Finite Group Databasebeta

← C13×#13449 #15699788

Subgroups — C13×#13449 #15699788

Order 3328.

446 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×SD32C211yesmaximal, characteristic
2C2×C13×C4⋊C16C211yesmaximal, characteristic, complemented
3C2×C13×#358C211yesmaximal, characteristic, complemented
4C2×C13×#357C211yesmaximal, characteristic
5C13×#1970C211yesmaximal, characteristic
6C13×#1969C211yesmaximal, characteristic, complemented
7C13×#1380C211yesmaximal, characteristic, complemented
8C22×C13×Q16C2211yescharacteristic
9C22×C13×D8C2211yescharacteristic
10C2×C13×SD32—22no—
11C2×C13×SD32—22no—
12C2×C13×SD32—22no—
13C22×C13×C16C2211yescharacteristic
14C22×C13×C16C2211yescharacteristic
15C2×C13×#107C2211yescharacteristic
16C2×C13×#107C2211yescharacteristic
17C2×C13×#103—21no—
18C2×C13×#102—21no—
19C2×C4×C8×C13C2211yescharacteristic
20C13×#391—21no—
21C13×#390—21no—
22C13×C4⋊C16—22no—
23C13×#358—22no—
24C13×#357—22no—
25C22×Q8×C13—21no—
26C22×D4×C13—21no—
27C2×C13×Q16—21no—
28C2×C13×Q16—21no—
29C2×C13×Q16—21no—
30C2×C13×Q16—21no—
31C2×C13×Q16—21no—
32C2×C13×Q16D412yes—
33C2×C13×D8—21no—
34C2×C13×D8—21no—
35C2×C13×D8—21no—
36C2×C13×D8—21no—
37C2×C13×D8—21no—
38C2×C13×D8D412yes—
39C22×C8×C13D411yescharacteristic
40C22×C8×C13C2311yescharacteristic
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C22⋊C4—41no—
44C2×C13×C22⋊C4—41no—
45C2×C42×C13D411yescharacteristic
46C13×SD32—28no—
47C2×C13×C16—21no—
48C2×C13×C16—21no—
49C2×C13×C16—21no—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C2×C13×C16D412yes—
53C13×#107—21no—
54C13×#107—21no—
55C13×#107—21no—
56C13×#107—21no—
57C13×#103—42no—
58C13×#102—42no—
59C4×C8×C13—21no—
60C4×C8×C13—21no—
61C13×#95—41no—
62C13×#95—41no—
63#13449C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13—41no—
65C2×Q8×C13—22no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×D4×C13—22no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13D811yescharacteristic
81C22×C4×C13D811yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×Q16—22no—
84C13×Q16—22no—
85C13×Q16—41no—
86C13×Q16—41no—
87C13×D8—22no—
88C13×D8—22no—
89C13×D8—41no—
90C13×D8—41no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13C2×D411yescharacteristic
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13C2×D411yescharacteristic
97C2×C8×C13#4111yescharacteristic
98C2×C8×C13#4111yescharacteristic
99C2×C8×C13#4111yescharacteristic
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C13×C22⋊C4—82no—
105C13×C22⋊C4—82no—
106C42×C13—21no—
107C42×C13—21no—
108C13×C16—22no—
109C13×C16—41no—
110C22×SD32C2×C1311yescharacteristic
111C2×C4⋊C16C2×C1311yescharacteristic, complemented
112C2×#358C2×C1311yescharacteristic, complemented
113C2×#357C2×C1311yescharacteristic
114#1970C2×C1311yescharacteristic
115#1969C2×C1311yescharacteristic, complemented
116#1380C2×C1311yescharacteristic, complemented
117C23×C13—42no—
118C23×C13—81no—
119C23×C13—81no—
120C23×C13—81no—
121C23×C13—81no—
122C23×C13—81no—
123C23×C13—81no—
124C23×C13C2×D811yescharacteristic
125Q8×C13—42no—
126Q8×C13—42no—
127Q8×C13—81no—
128Q8×C13—81no—
129D4×C13—42no—
130D4×C13—42no—
131D4×C13—81no—
132D4×C13—81no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—42no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13SD3212yescomplemented
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C8×C13—41no—
155C8×C13#12011yescharacteristic
156C8×C13#12311yescharacteristic
157C8×C13#12311yescharacteristic
158C8×C13#12411yescharacteristic
159C22×Q16C22×C1311yescharacteristic
160C22×D8C22×C1311yescharacteristic
161C2×SD32—22no—
162C2×SD32—22no—
163C2×SD32—22no—
164C22×C16C22×C1311yescharacteristic
165C22×C16C22×C1311yescharacteristic
166C2×#107C22×C1311yescharacteristic
167C2×#107C22×C1311yescharacteristic
168C2×#103—21no—
169C2×#102—21no—
170C2×C4×C8C22×C1311yescharacteristic
171#391—21no—
172#390—21no—
173C4⋊C16—22no—
174#358—22no—
175#357—22no—
176C22×C13—82no—
177C22×C13—82no—
178C22×C13—82no—
179C22×C13—161no—
180C22×C13—161no—
181C22×C13—161no—
182C22×C13—161no—
183C22×C13#45911yescharacteristic
184C22×C13#45911yescharacteristic
185C22×C13#46611yescharacteristic
186C22×C13C2×SD3211yescharacteristic
187C22×C13#50811yescharacteristic
188C22×C13#50911yescharacteristic
189C22×C13#51011yescharacteristic
190C4×C13—22no—
191C4×C13—41no—
192C4×C13—82no—
193C4×C13—161no—
194C4×C13—161no—
195C4×C13#39411yescharacteristic
196C4×C13#46311yescharacteristic
197C4×C13#46311yescharacteristic
198C4×C13#46911yescharacteristic
199C22×Q8—21no—
200C22×D4—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16D4×C1312yes—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8D4×C1312yes—
213C22×C8D4×C1311yescharacteristic
214C22×C8C23×C1311yescharacteristic
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C22⋊C4—41no—
218C2×C22⋊C4—41no—
219C2×C42D4×C1311yescharacteristic
220SD32—28no—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16—21no—
224C2×C16—21no—
225C2×C16—21no—
226C2×C16D4×C1312yes—
227#107—21no—
228#107—21no—
229#107—21no—
230#107—21no—
231#103—42no—
232#102—42no—
233C4×C8—21no—
234C4×C8—21no—
235#95—41no—
236#95—41no—
237C2×C13—162no—
238C2×C13#205411yescharacteristic
239C2×C13#220711yescharacteristic
240C2×C13#220811yescharacteristic
241C2×C13#221011yescharacteristic
242C2×C13#221111yescharacteristic
243C2×C13#221711yescharacteristic
244C2×C13#222011yescharacteristic
245C24—41no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4C13×D811yescharacteristic
262C22×C4C13×D811yescharacteristic
263C22×C4C2×D4×C1311yescharacteristic
264Q16—22no—
265Q16—22no—
266Q16—41no—
267Q16—41no—
268D8—22no—
269D8—22no—
270D8—41no—
271D8—41no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8C2×D4×C1311yescharacteristic
276C2×C8C2×D4×C1311yescharacteristic
277C2×C8C2×D4×C1311yescharacteristic
278C2×C8C13×#4111yescharacteristic
279C2×C8C13×#4111yescharacteristic
280C2×C8C13×#4111yescharacteristic
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—82no—
286C22⋊C4—82no—
287C42—21no—
288C42—21no—
289C16—22no—
290C16—41no—
291C13#1344911yescharacteristic, direct product factor, Sylow
292C23—42no—
293C23—81no—
294C23—81no—
295C23—81no—
296C23—81no—
297C23—81no—
298C23—81no—
299C23C2×C13×D811yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304D4—42no—
305D4—42no—
306D4—81no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4C13×SD3212yescomplemented
323C2×C4C13×#12111yescharacteristic
324C2×C4C13×#12111yescharacteristic
325C2×C4C13×#12111yescharacteristic
326C2×C4C13×#13511yescharacteristic
327C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
328C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
329C8—41no—
330C8C13×#12011yescharacteristic
331C8C13×#12311yescharacteristic
332C8C13×#12311yescharacteristic
333C8C13×#12411yescharacteristic
334C22—82no—
335C22—82no—
336C22—82no—
337C22—161no—
338C22—161no—
339C22—161no—
340C22—161no—
341C22C13×#45911yescharacteristic
342C22C13×#45911yescharacteristic
343C22C13×#46611yescharacteristic
344C22C2×C13×SD3211yescharacteristic
345C22C13×#50811yescharacteristic
346C22C13×#50911yescharacteristic
347C22C13×#51011yescharacteristic
348C4—22no—
349C4—41no—
350C4—82no—
351C4—161no—
352C4—161no—
353C4C13×#39411yescharacteristic
354C4C13×#46311yescharacteristic
355C4C13×#46311yescharacteristic
356C4C13×#46911yescharacteristic
357C2—162no—
358C2C13×#205411yescharacteristic
359C2C13×#220711yescharacteristic
360C2C13×#220811yescharacteristic
361C2C13×#221011yescharacteristic
362C2C13×#221111yescharacteristic
363C2C13×#221711yescharacteristic
364C2C13×#222011yescharacteristic
subgroupG/H
center, socleC23×C13C2×D8
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC22×C13×D8C22
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
2. C2×C13×C4⋊C16C2semidirect
3. C2×C13×#358C2semidirect
6. C13×#1969C2semidirect
7. C13×#1380C2semidirect
63. #13449C13direct (N × H)
111. C2×C4⋊C16C2×C13semidirect
112. C2×#358C2×C13semidirect
115. #1969C2×C13semidirect
116. #1380C2×C13semidirect
147. C2×C4×C13SD32semidirect
291. C13#13449direct (N × H)
322. C2×C4C13×SD32semidirect

Maximal subgroups

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

subgroupindex
C22×C13×SD322
C2×C13×C4⋊C162
C2×C13×#3582
C2×C13×#3572
C13×#19702
C13×#19692
C13×#13802
#1344913