Finite Group Databasebeta

← C13×#12806 #15699145

Subgroups — C13×#12806 #15699145

Order 3328.

420 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2930C211yesmaximal, characteristic
2C13×#2120C212yesmaximal
3C13×#1813C211yesmaximal, characteristic, complemented
4C13×#1812C211yesmaximal, characteristic, complemented
5C13×#1395C212yesmaximal, complemented
6C2×C13×#131C2211yescharacteristic
7C22×C13×M16C411yescharacteristic, complemented
8C13×#525C2211yescharacteristic
9C13×#436—21no—
10C13×#436—21no—
11C13×#435—21no—
12C13×#435—21no—
13C2×C13×#108—21no—
14C13×#427—21no—
15C13×#424C411yescharacteristic, complemented
16C13×#413C2212yes—
17C13×#410C2212yes—
18C13×#408C2211yescharacteristic
19C13×#407C411yescharacteristic, complemented
20C13×#405C411yescharacteristic, complemented
21C13×#352—22no—
22C13×AΣL(1,𝔽16)—22no—
23C13×#338—21no—
24C13×H(3,ℤ/4)—21no—
25C2×C13×#41C2311yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C13×#131—41no—
28C13×#131—41no—
29C2×C13×M16—21no—
30C2×C13×M16—21no—
31C2×C13×M16—22no—
32C2×C13×M16—41no—
33C2×C13×M16—41no—
34C2×C13×M16C2×C411yescharacteristic
35C2×C13×M16C2×C411yescharacteristic
36C2×C13×M16D411yescharacteristic
37C2×C13×M16D411yescharacteristic
38C22×C8×C13C2×C411yescharacteristic
39C22×C8×C13C2×C411yescharacteristic
40C22×C8×C13D411yescharacteristic
41C22×C8×C13D411yescharacteristic
42C13×#123D411yescharacteristic
43C13×#123Q811yescharacteristic
44C13×C22⋊Q8—21no—
45C13×#121—21no—
46C13×#120D411yescharacteristic
47C13×#120Q811yescharacteristic
48C4×D4×C13—21no—
49C4×D4×C13—21no—
50C13×#117—22no—
51C13×#117C2×C411yescharacteristic
52C13×#108—41no—
53C13×#108—41no—
54C13×#107—41no—
55C13×#106—41no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×#101—22no—
59C13×#100—22no—
60C13×#99—22no—
61C13×#99—22no—
62C13×C22⋊C8—21no—
63C13×C22⋊C8—21no—
64C13×C22⋊C8—21no—
65C13×C22⋊C8—21no—
66C13×#97—21no—
67C4×C8×C13—21no—
68#12806C1311yesmaximal, characteristic, direct product factor, Sylow
69C24×C13C4⋊C411yescharacteristic
70C13×#41—41no—
71C13×#41—41no—
72C2×Q8×C13#4111yescharacteristic
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13C2×D411yescharacteristic
76C2×D4×C13C2×Q811yescharacteristic
77C2×D4×C13#4111yescharacteristic
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13C4⋊C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C13×M16—41no—
87C13×M16—41no—
88C13×M16—41no—
89C13×M16—42no—
90C13×M16—41no—
91C13×M16—41no—
92C13×M16—41no—
93C13×M16—42no—
94C13×M16—42no—
95C2×C8×C13—21no—
96C2×C8×C13—21no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13—21no—
100C2×C8×C13—21no—
101C2×C8×C13—21no—
102C2×C8×C13—21no—
103C2×C8×C13—41no—
104C2×C8×C13—42no—
105C2×C8×C13C22⋊C411yescharacteristic
106C2×C8×C13C22⋊C411yescharacteristic
107C2×C8×C13C22⋊C411yescharacteristic
108C2×C8×C13C22⋊C411yescharacteristic
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—42no—
113C13×C22⋊C4—21no—
114C13×C22⋊C4—21no—
115C13×C22⋊C4—21no—
116C13×C22⋊C4—21no—
117C13×C22⋊C4—42no—
118C13×C22⋊C4C4⋊C411yescharacteristic
119C13×C22⋊C4C4⋊C411yescharacteristic
120C42×C13—21no—
121C42×C13—42no—
122#2930C2×C1311yescharacteristic
123#2120C2×C1312yes—
124#1813C2×C1311yescharacteristic, complemented
125#1812C2×C1311yescharacteristic, complemented
126#1395C2×C1312yescomplemented
127C23×C13—21no—
128C23×C13—41no—
129C23×C13—81no—
130C23×C13C2×C4⋊C411yescharacteristic
131C23×C13#12111yescharacteristic
132C23×C13C22⋊Q811yescharacteristic
133Q8×C13—41no—
134D4×C13—41no—
135D4×C13—41no—
136D4×C13—41no—
137D4×C13—81no—
138D4×C13—81no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—42no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—82no—
153C2×C4×C13C2×C22⋊C411yescharacteristic
154C2×C4×C13#11711yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13C22⋊Q811yescharacteristic
157C8×C13—21no—
158C8×C13—21no—
159C8×C13—21no—
160C8×C13—41no—
161C8×C13—41no—
162C8×C13—82no—
163C8×C13#9911yescharacteristic
164C8×C13#9911yescharacteristic
165C2×#131C22×C1311yescharacteristic
166C22×M16C4×C1311yescharacteristic, complemented
167#525C22×C1311yescharacteristic
168#436—21no—
169#436—21no—
170#435—21no—
171#435—21no—
172C2×#108—21no—
173#427—21no—
174#424C4×C1311yescharacteristic, complemented
175#413C22×C1312yes—
176#410C22×C1312yes—
177#408C22×C1311yescharacteristic
178#407C4×C1311yescharacteristic, complemented
179#405C4×C1311yescharacteristic, complemented
180#352—22no—
181AΣL(1,𝔽16)—22no—
182#338—21no—
183H(3,ℤ/4)—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—82no—
194C22×C13#38011yescharacteristic
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—162no—
202C4×C13C2×#9911yescharacteristic
203C4×C13#41011yescharacteristic
204C2×#41C23×C1311yescharacteristic
205C23×C4C2×C4×C1311yescharacteristic
206#131—41no—
207#131—41no—
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—22no—
211C2×M16—41no—
212C2×M16—41no—
213C2×M16C2×C4×C1311yescharacteristic
214C2×M16C2×C4×C1311yescharacteristic
215C2×M16D4×C1311yescharacteristic
216C2×M16D4×C1311yescharacteristic
217C22×C8C2×C4×C1311yescharacteristic
218C22×C8C2×C4×C1311yescharacteristic
219C22×C8D4×C1311yescharacteristic
220C22×C8D4×C1311yescharacteristic
221#123D4×C1311yescharacteristic
222#123Q8×C1311yescharacteristic
223C22⋊Q8—21no—
224#121—21no—
225#120D4×C1311yescharacteristic
226#120Q8×C1311yescharacteristic
227C4×D4—21no—
228C4×D4—21no—
229#117—22no—
230#117C2×C4×C1311yescharacteristic
231#108—41no—
232#108—41no—
233#107—41no—
234#106—41no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237#101—22no—
238#100—22no—
239#99—22no—
240#99—22no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245#97—21no—
246C4×C8—21no—
247C2×C13—21no—
248C2×C13—41no—
249C2×C13—41no—
250C2×C13—41no—
251C2×C13—81no—
252C2×C13#179911yescharacteristic
253C24C13×C4⋊C411yescharacteristic
254#41—41no—
255#41—41no—
256C2×Q8C13×#4111yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4C2×D4×C1311yescharacteristic
260C2×D4C2×Q8×C1311yescharacteristic
261C2×D4C13×#4111yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C13×C4⋊C411yescharacteristic
267C22×C4C22×C4×C1311yescharacteristic
268C22×C4C2×D4×C1311yescharacteristic
269C22×C4C2×D4×C1311yescharacteristic
270M16—41no—
271M16—41no—
272M16—41no—
273M16—42no—
274M16—41no—
275M16—41no—
276M16—41no—
277M16—42no—
278M16—42no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8—42no—
289C2×C8C13×C22⋊C411yescharacteristic
290C2×C8C13×C22⋊C411yescharacteristic
291C2×C8C13×C22⋊C411yescharacteristic
292C2×C8C13×C22⋊C411yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—42no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—42no—
302C22⋊C4C13×C4⋊C411yescharacteristic
303C22⋊C4C13×C4⋊C411yescharacteristic
304C42—21no—
305C42—42no—
306C13#1280611yescharacteristic, direct product factor, Sylow
307C23—21no—
308C23—41no—
309C23—81no—
310C23C2×C13×C4⋊C411yescharacteristic
311C23C13×#12111yescharacteristic
312C23C13×C22⋊Q811yescharacteristic
313Q8—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—82no—
333C2×C4C2×C13×C22⋊C411yescharacteristic
334C2×C4C13×#11711yescharacteristic
335C2×C4C13×#12111yescharacteristic
336C2×C4C13×C22⋊Q811yescharacteristic
337C8—21no—
338C8—21no—
339C8—21no—
340C8—41no—
341C8—41no—
342C8—82no—
343C8C13×#9911yescharacteristic
344C8C13×#9911yescharacteristic
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—82no—
355C22C13×#38011yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—162no—
363C4C2×C13×#9911yescharacteristic
364C4C13×#41011yescharacteristic
365C2—21no—
366C2—41no—
367C2—41no—
368C2—41no—
369C2—81no—
370C2C13×#179911yescharacteristic
subgroupG/H
centerC4×C13#410
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×#41C23×C13
socleC2×C13#1799
prime radicalC13×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C2×C8×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1813C2semidirect
4. C13×#1812C2semidirect
5. C13×#1395C2semidirect
7. C22×C13×M16C4semidirect
15. C13×#424C4semidirect
19. C13×#407C4semidirect
20. C13×#405C4semidirect
68. #12806C13direct (N × H)
124. #1813C2×C13semidirect
125. #1812C2×C13semidirect
126. #1395C2×C13semidirect
166. C22×M16C4×C13semidirect
174. #424C4×C13semidirect
178. #407C4×C13semidirect
179. #405C4×C13semidirect
306. C13#12806direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29302
C13×#21202
C13×#18132
C13×#18122
C13×#13952
#1280613