Subgroups — C₂×D₁₃×#401 #16029212

Order 3328.

2942 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊#401	C₂	1	7	yes	maximal, complemented
2	D₁₃×#401	C₂	1	16	yes	maximal, direct product factor
3	C₂×D₁₃×#95	C₂	1	7	yes	maximal
4	C₂×C₁₃×#401	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₄×D₁₃	C₂²	1	7	yes	—
6	C₁₃×#401	C₂²	1	8	yes	complemented
7	C₂×C₁₃×#95	C₂²	1	7	yes	—
8	C₂×#88071	C₂²	1	21	yes	—
9	D₁₃×#95	C₂²	1	56	yes	—
10	C₁₃⋊#401	C₂²	1	56	yes	complemented
11	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
12	C₂³×C₄×C₁₃	C₂³	1	7	yes	—
13	C₂³×Dic₁₃	C₂³	1	7	yes	—
14	C₂²×C₄×D₁₃	—	2	84	no	—
15	C₂²×C₄×D₁₃	C₂³	1	28	yes	—
16	C₁₃×#95	C₂³	1	28	yes	—
17	#88071	C₂³	1	84	yes	—
18	C₂²×#401	—	13	1	no	maximal, Sylow
19	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
20	C₂³×D₁₃	#41	1	28	yes	—
21	C₂³×D₁₃	C₂⁴	1	2	yes	—
22	C₂²×C₄×C₁₃	—	2	42	no	—
23	C₂²×C₄×C₁₃	C₂⁴	1	14	yes	—
24	C₂²×Dic₁₃	—	2	42	no	—
25	C₂²×Dic₁₃	C₂⁴	1	14	yes	—
26	C₂×C₄×D₁₃	—	2	168	no	—
27	C₂×C₄×D₁₃	—	4	112	no	—
28	C₂×#401	—	13	16	no	—
29	C₂×#401	—	13	7	no	—
30	C₂×#401	D₁₃	1	1	yes	characteristic, direct product factor
31	C₂²×#95	—	13	7	no	—
32	C₂³×C₁₃	C₂×#41	1	14	yes	—
33	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
34	C₂²×D₁₃	#126	1	112	yes	—
35	C₂²×D₁₃	C₂×#41	1	28	yes	—
36	C₂×C₄×C₁₃	—	2	42	no	—
37	C₂×C₄×C₁₃	—	4	28	no	—
38	C₂×Dic₁₃	—	2	42	no	—
39	C₂×Dic₁₃	—	4	28	no	—
40	C₄×D₁₃	—	4	112	no	—
41	C₂⁴×C₄	—	13	7	no	—
42	#401	—	13	56	no	—
43	#401	C₂×D₁₃	1	8	yes	direct product factor
44	C₂×#95	—	13	21	no	—
45	C₂×#95	—	13	56	no	—
46	C₂×#95	C₂×D₁₃	1	7	yes	—
47	C₂²×C₁₃	C₂×#126	1	28	yes	—
48	C₂²×C₁₃	C₂²×#41	1	7	yes	—
49	C₂×D₁₃	#401	1	64	yes	direct product factor
50	C₂×D₁₃	C₂×#126	1	56	yes	—
51	C₄×C₁₃	—	4	14	no	—
52	Dic₁₃	—	4	14	no	—
53	C₂⁵	—	13	1	no	—
54	C₂³×C₄	—	13	7	no	—
55	C₂³×C₄	—	13	28	no	—
56	C₂³×C₄	—	26	84	no	—
57	C₂³×C₄	C₂²×D₁₃	1	7	yes	—
58	#95	—	13	84	no	—
59	#95	C₂²×D₁₃	1	28	yes	—
60	C₂×C₁₃	C₂×#401	1	8	yes	complemented
61	C₂×C₁₃	C₂²×#126	1	7	yes	—
62	D₁₃	C₂×#401	1	16	yes	direct product factor
63	C₂⁴	—	13	28	no	—
64	C₂⁴	—	13	2	no	—
65	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
66	C₂²×C₄	—	2	42	no	—
67	C₂²×C₄	—	13	14	no	—
68	C₂²×C₄	—	26	168	no	—
69	C₂²×C₄	—	26	42	no	—
70	C₂²×C₄	—	52	112	no	—
71	C₂²×C₄	C₂³×D₁₃	1	14	yes	—
72	C₁₃	C₂²×#401	1	1	yes	characteristic, complemented, Sylow
73	C₂³	—	13	28	no	—
74	C₂³	—	13	112	no	—
75	C₂³	#41×D₁₃	1	14	yes	—
76	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
77	C₂×C₄	—	2	42	no	—
78	C₂×C₄	—	4	28	no	—
79	C₂×C₄	—	26	42	no	—
80	C₂×C₄	—	52	112	no	—
81	C₂×C₄	—	52	28	no	—
82	C₂²	—	13	56	no	—
83	C₂²	—	13	64	no	—
84	C₂²	D₁₃×#126	1	28	yes	—
85	C₂²	C₂×#41×D₁₃	1	7	yes	—
86	C₄	—	4	14	no	—
87	C₄	—	52	14	no	—
88	C₂	—	13	16	no	—
89	C₂	D₁₃×#401	1	8	yes	direct product factor
90	C₂	C₂×D₁₃×#126	1	7	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂³×C₁₃	C₂⁵
Frattini	C₂³	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#401	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂⁴×D₁₃	C₂³
hypercenter	C₂×#401	D₁₃
hypocenter	C₁₃	C₂²×#401
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#401

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃⋊#401	C₂	semidirect
2. D₁₃×#401	C₂	direct (N × H)
4. C₂×C₁₃×#401	C₂	semidirect
6. C₁₃×#401	C₂²	semidirect
10. C₁₃⋊#401	C₂²	semidirect
30. C₂×#401	D₁₃	direct (N × H)
43. #401	C₂×D₁₃	direct (N × H)
49. C₂×D₁₃	#401	direct (N × H)
60. C₂×C₁₃	C₂×#401	semidirect
62. D₁₃	C₂×#401	direct (N × H)
72. C₁₃	C₂²×#401	semidirect
89. C₂	D₁₃×#401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃⋊#401	2
D₁₃×#401	2
C₂×D₁₃×#95	2
C₂×C₁₃×#401	2
C₂²×#401	13

Subgroups — C2×D13×#401 #16029212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#401 #16029212