Finite Group Databasebeta

← C13×#18345 #15704684

Subgroups — C13×#18345 #15704684

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3461C211yesmaximal, characteristic
2C13×#3239C212yesmaximal, complemented
3C13×#2568C211yesmaximal, characteristic, complemented
4C13×#1617C212yesmaximal, complemented
5C13×#1616C212yesmaximal
6C13×#1615C214yesmaximal, complemented
7C13×#1509C212yesmaximal, complemented
8C13×#1467C211yesmaximal, characteristic, complemented
9C13×#544C2211yescharacteristic
10C13×#542—22no—
11C13×#541—22no—
12C13×#539—21no—
13C13×#539C2212yes—
14C13×#537C2211yescharacteristic
15C13×#536—21no—
16C13×#533—22no—
17C2×C13×C4⋊Q8C2211yescharacteristic
18C13×#529—22no—
19C13×#529—21no—
20C13×#529C2212yes—
21C4×C13×#41—21no—
22C2×C4×Q8×C13C2211yescharacteristic
23C13×#501—22no—
24C13×#489—22no—
25C13×#484C2214yes—
26C13×#481C2214yes—
27C13×#475—22no—
28C13×#474—22no—
29C13×#432C2212yes—
30C13×#400C2212yes—
31C13×#400C2212yes—
32C13×#391—21no—
33C13×#391—21no—
34C13×#391—21no—
35C13×#382—21no—
36C4×C13×C4⋊C4C2211yescharacteristic
37C13×#328C2214yes—
38C13×#327C2214yes—
39C13×#324C2212yes—
40C13×#324C2212yes—
41C2×C13×#41—21no—
42C22×Q8×C13—21no—
43C22×Q8×C13D411yescharacteristic
44C13×C4⋊Q8—22no—
45C13×C4⋊Q8—22no—
46C13×C4⋊Q8—22no—
47C13×C4⋊Q8—22no—
48C13×#126—22no—
49C13×#126—22no—
50C13×#126—22no—
51C13×#126—22no—
52C13×#125—21no—
53C13×#125—22no—
54C13×#125—22no—
55C13×#125—22no—
56C13×#125D412yes—
57C13×#124—22no—
58C13×#124—21no—
59C13×#124D412yes—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—22no—
63C13×#123—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8—22no—
70C13×C22⋊Q8C2312yes—
71C13×#121—22no—
72C13×#121—21no—
73C13×#121C2312yes—
74C4×Q8×C13—21no—
75C4×Q8×C13—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13—22no—
78C4×Q8×C13—22no—
79C4×Q8×C13D412yes—
80C4×D4×C13—21no—
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C4×D4×C13—22no—
84C4×D4×C13—22no—
85C4×D4×C13D412yes—
86C13×#117—22no—
87C13×#117—22no—
88C13×#117—21no—
89C13×#117—22no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4D411yescharacteristic
93C2×C13×C4⋊C4C2312yes—
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C42×C13—22no—
97C2×C42×C13—21no—
98C2×C42×C13D411yescharacteristic
99C2×C42×C13D411yescharacteristic
100C2×C42×C13C2311yescharacteristic
101C13×#107—24no—
102C13×#106—24no—
103C13×C4⋊C8—22no—
104C13×#103—24no—
105C13×#102—24no—
106C13×C22⋊C8C2314yes—
107C13×#97—22no—
108C13×#95—22no—
109C13×#95—22no—
110C13×#95—22no—
111C13×#95—22no—
112C13×#95C2312yes—
113#18345C1311yesmaximal, characteristic, direct product factor, Sylow
114C13×#41—42no—
115C13×#41—42no—
116C2×Q8×C13—21no—
117C2×Q8×C13—21no—
118C2×Q8×C13—22no—
119C2×Q8×C13—22no—
120C2×Q8×C13—41no—
121C2×Q8×C13—44no—
122C2×Q8×C13—41no—
123C2×Q8×C13—41no—
124C2×Q8×C13C2×D412yes—
125C2×D4×C13—21no—
126C2×D4×C13—22no—
127C2×D4×C13—21no—
128C2×D4×C13C2×D412yes—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C2×C8×C13—24no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—22no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—42no—
159C13×C4⋊C4—42no—
160C13×C4⋊C4C2×D412yes—
161C13×C4⋊C4C2×D412yes—
162C13×C22⋊C4—22no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—22no—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C42×C13—22no—
172C42×C13—22no—
173C42×C13—21no—
174C42×C13—22no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—42no—
179C42×C13C2×D412yes—
180C42×C13C2×D412yes—
181#3461C2×C1311yescharacteristic
182#3239C2×C1312yescomplemented
183#2568C2×C1311yescharacteristic, complemented
184#1617C2×C1312yescomplemented
185#1616C2×C1312yes—
186#1615C2×C1314yescomplemented
187#1509C2×C1312yescomplemented
188#1467C2×C1311yescharacteristic, complemented
189C23×C13—22no—
190C23×C13C22×D411yescharacteristic
191Q8×C13—44no—
192Q8×C13—42no—
193Q8×C13—42no—
194Q8×C13—82no—
195Q8×C13—81no—
196Q8×C13—82no—
197D4×C13—42no—
198D4×C13—42no—
199D4×C13—42no—
200D4×C13—42no—
201D4×C13—81no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—22no—
207C2×C4×C13—21no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—22no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—41no—
216C2×C4×C13—44no—
217C2×C4×C13—44no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—44no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—82no—
226C2×C4×C13#12011yescharacteristic
227C2×C4×C13#12012yes—
228C2×C4×C13#12011yescharacteristic
229C2×C4×C13#13712yes—
230C2×C4×C13C22×D412yes—
231C8×C13—44no—
232#544C22×C1311yescharacteristic
233#542—22no—
234#541—22no—
235#539—21no—
236#539C22×C1312yes—
237#537C22×C1311yescharacteristic
238#536—21no—
239#533—22no—
240C2×C4⋊Q8C22×C1311yescharacteristic
241#529—22no—
242#529—21no—
243#529C22×C1312yes—
244C4×#41—21no—
245C2×C4×Q8C22×C1311yescharacteristic
246#501—22no—
247#489—22no—
248#484C22×C1314yes—
249#481C22×C1314yes—
250#475—22no—
251#474—22no—
252#432C22×C1312yes—
253#400C22×C1312yes—
254#400C22×C1312yes—
255#391—21no—
256#391—21no—
257#391—21no—
258#382—21no—
259C4×C4⋊C4C22×C1311yescharacteristic
260#328C22×C1314yes—
261#327C22×C1314yes—
262#324C22×C1312yes—
263#324C22×C1312yes—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—42no—
269C22×C13C2×#12011yescharacteristic
270C22×C13C2×#13711yescharacteristic
271C22×C13#57511yescharacteristic
272C4×C13—22no—
273C4×C13—22no—
274C4×C13—21no—
275C4×C13—22no—
276C4×C13—41no—
277C4×C13—42no—
278C4×C13—42no—
279C4×C13—41no—
280C4×C13—41no—
281C4×C13—42no—
282C4×C13—82no—
283C4×C13—82no—
284C4×C13#45412yes—
285C2×#41—21no—
286C22×Q8—21no—
287C22×Q8D4×C1311yescharacteristic
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292#126—22no—
293#126—22no—
294#126—22no—
295#126—22no—
296#125—21no—
297#125—22no—
298#125—22no—
299#125—22no—
300#125D4×C1312yes—
301#124—22no—
302#124—21no—
303#124D4×C1312yes—
304#123—22no—
305#123—22no—
306#123—22no—
307#123—22no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—21no—
313C22⋊Q8—22no—
314C22⋊Q8C23×C1312yes—
315#121—22no—
316#121—21no—
317#121C23×C1312yes—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8D4×C1312yes—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4D4×C1312yes—
330#117—22no—
331#117—22no—
332#117—21no—
333#117—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4D4×C1311yescharacteristic
337C2×C4⋊C4C23×C1312yes—
338C2×C4⋊C4C23×C1311yescharacteristic
339C2×C4⋊C4C23×C1311yescharacteristic
340C2×C42—22no—
341C2×C42—21no—
342C2×C42D4×C1311yescharacteristic
343C2×C42D4×C1311yescharacteristic
344C2×C42C23×C1311yescharacteristic
345#107—24no—
346#106—24no—
347C4⋊C8—22no—
348#103—24no—
349#102—24no—
350C22⋊C8C23×C1314yes—
351#97—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95C23×C1312yes—
357C2×C13—21no—
358C2×C13—21no—
359C2×C13—82no—
360C2×C13#300711yescharacteristic
361C2×C13C2×#45411yescharacteristic
362C2×C13#302811yescharacteristic
363#41—42no—
364#41—42no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—41no—
370C2×Q8—44no—
371C2×Q8—41no—
372C2×Q8—41no—
373C2×Q8C2×D4×C1312yes—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4C2×D4×C1312yes—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4C2×D4×C1311yescharacteristic
384C22×C4C2×D4×C1311yescharacteristic
385C22×C4C2×D4×C1311yescharacteristic
386C22×C4C2×D4×C1311yescharacteristic
387C22×C4C2×D4×C1311yescharacteristic
388C22×C4C2×D4×C1311yescharacteristic
389C22×C4C24×C1311yescharacteristic
390C2×C8—24no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—24no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4C2×D4×C1312yes—
410C4⋊C4C2×D4×C1312yes—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C42—22no—
421C42—22no—
422C42—21no—
423C42—22no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—42no—
428C42C2×D4×C1312yes—
429C42C2×D4×C1312yes—
430C13#1834511yescharacteristic, direct product factor, Sylow
431C23—22no—
432C23C22×D4×C1311yescharacteristic
433Q8—44no—
434Q8—42no—
435Q8—42no—
436Q8—82no—
437Q8—81no—
438Q8—82no—
439D4—42no—
440D4—42no—
441D4—42no—
442D4—42no—
443D4—81no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—82no—
468C2×C4C13×#12011yescharacteristic
469C2×C4C13×#12012yes—
470C2×C4C13×#12011yescharacteristic
471C2×C4C13×#13712yes—
472C2×C4C22×D4×C1312yes—
473C8—44no—
474C22—21no—
475C22—21no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22C2×C13×#12011yescharacteristic
480C22C2×C13×#13711yescharacteristic
481C22C13×#57511yescharacteristic
482C4—22no—
483C4—22no—
484C4—21no—
485C4—22no—
486C4—41no—
487C4—42no—
488C4—42no—
489C4—41no—
490C4—41no—
491C4—42no—
492C4—82no—
493C4—82no—
494C4C13×#45412yes—
495C2—21no—
496C2—21no—
497C2—82no—
498C2C13×#300711yescharacteristic
499C2C2×C13×#45411yescharacteristic
500C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#537C22
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×#3239C2semidirect
3. C13×#2568C2semidirect
4. C13×#1617C2semidirect
6. C13×#1615C2semidirect
7. C13×#1509C2semidirect
8. C13×#1467C2semidirect
113. #18345C13direct (N × H)
182. #3239C2×C13semidirect
183. #2568C2×C13semidirect
184. #1617C2×C13semidirect
186. #1615C2×C13semidirect
187. #1509C2×C13semidirect
188. #1467C2×C13semidirect
430. C13#18345direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34612
C13×#32392
C13×#25682
C13×#16172
C13×#16162
C13×#16152
C13×#15092
C13×#14672
#1834513