Finite Group Databasebeta

← C13×#13999 #15700338

Subgroups — C13×#13999 #15700338

Order 3328.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#388C211yesmaximal, characteristic, complemented
2C2×C13×#386C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#386C211yesmaximal, characteristic
5C2×C13×#380C211yesmaximal, characteristic, complemented
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
7C22×C13×#95C211yesmaximal, characteristic, complemented
8C13×#1443C211yesmaximal, characteristic, complemented
9C13×#1442C211yesmaximal, characteristic, complemented
10C13×#1440C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1437C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1434C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C42×C13C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C13×#388—24no—
34C13×#386—24no—
35C13×#386—24no—
36C13×#386C418yescomplemented
37C13×#380—24no—
38C4×C13×C22⋊C4—24no—
39C2×C13×#95—24no—
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
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—22no—
65C22×D4×C13—22no—
66C22×D4×C13C2×C414yes—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—22no—
72C23×C4×C13—22no—
73C23×C4×C13—22no—
74C23×C4×C13—22no—
75C23×C4×C13—22no—
76C23×C4×C13—22no—
77C23×C4×C13—22no—
78C23×C4×C13—22no—
79C23×C4×C13—22no—
80C23×C4×C13—41no—
81C23×C4×C13—41no—
82C23×C4×C13—41no—
83C23×C4×C13—41no—
84C23×C4×C13—41no—
85C23×C4×C13—41no—
86C23×C4×C13C2×C414yes—
87C23×C4×C13D414yes—
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C23×C4×C13C2311yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—41no—
106C2×C13×C4⋊C4—41no—
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—22no—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4—22no—
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⋊C4C2×C414yes—
131C2×C13×C22⋊C4C2×C414yescomplemented
132C2×C13×C22⋊C4C2×C414yescomplemented
133C2×C13×C22⋊C4D414yes—
134C2×C42×C13—22no—
135C2×C42×C13—22no—
136C2×C42×C13—22no—
137C2×C42×C13—22no—
138C2×C42×C13—41no—
139C2×C42×C13—41no—
140C13×#95—22no—
141C13×#95—22no—
142C13×#95—22no—
143C13×#95—22no—
144C13×#95—22no—
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—41no—
154C13×#95—41no—
155C13×#95C2×C414yescomplemented
156C13×#95C2×C414yescomplemented
157C13×#95D414yescomplemented
158#13999C1311yesmaximal, characteristic, direct product factor, Sylow
159C24×C13—21no—
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×C13C22×C412yes—
182C24×C13C22×C412yes—
183C24×C13C2×D412yes—
184C24×C13C2×D412yes—
185C24×C13#4112yes—
186C24×C13#4112yes—
187C24×C13#4112yes—
188C24×C13#4112yes—
189C24×C13C2411yescharacteristic
190C2×D4×C13—28no—
191C2×D4×C13—28no—
192C2×D4×C13—28no—
193C2×D4×C13—44no—
194C2×D4×C13—44no—
195C2×D4×C13—44no—
196C2×D4×C13—44no—
197C22×C4×C13—21no—
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—28no—
206C22×C4×C13—28no—
207C22×C4×C13—28no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
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—21no—
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—28no—
263C22×C4×C13—28no—
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—21no—
277C22×C4×C13—21no—
278C22×C4×C13—44no—
279C22×C4×C13—44no—
280C22×C4×C13—44no—
281C22×C4×C13—44no—
282C22×C4×C13—44no—
283C22×C4×C13—44no—
284C22×C4×C13—44no—
285C22×C4×C13—44no—
286C22×C4×C13—44no—
287C22×C4×C13—44no—
288C22×C4×C13—44no—
289C22×C4×C13—44no—
290C22×C4×C13—44no—
291C22×C4×C13—44no—
292C22×C4×C13—44no—
293C22×C4×C13—44no—
294C22×C4×C13C22×C412yes—
295C22×C4×C13C22×C412yes—
296C22×C4×C13C22×C412yes—
297C22×C4×C13C22×C412yes—
298C22×C4×C13C22×C412yes—
299C22×C4×C13C2×D412yes—
300C22×C4×C13C2×D412yes—
301C22×C4×C13C2×D412yes—
302C22×C4×C13C2×D412yes—
303C22×C4×C13C2×D412yes—
304C22×C4×C13C2×D412yes—
305C22×C4×C13C2×D412yes—
306C22×C4×C13#4112yes—
307C22×C4×C13#4112yes—
308C22×C4×C13#4112yes—
309C13×C4⋊C4—44no—
310C13×C4⋊C4—44no—
311C13×C22⋊C4—28no—
312C13×C22⋊C4—28no—
313C13×C22⋊C4—28no—
314C13×C22⋊C4—44no—
315C13×C22⋊C4—44no—
316C13×C22⋊C4—44no—
317C13×C22⋊C4—44no—
318C13×C22⋊C4—44no—
319C13×C22⋊C4—44no—
320C42×C13—44no—
321C42×C13—44no—
322C2×#388C2×C1311yescharacteristic, complemented
323C2×#386C2×C1311yescharacteristic
324C2×#386C2×C1311yescharacteristic
325C2×#386C2×C1311yescharacteristic
326C2×#380C2×C1311yescharacteristic, complemented
327C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
328C22×#95C2×C1311yescharacteristic, complemented
329#1443C2×C1311yescharacteristic, complemented
330#1442C2×C1311yescharacteristic, complemented
331#1440C2×C1311yescharacteristic, complemented
332#1439C2×C1311yescharacteristic, complemented
333#1437C2×C1311yescharacteristic, complemented
334#1436C2×C1311yescharacteristic, complemented
335#1434C2×C1311yescharacteristic, complemented
336C22⋊#95C2×C1311yescharacteristic, complemented
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—22no—
356C23×C13—22no—
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—22no—
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
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×C13—41no—
400C23×C13#11714yes—
401C23×C13C4×D414yes—
402C23×C13C4×D414yes—
403C23×C13#12114yes—
404C23×C13#12314yes—
405C23×C13#12414yes—
406C23×C13#12614yes—
407C23×C13C23×C411yescharacteristic
408C23×C13C22×D411yescharacteristic
409C23×C13C22×D411yescharacteristic
410C23×C13C22×D411yescharacteristic
411C23×C13C2×#4111yescharacteristic
412C23×C13C2×#4111yescharacteristic
413C23×C13C2×#4111yescharacteristic
414C23×C13C2×#4111yescharacteristic
415C23×C13C2×#4111yescharacteristic
416C23×C13C2×#4111yescharacteristic
417C23×C13C2×#4111yescharacteristic
418C23×C13H(5,𝔽2)11yescharacteristic
419C23×C13H(5,𝔽2)11yescharacteristic
420C23×C13H(5,𝔽2)11yescharacteristic
421C23×C132−1+411yescharacteristic
422D4×C13—416no—
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—22no—
453C2×C4×C13—22no—
454C2×C4×C13—22no—
455C2×C4×C13—22no—
456C2×C4×C13—22no—
457C2×C4×C13—22no—
458C2×C4×C13—22no—
459C2×C4×C13—22no—
460C2×C4×C13—22no—
461C2×C4×C13—22no—
462C2×C4×C13—416no—
463C2×C4×C13—416no—
464C2×C4×C13—416no—
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×C13—41no—
506C2×C4×C13—41no—
507C2×C4×C13—41no—
508C2×C4×C13—41no—
509C2×C4×C13—41no—
510C2×C4×C13—41no—
511C2×C4×C13—41no—
512C2×C4×C13—41no—
513C2×C4×C13—41no—
514C2×C4×C13—41no—
515C2×C4×C13C4×D414yes—
516C2×C4×C13#12114yes—
517C23×D4C22×C1311yescharacteristic
518C24×C4C22×C1311yescharacteristic
519C24×C4C22×C1311yescharacteristic
520C24×C4C22×C1311yescharacteristic
521C22×C4⋊C4C22×C1311yescharacteristic
522C22×C4⋊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×C22⋊C4C22×C1311yescharacteristic
531C22×C22⋊C4C22×C1311yescharacteristic
532C22×C42C22×C1311yescharacteristic
533C22×C42C22×C1311yescharacteristic
534#388—24no—
535#386—24no—
536#386—24no—
537#386C4×C1318yescomplemented
538#380—24no—
539C4×C22⋊C4—24no—
540C2×#95—24no—
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
550C2×#95C22×C1311yescharacteristic
551C2×#95C22×C1311yescharacteristic
552C2×#95C22×C1311yescharacteristic
553C2×#95C22×C1311yescharacteristic
554C2×#95C22×C1311yescharacteristic
555C2×#95C22×C1311yescharacteristic
556C2×#95C22×C1311yescharacteristic
557C2×#95C22×C1311yescharacteristic
558C2×#95C22×C1311yescharacteristic
559C22×C13—24no—
560C22×C13—24no—
561C22×C13—24no—
562C22×C13—24no—
563C22×C13—24no—
564C22×C13—24no—
565C22×C13—24no—
566C22×C13—24no—
567C22×C13—24no—
568C22×C13—24no—
569C22×C13—24no—
570C22×C13—24no—
571C22×C13—24no—
572C22×C13—24no—
573C22×C13—42no—
574C22×C13—42no—
575C22×C13—42no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13—42no—
580C22×C13—81no—
581C22×C13—81no—
582C22×C13—81no—
583C22×C13—81no—
584C22×C13—81no—
585C22×C13—81no—
586C22×C13—81no—
587C22×C13—81no—
588C22×C13#38818yescomplemented
589C22×C13C2×#11711yescharacteristic
590C22×C13C2×C4×D411yescharacteristic
591C22×C13C2×C4×D411yescharacteristic
592C22×C13C2×C4×D411yescharacteristic
593C22×C13C4×#4111yescharacteristic
594C22×C13#51811yescharacteristic
595C22×C13#52011yescharacteristic
596C22×C13C2×#12111yescharacteristic
597C22×C13C2×#12111yescharacteristic
598C22×C13C2×#12311yescharacteristic
599C22×C13#52511yescharacteristic
600C22×C13C2×#12411yescharacteristic
601C22×C13C2×#12611yescharacteristic
602C22×C13#52911yescharacteristic
603C22×C13#53211yescharacteristic
604C22×C13#53411yescharacteristic
605C22×C13#53711yescharacteristic
606C22×C13#53811yescharacteristic
607C22×C13#53911yescharacteristic
608C22×C13D4211yescharacteristic
609C22×C13#54611yescharacteristic
610C22×C13#54611yescharacteristic
611C22×C13#54611yescharacteristic
612C22×C13#54611yescharacteristic
613C22×C13#54711yescharacteristic
614C22×C13#54811yescharacteristic
615C22×C13#55111yescharacteristic
616C22×C13#55111yescharacteristic
617C22×C13#55111yescharacteristic
618C22×C13#55111yescharacteristic
619C22×C13#55211yescharacteristic
620C22×C13#55211yescharacteristic
621C22×C13#55311yescharacteristic
622C22×C13#55311yescharacteristic
623C22×C13#55311yescharacteristic
624C4×C13—24no—
625C4×C13—24no—
626C4×C13—42no—
627C4×C13—42no—
628C4×C13—42no—
629C4×C13—42no—
630C4×C13—42no—
631C4×C13—42no—
632C4×C13—42no—
633C4×C13—42no—
634C4×C13—42no—
635C4×C13—81no—
636C4×C13—81no—
637C25C23×C1311yescharacteristic
638C25C23×C1311yescharacteristic
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—22no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—22no—
645C22×D4C2×C4×C1314yes—
646C23×C4—22no—
647C23×C4—22no—
648C23×C4—22no—
649C23×C4—22no—
650C23×C4—22no—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4—41no—
662C23×C4—41no—
663C23×C4—41no—
664C23×C4—41no—
665C23×C4C2×C4×C1314yes—
666C23×C4D4×C1314yes—
667C23×C4C23×C1311yescharacteristic
668C23×C4C23×C1311yescharacteristic
669C23×C4C23×C1311yescharacteristic
670C23×C4C23×C1311yescharacteristic
671C23×C4C23×C1311yescharacteristic
672C23×C4C23×C1311yescharacteristic
673C23×C4C23×C1311yescharacteristic
674C23×C4C23×C1311yescharacteristic
675C23×C4C23×C1311yescharacteristic
676C23×C4C23×C1311yescharacteristic
677C23×C4C23×C1311yescharacteristic
678C23×C4C23×C1311yescharacteristic
679C23×C4C23×C1311yescharacteristic
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4C2×C4×C1314yes—
710C2×C22⋊C4C2×C4×C1314yescomplemented
711C2×C22⋊C4C2×C4×C1314yescomplemented
712C2×C22⋊C4D4×C1314yes—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—22no—
716C2×C42—22no—
717C2×C42—41no—
718C2×C42—41no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—41no—
733#95—41no—
734#95C2×C4×C1314yescomplemented
735#95C2×C4×C1314yescomplemented
736#95D4×C1314yescomplemented
737C2×C13—28no—
738C2×C13—82no—
739C2×C13C2×#38811yescharacteristic
740C2×C13C4×#12111yescharacteristic
741C2×C13#232511yescharacteristic
742C2×C13#235211yescharacteristic
743C2×C13#235311yescharacteristic
744C2×C13#235811yescharacteristic
745C2×C13#235911yescharacteristic
746C2×C13#241211yescharacteristic
747C2×C13#241611yescharacteristic
748C2×C13#247211yescharacteristic
749C2×C13#248111yescharacteristic
750C2×C13#248811yescharacteristic
751C2×C13#249811yescharacteristic
752C2×C13#251011yescharacteristic
753C2×C13#254311yescharacteristic
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—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C22×C4×C1312yes—
777C24C22×C4×C1312yes—
778C24C2×D4×C1312yes—
779C24C2×D4×C1312yes—
780C24C13×#4112yes—
781C24C13×#4112yes—
782C24C13×#4112yes—
783C24C13×#4112yes—
784C24C24×C1311yescharacteristic
785C2×D4—28no—
786C2×D4—28no—
787C2×D4—28no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—28no—
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—21no—
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—28no—
858C22×C4—28no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4C22×C4×C1312yes—
890C22×C4C22×C4×C1312yes—
891C22×C4C22×C4×C1312yes—
892C22×C4C22×C4×C1312yes—
893C22×C4C22×C4×C1312yes—
894C22×C4C2×D4×C1312yes—
895C22×C4C2×D4×C1312yes—
896C22×C4C2×D4×C1312yes—
897C22×C4C2×D4×C1312yes—
898C22×C4C2×D4×C1312yes—
899C22×C4C2×D4×C1312yes—
900C22×C4C2×D4×C1312yes—
901C22×C4C13×#4112yes—
902C22×C4C13×#4112yes—
903C22×C4C13×#4112yes—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C42—44no—
916C42—44no—
917C13#1399911yescharacteristic, direct product factor, Sylow
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
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—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23C13×#11714yes—
982C23C4×D4×C1314yes—
983C23C4×D4×C1314yes—
984C23C13×#12114yes—
985C23C13×#12314yes—
986C23C13×#12414yes—
987C23C13×#12614yes—
988C23C23×C4×C1311yescharacteristic
989C23C22×D4×C1311yescharacteristic
990C23C22×D4×C1311yescharacteristic
991C23C22×D4×C1311yescharacteristic
992C23C2×C13×#4111yescharacteristic
993C23C2×C13×#4111yescharacteristic
994C23C2×C13×#4111yescharacteristic
995C23C2×C13×#4111yescharacteristic
996C23C2×C13×#4111yescharacteristic
997C23C2×C13×#4111yescharacteristic
998C23C2×C13×#4111yescharacteristic
999C23C13×H(5,𝔽2)11yescharacteristic
1000C23C13×H(5,𝔽2)11yescharacteristic
1001C23C13×H(5,𝔽2)11yescharacteristic
1002C23C13×2−1+411yescharacteristic
1003D4—416no—
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—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—416no—
1044C2×C4—416no—
1045C2×C4—416no—
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×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4C4×D4×C1314yes—
1097C2×C4C13×#12114yes—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22C13×#38818yescomplemented
1128C22C2×C13×#11711yescharacteristic
1129C22C2×C4×D4×C1311yescharacteristic
1130C22C2×C4×D4×C1311yescharacteristic
1131C22C2×C4×D4×C1311yescharacteristic
1132C22C4×C13×#4111yescharacteristic
1133C22C13×#51811yescharacteristic
1134C22C13×#52011yescharacteristic
1135C22C2×C13×#12111yescharacteristic
1136C22C2×C13×#12111yescharacteristic
1137C22C2×C13×#12311yescharacteristic
1138C22C13×#52511yescharacteristic
1139C22C2×C13×#12411yescharacteristic
1140C22C2×C13×#12611yescharacteristic
1141C22C13×#52911yescharacteristic
1142C22C13×#53211yescharacteristic
1143C22C13×#53411yescharacteristic
1144C22C13×#53711yescharacteristic
1145C22C13×#53811yescharacteristic
1146C22C13×#53911yescharacteristic
1147C22D42×C1311yescharacteristic
1148C22C13×#54611yescharacteristic
1149C22C13×#54611yescharacteristic
1150C22C13×#54611yescharacteristic
1151C22C13×#54611yescharacteristic
1152C22C13×#54711yescharacteristic
1153C22C13×#54811yescharacteristic
1154C22C13×#55111yescharacteristic
1155C22C13×#55111yescharacteristic
1156C22C13×#55111yescharacteristic
1157C22C13×#55111yescharacteristic
1158C22C13×#55211yescharacteristic
1159C22C13×#55211yescharacteristic
1160C22C13×#55311yescharacteristic
1161C22C13×#55311yescharacteristic
1162C22C13×#55311yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—81no—
1175C4—81no—
1176C2—28no—
1177C2—82no—
1178C2C2×C13×#38811yescharacteristic
1179C2C4×C13×#12111yescharacteristic
1180C2C13×#232511yescharacteristic
1181C2C13×#235211yescharacteristic
1182C2C13×#235311yescharacteristic
1183C2C13×#235811yescharacteristic
1184C2C13×#235911yescharacteristic
1185C2C13×#241211yescharacteristic
1186C2C13×#241611yescharacteristic
1187C2C13×#247211yescharacteristic
1188C2C13×#248111yescharacteristic
1189C2C13×#248811yescharacteristic
1190C2C13×#249811yescharacteristic
1191C2C13×#251011yescharacteristic
1192C2C13×#254311yescharacteristic
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
1. C2×C13×#388C2semidirect
5. C2×C13×#380C2semidirect
6. C2×C4×C13×C22⋊C4C2semidirect
7. C22×C13×#95C2semidirect
8. C13×#1443C2semidirect
9. C13×#1442C2semidirect
10. C13×#1440C2semidirect
11. C13×#1439C2semidirect
12. C13×#1437C2semidirect
13. C13×#1436C2semidirect
14. C13×#1434C2semidirect
15. C13×C22⋊#95C2semidirect
36. C13×#386C4semidirect
131. C2×C13×C22⋊C4C2×C4semidirect
132. C2×C13×C22⋊C4C2×C4semidirect
155. C13×#95C2×C4semidirect
156. C13×#95C2×C4semidirect
157. C13×#95D4semidirect
158. #13999C13direct (N × H)
322. C2×#388C2×C13semidirect
326. C2×#380C2×C13semidirect
327. C2×C4×C22⋊C4C2×C13semidirect
328. C22×#95C2×C13semidirect
329. #1443C2×C13semidirect
330. #1442C2×C13semidirect
331. #1440C2×C13semidirect
332. #1439C2×C13semidirect
333. #1437C2×C13semidirect
334. #1436C2×C13semidirect
335. #1434C2×C13semidirect
336. C22⋊#95C2×C13semidirect
537. #386C4×C13semidirect
588. C22×C13#388semidirect
710. C2×C22⋊C4C2×C4×C13semidirect
711. C2×C22⋊C4C2×C4×C13semidirect
734. #95C2×C4×C13semidirect
735. #95C2×C4×C13semidirect
736. #95D4×C13semidirect
917. C13#13999direct (N × H)
1127. C22C13×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#3882
C2×C13×#3862
C2×C13×#3802
C2×C4×C13×C22⋊C42
C22×C13×#952
C13×#14432
C13×#14422
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C13×#14342
C13×C22⋊#952
#1399913