Finite Group Databasebeta

← C13×#14825 #15701164

Subgroups — C13×#14825 #15701164

Order 3328.

2198 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C13C211yesmaximal, characteristic
2C2×C13×#400C211yesmaximal, characteristic, complemented
3C2×C13×#399C211yesmaximal, characteristic, complemented
4C2×C13×#380C211yesmaximal, characteristic, complemented
5C13×#1441C211yesmaximal, characteristic, complemented
6C13×#1439C212yesmaximal, complemented
7C13×#1439C211yesmaximal, characteristic, complemented
8C13×#1438C212yesmaximal
9C13×#1436C212yesmaximal, complemented
10C13×C22⋊#95C212yesmaximal, complemented
11C13×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C2×C4×D4×C13—24no—
16C2×C4×D4×C13—24no—
17C2×C4×D4×C13—24no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2212yes—
24C22×C13×C22⋊C4C2212yes—
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2212yes—
27C22×C13×C22⋊C4C2212yes—
28C22×C42×C13C2211yescharacteristic
29C13×#400—24no—
30C13×#399—24no—
31C13×#380—24no—
32C2×C13×#95C2212yes—
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2212yes—
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2212yes—
41C25×C13C2311yescharacteristic
42C25×C13C2311yescharacteristic
43C22×D4×C13—22no—
44C22×D4×C13—22no—
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13—22no—
49C22×D4×C13Q814yes—
50C23×C4×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—24no—
56C23×C4×C13—24no—
57C23×C4×C13—42no—
58C23×C4×C13—42no—
59C23×C4×C13D414yes—
60C23×C4×C13C2312yes—
61C23×C4×C13C2312yes—
62C23×C4×C13C2312yes—
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2312yes—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C4×D4×C13—232no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—24no—
78C2×C13×C4⋊C4—42no—
79C2×C13×C4⋊C4—42no—
80C2×C13×C4⋊C4D414yes—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—24no—
87C2×C13×C22⋊C4—24no—
88C2×C13×C22⋊C4—24no—
89C2×C13×C22⋊C4—24no—
90C2×C13×C22⋊C4—24no—
91C2×C13×C22⋊C4—24no—
92C2×C13×C22⋊C4—42no—
93C2×C13×C22⋊C4—42no—
94C2×C13×C22⋊C4—42no—
95C2×C13×C22⋊C4—42no—
96C2×C13×C22⋊C4—42no—
97C2×C13×C22⋊C4—42no—
98C2×C13×C22⋊C4D414yes—
99C2×C42×C13—22no—
100C2×C42×C13—22no—
101C2×C42×C13—22no—
102C13×#95—24no—
103C13×#95—22no—
104C13×#95—22no—
105C13×#95—24no—
106C13×#95—24no—
107C13×#95—24no—
108C13×#95—24no—
109C13×#95—42no—
110C13×#95—42no—
111#14825C1311yesmaximal, characteristic, direct product factor, Sylow
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—22no—
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—21no—
121C24×C13—21no—
122C24×C13—21no—
123C24×C13—21no—
124C24×C13—22no—
125C24×C13—22no—
126C24×C13—22no—
127C24×C13—22no—
128C24×C13C2×D412yes—
129C24×C13C2×D412yes—
130C24×C13C2×Q812yes—
131C24×C13C2×Q812yes—
132C24×C13#4112yes—
133C24×C13#4112yes—
134C24×C13C2411yescharacteristic
135C2×D4×C13—28no—
136C2×D4×C13—28no—
137C2×D4×C13—28no—
138C2×D4×C13—28no—
139C2×D4×C13—28no—
140C2×D4×C13—28no—
141C2×D4×C13—28no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—28no—
152C22×C4×C13—22no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—28no—
167C22×C4×C13—28no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—44no—
190C22×C4×C13—48no—
191C22×C4×C13—48no—
192C22×C4×C13—48no—
193C22×C4×C13—48no—
194C22×C4×C13—44no—
195C22×C4×C13—44no—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×D412yes—
198C22×C4×C13C2×D412yes—
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2×D412yes—
203C22×C4×C13C2×Q812yes—
204C22×C4×C13#4114yes—
205C22×C4×C13#4112yes—
206C22×C4×C13#4114yes—
207C13×C4⋊C4—28no—
208C13×C4⋊C4—48no—
209C13×C4⋊C4—44no—
210C13×C4⋊C4—44no—
211C13×C22⋊C4—28no—
212C13×C22⋊C4—28no—
213C13×C22⋊C4—48no—
214C13×C22⋊C4—48no—
215C13×C22⋊C4—48no—
216C13×C22⋊C4—48no—
217C42×C13—28no—
218C22×C4×D4C2×C1311yescharacteristic
219C2×#400C2×C1311yescharacteristic, complemented
220C2×#399C2×C1311yescharacteristic, complemented
221C2×#380C2×C1311yescharacteristic, complemented
222#1441C2×C1311yescharacteristic, complemented
223#1439C2×C1312yescomplemented
224#1439C2×C1311yescharacteristic, complemented
225#1438C2×C1312yes—
226#1436C2×C1312yescomplemented
227C22⋊#95C2×C1312yescomplemented
228C22⋊#95C2×C1311yescharacteristic, complemented
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13—24no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—22no—
246C23×C13—24no—
247C23×C13—24no—
248C23×C13—24no—
249C23×C13—24no—
250C23×C13—24no—
251C23×C13—24no—
252C23×C13—24no—
253C23×C13—24no—
254C23×C13—24no—
255C23×C13—41no—
256C23×C13—42no—
257C23×C13—42no—
258C23×C13—42no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—42no—
263C23×C13—42no—
264C23×C13—42no—
265C23×C13—42no—
266C23×C13—42no—
267C23×C13—42no—
268C23×C13—42no—
269C23×C13—42no—
270C23×C13—42no—
271C23×C13—42no—
272C23×C13—42no—
273C23×C13C22⋊Q814yes—
274C23×C13C22⋊Q814yes—
275C23×C13C22×D411yescharacteristic
276C23×C13C22×D411yescharacteristic
277C23×C13C22×D411yescharacteristic
278C23×C13C22×Q811yescharacteristic
279C23×C13C2×#4111yescharacteristic
280C23×C13C2×#4111yescharacteristic
281C23×C13C2×#4111yescharacteristic
282C23×C13C2×#4112yes—
283C23×C13C2×#4112yes—
284C23×C13H(5,𝔽2)12yes—
285C23×C13H(5,𝔽2)12yes—
286D4×C13—232no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—24no—
298C2×C4×C13—24no—
299C2×C4×C13—24no—
300C2×C4×C13—24no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—24no—
304C2×C4×C13—24no—
305C2×C4×C13—24no—
306C2×C4×C13—24no—
307C2×C4×C13—24no—
308C2×C4×C13—416no—
309C2×C4×C13—416no—
310C2×C4×C13—41no—
311C2×C4×C13—42no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13—42no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—42no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13—42no—
340C2×C4×C13—42no—
341C2×C4×C13#12014yes—
342C2×C4×C13C22⋊Q814yes—
343C2×C4×C13#12314yes—
344C23×D4C22×C1311yescharacteristic
345C24×C4C22×C1311yescharacteristic
346C24×C4C22×C1311yescharacteristic
347C2×C4×D4—24no—
348C2×C4×D4—24no—
349C2×C4×D4—24no—
350C22×C4⋊C4C22×C1311yescharacteristic
351C22×C4⋊C4C22×C1312yes—
352C22×C4⋊C4C22×C1311yescharacteristic
353C22×C4⋊C4C22×C1311yescharacteristic
354C22×C22⋊C4C22×C1311yescharacteristic
355C22×C22⋊C4C22×C1312yes—
356C22×C22⋊C4C22×C1312yes—
357C22×C22⋊C4C22×C1311yescharacteristic
358C22×C22⋊C4C22×C1312yes—
359C22×C22⋊C4C22×C1312yes—
360C22×C42C22×C1311yescharacteristic
361#400—24no—
362#399—24no—
363#380—24no—
364C2×#95C22×C1311yescharacteristic
365C2×#95C22×C1312yes—
366C2×#95C22×C1311yescharacteristic
367C2×#95C22×C1312yes—
368C2×#95C22×C1312yes—
369C2×#95C22×C1312yes—
370C2×#95C22×C1312yes—
371C2×#95C22×C1312yes—
372C2×#95C22×C1312yes—
373C22×C13—24no—
374C22×C13—24no—
375C22×C13—24no—
376C22×C13—28no—
377C22×C13—24no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13—42no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13—42no—
386C22×C13—42no—
387C22×C13—44no—
388C22×C13—44no—
389C22×C13—44no—
390C22×C13—44no—
391C22×C13—44no—
392C22×C13—44no—
393C22×C13—44no—
394C22×C13—42no—
395C22×C13C2×#12011yescharacteristic
396C22×C13C2×C22⋊Q811yescharacteristic
397C22×C13C2×C22⋊Q811yescharacteristic
398C22×C13C2×C22⋊Q811yescharacteristic
399C22×C13C2×#12311yescharacteristic
400C22×C13#52511yescharacteristic
401C22×C13#52511yescharacteristic
402C22×C13#52511yescharacteristic
403C22×C13#52912yes—
404C22×C13#52912yes—
405C22×C13#53211yescharacteristic
406C22×C13#53411yescharacteristic
407C22×C13#53511yescharacteristic
408C22×C13#53812yes—
409C22×C13#54012yes—
410C22×C13#54612yes—
411C22×C13#54612yes—
412C22×C13#54612yes—
413C22×C13#55012yes—
414C22×C13#55112yes—
415C22×C13#55312yes—
416C22×C13#55412yes—
417C22×C13#55412yes—
418C4×C13—24no—
419C4×C13—24no—
420C4×C13—24no—
421C4×C13—42no—
422C4×C13—42no—
423C4×C13—44no—
424C4×C13—82no—
425C4×C13—82no—
426C4×C13—82no—
427C25C23×C1311yescharacteristic
428C25C23×C1311yescharacteristic
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4Q8×C1314yes—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—24no—
442C23×C4—24no—
443C23×C4—42no—
444C23×C4—42no—
445C23×C4D4×C1314yes—
446C23×C4C23×C1312yes—
447C23×C4C23×C1312yes—
448C23×C4C23×C1312yes—
449C23×C4C23×C1311yescharacteristic
450C23×C4C23×C1311yescharacteristic
451C23×C4C23×C1312yes—
452C23×C4C23×C1311yescharacteristic
453C23×C4C23×C1311yescharacteristic
454C23×C4C23×C1311yescharacteristic
455C4×D4—232no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4D4×C1314yes—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4D4×C1314yes—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—22no—
488#95—24no—
489#95—22no—
490#95—22no—
491#95—24no—
492#95—24no—
493#95—24no—
494#95—24no—
495#95—42no—
496#95—42no—
497C2×C13—44no—
498C2×C13—44no—
499C2×C13#239511yescharacteristic
500C2×C13#240511yescharacteristic
501C2×C13#243111yescharacteristic
502C2×C13#245012yes—
503C2×C13#245412yes—
504C2×C13#245712yes—
505C2×C13#246712yes—
506C2×C13#248711yescharacteristic
507C2×C13#256411yescharacteristic
508C2×C13#263511yescharacteristic
509C2×C13#284811yescharacteristic
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24C2×D4×C1312yes—
527C24C2×D4×C1312yes—
528C24C2×Q8×C1312yes—
529C24C2×Q8×C1312yes—
530C24C13×#4112yes—
531C24C13×#4112yes—
532C24C24×C1311yescharacteristic
533C2×D4—28no—
534C2×D4—28no—
535C2×D4—28no—
536C2×D4—28no—
537C2×D4—28no—
538C2×D4—28no—
539C2×D4—28no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4C2×D4×C1312yes—
595C22×C4C2×D4×C1312yes—
596C22×C4C2×D4×C1312yes—
597C22×C4C2×D4×C1312yes—
598C22×C4C2×D4×C1312yes—
599C22×C4C2×D4×C1312yes—
600C22×C4C2×D4×C1312yes—
601C22×C4C2×Q8×C1312yes—
602C22×C4C13×#4114yes—
603C22×C4C13×#4112yes—
604C22×C4C13×#4114yes—
605C4⋊C4—28no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C42—28no—
616C13#1482511yescharacteristic, direct product factor, Sylow
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23C13×C22⋊Q814yes—
662C23C13×C22⋊Q814yes—
663C23C22×D4×C1311yescharacteristic
664C23C22×D4×C1311yescharacteristic
665C23C22×D4×C1311yescharacteristic
666C23C22×Q8×C1311yescharacteristic
667C23C2×C13×#4111yescharacteristic
668C23C2×C13×#4111yescharacteristic
669C23C2×C13×#4111yescharacteristic
670C23C2×C13×#4112yes—
671C23C2×C13×#4112yes—
672C23C13×H(5,𝔽2)12yes—
673C23C13×H(5,𝔽2)12yes—
674D4—232no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—416no—
697C2×C4—416no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4C13×#12014yes—
730C2×C4C13×C22⋊Q814yes—
731C2×C4C13×#12314yes—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—28no—
736C22—24no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—42no—
754C22C2×C13×#12011yescharacteristic
755C22C2×C13×C22⋊Q811yescharacteristic
756C22C2×C13×C22⋊Q811yescharacteristic
757C22C2×C13×C22⋊Q811yescharacteristic
758C22C2×C13×#12311yescharacteristic
759C22C13×#52511yescharacteristic
760C22C13×#52511yescharacteristic
761C22C13×#52511yescharacteristic
762C22C13×#52912yes—
763C22C13×#52912yes—
764C22C13×#53211yescharacteristic
765C22C13×#53411yescharacteristic
766C22C13×#53511yescharacteristic
767C22C13×#53812yes—
768C22C13×#54012yes—
769C22C13×#54612yes—
770C22C13×#54612yes—
771C22C13×#54612yes—
772C22C13×#55012yes—
773C22C13×#55112yes—
774C22C13×#55312yes—
775C22C13×#55412yes—
776C22C13×#55412yes—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—44no—
783C4—82no—
784C4—82no—
785C4—82no—
786C2—44no—
787C2—44no—
788C2C13×#239511yescharacteristic
789C2C13×#240511yescharacteristic
790C2C13×#243111yescharacteristic
791C2C13×#245012yes—
792C2C13×#245412yes—
793C2C13×#245712yes—
794C2C13×#246712yes—
795C2C13×#248711yescharacteristic
796C2C13×#256411yescharacteristic
797C2C13×#263511yescharacteristic
798C2C13×#284811yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#400C2semidirect
3. C2×C13×#399C2semidirect
4. C2×C13×#380C2semidirect
5. C13×#1441C2semidirect
6. C13×#1439C2semidirect
7. C13×#1439C2semidirect
9. C13×#1436C2semidirect
10. C13×C22⋊#95C2semidirect
11. C13×C22⋊#95C2semidirect
111. #14825C13direct (N × H)
219. C2×#400C2×C13semidirect
220. C2×#399C2×C13semidirect
221. C2×#380C2×C13semidirect
222. #1441C2×C13semidirect
223. #1439C2×C13semidirect
224. #1439C2×C13semidirect
226. #1436C2×C13semidirect
227. C22⋊#95C2×C13semidirect
228. C22⋊#95C2×C13semidirect
616. C13#14825direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C132
C2×C13×#4002
C2×C13×#3992
C2×C13×#3802
C13×#14412
C13×#14392
C13×#14382
C13×#14362
C13×C22⋊#952
#1482513