Finite Group Databasebeta

← C13×#10426 #15696765

Subgroups — C13×#10426 #15696765

Order 3328.

444 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2820C211yesmaximal, characteristic
2C13×#1992C211yesmaximal, characteristic, complemented
3C13×#1959C211yesmaximal, characteristic
4C13×#1836C211yesmaximal, characteristic, complemented
5C2×C13×#330C211yesmaximal, characteristic, complemented
6C2×C13×#329C211yesmaximal, characteristic
7C13×#1295C211yesmaximal, characteristic, complemented
8C2×C13×#125C2211yescharacteristic
9C2×C13×#124C2211yescharacteristic
10C2×C13×#103—21no—
11C2×C13×#102—21no—
12C2×C13×#97C2211yescharacteristic
13C2×C13×#97C2211yescharacteristic
14C2×C13×#97C2211yescharacteristic
15C13×#399—21no—
16C13×#397—21no—
17C13×#396—21no—
18C13×#396—21no—
19C13×#395—21no—
20C13×#394—21no—
21C13×#384C2211yescharacteristic
22C13×#382C2211yescharacteristic
23C13×#340—21no—
24C13×#340—21no—
25C13×#340—21no—
26C13×#340—21no—
27C13×#330—22no—
28C13×#329—22no—
29C22×Q8×C13D411yescharacteristic
30C22×D4×C13D411yescharacteristic
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C13×#125—21no—
35C13×#125—21no—
36C13×#125—21no—
37C13×#125—21no—
38C13×#124—21no—
39C13×#124—21no—
40C13×#124—21no—
41C13×#124—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C42×C13C2311yescharacteristic
60C13×#103—42no—
61C13×#102—42no—
62C13×#97—21no—
63C13×#97—21no—
64C13×#97—21no—
65C13×#97—21no—
66C13×#97—21no—
67C13×#97D412yes—
68C13×#95—21no—
69C13×#95—21no—
70C13×#95—21no—
71C13×#95—21no—
72#10426C1311yesmaximal, characteristic, direct product factor, Sylow
73C24×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13—21no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×D4×C13—21no—
79C2×D4×C13—21no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—41no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13—22no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—42no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—81no—
115C13×C4⋊C4—81no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—81no—
121C13×C22⋊C4—81no—
122C13×C22⋊C4—81no—
123C13×C22⋊C4—81no—
124C42×C13C2×D411yescharacteristic
125C42×C13#4111yescharacteristic
126C42×C13#4111yescharacteristic
127C42×C13#4111yescharacteristic
128#2820C2×C1311yescharacteristic
129#1992C2×C1311yescharacteristic, complemented
130#1959C2×C1311yescharacteristic
131#1836C2×C1311yescharacteristic, complemented
132C2×#330C2×C1311yescharacteristic, complemented
133C2×#329C2×C1311yescharacteristic
134#1295C2×C1311yescharacteristic, complemented
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13#12011yescharacteristic
143Q8×C13—42no—
144Q8×C13—81no—
145D4×C13—42no—
146D4×C13—81no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—81no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13#12111yescharacteristic
174C2×C4×C13#12311yescharacteristic
175C2×C4×C13#12311yescharacteristic
176C2×C4×C13#12411yescharacteristic
177C8×C13—42no—
178C8×C13—42no—
179C8×C13—42no—
180C2×#125C22×C1311yescharacteristic
181C2×#124C22×C1311yescharacteristic
182C2×#103—21no—
183C2×#102—21no—
184C2×#97C22×C1311yescharacteristic
185C2×#97C22×C1311yescharacteristic
186C2×#97C22×C1311yescharacteristic
187#399—21no—
188#397—21no—
189#396—21no—
190#396—21no—
191#395—21no—
192#394—21no—
193#384C22×C1311yescharacteristic
194#382C22×C1311yescharacteristic
195#340—21no—
196#340—21no—
197#340—21no—
198#340—21no—
199#330—22no—
200#329—22no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13#39411yescharacteristic
209C22×C13#45311yescharacteristic
210C22×C13#45411yescharacteristic
211C22×C13#45411yescharacteristic
212C22×C13#45511yescharacteristic
213C22×C13#45511yescharacteristic
214C22×C13#45611yescharacteristic
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—81no—
222C4×C13—81no—
223C4×C13—81no—
224C4×C13—81no—
225C4×C13—81no—
226C4×C13—161no—
227C22×Q8D4×C1311yescharacteristic
228C22×D4D4×C1311yescharacteristic
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232#125—21no—
233#125—21no—
234#125—21no—
235#125—21no—
236#124—21no—
237#124—21no—
238#124—21no—
239#124—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4D4×C1311yescharacteristic
248C2×C4⋊C4D4×C1311yescharacteristic
249C2×C4⋊C4D4×C1311yescharacteristic
250C2×C4⋊C4D4×C1311yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C42C23×C1311yescharacteristic
258#103—42no—
259#102—42no—
260#97—21no—
261#97—21no—
262#97—21no—
263#97—21no—
264#97—21no—
265#97D4×C1312yes—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270C2×C13—161no—
271C2×C13#165711yescharacteristic
272C2×C13#166111yescharacteristic
273C2×C13#166211yescharacteristic
274C2×C13#166411yescharacteristic
275C2×C13#203711yescharacteristic
276C2×C13#203811yescharacteristic
277C2×C13#204011yescharacteristic
278C24—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4C2×D4×C1311yescharacteristic
294C22×C4C2×D4×C1311yescharacteristic
295C22×C4C2×D4×C1311yescharacteristic
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—81no—
320C4⋊C4—81no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C42C2×D4×C1311yescharacteristic
330C42C13×#4111yescharacteristic
331C42C13×#4111yescharacteristic
332C42C13×#4111yescharacteristic
333C13#1042611yescharacteristic, direct product factor, Sylow
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23C13×#12011yescharacteristic
342Q8—42no—
343Q8—81no—
344D4—42no—
345D4—81no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4C13×#12111yescharacteristic
371C2×C4C13×#12111yescharacteristic
372C2×C4C13×#12111yescharacteristic
373C2×C4C13×#12311yescharacteristic
374C2×C4C13×#12311yescharacteristic
375C2×C4C13×#12411yescharacteristic
376C8—42no—
377C8—42no—
378C8—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C13×#39411yescharacteristic
387C22C13×#45311yescharacteristic
388C22C13×#45411yescharacteristic
389C22C13×#45411yescharacteristic
390C22C13×#45511yescharacteristic
391C22C13×#45511yescharacteristic
392C22C13×#45611yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—161no—
405C2—161no—
406C2C13×#165711yescharacteristic
407C2C13×#166111yescharacteristic
408C2C13×#166211yescharacteristic
409C2C13×#166411yescharacteristic
410C2C13×#203711yescharacteristic
411C2C13×#203811yescharacteristic
412C2C13×#204011yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1992C2semidirect
4. C13×#1836C2semidirect
5. C2×C13×#330C2semidirect
7. C13×#1295C2semidirect
72. #10426C13direct (N × H)
129. #1992C2×C13semidirect
131. #1836C2×C13semidirect
132. C2×#330C2×C13semidirect
134. #1295C2×C13semidirect
333. C13#10426direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28202
C13×#19922
C13×#19592
C13×#18362
C2×C13×#3302
C2×C13×#3292
C13×#12952
#1042613