Finite Group Databasebeta

← C13×#10434 #15696773

Subgroups — C13×#10434 #15696773

Order 3328.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2538C211yesmaximal, characteristic
2C13×#1845C211yesmaximal, characteristic, complemented
3C13×#1803C211yesmaximal, characteristic, complemented
4C13×#1802C211yesmaximal, characteristic
5C2×C13×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C13×D4⋊C8C211yesmaximal, characteristic
7C13×#1296C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8—21no—
9C2×C4×Q8×C13C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C2×C13×#107—22no—
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×#103—21no—
15C2×C13×#102—21no—
16C2×C4×C8×C13C2211yescharacteristic
17C13×#396—22no—
18C13×#390—21no—
19C13×#389—21no—
20C13×#384C2211yescharacteristic
21C13×#384C2211yescharacteristic
22C13×#380—21no—
23C13×#340—21no—
24C13×#340—21no—
25C13×Q8⋊C8—22no—
26C13×D4⋊C8—22no—
27C22×Q8×C13D411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C13×C22⋊Q8—42no—
34C13×C22⋊Q8—42no—
35C4×Q8×C13—21no—
36C4×Q8×C13—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C4×D4×C13—21no—
40C4×D4×C13—21no—
41C4×D4×C13—21no—
42C4×D4×C13—21no—
43C2×C13×C4⋊C4—22no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C4⋊C4D412yes—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—22no—
56C2×C42×C13—21no—
57C2×C42×C13C2311yescharacteristic
58C13×#107—44no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×#103—42no—
64C13×#102—42no—
65C4×C8×C13—21no—
66C4×C8×C13D412yes—
67C13×#95—22no—
68#10434C1311yesmaximal, characteristic, direct product factor, Sylow
69C24×C13—21no—
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—21no—
77C2×D4×C13—21no—
78C2×D4×C13—21no—
79C2×D4×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13Q1612yes—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—22no—
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×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—22no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4—44no—
111C13×C4⋊C4—42no—
112C13×C4⋊C4—41no—
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×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C22⋊C4—44no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—82no—
126C42×C13—41no—
127C42×C13—41no—
128C42×C13C2×D411yescharacteristic
129C42×C13#4111yescharacteristic
130C42×C13#4111yescharacteristic
131C42×C13#4111yescharacteristic
132#2538C2×C1311yescharacteristic
133#1845C2×C1311yescharacteristic, complemented
134#1803C2×C1311yescharacteristic, complemented
135#1802C2×C1311yescharacteristic
136C2×Q8⋊C8C2×C1311yescharacteristic, complemented
137C2×D4⋊C8C2×C1311yescharacteristic
138#1296C2×C1311yescharacteristic, complemented
139C23×C13—22no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13#12011yescharacteristic
147Q8×C13—22no—
148Q8×C13—22no—
149Q8×C13—41no—
150Q8×C13—41no—
151D4×C13—22no—
152D4×C13—22no—
153D4×C13—41no—
154D4×C13—41no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—22no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—42no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—42no—
168C2×C4×C13—41no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13—81no—
174C2×C4×C13—81no—
175C2×C4×C13—81no—
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13#12111yescharacteristic
178C2×C4×C13#12111yescharacteristic
179C2×C4×C13#12311yescharacteristic
180C2×C4×C13#12311yescharacteristic
181C2×C4×C13#12411yescharacteristic
182C2×C4×C13C2×D811yescharacteristic
183C2×C4×C13C2×Q1611yescharacteristic
184C2×C4×C13#13511yescharacteristic
185C2×C4×C13#13511yescharacteristic
186C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C13#13711yescharacteristic
189C2×C4×C13#13711yescharacteristic
190C8×C13—24no—
191C8×C13—81no—
192C8×C13—81no—
193C2×C22⋊Q8—21no—
194C2×C4×Q8C22×C1311yescharacteristic
195C2×C4×D4C22×C1311yescharacteristic
196C2×#107—22no—
197C2×C4⋊C8C22×C1311yescharacteristic
198C2×C4⋊C8C22×C1311yescharacteristic
199C2×#103—21no—
200C2×#102—21no—
201C2×C4×C8C22×C1311yescharacteristic
202#396—22no—
203#390—21no—
204#389—21no—
205#384C22×C1311yescharacteristic
206#384C22×C1311yescharacteristic
207#380—21no—
208#340—21no—
209#340—21no—
210Q8⋊C8—22no—
211D4⋊C8—22no—
212C22×C13—42no—
213C22×C13—42no—
214C22×C13—42no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13#39411yescharacteristic
220C22×C13#44711yescharacteristic
221C22×C13#44911yescharacteristic
222C22×C13#45111yescharacteristic
223C22×C13#45211yescharacteristic
224C22×C13#45311yescharacteristic
225C22×C13#45611yescharacteristic
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—42no—
229C4×C13—82no—
230C4×C13—81no—
231C4×C13—81no—
232C4×C13—161no—
233C4×C13#46611yescharacteristic
234C4×C13#46711yescharacteristic
235C4×C13#46811yescharacteristic
236C4×C13#46811yescharacteristic
237C4×C13#48011yescharacteristic
238C4×C13#48211yescharacteristic
239C4×C13#48411yescharacteristic
240C4×C13#48511yescharacteristic
241C22×Q8D4×C1311yescharacteristic
242C22×D4D4×C1311yescharacteristic
243C23×C4—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22⋊Q8—42no—
248C22⋊Q8—42no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4D4×C1311yescharacteristic
265C2×C4⋊C4D4×C1311yescharacteristic
266C2×C4⋊C4D4×C1312yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—22no—
270C2×C42—21no—
271C2×C42C23×C1311yescharacteristic
272#107—44no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277#103—42no—
278#102—42no—
279C4×C8—21no—
280C4×C8D4×C1312yes—
281#95—22no—
282C2×C13—82no—
283C2×C13#162111yescharacteristic
284C2×C13#163211yescharacteristic
285C2×C13#164911yescharacteristic
286C2×C13#165011yescharacteristic
287C2×C13#203311yescharacteristic
288C2×C13#203611yescharacteristic
289C2×C13#203911yescharacteristic
290C24—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8C13×D812yes—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4C13×Q1612yes—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4C2×D4×C1311yescharacteristic
315C22×C4C2×D4×C1311yescharacteristic
316C22×C4C2×D4×C1311yescharacteristic
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—42no—
331C4⋊C4—44no—
332C4⋊C4—42no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C22⋊C4—44no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—82no—
347C42—41no—
348C42—41no—
349C42C2×D4×C1311yescharacteristic
350C42C13×#4111yescharacteristic
351C42C13×#4111yescharacteristic
352C42C13×#4111yescharacteristic
353C13#1043411yescharacteristic, direct product factor, Sylow
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23C13×#12011yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—41no—
365Q8—41no—
366D4—22no—
367D4—22no—
368D4—41no—
369D4—41no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4C13×#12111yescharacteristic
392C2×C4C13×#12111yescharacteristic
393C2×C4C13×#12111yescharacteristic
394C2×C4C13×#12311yescharacteristic
395C2×C4C13×#12311yescharacteristic
396C2×C4C13×#12411yescharacteristic
397C2×C4C2×C13×D811yescharacteristic
398C2×C4C2×C13×Q1611yescharacteristic
399C2×C4C13×#13511yescharacteristic
400C2×C4C13×#13511yescharacteristic
401C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
402C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
403C2×C4C13×#13711yescharacteristic
404C2×C4C13×#13711yescharacteristic
405C8—24no—
406C8—81no—
407C8—81no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22C13×#39411yescharacteristic
416C22C13×#44711yescharacteristic
417C22C13×#44911yescharacteristic
418C22C13×#45111yescharacteristic
419C22C13×#45211yescharacteristic
420C22C13×#45311yescharacteristic
421C22C13×#45611yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—81no—
427C4—82no—
428C4—161no—
429C4C13×#46611yescharacteristic
430C4C13×#46711yescharacteristic
431C4C13×#46811yescharacteristic
432C4C13×#46811yescharacteristic
433C4C13×#48011yescharacteristic
434C4C13×#48211yescharacteristic
435C4C13×#48411yescharacteristic
436C4C13×#48511yescharacteristic
437C2—82no—
438C2C13×#162111yescharacteristic
439C2C13×#163211yescharacteristic
440C2C13×#164911yescharacteristic
441C2C13×#165011yescharacteristic
442C2C13×#203311yescharacteristic
443C2C13×#203611yescharacteristic
444C2C13×#203911yescharacteristic
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×#1845C2semidirect
3. C13×#1803C2semidirect
5. C2×C13×Q8⋊C8C2semidirect
7. C13×#1296C2semidirect
68. #10434C13direct (N × H)
133. #1845C2×C13semidirect
134. #1803C2×C13semidirect
136. C2×Q8⋊C8C2×C13semidirect
138. #1296C2×C13semidirect
353. C13#10434direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25382
C13×#18452
C13×#18032
C13×#18022
C2×C13×Q8⋊C82
C2×C13×D4⋊C82
C13×#12962
#1043413