Finite Group Databasebeta

← C13×#10323 #15696662

Subgroups — C13×#10323 #15696662

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3187C211yesmaximal, characteristic
2C13×#2855C211yesmaximal, characteristic, complemented
3C13×#2854C211yesmaximal, characteristic
4C13×#1817C211yesmaximal, characteristic, complemented
5C13×#1520C211yesmaximal, characteristic, complemented
6C13×#1519C211yesmaximal, characteristic
7C13×#1289C211yesmaximal, characteristic, complemented
8C2×C13×#123—21no—
9C2×C13×C22⋊Q8C2211yescharacteristic
10C2×C13×#121C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12C13×#483—21no—
13C13×#481—21no—
14C13×#465—22no—
15C13×#450—21no—
16C13×#448—21no—
17C2×C13×C22⋊C8C2211yescharacteristic
18C2×C13×C22⋊C8C2211yescharacteristic
19C13×#391—21no—
20C13×#390—21no—
21C13×#389—21no—
22C13×#389—21no—
23C13×#388—22no—
24C13×#387—22no—
25C13×#386—21no—
26C13×#385—21no—
27C13×#381—21no—
28C13×#380C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C13×#336—22no—
31C13×#328—22no—
32C13×#327—22no—
33C22×Q8×C13D411yescharacteristic
34C22×D4×C13—21no—
35C22×D4×C13D411yescharacteristic
36C23×C4×C13D411yescharacteristic
37C23×C4×C13D411yescharacteristic
38C23×C4×C13C2311yescharacteristic
39C2×C13×SD16—22no—
40C22×C8×C13—21no—
41C22×C8×C13D412yes—
42C13×#123—42no—
43C13×#123—42no—
44C13×C22⋊Q8—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8—21no—
48C13×#121—21no—
49C13×#121—21no—
50C13×#121—21no—
51C13×#121—21no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C4⋊C4D411yescharacteristic
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—21no—
65C2×C42×C13—21no—
66C2×C42×C13—21no—
67C2×C42×C13—21no—
68C2×C42×C13—21no—
69C2×C42×C13—21no—
70C2×C42×C13—21no—
71C13×#106—22no—
72C13×#103—22no—
73C13×#102—22no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×#95—22no—
79C13×#95—22no—
80C13×#95—22no—
81C13×#95—22no—
82C13×#95D412yes—
83C13×#95D412yes—
84#10323C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13—21no—
86C24×C13C2×D411yescharacteristic
87C2×Q8×C13—21no—
88C2×Q8×C13—21no—
89C2×Q8×C13—42no—
90C2×D4×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—42no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—42no—
114C22×C4×C13—42no—
115C22×C4×C13SD1612yescomplemented
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13#4111yescharacteristic
122C13×SD16—82no—
123C2×C8×C13—22no—
124C2×C8×C13—42no—
125C2×C8×C13—42no—
126C2×C8×C13—41no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—42no—
132C13×C4⋊C4—42no—
133C13×C4⋊C4—44no—
134C13×C4⋊C4—44no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C22⋊C4—44no—
138C13×C22⋊C4—44no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—41no—
146C13×C22⋊C4—41no—
147C42×C13—41no—
148C42×C13—41no—
149C42×C13—41no—
150C42×C13—41no—
151#3187C2×C1311yescharacteristic
152#2855C2×C1311yescharacteristic, complemented
153#2854C2×C1311yescharacteristic
154#1817C2×C1311yescharacteristic, complemented
155#1520C2×C1311yescharacteristic, complemented
156#1519C2×C1311yescharacteristic
157#1289C2×C1311yescharacteristic, complemented
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—42no—
161C23×C13—42no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13#12011yescharacteristic
166C23×C13#12011yescharacteristic
167C23×C13#12111yescharacteristic
168C23×C13C2×SD1611yescharacteristic
169C23×C13#13511yescharacteristic
170C23×C13AGL(1,ℤ/8)11yescharacteristic
171C23×C13#13711yescharacteristic
172Q8×C13—42no—
173Q8×C13—81no—
174D4×C13—42no—
175D4×C13—81no—
176D4×C13—81no—
177D4×C13—81no—
178D4×C13—81no—
179D4×C13—81no—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—22no—
183C2×C4×C13—22no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—22no—
187C2×C4×C13—22no—
188C2×C4×C13—22no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13#12011yescharacteristic
214C2×C4×C13#12111yescharacteristic
215C2×C4×C13#12111yescharacteristic
216C2×C4×C13#12711yescharacteristic
217C8×C13—42no—
218C8×C13—81no—
219C2×#123—21no—
220C2×C22⋊Q8C22×C1311yescharacteristic
221C2×#121C22×C1311yescharacteristic
222C22×C42C22×C1311yescharacteristic
223#483—21no—
224#481—21no—
225#465—22no—
226#450—21no—
227#448—21no—
228C2×C22⋊C8C22×C1311yescharacteristic
229C2×C22⋊C8C22×C1311yescharacteristic
230#391—21no—
231#390—21no—
232#389—21no—
233#389—21no—
234#388—22no—
235#387—22no—
236#386—21no—
237#385—21no—
238#381—21no—
239#380C22×C1311yescharacteristic
240#380C22×C1311yescharacteristic
241#336—22no—
242#328—22no—
243#327—22no—
244C22×C13—21no—
245C22×C13—21no—
246C22×C13—21no—
247C22×C13—21no—
248C22×C13—21no—
249C22×C13—21no—
250C22×C13—41no—
251C22×C13—41no—
252C22×C13—41no—
253C22×C13—41no—
254C22×C13—82no—
255C22×C13—82no—
256C22×C13—81no—
257C22×C13—81no—
258C22×C13—81no—
259C22×C13#39211yescharacteristic
260C22×C13#44811yescharacteristic
261C22×C13#44911yescharacteristic
262C22×C13#45011yescharacteristic
263C22×C13#45211yescharacteristic
264C22×C13#46511yescharacteristic
265C22×C13#46811yescharacteristic
266C4×C13—21no—
267C4×C13—21no—
268C4×C13—21no—
269C4×C13—42no—
270C4×C13—42no—
271C4×C13—82no—
272C4×C13—82no—
273C4×C13—81no—
274C4×C13—81no—
275C4×C13—81no—
276C4×C13#45812yes—
277C22×Q8D4×C1311yescharacteristic
278C22×D4—21no—
279C22×D4D4×C1311yescharacteristic
280C23×C4D4×C1311yescharacteristic
281C23×C4D4×C1311yescharacteristic
282C23×C4C23×C1311yescharacteristic
283C2×SD16—22no—
284C22×C8—21no—
285C22×C8D4×C1312yes—
286#123—42no—
287#123—42no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—21no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4D4×C1311yescharacteristic
302C2×C4⋊C4D4×C1311yescharacteristic
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315#106—22no—
316#103—22no—
317#102—22no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322#95—22no—
323#95—22no—
324#95—22no—
325#95—22no—
326#95D4×C1312yes—
327#95D4×C1312yes—
328C2×C13—21no—
329C2×C13—21no—
330C2×C13—21no—
331C2×C13—21no—
332C2×C13—21no—
333C2×C13—21no—
334C2×C13—161no—
335C2×C13#200011yescharacteristic
336C2×C13#201011yescharacteristic
337C2×C13#202211yescharacteristic
338C24—21no—
339C24C2×D4×C1311yescharacteristic
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—42no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—42no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4C13×SD1612yescomplemented
369C22×C4C2×D4×C1311yescharacteristic
370C22×C4C2×D4×C1311yescharacteristic
371C22×C4C2×D4×C1311yescharacteristic
372C22×C4C2×D4×C1311yescharacteristic
373C22×C4C2×D4×C1311yescharacteristic
374C22×C4C13×#4111yescharacteristic
375SD16—82no—
376C2×C8—22no—
377C2×C8—42no—
378C2×C8—42no—
379C2×C8—41no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—44no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—44no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C22⋊C4—44no—
391C22⋊C4—44no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C42—41no—
401C42—41no—
402C42—41no—
403C42—41no—
404C13#1032311yescharacteristic, direct product factor, Sylow
405C23—41no—
406C23—41no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23C13×#12011yescharacteristic
413C23C13×#12011yescharacteristic
414C23C13×#12111yescharacteristic
415C23C2×C13×SD1611yescharacteristic
416C23C13×#13511yescharacteristic
417C23C13×AGL(1,ℤ/8)11yescharacteristic
418C23C13×#13711yescharacteristic
419Q8—42no—
420Q8—81no—
421D4—42no—
422D4—81no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4C13×#12011yescharacteristic
461C2×C4C13×#12111yescharacteristic
462C2×C4C13×#12111yescharacteristic
463C2×C4C13×#12711yescharacteristic
464C8—42no—
465C8—81no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—82no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22C13×#39211yescharacteristic
482C22C13×#44811yescharacteristic
483C22C13×#44911yescharacteristic
484C22C13×#45011yescharacteristic
485C22C13×#45211yescharacteristic
486C22C13×#46511yescharacteristic
487C22C13×#46811yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—82no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4C13×#45812yes—
499C2—21no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—161no—
506C2C13×#200011yescharacteristic
507C2C13×#201011yescharacteristic
508C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2855C2semidirect
4. C13×#1817C2semidirect
5. C13×#1520C2semidirect
7. C13×#1289C2semidirect
84. #10323C13direct (N × H)
115. C22×C4×C13SD16semidirect
152. #2855C2×C13semidirect
154. #1817C2×C13semidirect
155. #1520C2×C13semidirect
157. #1289C2×C13semidirect
368. C22×C4C13×SD16semidirect
404. C13#10323direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31872
C13×#28552
C13×#28542
C13×#18172
C13×#15202
C13×#15192
C13×#12892
#1032313