Finite Group Databasebeta

← C13×#9880 #15696219

Subgroups — C13×#9880 #15696219

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#387C211yesmaximal, characteristic
2C13×#1797C211yesmaximal, characteristic
3C4×C13×C22⋊C8C211yesmaximal, characteristic
4C13×#1280C212yesmaximal
5C13×#1280C212yesmaximal
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C2×C13×C4⋊C8—21no—
10C2×C13×C22⋊C8C2212yes—
11C2×C13×C22⋊C8C2212yes—
12C2×C4×C8×C13—21no—
13C13×#387—21no—
14C13×#387—21no—
15C13×#387—21no—
16C13×#387—21no—
17C2×C13×#95C411yescharacteristic
18C2×C13×#95C411yescharacteristic
19C2×C13×#95C2211yescharacteristic
20C2×C13×#95C2211yescharacteristic
21C13×#336—21no—
22C13×#336—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C22×C8×C13—22no—
31C22×C8×C13—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—42no—
38C2×C13×C4⋊C4C814yescomplemented
39C2×C42×C13—42no—
40C2×C42×C13D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C13×C4⋊C8—42no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—24no—
47C13×C22⋊C8Q814yes—
48C4×C8×C13—42no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57#9880C1311yesmaximal, characteristic, direct product factor, Sylow
58C24×C13C22×C411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C2×C812yes—
87C22×C4×C13C2×C812yes—
88C22×C4×C13C2×C812yes—
89C22×C4×C13M1612yes—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×Q812yes—
93C22×C4×C13#4112yes—
94C2×C8×C13—24no—
95C2×C8×C13—42no—
96C2×C8×C13—42no—
97C2×C8×C13—42no—
98C2×C8×C13—42no—
99C2×C8×C13—42no—
100C13×C4⋊C4—24no—
101C13×C4⋊C4—24no—
102C13×C4⋊C4—42no—
103C13×C4⋊C4—42no—
104C42×C13—22no—
105C42×C13—22no—
106C42×C13—41no—
107C42×C13—41no—
108C2×#387C2×C1311yescharacteristic
109#1797C2×C1311yescharacteristic
110C4×C22⋊C8C2×C1311yescharacteristic
111#1280C2×C1312yes—
112#1280C2×C1312yes—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C2×C22⋊C411yescharacteristic
118C23×C13C4×Q812yes—
119C23×C13C22×C811yescharacteristic
120C23×C13C2×M1611yescharacteristic
121C23×C13#13112yes—
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—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—44no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
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—82no—
157C2×C4×C13—82no—
158C2×C4×C13C22⋊C812yes—
159C2×C4×C13C22⋊C812yes—
160C2×C4×C13#9912yes—
161C2×C4×C13C22⋊Q812yes—
162C2×C4×C13#12411yescharacteristic
163C2×C4×C13C4⋊Q811yescharacteristic
164C8×C13—44no—
165C8×C13—82no—
166C22×C4⋊C4C4×C1311yescharacteristic
167C22×C4⋊C4C4×C1311yescharacteristic
168C22×C42C22×C1311yescharacteristic
169C2×C4⋊C8—21no—
170C2×C22⋊C8C22×C1312yes—
171C2×C22⋊C8C22×C1312yes—
172C2×C4×C8—21no—
173#387—21no—
174#387—21no—
175#387—21no—
176#387—21no—
177C2×#95C4×C1311yescharacteristic
178C2×#95C4×C1311yescharacteristic
179C2×#95C22×C1311yescharacteristic
180C2×#95C22×C1311yescharacteristic
181#336—21no—
182#336—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13#39111yescharacteristic
192C22×C13C2×C22⋊C811yescharacteristic
193C22×C13#40811yescharacteristic
194C22×C13C2×#9911yescharacteristic
195C22×C13#41011yescharacteristic
196C22×C13#41311yescharacteristic
197C22×C13#41311yescharacteristic
198C22×C13C8×Q812yes—
199C22×C13#44612yes—
200C4×C13—22no—
201C4×C13—22no—
202C4×C13—22no—
203C4×C13—22no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—42no—
207C4×C13—42no—
208C4×C13—41no—
209C4×C13—81no—
210C4×C13—81no—
211C23×C4C2×C4×C1311yescharacteristic
212C23×C4C2×C4×C1311yescharacteristic
213C23×C4C2×C4×C1311yescharacteristic
214C23×C4C2×C4×C1311yescharacteristic
215C23×C4C2×C4×C1311yescharacteristic
216C23×C4C2×C4×C1311yescharacteristic
217C23×C4C23×C1311yescharacteristic
218C22×C8—22no—
219C22×C8—22no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4C8×C1314yescomplemented
227C2×C42—42no—
228C2×C42D4×C1311yescharacteristic
229C2×C42D4×C1311yescharacteristic
230C2×C42D4×C1311yescharacteristic
231C2×C42D4×C1311yescharacteristic
232C4⋊C8—42no—
233C22⋊C8—22no—
234C22⋊C8—24no—
235C22⋊C8Q8×C1314yes—
236C4×C8—42no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245C2×C13—22no—
246C2×C13—22no—
247C2×C13#145811yescharacteristic
248C2×C13#145911yescharacteristic
249C2×C13#146811yescharacteristic
250C2×C13#147311yescharacteristic
251C2×C13#198411yescharacteristic
252C2×C13#199611yescharacteristic
253C2×C13#199811yescharacteristic
254C24C22×C4×C1311yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C13×C22⋊C411yescharacteristic
279C22×C4C13×C22⋊C411yescharacteristic
280C22×C4C13×C22⋊C411yescharacteristic
281C22×C4C13×C22⋊C411yescharacteristic
282C22×C4C2×C8×C1312yes—
283C22×C4C2×C8×C1312yes—
284C22×C4C2×C8×C1312yes—
285C22×C4C13×M1612yes—
286C22×C4C2×D4×C1311yescharacteristic
287C22×C4C2×D4×C1311yescharacteristic
288C22×C4C2×Q8×C1312yes—
289C22×C4C13×#4112yes—
290C2×C8—24no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C42—22no—
301C42—22no—
302C42—41no—
303C42—41no—
304C13#988011yescharacteristic, direct product factor, Sylow
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×C13×C22⋊C411yescharacteristic
310C23C4×Q8×C1312yes—
311C23C22×C8×C1311yescharacteristic
312C23C2×C13×M1611yescharacteristic
313C23C13×#13112yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4C13×C22⋊C812yes—
351C2×C4C13×C22⋊C812yes—
352C2×C4C13×#9912yes—
353C2×C4C13×C22⋊Q812yes—
354C2×C4C13×#12411yescharacteristic
355C2×C4C13×C4⋊Q811yescharacteristic
356C8—44no—
357C8—82no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22C13×#39111yescharacteristic
367C22C2×C13×C22⋊C811yescharacteristic
368C22C13×#40811yescharacteristic
369C22C2×C13×#9911yescharacteristic
370C22C13×#41011yescharacteristic
371C22C13×#41311yescharacteristic
372C22C13×#41311yescharacteristic
373C22C8×Q8×C1312yes—
374C22C13×#44612yes—
375C4—22no—
376C4—21no—
377C4—21no—
378C4—22no—
379C4—22no—
380C4—22no—
381C4—42no—
382C4—42no—
383C4—41no—
384C4—81no—
385C4—81no—
386C2—22no—
387C2—22no—
388C2C13×#145811yescharacteristic
389C2C13×#145911yescharacteristic
390C2C13×#146811yescharacteristic
391C2C13×#147311yescharacteristic
392C2C13×#198411yescharacteristic
393C2C13×#199611yescharacteristic
394C2C13×#199811yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC23C22×C8×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
38. C2×C13×C4⋊C4C8semidirect
57. #9880C13direct (N × H)
226. C2×C4⋊C4C8×C13semidirect
304. C13#9880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3872
C13×#17972
C4×C13×C22⋊C82
C13×#12802
#988013