Subgroups — C₂³×C₄×#261 #13131806

Order 1664.

3000 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#261	C₂	1	2	yes	maximal
2	C₂³×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×#261	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×D₁₃	C₂²	1	1	yes	characteristic
5	C₂³×#261	C₄	1	32	yes	direct product factor
6	C₂³×#261	C₂²	1	28	yes	—
7	C₂³×C₄×C₁₃	C₄	1	1	yes	characteristic, complemented
8	C₂³×Dic₁₃	C₄	1	1	yes	characteristic, complemented
9	C₂²×C₄×D₁₃	C₄	1	14	yes	complemented
10	C₂²×C₄×D₁₃	C₂²	1	14	yes	—
11	C₂×C₄×#261	C₂²	1	112	yes	direct product factor
12	C₂⁴×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂³×D₁₃	C₂×C₄	1	7	yes	—
14	C₂³×D₁₃	C₂×C₄	1	16	yes	—
15	C₂³×D₁₃	C₂³	1	7	yes	—
16	C₂²×#261	C₂×C₄	1	224	yes	direct product factor
17	C₂²×#261	C₂³	1	56	yes	—
18	C₂²×C₄×C₁₃	C₂×C₄	1	14	yes	complemented
19	C₂²×Dic₁₃	C₂×C₄	1	14	yes	complemented
20	C₂×C₄×D₁₃	C₂×C₄	1	84	yes	complemented
21	C₂×C₄×D₁₃	C₂³	1	28	yes	—
22	C₄×#261	C₂³	1	64	yes	direct product factor
23	C₂³×C₄²	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	C₄²	1	8	yes	complemented
25	C₂³×C₁₃	C₂²×C₄	1	7	yes	—
26	C₂²×D₁₃	C₄²	1	56	yes	complemented
27	C₂²×D₁₃	C₂²×C₄	1	21	yes	—
28	C₂²×D₁₃	C₂²×C₄	1	56	yes	—
29	C₂²×D₁₃	C₂⁴	1	7	yes	—
30	C₂×#261	C₂²×C₄	1	224	yes	direct product factor
31	C₂×#261	C₂⁴	1	16	yes	—
32	C₂×C₄×C₁₃	C₂²×C₄	1	28	yes	complemented
33	C₂×Dic₁₃	C₂²×C₄	1	28	yes	complemented
34	C₄×D₁₃	C₂²×C₄	1	56	yes	complemented
35	C₄×D₁₃	C₂⁴	1	8	yes	—
36	C₂⁴×C₄	—	13	2	no	—
37	C₂⁴×C₄	—	13	1	no	—
38	C₂²×C₄²	—	13	28	no	—
39	C₂²×C₁₃	C₂×C₄²	1	28	yes	complemented
40	C₂²×C₁₃	C₂³×C₄	1	7	yes	—
41	C₂×D₁₃	C₂×C₄²	1	84	yes	complemented
42	C₂×D₁₃	C₂³×C₄	1	28	yes	—
43	C₂×D₁₃	C₂³×C₄	1	7	yes	—
44	C₂×D₁₃	C₂⁵	1	1	yes	characteristic
45	#261	C₂³×C₄	1	32	yes	direct product factor
46	C₄×C₁₃	C₂³×C₄	1	8	yes	complemented
47	Dic₁₃	C₂³×C₄	1	8	yes	complemented
48	C₂⁵	—	13	1	no	—
49	C₂³×C₄	—	13	32	no	—
50	C₂³×C₄	—	13	28	no	—
51	C₂³×C₄	—	13	1	no	—
52	C₂³×C₄	—	13	14	no	—
53	C₂³×C₄	—	13	14	no	—
54	C₂³×C₄	#261	1	1	yes	characteristic, direct product factor
55	C₂×C₄²	—	13	112	no	—
56	C₂×C₁₃	C₂²×C₄²	1	14	yes	complemented
57	C₂×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
58	D₁₃	C₂²×C₄²	1	14	yes	complemented
59	D₁₃	C₂⁴×C₄	1	2	yes	—
60	C₂⁴	—	13	16	no	—
61	C₂⁴	—	13	7	no	—
62	C₂⁴	—	13	7	no	—
63	C₂⁴	C₂×#261	1	1	yes	characteristic
64	C₂²×C₄	—	13	56	no	—
65	C₂²×C₄	—	13	224	no	—
66	C₂²×C₄	—	13	14	no	—
67	C₂²×C₄	—	13	28	no	—
68	C₂²×C₄	—	13	84	no	—
69	C₂²×C₄	C₂×#261	1	14	yes	direct product factor
70	C₄²	—	13	64	no	—
71	C₁₃	C₂³×C₄²	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	13	56	no	—
73	C₂³	—	13	56	no	—
74	C₂³	—	13	7	no	—
75	C₂³	—	13	21	no	—
76	C₂³	C₄×#261	1	8	yes	direct product factor
77	C₂³	C₂²×#261	1	7	yes	—
78	C₂×C₄	—	13	16	no	—
79	C₂×C₄	—	13	224	no	—
80	C₂×C₄	—	13	28	no	—
81	C₂×C₄	—	13	8	no	—
82	C₂×C₄	—	13	56	no	—
83	C₂×C₄	C₂²×#261	1	28	yes	direct product factor
84	C₂²	—	13	84	no	—
85	C₂²	—	13	28	no	—
86	C₂²	—	13	7	no	—
87	C₂²	—	13	1	no	—
88	C₂²	C₂×C₄×#261	1	28	yes	direct product factor
89	C₂²	C₂³×#261	1	7	yes	—
90	C₄	—	13	32	no	—
91	C₄	—	13	8	no	—
92	C₄	C₂³×#261	1	8	yes	direct product factor
93	C₂	—	13	2	no	—
94	C₂	—	13	14	no	—
95	C₂	C₂²×C₄×#261	1	14	yes	direct product factor
96	C₂	C₂⁴×#261	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	#261
commutator, hypocenter	C₁₃	C₂³×C₄²
Frattini	C₂	C₂⁴×#261
Fitting	C₂³×C₄×C₁₃	C₄
socle	C₂⁴×C₁₃	C₂×C₄
prime radical	C₂⁴×D₁₃	C₂²
cosocle	C₂×D₁₃	C₂⁵
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×#261	C₂	direct (N × H)
5. C₂³×#261	C₄	direct (N × H)
7. C₂³×C₄×C₁₃	C₄	semidirect
8. C₂³×Dic₁₃	C₄	semidirect
9. C₂²×C₄×D₁₃	C₄	semidirect
11. C₂×C₄×#261	C₂²	direct (N × H)
16. C₂²×#261	C₂×C₄	direct (N × H)
18. C₂²×C₄×C₁₃	C₂×C₄	semidirect
19. C₂²×Dic₁₃	C₂×C₄	semidirect
20. C₂×C₄×D₁₃	C₂×C₄	semidirect
22. C₄×#261	C₂³	direct (N × H)
24. C₂³×C₁₃	C₄²	semidirect
26. C₂²×D₁₃	C₄²	semidirect
30. C₂×#261	C₂²×C₄	direct (N × H)
32. C₂×C₄×C₁₃	C₂²×C₄	semidirect
33. C₂×Dic₁₃	C₂²×C₄	semidirect
34. C₄×D₁₃	C₂²×C₄	semidirect
39. C₂²×C₁₃	C₂×C₄²	semidirect
41. C₂×D₁₃	C₂×C₄²	semidirect
45. #261	C₂³×C₄	direct (N × H)
46. C₄×C₁₃	C₂³×C₄	semidirect
47. Dic₁₃	C₂³×C₄	semidirect
54. C₂³×C₄	#261	direct (N × H)
56. C₂×C₁₃	C₂²×C₄²	semidirect
58. D₁₃	C₂²×C₄²	semidirect
69. C₂²×C₄	C₂×#261	direct (N × H)
71. C₁₃	C₂³×C₄²	semidirect
76. C₂³	C₄×#261	direct (N × H)
83. C₂×C₄	C₂²×#261	direct (N × H)
88. C₂²	C₂×C₄×#261	direct (N × H)
92. C₄	C₂³×#261	direct (N × H)
95. C₂	C₂²×C₄×#261	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×#261	2
C₂³×C₄×D₁₃	2
C₂²×C₄×#261	2
C₂³×C₄²	13

Subgroups — C23×C4×#261 #13131806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×#261 #13131806