Finite Group Databasebeta

← C13×#33904 #15720243

Subgroups — C13×#33904 #15720243

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3339C211yesmaximal, characteristic
2C13×#3336C211yesmaximal, characteristic, complemented
3C13×#2253C211yesmaximal, characteristic, complemented
4C13×#2237C211yesmaximal, characteristic, complemented
5C13×#2236C211yesmaximal, characteristic, complemented
6C13×#2234C211yesmaximal, characteristic, complemented
7C13×#2232C211yesmaximal, characteristic, complemented
8C13×#2229C211yesmaximal, characteristic, complemented
9C13×#2228C211yesmaximal, characteristic, complemented
10C13×#2217C211yesmaximal, characteristic, complemented
11C13×#2217C211yesmaximal, characteristic, complemented
12C4×C13×SD32C211yesmaximal, characteristic, complemented
13D4×C13×C16C211yesmaximal, characteristic, complemented
14C13×#2158C211yesmaximal, characteristic, complemented
15C2×C13×#367C211yesmaximal, characteristic, complemented
16C13×#553—21no—
17C13×#552—21no—
18C2×C13×SD32C2211yescharacteristic
19C22×C13×C16C2211yescharacteristic
20C22×C13×C16C2211yescharacteristic
21C13×#499C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#485—21no—
24C13×#483—21no—
25C13×#482—21no—
26C13×#481—21no—
27C13×#479—21no—
28C13×#478—21no—
29C13×#467C2211yescharacteristic
30C13×#467C2211yescharacteristic
31C13×#466C2211yescharacteristic
32C13×#466C2211yescharacteristic
33C4×C13×Q16C2211yescharacteristic
34C4×C13×D8C2211yescharacteristic
35C8×D4×C13C2211yescharacteristic
36C13×#427C2211yescharacteristic
37C13×#427C2211yescharacteristic
38C2×C13×#107C2211yescharacteristic
39C2×C13×#107C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#367C2211yescharacteristic
44C13×#367C2211yescharacteristic
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
58C4×C13×C16C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×D8C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C13×#126—41no—
64C13×#126—41no—
65C13×#125—21no—
66C13×#125—21no—
67C13×#125—41no—
68C13×#123—41no—
69C13×#123—41no—
70C13×C22⋊Q8—21no—
71C13×C22⋊Q8—21no—
72C13×#121—21no—
73C13×#121—21no—
74C13×#121—41no—
75C4×Q8×C13—21no—
76C4×D4×C13—21no—
77C4×D4×C13—41no—
78C4×D4×C13D411yescharacteristic
79C13×#117—21no—
80C13×#117—21no—
81C13×#117—41no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—21no—
84C13×SD32—22no—
85C2×C13×C16—22no—
86C2×C13×C16—22no—
87C2×C13×C16C2311yescharacteristic
88C2×C13×C16C2311yescharacteristic
89C2×C13×C16C2311yescharacteristic
90C2×C13×C16C2311yescharacteristic
91C13×#107—21no—
92C13×#107—21no—
93C13×#107C2311yescharacteristic
94C13×#107C2311yescharacteristic
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×#106—21no—
100C13×#106—21no—
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#33904C1311yesmaximal, characteristic, direct product factor, Sylow
114C2×Q8×C13—21no—
115C2×D4×C13—21no—
116C2×D4×C13—41no—
117C2×D4×C13—41no—
118C2×D4×C13D811yescharacteristic
119C22×C4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C13×Q16—21no—
125C13×Q16—21no—
126C13×D8—21no—
127C13×D8—21no—
128C2×C8×C13—21no—
129C2×C8×C13—21no—
130C2×C8×C13—21no—
131C2×C8×C13—21no—
132C2×C8×C13C2×D411yescharacteristic
133C2×C8×C13C2×D411yescharacteristic
134C2×C8×C13C2×D411yescharacteristic
135C2×C8×C13C2411yescharacteristic
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—41no—
143C13×C4⋊C4—41no—
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⋊C4D811yescharacteristic
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C13×C22⋊C4—41no—
159C13×C22⋊C4D811yescharacteristic
160C13×C22⋊C4D811yescharacteristic
161C42×C13—41no—
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#3336C2×C1311yescharacteristic, complemented
171#2253C2×C1311yescharacteristic, complemented
172#2237C2×C1311yescharacteristic, complemented
173#2236C2×C1311yescharacteristic, complemented
174#2234C2×C1311yescharacteristic, complemented
175#2232C2×C1311yescharacteristic, complemented
176#2229C2×C1311yescharacteristic, complemented
177#2228C2×C1311yescharacteristic, complemented
178#2217C2×C1311yescharacteristic, complemented
179#2217C2×C1311yescharacteristic, complemented
180C4×SD32C2×C1311yescharacteristic, complemented
181D4×C16C2×C1311yescharacteristic, complemented
182#2158C2×C1311yescharacteristic, complemented
183C2×#367C2×C1311yescharacteristic, complemented
184C23×C13—41no—
185C23×C13C2×D811yescharacteristic
186C23×C13C2×D811yescharacteristic
187Q8×C13—41no—
188Q8×C13—41no—
189D4×C13—22no—
190D4×C13—41no—
191D4×C13—41no—
192D4×C13—82no—
193D4×C13—161no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—41no—
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—82no—
206C2×C4×C13—161no—
207C2×C4×C13—161no—
208C2×C4×C13C2×D811yescharacteristic
209C2×C4×C13C2×D811yescharacteristic
210C2×C4×C13C2×D811yescharacteristic
211C2×C4×C13C2×D811yescharacteristic
212C2×C4×C13C22×D411yescharacteristic
213C8×C13—21no—
214C8×C13—21no—
215C8×C13—21no—
216C8×C13C2×#4111yescharacteristic
217C8×C132−1+411yescharacteristic
218#553—21no—
219#552—21no—
220C2×SD32C22×C1311yescharacteristic
221C22×C16C22×C1311yescharacteristic
222C22×C16C22×C1311yescharacteristic
223#499C22×C1311yescharacteristic
224#499C22×C1311yescharacteristic
225#485—21no—
226#483—21no—
227#482—21no—
228#481—21no—
229#479—21no—
230#478—21no—
231#467C22×C1311yescharacteristic
232#467C22×C1311yescharacteristic
233#466C22×C1311yescharacteristic
234#466C22×C1311yescharacteristic
235C4×Q16C22×C1311yescharacteristic
236C4×D8C22×C1311yescharacteristic
237C8×D4C22×C1311yescharacteristic
238#427C22×C1311yescharacteristic
239#427C22×C1311yescharacteristic
240C2×#107C22×C1311yescharacteristic
241C2×#107C22×C1311yescharacteristic
242#367C22×C1311yescharacteristic
243#367C22×C1311yescharacteristic
244#367C22×C1311yescharacteristic
245#367C22×C1311yescharacteristic
246#367C22×C1311yescharacteristic
247#366C22×C1311yescharacteristic
248#366C22×C1311yescharacteristic
249#366C22×C1311yescharacteristic
250#366C22×C1311yescharacteristic
251C4⋊C16C22×C1311yescharacteristic
252#358C22×C1311yescharacteristic
253#358C22×C1311yescharacteristic
254#358C22×C1311yescharacteristic
255#357C22×C1311yescharacteristic
256#357C22×C1311yescharacteristic
257#357C22×C1311yescharacteristic
258C22⋊C16C22×C1311yescharacteristic
259C22⋊C16C22×C1311yescharacteristic
260C4×C16C22×C1311yescharacteristic
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13—81no—
269C22×C13#50812yes—
270C22×C13C22×D811yescharacteristic
271C4×C13—21no—
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—81no—
276C4×C13—81no—
277C4×C13—81no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13—81no—
281C4×C13—81no—
282C4×C13#54711yescharacteristic
283C4×C13#57811yescharacteristic
284C2×Q16C23×C1311yescharacteristic
285C2×D8C23×C1311yescharacteristic
286C22×C8C23×C1311yescharacteristic
287C22×C8C23×C1311yescharacteristic
288#126—41no—
289#126—41no—
290#125—21no—
291#125—21no—
292#125—41no—
293#123—41no—
294#123—41no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297#121—21no—
298#121—21no—
299#121—41no—
300C4×Q8—21no—
301C4×D4—21no—
302C4×D4—41no—
303C4×D4D4×C1311yescharacteristic
304#117—21no—
305#117—21no—
306#117—41no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309SD32—22no—
310C2×C16—22no—
311C2×C16—22no—
312C2×C16C23×C1311yescharacteristic
313C2×C16C23×C1311yescharacteristic
314C2×C16C23×C1311yescharacteristic
315C2×C16C23×C1311yescharacteristic
316#107—21no—
317#107—21no—
318#107C23×C1311yescharacteristic
319#107C23×C1311yescharacteristic
320#107C23×C1311yescharacteristic
321#107C23×C1311yescharacteristic
322#107C23×C1311yescharacteristic
323#107C23×C1311yescharacteristic
324#106—21no—
325#106—21no—
326#106—21no—
327#106—21no—
328C4⋊C8D4×C1311yescharacteristic
329#103—21no—
330#103—21no—
331#103—21no—
332#102—21no—
333#102—21no—
334#102—21no—
335C22⋊C8D4×C1311yescharacteristic
336C22⋊C8D4×C1311yescharacteristic
337C4×C8C23×C1311yescharacteristic
338C2×C13—22no—
339C2×C13—41no—
340C2×C13—161no—
341C2×C13#333411yescharacteristic
342C2×C13C2×#50811yescharacteristic
343C2×C13#341611yescharacteristic
344C2×Q8—21no—
345C2×D4—21no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4C13×D811yescharacteristic
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4C2×D4×C1311yescharacteristic
353C22×C4C2×D4×C1311yescharacteristic
354Q16—21no—
355Q16—21no—
356D8—21no—
357D8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8C2×D4×C1311yescharacteristic
363C2×C8C2×D4×C1311yescharacteristic
364C2×C8C2×D4×C1311yescharacteristic
365C2×C8C24×C1311yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4C13×D811yescharacteristic
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4C13×D811yescharacteristic
390C22⋊C4C13×D811yescharacteristic
391C42—41no—
392C42—41no—
393C42—41no—
394C42C2×D4×C1311yescharacteristic
395C16—21no—
396C16—21no—
397C16—21no—
398C16C13×#4112yes—
399C13#3390411yescharacteristic, direct product factor, Sylow
400C23—41no—
401C23C2×C13×D811yescharacteristic
402C23C2×C13×D811yescharacteristic
403Q8—41no—
404Q8—41no—
405D4—22no—
406D4—41no—
407D4—41no—
408D4—82no—
409D4—161no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—82no—
422C2×C4—161no—
423C2×C4—161no—
424C2×C4C2×C13×D811yescharacteristic
425C2×C4C2×C13×D811yescharacteristic
426C2×C4C2×C13×D811yescharacteristic
427C2×C4C2×C13×D811yescharacteristic
428C2×C4C22×D4×C1311yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8C2×C13×#4111yescharacteristic
433C8C13×2−1+411yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22C13×#50812yes—
443C22C22×C13×D811yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4C13×#54711yescharacteristic
456C4C13×#57811yescharacteristic
457C2—22no—
458C2—41no—
459C2—161no—
460C2C13×#333411yescharacteristic
461C2C2×C13×#50811yescharacteristic
462C2C13×#341611yescharacteristic
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×#3336C2semidirect
3. C13×#2253C2semidirect
4. C13×#2237C2semidirect
5. C13×#2236C2semidirect
6. C13×#2234C2semidirect
7. C13×#2232C2semidirect
8. C13×#2229C2semidirect
9. C13×#2228C2semidirect
10. C13×#2217C2semidirect
11. C13×#2217C2semidirect
12. C4×C13×SD32C2semidirect
13. D4×C13×C16C2semidirect
14. C13×#2158C2semidirect
15. C2×C13×#367C2semidirect
113. #33904C13direct (N × H)
170. #3336C2×C13semidirect
171. #2253C2×C13semidirect
172. #2237C2×C13semidirect
173. #2236C2×C13semidirect
174. #2234C2×C13semidirect
175. #2232C2×C13semidirect
176. #2229C2×C13semidirect
177. #2228C2×C13semidirect
178. #2217C2×C13semidirect
179. #2217C2×C13semidirect
180. C4×SD32C2×C13semidirect
181. D4×C16C2×C13semidirect
182. #2158C2×C13semidirect
183. C2×#367C2×C13semidirect
399. C13#33904direct (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×#33362
C13×#22532
C13×#22372
C13×#22362
C13×#22342
C13×#22322
C13×#22292
C13×#22282
C13×#22172
C4×C13×SD322
D4×C13×C162
C13×#21582
C2×C13×#3672
#3390413