Finite Group Databasebeta

← C13×#9813 #15696152

Subgroups — C13×#9813 #15696152

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#465C211yesmaximal, characteristic
2C13×#1810C211yesmaximal, characteristic, complemented
3C8×C13×C22⋊C4C211yesmaximal, characteristic, complemented
4C13×#1508C211yesmaximal, characteristic, complemented
5C13×#1507C211yesmaximal, characteristic
6C13×#1472C211yesmaximal, characteristic, complemented
7C13×#1471C211yesmaximal, characteristic
8C22×C13×SD16C411yescharacteristic, complemented
9C23×C8×C13C2211yescharacteristic
10C2×C13×C22⋊Q8C2211yescharacteristic
11C2×C13×#121C2211yescharacteristic
12C13×#465—21no—
13C13×#465—21no—
14C13×#465—21no—
15C13×#465—21no—
16C2×C13×#108—21no—
17C2×C13×#106C411yescharacteristic, complemented
18C2×C13×#103C411yescharacteristic, complemented
19C2×C13×#102C411yescharacteristic, complemented
20C13×#407C2211yescharacteristic
21C13×#407C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C4×C8×C13—21no—
24C4×C13×C22⋊C4C2211yescharacteristic
25C13×#341—21no—
26C13×#336—21no—
27C13×#328—22no—
28C13×#327—22no—
29C13×#324—22no—
30C13×#323—22no—
31C22×Q8×C13C2×C411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13C2×C411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C2×C13×SD16—21no—
36C2×C13×SD16—21no—
37C2×C13×SD16—42no—
38C2×C13×M16—21no—
39C2×C13×M16—21no—
40C22×C8×C13—21no—
41C22×C8×C13—42no—
42C22×C8×C13C2×C411yescharacteristic
43C22×C8×C13C2×C411yescharacteristic
44C22×C8×C13D411yescharacteristic
45C22×C8×C13D411yescharacteristic
46C22×C8×C13D411yescharacteristic
47C22×C8×C13D411yescharacteristic
48C13×C22⋊Q8—21no—
49C13×C22⋊Q8—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8—21no—
52C13×#121—21no—
53C13×#121—21no—
54C13×#121—21no—
55C13×#121—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C42×C13—21no—
63C13×#108—42no—
64C13×#106—21no—
65C13×#106—21no—
66C13×#103—21no—
67C13×#103—21no—
68C13×#102—21no—
69C13×#102—21no—
70C13×C22⋊C8—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8D412yes—
76C4×C8×C13—42no—
77C13×#95D412yes—
78#9813C1311yesmaximal, characteristic, direct product factor, Sylow
79C24×C13—21no—
80C24×C13#4111yescharacteristic
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×D4×C13—21no—
86C2×D4×C13—21no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—82no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C13×SD16—42no—
105C13×SD16—42no—
106C13×M16—41no—
107C13×M16—41no—
108C13×M16—41no—
109C13×M16—41no—
110C2×C8×C13—22no—
111C2×C8×C13—22no—
112C2×C8×C13—22no—
113C2×C8×C13—22no—
114C2×C8×C13—41no—
115C2×C8×C13—41no—
116C2×C8×C13—41no—
117C2×C8×C13—41no—
118C2×C8×C13—41no—
119C2×C8×C13—41no—
120C2×C8×C13—41no—
121C2×C8×C13C22⋊C411yescharacteristic
122C2×C8×C13C22⋊C411yescharacteristic
123C2×C8×C13C22⋊C411yescharacteristic
124C2×C8×C13C22⋊C411yescharacteristic
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—41no—
130C13×C4⋊C4—41no—
131C13×C22⋊C4—24no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C42×C13—41no—
137C42×C13—41no—
138C2×#465C2×C1311yescharacteristic
139#1810C2×C1311yescharacteristic, complemented
140C8×C22⋊C4C2×C1311yescharacteristic, complemented
141#1508C2×C1311yescharacteristic, complemented
142#1507C2×C1311yescharacteristic
143#1472C2×C1311yescharacteristic, complemented
144#1471C2×C1311yescharacteristic
145C23×C13—22no—
146C23×C13—22no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—42no—
150C23×C13—81no—
151C23×C13—81no—
152C23×C13C4×D411yescharacteristic
153C23×C13#12111yescharacteristic
154C23×C13#12411yescharacteristic
155Q8×C13—41no—
156Q8×C13—41no—
157Q8×C13—81no—
158D4×C13—41no—
159D4×C13—41no—
160D4×C13—81no—
161D4×C13—82no—
162D4×C13—82no—
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—24no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—42no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13C2×C22⋊C411yescharacteristic
182C2×C4×C13C4×D411yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C2×C4×C13#12711yescharacteristic
185C8×C13—21no—
186C8×C13—21no—
187C8×C13—21no—
188C8×C13—42no—
189C8×C13—81no—
190C8×C13—81no—
191C8×C13#9912yes—
192C22×SD16C4×C1311yescharacteristic, complemented
193C23×C8C22×C1311yescharacteristic
194C2×C22⋊Q8C22×C1311yescharacteristic
195C2×#121C22×C1311yescharacteristic
196#465—21no—
197#465—21no—
198#465—21no—
199#465—21no—
200C2×#108—21no—
201C2×#106C4×C1311yescharacteristic, complemented
202C2×#103C4×C1311yescharacteristic, complemented
203C2×#102C4×C1311yescharacteristic, complemented
204#407C22×C1311yescharacteristic
205#407C22×C1311yescharacteristic
206C2×C22⋊C8C22×C1311yescharacteristic
207C2×C4×C8—21no—
208C4×C22⋊C4C22×C1311yescharacteristic
209#341—21no—
210#336—21no—
211#328—22no—
212#327—22no—
213#324—22no—
214#323—22no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—44no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—162no—
227C22×C13#39011yescharacteristic
228C22×C13#44312yes—
229C22×C13#47112yes—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—21no—
233C4×C13—44no—
234C4×C13—81no—
235C4×C13—81no—
236C4×C13—81no—
237C4×C13C2×#9911yescharacteristic
238C4×C13#41011yescharacteristic
239C22×Q8C2×C4×C1311yescharacteristic
240C22×D4—21no—
241C22×D4C2×C4×C1311yescharacteristic
242C23×C4C23×C1311yescharacteristic
243C2×SD16—21no—
244C2×SD16—21no—
245C2×SD16—42no—
246C2×M16—21no—
247C2×M16—21no—
248C22×C8—21no—
249C22×C8—42no—
250C22×C8C2×C4×C1311yescharacteristic
251C22×C8C2×C4×C1311yescharacteristic
252C22×C8D4×C1311yescharacteristic
253C22×C8D4×C1311yescharacteristic
254C22×C8D4×C1311yescharacteristic
255C22×C8D4×C1311yescharacteristic
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263#121—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×C4×C1311yescharacteristic
266C2×C4⋊C4C2×C4×C1311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42—21no—
271#108—42no—
272#106—21no—
273#106—21no—
274#103—21no—
275#103—21no—
276#102—21no—
277#102—21no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8D4×C1312yes—
284C4×C8—42no—
285#95D4×C1312yes—
286C2×C13—22no—
287C2×C13—22no—
288C2×C13—41no—
289C2×C13—161no—
290C2×C13#196411yescharacteristic
291C2×C13#197411yescharacteristic
292C2×C13#197711yescharacteristic
293C24—21no—
294C24C13×#4111yescharacteristic
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—82no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4C22×C4×C1311yescharacteristic
313C22×C4C2×D4×C1311yescharacteristic
314C22×C4C2×D4×C1311yescharacteristic
315C22×C4C2×D4×C1311yescharacteristic
316C22×C4C2×D4×C1311yescharacteristic
317C22×C4C13×#4111yescharacteristic
318SD16—42no—
319SD16—42no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8C13×C22⋊C411yescharacteristic
336C2×C8C13×C22⋊C411yescharacteristic
337C2×C8C13×C22⋊C411yescharacteristic
338C2×C8C13×C22⋊C411yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C22⋊C4—24no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C42—41no—
351C42—41no—
352C13#981311yescharacteristic, direct product factor, Sylow
353C23—22no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23C4×D4×C1311yescharacteristic
361C23C13×#12111yescharacteristic
362C23C13×#12411yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—81no—
366D4—41no—
367D4—41no—
368D4—81no—
369D4—82no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4C2×C13×C22⋊C411yescharacteristic
390C2×C4C4×D4×C1311yescharacteristic
391C2×C4C13×#12111yescharacteristic
392C2×C4C13×#12711yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—42no—
397C8—81no—
398C8—81no—
399C8C13×#9912yes—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—44no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—162no—
412C22C13×#39011yescharacteristic
413C22C13×#44312yes—
414C22C13×#47112yes—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—44no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4C2×C13×#9911yescharacteristic
423C4C13×#41011yescharacteristic
424C2—22no—
425C2—22no—
426C2—41no—
427C2—161no—
428C2C13×#196411yescharacteristic
429C2C13×#197411yescharacteristic
430C2C13×#197711yescharacteristic
subgroupG/H
center, socleC22×C13#390
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
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×#1810C2semidirect
3. C8×C13×C22⋊C4C2semidirect
4. C13×#1508C2semidirect
6. C13×#1472C2semidirect
8. C22×C13×SD16C4semidirect
17. C2×C13×#106C4semidirect
18. C2×C13×#103C4semidirect
19. C2×C13×#102C4semidirect
78. #9813C13direct (N × H)
139. #1810C2×C13semidirect
140. C8×C22⋊C4C2×C13semidirect
141. #1508C2×C13semidirect
143. #1472C2×C13semidirect
192. C22×SD16C4×C13semidirect
201. C2×#106C4×C13semidirect
202. C2×#103C4×C13semidirect
203. C2×#102C4×C13semidirect
352. C13#9813direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4652
C13×#18102
C8×C13×C22⋊C42
C13×#15082
C13×#15072
C13×#14722
C13×#14712
#981313