Finite Group Databasebeta

← C13×#13081 #15699420

Subgroups — C13×#13081 #15699420

Order 3328.

722 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#413C211yesmaximal, characteristic
2C13×#2406C211yesmaximal, characteristic
3C2×C13×#352C212yesmaximal, complemented
4C13×#1782C211yesmaximal, characteristic
5C13×#1390C212yesmaximal, complemented
6C22×C13×#41C2211yescharacteristic
7C22×C13×M16—21no—
8C2×C13×#123C411yescharacteristic, complemented
9C2×C13×#123C2211yescharacteristic
10C22×C13×C4⋊C4C411yescharacteristic, complemented
11C13×#413—24no—
12C2×C13×#101—21no—
13C2×C13×#100C2212yes—
14C2×C13×#99—21no—
15C2×C13×#99C2212yes—
16C13×#395—21no—
17C13×#394—21no—
18C13×#386C411yescharacteristic, complemented
19C13×#386C2211yescharacteristic
20C13×#385—21no—
21C13×#385—21no—
22C13×#381—21no—
23C13×#381C411yescharacteristic, complemented
24C13×#352—24no—
25C2×C13×#41—22no—
26C2×C13×#41—22no—
27C2×C13×#41—41no—
28C2×C13×#41—41no—
29C2×C13×#41—42no—
30C22×Q8×C13D411yescharacteristic
31C22×D4×C13C2×C411yescharacteristic
32C22×D4×C13D411yescharacteristic
33C22×D4×C13C2311yescharacteristic
34C23×C4×C13C2×C411yescharacteristic
35C23×C4×C13C2×C411yescharacteristic
36C23×C4×C13C2×C411yescharacteristic
37C23×C4×C13D411yescharacteristic
38C23×C4×C13D411yescharacteristic
39C2×C13×M16—24no—
40C2×C13×M16—22no—
41C2×C13×M16—42no—
42C2×C13×M16—41no—
43C22×C8×C13—41no—
44C13×#123—22no—
45C13×#123—22no—
46C13×#123—42no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—41no—
52C2×C13×C4⋊C4—41no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4C2×C411yescharacteristic
59C2×C13×C22⋊C4C2×C411yescharacteristic
60C13×#101—24no—
61C13×#100—22no—
62C13×#100D414yes—
63C13×#99—22no—
64C13×#99—22no—
65C13×#99—42no—
66C13×#95—21no—
67C13×#95—21no—
68C13×#95—21no—
69C13×#95—21no—
70C13×#95—41no—
71C13×#95—41no—
72#13081C1311yesmaximal, characteristic, direct product factor, Sylow
73C24×C13C22⋊C411yescharacteristic
74C24×C13C22×C411yescharacteristic
75C24×C13C2×D411yescharacteristic
76C13×#41—44no—
77C13×#41—44no—
78C13×#41—44no—
79C13×#41—44no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×D4×C13—22no—
85C2×D4×C13—22no—
86C2×D4×C13—22no—
87C2×D4×C13—22no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13C2×D412yes—
93C2×D4×C13#4112yes—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13—42no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13—42no—
117C22×C4×C13C22⋊C411yescharacteristic
118C22×C4×C13C22⋊C411yescharacteristic
119C22×C4×C13C22⋊C411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C13×M16—24no—
122C13×M16—44no—
123C13×M16—42no—
124C2×C8×C13—44no—
125C2×C8×C13—42no—
126C13×C4⋊C4—42no—
127C13×C4⋊C4—42no—
128C13×C4⋊C4—41no—
129C13×C4⋊C4—41no—
130C13×C4⋊C4—41no—
131C13×C4⋊C4—41no—
132C13×C22⋊C4—22no—
133C13×C22⋊C4—42no—
134C13×C22⋊C4—42no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4—42no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—42no—
139C13×C22⋊C4—42no—
140C2×#413C2×C1311yescharacteristic
141#2406C2×C1311yescharacteristic
142C2×#352C2×C1312yescomplemented
143#1782C2×C1311yescharacteristic
144#1390C2×C1312yescomplemented
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—21no—
148C23×C13—21no—
149C23×C13—21no—
150C23×C13—21no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13#9912yes—
158C23×C13C2×C22⋊C411yescharacteristic
159C23×C13C4×D412yes—
160C23×C13#12112yes—
161Q8×C13—42no—
162Q8×C13—42no—
163D4×C13—42no—
164D4×C13—42no—
165D4×C13—44no—
166D4×C13—44no—
167C2×C4×C13—22no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—22no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—22no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13—42no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—42no—
186C2×C4×C13—41no—
187C2×C4×C13—42no—
188C2×C4×C13—41no—
189C2×C4×C13—42no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—82no—
200C2×C4×C13—82no—
201C2×C4×C13—82no—
202C2×C4×C13—82no—
203C2×C4×C13#9911yescharacteristic
204C2×C4×C13#9911yescharacteristic
205C2×C4×C13#12011yescharacteristic
206C2×C4×C13#12311yescharacteristic
207C8×C13—44no—
208C22×#41C22×C1311yescharacteristic
209C22×M16—21no—
210C2×#123C4×C1311yescharacteristic, complemented
211C2×#123C22×C1311yescharacteristic
212C22×C4⋊C4C4×C1311yescharacteristic, complemented
213#413—24no—
214C2×#101—21no—
215C2×#100C22×C1312yes—
216C2×#99—21no—
217C2×#99C22×C1312yes—
218#395—21no—
219#394—21no—
220#386C4×C1311yescharacteristic, complemented
221#386C22×C1311yescharacteristic
222#385—21no—
223#385—21no—
224#381—21no—
225#381C4×C1311yescharacteristic, complemented
226#352—24no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—22no—
230C22×C13—22no—
231C22×C13—22no—
232C22×C13—42no—
233C22×C13—42no—
234C22×C13—42no—
235C22×C13—42no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13—41no—
242C22×C13—81no—
243C22×C13—81no—
244C22×C13#38611yescharacteristic
245C22×C13C2×#9911yescharacteristic
246C22×C13C2×#9911yescharacteristic
247C4×C13—21no—
248C4×C13—21no—
249C4×C13—21no—
250C4×C13—21no—
251C4×C13—42no—
252C4×C13—41no—
253C4×C13—41no—
254C4×C13—81no—
255C4×C13—81no—
256C4×C13—81no—
257C4×C13—162no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—41no—
261C2×#41—41no—
262C2×#41—42no—
263C22×Q8D4×C1311yescharacteristic
264C22×D4C2×C4×C1311yescharacteristic
265C22×D4D4×C1311yescharacteristic
266C22×D4C23×C1311yescharacteristic
267C23×C4C2×C4×C1311yescharacteristic
268C23×C4C2×C4×C1311yescharacteristic
269C23×C4C2×C4×C1311yescharacteristic
270C23×C4D4×C1311yescharacteristic
271C23×C4D4×C1311yescharacteristic
272C2×M16—24no—
273C2×M16—22no—
274C2×M16—42no—
275C2×M16—41no—
276C22×C8—41no—
277#123—22no—
278#123—22no—
279#123—42no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4C2×C4×C1311yescharacteristic
292C2×C22⋊C4C2×C4×C1311yescharacteristic
293#101—24no—
294#100—22no—
295#100D4×C1314yes—
296#99—22no—
297#99—22no—
298#99—42no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—41no—
304#95—41no—
305C2×C13—21no—
306C2×C13—21no—
307C2×C13—42no—
308C2×C13—42no—
309C2×C13—42no—
310C2×C13#189811yescharacteristic
311C2×C13#212011yescharacteristic
312C2×C13#212311yescharacteristic
313C24C13×C22⋊C411yescharacteristic
314C24C22×C4×C1311yescharacteristic
315C24C2×D4×C1311yescharacteristic
316#41—44no—
317#41—44no—
318#41—44no—
319#41—44no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—41no—
323C2×Q8—41no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4C2×D4×C1312yes—
333C2×D4C13×#4112yes—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—42no—
357C22×C4C13×C22⋊C411yescharacteristic
358C22×C4C13×C22⋊C411yescharacteristic
359C22×C4C13×C22⋊C411yescharacteristic
360C22×C4C2×D4×C1311yescharacteristic
361M16—24no—
362M16—44no—
363M16—42no—
364C2×C8—44no—
365C2×C8—42no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C22⋊C4—22no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—42no—
377C22⋊C4—41no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C13#1308111yescharacteristic, direct product factor, Sylow
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23C13×#9912yes—
394C23C2×C13×C22⋊C411yescharacteristic
395C23C4×D4×C1312yes—
396C23C13×#12112yes—
397Q8—42no—
398Q8—42no—
399D4—42no—
400D4—42no—
401D4—44no—
402D4—44no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4C13×#9911yescharacteristic
440C2×C4C13×#9911yescharacteristic
441C2×C4C13×#12011yescharacteristic
442C2×C4C13×#12311yescharacteristic
443C8—44no—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—81no—
460C22—81no—
461C22C13×#38611yescharacteristic
462C22C2×C13×#9911yescharacteristic
463C22C2×C13×#9911yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—41no—
470C4—41no—
471C4—81no—
472C4—81no—
473C4—81no—
474C4—162no—
475C2—21no—
476C2—21no—
477C2—42no—
478C2—42no—
479C2—42no—
480C2C13×#189811yescharacteristic
481C2C13×#212011yescharacteristic
482C2C13×#212311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC22×C13×#41C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C13×#352C2semidirect
5. C13×#1390C2semidirect
8. C2×C13×#123C4semidirect
10. C22×C13×C4⋊C4C4semidirect
18. C13×#386C4semidirect
23. C13×#381C4semidirect
72. #13081C13direct (N × H)
142. C2×#352C2×C13semidirect
144. #1390C2×C13semidirect
210. C2×#123C4×C13semidirect
212. C22×C4⋊C4C4×C13semidirect
220. #386C4×C13semidirect
225. #381C4×C13semidirect
380. C13#13081direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4132
C13×#24062
C2×C13×#3522
C13×#17822
C13×#13902
#1308113