₁ #38737411