Finite Group Databasebeta

← C13×#33681 #15720020

Subgroups — C13×#33681 #15720020

Order 3328.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3175C211yesmaximal, characteristic
2C13×#2950C211yesmaximal, characteristic, complemented
3C13×#2237C211yesmaximal, characteristic, complemented
4C13×#2234C211yesmaximal, characteristic
5C13×#2227C211yesmaximal, characteristic, complemented
6C13×#2225C211yesmaximal, characteristic, complemented
7C13×#2211C211yesmaximal, characteristic, complemented
8C13×#2211C211yesmaximal, characteristic, complemented
9C13×#2188C211yesmaximal, characteristic, complemented
10C13×#2185C211yesmaximal, characteristic
11C13×#2176C211yesmaximal, characteristic, complemented
12C13×#2175C211yesmaximal, characteristic, complemented
13C4×C13×Q32C211yesmaximal, characteristic, complemented
14C4×C13×SD32C211yesmaximal, characteristic, complemented
15C13×#2164C211yesmaximal, characteristic, complemented
16C22×C13×Q16C2211yescharacteristic
17C13×#542—21no—
18C13×#519—21no—
19C2×C13×Q32C2211yescharacteristic
20C2×C13×Q32C2211yescharacteristic
21C2×C13×SD32C2211yescharacteristic
22C2×C13×SD32C2211yescharacteristic
23C13×#500C2211yescharacteristic
24C13×#495C2211yescharacteristic
25C13×#489—21no—
26C13×#468—21no—
27C13×#467C2211yescharacteristic
28C13×#466C2211yescharacteristic
29C13×#441—21no—
30C13×#441—21no—
31C13×#440—21no—
32C4×C13×Q16C2211yescharacteristic
33C4×C13×Q16C2211yescharacteristic
34C4×C13×Q16C2211yescharacteristic
35C4×C13×Q16C2211yescharacteristic
36C4×C13×Q16C2211yescharacteristic
37C4×C13×D8C2211yescharacteristic
38C13×#427C2211yescharacteristic
39C13×#419—21no—
40C13×#405C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×C4⋊C16C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×C22⋊C16C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C4×C13×C16C2211yescharacteristic
59C22×Q8×C13—21no—
60C2×C13×Q16—22no—
61C2×C13×Q16—22no—
62C2×C13×Q16—21no—
63C2×C13×Q16C2311yescharacteristic
64C2×C13×Q16C2311yescharacteristic
65C2×C13×Q16C2311yescharacteristic
66C2×C13×SD16—21no—
67C2×C13×D8C2311yescharacteristic
68C2×C13×M16D411yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C13×C4⋊Q8—21no—
71C13×#126—41no—
72C13×#124—21no—
73C13×#124—41no—
74C13×#123—41no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8—41no—
77C13×#121—21no—
78C4×Q8×C13—21no—
79C4×Q8×C13—21no—
80C4×Q8×C13—21no—
81C4×Q8×C13—21no—
82C4×Q8×C13—21no—
83C4×Q8×C13—41no—
84C4×Q8×C13—41no—
85C4×D4×C13—21no—
86C13×#117—21no—
87C13×#117—41no—
88C13×#117—41no—
89C13×#117D411yescharacteristic
90C13×Q32—22no—
91C13×Q32—22no—
92C13×SD32—22no—
93C13×SD32—22no—
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#33681C1311yesmaximal, characteristic, direct product factor, Sylow
117C2×Q8×C13—24no—
118C2×Q8×C13—21no—
119C2×Q8×C13—21no—
120C2×Q8×C13—21no—
121C2×Q8×C13—42no—
122C2×Q8×C13—41no—
123C2×Q8×C13—41no—
124C2×D4×C13—21no—
125C2×D4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13C2×D411yescharacteristic
129C13×Q16—24no—
130C13×Q16—21no—
131C13×Q16—21no—
132C13×Q16—21no—
133C13×Q16—21no—
134C13×Q16#4112yes—
135C13×Q16#4112yes—
136C13×SD16—42no—
137C13×D8—21no—
138C13×D8—21no—
139C13×M16—41no—
140C2×C8×C13—21no—
141C2×C8×C13—21no—
142C2×C8×C13C2×D411yescharacteristic
143C2×C8×C13C2×D411yescharacteristic
144C2×C8×C13C2×D411yescharacteristic
145C2×C8×C13C2411yescharacteristic
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
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⋊C4D811yescharacteristic
166C13×C22⋊C4D811yescharacteristic
167C42×C13—41no—
168C42×C13—41no—
169C42×C13—41no—
170C42×C13—41no—
171C42×C13—41no—
172C42×C13—41no—
173C42×C13C2×D411yescharacteristic
174C42×C13C2×D411yescharacteristic
175C13×C16—21no—
176C13×C16—21no—
177C13×C16—21no—
178C13×C16—21no—
179#3175C2×C1311yescharacteristic
180#2950C2×C1311yescharacteristic, complemented
181#2237C2×C1311yescharacteristic, complemented
182#2234C2×C1311yescharacteristic
183#2227C2×C1311yescharacteristic, complemented
184#2225C2×C1311yescharacteristic, complemented
185#2211C2×C1311yescharacteristic, complemented
186#2211C2×C1311yescharacteristic, complemented
187#2188C2×C1311yescharacteristic, complemented
188#2185C2×C1311yescharacteristic
189#2176C2×C1311yescharacteristic, complemented
190#2175C2×C1311yescharacteristic, complemented
191C4×Q32C2×C1311yescharacteristic, complemented
192C4×SD32C2×C1311yescharacteristic, complemented
193#2164C2×C1311yescharacteristic, complemented
194C23×C13—41no—
195C23×C13C2×D811yescharacteristic
196Q8×C13—22no—
197Q8×C13—22no—
198Q8×C13—44no—
199Q8×C13—41no—
200Q8×C13—41no—
201Q8×C13—41no—
202Q8×C13—41no—
203Q8×C13—161no—
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—161no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—44no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—161no—
218C2×C4×C13C2×D811yescharacteristic
219C2×C4×C13C2×D811yescharacteristic
220C2×C4×C13C2×D811yescharacteristic
221C2×C4×C13C2×D811yescharacteristic
222C2×C4×C13C2×D811yescharacteristic
223C2×C4×C13C22×D411yescharacteristic
224C8×C13—21no—
225C8×C13—21no—
226C8×C13—21no—
227C8×C13C2×#4111yescharacteristic
228C8×C13C2×#4111yescharacteristic
229C22×Q16C22×C1311yescharacteristic
230#542—21no—
231#519—21no—
232C2×Q32C22×C1311yescharacteristic
233C2×Q32C22×C1311yescharacteristic
234C2×SD32C22×C1311yescharacteristic
235C2×SD32C22×C1311yescharacteristic
236#500C22×C1311yescharacteristic
237#495C22×C1311yescharacteristic
238#489—21no—
239#468—21no—
240#467C22×C1311yescharacteristic
241#466C22×C1311yescharacteristic
242#441—21no—
243#441—21no—
244#440—21no—
245C4×Q16C22×C1311yescharacteristic
246C4×Q16C22×C1311yescharacteristic
247C4×Q16C22×C1311yescharacteristic
248C4×Q16C22×C1311yescharacteristic
249C4×Q16C22×C1311yescharacteristic
250C4×D8C22×C1311yescharacteristic
251#427C22×C1311yescharacteristic
252#419—21no—
253#405C22×C1311yescharacteristic
254#367C22×C1311yescharacteristic
255#367C22×C1311yescharacteristic
256#366C22×C1311yescharacteristic
257#366C22×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⋊C16C22×C1311yescharacteristic
269C22⋊C16C22×C1311yescharacteristic
270#346C22×C1311yescharacteristic
271C4×C16C22×C1311yescharacteristic
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—81no—
276C22×C13—81no—
277C22×C13—81no—
278C22×C13C22×D811yescharacteristic
279C4×C13—21no—
280C4×C13—21no—
281C4×C13—21no—
282C4×C13—21no—
283C4×C13—21no—
284C4×C13—42no—
285C4×C13—42no—
286C4×C13—81no—
287C4×C13—81no—
288C4×C13—81no—
289C4×C13—81no—
290C4×C13—81no—
291C4×C13#52511yescharacteristic
292C4×C13#57511yescharacteristic
293C22×Q8—21no—
294C2×Q16—22no—
295C2×Q16—22no—
296C2×Q16—21no—
297C2×Q16C23×C1311yescharacteristic
298C2×Q16C23×C1311yescharacteristic
299C2×Q16C23×C1311yescharacteristic
300C2×SD16—21no—
301C2×D8C23×C1311yescharacteristic
302C2×M16D4×C1311yescharacteristic
303C22×C8C23×C1311yescharacteristic
304C4⋊Q8—21no—
305#126—41no—
306#124—21no—
307#124—41no—
308#123—41no—
309C22⋊Q8—21no—
310C22⋊Q8—41no—
311#121—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—41no—
318C4×Q8—41no—
319C4×D4—21no—
320#117—21no—
321#117—41no—
322#117—41no—
323#117D4×C1311yescharacteristic
324Q32—22no—
325Q32—22no—
326SD32—22no—
327SD32—22no—
328C2×C16C23×C1311yescharacteristic
329C2×C16C23×C1311yescharacteristic
330C2×C16C23×C1311yescharacteristic
331C2×C16C23×C1311yescharacteristic
332#107—21no—
333#107C23×C1311yescharacteristic
334#107C23×C1311yescharacteristic
335#107C23×C1311yescharacteristic
336#107C23×C1311yescharacteristic
337#106—21no—
338#103—21no—
339#103—21no—
340#103—21no—
341#103—21no—
342#103—21no—
343#103—21no—
344#102—21no—
345#102—21no—
346#97D4×C1311yescharacteristic
347#97D4×C1311yescharacteristic
348C4×C8C23×C1311yescharacteristic
349C4×C8C23×C1311yescharacteristic
350C2×C13—41no—
351C2×C13—161no—
352C2×C13#310011yescharacteristic
353C2×C13#341611yescharacteristic
354C2×C13#341711yescharacteristic
355C2×Q8—24no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—42no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×D4—21no—
363C2×D4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4C2×D4×C1311yescharacteristic
367Q16—24no—
368Q16—21no—
369Q16—21no—
370Q16—21no—
371Q16—21no—
372Q16C13×#4112yes—
373Q16C13×#4112yes—
374SD16—42no—
375D8—21no—
376D8—21no—
377M16—41no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8C2×D4×C1311yescharacteristic
381C2×C8C2×D4×C1311yescharacteristic
382C2×C8C2×D4×C1311yescharacteristic
383C2×C8C24×C1311yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4C13×D811yescharacteristic
396C4⋊C4C13×D811yescharacteristic
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4C13×D811yescharacteristic
404C22⋊C4C13×D811yescharacteristic
405C42—41no—
406C42—41no—
407C42—41no—
408C42—41no—
409C42—41no—
410C42—41no—
411C42C2×D4×C1311yescharacteristic
412C42C2×D4×C1311yescharacteristic
413C16—21no—
414C16—21no—
415C16—21no—
416C16—21no—
417C13#3368111yescharacteristic, direct product factor, Sylow
418C23—41no—
419C23C2×C13×D811yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—44no—
423Q8—41no—
424Q8—41no—
425Q8—41no—
426Q8—41no—
427Q8—161no—
428D4—41no—
429D4—41no—
430D4—161no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—161no—
442C2×C4C2×C13×D811yescharacteristic
443C2×C4C2×C13×D811yescharacteristic
444C2×C4C2×C13×D811yescharacteristic
445C2×C4C2×C13×D811yescharacteristic
446C2×C4C2×C13×D811yescharacteristic
447C2×C4C22×D4×C1311yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8C2×C13×#4111yescharacteristic
452C8C2×C13×#4111yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22C22×C13×D811yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4C13×#52511yescharacteristic
473C4C13×#57511yescharacteristic
474C2—41no—
475C2—161no—
476C2C13×#310011yescharacteristic
477C2C13×#341611yescharacteristic
478C2C13×#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
2. C13×#2950C2semidirect
3. C13×#2237C2semidirect
5. C13×#2227C2semidirect
6. C13×#2225C2semidirect
7. C13×#2211C2semidirect
8. C13×#2211C2semidirect
9. C13×#2188C2semidirect
11. C13×#2176C2semidirect
12. C13×#2175C2semidirect
13. C4×C13×Q32C2semidirect
14. C4×C13×SD32C2semidirect
15. C13×#2164C2semidirect
116. #33681C13direct (N × H)
180. #2950C2×C13semidirect
181. #2237C2×C13semidirect
183. #2227C2×C13semidirect
184. #2225C2×C13semidirect
185. #2211C2×C13semidirect
186. #2211C2×C13semidirect
187. #2188C2×C13semidirect
189. #2176C2×C13semidirect
190. #2175C2×C13semidirect
191. C4×Q32C2×C13semidirect
192. C4×SD32C2×C13semidirect
193. #2164C2×C13semidirect
417. C13#33681direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31752
C13×#29502
C13×#22372
C13×#22342
C13×#22272
C13×#22252
C13×#22112
C13×#21882
C13×#21852
C13×#21762
C13×#21752
C4×C13×Q322
C4×C13×SD322
C13×#21642
#3368113