Finite Group Databasebeta

← C13×#10013 #15696352

Subgroups — C13×#10013 #15696352

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3103C211yesmaximal, characteristic, complemented
2C13×#3100C211yesmaximal, characteristic
3C13×#2398C211yesmaximal, characteristic, complemented
4C13×#1963C211yesmaximal, characteristic, complemented
5C13×#1487C211yesmaximal, characteristic, complemented
6C13×#1486C211yesmaximal, characteristic, complemented
7C13×#1274C211yesmaximal, characteristic, complemented
8C13×#532C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C13×#481—21no—
12C13×#480—21no—
13C13×#475—21no—
14C13×#474—21no—
15C13×#460—21no—
16C13×#459—21no—
17C13×#448—21no—
18C13×#447—21no—
19C4×C13×SD16—22no—
20C4×C13×D8—22no—
21C13×#431C2211yescharacteristic
22C13×#431C2211yescharacteristic
23C13×#423C2211yescharacteristic
24C2×C13×#104—22no—
25C13×#400—21no—
26C13×#397—21no—
27C13×#394—21no—
28C13×#393—21no—
29C4×C13×C22⋊C4—22no—
30C13×#376C2211yescharacteristic
31C13×Q8⋊C8—22no—
32C13×D4⋊C8—22no—
33C2×C13×#41—21no—
34C22×Q8×C13D411yescharacteristic
35C22×D4×C13D411yescharacteristic
36C23×C4×C13—21no—
37C2×C13×SD16—22no—
38C2×C13×D8—22no—
39C2×C13×M16—21no—
40C13×C4⋊Q8D411yescharacteristic
41C13×#127D411yescharacteristic
42C13×#124—21no—
43C13×#121—21no—
44C13×#121—21no—
45C4×Q8×C13—21no—
46C4×Q8×C13—21no—
47C4×Q8×C13—21no—
48C4×Q8×C13—21no—
49C4×D4×C13—21no—
50C4×D4×C13—21no—
51C4×D4×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4D411yescharacteristic
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—21no—
61C2×C42×C13—21no—
62C2×C42×C13D412yes—
63C2×C42×C13C2311yescharacteristic
64C13×#107—22no—
65C13×#106—22no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8—21no—
69C13×C4⋊C8—21no—
70C13×#104—44no—
71C13×#103—22no—
72C13×#102—22no—
73C13×#102—22no—
74C13×#102—22no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77C4×C8×C13D412yes—
78C4×C8×C13D412yes—
79C13×#95—22no—
80C13×#95—22no—
81C13×#95—21no—
82C13×#95—21no—
83#10013C1311yesmaximal, characteristic, direct product factor, Sylow
84C24×C13—21no—
85C13×#41—42no—
86C13×#41—42no—
87C2×Q8×C13—21no—
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—42no—
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—42no—
97C2×D4×C13—41no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13—42no—
106C22×C4×C13—42no—
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C13×SD16—44no—
111C13×D8—44no—
112C13×M16—42no—
113C2×C8×C13—22no—
114C2×C8×C13—22no—
115C2×C8×C13—41no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4—41no—
124C13×C22⋊C4—44no—
125C13×C22⋊C4—44no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C42×C13—22no—
131C42×C13—22no—
132C42×C13—41no—
133C42×C13—41no—
134C42×C13C2×D411yescharacteristic
135C42×C13C2×D411yescharacteristic
136C42×C13C2×D411yescharacteristic
137C42×C13#4111yescharacteristic
138#3103C2×C1311yescharacteristic, complemented
139#3100C2×C1311yescharacteristic
140#2398C2×C1311yescharacteristic, complemented
141#1963C2×C1311yescharacteristic, complemented
142#1487C2×C1311yescharacteristic, complemented
143#1486C2×C1311yescharacteristic, complemented
144#1274C2×C1311yescharacteristic, complemented
145C23×C13—22no—
146C23×C13—42no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—42no—
150C23×C13—41no—
151C23×C13#12011yescharacteristic
152Q8×C13—22no—
153Q8×C13—22no—
154Q8×C13—41no—
155Q8×C13—41no—
156Q8×C13—42no—
157D4×C13—22no—
158D4×C13—22no—
159D4×C13—41no—
160D4×C13—41no—
161D4×C13—42no—
162D4×C13—42no—
163D4×C13—42no—
164D4×C13—82no—
165C2×C4×C13—22no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—42no—
177C2×C4×C13—42no—
178C2×C4×C13—82no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13—81no—
182C2×C4×C13—81no—
183C2×C4×C13#12011yescharacteristic
184C2×C4×C13#12011yescharacteristic
185C2×C4×C13#12111yescharacteristic
186C2×C4×C13#12111yescharacteristic
187C2×C4×C13#12111yescharacteristic
188C2×C4×C13#12711yescharacteristic
189C2×C4×C13#13512yes—
190C2×C4×C13AGL(1,ℤ/8)12yes—
191C8×C13—42no—
192C8×C13—42no—
193C8×C13—81no—
194#532C22×C1311yescharacteristic
195C2×C4×Q8C22×C1311yescharacteristic
196C2×C4×D4C22×C1311yescharacteristic
197#481—21no—
198#480—21no—
199#475—21no—
200#474—21no—
201#460—21no—
202#459—21no—
203#448—21no—
204#447—21no—
205C4×SD16—22no—
206C4×D8—22no—
207#431C22×C1311yescharacteristic
208#431C22×C1311yescharacteristic
209#423C22×C1311yescharacteristic
210C2×#104—22no—
211#400—21no—
212#397—21no—
213#394—21no—
214#393—21no—
215C4×C22⋊C4—22no—
216#376C22×C1311yescharacteristic
217Q8⋊C8—22no—
218D4⋊C8—22no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—44no—
222C22×C13—42no—
223C22×C13—82no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—81no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13#39211yescharacteristic
230C22×C13#44912yes—
231C4×C13—21no—
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—42no—
236C4×C13—82no—
237C4×C13—81no—
238C4×C13—81no—
239C4×C13—81no—
240C4×C13#46312yes—
241C4×C13#49511yescharacteristic
242C4×C13#49611yescharacteristic
243C2×#41—21no—
244C22×Q8D4×C1311yescharacteristic
245C22×D4D4×C1311yescharacteristic
246C23×C4—21no—
247C2×SD16—22no—
248C2×D8—22no—
249C2×M16—21no—
250C4⋊Q8D4×C1311yescharacteristic
251#127D4×C1311yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C1311yescharacteristic
267C2×C4⋊C4D4×C1311yescharacteristic
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—21no—
271C2×C42—21no—
272C2×C42D4×C1312yes—
273C2×C42C23×C1311yescharacteristic
274#107—22no—
275#106—22no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280#104—44no—
281#103—22no—
282#102—22no—
283#102—22no—
284#102—22no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C4×C8D4×C1312yes—
288C4×C8D4×C1312yes—
289#95—22no—
290#95—22no—
291#95—21no—
292#95—21no—
293C2×C13—22no—
294C2×C13—82no—
295C2×C13—161no—
296C2×C13#201011yescharacteristic
297C2×C13#201011yescharacteristic
298C2×C13#201211yescharacteristic
299C24—21no—
300#41—42no—
301#41—42no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—42no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—41no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4C2×D4×C1311yescharacteristic
323C22×C4C2×D4×C1311yescharacteristic
324C22×C4C2×D4×C1311yescharacteristic
325SD16—44no—
326D8—44no—
327M16—42no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—41no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C22⋊C4—44no—
340C22⋊C4—44no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C42—22no—
346C42—22no—
347C42—41no—
348C42—41no—
349C42C2×D4×C1311yescharacteristic
350C42C2×D4×C1311yescharacteristic
351C42C2×D4×C1311yescharacteristic
352C42C13×#4111yescharacteristic
353C13#1001311yescharacteristic, direct product factor, Sylow
354C23—22no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—42no—
359C23—41no—
360C23C13×#12011yescharacteristic
361Q8—22no—
362Q8—22no—
363Q8—41no—
364Q8—41no—
365Q8—42no—
366D4—22no—
367D4—22no—
368D4—41no—
369D4—41no—
370D4—42no—
371D4—42no—
372D4—42no—
373D4—82no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—82no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4C13×#12011yescharacteristic
393C2×C4C13×#12011yescharacteristic
394C2×C4C13×#12111yescharacteristic
395C2×C4C13×#12111yescharacteristic
396C2×C4C13×#12111yescharacteristic
397C2×C4C13×#12711yescharacteristic
398C2×C4C13×#13512yes—
399C2×C4C13×AGL(1,ℤ/8)12yes—
400C8—42no—
401C8—42no—
402C8—81no—
403C22—21no—
404C22—21no—
405C22—44no—
406C22—42no—
407C22—82no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22C13×#39211yescharacteristic
414C22C13×#44912yes—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—82no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4C13×#46312yes—
425C4C13×#49511yescharacteristic
426C4C13×#49611yescharacteristic
427C2—22no—
428C2—82no—
429C2—161no—
430C2C13×#201011yescharacteristic
431C2C13×#201011yescharacteristic
432C2C13×#201211yescharacteristic
subgroupG/H
centerC2×C4×C13#127
commutator, Frattini, cosocleC2×C42C23×C13
socleC22×C13#392
prime radicalC13×#3100C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3103C2semidirect
3. C13×#2398C2semidirect
4. C13×#1963C2semidirect
5. C13×#1487C2semidirect
6. C13×#1486C2semidirect
7. C13×#1274C2semidirect
83. #10013C13direct (N × H)
138. #3103C2×C13semidirect
140. #2398C2×C13semidirect
141. #1963C2×C13semidirect
142. #1487C2×C13semidirect
143. #1486C2×C13semidirect
144. #1274C2×C13semidirect
353. C13#10013direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31032
C13×#31002
C13×#23982
C13×#19632
C13×#14872
C13×#14862
C13×#12742
#1001313