Finite Group Databasebeta

← C13×#33910 #15720249

Subgroups — C13×#33910 #15720249

Order 3328.

504 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3336C211yesmaximal, characteristic, complemented
2C13×#3334C211yesmaximal, characteristic
3C13×#2255C211yesmaximal, characteristic, complemented
4C13×#2236C211yesmaximal, characteristic, complemented
5C13×#2235C211yesmaximal, characteristic, complemented
6C13×#2234C211yesmaximal, characteristic, complemented
7C13×#2232C211yesmaximal, characteristic, complemented
8C13×#2228C211yesmaximal, characteristic, complemented
9C13×#2227C211yesmaximal, 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×#552—21no—
17C13×#547—21no—
18C2×C13×SD32C2211yescharacteristic
19C2×C13×M32C2211yescharacteristic
20C22×C13×C16C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#485—21no—
24C13×#483—21no—
25C13×#480—21no—
26C13×#480—21no—
27C13×#479—21no—
28C13×#474—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×#41—41no—
60C2×C13×Q16C2311yescharacteristic
61C2×C13×D8C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×C4⋊Q8—21no—
65C13×#126—41no—
66C13×#125—21no—
67C13×#125—41no—
68C13×#123—41no—
69C13×#123—41no—
70C13×#123—41no—
71C13×C22⋊Q8—21no—
72C13×C22⋊Q8—21no—
73C13×C22⋊Q8—41no—
74C13×#121—21no—
75C13×#121—21no—
76C4×Q8×C13—21no—
77C4×D4×C13—21no—
78C4×D4×C13D411yescharacteristic
79C13×#117—21no—
80C13×#117—41no—
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#33910C1311yesmaximal, characteristic, direct product factor, Sylow
114C13×#41—84no—
115C2×Q8×C13—21no—
116C2×Q8×C13—41no—
117C2×D4×C13—21no—
118C2×D4×C13—41no—
119C2×D4×C13—41no—
120C2×D4×C13D811yescharacteristic
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C13×Q16—21no—
128C13×Q16—21no—
129C13×D8—21no—
130C13×D8—21no—
131C2×C8×C13—21no—
132C2×C8×C13—21no—
133C2×C8×C13—21no—
134C2×C8×C13—21no—
135C2×C8×C13C2×D411yescharacteristic
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13C2×D411yescharacteristic
138C2×C8×C13C2411yescharacteristic
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
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⋊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⋊C4D811yescharacteristic
162C13×C22⋊C4D811yescharacteristic
163C42×C13—41no—
164C42×C13—41no—
165C42×C13C2×D411yescharacteristic
166C13×C16—21no—
167C13×C16—21no—
168C13×C16—21no—
169C13×C16#4112yescomplemented
170#3336C2×C1311yescharacteristic, complemented
171#3334C2×C1311yescharacteristic
172#2255C2×C1311yescharacteristic, complemented
173#2236C2×C1311yescharacteristic, complemented
174#2235C2×C1311yescharacteristic, complemented
175#2234C2×C1311yescharacteristic, complemented
176#2232C2×C1311yescharacteristic, complemented
177#2228C2×C1311yescharacteristic, complemented
178#2227C2×C1311yescharacteristic, complemented
179#2220C2×C1311yescharacteristic, complemented
180#2217C2×C1311yescharacteristic, complemented
181#2175C2×C1311yescharacteristic, complemented
182#2168C2×C1311yescharacteristic, complemented
183#2159C2×C1311yescharacteristic, complemented
184C2×#366C2×C1311yescharacteristic, complemented
185C23×C13—41no—
186C23×C13C2×D811yescharacteristic
187C23×C13C2×D811yescharacteristic
188Q8×C13—41no—
189Q8×C13—41no—
190Q8×C13—82no—
191D4×C13—22no—
192D4×C13—41no—
193D4×C13—41no—
194D4×C13—82no—
195D4×C13—82no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
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—41no—
207C2×C4×C13—82no—
208C2×C4×C13—82no—
209C2×C4×C13—82no—
210C2×C4×C13—82no—
211C2×C4×C13C2×D811yescharacteristic
212C2×C4×C13C2×D811yescharacteristic
213C2×C4×C13C2×D811yescharacteristic
214C2×C4×C13C2×D811yescharacteristic
215C2×C4×C13C22×D411yescharacteristic
216C8×C13—21no—
217C8×C13—21no—
218C8×C13—21no—
219C8×C13C2×#4111yescharacteristic
220C8×C132−1+411yescharacteristic
221#552—21no—
222#547—21no—
223C2×SD32C22×C1311yescharacteristic
224C2×M32C22×C1311yescharacteristic
225C22×C16C22×C1311yescharacteristic
226#500C22×C1311yescharacteristic
227#499C22×C1311yescharacteristic
228#485—21no—
229#483—21no—
230#480—21no—
231#480—21no—
232#479—21no—
233#474—21no—
234#467C22×C1311yescharacteristic
235#467C22×C1311yescharacteristic
236#466C22×C1311yescharacteristic
237#466C22×C1311yescharacteristic
238C4×Q16C22×C1311yescharacteristic
239C4×D8C22×C1311yescharacteristic
240C8×D4C22×C1311yescharacteristic
241#427C22×C1311yescharacteristic
242C2×#107C22×C1311yescharacteristic
243C2×#107C22×C1311yescharacteristic
244C2×#107C22×C1311yescharacteristic
245#367C22×C1311yescharacteristic
246#367C22×C1311yescharacteristic
247#367C22×C1311yescharacteristic
248#366C22×C1311yescharacteristic
249#366C22×C1311yescharacteristic
250#366C22×C1311yescharacteristic
251#366C22×C1311yescharacteristic
252#366C22×C1311yescharacteristic
253#366C22×C1311yescharacteristic
254C4⋊C16C22×C1311yescharacteristic
255#358C22×C1311yescharacteristic
256#358C22×C1311yescharacteristic
257#358C22×C1311yescharacteristic
258#357C22×C1311yescharacteristic
259#357C22×C1311yescharacteristic
260#357C22×C1311yescharacteristic
261C22⋊C16C22×C1311yescharacteristic
262C22⋊C16C22×C1311yescharacteristic
263#346C22×C1311yescharacteristic
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—21no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13#50912yes—
273C22×C13C22×D811yescharacteristic
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—21no—
277C4×C13—21no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13—81no—
281C4×C13—81no—
282C4×C13—81no—
283C4×C13—81no—
284C4×C13—81no—
285C4×C13#54711yescharacteristic
286C4×C13#57811yescharacteristic
287C2×#41—41no—
288C2×Q16C23×C1311yescharacteristic
289C2×D8C23×C1311yescharacteristic
290C22×C8C23×C1311yescharacteristic
291C22×C8C23×C1311yescharacteristic
292C4⋊Q8—21no—
293#126—41no—
294#125—21no—
295#125—41no—
296#123—41no—
297#123—41no—
298#123—41no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—41no—
302#121—21no—
303#121—21no—
304C4×Q8—21no—
305C4×D4—21no—
306C4×D4D4×C1311yescharacteristic
307#117—21no—
308#117—41no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312SD32—22no—
313M32—22no—
314C2×C16—22no—
315C2×C16C23×C1311yescharacteristic
316C2×C16C23×C1311yescharacteristic
317C2×C16C23×C1311yescharacteristic
318C2×C16C23×C1311yescharacteristic
319#107—21no—
320#107—21no—
321#107—21no—
322#107—21no—
323#107C23×C1311yescharacteristic
324#107C23×C1311yescharacteristic
325#107C23×C1311yescharacteristic
326#107C23×C1311yescharacteristic
327#107C23×C1311yescharacteristic
328#107C23×C1311yescharacteristic
329#106—21no—
330#106—21no—
331C4⋊C8D4×C1311yescharacteristic
332#103—21no—
333#103—21no—
334#103—21no—
335#102—21no—
336#102—21no—
337#102—21no—
338C22⋊C8D4×C1311yescharacteristic
339C22⋊C8D4×C1311yescharacteristic
340C4×C8C23×C1311yescharacteristic
341C2×C13—22no—
342C2×C13—41no—
343C2×C13—161no—
344C2×C13#333411yescharacteristic
345C2×C13C2×#50911yescharacteristic
346C2×C13#341711yescharacteristic
347#41—84no—
348C2×Q8—21no—
349C2×Q8—41no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4C13×D811yescharacteristic
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4C2×D4×C1311yescharacteristic
359C22×C4C2×D4×C1311yescharacteristic
360Q16—21no—
361Q16—21no—
362D8—21no—
363D8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8C2×D4×C1311yescharacteristic
369C2×C8C2×D4×C1311yescharacteristic
370C2×C8C2×D4×C1311yescharacteristic
371C2×C8C24×C1311yescharacteristic
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4C13×D811yescharacteristic
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4C13×D811yescharacteristic
395C22⋊C4C13×D811yescharacteristic
396C42—41no—
397C42—41no—
398C42C2×D4×C1311yescharacteristic
399C16—21no—
400C16—21no—
401C16—21no—
402C16C13×#4112yescomplemented
403C13#3391011yescharacteristic, direct product factor, Sylow
404C23—41no—
405C23C2×C13×D811yescharacteristic
406C23C2×C13×D811yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—82no—
410D4—22no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—82no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4C2×C13×D811yescharacteristic
431C2×C4C2×C13×D811yescharacteristic
432C2×C4C2×C13×D811yescharacteristic
433C2×C4C2×C13×D811yescharacteristic
434C2×C4C22×D4×C1311yescharacteristic
435C8—21no—
436C8—21no—
437C8—21no—
438C8C2×C13×#4111yescharacteristic
439C8C13×2−1+411yescharacteristic
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22C13×#50912yes—
449C22C22×C13×D811yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4C13×#54711yescharacteristic
462C4C13×#57811yescharacteristic
463C2—22no—
464C2—41no—
465C2—161no—
466C2C13×#333411yescharacteristic
467C2C2×C13×#50911yescharacteristic
468C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#3334C2
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×#3336C2semidirect
3. C13×#2255C2semidirect
4. C13×#2236C2semidirect
5. C13×#2235C2semidirect
6. C13×#2234C2semidirect
7. C13×#2232C2semidirect
8. C13×#2228C2semidirect
9. C13×#2227C2semidirect
10. C13×#2220C2semidirect
11. C13×#2217C2semidirect
12. C13×#2175C2semidirect
13. C13×#2168C2semidirect
14. C13×#2159C2semidirect
15. C2×C13×#366C2semidirect
113. #33910C13direct (N × H)
169. C13×C16#41semidirect
170. #3336C2×C13semidirect
172. #2255C2×C13semidirect
173. #2236C2×C13semidirect
174. #2235C2×C13semidirect
175. #2234C2×C13semidirect
176. #2232C2×C13semidirect
177. #2228C2×C13semidirect
178. #2227C2×C13semidirect
179. #2220C2×C13semidirect
180. #2217C2×C13semidirect
181. #2175C2×C13semidirect
182. #2168C2×C13semidirect
183. #2159C2×C13semidirect
184. C2×#366C2×C13semidirect
402. C16C13×#41semidirect
403. C13#33910direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33362
C13×#33342
C13×#22552
C13×#22362
C13×#22352
C13×#22342
C13×#22322
C13×#22282
C13×#22272
C13×#22202
C13×#22172
C13×#21752
C13×#21682
C13×#21592
C2×C13×#3662
#3391013