Finite Group Databasebeta

← C13×#33913 #15720252

Subgroups — C13×#33913 #15720252

Order 3328.

484 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3339C211yesmaximal, characteristic
2C13×#3338C211yesmaximal, characteristic, complemented
3C13×#2255C211yesmaximal, characteristic, complemented
4C13×#2237C211yesmaximal, characteristic, complemented
5C13×#2236C211yesmaximal, characteristic, complemented
6C13×#2233C211yesmaximal, characteristic, complemented
7C13×#2232C211yesmaximal, characteristic, complemented
8C13×#2229C211yesmaximal, characteristic, complemented
9C13×#2224C211yesmaximal, characteristic, complemented
10C13×#2220C211yesmaximal, characteristic, complemented
11C13×#2217C211yesmaximal, characteristic, complemented
12C13×#2175C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2159C211yesmaximal, characteristic, complemented
15C2×C13×#366C211yesmaximal, characteristic, complemented
16C13×#554—21no—
17C13×#553—21no—
18C2×C13×SD32C2211yescharacteristic
19C2×C13×M32C2211yescharacteristic
20C22×C13×C16C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#484—21no—
24C13×#484—21no—
25C13×#482—21no—
26C13×#481—21no—
27C13×#478—21no—
28C13×#477—21no—
29C13×#467C2211yescharacteristic
30C13×#467C2211yescharacteristic
31C13×#466C2211yescharacteristic
32C13×#466C2211yescharacteristic
33C4×C13×Q16C2211yescharacteristic
34C4×C13×D8C2211yescharacteristic
35C8×D4×C13C2211yescharacteristic
36C13×#427C2211yescharacteristic
37C2×C13×#107C2211yescharacteristic
38C2×C13×#107C2211yescharacteristic
39C2×C13×#107C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×#366C2211yescharacteristic
46C13×#366C2211yescharacteristic
47C13×#366C2211yescharacteristic
48C13×#366C2211yescharacteristic
49C13×C4⋊C16C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic
58C13×#346C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×D8C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C13×C4⋊Q8—21no—
64C13×#126—41no—
65C13×#125—21no—
66C13×#125—41no—
67C13×#123—41no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8—21no—
70C13×C22⋊Q8—41no—
71C13×C22⋊Q8—41no—
72C13×#121—21no—
73C13×#121—21no—
74C13×#121—41no—
75C4×Q8×C13—21no—
76C4×D4×C13—21no—
77C4×D4×C13—41no—
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×SD32—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×#103—21no—
105C13×#103—21no—
106C13×#103—21no—
107C13×#102—21no—
108C13×#102—21no—
109C13×#102—21no—
110C13×C22⋊C8D411yescharacteristic
111C13×C22⋊C8D411yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#33913C1311yesmaximal, characteristic, direct product factor, Sylow
114C2×Q8×C13—21no—
115C2×Q8×C13—41no—
116C2×D4×C13—21no—
117C2×D4×C13—41no—
118C2×D4×C13—41no—
119C2×D4×C13D811yescharacteristic
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C13×Q16—21no—
127C13×Q16—21no—
128C13×D8—21no—
129C13×D8—21no—
130C2×C8×C13—21no—
131C2×C8×C13—21no—
132C2×C8×C13—21no—
133C2×C8×C13—21no—
134C2×C8×C13C2×D411yescharacteristic
135C2×C8×C13C2×D411yescharacteristic
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13C2411yescharacteristic
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
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⋊C4—41no—
153C13×C4⋊C4D811yescharacteristic
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4D811yescharacteristic
161C13×C22⋊C4D811yescharacteristic
162C42×C13—41no—
163C42×C13—41no—
164C42×C13C2×D411yescharacteristic
165C13×C16—21no—
166C13×C16—21no—
167C13×C16—21no—
168C13×C16#4112yes—
169#3339C2×C1311yescharacteristic
170#3338C2×C1311yescharacteristic, complemented
171#2255C2×C1311yescharacteristic, complemented
172#2237C2×C1311yescharacteristic, complemented
173#2236C2×C1311yescharacteristic, complemented
174#2233C2×C1311yescharacteristic, complemented
175#2232C2×C1311yescharacteristic, complemented
176#2229C2×C1311yescharacteristic, complemented
177#2224C2×C1311yescharacteristic, complemented
178#2220C2×C1311yescharacteristic, complemented
179#2217C2×C1311yescharacteristic, complemented
180#2175C2×C1311yescharacteristic, complemented
181#2168C2×C1311yescharacteristic, complemented
182#2159C2×C1311yescharacteristic, complemented
183C2×#366C2×C1311yescharacteristic, complemented
184C23×C13—41no—
185C23×C13C2×D811yescharacteristic
186C23×C13C2×D811yescharacteristic
187Q8×C13—41no—
188Q8×C13—41no—
189Q8×C13—161no—
190D4×C13—22no—
191D4×C13—41no—
192D4×C13—41no—
193D4×C13—82no—
194D4×C13—161no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—161no—
207C2×C4×C13—161no—
208C2×C4×C13—161no—
209C2×C4×C13—161no—
210C2×C4×C13C2×D811yescharacteristic
211C2×C4×C13C2×D811yescharacteristic
212C2×C4×C13C2×D811yescharacteristic
213C2×C4×C13C2×D811yescharacteristic
214C2×C4×C13C22×D411yescharacteristic
215C8×C13—21no—
216C8×C13—21no—
217C8×C13—21no—
218C8×C13C2×#4111yescharacteristic
219C8×C132−1+411yescharacteristic
220#554—21no—
221#553—21no—
222C2×SD32C22×C1311yescharacteristic
223C2×M32C22×C1311yescharacteristic
224C22×C16C22×C1311yescharacteristic
225#500C22×C1311yescharacteristic
226#499C22×C1311yescharacteristic
227#484—21no—
228#484—21no—
229#482—21no—
230#481—21no—
231#478—21no—
232#477—21no—
233#467C22×C1311yescharacteristic
234#467C22×C1311yescharacteristic
235#466C22×C1311yescharacteristic
236#466C22×C1311yescharacteristic
237C4×Q16C22×C1311yescharacteristic
238C4×D8C22×C1311yescharacteristic
239C8×D4C22×C1311yescharacteristic
240#427C22×C1311yescharacteristic
241C2×#107C22×C1311yescharacteristic
242C2×#107C22×C1311yescharacteristic
243C2×#107C22×C1311yescharacteristic
244#367C22×C1311yescharacteristic
245#367C22×C1311yescharacteristic
246#367C22×C1311yescharacteristic
247#366C22×C1311yescharacteristic
248#366C22×C1311yescharacteristic
249#366C22×C1311yescharacteristic
250#366C22×C1311yescharacteristic
251#366C22×C1311yescharacteristic
252#366C22×C1311yescharacteristic
253C4⋊C16C22×C1311yescharacteristic
254#358C22×C1311yescharacteristic
255#358C22×C1311yescharacteristic
256#358C22×C1311yescharacteristic
257#357C22×C1311yescharacteristic
258#357C22×C1311yescharacteristic
259#357C22×C1311yescharacteristic
260C22⋊C16C22×C1311yescharacteristic
261C22⋊C16C22×C1311yescharacteristic
262#346C22×C1311yescharacteristic
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13#51012yes—
272C22×C13C22×D811yescharacteristic
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—21no—
277C4×C13—81no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13—81no—
281C4×C13—81no—
282C4×C13—81no—
283C4×C13—81no—
284C4×C13#54711yescharacteristic
285C4×C13#57811yescharacteristic
286C2×Q16C23×C1311yescharacteristic
287C2×D8C23×C1311yescharacteristic
288C22×C8C23×C1311yescharacteristic
289C22×C8C23×C1311yescharacteristic
290C4⋊Q8—21no—
291#126—41no—
292#125—21no—
293#125—41no—
294#123—41no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—41no—
298C22⋊Q8—41no—
299#121—21no—
300#121—21no—
301#121—41no—
302C4×Q8—21no—
303C4×D4—21no—
304C4×D4—41no—
305C4×D4—41no—
306C4×D4D4×C1311yescharacteristic
307#117—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311SD32—22no—
312M32—22no—
313C2×C16—22no—
314C2×C16C23×C1311yescharacteristic
315C2×C16C23×C1311yescharacteristic
316C2×C16C23×C1311yescharacteristic
317C2×C16C23×C1311yescharacteristic
318#107—21no—
319#107—21no—
320#107—21no—
321#107—21no—
322#107C23×C1311yescharacteristic
323#107C23×C1311yescharacteristic
324#107C23×C1311yescharacteristic
325#107C23×C1311yescharacteristic
326#107C23×C1311yescharacteristic
327#107C23×C1311yescharacteristic
328#106—21no—
329#106—21no—
330C4⋊C8D4×C1311yescharacteristic
331#103—21no—
332#103—21no—
333#103—21no—
334#102—21no—
335#102—21no—
336#102—21no—
337C22⋊C8D4×C1311yescharacteristic
338C22⋊C8D4×C1311yescharacteristic
339C4×C8C23×C1311yescharacteristic
340C2×C13—22no—
341C2×C13—41no—
342C2×C13—161no—
343C2×C13#333411yescharacteristic
344C2×C13C2×#51011yescharacteristic
345C2×C13#341511yescharacteristic
346C2×Q8—21no—
347C2×Q8—41no—
348C2×D4—21no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4C13×D811yescharacteristic
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4C2×D4×C1311yescharacteristic
357C22×C4C2×D4×C1311yescharacteristic
358Q16—21no—
359Q16—21no—
360D8—21no—
361D8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8C2×D4×C1311yescharacteristic
367C2×C8C2×D4×C1311yescharacteristic
368C2×C8C2×D4×C1311yescharacteristic
369C2×C8C24×C1311yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4C13×D811yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4C13×D811yescharacteristic
393C22⋊C4C13×D811yescharacteristic
394C42—41no—
395C42—41no—
396C42C2×D4×C1311yescharacteristic
397C16—21no—
398C16—21no—
399C16—21no—
400C16C13×#4112yes—
401C13#3391311yescharacteristic, direct product factor, Sylow
402C23—41no—
403C23C2×C13×D811yescharacteristic
404C23C2×C13×D811yescharacteristic
405Q8—41no—
406Q8—41no—
407Q8—161no—
408D4—22no—
409D4—41no—
410D4—41no—
411D4—82no—
412D4—161no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—161no—
425C2×C4—161no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4C2×C13×D811yescharacteristic
429C2×C4C2×C13×D811yescharacteristic
430C2×C4C2×C13×D811yescharacteristic
431C2×C4C2×C13×D811yescharacteristic
432C2×C4C22×D4×C1311yescharacteristic
433C8—21no—
434C8—21no—
435C8—21no—
436C8C2×C13×#4111yescharacteristic
437C8C13×2−1+411yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22C13×#51012yes—
447C22C22×C13×D811yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4C13×#54711yescharacteristic
460C4C13×#57811yescharacteristic
461C2—22no—
462C2—41no—
463C2—161no—
464C2C13×#333411yescharacteristic
465C2C2×C13×#51011yescharacteristic
466C2C13×#341511yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#3339C2
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
2. C13×#3338C2semidirect
3. C13×#2255C2semidirect
4. C13×#2237C2semidirect
5. C13×#2236C2semidirect
6. C13×#2233C2semidirect
7. C13×#2232C2semidirect
8. C13×#2229C2semidirect
9. C13×#2224C2semidirect
10. C13×#2220C2semidirect
11. C13×#2217C2semidirect
12. C13×#2175C2semidirect
13. C13×#2168C2semidirect
14. C13×#2159C2semidirect
15. C2×C13×#366C2semidirect
113. #33913C13direct (N × H)
170. #3338C2×C13semidirect
171. #2255C2×C13semidirect
172. #2237C2×C13semidirect
173. #2236C2×C13semidirect
174. #2233C2×C13semidirect
175. #2232C2×C13semidirect
176. #2229C2×C13semidirect
177. #2224C2×C13semidirect
178. #2220C2×C13semidirect
179. #2217C2×C13semidirect
180. #2175C2×C13semidirect
181. #2168C2×C13semidirect
182. #2159C2×C13semidirect
183. C2×#366C2×C13semidirect
401. C13#33913direct (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×#33382
C13×#22552
C13×#22372
C13×#22362
C13×#22332
C13×#22322
C13×#22292
C13×#22242
C13×#22202
C13×#22172
C13×#21752
C13×#21682
C13×#21592
C2×C13×#3662
#3391313