Finite Group Databasebeta

← C13×#13092 #15699431

Subgroups — C13×#13092 #15699431

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#101C211yesmaximal, characteristic, complemented
2C13×#2436C211yesmaximal, characteristic
3C2×C13×#355C212yesmaximal, complemented
4C13×#1784C211yesmaximal, characteristic, complemented
5C13×#1394C212yesmaximal, complemented
6C23×Q8×C13C2211yescharacteristic
7C22×C13×M16—21no—
8C2×C13×#124C411yescharacteristic
9C2×C13×#124C2211yescharacteristic
10C2×C13×#121C411yescharacteristic
11C2×C13×#101—21no—
12C2×C13×#101—24no—
13C2×C13×#101—21no—
14C2×C13×#101C2212yes—
15C2×C13×#101C2212yes—
16C13×#407—21no—
17C13×#393—21no—
18C13×#393—21no—
19C13×#391C411yescharacteristic
20C13×#391C2211yescharacteristic
21C13×#386—21no—
22C13×#386—21no—
23C4×C13×C22⋊C4C411yescharacteristic
24C13×#355—24no—
25C22×Q8×C13—22no—
26C22×Q8×C13—22no—
27C22×Q8×C13—41no—
28C22×Q8×C13—41no—
29C22×Q8×C13—42no—
30C22×Q8×C13C2×C411yescharacteristic
31C22×Q8×C13D411yescharacteristic
32C22×Q8×C13D411yescharacteristic
33C22×Q8×C13C2311yescharacteristic
34C22×D4×C13—21no—
35C22×D4×C13C2×C411yescharacteristic
36C23×C4×C13C2×C411yescharacteristic
37C23×C4×C13D411yescharacteristic
38C23×C4×C13D411yescharacteristic
39C2×C13×M16—24no—
40C2×C13×M16—22no—
41C2×C13×M16—22no—
42C2×C13×M16—41no—
43C2×C13×M16—42no—
44C22×C8×C13—41no—
45C13×#124—22no—
46C13×#124—22no—
47C13×#124—42no—
48C13×#121—41no—
49C13×#121—41no—
50C2×C13×C4⋊C4C2×C411yescharacteristic
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C42×C13C2×C411yescharacteristic
58C2×C42×C13C2×C411yescharacteristic
59C13×#101—24no—
60C13×#101—22no—
61C13×#101—22no—
62C13×#101—22no—
63C13×#101—42no—
64C13×#101D414yescomplemented
65C13×C22⋊C8—41no—
66C13×C22⋊C8—41no—
67C13×#95—21no—
68C13×#95—21no—
69C13×#95—21no—
70C13×#95—21no—
71C13×#95—21no—
72#13092C1311yesmaximal, characteristic, direct product factor, Sylow
73C24×C13—21no—
74C24×C13C22⋊C411yescharacteristic
75C2×Q8×C13—22no—
76C2×Q8×C13—22no—
77C2×Q8×C13—22no—
78C2×Q8×C13—21no—
79C2×Q8×C13—22no—
80C2×Q8×C13—21no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×Q8×C13—41no—
86C2×Q8×C13—41no—
87C2×Q8×C13—44no—
88C2×Q8×C13—44no—
89C2×Q8×C13—44no—
90C2×Q8×C13—44no—
91C2×Q8×C13C2×D412yes—
92C2×Q8×C13#4112yes—
93C2×D4×C13—22no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—44no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13C22⋊C411yescharacteristic
116C22×C4×C13C22⋊C411yescharacteristic
117C22×C4×C13C22⋊C411yescharacteristic
118C22×C4×C13C22×C411yescharacteristic
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C13×M16—24no—
122C13×M16—44no—
123C13×M16—42no—
124C13×M16—42no—
125C13×M16—42no—
126C2×C8×C13—44no—
127C2×C8×C13—42no—
128C2×C8×C13—42no—
129C13×C4⋊C4—41no—
130C13×C22⋊C4—42no—
131C13×C22⋊C4—42no—
132C13×C22⋊C4—42no—
133C13×C22⋊C4—42no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4—41no—
137C42×C13—22no—
138C42×C13—41no—
139C22×#101C2×C1311yescharacteristic, complemented
140#2436C2×C1311yescharacteristic
141C2×#355C2×C1312yescomplemented
142#1784C2×C1311yescharacteristic, complemented
143#1394C2×C1312yescomplemented
144C23×C13—22no—
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—41no—
148C23×C13—42no—
149C23×C13—42no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13#9911yescharacteristic
154C23×C13#9911yescharacteristic
155C23×C13C2×C22⋊C411yescharacteristic
156Q8×C13—42no—
157Q8×C13—42no—
158Q8×C13—44no—
159Q8×C13—44no—
160Q8×C13—42no—
161Q8×C13—42no—
162D4×C13—82no—
163D4×C13—82no—
164D4×C13—82no—
165C2×C4×C13—22no—
166C2×C4×C13—22no—
167C2×C4×C13—22no—
168C2×C4×C13—22no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—42no—
186C2×C4×C13—42no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—42no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13#9912yes—
196C2×C4×C13C4×D412yes—
197C2×C4×C13#12011yescharacteristic
198C2×C4×C13#12112yes—
199C2×C4×C13#12311yescharacteristic
200C8×C13—44no—
201C8×C13—82no—
202C23×Q8C22×C1311yescharacteristic
203C22×M16—21no—
204C2×#124C4×C1311yescharacteristic
205C2×#124C22×C1311yescharacteristic
206C2×#121C4×C1311yescharacteristic
207C2×#101—21no—
208C2×#101—24no—
209C2×#101—21no—
210C2×#101C22×C1312yes—
211C2×#101C22×C1312yes—
212#407—21no—
213#393—21no—
214#393—21no—
215#391C4×C1311yescharacteristic
216#391C22×C1311yescharacteristic
217#386—21no—
218#386—21no—
219C4×C22⋊C4C4×C1311yescharacteristic
220#355—24no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—42no—
229C22×C13—42no—
230C22×C13—82no—
231C22×C13—82no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13—81no—
235C22×C13#35512yescomplemented
236C22×C13#38611yescharacteristic
237C22×C13C2×#9911yescharacteristic
238C22×C13C2×#9911yescharacteristic
239C4×C13—21no—
240C4×C13—22no—
241C4×C13—22no—
242C4×C13—21no—
243C4×C13—22no—
244C4×C13—41no—
245C4×C13—41no—
246C4×C13—81no—
247C4×C13—81no—
248C4×C13—81no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—41no—
252C22×Q8—41no—
253C22×Q8—42no—
254C22×Q8C2×C4×C1311yescharacteristic
255C22×Q8D4×C1311yescharacteristic
256C22×Q8D4×C1311yescharacteristic
257C22×Q8C23×C1311yescharacteristic
258C22×D4—21no—
259C22×D4C2×C4×C1311yescharacteristic
260C23×C4C2×C4×C1311yescharacteristic
261C23×C4D4×C1311yescharacteristic
262C23×C4D4×C1311yescharacteristic
263C2×M16—24no—
264C2×M16—22no—
265C2×M16—22no—
266C2×M16—41no—
267C2×M16—42no—
268C22×C8—41no—
269#124—22no—
270#124—22no—
271#124—42no—
272#121—41no—
273#121—41no—
274C2×C4⋊C4C2×C4×C1311yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42C2×C4×C1311yescharacteristic
282C2×C42C2×C4×C1311yescharacteristic
283#101—24no—
284#101—22no—
285#101—22no—
286#101—22no—
287#101—42no—
288#101D4×C1314yescomplemented
289C22⋊C8—41no—
290C22⋊C8—41no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—21no—
295#95—21no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13—22no—
299C2×C13—41no—
300C2×C13—161no—
301C2×C13#189811yescharacteristic
302C2×C13C2×#35511yescharacteristic
303C2×C13#213311yescharacteristic
304C24—21no—
305C24C13×C22⋊C411yescharacteristic
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—21no—
310C2×Q8—22no—
311C2×Q8—21no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—44no—
319C2×Q8—44no—
320C2×Q8—44no—
321C2×Q8—44no—
322C2×Q8C2×D4×C1312yes—
323C2×Q8C13×#4112yes—
324C2×D4—22no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—44no—
328C2×D4—41no—
329C2×D4—41no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4C13×C22⋊C411yescharacteristic
347C22×C4C13×C22⋊C411yescharacteristic
348C22×C4C13×C22⋊C411yescharacteristic
349C22×C4C22×C4×C1311yescharacteristic
350C22×C4C2×D4×C1311yescharacteristic
351C22×C4C2×D4×C1311yescharacteristic
352M16—24no—
353M16—44no—
354M16—42no—
355M16—42no—
356M16—42no—
357C2×C8—44no—
358C2×C8—42no—
359C2×C8—42no—
360C4⋊C4—41no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C22⋊C4—41no—
366C22⋊C4—42no—
367C22⋊C4—41no—
368C42—22no—
369C42—41no—
370C13#1309211yescharacteristic, direct product factor, Sylow
371C23—21no—
372C23—21no—
373C23—22no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23C13×#9911yescharacteristic
381C23C13×#9911yescharacteristic
382C23C2×C13×C22⋊C411yescharacteristic
383Q8—42no—
384Q8—42no—
385Q8—44no—
386Q8—44no—
387Q8—42no—
388Q8—42no—
389D4—82no—
390D4—82no—
391D4—82no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4C13×#9912yes—
423C2×C4C4×D4×C1312yes—
424C2×C4C13×#12011yescharacteristic
425C2×C4C13×#12112yes—
426C2×C4C13×#12311yescharacteristic
427C8—44no—
428C8—82no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—82no—
439C22—82no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C13×#35512yescomplemented
444C22C13×#38611yescharacteristic
445C22C2×C13×#9911yescharacteristic
446C22C2×C13×#9911yescharacteristic
447C4—21no—
448C4—22no—
449C4—22no—
450C4—21no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—81no—
455C4—81no—
456C4—81no—
457C2—21no—
458C2—21no—
459C2—22no—
460C2—41no—
461C2—161no—
462C2C13×#189811yescharacteristic
463C2C2×C13×#35511yescharacteristic
464C2C13×#213311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×Q8C23×C13
prime radicalC2×C13×#121C4
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
1. C22×C13×#101C2semidirect
3. C2×C13×#355C2semidirect
4. C13×#1784C2semidirect
5. C13×#1394C2semidirect
64. C13×#101D4semidirect
72. #13092C13direct (N × H)
139. C22×#101C2×C13semidirect
141. C2×#355C2×C13semidirect
142. #1784C2×C13semidirect
143. #1394C2×C13semidirect
235. C22×C13#355semidirect
288. #101D4×C13semidirect
370. C13#13092direct (N × H)
443. C22C13×#355semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1012
C13×#24362
C2×C13×#3552
C13×#17842
C13×#13942
#1309213