Finite Group Databasebeta

← C13×#10354 #15696693

Subgroups — C13×#10354 #15696693

Order 3328.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2552C211yesmaximal, characteristic, complemented
2C13×#1982C211yesmaximal, characteristic
3C13×#1982C211yesmaximal, characteristic
4C13×#1957C211yesmaximal, characteristic
5C13×#1296C211yesmaximal, characteristic, complemented
6C13×#1279C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×C13×#127C2211yescharacteristic
9C2×C13×#125—21no—
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×#102—21no—
13C2×C13×#102—21no—
14C2×C13×#102—21no—
15C2×C13×#102—21no—
16C2×C13×#102—22no—
17C2×C4×C8×C13C2211yescharacteristic
18C13×#398—22no—
19C13×#389—21no—
20C13×#389—21no—
21C13×#384—21no—
22C13×#384C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C13×#127—21no—
32C13×#127—21no—
33C13×#127—21no—
34C13×#127Q812yes—
35C13×#125—42no—
36C13×#125—42no—
37C2×C13×C4⋊C4—22no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—22no—
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C4⋊C4D411yescharacteristic
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C4⋊C4D412yes—
47C2×C42×C13—21no—
48C2×C42×C13—21no—
49C2×C42×C13C2311yescharacteristic
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×#102—42no—
55C13×#102—42no—
56C13×#102—44no—
57C13×#102—42no—
58C13×#102—42no—
59C4×C8×C13—21no—
60C4×C8×C13—21no—
61C13×#95—22no—
62C13×#95—21no—
63C13×#95—21no—
64#10354C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13—41no—
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—22no—
69C2×D4×C13—42no—
70C2×D4×C13—42no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—22no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C2×C8×C13—22no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—42no—
106C13×C4⋊C4—44no—
107C13×C4⋊C4—44no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—82no—
113C13×C4⋊C4D812yes—
114C13×C4⋊C4SD1612yes—
115C42×C13—41no—
116C42×C13—41no—
117C42×C13—41no—
118C42×C13—41no—
119C42×C13C2×Q811yescharacteristic
120C42×C13#4111yescharacteristic
121C42×C13#4111yescharacteristic
122C42×C13#4111yescharacteristic
123#2552C2×C1311yescharacteristic, complemented
124#1982C2×C1311yescharacteristic
125#1982C2×C1311yescharacteristic
126#1957C2×C1311yescharacteristic
127#1296C2×C1311yescharacteristic, complemented
128#1279C2×C1311yescharacteristic, complemented
129#1279C2×C1311yescharacteristic, complemented
130C23×C13—42no—
131C23×C13—81no—
132C23×C13—81no—
133C23×C13—81no—
134C23×C13—81no—
135C23×C13—81no—
136C23×C13—81no—
137C23×C13#12011yescharacteristic
138D4×C13—44no—
139D4×C13—42no—
140D4×C13—42no—
141D4×C13—42no—
142D4×C13—42no—
143D4×C13—82no—
144D4×C13—81no—
145D4×C13—81no—
146D4×C13—81no—
147D4×C13—81no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13C22⋊Q811yescharacteristic
166C2×C4×C13C22⋊Q811yescharacteristic
167C2×C4×C13C22⋊Q811yescharacteristic
168C2×C4×C13#12411yescharacteristic
169C2×C4×C13#12411yescharacteristic
170C2×C4×C13#12411yescharacteristic
171C2×C4×C13C2×D811yescharacteristic
172C2×C4×C13C2×SD1611yescharacteristic
173C2×C4×C13#13511yescharacteristic
174C2×C4×C13#13511yescharacteristic
175C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C13#13711yescharacteristic
179C8×C13—42no—
180C8×C13—81no—
181C8×C13—81no—
182C2×#127C22×C1311yescharacteristic
183C2×#125—21no—
184C2×C4⋊C8C22×C1311yescharacteristic
185C2×C4⋊C8C22×C1311yescharacteristic
186C2×#102—22no—
187C2×#102—21no—
188C2×#102—21no—
189C2×#102—21no—
190C2×#102—21no—
191C2×C4×C8C22×C1311yescharacteristic
192#398—22no—
193#389—21no—
194#389—21no—
195#384—21no—
196#384C22×C1311yescharacteristic
197C4×C4⋊C4C22×C1311yescharacteristic
198C4×C4⋊C4C22×C1311yescharacteristic
199C22×C13—82no—
200C22×C13—82no—
201C22×C13—82no—
202C22×C13—161no—
203C22×C13—161no—
204C22×C13—161no—
205C22×C13—161no—
206C22×C13#39311yescharacteristic
207C22×C13#44711yescharacteristic
208C22×C13#44811yescharacteristic
209C22×C13#44911yescharacteristic
210C22×C13#44911yescharacteristic
211C22×C13#45311yescharacteristic
212C22×C13#45411yescharacteristic
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—42no—
216C4×C13—42no—
217C4×C13—81no—
218C4×C13—82no—
219C4×C13—81no—
220C4×C13#47411yescharacteristic
221C4×C13#47611yescharacteristic
222C4×C13#47811yescharacteristic
223C4×C13#47811yescharacteristic
224C4×C13#48611yescharacteristic
225C4×C13#48811yescharacteristic
226C4×C13#48911yescharacteristic
227C4×C13#49011yescharacteristic
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234#127—21no—
235#127—21no—
236#127—21no—
237#127Q8×C1312yes—
238#125—42no—
239#125—42no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4D4×C1311yescharacteristic
246C2×C4⋊C4D4×C1311yescharacteristic
247C2×C4⋊C4D4×C1311yescharacteristic
248C2×C4⋊C4D4×C1311yescharacteristic
249C2×C4⋊C4D4×C1312yes—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42C23×C1311yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257#102—42no—
258#102—42no—
259#102—44no—
260#102—42no—
261#102—42no—
262C4×C8—21no—
263C4×C8—21no—
264#95—22no—
265#95—21no—
266#95—21no—
267C2×C13—162no—
268C2×C13#162111yescharacteristic
269C2×C13#162211yescharacteristic
270C2×C13#162511yescharacteristic
271C2×C13#162611yescharacteristic
272C2×C13#202311yescharacteristic
273C2×C13#202511yescharacteristic
274C2×C13#202711yescharacteristic
275C24—41no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4C2×D4×C1311yescharacteristic
298C22×C4C2×D4×C1311yescharacteristic
299C22×C4C2×D4×C1311yescharacteristic
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—42no—
316C4⋊C4—44no—
317C4⋊C4—44no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—82no—
323C4⋊C4C13×D812yes—
324C4⋊C4C13×SD1612yes—
325C42—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42C2×Q8×C1311yescharacteristic
330C42C13×#4111yescharacteristic
331C42C13×#4111yescharacteristic
332C42C13×#4111yescharacteristic
333C13#1035411yescharacteristic, direct product factor, Sylow
334C23—42no—
335C23—81no—
336C23—81no—
337C23—81no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23C13×#12011yescharacteristic
342D4—44no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—42no—
347D4—82no—
348D4—81no—
349D4—81no—
350D4—81no—
351D4—81no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4C13×C22⋊Q811yescharacteristic
370C2×C4C13×C22⋊Q811yescharacteristic
371C2×C4C13×C22⋊Q811yescharacteristic
372C2×C4C13×#12411yescharacteristic
373C2×C4C13×#12411yescharacteristic
374C2×C4C13×#12411yescharacteristic
375C2×C4C2×C13×D811yescharacteristic
376C2×C4C2×C13×SD1611yescharacteristic
377C2×C4C13×#13511yescharacteristic
378C2×C4C13×#13511yescharacteristic
379C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
380C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
381C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
382C2×C4C13×#13711yescharacteristic
383C8—42no—
384C8—81no—
385C8—81no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—161no—
390C22—161no—
391C22—161no—
392C22—161no—
393C22C13×#39311yescharacteristic
394C22C13×#44711yescharacteristic
395C22C13×#44811yescharacteristic
396C22C13×#44911yescharacteristic
397C22C13×#44911yescharacteristic
398C22C13×#45311yescharacteristic
399C22C13×#45411yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—82no—
406C4—81no—
407C4C13×#47411yescharacteristic
408C4C13×#47611yescharacteristic
409C4C13×#47811yescharacteristic
410C4C13×#47811yescharacteristic
411C4C13×#48611yescharacteristic
412C4C13×#48811yescharacteristic
413C4C13×#48911yescharacteristic
414C4C13×#49011yescharacteristic
415C2—162no—
416C2C13×#162111yescharacteristic
417C2C13×#162211yescharacteristic
418C2C13×#162511yescharacteristic
419C2C13×#162611yescharacteristic
420C2C13×#202311yescharacteristic
421C2C13×#202511yescharacteristic
422C2C13×#202711yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC2×C13×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2552C2semidirect
5. C13×#1296C2semidirect
6. C13×#1279C2semidirect
7. C13×#1279C2semidirect
64. #10354C13direct (N × H)
123. #2552C2×C13semidirect
127. #1296C2×C13semidirect
128. #1279C2×C13semidirect
129. #1279C2×C13semidirect
333. C13#10354direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25522
C13×#19822
C13×#19572
C13×#12962
C13×#12792
#1035413