Finite Group Databasebeta

← C13×#14566 #15700905

Subgroups — C13×#14566 #15700905

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#394C211yesmaximal, characteristic
2C2×C13×#388C211yesmaximal, characteristic, complemented
3C2×C13×#388C211yesmaximal, characteristic, complemented
4C13×#1443C211yesmaximal, characteristic, complemented
5C13×#1439C211yesmaximal, characteristic, complemented
6C13×#1439C211yesmaximal, characteristic, complemented
7C13×#1438C211yesmaximal, characteristic
8C13×#1438C211yesmaximal, characteristic
9C13×#1437C211yesmaximal, characteristic, complemented
10C13×#1437C211yesmaximal, characteristic, complemented
11C13×#1437C211yesmaximal, characteristic, complemented
12C13×#1437C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊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×C13×C22⋊C4C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C22×C42×C13C2211yescharacteristic
35C13×#394C418yescomplemented
36C13×#388—24no—
37C13×#388—24no—
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
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
54C25×C13C2311yescharacteristic
55C25×C13C2311yescharacteristic
56C22×D4×C13—41no—
57C22×D4×C13—41no—
58C22×D4×C13—41no—
59C22×D4×C13—41no—
60C22×D4×C13—41no—
61C22×D4×C13—41no—
62C22×D4×C13C2×C414yes—
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—41no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C4⋊C4C2×C414yes—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—41no—
102C2×C13×C22⋊C4—41no—
103C2×C13×C22⋊C4—41no—
104C2×C13×C22⋊C4—41no—
105C2×C13×C22⋊C4—41no—
106C2×C13×C22⋊C4—41no—
107C2×C13×C22⋊C4—41no—
108C2×C13×C22⋊C4—41no—
109C2×C13×C22⋊C4—41no—
110C2×C13×C22⋊C4—41no—
111C2×C13×C22⋊C4—41no—
112C2×C13×C22⋊C4—41no—
113C2×C13×C22⋊C4—41no—
114C2×C13×C22⋊C4—41no—
115C2×C13×C22⋊C4—41no—
116C2×C13×C22⋊C4—41no—
117C2×C13×C22⋊C4C2×C414yes—
118C2×C13×C22⋊C4C2×C414yes—
119C2×C13×C22⋊C4C2×C414yes—
120C2×C13×C22⋊C4C2×C414yes—
121C2×C42×C13—22no—
122C2×C42×C13—22no—
123C2×C42×C13—22no—
124C2×C42×C13—41no—
125C2×C42×C13—41no—
126C2×C42×C13—41no—
127C2×C42×C13—41no—
128C2×C42×C13—41no—
129C2×C42×C13—41no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95—22no—
134C13×#95—41no—
135C13×#95—41no—
136C13×#95—41no—
137C13×#95—41no—
138C13×#95—41no—
139C13×#95—41no—
140C13×#95—41no—
141C13×#95—41no—
142C13×#95—41no—
143C13×#95—41no—
144C13×#95C2×C414yes—
145C13×#95D414yescomplemented
146#14566C1311yesmaximal, characteristic, direct product factor, Sylow
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
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×C13C22×C412yes—
176C24×C13C22×C412yes—
177C24×C13C2411yescharacteristic
178C2×D4×C13—44no—
179C2×D4×C13—44no—
180C2×D4×C13—44no—
181C2×D4×C13—44no—
182C2×D4×C13—44no—
183C2×D4×C13—44no—
184C2×D4×C13—44no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
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—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
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—21no—
263C22×C4×C13C22×C412yes—
264C22×C4×C13C22×C412yes—
265C22×C4×C13C22×C412yes—
266C22×C4×C13C22×C412yes—
267C22×C4×C13C22×C412yes—
268C22×C4×C13C2×D412yes—
269C22×C4×C13C2×D412yes—
270C22×C4×C13C2×D412yes—
271C22×C4×C13#4112yes—
272C22×C4×C13#4112yes—
273C22×C4×C13#4112yes—
274C22×C4×C13#4112yes—
275C22×C4×C13#4112yes—
276C13×C4⋊C4—44no—
277C13×C4⋊C4—44no—
278C13×C4⋊C4—44no—
279C13×C22⋊C4—28no—
280C13×C22⋊C4—28no—
281C13×C22⋊C4—44no—
282C13×C22⋊C4—44no—
283C13×C22⋊C4—44no—
284C13×C22⋊C4—44no—
285C13×C22⋊C4—44no—
286C13×C22⋊C4—44no—
287C13×C22⋊C4—44no—
288C13×C22⋊C4—44no—
289C13×C22⋊C4—44no—
290C13×C22⋊C4—44no—
291C42×C13—44no—
292C42×C13—44no—
293C42×C13—44no—
294C2×#394C2×C1311yescharacteristic
295C2×#388C2×C1311yescharacteristic, complemented
296C2×#388C2×C1311yescharacteristic, complemented
297#1443C2×C1311yescharacteristic, complemented
298#1439C2×C1311yescharacteristic, complemented
299#1439C2×C1311yescharacteristic, complemented
300#1438C2×C1311yescharacteristic
301#1438C2×C1311yescharacteristic
302#1437C2×C1311yescharacteristic, complemented
303#1437C2×C1311yescharacteristic, complemented
304#1437C2×C1311yescharacteristic, complemented
305#1437C2×C1311yescharacteristic, complemented
306#1436C2×C1311yescharacteristic, complemented
307#1436C2×C1311yescharacteristic, complemented
308C4⋊#95C2×C1311yescharacteristic, complemented
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13—41no—
340C23×C13—41no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—41no—
344C23×C13—41no—
345C23×C13—41no—
346C23×C13—41no—
347C23×C13—41no—
348C23×C13—41no—
349C23×C13—41no—
350C23×C13—41no—
351C23×C13—41no—
352C23×C13—41no—
353C23×C13—41no—
354C23×C13—41no—
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×C13C23×C411yescharacteristic
380C23×C13C22×D411yescharacteristic
381C23×C13C2×#4111yescharacteristic
382C23×C13C2×#4111yescharacteristic
383C23×C13C2×#4111yescharacteristic
384C23×C13C2×#4111yescharacteristic
385C23×C13C2×#4111yescharacteristic
386C23×C13H(5,𝔽2)11yescharacteristic
387C23×C13H(5,𝔽2)11yescharacteristic
388C23×C13H(5,𝔽2)11yescharacteristic
389C23×C13H(5,𝔽2)11yescharacteristic
390C23×C13H(5,𝔽2)11yescharacteristic
391C23×C13H(5,𝔽2)11yescharacteristic
392C23×C13H(5,𝔽2)11yescharacteristic
393C23×C132−1+411yescharacteristic
394D4×C13—416no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—22no—
402C2×C4×C13—22no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—22no—
406C2×C4×C13—22no—
407C2×C4×C13—22no—
408C2×C4×C13—22no—
409C2×C4×C13—22no—
410C2×C4×C13—22no—
411C2×C4×C13—22no—
412C2×C4×C13—22no—
413C2×C4×C13—22no—
414C2×C4×C13—22no—
415C2×C4×C13—22no—
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—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
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×C13C4×D414yes—
486C23×D4C22×C1311yescharacteristic
487C22×C4⋊C4C22×C1311yescharacteristic
488C22×C4⋊C4C22×C1311yescharacteristic
489C22×C4⋊C4C22×C1311yescharacteristic
490C22×C22⋊C4C22×C1311yescharacteristic
491C22×C22⋊C4C22×C1311yescharacteristic
492C22×C22⋊C4C22×C1311yescharacteristic
493C22×C22⋊C4C22×C1311yescharacteristic
494C22×C22⋊C4C22×C1311yescharacteristic
495C22×C22⋊C4C22×C1311yescharacteristic
496C22×C22⋊C4C22×C1311yescharacteristic
497C22×C22⋊C4C22×C1311yescharacteristic
498C22×C22⋊C4C22×C1311yescharacteristic
499C22×C22⋊C4C22×C1311yescharacteristic
500C22×C22⋊C4C22×C1311yescharacteristic
501C22×C22⋊C4C22×C1311yescharacteristic
502C22×C42C22×C1311yescharacteristic
503C22×C42C22×C1311yescharacteristic
504C22×C42C22×C1311yescharacteristic
505#394C4×C1318yescomplemented
506#388—24no—
507#388—24no—
508C2×#95C22×C1311yescharacteristic
509C2×#95C22×C1311yescharacteristic
510C2×#95C22×C1311yescharacteristic
511C2×#95C22×C1311yescharacteristic
512C2×#95C22×C1311yescharacteristic
513C2×#95C22×C1311yescharacteristic
514C2×#95C22×C1311yescharacteristic
515C2×#95C22×C1311yescharacteristic
516C2×#95C22×C1311yescharacteristic
517C2×#95C22×C1311yescharacteristic
518C2×#95C22×C1311yescharacteristic
519C2×#95C22×C1311yescharacteristic
520C2×#95C22×C1311yescharacteristic
521C2×#95C22×C1311yescharacteristic
522C2×#95C22×C1311yescharacteristic
523C2×#95C22×C1311yescharacteristic
524C22×C13—42no—
525C22×C13—42no—
526C22×C13—42no—
527C22×C13—42no—
528C22×C13—42no—
529C22×C13—42no—
530C22×C13—42no—
531C22×C13—42no—
532C22×C13—42no—
533C22×C13—42no—
534C22×C13—42no—
535C22×C13—42no—
536C22×C13—42no—
537C22×C13—42no—
538C22×C13—81no—
539C22×C13—81no—
540C22×C13—81no—
541C22×C13—81no—
542C22×C13—81no—
543C22×C13—81no—
544C22×C13—81no—
545C22×C13—81no—
546C22×C13—81no—
547C22×C13—81no—
548C22×C13—81no—
549C22×C13—81no—
550C22×C13—81no—
551C22×C13—81no—
552C22×C13—81no—
553C22×C13—81no—
554C22×C13C2×C4×D411yescharacteristic
555C22×C13C4×#4111yescharacteristic
556C22×C13C4×#4111yescharacteristic
557C22×C13#51811yescharacteristic
558C22×C13#51811yescharacteristic
559C22×C13#51811yescharacteristic
560C22×C13#52011yescharacteristic
561C22×C13#53511yescharacteristic
562C22×C13#53711yescharacteristic
563C22×C13#53811yescharacteristic
564C22×C13#53811yescharacteristic
565C22×C13#53811yescharacteristic
566C22×C13#53911yescharacteristic
567C22×C13#54011yescharacteristic
568C22×C13#54011yescharacteristic
569C22×C13#54211yescharacteristic
570C22×C13#54211yescharacteristic
571C22×C13#54211yescharacteristic
572C22×C13#54211yescharacteristic
573C22×C13#54611yescharacteristic
574C22×C13#54611yescharacteristic
575C22×C13#54611yescharacteristic
576C22×C13#55011yescharacteristic
577C22×C13#55111yescharacteristic
578C22×C13#55311yescharacteristic
579C22×C13#55311yescharacteristic
580C22×C13#55311yescharacteristic
581C22×C13#55311yescharacteristic
582C22×C13#55311yescharacteristic
583C22×C13#55511yescharacteristic
584C22×C13#55911yescharacteristic
585C22×C13#56011yescharacteristic
586C22×C13#56011yescharacteristic
587C22×C13#56011yescharacteristic
588C22×C13H(3,𝔽4)11yescharacteristic
589C4×C13—24no—
590C4×C13—42no—
591C4×C13—42no—
592C4×C13—42no—
593C4×C13—42no—
594C4×C13—42no—
595C4×C13—42no—
596C4×C13—42no—
597C4×C13—42no—
598C4×C13—42no—
599C4×C13—42no—
600C4×C13—81no—
601C4×C13—81no—
602C25C23×C1311yescharacteristic
603C25C23×C1311yescharacteristic
604C22×D4—41no—
605C22×D4—41no—
606C22×D4—41no—
607C22×D4—41no—
608C22×D4—41no—
609C22×D4—41no—
610C22×D4C2×C4×C1314yes—
611C23×C4C23×C1311yescharacteristic
612C23×C4C23×C1311yescharacteristic
613C23×C4C23×C1311yescharacteristic
614C23×C4C23×C1311yescharacteristic
615C23×C4C23×C1311yescharacteristic
616C23×C4C23×C1311yescharacteristic
617C23×C4C23×C1311yescharacteristic
618C23×C4C23×C1311yescharacteristic
619C23×C4C23×C1311yescharacteristic
620C23×C4C23×C1311yescharacteristic
621C23×C4C23×C1311yescharacteristic
622C23×C4C23×C1311yescharacteristic
623C23×C4C23×C1311yescharacteristic
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4C2×C4×C1314yes—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4C2×C4×C1314yes—
666C2×C22⋊C4C2×C4×C1314yes—
667C2×C22⋊C4C2×C4×C1314yes—
668C2×C22⋊C4C2×C4×C1314yes—
669C2×C42—22no—
670C2×C42—22no—
671C2×C42—22no—
672C2×C42—41no—
673C2×C42—41no—
674C2×C42—41no—
675C2×C42—41no—
676C2×C42—41no—
677C2×C42—41no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95C2×C4×C1314yes—
693#95D4×C1314yescomplemented
694C2×C13—82no—
695C2×C13—82no—
696C2×C13#232411yescharacteristic
697C2×C13#233511yescharacteristic
698C2×C13#233711yescharacteristic
699C2×C13#236311yescharacteristic
700C2×C13#236411yescharacteristic
701C2×C13#237411yescharacteristic
702C2×C13#237511yescharacteristic
703C2×C13#270311yescharacteristic
704C2×C13#270511yescharacteristic
705C2×C13#271211yescharacteristic
706C2×C13#271411yescharacteristic
707C2×C13#275311yescharacteristic
708C2×C13#279511yescharacteristic
709C2×C13#280111yescharacteristic
710C2×C13#280311yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24C22×C4×C1312yes—
740C24C22×C4×C1312yes—
741C24C24×C1311yescharacteristic
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
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—21no—
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×C4C22×C4×C1312yes—
828C22×C4C22×C4×C1312yes—
829C22×C4C22×C4×C1312yes—
830C22×C4C22×C4×C1312yes—
831C22×C4C22×C4×C1312yes—
832C22×C4C2×D4×C1312yes—
833C22×C4C2×D4×C1312yes—
834C22×C4C2×D4×C1312yes—
835C22×C4C13×#4112yes—
836C22×C4C13×#4112yes—
837C22×C4C13×#4112yes—
838C22×C4C13×#4112yes—
839C22×C4C13×#4112yes—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C42—44no—
856C42—44no—
857C42—44no—
858C13#1456611yescharacteristic, direct product factor, Sylow
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23C23×C4×C1311yescharacteristic
930C23C22×D4×C1311yescharacteristic
931C23C2×C13×#4111yescharacteristic
932C23C2×C13×#4111yescharacteristic
933C23C2×C13×#4111yescharacteristic
934C23C2×C13×#4111yescharacteristic
935C23C2×C13×#4111yescharacteristic
936C23C13×H(5,𝔽2)11yescharacteristic
937C23C13×H(5,𝔽2)11yescharacteristic
938C23C13×H(5,𝔽2)11yescharacteristic
939C23C13×H(5,𝔽2)11yescharacteristic
940C23C13×H(5,𝔽2)11yescharacteristic
941C23C13×H(5,𝔽2)11yescharacteristic
942C23C13×H(5,𝔽2)11yescharacteristic
943C23C13×2−1+411yescharacteristic
944D4—416no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
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×C4C4×D4×C1314yes—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22C2×C4×D4×C1311yescharacteristic
1067C22C4×C13×#4111yescharacteristic
1068C22C4×C13×#4111yescharacteristic
1069C22C13×#51811yescharacteristic
1070C22C13×#51811yescharacteristic
1071C22C13×#51811yescharacteristic
1072C22C13×#52011yescharacteristic
1073C22C13×#53511yescharacteristic
1074C22C13×#53711yescharacteristic
1075C22C13×#53811yescharacteristic
1076C22C13×#53811yescharacteristic
1077C22C13×#53811yescharacteristic
1078C22C13×#53911yescharacteristic
1079C22C13×#54011yescharacteristic
1080C22C13×#54011yescharacteristic
1081C22C13×#54211yescharacteristic
1082C22C13×#54211yescharacteristic
1083C22C13×#54211yescharacteristic
1084C22C13×#54211yescharacteristic
1085C22C13×#54611yescharacteristic
1086C22C13×#54611yescharacteristic
1087C22C13×#54611yescharacteristic
1088C22C13×#55011yescharacteristic
1089C22C13×#55111yescharacteristic
1090C22C13×#55311yescharacteristic
1091C22C13×#55311yescharacteristic
1092C22C13×#55311yescharacteristic
1093C22C13×#55311yescharacteristic
1094C22C13×#55311yescharacteristic
1095C22C13×#55511yescharacteristic
1096C22C13×#55911yescharacteristic
1097C22C13×#56011yescharacteristic
1098C22C13×#56011yescharacteristic
1099C22C13×#56011yescharacteristic
1100C22C13×H(3,𝔽4)11yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—81no—
1113C4—81no—
1114C2—82no—
1115C2—82no—
1116C2C13×#232411yescharacteristic
1117C2C13×#233511yescharacteristic
1118C2C13×#233711yescharacteristic
1119C2C13×#236311yescharacteristic
1120C2C13×#236411yescharacteristic
1121C2C13×#237411yescharacteristic
1122C2C13×#237511yescharacteristic
1123C2C13×#270311yescharacteristic
1124C2C13×#270511yescharacteristic
1125C2C13×#271211yescharacteristic
1126C2C13×#271411yescharacteristic
1127C2C13×#275311yescharacteristic
1128C2C13×#279511yescharacteristic
1129C2C13×#280111yescharacteristic
1130C2C13×#280311yescharacteristic
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
2. C2×C13×#388C2semidirect
3. C2×C13×#388C2semidirect
4. C13×#1443C2semidirect
5. C13×#1439C2semidirect
6. C13×#1439C2semidirect
9. C13×#1437C2semidirect
10. C13×#1437C2semidirect
11. C13×#1437C2semidirect
12. C13×#1437C2semidirect
13. C13×#1436C2semidirect
14. C13×#1436C2semidirect
15. C13×C4⋊#95C2semidirect
35. C13×#394C4semidirect
145. C13×#95D4semidirect
146. #14566C13direct (N × H)
295. C2×#388C2×C13semidirect
296. C2×#388C2×C13semidirect
297. #1443C2×C13semidirect
298. #1439C2×C13semidirect
299. #1439C2×C13semidirect
302. #1437C2×C13semidirect
303. #1437C2×C13semidirect
304. #1437C2×C13semidirect
305. #1437C2×C13semidirect
306. #1436C2×C13semidirect
307. #1436C2×C13semidirect
308. C4⋊#95C2×C13semidirect
505. #394C4×C13semidirect
693. #95D4×C13semidirect
858. C13#14566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3942
C2×C13×#3882
C13×#14432
C13×#14392
C13×#14382
C13×#14372
C13×#14362
C13×C4⋊#952
#1456613