Finite Group Databasebeta

← C13×#12702 #15699041

Subgroups — C13×#12702 #15699041

Order 3328.

962 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 962 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×C13×#536C211yesmaximal, characteristic
2C2×C13×#356C212yesmaximal, complemented
3C2×C13×#355C212yesmaximal, complemented
4C13×#1784C212yesmaximal, complemented
5C22×C13×#41C411yescharacteristic
6C23×Q8×C13C2211yescharacteristic
7C13×#536—24no—
8C13×#536—24no—
9C2×C13×C4⋊Q8C411yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C13×#124C411yescharacteristic
12C2×C13×#124C2211yescharacteristic
13C2×C13×#123—22no—
14C2×C13×C22⋊Q8—22no—
15C2×C13×#117C411yescharacteristic
16C2×C13×#101—22no—
17C2×C13×#101C2214yes—
18C13×#407—22no—
19C13×#356—24no—
20C13×#355—24no—
21C2×C13×#41—22no—
22C2×C13×#41—22no—
23C2×C13×#41—42no—
24C2×C13×#41—42no—
25C22×Q8×C13—22no—
26C22×Q8×C13—22no—
27C22×Q8×C13—42no—
28C22×Q8×C13—42no—
29C22×Q8×C13C2×C411yescharacteristic
30C22×Q8×C13C2×C411yescharacteristic
31C22×Q8×C13D412yes—
32C22×Q8×C13C2311yescharacteristic
33C22×D4×C13—21no—
34C22×D4×C13C2×C411yescharacteristic
35C23×C4×C13—21no—
36C23×C4×C13C2×C411yescharacteristic
37C23×C4×C13D412yes—
38C2×C13×M16—24no—
39C13×C4⋊Q8—22no—
40C13×C4⋊Q8—22no—
41C13×C4⋊Q8—22no—
42C13×C4⋊Q8D414yes—
43C13×#124—22no—
44C13×#124—22no—
45C13×#124—22no—
46C13×#124D414yes—
47C13×#123—216no—
48C13×C22⋊Q8—216no—
49C13×#117—22no—
50C13×#117—22no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—22no—
56C2×C13×C22⋊C4—22no—
57C2×C42×C13C2×C411yescharacteristic
58C2×C42×C13C2×C411yescharacteristic
59C13×#101—24no—
60C13×#101—24no—
61C13×#101—44no—
62C13×C22⋊C8—44no—
63#12702C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13—21no—
65C24×C13C22⋊C411yescharacteristic
66C13×#41—48no—
67C13×#41—48no—
68C2×Q8×C13—24no—
69C2×Q8×C13—21no—
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—24no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×Q8×C13—42no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—48no—
79C2×Q8×C13—48no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13C22⋊C412yes—
83C2×Q8×C13C2×D412yes—
84C2×Q8×C13C2×D412yes—
85C2×D4×C13—24no—
86C2×D4×C13—21no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—42no—
90C2×D4×C13—42no—
91C2×D4×C13C22⋊C412yes—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—24no—
97C22×C4×C13—24no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—24no—
102C22×C4×C13—42no—
103C22×C4×C13—42no—
104C22×C4×C13—42no—
105C22×C4×C13C22⋊C412yes—
106C22×C4×C13C22⋊C411yescharacteristic
107C22×C4×C13C22×C411yescharacteristic
108C22×C4×C13C2×D412yes—
109C13×M16—44no—
110C13×M16—44no—
111C2×C8×C13—44no—
112C13×C4⋊C4—24no—
113C13×C4⋊C4—28no—
114C13×C4⋊C4—28no—
115C13×C22⋊C4—24no—
116C13×C22⋊C4—28no—
117C13×C22⋊C4—28no—
118C42×C13—21no—
119C42×C13—21no—
120C42×C13C22⋊C412yes—
121C42×C13C22⋊C412yes—
122C2×#536C2×C1311yescharacteristic
123C2×#356C2×C1312yescomplemented
124C2×#355C2×C1312yescomplemented
125#1784C2×C1312yescomplemented
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—22no—
129C23×C13—42no—
130C23×C13—44no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13#9912yes—
134C23×C13C2×C22⋊C411yescharacteristic
135Q8×C13—42no—
136Q8×C13—42no—
137Q8×C13—48no—
138Q8×C13—42no—
139Q8×C13—42no—
140Q8×C13—42no—
141Q8×C13—42no—
142D4×C13—42no—
143D4×C13—42no—
144D4×C13—48no—
145C2×C4×C13—24no—
146C2×C4×C13—24no—
147C2×C4×C13—21no—
148C2×C4×C13—22no—
149C2×C4×C13—21no—
150C2×C4×C13—22no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—22no—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—22no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—48no—
160C2×C4×C13—48no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13#9912yes—
166C2×C4×C13C2×C22⋊C411yescharacteristic
167C2×C4×C13C2×C22⋊C411yescharacteristic
168C2×C4×C13#12014yes—
169C8×C13—84no—
170C22×#41C4×C1311yescharacteristic
171C23×Q8C22×C1311yescharacteristic
172#536—24no—
173#536—24no—
174C2×C4⋊Q8C4×C1311yescharacteristic
175C2×C4⋊Q8C22×C1311yescharacteristic
176C2×#124C4×C1311yescharacteristic
177C2×#124C22×C1311yescharacteristic
178C2×#123—22no—
179C2×C22⋊Q8—22no—
180C2×#117C4×C1311yescharacteristic
181C2×#101—22no—
182C2×#101C22×C1314yes—
183#407—22no—
184#356—24no—
185#355—24no—
186C22×C13—22no—
187C22×C13—24no—
188C22×C13—22no—
189C22×C13—42no—
190C22×C13—42no—
191C22×C13—44no—
192C22×C13—42no—
193C22×C13—82no—
194C22×C13—82no—
195C22×C13#37911yescharacteristic
196C22×C13C2×#9911yescharacteristic
197C22×C13C2×#9911yescharacteristic
198C4×C13—24no—
199C4×C13—22no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—42no—
203C4×C13—42no—
204C4×C13—42no—
205C4×C13—42no—
206C2×#41—22no—
207C2×#41—22no—
208C2×#41—42no—
209C2×#41—42no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—42no—
213C22×Q8—42no—
214C22×Q8C2×C4×C1311yescharacteristic
215C22×Q8C2×C4×C1311yescharacteristic
216C22×Q8D4×C1312yes—
217C22×Q8C23×C1311yescharacteristic
218C22×D4—21no—
219C22×D4C2×C4×C1311yescharacteristic
220C23×C4—21no—
221C23×C4C2×C4×C1311yescharacteristic
222C23×C4D4×C1312yes—
223C2×M16—24no—
224C4⋊Q8—22no—
225C4⋊Q8—22no—
226C4⋊Q8—22no—
227C4⋊Q8D4×C1314yes—
228#124—22no—
229#124—22no—
230#124—22no—
231#124D4×C1314yes—
232#123—216no—
233C22⋊Q8—216no—
234#117—22no—
235#117—22no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C42C2×C4×C1311yescharacteristic
243C2×C42C2×C4×C1311yescharacteristic
244#101—24no—
245#101—24no—
246#101—44no—
247C22⋊C8—44no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—42no—
251C2×C13—82no—
252C2×C13#178111yescharacteristic
253C2×C13#213312yes—
254C24—21no—
255C24C13×C22⋊C411yescharacteristic
256#41—48no—
257#41—48no—
258C2×Q8—24no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—24no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—48no—
269C2×Q8—48no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8C13×C22⋊C412yes—
273C2×Q8C2×D4×C1312yes—
274C2×Q8C2×D4×C1312yes—
275C2×D4—24no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4C13×C22⋊C412yes—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—24no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4C13×C22⋊C412yes—
296C22×C4C13×C22⋊C411yescharacteristic
297C22×C4C22×C4×C1311yescharacteristic
298C22×C4C2×D4×C1312yes—
299M16—44no—
300M16—44no—
301C2×C8—44no—
302C4⋊C4—24no—
303C4⋊C4—28no—
304C4⋊C4—28no—
305C22⋊C4—24no—
306C22⋊C4—28no—
307C22⋊C4—28no—
308C42—21no—
309C42—21no—
310C42C13×C22⋊C412yes—
311C42C13×C22⋊C412yes—
312C13#1270211yescharacteristic, direct product factor, Sylow
313C23—21no—
314C23—21no—
315C23—22no—
316C23—42no—
317C23—44no—
318C23—41no—
319C23—41no—
320C23C13×#9912yes—
321C23C2×C13×C22⋊C411yescharacteristic
322Q8—42no—
323Q8—42no—
324Q8—48no—
325Q8—42no—
326Q8—42no—
327Q8—42no—
328Q8—42no—
329D4—42no—
330D4—42no—
331D4—48no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—48no—
347C2×C4—48no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4C13×#9912yes—
353C2×C4C2×C13×C22⋊C411yescharacteristic
354C2×C4C2×C13×C22⋊C411yescharacteristic
355C2×C4C13×#12014yes—
356C8—84no—
357C22—22no—
358C22—22no—
359C22—24no—
360C22—42no—
361C22—42no—
362C22—44no—
363C22—42no—
364C22—82no—
365C22—82no—
366C22C13×#37911yescharacteristic
367C22C2×C13×#9911yescharacteristic
368C22C2×C13×#9911yescharacteristic
369C4—24no—
370C4—22no—
371C4—21no—
372C4—21no—
373C4—42no—
374C4—42no—
375C4—42no—
376C4—42no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—82no—
381C2C13×#178111yescharacteristic
382C2C13×#213312yes—
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×Q8C23×C13
prime radicalC22×C13×#41C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C23×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#356C2semidirect
3. C2×C13×#355C2semidirect
4. C13×#1784C2semidirect
63. #12702C13direct (N × H)
123. C2×#356C2×C13semidirect
124. C2×#355C2×C13semidirect
125. #1784C2×C13semidirect
312. C13#12702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5362
C2×C13×#3562
C2×C13×#3552
C13×#17842
#1270213