Finite Group Databasebeta

← C13×#9682 #15696021

Subgroups — C13×#9682 #15696021

Order 3328.

700 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2850C211yesmaximal, characteristic
2C13×#1749C211yesmaximal, characteristic, complemented
3C2×C13×#328C212yesmaximal, complemented
4C2×C13×#327C212yesmaximal
5C13×C4⋊#95C211yesmaximal, characteristic, complemented
6C2×C13×#124C411yescharacteristic, complemented
7C2×C13×C22⋊Q8C2211yescharacteristic
8C2×C13×#121C2211yescharacteristic
9C22×C13×C4⋊C4—21no—
10C22×C42×C13C2211yescharacteristic
11C2×C13×C22⋊C8C2212yes—
12C2×C13×#97—21no—
13C13×#391C411yescharacteristic, complemented
14C13×#390C411yescharacteristic, complemented
15C13×#388—21no—
16C13×#388—21no—
17C13×#386—21no—
18C13×#386—21no—
19C13×#382C411yescharacteristic, complemented
20C2×C13×#95—21no—
21C2×C13×#95C2212yes—
22C13×#336—21no—
23C13×#328—24no—
24C13×#327—24no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13—22no—
29C23×C4×C13D411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C22×C8×C13—22no—
33C13×#124—42no—
34C13×C22⋊Q8—22no—
35C13×C22⋊Q8—22no—
36C13×#121—22no—
37C13×#121—22no—
38C2×C13×C4⋊C4—24no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—42no—
41C2×C13×C4⋊C4—42no—
42C2×C13×C4⋊C4C2×C411yescharacteristic
43C2×C13×C4⋊C4C2×C411yescharacteristic
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C42×C13—42no—
51C2×C42×C13C2×C411yescharacteristic
52C2×C42×C13C2×C411yescharacteristic
53C2×C42×C13D411yescharacteristic
54C2×C42×C13D411yescharacteristic
55C13×C22⋊C8—22no—
56C13×C22⋊C8D414yes—
57C13×#97—42no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—22no—
63C13×#95—22no—
64C13×#95—42no—
65#9682C1311yesmaximal, characteristic, direct product factor, Sylow
66C24×C13—21no—
67C24×C13C2×D411yescharacteristic
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×D4×C13—22no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—24no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13—42no—
97C22×C4×C13—42no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13C22⋊C411yescharacteristic
101C22×C4×C13C22⋊C411yescharacteristic
102C22×C4×C13C22⋊C411yescharacteristic
103C22×C4×C13C22⋊C411yescharacteristic
104C22×C4×C13C22×C411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D412yes—
107C22×C4×C13#4112yes—
108C2×C8×C13—24no—
109C2×C8×C13—42no—
110C2×C8×C13—42no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—48no—
114C13×C4⋊C4—42no—
115C13×C22⋊C4—42no—
116C13×C22⋊C4—42no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C13×C22⋊C4—42no—
120C13×C22⋊C4—42no—
121C13×C22⋊C4—42no—
122C42×C13—22no—
123C42×C13—22no—
124C42×C13—41no—
125C42×C13—41no—
126#2850C2×C1311yescharacteristic
127#1749C2×C1311yescharacteristic, complemented
128C2×#328C2×C1312yescomplemented
129C2×#327C2×C1312yes—
130C4⋊#95C2×C1311yescharacteristic, complemented
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13C2×C22⋊C411yescharacteristic
143C23×C13#12411yescharacteristic
144C23×C13#12711yescharacteristic
145C23×C13AGL(1,ℤ/8)11yescharacteristic
146C23×C13AGL(1,ℤ/8)11yescharacteristic
147C23×C13#13711yescharacteristic
148C23×C13#13711yescharacteristic
149Q8×C13—82no—
150D4×C13—82no—
151D4×C13—81no—
152D4×C13—81no—
153D4×C13—81no—
154D4×C13—81no—
155C2×C4×C13—24no—
156C2×C4×C13—24no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—44no—
176C2×C4×C13—44no—
177C2×C4×C13—44no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—82no—
188C2×C4×C13—82no—
189C2×C4×C13—82no—
190C2×C4×C13—82no—
191C2×C4×C13#9912yes—
192C2×C4×C13#10412yes—
193C2×C4×C13C4×D412yes—
194C2×C4×C13#12112yes—
195C8×C13—44no—
196C2×#124C4×C1311yescharacteristic, complemented
197C2×C22⋊Q8C22×C1311yescharacteristic
198C2×#121C22×C1311yescharacteristic
199C22×C4⋊C4—21no—
200C22×C42C22×C1311yescharacteristic
201C2×C22⋊C8C22×C1312yes—
202C2×#97—21no—
203#391C4×C1311yescharacteristic, complemented
204#390C4×C1311yescharacteristic, complemented
205#388—21no—
206#388—21no—
207#386—21no—
208#386—21no—
209#382C4×C1311yescharacteristic, complemented
210C2×#95—21no—
211C2×#95C22×C1312yes—
212#336—21no—
213#328—24no—
214#327—24no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13—81no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13#39011yescharacteristic
235C22×C13C2×#9911yescharacteristic
236C22×C13#41011yescharacteristic
237C22×C13#41711yescharacteristic
238C22×C13#41711yescharacteristic
239C22×C13C2×#10411yescharacteristic
240C22×C13#42111yescharacteristic
241C22×C13#48911yescharacteristic
242C22×C13#48911yescharacteristic
243C22×C13#49611yescharacteristic
244C22×C13#49711yescharacteristic
245C4×C13—22no—
246C4×C13—22no—
247C4×C13—22no—
248C4×C13—22no—
249C4×C13—41no—
250C4×C13—41no—
251C4×C13—84no—
252C4×C13—81no—
253C4×C13—81no—
254C4×C13—81no—
255C22×Q8C2×C4×C1311yescharacteristic
256C22×D4—21no—
257C22×D4C2×C4×C1311yescharacteristic
258C23×C4—22no—
259C23×C4D4×C1311yescharacteristic
260C23×C4D4×C1311yescharacteristic
261C23×C4C23×C1311yescharacteristic
262C22×C8—22no—
263#124—42no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266#121—22no—
267#121—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4C2×C4×C1311yescharacteristic
273C2×C4⋊C4C2×C4×C1311yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C42—42no—
281C2×C42C2×C4×C1311yescharacteristic
282C2×C42C2×C4×C1311yescharacteristic
283C2×C42D4×C1311yescharacteristic
284C2×C42D4×C1311yescharacteristic
285C22⋊C8—22no—
286C22⋊C8D4×C1314yes—
287#97—42no—
288#95—21no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—22no—
293#95—22no—
294#95—42no—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13—21no—
299C2×C13—161no—
300C2×C13#150411yescharacteristic
301C2×C13#150911yescharacteristic
302C2×C13#151211yescharacteristic
303C2×C13#151311yescharacteristic
304C2×C13#195911yescharacteristic
305C2×C13#196411yescharacteristic
306C2×C13#198011yescharacteristic
307C24—21no—
308C24C2×D4×C1311yescharacteristic
309C2×Q8—22no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—24no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4C13×C22⋊C411yescharacteristic
342C22×C4C13×C22⋊C411yescharacteristic
343C22×C4C13×C22⋊C411yescharacteristic
344C22×C4C13×C22⋊C411yescharacteristic
345C22×C4C22×C4×C1311yescharacteristic
346C22×C4C2×D4×C1311yescharacteristic
347C22×C4C2×D4×C1312yes—
348C22×C4C13×#4112yes—
349C2×C8—24no—
350C2×C8—42no—
351C2×C8—42no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—48no—
355C4⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C42—22no—
364C42—22no—
365C42—41no—
366C42—41no—
367C13#968211yescharacteristic, direct product factor, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C2×C13×C22⋊C411yescharacteristic
380C23C13×#12411yescharacteristic
381C23C13×#12711yescharacteristic
382C23C13×AGL(1,ℤ/8)11yescharacteristic
383C23C13×AGL(1,ℤ/8)11yescharacteristic
384C23C13×#13711yescharacteristic
385C23C13×#13711yescharacteristic
386Q8—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—21no—
395C2×C4—21no—
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—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4C13×#9912yes—
429C2×C4C13×#10412yes—
430C2×C4C4×D4×C1312yes—
431C2×C4C13×#12112yes—
432C8—44no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22C13×#39011yescharacteristic
453C22C2×C13×#9911yescharacteristic
454C22C13×#41011yescharacteristic
455C22C13×#41711yescharacteristic
456C22C13×#41711yescharacteristic
457C22C2×C13×#10411yescharacteristic
458C22C13×#42111yescharacteristic
459C22C13×#48911yescharacteristic
460C22C13×#48911yescharacteristic
461C22C13×#49611yescharacteristic
462C22C13×#49711yescharacteristic
463C4—22no—
464C4—22no—
465C4—22no—
466C4—22no—
467C4—41no—
468C4—41no—
469C4—84no—
470C4—81no—
471C4—81no—
472C4—81no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—161no—
478C2C13×#150411yescharacteristic
479C2C13×#150911yescharacteristic
480C2C13×#151211yescharacteristic
481C2C13×#151311yescharacteristic
482C2C13×#195911yescharacteristic
483C2C13×#196411yescharacteristic
484C2C13×#198011yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1749C2semidirect
3. C2×C13×#328C2semidirect
5. C13×C4⋊#95C2semidirect
6. C2×C13×#124C4semidirect
13. C13×#391C4semidirect
14. C13×#390C4semidirect
19. C13×#382C4semidirect
65. #9682C13direct (N × H)
127. #1749C2×C13semidirect
128. C2×#328C2×C13semidirect
130. C4⋊#95C2×C13semidirect
196. C2×#124C4×C13semidirect
203. #391C4×C13semidirect
204. #390C4×C13semidirect
209. #382C4×C13semidirect
367. C13#9682direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28502
C13×#17492
C2×C13×#3282
C2×C13×#3272
C13×C4⋊#952
#968213