Finite Group Databasebeta

← C13×#18365 #15704704

Subgroups — C13×#18365 #15704704

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3507C211yesmaximal, characteristic
2C13×#3236C211yesmaximal, characteristic, complemented
3C13×#3234C211yesmaximal, characteristic
4C13×#2634C211yesmaximal, characteristic, complemented
5C13×#1615C214yesmaximal, complemented
6C13×#1609C214yesmaximal, complemented
7C13×#1515C211yesmaximal, characteristic, complemented
8C13×#1514C211yesmaximal, characteristic
9C13×#1467C211yesmaximal, characteristic, complemented
10C13×#559—21no—
11C13×#557—21no—
12C13×#556—21no—
13C13×#556—22no—
14C13×#554—21no—
15C13×#552—22no—
16C13×#539C2214yes—
17C13×#536—21no—
18C13×#533C2211yescharacteristic
19C13×#532C2211yescharacteristic
20C13×#529—22no—
21C2×C13×#125C2211yescharacteristic
22C13×#520—21no—
23C2×C4×Q8×C13C2211yescharacteristic
24C13×#501—21no—
25C13×#501—21no—
26C13×#491—21no—
27C13×#490—21no—
28C13×#484C2212yes—
29C13×#483C2212yes—
30C13×#481C2212yes—
31C13×#480C2212yes—
32C13×#479—22no—
33C13×#478—22no—
34C13×#432C2211yescharacteristic
35C13×#432C2211yescharacteristic
36C13×#400—21no—
37C13×#400C2212yes—
38C13×#398C2212yes—
39C13×#395—21no—
40C13×#387—22no—
41C13×#383C2211yescharacteristic
42C13×#328C2214yes—
43C13×#327C2214yes—
44C13×#324C2214yes—
45C2×C13×#41—21no—
46C22×Q8×C13D411yescharacteristic
47C13×C4⋊Q8—22no—
48C13×C4⋊Q8D411yescharacteristic
49C13×C4⋊Q8D411yescharacteristic
50C13×C4⋊Q8D411yescharacteristic
51C13×#127D411yescharacteristic
52C13×#126—24no—
53C13×#126—24no—
54C13×#125—22no—
55C13×#125—24no—
56C13×#125—21no—
57C13×#125—21no—
58C13×#125—21no—
59C13×#125—21no—
60C13×#125—21no—
61C13×#124—22no—
62C13×#124—22no—
63C13×#124—21no—
64C13×#123—24no—
65C13×#123—24no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—24no—
69C13×C22⋊Q8—21no—
70C13×C22⋊Q8C2312yes—
71C13×#121—21no—
72C13×#121C2312yes—
73C4×Q8×C13—22no—
74C4×Q8×C13—22no—
75C4×Q8×C13—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13—21no—
78C4×Q8×C13—21no—
79C4×Q8×C13—21no—
80C4×Q8×C13D412yes—
81C4×D4×C13—22no—
82C4×D4×C13—22no—
83C4×D4×C13—24no—
84C4×D4×C13—21no—
85C4×D4×C13D412yes—
86C13×#117—22no—
87C13×#117—24no—
88C13×#117—21no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2312yes—
97C2×C42×C13D412yes—
98C2×C42×C13C2311yescharacteristic
99C13×#107—22no—
100C13×#107—22no—
101C13×#106—22no—
102C13×#106—22no—
103C13×C4⋊C8—21no—
104C13×C4⋊C8—21no—
105C13×#103—22no—
106C13×#103—22no—
107C13×#102—22no—
108C13×#102—22no—
109C13×C22⋊C8C2312yes—
110C13×C22⋊C8C2312yes—
111C13×#97—21no—
112C13×#97—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—22no—
116C13×#95—22no—
117C13×#95—22no—
118C13×#95C2312yes—
119#18365C1311yesmaximal, characteristic, direct product factor, Sylow
120C13×#41—44no—
121C2×Q8×C13—21no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—42no—
126C2×Q8×C13C2×D412yes—
127C2×D4×C13—22no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13C2×D412yes—
131C22×C4×C13—24no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C2×C8×C13—22no—
142C2×C8×C13—22no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—24no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—44no—
161C13×C4⋊C4—41no—
162C13×C4⋊C4—41no—
163C13×C4⋊C4—41no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4C2×D412yes—
166C13×C4⋊C4C2×D412yes—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C42×C13—24no—
174C42×C13—22no—
175C42×C13—22no—
176C42×C13—22no—
177C42×C13C2×D411yescharacteristic
178C42×C13C2×D411yescharacteristic
179C42×C13C2×D411yescharacteristic
180C42×C13C2×D411yescharacteristic
181#3507C2×C1311yescharacteristic
182#3236C2×C1311yescharacteristic, complemented
183#3234C2×C1311yescharacteristic
184#2634C2×C1311yescharacteristic, complemented
185#1615C2×C1314yescomplemented
186#1609C2×C1314yescomplemented
187#1515C2×C1311yescharacteristic, complemented
188#1514C2×C1311yescharacteristic
189#1467C2×C1311yescharacteristic, complemented
190C23×C13—22no—
191C23×C13C22×D411yescharacteristic
192Q8×C13—42no—
193Q8×C13—42no—
194Q8×C13—42no—
195Q8×C13—42no—
196Q8×C13—42no—
197D4×C13—42no—
198D4×C13—42no—
199D4×C13—42no—
200D4×C13—44no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—44no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—84no—
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13#12011yescharacteristic
223C2×C4×C13#12011yescharacteristic
224C2×C4×C13#12011yescharacteristic
225C2×C4×C13C22×D411yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C8×C13—42no—
228C8×C13—42no—
229#559—21no—
230#557—21no—
231#556—21no—
232#556—22no—
233#554—21no—
234#552—22no—
235#539C22×C1314yes—
236#536—21no—
237#533C22×C1311yescharacteristic
238#532C22×C1311yescharacteristic
239#529—22no—
240C2×#125C22×C1311yescharacteristic
241#520—21no—
242C2×C4×Q8C22×C1311yescharacteristic
243#501—21no—
244#501—21no—
245#491—21no—
246#490—21no—
247#484C22×C1312yes—
248#483C22×C1312yes—
249#481C22×C1312yes—
250#480C22×C1312yes—
251#479—22no—
252#478—22no—
253#432C22×C1311yescharacteristic
254#432C22×C1311yescharacteristic
255#400—21no—
256#400C22×C1312yes—
257#398C22×C1312yes—
258#395—21no—
259#387—22no—
260#383C22×C1311yescharacteristic
261#328C22×C1314yes—
262#327C22×C1314yes—
263#324C22×C1314yes—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—42no—
269C22×C13C2×#12011yescharacteristic
270C22×C13#57512yes—
271C4×C13—21no—
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—21no—
277C4×C13—42no—
278C4×C13—42no—
279C4×C13—42no—
280C4×C13—42no—
281C4×C13—42no—
282C4×C13—82no—
283C4×C13—81no—
284C4×C13—81no—
285C2×#41—21no—
286C22×Q8D4×C1311yescharacteristic
287C4⋊Q8—22no—
288C4⋊Q8D4×C1311yescharacteristic
289C4⋊Q8D4×C1311yescharacteristic
290C4⋊Q8D4×C1311yescharacteristic
291#127D4×C1311yescharacteristic
292#126—24no—
293#126—24no—
294#125—22no—
295#125—24no—
296#125—21no—
297#125—21no—
298#125—21no—
299#125—21no—
300#125—21no—
301#124—22no—
302#124—22no—
303#124—21no—
304#123—24no—
305#123—24no—
306C22⋊Q8—22no—
307C22⋊Q8—22no—
308C22⋊Q8—24no—
309C22⋊Q8—21no—
310C22⋊Q8C23×C1312yes—
311#121—21no—
312#121C23×C1312yes—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8D4×C1312yes—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—24no—
324C4×D4—21no—
325C4×D4D4×C1312yes—
326#117—22no—
327#117—24no—
328#117—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4D4×C1311yescharacteristic
334C2×C4⋊C4C23×C1311yescharacteristic
335C2×C4⋊C4C23×C1311yescharacteristic
336C2×C4⋊C4C23×C1312yes—
337C2×C42D4×C1312yes—
338C2×C42C23×C1311yescharacteristic
339#107—22no—
340#107—22no—
341#106—22no—
342#106—22no—
343C4⋊C8—21no—
344C4⋊C8—21no—
345#103—22no—
346#103—22no—
347#102—22no—
348#102—22no—
349C22⋊C8C23×C1312yes—
350C22⋊C8C23×C1312yes—
351#97—21no—
352#97—21no—
353#95—21no—
354#95—21no—
355#95—22no—
356#95—22no—
357#95—22no—
358#95C23×C1312yes—
359C2×C13—22no—
360C2×C13—82no—
361C2×C13#300511yescharacteristic
362C2×C13#302011yescharacteristic
363C2×C13#302811yescharacteristic
364#41—44no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—42no—
370C2×Q8C2×D4×C1312yes—
371C2×D4—22no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4C2×D4×C1312yes—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4C2×D4×C1312yes—
381C22×C4C2×D4×C1311yescharacteristic
382C22×C4C2×D4×C1312yes—
383C22×C4C2×D4×C1311yescharacteristic
384C22×C4C24×C1311yescharacteristic
385C2×C8—22no—
386C2×C8—22no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—44no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4C2×D4×C1312yes—
410C4⋊C4C2×D4×C1312yes—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C42—24no—
418C42—22no—
419C42—22no—
420C42—22no—
421C42C2×D4×C1311yescharacteristic
422C42C2×D4×C1311yescharacteristic
423C42C2×D4×C1311yescharacteristic
424C42C2×D4×C1311yescharacteristic
425C13#1836511yescharacteristic, direct product factor, Sylow
426C23—22no—
427C23C22×D4×C1311yescharacteristic
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—42no—
433D4—42no—
434D4—42no—
435D4—42no—
436D4—44no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—84no—
457C2×C4C13×#12011yescharacteristic
458C2×C4C13×#12011yescharacteristic
459C2×C4C13×#12011yescharacteristic
460C2×C4C13×#12011yescharacteristic
461C2×C4C22×D4×C1311yescharacteristic
462C2×C4C22×D4×C1311yescharacteristic
463C8—42no—
464C8—42no—
465C22—21no—
466C22—21no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22C2×C13×#12011yescharacteristic
471C22C13×#57512yes—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4—42no—
483C4—82no—
484C4—81no—
485C4—81no—
486C2—22no—
487C2—82no—
488C2C13×#300511yescharacteristic
489C2C13×#302011yescharacteristic
490C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#532C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3236C2semidirect
4. C13×#2634C2semidirect
5. C13×#1615C2semidirect
6. C13×#1609C2semidirect
7. C13×#1515C2semidirect
9. C13×#1467C2semidirect
119. #18365C13direct (N × H)
182. #3236C2×C13semidirect
184. #2634C2×C13semidirect
185. #1615C2×C13semidirect
186. #1609C2×C13semidirect
187. #1515C2×C13semidirect
189. #1467C2×C13semidirect
425. C13#18365direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35072
C13×#32362
C13×#32342
C13×#26342
C13×#16152
C13×#16092
C13×#15152
C13×#15142
C13×#14672
#1836513