Finite Group Databasebeta

← C13×#14100 #15700439

Subgroups — C13×#14100 #15700439

Order 3328.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#121C211yesmaximal, characteristic
2C2×C13×#390C211yesmaximal, characteristic, complemented
3C2×C13×#388C211yesmaximal, characteristic, complemented
4C2×C13×#386C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic, complemented
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
7C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
8C13×#1441C211yesmaximal, characteristic, complemented
9C13×#1438C211yesmaximal, characteristic, complemented
10C13×#1438C211yesmaximal, characteristic, complemented
11C13×#1438C211yesmaximal, characteristic, complemented
12C13×#1437C211yesmaximal, characteristic, complemented
13C13×#1437C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic
21C2×C13×#121—24no—
22C2×C13×#121—24no—
23C2×C13×#121C418yescomplemented
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊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×C13×C22⋊C4C2211yescharacteristic
37C22×C13×C22⋊C4C2211yescharacteristic
38C22×C13×C22⋊C4C2211yescharacteristic
39C22×C42×C13C2211yescharacteristic
40C22×C42×C13C2211yescharacteristic
41C22×C42×C13C2211yescharacteristic
42C13×#390—24no—
43C13×#388—24no—
44C13×#386—24no—
45C13×#386—24no—
46C4×C13×C22⋊C4—24no—
47C4×C13×C22⋊C4—24no—
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
58C2×C13×#95C2211yescharacteristic
59C2×C13×#95C2211yescharacteristic
60C25×C13C2311yescharacteristic
61C25×C13C2311yescharacteristic
62C25×C13C2311yescharacteristic
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13—22no—
67C22×D4×C13—22no—
68C22×D4×C13—22no—
69C22×D4×C13—22no—
70C22×D4×C13—22no—
71C22×D4×C13—22no—
72C22×D4×C13—22no—
73C22×D4×C13—22no—
74C22×D4×C13—22no—
75C22×D4×C13—41no—
76C22×D4×C13—41no—
77C22×D4×C13—41no—
78C22×D4×C13—41no—
79C22×D4×C13—41no—
80C22×D4×C13—41no—
81C22×D4×C13C2×C414yes—
82C22×D4×C13C2×C414yes—
83C22×D4×C13C2×C414yescomplemented
84C23×C4×C13—22no—
85C23×C4×C13—22no—
86C23×C4×C13—22no—
87C23×C4×C13—22no—
88C23×C4×C13—22no—
89C23×C4×C13—22no—
90C23×C4×C13—22no—
91C23×C4×C13—22no—
92C23×C4×C13—22no—
93C23×C4×C13—41no—
94C23×C4×C13—41no—
95C23×C4×C13—41no—
96C23×C4×C13—41no—
97C23×C4×C13C2×C414yescomplemented
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C23×C4×C13C2311yescharacteristic
102C23×C4×C13C2311yescharacteristic
103C23×C4×C13C2311yescharacteristic
104C23×C4×C13C2311yescharacteristic
105C23×C4×C13C2311yescharacteristic
106C23×C4×C13C2311yescharacteristic
107C23×C4×C13C2311yescharacteristic
108C23×C4×C13C2311yescharacteristic
109C23×C4×C13C2311yescharacteristic
110C13×#121—232no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—22no—
113C2×C13×C4⋊C4—22no—
114C2×C13×C4⋊C4—22no—
115C2×C13×C4⋊C4—41no—
116C2×C13×C4⋊C4C2×C414yescomplemented
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—22no—
125C2×C13×C22⋊C4—22no—
126C2×C13×C22⋊C4—22no—
127C2×C13×C22⋊C4—22no—
128C2×C13×C22⋊C4—22no—
129C2×C13×C22⋊C4—22no—
130C2×C13×C22⋊C4—22no—
131C2×C13×C22⋊C4—22no—
132C2×C13×C22⋊C4—22no—
133C2×C13×C22⋊C4—22no—
134C2×C13×C22⋊C4—22no—
135C2×C13×C22⋊C4—22no—
136C2×C13×C22⋊C4—22no—
137C2×C13×C22⋊C4—22no—
138C2×C13×C22⋊C4—22no—
139C2×C13×C22⋊C4—22no—
140C2×C13×C22⋊C4—22no—
141C2×C13×C22⋊C4—22no—
142C2×C13×C22⋊C4—22no—
143C2×C13×C22⋊C4—41no—
144C2×C13×C22⋊C4—41no—
145C2×C13×C22⋊C4—41no—
146C2×C13×C22⋊C4—41no—
147C2×C13×C22⋊C4—41no—
148C2×C13×C22⋊C4—41no—
149C2×C13×C22⋊C4—41no—
150C2×C13×C22⋊C4—41no—
151C2×C13×C22⋊C4C2×C414yes—
152C2×C13×C22⋊C4C2×C414yescomplemented
153C2×C13×C22⋊C4D414yes—
154C2×C13×C22⋊C4D414yes—
155C2×C13×C22⋊C4D414yescomplemented
156C2×C42×C13—22no—
157C2×C42×C13—22no—
158C2×C42×C13—22no—
159C2×C42×C13—22no—
160C2×C42×C13—22no—
161C2×C42×C13—22no—
162C2×C42×C13—41no—
163C2×C42×C13—41no—
164C2×C42×C13—41no—
165C13×#95—22no—
166C13×#95—22no—
167C13×#95—22no—
168C13×#95—22no—
169C13×#95—22no—
170C13×#95—22no—
171C13×#95—22no—
172C13×#95—22no—
173C13×#95—22no—
174C13×#95—41no—
175C13×#95—41no—
176C13×#95D414yescomplemented
177#14100C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
187C24×C13—21no—
188C24×C13—21no—
189C24×C13—21no—
190C24×C13—21no—
191C24×C13—21no—
192C24×C13—21no—
193C24×C13—21no—
194C24×C13—21no—
195C24×C13—21no—
196C24×C13—21no—
197C24×C13—21no—
198C24×C13—21no—
199C24×C13—21no—
200C24×C13—21no—
201C24×C13—21no—
202C24×C13—21no—
203C24×C13—21no—
204C24×C13—21no—
205C24×C13—21no—
206C24×C13—21no—
207C24×C13—21no—
208C24×C13—21no—
209C24×C13—21no—
210C24×C13—21no—
211C24×C13—21no—
212C24×C13—21no—
213C24×C13—21no—
214C24×C13—21no—
215C24×C13—21no—
216C24×C13C22×C412yes—
217C24×C13C22×C412yes—
218C24×C13C22×C412yes—
219C24×C13C2×D412yes—
220C24×C13C2×D412yes—
221C24×C13C2×D412yes—
222C24×C13#4112yes—
223C24×C13C2411yescharacteristic
224C2×D4×C13—28no—
225C2×D4×C13—28no—
226C2×D4×C13—28no—
227C2×D4×C13—28no—
228C2×D4×C13—28no—
229C2×D4×C13—28no—
230C2×D4×C13—44no—
231C2×D4×C13—44no—
232C2×D4×C13—44no—
233C2×D4×C13—44no—
234C2×D4×C13—44no—
235C2×D4×C13—44no—
236C2×D4×C13—44no—
237C2×D4×C13—44no—
238C2×D4×C13—44no—
239C2×D4×C13—44no—
240C2×D4×C13—44no—
241C2×D4×C13—44no—
242C2×D4×C13—44no—
243C2×D4×C13—44no—
244C2×D4×C13—44no—
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—28no—
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×C13—21no—
278C22×C4×C13—21no—
279C22×C4×C13—21no—
280C22×C4×C13—21no—
281C22×C4×C13—21no—
282C22×C4×C13—21no—
283C22×C4×C13—21no—
284C22×C4×C13—21no—
285C22×C4×C13—21no—
286C22×C4×C13—21no—
287C22×C4×C13—21no—
288C22×C4×C13—21no—
289C22×C4×C13—21no—
290C22×C4×C13—21no—
291C22×C4×C13—21no—
292C22×C4×C13—21no—
293C22×C4×C13—21no—
294C22×C4×C13—21no—
295C22×C4×C13—21no—
296C22×C4×C13—21no—
297C22×C4×C13—21no—
298C22×C4×C13—28no—
299C22×C4×C13—28no—
300C22×C4×C13—21no—
301C22×C4×C13—21no—
302C22×C4×C13—21no—
303C22×C4×C13—21no—
304C22×C4×C13—21no—
305C22×C4×C13—21no—
306C22×C4×C13—21no—
307C22×C4×C13—21no—
308C22×C4×C13—21no—
309C22×C4×C13—21no—
310C22×C4×C13—21no—
311C22×C4×C13—21no—
312C22×C4×C13—21no—
313C22×C4×C13—21no—
314C22×C4×C13—44no—
315C22×C4×C13—44no—
316C22×C4×C13—44no—
317C22×C4×C13—44no—
318C22×C4×C13—44no—
319C22×C4×C13—44no—
320C22×C4×C13—44no—
321C22×C4×C13—44no—
322C22×C4×C13—44no—
323C22×C4×C13—44no—
324C22×C4×C13—44no—
325C22×C4×C13C22×C412yes—
326C22×C4×C13C22×C412yes—
327C22×C4×C13C22×C412yes—
328C22×C4×C13C22×C412yes—
329C22×C4×C13C2×D412yes—
330C22×C4×C13C2×D412yes—
331C22×C4×C13C2×D412yes—
332C22×C4×C13C2×D412yes—
333C22×C4×C13C2×D412yes—
334C22×C4×C13C2×D412yes—
335C22×C4×C13C2×D412yes—
336C22×C4×C13C2×D412yes—
337C22×C4×C13C2×D412yes—
338C22×C4×C13#4112yes—
339C22×C4×C13#4112yes—
340C22×C4×C13#4112yes—
341C22×C4×C13#4112yes—
342C22×C4×C13#4112yes—
343C13×C4⋊C4—28no—
344C13×C4⋊C4—44no—
345C13×C22⋊C4—28no—
346C13×C22⋊C4—28no—
347C13×C22⋊C4—28no—
348C13×C22⋊C4—28no—
349C13×C22⋊C4—44no—
350C13×C22⋊C4—44no—
351C13×C22⋊C4—44no—
352C13×C22⋊C4—44no—
353C13×C22⋊C4—44no—
354C13×C22⋊C4—44no—
355C13×C22⋊C4—44no—
356C13×C22⋊C4—44no—
357C13×C22⋊C4C22⋊C4116yescomplemented
358C42×C13—44no—
359C42×C13—44no—
360C42×C13—44no—
361C22×#121C2×C1311yescharacteristic
362C2×#390C2×C1311yescharacteristic, complemented
363C2×#388C2×C1311yescharacteristic, complemented
364C2×#386C2×C1311yescharacteristic, complemented
365C2×#386C2×C1311yescharacteristic, complemented
366C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
367C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
368#1441C2×C1311yescharacteristic, complemented
369#1438C2×C1311yescharacteristic, complemented
370#1438C2×C1311yescharacteristic, complemented
371#1438C2×C1311yescharacteristic, complemented
372#1437C2×C1311yescharacteristic, complemented
373#1437C2×C1311yescharacteristic, complemented
374#1436C2×C1311yescharacteristic, complemented
375C22⋊#95C2×C1311yescharacteristic, complemented
376C23×C13—22no—
377C23×C13—22no—
378C23×C13—22no—
379C23×C13—22no—
380C23×C13—22no—
381C23×C13—22no—
382C23×C13—22no—
383C23×C13—22no—
384C23×C13—22no—
385C23×C13—22no—
386C23×C13—22no—
387C23×C13—22no—
388C23×C13—22no—
389C23×C13—22no—
390C23×C13—22no—
391C23×C13—22no—
392C23×C13—22no—
393C23×C13—22no—
394C23×C13—22no—
395C23×C13—22no—
396C23×C13—22no—
397C23×C13—22no—
398C23×C13—22no—
399C23×C13—22no—
400C23×C13—22no—
401C23×C13—22no—
402C23×C13—22no—
403C23×C13—22no—
404C23×C13—22no—
405C23×C13—22no—
406C23×C13—22no—
407C23×C13—22no—
408C23×C13—22no—
409C23×C13—22no—
410C23×C13—22no—
411C23×C13—22no—
412C23×C13—22no—
413C23×C13—22no—
414C23×C13—22no—
415C23×C13—22no—
416C23×C13—22no—
417C23×C13—22no—
418C23×C13—22no—
419C23×C13—41no—
420C23×C13—41no—
421C23×C13—41no—
422C23×C13—41no—
423C23×C13—41no—
424C23×C13—41no—
425C23×C13—41no—
426C23×C13—41no—
427C23×C13—41no—
428C23×C13—41no—
429C23×C13—41no—
430C23×C13—41no—
431C23×C13—41no—
432C23×C13—41no—
433C23×C13—41no—
434C23×C13—41no—
435C23×C13—41no—
436C23×C13—41no—
437C23×C13—41no—
438C23×C13—41no—
439C23×C13—41no—
440C23×C13—41no—
441C23×C13—41no—
442C23×C13—41no—
443C23×C13—41no—
444C23×C13—41no—
445C23×C13—41no—
446C23×C13—41no—
447C23×C13—41no—
448C23×C13—41no—
449C23×C13—41no—
450C23×C13—41no—
451C23×C13—41no—
452C23×C13—41no—
453C23×C13—41no—
454C23×C13—41no—
455C23×C13—41no—
456C23×C13—41no—
457C23×C13—41no—
458C23×C13—41no—
459C23×C13—41no—
460C23×C13—41no—
461C23×C13—41no—
462C23×C13—41no—
463C23×C13—41no—
464C23×C13—41no—
465C23×C13—41no—
466C23×C13—41no—
467C23×C13—41no—
468C23×C13—41no—
469C23×C13—41no—
470C23×C13—41no—
471C23×C13—41no—
472C23×C13—41no—
473C23×C13—41no—
474C23×C13—41no—
475C23×C13—41no—
476C23×C13—41no—
477C23×C13—41no—
478C23×C13—41no—
479C23×C13C2×C22⋊C414yes—
480C23×C13C4×D414yes—
481C23×C13C23×C411yescharacteristic
482C23×C13C22×D411yescharacteristic
483C23×C13C22×D411yescharacteristic
484C23×C13C22×D411yescharacteristic
485C23×C13C22×D411yescharacteristic
486C23×C13C2×#4111yescharacteristic
487C23×C13C2×#4111yescharacteristic
488C23×C13C2×#4111yescharacteristic
489C23×C13C2×#4111yescharacteristic
490C23×C13C2×#4111yescharacteristic
491C23×C13C2×#4111yescharacteristic
492C23×C13H(5,𝔽2)11yescharacteristic
493C23×C13H(5,𝔽2)11yescharacteristic
494C23×C13H(5,𝔽2)11yescharacteristic
495C23×C13H(5,𝔽2)11yescharacteristic
496D4×C13—416no—
497D4×C13—416no—
498D4×C13—416no—
499C2×C4×C13—22no—
500C2×C4×C13—22no—
501C2×C4×C13—22no—
502C2×C4×C13—22no—
503C2×C4×C13—22no—
504C2×C4×C13—22no—
505C2×C4×C13—22no—
506C2×C4×C13—22no—
507C2×C4×C13—22no—
508C2×C4×C13—22no—
509C2×C4×C13—22no—
510C2×C4×C13—22no—
511C2×C4×C13—22no—
512C2×C4×C13—22no—
513C2×C4×C13—22no—
514C2×C4×C13—22no—
515C2×C4×C13—22no—
516C2×C4×C13—22no—
517C2×C4×C13—22no—
518C2×C4×C13—22no—
519C2×C4×C13—22no—
520C2×C4×C13—22no—
521C2×C4×C13—22no—
522C2×C4×C13—22no—
523C2×C4×C13—22no—
524C2×C4×C13—22no—
525C2×C4×C13—22no—
526C2×C4×C13—22no—
527C2×C4×C13—22no—
528C2×C4×C13—22no—
529C2×C4×C13—22no—
530C2×C4×C13—22no—
531C2×C4×C13—22no—
532C2×C4×C13—22no—
533C2×C4×C13—22no—
534C2×C4×C13—22no—
535C2×C4×C13—22no—
536C2×C4×C13—22no—
537C2×C4×C13—22no—
538C2×C4×C13—22no—
539C2×C4×C13—22no—
540C2×C4×C13—22no—
541C2×C4×C13—416no—
542C2×C4×C13—416no—
543C2×C4×C13—41no—
544C2×C4×C13—41no—
545C2×C4×C13—41no—
546C2×C4×C13—41no—
547C2×C4×C13—41no—
548C2×C4×C13—41no—
549C2×C4×C13—41no—
550C2×C4×C13—41no—
551C2×C4×C13—41no—
552C2×C4×C13—41no—
553C2×C4×C13—41no—
554C2×C4×C13—41no—
555C2×C4×C13—41no—
556C2×C4×C13—41no—
557C2×C4×C13—41no—
558C2×C4×C13—41no—
559C2×C4×C13—41no—
560C2×C4×C13—41no—
561C2×C4×C13—41no—
562C2×C4×C13—41no—
563C2×C4×C13—41no—
564C2×C4×C13—41no—
565C2×C4×C13—41no—
566C2×C4×C13—41no—
567C2×C4×C13—41no—
568C2×C4×C13—41no—
569C2×C4×C13—41no—
570C2×C4×C13—41no—
571C2×C4×C13—41no—
572C2×C4×C13—41no—
573C2×C4×C13—41no—
574C2×C4×C13—41no—
575C2×C4×C13—41no—
576C2×C4×C13—41no—
577C2×C4×C13—41no—
578C2×C4×C13—41no—
579C2×C4×C13—41no—
580C2×C4×C13—41no—
581C2×C4×C13C2×C22⋊C414yes—
582C2×C4×C13C2×C22⋊C414yes—
583C2×C4×C13C4×D414yes—
584C2×C4×C13#12114yescomplemented
585C23×D4C22×C1311yescharacteristic
586C23×D4C22×C1311yescharacteristic
587C23×D4C22×C1311yescharacteristic
588C24×C4C22×C1311yescharacteristic
589C24×C4C22×C1311yescharacteristic
590C2×#121—24no—
591C2×#121—24no—
592C2×#121C4×C1318yescomplemented
593C22×C4⋊C4C22×C1311yescharacteristic
594C22×C4⋊C4C22×C1311yescharacteristic
595C22×C22⋊C4C22×C1311yescharacteristic
596C22×C22⋊C4C22×C1311yescharacteristic
597C22×C22⋊C4C22×C1311yescharacteristic
598C22×C22⋊C4C22×C1311yescharacteristic
599C22×C22⋊C4C22×C1311yescharacteristic
600C22×C22⋊C4C22×C1311yescharacteristic
601C22×C22⋊C4C22×C1311yescharacteristic
602C22×C22⋊C4C22×C1311yescharacteristic
603C22×C22⋊C4C22×C1311yescharacteristic
604C22×C22⋊C4C22×C1311yescharacteristic
605C22×C22⋊C4C22×C1311yescharacteristic
606C22×C22⋊C4C22×C1311yescharacteristic
607C22×C22⋊C4C22×C1311yescharacteristic
608C22×C42C22×C1311yescharacteristic
609C22×C42C22×C1311yescharacteristic
610C22×C42C22×C1311yescharacteristic
611#390—24no—
612#388—24no—
613#386—24no—
614#386—24no—
615C4×C22⋊C4—24no—
616C4×C22⋊C4—24no—
617C2×#95C22×C1311yescharacteristic
618C2×#95C22×C1311yescharacteristic
619C2×#95C22×C1311yescharacteristic
620C2×#95C22×C1311yescharacteristic
621C2×#95C22×C1311yescharacteristic
622C2×#95C22×C1311yescharacteristic
623C2×#95C22×C1311yescharacteristic
624C2×#95C22×C1311yescharacteristic
625C2×#95C22×C1311yescharacteristic
626C2×#95C22×C1311yescharacteristic
627C2×#95C22×C1311yescharacteristic
628C2×#95C22×C1311yescharacteristic
629C22×C13—24no—
630C22×C13—24no—
631C22×C13—24no—
632C22×C13—24no—
633C22×C13—24no—
634C22×C13—24no—
635C22×C13—42no—
636C22×C13—42no—
637C22×C13—42no—
638C22×C13—42no—
639C22×C13—42no—
640C22×C13—42no—
641C22×C13—42no—
642C22×C13—42no—
643C22×C13—42no—
644C22×C13—42no—
645C22×C13—42no—
646C22×C13—42no—
647C22×C13—42no—
648C22×C13—42no—
649C22×C13—42no—
650C22×C13—42no—
651C22×C13—42no—
652C22×C13—42no—
653C22×C13—42no—
654C22×C13—42no—
655C22×C13—42no—
656C22×C13—42no—
657C22×C13—42no—
658C22×C13—42no—
659C22×C13—42no—
660C22×C13—42no—
661C22×C13—42no—
662C22×C13—42no—
663C22×C13—42no—
664C22×C13—42no—
665C22×C13—42no—
666C22×C13—81no—
667C22×C13—81no—
668C22×C13—81no—
669C22×C13—81no—
670C22×C13—81no—
671C22×C13—81no—
672C22×C13—81no—
673C22×C13—81no—
674C22×C13C22×C22⋊C411yescharacteristic
675C22×C13C2×C4×D411yescharacteristic
676C22×C13C2×C4×D411yescharacteristic
677C22×C13C4×#4111yescharacteristic
678C22×C13C4×#4111yescharacteristic
679C22×C13#51811yescharacteristic
680C22×C13#51811yescharacteristic
681C22×C13C2×#12111yescharacteristic
682C22×C13#52511yescharacteristic
683C22×C13#52511yescharacteristic
684C22×C13#52511yescharacteristic
685C22×C13#52911yescharacteristic
686C22×C13#53211yescharacteristic
687C22×C13#53211yescharacteristic
688C22×C13#53211yescharacteristic
689C22×C13#53811yescharacteristic
690C22×C13#53811yescharacteristic
691C22×C13#54011yescharacteristic
692C22×C13#54011yescharacteristic
693C22×C13D4211yescharacteristic
694C22×C13D4211yescharacteristic
695C22×C13D4211yescharacteristic
696C22×C13D4211yescharacteristic
697C22×C13#54611yescharacteristic
698C22×C13#54611yescharacteristic
699C22×C13#54611yescharacteristic
700C22×C13#54611yescharacteristic
701C22×C13#54611yescharacteristic
702C22×C13#54611yescharacteristic
703C22×C13#54611yescharacteristic
704C22×C13#55011yescharacteristic
705C22×C13#55311yescharacteristic
706C22×C13#55311yescharacteristic
707C22×C13#55311yescharacteristic
708C22×C13#55511yescharacteristic
709C4×C13—24no—
710C4×C13—24no—
711C4×C13—24no—
712C4×C13—24no—
713C4×C13—42no—
714C4×C13—42no—
715C4×C13—42no—
716C4×C13—42no—
717C4×C13—42no—
718C4×C13—42no—
719C4×C13—81no—
720C4×C13—81no—
721C25C23×C1311yescharacteristic
722C25C23×C1311yescharacteristic
723C25C23×C1311yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4C2×C4×C1314yes—
743C22×D4C2×C4×C1314yes—
744C22×D4C2×C4×C1314yescomplemented
745C23×C4—22no—
746C23×C4—22no—
747C23×C4—22no—
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—41no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4—41no—
758C23×C4C2×C4×C1314yescomplemented
759C23×C4C23×C1311yescharacteristic
760C23×C4C23×C1311yescharacteristic
761C23×C4C23×C1311yescharacteristic
762C23×C4C23×C1311yescharacteristic
763C23×C4C23×C1311yescharacteristic
764C23×C4C23×C1311yescharacteristic
765C23×C4C23×C1311yescharacteristic
766C23×C4C23×C1311yescharacteristic
767C23×C4C23×C1311yescharacteristic
768C23×C4C23×C1311yescharacteristic
769C23×C4C23×C1311yescharacteristic
770C23×C4C23×C1311yescharacteristic
771#121—232no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4C2×C4×C1314yescomplemented
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4C2×C4×C1314yes—
813C2×C22⋊C4C2×C4×C1314yescomplemented
814C2×C22⋊C4D4×C1314yes—
815C2×C22⋊C4D4×C1314yes—
816C2×C22⋊C4D4×C1314yescomplemented
817C2×C42—22no—
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—22no—
822C2×C42—22no—
823C2×C42—41no—
824C2×C42—41no—
825C2×C42—41no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—41no—
836#95—41no—
837#95D4×C1314yescomplemented
838C2×C13—44no—
839C2×C13—44no—
840C2×C13—82no—
841C2×C13#229711yescharacteristic
842C2×C13C4×#12111yescharacteristic
843C2×C13#233311yescharacteristic
844C2×C13D4×C22⋊C411yescharacteristic
845C2×C13D4×C22⋊C411yescharacteristic
846C2×C13#236311yescharacteristic
847C2×C13#236411yescharacteristic
848C2×C13#242411yescharacteristic
849C2×C13#242811yescharacteristic
850C2×C13#245611yescharacteristic
851C2×C13#246411yescharacteristic
852C2×C13#246411yescharacteristic
853C2×C13#247611yescharacteristic
854C2×C13#255511yescharacteristic
855C2×C13#255911yescharacteristic
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24C22×C4×C1312yes—
895C24C22×C4×C1312yes—
896C24C22×C4×C1312yes—
897C24C2×D4×C1312yes—
898C24C2×D4×C1312yes—
899C24C2×D4×C1312yes—
900C24C13×#4112yes—
901C24C24×C1311yescharacteristic
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—28no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—28no—
977C22×C4—28no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4C22×C4×C1312yes—
1004C22×C4C22×C4×C1312yes—
1005C22×C4C22×C4×C1312yes—
1006C22×C4C22×C4×C1312yes—
1007C22×C4C2×D4×C1312yes—
1008C22×C4C2×D4×C1312yes—
1009C22×C4C2×D4×C1312yes—
1010C22×C4C2×D4×C1312yes—
1011C22×C4C2×D4×C1312yes—
1012C22×C4C2×D4×C1312yes—
1013C22×C4C2×D4×C1312yes—
1014C22×C4C2×D4×C1312yes—
1015C22×C4C2×D4×C1312yes—
1016C22×C4C13×#4112yes—
1017C22×C4C13×#4112yes—
1018C22×C4C13×#4112yes—
1019C22×C4C13×#4112yes—
1020C22×C4C13×#4112yes—
1021C4⋊C4—28no—
1022C4⋊C4—44no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4C13×C22⋊C4116yescomplemented
1036C42—44no—
1037C42—44no—
1038C42—44no—
1039C13#1410011yescharacteristic, direct product factor, Sylow
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C13×C22⋊C414yes—
1144C23C4×D4×C1314yes—
1145C23C23×C4×C1311yescharacteristic
1146C23C22×D4×C1311yescharacteristic
1147C23C22×D4×C1311yescharacteristic
1148C23C22×D4×C1311yescharacteristic
1149C23C22×D4×C1311yescharacteristic
1150C23C2×C13×#4111yescharacteristic
1151C23C2×C13×#4111yescharacteristic
1152C23C2×C13×#4111yescharacteristic
1153C23C2×C13×#4111yescharacteristic
1154C23C2×C13×#4111yescharacteristic
1155C23C2×C13×#4111yescharacteristic
1156C23C13×H(5,𝔽2)11yescharacteristic
1157C23C13×H(5,𝔽2)11yescharacteristic
1158C23C13×H(5,𝔽2)11yescharacteristic
1159C23C13×H(5,𝔽2)11yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—416no—
1206C2×C4—416no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4C2×C13×C22⋊C414yes—
1246C2×C4C2×C13×C22⋊C414yes—
1247C2×C4C4×D4×C1314yes—
1248C2×C4C13×#12114yescomplemented
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C13×C22⋊C411yescharacteristic
1295C22C2×C4×D4×C1311yescharacteristic
1296C22C2×C4×D4×C1311yescharacteristic
1297C22C4×C13×#4111yescharacteristic
1298C22C4×C13×#4111yescharacteristic
1299C22C13×#51811yescharacteristic
1300C22C13×#51811yescharacteristic
1301C22C2×C13×#12111yescharacteristic
1302C22C13×#52511yescharacteristic
1303C22C13×#52511yescharacteristic
1304C22C13×#52511yescharacteristic
1305C22C13×#52911yescharacteristic
1306C22C13×#53211yescharacteristic
1307C22C13×#53211yescharacteristic
1308C22C13×#53211yescharacteristic
1309C22C13×#53811yescharacteristic
1310C22C13×#53811yescharacteristic
1311C22C13×#54011yescharacteristic
1312C22C13×#54011yescharacteristic
1313C22D42×C1311yescharacteristic
1314C22D42×C1311yescharacteristic
1315C22D42×C1311yescharacteristic
1316C22D42×C1311yescharacteristic
1317C22C13×#54611yescharacteristic
1318C22C13×#54611yescharacteristic
1319C22C13×#54611yescharacteristic
1320C22C13×#54611yescharacteristic
1321C22C13×#54611yescharacteristic
1322C22C13×#54611yescharacteristic
1323C22C13×#54611yescharacteristic
1324C22C13×#55011yescharacteristic
1325C22C13×#55311yescharacteristic
1326C22C13×#55311yescharacteristic
1327C22C13×#55311yescharacteristic
1328C22C13×#55511yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—81no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C13×#229711yescharacteristic
1345C2C4×C13×#12111yescharacteristic
1346C2C13×#233311yescharacteristic
1347C2D4×C13×C22⋊C411yescharacteristic
1348C2D4×C13×C22⋊C411yescharacteristic
1349C2C13×#236311yescharacteristic
1350C2C13×#236411yescharacteristic
1351C2C13×#242411yescharacteristic
1352C2C13×#242811yescharacteristic
1353C2C13×#245611yescharacteristic
1354C2C13×#246411yescharacteristic
1355C2C13×#246411yescharacteristic
1356C2C13×#247611yescharacteristic
1357C2C13×#255511yescharacteristic
1358C2C13×#255911yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC22×C13×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#390C2semidirect
3. C2×C13×#388C2semidirect
4. C2×C13×#386C2semidirect
5. C2×C13×#386C2semidirect
6. C2×C4×C13×C22⋊C4C2semidirect
7. C2×C4×C13×C22⋊C4C2semidirect
8. C13×#1441C2semidirect
9. C13×#1438C2semidirect
10. C13×#1438C2semidirect
11. C13×#1438C2semidirect
12. C13×#1437C2semidirect
13. C13×#1437C2semidirect
14. C13×#1436C2semidirect
15. C13×C22⋊#95C2semidirect
23. C2×C13×#121C4semidirect
83. C22×D4×C13C2×C4semidirect
97. C23×C4×C13C2×C4semidirect
116. C2×C13×C4⋊C4C2×C4semidirect
152. C2×C13×C22⋊C4C2×C4semidirect
155. C2×C13×C22⋊C4D4semidirect
176. C13×#95D4semidirect
177. #14100C13direct (N × H)
357. C13×C22⋊C4C22⋊C4semidirect
362. C2×#390C2×C13semidirect
363. C2×#388C2×C13semidirect
364. C2×#386C2×C13semidirect
365. C2×#386C2×C13semidirect
366. C2×C4×C22⋊C4C2×C13semidirect
367. C2×C4×C22⋊C4C2×C13semidirect
368. #1441C2×C13semidirect
369. #1438C2×C13semidirect
370. #1438C2×C13semidirect
371. #1438C2×C13semidirect
372. #1437C2×C13semidirect
373. #1437C2×C13semidirect
374. #1436C2×C13semidirect
375. C22⋊#95C2×C13semidirect
584. C2×C4×C13#121semidirect
592. C2×#121C4×C13semidirect
744. C22×D4C2×C4×C13semidirect
758. C23×C4C2×C4×C13semidirect
777. C2×C4⋊C4C2×C4×C13semidirect
813. C2×C22⋊C4C2×C4×C13semidirect
816. C2×C22⋊C4D4×C13semidirect
837. #95D4×C13semidirect
1035. C22⋊C4C13×C22⋊C4semidirect
1039. C13#14100direct (N × H)
1248. C2×C4C13×#121semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1212
C2×C13×#3902
C2×C13×#3882
C2×C13×#3862
C2×C4×C13×C22⋊C42
C13×#14412
C13×#14382
C13×#14372
C13×#14362
C13×C22⋊#952
#1410013