Finite Group Databasebeta

← C13×#10033 #15696372

Subgroups — C13×#10033 #15696372

Order 3328.

550 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3135C211yesmaximal, characteristic, complemented
2C13×#3101C211yesmaximal, characteristic, complemented
3C13×#3100C211yesmaximal, characteristic
4C13×#1955C211yesmaximal, characteristic, complemented
5C13×#1481C211yesmaximal, characteristic, complemented
6C13×#1480C211yesmaximal, characteristic, complemented
7C13×#1275C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#532C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C13×#491—21no—
12C13×#490—21no—
13C13×#489—21no—
14C13×#489—21no—
15C13×#483—21no—
16C13×#480—21no—
17C13×#476—21no—
18C13×#474—21no—
19C13×#461—21no—
20C13×#459—21no—
21C13×#450—21no—
22C13×#447—21no—
23C4×C13×SD16—22no—
24C4×C13×D8—22no—
25C13×#431C2211yescharacteristic
26C13×#431C2211yescharacteristic
27C2×C13×C4⋊C8C2211yescharacteristic
28C13×#416—22no—
29C2×C13×C22⋊C8—22no—
30C2×C13×#97C2211yescharacteristic
31C13×Q8⋊C8—22no—
32C13×D4⋊C8—22no—
33C2×C13×#41—21no—
34C22×D4×C13D411yescharacteristic
35C23×C4×C13—21no—
36C2×C13×SD16—22no—
37C2×C13×D8—22no—
38C22×C8×C13—21no—
39C22×C8×C13D412yes—
40C13×C4⋊Q8D411yescharacteristic
41C13×C4⋊Q8D411yescharacteristic
42C13×C4⋊Q8D411yescharacteristic
43C13×#127D411yescharacteristic
44C13×#125—21no—
45C13×#124—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8—21no—
48C13×#121—21no—
49C13×#121—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13—21no—
52C4×D4×C13—21no—
53C4×D4×C13—21no—
54C4×D4×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13—21no—
57C4×D4×C13—21no—
58C13×#117—21no—
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C13×C22⋊C4—21no—
61C2×C42×C13C2311yescharacteristic
62C13×#107—22no—
63C13×#106—22no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8—21no—
68C13×#103—22no—
69C13×#103—22no—
70C13×#103—22no—
71C13×#102—22no—
72C13×#102—22no—
73C13×#102—22no—
74C13×#102—22no—
75C13×#102—22no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—44no—
79C13×#97—21no—
80C13×#97—21no—
81C4×C8×C13D412yes—
82C4×C8×C13D412yes—
83#10033C1311yesmaximal, 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×D4×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—42no—
96C2×D4×C13—41no—
97C22×C4×C13—21no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13—42no—
102C22×C4×C13—42no—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13#4111yescharacteristic
106C13×SD16—44no—
107C13×D8—44no—
108C2×C8×C13—22no—
109C2×C8×C13—22no—
110C2×C8×C13—22no—
111C2×C8×C13—22no—
112C2×C8×C13—22no—
113C2×C8×C13—41no—
114C2×C8×C13—42no—
115C13×C4⋊C4—21no—
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—21no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—41no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C42×C13—41no—
131C42×C13C2×D411yescharacteristic
132C42×C13C2×D411yescharacteristic
133C42×C13C2×D411yescharacteristic
134C42×C13C2×D411yescharacteristic
135#3135C2×C1311yescharacteristic, complemented
136#3101C2×C1311yescharacteristic, complemented
137#3100C2×C1311yescharacteristic
138#1955C2×C1311yescharacteristic, complemented
139#1481C2×C1311yescharacteristic, complemented
140#1480C2×C1311yescharacteristic, complemented
141#1275C2×C1311yescharacteristic, complemented
142C23×C13—22no—
143C23×C13—41no—
144C23×C13—42no—
145C23×C13—41no—
146C23×C13—42no—
147C23×C13—41no—
148C23×C13#12111yescharacteristic
149Q8×C13—42no—
150Q8×C13—42no—
151Q8×C13—42no—
152D4×C13—22no—
153D4×C13—22no—
154D4×C13—41no—
155D4×C13—41no—
156D4×C13—42no—
157D4×C13—42no—
158D4×C13—42no—
159D4×C13—82no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—42no—
167C2×C4×C13—82no—
168C2×C4×C13—81no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13#12011yescharacteristic
173C2×C4×C13#12011yescharacteristic
174C2×C4×C13#12011yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13#12711yescharacteristic
178C2×C4×C13#13512yes—
179C2×C4×C13AGL(1,ℤ/8)12yes—
180C8×C13—42no—
181C8×C13—42no—
182C8×C13—42no—
183C8×C13—81no—
184#533C22×C1311yescharacteristic
185#532C22×C1311yescharacteristic
186C2×C4×D4C22×C1311yescharacteristic
187#491—21no—
188#490—21no—
189#489—21no—
190#489—21no—
191#483—21no—
192#480—21no—
193#476—21no—
194#474—21no—
195#461—21no—
196#459—21no—
197#450—21no—
198#447—21no—
199C4×SD16—22no—
200C4×D8—22no—
201#431C22×C1311yescharacteristic
202#431C22×C1311yescharacteristic
203C2×C4⋊C8C22×C1311yescharacteristic
204#416—22no—
205C2×C22⋊C8—22no—
206C2×#97C22×C1311yescharacteristic
207Q8⋊C8—22no—
208D4⋊C8—22no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—44no—
212C22×C13—42no—
213C22×C13—82no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13#39211yescharacteristic
220C22×C13#46312yes—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—81no—
226C4×C13—81no—
227C4×C13—81no—
228C4×C13—81no—
229C4×C13#44912yes—
230C4×C13#49511yescharacteristic
231C4×C13#49611yescharacteristic
232C2×#41—21no—
233C22×D4D4×C1311yescharacteristic
234C23×C4—21no—
235C2×SD16—22no—
236C2×D8—22no—
237C22×C8—21no—
238C22×C8D4×C1312yes—
239C4⋊Q8D4×C1311yescharacteristic
240C4⋊Q8D4×C1311yescharacteristic
241C4⋊Q8D4×C1311yescharacteristic
242#127D4×C1311yescharacteristic
243#125—21no—
244#124—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247#121—21no—
248#121—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257#117—21no—
258C2×C4⋊C4D4×C1311yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C23×C1311yescharacteristic
261#107—22no—
262#106—22no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267#103—22no—
268#103—22no—
269#103—22no—
270#102—22no—
271#102—22no—
272#102—22no—
273#102—22no—
274#102—22no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—44no—
278#97—21no—
279#97—21no—
280C4×C8D4×C1312yes—
281C4×C8D4×C1312yes—
282C2×C13—22no—
283C2×C13—82no—
284C2×C13—161no—
285C2×C13#201011yescharacteristic
286C2×C13#201211yescharacteristic
287C2×C13#201711yescharacteristic
288C24—21no—
289#41—42no—
290#41—42no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—42no—
300C2×D4—41no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4C2×D4×C1311yescharacteristic
308C22×C4C2×D4×C1311yescharacteristic
309C22×C4C13×#4111yescharacteristic
310SD16—44no—
311D8—44no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—41no—
318C2×C8—42no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C42—41no—
335C42C2×D4×C1311yescharacteristic
336C42C2×D4×C1311yescharacteristic
337C42C2×D4×C1311yescharacteristic
338C42C2×D4×C1311yescharacteristic
339C13#1003311yescharacteristic, direct product factor, Sylow
340C23—22no—
341C23—41no—
342C23—42no—
343C23—41no—
344C23—42no—
345C23—41no—
346C23C13×#12111yescharacteristic
347Q8—42no—
348Q8—42no—
349Q8—42no—
350D4—22no—
351D4—22no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—82no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4C13×#12011yescharacteristic
371C2×C4C13×#12011yescharacteristic
372C2×C4C13×#12011yescharacteristic
373C2×C4C13×#12111yescharacteristic
374C2×C4C13×#12111yescharacteristic
375C2×C4C13×#12711yescharacteristic
376C2×C4C13×#13512yes—
377C2×C4C13×AGL(1,ℤ/8)12yes—
378C8—42no—
379C8—42no—
380C8—42no—
381C8—81no—
382C22—21no—
383C22—21no—
384C22—44no—
385C22—42no—
386C22—82no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C13×#39211yescharacteristic
393C22C13×#46312yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4C13×#44912yes—
403C4C13×#49511yescharacteristic
404C4C13×#49611yescharacteristic
405C2—22no—
406C2—82no—
407C2—161no—
408C2C13×#201011yescharacteristic
409C2C13×#201211yescharacteristic
410C2C13×#201711yescharacteristic
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×#3135C2semidirect
2. C13×#3101C2semidirect
4. C13×#1955C2semidirect
5. C13×#1481C2semidirect
6. C13×#1480C2semidirect
7. C13×#1275C2semidirect
83. #10033C13direct (N × H)
135. #3135C2×C13semidirect
136. #3101C2×C13semidirect
138. #1955C2×C13semidirect
139. #1481C2×C13semidirect
140. #1480C2×C13semidirect
141. #1275C2×C13semidirect
339. C13#10033direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31352
C13×#31012
C13×#31002
C13×#19552
C13×#14812
C13×#14802
C13×#12752
#1003313