Finite Group Databasebeta

← C13×#14064 #15700403

Subgroups — C13×#14064 #15700403

Order 3328.

2330 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#117C211yesmaximal, characteristic, complemented
2C2×C13×#386C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#385C211yesmaximal, characteristic, complemented
5C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
6C13×#1442C211yesmaximal, 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×#1434C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C2×C13×#117—24no—
20C2×C13×#117—24no—
21C2×C13×#117—24no—
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×C42×C13C2211yescharacteristic
36C22×C42×C13C2211yescharacteristic
37C22×C42×C13C2211yescharacteristic
38C13×#386—24no—
39C13×#386C418yescomplemented
40C13×#385—24no—
41C4×C13×C22⋊C4—24no—
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—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×C13—22no—
74C23×C4×C13—22no—
75C23×C4×C13—22no—
76C23×C4×C13—22no—
77C23×C4×C13—22no—
78C23×C4×C13—41no—
79C23×C4×C13—41no—
80C23×C4×C13C2×C414yescomplemented
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C13×#117—232no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—41no—
103C2×C13×C4⋊C4D414yescomplemented
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—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×C414yes—
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—22no—
139C2×C42×C13—22no—
140C2×C42×C13—41no—
141C2×C42×C13—41no—
142C2×C42×C13D414yescomplemented
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—41no—
153C13×#95—41no—
154C13×#95—41no—
155C13×#95—41no—
156C13×#95—41no—
157C13×#95C2×C414yescomplemented
158C13×#95C2×C414yescomplemented
159#14064C1311yesmaximal, 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×C13C22×C412yes—
185C24×C13C22×C412yes—
186C24×C13C2×D412yes—
187C24×C13#4112yes—
188C24×C13#4112yes—
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—28no—
216C22×C4×C13—28no—
217C22×C4×C13—28no—
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×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—44no—
281C22×C4×C13—44no—
282C22×C4×C13—44no—
283C22×C4×C13—44no—
284C22×C4×C13—44no—
285C22×C4×C13—44no—
286C22×C4×C13C22×C412yes—
287C22×C4×C13C22×C412yes—
288C22×C4×C13C22×C412yes—
289C22×C4×C13C22×C412yes—
290C22×C4×C13C22×C412yes—
291C22×C4×C13C2×D412yes—
292C22×C4×C13C2×D412yes—
293C22×C4×C13C2×D412yes—
294C22×C4×C13C2×D412yes—
295C22×C4×C13C2×D412yes—
296C22×C4×C13C2×D412yes—
297C22×C4×C13C2×D412yes—
298C22×C4×C13C2×D412yes—
299C22×C4×C13#4112yes—
300C22×C4×C13#4112yes—
301C22×C4×C13#4112yes—
302C22×C4×C13#4112yes—
303C13×C4⋊C4—28no—
304C13×C4⋊C4—28no—
305C13×C4⋊C4—44no—
306C13×C22⋊C4—28no—
307C13×C22⋊C4—28no—
308C13×C22⋊C4—28no—
309C13×C22⋊C4—28no—
310C13×C22⋊C4—28no—
311C13×C22⋊C4—44no—
312C13×C22⋊C4—44no—
313C13×C22⋊C4—44no—
314C13×C22⋊C4—44no—
315C13×C22⋊C4—44no—
316C42×C13—28no—
317C42×C13—28no—
318C42×C13—44no—
319C22×#117C2×C1311yescharacteristic, complemented
320C2×#386C2×C1311yescharacteristic
321C2×#386C2×C1311yescharacteristic
322C2×#385C2×C1311yescharacteristic, complemented
323C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
324#1442C2×C1311yescharacteristic, complemented
325#1439C2×C1311yescharacteristic, complemented
326#1439C2×C1311yescharacteristic, complemented
327#1438C2×C1311yescharacteristic
328#1437C2×C1311yescharacteristic, complemented
329#1437C2×C1311yescharacteristic, complemented
330#1436C2×C1311yescharacteristic, complemented
331#1436C2×C1311yescharacteristic, complemented
332#1434C2×C1311yescharacteristic, complemented
333C22⋊#95C2×C1311yescharacteristic, complemented
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—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—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×C13—41no—
400C23×C13—41no—
401C23×C13—41no—
402C23×C13#11714yescomplemented
403C23×C13C4×D414yes—
404C23×C13C23×C411yescharacteristic
405C23×C13C22×D411yescharacteristic
406C23×C13C22×D411yescharacteristic
407C23×C13C22×D411yescharacteristic
408C23×C13C2×#4111yescharacteristic
409C23×C13C2×#4111yescharacteristic
410C23×C13C2×#4111yescharacteristic
411C23×C13C2×#4111yescharacteristic
412C23×C13C2×#4111yescharacteristic
413C23×C13C2×#4111yescharacteristic
414C23×C13C2×#4111yescharacteristic
415C23×C13H(5,𝔽2)11yescharacteristic
416C23×C13H(5,𝔽2)11yescharacteristic
417C23×C13H(5,𝔽2)11yescharacteristic
418C23×C132−1+411yescharacteristic
419D4×C13—416no—
420C2×C4×C13—232no—
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—22no—
463C2×C4×C13—416no—
464C2×C4×C13—41no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—41no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13—41no—
474C2×C4×C13—41no—
475C2×C4×C13—41no—
476C2×C4×C13—41no—
477C2×C4×C13—41no—
478C2×C4×C13—41no—
479C2×C4×C13—41no—
480C2×C4×C13—41no—
481C2×C4×C13—41no—
482C2×C4×C13—41no—
483C2×C4×C13—41no—
484C2×C4×C13—41no—
485C2×C4×C13—41no—
486C2×C4×C13—41no—
487C2×C4×C13—41no—
488C2×C4×C13—41no—
489C2×C4×C13—41no—
490C2×C4×C13—41no—
491C2×C4×C13—41no—
492C2×C4×C13—41no—
493C2×C4×C13—41no—
494C2×C4×C13—41no—
495C2×C4×C13—41no—
496C2×C4×C13—41no—
497C2×C4×C13—41no—
498C2×C4×C13—41no—
499C2×C4×C13—41no—
500C2×C4×C13—41no—
501C2×C4×C13—41no—
502C2×C4×C13—41no—
503C2×C4×C13—41no—
504C2×C4×C13—41no—
505C2×C4×C13—41no—
506C2×C4×C13—41no—
507C2×C4×C13—41no—
508C2×C4×C13—41no—
509C2×C4×C13—41no—
510C2×C4×C13C4×D414yes—
511C2×C4×C13C4×D414yes—
512C2×C4×C13#12014yes—
513C23×D4C22×C1311yescharacteristic
514C24×C4C22×C1311yescharacteristic
515C24×C4C22×C1311yescharacteristic
516C2×#117—24no—
517C2×#117—24no—
518C2×#117—24no—
519C22×C4⋊C4C22×C1311yescharacteristic
520C22×C4⋊C4C22×C1311yescharacteristic
521C22×C4⋊C4C22×C1311yescharacteristic
522C22×C22⋊C4C22×C1311yescharacteristic
523C22×C22⋊C4C22×C1311yescharacteristic
524C22×C22⋊C4C22×C1311yescharacteristic
525C22×C22⋊C4C22×C1311yescharacteristic
526C22×C22⋊C4C22×C1311yescharacteristic
527C22×C22⋊C4C22×C1311yescharacteristic
528C22×C22⋊C4C22×C1311yescharacteristic
529C22×C22⋊C4C22×C1311yescharacteristic
530C22×C22⋊C4C22×C1311yescharacteristic
531C22×C22⋊C4C22×C1311yescharacteristic
532C22×C42C22×C1311yescharacteristic
533C22×C42C22×C1311yescharacteristic
534C22×C42C22×C1311yescharacteristic
535#386—24no—
536#386C4×C1318yescomplemented
537#385—24no—
538C4×C22⋊C4—24no—
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
550C2×#95C22×C1311yescharacteristic
551C2×#95C22×C1311yescharacteristic
552C2×#95C22×C1311yescharacteristic
553C2×#95C22×C1311yescharacteristic
554C2×#95C22×C1311yescharacteristic
555C22×C13—24no—
556C22×C13—24no—
557C22×C13—24no—
558C22×C13—24no—
559C22×C13—24no—
560C22×C13—24no—
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—42no—
573C22×C13—42no—
574C22×C13—42no—
575C22×C13—42no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13—42no—
580C22×C13—42no—
581C22×C13—42no—
582C22×C13—42no—
583C22×C13—42no—
584C22×C13—42no—
585C22×C13C2×#11711yescharacteristic
586C22×C13C2×C4×D411yescharacteristic
587C22×C13C2×C4×D411yescharacteristic
588C22×C13C2×C4×D411yescharacteristic
589C22×C13C4×#4111yescharacteristic
590C22×C13#51811yescharacteristic
591C22×C13#52011yescharacteristic
592C22×C13C2×#12011yescharacteristic
593C22×C13#52511yescharacteristic
594C22×C13#52511yescharacteristic
595C22×C13#52511yescharacteristic
596C22×C13#52511yescharacteristic
597C22×C13#52511yescharacteristic
598C22×C13#52911yescharacteristic
599C22×C13#52911yescharacteristic
600C22×C13#53511yescharacteristic
601C22×C13#53711yescharacteristic
602C22×C13#54011yescharacteristic
603C22×C13#54211yescharacteristic
604C22×C13#54611yescharacteristic
605C22×C13#54611yescharacteristic
606C22×C13#54611yescharacteristic
607C22×C13#54611yescharacteristic
608C22×C13#54611yescharacteristic
609C22×C13#54711yescharacteristic
610C22×C13#54811yescharacteristic
611C22×C13#55011yescharacteristic
612C22×C13#55111yescharacteristic
613C22×C13#55111yescharacteristic
614C22×C13#55111yescharacteristic
615C22×C13#55211yescharacteristic
616C22×C13#55211yescharacteristic
617C22×C13#55311yescharacteristic
618C22×C13#55311yescharacteristic
619C22×C13#55511yescharacteristic
620C4×C13—24no—
621C4×C13—24no—
622C4×C13—24no—
623C4×C13—42no—
624C4×C13—42no—
625C4×C13—42no—
626C4×C13—42no—
627C4×C13—42no—
628C4×C13—42no—
629C4×C13—42no—
630C4×C13—42no—
631C4×C13—81no—
632C4×C13—81no—
633C25C23×C1311yescharacteristic
634C25C23×C1311yescharacteristic
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—41no—
640C22×D4—41no—
641C22×D4C2×C4×C1314yes—
642C23×C4—22no—
643C23×C4—22no—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—22no—
648C23×C4—22no—
649C23×C4—22no—
650C23×C4—22no—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—41no—
654C23×C4—41no—
655C23×C4C2×C4×C1314yescomplemented
656C23×C4C23×C1311yescharacteristic
657C23×C4C23×C1311yescharacteristic
658C23×C4C23×C1311yescharacteristic
659C23×C4C23×C1311yescharacteristic
660C23×C4C23×C1311yescharacteristic
661C23×C4C23×C1311yescharacteristic
662C23×C4C23×C1311yescharacteristic
663C23×C4C23×C1311yescharacteristic
664C23×C4C23×C1311yescharacteristic
665C23×C4C23×C1311yescharacteristic
666C23×C4C23×C1311yescharacteristic
667C23×C4C23×C1311yescharacteristic
668C23×C4C23×C1311yescharacteristic
669#117—232no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4D4×C1314yescomplemented
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—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—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4C2×C4×C1314yes—
706C2×C22⋊C4C2×C4×C1314yes—
707C2×C22⋊C4C2×C4×C1314yescomplemented
708C2×C22⋊C4D4×C1314yes—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42D4×C1314yescomplemented
718#95—22no—
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—41no—
728#95—41no—
729#95—41no—
730#95—41no—
731#95—41no—
732#95C2×C4×C1314yescomplemented
733#95C2×C4×C1314yescomplemented
734C2×C13—44no—
735C2×C13—44no—
736C2×C13#229011yescharacteristic
737C2×C13C4×#12011yescharacteristic
738C2×C13#232411yescharacteristic
739C2×C13#234211yescharacteristic
740C2×C13#235211yescharacteristic
741C2×C13#235911yescharacteristic
742C2×C13#236311yescharacteristic
743C2×C13#240411yescharacteristic
744C2×C13#240711yescharacteristic
745C2×C13#247011yescharacteristic
746C2×C13#247111yescharacteristic
747C2×C13#247611yescharacteristic
748C2×C13#247711yescharacteristic
749C2×C13#259811yescharacteristic
750C2×C13#260911yescharacteristic
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—
772C24—21no—
773C24—21no—
774C24—21no—
775C24C22×C4×C1312yes—
776C24C22×C4×C1312yes—
777C24C2×D4×C1312yes—
778C24C13×#4112yes—
779C24C13×#4112yes—
780C24C13×#4112yes—
781C24C24×C1311yescharacteristic
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
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—28no—
807C22×C4—28no—
808C22×C4—28no—
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×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—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4C22×C4×C1312yes—
878C22×C4C22×C4×C1312yes—
879C22×C4C22×C4×C1312yes—
880C22×C4C22×C4×C1312yes—
881C22×C4C22×C4×C1312yes—
882C22×C4C2×D4×C1312yes—
883C22×C4C2×D4×C1312yes—
884C22×C4C2×D4×C1312yes—
885C22×C4C2×D4×C1312yes—
886C22×C4C2×D4×C1312yes—
887C22×C4C2×D4×C1312yes—
888C22×C4C2×D4×C1312yes—
889C22×C4C2×D4×C1312yes—
890C22×C4C13×#4112yes—
891C22×C4C13×#4112yes—
892C22×C4C13×#4112yes—
893C22×C4C13×#4112yes—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—44no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C42—28no—
908C42—28no—
909C42—44no—
910C13#1406411yescharacteristic, direct product factor, Sylow
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—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—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—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C13×#11714yescomplemented
980C23C4×D4×C1314yes—
981C23C23×C4×C1311yescharacteristic
982C23C22×D4×C1311yescharacteristic
983C23C22×D4×C1311yescharacteristic
984C23C22×D4×C1311yescharacteristic
985C23C2×C13×#4111yescharacteristic
986C23C2×C13×#4111yescharacteristic
987C23C2×C13×#4111yescharacteristic
988C23C2×C13×#4111yescharacteristic
989C23C2×C13×#4111yescharacteristic
990C23C2×C13×#4111yescharacteristic
991C23C2×C13×#4111yescharacteristic
992C23C13×H(5,𝔽2)11yescharacteristic
993C23C13×H(5,𝔽2)11yescharacteristic
994C23C13×H(5,𝔽2)11yescharacteristic
995C23C13×2−1+411yescharacteristic
996D4—416no—
997C2×C4—232no—
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—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—416no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×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×C4C4×D4×C1314yes—
1088C2×C4C4×D4×C1314yes—
1089C2×C4C13×#12014yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C2×C13×#11711yescharacteristic
1121C22C2×C4×D4×C1311yescharacteristic
1122C22C2×C4×D4×C1311yescharacteristic
1123C22C2×C4×D4×C1311yescharacteristic
1124C22C4×C13×#4111yescharacteristic
1125C22C13×#51811yescharacteristic
1126C22C13×#52011yescharacteristic
1127C22C2×C13×#12011yescharacteristic
1128C22C13×#52511yescharacteristic
1129C22C13×#52511yescharacteristic
1130C22C13×#52511yescharacteristic
1131C22C13×#52511yescharacteristic
1132C22C13×#52511yescharacteristic
1133C22C13×#52911yescharacteristic
1134C22C13×#52911yescharacteristic
1135C22C13×#53511yescharacteristic
1136C22C13×#53711yescharacteristic
1137C22C13×#54011yescharacteristic
1138C22C13×#54211yescharacteristic
1139C22C13×#54611yescharacteristic
1140C22C13×#54611yescharacteristic
1141C22C13×#54611yescharacteristic
1142C22C13×#54611yescharacteristic
1143C22C13×#54611yescharacteristic
1144C22C13×#54711yescharacteristic
1145C22C13×#54811yescharacteristic
1146C22C13×#55011yescharacteristic
1147C22C13×#55111yescharacteristic
1148C22C13×#55111yescharacteristic
1149C22C13×#55111yescharacteristic
1150C22C13×#55211yescharacteristic
1151C22C13×#55211yescharacteristic
1152C22C13×#55311yescharacteristic
1153C22C13×#55311yescharacteristic
1154C22C13×#55511yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—44no—
1170C2C13×#229011yescharacteristic
1171C2C4×C13×#12011yescharacteristic
1172C2C13×#232411yescharacteristic
1173C2C13×#234211yescharacteristic
1174C2C13×#235211yescharacteristic
1175C2C13×#235911yescharacteristic
1176C2C13×#236311yescharacteristic
1177C2C13×#240411yescharacteristic
1178C2C13×#240711yescharacteristic
1179C2C13×#247011yescharacteristic
1180C2C13×#247111yescharacteristic
1181C2C13×#247611yescharacteristic
1182C2C13×#247711yescharacteristic
1183C2C13×#259811yescharacteristic
1184C2C13×#260911yescharacteristic
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
4. C2×C13×#385C2semidirect
5. C2×C4×C13×C22⋊C4C2semidirect
6. C13×#1442C2semidirect
7. C13×#1439C2semidirect
8. C13×#1439C2semidirect
10. C13×#1437C2semidirect
11. C13×#1437C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×#1434C2semidirect
15. C13×C22⋊#95C2semidirect
39. C13×#386C4semidirect
80. C23×C4×C13C2×C4semidirect
103. C2×C13×C4⋊C4D4semidirect
132. C2×C13×C22⋊C4C2×C4semidirect
142. C2×C42×C13D4semidirect
157. C13×#95C2×C4semidirect
158. C13×#95C2×C4semidirect
159. #14064C13direct (N × H)
319. C22×#117C2×C13semidirect
322. C2×#385C2×C13semidirect
323. C2×C4×C22⋊C4C2×C13semidirect
324. #1442C2×C13semidirect
325. #1439C2×C13semidirect
326. #1439C2×C13semidirect
328. #1437C2×C13semidirect
329. #1437C2×C13semidirect
330. #1436C2×C13semidirect
331. #1436C2×C13semidirect
332. #1434C2×C13semidirect
333. C22⋊#95C2×C13semidirect
402. C23×C13#117semidirect
536. #386C4×C13semidirect
655. C23×C4C2×C4×C13semidirect
678. C2×C4⋊C4D4×C13semidirect
707. C2×C22⋊C4C2×C4×C13semidirect
717. C2×C42D4×C13semidirect
732. #95C2×C4×C13semidirect
733. #95C2×C4×C13semidirect
910. C13#14064direct (N × H)
979. C23C13×#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×#3862
C2×C13×#3852
C2×C4×C13×C22⋊C42
C13×#14422
C13×#14392
C13×#14382
C13×#14372
C13×#14362
C13×#14342
C13×C22⋊#952
#1406413