Finite Group Databasebeta

← C13×#33809 #15720148

Subgroups — C13×#33809 #15720148

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3175C211yesmaximal, characteristic
2C13×#3164C211yesmaximal, characteristic, complemented
3C13×#2255C211yesmaximal, characteristic, complemented
4C13×#2252C211yesmaximal, characteristic, complemented
5C13×#2243C211yesmaximal, characteristic, complemented
6C13×#2242C211yesmaximal, characteristic, complemented
7C13×#2237C211yesmaximal, characteristic, complemented
8C13×#2236C211yesmaximal, characteristic, complemented
9C13×#2234C211yesmaximal, characteristic
10C13×#2232C211yesmaximal, characteristic
11C13×#2229C211yesmaximal, characteristic, complemented
12C13×#2228C211yesmaximal, characteristic, complemented
13C13×#2227C211yesmaximal, characteristic, complemented
14C13×#2224C211yesmaximal, characteristic, complemented
15C13×#2164C211yesmaximal, characteristic, complemented
16C13×#544—21no—
17C13×#542—21no—
18C13×#501—21no—
19C13×#501—21no—
20C13×#500C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#500C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#499C2211yescharacteristic
25C13×#495C2211yescharacteristic
26C13×#489—21no—
27C13×#468—21no—
28C13×#467C2211yescharacteristic
29C13×#466C2211yescharacteristic
30C13×#440—21no—
31C4×C13×Q16C2211yescharacteristic
32C4×C13×D8C2211yescharacteristic
33C13×#428—21no—
34C13×#427C2211yescharacteristic
35C2×C13×#107C2211yescharacteristic
36C13×#405C2211yescharacteristic
37C13×#367C2211yescharacteristic
38C13×#367C2211yescharacteristic
39C13×#366C2211yescharacteristic
40C13×#366C2211yescharacteristic
41C13×#366C2211yescharacteristic
42C13×#366C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×C4⋊C16C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×C22⋊C16C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C4×C13×C16C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×SD16—21no—
61C2×C13×D8C2311yescharacteristic
62C2×C13×M16D411yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—21no—
67C13×C4⋊Q8—41no—
68C13×#126—41no—
69C13×#125—21no—
70C13×#125—21no—
71C13×#125—41no—
72C13×#124—21no—
73C13×#124—41no—
74C13×#123—41no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8—41no—
77C13×C22⋊Q8—41no—
78C13×C22⋊Q8—41no—
79C13×#121—21no—
80C4×Q8×C13—21no—
81C4×D4×C13—21no—
82C13×#117—21no—
83C13×#117D411yescharacteristic
84C2×C13×C4⋊C4—21no—
85C2×C13×C16C2311yescharacteristic
86C2×C13×C16C2311yescharacteristic
87C2×C13×C16C2311yescharacteristic
88C2×C13×C16C2311yescharacteristic
89C13×#107—21no—
90C13×#107—21no—
91C13×#107—21no—
92C13×#107—21no—
93C13×#107C2311yescharacteristic
94C13×#107C2311yescharacteristic
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×#106—21no—
100C13×#106—21no—
101C13×#106—21no—
102C13×#103—21no—
103C13×#103—21no—
104C13×#102—21no—
105C13×#102—21no—
106C13×#97D411yescharacteristic
107C13×#97D411yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#33809C1311yesmaximal, characteristic, direct product factor, Sylow
111C2×Q8×C13—21no—
112C2×Q8×C13—41no—
113C2×Q8×C13—41no—
114C2×Q8×C13—41no—
115C2×D4×C13—21no—
116C2×D4×C13—41no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13C2×D411yescharacteristic
120C13×Q16—21no—
121C13×Q16—21no—
122C13×SD16—42no—
123C13×D8—21no—
124C13×D8—21no—
125C13×M16—22no—
126C2×C8×C13—21no—
127C2×C8×C13—21no—
128C2×C8×C13C2×D411yescharacteristic
129C2×C8×C13C2×D411yescharacteristic
130C2×C8×C13C2×D411yescharacteristic
131C2×C8×C13C2411yescharacteristic
132C13×C4⋊C4—21no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4—41no—
140C13×C4⋊C4—41no—
141C13×C4⋊C4—41no—
142C13×C4⋊C4—41no—
143C13×C4⋊C4—41no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C4⋊C4—41no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4D811yescharacteristic
149C13×C4⋊C4D811yescharacteristic
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4D811yescharacteristic
157C13×C22⋊C4D811yescharacteristic
158C42×C13—41no—
159C42×C13—41no—
160C42×C13C2×D411yescharacteristic
161C42×C13C2×D411yescharacteristic
162C13×C16—21no—
163C13×C16—21no—
164C13×C16—21no—
165C13×C16—21no—
166#3175C2×C1311yescharacteristic
167#3164C2×C1311yescharacteristic, complemented
168#2255C2×C1311yescharacteristic, complemented
169#2252C2×C1311yescharacteristic, complemented
170#2243C2×C1311yescharacteristic, complemented
171#2242C2×C1311yescharacteristic, complemented
172#2237C2×C1311yescharacteristic, complemented
173#2236C2×C1311yescharacteristic, complemented
174#2234C2×C1311yescharacteristic
175#2232C2×C1311yescharacteristic
176#2229C2×C1311yescharacteristic, complemented
177#2228C2×C1311yescharacteristic, complemented
178#2227C2×C1311yescharacteristic, complemented
179#2224C2×C1311yescharacteristic, complemented
180#2164C2×C1311yescharacteristic, complemented
181C23×C13—41no—
182C23×C13C2×D811yescharacteristic
183Q8×C13—41no—
184Q8×C13—41no—
185Q8×C13—161no—
186Q8×C13—161no—
187Q8×C13—161no—
188D4×C13—41no—
189D4×C13—41no—
190D4×C13—161no—
191C2×C4×C13—21no—
192C2×C4×C13—21no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—161no—
201C2×C4×C13—161no—
202C2×C4×C13C2×D811yescharacteristic
203C2×C4×C13C2×D811yescharacteristic
204C2×C4×C13C2×D811yescharacteristic
205C2×C4×C13C2×D811yescharacteristic
206C2×C4×C13C2×D811yescharacteristic
207C2×C4×C13C22×D411yescharacteristic
208C8×C13—21no—
209C8×C13—21no—
210C8×C13#13712yes—
211C8×C132−1+411yescharacteristic
212C8×C132−1+411yescharacteristic
213#544—21no—
214#542—21no—
215#501—21no—
216#501—21no—
217#500C22×C1311yescharacteristic
218#500C22×C1311yescharacteristic
219#500C22×C1311yescharacteristic
220#499C22×C1311yescharacteristic
221#499C22×C1311yescharacteristic
222#495C22×C1311yescharacteristic
223#489—21no—
224#468—21no—
225#467C22×C1311yescharacteristic
226#466C22×C1311yescharacteristic
227#440—21no—
228C4×Q16C22×C1311yescharacteristic
229C4×D8C22×C1311yescharacteristic
230#428—21no—
231#427C22×C1311yescharacteristic
232C2×#107C22×C1311yescharacteristic
233#405C22×C1311yescharacteristic
234#367C22×C1311yescharacteristic
235#367C22×C1311yescharacteristic
236#366C22×C1311yescharacteristic
237#366C22×C1311yescharacteristic
238#366C22×C1311yescharacteristic
239#366C22×C1311yescharacteristic
240#366C22×C1311yescharacteristic
241#366C22×C1311yescharacteristic
242C4⋊C16C22×C1311yescharacteristic
243C4⋊C16C22×C1311yescharacteristic
244#358C22×C1311yescharacteristic
245#358C22×C1311yescharacteristic
246#358C22×C1311yescharacteristic
247#358C22×C1311yescharacteristic
248#357C22×C1311yescharacteristic
249#357C22×C1311yescharacteristic
250#357C22×C1311yescharacteristic
251#357C22×C1311yescharacteristic
252C22⋊C16C22×C1311yescharacteristic
253C22⋊C16C22×C1311yescharacteristic
254#346C22×C1311yescharacteristic
255C4×C16C22×C1311yescharacteristic
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—81no—
260C22×C13—81no—
261C22×C13—81no—
262C22×C13C22×D811yescharacteristic
263C4×C13—21no—
264C4×C13—21no—
265C4×C13—21no—
266C4×C13—21no—
267C4×C13—21no—
268C4×C13—81no—
269C4×C13—81no—
270C4×C13—81no—
271C4×C13—81no—
272C4×C13—81no—
273C4×C13—81no—
274C4×C13—81no—
275C4×C13#53611yescharacteristic
276C4×C13C2×#13711yescharacteristic
277C2×Q16C23×C1311yescharacteristic
278C2×SD16—21no—
279C2×D8C23×C1311yescharacteristic
280C2×M16D4×C1311yescharacteristic
281C22×C8C23×C1311yescharacteristic
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—41no—
286#126—41no—
287#125—21no—
288#125—21no—
289#125—41no—
290#124—21no—
291#124—41no—
292#123—41no—
293C22⋊Q8—21no—
294C22⋊Q8—41no—
295C22⋊Q8—41no—
296C22⋊Q8—41no—
297#121—21no—
298C4×Q8—21no—
299C4×D4—21no—
300#117—21no—
301#117D4×C1311yescharacteristic
302C2×C4⋊C4—21no—
303C2×C16C23×C1311yescharacteristic
304C2×C16C23×C1311yescharacteristic
305C2×C16C23×C1311yescharacteristic
306C2×C16C23×C1311yescharacteristic
307#107—21no—
308#107—21no—
309#107—21no—
310#107—21no—
311#107C23×C1311yescharacteristic
312#107C23×C1311yescharacteristic
313#107C23×C1311yescharacteristic
314#107C23×C1311yescharacteristic
315#107C23×C1311yescharacteristic
316#107C23×C1311yescharacteristic
317#106—21no—
318#106—21no—
319#106—21no—
320#103—21no—
321#103—21no—
322#102—21no—
323#102—21no—
324#97D4×C1311yescharacteristic
325#97D4×C1311yescharacteristic
326C4×C8C23×C1311yescharacteristic
327C4×C8C23×C1311yescharacteristic
328C2×C13—41no—
329C2×C13—161no—
330C2×C13#322611yescharacteristic
331C2×C13#341511yescharacteristic
332C2×C13#341711yescharacteristic
333C2×Q8—21no—
334C2×Q8—41no—
335C2×Q8—41no—
336C2×Q8—41no—
337C2×D4—21no—
338C2×D4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4C2×D4×C1311yescharacteristic
342Q16—21no—
343Q16—21no—
344SD16—42no—
345D8—21no—
346D8—21no—
347M16—22no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8C2×D4×C1311yescharacteristic
351C2×C8C2×D4×C1311yescharacteristic
352C2×C8C2×D4×C1311yescharacteristic
353C2×C8C24×C1311yescharacteristic
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4C13×D811yescharacteristic
371C4⋊C4C13×D811yescharacteristic
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4C13×D811yescharacteristic
379C22⋊C4C13×D811yescharacteristic
380C42—41no—
381C42—41no—
382C42C2×D4×C1311yescharacteristic
383C42C2×D4×C1311yescharacteristic
384C16—21no—
385C16—21no—
386C16—21no—
387C16—21no—
388C13#3380911yescharacteristic, direct product factor, Sylow
389C23—41no—
390C23C2×C13×D811yescharacteristic
391Q8—41no—
392Q8—41no—
393Q8—161no—
394Q8—161no—
395Q8—161no—
396D4—41no—
397D4—41no—
398D4—161no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—161no—
409C2×C4—161no—
410C2×C4C2×C13×D811yescharacteristic
411C2×C4C2×C13×D811yescharacteristic
412C2×C4C2×C13×D811yescharacteristic
413C2×C4C2×C13×D811yescharacteristic
414C2×C4C2×C13×D811yescharacteristic
415C2×C4C22×D4×C1311yescharacteristic
416C8—21no—
417C8—21no—
418C8C13×#13712yes—
419C8C13×2−1+411yescharacteristic
420C8C13×2−1+411yescharacteristic
421C22—21no—
422C22—21no—
423C22—21no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22C22×C13×D811yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4C13×#53611yescharacteristic
441C4C2×C13×#13711yescharacteristic
442C2—41no—
443C2—161no—
444C2C13×#322611yescharacteristic
445C2C13×#341511yescharacteristic
446C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3164C2semidirect
3. C13×#2255C2semidirect
4. C13×#2252C2semidirect
5. C13×#2243C2semidirect
6. C13×#2242C2semidirect
7. C13×#2237C2semidirect
8. C13×#2236C2semidirect
11. C13×#2229C2semidirect
12. C13×#2228C2semidirect
13. C13×#2227C2semidirect
14. C13×#2224C2semidirect
15. C13×#2164C2semidirect
110. #33809C13direct (N × H)
167. #3164C2×C13semidirect
168. #2255C2×C13semidirect
169. #2252C2×C13semidirect
170. #2243C2×C13semidirect
171. #2242C2×C13semidirect
172. #2237C2×C13semidirect
173. #2236C2×C13semidirect
176. #2229C2×C13semidirect
177. #2228C2×C13semidirect
178. #2227C2×C13semidirect
179. #2224C2×C13semidirect
180. #2164C2×C13semidirect
388. C13#33809direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31752
C13×#31642
C13×#22552
C13×#22522
C13×#22432
C13×#22422
C13×#22372
C13×#22362
C13×#22342
C13×#22322
C13×#22292
C13×#22282
C13×#22272
C13×#22242
C13×#21642
#3380913