Finite Group Databasebeta

← C13×#9716 #15696055

Subgroups — C13×#9716 #15696055

Order 3328.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2850C211yesmaximal, characteristic
2C13×#1797C211yesmaximal, characteristic, complemented
3C2×C13×#328C212yesmaximal, complemented
4C2×C13×#327C212yesmaximal
5C13×#1434C211yesmaximal, characteristic, complemented
6C2×C13×#124C411yescharacteristic, complemented
7C2×C13×C22⋊Q8C2211yescharacteristic
8C2×C13×#121C2211yescharacteristic
9C22×C42×C13C2211yescharacteristic
10C2×C13×C4⋊C8—21no—
11C2×C13×C22⋊C8C2212yes—
12C13×#391C411yescharacteristic, complemented
13C13×#390C411yescharacteristic, complemented
14C13×#388—21no—
15C13×#388—21no—
16C13×#386—21no—
17C13×#386—21no—
18C13×#382C411yescharacteristic, complemented
19C2×C13×#95—21no—
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—21no—
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C4⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C42×C13—42no—
48C2×C42×C13C2×C411yescharacteristic
49C2×C42×C13C2×C411yescharacteristic
50C2×C42×C13D411yescharacteristic
51C2×C42×C13D411yescharacteristic
52C13×C4⋊C8—42no—
53C13×C22⋊C8—22no—
54C13×C22⋊C8—22no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—22no—
60C13×#95—42no—
61C13×#95—42no—
62C13×#95D414yes—
63#9716C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13—21no—
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×D4×C13—22no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C22×C4×C13—22no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—22no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—24no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—42no—
90C22×C4×C13—42no—
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13—42no—
94C22×C4×C13—42no—
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C22⋊C411yescharacteristic
99C22×C4×C13C22×C411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D412yes—
102C22×C4×C13#4112yes—
103C2×C8×C13—42no—
104C2×C8×C13—42no—
105C2×C8×C13—42no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—42no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117C42×C13—22no—
118C42×C13—22no—
119C42×C13—41no—
120C42×C13—41no—
121#2850C2×C1311yescharacteristic
122#1797C2×C1311yescharacteristic, complemented
123C2×#328C2×C1312yescomplemented
124C2×#327C2×C1312yes—
125#1434C2×C1311yescharacteristic, complemented
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13C2×C22⋊C411yescharacteristic
138C23×C13#12112yes—
139C23×C13#13512yes—
140C23×C13AGL(1,ℤ/8)11yescharacteristic
141C23×C13#13711yescharacteristic
142Q8×C13—82no—
143D4×C13—82no—
144D4×C13—82no—
145D4×C13—82no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—44no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—44no—
167C2×C4×C13—44no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—44no—
178C2×C4×C13—82no—
179C2×C4×C13—82no—
180C2×C4×C13—82no—
181C2×C4×C13—82no—
182C2×C4×C13#9912yes—
183C2×C4×C13C4×D412yes—
184C2×C4×C13#12411yescharacteristic
185C2×C4×C13#12711yescharacteristic
186C8×C13—82no—
187C2×#124C4×C1311yescharacteristic, complemented
188C2×C22⋊Q8C22×C1311yescharacteristic
189C2×#121C22×C1311yescharacteristic
190C22×C42C22×C1311yescharacteristic
191C2×C4⋊C8—21no—
192C2×C22⋊C8C22×C1312yes—
193#391C4×C1311yescharacteristic, complemented
194#390C4×C1311yescharacteristic, complemented
195#388—21no—
196#388—21no—
197#386—21no—
198#386—21no—
199#382C4×C1311yescharacteristic, complemented
200C2×#95—21no—
201C2×#95—21no—
202C2×#95C22×C1312yes—
203#336—21no—
204#328—24no—
205#327—24no—
206C22×C13—22no—
207C22×C13—22no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—22no—
213C22×C13—22no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13#39011yescharacteristic
222C22×C13C2×#9911yescharacteristic
223C22×C13#41011yescharacteristic
224C22×C13#41611yescharacteristic
225C22×C13#41711yescharacteristic
226C22×C13#42111yescharacteristic
227C22×C13#42111yescharacteristic
228C22×C13#46312yes—
229C22×C13#46412yes—
230C4×C13—21no—
231C4×C13—22no—
232C4×C13—21no—
233C4×C13—22no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237C4×C13—84no—
238C4×C13—81no—
239C4×C13—81no—
240C4×C13—81no—
241C22×Q8C2×C4×C1311yescharacteristic
242C22×D4—21no—
243C22×D4C2×C4×C1311yescharacteristic
244C23×C4—22no—
245C23×C4D4×C1311yescharacteristic
246C23×C4D4×C1311yescharacteristic
247C23×C4C23×C1311yescharacteristic
248C22×C8—22no—
249#124—42no—
250C22⋊Q8—22no—
251C22⋊Q8—22no—
252#121—22no—
253#121—22no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4C2×C4×C1311yescharacteristic
256C2×C4⋊C4C2×C4×C1311yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C42—42no—
264C2×C42C2×C4×C1311yescharacteristic
265C2×C42C2×C4×C1311yescharacteristic
266C2×C42D4×C1311yescharacteristic
267C2×C42D4×C1311yescharacteristic
268C4⋊C8—42no—
269C22⋊C8—22no—
270C22⋊C8—22no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—22no—
276#95—42no—
277#95—42no—
278#95D4×C1314yes—
279C2×C13—22no—
280C2×C13—22no—
281C2×C13—161no—
282C2×C13#151211yescharacteristic
283C2×C13#151311yescharacteristic
284C2×C13#151611yescharacteristic
285C2×C13#152111yescharacteristic
286C2×C13#196311yescharacteristic
287C2×C13#196411yescharacteristic
288C2×C13#198311yescharacteristic
289C24—21no—
290C24C2×D4×C1311yescharacteristic
291C2×Q8—22no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—41no—
300C2×D4—41no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—24no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4C13×C22⋊C411yescharacteristic
321C22×C4C13×C22⋊C411yescharacteristic
322C22×C4C13×C22⋊C411yescharacteristic
323C22×C4C13×C22⋊C411yescharacteristic
324C22×C4C22×C4×C1311yescharacteristic
325C22×C4C2×D4×C1311yescharacteristic
326C22×C4C2×D4×C1312yes—
327C22×C4C13×#4112yes—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—22no—
343C42—22no—
344C42—41no—
345C42—41no—
346C13#971611yescharacteristic, direct product factor, Sylow
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23C2×C13×C22⋊C411yescharacteristic
359C23C13×#12112yes—
360C23C13×#13512yes—
361C23C13×AGL(1,ℤ/8)11yescharacteristic
362C23C13×#13711yescharacteristic
363Q8—82no—
364D4—82no—
365D4—82no—
366D4—82no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—44no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4C13×#9912yes—
404C2×C4C4×D4×C1312yes—
405C2×C4C13×#12411yescharacteristic
406C2×C4C13×#12711yescharacteristic
407C8—82no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22C13×#39011yescharacteristic
424C22C2×C13×#9911yescharacteristic
425C22C13×#41011yescharacteristic
426C22C13×#41611yescharacteristic
427C22C13×#41711yescharacteristic
428C22C13×#42111yescharacteristic
429C22C13×#42111yescharacteristic
430C22C13×#46312yes—
431C22C13×#46412yes—
432C4—22no—
433C4—21no—
434C4—22no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—84no—
440C4—81no—
441C4—81no—
442C4—81no—
443C2—22no—
444C2—22no—
445C2—161no—
446C2C13×#151211yescharacteristic
447C2C13×#151311yescharacteristic
448C2C13×#151611yescharacteristic
449C2C13×#152111yescharacteristic
450C2C13×#196311yescharacteristic
451C2C13×#196411yescharacteristic
452C2C13×#198311yescharacteristic
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×#1797C2semidirect
3. C2×C13×#328C2semidirect
5. C13×#1434C2semidirect
6. C2×C13×#124C4semidirect
12. C13×#391C4semidirect
13. C13×#390C4semidirect
18. C13×#382C4semidirect
63. #9716C13direct (N × H)
122. #1797C2×C13semidirect
123. C2×#328C2×C13semidirect
125. #1434C2×C13semidirect
187. C2×#124C4×C13semidirect
193. #391C4×C13semidirect
194. #390C4×C13semidirect
199. #382C4×C13semidirect
346. C13#9716direct (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×#17972
C2×C13×#3282
C2×C13×#3272
C13×#14342
#971613