Finite Group Databasebeta

← C13×#10411 #15696750

Subgroups — C13×#10411 #15696750

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2548C211yesmaximal, characteristic
2C13×#1957C211yesmaximal, characteristic
3C13×#1947C211yesmaximal, characteristic, complemented
4C13×#1803C211yesmaximal, characteristic, complemented
5C2×C13×#331C211yesmaximal, characteristic
6C2×C13×Q8⋊C8C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×C13×#127C2211yescharacteristic
9C2×C13×#124—21no—
10C2×C4×Q8×C13C2211yescharacteristic
11C2×C13×#107—21no—
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×#103—21no—
15C2×C13×#102—22no—
16C2×C4×C8×C13C2211yescharacteristic
17C13×#394—22no—
18C13×#390—21no—
19C13×#390—21no—
20C13×#390—21no—
21C13×#384C2211yescharacteristic
22C4×C13×C4⋊C4C2211yescharacteristic
23C13×#340—21no—
24C13×#340—21no—
25C13×#331—22no—
26C13×Q8⋊C8—22no—
27C22×Q8×C13D411yescharacteristic
28C22×D4×C13—21no—
29C22×D4×C13—21no—
30C22×D4×C13D412yes—
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C13×#127—21no—
35C13×#127—21no—
36C13×#127—21no—
37C13×#127—21no—
38C13×#124—42no—
39C13×#124—42no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C4×Q8×C13—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C22⋊C4—22no—
52C2×C13×C22⋊C4—22no—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4—22no—
55C2×C42×C13—21no—
56C2×C42×C13—21no—
57C2×C42×C13C2311yescharacteristic
58C13×#107—42no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8D412yes—
63C13×#103—42no—
64C13×#102—44no—
65C4×C8×C13—21no—
66C4×C8×C13—21no—
67C13×#95—21no—
68#10411C1311yesmaximal, characteristic, direct product factor, Sylow
69C24×C13—22no—
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13D812yes—
76C2×D4×C13—22no—
77C2×D4×C13—22no—
78C2×D4×C13—42no—
79C2×D4×C13—42no—
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—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—41no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C2×C8×C13—22no—
101C2×C8×C13—22no—
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—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—42no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C22⋊C4—44no—
123C13×C22⋊C4—44no—
124C13×C22⋊C4—82no—
125C13×C22⋊C4—82no—
126C42×C13—41no—
127C42×C13—41no—
128C42×C13—41no—
129C42×C13—41no—
130C42×C13C2×D411yescharacteristic
131C42×C13#4111yescharacteristic
132C42×C13#4111yescharacteristic
133C42×C13#4111yescharacteristic
134#2548C2×C1311yescharacteristic
135#1957C2×C1311yescharacteristic
136#1947C2×C1311yescharacteristic, complemented
137#1803C2×C1311yescharacteristic, complemented
138C2×#331C2×C1311yescharacteristic
139C2×Q8⋊C8C2×C1311yescharacteristic, complemented
140#1279C2×C1311yescharacteristic, complemented
141C23×C13—42no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13—42no—
145C23×C13—42no—
146C23×C13—42no—
147C23×C13—42no—
148C23×C13#12011yescharacteristic
149Q8×C13—22no—
150Q8×C13—22no—
151Q8×C13—41no—
152Q8×C13—41no—
153D4×C13—44no—
154D4×C13—82no—
155D4×C13—81no—
156D4×C13—81no—
157D4×C13—81no—
158D4×C13—81no—
159D4×C13—81no—
160D4×C13—81no—
161D4×C13—81no—
162D4×C13—81no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—22no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12311yescharacteristic
184C2×C4×C13#12311yescharacteristic
185C2×C4×C13#12411yescharacteristic
186C2×C4×C13C2×D811yescharacteristic
187C2×C4×C13#13511yescharacteristic
188C2×C4×C13#13511yescharacteristic
189C2×C4×C13#13511yescharacteristic
190C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C13#13711yescharacteristic
193C2×C4×C13#13711yescharacteristic
194C8×C13—42no—
195C8×C13—42no—
196C8×C13—81no—
197C2×#127C22×C1311yescharacteristic
198C2×#124—21no—
199C2×C4×Q8C22×C1311yescharacteristic
200C2×#107—21no—
201C2×C4⋊C8C22×C1311yescharacteristic
202C2×C4⋊C8C22×C1311yescharacteristic
203C2×#103—21no—
204C2×#102—22no—
205C2×C4×C8C22×C1311yescharacteristic
206#394—22no—
207#390—21no—
208#390—21no—
209#390—21no—
210#384C22×C1311yescharacteristic
211C4×C4⋊C4C22×C1311yescharacteristic
212#340—21no—
213#340—21no—
214#331—22no—
215Q8⋊C8—22no—
216C22×C13—82no—
217C22×C13—82no—
218C22×C13—82no—
219C22×C13—82no—
220C22×C13—82no—
221C22×C13—82no—
222C22×C13—82no—
223C22×C13#39411yescharacteristic
224C22×C13#44711yescharacteristic
225C22×C13#44911yescharacteristic
226C22×C13#45211yescharacteristic
227C22×C13#45211yescharacteristic
228C22×C13#45311yescharacteristic
229C22×C13#45511yescharacteristic
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—42no—
233C4×C13—81no—
234C4×C13—81no—
235C4×C13—81no—
236C4×C13—161no—
237C4×C13#46311yescharacteristic
238C4×C13#46411yescharacteristic
239C4×C13#46611yescharacteristic
240C4×C13#46811yescharacteristic
241C4×C13#48011yescharacteristic
242C4×C13#48211yescharacteristic
243C4×C13#48811yescharacteristic
244C4×C13#48911yescharacteristic
245C22×Q8D4×C1311yescharacteristic
246C22×D4—21no—
247C22×D4—21no—
248C22×D4D4×C1312yes—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252#127—21no—
253#127—21no—
254#127—21no—
255#127—21no—
256#124—42no—
257#124—42no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C1311yescharacteristic
267C2×C4⋊C4D4×C1311yescharacteristic
268C2×C4⋊C4D4×C1311yescharacteristic
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42C23×C1311yescharacteristic
276#107—42no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8D4×C1312yes—
281#103—42no—
282#102—44no—
283C4×C8—21no—
284C4×C8—21no—
285#95—21no—
286C2×C13—162no—
287C2×C13#162111yescharacteristic
288C2×C13#163011yescharacteristic
289C2×C13#164011yescharacteristic
290C2×C13#164111yescharacteristic
291C2×C13#203311yescharacteristic
292C2×C13#203711yescharacteristic
293C2×C13#204211yescharacteristic
294C24—22no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8C13×D812yes—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4C2×D4×C1311yescharacteristic
323C22×C4C2×D4×C1311yescharacteristic
324C22×C4C2×D4×C1311yescharacteristic
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—42no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C22⋊C4—44no—
348C22⋊C4—44no—
349C22⋊C4—82no—
350C22⋊C4—82no—
351C42—41no—
352C42—41no—
353C42—41no—
354C42—41no—
355C42C2×D4×C1311yescharacteristic
356C42C13×#4111yescharacteristic
357C42C13×#4111yescharacteristic
358C42C13×#4111yescharacteristic
359C13#1041111yescharacteristic, direct product factor, Sylow
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23C13×#12011yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372D4—44no—
373D4—82no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C13×#12111yescharacteristic
400C2×C4C13×#12111yescharacteristic
401C2×C4C13×#12111yescharacteristic
402C2×C4C13×#12311yescharacteristic
403C2×C4C13×#12311yescharacteristic
404C2×C4C13×#12411yescharacteristic
405C2×C4C2×C13×D811yescharacteristic
406C2×C4C13×#13511yescharacteristic
407C2×C4C13×#13511yescharacteristic
408C2×C4C13×#13511yescharacteristic
409C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
410C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
411C2×C4C13×#13711yescharacteristic
412C2×C4C13×#13711yescharacteristic
413C8—42no—
414C8—42no—
415C8—81no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22C13×#39411yescharacteristic
424C22C13×#44711yescharacteristic
425C22C13×#44911yescharacteristic
426C22C13×#45211yescharacteristic
427C22C13×#45211yescharacteristic
428C22C13×#45311yescharacteristic
429C22C13×#45511yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—161no—
437C4C13×#46311yescharacteristic
438C4C13×#46411yescharacteristic
439C4C13×#46611yescharacteristic
440C4C13×#46811yescharacteristic
441C4C13×#48011yescharacteristic
442C4C13×#48211yescharacteristic
443C4C13×#48811yescharacteristic
444C4C13×#48911yescharacteristic
445C2—162no—
446C2C13×#162111yescharacteristic
447C2C13×#163011yescharacteristic
448C2C13×#164011yescharacteristic
449C2C13×#164111yescharacteristic
450C2C13×#203311yescharacteristic
451C2C13×#203711yescharacteristic
452C2C13×#204211yescharacteristic
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
3. C13×#1947C2semidirect
4. C13×#1803C2semidirect
6. C2×C13×Q8⋊C8C2semidirect
7. C13×#1279C2semidirect
68. #10411C13direct (N × H)
136. #1947C2×C13semidirect
137. #1803C2×C13semidirect
139. C2×Q8⋊C8C2×C13semidirect
140. #1279C2×C13semidirect
359. C13#10411direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25482
C13×#19572
C13×#19472
C13×#18032
C2×C13×#3312
C2×C13×Q8⋊C82
C13×#12792
#1041113