Finite Group Databasebeta

← C13×#9651 #15695990

Subgroups — C13×#9651 #15695990

Order 3328.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#388C211yesmaximal, characteristic
2C13×#1797C211yesmaximal, characteristic, complemented
3C4×C13×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×C13×#324C212yesmaximal, complemented
5C2×C13×#323C212yesmaximal
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C13×C22⋊C4C411yescharacteristic
8C22×C13×C22⋊C4C411yescharacteristic
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C42×C13C2211yescharacteristic
11C2×C13×C4⋊C8—21no—
12C2×C13×C22⋊C8C2212yes—
13C2×C13×C22⋊C8C2212yes—
14C2×C4×C8×C13—21no—
15C13×#388—21no—
16C13×#388—21no—
17C13×#388—21no—
18C13×#388—21no—
19C2×C13×#95C411yescharacteristic
20C2×C13×#95C411yescharacteristic
21C13×#336—21no—
22C13×#336—21no—
23C13×#324—24no—
24C13×#323—24no—
25C25×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13C2×C411yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C22×C8×C13—22no—
33C22×C8×C13—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4—22no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—22no—
46C2×C13×C22⋊C4—22no—
47C2×C13×C22⋊C4—42no—
48C2×C13×C22⋊C4C814yescomplemented
49C2×C42×C13—42no—
50C2×C42×C13D411yescharacteristic
51C2×C42×C13D411yescharacteristic
52C2×C42×C13D411yescharacteristic
53C2×C42×C13D411yescharacteristic
54C13×C4⋊C8—42no—
55C13×C22⋊C8—22no—
56C13×C22⋊C8—22no—
57C13×C22⋊C8—22no—
58C13×C22⋊C8D414yes—
59C4×C8×C13—42no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64#9651C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—21no—
66C24×C13—21no—
67C24×C13—22no—
68C24×C13—22no—
69C24×C13—41no—
70C24×C13—41no—
71C24×C13—41no—
72C24×C13—41no—
73C24×C13C2×C812yes—
74C24×C13C22×C411yescharacteristic
75C22×C4×C13—21no—
76C22×C4×C13—22no—
77C22×C4×C13—21no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—22no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—22no—
84C22×C4×C13—22no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C2×C812yes—
99C22×C4×C13C2×C812yes—
100C22×C4×C13M1612yes—
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D412yes—
104C22×C4×C13#4112yes—
105C2×C8×C13—24no—
106C2×C8×C13—42no—
107C2×C8×C13—42no—
108C2×C8×C13—42no—
109C2×C8×C13—42no—
110C2×C8×C13—42no—
111C13×C4⋊C4—42no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C22⋊C4—24no—
115C13×C22⋊C4—24no—
116C13×C22⋊C4—42no—
117C13×C22⋊C4—42no—
118C13×C22⋊C4—42no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—41no—
121C42×C13—22no—
122C42×C13—22no—
123C42×C13—41no—
124C42×C13—41no—
125C2×#388C2×C1311yescharacteristic
126#1797C2×C1311yescharacteristic, complemented
127C4×C22⋊C8C2×C1311yescharacteristic, complemented
128C2×#324C2×C1312yescomplemented
129C2×#323C2×C1312yes—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—22no—
135C23×C13—24no—
136C23×C13—42no—
137C23×C13—42no—
138C23×C13—42no—
139C23×C13—42no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—42no—
147C23×C13—82no—
148C23×C13—82no—
149C23×C13—82no—
150C23×C13—82no—
151C23×C13C2×C22⋊C411yescharacteristic
152C23×C13C4×D412yes—
153C23×C13C22×C811yescharacteristic
154C23×C13C2×M1611yescharacteristic
155C23×C13#13112yes—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—22no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—24no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—44no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—42no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—82no—
186C2×C4×C13—82no—
187C2×C4×C13C22⋊C812yes—
188C2×C4×C13C22⋊C812yes—
189C2×C4×C13#9912yes—
190C2×C4×C13#12112yes—
191C2×C4×C13#12411yescharacteristic
192C2×C4×C13#12711yescharacteristic
193C8×C13—44no—
194C8×C13—82no—
195C22×C4⋊C4C22×C1311yescharacteristic
196C22×C22⋊C4C4×C1311yescharacteristic
197C22×C22⋊C4C4×C1311yescharacteristic
198C22×C22⋊C4C22×C1311yescharacteristic
199C22×C42C22×C1311yescharacteristic
200C2×C4⋊C8—21no—
201C2×C22⋊C8C22×C1312yes—
202C2×C22⋊C8C22×C1312yes—
203C2×C4×C8—21no—
204#388—21no—
205#388—21no—
206#388—21no—
207#388—21no—
208C2×#95C4×C1311yescharacteristic
209C2×#95C4×C1311yescharacteristic
210#336—21no—
211#336—21no—
212#324—24no—
213#323—24no—
214C22×C13—22no—
215C22×C13—22no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—22no—
221C22×C13—22no—
222C22×C13—42no—
223C22×C13—42no—
224C22×C13—42no—
225C22×C13—84no—
226C22×C13—84no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13#39011yescharacteristic
232C22×C13C2×C22⋊C811yescharacteristic
233C22×C13#40811yescharacteristic
234C22×C13C2×#9911yescharacteristic
235C22×C13#41011yescharacteristic
236C22×C13#41311yescharacteristic
237C22×C13#41311yescharacteristic
238C22×C13C8×D412yes—
239C22×C13#43612yes—
240C4×C13—22no—
241C4×C13—21no—
242C4×C13—21no—
243C4×C13—22no—
244C4×C13—22no—
245C4×C13—22no—
246C4×C13—42no—
247C4×C13—41no—
248C4×C13—81no—
249C4×C13—81no—
250C25C2×C4×C1311yescharacteristic
251C23×C4C2×C4×C1311yescharacteristic
252C23×C4C2×C4×C1311yescharacteristic
253C23×C4C2×C4×C1311yescharacteristic
254C23×C4C2×C4×C1311yescharacteristic
255C23×C4C2×C4×C1311yescharacteristic
256C23×C4C23×C1311yescharacteristic
257C22×C8—22no—
258C22×C8—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—42no—
273C2×C22⋊C4C8×C1314yescomplemented
274C2×C42—42no—
275C2×C42D4×C1311yescharacteristic
276C2×C42D4×C1311yescharacteristic
277C2×C42D4×C1311yescharacteristic
278C2×C42D4×C1311yescharacteristic
279C4⋊C8—42no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282C22⋊C8—22no—
283C22⋊C8D4×C1314yes—
284C4×C8—42no—
285#95—21no—
286#95—21no—
287#95—21no—
288#95—21no—
289C2×C13—22no—
290C2×C13—22no—
291C2×C13—82no—
292C2×C13#145811yescharacteristic
293C2×C13#145911yescharacteristic
294C2×C13#146811yescharacteristic
295C2×C13#147311yescharacteristic
296C2×C13#195411yescharacteristic
297C2×C13#196411yescharacteristic
298C2×C13#196711yescharacteristic
299C24—21no—
300C24—21no—
301C24—22no—
302C24—22no—
303C24—41no—
304C24—41no—
305C24—41no—
306C24—41no—
307C24C2×C8×C1312yes—
308C24C22×C4×C1311yescharacteristic
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4C13×C22⋊C411yescharacteristic
329C22×C4C13×C22⋊C411yescharacteristic
330C22×C4C13×C22⋊C411yescharacteristic
331C22×C4C13×C22⋊C411yescharacteristic
332C22×C4C2×C8×C1312yes—
333C22×C4C2×C8×C1312yes—
334C22×C4C13×M1612yes—
335C22×C4C2×D4×C1311yescharacteristic
336C22×C4C2×D4×C1311yescharacteristic
337C22×C4C2×D4×C1312yes—
338C22×C4C13×#4112yes—
339C2×C8—24no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C4⋊C4—42no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—22no—
356C42—22no—
357C42—41no—
358C42—41no—
359C13#965111yescharacteristic, direct product factor, Sylow
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—22no—
365C23—24no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—82no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23C2×C13×C22⋊C411yescharacteristic
382C23C4×D4×C1312yes—
383C23C22×C8×C1311yescharacteristic
384C23C2×C13×M1611yescharacteristic
385C23C13×#13112yes—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—24no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4C13×C22⋊C812yes—
418C2×C4C13×C22⋊C812yes—
419C2×C4C13×#9912yes—
420C2×C4C13×#12112yes—
421C2×C4C13×#12411yescharacteristic
422C2×C4C13×#12711yescharacteristic
423C8—44no—
424C8—82no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—22no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—84no—
437C22—84no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22C13×#39011yescharacteristic
443C22C2×C13×C22⋊C811yescharacteristic
444C22C13×#40811yescharacteristic
445C22C2×C13×#9911yescharacteristic
446C22C13×#41011yescharacteristic
447C22C13×#41311yescharacteristic
448C22C13×#41311yescharacteristic
449C22C8×D4×C1312yes—
450C22C13×#43612yes—
451C4—22no—
452C4—21no—
453C4—21no—
454C4—22no—
455C4—22no—
456C4—22no—
457C4—42no—
458C4—41no—
459C4—81no—
460C4—81no—
461C2—22no—
462C2—22no—
463C2—82no—
464C2C13×#145811yescharacteristic
465C2C13×#145911yescharacteristic
466C2C13×#146811yescharacteristic
467C2C13×#147311yescharacteristic
468C2C13×#195411yescharacteristic
469C2C13×#196411yescharacteristic
470C2C13×#196711yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC23C22×C8×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC25×C13C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1797C2semidirect
3. C4×C13×C22⋊C8C2semidirect
4. C2×C13×#324C2semidirect
48. C2×C13×C22⋊C4C8semidirect
64. #9651C13direct (N × H)
126. #1797C2×C13semidirect
127. C4×C22⋊C8C2×C13semidirect
128. C2×#324C2×C13semidirect
273. C2×C22⋊C4C8×C13semidirect
359. C13#9651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3882
C13×#17972
C4×C13×C22⋊C82
C2×C13×#3242
C2×C13×#3232
#965113