Finite Group Databasebeta

← C13×#33596 #15719935

Subgroups — C13×#33596 #15719935

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3414C211yesmaximal, characteristic
2C2×C13×#510C211yesmaximal, characteristic, complemented
3C13×#3156C211yesmaximal, characteristic, complemented
4C13×#2957C211yesmaximal, characteristic, complemented
5C13×#2214C214yesmaximal, complemented
6C13×#2212C214yesmaximal, complemented
7C13×#2153C211yesmaximal, characteristic, complemented
8C13×#2148C211yesmaximal, characteristic, complemented
9C2×C13×#362C211yesmaximal, characteristic, complemented
10C2×C13×#137—21no—
11C2×C13×#135C2211yescharacteristic
12C2×C13×#135C2211yescharacteristic
13C22×C13×Q16C2211yescharacteristic
14C13×#568—21no—
15C13×#536—21no—
16C13×#510—22no—
17C13×#510—21no—
18C13×#510C2214yes—
19C13×#510C2212yes—
20C13×#509—21no—
21C13×#509C2212yes—
22C13×#508—22no—
23C2×C13×Q32—21no—
24C2×C13×SD32—21no—
25C2×C13×M32C2211yescharacteristic
26C2×C13×M32C2211yescharacteristic
27C13×#497—22no—
28C13×#495C2212yescomplemented
29C13×#494C2212yescomplemented
30C13×#444—22no—
31C13×#443C2214yes—
32C2×C13×#108C2211yescharacteristic
33C13×#421—21no—
34C13×#405C2211yescharacteristic
35C13×#364C2214yescomplemented
36C13×#362C2214yescomplemented
37C13×#362C2212yescomplemented
38C13×#361C2212yescomplemented
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C22×Q8×C13—21no—
42C13×#137—42no—
43C13×#137—42no—
44C13×#135—21no—
45C13×#135—21no—
46C13×#135—21no—
47C13×#135—21no—
48C13×#135—21no—
49C13×#135—21no—
50C13×#135D412yes—
51C13×#135C2312yes—
52C2×C13×Q16—21no—
53C2×C13×Q16—21no—
54C2×C13×Q16—22no—
55C2×C13×Q16—21no—
56C2×C13×Q16—21no—
57C2×C13×Q16—21no—
58C2×C13×Q16D411yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×Q16C2312yes—
61C2×C13×SD16—22no—
62C2×C13×SD16—21no—
63C2×C13×SD16—21no—
64C2×C13×D8D411yescharacteristic
65C2×C13×D8C2311yescharacteristic
66C13×#131—24no—
67C13×#131—42no—
68C2×C13×M16—21no—
69C2×C13×M16—42no—
70C2×C13×M16D411yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C13×C4⋊Q8—22no—
73C13×#124—22no—
74C13×#123—42no—
75C13×C22⋊Q8—42no—
76C13×#117D411yescharacteristic
77C13×Q32—24no—
78C13×Q32—22no—
79C13×SD32—22no—
80C13×SD32—24no—
81C13×SD32—22no—
82C13×D16—22no—
83C13×M32—21no—
84C13×M32—21no—
85C13×M32C2312yes—
86C13×M32C2312yes—
87C2×C13×C16—21no—
88C2×C13×C16—21no—
89C13×#108—21no—
90C13×#108C2312yes—
91C13×#104—24no—
92C13×#97D412yes—
93C4×C8×C13C2312yes—
94#33596C1311yesmaximal, characteristic, direct product factor, Sylow
95C13×#41—22no—
96C13×#41—22no—
97C13×#41—41no—
98C13×#41—41no—
99C13×#41—41no—
100C13×#41—41no—
101C13×#41—41no—
102C13×#41—41no—
103C2×Q8×C13—21no—
104C2×Q8×C13—22no—
105C2×Q8×C13—21no—
106C2×Q8×C13—41no—
107C2×Q8×C13—41no—
108C2×Q8×C13—41no—
109C2×Q8×C13—41no—
110C2×Q8×C13—41no—
111C2×D4×C13—21no—
112C2×D4×C13—21no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13—41no—
117C22×C4×C13—41no—
118C22×C4×C13C2×D411yescharacteristic
119C13×Q16—21no—
120C13×Q16—22no—
121C13×Q16—21no—
122C13×Q16—22no—
123C13×Q16—21no—
124C13×Q16—41no—
125C13×Q16—41no—
126C13×Q16—44no—
127C13×Q16C2×D412yes—
128C13×SD16—22no—
129C13×SD16—22no—
130C13×SD16—41no—
131C13×SD16—41no—
132C13×SD16—44no—
133C13×D8—21no—
134C13×D8—21no—
135C13×D8—21no—
136C13×D8C2×D412yes—
137C13×M16—22no—
138C13×M16—41no—
139C13×M16—44no—
140C13×M16D812yes—
141C13×M16D812yes—
142C2×C8×C13—41no—
143C2×C8×C13—44no—
144C2×C8×C13C2×D411yescharacteristic
145C2×C8×C13C2×D411yescharacteristic
146C2×C8×C13C2×D411yescharacteristic
147C2×C8×C13C2×D412yes—
148C2×C8×C13#4111yescharacteristic
149C2×C8×C13#4111yescharacteristic
150C2×C8×C13C2411yescharacteristic
151C13×C4⋊C4—21no—
152C13×C4⋊C4—44no—
153C13×C22⋊C4—21no—
154C13×C22⋊C4—44no—
155C42×C13C2×D412yes—
156C13×C16—22no—
157C13×C16—22no—
158#3414C2×C1311yescharacteristic
159C2×#510C2×C1311yescharacteristic, complemented
160#3156C2×C1311yescharacteristic, complemented
161#2957C2×C1311yescharacteristic, complemented
162#2214C2×C1314yescomplemented
163#2212C2×C1314yescomplemented
164#2153C2×C1311yescharacteristic, complemented
165#2148C2×C1311yescharacteristic, complemented
166C2×#362C2×C1311yescharacteristic, complemented
167C23×C13—41no—
168C23×C13—41no—
169C23×C13AGL(1,ℤ/8)11yescharacteristic
170Q8×C13—22no—
171Q8×C13—41no—
172Q8×C13—41no—
173Q8×C13—42no—
174Q8×C13—42no—
175Q8×C13—41no—
176Q8×C13—81no—
177Q8×C13—81no—
178D4×C13—22no—
179D4×C13—42no—
180D4×C13—42no—
181D4×C13—41no—
182D4×C13—41no—
183D4×C13—41no—
184D4×C13—81no—
185D4×C13—81no—
186C2×C4×C13—22no—
187C2×C4×C13—41no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—41no—
192C2×C4×C13—81no—
193C2×C4×C13—81no—
194C2×C4×C13—81no—
195C2×C4×C13—81no—
196C2×C4×C13#12111yescharacteristic
197C2×C4×C13#12111yescharacteristic
198C2×C4×C13C2×D811yescharacteristic
199C2×C4×C13C2×D811yescharacteristic
200C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C13C22×D411yescharacteristic
202C8×C13—42no—
203C8×C13#12111yescharacteristic
204C8×C13#12111yescharacteristic
205C8×C13C2×D814yes—
206C8×C13C22×D411yescharacteristic
207C8×C13C2×#4111yescharacteristic
208C2×#137—21no—
209C2×#135C22×C1311yescharacteristic
210C2×#135C22×C1311yescharacteristic
211C22×Q16C22×C1311yescharacteristic
212#568—21no—
213#536—21no—
214#510—22no—
215#510—21no—
216#510C22×C1314yes—
217#510C22×C1312yes—
218#509—21no—
219#509C22×C1312yes—
220#508—22no—
221C2×Q32—21no—
222C2×SD32—21no—
223C2×M32C22×C1311yescharacteristic
224C2×M32C22×C1311yescharacteristic
225#497—22no—
226#495C22×C1312yescomplemented
227#494C22×C1312yescomplemented
228#444—22no—
229#443C22×C1314yes—
230C2×#108C22×C1311yescharacteristic
231#421—21no—
232#405C22×C1311yescharacteristic
233#364C22×C1314yescomplemented
234#362C22×C1314yescomplemented
235#362C22×C1312yescomplemented
236#361C22×C1312yescomplemented
237C22×C13—41no—
238C22×C13—42no—
239C22×C13—82no—
240C22×C13—81no—
241C22×C13—161no—
242C22×C13#45911yescharacteristic
243C22×C13#45911yescharacteristic
244C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C13—42no—
246C4×C13—42no—
247C4×C13—81no—
248C4×C13—82no—
249C4×C13#45911yescharacteristic
250C4×C13#45911yescharacteristic
251C4×C13C2×#12111yescharacteristic
252C4×C13C22×D811yescharacteristic
253C2×#41—21no—
254C2×#41—21no—
255C22×Q8—21no—
256#137—42no—
257#137—42no—
258#135—21no—
259#135—21no—
260#135—21no—
261#135—21no—
262#135—21no—
263#135—21no—
264#135D4×C1312yes—
265#135C23×C1312yes—
266C2×Q16—21no—
267C2×Q16—21no—
268C2×Q16—21no—
269C2×Q16—22no—
270C2×Q16—21no—
271C2×Q16—21no—
272C2×Q16D4×C1311yescharacteristic
273C2×Q16C23×C1312yes—
274C2×Q16C23×C1311yescharacteristic
275C2×SD16—21no—
276C2×SD16—22no—
277C2×SD16—21no—
278C2×D8D4×C1311yescharacteristic
279C2×D8C23×C1311yescharacteristic
280#131—24no—
281#131—42no—
282C2×M16—21no—
283C2×M16—42no—
284C2×M16D4×C1311yescharacteristic
285C22×C8C23×C1311yescharacteristic
286C4⋊Q8—22no—
287#124—22no—
288#123—42no—
289C22⋊Q8—42no—
290#117D4×C1311yescharacteristic
291Q32—24no—
292Q32—22no—
293SD32—22no—
294SD32—24no—
295SD32—22no—
296D16—22no—
297M32—21no—
298M32—21no—
299M32C23×C1312yes—
300M32C23×C1312yes—
301C2×C16—21no—
302C2×C16—21no—
303#108—21no—
304#108C23×C1312yes—
305#104—24no—
306#97D4×C1312yes—
307C4×C8C23×C1312yes—
308C2×C13—21no—
309C2×C13—21no—
310C2×C13—21no—
311C2×C13—82no—
312C2×C13—161no—
313C2×C13C2×#45911yescharacteristic
314#41—22no—
315#41—22no—
316#41—41no—
317#41—41no—
318#41—41no—
319#41—41no—
320#41—41no—
321#41—41no—
322C2×Q8—21no—
323C2×Q8—22no—
324C2×Q8—21no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8—41no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—41no—
333C2×D4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4C2×D4×C1311yescharacteristic
338Q16—21no—
339Q16—22no—
340Q16—21no—
341Q16—22no—
342Q16—21no—
343Q16—41no—
344Q16—41no—
345Q16—44no—
346Q16C2×D4×C1312yes—
347SD16—22no—
348SD16—22no—
349SD16—41no—
350SD16—41no—
351SD16—44no—
352D8—21no—
353D8—21no—
354D8—21no—
355D8C2×D4×C1312yes—
356M16—22no—
357M16—41no—
358M16—44no—
359M16C13×D812yes—
360M16C13×D812yes—
361C2×C8—41no—
362C2×C8—44no—
363C2×C8C2×D4×C1311yescharacteristic
364C2×C8C2×D4×C1311yescharacteristic
365C2×C8C2×D4×C1311yescharacteristic
366C2×C8C2×D4×C1312yes—
367C2×C8C13×#4111yescharacteristic
368C2×C8C13×#4111yescharacteristic
369C2×C8C24×C1311yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—44no—
372C22⋊C4—21no—
373C22⋊C4—44no—
374C42C2×D4×C1312yes—
375C16—22no—
376C16—22no—
377C13#3359611yescharacteristic, direct product factor, Sylow
378C23—41no—
379C23—41no—
380C23C13×AGL(1,ℤ/8)11yescharacteristic
381Q8—22no—
382Q8—41no—
383Q8—41no—
384Q8—42no—
385Q8—42no—
386Q8—41no—
387Q8—81no—
388Q8—81no—
389D4—22no—
390D4—42no—
391D4—42no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—81no—
396D4—81no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4C13×#12111yescharacteristic
408C2×C4C13×#12111yescharacteristic
409C2×C4C2×C13×D811yescharacteristic
410C2×C4C2×C13×D811yescharacteristic
411C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
412C2×C4C22×D4×C1311yescharacteristic
413C8—42no—
414C8C13×#12111yescharacteristic
415C8C13×#12111yescharacteristic
416C8C2×C13×D814yes—
417C8C22×D4×C1311yescharacteristic
418C8C2×C13×#4111yescharacteristic
419C22—41no—
420C22—42no—
421C22—82no—
422C22—81no—
423C22—161no—
424C22C13×#45911yescharacteristic
425C22C13×#45911yescharacteristic
426C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
427C4—42no—
428C4—42no—
429C4—81no—
430C4—82no—
431C4C13×#45911yescharacteristic
432C4C13×#45911yescharacteristic
433C4C2×C13×#12111yescharacteristic
434C4C22×C13×D811yescharacteristic
435C2—21no—
436C2—21no—
437C2—21no—
438C2—82no—
439C2—161no—
440C2C2×C13×#45911yescharacteristic
subgroupG/H
center, socleC2×C13C2×#459
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#3414C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#510C2semidirect
3. C13×#3156C2semidirect
4. C13×#2957C2semidirect
5. C13×#2214C2semidirect
6. C13×#2212C2semidirect
7. C13×#2153C2semidirect
8. C13×#2148C2semidirect
9. C2×C13×#362C2semidirect
28. C13×#495C22semidirect
29. C13×#494C22semidirect
35. C13×#364C22semidirect
36. C13×#362C22semidirect
37. C13×#362C22semidirect
38. C13×#361C22semidirect
94. #33596C13direct (N × H)
159. C2×#510C2×C13semidirect
160. #3156C2×C13semidirect
161. #2957C2×C13semidirect
162. #2214C2×C13semidirect
163. #2212C2×C13semidirect
164. #2153C2×C13semidirect
165. #2148C2×C13semidirect
166. C2×#362C2×C13semidirect
226. #495C22×C13semidirect
227. #494C22×C13semidirect
233. #364C22×C13semidirect
234. #362C22×C13semidirect
235. #362C22×C13semidirect
236. #361C22×C13semidirect
377. C13#33596direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34142
C2×C13×#5102
C13×#31562
C13×#29572
C13×#22142
C13×#22122
C13×#21532
C13×#21482
C2×C13×#3622
#3359613