Finite Group Databasebeta

← C13×#61877 #15748216

Subgroups — C13×#61877 #15748216

Order 3328.

1600 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3556C211yesmaximal, characteristic, complemented
2C13×#3504C211yesmaximal, characteristic
3C13×#3390C214yesmaximal, complemented
4C13×#3388C214yesmaximal, complemented
5C13×#3374C214yesmaximal, complemented
6C13×#3372C214yesmaximal, complemented
7C13×#3242C214yesmaximal, complemented
8C13×#3236C212yesmaximal, complemented
9C13×#3120C214yesmaximal
10C13×#3116C212yesmaximal
11C13×#2987C211yesmaximal, characteristic, complemented
12C13×#564—21no—
13C13×#564—21no—
14C13×#557—22no—
15C13×#557C2214yes—
16C13×#557C2214yes—
17C13×#557C2214yes—
18C13×#554—24no—
19C13×#554C2214yes—
20C13×#544—22no—
21C13×#544C2212yes—
22C13×#541—24no—
23C13×#541C2214yes—
24C13×#533—21no—
25C13×#533C2212yes—
26C13×#533C2211yescharacteristic
27C2×C13×#125—21no—
28C2×C13×#125C2211yescharacteristic
29C13×#520C2212yes—
30C4×C13×#41C2211yescharacteristic
31C13×#501C2214yes—
32C13×#501C2214yes—
33C13×#499C2214yes—
34C13×#491C2214yes—
35C13×#491C2214yes—
36C13×#487C2214yes—
37C13×#485C2214yes—
38C13×#484C2214yes—
39C13×#483C2214yes—
40C13×#479C2214yes—
41C13×#479C2214yes—
42C13×#479C2214yes—
43C13×#479C2214yes—
44C13×#479C2214yes—
45C13×#478C2214yes—
46C13×#477C2212yes—
47C13×#477C2214yes—
48C13×#476C2212yes—
49C13×#475C2214yes—
50C13×#462C2212yes—
51C13×#462C2214yes—
52C13×#461C2212yes—
53C13×#461C2214yes—
54C13×#452C2214yes—
55C13×#446C2214yes—
56C13×#446C2214yes—
57C13×#441C2214yes—
58C13×#441C2214yes—
59C13×#440C2214yes—
60C13×#440C2214yes—
61C4×C13×Q16C2214yes—
62C4×C13×SD16C2214yes—
63C13×#433C2214yes—
64C13×#432C2212yes—
65C2×C13×#41C2311yescharacteristic
66C2×C13×Q16C2314yes—
67C2×C13×SD16C2314yes—
68C13×C4⋊Q8—24no—
69C13×C4⋊Q8—24no—
70C13×C4⋊Q8—22no—
71C13×C4⋊Q8D412yes—
72C13×C4⋊Q8C2314yes—
73C13×C4⋊Q8C2312yes—
74C13×C4⋊Q8C2314yes—
75C13×C4⋊Q8C2312yes—
76C13×#126—24no—
77C13×#126—24no—
78C13×#125—22no—
79C13×#125—24no—
80C13×#125—24no—
81C13×#125—24no—
82C13×#125—24no—
83C13×#125—24no—
84C13×#125—24no—
85C13×#125—24no—
86C13×#125—24no—
87C13×#125—24no—
88C13×#125—21no—
89C13×#125—21no—
90C13×#125—22no—
91C13×#125D411yescharacteristic
92C13×#125D411yescharacteristic
93C13×#125C2314yes—
94C13×#125C2314yes—
95C13×#125C2314yes—
96C13×C22⋊Q8—24no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8—24no—
99C13×C22⋊Q8—24no—
100C13×C22⋊Q8—24no—
101C13×C22⋊Q8D414yes—
102C13×C22⋊Q8C2314yes—
103C4×Q8×C13—24no—
104C4×Q8×C13—24no—
105C4×Q8×C13—24no—
106C4×Q8×C13—22no—
107C4×Q8×C13C2314yes—
108C4×Q8×C13C2314yes—
109C4×Q8×C13C2314yes—
110C4×Q8×C13C2314yes—
111C4×Q8×C13C2312yes—
112C4×Q8×C13C2314yes—
113C4×D4×C13—22no—
114C4×D4×C13—24no—
115C4×D4×C13C2314yes—
116C4×D4×C13C2312yes—
117C13×#117—22no—
118C13×#117—22no—
119C13×#117—21no—
120C13×#117C2311yescharacteristic
121C13×#117C2312yes—
122C2×C13×C4⋊C4—22no—
123C2×C13×C4⋊C4—22no—
124C2×C13×C4⋊C4—24no—
125C2×C13×C4⋊C4C2312yes—
126C2×C42×C13—21no—
127C2×C42×C13C2311yescharacteristic
128C13×#107C2314yes—
129C13×#107C2314yes—
130C13×#107C2314yes—
131C13×#106C2314yes—
132C13×#106C2314yes—
133C13×#106C2314yes—
134C13×C4⋊C8C2312yes—
135C13×C4⋊C8C2312yes—
136C13×C4⋊C8C2314yes—
137C13×C4⋊C8C2314yes—
138C13×#103C2314yes—
139C13×#103C2314yes—
140C13×#103C2314yes—
141C13×#103C2314yes—
142C13×#103C2314yes—
143C13×#103C2314yes—
144C13×#103C2314yes—
145C13×#102C2314yes—
146C13×C22⋊C8C2314yes—
147C13×#97C2314yes—
148C13×#97C2314yes—
149C4×C8×C13C2314yes—
150#61877C1311yesmaximal, characteristic, direct product factor, Sylow
151C13×#41—22no—
152C13×#41—22no—
153C2×Q8×C13—22no—
154C2×Q8×C13—24no—
155C2×Q8×C13C2×D414yes—
156C2×Q8×C13C2414yes—
157C2×Q8×C13C2411yescharacteristic
158C2×D4×C13—21no—
159C2×D4×C13C2411yescharacteristic
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—24no—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2411yescharacteristic
166C13×Q16—28no—
167C13×SD16—28no—
168C2×C8×C13C2414yes—
169C2×C8×C13C2414yes—
170C13×C4⋊C4—24no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—24no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—24no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—24no—
181C13×C4⋊C4—24no—
182C13×C4⋊C4—24no—
183C13×C4⋊C4—24no—
184C13×C4⋊C4—24no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—24no—
187C13×C4⋊C4—24no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4C2×D412yes—
190C13×C4⋊C4C2×D414yes—
191C13×C4⋊C4C2×D412yes—
192C13×C4⋊C4C2×D414yes—
193C13×C4⋊C4C2×D414yes—
194C13×C4⋊C4C2414yes—
195C13×C4⋊C4C2414yes—
196C13×C4⋊C4C2412yes—
197C13×C22⋊C4—24no—
198C13×C22⋊C4—21no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—24no—
201C13×C22⋊C4C2×D414yes—
202C42×C13—21no—
203C42×C13—22no—
204C42×C13—24no—
205C42×C13—24no—
206C42×C13—24no—
207C42×C13—24no—
208C42×C13C2×D411yescharacteristic
209C42×C13C2×D411yescharacteristic
210C42×C13C2414yes—
211C42×C13C2412yes—
212#3556C2×C1311yescharacteristic, complemented
213#3504C2×C1311yescharacteristic
214#3390C2×C1314yescomplemented
215#3388C2×C1314yescomplemented
216#3374C2×C1314yescomplemented
217#3372C2×C1314yescomplemented
218#3242C2×C1314yescomplemented
219#3236C2×C1312yescomplemented
220#3120C2×C1314yes—
221#3116C2×C1312yes—
222#2987C2×C1311yescharacteristic, complemented
223C23×C13—21no—
224C23×C13C22×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—24no—
227Q8×C13—24no—
228Q8×C13—44no—
229Q8×C13—44no—
230Q8×C13—84no—
231Q8×C132−1+412yes—
232D4×C13—24no—
233D4×C13—21no—
234D4×C132−1+412yes—
235C2×C4×C13—24no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—42no—
244C2×C4×C13—82no—
245C2×C4×C13—84no—
246C2×C4×C13—82no—
247C2×C4×C13C22×D412yes—
248C2×C4×C13C22×D414yes—
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C22×D412yes—
251C2×C4×C13C22×D414yes—
252C2×C4×C13C2511yescharacteristic
253C8×C13—24no—
254C8×C13—24no—
255#564—21no—
256#564—21no—
257#557—22no—
258#557C22×C1314yes—
259#557C22×C1314yes—
260#557C22×C1314yes—
261#554—24no—
262#554C22×C1314yes—
263#544—22no—
264#544C22×C1312yes—
265#541—24no—
266#541C22×C1314yes—
267#533—21no—
268#533C22×C1312yes—
269#533C22×C1311yescharacteristic
270C2×#125—21no—
271C2×#125C22×C1311yescharacteristic
272#520C22×C1312yes—
273C4×#41C22×C1311yescharacteristic
274#501C22×C1314yes—
275#501C22×C1314yes—
276#499C22×C1314yes—
277#491C22×C1314yes—
278#491C22×C1314yes—
279#487C22×C1314yes—
280#485C22×C1314yes—
281#484C22×C1314yes—
282#483C22×C1314yes—
283#479C22×C1314yes—
284#479C22×C1314yes—
285#479C22×C1314yes—
286#479C22×C1314yes—
287#479C22×C1314yes—
288#478C22×C1314yes—
289#477C22×C1312yes—
290#477C22×C1314yes—
291#476C22×C1312yes—
292#475C22×C1314yes—
293#462C22×C1312yes—
294#462C22×C1314yes—
295#461C22×C1312yes—
296#461C22×C1314yes—
297#452C22×C1314yes—
298#446C22×C1314yes—
299#446C22×C1314yes—
300#441C22×C1314yes—
301#441C22×C1314yes—
302#440C22×C1314yes—
303#440C22×C1314yes—
304C4×Q16C22×C1314yes—
305C4×SD16C22×C1314yes—
306#433C22×C1314yes—
307#432C22×C1312yes—
308C22×C13—22no—
309C22×C13—21no—
310C22×C13—22no—
311C22×C13—42no—
312C22×C13C23×D411yescharacteristic
313C4×C13—22no—
314C4×C13—22no—
315C4×C13—24no—
316C4×C13—24no—
317C4×C13—21no—
318C4×C13—22no—
319C4×C13—44no—
320C4×C13—42no—
321C4×C13—44no—
322C4×C13—44no—
323C4×C13C2×2−1+411yescharacteristic
324C4×C13C2×2−1+411yescharacteristic
325C2×#41C23×C1311yescharacteristic
326C2×Q16C23×C1314yes—
327C2×SD16C23×C1314yes—
328C4⋊Q8—24no—
329C4⋊Q8—24no—
330C4⋊Q8—22no—
331C4⋊Q8D4×C1312yes—
332C4⋊Q8C23×C1312yes—
333C4⋊Q8C23×C1314yes—
334C4⋊Q8C23×C1312yes—
335C4⋊Q8C23×C1314yes—
336#126—24no—
337#126—24no—
338#125—22no—
339#125—24no—
340#125—24no—
341#125—24no—
342#125—24no—
343#125—24no—
344#125—24no—
345#125—24no—
346#125—24no—
347#125—24no—
348#125—21no—
349#125—21no—
350#125—22no—
351#125D4×C1311yescharacteristic
352#125D4×C1311yescharacteristic
353#125C23×C1314yes—
354#125C23×C1314yes—
355#125C23×C1314yes—
356C22⋊Q8—24no—
357C22⋊Q8—22no—
358C22⋊Q8—24no—
359C22⋊Q8—24no—
360C22⋊Q8—24no—
361C22⋊Q8D4×C1314yes—
362C22⋊Q8C23×C1314yes—
363C4×Q8—24no—
364C4×Q8—24no—
365C4×Q8—24no—
366C4×Q8—22no—
367C4×Q8C23×C1312yes—
368C4×Q8C23×C1314yes—
369C4×Q8C23×C1314yes—
370C4×Q8C23×C1314yes—
371C4×Q8C23×C1314yes—
372C4×Q8C23×C1314yes—
373C4×D4—22no—
374C4×D4—24no—
375C4×D4C23×C1312yes—
376C4×D4C23×C1314yes—
377#117—22no—
378#117—22no—
379#117—21no—
380#117C23×C1311yescharacteristic
381#117C23×C1312yes—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4C23×C1312yes—
386C2×C42—21no—
387C2×C42C23×C1311yescharacteristic
388#107C23×C1314yes—
389#107C23×C1314yes—
390#107C23×C1314yes—
391#106C23×C1314yes—
392#106C23×C1314yes—
393#106C23×C1314yes—
394C4⋊C8C23×C1312yes—
395C4⋊C8C23×C1312yes—
396C4⋊C8C23×C1314yes—
397C4⋊C8C23×C1314yes—
398#103C23×C1314yes—
399#103C23×C1314yes—
400#103C23×C1314yes—
401#103C23×C1314yes—
402#103C23×C1314yes—
403#103C23×C1314yes—
404#103C23×C1314yes—
405#102C23×C1314yes—
406C22⋊C8C23×C1314yes—
407#97C23×C1314yes—
408#97C23×C1314yes—
409C4×C8C23×C1314yes—
410C2×C13—41no—
411C2×C13—42no—
412C2×C13#348611yescharacteristic
413C2×C13#358612yes—
414#41—22no—
415#41—22no—
416C2×Q8—22no—
417C2×Q8—24no—
418C2×Q8C2×D4×C1314yes—
419C2×Q8C24×C1314yes—
420C2×Q8C24×C1311yescharacteristic
421C2×D4—21no—
422C2×D4C24×C1311yescharacteristic
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4C2×D4×C1312yes—
428C22×C4C24×C1311yescharacteristic
429Q16—28no—
430SD16—28no—
431C2×C8C24×C1314yes—
432C2×C8C24×C1314yes—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4C2×D4×C1312yes—
453C4⋊C4C2×D4×C1314yes—
454C4⋊C4C2×D4×C1312yes—
455C4⋊C4C2×D4×C1314yes—
456C4⋊C4C2×D4×C1314yes—
457C4⋊C4C24×C1314yes—
458C4⋊C4C24×C1314yes—
459C4⋊C4C24×C1312yes—
460C22⋊C4—24no—
461C22⋊C4—21no—
462C22⋊C4—22no—
463C22⋊C4—24no—
464C22⋊C4C2×D4×C1314yes—
465C42—21no—
466C42—22no—
467C42—24no—
468C42—24no—
469C42—24no—
470C42—24no—
471C42C2×D4×C1311yescharacteristic
472C42C2×D4×C1311yescharacteristic
473C42C24×C1314yes—
474C42C24×C1312yes—
475C13#6187711yescharacteristic, direct product factor, Sylow
476C23—21no—
477C23C22×D4×C1311yescharacteristic
478Q8—21no—
479Q8—24no—
480Q8—24no—
481Q8—44no—
482Q8—44no—
483Q8—84no—
484Q8C13×2−1+412yes—
485D4—24no—
486D4—21no—
487D4C13×2−1+412yes—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—82no—
498C2×C4—84no—
499C2×C4—82no—
500C2×C4C22×D4×C1312yes—
501C2×C4C22×D4×C1314yes—
502C2×C4C22×D4×C1311yescharacteristic
503C2×C4C22×D4×C1312yes—
504C2×C4C22×D4×C1314yes—
505C2×C4C25×C1311yescharacteristic
506C8—24no—
507C8—24no—
508C22—22no—
509C22—21no—
510C22—22no—
511C22—42no—
512C22C23×D4×C1311yescharacteristic
513C4—22no—
514C4—22no—
515C4—24no—
516C4—24no—
517C4—21no—
518C4—22no—
519C4—44no—
520C4—42no—
521C4—44no—
522C4—44no—
523C4C2×C13×2−1+411yescharacteristic
524C4C2×C13×2−1+411yescharacteristic
525C2—41no—
526C2—42no—
527C2C13×#348611yescharacteristic
528C2C13×#358612yes—
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
prime radicalC2×C13×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3556C2semidirect
3. C13×#3390C2semidirect
4. C13×#3388C2semidirect
5. C13×#3374C2semidirect
6. C13×#3372C2semidirect
7. C13×#3242C2semidirect
8. C13×#3236C2semidirect
11. C13×#2987C2semidirect
150. #61877C13direct (N × H)
212. #3556C2×C13semidirect
214. #3390C2×C13semidirect
215. #3388C2×C13semidirect
216. #3374C2×C13semidirect
217. #3372C2×C13semidirect
218. #3242C2×C13semidirect
219. #3236C2×C13semidirect
222. #2987C2×C13semidirect
475. C13#61877direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35562
C13×#35042
C13×#33902
C13×#33882
C13×#33742
C13×#33722
C13×#32422
C13×#32362
C13×#31202
C13×#31162
C13×#29872
#6187713