Finite Group Databasebeta

← C13×#33882 #15720221

Subgroups — C13×#33882 #15720221

Order 3328.

542 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3336C211yesmaximal, characteristic, complemented
2C13×#3283C211yesmaximal, characteristic
3C13×#2245C211yesmaximal, characteristic, complemented
4C13×#2237C211yesmaximal, characteristic, complemented
5C13×#2236C211yesmaximal, characteristic, complemented
6C13×#2228C211yesmaximal, characteristic, complemented
7C13×#2219C211yesmaximal, characteristic, complemented
8C13×#2216C211yesmaximal, characteristic, complemented
9C13×#2209C211yesmaximal, characteristic, complemented
10C13×#2189C211yesmaximal, characteristic, complemented
11C13×#2189C211yesmaximal, characteristic, complemented
12C13×#2175C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2139C211yesmaximal, characteristic, complemented
15C13×#2138C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C2×C13×#135C2211yescharacteristic
18C13×#552—21no—
19C13×#547—21no—
20C2×C13×Q32C2211yescharacteristic
21C2×C13×Q32C2211yescharacteristic
22C2×C13×SD32C2211yescharacteristic
23C2×C13×M32C2211yescharacteristic
24C22×C13×C16C2211yescharacteristic
25C13×#499C2211yescharacteristic
26C13×#494C2211yescharacteristic
27C13×#485—21no—
28C13×#483—21no—
29C13×#479—21no—
30C13×#467C2211yescharacteristic
31C13×#467C2211yescharacteristic
32C13×#467C2211yescharacteristic
33C13×#467C2211yescharacteristic
34C13×#461—21no—
35C13×#452—21no—
36C13×#452—21no—
37C4×C13×Q16C2211yescharacteristic
38C4×C13×D8C2211yescharacteristic
39C8×D4×C13C2211yescharacteristic
40C13×#427C2211yescharacteristic
41C2×C13×#107C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
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—
60C2×C13×#41—21no—
61C13×#135—22no—
62C13×#135—22no—
63C13×#135—41no—
64C13×#135—41no—
65C2×C13×Q16—21no—
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×#126—41no—
76C13×#125—21no—
77C13×#125—41no—
78C13×#123—41no—
79C13×#123—41no—
80C13×#123—41no—
81C13×C22⋊Q8—21no—
82C13×C22⋊Q8—21no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—21no—
85C13×#121—41no—
86C4×Q8×C13—21no—
87C4×D4×C13—21no—
88C4×D4×C13D411yescharacteristic
89C13×#117—21no—
90C13×#117—41no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—41no—
93C13×Q32—41no—
94C13×Q32—41no—
95C13×SD32—22no—
96C13×M32—41no—
97C2×C13×C16—41no—
98C2×C13×C16C2311yescharacteristic
99C2×C13×C16C2311yescharacteristic
100C2×C13×C16C2311yescharacteristic
101C2×C13×C16C2311yescharacteristic
102C13×#107—21no—
103C13×#107C2311yescharacteristic
104C13×#107C2311yescharacteristic
105C13×#107C2311yescharacteristic
106C13×#107C2311yescharacteristic
107C13×#106—21no—
108C13×#106—21no—
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#33882C1311yesmaximal, characteristic, direct product factor, Sylow
120C13×#41—42no—
121C13×#41—42no—
122C13×#41—81no—
123C13×#41—81no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13D811yescharacteristic
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13—41no—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C13×Q16—21no—
138C13×Q16—21no—
139C13×Q16—21no—
140C13×Q16—21no—
141C13×Q16—21no—
142C13×Q16—21no—
143C13×Q16—81no—
144C13×SD16—42no—
145C13×SD16—42no—
146C13×D8—21no—
147C13×D8#4112yes—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13C2×D411yescharacteristic
153C2×C8×C13C2×D411yescharacteristic
154C2×C8×C13C2×D411yescharacteristic
155C2×C8×C13C2411yescharacteristic
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—41no—
161C13×C4⋊C4—41no—
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#3336C2×C1311yescharacteristic, complemented
187#3283C2×C1311yescharacteristic
188#2245C2×C1311yescharacteristic, complemented
189#2237C2×C1311yescharacteristic, complemented
190#2236C2×C1311yescharacteristic, complemented
191#2228C2×C1311yescharacteristic, complemented
192#2219C2×C1311yescharacteristic, complemented
193#2216C2×C1311yescharacteristic, complemented
194#2209C2×C1311yescharacteristic, complemented
195#2189C2×C1311yescharacteristic, complemented
196#2189C2×C1311yescharacteristic, complemented
197#2175C2×C1311yescharacteristic, complemented
198#2168C2×C1311yescharacteristic, complemented
199#2139C2×C1311yescharacteristic, complemented
200#2138C2×C1311yescharacteristic, complemented
201C23×C13—41no—
202C23×C13C2×D811yescharacteristic
203C23×C13C2×D811yescharacteristic
204Q8×C13—41no—
205Q8×C13—41no—
206Q8×C13—41no—
207Q8×C13—41no—
208Q8×C13—41no—
209Q8×C13—41no—
210D4×C13—22no—
211D4×C13—41no—
212D4×C13—41no—
213D4×C13—82no—
214D4×C13—82no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—82no—
227C2×C4×C13—82no—
228C2×C4×C13—82no—
229C2×C4×C13—82no—
230C2×C4×C13C2×D811yescharacteristic
231C2×C4×C13C2×D811yescharacteristic
232C2×C4×C13C2×D811yescharacteristic
233C2×C4×C13C2×D811yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C8×C13—21no—
236C8×C13—21no—
237C8×C13—21no—
238C8×C13C2×#4111yescharacteristic
239C8×C13H(5,𝔽2)11yescharacteristic
240C2×#135C22×C1311yescharacteristic
241C2×#135C22×C1311yescharacteristic
242#552—21no—
243#547—21no—
244C2×Q32C22×C1311yescharacteristic
245C2×Q32C22×C1311yescharacteristic
246C2×SD32C22×C1311yescharacteristic
247C2×M32C22×C1311yescharacteristic
248C22×C16C22×C1311yescharacteristic
249#499C22×C1311yescharacteristic
250#494C22×C1311yescharacteristic
251#485—21no—
252#483—21no—
253#479—21no—
254#467C22×C1311yescharacteristic
255#467C22×C1311yescharacteristic
256#467C22×C1311yescharacteristic
257#467C22×C1311yescharacteristic
258#461—21no—
259#452—21no—
260#452—21no—
261C4×Q16C22×C1311yescharacteristic
262C4×D8C22×C1311yescharacteristic
263C8×D4C22×C1311yescharacteristic
264#427C22×C1311yescharacteristic
265C2×#107C22×C1311yescharacteristic
266#367C22×C1311yescharacteristic
267#366C22×C1311yescharacteristic
268#366C22×C1311yescharacteristic
269C4⋊C16C22×C1311yescharacteristic
270#358C22×C1311yescharacteristic
271#358C22×C1311yescharacteristic
272#358C22×C1311yescharacteristic
273#358C22×C1311yescharacteristic
274#358C22×C1311yescharacteristic
275#358C22×C1311yescharacteristic
276#358C22×C1311yescharacteristic
277#357C22×C1311yescharacteristic
278#357C22×C1311yescharacteristic
279#357C22×C1311yescharacteristic
280C22⋊C16C22×C1311yescharacteristic
281C22⋊C16C22×C1311yescharacteristic
282#346C22×C1311yescharacteristic
283C22×C13—21no—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—42no—
290C22×C13—81no—
291C22×C13—81no—
292C22×C13C22×D811yescharacteristic
293C4×C13—21no—
294C4×C13—21no—
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—81no—
298C4×C13—81no—
299C4×C13—81no—
300C4×C13—81no—
301C4×C13—81no—
302C4×C13—81no—
303C4×C13—81no—
304C4×C13#54611yescharacteristic
305C4×C13#57711yescharacteristic
306C2×#41—21no—
307C2×#41—21no—
308#135—22no—
309#135—22no—
310#135—41no—
311#135—41no—
312C2×Q16—21no—
313C2×Q16C23×C1311yescharacteristic
314C2×Q16C23×C1311yescharacteristic
315C2×Q16C23×C1311yescharacteristic
316C2×SD16—21no—
317C2×SD16—21no—
318C2×D8C23×C1311yescharacteristic
319C22×C8C23×C1311yescharacteristic
320C22×C8C23×C1311yescharacteristic
321C4⋊Q8—21no—
322#126—41no—
323#125—21no—
324#125—41no—
325#123—41no—
326#123—41no—
327#123—41no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332#121—41no—
333C4×Q8—21no—
334C4×D4—21no—
335C4×D4D4×C1311yescharacteristic
336#117—21no—
337#117—41no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—41no—
340Q32—41no—
341Q32—41no—
342SD32—22no—
343M32—41no—
344C2×C16—41no—
345C2×C16C23×C1311yescharacteristic
346C2×C16C23×C1311yescharacteristic
347C2×C16C23×C1311yescharacteristic
348C2×C16C23×C1311yescharacteristic
349#107—21no—
350#107C23×C1311yescharacteristic
351#107C23×C1311yescharacteristic
352#107C23×C1311yescharacteristic
353#107C23×C1311yescharacteristic
354#106—21no—
355#106—21no—
356C4⋊C8D4×C1311yescharacteristic
357#103—21no—
358#103—21no—
359#103—21no—
360#103—21no—
361#103—21no—
362#102—21no—
363C22⋊C8D4×C1311yescharacteristic
364C22⋊C8D4×C1311yescharacteristic
365C4×C8C23×C1311yescharacteristic
366C2×C13—41no—
367C2×C13—41no—
368C2×C13—82no—
369C2×C13#329411yescharacteristic
370C2×C13#341411yescharacteristic
371C2×C13#341711yescharacteristic
372#41—42no—
373#41—42no—
374#41—81no—
375#41—81no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×D4—21no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4C13×D811yescharacteristic
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4C2×D4×C1311yescharacteristic
388C22×C4C2×D4×C1311yescharacteristic
389Q16—21no—
390Q16—21no—
391Q16—21no—
392Q16—21no—
393Q16—21no—
394Q16—21no—
395Q16—81no—
396SD16—42no—
397SD16—42no—
398D8—21no—
399D8C13×#4112yes—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8C2×D4×C1311yescharacteristic
405C2×C8C2×D4×C1311yescharacteristic
406C2×C8C2×D4×C1311yescharacteristic
407C2×C8C24×C1311yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4C13×D811yescharacteristic
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4C13×D811yescharacteristic
430C22⋊C4C13×D811yescharacteristic
431C42—41no—
432C42—41no—
433C42C2×D4×C1311yescharacteristic
434C16—21no—
435C16—21no—
436C16—21no—
437C16—21no—
438C13#3388211yescharacteristic, direct product factor, Sylow
439C23—41no—
440C23C2×C13×D811yescharacteristic
441C23C2×C13×D811yescharacteristic
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446Q8—41no—
447Q8—41no—
448D4—22no—
449D4—41no—
450D4—41no—
451D4—82no—
452D4—82no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4C2×C13×D811yescharacteristic
469C2×C4C2×C13×D811yescharacteristic
470C2×C4C2×C13×D811yescharacteristic
471C2×C4C2×C13×D811yescharacteristic
472C2×C4C22×D4×C1311yescharacteristic
473C8—21no—
474C8—21no—
475C8—21no—
476C8C2×C13×#4111yescharacteristic
477C8C13×H(5,𝔽2)11yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—81no—
486C22—81no—
487C22C22×C13×D811yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—81no—
499C4C13×#54611yescharacteristic
500C4C13×#57711yescharacteristic
501C2—41no—
502C2—41no—
503C2—82no—
504C2C13×#329411yescharacteristic
505C2C13×#341411yescharacteristic
506C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#3283C2
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×#3336C2semidirect
3. C13×#2245C2semidirect
4. C13×#2237C2semidirect
5. C13×#2236C2semidirect
6. C13×#2228C2semidirect
7. C13×#2219C2semidirect
8. C13×#2216C2semidirect
9. C13×#2209C2semidirect
10. C13×#2189C2semidirect
11. C13×#2189C2semidirect
12. C13×#2175C2semidirect
13. C13×#2168C2semidirect
14. C13×#2139C2semidirect
15. C13×#2138C2semidirect
119. #33882C13direct (N × H)
186. #3336C2×C13semidirect
188. #2245C2×C13semidirect
189. #2237C2×C13semidirect
190. #2236C2×C13semidirect
191. #2228C2×C13semidirect
192. #2219C2×C13semidirect
193. #2216C2×C13semidirect
194. #2209C2×C13semidirect
195. #2189C2×C13semidirect
196. #2189C2×C13semidirect
197. #2175C2×C13semidirect
198. #2168C2×C13semidirect
199. #2139C2×C13semidirect
200. #2138C2×C13semidirect
438. C13#33882direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33362
C13×#32832
C13×#22452
C13×#22372
C13×#22362
C13×#22282
C13×#22192
C13×#22162
C13×#22092
C13×#21892
C13×#21752
C13×#21682
C13×#21392
C13×#21382
#3388213