Finite Group Databasebeta

← C13×#33879 #15720218

Subgroups — C13×#33879 #15720218

Order 3328.

536 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3336C211yesmaximal, characteristic
2D4×C13×Q16C211yesmaximal, characteristic
3C13×#2245C211yesmaximal, characteristic, complemented
4C13×#2237C211yesmaximal, characteristic, complemented
5C13×#2235C211yesmaximal, characteristic, complemented
6C13×#2229C211yesmaximal, characteristic, complemented
7C13×#2219C211yesmaximal, characteristic, complemented
8C13×#2216C211yesmaximal, characteristic, complemented
9C13×#2209C211yesmaximal, characteristic, complemented
10C13×#2188C211yesmaximal, characteristic, complemented
11C13×#2188C211yesmaximal, characteristic, complemented
12C13×#2176C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic
14C13×#2141C211yesmaximal, characteristic, complemented
15C2×C13×#358C211yesmaximal, characteristic, complemented
16C22×C13×Q16C2211yescharacteristic
17C22×C13×Q16C2211yescharacteristic
18C13×#552—21no—
19D4×Q8×C13—21no—
20C2×C13×Q32C2211yescharacteristic
21C2×C13×Q32C2211yescharacteristic
22C2×C13×Q32C2211yescharacteristic
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×#462—21no—
35C13×#451—21no—
36C13×#451—21no—
37C4×C13×Q16C2211yescharacteristic
38C4×C13×Q16C2211yescharacteristic
39C8×D4×C13C2211yescharacteristic
40C13×#427C2211yescharacteristic
41C2×C13×#107C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#367C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×#358C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#358C2211yescharacteristic
54C13×#358C2211yescharacteristic
55C13×#358C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic
58C13×#346C2211yescharacteristic
59C22×Q8×C13—21no—
60C22×Q8×C13—21no—
61C2×C13×Q16—22no—
62C2×C13×Q16—22no—
63C2×C13×Q16—21no—
64C2×C13×Q16—21no—
65C2×C13×Q16—21no—
66C2×C13×Q16—41no—
67C2×C13×Q16—41no—
68C2×C13×Q16C2311yescharacteristic
69C2×C13×Q16C2311yescharacteristic
70C2×C13×Q16C2311yescharacteristic
71C2×C13×Q16C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C13×C4⋊Q8—21no—
75C13×C4⋊Q8—41no—
76C13×#126—41no—
77C13×#125—21no—
78C13×#125—41no—
79C13×#123—41no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—21no—
82C13×C22⋊Q8—21no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—41no—
85C13×C22⋊Q8—41no—
86C4×Q8×C13—21no—
87C4×Q8×C13—21no—
88C4×D4×C13—41no—
89C4×D4×C13D411yescharacteristic
90C13×#117—21no—
91C13×#117—41no—
92C2×C13×C4⋊C4—21no—
93C13×Q32—22no—
94C13×Q32—41no—
95C13×Q32—41no—
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×#103—21no—
116C13×C22⋊C8D411yescharacteristic
117C13×C22⋊C8D411yescharacteristic
118C4×C8×C13C2311yescharacteristic
119#33879C1311yesmaximal, characteristic, direct product factor, Sylow
120C2×Q8×C13—21no—
121C2×Q8×C13—21no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—42no—
125C2×Q8×C13—42no—
126C2×Q8×C13—41no—
127C2×Q8×C13—41no—
128C2×Q8×C13—81no—
129C2×Q8×C13—81no—
130C2×D4×C13D811yescharacteristic
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C13×Q16—21no—
137C13×Q16—21no—
138C13×Q16—21no—
139C13×Q16—21no—
140C13×Q16—21no—
141C13×Q16—21no—
142C13×Q16—21no—
143C13×Q16—42no—
144C13×Q16—42no—
145C13×Q16—81no—
146C13×Q16#4112yes—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13C2×D411yescharacteristic
152C2×C8×C13C2×D411yescharacteristic
153C2×C8×C13C2×D411yescharacteristic
154C2×C8×C13C2411yescharacteristic
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—41no—
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⋊C4D811yescharacteristic
177C13×C22⋊C4D811yescharacteristic
178C42×C13—41no—
179C42×C13—41no—
180C42×C13—41no—
181C42×C13C2×D411yescharacteristic
182C13×C16—21no—
183C13×C16—21no—
184C13×C16—21no—
185C13×C16—21no—
186#3336C2×C1311yescharacteristic
187D4×Q16C2×C1311yescharacteristic
188#2245C2×C1311yescharacteristic, complemented
189#2237C2×C1311yescharacteristic, complemented
190#2235C2×C1311yescharacteristic, complemented
191#2229C2×C1311yescharacteristic, complemented
192#2219C2×C1311yescharacteristic, complemented
193#2216C2×C1311yescharacteristic, complemented
194#2209C2×C1311yescharacteristic, complemented
195#2188C2×C1311yescharacteristic, complemented
196#2188C2×C1311yescharacteristic, complemented
197#2176C2×C1311yescharacteristic, complemented
198#2168C2×C1311yescharacteristic
199#2141C2×C1311yescharacteristic, complemented
200C2×#358C2×C1311yescharacteristic, complemented
201C23×C13C2×D811yescharacteristic
202C23×C13C2×D811yescharacteristic
203Q8×C13—22no—
204Q8×C13—41no—
205Q8×C13—41no—
206Q8×C13—41no—
207Q8×C13—41no—
208Q8×C13—41no—
209Q8×C13—41no—
210Q8×C13—41no—
211Q8×C13—82no—
212Q8×C13—82no—
213D4×C13—22no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—41no—
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×C13C2×D811yescharacteristic
230C2×C4×C13C2×D811yescharacteristic
231C2×C4×C13C2×D811yescharacteristic
232C2×C4×C13C2×D811yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C8×C13—21no—
235C8×C13—21no—
236C8×C13—21no—
237C8×C13C2×#4111yescharacteristic
238C8×C13H(5,𝔽2)11yescharacteristic
239C22×Q16C22×C1311yescharacteristic
240C22×Q16C22×C1311yescharacteristic
241#552—21no—
242D4×Q8—21no—
243C2×Q32C22×C1311yescharacteristic
244C2×Q32C22×C1311yescharacteristic
245C2×Q32C22×C1311yescharacteristic
246C2×M32C22×C1311yescharacteristic
247C22×C16C22×C1311yescharacteristic
248#499C22×C1311yescharacteristic
249#494C22×C1311yescharacteristic
250#485—21no—
251#483—21no—
252#479—21no—
253#467C22×C1311yescharacteristic
254#467C22×C1311yescharacteristic
255#467C22×C1311yescharacteristic
256#467C22×C1311yescharacteristic
257#462—21no—
258#451—21no—
259#451—21no—
260C4×Q16C22×C1311yescharacteristic
261C4×Q16C22×C1311yescharacteristic
262C8×D4C22×C1311yescharacteristic
263#427C22×C1311yescharacteristic
264C2×#107C22×C1311yescharacteristic
265#367C22×C1311yescharacteristic
266#367C22×C1311yescharacteristic
267#366C22×C1311yescharacteristic
268C4⋊C16C22×C1311yescharacteristic
269#358C22×C1311yescharacteristic
270#358C22×C1311yescharacteristic
271#358C22×C1311yescharacteristic
272#358C22×C1311yescharacteristic
273#358C22×C1311yescharacteristic
274#358C22×C1311yescharacteristic
275#358C22×C1311yescharacteristic
276#358C22×C1311yescharacteristic
277#358C22×C1311yescharacteristic
278#358C22×C1311yescharacteristic
279C22⋊C16C22×C1311yescharacteristic
280C22⋊C16C22×C1311yescharacteristic
281#346C22×C1311yescharacteristic
282C22×C13—21no—
283C22×C13—21no—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13—21no—
287C22×C13#51012yes—
288C22×C13C22×D811yescharacteristic
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—42no—
294C4×C13—81no—
295C4×C13—81no—
296C4×C13—81no—
297C4×C13—81no—
298C4×C13—81no—
299C4×C13—81no—
300C4×C13—81no—
301C4×C13#54611yescharacteristic
302C4×C13#57711yescharacteristic
303C22×Q8—21no—
304C22×Q8—21no—
305C2×Q16—22no—
306C2×Q16—22no—
307C2×Q16—21no—
308C2×Q16—21no—
309C2×Q16—21no—
310C2×Q16—41no—
311C2×Q16—41no—
312C2×Q16C23×C1311yescharacteristic
313C2×Q16C23×C1311yescharacteristic
314C2×Q16C23×C1311yescharacteristic
315C2×Q16C23×C1311yescharacteristic
316C22×C8C23×C1311yescharacteristic
317C22×C8C23×C1311yescharacteristic
318C4⋊Q8—21no—
319C4⋊Q8—41no—
320#126—41no—
321#125—21no—
322#125—41no—
323#123—41no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—41no—
329C22⋊Q8—41no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×D4—41no—
333C4×D4D4×C1311yescharacteristic
334#117—21no—
335#117—41no—
336C2×C4⋊C4—21no—
337Q32—22no—
338Q32—41no—
339Q32—41no—
340M32—41no—
341C2×C16—41no—
342C2×C16C23×C1311yescharacteristic
343C2×C16C23×C1311yescharacteristic
344C2×C16C23×C1311yescharacteristic
345C2×C16C23×C1311yescharacteristic
346#107—21no—
347#107C23×C1311yescharacteristic
348#107C23×C1311yescharacteristic
349#107C23×C1311yescharacteristic
350#107C23×C1311yescharacteristic
351#106—21no—
352#106—21no—
353C4⋊C8D4×C1311yescharacteristic
354#103—21no—
355#103—21no—
356#103—21no—
357#103—21no—
358#103—21no—
359#103—21no—
360C22⋊C8D4×C1311yescharacteristic
361C22⋊C8D4×C1311yescharacteristic
362C4×C8C23×C1311yescharacteristic
363C2×C13—22no—
364C2×C13—41no—
365C2×C13#329411yescharacteristic
366C2×C13C2×#51011yescharacteristic
367C2×C13#341711yescharacteristic
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—42no—
373C2×Q8—42no—
374C2×Q8—41no—
375C2×Q8—41no—
376C2×Q8—81no—
377C2×Q8—81no—
378C2×D4C13×D811yescharacteristic
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4C2×D4×C1311yescharacteristic
383C22×C4C2×D4×C1311yescharacteristic
384Q16—21no—
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—21no—
389Q16—21no—
390Q16—21no—
391Q16—42no—
392Q16—42no—
393Q16—81no—
394Q16C13×#4112yes—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×D4×C1311yescharacteristic
400C2×C8C2×D4×C1311yescharacteristic
401C2×C8C2×D4×C1311yescharacteristic
402C2×C8C24×C1311yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4C13×D811yescharacteristic
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4C13×D811yescharacteristic
425C22⋊C4C13×D811yescharacteristic
426C42—41no—
427C42—41no—
428C42—41no—
429C42C2×D4×C1311yescharacteristic
430C16—21no—
431C16—21no—
432C16—21no—
433C16—21no—
434C13#3387911yescharacteristic, direct product factor, Sylow
435C23C2×C13×D811yescharacteristic
436C23C2×C13×D811yescharacteristic
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—82no—
446Q8—82no—
447D4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4C2×C13×D811yescharacteristic
464C2×C4C2×C13×D811yescharacteristic
465C2×C4C2×C13×D811yescharacteristic
466C2×C4C2×C13×D811yescharacteristic
467C2×C4C22×D4×C1311yescharacteristic
468C8—21no—
469C8—21no—
470C8—21no—
471C8C2×C13×#4111yescharacteristic
472C8C13×H(5,𝔽2)11yescharacteristic
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22C13×#51012yes—
479C22C22×C13×D811yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—81no—
492C4C13×#54611yescharacteristic
493C4C13×#57711yescharacteristic
494C2—22no—
495C2—41no—
496C2C13×#329411yescharacteristic
497C2C2×C13×#51011yescharacteristic
498C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC2×D4×C13D8
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
3. C13×#2245C2semidirect
4. C13×#2237C2semidirect
5. C13×#2235C2semidirect
6. C13×#2229C2semidirect
7. C13×#2219C2semidirect
8. C13×#2216C2semidirect
9. C13×#2209C2semidirect
10. C13×#2188C2semidirect
11. C13×#2188C2semidirect
12. C13×#2176C2semidirect
14. C13×#2141C2semidirect
15. C2×C13×#358C2semidirect
119. #33879C13direct (N × H)
188. #2245C2×C13semidirect
189. #2237C2×C13semidirect
190. #2235C2×C13semidirect
191. #2229C2×C13semidirect
192. #2219C2×C13semidirect
193. #2216C2×C13semidirect
194. #2209C2×C13semidirect
195. #2188C2×C13semidirect
196. #2188C2×C13semidirect
197. #2176C2×C13semidirect
199. #2141C2×C13semidirect
200. C2×#358C2×C13semidirect
434. C13#33879direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33362
D4×C13×Q162
C13×#22452
C13×#22372
C13×#22352
C13×#22292
C13×#22192
C13×#22162
C13×#22092
C13×#21882
C13×#21762
C13×#21682
C13×#21412
C2×C13×#3582
#3387913