Finite Group Databasebeta

← C13×#13417 #15699756

Subgroups — C13×#13417 #15699756

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3155C211yesmaximal, characteristic
2C13×#2148C211yesmaximal, characteristic, complemented
3C2×C13×#361C211yesmaximal, characteristic, complemented
4C2×C13×#361C211yesmaximal, characteristic, complemented
5C13×#2143C211yesmaximal, characteristic, complemented
6C13×#1953C211yesmaximal, characteristic, complemented
7C13×#1378C211yesmaximal, characteristic, complemented
8C2×C13×AGL(1,ℤ/8)—21no—
9C2×C13×#135C2211yescharacteristic
10C22×C13×D8C2211yescharacteristic
11C13×#535—21no—
12C2×C13×M32C2211yescharacteristic
13C2×C13×M32C2211yescharacteristic
14C13×#496—22no—
15C13×#495—21no—
16C13×#493—21no—
17C13×#430—21no—
18C2×C13×#108C2211yescharacteristic
19C2×C13×#108C2211yescharacteristic
20C13×#405C2211yescharacteristic
21C13×#362—21no—
22C13×#361—22no—
23C13×#361—21no—
24C13×#361—22no—
25C13×#359—22no—
26C13×#344—21no—
27C2×C13×#41—21no—
28C22×D4×C13—21no—
29C13×AGL(1,ℤ/8)—42no—
30C13×AGL(1,ℤ/8)—42no—
31C13×#135—21no—
32C13×#135—21no—
33C13×#135—21no—
34C13×#135—21no—
35C2×C13×Q16D411yescharacteristic
36C2×C13×SD16—22no—
37C2×C13×SD16—21no—
38C2×C13×D8—22no—
39C2×C13×D8—21no—
40C2×C13×D8—21no—
41C2×C13×D8—21no—
42C2×C13×D8—21no—
43C2×C13×D8—21no—
44C2×C13×D8D411yescharacteristic
45C2×C13×D8D412yes—
46C2×C13×M16—21no—
47C2×C13×M16—21no—
48C2×C13×M16D411yescharacteristic
49C22×C8×C13C2311yescharacteristic
50C13×#127—22no—
51C13×#124—22no—
52C13×#121—42no—
53C13×#120—42no—
54C13×#117D411yescharacteristic
55C13×M32—21no—
56C13×M32—21no—
57C13×M32—21no—
58C13×M32—21no—
59C2×C13×C16—21no—
60C2×C13×C16—21no—
61C13×#108—21no—
62C13×#108—21no—
63C13×#108—21no—
64C13×#108—42no—
65C13×#108D412yescomplemented
66C13×#97—21no—
67C4×C8×C13—21no—
68#13417C1311yesmaximal, characteristic, direct product factor, Sylow
69C24×C13—41no—
70C13×#41—41no—
71C13×#41—41no—
72C13×#41—41no—
73C13×#41—41no—
74C2×Q8×C13—21no—
75C2×D4×C13—22no—
76C2×D4×C13—21no—
77C2×D4×C13—44no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C13×Q16—21no—
87C13×Q16—21no—
88C13×SD16—44no—
89C13×SD16—41no—
90C13×SD16—41no—
91C13×D8—22no—
92C13×D8—21no—
93C13×D8—22no—
94C13×D8—21no—
95C13×D8—44no—
96C13×D8—41no—
97C13×D8—41no—
98C13×M16—21no—
99C13×M16—22no—
100C13×M16—41no—
101C13×M16—41no—
102C13×M16—41no—
103C13×M16D812yes—
104C2×C8×C13—21no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C2×C8×C13C2×D411yescharacteristic
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13#4111yescharacteristic
111C2×C8×C13#4111yescharacteristic
112C2×C8×C13#4111yescharacteristic
113C13×C4⋊C4—21no—
114C13×C22⋊C4—44no—
115C13×C22⋊C4SD1612yes—
116C42×C13—21no—
117C13×C16—41no—
118C13×C16—41no—
119#3155C2×C1311yescharacteristic
120#2148C2×C1311yescharacteristic, complemented
121C2×#361C2×C1311yescharacteristic, complemented
122C2×#361C2×C1311yescharacteristic, complemented
123#2143C2×C1311yescharacteristic, complemented
124#1953C2×C1311yescharacteristic, complemented
125#1378C2×C1311yescharacteristic, complemented
126C23×C13—42no—
127C23×C13—41no—
128C23×C13—81no—
129C23×C13—81no—
130C23×C13—162no—
131C23×C13C2×SD1611yescharacteristic
132Q8×C13—41no—
133Q8×C13—41no—
134D4×C13—42no—
135D4×C13—41no—
136D4×C13—41no—
137D4×C13—42no—
138D4×C13—81no—
139D4×C13—81no—
140D4×C13—81no—
141D4×C13—81no—
142D4×C13—164no—
143C2×C4×C13—22no—
144C2×C4×C13—41no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12411yescharacteristic
150C2×C4×C13C2×D811yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C8×C13—22no—
154C8×C13—42no—
155C8×C13—81no—
156C8×C13#12111yescharacteristic
157C8×C13#12111yescharacteristic
158C8×C13#12311yescharacteristic
159C8×C13#12311yescharacteristic
160C2×AGL(1,ℤ/8)—21no—
161C2×#135C22×C1311yescharacteristic
162C22×D8C22×C1311yescharacteristic
163#535—21no—
164C2×M32C22×C1311yescharacteristic
165C2×M32C22×C1311yescharacteristic
166#496—22no—
167#495—21no—
168#493—21no—
169#430—21no—
170C2×#108C22×C1311yescharacteristic
171C2×#108C22×C1311yescharacteristic
172#405C22×C1311yescharacteristic
173#362—21no—
174#361—22no—
175#361—21no—
176#361—22no—
177#359—22no—
178#344—21no—
179C22×C13—41no—
180C22×C13—82no—
181C22×C13—84no—
182C22×C13—81no—
183C22×C13—82no—
184C22×C13—162no—
185C22×C13—162no—
186C22×C13#45011yescharacteristic
187C22×C13#46011yescharacteristic
188C22×C13#48611yescharacteristic
189C4×C13—42no—
190C4×C13—81no—
191C4×C13#39411yescharacteristic
192C4×C13#44711yescharacteristic
193C4×C13#45911yescharacteristic
194C4×C13#49011yescharacteristic
195C2×#41—21no—
196C22×D4—21no—
197AGL(1,ℤ/8)—42no—
198AGL(1,ℤ/8)—42no—
199#135—21no—
200#135—21no—
201#135—21no—
202#135—21no—
203C2×Q16D4×C1311yescharacteristic
204C2×SD16—22no—
205C2×SD16—21no—
206C2×D8—22no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8D4×C1312yes—
213C2×D8D4×C1311yescharacteristic
214C2×M16—21no—
215C2×M16—21no—
216C2×M16D4×C1311yescharacteristic
217C22×C8C23×C1311yescharacteristic
218#127—22no—
219#124—22no—
220#121—42no—
221#120—42no—
222#117D4×C1311yescharacteristic
223M32—21no—
224M32—21no—
225M32—21no—
226M32—21no—
227C2×C16—21no—
228C2×C16—21no—
229#108—21no—
230#108—21no—
231#108—21no—
232#108—42no—
233#108D4×C1312yescomplemented
234#97—21no—
235C4×C8—21no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—161no—
240C2×C13—162no—
241C2×C13#204111yescharacteristic
242C24—41no—
243#41—41no—
244#41—41no—
245#41—41no—
246#41—41no—
247C2×Q8—21no—
248C2×D4—22no—
249C2×D4—21no—
250C2×D4—44no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C22×C4—41no—
258C22×C4C2×D4×C1311yescharacteristic
259Q16—21no—
260Q16—21no—
261SD16—44no—
262SD16—41no—
263SD16—41no—
264D8—22no—
265D8—21no—
266D8—22no—
267D8—21no—
268D8—44no—
269D8—41no—
270D8—41no—
271M16—21no—
272M16—22no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16C13×D812yes—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8C2×D4×C1311yescharacteristic
281C2×C8C2×D4×C1311yescharacteristic
282C2×C8C2×D4×C1311yescharacteristic
283C2×C8C13×#4111yescharacteristic
284C2×C8C13×#4111yescharacteristic
285C2×C8C13×#4111yescharacteristic
286C4⋊C4—21no—
287C22⋊C4—44no—
288C22⋊C4C13×SD1612yes—
289C42—21no—
290C16—41no—
291C16—41no—
292C13#1341711yescharacteristic, direct product factor, Sylow
293C23—42no—
294C23—41no—
295C23—81no—
296C23—81no—
297C23—162no—
298C23C2×C13×SD1611yescharacteristic
299Q8—41no—
300Q8—41no—
301D4—42no—
302D4—41no—
303D4—41no—
304D4—42no—
305D4—81no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—164no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4C13×#12011yescharacteristic
315C2×C4C13×#12111yescharacteristic
316C2×C4C13×#12411yescharacteristic
317C2×C4C2×C13×D811yescharacteristic
318C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
319C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
320C8—22no—
321C8—42no—
322C8—81no—
323C8C13×#12111yescharacteristic
324C8C13×#12111yescharacteristic
325C8C13×#12311yescharacteristic
326C8C13×#12311yescharacteristic
327C22—41no—
328C22—82no—
329C22—84no—
330C22—81no—
331C22—82no—
332C22—162no—
333C22—162no—
334C22C13×#45011yescharacteristic
335C22C13×#46011yescharacteristic
336C22C13×#48611yescharacteristic
337C4—42no—
338C4—81no—
339C4C13×#39411yescharacteristic
340C4C13×#44711yescharacteristic
341C4C13×#45911yescharacteristic
342C4C13×#49011yescharacteristic
343C2—21no—
344C2—21no—
345C2—21no—
346C2—162no—
347C2—161no—
348C2C13×#204111yescharacteristic
subgroupG/H
center, socleC2×C13#2041
commutator, Frattini, cosocleC22×C8C23×C13
prime radicalC13×#3155C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2148C2semidirect
3. C2×C13×#361C2semidirect
4. C2×C13×#361C2semidirect
5. C13×#2143C2semidirect
6. C13×#1953C2semidirect
7. C13×#1378C2semidirect
65. C13×#108D4semidirect
68. #13417C13direct (N × H)
120. #2148C2×C13semidirect
121. C2×#361C2×C13semidirect
122. C2×#361C2×C13semidirect
123. #2143C2×C13semidirect
124. #1953C2×C13semidirect
125. #1378C2×C13semidirect
233. #108D4×C13semidirect
292. C13#13417direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31552
C13×#21482
C2×C13×#3612
C13×#21432
C13×#19532
C13×#13782
#1341713