Finite Group Databasebeta

← C13×#34976 #15721315

Subgroups — C13×#34976 #15721315

Order 3328.

2810 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C13×#41C212yesmaximal, complemented
2C13×#2609C214yesmaximal, complemented
3C13×#2582C211yesmaximal, characteristic, complemented
4C13×#2538C212yesmaximal, complemented
5C13×#2537C211yesmaximal, characteristic, complemented
6C13×#2485C214yesmaximal, complemented
7C13×#2407C214yesmaximal, complemented
8C13×#2392C214yesmaximal, complemented
9C4×C13×C22⋊Q8C214yesmaximal, complemented
10C4×C13×#121C214yesmaximal, complemented
11C13×#2285C211yesmaximal, characteristic, complemented
12C22×C13×#41C2212yes—
13C2×C13×C22⋊Q8C2214yes—
14C2×C13×#121C2214yes—
15C4×C13×#41—216no—
16C2×C4×Q8×C13C2212yes—
17C2×C4×Q8×C13C2212yes—
18C2×C4×D4×C13C2212yes—
19C2×C4×D4×C13C2212yes—
20C2×C4×D4×C13C2214yes—
21C2×C4×D4×C13C2214yes—
22C2×C4×D4×C13C2214yes—
23C2×C13×#117C2214yes—
24C2×C13×#117C2212yes—
25C2×C13×#117C2212yes—
26C22×C42×C13C2214yes—
27C22×C42×C13C2211yescharacteristic
28C13×#398C2214yes—
29C13×#397C2214yes—
30C13×#396C2218yes—
31C13×#394C2214yes—
32C13×#394C2218yes—
33C13×#392C2214yes—
34C13×#391C2214yes—
35C13×#390C2214yes—
36C13×#389C2214yes—
37C13×#389C2214yes—
38C13×#388C2218yes—
39C13×#387C2218yes—
40C13×#386C2218yes—
41C13×#385C2218yes—
42C13×#384C2211yescharacteristic
43C13×#384C2211yescharacteristic
44C13×#382C2212yes—
45C13×#380C2214yes—
46C13×#380C2214yes—
47C13×#380C2214yes—
48C4×C13×C4⋊C4C2214yes—
49C4×C13×C4⋊C4C2214yes—
50C4×C13×C22⋊C4C2218yes—
51C2×C13×#41—28no—
52C2×C13×#41—28no—
53C2×C13×#41—28no—
54C22×Q8×C13C2312yes—
55C22×D4×C13C2314yes—
56C22×D4×C13C2314yes—
57C22×D4×C13C2312yes—
58C23×C4×C13C2314yes—
59C23×C4×C13C2314yes—
60C23×C4×C13C2314yes—
61C23×C4×C13C2312yes—
62C23×C4×C13C2311yescharacteristic
63C13×C22⋊Q8—216no—
64C13×#121—216no—
65C4×Q8×C13—28no—
66C4×Q8×C13—28no—
67C4×D4×C13—216no—
68C4×D4×C13—216no—
69C4×D4×C13—28no—
70C4×D4×C13—28no—
71C4×D4×C13—48no—
72C13×#117—28no—
73C13×#117—216no—
74C13×#117—44no—
75C2×C13×C4⋊C4C2314yes—
76C2×C13×C4⋊C4C2314yes—
77C2×C13×C4⋊C4C2318yes—
78C2×C13×C4⋊C4C2312yes—
79C2×C13×C4⋊C4C2312yes—
80C2×C13×C4⋊C4C2314yes—
81C2×C13×C4⋊C4C2314yes—
82C2×C13×C4⋊C4C2312yes—
83C2×C13×C4⋊C4C2312yes—
84C2×C13×C4⋊C4C2314yes—
85C2×C13×C22⋊C4C2318yes—
86C2×C13×C22⋊C4C2318yes—
87C2×C13×C22⋊C4C2314yes—
88C2×C13×C22⋊C4C2314yes—
89C2×C13×C22⋊C4C2314yes—
90C2×C13×C22⋊C4C2314yes—
91C2×C13×C22⋊C4C2318yes—
92C2×C42×C13—216no—
93C2×C42×C13D418yescomplemented
94C2×C42×C13C2314yes—
95C2×C42×C13C2314yes—
96C2×C42×C13C2314yes—
97C2×C42×C13C2314yes—
98C2×C42×C13C2311yescharacteristic
99C2×C42×C13C2311yescharacteristic
100C2×C42×C13C2312yes—
101C13×#95C2318yes—
102C13×#95C2318yes—
103C13×#95C2314yes—
104C13×#95C2318yes—
105C13×#95C2314yes—
106#34976C1311yesmaximal, characteristic, direct product factor, Sylow
107C24×C13C2411yescharacteristic
108C24×C13C2414yes—
109C13×#41—264no—
110C2×Q8×C13—24no—
111C2×Q8×C13—24no—
112C2×Q8×C13#4118yescomplemented
113C2×D4×C13—28no—
114C2×D4×C13—28no—
115C2×D4×C13—216no—
116C2×D4×C13—24no—
117C2×D4×C13—28no—
118C2×D4×C13—24no—
119C2×D4×C13—44no—
120C2×D4×C13#4118yescomplemented
121C22×C4×C13—28no—
122C22×C4×C13—28no—
123C22×C4×C13—28no—
124C22×C4×C13—24no—
125C22×C4×C13—24no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—28no—
129C22×C4×C13—28no—
130C22×C4×C13—28no—
131C22×C4×C13—28no—
132C22×C4×C13—28no—
133C22×C4×C13—28no—
134C22×C4×C13C2×D418yes—
135C22×C4×C13C2×D414yes—
136C22×C4×C13C2414yes—
137C22×C4×C13C2414yes—
138C22×C4×C13C2414yes—
139C22×C4×C13C2414yes—
140C22×C4×C13C2412yes—
141C22×C4×C13C2411yescharacteristic
142C22×C4×C13C2414yes—
143C22×C4×C13C2412yes—
144C22×C4×C13C2411yescharacteristic
145C13×C4⋊C4—28no—
146C13×C4⋊C4—28no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—24no—
149C13×C4⋊C4—28no—
150C13×C4⋊C4—28no—
151C13×C4⋊C4—216no—
152C13×C4⋊C4—42no—
153C13×C4⋊C4—42no—
154C13×C4⋊C4—44no—
155C13×C22⋊C4—28no—
156C13×C22⋊C4—216no—
157C13×C22⋊C4—28no—
158C13×C22⋊C4—28no—
159C13×C22⋊C4—216no—
160C13×C22⋊C4—44no—
161C13×C22⋊C4—48no—
162C42×C13—28no—
163C42×C13—28no—
164C42×C13—28no—
165C42×C13—28no—
166C42×C13C2×D418yes—
167C42×C13C2×D414yes—
168C42×C13C2×D414yes—
169C2×C4×#41C2×C1312yescomplemented
170#2609C2×C1314yescomplemented
171#2582C2×C1311yescharacteristic, complemented
172#2538C2×C1312yescomplemented
173#2537C2×C1311yescharacteristic, complemented
174#2485C2×C1314yescomplemented
175#2407C2×C1314yescomplemented
176#2392C2×C1314yescomplemented
177C4×C22⋊Q8C2×C1314yescomplemented
178C4×#121C2×C1314yescomplemented
179#2285C2×C1311yescharacteristic, complemented
180C23×C13—24no—
181C23×C13—24no—
182C23×C13—22no—
183C23×C13—22no—
184C23×C13—24no—
185C23×C13—24no—
186C23×C13—21no—
187C23×C13—24no—
188C23×C13—21no—
189C23×C13—24no—
190C23×C13C22×D412yes—
191C23×C13C2×#4118yes—
192C23×C13C2511yescharacteristic
193Q8×C13—216no—
194D4×C13—232no—
195D4×C13—216no—
196D4×C13—416no—
197C2×C4×C13—232no—
198C2×C4×C13—24no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—24no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—216no—
205C2×C4×C13—28no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—28no—
210C2×C4×C13—28no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—24no—
216C2×C4×C13—416no—
217C2×C4×C13—416no—
218C2×C4×C13C22×D414yes—
219C2×C4×C13C22×D412yes—
220C2×C4×C13C22×D414yes—
221C2×C4×C13C22×D412yes—
222C2×C4×C13C2×#4118yes—
223C2×C4×C13C2×#4114yes—
224C2×C4×C13C2×#4114yes—
225C2×C4×C13H(5,𝔽2)12yes—
226C2×C4×C132−1+412yes—
227C22×#41C22×C1312yes—
228C2×C22⋊Q8C22×C1314yes—
229C2×#121C22×C1314yes—
230C4×#41—216no—
231C2×C4×Q8C22×C1312yes—
232C2×C4×Q8C22×C1312yes—
233C2×C4×D4C22×C1314yes—
234C2×C4×D4C22×C1314yes—
235C2×C4×D4C22×C1312yes—
236C2×C4×D4C22×C1312yes—
237C2×C4×D4C22×C1314yes—
238C2×#117C22×C1314yes—
239C2×#117C22×C1312yes—
240C2×#117C22×C1312yes—
241C22×C42C22×C1314yes—
242C22×C42C22×C1311yescharacteristic
243#398C22×C1314yes—
244#397C22×C1314yes—
245#396C22×C1318yes—
246#394C22×C1314yes—
247#394C22×C1318yes—
248#392C22×C1314yes—
249#391C22×C1314yes—
250#390C22×C1314yes—
251#389C22×C1314yes—
252#389C22×C1314yes—
253#388C22×C1318yes—
254#387C22×C1318yes—
255#386C22×C1318yes—
256#385C22×C1318yes—
257#384C22×C1311yescharacteristic
258#384C22×C1311yescharacteristic
259#382C22×C1312yes—
260#380C22×C1314yes—
261#380C22×C1314yes—
262#380C22×C1314yes—
263C4×C4⋊C4C22×C1314yes—
264C4×C4⋊C4C22×C1314yes—
265C4×C22⋊C4C22×C1318yes—
266C22×C13—24no—
267C22×C13—28no—
268C22×C13—22no—
269C22×C13—28no—
270C22×C13—28no—
271C22×C13—44no—
272C22×C13—44no—
273C22×C13—41no—
274C22×C13—42no—
275C22×C13—44no—
276C22×C13—44no—
277C22×C13—41no—
278C22×C13C23×D411yescharacteristic
279C22×C13C22×#4112yes—
280C22×C13C22×#4112yes—
281C22×C13C2×H(5,𝔽2)11yescharacteristic
282C22×C13C2×2−1+411yescharacteristic
283C4×C13—24no—
284C4×C13—28no—
285C4×C13—22no—
286C4×C13—44no—
287C4×C13—44no—
288C4×C13—44no—
289C4×C13—44no—
290C4×C13#52518yes—
291C4×C13#53714yes—
292C2×#41—28no—
293C2×#41—28no—
294C2×#41—28no—
295C22×Q8C23×C1312yes—
296C22×D4C23×C1314yes—
297C22×D4C23×C1314yes—
298C22×D4C23×C1312yes—
299C23×C4C23×C1314yes—
300C23×C4C23×C1314yes—
301C23×C4C23×C1314yes—
302C23×C4C23×C1311yescharacteristic
303C23×C4C23×C1312yes—
304C22⋊Q8—216no—
305#121—216no—
306C4×Q8—28no—
307C4×Q8—28no—
308C4×D4—216no—
309C4×D4—216no—
310C4×D4—28no—
311C4×D4—28no—
312C4×D4—48no—
313#117—28no—
314#117—216no—
315#117—44no—
316C2×C4⋊C4C23×C1312yes—
317C2×C4⋊C4C23×C1312yes—
318C2×C4⋊C4C23×C1314yes—
319C2×C4⋊C4C23×C1314yes—
320C2×C4⋊C4C23×C1314yes—
321C2×C4⋊C4C23×C1314yes—
322C2×C4⋊C4C23×C1318yes—
323C2×C4⋊C4C23×C1312yes—
324C2×C4⋊C4C23×C1312yes—
325C2×C4⋊C4C23×C1314yes—
326C2×C22⋊C4C23×C1314yes—
327C2×C22⋊C4C23×C1314yes—
328C2×C22⋊C4C23×C1314yes—
329C2×C22⋊C4C23×C1318yes—
330C2×C22⋊C4C23×C1318yes—
331C2×C22⋊C4C23×C1314yes—
332C2×C22⋊C4C23×C1318yes—
333C2×C42—216no—
334C2×C42D4×C1318yescomplemented
335C2×C42C23×C1314yes—
336C2×C42C23×C1314yes—
337C2×C42C23×C1314yes—
338C2×C42C23×C1314yes—
339C2×C42C23×C1311yescharacteristic
340C2×C42C23×C1311yescharacteristic
341C2×C42C23×C1312yes—
342#95C23×C1318yes—
343#95C23×C1318yes—
344#95C23×C1314yes—
345#95C23×C1318yes—
346#95C23×C1314yes—
347C2×C13—42no—
348C2×C13—48no—
349C2×C13C2×#52512yes—
350C2×C13C2×#53711yescharacteristic
351C2×C13#348111yescharacteristic
352C2×C13#348212yes—
353C2×C13#348311yescharacteristic
354C24C24×C1311yescharacteristic
355C24C24×C1314yes—
356#41—264no—
357C2×Q8—24no—
358C2×Q8—24no—
359C2×Q8C13×#4118yescomplemented
360C2×D4—28no—
361C2×D4—28no—
362C2×D4—216no—
363C2×D4—24no—
364C2×D4—28no—
365C2×D4—24no—
366C2×D4—44no—
367C2×D4C13×#4118yescomplemented
368C22×C4—28no—
369C22×C4—28no—
370C22×C4—28no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—28no—
376C22×C4—28no—
377C22×C4—28no—
378C22×C4—28no—
379C22×C4—28no—
380C22×C4—28no—
381C22×C4C2×D4×C1318yes—
382C22×C4C2×D4×C1314yes—
383C22×C4C24×C1314yes—
384C22×C4C24×C1314yes—
385C22×C4C24×C1314yes—
386C22×C4C24×C1314yes—
387C22×C4C24×C1312yes—
388C22×C4C24×C1311yescharacteristic
389C22×C4C24×C1314yes—
390C22×C4C24×C1312yes—
391C22×C4C24×C1311yescharacteristic
392C4⋊C4—28no—
393C4⋊C4—28no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—28no—
397C4⋊C4—28no—
398C4⋊C4—216no—
399C4⋊C4—42no—
400C4⋊C4—42no—
401C4⋊C4—44no—
402C22⋊C4—28no—
403C22⋊C4—216no—
404C22⋊C4—28no—
405C22⋊C4—28no—
406C22⋊C4—216no—
407C22⋊C4—44no—
408C22⋊C4—48no—
409C42—28no—
410C42—28no—
411C42—28no—
412C42—28no—
413C42C2×D4×C1318yes—
414C42C2×D4×C1314yes—
415C42C2×D4×C1314yes—
416C13#3497611yescharacteristic, direct product factor, Sylow
417C23—24no—
418C23—24no—
419C23—22no—
420C23—22no—
421C23—24no—
422C23—24no—
423C23—21no—
424C23—24no—
425C23—21no—
426C23—24no—
427C23C22×D4×C1312yes—
428C23C2×C13×#4118yes—
429C23C25×C1311yescharacteristic
430Q8—216no—
431D4—232no—
432D4—216no—
433D4—416no—
434C2×C4—232no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—216no—
442C2×C4—28no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—28no—
447C2×C4—28no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—416no—
454C2×C4—416no—
455C2×C4C22×D4×C1314yes—
456C2×C4C22×D4×C1312yes—
457C2×C4C22×D4×C1314yes—
458C2×C4C22×D4×C1312yes—
459C2×C4C2×C13×#4118yes—
460C2×C4C2×C13×#4114yes—
461C2×C4C2×C13×#4114yes—
462C2×C4C13×H(5,𝔽2)12yes—
463C2×C4C13×2−1+412yes—
464C22—24no—
465C22—28no—
466C22—22no—
467C22—28no—
468C22—28no—
469C22—44no—
470C22—44no—
471C22—41no—
472C22—42no—
473C22—44no—
474C22—44no—
475C22—41no—
476C22C23×D4×C1311yescharacteristic
477C22C22×C13×#4112yes—
478C22C22×C13×#4112yes—
479C22C2×C13×H(5,𝔽2)11yescharacteristic
480C22C2×C13×2−1+411yescharacteristic
481C4—24no—
482C4—28no—
483C4—22no—
484C4—44no—
485C4—44no—
486C4—44no—
487C4—44no—
488C4C13×#52518yes—
489C4C13×#53714yes—
490C2—42no—
491C2—48no—
492C2C2×C13×#52512yes—
493C2C2×C13×#53711yescharacteristic
494C2C13×#348111yescharacteristic
495C2C13×#348212yes—
496C2C13×#348311yescharacteristic
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×C13×#41C2semidirect
2. C13×#2609C2semidirect
3. C13×#2582C2semidirect
4. C13×#2538C2semidirect
5. C13×#2537C2semidirect
6. C13×#2485C2semidirect
7. C13×#2407C2semidirect
8. C13×#2392C2semidirect
9. C4×C13×C22⋊Q8C2semidirect
10. C4×C13×#121C2semidirect
11. C13×#2285C2semidirect
93. C2×C42×C13D4semidirect
106. #34976C13direct (N × H)
112. C2×Q8×C13#41semidirect
120. C2×D4×C13#41semidirect
169. C2×C4×#41C2×C13semidirect
170. #2609C2×C13semidirect
171. #2582C2×C13semidirect
172. #2538C2×C13semidirect
173. #2537C2×C13semidirect
174. #2485C2×C13semidirect
175. #2407C2×C13semidirect
176. #2392C2×C13semidirect
177. C4×C22⋊Q8C2×C13semidirect
178. C4×#121C2×C13semidirect
179. #2285C2×C13semidirect
334. C2×C42D4×C13semidirect
359. C2×Q8C13×#41semidirect
367. C2×D4C13×#41semidirect
416. C13#34976direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C13×#412
C13×#26092
C13×#25822
C13×#25382
C13×#25372
C13×#24852
C13×#24072
C13×#23922
C4×C13×C22⋊Q82
C4×C13×#1212
C13×#22852
#3497613