Finite Group Databasebeta

← C13×#33883 #15720222

Subgroups — C13×#33883 #15720222

Order 3328.

548 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3338C211yesmaximal, characteristic, complemented
2C13×#3285C211yesmaximal, characteristic
3C13×#2243C211yesmaximal, characteristic, complemented
4C13×#2235C211yesmaximal, characteristic, complemented
5C13×#2233C211yesmaximal, characteristic, complemented
6C13×#2225C211yesmaximal, characteristic, complemented
7C13×#2219C211yesmaximal, characteristic, complemented
8C13×#2217C211yesmaximal, characteristic, complemented
9C13×#2211C211yesmaximal, characteristic, complemented
10C13×#2189C211yesmaximal, characteristic, complemented
11C13×#2188C211yesmaximal, characteristic, complemented
12C13×#2176C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2139C211yesmaximal, characteristic, complemented
15C2×C13×#358C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C22×C13×Q16C2211yescharacteristic
18C13×#554—21no—
19C13×#548—21no—
20C2×C13×Q32C2211yescharacteristic
21C2×C13×Q32C2211yescharacteristic
22C2×C13×SD32C2211yescharacteristic
23C2×C13×M32C2211yescharacteristic
24C22×C13×C16C2211yescharacteristic
25C13×#500C2211yescharacteristic
26C13×#495C2211yescharacteristic
27C13×#484—21no—
28C13×#484—21no—
29C13×#477—21no—
30C13×#467C2211yescharacteristic
31C13×#467C2211yescharacteristic
32C13×#467C2211yescharacteristic
33C13×#466C2211yescharacteristic
34C13×#464—21no—
35C13×#452—21no—
36C13×#448—21no—
37C4×C13×Q16C2211yescharacteristic
38C4×C13×Q16C2211yescharacteristic
39C8×D4×C13C2211yescharacteristic
40C2×C13×#107C2211yescharacteristic
41C2×C13×#107C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#367C2211yescharacteristic
44C13×#367C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×#358C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic
58C13×#346C2211yescharacteristic
59C2×C13×#41—21no—
60C22×Q8×C13—21no—
61C13×#135—22no—
62C13×#135—41no—
63C2×C13×Q16—22no—
64C2×C13×Q16—21no—
65C2×C13×Q16—41no—
66C2×C13×Q16C2311yescharacteristic
67C2×C13×Q16C2311yescharacteristic
68C2×C13×Q16C2311yescharacteristic
69C2×C13×SD16—21no—
70C2×C13×SD16—21no—
71C2×C13×D8C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C13×C4⋊Q8—21no—
75C13×#125—41no—
76C13×#124—21no—
77C13×#124—41no—
78C13×C22⋊Q8—21no—
79C13×C22⋊Q8—21no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—41no—
82C13×C22⋊Q8—41no—
83C13×C22⋊Q8—41no—
84C13×#121—21no—
85C13×#121—41no—
86C4×Q8×C13—21no—
87C4×Q8×C13—21no—
88C4×D4×C13—41no—
89C4×D4×C13—41no—
90C4×D4×C13D411yescharacteristic
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—21no—
93C13×Q32—22no—
94C13×Q32—41no—
95C13×SD32—41no—
96C13×M32—41no—
97C2×C13×C16—41no—
98C2×C13×C16C2311yescharacteristic
99C2×C13×C16C2311yescharacteristic
100C2×C13×C16C2311yescharacteristic
101C2×C13×C16C2311yescharacteristic
102C13×#107—21no—
103C13×#107—21no—
104C13×#107—21no—
105C13×#107C2311yescharacteristic
106C13×#107C2311yescharacteristic
107C13×#107C2311yescharacteristic
108C13×#107C2311yescharacteristic
109C13×C4⋊C8D411yescharacteristic
110C13×#103—21no—
111C13×#103—21no—
112C13×#103—21no—
113C13×#103—21no—
114C13×#103—21no—
115C13×#102—21no—
116C13×C22⋊C8D411yescharacteristic
117C13×C22⋊C8D411yescharacteristic
118C4×C8×C13C2311yescharacteristic
119#33883C1311yesmaximal, characteristic, direct product factor, Sylow
120C13×#41—42no—
121C13×#41—81no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—42no—
126C2×Q8×C13—41no—
127C2×Q8×C13—41no—
128C2×Q8×C13—81no—
129C2×D4×C13—21no—
130C2×D4×C13—41no—
131C2×D4×C13—41no—
132C2×D4×C13D811yescharacteristic
133C22×C4×C13—41no—
134C22×C4×C13—41no—
135C22×C4×C13—41no—
136C22×C4×C13—41no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C13×Q16—21no—
140C13×Q16—21no—
141C13×Q16—21no—
142C13×Q16—21no—
143C13×Q16—21no—
144C13×Q16—42no—
145C13×Q16#4112yes—
146C13×SD16—42no—
147C13×SD16—81no—
148C13×D8—21no—
149C13×D8—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13C2×D411yescharacteristic
155C2×C8×C13C2×D411yescharacteristic
156C2×C8×C13C2×D411yescharacteristic
157C2×C8×C13C2411yescharacteristic
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—41no—
163C13×C4⋊C4—41no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—41no—
166C13×C4⋊C4—41no—
167C13×C4⋊C4—41no—
168C13×C4⋊C4—41no—
169C13×C4⋊C4—41no—
170C13×C4⋊C4D811yescharacteristic
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—41no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4D811yescharacteristic
178C13×C22⋊C4D811yescharacteristic
179C42×C13—41no—
180C42×C13—41no—
181C42×C13C2×D411yescharacteristic
182C13×C16—21no—
183C13×C16—21no—
184C13×C16—21no—
185C13×C16—21no—
186#3338C2×C1311yescharacteristic, complemented
187#3285C2×C1311yescharacteristic
188#2243C2×C1311yescharacteristic, complemented
189#2235C2×C1311yescharacteristic, complemented
190#2233C2×C1311yescharacteristic, complemented
191#2225C2×C1311yescharacteristic, complemented
192#2219C2×C1311yescharacteristic, complemented
193#2217C2×C1311yescharacteristic, complemented
194#2211C2×C1311yescharacteristic, complemented
195#2189C2×C1311yescharacteristic, complemented
196#2188C2×C1311yescharacteristic, complemented
197#2176C2×C1311yescharacteristic, complemented
198#2168C2×C1311yescharacteristic, complemented
199#2139C2×C1311yescharacteristic, complemented
200C2×#358C2×C1311yescharacteristic, complemented
201C23×C13—41no—
202C23×C13C2×D811yescharacteristic
203C23×C13C2×D811yescharacteristic
204Q8×C13—22no—
205Q8×C13—41no—
206Q8×C13—41no—
207Q8×C13—41no—
208Q8×C13—41no—
209Q8×C13—41no—
210Q8×C13—82no—
211Q8×C13—161no—
212D4×C13—22no—
213D4×C13—41no—
214D4×C13—41no—
215D4×C13—82no—
216D4×C13—82no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—82no—
229C2×C4×C13—82no—
230C2×C4×C13—161no—
231C2×C4×C13—161no—
232C2×C4×C13C2×D811yescharacteristic
233C2×C4×C13C2×D811yescharacteristic
234C2×C4×C13C2×D811yescharacteristic
235C2×C4×C13C2×D811yescharacteristic
236C2×C4×C13C22×D411yescharacteristic
237C8×C13—21no—
238C8×C13—21no—
239C8×C13—21no—
240C8×C13C2×#4111yescharacteristic
241C8×C13H(5,𝔽2)11yescharacteristic
242C2×#135C22×C1311yescharacteristic
243C22×Q16C22×C1311yescharacteristic
244#554—21no—
245#548—21no—
246C2×Q32C22×C1311yescharacteristic
247C2×Q32C22×C1311yescharacteristic
248C2×SD32C22×C1311yescharacteristic
249C2×M32C22×C1311yescharacteristic
250C22×C16C22×C1311yescharacteristic
251#500C22×C1311yescharacteristic
252#495C22×C1311yescharacteristic
253#484—21no—
254#484—21no—
255#477—21no—
256#467C22×C1311yescharacteristic
257#467C22×C1311yescharacteristic
258#467C22×C1311yescharacteristic
259#466C22×C1311yescharacteristic
260#464—21no—
261#452—21no—
262#448—21no—
263C4×Q16C22×C1311yescharacteristic
264C4×Q16C22×C1311yescharacteristic
265C8×D4C22×C1311yescharacteristic
266C2×#107C22×C1311yescharacteristic
267C2×#107C22×C1311yescharacteristic
268#367C22×C1311yescharacteristic
269#367C22×C1311yescharacteristic
270#367C22×C1311yescharacteristic
271C4⋊C16C22×C1311yescharacteristic
272#358C22×C1311yescharacteristic
273#358C22×C1311yescharacteristic
274#358C22×C1311yescharacteristic
275#358C22×C1311yescharacteristic
276#358C22×C1311yescharacteristic
277#358C22×C1311yescharacteristic
278#358C22×C1311yescharacteristic
279#357C22×C1311yescharacteristic
280#357C22×C1311yescharacteristic
281#357C22×C1311yescharacteristic
282C22⋊C16C22×C1311yescharacteristic
283C22⋊C16C22×C1311yescharacteristic
284#346C22×C1311yescharacteristic
285C22×C13—21no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—81no—
291C22×C13—81no—
292C22×C13—81no—
293C22×C13#51012yes—
294C22×C13C22×D811yescharacteristic
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—42no—
300C4×C13—81no—
301C4×C13—81no—
302C4×C13—81no—
303C4×C13—81no—
304C4×C13—81no—
305C4×C13—81no—
306C4×C13#54611yescharacteristic
307C4×C13#57711yescharacteristic
308C2×#41—21no—
309C22×Q8—21no—
310#135—22no—
311#135—41no—
312C2×Q16—22no—
313C2×Q16—21no—
314C2×Q16—41no—
315C2×Q16C23×C1311yescharacteristic
316C2×Q16C23×C1311yescharacteristic
317C2×Q16C23×C1311yescharacteristic
318C2×SD16—21no—
319C2×SD16—21no—
320C2×D8C23×C1311yescharacteristic
321C22×C8C23×C1311yescharacteristic
322C22×C8C23×C1311yescharacteristic
323C4⋊Q8—21no—
324#125—41no—
325#124—21no—
326#124—41no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—41no—
331C22⋊Q8—41no—
332C22⋊Q8—41no—
333#121—21no—
334#121—41no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×D4—41no—
338C4×D4—41no—
339C4×D4D4×C1311yescharacteristic
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342Q32—22no—
343Q32—41no—
344SD32—41no—
345M32—41no—
346C2×C16—41no—
347C2×C16C23×C1311yescharacteristic
348C2×C16C23×C1311yescharacteristic
349C2×C16C23×C1311yescharacteristic
350C2×C16C23×C1311yescharacteristic
351#107—21no—
352#107—21no—
353#107—21no—
354#107C23×C1311yescharacteristic
355#107C23×C1311yescharacteristic
356#107C23×C1311yescharacteristic
357#107C23×C1311yescharacteristic
358C4⋊C8D4×C1311yescharacteristic
359#103—21no—
360#103—21no—
361#103—21no—
362#103—21no—
363#103—21no—
364#102—21no—
365C22⋊C8D4×C1311yescharacteristic
366C22⋊C8D4×C1311yescharacteristic
367C4×C8C23×C1311yescharacteristic
368C2×C13—22no—
369C2×C13—41no—
370C2×C13—161no—
371C2×C13#329411yescharacteristic
372C2×C13C2×#51011yescharacteristic
373C2×C13#341611yescharacteristic
374#41—42no—
375#41—81no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—42no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—81no—
383C2×D4—21no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4C13×D811yescharacteristic
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4C2×D4×C1311yescharacteristic
392C22×C4C2×D4×C1311yescharacteristic
393Q16—21no—
394Q16—21no—
395Q16—21no—
396Q16—21no—
397Q16—21no—
398Q16—42no—
399Q16C13×#4112yes—
400SD16—42no—
401SD16—81no—
402D8—21no—
403D8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8C2×D4×C1311yescharacteristic
409C2×C8C2×D4×C1311yescharacteristic
410C2×C8C2×D4×C1311yescharacteristic
411C2×C8C24×C1311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4C13×D811yescharacteristic
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4C13×D811yescharacteristic
432C22⋊C4C13×D811yescharacteristic
433C42—41no—
434C42—41no—
435C42C2×D4×C1311yescharacteristic
436C16—21no—
437C16—21no—
438C16—21no—
439C16—21no—
440C13#3388311yescharacteristic, direct product factor, Sylow
441C23—41no—
442C23C2×C13×D811yescharacteristic
443C23C2×C13×D811yescharacteristic
444Q8—22no—
445Q8—41no—
446Q8—41no—
447Q8—41no—
448Q8—41no—
449Q8—41no—
450Q8—82no—
451Q8—161no—
452D4—22no—
453D4—41no—
454D4—41no—
455D4—82no—
456D4—82no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—161no—
471C2×C4—161no—
472C2×C4C2×C13×D811yescharacteristic
473C2×C4C2×C13×D811yescharacteristic
474C2×C4C2×C13×D811yescharacteristic
475C2×C4C2×C13×D811yescharacteristic
476C2×C4C22×D4×C1311yescharacteristic
477C8—21no—
478C8—21no—
479C8—21no—
480C8C2×C13×#4111yescharacteristic
481C8C13×H(5,𝔽2)11yescharacteristic
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22C13×#51012yes—
491C22C22×C13×D811yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—81no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4C13×#54611yescharacteristic
504C4C13×#57711yescharacteristic
505C2—22no—
506C2—41no—
507C2—161no—
508C2C13×#329411yescharacteristic
509C2C2×C13×#51011yescharacteristic
510C2C13×#341611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#3285C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3338C2semidirect
3. C13×#2243C2semidirect
4. C13×#2235C2semidirect
5. C13×#2233C2semidirect
6. C13×#2225C2semidirect
7. C13×#2219C2semidirect
8. C13×#2217C2semidirect
9. C13×#2211C2semidirect
10. C13×#2189C2semidirect
11. C13×#2188C2semidirect
12. C13×#2176C2semidirect
13. C13×#2168C2semidirect
14. C13×#2139C2semidirect
15. C2×C13×#358C2semidirect
119. #33883C13direct (N × H)
186. #3338C2×C13semidirect
188. #2243C2×C13semidirect
189. #2235C2×C13semidirect
190. #2233C2×C13semidirect
191. #2225C2×C13semidirect
192. #2219C2×C13semidirect
193. #2217C2×C13semidirect
194. #2211C2×C13semidirect
195. #2189C2×C13semidirect
196. #2188C2×C13semidirect
197. #2176C2×C13semidirect
198. #2168C2×C13semidirect
199. #2139C2×C13semidirect
200. C2×#358C2×C13semidirect
440. C13#33883direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33382
C13×#32852
C13×#22432
C13×#22352
C13×#22332
C13×#22252
C13×#22192
C13×#22172
C13×#22112
C13×#21892
C13×#21882
C13×#21762
C13×#21682
C13×#21392
C2×C13×#3582
#3388313