Finite Group Databasebeta

← C13×#13225 #15699564

Subgroups — C13×#13225 #15699564

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2544C211yesmaximal, characteristic
2C2×C13×#354C212yesmaximal, complemented
3C2×C13×#353C212yesmaximal
4C13×#1799C211yesmaximal, characteristic, complemented
5C4×C13×#99C211yesmaximal, characteristic, complemented
6C2×C13×#127C2211yescharacteristic
7C2×C13×#124C411yescharacteristic, complemented
8C2×C13×#124C2211yescharacteristic
9C2×C4×D4×C13C2211yescharacteristic
10C2×C13×#99C2212yes—
11C2×C13×#99C2212yes—
12C13×#394—21no—
13C13×#394—21no—
14C13×#391C411yescharacteristic, complemented
15C13×#390C411yescharacteristic, complemented
16C13×#386—21no—
17C13×#386—21no—
18C13×#380—21no—
19C4×C13×C4⋊C4C411yescharacteristic, complemented
20C4×C13×C22⋊C4—21no—
21C13×#354—24no—
22C13×#353—24no—
23C13×#342—21no—
24C13×#342—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13—21no—
28C22×D4×C13C2×C411yescharacteristic
29C22×D4×C13C2311yescharacteristic
30C23×C4×C13D411yescharacteristic
31C23×C4×C13D411yescharacteristic
32C13×#127—22no—
33C13×#127—22no—
34C13×#124—22no—
35C13×#124—22no—
36C13×#124—41no—
37C13×#124—41no—
38C4×D4×C13—41no—
39C4×D4×C13—41no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—41no—
42C2×C13×C4⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4—22no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—22no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4D411yescharacteristic
52C2×C13×C22⋊C4D411yescharacteristic
53C2×C42×C13—41no—
54C2×C42×C13C2×C411yescharacteristic
55C2×C42×C13C2×C411yescharacteristic
56C2×C42×C13C2×C411yescharacteristic
57C13×#99—22no—
58C13×#99—22no—
59C13×#99—22no—
60C13×#99D414yes—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64C13×#95—41no—
65C13×#95—41no—
66#13225C1311yesmaximal, characteristic, direct product factor, Sylow
67C24×C13—21no—
68C24×C13C2×D411yescharacteristic
69C24×C13C2×D411yescharacteristic
70C2×Q8×C13—22no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×D4×C13—22no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—42no—
79C2×D4×C13—42no—
80C2×D4×C13—42no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—81no—
84C2×D4×C13—81no—
85C2×D4×C13C2×D412yes—
86C2×D4×C13#4112yes—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13—81no—
97C22×C4×C13—81no—
98C22×C4×C13C22⋊C411yescharacteristic
99C22×C4×C13C22⋊C411yescharacteristic
100C22×C4×C13C22⋊C411yescharacteristic
101C22×C4×C13C22⋊C411yescharacteristic
102C22×C4×C13C22×C411yescharacteristic
103C13×C4⋊C4—41no—
104C13×C4⋊C4—42no—
105C13×C4⋊C4—82no—
106C13×C22⋊C4—24no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—42no—
117C13×C22⋊C4—42no—
118C13×C22⋊C4—81no—
119C13×C22⋊C4—81no—
120C42×C13—21no—
121C42×C13—21no—
122C42×C13—22no—
123C42×C13—22no—
124C42×C13—82no—
125#2544C2×C1311yescharacteristic
126C2×#354C2×C1312yescomplemented
127C2×#353C2×C1312yes—
128#1799C2×C1311yescharacteristic, complemented
129C4×#99C2×C1311yescharacteristic, complemented
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13C2×C22⋊C411yescharacteristic
146C23×C13#12112yes—
147C23×C13#12411yescharacteristic
148C23×C13#12711yescharacteristic
149Q8×C13—82no—
150D4×C13—42no—
151D4×C13—42no—
152D4×C13—82no—
153D4×C13—84no—
154D4×C13—82no—
155D4×C13—82no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—22no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—44no—
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—81no—
178C2×C4×C13—81no—
179C2×C4×C13—82no—
180C2×C4×C13—82no—
181C2×C4×C13—82no—
182C2×C4×C13—82no—
183C2×C4×C13—82no—
184C2×C4×C13#9911yescharacteristic
185C2×C4×C13#9911yescharacteristic
186C2×C4×C13C4×D412yes—
187C2×#127C22×C1311yescharacteristic
188C2×#124C4×C1311yescharacteristic, complemented
189C2×#124C22×C1311yescharacteristic
190C2×C4×D4C22×C1311yescharacteristic
191C2×#99C22×C1312yes—
192C2×#99C22×C1312yes—
193#394—21no—
194#394—21no—
195#391C4×C1311yescharacteristic, complemented
196#390C4×C1311yescharacteristic, complemented
197#386—21no—
198#386—21no—
199#380—21no—
200C4×C4⋊C4C4×C1311yescharacteristic, complemented
201C4×C22⋊C4—21no—
202#354—24no—
203#353—24no—
204#342—21no—
205#342—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—22no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—42no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—81no—
227C22×C13#39011yescharacteristic
228C22×C13C2×#9911yescharacteristic
229C22×C13#41011yescharacteristic
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—22no—
233C4×C13—42no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237C4×C13—81no—
238C4×C13—84no—
239C4×C13—81no—
240C4×C13—162no—
241C22×Q8C2×C4×C1311yescharacteristic
242C22×D4—21no—
243C22×D4—21no—
244C22×D4C2×C4×C1311yescharacteristic
245C22×D4C23×C1311yescharacteristic
246C23×C4D4×C1311yescharacteristic
247C23×C4D4×C1311yescharacteristic
248#127—22no—
249#127—22no—
250#124—22no—
251#124—22no—
252#124—41no—
253#124—41no—
254C4×D4—41no—
255C4×D4—41no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—41no—
258C2×C4⋊C4C2×C4×C1311yescharacteristic
259C2×C22⋊C4—22no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4D4×C1311yescharacteristic
268C2×C22⋊C4D4×C1311yescharacteristic
269C2×C42—41no—
270C2×C42C2×C4×C1311yescharacteristic
271C2×C42C2×C4×C1311yescharacteristic
272C2×C42C2×C4×C1311yescharacteristic
273#99—22no—
274#99—22no—
275#99—22no—
276#99D4×C1314yes—
277#95—21no—
278#95—21no—
279#95—21no—
280#95—41no—
281#95—41no—
282C2×C13—21no—
283C2×C13—21no—
284C2×C13—42no—
285C2×C13—41no—
286C2×C13—41no—
287C2×C13—161no—
288C2×C13#196411yescharacteristic
289C2×C13#212611yescharacteristic
290C2×C13#212711yescharacteristic
291C24—21no—
292C24C2×D4×C1311yescharacteristic
293C24C2×D4×C1311yescharacteristic
294C2×Q8—22no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—81no—
308C2×D4—81no—
309C2×D4C2×D4×C1312yes—
310C2×D4C13×#4112yes—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—81no—
321C22×C4—81no—
322C22×C4C13×C22⋊C411yescharacteristic
323C22×C4C13×C22⋊C411yescharacteristic
324C22×C4C13×C22⋊C411yescharacteristic
325C22×C4C13×C22⋊C411yescharacteristic
326C22×C4C22×C4×C1311yescharacteristic
327C4⋊C4—41no—
328C4⋊C4—42no—
329C4⋊C4—82no—
330C22⋊C4—24no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—81no—
343C22⋊C4—81no—
344C42—21no—
345C42—21no—
346C42—22no—
347C42—22no—
348C42—82no—
349C13#1322511yescharacteristic, direct product factor, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23C2×C13×C22⋊C411yescharacteristic
366C23C13×#12112yes—
367C23C13×#12411yescharacteristic
368C23C13×#12711yescharacteristic
369Q8—82no—
370D4—42no—
371D4—42no—
372D4—82no—
373D4—84no—
374D4—82no—
375D4—82no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4C13×#9911yescharacteristic
405C2×C4C13×#9911yescharacteristic
406C2×C4C4×D4×C1312yes—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—42no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22C13×#39011yescharacteristic
429C22C2×C13×#9911yescharacteristic
430C22C13×#41011yescharacteristic
431C4—21no—
432C4—21no—
433C4—22no—
434C4—42no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—81no—
439C4—84no—
440C4—81no—
441C4—162no—
442C2—21no—
443C2—21no—
444C2—42no—
445C2—41no—
446C2—41no—
447C2—161no—
448C2C13×#196411yescharacteristic
449C2C13×#212611yescharacteristic
450C2C13×#212711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC2×C13×#127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#354C2semidirect
4. C13×#1799C2semidirect
5. C4×C13×#99C2semidirect
7. C2×C13×#124C4semidirect
14. C13×#391C4semidirect
15. C13×#390C4semidirect
19. C4×C13×C4⋊C4C4semidirect
66. #13225C13direct (N × H)
126. C2×#354C2×C13semidirect
128. #1799C2×C13semidirect
129. C4×#99C2×C13semidirect
188. C2×#124C4×C13semidirect
195. #391C4×C13semidirect
196. #390C4×C13semidirect
200. C4×C4⋊C4C4×C13semidirect
349. C13#13225direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25442
C2×C13×#3542
C2×C13×#3532
C13×#17992
C4×C13×#992
#1322513