Finite Group Databasebeta

← C13×#14360 #15700699

Subgroups — C13×#14360 #15700699

Order 3328.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#123C211yesmaximal, characteristic
2C2×C13×#390C211yesmaximal, characteristic
3C2×C13×#389C211yesmaximal, characteristic, complemented
4C2×C13×#387C211yesmaximal, characteristic, complemented
5C2×C13×#380C211yesmaximal, characteristic, complemented
6C13×#1441C211yesmaximal, characteristic, complemented
7C13×#1439C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1438C211yesmaximal, characteristic
12C13×#1437C211yesmaximal, characteristic, complemented
13C13×#1437C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×#123—24no—
19C2×C13×#123—24no—
20C2×C13×#123C418yescomplemented
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2211yescharacteristic
34C22×C13×C22⋊C4C2211yescharacteristic
35C22×C13×C22⋊C4C2211yescharacteristic
36C22×C13×C22⋊C4C2211yescharacteristic
37C22×C13×C22⋊C4C2211yescharacteristic
38C22×C42×C13C2211yescharacteristic
39C22×C42×C13C2211yescharacteristic
40C13×#390—24no—
41C13×#389—24no—
42C13×#387—24no—
43C13×#380—24no—
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C2×C13×#95C2211yescharacteristic
58C25×C13C2311yescharacteristic
59C25×C13C2311yescharacteristic
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—41no—
65C22×D4×C13—41no—
66C22×D4×C13C2×C414yes—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—41no—
72C23×C4×C13—41no—
73C23×C4×C13C2×C414yes—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C13×#123—232no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—41no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4C2×C414yes—
103C2×C13×C4⋊C4C2×C414yes—
104C2×C13×C4⋊C4D414yes—
105C2×C13×C4⋊C4D414yes—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—22no—
117C2×C13×C22⋊C4—22no—
118C2×C13×C22⋊C4—22no—
119C2×C13×C22⋊C4—22no—
120C2×C13×C22⋊C4—22no—
121C2×C13×C22⋊C4—41no—
122C2×C13×C22⋊C4—41no—
123C2×C13×C22⋊C4—41no—
124C2×C13×C22⋊C4—41no—
125C2×C13×C22⋊C4—41no—
126C2×C13×C22⋊C4—41no—
127C2×C13×C22⋊C4—41no—
128C2×C13×C22⋊C4—41no—
129C2×C13×C22⋊C4—41no—
130C2×C13×C22⋊C4—41no—
131C2×C13×C22⋊C4—41no—
132C2×C13×C22⋊C4—41no—
133C2×C13×C22⋊C4—41no—
134C2×C13×C22⋊C4—41no—
135C2×C13×C22⋊C4C2×C414yes—
136C2×C13×C22⋊C4C2×C414yes—
137C2×C13×C22⋊C4C2×C414yes—
138C2×C13×C22⋊C4D414yes—
139C2×C42×C13—22no—
140C2×C42×C13—22no—
141C2×C42×C13—22no—
142C2×C42×C13—41no—
143C2×C42×C13—41no—
144C2×C42×C13—41no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95—22no—
148C13×#95—22no—
149C13×#95—22no—
150C13×#95—22no—
151C13×#95—22no—
152C13×#95—22no—
153C13×#95—22no—
154C13×#95—22no—
155C13×#95—41no—
156C13×#95—41no—
157C13×#95—41no—
158C13×#95—41no—
159#14360C1311yesmaximal, characteristic, direct product factor, Sylow
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13—21no—
179C24×C13—21no—
180C24×C13—21no—
181C24×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13—21no—
185C24×C13—21no—
186C24×C13C22×C412yes—
187C24×C13C22×C412yes—
188C24×C13C2×D412yes—
189C24×C13#4112yes—
190C24×C13C2411yescharacteristic
191C2×D4×C13—28no—
192C2×D4×C13—28no—
193C2×D4×C13—44no—
194C2×D4×C13—44no—
195C2×D4×C13—44no—
196C2×D4×C13—44no—
197C2×D4×C13—44no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—28no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—28no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—21no—
264C22×C4×C13—21no—
265C22×C4×C13—21no—
266C22×C4×C13—21no—
267C22×C4×C13—21no—
268C22×C4×C13—21no—
269C22×C4×C13—21no—
270C22×C4×C13—21no—
271C22×C4×C13—21no—
272C22×C4×C13—21no—
273C22×C4×C13—21no—
274C22×C4×C13—21no—
275C22×C4×C13—21no—
276C22×C4×C13—44no—
277C22×C4×C13—44no—
278C22×C4×C13—44no—
279C22×C4×C13—44no—
280C22×C4×C13—44no—
281C22×C4×C13C22×C412yes—
282C22×C4×C13C22×C412yes—
283C22×C4×C13C22×C412yes—
284C22×C4×C13C22×C412yes—
285C22×C4×C13C22×C412yes—
286C22×C4×C13C2×D412yes—
287C22×C4×C13C2×D412yes—
288C22×C4×C13C2×D412yes—
289C22×C4×C13C2×D412yes—
290C22×C4×C13C2×D412yes—
291C22×C4×C13C2×D412yes—
292C22×C4×C13C2×D412yes—
293C22×C4×C13C2×D412yes—
294C22×C4×C13#4112yes—
295C22×C4×C13#4112yes—
296C13×C4⋊C4—28no—
297C13×C4⋊C4—44no—
298C13×C4⋊C4—44no—
299C13×C4⋊C4—44no—
300C13×C4⋊C4—44no—
301C13×C4⋊C4C22⋊C4116yescomplemented
302C13×C22⋊C4—28no—
303C13×C22⋊C4—28no—
304C13×C22⋊C4—28no—
305C13×C22⋊C4—44no—
306C13×C22⋊C4—44no—
307C13×C22⋊C4—44no—
308C13×C22⋊C4—44no—
309C13×C22⋊C4—44no—
310C13×C22⋊C4—44no—
311C13×C22⋊C4—44no—
312C13×C22⋊C4—44no—
313C42×C13—44no—
314C42×C13—44no—
315C22×#123C2×C1311yescharacteristic
316C2×#390C2×C1311yescharacteristic
317C2×#389C2×C1311yescharacteristic, complemented
318C2×#387C2×C1311yescharacteristic, complemented
319C2×#380C2×C1311yescharacteristic, complemented
320#1441C2×C1311yescharacteristic, complemented
321#1439C2×C1311yescharacteristic, complemented
322#1439C2×C1311yescharacteristic, complemented
323#1439C2×C1311yescharacteristic, complemented
324#1439C2×C1311yescharacteristic, complemented
325#1438C2×C1311yescharacteristic
326#1437C2×C1311yescharacteristic, complemented
327#1437C2×C1311yescharacteristic, complemented
328#1436C2×C1311yescharacteristic, complemented
329C22⋊#95C2×C1311yescharacteristic, complemented
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13—22no—
341C23×C13—22no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—22no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—22no—
349C23×C13—22no—
350C23×C13—22no—
351C23×C13—22no—
352C23×C13—22no—
353C23×C13—22no—
354C23×C13—22no—
355C23×C13—41no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—41no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13—41no—
366C23×C13—41no—
367C23×C13—41no—
368C23×C13—41no—
369C23×C13—41no—
370C23×C13—41no—
371C23×C13—41no—
372C23×C13—41no—
373C23×C13—41no—
374C23×C13—41no—
375C23×C13—41no—
376C23×C13—41no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13—41no—
383C23×C13—41no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13—41no—
387C23×C13—41no—
388C23×C13—41no—
389C23×C13—41no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—41no—
394C23×C13—41no—
395C23×C13—41no—
396C23×C13—41no—
397C23×C13—41no—
398C23×C13—41no—
399C23×C13C4×D414yes—
400C23×C13C23×C411yescharacteristic
401C23×C13C22×D411yescharacteristic
402C23×C13C22×D411yescharacteristic
403C23×C13C22×D411yescharacteristic
404C23×C13C2×#4111yescharacteristic
405C23×C13C2×#4111yescharacteristic
406C23×C13C2×#4111yescharacteristic
407C23×C13H(5,𝔽2)11yescharacteristic
408C23×C13H(5,𝔽2)11yescharacteristic
409C23×C13H(5,𝔽2)11yescharacteristic
410C23×C13H(5,𝔽2)11yescharacteristic
411C23×C13H(5,𝔽2)11yescharacteristic
412C23×C132−1+411yescharacteristic
413C23×C132−1+411yescharacteristic
414C23×C132−1+411yescharacteristic
415D4×C13—416no—
416C2×C4×C13—22no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—22no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—22no—
426C2×C4×C13—22no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—22no—
430C2×C4×C13—22no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—22no—
440C2×C4×C13—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—22no—
447C2×C4×C13—22no—
448C2×C4×C13—22no—
449C2×C4×C13—22no—
450C2×C4×C13—22no—
451C2×C4×C13—22no—
452C2×C4×C13—416no—
453C2×C4×C13—41no—
454C2×C4×C13—41no—
455C2×C4×C13—41no—
456C2×C4×C13—41no—
457C2×C4×C13—41no—
458C2×C4×C13—41no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—41no—
463C2×C4×C13—41no—
464C2×C4×C13—41no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—41no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13—41no—
474C2×C4×C13—41no—
475C2×C4×C13—41no—
476C2×C4×C13—41no—
477C2×C4×C13—41no—
478C2×C4×C13—41no—
479C2×C4×C13—41no—
480C2×C4×C13—41no—
481C2×C4×C13—41no—
482C2×C4×C13—41no—
483C2×C4×C13—41no—
484C2×C4×C13—41no—
485C2×C4×C13—41no—
486C2×C4×C13—41no—
487C2×C4×C13—41no—
488C2×C4×C13—41no—
489C2×C4×C13—41no—
490C2×C4×C13—41no—
491C2×C4×C13—41no—
492C2×C4×C13—41no—
493C2×C4×C13—41no—
494C2×C4×C13—41no—
495C2×C4×C13—41no—
496C2×C4×C13—41no—
497C2×C4×C13—41no—
498C2×C4×C13—41no—
499C2×C4×C13—41no—
500C2×C4×C13—41no—
501C2×C4×C13—41no—
502C2×C4×C13—41no—
503C2×C4×C13—41no—
504C2×C4×C13—41no—
505C2×C4×C13C2×C22⋊C414yes—
506C2×C4×C13C2×C22⋊C414yes—
507C2×C4×C13C2×C22⋊C414yes—
508C23×D4C22×C1311yescharacteristic
509C24×C4C22×C1311yescharacteristic
510C2×#123—24no—
511C2×#123—24no—
512C2×#123C4×C1318yescomplemented
513C22×C4⋊C4C22×C1311yescharacteristic
514C22×C4⋊C4C22×C1311yescharacteristic
515C22×C4⋊C4C22×C1311yescharacteristic
516C22×C4⋊C4C22×C1311yescharacteristic
517C22×C4⋊C4C22×C1311yescharacteristic
518C22×C4⋊C4C22×C1311yescharacteristic
519C22×C22⋊C4C22×C1311yescharacteristic
520C22×C22⋊C4C22×C1311yescharacteristic
521C22×C22⋊C4C22×C1311yescharacteristic
522C22×C22⋊C4C22×C1311yescharacteristic
523C22×C22⋊C4C22×C1311yescharacteristic
524C22×C22⋊C4C22×C1311yescharacteristic
525C22×C22⋊C4C22×C1311yescharacteristic
526C22×C22⋊C4C22×C1311yescharacteristic
527C22×C22⋊C4C22×C1311yescharacteristic
528C22×C22⋊C4C22×C1311yescharacteristic
529C22×C22⋊C4C22×C1311yescharacteristic
530C22×C42C22×C1311yescharacteristic
531C22×C42C22×C1311yescharacteristic
532#390—24no—
533#389—24no—
534#387—24no—
535#380—24no—
536C2×#95C22×C1311yescharacteristic
537C2×#95C22×C1311yescharacteristic
538C2×#95C22×C1311yescharacteristic
539C2×#95C22×C1311yescharacteristic
540C2×#95C22×C1311yescharacteristic
541C2×#95C22×C1311yescharacteristic
542C2×#95C22×C1311yescharacteristic
543C2×#95C22×C1311yescharacteristic
544C2×#95C22×C1311yescharacteristic
545C2×#95C22×C1311yescharacteristic
546C2×#95C22×C1311yescharacteristic
547C2×#95C22×C1311yescharacteristic
548C2×#95C22×C1311yescharacteristic
549C2×#95C22×C1311yescharacteristic
550C22×C13—24no—
551C22×C13—24no—
552C22×C13—24no—
553C22×C13—42no—
554C22×C13—42no—
555C22×C13—42no—
556C22×C13—42no—
557C22×C13—42no—
558C22×C13—42no—
559C22×C13—42no—
560C22×C13—42no—
561C22×C13—42no—
562C22×C13—42no—
563C22×C13—42no—
564C22×C13—42no—
565C22×C13—42no—
566C22×C13—42no—
567C22×C13—42no—
568C22×C13—42no—
569C22×C13—42no—
570C22×C13—42no—
571C22×C13—42no—
572C22×C13—81no—
573C22×C13—81no—
574C22×C13—81no—
575C22×C13—81no—
576C22×C13—81no—
577C22×C13—81no—
578C22×C13—81no—
579C22×C13—81no—
580C22×C13C22×C22⋊C411yescharacteristic
581C22×C13C2×C4×D411yescharacteristic
582C22×C13C4×#4111yescharacteristic
583C22×C13#51811yescharacteristic
584C22×C13#52011yescharacteristic
585C22×C13#52011yescharacteristic
586C22×C13#52011yescharacteristic
587C22×C13#53411yescharacteristic
588C22×C13#53511yescharacteristic
589C22×C13#53611yescharacteristic
590C22×C13#53611yescharacteristic
591C22×C13#53711yescharacteristic
592C22×C13#53711yescharacteristic
593C22×C13#53811yescharacteristic
594C22×C13#53911yescharacteristic
595C22×C13#53911yescharacteristic
596C22×C13#53911yescharacteristic
597C22×C13#54011yescharacteristic
598C22×C13#54211yescharacteristic
599C22×C13D4211yescharacteristic
600C22×C13D4211yescharacteristic
601C22×C13#54611yescharacteristic
602C22×C13#54611yescharacteristic
603C22×C13#54611yescharacteristic
604C22×C13#54711yescharacteristic
605C22×C13#54811yescharacteristic
606C22×C13#54811yescharacteristic
607C22×C13#55011yescharacteristic
608C22×C13#55011yescharacteristic
609C22×C13#55111yescharacteristic
610C22×C13#55211yescharacteristic
611C22×C13#56011yescharacteristic
612C22×C13#56211yescharacteristic
613C22×C13#56211yescharacteristic
614C22×C13#56311yescharacteristic
615C4×C13—24no—
616C4×C13—24no—
617C4×C13—24no—
618C4×C13—42no—
619C4×C13—42no—
620C4×C13—42no—
621C4×C13—42no—
622C4×C13—42no—
623C4×C13—42no—
624C4×C13—81no—
625C4×C13—81no—
626C4×C13—81no—
627C4×C13—81no—
628C25C23×C1311yescharacteristic
629C25C23×C1311yescharacteristic
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—22no—
634C22×D4—41no—
635C22×D4—41no—
636C22×D4C2×C4×C1314yes—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—22no—
640C23×C4—22no—
641C23×C4—41no—
642C23×C4—41no—
643C23×C4C2×C4×C1314yes—
644C23×C4C23×C1311yescharacteristic
645C23×C4C23×C1311yescharacteristic
646C23×C4C23×C1311yescharacteristic
647C23×C4C23×C1311yescharacteristic
648C23×C4C23×C1311yescharacteristic
649C23×C4C23×C1311yescharacteristic
650C23×C4C23×C1311yescharacteristic
651C23×C4C23×C1311yescharacteristic
652C23×C4C23×C1311yescharacteristic
653C23×C4C23×C1311yescharacteristic
654C23×C4C23×C1311yescharacteristic
655C23×C4C23×C1311yescharacteristic
656C23×C4C23×C1311yescharacteristic
657#123—232no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4C2×C4×C1314yes—
673C2×C4⋊C4C2×C4×C1314yes—
674C2×C4⋊C4D4×C1314yes—
675C2×C4⋊C4D4×C1314yes—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4C2×C4×C1314yes—
706C2×C22⋊C4C2×C4×C1314yes—
707C2×C22⋊C4C2×C4×C1314yes—
708C2×C22⋊C4D4×C1314yes—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42—41no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95—41no—
729C2×C13—44no—
730C2×C13—82no—
731C2×C13#231111yescharacteristic
732C2×C13#232211yescharacteristic
733C2×C13#233511yescharacteristic
734C2×C13D4×C22⋊C411yescharacteristic
735C2×C13#234111yescharacteristic
736C2×C13#235911yescharacteristic
737C2×C13#237611yescharacteristic
738C2×C13#267311yescharacteristic
739C2×C13#267411yescharacteristic
740C2×C13#268111yescharacteristic
741C2×C13#268211yescharacteristic
742C2×C13#269411yescharacteristic
743C2×C13#269611yescharacteristic
744C2×C13#270511yescharacteristic
745C2×C13#270711yescharacteristic
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24C22×C4×C1312yes—
773C24C22×C4×C1312yes—
774C24C2×D4×C1312yes—
775C24C13×#4112yes—
776C24C24×C1311yescharacteristic
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—28no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—28no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4C22×C4×C1312yes—
868C22×C4C22×C4×C1312yes—
869C22×C4C22×C4×C1312yes—
870C22×C4C22×C4×C1312yes—
871C22×C4C22×C4×C1312yes—
872C22×C4C2×D4×C1312yes—
873C22×C4C2×D4×C1312yes—
874C22×C4C2×D4×C1312yes—
875C22×C4C2×D4×C1312yes—
876C22×C4C2×D4×C1312yes—
877C22×C4C2×D4×C1312yes—
878C22×C4C2×D4×C1312yes—
879C22×C4C2×D4×C1312yes—
880C22×C4C13×#4112yes—
881C22×C4C13×#4112yes—
882C4⋊C4—28no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4C13×C22⋊C4116yescomplemented
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C42—44no—
900C42—44no—
901C13#1436011yescharacteristic, direct product factor, Sylow
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C4×D4×C1314yes—
972C23C23×C4×C1311yescharacteristic
973C23C22×D4×C1311yescharacteristic
974C23C22×D4×C1311yescharacteristic
975C23C22×D4×C1311yescharacteristic
976C23C2×C13×#4111yescharacteristic
977C23C2×C13×#4111yescharacteristic
978C23C2×C13×#4111yescharacteristic
979C23C13×H(5,𝔽2)11yescharacteristic
980C23C13×H(5,𝔽2)11yescharacteristic
981C23C13×H(5,𝔽2)11yescharacteristic
982C23C13×H(5,𝔽2)11yescharacteristic
983C23C13×H(5,𝔽2)11yescharacteristic
984C23C13×2−1+411yescharacteristic
985C23C13×2−1+411yescharacteristic
986C23C13×2−1+411yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—416no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4C2×C13×C22⋊C414yes—
1078C2×C4C2×C13×C22⋊C414yes—
1079C2×C4C2×C13×C22⋊C414yes—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C13×C22⋊C411yescharacteristic
1111C22C2×C4×D4×C1311yescharacteristic
1112C22C4×C13×#4111yescharacteristic
1113C22C13×#51811yescharacteristic
1114C22C13×#52011yescharacteristic
1115C22C13×#52011yescharacteristic
1116C22C13×#52011yescharacteristic
1117C22C13×#53411yescharacteristic
1118C22C13×#53511yescharacteristic
1119C22C13×#53611yescharacteristic
1120C22C13×#53611yescharacteristic
1121C22C13×#53711yescharacteristic
1122C22C13×#53711yescharacteristic
1123C22C13×#53811yescharacteristic
1124C22C13×#53911yescharacteristic
1125C22C13×#53911yescharacteristic
1126C22C13×#53911yescharacteristic
1127C22C13×#54011yescharacteristic
1128C22C13×#54211yescharacteristic
1129C22D42×C1311yescharacteristic
1130C22D42×C1311yescharacteristic
1131C22C13×#54611yescharacteristic
1132C22C13×#54611yescharacteristic
1133C22C13×#54611yescharacteristic
1134C22C13×#54711yescharacteristic
1135C22C13×#54811yescharacteristic
1136C22C13×#54811yescharacteristic
1137C22C13×#55011yescharacteristic
1138C22C13×#55011yescharacteristic
1139C22C13×#55111yescharacteristic
1140C22C13×#55211yescharacteristic
1141C22C13×#56011yescharacteristic
1142C22C13×#56211yescharacteristic
1143C22C13×#56211yescharacteristic
1144C22C13×#56311yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C13×#231111yescharacteristic
1161C2C13×#232211yescharacteristic
1162C2C13×#233511yescharacteristic
1163C2D4×C13×C22⋊C411yescharacteristic
1164C2C13×#234111yescharacteristic
1165C2C13×#235911yescharacteristic
1166C2C13×#237611yescharacteristic
1167C2C13×#267311yescharacteristic
1168C2C13×#267411yescharacteristic
1169C2C13×#268111yescharacteristic
1170C2C13×#268211yescharacteristic
1171C2C13×#269411yescharacteristic
1172C2C13×#269611yescharacteristic
1173C2C13×#270511yescharacteristic
1174C2C13×#270711yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C13×#389C2semidirect
4. C2×C13×#387C2semidirect
5. C2×C13×#380C2semidirect
6. C13×#1441C2semidirect
7. C13×#1439C2semidirect
8. C13×#1439C2semidirect
9. C13×#1439C2semidirect
10. C13×#1439C2semidirect
12. C13×#1437C2semidirect
13. C13×#1437C2semidirect
14. C13×#1436C2semidirect
15. C13×C22⋊#95C2semidirect
20. C2×C13×#123C4semidirect
159. #14360C13direct (N × H)
301. C13×C4⋊C4C22⋊C4semidirect
317. C2×#389C2×C13semidirect
318. C2×#387C2×C13semidirect
319. C2×#380C2×C13semidirect
320. #1441C2×C13semidirect
321. #1439C2×C13semidirect
322. #1439C2×C13semidirect
323. #1439C2×C13semidirect
324. #1439C2×C13semidirect
326. #1437C2×C13semidirect
327. #1437C2×C13semidirect
328. #1436C2×C13semidirect
329. C22⋊#95C2×C13semidirect
512. C2×#123C4×C13semidirect
887. C4⋊C4C13×C22⋊C4semidirect
901. C13#14360direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×#1232
C2×C13×#3902
C2×C13×#3892
C2×C13×#3872
C2×C13×#3802
C13×#14412
C13×#14392
C13×#14382
C13×#14372
C13×#14362
C13×C22⋊#952
#1436013