Finite Group Databasebeta

← C13×#3118 #13112176

Subgroups — C13×#3118 #13112176

Order 1664.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#542C211yesmaximal, characteristic, complemented
2C13×#518C211yesmaximal, characteristic, complemented
3C13×#485C211yesmaximal, characteristic, complemented
4C13×#482C211yesmaximal, characteristic, complemented
5C13×#476C211yesmaximal, characteristic, complemented
6C13×#474C211yesmaximal, characteristic, complemented
7C13×#463C211yesmaximal, characteristic, complemented
8C13×#463C211yesmaximal, characteristic, complemented
9C13×#450C211yesmaximal, characteristic, complemented
10C13×#447C211yesmaximal, characteristic
11C13×#442C211yesmaximal, characteristic, complemented
12C13×#440C211yesmaximal, characteristic, complemented
13C4×C13×SD16C211yesmaximal, characteristic, complemented
14C4×C13×D8C211yesmaximal, characteristic, complemented
15C13×#433C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic
21C13×C4⋊Q8C2211yescharacteristic, complemented
22C13×#126—21no—
23C13×#124—21no—
24C13×#124C2211yescharacteristic, complemented
25C13×#123—21no—
26C13×C22⋊Q8—21no—
27C13×C22⋊Q8C2211yescharacteristic
28C13×#121C2211yescharacteristic
29C4×Q8×C13C2211yescharacteristic, complemented
30C4×D4×C13—21no—
31C4×D4×C13—21no—
32C4×D4×C13C2211yescharacteristic
33C4×D4×C13C2211yescharacteristic
34C4×D4×C13C2211yescharacteristic
35C4×D4×C13C2211yescharacteristic
36C4×D4×C13C2211yescharacteristic, complemented
37C13×#117C2211yescharacteristic
38C13×#117C2211yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C13×#107C2211yescharacteristic, complemented
42C13×#107C2211yescharacteristic, complemented
43C13×#106C2211yescharacteristic, complemented
44C13×#106C2211yescharacteristic, complemented
45C13×C4⋊C8C2211yescharacteristic, complemented
46C13×C4⋊C8C2211yescharacteristic, complemented
47C13×#103C2211yescharacteristic, complemented
48C13×#103C2211yescharacteristic, complemented
49C13×#102C2211yescharacteristic
50C13×#102C2211yescharacteristic
51C13×#102C2211yescharacteristic
52C13×#102C2211yescharacteristic
53C13×#102C2211yescharacteristic, complemented
54C13×#102C2211yescharacteristic, complemented
55C13×C22⋊C8C2211yescharacteristic
56C13×C22⋊C8C2211yescharacteristic
57C13×#97C2211yescharacteristic, complemented
58C4×C8×C13C2211yescharacteristic, complemented
59C24×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—22no—
63C2×D4×C13—22no—
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13C2311yescharacteristic
67C2×D4×C13C2311yescharacteristic
68C2×D4×C13C2311yescharacteristic
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13C2311yescharacteristic
75C13×SD16—22no—
76C13×SD16—22no—
77C13×D8—22no—
78C13×D8—22no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4D411yescharacteristic
87C13×C4⋊C4D411yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C4⋊C4C2311yescharacteristic
90C13×C4⋊C4C2311yescharacteristic
91C13×C4⋊C4C2311yescharacteristic
92C13×C22⋊C4—21no—
93C13×C22⋊C4—21no—
94C13×C22⋊C4—21no—
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C13×C22⋊C4—21no—
99C13×C22⋊C4—21no—
100C13×C22⋊C4—21no—
101C13×C22⋊C4—21no—
102C13×C22⋊C4D411yescharacteristic
103C13×C22⋊C4D411yescharacteristic
104C42×C13—21no—
105C42×C13—21no—
106C42×C13C2311yescharacteristic
107C42×C13C2311yescharacteristic
108#3118C1311yesmaximal, characteristic, direct product factor, Sylow
109C23×C13—24no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—81no—
114C23×C13—81no—
115C23×C13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—81no—
119D4×C13—24no—
120D4×C13—21no—
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—81no—
125D4×C13#4112yes—
126D4×C13#4112yes—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2×D411yescharacteristic
142C2×C4×C13C2×D411yescharacteristic
143C2×C4×C13C2×D411yescharacteristic
144C2×C4×C13C2411yescharacteristic
145C8×C13—21no—
146C8×C13—21no—
147C8×C13—21no—
148C8×C13—21no—
149#542C2×C1311yescharacteristic, complemented
150#518C2×C1311yescharacteristic, complemented
151#485C2×C1311yescharacteristic, complemented
152#482C2×C1311yescharacteristic, complemented
153#476C2×C1311yescharacteristic, complemented
154#474C2×C1311yescharacteristic, complemented
155#463C2×C1311yescharacteristic, complemented
156#463C2×C1311yescharacteristic, complemented
157#450C2×C1311yescharacteristic, complemented
158#447C2×C1311yescharacteristic
159#442C2×C1311yescharacteristic, complemented
160#440C2×C1311yescharacteristic, complemented
161C4×SD16C2×C1311yescharacteristic, complemented
162C4×D8C2×C1311yescharacteristic, complemented
163#433C2×C1311yescharacteristic, complemented
164C22×C13—21no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—84no—
177C22×C13C22×D411yescharacteristic
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13C2×#4111yescharacteristic
189C4×C13C2×#4111yescharacteristic
190C22×D4C22×C1311yescharacteristic
191C2×SD16C22×C1311yescharacteristic
192C2×SD16C22×C1311yescharacteristic
193C2×D8C22×C1311yescharacteristic
194C2×D8C22×C1311yescharacteristic
195C4⋊Q8C22×C1311yescharacteristic, complemented
196#126—21no—
197#124—21no—
198#124C22×C1311yescharacteristic, complemented
199#123—21no—
200C22⋊Q8—21no—
201C22⋊Q8C22×C1311yescharacteristic
202#121C22×C1311yescharacteristic
203C4×Q8C22×C1311yescharacteristic, complemented
204C4×D4—21no—
205C4×D4—21no—
206C4×D4C22×C1311yescharacteristic
207C4×D4C22×C1311yescharacteristic
208C4×D4C22×C1311yescharacteristic
209C4×D4C22×C1311yescharacteristic
210C4×D4C22×C1311yescharacteristic, complemented
211#117C22×C1311yescharacteristic
212#117C22×C1311yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215#107C22×C1311yescharacteristic, complemented
216#107C22×C1311yescharacteristic, complemented
217#106C22×C1311yescharacteristic, complemented
218#106C22×C1311yescharacteristic, complemented
219C4⋊C8C22×C1311yescharacteristic, complemented
220C4⋊C8C22×C1311yescharacteristic, complemented
221#103C22×C1311yescharacteristic, complemented
222#103C22×C1311yescharacteristic, complemented
223#102C22×C1311yescharacteristic
224#102C22×C1311yescharacteristic
225#102C22×C1311yescharacteristic
226#102C22×C1311yescharacteristic
227#102C22×C1311yescharacteristic, complemented
228#102C22×C1311yescharacteristic, complemented
229C22⋊C8C22×C1311yescharacteristic
230C22⋊C8C22×C1311yescharacteristic
231#97C22×C1311yescharacteristic, complemented
232C4×C8C22×C1311yescharacteristic, complemented
233C2×C13—41no—
234C2×C13—42no—
235C2×C13—42no—
236C2×C13—81no—
237C2×C13#52511yescharacteristic
238C2×C13#57611yescharacteristic
239C2×C13#57711yescharacteristic
240C24—21no—
241C2×Q8—21no—
242C2×Q8C23×C1311yescharacteristic
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4C23×C1311yescharacteristic
248C2×D4C23×C1311yescharacteristic
249C2×D4C23×C1311yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4C23×C1311yescharacteristic
256SD16—22no—
257SD16—22no—
258D8—22no—
259D8—22no—
260C2×C8C23×C1311yescharacteristic
261C2×C8C23×C1311yescharacteristic
262C2×C8C23×C1311yescharacteristic
263C2×C8C23×C1311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4D4×C1311yescharacteristic
268C4⋊C4D4×C1311yescharacteristic
269C4⋊C4C23×C1311yescharacteristic
270C4⋊C4C23×C1311yescharacteristic
271C4⋊C4C23×C1311yescharacteristic
272C4⋊C4C23×C1311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4D4×C1311yescharacteristic
284C22⋊C4D4×C1311yescharacteristic
285C42—21no—
286C42—21no—
287C42C23×C1311yescharacteristic
288C42C23×C1311yescharacteristic
289C13#311811yescharacteristic, direct product factor, Sylow
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23C2×D4×C1311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4C13×#4112yes—
307D4C13×#4112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4C2×D4×C1311yescharacteristic
321C2×C4C2×D4×C1311yescharacteristic
322C2×C4C2×D4×C1311yescharacteristic
323C2×C4C2×D4×C1311yescharacteristic
324C2×C4C2×D4×C1311yescharacteristic
325C2×C4C24×C1311yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C22×D4×C1311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4C2×C13×#4111yescharacteristic
355C4C2×C13×#4111yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2C13×#52511yescharacteristic
361C2C13×#57611yescharacteristic
362C2C13×#57711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
prime radicalC13×#447C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#542C2semidirect
2. C13×#518C2semidirect
3. C13×#485C2semidirect
4. C13×#482C2semidirect
5. C13×#476C2semidirect
6. C13×#474C2semidirect
7. C13×#463C2semidirect
8. C13×#463C2semidirect
9. C13×#450C2semidirect
11. C13×#442C2semidirect
12. C13×#440C2semidirect
13. C4×C13×SD16C2semidirect
14. C4×C13×D8C2semidirect
15. C13×#433C2semidirect
21. C13×C4⋊Q8C22semidirect
24. C13×#124C22semidirect
29. C4×Q8×C13C22semidirect
36. C4×D4×C13C22semidirect
41. C13×#107C22semidirect
42. C13×#107C22semidirect
43. C13×#106C22semidirect
44. C13×#106C22semidirect
45. C13×C4⋊C8C22semidirect
46. C13×C4⋊C8C22semidirect
47. C13×#103C22semidirect
48. C13×#103C22semidirect
53. C13×#102C22semidirect
54. C13×#102C22semidirect
57. C13×#97C22semidirect
58. C4×C8×C13C22semidirect
108. #3118C13direct (N × H)
149. #542C2×C13semidirect
150. #518C2×C13semidirect
151. #485C2×C13semidirect
152. #482C2×C13semidirect
153. #476C2×C13semidirect
154. #474C2×C13semidirect
155. #463C2×C13semidirect
156. #463C2×C13semidirect
157. #450C2×C13semidirect
159. #442C2×C13semidirect
160. #440C2×C13semidirect
161. C4×SD16C2×C13semidirect
162. C4×D8C2×C13semidirect
163. #433C2×C13semidirect
195. C4⋊Q8C22×C13semidirect
198. #124C22×C13semidirect
203. C4×Q8C22×C13semidirect
210. C4×D4C22×C13semidirect
215. #107C22×C13semidirect
216. #107C22×C13semidirect
217. #106C22×C13semidirect
218. #106C22×C13semidirect
219. C4⋊C8C22×C13semidirect
220. C4⋊C8C22×C13semidirect
221. #103C22×C13semidirect
222. #103C22×C13semidirect
227. #102C22×C13semidirect
228. #102C22×C13semidirect
231. #97C22×C13semidirect
232. C4×C8C22×C13semidirect
289. C13#3118direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5422
C13×#5182
C13×#4852
C13×#4822
C13×#4762
C13×#4742
C13×#4632
C13×#4502
C13×#4472
C13×#4422
C13×#4402
C4×C13×SD162
C4×C13×D82
C13×#4332
#311813