Finite Group Databasebeta

← C13×#9369 #15695708

Subgroups — C13×#9369 #15695708

Order 3328.

390 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3240C211yesmaximal, characteristic
2C13×#2967C211yesmaximal, characteristic
3C13×#1521C211yesmaximal, characteristic
4C13×#1515C211yesmaximal, characteristic, complemented
5C13×#1485C211yesmaximal, characteristic, complemented
6C13×#1288C211yesmaximal, characteristic, complemented
7C13×#1287C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#501C411yescharacteristic, complemented
11C13×#501C411yescharacteristic, complemented
12C13×#489C411yescharacteristic, complemented
13C13×#489C411yescharacteristic, complemented
14C13×#485—21no—
15C13×#482—21no—
16C13×#479—21no—
17C13×#478—21no—
18C13×#446—21no—
19C13×#436—21no—
20C13×#435—21no—
21C13×#435—21no—
22C13×#433—21no—
23C13×#432C2211yescharacteristic
24C13×#432C2211yescharacteristic
25C13×#431C2211yescharacteristic
26C13×#405—21no—
27C4×C13×M16C2211yescharacteristic
28C13×#383C2211yescharacteristic
29C13×#328—21no—
30C13×#328—21no—
31C13×#328—21no—
32C13×#327—21no—
33C13×Q8⋊C8—21no—
34C13×Q8⋊C8—21no—
35C2×C13×M16—21no—
36C2×C13×M16—21no—
37C22×C8×C13—21no—
38C13×C4⋊Q8C2×C411yescharacteristic
39C13×C4⋊Q8C2×C411yescharacteristic
40C13×#126—21no—
41C13×#125—21no—
42C13×#125C2×C411yescharacteristic
43C13×#124C2×C411yescharacteristic
44C13×#123—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8D411yescharacteristic
48C13×#121D411yescharacteristic
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13D411yescharacteristic
52C4×D4×C13—21no—
53C4×D4×C13D411yescharacteristic
54C13×#117—21no—
55C13×#117—21no—
56C2×C42×C13C2311yescharacteristic
57C13×#107—21no—
58C13×#107—21no—
59C13×#106—21no—
60C13×#106—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×#103—21no—
67C13×#103—21no—
68C13×#102—21no—
69C13×#102—21no—
70C13×C22⋊C8—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8D411yescharacteristic
75C13×C22⋊C8D411yescharacteristic
76C13×#97—21no—
77C13×#97—21no—
78C13×#97—21no—
79C13×#97C2×C411yescharacteristic
80C13×#97C2×C411yescharacteristic
81C4×C8×C13—21no—
82C4×C8×C13—21no—
83C4×C8×C13D411yescharacteristic
84C4×C8×C13D411yescharacteristic
85C13×#95—21no—
86C13×#95—21no—
87C13×#95—21no—
88#9369C1311yesmaximal, characteristic, direct product factor, Sylow
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13C22⋊C411yescharacteristic
92C2×D4×C13—21no—
93C2×D4×C13C22⋊C411yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13—41no—
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13#4111yescharacteristic
99C13×M16—42no—
100C13×M16—42no—
101C2×C8×C13—21no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13—21no—
105C2×C8×C13—21no—
106C2×C8×C13—21no—
107C2×C8×C13—42no—
108C2×C8×C13—41no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4C22⋊C411yescharacteristic
120C13×C4⋊C4C22⋊C411yescharacteristic
121C13×C22⋊C4—21no—
122C13×C22⋊C4—21no—
123C13×C22⋊C4—21no—
124C13×C22⋊C4—21no—
125C13×C22⋊C4—21no—
126C13×C22⋊C4—41no—
127C42×C13—21no—
128C42×C13—41no—
129C42×C13C22×C411yescharacteristic
130C42×C13C2×D411yescharacteristic
131C42×C13C2×D411yescharacteristic
132C42×C13#4111yescharacteristic
133#3240C2×C1311yescharacteristic
134#2967C2×C1311yescharacteristic
135#1521C2×C1311yescharacteristic
136#1515C2×C1311yescharacteristic, complemented
137#1485C2×C1311yescharacteristic, complemented
138#1288C2×C1311yescharacteristic, complemented
139#1287C2×C1311yescharacteristic, complemented
140C23×C13—21no—
141C23×C13#12111yescharacteristic
142Q8×C13—41no—
143Q8×C13—42no—
144Q8×C13—81no—
145D4×C13—41no—
146D4×C13—81no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13C2×C22⋊C411yescharacteristic
161C2×C4×C13C4×D411yescharacteristic
162C2×C4×C13C4×D411yescharacteristic
163C2×C4×C13#12011yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13#12311yescharacteristic
166C8×C13—22no—
167C8×C13—41no—
168C8×C13—41no—
169C8×C13—41no—
170C8×C13—41no—
171C8×C13—41no—
172C8×C13—81no—
173#533C22×C1311yescharacteristic
174#529C22×C1311yescharacteristic
175#501C4×C1311yescharacteristic, complemented
176#501C4×C1311yescharacteristic, complemented
177#489C4×C1311yescharacteristic, complemented
178#489C4×C1311yescharacteristic, complemented
179#485—21no—
180#482—21no—
181#479—21no—
182#478—21no—
183#446—21no—
184#436—21no—
185#435—21no—
186#435—21no—
187#433—21no—
188#432C22×C1311yescharacteristic
189#432C22×C1311yescharacteristic
190#431C22×C1311yescharacteristic
191#405—21no—
192C4×M16C22×C1311yescharacteristic
193#383C22×C1311yescharacteristic
194#328—21no—
195#328—21no—
196#328—21no—
197#327—21no—
198Q8⋊C8—21no—
199Q8⋊C8—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13#38611yescharacteristic
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—41no—
214C4×C13—41no—
215C4×C13—41no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13—161no—
219C2×M16—21no—
220C2×M16—21no—
221C22×C8—21no—
222C4⋊Q8C2×C4×C1311yescharacteristic
223C4⋊Q8C2×C4×C1311yescharacteristic
224#126—21no—
225#125—21no—
226#125C2×C4×C1311yescharacteristic
227#124C2×C4×C1311yescharacteristic
228#123—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231C22⋊Q8D4×C1311yescharacteristic
232#121D4×C1311yescharacteristic
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8D4×C1311yescharacteristic
236C4×D4—21no—
237C4×D4D4×C1311yescharacteristic
238#117—21no—
239#117—21no—
240C2×C42C23×C1311yescharacteristic
241#107—21no—
242#107—21no—
243#106—21no—
244#106—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250#103—21no—
251#103—21no—
252#102—21no—
253#102—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8D4×C1311yescharacteristic
259C22⋊C8D4×C1311yescharacteristic
260#97—21no—
261#97—21no—
262#97—21no—
263#97C2×C4×C1311yescharacteristic
264#97C2×C4×C1311yescharacteristic
265C4×C8—21no—
266C4×C8—21no—
267C4×C8D4×C1311yescharacteristic
268C4×C8D4×C1311yescharacteristic
269#95—21no—
270#95—21no—
271#95—21no—
272C2×C13—41no—
273C2×C13—81no—
274C2×C13#188111yescharacteristic
275C2×C13#190611yescharacteristic
276C2×C13#190911yescharacteristic
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8C13×C22⋊C411yescharacteristic
280C2×D4—21no—
281C2×D4C13×C22⋊C411yescharacteristic
282C22×C4—21no—
283C22×C4—41no—
284C22×C4C2×D4×C1311yescharacteristic
285C22×C4C2×D4×C1311yescharacteristic
286C22×C4C13×#4111yescharacteristic
287M16—42no—
288M16—42no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—42no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4C13×C22⋊C411yescharacteristic
308C4⋊C4C13×C22⋊C411yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—41no—
315C42—21no—
316C42—41no—
317C42C22×C4×C1311yescharacteristic
318C42C2×D4×C1311yescharacteristic
319C42C2×D4×C1311yescharacteristic
320C42C13×#4111yescharacteristic
321C13#936911yescharacteristic, direct product factor, Sylow
322C23—21no—
323C23C13×#12111yescharacteristic
324Q8—41no—
325Q8—42no—
326Q8—81no—
327D4—41no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4C2×C13×C22⋊C411yescharacteristic
343C2×C4C4×D4×C1311yescharacteristic
344C2×C4C4×D4×C1311yescharacteristic
345C2×C4C13×#12011yescharacteristic
346C2×C4C13×#12111yescharacteristic
347C2×C4C13×#12311yescharacteristic
348C8—22no—
349C8—41no—
350C8—41no—
351C8—41no—
352C8—41no—
353C8—41no—
354C8—81no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C13×#38611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—81no—
372C4—81no—
373C4—161no—
374C2—41no—
375C2—81no—
376C2C13×#188111yescharacteristic
377C2C13×#190611yescharacteristic
378C2C13×#190911yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1515C2semidirect
5. C13×#1485C2semidirect
6. C13×#1288C2semidirect
7. C13×#1287C2semidirect
10. C13×#501C4semidirect
11. C13×#501C4semidirect
12. C13×#489C4semidirect
13. C13×#489C4semidirect
88. #9369C13direct (N × H)
136. #1515C2×C13semidirect
137. #1485C2×C13semidirect
138. #1288C2×C13semidirect
139. #1287C2×C13semidirect
175. #501C4×C13semidirect
176. #501C4×C13semidirect
177. #489C4×C13semidirect
178. #489C4×C13semidirect
321. C13#9369direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32402
C13×#29672
C13×#15212
C13×#15152
C13×#14852
C13×#12882
C13×#12872
#936913