Finite Group Databasebeta

← C13×#13318 #15699657

Subgroups — C13×#13318 #15699657

Order 3328.

532 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3414C211yesmaximal, characteristic, complemented
2C13×#3067C211yesmaximal, characteristic, complemented
3C13×#3060C211yesmaximal, characteristic, complemented
4C2×C13×#360C211yesmaximal, characteristic, complemented
5C13×#2143C211yesmaximal, characteristic, complemented
6C13×#2117C211yesmaximal, characteristic, complemented
7C13×#1383C211yesmaximal, characteristic, complemented
8C13×#575—21no—
9C2×C13×#135C2211yescharacteristic
10C2×C13×#135C2211yescharacteristic
11C2×C13×#131C2211yescharacteristic
12C13×#537—21no—
13C13×#510—21no—
14C13×#510—21no—
15C13×#509—21no—
16C13×#509—21no—
17C13×#508—22no—
18C2×C13×M32C2211yescharacteristic
19C2×C13×M32C2211yescharacteristic
20C13×#473—21no—
21C13×#472—21no—
22C13×#471—22no—
23C13×#470—21no—
24C13×#469—21no—
25C13×#465—22no—
26C2×C13×#108C2211yescharacteristic
27C2×C13×#106C2211yescharacteristic
28C13×#417—21no—
29C13×#413—21no—
30C13×#360—22no—
31C13×#359—22no—
32C13×#350—22no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41D411yescharacteristic
36C13×#137—22no—
37C13×#137—41no—
38C13×AGL(1,ℤ/8)—22no—
39C13×AGL(1,ℤ/8)—41no—
40C13×#135—21no—
41C13×#135—21no—
42C13×#135—21no—
43C13×#135—21no—
44C13×#135—21no—
45C13×#135—21no—
46C13×#135—21no—
47C13×#135—21no—
48C13×#135—42no—
49C2×C13×Q16D411yescharacteristic
50C2×C13×Q16D411yescharacteristic, complemented
51C2×C13×SD16—21no—
52C2×C13×SD16—21no—
53C2×C13×D8D411yescharacteristic
54C2×C13×D8D411yescharacteristic, complemented
55C13×#131—21no—
56C13×#131—21no—
57C13×#131—21no—
58C13×#131—21no—
59C2×C13×M16—21no—
60C2×C13×M16—21no—
61C2×C13×M16D411yescharacteristic
62C22×C8×C13—21no—
63C22×C8×C13C2311yescharacteristic
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—41no—
66C13×#121—22no—
67C13×#121—42no—
68C13×#121—41no—
69C2×C13×C4⋊C4—21no—
70C13×Q32—22no—
71C13×SD32—22no—
72C13×SD32—22no—
73C13×D16—22no—
74C13×M32—21no—
75C13×M32—21no—
76C13×M32—21no—
77C13×M32—21no—
78C2×C13×C16—21no—
79C2×C13×C16D412yescomplemented
80C13×#108—21no—
81C13×#108D412yescomplemented
82C13×#106—21no—
83C13×#106D412yes—
84C13×#103—22no—
85C13×#102—22no—
86C13×#101—22no—
87C13×#100—22no—
88#13318C1311yesmaximal, characteristic, direct product factor, Sylow
89C13×#41—21no—
90C13×#41—21no—
91C13×#41—21no—
92C13×#41—21no—
93C13×#41—41no—
94C13×#41—41no—
95C13×#41—41no—
96C13×#41—41no—
97C13×#41—41no—
98C13×#41—41no—
99C13×#41—41no—
100C13×#41—41no—
101C2×Q8×C13—21no—
102C2×Q8×C13—21no—
103C2×Q8×C13D811yescharacteristic
104C2×D4×C13—21no—
105C2×D4×C13—21no—
106C2×D4×C13—21no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C2×D4×C13—42no—
110C2×D4×C13D811yescharacteristic
111C22×C4×C13—21no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13C2×D411yescharacteristic
116C13×Q16—21no—
117C13×Q16—21no—
118C13×Q16—21no—
119C13×Q16—21no—
120C13×Q16—42no—
121C13×SD16—42no—
122C13×SD16—42no—
123C13×SD16—41no—
124C13×SD16—41no—
125C13×SD16—41no—
126C13×SD16—41no—
127C13×D8—21no—
128C13×D8—21no—
129C13×D8—21no—
130C13×D8—21no—
131C13×D8—42no—
132C13×M16—21no—
133C13×M16—22no—
134C13×M16—21no—
135C13×M16—41no—
136C13×M16—41no—
137C13×M16—41no—
138C2×C8×C13—21no—
139C2×C8×C13—41no—
140C2×C8×C13—41no—
141C2×C8×C13—41no—
142C2×C8×C13C2×D411yescharacteristic
143C2×C8×C13C2×D411yescharacteristic
144C2×C8×C13C2×D411yescharacteristic
145C2×C8×C13C2×D411yescharacteristic
146C2×C8×C13C2×D411yescharacteristic
147C2×C8×C13#4111yescharacteristic
148C13×C4⋊C4—22no—
149C13×C4⋊C4—42no—
150C13×C4⋊C4—41no—
151C13×C22⋊C4—42no—
152C13×C22⋊C4—42no—
153C13×C16—22no—
154C13×C16—41no—
155#3414C2×C1311yescharacteristic, complemented
156#3067C2×C1311yescharacteristic, complemented
157#3060C2×C1311yescharacteristic, complemented
158C2×#360C2×C1311yescharacteristic, complemented
159#2143C2×C1311yescharacteristic, complemented
160#2117C2×C1311yescharacteristic, complemented
161#1383C2×C1311yescharacteristic, complemented
162C23×C13—21no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13AGL(1,ℤ/8)11yescharacteristic
166Q8×C13—21no—
167Q8×C13—21no—
168Q8×C13—41no—
169Q8×C13—41no—
170Q8×C13—41no—
171Q8×C13—41no—
172D4×C13—21no—
173D4×C13—21no—
174D4×C13—41no—
175D4×C13—41no—
176D4×C13—41no—
177D4×C13—41no—
178D4×C13—41no—
179D4×C13—41no—
180D4×C13—81no—
181D4×C13—81no—
182D4×C13—81no—
183D4×C13—81no—
184D4×C13—162no—
185C2×C4×C13—21no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—42no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—81no—
192C2×C4×C13—81no—
193C2×C4×C13—81no—
194C2×C4×C13—81no—
195C2×C4×C13—161no—
196C2×C4×C13#12011yescharacteristic
197C2×C4×C13#12011yescharacteristic
198C2×C4×C13#12111yescharacteristic
199C2×C4×C13C2×D811yescharacteristic
200C2×C4×C13#13511yescharacteristic
201C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
202C8×C13—41no—
203C8×C13—42no—
204C8×C13#12011yescharacteristic
205C8×C13#12111yescharacteristic
206C8×C13#12111yescharacteristic
207C8×C13#12711yescharacteristic
208#575—21no—
209C2×#135C22×C1311yescharacteristic
210C2×#135C22×C1311yescharacteristic
211C2×#131C22×C1311yescharacteristic
212#537—21no—
213#510—21no—
214#510—21no—
215#509—21no—
216#509—21no—
217#508—22no—
218C2×M32C22×C1311yescharacteristic
219C2×M32C22×C1311yescharacteristic
220#473—21no—
221#472—21no—
222#471—22no—
223#470—21no—
224#469—21no—
225#465—22no—
226C2×#108C22×C1311yescharacteristic
227C2×#106C22×C1311yescharacteristic
228#417—21no—
229#413—21no—
230#360—22no—
231#359—22no—
232#350—22no—
233C22×C13—41no—
234C22×C13—42no—
235C22×C13—41no—
236C22×C13—81no—
237C22×C13—81no—
238C22×C13—81no—
239C22×C13—81no—
240C22×C13—161no—
241C22×C13#44711yescharacteristic
242C22×C13#44911yescharacteristic
243C22×C13#46911yescharacteristic
244C4×C13—41no—
245C4×C13—82no—
246C4×C13—81no—
247C4×C13—81no—
248C4×C13#39211yescharacteristic
249C4×C13#44711yescharacteristic
250C4×C13#44911yescharacteristic
251C4×C13#46611yescharacteristic
252C2×#41—21no—
253C2×#41—21no—
254C2×#41D4×C1311yescharacteristic
255#137—22no—
256#137—41no—
257AGL(1,ℤ/8)—22no—
258AGL(1,ℤ/8)—41no—
259#135—21no—
260#135—21no—
261#135—21no—
262#135—21no—
263#135—21no—
264#135—21no—
265#135—21no—
266#135—21no—
267#135—42no—
268C2×Q16D4×C1311yescharacteristic
269C2×Q16D4×C1311yescharacteristic, complemented
270C2×SD16—21no—
271C2×SD16—21no—
272C2×D8D4×C1311yescharacteristic
273C2×D8D4×C1311yescharacteristic, complemented
274#131—21no—
275#131—21no—
276#131—21no—
277#131—21no—
278C2×M16—21no—
279C2×M16—21no—
280C2×M16D4×C1311yescharacteristic
281C22×C8—21no—
282C22×C8C23×C1311yescharacteristic
283C22⋊Q8—22no—
284C22⋊Q8—41no—
285#121—22no—
286#121—42no—
287#121—41no—
288C2×C4⋊C4—21no—
289Q32—22no—
290SD32—22no—
291SD32—22no—
292D16—22no—
293M32—21no—
294M32—21no—
295M32—21no—
296M32—21no—
297C2×C16—21no—
298C2×C16D4×C1312yescomplemented
299#108—21no—
300#108D4×C1312yescomplemented
301#106—21no—
302#106D4×C1312yes—
303#103—22no—
304#102—22no—
305#101—22no—
306#100—22no—
307C2×C13—21no—
308C2×C13—21no—
309C2×C13—21no—
310C2×C13—81no—
311C2×C13—161no—
312C2×C13—161no—
313C2×C13#199911yescharacteristic
314#41—21no—
315#41—21no—
316#41—21no—
317#41—21no—
318#41—41no—
319#41—41no—
320#41—41no—
321#41—41no—
322#41—41no—
323#41—41no—
324#41—41no—
325#41—41no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8C13×D811yescharacteristic
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—42no—
335C2×D4C13×D811yescharacteristic
336C22×C4—21no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4C2×D4×C1311yescharacteristic
341Q16—21no—
342Q16—21no—
343Q16—21no—
344Q16—21no—
345Q16—42no—
346SD16—42no—
347SD16—42no—
348SD16—41no—
349SD16—41no—
350SD16—41no—
351SD16—41no—
352D8—21no—
353D8—21no—
354D8—21no—
355D8—21no—
356D8—42no—
357M16—21no—
358M16—22no—
359M16—21no—
360M16—41no—
361M16—41no—
362M16—41no—
363C2×C8—21no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8C2×D4×C1311yescharacteristic
368C2×C8C2×D4×C1311yescharacteristic
369C2×C8C2×D4×C1311yescharacteristic
370C2×C8C2×D4×C1311yescharacteristic
371C2×C8C2×D4×C1311yescharacteristic
372C2×C8C13×#4111yescharacteristic
373C4⋊C4—22no—
374C4⋊C4—42no—
375C4⋊C4—41no—
376C22⋊C4—42no—
377C22⋊C4—42no—
378C16—22no—
379C16—41no—
380C13#1331811yescharacteristic, direct product factor, Sylow
381C23—21no—
382C23—41no—
383C23—41no—
384C23C13×AGL(1,ℤ/8)11yescharacteristic
385Q8—21no—
386Q8—21no—
387Q8—41no—
388Q8—41no—
389Q8—41no—
390Q8—41no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—162no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—161no—
415C2×C4C13×#12011yescharacteristic
416C2×C4C13×#12011yescharacteristic
417C2×C4C13×#12111yescharacteristic
418C2×C4C2×C13×D811yescharacteristic
419C2×C4C13×#13511yescharacteristic
420C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
421C8—41no—
422C8—42no—
423C8C13×#12011yescharacteristic
424C8C13×#12111yescharacteristic
425C8C13×#12111yescharacteristic
426C8C13×#12711yescharacteristic
427C22—41no—
428C22—42no—
429C22—41no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—161no—
435C22C13×#44711yescharacteristic
436C22C13×#44911yescharacteristic
437C22C13×#46911yescharacteristic
438C4—41no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4C13×#39211yescharacteristic
443C4C13×#44711yescharacteristic
444C4C13×#44911yescharacteristic
445C4C13×#46611yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—81no—
450C2—161no—
451C2—161no—
452C2C13×#199911yescharacteristic
subgroupG/H
center, socleC2×C13#1999
commutator, Frattini, cosocleC22×C8C23×C13
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3414C2semidirect
2. C13×#3067C2semidirect
3. C13×#3060C2semidirect
4. C2×C13×#360C2semidirect
5. C13×#2143C2semidirect
6. C13×#2117C2semidirect
7. C13×#1383C2semidirect
50. C2×C13×Q16D4semidirect
54. C2×C13×D8D4semidirect
79. C2×C13×C16D4semidirect
81. C13×#108D4semidirect
88. #13318C13direct (N × H)
155. #3414C2×C13semidirect
156. #3067C2×C13semidirect
157. #3060C2×C13semidirect
158. C2×#360C2×C13semidirect
159. #2143C2×C13semidirect
160. #2117C2×C13semidirect
161. #1383C2×C13semidirect
269. C2×Q16D4×C13semidirect
273. C2×D8D4×C13semidirect
298. C2×C16D4×C13semidirect
300. #108D4×C13semidirect
380. C13#13318direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34142
C13×#30672
C13×#30602
C2×C13×#3602
C13×#21432
C13×#21172
C13×#13832
#1331813