Finite Group Databasebeta

← C13×#8999 #15695338

Subgroups — C13×#8999 #15695338

Order 3328.

530 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#489C211yesmaximal, characteristic
2C13×#2379C211yesmaximal, characteristic
3C13×#1993C211yesmaximal, characteristic, complemented
4C13×#1960C211yesmaximal, characteristic, complemented
5C2×C13×#329C211yesmaximal, characteristic
6C13×#1295C211yesmaximal, characteristic, complemented
7C13×#1295C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×#124C2211yescharacteristic
10C13×#489—22no—
11C13×#489C414yescomplemented
12C2×C13×#103—21no—
13C2×C13×#103—21no—
14C2×C13×#103—21no—
15C2×C13×#102—21no—
16C2×C13×#97C2211yescharacteristic
17C2×C13×#97C2211yescharacteristic
18C2×C13×#97C2211yescharacteristic
19C13×#391—21no—
20C13×#388—21no—
21C13×#388—21no—
22C13×#386—21no—
23C13×#385—21no—
24C13×#385—21no—
25C13×#382C2211yescharacteristic
26C13×#382C2211yescharacteristic
27C13×#340—21no—
28C13×#340—21no—
29C13×#329—22no—
30C22×Q8×C13—21no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C22×C8×C13—21no—
35C22×C8×C13—21no—
36C22×C8×C13—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8C2×C412yescomplemented
41C13×#124—21no—
42C13×#124—21no—
43C13×#124C2×C412yes—
44C13×#124D412yes—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C42×C13—21no—
58C2×C42×C13C2311yescharacteristic
59C13×#103—24no—
60C13×#103—42no—
61C13×#103—42no—
62C13×#102—24no—
63C13×#97—21no—
64C13×#97—21no—
65C13×#97—21no—
66C13×#97—21no—
67C13×#97—21no—
68C13×#97C2×C412yescomplemented
69C13×#95—21no—
70C13×#95—21no—
71C13×#95—21no—
72C13×#95—21no—
73C13×#95—21no—
74C13×#95—21no—
75#8999C1311yesmaximal, characteristic, direct product factor, Sylow
76C24×C13—21no—
77C2×Q8×C13—21no—
78C2×Q8×C13—22no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×Q8×C13—41no—
86C2×Q8×C13C22⋊C412yes—
87C2×D4×C13—21no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13C22⋊C412yes—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—41no—
97C22×C4×C13—81no—
98C22×C4×C13—81no—
99C22×C4×C13—81no—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C2×C8×C13—22no—
104C2×C8×C13—22no—
105C2×C8×C13—22no—
106C2×C8×C13—41no—
107C2×C8×C13—41no—
108C2×C8×C13—41no—
109C2×C8×C13—41no—
110C2×C8×C13—41no—
111C2×C8×C13—41no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—81no—
121C13×C22⋊C4—22no—
122C13×C22⋊C4—22no—
123C13×C22⋊C4—22no—
124C13×C22⋊C4—22no—
125C13×C22⋊C4—81no—
126C13×C22⋊C4—81no—
127C13×C22⋊C4—81no—
128C42×C13—81no—
129C42×C13C22×C411yescharacteristic
130C42×C13C2×D411yescharacteristic
131C42×C13#4111yescharacteristic
132C42×C13#4111yescharacteristic
133C2×#489C2×C1311yescharacteristic
134#2379C2×C1311yescharacteristic
135#1993C2×C1311yescharacteristic, complemented
136#1960C2×C1311yescharacteristic, complemented
137C2×#329C2×C1311yescharacteristic
138#1295C2×C1311yescharacteristic, complemented
139#1295C2×C1311yescharacteristic, complemented
140C23×C13—22no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13#12011yescharacteristic
148Q8×C13—42no—
149Q8×C13—42no—
150Q8×C13—42no—
151Q8×C13—81no—
152Q8×C13—81no—
153Q8×C13—81no—
154D4×C13—42no—
155D4×C13—81no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—22no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—42no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—84no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13C2×C22⋊C411yescharacteristic
182C2×C4×C13C4×D411yescharacteristic
183C2×C4×C13C4×D411yescharacteristic
184C2×C4×C13#12111yescharacteristic
185C2×C4×C13#12111yescharacteristic
186C2×C4×C13#12311yescharacteristic
187C8×C13—42no—
188C8×C13—42no—
189C8×C13—42no—
190C2×C4⋊Q8C22×C1311yescharacteristic
191C2×#124C22×C1311yescharacteristic
192#489—22no—
193#489C4×C1314yescomplemented
194C2×#103—21no—
195C2×#103—21no—
196C2×#103—21no—
197C2×#102—21no—
198C2×#97C22×C1311yescharacteristic
199C2×#97C22×C1311yescharacteristic
200C2×#97C22×C1311yescharacteristic
201#391—21no—
202#388—21no—
203#388—21no—
204#386—21no—
205#385—21no—
206#385—21no—
207#382C22×C1311yescharacteristic
208#382C22×C1311yescharacteristic
209#340—21no—
210#340—21no—
211#329—22no—
212C22×C13—42no—
213C22×C13—42no—
214C22×C13—42no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13#38611yescharacteristic
220C22×C13#45311yescharacteristic
221C22×C13#45411yescharacteristic
222C22×C13#45511yescharacteristic
223C22×C13#45511yescharacteristic
224C22×C13#45511yescharacteristic
225C22×C13#45611yescharacteristic
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—42no—
233C4×C13—82no—
234C4×C13—81no—
235C4×C13—81no—
236C4×C13—81no—
237C4×C13—81no—
238C22×Q8—21no—
239C22×Q8D4×C1311yescharacteristic
240C22×D4D4×C1311yescharacteristic
241C23×C4—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8C2×C4×C1312yescomplemented
249#124—21no—
250#124—21no—
251#124C2×C4×C1312yes—
252#124D4×C1312yes—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C1311yescharacteristic
257C2×C4⋊C4D4×C1311yescharacteristic
258C2×C4⋊C4D4×C1311yescharacteristic
259C2×C4⋊C4D4×C1311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C42—21no—
266C2×C42C23×C1311yescharacteristic
267#103—24no—
268#103—42no—
269#103—42no—
270#102—24no—
271#97—21no—
272#97—21no—
273#97—21no—
274#97—21no—
275#97—21no—
276#97C2×C4×C1312yescomplemented
277#95—21no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283C2×C13—82no—
284C2×C13#165911yescharacteristic
285C2×C13#166111yescharacteristic
286C2×C13#166211yescharacteristic
287C2×C13#166411yescharacteristic
288C2×C13#188211yescharacteristic
289C2×C13#188311yescharacteristic
290C2×C13#188511yescharacteristic
291C24—21no—
292C2×Q8—21no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8C13×C22⋊C412yes—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4C13×C22⋊C412yes—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—81no—
313C22×C4—81no—
314C22×C4—81no—
315C22×C4C2×D4×C1311yescharacteristic
316C22×C4C2×D4×C1311yescharacteristic
317C22×C4C2×D4×C1311yescharacteristic
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—81no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—81no—
341C22⋊C4—81no—
342C22⋊C4—81no—
343C42—81no—
344C42C22×C4×C1311yescharacteristic
345C42C2×D4×C1311yescharacteristic
346C42C13×#4111yescharacteristic
347C42C13×#4111yescharacteristic
348C13#899911yescharacteristic, direct product factor, Sylow
349C23—22no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23C13×#12011yescharacteristic
357Q8—42no—
358Q8—42no—
359Q8—42no—
360Q8—81no—
361Q8—81no—
362Q8—81no—
363D4—42no—
364D4—81no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—84no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4C2×C13×C22⋊C411yescharacteristic
391C2×C4C4×D4×C1311yescharacteristic
392C2×C4C4×D4×C1311yescharacteristic
393C2×C4C13×#12111yescharacteristic
394C2×C4C13×#12111yescharacteristic
395C2×C4C13×#12311yescharacteristic
396C8—42no—
397C8—42no—
398C8—42no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22C13×#38611yescharacteristic
407C22C13×#45311yescharacteristic
408C22C13×#45411yescharacteristic
409C22C13×#45511yescharacteristic
410C22C13×#45511yescharacteristic
411C22C13×#45511yescharacteristic
412C22C13×#45611yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—82no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—81no—
425C2—82no—
426C2C13×#165911yescharacteristic
427C2C13×#166111yescharacteristic
428C2C13×#166211yescharacteristic
429C2C13×#166411yescharacteristic
430C2C13×#188211yescharacteristic
431C2C13×#188311yescharacteristic
432C2C13×#188511yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1993C2semidirect
4. C13×#1960C2semidirect
6. C13×#1295C2semidirect
7. C13×#1295C2semidirect
11. C13×#489C4semidirect
40. C13×C4⋊Q8C2×C4semidirect
68. C13×#97C2×C4semidirect
75. #8999C13direct (N × H)
135. #1993C2×C13semidirect
136. #1960C2×C13semidirect
138. #1295C2×C13semidirect
139. #1295C2×C13semidirect
193. #489C4×C13semidirect
248. C4⋊Q8C2×C4×C13semidirect
276. #97C2×C4×C13semidirect
348. C13#8999direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4892
C13×#23792
C13×#19932
C13×#19602
C2×C13×#3292
C13×#12952
#899913