Finite Group Databasebeta

← C13×#10540 #15696879

Subgroups — C13×#10540 #15696879

Order 3328.

506 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
1C2×C13×#486C211yesmaximal, characteristic
2C13×#1982C211yesmaximal, characteristic
3C13×#1981C211yesmaximal, characteristic, complemented
4C13×#1939C211yesmaximal, characteristic, complemented
5C2×C13×#332C211yesmaximal, characteristic, complemented
6C2×C13×#331C211yesmaximal, characteristic
7C13×#1277C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×#127C2211yescharacteristic
10C13×#486—22no—
11C13×#486—22no—
12C2×C13×C4⋊C8—21no—
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×C4⋊C8C2211yescharacteristic
15C2×C13×C4⋊C8C2211yescharacteristic
16C2×C13×#103—21no—
17C2×C13×#103—21no—
18C2×C13×#102—21no—
19C2×C13×#102—21no—
20C2×C13×#102—21no—
21C2×C13×#102—21no—
22C2×C4×C8×C13C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C13×#336—21no—
25C13×#332—22no—
26C13×#331—22no—
27C22×Q8×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C22×C8×C13D411yescharacteristic
35C22×C8×C13D411yescharacteristic
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8D412yes—
40C13×#127—21no—
41C13×#127—21no—
42C13×#127—21no—
43C13×#127D412yes—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C42×C13—21no—
49C2×C42×C13C2311yescharacteristic
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—42no—
57C13×#103—42no—
58C13×#103—42no—
59C13×#102—24no—
60C13×#102—24no—
61C13×#102—42no—
62C13×#102—42no—
63C4×C8×C13—21no—
64C4×C8×C13—21no—
65C13×#95—21no—
66#10540C1311yesmaximal, characteristic, direct product factor, Sylow
67C24×C13—41no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×D4×C13—22no—
75C2×D4×C13—22no—
76C2×D4×C13—22no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—81no—
89C2×D4×C13—81no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—41no—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C2×C8×C13—21no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13—21no—
100C2×C8×C13—21no—
101C2×C8×C13—21no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C2×C8×C13—41no—
110C2×C8×C13—41no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4D812yes—
119C42×C13—41no—
120C42×C13—41no—
121C42×C13C2×D411yescharacteristic
122C42×C13C2×D411yescharacteristic
123C42×C13#4111yescharacteristic
124C42×C13#4111yescharacteristic
125C2×#486C2×C1311yescharacteristic
126#1982C2×C1311yescharacteristic
127#1981C2×C1311yescharacteristic, complemented
128#1939C2×C1311yescharacteristic, complemented
129C2×#332C2×C1311yescharacteristic, complemented
130C2×#331C2×C1311yescharacteristic
131#1277C2×C1311yescharacteristic, complemented
132C23×C13—42no—
133C23×C13—81no—
134C23×C13—81no—
135C23×C13—81no—
136C23×C13—81no—
137C23×C13—81no—
138C23×C13—81no—
139C23×C13#12111yescharacteristic
140Q8×C13—42no—
141Q8×C13—42no—
142Q8×C13—81no—
143Q8×C13—81no—
144D4×C13—42no—
145D4×C13—42no—
146D4×C13—42no—
147D4×C13—42no—
148D4×C13—82no—
149D4×C13—82no—
150D4×C13—81no—
151D4×C13—81no—
152D4×C13—81no—
153D4×C13—81no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—22no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—42no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—81no—
164C2×C4×C13—81no—
165C2×C4×C13#12011yescharacteristic
166C2×C4×C13#12111yescharacteristic
167C2×C4×C13#12111yescharacteristic
168C2×C4×C13#12311yescharacteristic
169C2×C4×C13#12311yescharacteristic
170C2×C4×C13#12411yescharacteristic
171C2×C4×C13C2×D811yescharacteristic
172C2×C4×C13#13511yescharacteristic
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—41no—
180C8×C13—41no—
181C8×C13—81no—
182C8×C13—81no—
183C8×C13—81no—
184C2×C4⋊Q8C22×C1311yescharacteristic
185C2×#127C22×C1311yescharacteristic
186#486—22no—
187#486—22no—
188C2×C4⋊C8—21no—
189C2×C4⋊C8C22×C1311yescharacteristic
190C2×C4⋊C8C22×C1311yescharacteristic
191C2×C4⋊C8C22×C1311yescharacteristic
192C2×#103—21no—
193C2×#103—21no—
194C2×#102—21no—
195C2×#102—21no—
196C2×#102—21no—
197C2×#102—21no—
198C2×C4×C8C22×C1311yescharacteristic
199C4×C4⋊C4C22×C1311yescharacteristic
200#336—21no—
201#332—22no—
202#331—22no—
203C22×C13—82no—
204C22×C13—82no—
205C22×C13—82no—
206C22×C13—161no—
207C22×C13—161no—
208C22×C13—161no—
209C22×C13—161no—
210C22×C13#39411yescharacteristic
211C22×C13#46311yescharacteristic
212C22×C13#46411yescharacteristic
213C22×C13#46611yescharacteristic
214C22×C13#46911yescharacteristic
215C22×C13#47111yescharacteristic
216C22×C13#47111yescharacteristic
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—42no—
220C4×C13—82no—
221C4×C13—81no—
222C4×C13#44911yescharacteristic
223C4×C13#45211yescharacteristic
224C4×C13#45911yescharacteristic
225C4×C13#45911yescharacteristic
226C4×C13#46311yescharacteristic
227C4×C13#46311yescharacteristic
228C4×C13#48811yescharacteristic
229C4×C13#48911yescharacteristic
230C22×Q8—21no—
231C22×D4—21no—
232C22×D4—21no—
233C22×D4—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8D4×C1311yescharacteristic
238C22×C8D4×C1311yescharacteristic
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8D4×C1312yes—
243#127—21no—
244#127—21no—
245#127—21no—
246#127D4×C1312yes—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C1311yescharacteristic
250C2×C4⋊C4D4×C1311yescharacteristic
251C2×C42—21no—
252C2×C42C23×C1311yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—42no—
260#103—42no—
261#103—42no—
262#102—24no—
263#102—24no—
264#102—42no—
265#102—42no—
266C4×C8—21no—
267C4×C8—21no—
268#95—21no—
269C2×C13—162no—
270C2×C13#168111yescharacteristic
271C2×C13#168211yescharacteristic
272C2×C13#170111yescharacteristic
273C2×C13#170211yescharacteristic
274C2×C13#204211yescharacteristic
275C2×C13#204611yescharacteristic
276C2×C13#205411yescharacteristic
277C24—41no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—81no—
299C2×D4—81no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4C2×D4×C1311yescharacteristic
304C22×C4C2×D4×C1311yescharacteristic
305C22×C4C13×#4111yescharacteristic
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4C13×D812yes—
329C42—41no—
330C42—41no—
331C42C2×D4×C1311yescharacteristic
332C42C2×D4×C1311yescharacteristic
333C42C13×#4111yescharacteristic
334C42C13×#4111yescharacteristic
335C13#1054011yescharacteristic, direct product factor, Sylow
336C23—42no—
337C23—81no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23—81no—
342C23—81no—
343C23C13×#12111yescharacteristic
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—42no—
352D4—82no—
353D4—82no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4C13×#12011yescharacteristic
370C2×C4C13×#12111yescharacteristic
371C2×C4C13×#12111yescharacteristic
372C2×C4C13×#12311yescharacteristic
373C2×C4C13×#12311yescharacteristic
374C2×C4C13×#12411yescharacteristic
375C2×C4C2×C13×D811yescharacteristic
376C2×C4C13×#13511yescharacteristic
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—41no—
384C8—41no—
385C8—81no—
386C8—81no—
387C8—81no—
388C22—82no—
389C22—82no—
390C22—82no—
391C22—161no—
392C22—161no—
393C22—161no—
394C22—161no—
395C22C13×#39411yescharacteristic
396C22C13×#46311yescharacteristic
397C22C13×#46411yescharacteristic
398C22C13×#46611yescharacteristic
399C22C13×#46911yescharacteristic
400C22C13×#47111yescharacteristic
401C22C13×#47111yescharacteristic
402C4—21no—
403C4—21no—
404C4—42no—
405C4—82no—
406C4—81no—
407C4C13×#44911yescharacteristic
408C4C13×#45211yescharacteristic
409C4C13×#45911yescharacteristic
410C4C13×#45911yescharacteristic
411C4C13×#46311yescharacteristic
412C4C13×#46311yescharacteristic
413C4C13×#48811yescharacteristic
414C4C13×#48911yescharacteristic
415C2—162no—
416C2C13×#168111yescharacteristic
417C2C13×#168211yescharacteristic
418C2C13×#170111yescharacteristic
419C2C13×#170211yescharacteristic
420C2C13×#204211yescharacteristic
421C2C13×#204611yescharacteristic
422C2C13×#205411yescharacteristic
subgroupG/H
center, socleC23×C13#121
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
3. C13×#1981C2semidirect
4. C13×#1939C2semidirect
5. C2×C13×#332C2semidirect
7. C13×#1277C2semidirect
66. #10540C13direct (N × H)
127. #1981C2×C13semidirect
128. #1939C2×C13semidirect
129. C2×#332C2×C13semidirect
131. #1277C2×C13semidirect
335. C13#10540direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4862
C13×#19822
C13×#19812
C13×#19392
C2×C13×#3322
C2×C13×#3312
C13×#12772
#1054013