Finite Group Databasebeta

← C13×#8495 #15694834

Subgroups — C13×#8495 #15694834

Order 3328.

620 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3556C211yesmaximal, characteristic
2C13×#1995C211yesmaximal, characteristic
3C13×#1559C212yesmaximal
4C13×#1537C211yesmaximal, characteristic
5C13×#1506C212yesmaximal
6C13×#564—22no—
7C13×#557—22no—
8C13×#557—22no—
9C13×#557C414yescomplemented
10C13×#541—24no—
11C13×#541—22no—
12C13×#533C2212yes—
13C13×#533C2211yescharacteristic
14C13×#432C2212yes—
15C13×#423C2211yescharacteristic
16C13×#376C2211yescharacteristic
17C13×#339—22no—
18C13×#333—22no—
19C13×#332—22no—
20C13×#330—22no—
21C13×#328—24no—
22C2×C13×M16—21no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—24no—
25C13×C4⋊Q8C2×C412yes—
26C13×C4⋊Q8D412yes—
27C13×C4⋊Q8D412yes—
28C13×#126—28no—
29C13×#125—22no—
30C13×#125—28no—
31C13×#125—28no—
32C13×#125—24no—
33C13×#125—28no—
34C13×#125—22no—
35C13×#125D412yes—
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8—22no—
38C13×C22⋊Q8D414yes—
39C4×Q8×C13—24no—
40C4×Q8×C13—24no—
41C4×Q8×C13—24no—
42C4×Q8×C13—22no—
43C4×Q8×C13—22no—
44C4×Q8×C13C2×C414yes—
45C13×#117—22no—
46C13×#117D412yes—
47C2×C42×C13—21no—
48C2×C42×C13C2311yescharacteristic
49C13×C4⋊C8—22no—
50C13×C4⋊C8—22no—
51C13×C22⋊C8—22no—
52C13×#97—22no—
53C13×#95—22no—
54#8495C1311yesmaximal, characteristic, direct product factor, Sylow
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13C22⋊C414yes—
58C22×C4×C13—41no—
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D412yes—
61C13×M16—42no—
62C2×C8×C13—42no—
63C2×C8×C13—41no—
64C13×C4⋊C4—28no—
65C13×C4⋊C4—28no—
66C13×C4⋊C4—28no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—24no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—22no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4C22⋊C414yes—
75C13×C4⋊C4C22⋊C414yes—
76C13×C22⋊C4—24no—
77C13×C22⋊C4—22no—
78C42×C13—28no—
79C42×C13—24no—
80C42×C13—22no—
81C42×C13—22no—
82C42×C13—41no—
83C42×C13C22×C411yescharacteristic
84C42×C13C2×D411yescharacteristic
85C42×C13C2×D412yes—
86#3556C2×C1311yescharacteristic
87#1995C2×C1311yescharacteristic
88#1559C2×C1312yes—
89#1537C2×C1311yescharacteristic
90#1506C2×C1312yes—
91C23×C13#12011yescharacteristic
92Q8×C13—44no—
93Q8×C13—44no—
94Q8×C13—42no—
95Q8×C13—42no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—24no—
99C2×C4×C13—24no—
100C2×C4×C13—24no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—82no—
104C2×C4×C13C2×C22⋊C412yes—
105C2×C4×C13C2×C22⋊C411yescharacteristic
106C2×C4×C13#12012yes—
107C2×C4×C13#12011yescharacteristic
108C8×C13—82no—
109C8×C13—81no—
110#564—22no—
111#557—22no—
112#557—22no—
113#557C4×C1314yescomplemented
114#541—24no—
115#541—22no—
116#533C22×C1312yes—
117#533C22×C1311yescharacteristic
118#432C22×C1312yes—
119#423C22×C1311yescharacteristic
120#376C22×C1311yescharacteristic
121#339—22no—
122#333—22no—
123#332—22no—
124#330—22no—
125#328—24no—
126C22×C13—21no—
127C22×C13—22no—
128C22×C13#37911yescharacteristic
129C4×C13—21no—
130C4×C13—22no—
131C4×C13—22no—
132C4×C13—44no—
133C4×C13—44no—
134C4×C13—44no—
135C4×C13—82no—
136C4×C13#45411yescharacteristic
137C4×C13#45611yescharacteristic
138C2×M16—21no—
139C4⋊Q8—22no—
140C4⋊Q8—24no—
141C4⋊Q8C2×C4×C1312yes—
142C4⋊Q8D4×C1312yes—
143C4⋊Q8D4×C1312yes—
144#126—28no—
145#125—22no—
146#125—28no—
147#125—28no—
148#125—24no—
149#125—28no—
150#125—22no—
151#125D4×C1312yes—
152C22⋊Q8—22no—
153C22⋊Q8—22no—
154C22⋊Q8D4×C1314yes—
155C4×Q8—24no—
156C4×Q8—24no—
157C4×Q8—24no—
158C4×Q8—22no—
159C4×Q8—22no—
160C4×Q8C2×C4×C1314yes—
161#117—22no—
162#117D4×C1312yes—
163C2×C42—21no—
164C2×C42C23×C1311yescharacteristic
165C4⋊C8—22no—
166C4⋊C8—22no—
167C22⋊C8—22no—
168#97—22no—
169#95—22no—
170C2×C13—41no—
171C2×C13#179311yescharacteristic
172C2×C13#179612yes—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8C13×C22⋊C414yes—
176C22×C4—41no—
177C22×C4C2×D4×C1311yescharacteristic
178C22×C4C2×D4×C1312yes—
179M16—42no—
180C2×C8—42no—
181C2×C8—41no—
182C4⋊C4—28no—
183C4⋊C4—28no—
184C4⋊C4—28no—
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—24no—
191C4⋊C4—24no—
192C4⋊C4C13×C22⋊C414yes—
193C4⋊C4C13×C22⋊C414yes—
194C22⋊C4—24no—
195C22⋊C4—22no—
196C42—28no—
197C42—24no—
198C42—22no—
199C42—22no—
200C42—41no—
201C42C22×C4×C1311yescharacteristic
202C42C2×D4×C1311yescharacteristic
203C42C2×D4×C1312yes—
204C13#849511yescharacteristic, direct product factor, Sylow
205C23C13×#12011yescharacteristic
206Q8—44no—
207Q8—44no—
208Q8—42no—
209Q8—42no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—24no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4C2×C13×C22⋊C412yes—
219C2×C4C2×C13×C22⋊C411yescharacteristic
220C2×C4C13×#12012yes—
221C2×C4C13×#12011yescharacteristic
222C8—82no—
223C8—81no—
224C22—21no—
225C22—22no—
226C22C13×#37911yescharacteristic
227C4—21no—
228C4—22no—
229C4—22no—
230C4—44no—
231C4—44no—
232C4—44no—
233C4—82no—
234C4C13×#45411yescharacteristic
235C4C13×#45611yescharacteristic
236C2—41no—
237C2C13×#179311yescharacteristic
238C2C13×#179612yes—
subgroupG/H
center, socleC22×C13#379
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC23×C13#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
9. C13×#557C4semidirect
54. #8495C13direct (N × H)
113. #557C4×C13semidirect
204. C13#8495direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35562
C13×#19952
C13×#15592
C13×#15372
C13×#15062
#849513