Finite Group Databasebeta

← C13×#10376 #15696715

Subgroups — C13×#10376 #15696715

Order 3328.

464 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2569C211yesmaximal, characteristic, complemented
2C13×#1964C211yesmaximal, characteristic
3C13×#1519C211yesmaximal, characteristic
4C2×C13×#327C211yesmaximal, characteristic
5C13×#1294C211yesmaximal, characteristic, complemented
6C13×#1289C211yesmaximal, characteristic, complemented
7C13×#1282C211yesmaximal, characteristic, complemented
8C2×C13×#121C2211yescharacteristic
9C2×C13×#99—21no—
10C2×C13×#99—21no—
11C2×C13×C22⋊C8C2211yescharacteristic
12C2×C13×C22⋊C8C2211yescharacteristic
13C13×#400—21no—
14C13×#398—21no—
15C13×#387—21no—
16C13×#387—21no—
17C13×#385—21no—
18C13×#380—21no—
19C13×#380C2211yescharacteristic
20C13×#380C2211yescharacteristic
21C4×C13×C22⋊C4C2211yescharacteristic
22C2×C13×#95C2211yescharacteristic
23C13×#327—21no—
24C13×#327—21no—
25C13×#327—21no—
26C13×#327—21no—
27C22×D4×C13—21no—
28C22×D4×C13Q811yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13C2311yescharacteristic
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C13×#121—21no—
34C13×#121—21no—
35C13×#121—21no—
36C13×#121—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4Q811yescharacteristic
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C42×C13—21no—
50C13×#99—42no—
51C13×#99—42no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95D411yescharacteristic
64C13×#95D411yescharacteristic
65C13×#95D411yescharacteristic
66C13×#95D411yescharacteristic
67#10376C1311yesmaximal, characteristic, direct product factor, Sylow
68C24×C13—21no—
69C24×C13C2×D411yescharacteristic
70C2×D4×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—81no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—42no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—81no—
91C22×C4×C13—81no—
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×Q811yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C22×C4×C13#4111yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—81no—
101C2×C8×C13—81no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—42no—
105C13×C4⋊C4—42no—
106C13×C4⋊C4—81no—
107C13×C4⋊C4—81no—
108C13×C4⋊C4—81no—
109C13×C4⋊C4—81no—
110C13×C22⋊C4—21no—
111C13×C22⋊C4—21no—
112C13×C22⋊C4—21no—
113C13×C22⋊C4—21no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C13×C22⋊C4—41no—
120C42×C13—81no—
121#2569C2×C1311yescharacteristic, complemented
122#1964C2×C1311yescharacteristic
123#1519C2×C1311yescharacteristic
124C2×#327C2×C1311yescharacteristic
125#1294C2×C1311yescharacteristic, complemented
126#1289C2×C1311yescharacteristic, complemented
127#1282C2×C1311yescharacteristic, complemented
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—81no—
134C23×C13—81no—
135C23×C13#12011yescharacteristic
136C23×C13C22⋊Q811yescharacteristic
137C23×C13#12411yescharacteristic
138C23×C13#13511yescharacteristic
139C23×C13#13511yescharacteristic
140C23×C13AGL(1,ℤ/8)11yescharacteristic
141C23×C13AGL(1,ℤ/8)11yescharacteristic
142D4×C13—81no—
143D4×C13—81no—
144D4×C13—81no—
145D4×C13—81no—
146D4×C13—81no—
147D4×C13—81no—
148C2×C4×C13—22no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—82no—
176C2×C4×C13—82no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13C22⋊Q811yescharacteristic
181C2×C4×C13C22⋊Q811yescharacteristic
182C2×C4×C13#12411yescharacteristic
183C2×C4×C13#12411yescharacteristic
184C8×C13—81no—
185C8×C13—81no—
186C2×#121C22×C1311yescharacteristic
187C2×#99—21no—
188C2×#99—21no—
189C2×C22⋊C8C22×C1311yescharacteristic
190C2×C22⋊C8C22×C1311yescharacteristic
191#400—21no—
192#398—21no—
193#387—21no—
194#387—21no—
195#385—21no—
196#380—21no—
197#380C22×C1311yescharacteristic
198#380C22×C1311yescharacteristic
199C4×C22⋊C4C22×C1311yescharacteristic
200C2×#95C22×C1311yescharacteristic
201#327—21no—
202#327—21no—
203#327—21no—
204#327—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—161no—
219C22×C13—161no—
220C22×C13#39311yescharacteristic
221C22×C13#44911yescharacteristic
222C22×C13#44911yescharacteristic
223C22×C13#47811yescharacteristic
224C22×C13#47811yescharacteristic
225C22×C13#48811yescharacteristic
226C22×C13#49011yescharacteristic
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—42no—
232C4×C13—81no—
233C4×C13—81no—
234C4×C13—81no—
235C4×C13—81no—
236C4×C13—81no—
237C4×C13—81no—
238C4×C13—161no—
239C22×D4—21no—
240C22×D4Q8×C1311yescharacteristic
241C23×C4—21no—
242C23×C4C23×C1311yescharacteristic
243C22×C8—21no—
244C22×C8—21no—
245#121—21no—
246#121—21no—
247#121—21no—
248#121—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4Q8×C1311yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4D4×C1311yescharacteristic
260C2×C22⋊C4D4×C1311yescharacteristic
261C2×C42—21no—
262#99—42no—
263#99—42no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95D4×C1311yescharacteristic
276#95D4×C1311yescharacteristic
277#95D4×C1311yescharacteristic
278#95D4×C1311yescharacteristic
279C2×C13—21no—
280C2×C13—21no—
281C2×C13—21no—
282C2×C13—21no—
283C2×C13—21no—
284C2×C13—21no—
285C2×C13—161no—
286C2×C13#202511yescharacteristic
287C2×C13#203111yescharacteristic
288C2×C13#203211yescharacteristic
289C24—21no—
290C24C2×D4×C1311yescharacteristic
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—81no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—81no—
312C22×C4—81no—
313C22×C4C2×D4×C1311yescharacteristic
314C22×C4C2×D4×C1311yescharacteristic
315C22×C4C2×Q8×C1311yescharacteristic
316C22×C4C13×#4111yescharacteristic
317C22×C4C13×#4111yescharacteristic
318C22×C4C13×#4111yescharacteristic
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—81no—
322C2×C8—81no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—81no—
328C4⋊C4—81no—
329C4⋊C4—81no—
330C4⋊C4—81no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C42—81no—
342C13#1037611yescharacteristic, direct product factor, Sylow
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—81no—
349C23—81no—
350C23C13×#12011yescharacteristic
351C23C13×C22⋊Q811yescharacteristic
352C23C13×#12411yescharacteristic
353C23C13×#13511yescharacteristic
354C23C13×#13511yescharacteristic
355C23C13×AGL(1,ℤ/8)11yescharacteristic
356C23C13×AGL(1,ℤ/8)11yescharacteristic
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4C13×C22⋊Q811yescharacteristic
396C2×C4C13×C22⋊Q811yescharacteristic
397C2×C4C13×#12411yescharacteristic
398C2×C4C13×#12411yescharacteristic
399C8—81no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—161no—
415C22—161no—
416C22C13×#39311yescharacteristic
417C22C13×#44911yescharacteristic
418C22C13×#44911yescharacteristic
419C22C13×#47811yescharacteristic
420C22C13×#47811yescharacteristic
421C22C13×#48811yescharacteristic
422C22C13×#49011yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—42no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4—81no—
432C4—81no—
433C4—81no—
434C4—161no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—161no—
442C2C13×#202511yescharacteristic
443C2C13×#203111yescharacteristic
444C2C13×#203211yescharacteristic
subgroupG/H
center, socleC22×C13#393
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
1. C13×#2569C2semidirect
5. C13×#1294C2semidirect
6. C13×#1289C2semidirect
7. C13×#1282C2semidirect
67. #10376C13direct (N × H)
121. #2569C2×C13semidirect
125. #1294C2×C13semidirect
126. #1289C2×C13semidirect
127. #1282C2×C13semidirect
342. C13#10376direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25692
C13×#19642
C13×#15192
C2×C13×#3272
C13×#12942
C13×#12892
C13×#12822
#1037613