Finite Group Databasebeta

← C13×#33912 #15720251

Subgroups — C13×#33912 #15720251

Order 3328.

516 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3339C211yesmaximal, characteristic, complemented
2C13×#3334C211yesmaximal, characteristic, complemented
3C13×#2255C211yesmaximal, characteristic, complemented
4C13×#2234C211yesmaximal, characteristic, complemented
5C13×#2233C211yesmaximal, characteristic, complemented
6C13×#2233C211yesmaximal, characteristic, complemented
7C13×#2232C211yesmaximal, characteristic, complemented
8C13×#2228C211yesmaximal, characteristic, complemented
9C13×#2226C211yesmaximal, characteristic, complemented
10C13×#2218C211yesmaximal, characteristic, complemented
11C13×#2215C211yesmaximal, characteristic, complemented
12C13×#2177C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2159C211yesmaximal, characteristic, complemented
15C2×C13×#367C211yesmaximal, characteristic, complemented
16C13×#553—21no—
17C13×#547—21no—
18C2×C13×D16C2211yescharacteristic
19C2×C13×M32C2211yescharacteristic
20C22×C13×C16C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#482—21no—
24C13×#481—21no—
25C13×#480—21no—
26C13×#480—21no—
27C13×#478—21no—
28C13×#474—21no—
29C13×#466C2211yescharacteristic
30C13×#466C2211yescharacteristic
31C13×#466C2211yescharacteristic
32C13×#466C2211yescharacteristic
33C4×C13×D8C2211yescharacteristic
34C4×C13×D8C2211yescharacteristic
35C8×D4×C13C2211yescharacteristic
36C13×#427C2211yescharacteristic
37C2×C13×#107C2211yescharacteristic
38C2×C13×#107C2211yescharacteristic
39C2×C13×#107C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#367C2211yescharacteristic
44C13×#367C2211yescharacteristic
45C13×#367C2211yescharacteristic
46C13×#366C2211yescharacteristic
47C13×#366C2211yescharacteristic
48C13×#366C2211yescharacteristic
49C13×C4⋊C16C2211yescharacteristic
50C13×#357C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic
58C13×#346C2211yescharacteristic
59C2×C13×#41—41no—
60C2×C13×D8C2311yescharacteristic
61C2×C13×D8C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×C4⋊Q8—21no—
65C13×#126—41no—
66C13×#125—21no—
67C13×#123—41no—
68C13×#123—41no—
69C13×#123—41no—
70C13×C22⋊Q8—41no—
71C13×#121—21no—
72C13×#121—21no—
73C13×#121—21no—
74C13×#121—21no—
75C13×#121—41no—
76C4×D4×C13—21no—
77C4×D4×C13—21no—
78C4×D4×C13—41no—
79C4×D4×C13D411yescharacteristic
80C13×#117—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—21no—
84C13×D16—22no—
85C13×M32—22no—
86C2×C13×C16—22no—
87C2×C13×C16C2311yescharacteristic
88C2×C13×C16C2311yescharacteristic
89C2×C13×C16C2311yescharacteristic
90C2×C13×C16C2311yescharacteristic
91C13×#107—21no—
92C13×#107—21no—
93C13×#107—21no—
94C13×#107—21no—
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×#107C2311yescharacteristic
100C13×#107C2311yescharacteristic
101C13×#106—21no—
102C13×#106—21no—
103C13×C4⋊C8D411yescharacteristic
104C13×#102—21no—
105C13×#102—21no—
106C13×#102—21no—
107C13×#102—21no—
108C13×#102—21no—
109C13×#102—21no—
110C13×C22⋊C8D411yescharacteristic
111C13×C22⋊C8D411yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#33912C1311yesmaximal, characteristic, direct product factor, Sylow
114C13×#41—84no—
115C2×Q8×C13—41no—
116C2×D4×C13—21no—
117C2×D4×C13—21no—
118C2×D4×C13—41no—
119C2×D4×C13—41no—
120C2×D4×C13—41no—
121C2×D4×C13—41no—
122C2×D4×C13D811yescharacteristic
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C13×D8—21no—
131C13×D8—21no—
132C13×D8—21no—
133C13×D8—21no—
134C2×C8×C13—21no—
135C2×C8×C13—21no—
136C2×C8×C13—21no—
137C2×C8×C13—21no—
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—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—41no—
149C13×C4⋊C4—41no—
150C13×C4⋊C4—41no—
151C13×C4⋊C4—41no—
152C13×C4⋊C4—41no—
153C13×C4⋊C4—41no—
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⋊C4D811yescharacteristic
163C13×C22⋊C4D811yescharacteristic
164C42×C13—41no—
165C42×C13C2×D411yescharacteristic
166C13×C16—21no—
167C13×C16—21no—
168C13×C16—21no—
169C13×C16#4112yescomplemented
170#3339C2×C1311yescharacteristic, complemented
171#3334C2×C1311yescharacteristic, complemented
172#2255C2×C1311yescharacteristic, complemented
173#2234C2×C1311yescharacteristic, complemented
174#2233C2×C1311yescharacteristic, complemented
175#2233C2×C1311yescharacteristic, complemented
176#2232C2×C1311yescharacteristic, complemented
177#2228C2×C1311yescharacteristic, complemented
178#2226C2×C1311yescharacteristic, complemented
179#2218C2×C1311yescharacteristic, complemented
180#2215C2×C1311yescharacteristic, complemented
181#2177C2×C1311yescharacteristic, complemented
182#2168C2×C1311yescharacteristic, complemented
183#2159C2×C1311yescharacteristic, complemented
184C2×#367C2×C1311yescharacteristic, complemented
185C23×C13—41no—
186C23×C13—41no—
187C23×C13C2×D811yescharacteristic
188C23×C13C2×D811yescharacteristic
189Q8×C13—82no—
190D4×C13—22no—
191D4×C13—41no—
192D4×C13—41no—
193D4×C13—41no—
194D4×C13—41no—
195D4×C13—82no—
196D4×C13—82no—
197D4×C13—82no—
198D4×C13—161no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—82no—
210C2×C4×C13—82no—
211C2×C4×C13—82no—
212C2×C4×C13—161no—
213C2×C4×C13—161no—
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#553—21no—
225#547—21no—
226C2×D16C22×C1311yescharacteristic
227C2×M32C22×C1311yescharacteristic
228C22×C16C22×C1311yescharacteristic
229#500C22×C1311yescharacteristic
230#499C22×C1311yescharacteristic
231#482—21no—
232#481—21no—
233#480—21no—
234#480—21no—
235#478—21no—
236#474—21no—
237#466C22×C1311yescharacteristic
238#466C22×C1311yescharacteristic
239#466C22×C1311yescharacteristic
240#466C22×C1311yescharacteristic
241C4×D8C22×C1311yescharacteristic
242C4×D8C22×C1311yescharacteristic
243C8×D4C22×C1311yescharacteristic
244#427C22×C1311yescharacteristic
245C2×#107C22×C1311yescharacteristic
246C2×#107C22×C1311yescharacteristic
247C2×#107C22×C1311yescharacteristic
248#367C22×C1311yescharacteristic
249#367C22×C1311yescharacteristic
250#367C22×C1311yescharacteristic
251#367C22×C1311yescharacteristic
252#367C22×C1311yescharacteristic
253#367C22×C1311yescharacteristic
254#366C22×C1311yescharacteristic
255#366C22×C1311yescharacteristic
256#366C22×C1311yescharacteristic
257C4⋊C16C22×C1311yescharacteristic
258#357C22×C1311yescharacteristic
259#357C22×C1311yescharacteristic
260#357C22×C1311yescharacteristic
261#357C22×C1311yescharacteristic
262#357C22×C1311yescharacteristic
263#357C22×C1311yescharacteristic
264C22⋊C16C22×C1311yescharacteristic
265C22⋊C16C22×C1311yescharacteristic
266#346C22×C1311yescharacteristic
267C22×C13—21no—
268C22×C13—21no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—21no—
272C22×C13—81no—
273C22×C13—81no—
274C22×C13—81no—
275C22×C13—81no—
276C22×C13—81no—
277C22×C13—81no—
278C22×C13#50912yes—
279C22×C13C22×D811yescharacteristic
280C4×C13—21no—
281C4×C13—21no—
282C4×C13—21no—
283C4×C13—21no—
284C4×C13—81no—
285C4×C13—81no—
286C4×C13—81no—
287C4×C13—81no—
288C4×C13—81no—
289C4×C13—81no—
290C4×C13#54711yescharacteristic
291C4×C13#57811yescharacteristic
292C2×#41—41no—
293C2×D8C23×C1311yescharacteristic
294C2×D8C23×C1311yescharacteristic
295C22×C8C23×C1311yescharacteristic
296C22×C8C23×C1311yescharacteristic
297C4⋊Q8—21no—
298#126—41no—
299#125—21no—
300#123—41no—
301#123—41no—
302#123—41no—
303C22⋊Q8—41no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—41no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—41no—
312C4×D4D4×C1311yescharacteristic
313#117—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317D16—22no—
318M32—22no—
319C2×C16—22no—
320C2×C16C23×C1311yescharacteristic
321C2×C16C23×C1311yescharacteristic
322C2×C16C23×C1311yescharacteristic
323C2×C16C23×C1311yescharacteristic
324#107—21no—
325#107—21no—
326#107—21no—
327#107—21no—
328#107C23×C1311yescharacteristic
329#107C23×C1311yescharacteristic
330#107C23×C1311yescharacteristic
331#107C23×C1311yescharacteristic
332#107C23×C1311yescharacteristic
333#107C23×C1311yescharacteristic
334#106—21no—
335#106—21no—
336C4⋊C8D4×C1311yescharacteristic
337#102—21no—
338#102—21no—
339#102—21no—
340#102—21no—
341#102—21no—
342#102—21no—
343C22⋊C8D4×C1311yescharacteristic
344C22⋊C8D4×C1311yescharacteristic
345C4×C8C23×C1311yescharacteristic
346C2×C13—22no—
347C2×C13—41no—
348C2×C13—161no—
349C2×C13—161no—
350C2×C13#333411yescharacteristic
351C2×C13C2×#50911yescharacteristic
352C2×C13#341611yescharacteristic
353#41—84no—
354C2×Q8—41no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4C13×D811yescharacteristic
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C2×D4×C1311yescharacteristic
368C22×C4C2×D4×C1311yescharacteristic
369D8—21no—
370D8—21no—
371D8—21no—
372D8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8C2×D4×C1311yescharacteristic
378C2×C8C2×D4×C1311yescharacteristic
379C2×C8C2×D4×C1311yescharacteristic
380C2×C8C24×C1311yescharacteristic
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4C13×D811yescharacteristic
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4C13×D811yescharacteristic
402C22⋊C4C13×D811yescharacteristic
403C42—41no—
404C42C2×D4×C1311yescharacteristic
405C16—21no—
406C16—21no—
407C16—21no—
408C16C13×#4112yescomplemented
409C13#3391211yescharacteristic, direct product factor, Sylow
410C23—41no—
411C23—41no—
412C23C2×C13×D811yescharacteristic
413C23C2×C13×D811yescharacteristic
414Q8—82no—
415D4—22no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—82no—
422D4—82no—
423D4—161no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—161no—
438C2×C4—161no—
439C2×C4C2×C13×D811yescharacteristic
440C2×C4C2×C13×D811yescharacteristic
441C2×C4C2×C13×D811yescharacteristic
442C2×C4C2×C13×D811yescharacteristic
443C2×C4C22×D4×C1311yescharacteristic
444C8—21no—
445C8—21no—
446C8—21no—
447C8C2×C13×#4111yescharacteristic
448C8C13×2−1+411yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22C13×#50912yes—
461C22C22×C13×D811yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4C13×#54711yescharacteristic
473C4C13×#57811yescharacteristic
474C2—22no—
475C2—41no—
476C2—161no—
477C2—161no—
478C2C13×#333411yescharacteristic
479C2C2×C13×#50911yescharacteristic
480C2C13×#341611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
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×#3339C2semidirect
2. C13×#3334C2semidirect
3. C13×#2255C2semidirect
4. C13×#2234C2semidirect
5. C13×#2233C2semidirect
6. C13×#2233C2semidirect
7. C13×#2232C2semidirect
8. C13×#2228C2semidirect
9. C13×#2226C2semidirect
10. C13×#2218C2semidirect
11. C13×#2215C2semidirect
12. C13×#2177C2semidirect
13. C13×#2168C2semidirect
14. C13×#2159C2semidirect
15. C2×C13×#367C2semidirect
113. #33912C13direct (N × H)
169. C13×C16#41semidirect
170. #3339C2×C13semidirect
171. #3334C2×C13semidirect
172. #2255C2×C13semidirect
173. #2234C2×C13semidirect
174. #2233C2×C13semidirect
175. #2233C2×C13semidirect
176. #2232C2×C13semidirect
177. #2228C2×C13semidirect
178. #2226C2×C13semidirect
179. #2218C2×C13semidirect
180. #2215C2×C13semidirect
181. #2177C2×C13semidirect
182. #2168C2×C13semidirect
183. #2159C2×C13semidirect
184. C2×#367C2×C13semidirect
408. C16C13×#41semidirect
409. C13#33912direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33392
C13×#33342
C13×#22552
C13×#22342
C13×#22332
C13×#22322
C13×#22282
C13×#22262
C13×#22182
C13×#22152
C13×#21772
C13×#21682
C13×#21592
C2×C13×#3672
#3391213