Subgroups — C₂×C₁₃×#1397 #15699886

Order 3328.

254 conjugacy classes of subgroups.

The subgroup lattice has 114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1397	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₁₃×C₃₂	C₄	1	8	yes	complemented
8	C₂×C₁₃×C₃₂	C₂²	1	4	yes	—
9	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
10	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₃	C₈	1	1	yes	characteristic
14	C₂×C₁₃×C₁₆	C₈	1	4	yes	—
15	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
17	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
18	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
19	C₄×C₈×C₁₃	C₈	1	2	yes	—
20	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₁₃×C₃₂	C₂×C₄	1	8	yes	complemented
22	C₂×#1397	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂²×C₄×C₁₃	C₁₆	1	2	yes	—
24	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₂×C₈×C₁₃	C₁₆	1	4	yes	—
26	C₂×C₈×C₁₃	C₄²	1	2	yes	—
27	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
29	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
30	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₄²×C₁₃	C₁₆	1	2	yes	—
32	C₄²×C₁₃	C₂×C₈	1	2	yes	—
33	C₁₃×C₁₆	C₄²	1	2	yes	—
34	C₁₃×C₁₆	C₂×C₈	1	4	yes	—
35	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
36	C₂²×C₃₂	C₂×C₁₃	1	2	yes	—
37	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
38	#1397	C₂×C₁₃	1	4	yes	direct product factor
39	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
40	C₂×C₄×C₁₃	—	2	4	no	—
41	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
42	C₂×C₄×C₁₃	C₂×C₁₆	1	4	yes	—
43	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
44	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
45	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
46	C₈×C₁₃	C₄×C₈	1	2	yes	—
47	C₈×C₁₃	C₂×C₁₆	1	4	yes	—
48	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
49	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
50	C₂²×C₁₆	C₄×C₁₃	1	1	yes	characteristic
51	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
52	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
53	C₂×C₃₂	C₄×C₁₃	1	8	yes	complemented
54	C₂×C₃₂	C₂²×C₁₃	1	4	yes	—
55	C₄×C₁₆	C₄×C₁₃	1	2	yes	—
56	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
57	C₂²×C₁₃	C₄×C₁₆	1	2	yes	—
58	C₂²×C₁₃	M₆₄	1	4	yes	—
59	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
60	C₄×C₁₃	—	2	4	no	—
61	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
62	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
63	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
64	C₂²×C₈	C₈×C₁₃	1	1	yes	characteristic
65	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
66	C₂×C₄²	C₈×C₁₃	1	1	yes	characteristic
67	C₂×C₁₆	C₈×C₁₃	1	4	yes	—
68	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
69	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
70	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
71	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
72	C₄×C₈	C₈×C₁₃	1	2	yes	—
73	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
74	C₃₂	C₂×C₄×C₁₃	1	8	yes	complemented
75	C₂×C₁₃	#1397	1	4	yes	direct product factor
76	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
77	C₂×C₁₃	C₂×M₆₄	1	2	yes	—
78	C₂²×C₄	C₁₃×C₁₆	1	2	yes	—
79	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
80	C₂×C₈	C₁₃×C₁₆	1	4	yes	—
81	C₂×C₈	C₄²×C₁₃	1	2	yes	—
82	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
83	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
84	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
85	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
86	C₄²	C₁₃×C₁₆	1	2	yes	—
87	C₄²	C₂×C₈×C₁₃	1	2	yes	—
88	C₁₆	C₄²×C₁₃	1	2	yes	—
89	C₁₆	C₂×C₈×C₁₃	1	4	yes	—
90	C₁₆	C₂²×C₄×C₁₃	1	2	yes	—
91	C₁₃	C₂×#1397	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³	C₂×C₁₃×C₁₆	1	1	yes	characteristic
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	C₄×C₈×C₁₃	1	2	yes	—
95	C₂×C₄	C₂×C₁₃×C₁₆	1	4	yes	—
96	C₂×C₄	C₂×C₁₃×C₁₆	1	1	yes	characteristic
97	C₂×C₄	C₂×C₁₃×C₁₆	1	2	yes	—
98	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
99	C₈	C₄×C₈×C₁₃	1	2	yes	—
100	C₈	C₂×C₁₃×C₁₆	1	4	yes	—
101	C₈	C₂×C₄²×C₁₃	1	1	yes	characteristic
102	C₈	C₂²×C₈×C₁₃	1	1	yes	characteristic
103	C₂²	C₄×C₁₃×C₁₆	1	2	yes	—
104	C₂²	C₁₃×M₆₄	1	4	yes	—
105	C₂²	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
106	C₄	—	2	4	no	—
107	C₄	C₄×C₁₃×C₁₆	1	2	yes	—
108	C₄	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
109	C₄	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
110	C₂	C₁₃×#1397	1	4	yes	direct product factor
111	C₂	C₂×C₄×C₁₃×C₁₆	1	1	yes	characteristic
112	C₂	C₂×C₁₃×M₆₄	1	2	yes	—

	subgroup	G/H
center	C₂²×C₁₃×C₁₆	C₂²
commutator	C₂	C₂×C₄×C₁₃×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1397	C₂	direct (N × H)
7. C₂×C₁₃×C₃₂	C₄	semidirect
21. C₁₃×C₃₂	C₂×C₄	semidirect
22. C₂×#1397	C₁₃	direct (N × H)
38. #1397	C₂×C₁₃	direct (N × H)
53. C₂×C₃₂	C₄×C₁₃	semidirect
74. C₃₂	C₂×C₄×C₁₃	semidirect
75. C₂×C₁₃	#1397	direct (N × H)
91. C₁₃	C₂×#1397	direct (N × H)
110. C₂	C₁₃×#1397	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₃₂	2
C₂×C₄×C₁₃×C₁₆	2
C₁₃×#1397	2
C₂×#1397	13

Subgroups — C2×C13×#1397 #15699886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1397 #15699886