Finite Group Databasebeta

← C13×#36640 #15722979

Subgroups — C13×#36640 #15722979

Order 3328.

1990 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2864C214yesmaximal, complemented
2C13×#2859C214yesmaximal, complemented
3C13×#2851C218yesmaximal
4C4×C13×#125C218yesmaximal, complemented
5C13×#2296C214yesmaximal
6C13×#2285C212yesmaximal
7C2×C43×C13C211yesmaximal, characteristic
8C2×C13×#125C2218yes—
9C2×C13×#117C2214yes—
10C22×C42×C13C2212yes—
11C22×C42×C13C2214yes—
12C22×C42×C13C2211yescharacteristic
13C13×#389C22116yes—
14C13×#389C22116yes—
15C13×#387C22132yes—
16C13×#385C22116yes—
17C13×#384C2214yes—
18C13×#382C2214yes—
19C13×#382C2218yes—
20C13×#380C2218yes—
21C4×C13×C4⋊C4C2218yes—
22C4×C13×C4⋊C4C22116yes—
23C43×C13C2214yes—
24C43×C13C2212yes—
25C43×C13C2212yes—
26C23×C4×C13C2314yes—
27C23×C4×C13C2312yes—
28C23×C4×C13C2311yescharacteristic
29C13×#125—232no—
30C13×#117—216no—
31C2×C13×C4⋊C4C23116yes—
32C2×C13×C4⋊C4C23132yes—
33C2×C13×C4⋊C4C2318yes—
34C2×C13×C22⋊C4C2318yes—
35C2×C42×C13—28no—
36C2×C42×C13—216no—
37C2×C42×C13Q818yes—
38C2×C42×C13C2318yes—
39C2×C42×C13C2314yes—
40C2×C42×C13C2314yes—
41C2×C42×C13C2318yes—
42C2×C42×C13C2314yes—
43C2×C42×C13C2311yescharacteristic
44C2×C42×C13C2311yescharacteristic
45C2×C42×C13C2312yes—
46C2×C42×C13C2314yes—
47C13×#95C23116yes—
48C13×#95C23132yes—
49#36640C1311yesmaximal, characteristic, direct product factor, Sylow
50C24×C13C2411yescharacteristic
51C22×C4×C13—28no—
52C22×C4×C13—216no—
53C22×C4×C13—28no—
54C22×C4×C13C2×Q818yes—
55C22×C4×C13C2×Q814yes—
56C22×C4×C13#4118yes—
57C22×C4×C13C24116yes—
58C22×C4×C13C2412yes—
59C22×C4×C13C2418yes—
60C22×C4×C13C2411yescharacteristic
61C22×C4×C13C2412yes—
62C22×C4×C13C2411yescharacteristic
63C13×C4⋊C4—216no—
64C13×C4⋊C4—264no—
65C13×C4⋊C4—232no—
66C13×C22⋊C4—216no—
67C42×C13—216no—
68C42×C13—28no—
69C42×C13—28no—
70C42×C13—28no—
71C42×C13—216no—
72C42×C13C2×Q814yes—
73C42×C13C2×Q818yes—
74C42×C13C2×Q814yes—
75C42×C13#41116yes—
76#2864C2×C1314yescomplemented
77#2859C2×C1314yescomplemented
78#2851C2×C1318yes—
79C4×#125C2×C1318yescomplemented
80#2296C2×C1314yes—
81#2285C2×C1312yes—
82C2×C43C2×C1311yescharacteristic
83C23×C13—24no—
84C23×C13C22×Q812yes—
85C23×C13C2×#4114yes—
86C23×C13C2511yescharacteristic
87C2×C4×C13—232no—
88C2×C4×C13—24no—
89C2×C4×C13—28no—
90C2×C4×C13—28no—
91C2×C4×C13—216no—
92C2×C4×C13—216no—
93C2×C4×C13—232no—
94C2×C4×C13#125116yescomplemented
95C2×C4×C13C22×Q814yes—
96C2×C4×C13C22×Q812yes—
97C2×C4×C13C22×Q812yes—
98C2×C4×C13C22×Q814yes—
99C2×C4×C13C2×#41116yes—
100C2×C4×C13C2×#4114yes—
101C2×C4×C13C2×#4114yes—
102C2×C4×C13C2×#4118yes—
103C2×#125C22×C1318yes—
104C2×#117C22×C1314yes—
105C22×C42C22×C1314yes—
106C22×C42C22×C1312yes—
107C22×C42C22×C1311yescharacteristic
108#389C22×C13116yes—
109#389C22×C13116yes—
110#387C22×C13132yes—
111#385C22×C13116yes—
112#384C22×C1314yes—
113#382C22×C1318yes—
114#382C22×C1314yes—
115#380C22×C1318yes—
116C4×C4⋊C4C22×C1318yes—
117C4×C4⋊C4C22×C13116yes—
118C43C22×C1314yes—
119C43C22×C1312yes—
120C43C22×C1312yes—
121C22×C13—24no—
122C22×C13—28no—
123C22×C13C2×#12514yes—
124C22×C13C23×Q811yescharacteristic
125C22×C13C22×#4112yes—
126C22×C13C22×#4114yes—
127C4×C13—24no—
128C4×C13—216no—
129C4×C13—416no—
130C4×C13C2×#12514yes—
131C4×C13C2×#12514yes—
132C4×C13#53318yes—
133C23×C4C23×C1314yes—
134C23×C4C23×C1312yes—
135C23×C4C23×C1311yescharacteristic
136#125—232no—
137#117—216no—
138C2×C4⋊C4C23×C1318yes—
139C2×C4⋊C4C23×C13116yes—
140C2×C4⋊C4C23×C13132yes—
141C2×C22⋊C4C23×C1318yes—
142C2×C42—28no—
143C2×C42—216no—
144C2×C42Q8×C1318yes—
145C2×C42C23×C1318yes—
146C2×C42C23×C1314yes—
147C2×C42C23×C1318yes—
148C2×C42C23×C1314yes—
149C2×C42C23×C1314yes—
150C2×C42C23×C1312yes—
151C2×C42C23×C1311yescharacteristic
152C2×C42C23×C1311yescharacteristic
153C2×C42C23×C1314yes—
154#95C23×C13116yes—
155#95C23×C13132yes—
156C2×C13—24no—
157C2×C13C22×#12511yescharacteristic
158C2×C13C2×#53312yes—
159C2×C13#344414yes—
160C24C24×C1311yescharacteristic
161C22×C4—28no—
162C22×C4—216no—
163C22×C4—28no—
164C22×C4C2×Q8×C1318yes—
165C22×C4C2×Q8×C1314yes—
166C22×C4C13×#4118yes—
167C22×C4C24×C13116yes—
168C22×C4C24×C1312yes—
169C22×C4C24×C1318yes—
170C22×C4C24×C1311yescharacteristic
171C22×C4C24×C1311yescharacteristic
172C22×C4C24×C1312yes—
173C4⋊C4—216no—
174C4⋊C4—264no—
175C4⋊C4—232no—
176C22⋊C4—216no—
177C42—216no—
178C42—28no—
179C42—28no—
180C42—28no—
181C42—216no—
182C42C2×Q8×C1314yes—
183C42C2×Q8×C1318yes—
184C42C2×Q8×C1314yes—
185C42C13×#41116yes—
186C13#3664011yescharacteristic, direct product factor, Sylow
187C23—24no—
188C23C22×Q8×C1312yes—
189C23C2×C13×#4114yes—
190C23C25×C1311yescharacteristic
191C2×C4—232no—
192C2×C4—24no—
193C2×C4—28no—
194C2×C4—28no—
195C2×C4—216no—
196C2×C4—216no—
197C2×C4—232no—
198C2×C4C13×#125116yescomplemented
199C2×C4C22×Q8×C1314yes—
200C2×C4C22×Q8×C1312yes—
201C2×C4C22×Q8×C1312yes—
202C2×C4C22×Q8×C1314yes—
203C2×C4C2×C13×#41116yes—
204C2×C4C2×C13×#4114yes—
205C2×C4C2×C13×#4114yes—
206C2×C4C2×C13×#4118yes—
207C22—24no—
208C22—28no—
209C22C2×C13×#12514yes—
210C22C23×Q8×C1311yescharacteristic
211C22C22×C13×#4112yes—
212C22C22×C13×#4114yes—
213C4—24no—
214C4—216no—
215C4—416no—
216C4C2×C13×#12514yes—
217C4C2×C13×#12514yes—
218C4C13×#53318yes—
219C2—24no—
220C2C22×C13×#12511yescharacteristic
221C2C2×C13×#53312yes—
222C2C13×#344414yes—
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC24×C13C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2864C2semidirect
2. C13×#2859C2semidirect
4. C4×C13×#125C2semidirect
49. #36640C13direct (N × H)
76. #2864C2×C13semidirect
77. #2859C2×C13semidirect
79. C4×#125C2×C13semidirect
94. C2×C4×C13#125semidirect
186. C13#36640direct (N × H)
198. C2×C4C13×#125semidirect

Maximal subgroups

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

subgroupindex
C13×#28642
C13×#28592
C13×#28512
C4×C13×#1252
C13×#22962
C13×#22852
C2×C43×C132
#3664013