Finite Group Databasebeta

← C13×#9337 #15695676

Subgroups — C13×#9337 #15695676

Order 3328.

412 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×#3218C211yesmaximal, characteristic
2C13×#2995C211yesmaximal, characteristic
3C13×#1997C211yesmaximal, characteristic, complemented
4C13×#1558C211yesmaximal, characteristic, complemented
5C13×#1529C211yesmaximal, characteristic
6C13×#1307C211yesmaximal, characteristic, complemented
7C13×#1291C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#497—21no—
11C13×#491—21no—
12C13×#462—21no—
13C13×#461—21no—
14C13×#451C412yes—
15C13×#448C412yes—
16C13×#446—21no—
17C13×#436—21no—
18C13×#435—21no—
19C13×#435—21no—
20C13×#433—21no—
21C13×#432C2211yescharacteristic
22C13×#432C2211yescharacteristic
23C13×#432C2211yescharacteristic
24C13×#424—21no—
25C13×#423C2211yescharacteristic
26C4×C13×M16C2211yescharacteristic
27C13×#343—21no—
28C13×#343—21no—
29C13×#333—21no—
30C13×#333—21no—
31C13×#330—21no—
32C13×#329—21no—
33C22×Q8×C13C2×C412yes—
34C2×C13×Q16—22no—
35C2×C13×SD16—22no—
36C2×C13×M16—21no—
37C2×C13×M16—21no—
38C2×C13×M16D411yescharacteristic
39C2×C13×M16D411yescharacteristic
40C22×C8×C13—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8—21no—
45C13×#126—21no—
46C13×#125D411yescharacteristic
47C13×#124D411yescharacteristic
48C13×#123—21no—
49C13×C22⋊Q8C2×C411yescharacteristic
50C13×#121C2×C411yescharacteristic
51C4×Q8×C13D411yescharacteristic
52C4×D4×C13—21no—
53C4×D4×C13D411yescharacteristic
54C13×#117—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C42×C13C2311yescharacteristic
58C13×C4⋊C8—21no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8D411yescharacteristic
65C13×C4⋊C8D411yescharacteristic
66C13×#103—22no—
67C13×#103—22no—
68C13×C22⋊C8—21no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8C2×C412yes—
73C13×#97—21no—
74C13×#97—21no—
75C13×#97—21no—
76C13×#97—21no—
77C13×#97—21no—
78C4×C8×C13—21no—
79C4×C8×C13—21no—
80#9337C1311yesmaximal, characteristic, direct product factor, Sylow
81C2×Q8×C13—22no—
82C2×Q8×C13—22no—
83C2×Q8×C13—82no—
84C2×Q8×C13C22⋊C411yescharacteristic
85C2×D4×C13—21no—
86C2×D4×C13C22⋊C411yescharacteristic
87C22×C4×C13—21no—
88C22×C4×C13—22no—
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13#4111yescharacteristic
92C13×Q16—82no—
93C13×SD16—82no—
94C13×M16—22no—
95C13×M16—41no—
96C13×M16—41no—
97C13×M16—41no—
98C13×M16—81no—
99C2×C8×C13—22no—
100C2×C8×C13—21no—
101C2×C8×C13—21no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C2×C8×C13—81no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4C22⋊C411yescharacteristic
116C13×C4⋊C4C22⋊C411yescharacteristic
117C13×C22⋊C4—21no—
118C13×C22⋊C4—21no—
119C13×C22⋊C4—21no—
120C13×C22⋊C4—21no—
121C13×C22⋊C4—21no—
122C42×C13—21no—
123C42×C13C2×D411yescharacteristic
124C42×C13C2×D411yescharacteristic
125C42×C13C2×D411yescharacteristic
126C42×C13#4111yescharacteristic
127#3218C2×C1311yescharacteristic
128#2995C2×C1311yescharacteristic
129#1997C2×C1311yescharacteristic, complemented
130#1558C2×C1311yescharacteristic, complemented
131#1529C2×C1311yescharacteristic
132#1307C2×C1311yescharacteristic, complemented
133#1291C2×C1311yescharacteristic, complemented
134C23×C13—21no—
135C23×C13C4×D411yescharacteristic
136Q8×C13—41no—
137Q8×C13—42no—
138Q8×C13—42no—
139Q8×C13—82no—
140D4×C13—41no—
141D4×C13—81no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—82no—
153C2×C4×C13C2×C22⋊C411yescharacteristic
154C2×C4×C13C4×D411yescharacteristic
155C2×C4×C13#12011yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12311yescharacteristic
159C8×C13—42no—
160C8×C13—42no—
161C8×C13—41no—
162C8×C13—41no—
163C8×C13—41no—
164C8×C13—41no—
165C8×C13—81no—
166C2×C4⋊Q8C22×C1311yescharacteristic
167#529C22×C1311yescharacteristic
168#497—21no—
169#491—21no—
170#462—21no—
171#461—21no—
172#451C4×C1312yes—
173#448C4×C1312yes—
174#446—21no—
175#436—21no—
176#435—21no—
177#435—21no—
178#433—21no—
179#432C22×C1311yescharacteristic
180#432C22×C1311yescharacteristic
181#432C22×C1311yescharacteristic
182#424—21no—
183#423C22×C1311yescharacteristic
184C4×M16C22×C1311yescharacteristic
185#343—21no—
186#343—21no—
187#333—21no—
188#333—21no—
189#330—21no—
190#329—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13#38611yescharacteristic
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—82no—
207C4×C13#45511yescharacteristic
208C4×C13#45611yescharacteristic
209C22×Q8C2×C4×C1312yes—
210C2×Q16—22no—
211C2×SD16—22no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16D4×C1311yescharacteristic
215C2×M16D4×C1311yescharacteristic
216C22×C8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221#126—21no—
222#125D4×C1311yescharacteristic
223#124D4×C1311yescharacteristic
224#123—21no—
225C22⋊Q8C2×C4×C1311yescharacteristic
226#121C2×C4×C1311yescharacteristic
227C4×Q8D4×C1311yescharacteristic
228C4×D4—21no—
229C4×D4D4×C1311yescharacteristic
230#117—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C42C23×C1311yescharacteristic
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8D4×C1311yescharacteristic
241C4⋊C8D4×C1311yescharacteristic
242#103—22no—
243#103—22no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8C2×C4×C1312yes—
249#97—21no—
250#97—21no—
251#97—21no—
252#97—21no—
253#97—21no—
254C4×C8—21no—
255C4×C8—21no—
256C2×C13—41no—
257C2×C13—81no—
258C2×C13#188211yescharacteristic
259C2×C13#190211yescharacteristic
260C2×C13#191411yescharacteristic
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—82no—
264C2×Q8C13×C22⋊C411yescharacteristic
265C2×D4—21no—
266C2×D4C13×C22⋊C411yescharacteristic
267C22×C4—21no—
268C22×C4—22no—
269C22×C4C22×C4×C1311yescharacteristic
270C22×C4C2×D4×C1311yescharacteristic
271C22×C4C13×#4111yescharacteristic
272Q16—82no—
273SD16—82no—
274M16—22no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—81no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—81no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4C13×C22⋊C411yescharacteristic
296C4⋊C4C13×C22⋊C411yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C42—21no—
303C42C2×D4×C1311yescharacteristic
304C42C2×D4×C1311yescharacteristic
305C42C2×D4×C1311yescharacteristic
306C42C13×#4111yescharacteristic
307C13#933711yescharacteristic, direct product factor, Sylow
308C23—21no—
309C23C4×D4×C1311yescharacteristic
310Q8—41no—
311Q8—42no—
312Q8—42no—
313Q8—82no—
314D4—41no—
315D4—81no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4C2×C13×C22⋊C411yescharacteristic
328C2×C4C4×D4×C1311yescharacteristic
329C2×C4C13×#12011yescharacteristic
330C2×C4C13×#12111yescharacteristic
331C2×C4C13×#12111yescharacteristic
332C2×C4C13×#12311yescharacteristic
333C8—42no—
334C8—42no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—41no—
339C8—81no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C13×#38611yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—82no—
356C4C13×#45511yescharacteristic
357C4C13×#45611yescharacteristic
358C2—41no—
359C2—81no—
360C2C13×#188211yescharacteristic
361C2C13×#190211yescharacteristic
362C2C13×#191411yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC13×#121C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1997C2semidirect
4. C13×#1558C2semidirect
6. C13×#1307C2semidirect
7. C13×#1291C2semidirect
80. #9337C13direct (N × H)
129. #1997C2×C13semidirect
130. #1558C2×C13semidirect
132. #1307C2×C13semidirect
133. #1291C2×C13semidirect
307. C13#9337direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32182
C13×#29952
C13×#19972
C13×#15582
C13×#15292
C13×#13072
C13×#12912
#933713