Finite Group Databasebeta

← C13×#10374 #15696713

Subgroups — C13×#10374 #15696713

Order 3328.

508 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2549C211yesmaximal, 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×C22⋊Q8—21no—
9C2×C13×#121C2211yescharacteristic
10C2×C13×#99—21no—
11C2×C13×#99—21no—
12C2×C13×C22⋊C8C2211yescharacteristic
13C2×C13×C22⋊C8C2211yescharacteristic
14C13×#398—21no—
15C13×#395—21no—
16C13×#391—21no—
17C13×#389—21no—
18C13×#385—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×Q8×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13Q811yescharacteristic, complemented
30C23×C4×C13—21no—
31C23×C4×C13C2311yescharacteristic
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C13×C22⋊Q8—42no—
35C13×C22⋊Q8—42no—
36C13×#121—21no—
37C13×#121—21no—
38C13×#121—21no—
39C13×#121—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4Q811yescharacteristic, complemented
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4D411yescharacteristic
52C2×C13×C22⋊C4D411yescharacteristic
53C2×C42×C13—21no—
54C13×#99—42no—
55C13×#99—42no—
56C13×C22⋊C8—21no—
57C13×C22⋊C8—21no—
58C13×C22⋊C8—21no—
59C13×C22⋊C8—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64C13×#95—21no—
65C13×#95D411yescharacteristic
66C13×#95D411yescharacteristic
67C13×#95D411yescharacteristic
68C13×#95D411yescharacteristic
69#10374C1311yesmaximal, characteristic, direct product factor, Sylow
70C24×C13—21no—
71C24×C13C2×D411yescharacteristic
72C2×Q8×C13—42no—
73C2×Q8×C13—42no—
74C2×Q8×C13—81no—
75C2×D4×C13—21no—
76C2×D4×C13—21no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—81no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—42no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—81no—
96C22×C4×C13—81no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×Q811yescharacteristic
100C22×C4×C13#4111yescharacteristic
101C22×C4×C13#4111yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C2×C8×C13—81no—
106C2×C8×C13—81no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4—42no—
111C13×C4⋊C4—42no—
112C13×C4⋊C4—42no—
113C13×C4⋊C4—81no—
114C13×C4⋊C4—81no—
115C13×C4⋊C4—81no—
116C13×C22⋊C4—21no—
117C13×C22⋊C4—21no—
118C13×C22⋊C4—41no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4D812yes—
125C13×C22⋊C4SD1612yes—
126C42×C13—81no—
127#2549C2×C1311yescharacteristic, complemented
128#1964C2×C1311yescharacteristic
129#1519C2×C1311yescharacteristic
130C2×#327C2×C1311yescharacteristic
131#1294C2×C1311yescharacteristic, complemented
132#1289C2×C1311yescharacteristic, complemented
133#1282C2×C1311yescharacteristic, complemented
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—81no—
140C23×C13—81no—
141C23×C13#12011yescharacteristic
142C23×C13C22⋊Q811yescharacteristic
143C23×C13#12411yescharacteristic
144C23×C13C2×D811yescharacteristic
145C23×C13C2×SD1611yescharacteristic
146C23×C13AGL(1,ℤ/8)11yescharacteristic
147C23×C13#13711yescharacteristic
148Q8×C13—84no—
149D4×C13—81no—
150D4×C13—81no—
151D4×C13—81no—
152D4×C13—81no—
153D4×C13—81no—
154D4×C13—81no—
155C2×C4×C13—22no—
156C2×C4×C13—22no—
157C2×C4×C13—22no—
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—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—82no—
183C2×C4×C13—82no—
184C2×C4×C13—81no—
185C2×C4×C13—81no—
186C2×C4×C13—81no—
187C2×C4×C13C22⋊Q811yescharacteristic
188C2×C4×C13C22⋊Q811yescharacteristic
189C2×C4×C13#12411yescharacteristic
190C2×C4×C13#12411yescharacteristic
191C8×C13—81no—
192C8×C13—81no—
193C2×C22⋊Q8—21no—
194C2×#121C22×C1311yescharacteristic
195C2×#99—21no—
196C2×#99—21no—
197C2×C22⋊C8C22×C1311yescharacteristic
198C2×C22⋊C8C22×C1311yescharacteristic
199#398—21no—
200#395—21no—
201#391—21no—
202#389—21no—
203#385—21no—
204#380C22×C1311yescharacteristic
205#380C22×C1311yescharacteristic
206C4×C22⋊C4C22×C1311yescharacteristic
207C2×#95C22×C1311yescharacteristic
208#327—21no—
209#327—21no—
210#327—21no—
211#327—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—161no—
226C22×C13—161no—
227C22×C13#39311yescharacteristic
228C22×C13#44711yescharacteristic
229C22×C13#44811yescharacteristic
230C22×C13#47411yescharacteristic
231C22×C13#47611yescharacteristic
232C22×C13#48611yescharacteristic
233C22×C13#48911yescharacteristic
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—21no—
238C4×C13—42no—
239C4×C13—42no—
240C4×C13—42no—
241C4×C13—81no—
242C4×C13—81no—
243C4×C13—81no—
244C4×C13—81no—
245C4×C13—161no—
246C22×Q8—21no—
247C22×D4—21no—
248C22×D4Q8×C1311yescharacteristic, complemented
249C23×C4—21no—
250C23×C4C23×C1311yescharacteristic
251C22×C8—21no—
252C22×C8—21no—
253C22⋊Q8—42no—
254C22⋊Q8—42no—
255#121—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4Q8×C1311yescharacteristic, complemented
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4D4×C1311yescharacteristic
271C2×C22⋊C4D4×C1311yescharacteristic
272C2×C42—21no—
273#99—42no—
274#99—42no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95D4×C1311yescharacteristic
285#95D4×C1311yescharacteristic
286#95D4×C1311yescharacteristic
287#95D4×C1311yescharacteristic
288C2×C13—21no—
289C2×C13—21no—
290C2×C13—21no—
291C2×C13—21no—
292C2×C13—21no—
293C2×C13—21no—
294C2×C13—161no—
295C2×C13#202311yescharacteristic
296C2×C13#203111yescharacteristic
297C2×C13#203211yescharacteristic
298C24—21no—
299C24C2×D4×C1311yescharacteristic
300C2×Q8—42no—
301C2×Q8—42no—
302C2×Q8—81no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—81no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—81no—
324C22×C4—81no—
325C22×C4C2×D4×C1311yescharacteristic
326C22×C4C2×D4×C1311yescharacteristic
327C22×C4C2×Q8×C1311yescharacteristic
328C22×C4C13×#4111yescharacteristic
329C22×C4C13×#4111yescharacteristic
330C22×C4C13×#4111yescharacteristic
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—81no—
334C2×C8—81no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—81no—
342C4⋊C4—81no—
343C4⋊C4—81no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4C13×D812yes—
353C22⋊C4C13×SD1612yes—
354C42—81no—
355C13#1037411yescharacteristic, direct product factor, Sylow
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—81no—
362C23—81no—
363C23C13×#12011yescharacteristic
364C23C13×C22⋊Q811yescharacteristic
365C23C13×#12411yescharacteristic
366C23C2×C13×D811yescharacteristic
367C23C2×C13×SD1611yescharacteristic
368C23C13×AGL(1,ℤ/8)11yescharacteristic
369C23C13×#13711yescharacteristic
370Q8—84no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
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—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4C13×C22⋊Q811yescharacteristic
410C2×C4C13×C22⋊Q811yescharacteristic
411C2×C4C13×#12411yescharacteristic
412C2×C4C13×#12411yescharacteristic
413C8—81no—
414C8—81no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—161no—
429C22—161no—
430C22C13×#39311yescharacteristic
431C22C13×#44711yescharacteristic
432C22C13×#44811yescharacteristic
433C22C13×#47411yescharacteristic
434C22C13×#47611yescharacteristic
435C22C13×#48611yescharacteristic
436C22C13×#48911yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—42no—
443C4—42no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—161no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—161no—
456C2C13×#202311yescharacteristic
457C2C13×#203111yescharacteristic
458C2C13×#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×#2549C2semidirect
5. C13×#1294C2semidirect
6. C13×#1289C2semidirect
7. C13×#1282C2semidirect
29. C22×D4×C13Q8semidirect
47. C2×C13×C4⋊C4Q8semidirect
69. #10374C13direct (N × H)
127. #2549C2×C13semidirect
131. #1294C2×C13semidirect
132. #1289C2×C13semidirect
133. #1282C2×C13semidirect
248. C22×D4Q8×C13semidirect
266. C2×C4⋊C4Q8×C13semidirect
355. C13#10374direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25492
C13×#19642
C13×#15192
C2×C13×#3272
C13×#12942
C13×#12892
C13×#12822
#1037413