Finite Group Databasebeta

← #626×AGL(1,𝔽13) #72242016

Subgroups — #626×AGL(1,𝔽13) #72242016

Order 11232.

1060 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72242009C211yesmaximal, characteristic, complemented
2#72242003C211yesmaximal, characteristic, complemented
3#72241998C211yesmaximal, characteristic, complemented
4#626×D13⋊C3C211yesmaximal, characteristic
5#72241984C411yescharacteristic, complemented
6#72241982C411yescharacteristic, complemented
7#72241981C411yescharacteristic, complemented
8C13⋊C3×#626C411yescharacteristic, complemented
9C2×C3×D3×AGL(1,𝔽13)C211yesmaximal, characteristic, complemented
10C2×C3×D3×D13⋊C3C2211yescharacteristic
11C3×Dic3×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#261×#626C311yesmaximal, characteristic, complemented
16D12×AGL(1,𝔽13)—31nomaximal
17#67×AGL(1,𝔽13)—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
22C3×D3×AGL(1,𝔽13)—22no—
23C3⋊D3×AGL(1,𝔽13)—22no—
24C2×C3⋊D3×#261C2×C311yescharacteristic, complemented
25C2×C3×D3×#261C2×C311yescharacteristic, complemented
26C22×C3×AGL(1,𝔽13)—31no—
27C2×D3×AGL(1,𝔽13)—21no—
28C2×D3×AGL(1,𝔽13)—31no—
29C2×D3×AGL(1,𝔽13)—31no—
30C2×D3×AGL(1,𝔽13)—61no—
31C2×D3×AGL(1,𝔽13)D311yescharacteristic, complemented
32D13×#626C2×C311yescharacteristic
33#14273015C2×C311yescharacteristic, complemented
34Dic3⋊(C3⋊#261)C2×C311yescharacteristic, complemented
35(C2×D3)⋊(C3⋊#261)C2×C311yescharacteristic, complemented
36C3×Dic3×#261C2×C311yescharacteristic, complemented
37#67×D13⋊C3—31no—
38D12×D13⋊C3—31no—
39#10597729⋊C3—31no—
40C4⋊(C3⋊AGL(1,𝔽13))—31no—
41C3×C4×AGL(1,𝔽13)—31no—
42Dic3⋊AGL(1,𝔽13)—31no—
43(C2×D3)⋊AGL(1,𝔽13)—31no—
44(C2×D3)⋊AGL(1,𝔽13)—31no—
45(C2×D3)⋊AGL(1,𝔽13)—31no—
46Dic3×AGL(1,𝔽13)—21no—
47Dic3×AGL(1,𝔽13)D311yescharacteristic, complemented
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))—21no—
58C3×C3⋊AGL(1,𝔽13)—21no—
59C3×C3⋊AGL(1,𝔽13)—21no—
60C32×AGL(1,𝔽13)D412yescomplemented
61C3×C3⋊(Dic13⋊C3)C2×C411yescharacteristic, complemented
62C3×Dic3×C13⋊C3C2×C411yescharacteristic, complemented
63#67×#261—31no—
64D12×#261—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—
73C3⋊D3×#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)C2×D311yescharacteristic
86C2×C3⋊AGL(1,𝔽13)C2×D311yescharacteristic
87C2×C3×AGL(1,𝔽13)—21no—
88C2×C3×AGL(1,𝔽13)—21no—
89C2×C3×AGL(1,𝔽13)—21no—
90C2×C3×AGL(1,𝔽13)—31no—
91C2×C3×AGL(1,𝔽13)—31no—
92C2×C3×AGL(1,𝔽13)—41no—
93C2×C3×AGL(1,𝔽13)—62no—
94C2×C3×AGL(1,𝔽13)C2×D311yescharacteristic
95C2×C3×AGL(1,𝔽13)C2×D311yescharacteristic
96D3×AGL(1,𝔽13)—22no—
97D3×AGL(1,𝔽13)—22no—
98D3×AGL(1,𝔽13)—22no—
99D3×AGL(1,𝔽13)—62no—
100D3×AGL(1,𝔽13)—62no—
101D3×AGL(1,𝔽13)—62no—
102D3×AGL(1,𝔽13)—62no—
103#11745538C3×C411yescharacteristic, complemented
104#11745534C3×C411yescharacteristic, complemented
105#11745533C3×C411yescharacteristic, complemented
106C13×#626C3×C411yescharacteristic, complemented
107C3×Dic3×D13C22×C311yescharacteristic
108#64625⋊C3—31no—
109C4⋊(C3⋊(D13⋊C3))—31no—
110#67×C13⋊C3—31no—
111D12×C13⋊C3—31no—
112C3×C4×D13⋊C3—31no—
113#64604⋊C3—31no—
114#64604⋊C3—31no—
115#64603⋊C3—31no—
116#64602⋊C3—31no—
117Dic3×D13⋊C3—21no—
118Dic3×D13⋊C3C2×D311yescharacteristic
119C3×C4×#626—131nomaximal, Hall
120C2×C32×C13⋊C3C22×C411yescharacteristic
121C3⋊(C3⋊(D13⋊C3))—21no—
122C3⋊D3×C13⋊C3—21no—
123C3×C3⋊(D13⋊C3)—21no—
124C3×D3×C13⋊C3—21no—
125C32×D13⋊C3C2×D411yescharacteristic
126C32×D13⋊C3#4111yescharacteristic
127C22×C3×#261—31no—
128C2×D3×#261—31no—
129C2×D3×#261—31no—
130C2×D3×#261—61no—
131C2×D3×#261C3×D311yescharacteristic, complemented
132C22×AGL(1,𝔽13)—31no—
133C22×AGL(1,𝔽13)—61no—
134C22×AGL(1,𝔽13)—91no—
135#67×D13—31no—
136D12×D13—31no—
137#10597729—31no—
138C4⋊(C3⋊#261)—31no—
139C3×C4×#261—31no—
140D4×D13⋊C3—91no—
141Dic3⋊#261—31no—
142(C2×D3)⋊#261—31no—
143(C2×D3)⋊#261—31no—
144(C2×D3)⋊#261—31no—
145Dic3×#261C3×D311yescharacteristic, complemented
146(C22⋊#261)⋊C3—91no—
147(C22⋊#261)⋊C3—91no—
148C4⋊AGL(1,𝔽13)—91no—
149C4×AGL(1,𝔽13)—31no—
150C4×AGL(1,𝔽13)—61no—
151C2×C3⋊D39C2×C3×C411yescharacteristic, complemented
152C2×C13×C3⋊D3C2×C3×C411yescharacteristic, complemented
153C2×C3×D39C2×C3×C411yescharacteristic, complemented
154C2×C3×D3×C13C2×C3×C411yescharacteristic, complemented
155C2×C32×D13C23×C311yescharacteristic
156C22×C3×C13⋊C3—31no—
157C3⋊D3×D13—21no—
158C3⋊D3×D13—21no—
159C3×D3×D13—21no—
160C3×D3×D13—21no—
161C3⋊(C3⋊#261)—21no—
162C3×C3⋊#261—21no—
163C3×C3⋊#261—21no—
164C32×#261C3×D412yescomplemented
165C2×C3⋊(D13⋊C3)—21no—
166C2×C3⋊(D13⋊C3)—31no—
167C2×C3⋊(D13⋊C3)—31no—
168C2×C3⋊(D13⋊C3)—61no—
169C2×C3⋊(D13⋊C3)C4×D311yescharacteristic, complemented
170C2×D3×C13⋊C3—21no—
171C2×D3×C13⋊C3—31no—
172C2×D3×C13⋊C3—31no—
173C2×D3×C13⋊C3—61no—
174C2×D3×C13⋊C3C4×D311yescharacteristic, complemented
175C2×C3×D13⋊C3—21no—
176C2×C3×D13⋊C3—21no—
177C2×C3×D13⋊C3—21no—
178C2×C3×D13⋊C3—31no—
179C2×C3×D13⋊C3—41no—
180C2×C3×D13⋊C3—61no—
181C2×C3×D13⋊C3—61no—
182C2×C3×D13⋊C3C22×D311yescharacteristic
183C2×C3×D13⋊C3C22×D311yescharacteristic
184D3×D13⋊C3—21no—
185D3×D13⋊C3—21no—
186D3×D13⋊C3—21no—
187D3×D13⋊C3—21no—
188D3×D13⋊C3—21no—
189D3×D13⋊C3—21no—
190D3×D13⋊C3—61no—
191D3×D13⋊C3—61no—
192D3×D13⋊C3—61no—
193D3×D13⋊C3—61no—
194D3×D13⋊C3—61no—
195D3×D13⋊C3—61no—
196D3×D13⋊C3—61no—
197D3×D13⋊C3—61no—
198C3⋊AGL(1,𝔽13)—21no—
199C3⋊AGL(1,𝔽13)—21no—
200C3⋊AGL(1,𝔽13)—21no—
201C3⋊AGL(1,𝔽13)—21no—
202C3⋊AGL(1,𝔽13)—21no—
203C3⋊AGL(1,𝔽13)—21no—
204C3⋊AGL(1,𝔽13)—61no—
205C3⋊AGL(1,𝔽13)—61no—
206C3⋊AGL(1,𝔽13)—61no—
207C3⋊AGL(1,𝔽13)—61no—
208C3×AGL(1,𝔽13)—22no—
209C3×AGL(1,𝔽13)—22no—
210C3×AGL(1,𝔽13)—22no—
211C3×AGL(1,𝔽13)—42no—
212C3×AGL(1,𝔽13)—61no—
213C3×AGL(1,𝔽13)—61no—
214C3×AGL(1,𝔽13)D1212yescomplemented
215C3×AGL(1,𝔽13)#6712yescomplemented
216C3×Dic39C2×C3×C411yescharacteristic, complemented
217C3×Dic3×C13C2×C3×C411yescharacteristic, complemented
218C3×C4×C13⋊C3—31no—
219C3⋊(Dic13⋊C3)—21no—
220C3⋊(Dic13⋊C3)C4×D311yescharacteristic, complemented
221Dic3×C13⋊C3—21no—
222Dic3×C13⋊C3C4×D311yescharacteristic, complemented
223C3×Dic13⋊C3—31no—
224C2×C3×C4×C3⋊D3—131no—
225C2×C32×C4×D3—131no—
226C2×C3×#626—131no—
227C32×C4×Dic3—131no—
228C3×Dic3⋊Dic3—131no—
229C3×#3722—131no—
230C3×(C2×D3)⋊Dic3—131no—
231D4×#261—91noHall
232C32×C13⋊C3C4×D411yescharacteristic, complemented, Hall
233C22×C3×D13—31no—
234C2×D3×D13—31no—
235C2×D3×D13—31no—
236C2×D3×D13—61no—
237C2×D3×D13C2×C3×D311yescharacteristic
238C2×C3⋊#261—31no—
239C2×C3⋊#261—31no—
240C2×C3⋊#261—61no—
241C2×C3⋊#261C2×C3×D311yescharacteristic
242C2×C3⋊#261C2×C3×D311yescharacteristic
243C2×C3×#261—21no—
244C2×C3×#261—31no—
245C2×C3×#261—31no—
246C2×C3×#261—62no—
247C2×C3×#261C2×C3×D311yescharacteristic
248C2×C3×#261C2×C3×D311yescharacteristic
249C22×D13⋊C3—31no—
250C22×D13⋊C3—61no—
251C22×D13⋊C3—91no—
252D3×#261—22no—
253D3×#261—62no—
254D3×#261—62no—
255D3×#261—62no—
256D3×#261—62no—
257C2×AGL(1,𝔽13)—21no—
258C2×AGL(1,𝔽13)—21no—
259C2×AGL(1,𝔽13)—31no—
260C2×AGL(1,𝔽13)—31no—
261C2×AGL(1,𝔽13)—41no—
262C2×AGL(1,𝔽13)—61no—
263C2×AGL(1,𝔽13)—61no—
264C2×AGL(1,𝔽13)—62no—
265C2×AGL(1,𝔽13)—62no—
266C2×AGL(1,𝔽13)—62no—
267C2×AGL(1,𝔽13)—91no—
268C2×AGL(1,𝔽13)—182no—
269C2×AGL(1,𝔽13)D3211yescharacteristic
270#64625—31no—
271D156—31no—
272C13×#67—31no—
273C13×D12—31no—
274C3×C4×D13—31no—
275D4×C13⋊C3—91no—
276#64604—31no—
277#64604—31no—
278#64603—31no—
279#64602—31no—
280Dic3×D13C2×C3×D311yescharacteristic
281(C22⋊D13)⋊C3—91no—
282(C22⋊D13)⋊C3—91no—
283C4⋊(D13⋊C3)—91no—
284C4×D13⋊C3—31no—
285C4×D13⋊C3—61no—
286C3×C4×#67—391no—
287C3×C4×D12—391no—
288C4×#626—131no—
289C2×C32×C13C22×C3×C411yescharacteristic
290C3⋊D39—21no—
291C13×C3⋊D3—21no—
292C3×D39—21no—
293C3×D3×C13—21no—
294C32×D13C2×C3×D411yescharacteristic
295C32×D13C3×#4111yescharacteristic
296C2×C3×C13⋊C3—21no—
297C2×C3×C13⋊C3—21no—
298C2×C3×C13⋊C3—21no—
299C2×C3×C13⋊C3—41no—
300C2×C3×C13⋊C3—61no—
301C2×C3×C13⋊C3C2×C4×D311yescharacteristic
302C2×C3×C13⋊C3C2×C4×D311yescharacteristic
303C3⋊(D13⋊C3)—21no—
304C3⋊(D13⋊C3)—21no—
305C3⋊(D13⋊C3)—21no—
306C3⋊(D13⋊C3)—61no—
307C3⋊(D13⋊C3)—61no—
308C3⋊(D13⋊C3)—61no—
309C3⋊(D13⋊C3)—61no—
310D3×C13⋊C3—21no—
311D3×C13⋊C3—21no—
312D3×C13⋊C3—21no—
313D3×C13⋊C3—61no—
314D3×C13⋊C3—61no—
315D3×C13⋊C3—61no—
316D3×C13⋊C3—61no—
317C3×D13⋊C3—21no—
318C3×D13⋊C3—21no—
319C3×D13⋊C3—21no—
320C3×D13⋊C3—21no—
321C3×D13⋊C3—21no—
322C3×D13⋊C3—21no—
323C3×D13⋊C3—41no—
324C3×D13⋊C3—41no—
325C3×D13⋊C3—61no—
326C3×D13⋊C3C2×D1211yescharacteristic
327C3×D13⋊C3#23511yescharacteristic
328C3×D13⋊C3#23511yescharacteristic
329C3×D13⋊C3C2×#6711yescharacteristic
330C22×C3×C3⋊D3—131no—
331C22×C32×D3—131no—
332C2×C33×C4—131no—
333C2×C3×C3⋊Dic3—131no—
334C3×C4×C3⋊D3—262no—
335C2×C32×Dic3—131no—
336C2×C32×Dic3—131no—
337C2×C32×Dic3—131no—
338C32×C4×D3—262no—
339C3×#626—131no—
340C3×#626—131no—
341C3×#626—131no—
342C3×#626—521no—
343C22×#261—31no—
344C22×#261—91no—
345D4×D13—91no—
346C22⋊#261—91no—
347C22⋊#261—91no—
348C4⋊#261—91no—
349C4×#261—31no—
350C22×C3×C13—31no—
351C2×D39—31no—
352C2×D39—31no—
353C2×D39—61no—
354C2×D39C3×C4×D311yescharacteristic, complemented
355C2×D3×C13—31no—
356C2×D3×C13—31no—
357C2×D3×C13—61no—
358C2×D3×C13C3×C4×D311yescharacteristic, complemented
359C2×C3×D13—21no—
360C2×C3×D13—31no—
361C2×C3×D13—61no—
362C2×C3×D13—61no—
363C2×C3×D13C22×C3×D311yescharacteristic
364C2×C3×D13C22×C3×D311yescharacteristic
365C22×C13⋊C3—31no—
366C22×C13⋊C3—61no—
367C22×C13⋊C3—91no—
368D3×D13—21no—
369D3×D13—21no—
370D3×D13—61no—
371D3×D13—61no—
372D3×D13—61no—
373D3×D13—61no—
374D3×D13—61no—
375D3×D13—61no—
376D3×D13—61no—
377D3×D13—61no—
378C3⋊#261—21no—
379C3⋊#261—21no—
380C3⋊#261—61no—
381C3⋊#261—61no—
382C3⋊#261—61no—
383C3⋊#261—61no—
384C3×#261—22no—
385C3×#261—61no—
386C3×#261—61no—
387C3×#261C3×D1212yescomplemented
388C3×#261C3×#6712yescomplemented
389C2×D13⋊C3—21no—
390C2×D13⋊C3—21no—
391C2×D13⋊C3—31no—
392C2×D13⋊C3—41no—
393C2×D13⋊C3—61no—
394C2×D13⋊C3—61no—
395C2×D13⋊C3—61no—
396C2×D13⋊C3—61no—
397C2×D13⋊C3—61no—
398C2×D13⋊C3—61no—
399C2×D13⋊C3—61no—
400C2×D13⋊C3—91no—
401C2×D13⋊C3—181no—
402C2×D13⋊C3—181no—
403C2×D13⋊C3C2×D3211yescharacteristic
404AGL(1,𝔽13)—22no—
405AGL(1,𝔽13)—22no—
406AGL(1,𝔽13)—42no—
407AGL(1,𝔽13)—61no—
408AGL(1,𝔽13)—61no—
409AGL(1,𝔽13)—61no—
410AGL(1,𝔽13)—61no—
411AGL(1,𝔽13)—61no—
412AGL(1,𝔽13)—61no—
413AGL(1,𝔽13)—181no—
414AGL(1,𝔽13)#62612yesdirect product factor
415C3×C4×C13—31no—
416Dic39C3×C4×D311yescharacteristic, complemented
417C3×Dic13—31no—
418Dic3×C13C3×C4×D311yescharacteristic, complemented
419C4×C13⋊C3—31no—
420C4×C13⋊C3—61no—
421Dic13⋊C3—31no—
422Dic13⋊C3—61no—
423C22×C32×C4—391no—
424C2×C4×C3⋊D3—131no—
425C2×C3×#67—391no—
426C2×C3×D12—391no—
427C2×C3×C4×D3—131no—
428C2×C3×C4×D3—131no—
429C2×C3×C4×D3—261no—
430C2×C3×C4×D3—391no—
431C2×C3×C4×D3—391no—
432C2×C3×C4×D3—781no—
433C2×#626—131no—
434C32×C42—391no—
435C3×#217—391no—
436C3×(C2×D3)⋊C4—391no—
437C3×(C2×D3)⋊C4—391no—
438C3×(C2×D3)⋊C4—391no—
439C3×C4⋊Dic3—391no—
440C3×Dic3⋊C4—391no—
441C3×C4×Dic3—131no—
442C3×C4×Dic3—131no—
443C3×C4×Dic3—261no—
444Dic3⋊Dic3—131no—
445#3722—131no—
446(C2×D3)⋊Dic3—131no—
447C32×C13C3×C4×D411yescharacteristic, complemented
448C3×C13⋊C3—21no—
449C3×C13⋊C3—21no—
450C3×C13⋊C3—21no—
451C3×C13⋊C3—41no—
452C3×C13⋊C3C4×D1211yescharacteristic, complemented
453C3×C13⋊C3C4×#6711yescharacteristic, complemented
454C22×C33—131no—
455C2×C3×C3⋊D3—131no—
456C2×C3×C3⋊D3—261no—
457C2×C3×C3⋊D3—261no—
458C2×C3×C3⋊D3—521no—
459C2×C32×D3—131no—
460C2×C32×D3—261no—
461C2×C32×D3—261no—
462C2×C32×D3—521no—
463C33×C4—132no—
464C3×C3⋊Dic3—261no—
465C32×Dic3—131no—
466C32×Dic3—261no—
467C32×Dic3—261no—
468C32×Dic3—521no—
469C22×D13—31no—
470C22×D13—91no—
471C2×#261—31no—
472C2×#261—31no—
473C2×#261—62no—
474C2×#261—91no—
475C2×#261—182no—
476C2×#261C3×D3211yescharacteristic
477D4×C13—91no—
478C22⋊D13—91no—
479C22⋊D13—91no—
480D52—91no—
481C4×D13—31no—
482C3×C4×D4—1171no—
483C4×#67—391no—
484C4×D12—391no—
485C2×C3×C13—21no—
486C2×C3×C13—61no—
487C2×C3×C13C2×C3×C4×D311yescharacteristic
488C2×C3×C13C2×C3×C4×D311yescharacteristic
489D39—21no—
490D39—61no—
491D39—61no—
492D39—61no—
493D39—61no—
494C3×D13—21no—
495C3×D13—21no—
496C3×D13—61no—
497C3×D13C2×C3×D1211yescharacteristic
498C3×D13C3×#23511yescharacteristic
499C3×D13C3×#23511yescharacteristic
500C3×D13C2×C3×#6711yescharacteristic
501D3×C13—21no—
502D3×C13—61no—
503D3×C13—61no—
504D3×C13—61no—
505D3×C13—61no—
506C2×C13⋊C3—21no—
507C2×C13⋊C3—21no—
508C2×C13⋊C3—41no—
509C2×C13⋊C3—61no—
510C2×C13⋊C3—61no—
511C2×C13⋊C3—61no—
512C2×C13⋊C3—181no—
513C2×C13⋊C3C4×D3211yescharacteristic
514D13⋊C3—21no—
515D13⋊C3—21no—
516D13⋊C3—21no—
517D13⋊C3—21no—
518D13⋊C3—41no—
519D13⋊C3—41no—
520D13⋊C3—61no—
521D13⋊C3—61no—
522D13⋊C3—61no—
523D13⋊C3—181no—
524D13⋊C3#379811yescharacteristic
525D13⋊C3C2×#62611yescharacteristic
526C23×C32—391no—
527C22×C3⋊D3—131no—
528C22×C3×D3—131no—
529C22×C3×D3—131no—
530C22×C3×D3—261no—
531C22×C3×D3—391no—
532C22×C3×D3—391no—
533C22×C3×D3—781no—
534C2×C32×C4—131no—
535C2×C32×C4—131no—
536C2×C32×C4—131no—
537C2×C32×C4—261no—
538C2×C32×C4—261no—
539C2×C32×C4—261no—
540C2×C32×C4—391no—
541C2×C32×C4—391no—
542C2×C32×C4—391no—
543C2×C32×C4—521no—
544C2×C32×C4—782no—
545C2×C3⋊Dic3—131no—
546C4×C3⋊D3—262no—
547C3×#67—391no—
548C3×#67—391no—
549C3×#67—391no—
550C3×#67—1561no—
551C2×C3×Dic3—131no—
552C2×C3×Dic3—131no—
553C2×C3×Dic3—131no—
554C2×C3×Dic3—131no—
555C2×C3×Dic3—131no—
556C2×C3×Dic3—131no—
557C2×C3×Dic3—261no—
558C2×C3×Dic3—261no—
559C2×C3×Dic3—261no—
560C2×C3×Dic3—391no—
561C2×C3×Dic3—391no—
562C2×C3×Dic3—781no—
563C3×D12—391no—
564C3×D12—391no—
565C3×D12—391no—
566C3×D12—1561no—
567C3×C4×D3—262no—
568C3×C4×D3—262no—
569C3×C4×D3—262no—
570C3×C4×D3—262no—
571C3×C4×D3—782no—
572C3×C4×D3—782no—
573C3×C4×D3—782no—
574C3×C4×D3—782no—
575#626—131no—
576#626—131no—
577#626—131no—
578#626AGL(1,𝔽13)11yescharacteristic, direct product factor
579C2×C33—131no—
580C2×C33—131no—
581C2×C33—521no—
582C3×C3⋊D3—261no—
583C3×C3⋊D3—1041no—
584C32×D3—261no—
585C32×D3—1041no—
586C22×C13—31no—
587C22×C13—91no—
588C2×D13—31no—
589C2×D13—61no—
590C2×D13—61no—
591C2×D13—91no—
592C2×D13—181no—
593C2×D13—181no—
594C2×D13C2×C3×D3211yescharacteristic
595#261—61no—
596#261—61no—
597#261—181no—
598#261C3×#62612yescomplemented
599C4×C13—31no—
600Dic13—31no—
601C2×C3×D4—1171no—
602C22×C3×C4—391no—
603C22×C3×C4—391no—
604C22×C3×C4—781no—
605C22×C3×C4—1171no—
606C2×#67—391no—
607C2×D12—391no—
608C2×C4×D3—131no—
609C2×C4×D3—391no—
610C2×C4×D3—391no—
611C2×C4×D3—781no—
612C3×C4⋊C4—1171no—
613C3×C22⋊C4—1171no—
614C3×C22⋊C4—1171no—
615C3×C42—391no—
616C3×C42—391no—
617C3×C42—781no—
618#217—391no—
619(C2×D3)⋊C4—391no—
620(C2×D3)⋊C4—391no—
621(C2×D3)⋊C4—391no—
622C4⋊Dic3—391no—
623Dic3⋊C4—391no—
624C4×Dic3—131no—
625C3×C13—21no—
626C3×C13C3×C4×D1211yescharacteristic, complemented
627C3×C13C3×C4×#6711yescharacteristic, complemented
628C13⋊C3—21no—
629C13⋊C3—21no—
630C13⋊C3—41no—
631C13⋊C3C4×#62611yescharacteristic, complemented
632C22×C32—131no—
633C22×C32—131no—
634C22×C32—131no—
635C22×C32—261no—
636C22×C32—261no—
637C22×C32—261no—
638C22×C32—391no—
639C22×C32—521no—
640C22×C32—781no—
641C22×C32—781no—
642C22×C32—1561no—
643C2×C3⋊D3—131no—
644C2×C3⋊D3—261no—
645C2×C3⋊D3—261no—
646C2×C3⋊D3C2×AGL(1,𝔽13)11yescharacteristic, complemented
647C2×C3×D3—131no—
648C2×C3×D3—131no—
649C2×C3×D3—261no—
650C2×C3×D3—261no—
651C2×C3×D3—261no—
652C2×C3×D3—261no—
653C2×C3×D3—261no—
654C2×C3×D3—261no—
655C2×C3×D3—261no—
656C2×C3×D3—261no—
657C2×C3×D3—261no—
658C2×C3×D3—391no—
659C2×C3×D3—391no—
660C2×C3×D3—521no—
661C2×C3×D3—3121no—
662C2×C3×D3—781no—
663C2×C3×D3—781no—
664C2×C3×D3—781no—
665C2×C3×D3—781no—
666C2×C3×D3—781no—
667C2×C3×D3—781no—
668C2×C3×D3—781no—
669C2×C3×D3—781no—
670C2×C3×D3—781no—
671C2×C3×D3—1041no—
672C2×C3×D3—1561no—
673C2×C3×D3—1561no—
674C2×C3×D3C2×AGL(1,𝔽13)11yescharacteristic, complemented
675C32×C4—132no—
676C32×C4—132no—
677C32×C4—132no—
678C32×C4—262no—
679C32×C4—262no—
680C32×C4—262no—
681C32×C4—391no—
682C32×C4—522no—
683C32×C4—781no—
684C32×C4—781no—
685C32×C4—1561no—
686C3⋊Dic3—261no—
687C3×Dic3—131no—
688C3×Dic3—131no—
689C3×Dic3—261no—
690C3×Dic3—261no—
691C3×Dic3—261no—
692C3×Dic3—261no—
693C3×Dic3—261no—
694C3×Dic3—261no—
695C3×Dic3—261no—
696C3×Dic3—261no—
697C3×Dic3—261no—
698C3×Dic3—521no—
699C3×Dic3—781no—
700C3×Dic3—781no—
701C3×Dic3—781no—
702C3×Dic3—781no—
703C3×Dic3—1041no—
704C3×Dic3C2×AGL(1,𝔽13)11yescharacteristic, complemented
705C4×D4—1171noSylow
706C33—521noSylow
707C2×C13—61no—
708C2×C13—181no—
709C2×C13C3×C4×D3211yescharacteristic
710D13—61no—
711D13—181no—
712D13C3×#379811yescharacteristic
713D13C2×C3×#62611yescharacteristic
714C23×C3—391no—
715C23×C3—391no—
716C23×C3—781no—
717C23×C3—1171no—
718C22×D3—131no—
719C22×D3—391no—
720C22×D3—391no—
721C22×D3—781no—
722C3×D4—1171no—
723C3×D4—1171no—
724C3×D4—1171no—
725C3×D4—4681no—
726C2×C3×C4—131no—
727C2×C3×C4—131no—
728C2×C3×C4—131no—
729C2×C3×C4—261no—
730C2×C3×C4—261no—
731C2×C3×C4—261no—
732C2×C3×C4—391no—
733C2×C3×C4—391no—
734C2×C3×C4—391no—
735C2×C3×C4—391no—
736C2×C3×C4—391no—
737C2×C3×C4—391no—
738C2×C3×C4—521no—
739C2×C3×C4—781no—
740C2×C3×C4—781no—
741C2×C3×C4—781no—
742C2×C3×C4—782no—
743C2×C3×C4—782no—
744C2×C3×C4—782no—
745C2×C3×C4—782no—
746C2×C3×C4—1171no—
747C2×C3×C4—2342no—
748#67—31no—
749#67—391no—
750#67—391no—
751#67—391no—
752C2×Dic3—131no—
753C2×Dic3—131no—
754C2×Dic3—131no—
755C2×Dic3—391no—
756C2×Dic3—391no—
757C2×Dic3—781no—
758D12—31no—
759D12—391no—
760D12—391no—
761D12—391no—
762C4×D3—262no—
763C4×D3—782no—
764C4×D3—782no—
765C4×D3—782no—
766C4×D3—782no—
767C2×C32—131no—
768C2×C32—131no—
769C2×C32—131no—
770C2×C32—131no—
771C2×C32—131no—
772C2×C32—131no—
773C2×C32—261no—
774C2×C32—261no—
775C2×C32—261no—
776C2×C32—261no—
777C2×C32—261no—
778C2×C32—261no—
779C2×C32—521no—
780C2×C32—521no—
781C2×C32—521no—
782C2×C32—521no—
783C2×C32—3121no—
784C2×C32—781no—
785C2×C32—1041no—
786C2×C32—1041no—
787C2×C32—1041no—
788C2×C32—2081no—
789C2×C32C22×AGL(1,𝔽13)11yescharacteristic
790C3⋊D3—21no—
791C3⋊D3—261no—
792C3×D3—21no—
793C3×D3—261no—
794C3×D3—261no—
795C3×D3—261no—
796C3×D3—261no—
797C3×D3—261no—
798C3×D3—3121no—
799C3×D3—3121no—
800C3×D3—3121no—
801C3×D3—3121no—
802C3×D3—781no—
803C3×D3—781no—
804C3×D3—781no—
805C3×D3—781no—
806C3×D3—1041no—
807C3×D3—1041no—
808C2×D4—1171no—
809C22×C4—391no—
810C22×C4—1171no—
811C4⋊C4—1171no—
812C22⋊C4—1171no—
813C22⋊C4—1171no—
814C42—391no—
815C13C3×C4×#62611yescharacteristic, complemented, Sylow
816C22×C3—31no—
817C22×C3—131no—
818C22×C3—131no—
819C22×C3—131no—
820C22×C3—261no—
821C22×C3—261no—
822C22×C3—261no—
823C22×C3—391no—
824C22×C3—391no—
825C22×C3—521no—
826C22×C3—3121no—
827C22×C3—781no—
828C22×C3—781no—
829C22×C3—781no—
830C22×C3—781no—
831C22×C3—781no—
832C22×C3—781no—
833C22×C3—781no—
834C22×C3—781no—
835C22×C3—781no—
836C22×C3—1171no—
837C22×C3—1561no—
838C22×C3—4681no—
839C22×C3—2341no—
840C22×C3—2341no—
841C2×D3—31no—
842C2×D3—31no—
843C2×D3—61no—
844C2×D3—131no—
845C2×D3—261no—
846C2×D3—261no—
847C2×D3—391no—
848C2×D3—391no—
849C2×D3—781no—
850C2×D3—781no—
851C2×D3—781no—
852C2×D3—781no—
853C2×D3—781no—
854C2×D3—781no—
855C2×D3—781no—
856C2×D3—781no—
857C2×D3—781no—
858C2×D3D3×AGL(1,𝔽13)11yescharacteristic, complemented
859C3×C4—31no—
860C3×C4—132no—
861C3×C4—132no—
862C3×C4—132no—
863C3×C4—262no—
864C3×C4—262no—
865C3×C4—262no—
866C3×C4—391no—
867C3×C4—391no—
868C3×C4—522no—
869C3×C4—3121no—
870C3×C4—781no—
871C3×C4—781no—
872C3×C4—781no—
873C3×C4—781no—
874C3×C4—781no—
875C3×C4—781no—
876C3×C4—781no—
877C3×C4—781no—
878C3×C4—781no—
879C3×C4—1561no—
880C3×C4—2341no—
881Dic3—131no—
882Dic3—261no—
883Dic3—261no—
884Dic3—781no—
885Dic3—781no—
886Dic3—781no—
887Dic3—781no—
888Dic3D3×AGL(1,𝔽13)11yescharacteristic, complemented
889C32—521no—
890C32—521no—
891C32—1041no—
892C32—1041no—
893C32—1041no—
894C32—2081no—
895C32D4×AGL(1,𝔽13)11yescharacteristic, complemented
896C23—391no—
897C23—1171no—
898D4—91no—
899D4—1171no—
900D4—1171no—
901D4—1171no—
902C2×C4—131no—
903C2×C4—391no—
904C2×C4—391no—
905C2×C4—391no—
906C2×C4—782no—
907C2×C4—1171no—
908C2×C4—2342no—
909C2×C3—21no—
910C2×C3—61no—
911C2×C3—131no—
912C2×C3—131no—
913C2×C3—131no—
914C2×C3—131no—
915C2×C3—131no—
916C2×C3—131no—
917C2×C3—261no—
918C2×C3—261no—
919C2×C3—261no—
920C2×C3—261no—
921C2×C3—261no—
922C2×C3—261no—
923C2×C3—521no—
924C2×C3—521no—
925C2×C3—521no—
926C2×C3—3121no—
927C2×C3—3121no—
928C2×C3—3121no—
929C2×C3—781no—
930C2×C3—781no—
931C2×C3—781no—
932C2×C3—781no—
933C2×C3—1041no—
934C2×C3—1041no—
935C2×C3—9361no—
936C2×C3—2081no—
937C2×C3—2341no—
938C2×C3C2×D3×AGL(1,𝔽13)11yescharacteristic
939C2×C3C2×D3×AGL(1,𝔽13)11yescharacteristic
940D3—21no—
941D3—61no—
942D3—61no—
943D3—61no—
944D3—61no—
945D3—261no—
946D3—781no—
947D3—781no—
948D3—781no—
949D3—781no—
950C22—31no—
951C22—91no—
952C22—131no—
953C22—391no—
954C22—781no—
955C22—781no—
956C22—1171no—
957C22—2341no—
958C22—2341no—
959C4—31no—
960C4—132no—
961C4—391no—
962C4—781no—
963C4—781no—
964C4—2341no—
965C3—21no—
966C3—521no—
967C3—1041no—
968C3—1041no—
969C3—2081no—
970C3#67×AGL(1,𝔽13)11yescharacteristic, complemented
971C3D12×AGL(1,𝔽13)11yescharacteristic, complemented
972C2—61no—
973C2—131no—
974C2—131no—
975C2—181no—
976C2—781no—
977C2—2341no—
978C2D32×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. #72242009C2semidirect
2. #72242003C2semidirect
3. #72241998C2semidirect
5. #72241984C4semidirect
6. #72241982C4semidirect
7. #72241981C4semidirect
8. C13⋊C3×#626C4semidirect
9. C2×C3×D3×AGL(1,𝔽13)C2semidirect
11. C3×Dic3×AGL(1,𝔽13)C2semidirect
15. #261×#626C3semidirect
18. C2×C3⋊D3×AGL(1,𝔽13)C2semidirect
24. C2×C3⋊D3×#261C2×C3semidirect
25. C2×C3×D3×#261C2×C3semidirect
31. C2×D3×AGL(1,𝔽13)D3semidirect
33. #14273015C2×C3semidirect
34. Dic3⋊(C3⋊#261)C2×C3semidirect
35. (C2×D3)⋊(C3⋊#261)C2×C3semidirect
36. C3×Dic3×#261C2×C3semidirect
47. Dic3×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
60. C32×AGL(1,𝔽13)D4semidirect
61. C3×C3⋊(Dic13⋊C3)C2×C4semidirect
62. C3×Dic3×C13⋊C3C2×C4semidirect
103. #11745538C3×C4semidirect
104. #11745534C3×C4semidirect
105. #11745533C3×C4semidirect
106. C13×#626C3×C4semidirect
131. C2×D3×#261C3×D3semidirect
145. Dic3×#261C3×D3semidirect
151. C2×C3⋊D39C2×C3×C4semidirect
152. C2×C13×C3⋊D3C2×C3×C4semidirect
153. C2×C3×D39C2×C3×C4semidirect
154. C2×C3×D3×C13C2×C3×C4semidirect
164. C32×#261C3×D4semidirect
169. C2×C3⋊(D13⋊C3)C4×D3semidirect
174. C2×D3×C13⋊C3C4×D3semidirect
214. C3×AGL(1,𝔽13)D12semidirect
215. C3×AGL(1,𝔽13)#67semidirect
216. C3×Dic39C2×C3×C4semidirect
217. C3×Dic3×C13C2×C3×C4semidirect
220. C3⋊(Dic13⋊C3)C4×D3semidirect
222. Dic3×C13⋊C3C4×D3semidirect
232. C32×C13⋊C3C4×D4semidirect
354. C2×D39C3×C4×D3semidirect
358. C2×D3×C13C3×C4×D3semidirect
387. C3×#261C3×D12semidirect
388. C3×#261C3×#67semidirect
414. AGL(1,𝔽13)#626direct (N × H)
416. Dic39C3×C4×D3semidirect
418. Dic3×C13C3×C4×D3semidirect
447. C32×C13C3×C4×D4semidirect
452. C3×C13⋊C3C4×D12semidirect
453. C3×C13⋊C3C4×#67semidirect
578. #626AGL(1,𝔽13)direct (N × H)
598. #261C3×#626semidirect
626. C3×C13C3×C4×D12semidirect
627. C3×C13C3×C4×#67semidirect
631. C13⋊C3C4×#626semidirect
646. C2×C3⋊D3C2×AGL(1,𝔽13)semidirect
674. C2×C3×D3C2×AGL(1,𝔽13)semidirect
704. C3×Dic3C2×AGL(1,𝔽13)semidirect
815. C13C3×C4×#626semidirect
858. C2×D3D3×AGL(1,𝔽13)semidirect
888. Dic3D3×AGL(1,𝔽13)semidirect
895. C32D4×AGL(1,𝔽13)semidirect
970. C3#67×AGL(1,𝔽13)semidirect
971. C3D12×AGL(1,𝔽13)semidirect

Maximal subgroups

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

subgroupindex
#722420092
#722420032
#722419982
#626×D13⋊C32
C2×C3×D3×AGL(1,𝔽13)2
C3×Dic3×AGL(1,𝔽13)2
#261×#6263
D12×AGL(1,𝔽13)3
#67×AGL(1,𝔽13)3
C2×C3⋊D3×AGL(1,𝔽13)2
C3×C4×#62613