Finite Group Databasebeta

← C13×#9203 #15695542

Subgroups — C13×#9203 #15695542

Order 3328.

762 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2617C211yesmaximal, characteristic
2C13×#2315C211yesmaximal, characteristic, complemented
3C13×#1519C212yesmaximal, complemented
4C2×C13×#323C211yesmaximal, characteristic, complemented
5C13×#1289C212yesmaximal, complemented
6C2×C13×#121C2211yescharacteristic
7C2×C13×#120—21no—
8C22×C13×C22⋊C4—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C2×C13×C22⋊C8C2212yes—
11C13×#397C412yescomplemented
12C13×#394—22no—
13C13×#392C412yescomplemented
14C13×#386—21no—
15C13×#385—24no—
16C13×#380—21no—
17C13×#380C2211yescharacteristic
18C13×#380C2212yes—
19C13×#327—24no—
20C13×#323—22no—
21C25×C13D411yescharacteristic
22C22×D4×C13—21no—
23C22×D4×C13—22no—
24C22×D4×C13C2×C411yescharacteristic, complemented
25C23×C4×C13—22no—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C22×C8×C13—22no—
29C13×#121—22no—
30C13×#121—22no—
31C13×#120—42no—
32C13×#120—42no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—22no—
45C2×C13×C22⋊C4—42no—
46C2×C13×C22⋊C4—42no—
47C2×C13×C22⋊C4C2×C412yes—
48C2×C13×C22⋊C4D412yes—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—22no—
51C13×#95—22no—
52C13×#95—22no—
53C13×#95C2×C412yescomplemented
54C13×#95D414yescomplemented
55#9203C1311yesmaximal, characteristic, direct product factor, Sylow
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—21no—
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—81no—
62C24×C13—81no—
63C24×C13C22⋊C412yes—
64C24×C13D812yes—
65C24×C13SD1612yes—
66C24×C13C2×D411yescharacteristic
67C2×D4×C13—22no—
68C2×D4×C13—44no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—82no—
76C2×D4×C13—82no—
77C2×D4×C13—81no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—22no—
82C22×C4×C13—24no—
83C22×C4×C13—44no—
84C22×C4×C13—81no—
85C22×C4×C13—81no—
86C22×C4×C13—82no—
87C22×C4×C13—82no—
88C22×C4×C13C22⋊C412yes—
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13#4112yes—
93C2×C8×C13—42no—
94C2×C8×C13—82no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—82no—
97C13×C4⋊C4—81no—
98C13×C4⋊C4—82no—
99C13×C22⋊C4—24no—
100C13×C22⋊C4—24no—
101C13×C22⋊C4—44no—
102C13×C22⋊C4—44no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—42no—
108C13×C22⋊C4—82no—
109#2617C2×C1311yescharacteristic
110#2315C2×C1311yescharacteristic, complemented
111#1519C2×C1312yescomplemented
112C2×#323C2×C1311yescharacteristic, complemented
113#1289C2×C1312yescomplemented
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13—42no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—81no—
132C23×C13—81no—
133C23×C13—82no—
134C23×C13—82no—
135C23×C13—82no—
136C23×C13—82no—
137C23×C13#10214yes—
138C23×C13C2×C22⋊C411yescharacteristic
139C23×C13#12011yescharacteristic
140C23×C13#12311yescharacteristic
141C23×C13C2×D811yescharacteristic
142C23×C13C2×SD1611yescharacteristic
143C23×C13AGL(1,ℤ/8)11yescharacteristic
144C23×C13#13711yescharacteristic
145D4×C13—82no—
146D4×C13—88no—
147D4×C13—81no—
148D4×C13—81no—
149D4×C13—81no—
150D4×C13—81no—
151C2×C4×C13—22no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—44no—
160C2×C4×C13—44no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—44no—
167C2×C4×C13—81no—
168C2×C4×C13—88no—
169C2×C4×C13C4×D412yes—
170C2×C4×C13#12112yes—
171C8×C13—82no—
172C2×#121C22×C1311yescharacteristic
173C2×#120—21no—
174C22×C22⋊C4—21no—
175C22×C22⋊C4C22×C1311yescharacteristic
176C2×C22⋊C8C22×C1312yes—
177#397C4×C1312yescomplemented
178#394—22no—
179#392C4×C1312yescomplemented
180#386—21no—
181#385—24no—
182#380—21no—
183#380C22×C1311yescharacteristic
184#380C22×C1312yes—
185#327—24no—
186#323—22no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—24no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—44no—
199C22×C13—44no—
200C22×C13—44no—
201C22×C13—42no—
202C22×C13—42no—
203C22×C13—82no—
204C22×C13—82no—
205C22×C13—82no—
206C22×C13—82no—
207C22×C13—82no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13#38611yescharacteristic
212C22×C13C2×#10211yescharacteristic
213C22×C13#41711yescharacteristic
214C22×C13#44711yescharacteristic
215C22×C13#44811yescharacteristic
216C22×C13#48011yescharacteristic
217C22×C13#48111yescharacteristic
218C4×C13—22no—
219C4×C13—22no—
220C4×C13—42no—
221C4×C13—84no—
222C4×C13—82no—
223C4×C13—81no—
224C25D4×C1311yescharacteristic
225C22×D4—21no—
226C22×D4—22no—
227C22×D4C2×C4×C1311yescharacteristic, complemented
228C23×C4—22no—
229C23×C4D4×C1311yescharacteristic
230C23×C4C23×C1311yescharacteristic
231C22×C8—22no—
232#121—22no—
233#121—22no—
234#120—42no—
235#120—42no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4C2×C4×C1311yescharacteristic, complemented
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—42no—
249C2×C22⋊C4—42no—
250C2×C22⋊C4C2×C4×C1312yes—
251C2×C22⋊C4D4×C1312yes—
252C22⋊C8—22no—
253C22⋊C8—22no—
254#95—22no—
255#95—22no—
256#95C2×C4×C1312yescomplemented
257#95D4×C1314yescomplemented
258C2×C13—21no—
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—44no—
265C2×C13—161no—
266C2×C13#187411yescharacteristic
267C2×C13#191111yescharacteristic
268C2×C13#191311yescharacteristic
269C24—21no—
270C24—21no—
271C24—21no—
272C24—21no—
273C24—21no—
274C24—81no—
275C24—81no—
276C24C13×C22⋊C412yes—
277C24C13×D812yes—
278C24C13×SD1612yes—
279C24C2×D4×C1311yescharacteristic
280C2×D4—22no—
281C2×D4—44no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—82no—
289C2×D4—82no—
290C2×D4—81no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—24no—
296C22×C4—44no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4—82no—
300C22×C4—82no—
301C22×C4C13×C22⋊C412yes—
302C22×C4C22×C4×C1311yescharacteristic
303C22×C4C2×D4×C1312yes—
304C22×C4C2×D4×C1311yescharacteristic
305C22×C4C13×#4112yes—
306C2×C8—42no—
307C2×C8—82no—
308C4⋊C4—22no—
309C4⋊C4—82no—
310C4⋊C4—81no—
311C4⋊C4—82no—
312C22⋊C4—24no—
313C22⋊C4—24no—
314C22⋊C4—44no—
315C22⋊C4—44no—
316C22⋊C4—42no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—82no—
322C13#920311yescharacteristic, direct product factor, Sylow
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—41no—
330C23—41no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—81no—
341C23—81no—
342C23—82no—
343C23—82no—
344C23—82no—
345C23—82no—
346C23C13×#10214yes—
347C23C2×C13×C22⋊C411yescharacteristic
348C23C13×#12011yescharacteristic
349C23C13×#12311yescharacteristic
350C23C2×C13×D811yescharacteristic
351C23C2×C13×SD1611yescharacteristic
352C23C13×AGL(1,ℤ/8)11yescharacteristic
353C23C13×#13711yescharacteristic
354D4—82no—
355D4—88no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—44no—
376C2×C4—81no—
377C2×C4—88no—
378C2×C4C4×D4×C1312yes—
379C2×C4C13×#12112yes—
380C8—82no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—24no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—44no—
393C22—44no—
394C22—44no—
395C22—42no—
396C22—42no—
397C22—82no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C13×#38611yescharacteristic
406C22C2×C13×#10211yescharacteristic
407C22C13×#41711yescharacteristic
408C22C13×#44711yescharacteristic
409C22C13×#44811yescharacteristic
410C22C13×#48011yescharacteristic
411C22C13×#48111yescharacteristic
412C4—22no—
413C4—22no—
414C4—42no—
415C4—84no—
416C4—82no—
417C4—81no—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2—44no—
425C2—161no—
426C2C13×#187411yescharacteristic
427C2C13×#191111yescharacteristic
428C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2617C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2315C2semidirect
3. C13×#1519C2semidirect
4. C2×C13×#323C2semidirect
5. C13×#1289C2semidirect
11. C13×#397C4semidirect
13. C13×#392C4semidirect
24. C22×D4×C13C2×C4semidirect
36. C2×C13×C4⋊C4C2×C4semidirect
53. C13×#95C2×C4semidirect
54. C13×#95D4semidirect
55. #9203C13direct (N × H)
110. #2315C2×C13semidirect
111. #1519C2×C13semidirect
112. C2×#323C2×C13semidirect
113. #1289C2×C13semidirect
177. #397C4×C13semidirect
179. #392C4×C13semidirect
227. C22×D4C2×C4×C13semidirect
239. C2×C4⋊C4C2×C4×C13semidirect
256. #95C2×C4×C13semidirect
257. #95D4×C13semidirect
322. C13#9203direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26172
C13×#23152
C13×#15192
C2×C13×#3232
C13×#12892
#920313