Finite Group Databasebeta

← C13×#13326 #15699665

Subgroups — C13×#13326 #15699665

Order 3328.

614 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×SD32C211yesmaximal, characteristic, complemented
2C22×C13×D16C211yesmaximal, characteristic
3C2×C13×#495C211yesmaximal, characteristic, complemented
4C2×C13×#358C211yesmaximal, characteristic, complemented
5C2×C13×#357C211yesmaximal, characteristic, complemented
6C13×#1970C211yesmaximal, characteristic, complemented
7C13×#1374C211yesmaximal, characteristic, complemented
8C22×C13×Q16C2211yescharacteristic
9C22×C13×SD16—21no—
10C22×C13×D8C2211yescharacteristic
11C22×C13×D8C2211yescharacteristic
12C2×C13×#124—21no—
13C2×C13×SD32—22no—
14C2×C13×SD32—22no—
15C2×C13×SD32—22no—
16C2×C13×D16—22no—
17C2×C13×D16—22no—
18C2×C13×D16—22no—
19C22×C13×C16C2211yescharacteristic
20C22×C13×C16C2211yescharacteristic
21C13×#495—22no—
22C13×#495—22no—
23C2×C13×#107C2211yescharacteristic
24C2×C13×#102—21no—
25C2×C4×C8×C13C2211yescharacteristic
26C13×#390—21no—
27C13×#358—22no—
28C13×#357—22no—
29C22×Q8×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13—21no—
32C2×C13×Q16—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16—21no—
35C2×C13×Q16—21no—
36C2×C13×Q16—21no—
37C2×C13×Q16D412yes—
38C2×C13×SD16—24no—
39C2×C13×SD16—42no—
40C2×C13×SD16—42no—
41C2×C13×D8—21no—
42C2×C13×D8—21no—
43C2×C13×D8—21no—
44C2×C13×D8—21no—
45C2×C13×D8—21no—
46C2×C13×D8—21no—
47C2×C13×D8—21no—
48C2×C13×D8—21no—
49C2×C13×D8—21no—
50C2×C13×D8—21no—
51C2×C13×D8D412yes—
52C2×C13×D8D412yes—
53C22×C8×C13D411yescharacteristic
54C22×C8×C13C2311yescharacteristic
55C13×#124—24no—
56C13×#124—42no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C22⋊C4—42no—
59C2×C13×C22⋊C4—42no—
60C2×C42×C13D411yescharacteristic
61C13×SD32—28no—
62C13×D16—28no—
63C2×C13×C16—21no—
64C2×C13×C16—21no—
65C2×C13×C16—21no—
66C2×C13×C16—21no—
67C2×C13×C16D412yes—
68C2×C13×C16D412yes—
69C13×#107—21no—
70C13×#107—21no—
71C13×#102—42no—
72C4×C8×C13—21no—
73C4×C8×C13—21no—
74#13326C1311yesmaximal, characteristic, direct product factor, Sylow
75C24×C13—41no—
76C24×C13—41no—
77C2×Q8×C13—22no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×D4×C13—22no—
84C2×D4×C13—22no—
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—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13D812yes—
98C22×C4×C13C2×D411yescharacteristic
99C13×Q16—22no—
100C13×Q16—22no—
101C13×Q16—41no—
102C13×Q16—41no—
103C13×SD16—48no—
104C13×D8—22no—
105C13×D8—22no—
106C13×D8—22no—
107C13×D8—22no—
108C13×D8—41no—
109C13×D8—41no—
110C13×D8—41no—
111C13×D8—41no—
112C2×C8×C13—21no—
113C2×C8×C13—21no—
114C2×C8×C13D812yes—
115C2×C8×C13C2×D411yescharacteristic
116C2×C8×C13C2×D411yescharacteristic
117C2×C8×C13C2×D411yescharacteristic
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13#4111yescharacteristic
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C22⋊C4—48no—
124C13×C22⋊C4—84no—
125C42×C13—21no—
126C42×C13—21no—
127C13×C16—22no—
128C13×C16—22no—
129C22×SD32C2×C1311yescharacteristic, complemented
130C22×D16C2×C1311yescharacteristic
131C2×#495C2×C1311yescharacteristic, complemented
132C2×#358C2×C1311yescharacteristic, complemented
133C2×#357C2×C1311yescharacteristic, complemented
134#1970C2×C1311yescharacteristic, complemented
135#1374C2×C1311yescharacteristic, complemented
136C23×C13—42no—
137C23×C13—42no—
138C23×C13—81no—
139C23×C13—81no—
140C23×C13—81no—
141C23×C13—81no—
142C23×C13—82no—
143C23×C13—82no—
144C23×C13—82no—
145C23×C13—82no—
146C23×C13C2×D811yescharacteristic
147Q8×C13—42no—
148Q8×C13—42no—
149Q8×C13—81no—
150Q8×C13—81no—
151D4×C13—42no—
152D4×C13—42no—
153D4×C13—42no—
154D4×C13—42no—
155D4×C13—81no—
156D4×C13—81no—
157D4×C13—81no—
158D4×C13—81no—
159C2×C4×C13—22no—
160C2×C4×C13—22no—
161C2×C4×C13—22no—
162C2×C4×C13—42no—
163C2×C4×C13—81no—
164C2×C4×C13—81no—
165C2×C4×C13—81no—
166C2×C4×C13—82no—
167C2×C4×C13#12011yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12711yescharacteristic
170C2×C4×C13C2×D811yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
173C8×C13—22no—
174C8×C13#12011yescharacteristic
175C8×C13#12011yescharacteristic
176C8×C13#12111yescharacteristic
177C8×C13#12111yescharacteristic
178C22×Q16C22×C1311yescharacteristic
179C22×SD16—21no—
180C22×D8C22×C1311yescharacteristic
181C22×D8C22×C1311yescharacteristic
182C2×#124—21no—
183C2×SD32—22no—
184C2×SD32—22no—
185C2×SD32—22no—
186C2×D16—22no—
187C2×D16—22no—
188C2×D16—22no—
189C22×C16C22×C1311yescharacteristic
190C22×C16C22×C1311yescharacteristic
191#495—22no—
192#495—22no—
193C2×#107C22×C1311yescharacteristic
194C2×#102—21no—
195C2×C4×C8C22×C1311yescharacteristic
196#390—21no—
197#358—22no—
198#357—22no—
199C22×C13—84no—
200C22×C13—84no—
201C22×C13—82no—
202C22×C13—82no—
203C22×C13—162no—
204C22×C13—162no—
205C22×C13—161no—
206C22×C13—161no—
207C22×C13—161no—
208C22×C13—161no—
209C22×C13#44711yescharacteristic
210C22×C13#45911yescharacteristic
211C22×C13#49311yescharacteristic
212C22×C13#50812yes—
213C22×C13#50912yes—
214C4×C13—42no—
215C4×C13—82no—
216C4×C13—161no—
217C4×C13#39211yescharacteristic
218C4×C13#44711yescharacteristic
219C4×C13#45911yescharacteristic
220C4×C13#49611yescharacteristic
221C22×Q8—21no—
222C22×D4—21no—
223C22×D4—21no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16—21no—
227C2×Q16—21no—
228C2×Q16—21no—
229C2×Q16D4×C1312yes—
230C2×SD16—24no—
231C2×SD16—42no—
232C2×SD16—42no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8—21no—
240C2×D8—21no—
241C2×D8—21no—
242C2×D8—21no—
243C2×D8D4×C1312yes—
244C2×D8D4×C1312yes—
245C22×C8D4×C1311yescharacteristic
246C22×C8C23×C1311yescharacteristic
247#124—24no—
248#124—42no—
249C2×C4⋊C4—21no—
250C2×C22⋊C4—42no—
251C2×C22⋊C4—42no—
252C2×C42D4×C1311yescharacteristic
253SD32—28no—
254D16—28no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16D4×C1312yes—
260C2×C16D4×C1312yes—
261#107—21no—
262#107—21no—
263#102—42no—
264C4×C8—21no—
265C4×C8—21no—
266C2×C13—162no—
267C2×C13—162no—
268C2×C13#201111yescharacteristic
269C2×C13#218612yes—
270C2×C13#221012yes—
271C2×C13#224911yescharacteristic
272C2×C13#225011yescharacteristic
273C24—41no—
274C24—41no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4C13×D812yes—
296C22×C4C2×D4×C1311yescharacteristic
297Q16—22no—
298Q16—22no—
299Q16—41no—
300Q16—41no—
301SD16—48no—
302D8—22no—
303D8—22no—
304D8—22no—
305D8—22no—
306D8—41no—
307D8—41no—
308D8—41no—
309D8—41no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8C13×D812yes—
313C2×C8C2×D4×C1311yescharacteristic
314C2×C8C2×D4×C1311yescharacteristic
315C2×C8C2×D4×C1311yescharacteristic
316C2×C8C2×D4×C1311yescharacteristic
317C2×C8C2×D4×C1311yescharacteristic
318C2×C8C13×#4111yescharacteristic
319C4⋊C4—41no—
320C4⋊C4—41no—
321C22⋊C4—48no—
322C22⋊C4—84no—
323C42—21no—
324C42—21no—
325C16—22no—
326C16—22no—
327C13#1332611yescharacteristic, direct product factor, Sylow
328C23—42no—
329C23—42no—
330C23—81no—
331C23—81no—
332C23—81no—
333C23—81no—
334C23—82no—
335C23—82no—
336C23—82no—
337C23—82no—
338C23C2×C13×D811yescharacteristic
339Q8—42no—
340Q8—42no—
341Q8—81no—
342Q8—81no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—42no—
347D4—81no—
348D4—81no—
349D4—81no—
350D4—81no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—82no—
359C2×C4C13×#12011yescharacteristic
360C2×C4C13×#12111yescharacteristic
361C2×C4C13×#12711yescharacteristic
362C2×C4C2×C13×D811yescharacteristic
363C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
364C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
365C8—22no—
366C8C13×#12011yescharacteristic
367C8C13×#12011yescharacteristic
368C8C13×#12111yescharacteristic
369C8C13×#12111yescharacteristic
370C22—82no—
371C22—82no—
372C22—84no—
373C22—84no—
374C22—161no—
375C22—161no—
376C22—161no—
377C22—161no—
378C22—162no—
379C22—162no—
380C22C13×#44711yescharacteristic
381C22C13×#45911yescharacteristic
382C22C13×#49311yescharacteristic
383C22C13×#50812yes—
384C22C13×#50912yes—
385C4—42no—
386C4—82no—
387C4—161no—
388C4C13×#39211yescharacteristic
389C4C13×#44711yescharacteristic
390C4C13×#45911yescharacteristic
391C4C13×#49611yescharacteristic
392C2—162no—
393C2—162no—
394C2C13×#201111yescharacteristic
395C2C13×#218612yes—
396C2C13×#221012yes—
397C2C13×#224911yescharacteristic
398C2C13×#225011yescharacteristic
subgroupG/H
center, socleC23×C13C2×D8
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC22×C13×D16C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C13×SD32C2semidirect
3. C2×C13×#495C2semidirect
4. C2×C13×#358C2semidirect
5. C2×C13×#357C2semidirect
6. C13×#1970C2semidirect
7. C13×#1374C2semidirect
74. #13326C13direct (N × H)
129. C22×SD32C2×C13semidirect
131. C2×#495C2×C13semidirect
132. C2×#358C2×C13semidirect
133. C2×#357C2×C13semidirect
134. #1970C2×C13semidirect
135. #1374C2×C13semidirect
327. C13#13326direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×SD322
C22×C13×D162
C2×C13×#4952
C2×C13×#3582
C2×C13×#3572
C13×#19702
C13×#13742
#1332613