Finite Group Databasebeta

← #72242017

Subgroups — #72242017

Order 11232.

1012 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×(C2×D3)⋊AGL(1,𝔽13)C211yesmaximal, characteristic, complemented
2#72242003C211yesmaximal, characteristic, complemented
3C3×Dic3⋊AGL(1,𝔽13)C211yesmaximal, characteristic, complemented
4#626×D13⋊C3C211yesmaximal, characteristic
5#72241984C411yescharacteristic, complemented
6#72241982C411yescharacteristic, complemented
7#72241981C411yescharacteristic, complemented
8C13⋊C3×#626C411yescharacteristic, complemented
9C2×D3×C3⋊AGL(1,𝔽13)C211yesmaximal, characteristic, complemented
10C2×C3×D3×D13⋊C3C2211yescharacteristic
11Dic3×C3⋊AGL(1,𝔽13)C211yesmaximal, characteristic, complemented
12C2×C3×C3⋊AGL(1,𝔽13)C2211yescharacteristic
13C2×C3×C3⋊AGL(1,𝔽13)C2211yescharacteristic
14C3×Dic3×D13⋊C3C2211yescharacteristic
15#72241926C311yesmaximal, characteristic, complemented
16#72241925—31nomaximal
17#72241913—31nomaximal
18C2×C3⋊D3×AGL(1,𝔽13)C211yesmaximal, characteristic, complemented
19C2×C3⋊(C3⋊AGL(1,𝔽13))C2211yescharacteristic
20C2×C32×AGL(1,𝔽13)C2211yescharacteristic
21C2×C3⋊D3×D13⋊C3C2211yescharacteristic
22D3×C3⋊AGL(1,𝔽13)—22no—
23C3⋊D3×AGL(1,𝔽13)—22no—
24C2×D3×C3⋊#261C2×C311yescharacteristic, complemented
25C2×C3⋊D3×#261C2×C311yescharacteristic, complemented
26C22×C3⋊AGL(1,𝔽13)—31no—
27C2×D3×AGL(1,𝔽13)—31no—
28C2×D3×AGL(1,𝔽13)—31no—
29C2×D3×AGL(1,𝔽13)—31no—
30C2×D3×AGL(1,𝔽13)—61no—
31D13×#626C2×C311yescharacteristic
32#14273015C2×C311yescharacteristic, complemented
33Dic3×C3⋊#261C2×C311yescharacteristic, complemented
34C3×Dic3⋊#261C2×C311yescharacteristic, complemented
35C3×(C2×D3)⋊#261C2×C311yescharacteristic, complemented
36#67×D13⋊C3—31no—
37D12×D13⋊C3—31no—
38C4×C3⋊AGL(1,𝔽13)—31no—
39C3×(C22⋊#261)⋊C3—31no—
40C3×C4⋊AGL(1,𝔽13)—31no—
41Dic3⋊AGL(1,𝔽13)—21no—
42Dic3⋊AGL(1,𝔽13)D311yescharacteristic, complemented
43(C2×D3)⋊AGL(1,𝔽13)—21no—
44(C2×D3)⋊AGL(1,𝔽13)—31no—
45(C2×D3)⋊AGL(1,𝔽13)—31no—
46(C2×D3)⋊AGL(1,𝔽13)D311yescharacteristic, complemented
47Dic3×AGL(1,𝔽13)—31no—
48C2×C3⋊(C3⋊(D13⋊C3))C2×C411yescharacteristic, complemented
49C2×C3⋊D3×C13⋊C3C2×C411yescharacteristic, complemented
50C2×C3×C3⋊(D13⋊C3)C2×C411yescharacteristic, complemented
51C2×C3×D3×C13⋊C3C2×C411yescharacteristic, complemented
52C2×C32×D13⋊C3C2311yescharacteristic
53C3⋊D3×D13⋊C3—21no—
54C3⋊D3×D13⋊C3—21no—
55C3×D3×D13⋊C3—21no—
56C3×D3×D13⋊C3—21no—
57C3⋊(C3⋊AGL(1,𝔽13))D412yescomplemented
58C3×C3⋊AGL(1,𝔽13)—21no—
59C3×C3⋊AGL(1,𝔽13)—21no—
60C32×AGL(1,𝔽13)—21no—
61C3×C3⋊(Dic13⋊C3)C2×C411yescharacteristic, complemented
62C3×Dic3×C13⋊C3C2×C411yescharacteristic, complemented
63#67⋊#261—31no—
64#11929092—31no—
65D4×AGL(1,𝔽13)—91no—
66C2×C3⋊D3×D13C22×C311yescharacteristic
67C2×C3×D3×D13C22×C311yescharacteristic
68C2×C3⋊(C3⋊#261)C22×C311yescharacteristic
69C2×C3×C3⋊#261C22×C311yescharacteristic
70C2×C3×C3⋊#261C22×C311yescharacteristic
71C2×C32×#261C22×C311yescharacteristic
72C22×C3×D13⋊C3—31no—
73D3×C3⋊#261—22no—
74C3⋊D3×#261—22no—
75C2×D3×D13⋊C3—21no—
76C2×D3×D13⋊C3—31no—
77C2×D3×D13⋊C3—31no—
78C2×D3×D13⋊C3—61no—
79C2×D3×D13⋊C3C2×D311yescharacteristic
80C2×C3⋊AGL(1,𝔽13)—21no—
81C2×C3⋊AGL(1,𝔽13)—21no—
82C2×C3⋊AGL(1,𝔽13)—31no—
83C2×C3⋊AGL(1,𝔽13)—31no—
84C2×C3⋊AGL(1,𝔽13)—61no—
85C2×C3⋊AGL(1,𝔽13)—62no—
86C2×C3⋊AGL(1,𝔽13)C2×D311yescharacteristic
87C2×C3⋊AGL(1,𝔽13)C2×D311yescharacteristic
88C2×C3×AGL(1,𝔽13)—21no—
89C2×C3×AGL(1,𝔽13)—21no—
90C2×C3×AGL(1,𝔽13)—21no—
91C2×C3×AGL(1,𝔽13)—31no—
92C2×C3×AGL(1,𝔽13)—31no—
93C2×C3×AGL(1,𝔽13)—41no—
94C2×C3×AGL(1,𝔽13)C2×D311yescharacteristic
95C2×C3×AGL(1,𝔽13)C2×D311yescharacteristic
96D3×AGL(1,𝔽13)—62no—
97D3×AGL(1,𝔽13)—62no—
98D3×AGL(1,𝔽13)—62no—
99D3×AGL(1,𝔽13)—62no—
100D3×AGL(1,𝔽13)—62no—
101#11745538C3×C411yescharacteristic, complemented
102#11745534C3×C411yescharacteristic, complemented
103#11745533C3×C411yescharacteristic, complemented
104C13×#626C3×C411yescharacteristic, complemented
105C3×Dic3×D13C22×C311yescharacteristic
106#64625⋊C3—31no—
107C4⋊(C3⋊(D13⋊C3))—31no—
108#67×C13⋊C3—31no—
109D12×C13⋊C3—31no—
110C3×C4×D13⋊C3—31no—
111#64604⋊C3—31no—
112#64604⋊C3—31no—
113#64603⋊C3—31no—
114#64602⋊C3—31no—
115Dic3×D13⋊C3—21no—
116Dic3×D13⋊C3C2×D311yescharacteristic
117C3×#63881—131nomaximal, Hall
118C2×C32×C13⋊C3C22×C411yescharacteristic
119C3⋊(C3⋊(D13⋊C3))—21no—
120C3⋊D3×C13⋊C3—21no—
121C3×C3⋊(D13⋊C3)—21no—
122C3×D3×C13⋊C3—21no—
123C32×D13⋊C3C2×D411yescharacteristic
124C32×D13⋊C3#4111yescharacteristic
125C22×C3⋊#261—31no—
126C2×D3×#261—31no—
127C2×D3×#261—31no—
128C2×D3×#261—31no—
129C2×D3×#261—61no—
130C22×AGL(1,𝔽13)—91no—
131C22×AGL(1,𝔽13)—91no—
132#67×D13—31no—
133D12×D13—31no—
134C4×C3⋊#261—31no—
135C3×C22⋊#261—31no—
136C3×C4⋊#261—31no—
137D4×D13⋊C3—91no—
138Dic3⋊#261C3×D311yescharacteristic, complemented
139(C2×D3)⋊#261—31no—
140(C2×D3)⋊#261—31no—
141(C2×D3)⋊#261C3×D311yescharacteristic, complemented
142Dic3×#261—31no—
143(C22⋊#261)⋊C3—31no—
144(C22⋊#261)⋊C3—61no—
145(C22⋊#261)⋊C3—91no—
146C4⋊AGL(1,𝔽13)—31no—
147C4⋊AGL(1,𝔽13)—61no—
148C4×AGL(1,𝔽13)—91no—
149C2×C3⋊D39C2×C3×C411yescharacteristic, complemented
150C2×C13×C3⋊D3C2×C3×C411yescharacteristic, complemented
151C2×C3×D39C2×C3×C411yescharacteristic, complemented
152C2×C3×D3×C13C2×C3×C411yescharacteristic, complemented
153C2×C32×D13C23×C311yescharacteristic
154C22×C3×C13⋊C3—31no—
155C3⋊D3×D13—21no—
156C3⋊D3×D13—21no—
157C3×D3×D13—21no—
158C3×D3×D13—21no—
159C3⋊(C3⋊#261)C3×D412yescomplemented
160C3×C3⋊#261—21no—
161C3×C3⋊#261—21no—
162C32×#261—21no—
163C2×C3⋊(D13⋊C3)—21no—
164C2×C3⋊(D13⋊C3)—31no—
165C2×C3⋊(D13⋊C3)—31no—
166C2×C3⋊(D13⋊C3)—61no—
167C2×C3⋊(D13⋊C3)C4×D311yescharacteristic, complemented
168C2×D3×C13⋊C3—21no—
169C2×D3×C13⋊C3—31no—
170C2×D3×C13⋊C3—31no—
171C2×D3×C13⋊C3—61no—
172C2×D3×C13⋊C3C4×D311yescharacteristic, complemented
173C2×C3×D13⋊C3—21no—
174C2×C3×D13⋊C3—21no—
175C2×C3×D13⋊C3—21no—
176C2×C3×D13⋊C3—31no—
177C2×C3×D13⋊C3—41no—
178C2×C3×D13⋊C3—61no—
179C2×C3×D13⋊C3—61no—
180C2×C3×D13⋊C3C22×D311yescharacteristic
181C2×C3×D13⋊C3C22×D311yescharacteristic
182D3×D13⋊C3—21no—
183D3×D13⋊C3—21no—
184D3×D13⋊C3—41no—
185D3×D13⋊C3—41no—
186D3×D13⋊C3—61no—
187D3×D13⋊C3—61no—
188D3×D13⋊C3—61no—
189D3×D13⋊C3—61no—
190D3×D13⋊C3—61no—
191D3×D13⋊C3—61no—
192D3×D13⋊C3—61no—
193D3×D13⋊C3—61no—
194C3⋊AGL(1,𝔽13)—21no—
195C3⋊AGL(1,𝔽13)—21no—
196C3⋊AGL(1,𝔽13)—32no—
197C3⋊AGL(1,𝔽13)—32no—
198C3⋊AGL(1,𝔽13)—41no—
199C3⋊AGL(1,𝔽13)—41no—
200C3⋊AGL(1,𝔽13)—62no—
201C3×AGL(1,𝔽13)—21no—
202C3×AGL(1,𝔽13)—21no—
203C3×AGL(1,𝔽13)—21no—
204C3×AGL(1,𝔽13)—21no—
205C3×AGL(1,𝔽13)—41no—
206C3×AGL(1,𝔽13)—41no—
207C3×AGL(1,𝔽13)—41no—
208C3×AGL(1,𝔽13)—41no—
209C3×AGL(1,𝔽13)—61no—
210C3×AGL(1,𝔽13)—61no—
211C3×Dic39C2×C3×C411yescharacteristic, complemented
212C3×Dic3×C13C2×C3×C411yescharacteristic, complemented
213C3×C4×C13⋊C3—31no—
214C3⋊(Dic13⋊C3)—21no—
215C3⋊(Dic13⋊C3)C4×D311yescharacteristic, complemented
216Dic3×C13⋊C3—21no—
217Dic3×C13⋊C3C4×D311yescharacteristic, complemented
218C3×Dic13⋊C3—31no—
219C2×C3×C4×C3⋊D3—131no—
220C2×C3×#626—131no—
221C2×C3×D3×Dic3—131no—
222C32×(C2×D3)⋊C4—131no—
223C32×Dic3⋊C4—131no—
224C3×#3722—131no—
225C3×Dic32—131no—
226D4×#261—91noHall
227C32×C13⋊C3C4×D411yescharacteristic, complemented, Hall
228C22×C3×D13—31no—
229C2×D3×D13—31no—
230C2×D3×D13—31no—
231C2×D3×D13—61no—
232C2×D3×D13C2×C3×D311yescharacteristic
233C2×C3⋊#261—31no—
234C2×C3⋊#261—31no—
235C2×C3⋊#261—61no—
236C2×C3⋊#261—62no—
237C2×C3⋊#261C2×C3×D311yescharacteristic
238C2×C3⋊#261C2×C3×D311yescharacteristic
239C2×C3×#261—21no—
240C2×C3×#261—31no—
241C2×C3×#261—31no—
242C2×C3×#261C2×C3×D311yescharacteristic
243C2×C3×#261C2×C3×D311yescharacteristic
244C22×D13⋊C3—31no—
245C22×D13⋊C3—61no—
246C22×D13⋊C3—91no—
247D3×#261—62no—
248D3×#261—62no—
249D3×#261—62no—
250D3×#261—62no—
251D3×#261—62no—
252C2×AGL(1,𝔽13)—21no—
253C2×AGL(1,𝔽13)—21no—
254C2×AGL(1,𝔽13)—31no—
255C2×AGL(1,𝔽13)—31no—
256C2×AGL(1,𝔽13)—41no—
257C2×AGL(1,𝔽13)—61no—
258C2×AGL(1,𝔽13)—61no—
259C2×AGL(1,𝔽13)—91no—
260C2×AGL(1,𝔽13)—182no—
261C2×AGL(1,𝔽13)—182no—
262C2×AGL(1,𝔽13)D3211yescharacteristic
263#64625—31no—
264D156—31no—
265C13×#67—31no—
266C13×D12—31no—
267C3×C4×D13—31no—
268D4×C13⋊C3—91no—
269#64604—31no—
270#64604—31no—
271#64603—31no—
272#64602—31no—
273Dic3×D13C2×C3×D311yescharacteristic
274(C22⋊D13)⋊C3—91no—
275(C22⋊D13)⋊C3—91no—
276C4⋊(D13⋊C3)—91no—
277C4×D13⋊C3—31no—
278C4×D13⋊C3—61no—
279C3×#893—391no—
280C3×#67⋊C4—391no—
281#63881—131no—
282C2×C32×C13C22×C3×C411yescharacteristic
283C3⋊D39—21no—
284C13×C3⋊D3—21no—
285C3×D39—21no—
286C3×D3×C13—21no—
287C32×D13C2×C3×D411yescharacteristic
288C32×D13C3×#4111yescharacteristic
289C2×C3×C13⋊C3—21no—
290C2×C3×C13⋊C3—21no—
291C2×C3×C13⋊C3—21no—
292C2×C3×C13⋊C3—41no—
293C2×C3×C13⋊C3—61no—
294C2×C3×C13⋊C3C2×C4×D311yescharacteristic
295C2×C3×C13⋊C3C2×C4×D311yescharacteristic
296C3⋊(D13⋊C3)—21no—
297C3⋊(D13⋊C3)—41no—
298C3⋊(D13⋊C3)—61no—
299C3⋊(D13⋊C3)—61no—
300C3⋊(D13⋊C3)—61no—
301C3⋊(D13⋊C3)—61no—
302D3×C13⋊C3—21no—
303D3×C13⋊C3—41no—
304D3×C13⋊C3—61no—
305D3×C13⋊C3—61no—
306D3×C13⋊C3—61no—
307D3×C13⋊C3—61no—
308C3×D13⋊C3—21no—
309C3×D13⋊C3—21no—
310C3×D13⋊C3—21no—
311C3×D13⋊C3—21no—
312C3×D13⋊C3—21no—
313C3×D13⋊C3—21no—
314C3×D13⋊C3—41no—
315C3×D13⋊C3—41no—
316C3×D13⋊C3—61no—
317C3×D13⋊C3D3×D411yescharacteristic
318C3×D13⋊C3D3×D411yescharacteristic
319C3×D13⋊C3#23711yescharacteristic
320C3×D13⋊C3#23911yescharacteristic
321C22×C3×C3⋊D3—131no—
322C22×C32×D3—131no—
323C2×C33×C4—131no—
324C2×C3×C3⋊Dic3—131no—
325C3×C4×C3⋊D3—262no—
326C2×C32×Dic3—131no—
327C2×C32×Dic3—131no—
328C2×C32×Dic3—131no—
329C3×#626—131no—
330C3×#626—131no—
331C3×#626—131no—
332C3×#626—521no—
333C3×D3×Dic3—262no—
334C22×#261—91no—
335C22×#261—91no—
336D4×D13—91no—
337C22⋊#261—31no—
338C22⋊#261—91no—
339C4⋊#261—31no—
340C4×#261—91no—
341C22×C3×C13—31no—
342C2×D39—31no—
343C2×D39—31no—
344C2×D39—61no—
345C2×D39C3×C4×D311yescharacteristic, complemented
346C2×D3×C13—31no—
347C2×D3×C13—31no—
348C2×D3×C13—61no—
349C2×D3×C13C3×C4×D311yescharacteristic, complemented
350C2×C3×D13—21no—
351C2×C3×D13—31no—
352C2×C3×D13—61no—
353C2×C3×D13—61no—
354C2×C3×D13C22×C3×D311yescharacteristic
355C2×C3×D13C22×C3×D311yescharacteristic
356C22×C13⋊C3—31no—
357C22×C13⋊C3—61no—
358C22×C13⋊C3—91no—
359D3×D13—21no—
360D3×D13—21no—
361D3×D13—61no—
362D3×D13—61no—
363D3×D13—61no—
364D3×D13—61no—
365D3×D13—61no—
366D3×D13—61no—
367D3×D13—61no—
368D3×D13—61no—
369C3⋊#261—21no—
370C3⋊#261—21no—
371C3⋊#261—32no—
372C3⋊#261—32no—
373C3⋊#261—62no—
374C3×#261—21no—
375C3×#261—21no—
376C3×#261—21no—
377C3×#261—21no—
378C3×#261—61no—
379C3×#261—61no—
380C2×D13⋊C3—21no—
381C2×D13⋊C3—21no—
382C2×D13⋊C3—31no—
383C2×D13⋊C3—41no—
384C2×D13⋊C3—61no—
385C2×D13⋊C3—61no—
386C2×D13⋊C3—61no—
387C2×D13⋊C3—91no—
388C2×D13⋊C3—121no—
389C2×D13⋊C3—121no—
390C2×D13⋊C3—181no—
391C2×D13⋊C3—181no—
392C2×D13⋊C3C2×D3211yescharacteristic
393AGL(1,𝔽13)—21no—
394AGL(1,𝔽13)—41no—
395AGL(1,𝔽13)—41no—
396AGL(1,𝔽13)—41no—
397AGL(1,𝔽13)—41no—
398AGL(1,𝔽13)—61no—
399AGL(1,𝔽13)—61no—
400AGL(1,𝔽13)—92no—
401AGL(1,𝔽13)—121no—
402AGL(1,𝔽13)—121no—
403C3×C4×C13—31no—
404Dic39C3×C4×D311yescharacteristic, complemented
405C3×Dic13—31no—
406Dic3×C13C3×C4×D311yescharacteristic, complemented
407C4×C13⋊C3—31no—
408C4×C13⋊C3—61no—
409Dic13⋊C3—31no—
410Dic13⋊C3—61no—
411C2×C4×C3⋊D3—131no—
412C2×C3×#67—391no—
413C22×C3×Dic3—391no—
414C2×C3×D12—391no—
415C2×C3×C4×D3—391no—
416C2×C3×C4×D3—391no—
417C2×C3×C4×D3—391no—
418C2×C3×C4×D3—781no—
419C2×#626—131no—
420C2×D3×Dic3—131no—
421C32×C4⋊C4—391no—
422C32×C22⋊C4—391no—
423C3×(C2×D3)⋊C4—131no—
424C3×(C2×D3)⋊C4—131no—
425C3×(C2×D3)⋊C4—261no—
426C3×(C2×D3)⋊C4—391no—
427C3×(C2×D3)⋊C4—391no—
428C3×Dic3⋊C4—131no—
429C3×Dic3⋊C4—131no—
430C3×Dic3⋊C4—261no—
431C3×C4×Dic3—391no—
432C3×C4×Dic3—391no—
433#3722—131no—
434Dic32—131no—
435C32×C13C3×C4×D411yescharacteristic, complemented
436C3×C13⋊C3—21no—
437C3×C13⋊C3—21no—
438C3×C13⋊C3—21no—
439C3×C13⋊C3—41no—
440C3×C13⋊C3#67⋊C411yescharacteristic, complemented
441C3×C13⋊C3#89311yescharacteristic, complemented
442C22×C33—131no—
443C2×C3×C3⋊D3—131no—
444C2×C3×C3⋊D3—261no—
445C2×C3×C3⋊D3—261no—
446C2×C3×C3⋊D3—521no—
447C2×C32×D3—131no—
448C2×C32×D3—261no—
449C2×C32×D3—261no—
450C2×C32×D3—521no—
451C33×C4—261no—
452C3×C3⋊Dic3—132no—
453C32×Dic3—131no—
454C32×Dic3—261no—
455C32×Dic3—261no—
456C32×Dic3—521no—
457C22×D13—31no—
458C22×D13—91no—
459C2×#261—31no—
460C2×#261—31no—
461C2×#261—91no—
462C2×#261—182no—
463C2×#261—182no—
464C2×#261C3×D3211yescharacteristic
465D4×C13—91no—
466C22⋊D13—91no—
467C22⋊D13—91no—
468D52—91no—
469C4×D13—31no—
470C3×C4×D4—1171no—
471#893—391no—
472#67⋊C4—391no—
473C2×C3×C13—21no—
474C2×C3×C13—61no—
475C2×C3×C13C2×C3×C4×D311yescharacteristic
476C2×C3×C13C2×C3×C4×D311yescharacteristic
477D39—21no—
478D39—61no—
479D39—61no—
480D39—61no—
481D39—61no—
482C3×D13—21no—
483C3×D13—21no—
484C3×D13—61no—
485C3×D13C3×D3×D411yescharacteristic
486C3×D13C3×D3×D411yescharacteristic
487C3×D13C3×#23711yescharacteristic
488C3×D13C3×#23911yescharacteristic
489D3×C13—21no—
490D3×C13—61no—
491D3×C13—61no—
492D3×C13—61no—
493D3×C13—61no—
494C2×C13⋊C3—21no—
495C2×C13⋊C3—21no—
496C2×C13⋊C3—41no—
497C2×C13⋊C3—61no—
498C2×C13⋊C3—121no—
499C2×C13⋊C3—181no—
500C2×C13⋊C3C4×D3211yescharacteristic
501D13⋊C3—21no—
502D13⋊C3—21no—
503D13⋊C3—21no—
504D13⋊C3—21no—
505D13⋊C3—41no—
506D13⋊C3—41no—
507D13⋊C3—61no—
508D13⋊C3—121no—
509D13⋊C3—181no—
510D13⋊C3#379611yescharacteristic
511D13⋊C3#381111yescharacteristic
512C23×C32—391no—
513C22×C3⋊D3—131no—
514C22×C3×D3—131no—
515C22×C3×D3—131no—
516C22×C3×D3—261no—
517C22×C3×D3—391no—
518C22×C3×D3—391no—
519C22×C3×D3—781no—
520C2×C32×C4—131no—
521C2×C32×C4—131no—
522C2×C32×C4—131no—
523C2×C32×C4—261no—
524C2×C32×C4—261no—
525C2×C32×C4—261no—
526C2×C32×C4—391no—
527C2×C32×C4—391no—
528C2×C32×C4—391no—
529C2×C32×C4—521no—
530C2×C3⋊Dic3—131no—
531C4×C3⋊D3—262no—
532C3×#67—391no—
533C3×#67—391no—
534C3×#67—391no—
535C3×#67—1561no—
536C2×C3×Dic3—131no—
537C2×C3×Dic3—131no—
538C2×C3×Dic3—131no—
539C2×C3×Dic3—131no—
540C2×C3×Dic3—131no—
541C2×C3×Dic3—131no—
542C2×C3×Dic3—261no—
543C2×C3×Dic3—261no—
544C2×C3×Dic3—261no—
545C2×C3×Dic3—391no—
546C2×C3×Dic3—391no—
547C2×C3×Dic3—781no—
548C2×C3×Dic3—782no—
549C3×D12—391no—
550C3×D12—391no—
551C3×D12—391no—
552C3×D12—1561no—
553C3×C4×D3—782no—
554C3×C4×D3—782no—
555C3×C4×D3—782no—
556C3×C4×D3—782no—
557C3×C4×D3—782no—
558#626—131no—
559#626—131no—
560#626—131no—
561#626AGL(1,𝔽13)11yescharacteristic, complemented
562D3×Dic3—262no—
563C2×C33—131no—
564C2×C33—131no—
565C2×C33—521no—
566C3×C3⋊D3—261no—
567C3×C3⋊D3—1041no—
568C32×D3—261no—
569C32×D3—1041no—
570C22×C13—31no—
571C22×C13—91no—
572C2×D13—31no—
573C2×D13—61no—
574C2×D13—61no—
575C2×D13—91no—
576C2×D13—181no—
577C2×D13—181no—
578C2×D13C2×C3×D3211yescharacteristic
579#261—21no—
580#261—61no—
581#261—61no—
582#261—92no—
583C4×C13—31no—
584Dic13—31no—
585C2×C3×D4—1171no—
586C22×C3×C4—1171no—
587C22×C3×C4—1171no—
588C2×#67—391no—
589C22×Dic3—391no—
590C2×D12—391no—
591C2×C4×D3—391no—
592C2×C4×D3—391no—
593C2×C4×D3—391no—
594C2×C4×D3—781no—
595C3×C4⋊C4—391no—
596C3×C4⋊C4—391no—
597C3×C4⋊C4—781no—
598C3×C22⋊C4—391no—
599C3×C22⋊C4—391no—
600C3×C22⋊C4—781no—
601C3×C22⋊C4—1171no—
602C3×C42—1171no—
603(C2×D3)⋊C4—131no—
604(C2×D3)⋊C4—391no—
605(C2×D3)⋊C4—391no—
606Dic3⋊C4—131no—
607C4×Dic3—391no—
608C4×Dic3—391no—
609C3×C13—21no—
610C3×C13C3×#67⋊C411yescharacteristic, complemented
611C3×C13C3×#89311yescharacteristic, complemented
612C13⋊C3—21no—
613C13⋊C3—21no—
614C13⋊C3—41no—
615C13⋊C3#6388111yescharacteristic, complemented
616C22×C32—131no—
617C22×C32—131no—
618C22×C32—131no—
619C22×C32—261no—
620C22×C32—261no—
621C22×C32—261no—
622C22×C32—391no—
623C22×C32—521no—
624C22×C32—781no—
625C22×C32—781no—
626C22×C32—1561no—
627C2×C3⋊D3—131no—
628C2×C3⋊D3—261no—
629C2×C3⋊D3—261no—
630C2×C3⋊D3C2×AGL(1,𝔽13)11yescharacteristic, complemented
631C2×C3×D3—131no—
632C2×C3×D3—131no—
633C2×C3×D3—261no—
634C2×C3×D3—261no—
635C2×C3×D3—261no—
636C2×C3×D3—261no—
637C2×C3×D3—261no—
638C2×C3×D3—391no—
639C2×C3×D3—391no—
640C2×C3×D3—521no—
641C2×C3×D3—521no—
642C2×C3×D3—521no—
643C2×C3×D3—3121no—
644C2×C3×D3—781no—
645C2×C3×D3—781no—
646C2×C3×D3—781no—
647C2×C3×D3—781no—
648C2×C3×D3—781no—
649C2×C3×D3—781no—
650C2×C3×D3—781no—
651C2×C3×D3—781no—
652C2×C3×D3—781no—
653C2×C3×D3—1041no—
654C2×C3×D3—1561no—
655C2×C3×D3—1561no—
656C2×C3×D3C2×AGL(1,𝔽13)11yescharacteristic, complemented
657C32×C4—261no—
658C32×C4—261no—
659C32×C4—261no—
660C32×C4—261no—
661C32×C4—261no—
662C32×C4—391no—
663C32×C4—521no—
664C32×C4—521no—
665C32×C4—521no—
666C32×C4—521no—
667C32×C4—781no—
668C32×C4—781no—
669C32×C4—1561no—
670C3⋊Dic3—132no—
671C3×Dic3—131no—
672C3×Dic3—131no—
673C3×Dic3—261no—
674C3×Dic3—261no—
675C3×Dic3—261no—
676C3×Dic3—261no—
677C3×Dic3—261no—
678C3×Dic3—392no—
679C3×Dic3—392no—
680C3×Dic3—521no—
681C3×Dic3—521no—
682C3×Dic3—521no—
683C3×Dic3—782no—
684C3×Dic3—1041no—
685C3×Dic3C2×AGL(1,𝔽13)11yescharacteristic, complemented
686C4×D4—1171noSylow
687C33—521noSylow
688C2×C13—61no—
689C2×C13—181no—
690C2×C13C3×C4×D3211yescharacteristic
691D13—61no—
692D13—181no—
693D13C3×#379611yescharacteristic
694D13C3×#381111yescharacteristic
695C23×C3—391no—
696C23×C3—391no—
697C23×C3—781no—
698C23×C3—1171no—
699C22×D3—131no—
700C22×D3—391no—
701C22×D3—391no—
702C22×D3—781no—
703C3×D4—1171no—
704C3×D4—1171no—
705C3×D4—1171no—
706C3×D4—4681no—
707C2×C3×C4—131no—
708C2×C3×C4—131no—
709C2×C3×C4—131no—
710C2×C3×C4—261no—
711C2×C3×C4—261no—
712C2×C3×C4—261no—
713C2×C3×C4—391no—
714C2×C3×C4—391no—
715C2×C3×C4—391no—
716C2×C3×C4—391no—
717C2×C3×C4—391no—
718C2×C3×C4—391no—
719C2×C3×C4—521no—
720C2×C3×C4—781no—
721C2×C3×C4—781no—
722C2×C3×C4—781no—
723C2×C3×C4—1171no—
724C2×C3×C4—2342no—
725C2×C3×C4—2342no—
726#67—31no—
727#67—391no—
728#67—391no—
729#67—391no—
730C2×Dic3—131no—
731C2×Dic3—131no—
732C2×Dic3—131no—
733C2×Dic3—391no—
734C2×Dic3—391no—
735C2×Dic3—781no—
736C2×Dic3—782no—
737D12—31no—
738D12—391no—
739D12—391no—
740D12—391no—
741C4×D3—782no—
742C4×D3—782no—
743C4×D3—782no—
744C4×D3—782no—
745C4×D3—782no—
746C2×C32—131no—
747C2×C32—131no—
748C2×C32—131no—
749C2×C32—131no—
750C2×C32—131no—
751C2×C32—131no—
752C2×C32—261no—
753C2×C32—261no—
754C2×C32—261no—
755C2×C32—261no—
756C2×C32—261no—
757C2×C32—261no—
758C2×C32—521no—
759C2×C32—521no—
760C2×C32—521no—
761C2×C32—521no—
762C2×C32—3121no—
763C2×C32—781no—
764C2×C32—1041no—
765C2×C32—1041no—
766C2×C32—1041no—
767C2×C32—2081no—
768C2×C32C22×AGL(1,𝔽13)11yescharacteristic
769C3⋊D3—21no—
770C3⋊D3—261no—
771C3×D3—21no—
772C3×D3—261no—
773C3×D3—261no—
774C3×D3—521no—
775C3×D3—3121no—
776C3×D3—3121no—
777C3×D3—3121no—
778C3×D3—3121no—
779C3×D3—781no—
780C3×D3—781no—
781C3×D3—781no—
782C3×D3—781no—
783C3×D3—1041no—
784C3×D3—1041no—
785C2×D4—1171no—
786C22×C4—1171no—
787C22×C4—1171no—
788C4⋊C4—391no—
789C22⋊C4—391no—
790C22⋊C4—1171no—
791C42—1171no—
792C13C3×#6388111yescharacteristic, complemented, Sylow
793C22×C3—31no—
794C22×C3—131no—
795C22×C3—131no—
796C22×C3—131no—
797C22×C3—261no—
798C22×C3—261no—
799C22×C3—261no—
800C22×C3—391no—
801C22×C3—391no—
802C22×C3—521no—
803C22×C3—3121no—
804C22×C3—781no—
805C22×C3—781no—
806C22×C3—781no—
807C22×C3—781no—
808C22×C3—781no—
809C22×C3—1171no—
810C22×C3—1561no—
811C22×C3—1561no—
812C22×C3—1561no—
813C22×C3—4681no—
814C22×C3—2341no—
815C22×C3—2341no—
816C2×D3—31no—
817C2×D3—31no—
818C2×D3—61no—
819C2×D3—131no—
820C2×D3—261no—
821C2×D3—261no—
822C2×D3—391no—
823C2×D3—391no—
824C2×D3—781no—
825C2×D3—781no—
826C2×D3—781no—
827C2×D3—781no—
828C2×D3—781no—
829C2×D3—781no—
830C2×D3—781no—
831C2×D3—781no—
832C2×D3—781no—
833C2×D3D3×AGL(1,𝔽13)11yescharacteristic, complemented
834C3×C4—31no—
835C3×C4—261no—
836C3×C4—261no—
837C3×C4—261no—
838C3×C4—261no—
839C3×C4—261no—
840C3×C4—391no—
841C3×C4—391no—
842C3×C4—521no—
843C3×C4—521no—
844C3×C4—521no—
845C3×C4—521no—
846C3×C4—3121no—
847C3×C4—781no—
848C3×C4—781no—
849C3×C4—781no—
850C3×C4—781no—
851C3×C4—781no—
852C3×C4—1172no—
853C3×C4—1561no—
854C3×C4—1561no—
855C3×C4—1561no—
856Dic3—131no—
857Dic3—261no—
858Dic3—261no—
859Dic3—392no—
860Dic3—392no—
861Dic3—782no—
862Dic3D3×AGL(1,𝔽13)11yescharacteristic, complemented
863C32—521no—
864C32—521no—
865C32—1041no—
866C32—1041no—
867C32—1041no—
868C32—2081no—
869C32D4×AGL(1,𝔽13)11yescharacteristic, complemented
870C23—391no—
871C23—1171no—
872D4—91no—
873D4—1171no—
874D4—1171no—
875D4—1171no—
876C2×C4—131no—
877C2×C4—391no—
878C2×C4—391no—
879C2×C4—391no—
880C2×C4—1171no—
881C2×C4—2342no—
882C2×C4—2342no—
883C2×C3—21no—
884C2×C3—61no—
885C2×C3—131no—
886C2×C3—131no—
887C2×C3—131no—
888C2×C3—131no—
889C2×C3—131no—
890C2×C3—131no—
891C2×C3—261no—
892C2×C3—261no—
893C2×C3—261no—
894C2×C3—261no—
895C2×C3—261no—
896C2×C3—261no—
897C2×C3—521no—
898C2×C3—521no—
899C2×C3—521no—
900C2×C3—3121no—
901C2×C3—3121no—
902C2×C3—781no—
903C2×C3—781no—
904C2×C3—1041no—
905C2×C3—1041no—
906C2×C3—1561no—
907C2×C3—9361no—
908C2×C3—2081no—
909C2×C3—2341no—
910C2×C3C2×D3×AGL(1,𝔽13)11yescharacteristic
911C2×C3C2×D3×AGL(1,𝔽13)11yescharacteristic
912D3—21no—
913D3—61no—
914D3—61no—
915D3—61no—
916D3—61no—
917D3—261no—
918D3—781no—
919D3—781no—
920D3—781no—
921D3—781no—
922C22—31no—
923C22—91no—
924C22—131no—
925C22—391no—
926C22—781no—
927C22—781no—
928C22—1171no—
929C22—2341no—
930C22—2341no—
931C4—31no—
932C4—261no—
933C4—391no—
934C4—781no—
935C4—781no—
936C4—1172no—
937C3—21no—
938C3—521no—
939C3—1041no—
940C3—1041no—
941C3—2081no—
942C3#7224191311yescharacteristic, complemented
943C3#7224192511yescharacteristic, complemented
944C2—61no—
945C2—131no—
946C2—131no—
947C2—181no—
948C2—781no—
949C2—2341no—
950C2D32×AGL(1,𝔽13)11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D32×AGL(1,𝔽13)
commutator, Fitting, socleC2×C32×C13C22×C3×C4
prime radical#626×D13⋊C3C2
cosocleC2×C32×D13C23×C3
hypocenterC32×C13C3×C4×D4
LCSG ▷ C2×C32×C13 ▷ C32×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×(C2×D3)⋊AGL(1,𝔽13)C2semidirect
2. #72242003C2semidirect
3. C3×Dic3⋊AGL(1,𝔽13)C2semidirect
5. #72241984C4semidirect
6. #72241982C4semidirect
7. #72241981C4semidirect
8. C13⋊C3×#626C4semidirect
9. C2×D3×C3⋊AGL(1,𝔽13)C2semidirect
11. Dic3×C3⋊AGL(1,𝔽13)C2semidirect
15. #72241926C3semidirect
18. C2×C3⋊D3×AGL(1,𝔽13)C2semidirect
24. C2×D3×C3⋊#261C2×C3semidirect
25. C2×C3⋊D3×#261C2×C3semidirect
32. #14273015C2×C3semidirect
33. Dic3×C3⋊#261C2×C3semidirect
34. C3×Dic3⋊#261C2×C3semidirect
35. C3×(C2×D3)⋊#261C2×C3semidirect
42. Dic3⋊AGL(1,𝔽13)D3semidirect
46. (C2×D3)⋊AGL(1,𝔽13)D3semidirect
48. C2×C3⋊(C3⋊(D13⋊C3))C2×C4semidirect
49. C2×C3⋊D3×C13⋊C3C2×C4semidirect
50. C2×C3×C3⋊(D13⋊C3)C2×C4semidirect
51. C2×C3×D3×C13⋊C3C2×C4semidirect
57. C3⋊(C3⋊AGL(1,𝔽13))D4semidirect
61. C3×C3⋊(Dic13⋊C3)C2×C4semidirect
62. C3×Dic3×C13⋊C3C2×C4semidirect
101. #11745538C3×C4semidirect
102. #11745534C3×C4semidirect
103. #11745533C3×C4semidirect
104. C13×#626C3×C4semidirect
138. Dic3⋊#261C3×D3semidirect
141. (C2×D3)⋊#261C3×D3semidirect
149. C2×C3⋊D39C2×C3×C4semidirect
150. C2×C13×C3⋊D3C2×C3×C4semidirect
151. C2×C3×D39C2×C3×C4semidirect
152. C2×C3×D3×C13C2×C3×C4semidirect
159. C3⋊(C3⋊#261)C3×D4semidirect
167. C2×C3⋊(D13⋊C3)C4×D3semidirect
172. C2×D3×C13⋊C3C4×D3semidirect
211. C3×Dic39C2×C3×C4semidirect
212. C3×Dic3×C13C2×C3×C4semidirect
215. C3⋊(Dic13⋊C3)C4×D3semidirect
217. Dic3×C13⋊C3C4×D3semidirect
227. C32×C13⋊C3C4×D4semidirect
345. C2×D39C3×C4×D3semidirect
349. C2×D3×C13C3×C4×D3semidirect
404. Dic39C3×C4×D3semidirect
406. Dic3×C13C3×C4×D3semidirect
435. C32×C13C3×C4×D4semidirect
440. C3×C13⋊C3#67⋊C4semidirect
441. C3×C13⋊C3#893semidirect
561. #626AGL(1,𝔽13)semidirect
610. C3×C13C3×#67⋊C4semidirect
611. C3×C13C3×#893semidirect
615. C13⋊C3#63881semidirect
630. C2×C3⋊D3C2×AGL(1,𝔽13)semidirect
656. C2×C3×D3C2×AGL(1,𝔽13)semidirect
685. C3×Dic3C2×AGL(1,𝔽13)semidirect
792. C13C3×#63881semidirect
833. C2×D3D3×AGL(1,𝔽13)semidirect
862. Dic3D3×AGL(1,𝔽13)semidirect
869. C32D4×AGL(1,𝔽13)semidirect
942. C3#72241913semidirect
943. C3#72241925semidirect

Maximal subgroups

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

subgroupindex
C3×(C2×D3)⋊AGL(1,𝔽13)2
#722420032
C3×Dic3⋊AGL(1,𝔽13)2
#626×D13⋊C32
C2×D3×C3⋊AGL(1,𝔽13)2
Dic3×C3⋊AGL(1,𝔽13)2
#722419263
#722419253
#722419133
C2×C3⋊D3×AGL(1,𝔽13)2
C3×#6388113