Finite Group Databasebeta

← C13×#33914 #15720253

Subgroups — C13×#33914 #15720253

Order 3328.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3341C211yesmaximal, characteristic, complemented
2C13×#3339C211yesmaximal, characteristic, complemented
3C13×#2255C211yesmaximal, characteristic, complemented
4C13×#2234C211yesmaximal, characteristic, complemented
5C13×#2234C211yesmaximal, characteristic, complemented
6C13×#2234C211yesmaximal, characteristic, complemented
7C13×#2232C211yesmaximal, characteristic, complemented
8C13×#2228C211yesmaximal, characteristic, complemented
9C13×#2224C211yesmaximal, characteristic, complemented
10C13×#2218C211yesmaximal, characteristic, complemented
11C13×#2215C211yesmaximal, characteristic, complemented
12C13×#2177C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2159C211yesmaximal, characteristic, complemented
15C13×#2158C211yesmaximal, characteristic, complemented
16C13×#555—21no—
17C13×#553—21no—
18C2×C13×D16C2211yescharacteristic
19C2×C13×M32C2211yescharacteristic
20C22×C13×C16C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#482—21no—
24C13×#482—21no—
25C13×#482—21no—
26C13×#481—21no—
27C13×#478—21no—
28C13×#476—21no—
29C13×#466C2211yescharacteristic
30C13×#466C2211yescharacteristic
31C13×#466C2211yescharacteristic
32C13×#466C2211yescharacteristic
33C4×C13×D8C2211yescharacteristic
34C4×C13×D8C2211yescharacteristic
35C8×D4×C13C2211yescharacteristic
36C13×#427C2211yescharacteristic
37C13×#427C2211yescharacteristic
38C13×#427C2211yescharacteristic
39C2×C13×#107C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#367C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×#366C2211yescharacteristic
46C13×#366C2211yescharacteristic
47C13×#366C2211yescharacteristic
48C13×#366C2211yescharacteristic
49C13×C4⋊C16C2211yescharacteristic
50C13×#357C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic
58C13×#346C2211yescharacteristic
59C2×C13×D8C2311yescharacteristic
60C2×C13×D8C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C13×C4⋊Q8—21no—
64C13×#126—41no—
65C13×#125—21no—
66C13×#124—41no—
67C13×#124—41no—
68C13×#123—41no—
69C13×#121—21no—
70C13×#121—21no—
71C13×#121—21no—
72C13×#121—21no—
73C13×#121—41no—
74C13×#121—41no—
75C4×D4×C13—21no—
76C4×D4×C13—21no—
77C4×D4×C13—41no—
78C4×D4×C13D411yescharacteristic
79C13×#117—21no—
80C13×#117—21no—
81C13×#117—21no—
82C13×#117—41no—
83C2×C13×C4⋊C4—21no—
84C13×D16—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×#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×#102—21no—
105C13×#102—21no—
106C13×#102—21no—
107C13×#102—21no—
108C13×#102—21no—
109C13×#102—21no—
110C13×C22⋊C8D411yescharacteristic
111C13×C22⋊C8D411yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#33914C1311yesmaximal, characteristic, direct product factor, Sylow
114C2×Q8×C13—41no—
115C2×D4×C13—21no—
116C2×D4×C13—21no—
117C2×D4×C13—41no—
118C2×D4×C13—41no—
119C2×D4×C13—41no—
120C2×D4×C13—41no—
121C2×D4×C13D811yescharacteristic
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C13×D8—21no—
128C13×D8—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⋊C4D811yescharacteristic
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
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#3341C2×C1311yescharacteristic, complemented
170#3339C2×C1311yescharacteristic, complemented
171#2255C2×C1311yescharacteristic, complemented
172#2234C2×C1311yescharacteristic, complemented
173#2234C2×C1311yescharacteristic, complemented
174#2234C2×C1311yescharacteristic, complemented
175#2232C2×C1311yescharacteristic, complemented
176#2228C2×C1311yescharacteristic, complemented
177#2224C2×C1311yescharacteristic, complemented
178#2218C2×C1311yescharacteristic, complemented
179#2215C2×C1311yescharacteristic, complemented
180#2177C2×C1311yescharacteristic, complemented
181#2168C2×C1311yescharacteristic, complemented
182#2159C2×C1311yescharacteristic, complemented
183#2158C2×C1311yescharacteristic, complemented
184C23×C13—41no—
185C23×C13—41no—
186C23×C13C2×D811yescharacteristic
187C23×C13C2×D811yescharacteristic
188Q8×C13—161no—
189D4×C13—41no—
190D4×C13—41no—
191D4×C13—41no—
192D4×C13—41no—
193D4×C13—41no—
194D4×C13—82no—
195D4×C13—161no—
196D4×C13—161no—
197D4×C13—161no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—82no—
209C2×C4×C13—161no—
210C2×C4×C13—161no—
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#555—21no—
222#553—21no—
223C2×D16C22×C1311yescharacteristic
224C2×M32C22×C1311yescharacteristic
225C22×C16C22×C1311yescharacteristic
226#500C22×C1311yescharacteristic
227#499C22×C1311yescharacteristic
228#482—21no—
229#482—21no—
230#482—21no—
231#481—21no—
232#478—21no—
233#476—21no—
234#466C22×C1311yescharacteristic
235#466C22×C1311yescharacteristic
236#466C22×C1311yescharacteristic
237#466C22×C1311yescharacteristic
238C4×D8C22×C1311yescharacteristic
239C4×D8C22×C1311yescharacteristic
240C8×D4C22×C1311yescharacteristic
241#427C22×C1311yescharacteristic
242#427C22×C1311yescharacteristic
243#427C22×C1311yescharacteristic
244C2×#107C22×C1311yescharacteristic
245#367C22×C1311yescharacteristic
246#367C22×C1311yescharacteristic
247#367C22×C1311yescharacteristic
248#367C22×C1311yescharacteristic
249#366C22×C1311yescharacteristic
250#366C22×C1311yescharacteristic
251#366C22×C1311yescharacteristic
252#366C22×C1311yescharacteristic
253#366C22×C1311yescharacteristic
254C4⋊C16C22×C1311yescharacteristic
255#357C22×C1311yescharacteristic
256#357C22×C1311yescharacteristic
257#357C22×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—21no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13—81no—
273C22×C13—81no—
274C22×C13—81no—
275C22×C13—81no—
276C22×C13C22×D811yescharacteristic
277C4×C13—21no—
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—21no—
281C4×C13—81no—
282C4×C13—81no—
283C4×C13—81no—
284C4×C13—81no—
285C4×C13—81no—
286C4×C13—81no—
287C4×C13#54711yescharacteristic
288C4×C13#57811yescharacteristic
289C2×D8C23×C1311yescharacteristic
290C2×D8C23×C1311yescharacteristic
291C22×C8C23×C1311yescharacteristic
292C22×C8C23×C1311yescharacteristic
293C4⋊Q8—21no—
294#126—41no—
295#125—21no—
296#124—41no—
297#124—41no—
298#123—41no—
299#121—21no—
300#121—21no—
301#121—21no—
302#121—21no—
303#121—41no—
304#121—41no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4—41no—
308C4×D4D4×C1311yescharacteristic
309#117—21no—
310#117—21no—
311#117—21no—
312#117—41no—
313C2×C4⋊C4—21no—
314D16—22no—
315M32—22no—
316C2×C16—22no—
317C2×C16C23×C1311yescharacteristic
318C2×C16C23×C1311yescharacteristic
319C2×C16C23×C1311yescharacteristic
320C2×C16C23×C1311yescharacteristic
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—
331#106—21no—
332#106—21no—
333C4⋊C8D4×C1311yescharacteristic
334#102—21no—
335#102—21no—
336#102—21no—
337#102—21no—
338#102—21no—
339#102—21no—
340C22⋊C8D4×C1311yescharacteristic
341C22⋊C8D4×C1311yescharacteristic
342C4×C8C23×C1311yescharacteristic
343C2×C13—41no—
344C2×C13—41no—
345C2×C13—161no—
346C2×C13—161no—
347C2×C13#333411yescharacteristic
348C2×C13#341411yescharacteristic
349C2×C13#341511yescharacteristic
350C2×Q8—41no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4C13×D811yescharacteristic
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4C2×D4×C1311yescharacteristic
362C22×C4C2×D4×C1311yescharacteristic
363D8—21no—
364D8—21no—
365D8—21no—
366D8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8C2×D4×C1311yescharacteristic
372C2×C8C2×D4×C1311yescharacteristic
373C2×C8C2×D4×C1311yescharacteristic
374C2×C8C24×C1311yescharacteristic
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
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⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4C13×D811yescharacteristic
396C22⋊C4C13×D811yescharacteristic
397C42—41no—
398C42—41no—
399C42—41no—
400C42C2×D4×C1311yescharacteristic
401C16—21no—
402C16—21no—
403C16—21no—
404C16C13×#4112yes—
405C13#3391411yescharacteristic, direct product factor, Sylow
406C23—41no—
407C23—41no—
408C23C2×C13×D811yescharacteristic
409C23C2×C13×D811yescharacteristic
410Q8—161no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—82no—
417D4—161no—
418D4—161no—
419D4—161no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—82no—
431C2×C4—161no—
432C2×C4—161no—
433C2×C4C2×C13×D811yescharacteristic
434C2×C4C2×C13×D811yescharacteristic
435C2×C4C2×C13×D811yescharacteristic
436C2×C4C2×C13×D811yescharacteristic
437C2×C4C22×D4×C1311yescharacteristic
438C8—21no—
439C8—21no—
440C8—21no—
441C8C2×C13×#4111yescharacteristic
442C8C13×2−1+411yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C22×C13×D811yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4C13×#54711yescharacteristic
467C4C13×#57811yescharacteristic
468C2—41no—
469C2—41no—
470C2—161no—
471C2—161no—
472C2C13×#333411yescharacteristic
473C2C13×#341411yescharacteristic
474C2C13×#341511yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
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×#3341C2semidirect
2. C13×#3339C2semidirect
3. C13×#2255C2semidirect
4. C13×#2234C2semidirect
5. C13×#2234C2semidirect
6. C13×#2234C2semidirect
7. C13×#2232C2semidirect
8. C13×#2228C2semidirect
9. C13×#2224C2semidirect
10. C13×#2218C2semidirect
11. C13×#2215C2semidirect
12. C13×#2177C2semidirect
13. C13×#2168C2semidirect
14. C13×#2159C2semidirect
15. C13×#2158C2semidirect
113. #33914C13direct (N × H)
169. #3341C2×C13semidirect
170. #3339C2×C13semidirect
171. #2255C2×C13semidirect
172. #2234C2×C13semidirect
173. #2234C2×C13semidirect
174. #2234C2×C13semidirect
175. #2232C2×C13semidirect
176. #2228C2×C13semidirect
177. #2224C2×C13semidirect
178. #2218C2×C13semidirect
179. #2215C2×C13semidirect
180. #2177C2×C13semidirect
181. #2168C2×C13semidirect
182. #2159C2×C13semidirect
183. #2158C2×C13semidirect
405. C13#33914direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33412
C13×#33392
C13×#22552
C13×#22342
C13×#22322
C13×#22282
C13×#22242
C13×#22182
C13×#22152
C13×#21772
C13×#21682
C13×#21592
C13×#21582
#3391413