Finite Group Databasebeta

← C13×#3346 #13112404

Subgroups — C13×#3346 #13112404

Order 1664.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#554C211yesmaximal, characteristic, complemented
2C13×#553C211yesmaximal, characteristic
3C13×#501C211yesmaximal, characteristic, complemented
4C13×#485C211yesmaximal, characteristic, complemented
5C13×#484C211yesmaximal, characteristic, complemented
6C13×#481C211yesmaximal, characteristic, complemented
7C13×#480C211yesmaximal, characteristic, complemented
8C13×#479C211yesmaximal, characteristic, complemented
9C13×#474C211yesmaximal, characteristic, complemented
10C13×#468C211yesmaximal, characteristic, complemented
11C13×#465C211yesmaximal, characteristic, complemented
12C13×#440C211yesmaximal, characteristic, complemented
13C13×#435C211yesmaximal, characteristic, complemented
14C13×#428C211yesmaximal, characteristic, complemented
15C2×C13×#107C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C22×C8×C13C2211yescharacteristic
19C13×C4⋊Q8C2211yescharacteristic
20C13×#126—21no—
21C13×#125—21no—
22C13×#125C2211yescharacteristic
23C13×#123—21no—
24C13×C22⋊Q8—21no—
25C13×C22⋊Q8—21no—
26C13×C22⋊Q8C2211yescharacteristic
27C13×C22⋊Q8C2211yescharacteristic
28C13×#121—21no—
29C13×#121C2211yescharacteristic
30C13×#121C2211yescharacteristic
31C4×Q8×C13C2211yescharacteristic
32C4×D4×C13—21no—
33C4×D4×C13—21no—
34C4×D4×C13C2211yescharacteristic
35C4×D4×C13C2211yescharacteristic
36C13×#117C2211yescharacteristic
37C2×C13×C4⋊C4C2211yescharacteristic
38C2×C13×C4⋊C4C2211yescharacteristic
39C2×C13×C4⋊C4C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#107C2211yescharacteristic
43C13×#107C2211yescharacteristic
44C13×#107C2211yescharacteristic
45C13×#107C2211yescharacteristic
46C13×#106C2211yescharacteristic
47C13×#106C2211yescharacteristic
48C13×#106C2211yescharacteristic
49C13×C4⋊C8C2211yescharacteristic
50C13×#103C2211yescharacteristic
51C13×#103C2211yescharacteristic
52C13×#103C2211yescharacteristic
53C13×#102C2211yescharacteristic
54C13×#102C2211yescharacteristic
55C13×#102C2211yescharacteristic
56C13×C22⋊C8C2211yescharacteristic
57C13×C22⋊C8C2211yescharacteristic
58C13×#97C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13D411yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C13×SD16—22no—
72C13×M16—22no—
73C2×C8×C13—22no—
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4D411yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C4⋊C4C2311yescharacteristic
90C13×C4⋊C4C2311yescharacteristic
91C13×C4⋊C4C2311yescharacteristic
92C13×C4⋊C4C2311yescharacteristic
93C13×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
101C13×C22⋊C4D411yescharacteristic
102C42×C13—21no—
103C42×C13—21no—
104C42×C13C2311yescharacteristic
105#3346C1311yesmaximal, characteristic, direct product factor, Sylow
106C23×C13—21no—
107C23×C13C2×D411yescharacteristic
108C23×C13C2×D411yescharacteristic
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—81no—
112D4×C13—22no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13—42no—
116D4×C13—81no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13C2×D411yescharacteristic
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2411yescharacteristic
137C8×C13—21no—
138C8×C13—21no—
139C8×C13—21no—
140C8×C13#4112yes—
141#554C2×C1311yescharacteristic, complemented
142#553C2×C1311yescharacteristic
143#501C2×C1311yescharacteristic, complemented
144#485C2×C1311yescharacteristic, complemented
145#484C2×C1311yescharacteristic, complemented
146#481C2×C1311yescharacteristic, complemented
147#480C2×C1311yescharacteristic, complemented
148#479C2×C1311yescharacteristic, complemented
149#474C2×C1311yescharacteristic, complemented
150#468C2×C1311yescharacteristic, complemented
151#465C2×C1311yescharacteristic, complemented
152#440C2×C1311yescharacteristic, complemented
153#435C2×C1311yescharacteristic, complemented
154#428C2×C1311yescharacteristic, complemented
155C2×#107C2×C1311yescharacteristic, complemented
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13#13712yes—
165C22×C13C22×D411yescharacteristic
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13C2×#4111yescharacteristic
178C4×C132−1+411yescharacteristic
179C2×SD16C22×C1311yescharacteristic
180C2×M16C22×C1311yescharacteristic
181C22×C8C22×C1311yescharacteristic
182C4⋊Q8C22×C1311yescharacteristic
183#126—21no—
184#125—21no—
185#125C22×C1311yescharacteristic
186#123—21no—
187C22⋊Q8—21no—
188C22⋊Q8—21no—
189C22⋊Q8C22×C1311yescharacteristic
190C22⋊Q8C22×C1311yescharacteristic
191#121—21no—
192#121C22×C1311yescharacteristic
193#121C22×C1311yescharacteristic
194C4×Q8C22×C1311yescharacteristic
195C4×D4—21no—
196C4×D4—21no—
197C4×D4C22×C1311yescharacteristic
198C4×D4C22×C1311yescharacteristic
199#117C22×C1311yescharacteristic
200C2×C4⋊C4C22×C1311yescharacteristic
201C2×C4⋊C4C22×C1311yescharacteristic
202C2×C4⋊C4C22×C1311yescharacteristic
203#107C22×C1311yescharacteristic
204#107C22×C1311yescharacteristic
205#107C22×C1311yescharacteristic
206#107C22×C1311yescharacteristic
207#107C22×C1311yescharacteristic
208#107C22×C1311yescharacteristic
209#106C22×C1311yescharacteristic
210#106C22×C1311yescharacteristic
211#106C22×C1311yescharacteristic
212C4⋊C8C22×C1311yescharacteristic
213#103C22×C1311yescharacteristic
214#103C22×C1311yescharacteristic
215#103C22×C1311yescharacteristic
216#102C22×C1311yescharacteristic
217#102C22×C1311yescharacteristic
218#102C22×C1311yescharacteristic
219C22⋊C8C22×C1311yescharacteristic
220C22⋊C8C22×C1311yescharacteristic
221#97C22×C1311yescharacteristic
222C2×C13—22no—
223C2×C13—41no—
224C2×C13—81no—
225C2×C13#54711yescharacteristic
226C2×C13C2×#13711yescharacteristic
227C2×C13#57611yescharacteristic
228C2×Q8—21no—
229C2×Q8C23×C1311yescharacteristic
230C2×D4—21no—
231C2×D4—21no—
232C2×D4D4×C1311yescharacteristic
233C2×D4C23×C1311yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4C23×C1311yescharacteristic
239C22×C4C23×C1311yescharacteristic
240SD16—22no—
241M16—22no—
242C2×C8—22no—
243C2×C8C23×C1311yescharacteristic
244C2×C8C23×C1311yescharacteristic
245C2×C8C23×C1311yescharacteristic
246C2×C8C23×C1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4D4×C1311yescharacteristic
257C4⋊C4C23×C1311yescharacteristic
258C4⋊C4C23×C1311yescharacteristic
259C4⋊C4C23×C1311yescharacteristic
260C4⋊C4C23×C1311yescharacteristic
261C4⋊C4C23×C1311yescharacteristic
262C4⋊C4C23×C1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4D4×C1311yescharacteristic
270C22⋊C4D4×C1311yescharacteristic
271C42—21no—
272C42—21no—
273C42C23×C1311yescharacteristic
274C13#334611yescharacteristic, direct product factor, Sylow
275C23—21no—
276C23C2×D4×C1311yescharacteristic
277C23C2×D4×C1311yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—81no—
281D4—22no—
282D4—21no—
283D4—21no—
284D4—42no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4C2×D4×C1311yescharacteristic
302C2×C4C2×D4×C1311yescharacteristic
303C2×C4C2×D4×C1311yescharacteristic
304C2×C4C2×D4×C1311yescharacteristic
305C2×C4C24×C1311yescharacteristic
306C8—21no—
307C8—21no—
308C8—21no—
309C8C13×#4112yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C13×#13712yes—
319C22C22×D4×C1311yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4C2×C13×#4111yescharacteristic
332C4C13×2−1+411yescharacteristic
333C2—22no—
334C2—41no—
335C2—81no—
336C2C13×#54711yescharacteristic
337C2C2×C13×#13711yescharacteristic
338C2C13×#57611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D4
commutator, Frattini, cosocleC2×C4C24×C13
prime radicalC13×#553C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#554C2semidirect
3. C13×#501C2semidirect
4. C13×#485C2semidirect
5. C13×#484C2semidirect
6. C13×#481C2semidirect
7. C13×#480C2semidirect
8. C13×#479C2semidirect
9. C13×#474C2semidirect
10. C13×#468C2semidirect
11. C13×#465C2semidirect
12. C13×#440C2semidirect
13. C13×#435C2semidirect
14. C13×#428C2semidirect
15. C2×C13×#107C2semidirect
105. #3346C13direct (N × H)
141. #554C2×C13semidirect
143. #501C2×C13semidirect
144. #485C2×C13semidirect
145. #484C2×C13semidirect
146. #481C2×C13semidirect
147. #480C2×C13semidirect
148. #479C2×C13semidirect
149. #474C2×C13semidirect
150. #468C2×C13semidirect
151. #465C2×C13semidirect
152. #440C2×C13semidirect
153. #435C2×C13semidirect
154. #428C2×C13semidirect
155. C2×#107C2×C13semidirect
274. C13#3346direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5542
C13×#5532
C13×#5012
C13×#4852
C13×#4842
C13×#4812
C13×#4802
C13×#4792
C13×#4742
C13×#4682
C13×#4652
C13×#4402
C13×#4352
C13×#4282
C2×C13×#1072
#334613