Finite Group Databasebeta

← C13×#10417 #15696756

Subgroups — C13×#10417 #15696756

Order 3328.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2547C211yesmaximal, characteristic
2C13×#1990C211yesmaximal, characteristic, complemented
3C13×#1948C211yesmaximal, characteristic, complemented
4C13×#1802C211yesmaximal, characteristic
5C2×C13×#332C211yesmaximal, characteristic, complemented
6C2×C13×D4⋊C8C211yesmaximal, characteristic
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×#124—21no—
10C2×C4×D4×C13C2211yescharacteristic
11C2×C13×#106—21no—
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×#102—21no—
15C2×C4×C8×C13C2211yescharacteristic
16C13×#397—22no—
17C13×#391—21no—
18C13×#384C2211yescharacteristic
19C13×#380—21no—
20C13×#380—21no—
21C4×C13×C4⋊C4C2211yescharacteristic
22C13×#340—22no—
23C13×#340—21no—
24C13×#340—21no—
25C13×#332—22no—
26C13×D4⋊C8—22no—
27C22×Q8×C13—21no—
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×#124—42no—
38C13×#124—42no—
39C4×D4×C13—21no—
40C4×D4×C13—21no—
41C4×D4×C13—21no—
42C4×D4×C13—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D412yes—
51C2×C13×C22⋊C4—22no—
52C2×C13×C22⋊C4—22no—
53C2×C13×C22⋊C4—21no—
54C2×C42×C13—21no—
55C2×C42×C13C2311yescharacteristic
56C13×#106—42no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8D412yes—
61C13×#102—42no—
62C4×C8×C13—21no—
63C4×C8×C13—21no—
64C13×#95—22no—
65C13×#95—22no—
66C13×#95—21no—
67#10417C1311yesmaximal, characteristic, direct product factor, Sylow
68C24×C13—21no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×D4×C13—21no—
76C2×D4×C13—21no—
77C2×D4×C13—21no—
78C2×D4×C13—21no—
79C2×D4×C13—21no—
80C2×D4×C13SD1612yes—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
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×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—42no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C22⋊C4—44no—
120C13×C22⋊C4—44no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C42×C13—41no—
124C42×C13—41no—
125C42×C13C2×D411yescharacteristic
126C42×C13#4111yescharacteristic
127C42×C13#4111yescharacteristic
128C42×C13#4111yescharacteristic
129#2547C2×C1311yescharacteristic
130#1990C2×C1311yescharacteristic, complemented
131#1948C2×C1311yescharacteristic, complemented
132#1802C2×C1311yescharacteristic
133C2×#332C2×C1311yescharacteristic, complemented
134C2×D4⋊C8C2×C1311yescharacteristic
135#1279C2×C1311yescharacteristic, complemented
136C23×C13—22no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13#12011yescharacteristic
144Q8×C13—81no—
145Q8×C13—81no—
146Q8×C13—81no—
147Q8×C13—81no—
148D4×C13—22no—
149D4×C13—22no—
150D4×C13—41no—
151D4×C13—41no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—41no—
155C2×C4×C13—42no—
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—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13#12111yescharacteristic
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12311yescharacteristic
177C2×C4×C13#12311yescharacteristic
178C2×C4×C13#12411yescharacteristic
179C2×C4×C13C2×SD1611yescharacteristic
180C2×C4×C13#13511yescharacteristic
181C2×C4×C13#13511yescharacteristic
182C2×C4×C13#13511yescharacteristic
183C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C13#13711yescharacteristic
187C8×C13—42no—
188C8×C13—42no—
189C8×C13—81no—
190C2×C4⋊Q8C22×C1311yescharacteristic
191C2×#124—21no—
192C2×C4×D4C22×C1311yescharacteristic
193C2×#106—21no—
194C2×C4⋊C8C22×C1311yescharacteristic
195C2×C4⋊C8C22×C1311yescharacteristic
196C2×#102—21no—
197C2×C4×C8C22×C1311yescharacteristic
198#397—22no—
199#391—21no—
200#384C22×C1311yescharacteristic
201#380—21no—
202#380—21no—
203C4×C4⋊C4C22×C1311yescharacteristic
204#340—21no—
205#340—21no—
206#340—22no—
207#332—22no—
208D4⋊C8—22no—
209C22×C13—42no—
210C22×C13—42no—
211C22×C13—42no—
212C22×C13—81no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13#39411yescharacteristic
217C22×C13#44911yescharacteristic
218C22×C13#44911yescharacteristic
219C22×C13#45011yescharacteristic
220C22×C13#45211yescharacteristic
221C22×C13#45411yescharacteristic
222C22×C13#45611yescharacteristic
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—81no—
226C4×C13—81no—
227C4×C13—82no—
228C4×C13—81no—
229C4×C13—161no—
230C4×C13#46311yescharacteristic
231C4×C13#46411yescharacteristic
232C4×C13#46511yescharacteristic
233C4×C13#46911yescharacteristic
234C4×C13#48111yescharacteristic
235C4×C13#48211yescharacteristic
236C4×C13#48811yescharacteristic
237C4×C13#48911yescharacteristic
238C22×Q8—21no—
239C22×D4D4×C1311yescharacteristic
240C23×C4—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248#124—42no—
249#124—42no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4D4×C1311yescharacteristic
259C2×C4⋊C4D4×C1312yes—
260C2×C4⋊C4D4×C1311yescharacteristic
261C2×C4⋊C4D4×C1311yescharacteristic
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—21no—
265C2×C42—21no—
266C2×C42C23×C1311yescharacteristic
267#106—42no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8D4×C1312yes—
272#102—42no—
273C4×C8—21no—
274C4×C8—21no—
275#95—22no—
276#95—22no—
277#95—21no—
278C2×C13—82no—
279C2×C13#162811yescharacteristic
280C2×C13#163511yescharacteristic
281C2×C13#165011yescharacteristic
282C2×C13#165411yescharacteristic
283C2×C13#203411yescharacteristic
284C2×C13#203811yescharacteristic
285C2×C13#204211yescharacteristic
286C24—21no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4C13×SD1612yes—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4C2×D4×C1311yescharacteristic
311C22×C4C2×D4×C1311yescharacteristic
312C22×C4C2×D4×C1311yescharacteristic
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—42no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C22⋊C4—44no—
338C22⋊C4—44no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C42—41no—
342C42—41no—
343C42C2×D4×C1311yescharacteristic
344C42C13×#4111yescharacteristic
345C42C13×#4111yescharacteristic
346C42C13×#4111yescharacteristic
347C13#1041711yescharacteristic, direct product factor, Sylow
348C23—22no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23C13×#12011yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—22no—
361D4—22no—
362D4—41no—
363D4—41no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C13×#12111yescharacteristic
386C2×C4C13×#12111yescharacteristic
387C2×C4C13×#12111yescharacteristic
388C2×C4C13×#12311yescharacteristic
389C2×C4C13×#12311yescharacteristic
390C2×C4C13×#12411yescharacteristic
391C2×C4C2×C13×SD1611yescharacteristic
392C2×C4C13×#13511yescharacteristic
393C2×C4C13×#13511yescharacteristic
394C2×C4C13×#13511yescharacteristic
395C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
396C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
397C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
398C2×C4C13×#13711yescharacteristic
399C8—42no—
400C8—42no—
401C8—81no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22C13×#39411yescharacteristic
410C22C13×#44911yescharacteristic
411C22C13×#44911yescharacteristic
412C22C13×#45011yescharacteristic
413C22C13×#45211yescharacteristic
414C22C13×#45411yescharacteristic
415C22C13×#45611yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—161no—
423C4C13×#46311yescharacteristic
424C4C13×#46411yescharacteristic
425C4C13×#46511yescharacteristic
426C4C13×#46911yescharacteristic
427C4C13×#48111yescharacteristic
428C4C13×#48211yescharacteristic
429C4C13×#48811yescharacteristic
430C4C13×#48911yescharacteristic
431C2—82no—
432C2C13×#162811yescharacteristic
433C2C13×#163511yescharacteristic
434C2C13×#165011yescharacteristic
435C2C13×#165411yescharacteristic
436C2C13×#203411yescharacteristic
437C2C13×#203811yescharacteristic
438C2C13×#204211yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
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
2. C13×#1990C2semidirect
3. C13×#1948C2semidirect
5. C2×C13×#332C2semidirect
7. C13×#1279C2semidirect
67. #10417C13direct (N × H)
130. #1990C2×C13semidirect
131. #1948C2×C13semidirect
133. C2×#332C2×C13semidirect
135. #1279C2×C13semidirect
347. C13#10417direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25472
C13×#19902
C13×#19482
C13×#18022
C2×C13×#3322
C2×C13×D4⋊C82
C13×#12792
#1041713