Finite Group Databasebeta

← C13×#33937 #15720276

Subgroups — C13×#33937 #15720276

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3396C211yesmaximal, characteristic, complemented
2C13×#3380C211yesmaximal, characteristic, complemented
3C13×#2244C211yesmaximal, characteristic, complemented
4C13×#2243C211yesmaximal, characteristic, complemented
5C13×#2242C211yesmaximal, characteristic, complemented
6C13×#2229C211yesmaximal, characteristic, complemented
7C13×#2228C211yesmaximal, characteristic, complemented
8C13×#2224C211yesmaximal, characteristic, complemented
9C13×#2210C211yesmaximal, characteristic, complemented
10C13×#2210C211yesmaximal, characteristic, complemented
11C13×#2206C211yesmaximal, characteristic
12C13×#2183C211yesmaximal, characteristic, complemented
13C13×#2177C211yesmaximal, characteristic, complemented
14C13×#2175C211yesmaximal, characteristic, complemented
15C4×C13×D16C211yesmaximal, characteristic, complemented
16C13×#559—21no—
17C13×#554—21no—
18C2×C13×SD32C2211yescharacteristic
19C2×C13×D16C2211yescharacteristic
20C2×C13×D16C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#495C2211yescharacteristic
25C13×#495C2211yescharacteristic
26C13×#493C2211yescharacteristic
27C13×#478—21no—
28C13×#478—21no—
29C13×#476—21no—
30C13×#463—21no—
31C13×#463—21no—
32C13×#460—21no—
33C8×Q8×C13C2211yescharacteristic
34C4×C13×Q16C2211yescharacteristic
35C4×C13×D8C2211yescharacteristic
36C4×C13×D8C2211yescharacteristic
37C4×C13×D8C2211yescharacteristic
38C4×C13×D8C2211yescharacteristic
39C4×C13×D8C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#366C2211yescharacteristic
42C13×#366C2211yescharacteristic
43C13×C4⋊C16C2211yescharacteristic
44C13×C4⋊C16C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×#358C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#357C2211yescharacteristic
50C13×#357C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×#346C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C4×C13×C16C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×SD16—21no—
61C2×C13×SD16—21no—
62C2×C13×D8—21no—
63C2×C13×D8C2311yescharacteristic
64C2×C13×D8C2311yescharacteristic
65C2×C13×D8C2311yescharacteristic
66C13×C4⋊Q8—21no—
67C13×#127—21no—
68C13×#125—21no—
69C13×#125—21no—
70C13×#124—21no—
71C13×#124—21no—
72C13×#124—41no—
73C13×#123—41no—
74C13×#123—41no—
75C13×C22⋊Q8—41no—
76C13×C22⋊Q8—41no—
77C13×C22⋊Q8—41no—
78C4×Q8×C13—21no—
79C4×Q8×C13D411yescharacteristic
80C4×D4×C13—21no—
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C4×D4×C13—21no—
84C4×D4×C13—21no—
85C4×D4×C13—41no—
86C2×C13×C4⋊C4—41no—
87C13×SD32—22no—
88C13×D16—22no—
89C13×D16—22no—
90C2×C13×C16C2311yescharacteristic
91C2×C13×C16C2311yescharacteristic
92C2×C13×C16C2311yescharacteristic
93C2×C13×C16C2311yescharacteristic
94C13×#107—21no—
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×#106—21no—
100C13×#106—21no—
101C13×C4⋊C8D411yescharacteristic
102C13×C4⋊C8D411yescharacteristic
103C13×C4⋊C8D411yescharacteristic
104C13×#103—21no—
105C13×#102—21no—
106C13×#102—21no—
107C13×#102—21no—
108C13×#102—21no—
109C13×#102—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#33937C1311yesmaximal, characteristic, direct product factor, Sylow
114C2×Q8×C13—21no—
115C2×Q8×C13—41no—
116C2×Q8×C13D811yescharacteristic
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—41no—
121C2×D4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C13×Q16—21no—
128C13×Q16—21no—
129C13×SD16—81no—
130C13×SD16—81no—
131C13×D8—21no—
132C13×D8—21no—
133C13×D8—21no—
134C13×D8—21no—
135C13×D8—21no—
136C13×D8—81no—
137C13×D8#4112yes—
138C2×C8×C13C2×D411yescharacteristic
139C2×C8×C13C2×D411yescharacteristic
140C2×C8×C13C2×D411yescharacteristic
141C2×C8×C13C2411yescharacteristic
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—41no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4—41no—
149C13×C4⋊C4—41no—
150C13×C4⋊C4—41no—
151C13×C4⋊C4—41no—
152C13×C4⋊C4D811yescharacteristic
153C13×C4⋊C4D811yescharacteristic
154C13×C4⋊C4D811yescharacteristic
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4—41no—
164C42×C13—41no—
165C42×C13C2×D411yescharacteristic
166C42×C13C2×D411yescharacteristic
167C42×C13C2×D411yescharacteristic
168C13×C16—21no—
169C13×C16—21no—
170C13×C16—21no—
171C13×C16—21no—
172#3396C2×C1311yescharacteristic, complemented
173#3380C2×C1311yescharacteristic, complemented
174#2244C2×C1311yescharacteristic, complemented
175#2243C2×C1311yescharacteristic, complemented
176#2242C2×C1311yescharacteristic, complemented
177#2229C2×C1311yescharacteristic, complemented
178#2228C2×C1311yescharacteristic, complemented
179#2224C2×C1311yescharacteristic, complemented
180#2210C2×C1311yescharacteristic, complemented
181#2210C2×C1311yescharacteristic, complemented
182#2206C2×C1311yescharacteristic
183#2183C2×C1311yescharacteristic, complemented
184#2177C2×C1311yescharacteristic, complemented
185#2175C2×C1311yescharacteristic, complemented
186C4×D16C2×C1311yescharacteristic, complemented
187C23×C13—41no—
188C23×C13—41no—
189C23×C13—41no—
190Q8×C13—41no—
191Q8×C13—41no—
192Q8×C13—41no—
193Q8×C13—161no—
194D4×C13—22no—
195D4×C13—41no—
196D4×C13—41no—
197D4×C13—41no—
198D4×C13—41no—
199D4×C13—41no—
200D4×C13—82no—
201D4×C13—161no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—82no—
208C2×C4×C13—161no—
209C2×C4×C13—161no—
210C2×C4×C13—161no—
211C2×C4×C13—161no—
212C2×C4×C13C2×D811yescharacteristic
213C2×C4×C13C2×D811yescharacteristic
214C2×C4×C13C2×D811yescharacteristic
215C2×C4×C13C2×D811yescharacteristic
216C2×C4×C13C2×D811yescharacteristic
217C2×C4×C13C2×D811yescharacteristic
218C2×C4×C13C22×D411yescharacteristic
219C8×C13—21no—
220C8×C13—21no—
221C8×C13—21no—
222C8×C13C2×#4111yescharacteristic
223C8×C132−1+411yescharacteristic
224#559—21no—
225#554—21no—
226C2×SD32C22×C1311yescharacteristic
227C2×D16C22×C1311yescharacteristic
228C2×D16C22×C1311yescharacteristic
229#500C22×C1311yescharacteristic
230#499C22×C1311yescharacteristic
231#499C22×C1311yescharacteristic
232#495C22×C1311yescharacteristic
233#495C22×C1311yescharacteristic
234#493C22×C1311yescharacteristic
235#478—21no—
236#478—21no—
237#476—21no—
238#463—21no—
239#463—21no—
240#460—21no—
241C8×Q8C22×C1311yescharacteristic
242C4×Q16C22×C1311yescharacteristic
243C4×D8C22×C1311yescharacteristic
244C4×D8C22×C1311yescharacteristic
245C4×D8C22×C1311yescharacteristic
246C4×D8C22×C1311yescharacteristic
247C4×D8C22×C1311yescharacteristic
248#367C22×C1311yescharacteristic
249#366C22×C1311yescharacteristic
250#366C22×C1311yescharacteristic
251C4⋊C16C22×C1311yescharacteristic
252C4⋊C16C22×C1311yescharacteristic
253C4⋊C16C22×C1311yescharacteristic
254#358C22×C1311yescharacteristic
255#358C22×C1311yescharacteristic
256#358C22×C1311yescharacteristic
257#357C22×C1311yescharacteristic
258#357C22×C1311yescharacteristic
259#357C22×C1311yescharacteristic
260#357C22×C1311yescharacteristic
261#357C22×C1311yescharacteristic
262#357C22×C1311yescharacteristic
263#357C22×C1311yescharacteristic
264#346C22×C1311yescharacteristic
265#346C22×C1311yescharacteristic
266C4×C16C22×C1311yescharacteristic
267C22×C13—42no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13—81no—
273C22×C13—81no—
274C22×C13—81no—
275C22×C13—81no—
276C22×C13C22×D811yescharacteristic
277C4×C13—21no—
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—21no—
281C4×C13—21no—
282C4×C13—21no—
283C4×C13—81no—
284C4×C13—81no—
285C4×C13—81no—
286C4×C13—81no—
287C4×C13—81no—
288C4×C13#54811yescharacteristic
289C4×C13#57711yescharacteristic
290C2×Q16C23×C1311yescharacteristic
291C2×SD16—21no—
292C2×SD16—21no—
293C2×D8—21no—
294C2×D8C23×C1311yescharacteristic
295C2×D8C23×C1311yescharacteristic
296C2×D8C23×C1311yescharacteristic
297C4⋊Q8—21no—
298#127—21no—
299#125—21no—
300#125—21no—
301#124—21no—
302#124—21no—
303#124—41no—
304#123—41no—
305#123—41no—
306C22⋊Q8—41no—
307C22⋊Q8—41no—
308C22⋊Q8—41no—
309C4×Q8—21no—
310C4×Q8D4×C1311yescharacteristic
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—41no—
317C2×C4⋊C4—41no—
318SD32—22no—
319D16—22no—
320D16—22no—
321C2×C16C23×C1311yescharacteristic
322C2×C16C23×C1311yescharacteristic
323C2×C16C23×C1311yescharacteristic
324C2×C16C23×C1311yescharacteristic
325#107—21no—
326#107C23×C1311yescharacteristic
327#107C23×C1311yescharacteristic
328#107C23×C1311yescharacteristic
329#107C23×C1311yescharacteristic
330#106—21no—
331#106—21no—
332C4⋊C8D4×C1311yescharacteristic
333C4⋊C8D4×C1311yescharacteristic
334C4⋊C8D4×C1311yescharacteristic
335#103—21no—
336#102—21no—
337#102—21no—
338#102—21no—
339#102—21no—
340#102—21no—
341C4×C8C23×C1311yescharacteristic
342C4×C8C23×C1311yescharacteristic
343C4×C8C23×C1311yescharacteristic
344C2×C13—82no—
345C2×C13—161no—
346C2×C13—161no—
347C2×C13#335811yescharacteristic
348C2×C13#341411yescharacteristic
349C2×C13#341511yescharacteristic
350C2×Q8—21no—
351C2×Q8—41no—
352C2×Q8C13×D811yescharacteristic
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363Q16—21no—
364Q16—21no—
365SD16—81no—
366SD16—81no—
367D8—21no—
368D8—21no—
369D8—21no—
370D8—21no—
371D8—21no—
372D8—81no—
373D8C13×#4112yes—
374C2×C8C2×D4×C1311yescharacteristic
375C2×C8C2×D4×C1311yescharacteristic
376C2×C8C2×D4×C1311yescharacteristic
377C2×C8C24×C1311yescharacteristic
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4C13×D811yescharacteristic
389C4⋊C4C13×D811yescharacteristic
390C4⋊C4C13×D811yescharacteristic
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C42—41no—
401C42C2×D4×C1311yescharacteristic
402C42C2×D4×C1311yescharacteristic
403C42C2×D4×C1311yescharacteristic
404C16—21no—
405C16—21no—
406C16—21no—
407C16—21no—
408C13#3393711yescharacteristic, direct product factor, Sylow
409C23—41no—
410C23—41no—
411C23—41no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—161no—
416D4—22no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—82no—
423D4—161no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—82no—
430C2×C4—161no—
431C2×C4—161no—
432C2×C4—161no—
433C2×C4—161no—
434C2×C4C2×C13×D811yescharacteristic
435C2×C4C2×C13×D811yescharacteristic
436C2×C4C2×C13×D811yescharacteristic
437C2×C4C2×C13×D811yescharacteristic
438C2×C4C2×C13×D811yescharacteristic
439C2×C4C2×C13×D811yescharacteristic
440C2×C4C22×D4×C1311yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8C2×C13×#4111yescharacteristic
445C8C13×2−1+411yescharacteristic
446C22—42no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C22×C13×D811yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4C13×#54811yescharacteristic
468C4C13×#57711yescharacteristic
469C2—82no—
470C2—161no—
471C2—161no—
472C2C13×#335811yescharacteristic
473C2C13×#341411yescharacteristic
474C2C13×#341511yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#2206C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×Q8×C13 ◁ C8×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3396C2semidirect
2. C13×#3380C2semidirect
3. C13×#2244C2semidirect
4. C13×#2243C2semidirect
5. C13×#2242C2semidirect
6. C13×#2229C2semidirect
7. C13×#2228C2semidirect
8. C13×#2224C2semidirect
9. C13×#2210C2semidirect
10. C13×#2210C2semidirect
12. C13×#2183C2semidirect
13. C13×#2177C2semidirect
14. C13×#2175C2semidirect
15. C4×C13×D16C2semidirect
113. #33937C13direct (N × H)
172. #3396C2×C13semidirect
173. #3380C2×C13semidirect
174. #2244C2×C13semidirect
175. #2243C2×C13semidirect
176. #2242C2×C13semidirect
177. #2229C2×C13semidirect
178. #2228C2×C13semidirect
179. #2224C2×C13semidirect
180. #2210C2×C13semidirect
181. #2210C2×C13semidirect
183. #2183C2×C13semidirect
184. #2177C2×C13semidirect
185. #2175C2×C13semidirect
186. C4×D16C2×C13semidirect
408. C13#33937direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33962
C13×#33802
C13×#22442
C13×#22432
C13×#22422
C13×#22292
C13×#22282
C13×#22242
C13×#22102
C13×#22062
C13×#21832
C13×#21772
C13×#21752
C4×C13×D162
#3393713