Finite Group Databasebeta

← C13×#13085 #15699424

Subgroups — C13×#13085 #15699424

Order 3328.

724 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#410C211yesmaximal, characteristic
2C13×#2406C211yesmaximal, characteristic
3C2×C13×#352C212yesmaximal, complemented
4C13×#1785C211yesmaximal, characteristic
5C13×#1390C212yesmaximal, complemented
6C22×C13×#41C2211yescharacteristic
7C2×C13×#123C411yescharacteristic, complemented
8C2×C13×#123C2211yescharacteristic
9C2×C13×#117—21no—
10C22×C13×C4⋊C4C411yescharacteristic, complemented
11C2×C13×#101—21no—
12C2×C13×#100C2212yes—
13C13×#410—24no—
14C2×C13×#99—21no—
15C2×C13×#99C2212yes—
16C13×#407—21no—
17C13×#395—21no—
18C13×#394—21no—
19C13×#386C411yescharacteristic, complemented
20C13×#386C2211yescharacteristic
21C13×#385—21no—
22C13×#385—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—22no—
40C13×#123—22no—
41C13×#123—22no—
42C13×#123—42no—
43C13×#117—24no—
44C13×#117—42no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—41no—
50C2×C13×C4⋊C4—41no—
51C2×C13×C4⋊C4—41no—
52C2×C13×C22⋊C4—22no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4C2×C411yescharacteristic
58C2×C13×C22⋊C4C2×C411yescharacteristic
59C2×C42×C13—41no—
60C13×#101—42no—
61C13×#100—22no—
62C13×#100—22no—
63C13×#99—24no—
64C13×#99—22no—
65C13×#99D414yes—
66C13×C22⋊C8—41no—
67C13×C22⋊C8—41no—
68C13×#95—21no—
69C13×#95—21no—
70C13×#95—21no—
71C13×#95—21no—
72#13085C1311yesmaximal, 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—22no—
81C2×Q8×C13—22no—
82C2×Q8×C13—41no—
83C2×D4×C13—22no—
84C2×D4×C13—21no—
85C2×D4×C13—21no—
86C2×D4×C13—22no—
87C2×D4×C13—41no—
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—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—22no—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
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—42no—
115C22×C4×C13—41no—
116C22×C4×C13—41no—
117C22×C4×C13C22⋊C411yescharacteristic
118C22×C4×C13C22⋊C411yescharacteristic
119C22×C4×C13C22⋊C411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C13×M16—42no—
122C13×M16—42no—
123C2×C8×C13—42no—
124C13×C4⋊C4—42no—
125C13×C4⋊C4—44no—
126C13×C4⋊C4—41no—
127C13×C4⋊C4—41no—
128C13×C4⋊C4—42no—
129C13×C4⋊C4—42no—
130C13×C22⋊C4—22no—
131C13×C22⋊C4—24no—
132C13×C22⋊C4—42no—
133C13×C22⋊C4—42no—
134C13×C22⋊C4—42no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C42×C13—44no—
140C2×#410C2×C1311yescharacteristic
141#2406C2×C1311yescharacteristic
142C2×#352C2×C1312yescomplemented
143#1785C2×C1311yescharacteristic
144#1390C2×C1312yescomplemented
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—21no—
148C23×C13—21no—
149C23×C13—21no—
150C23×C13—21no—
151C23×C13—21no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13—41no—
158C23×C13C2×C22⋊C411yescharacteristic
159C23×C13C4×D412yes—
160C23×C13#12011yescharacteristic
161C23×C13#12311yescharacteristic
162Q8×C13—44no—
163D4×C13—42no—
164D4×C13—42no—
165D4×C13—44no—
166D4×C13—42no—
167D4×C13—42no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—22no—
171C2×C4×C13—22no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—22no—
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—44no—
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—41no—
200C2×C4×C13—82no—
201C2×C4×C13—82no—
202C2×C4×C13—82no—
203C2×C4×C13#9912yes—
204C2×C4×C13#9911yescharacteristic
205C2×C4×C13#9911yescharacteristic
206C2×C4×C13#12112yes—
207C8×C13—82no—
208C22×#41C22×C1311yescharacteristic
209C2×#123C4×C1311yescharacteristic, complemented
210C2×#123C22×C1311yescharacteristic
211C2×#117—21no—
212C22×C4⋊C4C4×C1311yescharacteristic, complemented
213C2×#101—21no—
214C2×#100C22×C1312yes—
215#410—24no—
216C2×#99—21no—
217C2×#99C22×C1312yes—
218#407—21no—
219#395—21no—
220#394—21no—
221#386C4×C1311yescharacteristic, complemented
222#386C22×C1311yescharacteristic
223#385—21no—
224#385—21no—
225#381C4×C1311yescharacteristic, complemented
226#352—24no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—21no—
231C22×C13—22no—
232C22×C13—42no—
233C22×C13—41no—
234C22×C13—41no—
235C22×C13—42no—
236C22×C13—42no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13—41no—
242C22×C13—41no—
243C22×C13—41no—
244C22×C13—81no—
245C22×C13—81no—
246C22×C13#38611yescharacteristic
247C22×C13C2×#9911yescharacteristic
248C22×C13C2×#9911yescharacteristic
249C4×C13—22no—
250C4×C13—21no—
251C4×C13—21no—
252C4×C13—22no—
253C4×C13—42no—
254C4×C13—41no—
255C4×C13—81no—
256C4×C13—81no—
257C4×C13—84no—
258C4×C13—81no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—41no—
262C2×#41—41no—
263C2×#41—42no—
264C22×Q8D4×C1311yescharacteristic
265C22×D4C2×C4×C1311yescharacteristic
266C22×D4D4×C1311yescharacteristic
267C22×D4C23×C1311yescharacteristic
268C23×C4C2×C4×C1311yescharacteristic
269C23×C4C2×C4×C1311yescharacteristic
270C23×C4C2×C4×C1311yescharacteristic
271C23×C4D4×C1311yescharacteristic
272C23×C4D4×C1311yescharacteristic
273C2×M16—22no—
274#123—22no—
275#123—22no—
276#123—42no—
277#117—24no—
278#117—42no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4C2×C4×C1311yescharacteristic
292C2×C22⋊C4C2×C4×C1311yescharacteristic
293C2×C42—41no—
294#101—42no—
295#100—22no—
296#100—22no—
297#99—24no—
298#99—22no—
299#99D4×C1314yes—
300C22⋊C8—41no—
301C22⋊C8—41no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—21no—
306C2×C13—21no—
307C2×C13—21no—
308C2×C13—41no—
309C2×C13—42no—
310C2×C13—41no—
311C2×C13—81no—
312C2×C13#189811yescharacteristic
313C2×C13#212011yescharacteristic
314C2×C13#212311yescharacteristic
315C24C13×C22⋊C411yescharacteristic
316C24C22×C4×C1311yescharacteristic
317C24C2×D4×C1311yescharacteristic
318#41—44no—
319#41—44no—
320#41—44no—
321#41—44no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—41no—
325C2×D4—22no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—22no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4C2×D4×C1312yes—
335C2×D4C13×#4112yes—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—42no—
355C22×C4—41no—
356C22×C4—42no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4C13×C22⋊C411yescharacteristic
360C22×C4C13×C22⋊C411yescharacteristic
361C22×C4C13×C22⋊C411yescharacteristic
362C22×C4C2×D4×C1311yescharacteristic
363M16—42no—
364M16—42no—
365C2×C8—42no—
366C4⋊C4—42no—
367C4⋊C4—44no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C22⋊C4—22no—
373C22⋊C4—24no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—42no—
377C22⋊C4—42no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C42—44no—
382C13#1308511yescharacteristic, direct product factor, Sylow
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23C2×C13×C22⋊C411yescharacteristic
397C23C4×D4×C1312yes—
398C23C13×#12011yescharacteristic
399C23C13×#12311yescharacteristic
400Q8—44no—
401D4—42no—
402D4—42no—
403D4—44no—
404D4—42no—
405D4—42no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4C13×#9911yescharacteristic
442C2×C4C13×#9911yescharacteristic
443C2×C4C13×#9912yes—
444C2×C4C13×#12112yes—
445C8—82no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—42no—
452C22—41no—
453C22—41no—
454C22—42no—
455C22—42no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—81no—
464C22—81no—
465C22C13×#38611yescharacteristic
466C22C2×C13×#9911yescharacteristic
467C22C2×C13×#9911yescharacteristic
468C4—22no—
469C4—21no—
470C4—21no—
471C4—22no—
472C4—42no—
473C4—41no—
474C4—81no—
475C4—81no—
476C4—84no—
477C4—81no—
478C2—21no—
479C2—21no—
480C2—41no—
481C2—42no—
482C2—41no—
483C2—81no—
484C2C13×#189811yescharacteristic
485C2C13×#212011yescharacteristic
486C2C13×#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
7. C2×C13×#123C4semidirect
10. C22×C13×C4⋊C4C4semidirect
19. C13×#386C4semidirect
23. C13×#381C4semidirect
72. #13085C13direct (N × H)
142. C2×#352C2×C13semidirect
144. #1390C2×C13semidirect
209. C2×#123C4×C13semidirect
212. C22×C4⋊C4C4×C13semidirect
221. #386C4×C13semidirect
225. #381C4×C13semidirect
382. C13#13085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4102
C13×#24062
C2×C13×#3522
C13×#17852
C13×#13902
#1308513