Finite Group Databasebeta

← C13×#33824 #15720163

Subgroups — C13×#33824 #15720163

Order 3328.

476 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3177C211yesmaximal, characteristic, complemented
2C13×#3175C211yesmaximal, characteristic
3C13×#2229C211yesmaximal, characteristic, complemented
4C13×#2228C211yesmaximal, characteristic, complemented
5C13×#2227C211yesmaximal, characteristic, complemented
6C13×#2225C211yesmaximal, characteristic, complemented
7C13×#2220C211yesmaximal, characteristic
8C13×#2219C211yesmaximal, characteristic, complemented
9C13×#2217C211yesmaximal, characteristic
10C13×#2216C211yesmaximal, characteristic, complemented
11C13×#2211C211yesmaximal, characteristic, complemented
12C13×#2211C211yesmaximal, characteristic, complemented
13C13×#2209C211yesmaximal, characteristic, complemented
14C13×#2208C211yesmaximal, characteristic, complemented
15C13×#2151C211yesmaximal, characteristic, complemented
16C13×#542—21no—
17C13×#541—21no—
18C2×C13×Q32C2211yescharacteristic
19C2×C13×Q32C2211yescharacteristic
20C2×C13×SD32C2211yescharacteristic
21C2×C13×SD32C2211yescharacteristic
22C2×C13×M32C2211yescharacteristic
23C22×C13×C16C2211yescharacteristic
24C13×#500C2211yescharacteristic
25C13×#499C2211yescharacteristic
26C13×#495C2211yescharacteristic
27C13×#494C2211yescharacteristic
28C13×#491—21no—
29C13×#489—21no—
30C13×#470—21no—
31C13×#468—21no—
32C13×#467C2211yescharacteristic
33C13×#467C2211yescharacteristic
34C13×#467C2211yescharacteristic
35C13×#466C2211yescharacteristic
36C13×#441—21no—
37C13×#440—21no—
38C4×C13×Q16C2211yescharacteristic
39C4×C13×Q16C2211yescharacteristic
40C4×C13×Q16C2211yescharacteristic
41C4×C13×D8C2211yescharacteristic
42C13×#405C2211yescharacteristic
43C13×#367C2211yescharacteristic
44C13×#367C2211yescharacteristic
45C13×#366C2211yescharacteristic
46C13×#366C2211yescharacteristic
47C13×C4⋊C16C2211yescharacteristic
48C13×C4⋊C16C2211yescharacteristic
49C13×C4⋊C16C2211yescharacteristic
50C13×C4⋊C16C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#358C2211yescharacteristic
54C13×#358C2211yescharacteristic
55C13×#358C2211yescharacteristic
56C13×#358C2211yescharacteristic
57C13×#357C2211yescharacteristic
58C13×#357C2211yescharacteristic
59C2×C13×Q16—21no—
60C2×C13×Q16C2311yescharacteristic
61C2×C13×Q16C2311yescharacteristic
62C2×C13×Q16C2311yescharacteristic
63C2×C13×SD16—21no—
64C2×C13×D8C2311yescharacteristic
65C2×C13×M16D411yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—21no—
69C13×#126—41no—
70C13×#126—41no—
71C13×#126—41no—
72C13×#125—21no—
73C13×#125—41no—
74C13×#125—41no—
75C13×#124—21no—
76C13×#124—41no—
77C13×#123—41no—
78C13×C22⋊Q8—21no—
79C13×C22⋊Q8—21no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—41no—
82C13×#121—21no—
83C4×Q8×C13—21no—
84C4×Q8×C13—21no—
85C4×Q8×C13—21no—
86C4×D4×C13—21no—
87C13×#117D411yescharacteristic
88C13×Q32—41no—
89C13×Q32—41no—
90C13×SD32—41no—
91C13×SD32—41no—
92C13×M32—41no—
93C2×C13×C16—41no—
94C2×C13×C16C2311yescharacteristic
95C2×C13×C16C2311yescharacteristic
96C2×C13×C16C2311yescharacteristic
97C2×C13×C16C2311yescharacteristic
98C13×#107—21no—
99C13×#107C2311yescharacteristic
100C13×#107C2311yescharacteristic
101C13×#107C2311yescharacteristic
102C13×#107C2311yescharacteristic
103C13×#106—21no—
104C13×#103—21no—
105C13×#103—21no—
106C13×#103—21no—
107C13×#103—21no—
108C13×#103—21no—
109C13×#103—21no—
110C13×#102—21no—
111C13×#102—21no—
112C13×#97D411yescharacteristic
113C13×#97D411yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116#33824C1311yesmaximal, characteristic, direct product factor, Sylow
117C2×Q8×C13—21no—
118C2×Q8×C13—21no—
119C2×Q8×C13—21no—
120C2×Q8×C13—41no—
121C2×D4×C13—21no—
122C2×D4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13C2×D411yescharacteristic
125C13×Q16—21no—
126C13×Q16—21no—
127C13×Q16—21no—
128C13×Q16—21no—
129C13×Q16—21no—
130C13×Q16—21no—
131C13×Q16—42no—
132C13×SD16—42no—
133C13×D8—21no—
134C13×D8—21no—
135C13×M16—41no—
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—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⋊C4—41no—
154C13×C4⋊C4—41no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4D811yescharacteristic
158C13×C4⋊C4D811yescharacteristic
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4—41no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4D811yescharacteristic
167C13×C22⋊C4D811yescharacteristic
168C42×C13—41no—
169C42×C13—41no—
170C42×C13—41no—
171C42×C13C2×D411yescharacteristic
172C42×C13C2×D411yescharacteristic
173C13×C16—21no—
174C13×C16—21no—
175C13×C16—21no—
176C13×C16—21no—
177#3177C2×C1311yescharacteristic, complemented
178#3175C2×C1311yescharacteristic
179#2229C2×C1311yescharacteristic, complemented
180#2228C2×C1311yescharacteristic, complemented
181#2227C2×C1311yescharacteristic, complemented
182#2225C2×C1311yescharacteristic, complemented
183#2220C2×C1311yescharacteristic
184#2219C2×C1311yescharacteristic, complemented
185#2217C2×C1311yescharacteristic
186#2216C2×C1311yescharacteristic, complemented
187#2211C2×C1311yescharacteristic, complemented
188#2211C2×C1311yescharacteristic, complemented
189#2209C2×C1311yescharacteristic, complemented
190#2208C2×C1311yescharacteristic, complemented
191#2151C2×C1311yescharacteristic, complemented
192C23×C13—41no—
193C23×C13C2×D811yescharacteristic
194Q8×C13—41no—
195Q8×C13—41no—
196Q8×C13—41no—
197Q8×C13—41no—
198Q8×C13—41no—
199Q8×C13—41no—
200Q8×C13—161no—
201D4×C13—41no—
202D4×C13—41no—
203D4×C13—161no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—161no—
214C2×C4×C13C2×D811yescharacteristic
215C2×C4×C13C2×D811yescharacteristic
216C2×C4×C13C2×D811yescharacteristic
217C2×C4×C13C2×D811yescharacteristic
218C2×C4×C13C2×D811yescharacteristic
219C2×C4×C13C22×D411yescharacteristic
220C8×C13—21no—
221C8×C13—21no—
222C8×C13—21no—
223C8×C13H(5,𝔽2)11yescharacteristic
224C8×C132−1+411yescharacteristic
225#542—21no—
226#541—21no—
227C2×Q32C22×C1311yescharacteristic
228C2×Q32C22×C1311yescharacteristic
229C2×SD32C22×C1311yescharacteristic
230C2×SD32C22×C1311yescharacteristic
231C2×M32C22×C1311yescharacteristic
232C22×C16C22×C1311yescharacteristic
233#500C22×C1311yescharacteristic
234#499C22×C1311yescharacteristic
235#495C22×C1311yescharacteristic
236#494C22×C1311yescharacteristic
237#491—21no—
238#489—21no—
239#470—21no—
240#468—21no—
241#467C22×C1311yescharacteristic
242#467C22×C1311yescharacteristic
243#467C22×C1311yescharacteristic
244#466C22×C1311yescharacteristic
245#441—21no—
246#440—21no—
247C4×Q16C22×C1311yescharacteristic
248C4×Q16C22×C1311yescharacteristic
249C4×Q16C22×C1311yescharacteristic
250C4×D8C22×C1311yescharacteristic
251#405C22×C1311yescharacteristic
252#367C22×C1311yescharacteristic
253#367C22×C1311yescharacteristic
254#366C22×C1311yescharacteristic
255#366C22×C1311yescharacteristic
256C4⋊C16C22×C1311yescharacteristic
257C4⋊C16C22×C1311yescharacteristic
258C4⋊C16C22×C1311yescharacteristic
259C4⋊C16C22×C1311yescharacteristic
260#358C22×C1311yescharacteristic
261#358C22×C1311yescharacteristic
262#358C22×C1311yescharacteristic
263#358C22×C1311yescharacteristic
264#358C22×C1311yescharacteristic
265#358C22×C1311yescharacteristic
266#357C22×C1311yescharacteristic
267#357C22×C1311yescharacteristic
268C22×C13—21no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—81no—
272C22×C13—81no—
273C22×C13—81no—
274C22×C13C22×D811yescharacteristic
275C4×C13—21no—
276C4×C13—21no—
277C4×C13—21no—
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—81no—
281C4×C13—81no—
282C4×C13—81no—
283C4×C13—81no—
284C4×C13—81no—
285C4×C13—81no—
286C4×C13—81no—
287C4×C13#53711yescharacteristic
288C4×C13#57511yescharacteristic
289C2×Q16—21no—
290C2×Q16C23×C1311yescharacteristic
291C2×Q16C23×C1311yescharacteristic
292C2×Q16C23×C1311yescharacteristic
293C2×SD16—21no—
294C2×D8C23×C1311yescharacteristic
295C2×M16D4×C1311yescharacteristic
296C22×C8C23×C1311yescharacteristic
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299#126—41no—
300#126—41no—
301#126—41no—
302#125—21no—
303#125—41no—
304#125—41no—
305#124—21no—
306#124—41no—
307#123—41no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—41no—
312#121—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×D4—21no—
317#117D4×C1311yescharacteristic
318Q32—41no—
319Q32—41no—
320SD32—41no—
321SD32—41no—
322M32—41no—
323C2×C16—41no—
324C2×C16C23×C1311yescharacteristic
325C2×C16C23×C1311yescharacteristic
326C2×C16C23×C1311yescharacteristic
327C2×C16C23×C1311yescharacteristic
328#107—21no—
329#107C23×C1311yescharacteristic
330#107C23×C1311yescharacteristic
331#107C23×C1311yescharacteristic
332#107C23×C1311yescharacteristic
333#106—21no—
334#103—21no—
335#103—21no—
336#103—21no—
337#103—21no—
338#103—21no—
339#103—21no—
340#102—21no—
341#102—21no—
342#97D4×C1311yescharacteristic
343#97D4×C1311yescharacteristic
344C4×C8C23×C1311yescharacteristic
345C4×C8C23×C1311yescharacteristic
346C2×C13—41no—
347C2×C13—161no—
348C2×C13#324511yescharacteristic
349C2×C13#341611yescharacteristic
350C2×C13#341711yescharacteristic
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—41no—
355C2×D4—21no—
356C2×D4—41no—
357C22×C4—41no—
358C22×C4C2×D4×C1311yescharacteristic
359Q16—21no—
360Q16—21no—
361Q16—21no—
362Q16—21no—
363Q16—21no—
364Q16—21no—
365Q16—42no—
366SD16—42no—
367D8—21no—
368D8—21no—
369M16—41no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×D4×C1311yescharacteristic
373C2×C8C2×D4×C1311yescharacteristic
374C2×C8C2×D4×C1311yescharacteristic
375C2×C8C24×C1311yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C13×D811yescharacteristic
392C4⋊C4C13×D811yescharacteristic
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4C13×D811yescharacteristic
401C22⋊C4C13×D811yescharacteristic
402C42—41no—
403C42—41no—
404C42—41no—
405C42C2×D4×C1311yescharacteristic
406C42C2×D4×C1311yescharacteristic
407C16—21no—
408C16—21no—
409C16—21no—
410C16—21no—
411C13#3382411yescharacteristic, direct product factor, Sylow
412C23—41no—
413C23C2×C13×D811yescharacteristic
414Q8—41no—
415Q8—41no—
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—161no—
421D4—41no—
422D4—41no—
423D4—161no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—161no—
434C2×C4C2×C13×D811yescharacteristic
435C2×C4C2×C13×D811yescharacteristic
436C2×C4C2×C13×D811yescharacteristic
437C2×C4C2×C13×D811yescharacteristic
438C2×C4C2×C13×D811yescharacteristic
439C2×C4C22×D4×C1311yescharacteristic
440C8—21no—
441C8—21no—
442C8—21no—
443C8C13×H(5,𝔽2)11yescharacteristic
444C8C13×2−1+411yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22C22×C13×D811yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4C13×#53711yescharacteristic
465C4C13×#57511yescharacteristic
466C2—41no—
467C2—161no—
468C2C13×#324511yescharacteristic
469C2C13×#341611yescharacteristic
470C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3177C2semidirect
3. C13×#2229C2semidirect
4. C13×#2228C2semidirect
5. C13×#2227C2semidirect
6. C13×#2225C2semidirect
8. C13×#2219C2semidirect
10. C13×#2216C2semidirect
11. C13×#2211C2semidirect
12. C13×#2211C2semidirect
13. C13×#2209C2semidirect
14. C13×#2208C2semidirect
15. C13×#2151C2semidirect
116. #33824C13direct (N × H)
177. #3177C2×C13semidirect
179. #2229C2×C13semidirect
180. #2228C2×C13semidirect
181. #2227C2×C13semidirect
182. #2225C2×C13semidirect
184. #2219C2×C13semidirect
186. #2216C2×C13semidirect
187. #2211C2×C13semidirect
188. #2211C2×C13semidirect
189. #2209C2×C13semidirect
190. #2208C2×C13semidirect
191. #2151C2×C13semidirect
411. C13#33824direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31772
C13×#31752
C13×#22292
C13×#22282
C13×#22272
C13×#22252
C13×#22202
C13×#22192
C13×#22172
C13×#22162
C13×#22112
C13×#22092
C13×#22082
C13×#21512
#3382413