Finite Group Databasebeta

← C13×#34329 #15720668

Subgroups — C13×#34329 #15720668

Order 3328.

2352 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#559C211yesmaximal, characteristic
2C13×#2374C212yesmaximal, complemented
3C13×#2372C212yesmaximal, complemented
4C13×#2367C211yesmaximal, characteristic, complemented
5C13×#2367C211yesmaximal, characteristic, complemented
6C13×#2366C211yesmaximal, characteristic
7C13×#2359C212yesmaximal, complemented
8C13×#2357C211yesmaximal, characteristic, complemented
9C13×#2356C211yesmaximal, characteristic, complemented
10C13×#2355C211yesmaximal, characteristic, complemented
11C13×#2354C211yesmaximal, characteristic, complemented
12C13×#2353C212yesmaximal, complemented
13C13×#2337C212yesmaximal, complemented
14C13×#2335C212yesmaximal, complemented
15C13×#2328C211yesmaximal, characteristic
16C13×#2326C211yesmaximal, characteristic, complemented
17C4×C13×#124C211yesmaximal, characteristic, complemented
18C4×C13×#123C212yesmaximal, complemented
19C13×#2295C211yesmaximal, characteristic, complemented
20C13×#2290C212yesmaximal, complemented
21C13×#2276C211yesmaximal, characteristic, complemented
22C13×#2275C211yesmaximal, characteristic, complemented
23C42×D4×C13C211yesmaximal, characteristic, complemented
24C13×#559C4116yescomplemented
25C2×C13×#127C2211yescharacteristic
26C2×C13×#124C2211yescharacteristic
27C2×C13×#124C2211yescharacteristic
28C2×C13×#124C2212yes—
29C2×C13×#123C2212yes—
30C2×C13×#123C2212yes—
31C2×C4×Q8×C13C2211yescharacteristic
32C2×C4×Q8×C13C2211yescharacteristic
33C2×C4×Q8×C13C2211yescharacteristic
34C2×C4×Q8×C13C2211yescharacteristic
35C2×C4×D4×C13C2211yescharacteristic
36C2×C4×D4×C13C2211yescharacteristic
37C2×C4×D4×C13C2211yescharacteristic
38C2×C4×D4×C13C2211yescharacteristic
39C2×C4×D4×C13C2212yes—
40C2×C4×D4×C13C2211yescharacteristic
41C2×C4×D4×C13C2211yescharacteristic
42C2×C4×D4×C13C2212yes—
43C2×C13×#117C2212yes—
44C22×C42×C13C2212yes—
45C13×#391C2211yescharacteristic
46C13×#391C2211yescharacteristic
47C13×#391C2211yescharacteristic
48C13×#391C2211yescharacteristic
49C13×#391C2212yes—
50C13×#390C2211yescharacteristic
51C13×#390C2211yescharacteristic
52C13×#390C2211yescharacteristic
53C13×#390C2211yescharacteristic
54C13×#390C2212yes—
55C13×#389C2211yescharacteristic
56C13×#389C2211yescharacteristic
57C13×#388C2212yes—
58C13×#388C2212yes—
59C13×#388C2212yes—
60C13×#388C2212yes—
61C13×#388C2212yes—
62C13×#388C2212yes—
63C13×#388C2212yes—
64C13×#388C2212yes—
65C13×#388C2212yes—
66C13×#388C2212yes—
67C13×#388C2212yes—
68C13×#388C2212yes—
69C13×#387C2211yescharacteristic
70C13×#387C2212yes—
71C13×#387C2211yescharacteristic
72C13×#387C2211yescharacteristic
73C13×#387C2211yescharacteristic
74C13×#387C2212yes—
75C13×#387C2212yes—
76C13×#387C2212yes—
77C13×#386C2212yes—
78C13×#386C2212yes—
79C13×#386C2212yes—
80C13×#386C2212yes—
81C13×#386C2212yes—
82C13×#386C2212yes—
83C13×#385C2212yes—
84C13×#385C2212yes—
85C13×#385C2212yes—
86C13×#385C2212yes—
87C13×#384C2211yescharacteristic
88C13×#383C2212yes—
89C13×#382C2211yescharacteristic
90C13×#382C2211yescharacteristic
91C13×#381C2212yes—
92C13×#380C2212yes—
93C4×C13×C4⋊C4C2211yescharacteristic
94C4×C13×C4⋊C4C2211yescharacteristic
95C4×C13×C4⋊C4C2211yescharacteristic
96C4×C13×C4⋊C4C2211yescharacteristic
97C4×C13×C4⋊C4C2211yescharacteristic
98C4×C13×C4⋊C4C2212yes—
99C4×C13×C4⋊C4C2212yes—
100C4×C13×C4⋊C4C2211yescharacteristic
101C4×C13×C4⋊C4C2211yescharacteristic
102C4×C13×C4⋊C4C2212yes—
103C4×C13×C4⋊C4C2211yescharacteristic
104C4×C13×C4⋊C4C2211yescharacteristic
105C4×C13×C4⋊C4C2211yescharacteristic
106C4×C13×C4⋊C4C2212yes—
107C4×C13×C22⋊C4C2212yes—
108C4×C13×C22⋊C4C2212yes—
109C4×C13×C22⋊C4C2212yes—
110C4×C13×C22⋊C4C2212yes—
111C4×C13×C22⋊C4C2212yes—
112C4×C13×C22⋊C4C2212yes—
113C4×C13×C22⋊C4C2212yes—
114C4×C13×C22⋊C4C2212yes—
115C4×C13×C22⋊C4C2212yes—
116C4×C13×C22⋊C4C2212yes—
117C4×C13×C22⋊C4C2212yes—
118C13×#376C2211yescharacteristic
119C13×#376C2211yescharacteristic
120C13×#376C2212yes—
121C13×#376C2212yes—
122C2×C13×#95C2212yes—
123C43×C13C2211yescharacteristic
124C22×Q8×C13C2311yescharacteristic
125C22×Q8×C13C2311yescharacteristic
126C22×D4×C13C2311yescharacteristic
127C22×D4×C13C2311yescharacteristic
128C22×D4×C13C2312yes—
129C22×D4×C13C2312yes—
130C23×C4×C13C2312yes—
131C23×C4×C13C2312yes—
132C23×C4×C13C2312yes—
133C23×C4×C13C2312yes—
134C23×C4×C13C2312yes—
135C23×C4×C13C2312yes—
136C13×#127C2×C418yes—
137C13×#124C2×C418yescomplemented
138C13×#124C2×C418yescomplemented
139C13×#124C2×C4116yescomplemented
140C13×#123C2×C4116yescomplemented
141C13×#123C2×C4116yescomplemented
142C4×Q8×C13—24no—
143C4×Q8×C13—24no—
144C4×Q8×C13C2×C418yescomplemented
145C4×Q8×C13C2×C418yescomplemented
146C4×D4×C13—24no—
147C4×D4×C13—24no—
148C4×D4×C13—24no—
149C4×D4×C13—24no—
150C4×D4×C13—44no—
151C4×D4×C13C2×C418yescomplemented
152C4×D4×C13C2×C418yescomplemented
153C4×D4×C13C2×C4116yescomplemented
154C13×#117—44no—
155C2×C13×C4⋊C4C2311yescharacteristic
156C2×C13×C4⋊C4C2311yescharacteristic
157C2×C13×C4⋊C4C2311yescharacteristic
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2312yes—
160C2×C13×C4⋊C4C2311yescharacteristic
161C2×C13×C4⋊C4C2311yescharacteristic
162C2×C13×C4⋊C4C2311yescharacteristic
163C2×C13×C4⋊C4C2312yes—
164C2×C13×C4⋊C4C2311yescharacteristic
165C2×C13×C4⋊C4C2311yescharacteristic
166C2×C13×C4⋊C4C2311yescharacteristic
167C2×C13×C4⋊C4C2312yes—
168C2×C13×C4⋊C4C2311yescharacteristic
169C2×C13×C4⋊C4C2312yes—
170C2×C13×C4⋊C4C2311yescharacteristic
171C2×C13×C4⋊C4C2311yescharacteristic
172C2×C13×C4⋊C4C2311yescharacteristic
173C2×C13×C4⋊C4C2311yescharacteristic
174C2×C13×C22⋊C4C2312yes—
175C2×C13×C22⋊C4C2312yes—
176C2×C13×C22⋊C4C2312yes—
177C2×C13×C22⋊C4C2312yes—
178C2×C13×C22⋊C4C2312yes—
179C2×C13×C22⋊C4C2312yes—
180C2×C13×C22⋊C4C2312yes—
181C2×C13×C22⋊C4C2312yes—
182C2×C13×C22⋊C4C2312yes—
183C2×C13×C22⋊C4C2312yes—
184C2×C13×C22⋊C4C2312yes—
185C2×C13×C22⋊C4C2312yes—
186C2×C13×C22⋊C4C2312yes—
187C2×C13×C22⋊C4C2312yes—
188C2×C13×C22⋊C4C2312yes—
189C2×C13×C22⋊C4C2312yes—
190C2×C13×C22⋊C4C2312yes—
191C2×C13×C22⋊C4C2312yes—
192C2×C42×C13—44no—
193C2×C42×C13C2312yes—
194C2×C42×C13C2312yes—
195C2×C42×C13C2312yes—
196C2×C42×C13C2311yescharacteristic
197C2×C42×C13C2311yescharacteristic
198C2×C42×C13C2311yescharacteristic
199C2×C42×C13C2311yescharacteristic
200C2×C42×C13C2311yescharacteristic
201C2×C42×C13C2311yescharacteristic
202C2×C42×C13C2312yes—
203C2×C42×C13C2312yes—
204C2×C42×C13C2312yes—
205C2×C42×C13C2312yes—
206C2×C42×C13C2311yescharacteristic
207C2×C42×C13C2312yes—
208C2×C42×C13C2312yes—
209C2×C42×C13C2311yescharacteristic
210C2×C42×C13C2311yescharacteristic
211C2×C42×C13C2311yescharacteristic
212C2×C42×C13C2312yes—
213C2×C42×C13C2311yescharacteristic
214C13×#95C2312yes—
215C13×#95C2312yes—
216C13×#95C2311yescharacteristic
217C13×#95C2312yes—
218C13×#95C2312yes—
219C13×#95C2311yescharacteristic
220C13×#95C2311yescharacteristic
221C13×#95C2311yescharacteristic
222C13×#95C2311yescharacteristic
223C13×#95C2312yes—
224C13×#95C2311yescharacteristic
225C13×#95C2312yes—
226C13×#95C2312yes—
227C13×#95C2312yes—
228C13×#95C2312yes—
229C13×#95C2312yes—
230C13×#95C2312yes—
231C13×#95C2311yescharacteristic
232C13×#95C2311yescharacteristic
233C13×#95C2311yescharacteristic
234C13×#95C2312yes—
235C13×#95C2312yes—
236C13×#95C2311yescharacteristic
237C13×#95C2311yescharacteristic
238C13×#95C2311yescharacteristic
239C13×#95C2312yes—
240C13×#95C2312yes—
241C13×#95C2311yescharacteristic
242C13×#95C2311yescharacteristic
243#34329C1311yesmaximal, characteristic, direct product factor, Sylow
244C24×C13C2412yes—
245C24×C13C2412yes—
246C2×Q8×C13—22no—
247C2×Q8×C13—22no—
248C2×Q8×C13—41no—
249C2×Q8×C13—41no—
250C2×Q8×C13C22×C414yes—
251C2×Q8×C13C22×C414yes—
252C2×D4×C13—22no—
253C2×D4×C13—22no—
254C2×D4×C13—22no—
255C2×D4×C13—22no—
256C2×D4×C13—42no—
257C2×D4×C13—42no—
258C2×D4×C13—42no—
259C2×D4×C13—42no—
260C2×D4×C13C22×C414yes—
261C2×D4×C13C22×C414yes—
262C2×D4×C13C22×C418yes—
263C2×D4×C13C22×C418yes—
264C22×C4×C13—24no—
265C22×C4×C13—24no—
266C22×C4×C13—24no—
267C22×C4×C13—24no—
268C22×C4×C13—24no—
269C22×C4×C13—42no—
270C22×C4×C13—42no—
271C22×C4×C13—42no—
272C22×C4×C13—42no—
273C22×C4×C13—42no—
274C22×C4×C13—42no—
275C22×C4×C13—42no—
276C22×C4×C13—42no—
277C22×C4×C13—42no—
278C22×C4×C13—42no—
279C22×C4×C13—42no—
280C22×C4×C13C22×C418yes—
281C22×C4×C13C22×C418yes—
282C22×C4×C13C2412yes—
283C22×C4×C13C2411yescharacteristic
284C22×C4×C13C2411yescharacteristic
285C22×C4×C13C2411yescharacteristic
286C22×C4×C13C2411yescharacteristic
287C22×C4×C13C2412yes—
288C22×C4×C13C2412yes—
289C22×C4×C13C2411yescharacteristic
290C22×C4×C13C2411yescharacteristic
291C22×C4×C13C2412yes—
292C22×C4×C13C2411yescharacteristic
293C22×C4×C13C2412yes—
294C22×C4×C13C2411yescharacteristic
295C22×C4×C13C2411yescharacteristic
296C22×C4×C13C2411yescharacteristic
297C22×C4×C13C2411yescharacteristic
298C22×C4×C13C2411yescharacteristic
299C22×C4×C13C2411yescharacteristic
300C22×C4×C13C2412yes—
301C22×C4×C13C2411yescharacteristic
302C22×C4×C13C2411yescharacteristic
303C13×C4⋊C4—22no—
304C13×C4⋊C4—22no—
305C13×C4⋊C4—24no—
306C13×C4⋊C4—24no—
307C13×C4⋊C4—22no—
308C13×C4⋊C4—22no—
309C13×C4⋊C4—22no—
310C13×C4⋊C4—41no—
311C13×C4⋊C4—41no—
312C13×C4⋊C4—42no—
313C13×C4⋊C4—41no—
314C13×C4⋊C4—41no—
315C13×C4⋊C4—42no—
316C13×C4⋊C4C22×C414yes—
317C13×C4⋊C4C22×C414yes—
318C13×C4⋊C4C22×C418yes—
319C13×C4⋊C4C22×C414yes—
320C13×C4⋊C4C22×C414yes—
321C13×C4⋊C4#4114yes—
322C13×C22⋊C4—24no—
323C13×C22⋊C4—24no—
324C13×C22⋊C4—24no—
325C13×C22⋊C4—24no—
326C13×C22⋊C4—24no—
327C13×C22⋊C4—42no—
328C13×C22⋊C4—42no—
329C13×C22⋊C4—42no—
330C13×C22⋊C4—42no—
331C13×C22⋊C4—42no—
332C13×C22⋊C4—42no—
333C13×C22⋊C4—42no—
334C13×C22⋊C4C22×C418yes—
335C13×C22⋊C4C22×C418yes—
336C13×C22⋊C4C22×C418yes—
337C13×C22⋊C4C22×C418yes—
338C13×C22⋊C4C22×C418yes—
339C13×C22⋊C4C22×C418yes—
340C42×C13—22no—
341C42×C13—22no—
342C42×C13—24no—
343C42×C13—24no—
344C42×C13—22no—
345C42×C13—22no—
346C42×C13—24no—
347C42×C13—42no—
348C42×C13—42no—
349C42×C13—42no—
350C42×C13—41no—
351C42×C13—41no—
352C42×C13—41no—
353C42×C13—42no—
354C42×C13—42no—
355C42×C13—42no—
356C42×C13C22×C418yes—
357C42×C13C22×C414yes—
358C42×C13C22×C414yes—
359C42×C13C22×C414yes—
360C42×C13#4114yes—
361C2×#559C2×C1311yescharacteristic
362#2374C2×C1312yescomplemented
363#2372C2×C1312yescomplemented
364#2367C2×C1311yescharacteristic, complemented
365#2367C2×C1311yescharacteristic, complemented
366#2366C2×C1311yescharacteristic
367#2359C2×C1312yescomplemented
368#2357C2×C1311yescharacteristic, complemented
369#2356C2×C1311yescharacteristic, complemented
370#2355C2×C1311yescharacteristic, complemented
371#2354C2×C1311yescharacteristic, complemented
372#2353C2×C1312yescomplemented
373#2337C2×C1312yescomplemented
374#2335C2×C1312yescomplemented
375#2328C2×C1311yescharacteristic
376#2326C2×C1311yescharacteristic, complemented
377C4×#124C2×C1311yescharacteristic, complemented
378C4×#123C2×C1312yescomplemented
379#2295C2×C1311yescharacteristic, complemented
380#2290C2×C1312yescomplemented
381#2276C2×C1311yescharacteristic, complemented
382#2275C2×C1311yescharacteristic, complemented
383C42×D4C2×C1311yescharacteristic, complemented
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×C13C23×C414yes—
397C23×C13C23×C414yes—
398C23×C13C2511yescharacteristic
399Q8×C13—28no—
400Q8×C13—44no—
401D4×C13—28no—
402D4×C13—28no—
403D4×C13—48no—
404D4×C13—48no—
405C2×C4×C13—22no—
406C2×C4×C13—22no—
407C2×C4×C13—21no—
408C2×C4×C13—21no—
409C2×C4×C13—22no—
410C2×C4×C13—21no—
411C2×C4×C13—22no—
412C2×C4×C13—21no—
413C2×C4×C13—21no—
414C2×C4×C13—21no—
415C2×C4×C13—21no—
416C2×C4×C13—21no—
417C2×C4×C13—21no—
418C2×C4×C13—22no—
419C2×C4×C13—21no—
420C2×C4×C13—21no—
421C2×C4×C13—21no—
422C2×C4×C13—21no—
423C2×C4×C13—22no—
424C2×C4×C13—21no—
425C2×C4×C13—21no—
426C2×C4×C13—21no—
427C2×C4×C13—21no—
428C2×C4×C13—21no—
429C2×C4×C13—21no—
430C2×C4×C13—21no—
431C2×C4×C13—21no—
432C2×C4×C13—22no—
433C2×C4×C13—21no—
434C2×C4×C13—21no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—21no—
440C2×C4×C13—21no—
441C2×C4×C13—21no—
442C2×C4×C13—21no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—21no—
446C2×C4×C13—22no—
447C2×C4×C13—21no—
448C2×C4×C13—21no—
449C2×C4×C13—21no—
450C2×C4×C13—21no—
451C2×C4×C13—22no—
452C2×C4×C13—21no—
453C2×C4×C13—48no—
454C2×C4×C13—48no—
455C2×C4×C13—48no—
456C2×C4×C13—48no—
457C2×C4×C13—84no—
458C2×C4×C13—84no—
459C2×C4×C13C23×C412yes—
460C2×C4×C13C23×C414yes—
461C2×C4×C13C23×C412yes—
462C2×C4×C13C23×C412yes—
463C2×C4×C13C23×C414yes—
464C2×C4×C13C23×C412yes—
465C2×C4×C13C23×C412yes—
466C2×C4×C13C23×C412yes—
467C2×C4×C13C23×C412yes—
468C2×C4×C13C2×#4112yes—
469C2×C4×C13C2×#4114yes—
470C2×C4×C13C2×#4112yes—
471C2×C4×C13C2×#4112yes—
472C2×C4×C13C2×#4112yes—
473C2×C4×C13H(5,𝔽2)12yes—
474#559C4×C13116yescomplemented
475C2×#127C22×C1311yescharacteristic
476C2×#124C22×C1311yescharacteristic
477C2×#124C22×C1312yes—
478C2×#124C22×C1311yescharacteristic
479C2×#123C22×C1312yes—
480C2×#123C22×C1312yes—
481C2×C4×Q8C22×C1311yescharacteristic
482C2×C4×Q8C22×C1311yescharacteristic
483C2×C4×Q8C22×C1311yescharacteristic
484C2×C4×Q8C22×C1311yescharacteristic
485C2×C4×D4C22×C1311yescharacteristic
486C2×C4×D4C22×C1311yescharacteristic
487C2×C4×D4C22×C1311yescharacteristic
488C2×C4×D4C22×C1311yescharacteristic
489C2×C4×D4C22×C1312yes—
490C2×C4×D4C22×C1312yes—
491C2×C4×D4C22×C1311yescharacteristic
492C2×C4×D4C22×C1311yescharacteristic
493C2×#117C22×C1312yes—
494C22×C42C22×C1312yes—
495#391C22×C1311yescharacteristic
496#391C22×C1311yescharacteristic
497#391C22×C1312yes—
498#391C22×C1311yescharacteristic
499#391C22×C1311yescharacteristic
500#390C22×C1311yescharacteristic
501#390C22×C1311yescharacteristic
502#390C22×C1311yescharacteristic
503#390C22×C1312yes—
504#390C22×C1311yescharacteristic
505#389C22×C1311yescharacteristic
506#389C22×C1311yescharacteristic
507#388C22×C1312yes—
508#388C22×C1312yes—
509#388C22×C1312yes—
510#388C22×C1312yes—
511#388C22×C1312yes—
512#388C22×C1312yes—
513#388C22×C1312yes—
514#388C22×C1312yes—
515#388C22×C1312yes—
516#388C22×C1312yes—
517#388C22×C1312yes—
518#388C22×C1312yes—
519#387C22×C1312yes—
520#387C22×C1312yes—
521#387C22×C1311yescharacteristic
522#387C22×C1312yes—
523#387C22×C1312yes—
524#387C22×C1311yescharacteristic
525#387C22×C1311yescharacteristic
526#387C22×C1311yescharacteristic
527#386C22×C1312yes—
528#386C22×C1312yes—
529#386C22×C1312yes—
530#386C22×C1312yes—
531#386C22×C1312yes—
532#386C22×C1312yes—
533#385C22×C1312yes—
534#385C22×C1312yes—
535#385C22×C1312yes—
536#385C22×C1312yes—
537#384C22×C1311yescharacteristic
538#383C22×C1312yes—
539#382C22×C1311yescharacteristic
540#382C22×C1311yescharacteristic
541#381C22×C1312yes—
542#380C22×C1312yes—
543C4×C4⋊C4C22×C1312yes—
544C4×C4⋊C4C22×C1312yes—
545C4×C4⋊C4C22×C1311yescharacteristic
546C4×C4⋊C4C22×C1311yescharacteristic
547C4×C4⋊C4C22×C1311yescharacteristic
548C4×C4⋊C4C22×C1311yescharacteristic
549C4×C4⋊C4C22×C1311yescharacteristic
550C4×C4⋊C4C22×C1311yescharacteristic
551C4×C4⋊C4C22×C1312yes—
552C4×C4⋊C4C22×C1311yescharacteristic
553C4×C4⋊C4C22×C1311yescharacteristic
554C4×C4⋊C4C22×C1311yescharacteristic
555C4×C4⋊C4C22×C1312yes—
556C4×C4⋊C4C22×C1311yescharacteristic
557C4×C22⋊C4C22×C1312yes—
558C4×C22⋊C4C22×C1312yes—
559C4×C22⋊C4C22×C1312yes—
560C4×C22⋊C4C22×C1312yes—
561C4×C22⋊C4C22×C1312yes—
562C4×C22⋊C4C22×C1312yes—
563C4×C22⋊C4C22×C1312yes—
564C4×C22⋊C4C22×C1312yes—
565C4×C22⋊C4C22×C1312yes—
566C4×C22⋊C4C22×C1312yes—
567C4×C22⋊C4C22×C1312yes—
568#376C22×C1311yescharacteristic
569#376C22×C1311yescharacteristic
570#376C22×C1312yes—
571#376C22×C1312yes—
572C2×#95C22×C1312yes—
573C43C22×C1311yescharacteristic
574C22×C13—24no—
575C22×C13—24no—
576C22×C13—24no—
577C22×C13—24no—
578C22×C13—24no—
579C22×C13—24no—
580C22×C13—42no—
581C22×C13—42no—
582C22×C13—42no—
583C22×C13—42no—
584C22×C13—42no—
585C22×C13—42no—
586C22×C13—42no—
587C22×C13—42no—
588C22×C13C24×C411yescharacteristic
589C22×C13C22×#4111yescharacteristic
590C22×C13C22×#4111yescharacteristic
591C22×C13C2×H(5,𝔽2)11yescharacteristic
592C22×C13#58511yescharacteristic
593C22×C13#58511yescharacteristic
594C22×C13#58511yescharacteristic
595C4×C13—24no—
596C4×C13—22no—
597C4×C13—22no—
598C4×C13—22no—
599C4×C13—22no—
600C4×C13—24no—
601C4×C13—22no—
602C4×C13—22no—
603C4×C13—22no—
604C4×C13—22no—
605C4×C13—22no—
606C4×C13—24no—
607C4×C13—42no—
608C4×C13—42no—
609C4×C13—42no—
610C4×C13—41no—
611C4×C13—41no—
612C4×C13—41no—
613C4×C13—41no—
614C4×C13—41no—
615C4×C13C4×#4114yes—
616C22×Q8C23×C1311yescharacteristic
617C22×Q8C23×C1311yescharacteristic
618C22×D4C23×C1311yescharacteristic
619C22×D4C23×C1311yescharacteristic
620C22×D4C23×C1312yes—
621C22×D4C23×C1312yes—
622C23×C4C23×C1312yes—
623C23×C4C23×C1312yes—
624C23×C4C23×C1312yes—
625C23×C4C23×C1312yes—
626C23×C4C23×C1312yes—
627C23×C4C23×C1312yes—
628#127C2×C4×C1318yes—
629#124C2×C4×C1318yescomplemented
630#124C2×C4×C1318yescomplemented
631#124C2×C4×C13116yescomplemented
632#123C2×C4×C13116yescomplemented
633#123C2×C4×C13116yescomplemented
634C4×Q8—24no—
635C4×Q8—24no—
636C4×Q8C2×C4×C1318yescomplemented
637C4×Q8C2×C4×C1318yescomplemented
638C4×D4—24no—
639C4×D4—24no—
640C4×D4—24no—
641C4×D4—24no—
642C4×D4—44no—
643C4×D4C2×C4×C1318yescomplemented
644C4×D4C2×C4×C1318yescomplemented
645C4×D4C2×C4×C13116yescomplemented
646#117—44no—
647C2×C4⋊C4C23×C1311yescharacteristic
648C2×C4⋊C4C23×C1311yescharacteristic
649C2×C4⋊C4C23×C1311yescharacteristic
650C2×C4⋊C4C23×C1311yescharacteristic
651C2×C4⋊C4C23×C1311yescharacteristic
652C2×C4⋊C4C23×C1312yes—
653C2×C4⋊C4C23×C1312yes—
654C2×C4⋊C4C23×C1312yes—
655C2×C4⋊C4C23×C1311yescharacteristic
656C2×C4⋊C4C23×C1312yes—
657C2×C4⋊C4C23×C1311yescharacteristic
658C2×C4⋊C4C23×C1311yescharacteristic
659C2×C4⋊C4C23×C1311yescharacteristic
660C2×C4⋊C4C23×C1311yescharacteristic
661C2×C4⋊C4C23×C1311yescharacteristic
662C2×C4⋊C4C23×C1311yescharacteristic
663C2×C4⋊C4C23×C1312yes—
664C2×C4⋊C4C23×C1311yescharacteristic
665C2×C4⋊C4C23×C1311yescharacteristic
666C2×C22⋊C4C23×C1312yes—
667C2×C22⋊C4C23×C1312yes—
668C2×C22⋊C4C23×C1312yes—
669C2×C22⋊C4C23×C1312yes—
670C2×C22⋊C4C23×C1312yes—
671C2×C22⋊C4C23×C1312yes—
672C2×C22⋊C4C23×C1312yes—
673C2×C22⋊C4C23×C1312yes—
674C2×C22⋊C4C23×C1312yes—
675C2×C22⋊C4C23×C1312yes—
676C2×C22⋊C4C23×C1312yes—
677C2×C22⋊C4C23×C1312yes—
678C2×C22⋊C4C23×C1312yes—
679C2×C22⋊C4C23×C1312yes—
680C2×C22⋊C4C23×C1312yes—
681C2×C22⋊C4C23×C1312yes—
682C2×C22⋊C4C23×C1312yes—
683C2×C22⋊C4C23×C1312yes—
684C2×C42—44no—
685C2×C42C23×C1312yes—
686C2×C42C23×C1311yescharacteristic
687C2×C42C23×C1311yescharacteristic
688C2×C42C23×C1312yes—
689C2×C42C23×C1312yes—
690C2×C42C23×C1311yescharacteristic
691C2×C42C23×C1311yescharacteristic
692C2×C42C23×C1312yes—
693C2×C42C23×C1312yes—
694C2×C42C23×C1311yescharacteristic
695C2×C42C23×C1311yescharacteristic
696C2×C42C23×C1311yescharacteristic
697C2×C42C23×C1312yes—
698C2×C42C23×C1312yes—
699C2×C42C23×C1312yes—
700C2×C42C23×C1312yes—
701C2×C42C23×C1311yescharacteristic
702C2×C42C23×C1312yes—
703C2×C42C23×C1311yescharacteristic
704C2×C42C23×C1311yescharacteristic
705C2×C42C23×C1311yescharacteristic
706#95C23×C1311yescharacteristic
707#95C23×C1312yes—
708#95C23×C1312yes—
709#95C23×C1312yes—
710#95C23×C1311yescharacteristic
711#95C23×C1311yescharacteristic
712#95C23×C1311yescharacteristic
713#95C23×C1311yescharacteristic
714#95C23×C1312yes—
715#95C23×C1311yescharacteristic
716#95C23×C1312yes—
717#95C23×C1311yescharacteristic
718#95C23×C1311yescharacteristic
719#95C23×C1311yescharacteristic
720#95C23×C1312yes—
721#95C23×C1312yes—
722#95C23×C1312yes—
723#95C23×C1312yes—
724#95C23×C1311yescharacteristic
725#95C23×C1312yes—
726#95C23×C1312yes—
727#95C23×C1311yescharacteristic
728#95C23×C1311yescharacteristic
729#95C23×C1312yes—
730#95C23×C1312yes—
731#95C23×C1312yes—
732#95C23×C1312yes—
733#95C23×C1311yescharacteristic
734#95C23×C1311yescharacteristic
735C2×C13—44no—
736C2×C13—44no—
737C2×C13C2×C4×#4111yescharacteristic
738C2×C13#342811yescharacteristic
739C2×C13C4×H(5,𝔽2)11yescharacteristic
740C2×C13#350611yescharacteristic
741C2×C13#351011yescharacteristic
742C2×C13#351311yescharacteristic
743C2×C13#352411yescharacteristic
744C24C24×C1312yes—
745C24C24×C1312yes—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—41no—
749C2×Q8—41no—
750C2×Q8C22×C4×C1314yes—
751C2×Q8C22×C4×C1314yes—
752C2×D4—22no—
753C2×D4—22no—
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—42no—
760C2×D4C22×C4×C1314yes—
761C2×D4C22×C4×C1314yes—
762C2×D4C22×C4×C1318yes—
763C2×D4C22×C4×C1318yes—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4C22×C4×C1318yes—
781C22×C4C22×C4×C1318yes—
782C22×C4C24×C1312yes—
783C22×C4C24×C1311yescharacteristic
784C22×C4C24×C1311yescharacteristic
785C22×C4C24×C1311yescharacteristic
786C22×C4C24×C1311yescharacteristic
787C22×C4C24×C1312yes—
788C22×C4C24×C1312yes—
789C22×C4C24×C1311yescharacteristic
790C22×C4C24×C1311yescharacteristic
791C22×C4C24×C1312yes—
792C22×C4C24×C1311yescharacteristic
793C22×C4C24×C1312yes—
794C22×C4C24×C1311yescharacteristic
795C22×C4C24×C1311yescharacteristic
796C22×C4C24×C1311yescharacteristic
797C22×C4C24×C1311yescharacteristic
798C22×C4C24×C1311yescharacteristic
799C22×C4C24×C1311yescharacteristic
800C22×C4C24×C1312yes—
801C22×C4C24×C1311yescharacteristic
802C22×C4C24×C1311yescharacteristic
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—22no—
810C4⋊C4—42no—
811C4⋊C4—41no—
812C4⋊C4—41no—
813C4⋊C4—42no—
814C4⋊C4—41no—
815C4⋊C4—41no—
816C4⋊C4C22×C4×C1314yes—
817C4⋊C4C22×C4×C1314yes—
818C4⋊C4C22×C4×C1318yes—
819C4⋊C4C22×C4×C1314yes—
820C4⋊C4C22×C4×C1314yes—
821C4⋊C4C13×#4114yes—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—42no—
831C22⋊C4—42no—
832C22⋊C4—42no—
833C22⋊C4—42no—
834C22⋊C4C22×C4×C1318yes—
835C22⋊C4C22×C4×C1318yes—
836C22⋊C4C22×C4×C1318yes—
837C22⋊C4C22×C4×C1318yes—
838C22⋊C4C22×C4×C1318yes—
839C22⋊C4C22×C4×C1318yes—
840C42—22no—
841C42—22no—
842C42—24no—
843C42—24no—
844C42—22no—
845C42—22no—
846C42—24no—
847C42—42no—
848C42—42no—
849C42—42no—
850C42—42no—
851C42—42no—
852C42—41no—
853C42—41no—
854C42—41no—
855C42—42no—
856C42C22×C4×C1318yes—
857C42C22×C4×C1314yes—
858C42C22×C4×C1314yes—
859C42C22×C4×C1314yes—
860C42C13×#4114yes—
861C13#3432911yescharacteristic, direct product factor, Sylow
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23C23×C4×C1314yes—
875C23C23×C4×C1314yes—
876C23C25×C1311yescharacteristic
877Q8—28no—
878Q8—44no—
879D4—28no—
880D4—28no—
881D4—48no—
882D4—48no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—48no—
933C2×C4—48no—
934C2×C4—48no—
935C2×C4—84no—
936C2×C4—84no—
937C2×C4C23×C4×C1312yes—
938C2×C4C23×C4×C1314yes—
939C2×C4C23×C4×C1312yes—
940C2×C4C23×C4×C1312yes—
941C2×C4C23×C4×C1314yes—
942C2×C4C23×C4×C1312yes—
943C2×C4C23×C4×C1312yes—
944C2×C4C23×C4×C1312yes—
945C2×C4C23×C4×C1312yes—
946C2×C4C2×C13×#4112yes—
947C2×C4C2×C13×#4114yes—
948C2×C4C2×C13×#4112yes—
949C2×C4C2×C13×#4112yes—
950C2×C4C2×C13×#4112yes—
951C2×C4C13×H(5,𝔽2)12yes—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22C24×C4×C1311yescharacteristic
967C22C22×C13×#4111yescharacteristic
968C22C22×C13×#4111yescharacteristic
969C22C2×C13×H(5,𝔽2)11yescharacteristic
970C22C13×#58511yescharacteristic
971C22C13×#58511yescharacteristic
972C22C13×#58511yescharacteristic
973C4—24no—
974C4—22no—
975C4—22no—
976C4—22no—
977C4—22no—
978C4—24no—
979C4—22no—
980C4—22no—
981C4—22no—
982C4—22no—
983C4—22no—
984C4—24no—
985C4—41no—
986C4—41no—
987C4—41no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—41no—
992C4—41no—
993C4C4×C13×#4114yes—
994C2—44no—
995C2—44no—
996C2C2×C4×C13×#4111yescharacteristic
997C2C13×#342811yescharacteristic
998C2C4×C13×H(5,𝔽2)11yescharacteristic
999C2C13×#350611yescharacteristic
1000C2C13×#351011yescharacteristic
1001C2C13×#351311yescharacteristic
1002C2C13×#352411yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC2×C13×#127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2374C2semidirect
3. C13×#2372C2semidirect
4. C13×#2367C2semidirect
5. C13×#2367C2semidirect
7. C13×#2359C2semidirect
8. C13×#2357C2semidirect
9. C13×#2356C2semidirect
10. C13×#2355C2semidirect
11. C13×#2354C2semidirect
12. C13×#2353C2semidirect
13. C13×#2337C2semidirect
14. C13×#2335C2semidirect
16. C13×#2326C2semidirect
17. C4×C13×#124C2semidirect
18. C4×C13×#123C2semidirect
19. C13×#2295C2semidirect
20. C13×#2290C2semidirect
21. C13×#2276C2semidirect
22. C13×#2275C2semidirect
23. C42×D4×C13C2semidirect
24. C13×#559C4semidirect
137. C13×#124C2×C4semidirect
138. C13×#124C2×C4semidirect
139. C13×#124C2×C4semidirect
140. C13×#123C2×C4semidirect
141. C13×#123C2×C4semidirect
144. C4×Q8×C13C2×C4semidirect
145. C4×Q8×C13C2×C4semidirect
151. C4×D4×C13C2×C4semidirect
152. C4×D4×C13C2×C4semidirect
153. C4×D4×C13C2×C4semidirect
243. #34329C13direct (N × H)
362. #2374C2×C13semidirect
363. #2372C2×C13semidirect
364. #2367C2×C13semidirect
365. #2367C2×C13semidirect
367. #2359C2×C13semidirect
368. #2357C2×C13semidirect
369. #2356C2×C13semidirect
370. #2355C2×C13semidirect
371. #2354C2×C13semidirect
372. #2353C2×C13semidirect
373. #2337C2×C13semidirect
374. #2335C2×C13semidirect
376. #2326C2×C13semidirect
377. C4×#124C2×C13semidirect
378. C4×#123C2×C13semidirect
379. #2295C2×C13semidirect
380. #2290C2×C13semidirect
381. #2276C2×C13semidirect
382. #2275C2×C13semidirect
383. C42×D4C2×C13semidirect
474. #559C4×C13semidirect
629. #124C2×C4×C13semidirect
630. #124C2×C4×C13semidirect
631. #124C2×C4×C13semidirect
632. #123C2×C4×C13semidirect
633. #123C2×C4×C13semidirect
636. C4×Q8C2×C4×C13semidirect
637. C4×Q8C2×C4×C13semidirect
643. C4×D4C2×C4×C13semidirect
644. C4×D4C2×C4×C13semidirect
645. C4×D4C2×C4×C13semidirect
861. C13#34329direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5592
C13×#23742
C13×#23722
C13×#23672
C13×#23662
C13×#23592
C13×#23572
C13×#23562
C13×#23552
C13×#23542
C13×#23532
C13×#23372
C13×#23352
C13×#23282
C13×#23262
C4×C13×#1242
C4×C13×#1232
C13×#22952
C13×#22902
C13×#22762
C13×#22752
C42×D4×C132
#3432913