Finite Group Databasebeta

← C13×#13303 #15699642

Subgroups — C13×#13303 #15699642

Order 3328.

396 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2565C211yesmaximal, characteristic
2C13×#1801C211yesmaximal, characteristic
3C4×C13×#101C211yesmaximal, characteristic
4C13×#1394C212yesmaximal
5C13×#1394C212yesmaximal
6C2×C13×#125C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#423—21no—
9C2×C13×#101C2212yes—
10C2×C13×#101C2212yes—
11C4×C13×M16—21no—
12C13×#398—21no—
13C13×#398—21no—
14C13×#391C2211yescharacteristic
15C13×#391C2211yescharacteristic
16C13×#387—21no—
17C13×#387—21no—
18C13×#384C411yescharacteristic
19C13×#382C411yescharacteristic
20C4×C13×C4⋊C4C411yescharacteristic
21C13×#343—21no—
22C13×#343—21no—
23C22×Q8×C13C2311yescharacteristic
24C2×C13×M16—22no—
25C2×C13×M16—22no—
26C13×#125—41no—
27C13×#125—41no—
28C4×Q8×C13—41no—
29C4×Q8×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C13×C4⋊C8—41no—
46C13×C4⋊C8—41no—
47C13×#101—22no—
48C13×#101—24no—
49C13×#101Q814yes—
50C13×#97—41no—
51C4×C8×C13—41no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59#13303C1311yesmaximal, characteristic, direct product factor, Sylow
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2×Q812yes—
63C2×Q8×C13#4112yes—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C13×M16—24no—
76C13×M16—42no—
77C13×M16—42no—
78C13×M16—42no—
79C2×C8×C13—42no—
80C2×C8×C13—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—41no—
99C42×C13—41no—
100#2565C2×C1311yescharacteristic
101#1801C2×C1311yescharacteristic
102C4×#101C2×C1311yescharacteristic
103#1394C2×C1312yes—
104#1394C2×C1312yes—
105C23×C13C2×C22⋊C411yescharacteristic
106Q8×C13—42no—
107Q8×C13—42no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13#9911yescharacteristic
134C2×C4×C13C4×Q812yes—
135C2×C4×C13C22⋊Q812yes—
136C2×C4×C13#12411yescharacteristic
137C2×C4×C13C4⋊Q811yescharacteristic
138C8×C13—44no—
139C8×C13—82no—
140C2×#125C4×C1311yescharacteristic
141C2×C4×Q8C22×C1311yescharacteristic
142#423—21no—
143C2×#101C22×C1312yes—
144C2×#101C22×C1312yes—
145C4×M16—21no—
146#398—21no—
147#398—21no—
148#391C22×C1311yescharacteristic
149#391C22×C1311yescharacteristic
150#387—21no—
151#387—21no—
152#384C4×C1311yescharacteristic
153#382C4×C1311yescharacteristic
154C4×C4⋊C4C4×C1311yescharacteristic
155#343—21no—
156#343—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13#39111yescharacteristic
160C22×C13C2×#9911yescharacteristic
161C22×C13#41011yescharacteristic
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—21no—
168C4×C13—42no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—81no—
173C4×C13—81no—
174C4×C13—81no—
175C22×Q8C23×C1311yescharacteristic
176C2×M16—22no—
177C2×M16—22no—
178#125—41no—
179#125—41no—
180C4×Q8—41no—
181C4×Q8—41no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4C2×C4×C1311yescharacteristic
188C2×C4⋊C4C2×C4×C1311yescharacteristic
189C2×C4⋊C4C2×C4×C1311yescharacteristic
190C2×C4⋊C4D4×C1311yescharacteristic
191C2×C4⋊C4D4×C1311yescharacteristic
192C2×C42C2×C4×C1311yescharacteristic
193C2×C42C2×C4×C1311yescharacteristic
194C2×C42C2×C4×C1311yescharacteristic
195C2×C42D4×C1311yescharacteristic
196C2×C42D4×C1311yescharacteristic
197C4⋊C8—41no—
198C4⋊C8—41no—
199#101—22no—
200#101—24no—
201#101Q8×C1314yes—
202#97—41no—
203C4×C8—41no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13#199611yescharacteristic
214C2×C13#213211yescharacteristic
215C2×C13#213311yescharacteristic
216C2×Q8—41no—
217C2×Q8—41no—
218C2×Q8C2×Q8×C1312yes—
219C2×Q8C13×#4112yes—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4C13×C22⋊C411yescharacteristic
225C22×C4C13×C22⋊C411yescharacteristic
226C22×C4C13×C22⋊C411yescharacteristic
227C22×C4C13×C22⋊C411yescharacteristic
228C22×C4C22×C4×C1311yescharacteristic
229C22×C4C2×D4×C1311yescharacteristic
230C22×C4C2×D4×C1311yescharacteristic
231M16—24no—
232M16—42no—
233M16—42no—
234M16—42no—
235C2×C8—42no—
236C2×C8—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—41no—
255C42—41no—
256C13#1330311yescharacteristic, direct product factor, Sylow
257C23C2×C13×C22⋊C411yescharacteristic
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4C13×#9911yescharacteristic
285C2×C4C13×#9911yescharacteristic
286C2×C4C4×Q8×C1312yes—
287C2×C4C13×C22⋊Q812yes—
288C2×C4C13×#12411yescharacteristic
289C2×C4C13×C4⋊Q811yescharacteristic
290C8—44no—
291C8—82no—
292C22—21no—
293C22—21no—
294C22C13×#39111yescharacteristic
295C22C2×C13×#9911yescharacteristic
296C22C13×#41011yescharacteristic
297C4—22no—
298C4—21no—
299C4—22no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—81no—
308C4—81no—
309C4—81no—
310C2—21no—
311C2—21no—
312C2C13×#199611yescharacteristic
313C2C13×#213211yescharacteristic
314C2C13×#213311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×Q8C23×C13
prime radicalC23×C13C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
59. #13303C13direct (N × H)
256. C13#13303direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25652
C13×#18012
C4×C13×#1012
C13×#13942
#1330313