Finite Group Databasebeta

← #72242011

Subgroups — #72242011

Order 11232.

1332 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 1332 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72242009C212yesmaximal, complemented
2C3×(C2×D3)⋊AGL(1,𝔽13)C212yesmaximal, complemented
3C2×D32×D13⋊C3C211yesmaximal, characteristic
4C2×(C3⋊(D13⋊C3))⋊D3C411yescharacteristic, complemented
5C2×D3×C3⋊(D13⋊C3)C412yescomplemented
6C2×D32×C13⋊C3C411yescharacteristic, complemented
7C2×C3×D3×D13⋊C3C2212yes—
8C2×#72220635C211yesmaximal, characteristic, complemented
9C2×C3×C3⋊AGL(1,𝔽13)C2212yescomplemented
10#72241914C311yesmaximal, characteristic, complemented
11D3×(C22⋊#261)⋊C3—32nomaximal
12C2×C3⋊D3×AGL(1,𝔽13)C211yesmaximal, characteristic, complemented
13C2×C3⋊(C3⋊AGL(1,𝔽13))C2211yescharacteristic, complemented
14C2×C32×AGL(1,𝔽13)C2211yescharacteristic, complemented
15C2×C3⋊D3×D13⋊C3C2211yescharacteristic
16#72220635—22no—
17D32×D13⋊C3—22no—
18D32×D13⋊C3—22no—
19C3⋊D3×AGL(1,𝔽13)—22no—
20C2×D32×D13C2×C311yescharacteristic
21C2×(C3⋊#261)⋊D3C2×C311yescharacteristic, complemented
22C2×C3⋊D3×#261C2×C311yescharacteristic, complemented
23C22×D3×D13⋊C3—32no—
24C2×D3×AGL(1,𝔽13)—32no—
25C2×D3×AGL(1,𝔽13)—32no—
26C2×D3×AGL(1,𝔽13)—61no—
27(C2×D3)⋊(C3⋊#261)C2×C312yescomplemented
28C3×(C2×D3)⋊#261C2×C312yescomplemented
29#10597729⋊C3—32no—
30C3×(C22⋊#261)⋊C3—32no—
31(C2×D3)⋊AGL(1,𝔽13)—22no—
32(C2×D3)⋊AGL(1,𝔽13)—32no—
33(C2×D3)⋊AGL(1,𝔽13)D312yescomplemented
34C2×C3⋊(C3⋊(D13⋊C3))C2×C411yescharacteristic
35C2×C3⋊D3×C13⋊C3C2×C411yescharacteristic
36C2×C3×C3⋊(D13⋊C3)C2×C412yescomplemented
37C2×C3×D3×C13⋊C3C2×C412yescomplemented
38C2×C32×D13⋊C3C2311yescharacteristic
39(C3⋊(D13⋊C3))⋊D3—22no—
40D3×C3⋊(D13⋊C3)—24no—
41D32×C13⋊C3—22no—
42C3⋊D3×D13⋊C3D412yes—
43C3⋊D3×D13⋊C3D412yes—
44C3×D3×D13⋊C3—22no—
45C3×D3×D13⋊C3—22no—
46C3⋊(C3⋊AGL(1,𝔽13))—21no—
47C3×C3⋊AGL(1,𝔽13)—22no—
48C32×AGL(1,𝔽13)—21no—
49D3×C22⋊#261—32no—
50C2×(C22⋊#261)⋊C3—91no—
51C2×(C3⋊D3)⋊D13C3×C411yescharacteristic, complemented
52C2×D3×D39C3×C412yescomplemented
53C2×D32×C13C3×C411yescharacteristic, complemented
54C2×C3⋊D3×D13C22×C311yescharacteristic
55C2×C3×D3×D13C22×C312yes—
56C2×C3⋊(C3⋊#261)C22×C311yescharacteristic, complemented
57C2×C3×C3⋊#261C22×C312yescomplemented
58C2×C32×#261C22×C311yescharacteristic, complemented
59C22×C3⋊(D13⋊C3)—32no—
60C22×D3×C13⋊C3—32no—
61C22×C3×D13⋊C3—32no—
62D32×D13—22no—
63D32×D13—22no—
64(C3⋊#261)⋊D3—22no—
65C3⋊D3×#261—22no—
66C2×D3×D13⋊C3—22no—
67C2×D3×D13⋊C3—32no—
68C2×D3×D13⋊C3—32no—
69C2×D3×D13⋊C3—32no—
70C2×D3×D13⋊C3—61no—
71C2×D3×D13⋊C3—64no—
72C2×D3×D13⋊C3—64no—
73C2×D3×D13⋊C3C2×D312yes—
74C2×C3⋊AGL(1,𝔽13)—22no—
75C2×C3⋊AGL(1,𝔽13)—32no—
76C2×C3⋊AGL(1,𝔽13)—61no—
77C2×C3⋊AGL(1,𝔽13)C2×D312yescomplemented
78C2×C3×AGL(1,𝔽13)—22no—
79C2×C3×AGL(1,𝔽13)—21no—
80C2×C3×AGL(1,𝔽13)—32no—
81C2×C3×AGL(1,𝔽13)—41no—
82C2×C3×AGL(1,𝔽13)C2×D312yescomplemented
83D3×AGL(1,𝔽13)—64no—
84D3×AGL(1,𝔽13)—62no—
85D3×AGL(1,𝔽13)—62no—
86D3×AGL(1,𝔽13)—64no—
87C3×#63921—131nomaximal, Hall
88C2×C32×C13⋊C3C22×C411yescharacteristic
89C3⋊(C3⋊(D13⋊C3))C22⋊C412yescomplemented
90C3⋊D3×C13⋊C3C22⋊C412yescomplemented
91C3×C3⋊(D13⋊C3)—22no—
92C3×D3×C13⋊C3—22no—
93C32×D13⋊C3C2×D411yescharacteristic
94C32×D13⋊C3C2×D411yescharacteristic
95C22×D3×D13—32no—
96C23×D13⋊C3—91no—
97C2×D3×#261—32no—
98C2×D3×#261—32no—
99C2×D3×#261—61no—
100C22×AGL(1,𝔽13)—91no—
101C22×AGL(1,𝔽13)—91no—
102#10597729—32no—
103C3×C22⋊#261—32no—
104(C2×D3)⋊#261—32no—
105(C2×D3)⋊#261C3×D312yescomplemented
106(C22⋊#261)⋊C3—32no—
107(C22⋊#261)⋊C3—62no—
108(C22⋊#261)⋊C3—92no—
109C2×C3⋊D39C2×C3×C411yescharacteristic
110C2×C13×C3⋊D3C2×C3×C411yescharacteristic
111C2×C3×D39C2×C3×C412yescomplemented
112C2×C3×D3×C13C2×C3×C412yescomplemented
113C2×C32×D13C23×C311yescharacteristic
114C22×C3×C13⋊C3—32no—
115(C3⋊D3)⋊D13—22no—
116D3×D39—24no—
117D32×C13—22no—
118C3⋊D3×D13C3×D412yes—
119C3⋊D3×D13C3×D412yes—
120C3×D3×D13—22no—
121C3×D3×D13—22no—
122C3⋊(C3⋊#261)—21no—
123C3×C3⋊#261—22no—
124C32×#261—21no—
125C2×C3⋊(D13⋊C3)—22no—
126C2×C3⋊(D13⋊C3)—32no—
127C2×C3⋊(D13⋊C3)—61no—
128C2×C3⋊(D13⋊C3)—64no—
129C2×C3⋊(D13⋊C3)C4×D312yescomplemented
130C2×D3×C13⋊C3—22no—
131C2×D3×C13⋊C3—32no—
132C2×D3×C13⋊C3—61no—
133C2×D3×C13⋊C3—64no—
134C2×D3×C13⋊C3C4×D312yescomplemented
135C2×C3×D13⋊C3—22no—
136C2×C3×D13⋊C3—21no—
137C2×C3×D13⋊C3—32no—
138C2×C3×D13⋊C3—41no—
139C2×C3×D13⋊C3—62no—
140C2×C3×D13⋊C3—62no—
141C2×C3×D13⋊C3C22×D312yes—
142D3×D13⋊C3—22no—
143D3×D13⋊C3—22no—
144D3×D13⋊C3—34no—
145D3×D13⋊C3—34no—
146D3×D13⋊C3—42no—
147D3×D13⋊C3—42no—
148D3×D13⋊C3—62no—
149D3×D13⋊C3—62no—
150D3×D13⋊C3—64no—
151D3×D13⋊C3—64no—
152C3⋊AGL(1,𝔽13)—22no—
153C3⋊AGL(1,𝔽13)—42no—
154C3⋊AGL(1,𝔽13)—61no—
155C3⋊AGL(1,𝔽13)—61no—
156C3⋊AGL(1,𝔽13)—62no—
157C3×AGL(1,𝔽13)—21no—
158C3×AGL(1,𝔽13)—21no—
159C3×AGL(1,𝔽13)—22no—
160C3×AGL(1,𝔽13)—42no—
161C3×AGL(1,𝔽13)—41no—
162C3×AGL(1,𝔽13)—41no—
163C3×AGL(1,𝔽13)—62no—
164C22×C3×D32—131no—
165C2×C3×C4×C3⋊D3—131no—
166C2×C3×#624—131no—
167C32×(C2×D3)⋊C4—132no—
168C3×(C2×D3)⋊Dic3—132no—
169C2×C22⋊#261—91noHall
170C32×C13⋊C3C2×C22⋊C411yescharacteristic, complemented, Hall
171C22×D39—32no—
172C22×D3×C13—32no—
173C22×C3×D13—32no—
174C23×C13⋊C3—91no—
175C2×D3×D13—32no—
176C2×D3×D13—32no—
177C2×D3×D13—32no—
178C2×D3×D13—61no—
179C2×D3×D13—64no—
180C2×D3×D13—64no—
181C2×D3×D13C2×C3×D312yes—
182C2×C3⋊#261—32no—
183C2×C3⋊#261—61no—
184C2×C3⋊#261C2×C3×D312yescomplemented
185C2×C3×#261—21no—
186C2×C3×#261—32no—
187C2×C3×#261C2×C3×D312yescomplemented
188C22×D13⋊C3—32no—
189C22×D13⋊C3—62no—
190C22×D13⋊C3—91no—
191C22×D13⋊C3—92no—
192C22×D13⋊C3—91no—
193C22×D13⋊C3—182no—
194C22×D13⋊C3—182no—
195D3×#261—64no—
196D3×#261—62no—
197D3×#261—62no—
198D3×#261—64no—
199C2×AGL(1,𝔽13)—22no—
200C2×AGL(1,𝔽13)—32no—
201C2×AGL(1,𝔽13)—41no—
202C2×AGL(1,𝔽13)—62no—
203C2×AGL(1,𝔽13)—91no—
204C2×AGL(1,𝔽13)—182no—
205C2×AGL(1,𝔽13)—182no—
206C2×AGL(1,𝔽13)D3211yescharacteristic, complemented
207C3×D3×C22⋊C4—392no—
208#63921—131no—
209C2×C32×C13C22×C3×C411yescharacteristic
210C3⋊D39C3×C22⋊C412yescomplemented
211C13×C3⋊D3C3×C22⋊C412yescomplemented
212C3×D39—22no—
213C3×D3×C13—22no—
214C32×D13C2×C3×D411yescharacteristic
215C32×D13C2×C3×D411yescharacteristic
216C2×C3×C13⋊C3—22no—
217C2×C3×C13⋊C3—21no—
218C2×C3×C13⋊C3—41no—
219C2×C3×C13⋊C3—62no—
220C2×C3×C13⋊C3C2×C4×D312yes—
221C3⋊(D13⋊C3)—22no—
222C3⋊(D13⋊C3)—34no—
223C3⋊(D13⋊C3)—42no—
224C3⋊(D13⋊C3)—62no—
225D3×C13⋊C3—22no—
226D3×C13⋊C3—34no—
227D3×C13⋊C3—42no—
228D3×C13⋊C3—62no—
229C3×D13⋊C3—22no—
230C3×D13⋊C3—22no—
231C3×D13⋊C3—21no—
232C3×D13⋊C3—21no—
233C3×D13⋊C3—41no—
234C3×D13⋊C3—41no—
235C3×D13⋊C3—62no—
236C3×D13⋊C3D3×D412yes—
237C3×D13⋊C3D3×D412yes—
238C22×C3×C3⋊D3—131no—
239C22×C32×D3—132no—
240C2×C3×D32—131no—
241C2×C3×D32—132no—
242C2×C3×D32—262no—
243C2×C3×D32—262no—
244C2×C3×D32—521no—
245C2×C33×C4—131no—
246C2×C3×C3⋊Dic3—131no—
247C3×C4×C3⋊D3—262no—
248C2×C32×Dic3—132no—
249C3×#624—262no—
250C23×D13—91no—
251C22×#261—91no—
252C22×#261—91no—
253C22⋊#261—32no—
254C22⋊#261—92no—
255C22×C3×C13—32no—
256C2×D39—32no—
257C2×D39—61no—
258C2×D39—64no—
259C2×D39C3×C4×D312yescomplemented
260C2×D3×C13—32no—
261C2×D3×C13—61no—
262C2×D3×C13—64no—
263C2×D3×C13C3×C4×D312yescomplemented
264C2×C3×D13—21no—
265C2×C3×D13—32no—
266C2×C3×D13—62no—
267C2×C3×D13—62no—
268C2×C3×D13C22×C3×D312yes—
269C22×C13⋊C3—32no—
270C22×C13⋊C3—62no—
271C22×C13⋊C3—91no—
272C22×C13⋊C3—182no—
273D3×D13—22no—
274D3×D13—22no—
275D3×D13—34no—
276D3×D13—34no—
277D3×D13—62no—
278D3×D13—62no—
279D3×D13—64no—
280D3×D13—64no—
281C3⋊#261—22no—
282C3⋊#261—61no—
283C3⋊#261—61no—
284C3⋊#261—62no—
285C3×#261—21no—
286C3×#261—21no—
287C3×#261—22no—
288C3×#261—62no—
289C2×D13⋊C3—22no—
290C2×D13⋊C3—32no—
291C2×D13⋊C3—41no—
292C2×D13⋊C3—62no—
293C2×D13⋊C3—62no—
294C2×D13⋊C3—62no—
295C2×D13⋊C3—91no—
296C2×D13⋊C3—92no—
297C2×D13⋊C3—92no—
298C2×D13⋊C3—122no—
299C2×D13⋊C3—122no—
300C2×D13⋊C3—182no—
301C2×D13⋊C3—184no—
302C2×D13⋊C3C2×D3211yescharacteristic
303AGL(1,𝔽13)—21no—
304AGL(1,𝔽13)—42no—
305AGL(1,𝔽13)—41no—
306AGL(1,𝔽13)—41no—
307AGL(1,𝔽13)—62no—
308AGL(1,𝔽13)—122no—
309AGL(1,𝔽13)—181no—
310C23×C3×D3—392no—
311C22×D32—131no—
312C2×C4×C3⋊D3—131no—
313C2×C3×C4×D3—392no—
314C2×C3×C4×D3—392no—
315C2×C3×C4×D3—781no—
316C2×#624—131no—
317C32×C22⋊C4—392no—
318C3×#217—392no—
319C3×(C2×D3)⋊C4—132no—
320C3×(C2×D3)⋊C4—132no—
321C3×(C2×D3)⋊C4—262no—
322C3×(C2×D3)⋊C4—392no—
323(C2×D3)⋊Dic3—132no—
324C32×C13C2×C3×C22⋊C411yescharacteristic, complemented
325C3×C13⋊C3—22no—
326C3×C13⋊C3—21no—
327C3×C13⋊C3—41no—
328C3×C13⋊C3D3×C22⋊C412yescomplemented
329C22×C33—131no—
330C2×C3×C3⋊D3—131no—
331C2×C3×C3⋊D3—132no—
332C2×C3×C3⋊D3—132no—
333C2×C3×C3⋊D3—521no—
334C2×C32×D3—132no—
335C2×C32×D3—262no—
336C2×C32×D3—262no—
337C2×C32×D3—522no—
338C3×D32—262no—
339C3×D32—264no—
340C3×D32—522no—
341C33×C4—261no—
342C3×C3⋊Dic3—261no—
343C32×Dic3—262no—
344C23×C13—91no—
345C22×D13—32no—
346C22×D13—91no—
347C22×D13—92no—
348C22×D13—91no—
349C22×D13—182no—
350C22×D13—182no—
351C2×#261—32no—
352C2×#261—91no—
353C2×#261—182no—
354C2×#261—182no—
355C2×#261C3×D3211yescharacteristic, complemented
356C2×C3×C22⋊C4—1171no—
357D3×C22⋊C4—392no—
358C2×C3×C13—21no—
359C2×C3×C13—62no—
360C2×C3×C13C2×C3×C4×D312yes—
361D39—22no—
362D39—34no—
363D39—62no—
364C3×D13—21no—
365C3×D13—21no—
366C3×D13—62no—
367C3×D13C3×D3×D412yes—
368C3×D13C3×D3×D412yes—
369D3×C13—22no—
370D3×C13—34no—
371D3×C13—62no—
372C2×C13⋊C3—22no—
373C2×C13⋊C3—41no—
374C2×C13⋊C3—62no—
375C2×C13⋊C3—92no—
376C2×C13⋊C3—122no—
377C2×C13⋊C3C4×D3211yescharacteristic
378D13⋊C3—22no—
379D13⋊C3—22no—
380D13⋊C3—41no—
381D13⋊C3—41no—
382D13⋊C3—62no—
383D13⋊C3—92no—
384D13⋊C3—122no—
385D13⋊C3#380211yescharacteristic
386D13⋊C3#381111yescharacteristic
387C23×C32—392no—
388C22×C3⋊D3—131no—
389C22×C3×D3—132no—
390C22×C3×D3—132no—
391C22×C3×D3—262no—
392C22×C3×D3—392no—
393C22×C3×D3—392no—
394C22×C3×D3—392no—
395C22×C3×D3—392no—
396C22×C3×D3—781no—
397C22×C3×D3—784no—
398C22×C3×D3—784no—
399C22×C3×D3—1562no—
400C2×D32—131no—
401C2×D32—132no—
402C2×D32—262no—
403C2×D32—262no—
404C2×D32AGL(1,𝔽13)11yescharacteristic, complemented
405C2×C32×C4—132no—
406C2×C32×C4—131no—
407C2×C32×C4—261no—
408C2×C32×C4—262no—
409C2×C32×C4—392no—
410C2×C32×C4—521no—
411C2×C3⋊Dic3—131no—
412C4×C3⋊D3—262no—
413C2×C3×Dic3—132no—
414C2×C3×Dic3—132no—
415C2×C3×Dic3—262no—
416C2×C3×Dic3—392no—
417C2×C3×Dic3—781no—
418C3×C4×D3—784no—
419C3×C4×D3—784no—
420C3×C4×D3—782no—
421C3×C4×D3—782no—
422#624—262no—
423C2×C33—131no—
424C2×C33—131no—
425C2×C33—521no—
426C3×C3⋊D3—132no—
427C3×C3⋊D3—522no—
428C32×D3—262no—
429C32×D3—522no—
430C22×C13—32no—
431C22×C13—91no—
432C22×C13—182no—
433C2×D13—32no—
434C2×D13—62no—
435C2×D13—62no—
436C2×D13—91no—
437C2×D13—92no—
438C2×D13—92no—
439C2×D13—182no—
440C2×D13—184no—
441C2×D13C2×C3×D3211yescharacteristic
442#261—21no—
443#261—62no—
444#261—181no—
445C24×C3—1171no—
446C23×D3—392no—
447C22×C3×C4—1171no—
448C22×C3×C4—1171no—
449C2×C4×D3—392no—
450C2×C4×D3—392no—
451C2×C4×D3—781no—
452C3×C22⋊C4—392no—
453C3×C22⋊C4—392no—
454C3×C22⋊C4—782no—
455C3×C22⋊C4—1172no—
456#217—392no—
457(C2×D3)⋊C4—132no—
458(C2×D3)⋊C4—392no—
459C3×C13—21no—
460C3×C13C3×D3×C22⋊C412yescomplemented
461C13⋊C3—22no—
462C13⋊C3—41no—
463C13⋊C3#6392111yescharacteristic, complemented
464C22×C32—132no—
465C22×C32—131no—
466C22×C32—262no—
467C22×C32—261no—
468C22×C32—392no—
469C22×C32—521no—
470C22×C32—782no—
471C22×C32—782no—
472C22×C32—1562no—
473C2×C3⋊D3—131no—
474C2×C3⋊D3—132no—
475C2×C3⋊D3—132no—
476C2×C3⋊D3C2×AGL(1,𝔽13)11yescharacteristic
477C2×C3×D3—132no—
478C2×C3×D3—132no—
479C2×C3×D3—262no—
480C2×C3×D3—262no—
481C2×C3×D3—262no—
482C2×C3×D3—262no—
483C2×C3×D3—262no—
484C2×C3×D3—392no—
485C2×C3×D3—394no—
486C2×C3×D3—394no—
487C2×C3×D3—522no—
488C2×C3×D3—522no—
489C2×C3×D3—522no—
490C2×C3×D3—3121no—
491C2×C3×D3—782no—
492C2×C3×D3—782no—
493C2×C3×D3—781no—
494C2×C3×D3—784no—
495C2×C3×D3—784no—
496C2×C3×D3—784no—
497C2×C3×D3—1042no—
498C2×C3×D3—1562no—
499C2×C3×D3—1564no—
500C2×C3×D3C2×AGL(1,𝔽13)12yescomplemented
501D32—22no—
502D32—264no—
503D32—262no—
504C32×C4—261no—
505C32×C4—262no—
506C32×C4—261no—
507C32×C4—261no—
508C32×C4—522no—
509C32×C4—521no—
510C32×C4—521no—
511C32×C4—782no—
512C3⋊Dic3—261no—
513C3×Dic3—262no—
514C3×Dic3—262no—
515C3×Dic3—522no—
516C3×Dic3—782no—
517C3×Dic3—781no—
518C3×Dic3—781no—
519C2×C22⋊C4—1171noSylow
520C33—521noSylow
521C2×C13—62no—
522C2×C13—92no—
523C2×C13C3×C4×D3211yescharacteristic
524D13—62no—
525D13—92no—
526D13C3×#380211yescharacteristic
527D13C3×#381111yescharacteristic
528C23×C3—392no—
529C23×C3—392no—
530C23×C3—782no—
531C23×C3—1171no—
532C23×C3—1171no—
533C23×C3—1172no—
534C23×C3—4681no—
535C23×C3—2342no—
536C23×C3—2342no—
537C22×D3—32no—
538C22×D3—132no—
539C22×D3—392no—
540C22×D3—392no—
541C22×D3—392no—
542C22×D3—392no—
543C22×D3—781no—
544C22×D3—784no—
545C22×D3—784no—
546C2×C3×C4—131no—
547C2×C3×C4—132no—
548C2×C3×C4—261no—
549C2×C3×C4—262no—
550C2×C3×C4—392no—
551C2×C3×C4—392no—
552C2×C3×C4—521no—
553C2×C3×C4—782no—
554C2×C3×C4—1171no—
555C2×C3×C4—2342no—
556C2×C3×C4—2342no—
557C2×Dic3—132no—
558C2×Dic3—392no—
559C2×Dic3—781no—
560C4×D3—784no—
561C4×D3—784no—
562C4×D3—782no—
563C4×D3—782no—
564C2×C32—132no—
565C2×C32—132no—
566C2×C32—131no—
567C2×C32—131no—
568C2×C32—262no—
569C2×C32—261no—
570C2×C32—262no—
571C2×C32—261no—
572C2×C32—521no—
573C2×C32—521no—
574C2×C32—522no—
575C2×C32—782no—
576C2×C32—1041no—
577C2×C32—1042no—
578C2×C32—1562no—
579C2×C32—2081no—
580C2×C32C22×AGL(1,𝔽13)11yescharacteristic
581C3⋊D3—132no—
582C3⋊D3(C22⋊#261)⋊C312yescomplemented
583C3×D3—22no—
584C3×D3—262no—
585C3×D3—262no—
586C3×D3—394no—
587C3×D3—522no—
588C3×D3—522no—
589C3×D3—3122no—
590C3×D3—782no—
591C3×D3—1042no—
592C3×D3—1564no—
593C24—1171no—
594C22×C4—1171no—
595C22×C4—1171no—
596C22⋊C4—392no—
597C22⋊C4—1172no—
598C13C3×#6392111yescharacteristic, complemented, Sylow
599C22×C3—32no—
600C22×C3—131no—
601C22×C3—132no—
602C22×C3—261no—
603C22×C3—262no—
604C22×C3—392no—
605C22×C3—392no—
606C22×C3—521no—
607C22×C3—3122no—
608C22×C3—782no—
609C22×C3—782no—
610C22×C3—782no—
611C22×C3—782no—
612C22×C3—782no—
613C22×C3—1172no—
614C22×C3—1172no—
615C22×C3—1171no—
616C22×C3—1562no—
617C22×C3—1562no—
618C22×C3—1562no—
619C22×C3—4681no—
620C22×C3—4682no—
621C22×C3—2342no—
622C22×C3—2344no—
623C2×D3—32no—
624C2×D3—61no—
625C2×D3—64no—
626C2×D3—132no—
627C2×D3—262no—
628C2×D3—262no—
629C2×D3—394no—
630C2×D3—394no—
631C2×D3—392no—
632C2×D3—782no—
633C2×D3—782no—
634C2×D3—781no—
635C2×D3—784no—
636C2×D3—784no—
637C2×D3—784no—
638C2×D3D3×AGL(1,𝔽13)12yescomplemented
639C3×C4—262no—
640C3×C4—261no—
641C3×C4—261no—
642C3×C4—261no—
643C3×C4—522no—
644C3×C4—521no—
645C3×C4—521no—
646C3×C4—782no—
647C3×C4—782no—
648C3×C4—1562no—
649C3×C4—2341no—
650Dic3—262no—
651Dic3—782no—
652Dic3—781no—
653Dic3—781no—
654C32—522no—
655C32—1041no—
656C32—1042no—
657C32—2081no—
658C32C2×(C22⋊#261)⋊C311yescharacteristic, complemented
659C23—91no—
660C23—392no—
661C23—1172no—
662C23—1171no—
663C23—1171no—
664C23—2342no—
665C23—2342no—
666C2×C4—131no—
667C2×C4—392no—
668C2×C4—1171no—
669C2×C4—2342no—
670C2×C4—2342no—
671C2×C3—21no—
672C2×C3—62no—
673C2×C3—131no—
674C2×C3—131no—
675C2×C3—132no—
676C2×C3—132no—
677C2×C3—261no—
678C2×C3—261no—
679C2×C3—262no—
680C2×C3—262no—
681C2×C3—521no—
682C2×C3—521no—
683C2×C3—521no—
684C2×C3—3122no—
685C2×C3—782no—
686C2×C3—782no—
687C2×C3—1042no—
688C2×C3—1172no—
689C2×C3—1562no—
690C2×C3—1562no—
691C2×C3—2081no—
692C2×C3—4682no—
693C2×C3C2×D3×AGL(1,𝔽13)12yes—
694D3—22no—
695D3—34no—
696D3—62no—
697D3—262no—
698D3—394no—
699D3—782no—
700C22—32no—
701C22—91no—
702C22—131no—
703C22—182no—
704C22—392no—
705C22—782no—
706C22—782no—
707C22—1172no—
708C22—1172no—
709C22—1171no—
710C22—2344no—
711C22—2342no—
712C4—261no—
713C4—782no—
714C4—2341no—
715C3—21no—
716C3—521no—
717C3—1042no—
718C3—2081no—
719C3D3×(C22⋊#261)⋊C312yescomplemented
720C2—62no—
721C2—92no—
722C2—131no—
723C2—131no—
724C2—782no—
725C2—1172no—
726C2D32×AGL(1,𝔽13)11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D32×AGL(1,𝔽13)
commutator, Fitting, socleC2×C32×C13C22×C3×C4
prime radicalC2×D32×D13⋊C3C2
cosocleC2×C32×D13C23×C3
hypocenterC32×C13C2×C3×C22⋊C4
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. C3×(C2×D3)⋊AGL(1,𝔽13)C2semidirect
4. C2×(C3⋊(D13⋊C3))⋊D3C4semidirect
5. C2×D3×C3⋊(D13⋊C3)C4semidirect
6. C2×D32×C13⋊C3C4semidirect
8. C2×#72220635C2semidirect
9. C2×C3×C3⋊AGL(1,𝔽13)C22semidirect
10. #72241914C3semidirect
12. C2×C3⋊D3×AGL(1,𝔽13)C2semidirect
13. C2×C3⋊(C3⋊AGL(1,𝔽13))C22semidirect
14. C2×C32×AGL(1,𝔽13)C22semidirect
21. C2×(C3⋊#261)⋊D3C2×C3semidirect
22. C2×C3⋊D3×#261C2×C3semidirect
27. (C2×D3)⋊(C3⋊#261)C2×C3semidirect
28. C3×(C2×D3)⋊#261C2×C3semidirect
33. (C2×D3)⋊AGL(1,𝔽13)D3semidirect
36. C2×C3×C3⋊(D13⋊C3)C2×C4semidirect
37. C2×C3×D3×C13⋊C3C2×C4semidirect
51. C2×(C3⋊D3)⋊D13C3×C4semidirect
52. C2×D3×D39C3×C4semidirect
53. C2×D32×C13C3×C4semidirect
56. C2×C3⋊(C3⋊#261)C22×C3semidirect
57. C2×C3×C3⋊#261C22×C3semidirect
58. C2×C32×#261C22×C3semidirect
77. C2×C3⋊AGL(1,𝔽13)C2×D3semidirect
82. C2×C3×AGL(1,𝔽13)C2×D3semidirect
89. C3⋊(C3⋊(D13⋊C3))C22⋊C4semidirect
90. C3⋊D3×C13⋊C3C22⋊C4semidirect
105. (C2×D3)⋊#261C3×D3semidirect
111. C2×C3×D39C2×C3×C4semidirect
112. C2×C3×D3×C13C2×C3×C4semidirect
129. C2×C3⋊(D13⋊C3)C4×D3semidirect
134. C2×D3×C13⋊C3C4×D3semidirect
170. C32×C13⋊C3C2×C22⋊C4semidirect
184. C2×C3⋊#261C2×C3×D3semidirect
187. C2×C3×#261C2×C3×D3semidirect
206. C2×AGL(1,𝔽13)D32semidirect
210. C3⋊D39C3×C22⋊C4semidirect
211. C13×C3⋊D3C3×C22⋊C4semidirect
259. C2×D39C3×C4×D3semidirect
263. C2×D3×C13C3×C4×D3semidirect
324. C32×C13C2×C3×C22⋊C4semidirect
328. C3×C13⋊C3D3×C22⋊C4semidirect
355. C2×#261C3×D32semidirect
404. C2×D32AGL(1,𝔽13)semidirect
460. C3×C13C3×D3×C22⋊C4semidirect
463. C13⋊C3#63921semidirect
500. C2×C3×D3C2×AGL(1,𝔽13)semidirect
582. C3⋊D3(C22⋊#261)⋊C3semidirect
598. C13C3×#63921semidirect
638. C2×D3D3×AGL(1,𝔽13)semidirect
658. C32C2×(C22⋊#261)⋊C3semidirect
719. C3D3×(C22⋊#261)⋊C3semidirect

Maximal subgroups

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

subgroupindex
#722420092
C3×(C2×D3)⋊AGL(1,𝔽13)2
C2×D32×D13⋊C32
C2×#722206352
#722419143
D3×(C22⋊#261)⋊C33
C2×C3⋊D3×AGL(1,𝔽13)2
C3×#6392113