Subgroups — C₂²×C₁₃×#67 #11929299

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#67	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄×C₁₃	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₃	—	2	4	no	—
7	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₁₃	C₂²	1	6	yes	complemented
9	C₂²×D₃×C₁₃	—	2	4	no	—
10	C₂²×D₃×C₁₃	C₂²	1	6	yes	complemented
11	C₁₃×#67	C₂²	1	16	yes	direct product factor
12	C₂×Dic₃×C₁₃	C₂²	1	6	yes	complemented
13	C₂⁴×C₁₃	—	3	1	no	—
14	C₂⁴×C₁₃	D₃	1	1	yes	characteristic, complemented
15	C₂×D₄×C₁₃	—	3	12	no	—
16	C₂²×C₄×C₁₃	—	3	1	no	—
17	C₂²×C₃×C₁₃	—	2	12	no	—
18	C₂²×C₃×C₁₃	D₄	1	4	yes	complemented
19	C₂²×C₃×C₁₃	C₂³	1	3	yes	—
20	C₂²×C₃×C₁₃	C₂³	1	4	yes	complemented
21	C₂×D₃×C₁₃	—	2	12	no	—
22	C₂×D₃×C₁₃	C₂³	1	4	yes	complemented
23	Dic₃×C₁₃	C₂³	1	4	yes	complemented
24	C₂³×C₁₃	—	2	4	no	—
25	C₂³×C₁₃	—	3	6	no	—
26	C₂³×C₁₃	—	6	4	no	—
27	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
28	C₂³×C₁₃	C₂×D₃	1	6	yes	complemented
29	D₄×C₁₃	—	3	16	no	—
30	C₂×C₄×C₁₃	—	3	6	no	—
31	C₂²×#67	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₃×C₁₃	—	2	4	no	—
33	C₂×C₃×C₁₃	C₂×D₄	1	6	yes	complemented
34	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
35	D₃×C₁₃	—	2	4	no	—
36	C₂²×C₁₃	—	2	12	no	—
37	C₂²×C₁₃	—	3	4	no	—
38	C₂²×C₁₃	—	6	12	no	—
39	C₂²×C₁₃	#67	1	4	yes	direct product factor
40	C₂²×C₁₃	C₂²×D₃	1	3	yes	—
41	C₂²×C₁₃	C₂²×D₃	1	4	yes	complemented
42	C₄×C₁₃	—	3	4	no	—
43	C₂⁴×C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
44	C₂³×D₃	C₂×C₁₃	1	1	yes	characteristic, complemented
45	C₂×#67	C₂×C₁₃	1	12	yes	direct product factor
46	C₂²×Dic₃	C₂×C₁₃	1	1	yes	characteristic, complemented
47	C₃×C₁₃	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
48	C₂²×D₄	—	3	1	no	Sylow
49	C₂×C₁₃	—	2	4	no	—
50	C₂×C₁₃	—	6	4	no	—
51	C₂×C₁₃	C₂×#67	1	6	yes	direct product factor
52	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
53	C₂³×C₃	—	2	4	no	—
54	C₂³×C₃	C₂²×C₁₃	1	1	yes	characteristic
55	C₂³×C₃	C₂²×C₁₃	1	6	yes	complemented
56	C₂²×D₃	—	2	4	no	—
57	C₂²×D₃	C₂²×C₁₃	1	6	yes	complemented
58	#67	C₂²×C₁₃	1	16	yes	direct product factor
59	C₂×Dic₃	C₂²×C₁₃	1	6	yes	complemented
60	C₂⁴	—	3	1	no	—
61	C₂⁴	D₃×C₁₃	1	1	yes	characteristic, complemented
62	C₂×D₄	—	3	12	no	—
63	C₂²×C₄	—	3	1	no	—
64	C₁₃	C₂²×#67	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²×C₃	—	2	12	no	—
66	C₂²×C₃	D₄×C₁₃	1	4	yes	complemented
67	C₂²×C₃	C₂³×C₁₃	1	3	yes	—
68	C₂²×C₃	C₂³×C₁₃	1	4	yes	complemented
69	C₂×D₃	—	2	12	no	—
70	C₂×D₃	C₂³×C₁₃	1	4	yes	complemented
71	Dic₃	C₂³×C₁₃	1	4	yes	complemented
72	C₂³	—	2	4	no	—
73	C₂³	—	3	6	no	—
74	C₂³	—	6	4	no	—
75	C₂³	C₂×D₃×C₁₃	1	1	yes	characteristic
76	C₂³	C₂×D₃×C₁₃	1	6	yes	complemented
77	D₄	—	3	16	no	—
78	C₂×C₄	—	3	6	no	—
79	C₂×C₃	—	2	4	no	—
80	C₂×C₃	C₂×D₄×C₁₃	1	6	yes	complemented
81	C₂×C₃	C₂⁴×C₁₃	1	1	yes	characteristic
82	D₃	—	2	4	no	—
83	C₂²	—	2	12	no	—
84	C₂²	—	3	4	no	—
85	C₂²	—	6	12	no	—
86	C₂²	C₁₃×#67	1	4	yes	direct product factor
87	C₂²	C₂²×D₃×C₁₃	1	3	yes	—
88	C₂²	C₂²×D₃×C₁₃	1	4	yes	complemented
89	C₄	—	3	4	no	—
90	C₃	C₂²×D₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	2	4	no	—
92	C₂	—	6	4	no	—
93	C₂	C₂×C₁₃×#67	1	6	yes	direct product factor
94	C₂	C₂³×D₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₁₃	C₂×D₃
commutator, cosocle	C₂×C₃	C₂⁴×C₁₃
Frattini	C₂	C₂³×D₃×C₁₃
Fitting	C₂⁴×C₃×C₁₃	C₂
socle	C₂³×C₃×C₁₃	C₂²
hypercenter	C₂⁴×C₁₃	D₃
hypocenter	C₃	C₂²×D₄×C₁₃
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂⁴×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₁₃	C₂	semidirect
2. C₂³×D₃×C₁₃	C₂	semidirect
3. C₂×C₁₃×#67	C₂	direct (N × H)
4. C₂²×Dic₃×C₁₃	C₂	semidirect
8. C₂³×C₃×C₁₃	C₂²	semidirect
10. C₂²×D₃×C₁₃	C₂²	semidirect
11. C₁₃×#67	C₂²	direct (N × H)
12. C₂×Dic₃×C₁₃	C₂²	semidirect
14. C₂⁴×C₁₃	D₃	semidirect
18. C₂²×C₃×C₁₃	D₄	semidirect
20. C₂²×C₃×C₁₃	C₂³	semidirect
22. C₂×D₃×C₁₃	C₂³	semidirect
23. Dic₃×C₁₃	C₂³	semidirect
28. C₂³×C₁₃	C₂×D₃	semidirect
31. C₂²×#67	C₁₃	direct (N × H)
33. C₂×C₃×C₁₃	C₂×D₄	semidirect
39. C₂²×C₁₃	#67	direct (N × H)
41. C₂²×C₁₃	C₂²×D₃	semidirect
43. C₂⁴×C₃	C₂×C₁₃	semidirect
44. C₂³×D₃	C₂×C₁₃	semidirect
45. C₂×#67	C₂×C₁₃	direct (N × H)
46. C₂²×Dic₃	C₂×C₁₃	semidirect
47. C₃×C₁₃	C₂²×D₄	semidirect
51. C₂×C₁₃	C₂×#67	direct (N × H)
55. C₂³×C₃	C₂²×C₁₃	semidirect
57. C₂²×D₃	C₂²×C₁₃	semidirect
58. #67	C₂²×C₁₃	direct (N × H)
59. C₂×Dic₃	C₂²×C₁₃	semidirect
61. C₂⁴	D₃×C₁₃	semidirect
64. C₁₃	C₂²×#67	direct (N × H)
66. C₂²×C₃	D₄×C₁₃	semidirect
68. C₂²×C₃	C₂³×C₁₃	semidirect
70. C₂×D₃	C₂³×C₁₃	semidirect
71. Dic₃	C₂³×C₁₃	semidirect
76. C₂³	C₂×D₃×C₁₃	semidirect
80. C₂×C₃	C₂×D₄×C₁₃	semidirect
86. C₂²	C₁₃×#67	direct (N × H)
88. C₂²	C₂²×D₃×C₁₃	semidirect
90. C₃	C₂²×D₄×C₁₃	semidirect
93. C₂	C₂×C₁₃×#67	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₁₃	2
C₂³×D₃×C₁₃	2
C₂×C₁₃×#67	2
C₂²×Dic₃×C₁₃	2
C₂²×D₄×C₁₃	3
C₂²×#67	13

Subgroups — C22×C13×#67 #11929299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#67 #11929299