Finite Group Databasebeta

← C13×#14071 #15700410

Subgroups — C13×#14071 #15700410

Order 3328.

2206 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×#117C211yesmaximal, characteristic, complemented
2C2×C13×#390C211yesmaximal, characteristic
3C2×C13×#388C211yesmaximal, characteristic, complemented
4C2×C13×#388C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic
6C13×#1444C211yesmaximal, characteristic, complemented
7C13×#1439C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic, complemented
9C13×#1438C211yesmaximal, characteristic
10C13×#1437C211yesmaximal, characteristic, complemented
11C13×#1437C211yesmaximal, characteristic, complemented
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×C22⋊#95C211yesmaximal, characteristic, complemented
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×#117—24no—
19C2×C13×#117—24no—
20C2×C13×#117—24no—
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊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×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2211yescharacteristic
34C22×C13×C22⋊C4C2211yescharacteristic
35C22×C13×C22⋊C4C2211yescharacteristic
36C22×C42×C13C2211yescharacteristic
37C22×C42×C13C2211yescharacteristic
38C22×C42×C13C2211yescharacteristic
39C22×C42×C13C2211yescharacteristic
40C13×#390—24no—
41C13×#388—24no—
42C13×#388—24no—
43C13×#386C418yescomplemented
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—22no—
72C23×C4×C13—22no—
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×#117—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—41no—
97C2×C13×C4⋊C4—41no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4D414yescomplemented
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
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⋊C4C2×C414yes—
130C2×C13×C22⋊C4C2×C414yes—
131C2×C13×C22⋊C4C2×C414yes—
132C2×C13×C22⋊C4D414yes—
133C2×C42×C13—22no—
134C2×C42×C13—22no—
135C2×C42×C13—22no—
136C2×C42×C13—22no—
137C2×C42×C13—22no—
138C2×C42×C13—22no—
139C2×C42×C13—22no—
140C2×C42×C13—22no—
141C2×C42×C13—22no—
142C2×C42×C13—41no—
143C2×C42×C13—41no—
144C2×C42×C13D414yescomplemented
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—41no—
155C13×#95—41no—
156C13×#95—41no—
157C13×#95C2×C414yes—
158C13×#95C2×C414yes—
159#14071C1311yesmaximal, 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—28no—
199C22×C4×C13—28no—
200C22×C4×C13—28no—
201C22×C4×C13—28no—
202C22×C4×C13—28no—
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—28no—
220C22×C4×C13—28no—
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×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—21no—
277C22×C4×C13C22×C412yes—
278C22×C4×C13C22×C412yes—
279C22×C4×C13C22×C412yes—
280C22×C4×C13C22×C412yes—
281C22×C4×C13C22×C412yes—
282C22×C4×C13C2×D412yes—
283C22×C4×C13C2×D412yes—
284C22×C4×C13C2×D412yes—
285C22×C4×C13C2×D412yes—
286C22×C4×C13C2×D412yes—
287C22×C4×C13C2×D412yes—
288C22×C4×C13C2×D412yes—
289C22×C4×C13C2×D412yes—
290C22×C4×C13#4112yes—
291C22×C4×C13#4112yes—
292C22×C4×C13#4112yes—
293C22×C4×C13#4112yes—
294C22×C4×C13#4112yes—
295C22×C4×C13#4112yes—
296C13×C4⋊C4—28no—
297C13×C4⋊C4—28no—
298C13×C4⋊C4—44no—
299C13×C4⋊C4—44no—
300C13×C22⋊C4—28no—
301C13×C22⋊C4—28no—
302C13×C22⋊C4—28no—
303C13×C22⋊C4—28no—
304C13×C22⋊C4—44no—
305C13×C22⋊C4—44no—
306C13×C22⋊C4—44no—
307C13×C22⋊C4—44no—
308C13×C22⋊C4—44no—
309C13×C22⋊C4—44no—
310C13×C22⋊C4—44no—
311C42×C13—28no—
312C42×C13—28no—
313C42×C13—44no—
314C42×C13—44no—
315C22×#117C2×C1311yescharacteristic, complemented
316C2×#390C2×C1311yescharacteristic
317C2×#388C2×C1311yescharacteristic, complemented
318C2×#388C2×C1311yescharacteristic, complemented
319C2×#386C2×C1311yescharacteristic
320#1444C2×C1311yescharacteristic, complemented
321#1439C2×C1311yescharacteristic, complemented
322#1439C2×C1311yescharacteristic, complemented
323#1438C2×C1311yescharacteristic
324#1437C2×C1311yescharacteristic, complemented
325#1437C2×C1311yescharacteristic, complemented
326#1436C2×C1311yescharacteristic, complemented
327#1436C2×C1311yescharacteristic, complemented
328C22⋊#95C2×C1311yescharacteristic, complemented
329C4×#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×C13C2×#4111yescharacteristic
408C23×C13C2×#4111yescharacteristic
409C23×C13C2×#4111yescharacteristic
410C23×C13C2×#4111yescharacteristic
411C23×C13H(5,𝔽2)11yescharacteristic
412C23×C13H(5,𝔽2)11yescharacteristic
413C23×C13H(5,𝔽2)11yescharacteristic
414C23×C132−1+411yescharacteristic
415D4×C13—416no—
416C2×C4×C13—232no—
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—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—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#11714yescomplemented
505C2×C4×C13C4×D414yes—
506C2×C4×C13C4×D414yes—
507C2×C4×C13#12014yes—
508C23×D4C22×C1311yescharacteristic
509C24×C4C22×C1311yescharacteristic
510C2×#117—24no—
511C2×#117—24no—
512C2×#117—24no—
513C22×C4⋊C4C22×C1311yescharacteristic
514C22×C4⋊C4C22×C1311yescharacteristic
515C22×C4⋊C4C22×C1311yescharacteristic
516C22×C4⋊C4C22×C1311yescharacteristic
517C22×C22⋊C4C22×C1311yescharacteristic
518C22×C22⋊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×C42C22×C1311yescharacteristic
529C22×C42C22×C1311yescharacteristic
530C22×C42C22×C1311yescharacteristic
531C22×C42C22×C1311yescharacteristic
532#390—24no—
533#388—24no—
534#388—24no—
535#386C4×C1318yescomplemented
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×C13C2×#11711yescharacteristic
581C22×C13C2×C4×D411yescharacteristic
582C22×C13C2×C4×D411yescharacteristic
583C22×C13C2×C4×D411yescharacteristic
584C22×C13C4×#4111yescharacteristic
585C22×C13#51811yescharacteristic
586C22×C13#52011yescharacteristic
587C22×C13C2×#12011yescharacteristic
588C22×C13#52511yescharacteristic
589C22×C13#52511yescharacteristic
590C22×C13#52511yescharacteristic
591C22×C13#52911yescharacteristic
592C22×C13#52911yescharacteristic
593C22×C13#53211yescharacteristic
594C22×C13#53211yescharacteristic
595C22×C13#53511yescharacteristic
596C22×C13#53711yescharacteristic
597C22×C13#54011yescharacteristic
598C22×C13#54211yescharacteristic
599C22×C13#54611yescharacteristic
600C22×C13#54611yescharacteristic
601C22×C13#54611yescharacteristic
602C22×C13#54611yescharacteristic
603C22×C13#54711yescharacteristic
604C22×C13#54711yescharacteristic
605C22×C13#55011yescharacteristic
606C22×C13#55011yescharacteristic
607C22×C13#55111yescharacteristic
608C22×C13#55111yescharacteristic
609C22×C13#55111yescharacteristic
610C22×C13#55211yescharacteristic
611C22×C13#55311yescharacteristic
612C22×C13#55511yescharacteristic
613C22×C13#55511yescharacteristic
614C22×C13#55611yescharacteristic
615C4×C13—24no—
616C4×C13—24no—
617C4×C13—24no—
618C4×C13—24no—
619C4×C13—42no—
620C4×C13—42no—
621C4×C13—42no—
622C4×C13—42no—
623C4×C13—42no—
624C4×C13—42no—
625C4×C13—42no—
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—22no—
642C23×C4—22no—
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#117—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—41no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4D4×C1314yescomplemented
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
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⋊C4C2×C4×C1314yes—
700C2×C22⋊C4C2×C4×C1314yes—
701C2×C22⋊C4C2×C4×C1314yes—
702C2×C22⋊C4D4×C1314yes—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42D4×C1314yescomplemented
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—41no—
725#95—41no—
726#95—41no—
727#95C2×C4×C1314yes—
728#95C2×C4×C1314yes—
729C2×C13—44no—
730C2×C13—82no—
731C2×C13#229311yescharacteristic
732C2×C13C4×#12011yescharacteristic
733C2×C13#232411yescharacteristic
734C2×C13#234211yescharacteristic
735C2×C13#235411yescharacteristic
736C2×C13#235911yescharacteristic
737C2×C13#236311yescharacteristic
738C2×C13#243011yescharacteristic
739C2×C13#243111yescharacteristic
740C2×C13#247111yescharacteristic
741C2×C13#247411yescharacteristic
742C2×C13#247611yescharacteristic
743C2×C13#247911yescharacteristic
744C2×C13#260111yescharacteristic
745C2×C13#261011yescharacteristic
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—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
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—28no—
806C22×C4—28no—
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—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4C22×C4×C1312yes—
864C22×C4C22×C4×C1312yes—
865C22×C4C22×C4×C1312yes—
866C22×C4C22×C4×C1312yes—
867C22×C4C22×C4×C1312yes—
868C22×C4C2×D4×C1312yes—
869C22×C4C2×D4×C1312yes—
870C22×C4C2×D4×C1312yes—
871C22×C4C2×D4×C1312yes—
872C22×C4C2×D4×C1312yes—
873C22×C4C2×D4×C1312yes—
874C22×C4C2×D4×C1312yes—
875C22×C4C2×D4×C1312yes—
876C22×C4C13×#4112yes—
877C22×C4C13×#4112yes—
878C22×C4C13×#4112yes—
879C22×C4C13×#4112yes—
880C22×C4C13×#4112yes—
881C22×C4C13×#4112yes—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C42—28no—
898C42—28no—
899C42—44no—
900C42—44no—
901C13#1407111yescharacteristic, 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
979C23C2×C13×#4111yescharacteristic
980C23C2×C13×#4111yescharacteristic
981C23C2×C13×#4111yescharacteristic
982C23C2×C13×#4111yescharacteristic
983C23C13×H(5,𝔽2)11yescharacteristic
984C23C13×H(5,𝔽2)11yescharacteristic
985C23C13×H(5,𝔽2)11yescharacteristic
986C23C13×2−1+411yescharacteristic
987D4—416no—
988C2×C4—232no—
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—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—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×C4C13×#11714yescomplemented
1077C2×C4C4×D4×C1314yes—
1078C2×C4C4×D4×C1314yes—
1079C2×C4C13×#12014yes—
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—
1110C22C2×C13×#11711yescharacteristic
1111C22C2×C4×D4×C1311yescharacteristic
1112C22C2×C4×D4×C1311yescharacteristic
1113C22C2×C4×D4×C1311yescharacteristic
1114C22C4×C13×#4111yescharacteristic
1115C22C13×#51811yescharacteristic
1116C22C13×#52011yescharacteristic
1117C22C2×C13×#12011yescharacteristic
1118C22C13×#52511yescharacteristic
1119C22C13×#52511yescharacteristic
1120C22C13×#52511yescharacteristic
1121C22C13×#52911yescharacteristic
1122C22C13×#52911yescharacteristic
1123C22C13×#53211yescharacteristic
1124C22C13×#53211yescharacteristic
1125C22C13×#53511yescharacteristic
1126C22C13×#53711yescharacteristic
1127C22C13×#54011yescharacteristic
1128C22C13×#54211yescharacteristic
1129C22C13×#54611yescharacteristic
1130C22C13×#54611yescharacteristic
1131C22C13×#54611yescharacteristic
1132C22C13×#54611yescharacteristic
1133C22C13×#54711yescharacteristic
1134C22C13×#54711yescharacteristic
1135C22C13×#55011yescharacteristic
1136C22C13×#55011yescharacteristic
1137C22C13×#55111yescharacteristic
1138C22C13×#55111yescharacteristic
1139C22C13×#55111yescharacteristic
1140C22C13×#55211yescharacteristic
1141C22C13×#55311yescharacteristic
1142C22C13×#55511yescharacteristic
1143C22C13×#55511yescharacteristic
1144C22C13×#55611yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C13×#229311yescharacteristic
1161C2C4×C13×#12011yescharacteristic
1162C2C13×#232411yescharacteristic
1163C2C13×#234211yescharacteristic
1164C2C13×#235411yescharacteristic
1165C2C13×#235911yescharacteristic
1166C2C13×#236311yescharacteristic
1167C2C13×#243011yescharacteristic
1168C2C13×#243111yescharacteristic
1169C2C13×#247111yescharacteristic
1170C2C13×#247411yescharacteristic
1171C2C13×#247611yescharacteristic
1172C2C13×#247911yescharacteristic
1173C2C13×#260111yescharacteristic
1174C2C13×#261011yescharacteristic
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. C22×C13×#117C2semidirect
3. C2×C13×#388C2semidirect
4. C2×C13×#388C2semidirect
6. C13×#1444C2semidirect
7. C13×#1439C2semidirect
8. C13×#1439C2semidirect
10. C13×#1437C2semidirect
11. C13×#1437C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×C22⋊#95C2semidirect
15. C4×C13×#95C2semidirect
43. C13×#386C4semidirect
99. C2×C13×C4⋊C4D4semidirect
144. C2×C42×C13D4semidirect
159. #14071C13direct (N × H)
315. C22×#117C2×C13semidirect
317. C2×#388C2×C13semidirect
318. C2×#388C2×C13semidirect
320. #1444C2×C13semidirect
321. #1439C2×C13semidirect
322. #1439C2×C13semidirect
324. #1437C2×C13semidirect
325. #1437C2×C13semidirect
326. #1436C2×C13semidirect
327. #1436C2×C13semidirect
328. C22⋊#95C2×C13semidirect
329. C4×#95C2×C13semidirect
504. C2×C4×C13#117semidirect
535. #386C4×C13semidirect
669. C2×C4⋊C4D4×C13semidirect
714. C2×C42D4×C13semidirect
901. C13#14071direct (N × H)
1076. C2×C4C13×#117semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1172
C2×C13×#3902
C2×C13×#3882
C2×C13×#3862
C13×#14442
C13×#14392
C13×#14382
C13×#14372
C13×#14362
C13×C22⋊#952
C4×C13×#952
#1407113