Subgroups — C₁₃×#12592 #15698931

Order 3328.

358 conjugacy classes of subgroups.

The subgroup lattice has 142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1374	C₂	1	4	yes	maximal
5	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
6	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×#97	C₄	1	2	yes	—
8	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#376	C₄	1	1	yes	characteristic
12	C₁₃×#346	C₄	1	4	yes	complemented
13	C₄×C₁₃×C₁₆	C₄	1	4	yes	complemented
14	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₃×C₁₆	—	2	4	no	—
20	C₂×C₁₃×C₁₆	—	2	4	no	—
21	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
22	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
23	C₁₃×#97	—	2	4	no	—
24	C₁₃×#97	C₈	1	4	yes	—
25	C₄×C₈×C₁₃	—	2	4	no	—
26	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₁₃×#95	C₈	1	4	yes	—
29	#12592	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
31	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
32	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	—	2	2	no	—
34	C₂×C₈×C₁₃	—	2	2	no	—
35	C₂×C₈×C₁₃	C₄²	1	2	yes	—
36	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
37	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
38	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	#41	1	4	yes	—
41	C₄²×C₁₃	—	2	2	no	—
42	C₄²×C₁₃	—	2	2	no	—
43	C₄²×C₁₃	C₄²	1	2	yes	—
44	C₄²×C₁₃	C₂×C₈	1	2	yes	—
45	C₁₃×C₁₆	—	2	4	no	—
46	C₁₃×C₁₆	—	2	4	no	—
47	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
48	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
49	#1726	C₂×C₁₃	1	1	yes	characteristic
50	#1374	C₂×C₁₃	1	4	yes	—
51	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₃	—	2	4	no	—
53	C₂×C₄×C₁₃	—	2	4	no	—
54	C₂×C₄×C₁₃	—	2	8	no	—
55	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
56	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₄×C₁₃	#117	1	2	yes	—
58	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
60	C₈×C₁₃	—	2	4	no	—
61	C₈×C₁₃	#97	1	4	yes	—
62	C₈×C₁₃	#117	1	2	yes	—
63	C₈×C₁₃	#117	1	2	yes	—
64	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
65	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
66	C₂×#97	C₄×C₁₃	1	2	yes	—
67	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
68	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
69	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
70	#376	C₄×C₁₃	1	1	yes	characteristic
71	#346	C₄×C₁₃	1	4	yes	complemented
72	C₄×C₁₆	C₄×C₁₃	1	4	yes	complemented
73	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
74	C₂²×C₁₃	#431	1	2	yes	—
75	C₂²×C₁₃	#504	1	4	yes	—
76	C₄×C₁₃	—	2	4	no	—
77	C₄×C₁₃	—	4	4	no	—
78	C₄×C₁₃	#376	1	1	yes	characteristic
79	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
80	C₄×C₁₃	#431	1	2	yes	—
81	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
82	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
83	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
84	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
85	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
86	C₂×C₁₆	—	2	4	no	—
87	C₂×C₁₆	—	2	4	no	—
88	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
89	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
90	#97	—	2	4	no	—
91	#97	C₈×C₁₃	1	4	yes	—
92	C₄×C₈	—	2	4	no	—
93	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
94	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
95	#95	C₈×C₁₃	1	4	yes	—
96	C₂×C₁₃	#1744	1	1	yes	characteristic
97	C₂×C₁₃	#2108	1	2	yes	—
98	C₂×C₁₃	#2164	1	4	yes	—
99	C₂²×C₄	C₂×C₈×C₁₃	1	4	yes	—
100	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
101	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
102	C₂×C₈	—	2	2	no	—
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	C₄²×C₁₃	1	2	yes	—
105	C₂×C₈	C₂×C₈×C₁₃	1	4	yes	—
106	C₂×C₈	C₁₃×M₁₆	1	4	yes	—
107	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
108	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
109	C₂×C₈	C₁₃×#41	1	4	yes	—
110	C₄²	—	2	2	no	—
111	C₄²	—	2	2	no	—
112	C₄²	C₄²×C₁₃	1	2	yes	—
113	C₄²	C₂×C₈×C₁₃	1	2	yes	—
114	C₁₆	—	2	4	no	—
115	C₁₆	—	2	4	no	—
116	C₁₃	#12592	1	1	yes	characteristic, direct product factor, Sylow
117	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	2	8	no	—
121	C₂×C₄	C₄×C₈×C₁₃	1	4	yes	—
122	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
123	C₂×C₄	C₁₃×#117	1	2	yes	—
124	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
125	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
126	C₈	—	2	4	no	—
127	C₈	C₁₃×#97	1	4	yes	—
128	C₈	C₁₃×#117	1	2	yes	—
129	C₈	C₁₃×#117	1	2	yes	—
130	C₂²	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
131	C₂²	C₁₃×#431	1	2	yes	—
132	C₂²	C₁₃×#504	1	4	yes	—
133	C₄	—	2	4	no	—
134	C₄	—	4	4	no	—
135	C₄	C₁₃×#376	1	1	yes	characteristic
136	C₄	C₂×C₁₃×#97	1	1	yes	characteristic
137	C₄	C₁₃×#431	1	2	yes	—
138	C₂	C₁₃×#1744	1	1	yes	characteristic
139	C₂	C₁₃×#2108	1	2	yes	—
140	C₂	C₁₃×#2164	1	4	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂²	C₂×C₄×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₁₃×#346	C₄	semidirect
13. C₄×C₁₃×C₁₆	C₄	semidirect
29. #12592	C₁₃	direct (N × H)
71. #346	C₄×C₁₃	semidirect
72. C₄×C₁₆	C₄×C₁₃	semidirect
116. C₁₃	#12592	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×#346	2
C₂×C₄×C₁₃×C₁₆	2
C₁₃×#1726	2
C₁₃×#1374	2
#12592	13

Subgroups — C13×#12592 #15698931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12592 #15698931