Finite Group Databasebeta

← C13×#63046 #15749385

Subgroups — C13×#63046 #15749385

Order 3328.

6790 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3568C216yesmaximal, complemented
2C13×#3561C216yesmaximal, complemented
3C13×#3558C216yesmaximal, complemented
4C13×#3545C213yesmaximal, complemented
5C13×#3545C216yesmaximal, complemented
6C13×#3540C2112yesmaximal, complemented
7C13×#3532C216yesmaximal, complemented
8C13×#3529C212yesmaximal, complemented
9C2×C13×H(3,𝔽4)C211yesmaximal, characteristic, complemented
10C13×#3514C216yesmaximal, complemented
11C13×#3510C213yesmaximal, complemented
12C13×#3490C216yesmaximal, complemented
13C13×#563C2216yescomplemented
14C13×#563C2216yescomplemented
15C13×#563C2213yescomplemented
16C13×#562C2216yescomplemented
17C13×#562C2216yescomplemented
18C13×#562C2216yescomplemented
19C13×H(3,𝔽4)C2211yescharacteristic, complemented
20C13×H(3,𝔽4)C2216yescomplemented
21C13×H(3,𝔽4)C2213yescomplemented
22C13×H(3,𝔽4)C2216yescomplemented
23C13×H(3,𝔽4)C2216yescomplemented
24C13×H(3,𝔽4)C2213yescomplemented
25C13×#560C22112yescomplemented
26C13×#560C2216yescomplemented
27C13×#559C2216yescomplemented
28C13×#559C22112yescomplemented
29C13×#556C22112yescomplemented
30C13×#556C22112yescomplemented
31C13×#556C2216yescomplemented
32C13×#555C2216yescomplemented
33C13×#555C22112yescomplemented
34C13×#551C22112yescomplemented
35C13×#551C22112yescomplemented
36C13×#551C22112yescomplemented
37C13×#551C2216yescomplemented
38C13×#551C22112yescomplemented
39C13×#551C22112yescomplemented
40C13×#551C22112yescomplemented
41C13×#551C2216yescomplemented
42D4×Q8×C13C2216yescomplemented
43C13×#548C2212yescomplemented
44C13×#548C2216yescomplemented
45C13×#548C22112yescomplemented
46C13×#546C22112yescomplemented
47C13×#546C2216yescomplemented
48C13×#546C22112yescomplemented
49C13×#546C22112yescomplemented
50C13×#546C22112yescomplemented
51C13×#546C22112yescomplemented
52C13×#546C2216yescomplemented
53D42×C13C2216yescomplemented
54D42×C13C2216yescomplemented
55C13×#543C2216yescomplemented
56C13×#542C2216yescomplemented
57C13×#542C22112yescomplemented
58C13×#542C2216yescomplemented
59C13×#542C22112yescomplemented
60C13×#542C22112yescomplemented
61C13×#542C22112yescomplemented
62C13×#542C22112yescomplemented
63C13×#538C22112yescomplemented
64C13×#538C22112yescomplemented
65C13×#538C22112yescomplemented
66C13×#538C22112yescomplemented
67C13×#538C22112yescomplemented
68C13×#538C22112yescomplemented
69C13×#538C22112yescomplemented
70C13×#536C2213yescomplemented
71C13×#536C22112yescomplemented
72C13×#535C2213yes—
73C13×#535C22112yescomplemented
74C13×#534C2216yescomplemented
75C13×#534C22112yescomplemented
76C13×#533C2213yescomplemented
77C13×#532C2216yescomplemented
78C13×#529C2216yescomplemented
79C13×#529C2216yescomplemented
80C13×#529C2216yescomplemented
81C13×#529C2216yescomplemented
82C13×#529C2216yescomplemented
83C2×C13×#124C2213yescomplemented
84C2×C13×#124C2216yescomplemented
85C2×C13×#124C2216yescomplemented
86C13×#525C22112yescomplemented
87C13×#525C22112yescomplemented
88C2×C13×#120C2216yescomplemented
89C2×C13×#120C2216yescomplemented
90C13×#519C2211yescharacteristic, complemented
91C13×#518C2213yescomplemented
92C13×#518C2216yescomplemented
93C4×C13×#41C2213yescomplemented
94C22×C13×C22⋊C4C2212yescomplemented
95C25×C13C2312yes—
96C2×C13×#41C2313yes—
97C2×C13×#41C2316yes—
98C2×C13×#41C23112yes—
99C2×C13×#41C2312yescomplemented
100C22×Q8×C13C2311yescharacteristic
101C22×Q8×C13C2312yes—
102C22×Q8×C13C2316yescomplemented
103C22×D4×C13C2313yes—
104C22×D4×C13C2316yes—
105C22×D4×C13C2316yes—
106C22×D4×C13C2316yes—
107C22×D4×C13C23112yescomplemented
108C23×C4×C13C2314yescomplemented
109C13×C4⋊Q8C2316yescomplemented
110C13×C4⋊Q8C2316yescomplemented
111C13×C4⋊Q8C23112yescomplemented
112C13×C4⋊Q8C2316yescomplemented
113C13×#127C2316yes—
114C13×#127C2316yes—
115C13×#126C23112yescomplemented
116C13×#126C23112yescomplemented
117C13×#126C23112yescomplemented
118C13×#126C23112yescomplemented
119C13×#126C23112yescomplemented
120C13×#126C23112yescomplemented
121C13×#126C23112yescomplemented
122C13×#126C23112yescomplemented
123C13×#126C23112yescomplemented
124C13×#125C2316yescomplemented
125C13×#125C2316yescomplemented
126C13×#124C2316yes—
127C13×#124C2313yes—
128C13×#124C2313yes—
129C13×#124C2316yes—
130C13×#124C23112yes—
131C13×#124C2316yes—
132C13×#124C23112yes—
133C13×#124C23112yes—
134C13×#124C2316yes—
135C13×#124C2316yes—
136C13×#124C2313yes—
137C13×#124C2313yes—
138C13×#124C2316yes—
139C13×#124C23112yes—
140C13×#124C2316yescomplemented
141C13×#124C23112yescomplemented
142C13×#124C2316yescomplemented
143C13×#124C23112yescomplemented
144C13×#124C23112yescomplemented
145C13×#124C2316yescomplemented
146C13×#124C23112yescomplemented
147C13×#124C23112yescomplemented
148C13×#124C23112yescomplemented
149C13×#123C23112yes—
150C13×#123C23112yes—
151C13×#123C23112yes—
152C13×#123C2316yes—
153C13×#123C23112yes—
154C13×#123C2316yes—
155C13×#123C23112yescomplemented
156C13×#123C23112yescomplemented
157C13×#123C23112yescomplemented
158C13×#123C23112yescomplemented
159C13×#123C23112yescomplemented
160C13×#123C23112yescomplemented
161C13×#123C23112yescomplemented
162C13×#123C23112yescomplemented
163C13×#123C23112yescomplemented
164C13×C22⋊Q8C2316yes—
165C13×C22⋊Q8C23112yes—
166C13×C22⋊Q8C23112yescomplemented
167C13×C22⋊Q8C23112yescomplemented
168C13×C22⋊Q8C23112yescomplemented
169C13×C22⋊Q8C23112yescomplemented
170C13×C22⋊Q8C2316yescomplemented
171C13×C22⋊Q8C2316yescomplemented
172C13×C22⋊Q8C2316yescomplemented
173C13×C22⋊Q8C2316yescomplemented
174C13×C22⋊Q8C23112yescomplemented
175C13×C22⋊Q8C23112yescomplemented
176C13×C22⋊Q8C23112yescomplemented
177C13×C22⋊Q8C23112yescomplemented
178C13×C22⋊Q8C23112yescomplemented
179C13×#121C23112yes—
180C13×#121C23112yes—
181C13×#121C23112yes—
182C13×#121C23112yes—
183C13×#121C2316yes—
184C13×#121C2316yes—
185C13×#121C2316yes—
186C13×#121C2316yes—
187C13×#121C2316yes—
188C13×#121C23112yes—
189C13×#121C23112yes—
190C13×#121C23112yes—
191C13×#121C23112yescomplemented
192C13×#121C23112yescomplemented
193C13×#121C23112yescomplemented
194C13×#121C23112yescomplemented
195C13×#120C2316yes—
196C13×#120C2316yes—
197C13×#120C23112yes—
198C13×#120C23112yes—
199C13×#120C23112yes—
200C13×#120C23112yes—
201C13×#120C2316yes—
202C13×#120C2316yes—
203C13×#120C2316yes—
204C13×#120C23112yes—
205C13×#120C2316yes—
206C13×#120C23112yescomplemented
207C13×#120C23112yescomplemented
208C13×#120C23112yescomplemented
209C4×Q8×C13C2316yescomplemented
210C4×Q8×C13C2312yescomplemented
211C4×Q8×C13C2316yescomplemented
212C4×Q8×C13C2312yescomplemented
213C4×Q8×C13C2316yescomplemented
214C4×Q8×C13C2316yescomplemented
215C4×Q8×C13C23112yescomplemented
216C4×D4×C13C2316yes—
217C4×D4×C13C2316yes—
218C4×D4×C13C2316yes—
219C4×D4×C13C23112yes—
220C4×D4×C13C23112yes—
221C4×D4×C13C2316yes—
222C4×D4×C13C2316yes—
223C4×D4×C13C23112yes—
224C4×D4×C13C2316yes—
225C4×D4×C13C2316yescomplemented
226C4×D4×C13C23112yescomplemented
227C4×D4×C13C23112yescomplemented
228C4×D4×C13C23112yescomplemented
229C4×D4×C13C23112yescomplemented
230C4×D4×C13C2316yescomplemented
231C4×D4×C13C23112yescomplemented
232C4×D4×C13C23112yescomplemented
233C13×#117C2313yes—
234C13×#117C2313yes—
235C13×#117C2313yes—
236C13×#117C2316yescomplemented
237C13×#117C23112yescomplemented
238C13×#117C23112yescomplemented
239C13×#117C23112yescomplemented
240C13×#117C23112yescomplemented
241C13×#117C23112yescomplemented
242C2×C13×C22⋊C4C2316yes—
243C2×C13×C22⋊C4C2316yes—
244C2×C13×C22⋊C4C2316yes—
245C2×C13×C22⋊C4C2316yes—
246C2×C13×C22⋊C4C23112yes—
247C2×C13×C22⋊C4C23112yescomplemented
248C2×C13×C22⋊C4C23112yescomplemented
249C2×C13×C22⋊C4C23112yescomplemented
250C2×C13×C22⋊C4C23112yescomplemented
251C2×C42×C13C2313yes—
252C2×C42×C13C2316yescomplemented
253#63046C1311yesmaximal, characteristic, direct product factor, Sylow
254C24×C13—44no—
255C24×C13—84no—
256C24×C13C2416yes—
257C24×C13C2416yes—
258C24×C13C2416yes—
259C24×C13C2412yes—
260C13×#41—46no—
261C13×#41—86no—
262C13×#41—812no—
263C13×#41—82no—
264C2×Q8×C13—42no—
265C2×Q8×C13—82no—
266C2×Q8×C13—86no—
267C2×Q8×C13C2411yescharacteristic
268C2×Q8×C13C2413yes—
269C2×Q8×C13C2413yes—
270C2×Q8×C13C2416yes—
271C2×Q8×C13C24112yes—
272C2×Q8×C13C2416yes—
273C2×Q8×C13C2412yes—
274C2×D4×C13—46no—
275C2×D4×C13—412no—
276C2×D4×C13—86no—
277C2×D4×C13—86no—
278C2×D4×C13—812no—
279C2×D4×C13C2416yes—
280C2×D4×C13C2413yes—
281C2×D4×C13C2416yes—
282C2×D4×C13C2413yes—
283C2×D4×C13C24112yes—
284C2×D4×C13C2416yes—
285C2×D4×C13C2416yes—
286C2×D4×C13C24112yes—
287C2×D4×C13C2413yes—
288C2×D4×C13C24112yes—
289C2×D4×C13C24112yes—
290C2×D4×C13C24112yes—
291C2×D4×C13C24112yes—
292C2×D4×C13C2416yes—
293C22×C4×C13—84no—
294C22×C4×C13C2413yes—
295C22×C4×C13C2416yes—
296C22×C4×C13C2416yes—
297C22×C4×C13C2416yes—
298C22×C4×C13C2416yes—
299C22×C4×C13C24112yes—
300C22×C4×C13C24112yes—
301C22×C4×C13C24112yes—
302C22×C4×C13C2416yes—
303C22×C4×C13C24112yes—
304C13×C4⋊C4C2416yes—
305C13×C4⋊C4C2416yes—
306C13×C4⋊C4C2416yes—
307C13×C4⋊C4C2416yes—
308C13×C4⋊C4C24112yes—
309C13×C4⋊C4C24112yes—
310C13×C4⋊C4C24112yes—
311C13×C4⋊C4C24112yes—
312C13×C4⋊C4C24112yes—
313C13×C4⋊C4C2416yes—
314C13×C4⋊C4C2416yes—
315C13×C4⋊C4C2416yes—
316C13×C4⋊C4C24112yes—
317C13×C4⋊C4C24112yes—
318C13×C22⋊C4C2411yescharacteristic
319C13×C22⋊C4C2416yes—
320C13×C22⋊C4C2413yes—
321C13×C22⋊C4C24112yes—
322C13×C22⋊C4C2416yes—
323C13×C22⋊C4C2416yes—
324C13×C22⋊C4C24112yes—
325C13×C22⋊C4C24112yes—
326C13×C22⋊C4C24112yes—
327C13×C22⋊C4C24112yes—
328C13×C22⋊C4C24112yes—
329C13×C22⋊C4C24112yes—
330C13×C22⋊C4C2416yes—
331C13×C22⋊C4C2416yes—
332C13×C22⋊C4C2416yes—
333C13×C22⋊C4C24112yes—
334C13×C22⋊C4C24112yes—
335C13×C22⋊C4C24112yes—
336C13×C22⋊C4C24112yes—
337C13×C22⋊C4C24112yes—
338C13×C22⋊C4C24112yes—
339C13×C22⋊C4C24112yes—
340C13×C22⋊C4C2416yes—
341C13×C22⋊C4C24112yes—
342C42×C13C2413yes—
343C42×C13C2413yes—
344C42×C13C2416yes—
345C42×C13C2416yes—
346C42×C13C2416yes—
347C42×C13C2416yes—
348C42×C13C2416yes—
349C42×C13C2416yes—
350C42×C13C24112yes—
351#3568C2×C1316yescomplemented
352#3561C2×C1316yescomplemented
353#3558C2×C1316yescomplemented
354#3545C2×C1313yescomplemented
355#3545C2×C1316yescomplemented
356#3540C2×C13112yescomplemented
357#3532C2×C1316yescomplemented
358#3529C2×C1312yescomplemented
359C2×H(3,𝔽4)C2×C1311yescharacteristic, complemented
360#3514C2×C1316yescomplemented
361#3510C2×C1313yescomplemented
362#3490C2×C1316yescomplemented
363C23×C13—212no—
364C23×C13—44no—
365C23×C13—42no—
366C23×C13—412no—
367C23×C13—412no—
368C23×C13—46no—
369C23×C13—46no—
370C23×C13—412no—
371C23×C13—816no—
372C23×C13C2516yes—
373C23×C13C2516yes—
374C23×C13C2516yes—
375C23×C13C2511yescharacteristic
376Q8×C13—41no—
377Q8×C13—43no—
378Q8×C13—46no—
379Q8×C13—46no—
380Q8×C13—412no—
381Q8×C13—42no—
382Q8×C13—43no—
383D4×C13—212no—
384D4×C13—43no—
385D4×C13—43no—
386D4×C13—46no—
387D4×C13—412no—
388D4×C13—412no—
389D4×C13—46no—
390D4×C13—412no—
391D4×C13—412no—
392D4×C13—412no—
393D4×C13—46no—
394D4×C13—46no—
395D4×C13—412no—
396D4×C13—43no—
397C2×C4×C13—26no—
398C2×C4×C13—412no—
399C2×C4×C13—412no—
400C2×C4×C13—46no—
401C2×C4×C13—46no—
402C2×C4×C13—46no—
403C2×C4×C13—412no—
404C2×C4×C13—412no—
405C2×C4×C13—46no—
406C2×C4×C13—46no—
407C2×C4×C13C2513yes—
408C2×C4×C13C2512yes—
409C2×C4×C13C2513yes—
410C2×C4×C13C2516yes—
411C2×C4×C13C2516yes—
412C2×C4×C13C2516yes—
413C2×C4×C13C2516yes—
414C2×C4×C13C25112yes—
415#563C22×C1316yescomplemented
416#563C22×C1316yescomplemented
417#563C22×C1313yescomplemented
418#562C22×C1316yescomplemented
419#562C22×C1316yescomplemented
420#562C22×C1316yescomplemented
421H(3,𝔽4)C22×C1311yescharacteristic, complemented
422H(3,𝔽4)C22×C1316yescomplemented
423H(3,𝔽4)C22×C1313yescomplemented
424H(3,𝔽4)C22×C1316yescomplemented
425H(3,𝔽4)C22×C1316yescomplemented
426H(3,𝔽4)C22×C1313yescomplemented
427#560C22×C13112yescomplemented
428#560C22×C1316yescomplemented
429#559C22×C13112yescomplemented
430#559C22×C1316yescomplemented
431#556C22×C13112yescomplemented
432#556C22×C1316yescomplemented
433#556C22×C13112yescomplemented
434#555C22×C13112yescomplemented
435#555C22×C1316yescomplemented
436#551C22×C13112yescomplemented
437#551C22×C13112yescomplemented
438#551C22×C13112yescomplemented
439#551C22×C13112yescomplemented
440#551C22×C13112yescomplemented
441#551C22×C1316yescomplemented
442#551C22×C13112yescomplemented
443#551C22×C1316yescomplemented
444D4×Q8C22×C1316yescomplemented
445#548C22×C1312yescomplemented
446#548C22×C1316yescomplemented
447#548C22×C13112yescomplemented
448#546C22×C1316yescomplemented
449#546C22×C13112yescomplemented
450#546C22×C13112yescomplemented
451#546C22×C13112yescomplemented
452#546C22×C13112yescomplemented
453#546C22×C13112yescomplemented
454#546C22×C1316yescomplemented
455D42C22×C1316yescomplemented
456D42C22×C1316yescomplemented
457#543C22×C1316yescomplemented
458#542C22×C1316yescomplemented
459#542C22×C1316yescomplemented
460#542C22×C13112yescomplemented
461#542C22×C13112yescomplemented
462#542C22×C13112yescomplemented
463#542C22×C13112yescomplemented
464#542C22×C13112yescomplemented
465#538C22×C13112yescomplemented
466#538C22×C13112yescomplemented
467#538C22×C13112yescomplemented
468#538C22×C13112yescomplemented
469#538C22×C13112yescomplemented
470#538C22×C13112yescomplemented
471#538C22×C13112yescomplemented
472#536C22×C1313yescomplemented
473#536C22×C13112yescomplemented
474#535C22×C1313yes—
475#535C22×C13112yescomplemented
476#534C22×C1316yescomplemented
477#534C22×C13112yescomplemented
478#533C22×C1313yescomplemented
479#532C22×C1316yescomplemented
480#529C22×C1316yescomplemented
481#529C22×C1316yescomplemented
482#529C22×C1316yescomplemented
483#529C22×C1316yescomplemented
484#529C22×C1316yescomplemented
485C2×#124C22×C1313yescomplemented
486C2×#124C22×C1316yescomplemented
487C2×#124C22×C1316yescomplemented
488#525C22×C13112yescomplemented
489#525C22×C13112yescomplemented
490C2×#120C22×C1316yescomplemented
491C2×#120C22×C1316yescomplemented
492#519C22×C1311yescharacteristic, complemented
493#518C22×C1313yescomplemented
494#518C22×C1316yescomplemented
495C4×#41C22×C1313yescomplemented
496C22×C22⋊C4C22×C1312yescomplemented
497C22×C13—22no—
498C22×C13—26no—
499C22×C13—26no—
500C22×C13—26no—
501C22×C13—26no—
502C22×C13—212no—
503C22×C13—26no—
504C22×C13—212no—
505C22×C13—48no—
506C22×C13—812no—
507C22×C13—812no—
508C22×C13—166no—
509C22×C13#58512yes—
510C22×C13C2611yescharacteristic
511C4×C13—23no—
512C4×C13—23no—
513C4×C13—26no—
514C4×C13—22no—
515C4×C13—212no—
516C4×C13—26no—
517C4×C13—26no—
518C4×C13—26no—
519C25C23×C1312yes—
520C2×#41C23×C1313yes—
521C2×#41C23×C1316yes—
522C2×#41C23×C13112yes—
523C2×#41C23×C1312yescomplemented
524C22×Q8C23×C1311yescharacteristic
525C22×Q8C23×C1312yes—
526C22×Q8C23×C1316yescomplemented
527C22×D4C23×C1313yes—
528C22×D4C23×C1316yes—
529C22×D4C23×C1316yes—
530C22×D4C23×C1316yes—
531C22×D4C23×C13112yescomplemented
532C23×C4C23×C1314yescomplemented
533C4⋊Q8C23×C1316yescomplemented
534C4⋊Q8C23×C1316yescomplemented
535C4⋊Q8C23×C13112yescomplemented
536C4⋊Q8C23×C1316yescomplemented
537#127C23×C1316yes—
538#127C23×C1316yes—
539#126C23×C13112yescomplemented
540#126C23×C13112yescomplemented
541#126C23×C13112yescomplemented
542#126C23×C13112yescomplemented
543#126C23×C13112yescomplemented
544#126C23×C13112yescomplemented
545#126C23×C13112yescomplemented
546#126C23×C13112yescomplemented
547#126C23×C13112yescomplemented
548#125C23×C1316yescomplemented
549#125C23×C1316yescomplemented
550#124C23×C1316yes—
551#124C23×C1313yes—
552#124C23×C1313yes—
553#124C23×C1316yes—
554#124C23×C13112yes—
555#124C23×C1316yes—
556#124C23×C13112yes—
557#124C23×C13112yes—
558#124C23×C1316yes—
559#124C23×C1316yes—
560#124C23×C1313yes—
561#124C23×C1313yes—
562#124C23×C1316yes—
563#124C23×C13112yes—
564#124C23×C1316yescomplemented
565#124C23×C13112yescomplemented
566#124C23×C1316yescomplemented
567#124C23×C13112yescomplemented
568#124C23×C13112yescomplemented
569#124C23×C1316yescomplemented
570#124C23×C13112yescomplemented
571#124C23×C13112yescomplemented
572#124C23×C13112yescomplemented
573#123C23×C13112yes—
574#123C23×C13112yes—
575#123C23×C13112yes—
576#123C23×C1316yes—
577#123C23×C13112yes—
578#123C23×C1316yes—
579#123C23×C13112yescomplemented
580#123C23×C13112yescomplemented
581#123C23×C13112yescomplemented
582#123C23×C13112yescomplemented
583#123C23×C13112yescomplemented
584#123C23×C13112yescomplemented
585#123C23×C13112yescomplemented
586#123C23×C13112yescomplemented
587#123C23×C13112yescomplemented
588C22⋊Q8C23×C1316yes—
589C22⋊Q8C23×C13112yes—
590C22⋊Q8C23×C13112yescomplemented
591C22⋊Q8C23×C13112yescomplemented
592C22⋊Q8C23×C13112yescomplemented
593C22⋊Q8C23×C13112yescomplemented
594C22⋊Q8C23×C1316yescomplemented
595C22⋊Q8C23×C1316yescomplemented
596C22⋊Q8C23×C1316yescomplemented
597C22⋊Q8C23×C1316yescomplemented
598C22⋊Q8C23×C13112yescomplemented
599C22⋊Q8C23×C13112yescomplemented
600C22⋊Q8C23×C13112yescomplemented
601C22⋊Q8C23×C13112yescomplemented
602C22⋊Q8C23×C13112yescomplemented
603#121C23×C13112yes—
604#121C23×C13112yes—
605#121C23×C13112yes—
606#121C23×C13112yes—
607#121C23×C1316yes—
608#121C23×C1316yes—
609#121C23×C1316yes—
610#121C23×C1316yes—
611#121C23×C1316yes—
612#121C23×C13112yes—
613#121C23×C13112yes—
614#121C23×C13112yes—
615#121C23×C13112yescomplemented
616#121C23×C13112yescomplemented
617#121C23×C13112yescomplemented
618#121C23×C13112yescomplemented
619#120C23×C1316yes—
620#120C23×C1316yes—
621#120C23×C13112yes—
622#120C23×C13112yes—
623#120C23×C13112yes—
624#120C23×C13112yes—
625#120C23×C1316yes—
626#120C23×C1316yes—
627#120C23×C1316yes—
628#120C23×C13112yes—
629#120C23×C1316yes—
630#120C23×C13112yescomplemented
631#120C23×C13112yescomplemented
632#120C23×C13112yescomplemented
633C4×Q8C23×C1316yescomplemented
634C4×Q8C23×C1312yescomplemented
635C4×Q8C23×C1316yescomplemented
636C4×Q8C23×C1312yescomplemented
637C4×Q8C23×C1316yescomplemented
638C4×Q8C23×C1316yescomplemented
639C4×Q8C23×C13112yescomplemented
640C4×D4C23×C1316yes—
641C4×D4C23×C1316yes—
642C4×D4C23×C1316yes—
643C4×D4C23×C13112yes—
644C4×D4C23×C13112yes—
645C4×D4C23×C1316yes—
646C4×D4C23×C1316yes—
647C4×D4C23×C13112yes—
648C4×D4C23×C1316yes—
649C4×D4C23×C1316yescomplemented
650C4×D4C23×C13112yescomplemented
651C4×D4C23×C13112yescomplemented
652C4×D4C23×C13112yescomplemented
653C4×D4C23×C13112yescomplemented
654C4×D4C23×C1316yescomplemented
655C4×D4C23×C13112yescomplemented
656C4×D4C23×C13112yescomplemented
657#117C23×C1313yes—
658#117C23×C1313yes—
659#117C23×C1313yes—
660#117C23×C1316yescomplemented
661#117C23×C13112yescomplemented
662#117C23×C13112yescomplemented
663#117C23×C13112yescomplemented
664#117C23×C13112yescomplemented
665#117C23×C13112yescomplemented
666C2×C22⋊C4C23×C1316yes—
667C2×C22⋊C4C23×C1316yes—
668C2×C22⋊C4C23×C1316yes—
669C2×C22⋊C4C23×C1316yes—
670C2×C22⋊C4C23×C13112yes—
671C2×C22⋊C4C23×C13112yescomplemented
672C2×C22⋊C4C23×C13112yescomplemented
673C2×C22⋊C4C23×C13112yescomplemented
674C2×C22⋊C4C23×C13112yescomplemented
675C2×C42C23×C1313yes—
676C2×C42C23×C1316yescomplemented
677C2×C13—22no—
678C2×C13—46no—
679C2×C13—46no—
680C2×C13—46no—
681C2×C13C2×#58511yescharacteristic
682C2×C13H(7,𝔽2)12yes—
683C24—44no—
684C24—84no—
685C24C24×C1316yes—
686C24C24×C1316yes—
687C24C24×C1316yes—
688C24C24×C1312yes—
689#41—46no—
690#41—86no—
691#41—812no—
692#41—82no—
693C2×Q8—42no—
694C2×Q8—82no—
695C2×Q8—86no—
696C2×Q8C24×C1311yescharacteristic
697C2×Q8C24×C1313yes—
698C2×Q8C24×C1313yes—
699C2×Q8C24×C1316yes—
700C2×Q8C24×C13112yes—
701C2×Q8C24×C1316yes—
702C2×Q8C24×C1312yes—
703C2×D4—46no—
704C2×D4—412no—
705C2×D4—86no—
706C2×D4—86no—
707C2×D4—812no—
708C2×D4C24×C1316yes—
709C2×D4C24×C1313yes—
710C2×D4C24×C1316yes—
711C2×D4C24×C1313yes—
712C2×D4C24×C13112yes—
713C2×D4C24×C1316yes—
714C2×D4C24×C1316yes—
715C2×D4C24×C13112yes—
716C2×D4C24×C1313yes—
717C2×D4C24×C13112yes—
718C2×D4C24×C13112yes—
719C2×D4C24×C13112yes—
720C2×D4C24×C13112yes—
721C2×D4C24×C1316yes—
722C22×C4—84no—
723C22×C4C24×C1313yes—
724C22×C4C24×C1316yes—
725C22×C4C24×C1316yes—
726C22×C4C24×C1316yes—
727C22×C4C24×C1316yes—
728C22×C4C24×C13112yes—
729C22×C4C24×C13112yes—
730C22×C4C24×C13112yes—
731C22×C4C24×C1316yes—
732C22×C4C24×C13112yes—
733C4⋊C4C24×C1316yes—
734C4⋊C4C24×C1316yes—
735C4⋊C4C24×C1316yes—
736C4⋊C4C24×C1316yes—
737C4⋊C4C24×C13112yes—
738C4⋊C4C24×C13112yes—
739C4⋊C4C24×C13112yes—
740C4⋊C4C24×C13112yes—
741C4⋊C4C24×C13112yes—
742C4⋊C4C24×C1316yes—
743C4⋊C4C24×C1316yes—
744C4⋊C4C24×C1316yes—
745C4⋊C4C24×C13112yes—
746C4⋊C4C24×C13112yes—
747C22⋊C4C24×C1311yescharacteristic
748C22⋊C4C24×C1316yes—
749C22⋊C4C24×C1313yes—
750C22⋊C4C24×C13112yes—
751C22⋊C4C24×C1316yes—
752C22⋊C4C24×C1316yes—
753C22⋊C4C24×C13112yes—
754C22⋊C4C24×C13112yes—
755C22⋊C4C24×C13112yes—
756C22⋊C4C24×C13112yes—
757C22⋊C4C24×C13112yes—
758C22⋊C4C24×C13112yes—
759C22⋊C4C24×C1316yes—
760C22⋊C4C24×C1316yes—
761C22⋊C4C24×C1316yes—
762C22⋊C4C24×C13112yes—
763C22⋊C4C24×C13112yes—
764C22⋊C4C24×C13112yes—
765C22⋊C4C24×C13112yes—
766C22⋊C4C24×C13112yes—
767C22⋊C4C24×C13112yes—
768C22⋊C4C24×C13112yes—
769C22⋊C4C24×C1316yes—
770C22⋊C4C24×C13112yes—
771C42C24×C1313yes—
772C42C24×C1313yes—
773C42C24×C1316yes—
774C42C24×C1316yes—
775C42C24×C1316yes—
776C42C24×C1316yes—
777C42C24×C1316yes—
778C42C24×C1316yes—
779C42C24×C13112yes—
780C13#6304611yescharacteristic, direct product factor, Sylow
781C23—212no—
782C23—44no—
783C23—42no—
784C23—412no—
785C23—412no—
786C23—46no—
787C23—46no—
788C23—412no—
789C23—816no—
790C23C25×C1316yes—
791C23C25×C1316yes—
792C23C25×C1316yes—
793C23C25×C1311yescharacteristic
794Q8—41no—
795Q8—43no—
796Q8—46no—
797Q8—46no—
798Q8—412no—
799Q8—42no—
800Q8—43no—
801D4—212no—
802D4—43no—
803D4—43no—
804D4—46no—
805D4—412no—
806D4—412no—
807D4—46no—
808D4—412no—
809D4—412no—
810D4—412no—
811D4—46no—
812D4—46no—
813D4—412no—
814D4—43no—
815C2×C4—26no—
816C2×C4—412no—
817C2×C4—412no—
818C2×C4—46no—
819C2×C4—46no—
820C2×C4—46no—
821C2×C4—412no—
822C2×C4—412no—
823C2×C4—46no—
824C2×C4—46no—
825C2×C4C25×C1313yes—
826C2×C4C25×C1312yes—
827C2×C4C25×C1313yes—
828C2×C4C25×C1316yes—
829C2×C4C25×C1316yes—
830C2×C4C25×C1316yes—
831C2×C4C25×C1316yes—
832C2×C4C25×C13112yes—
833C22—22no—
834C22—26no—
835C22—26no—
836C22—26no—
837C22—26no—
838C22—212no—
839C22—26no—
840C22—212no—
841C22—48no—
842C22—812no—
843C22—812no—
844C22—166no—
845C22C13×#58512yes—
846C22C26×C1311yescharacteristic
847C4—23no—
848C4—23no—
849C4—26no—
850C4—22no—
851C4—212no—
852C4—26no—
853C4—26no—
854C4—26no—
855C2—22no—
856C2—46no—
857C2—46no—
858C2—46no—
859C2C2×C13×#58511yescharacteristic
860C2C13×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C13C26
commutator, Frattini, cosocleC22C26×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3568C2semidirect
2. C13×#3561C2semidirect
3. C13×#3558C2semidirect
4. C13×#3545C2semidirect
5. C13×#3545C2semidirect
6. C13×#3540C2semidirect
7. C13×#3532C2semidirect
8. C13×#3529C2semidirect
9. C2×C13×H(3,𝔽4)C2semidirect
10. C13×#3514C2semidirect
11. C13×#3510C2semidirect
12. C13×#3490C2semidirect
13. C13×#563C22semidirect
14. C13×#563C22semidirect
15. C13×#563C22semidirect
16. C13×#562C22semidirect
17. C13×#562C22semidirect
18. C13×#562C22semidirect
19. C13×H(3,𝔽4)C22semidirect
20. C13×H(3,𝔽4)C22semidirect
21. C13×H(3,𝔽4)C22semidirect
22. C13×H(3,𝔽4)C22semidirect
23. C13×H(3,𝔽4)C22semidirect
24. C13×H(3,𝔽4)C22semidirect
25. C13×#560C22semidirect
26. C13×#560C22semidirect
27. C13×#559C22semidirect
28. C13×#559C22semidirect
29. C13×#556C22semidirect
30. C13×#556C22semidirect
31. C13×#556C22semidirect
32. C13×#555C22semidirect
33. C13×#555C22semidirect
34. C13×#551C22semidirect
35. C13×#551C22semidirect
36. C13×#551C22semidirect
37. C13×#551C22semidirect
38. C13×#551C22semidirect
39. C13×#551C22semidirect
40. C13×#551C22semidirect
41. C13×#551C22semidirect
42. D4×Q8×C13C22semidirect
43. C13×#548C22semidirect
44. C13×#548C22semidirect
45. C13×#548C22semidirect
46. C13×#546C22semidirect
47. C13×#546C22semidirect
48. C13×#546C22semidirect
49. C13×#546C22semidirect
50. C13×#546C22semidirect
51. C13×#546C22semidirect
52. C13×#546C22semidirect
53. D42×C13C22semidirect
54. D42×C13C22semidirect
55. C13×#543C22semidirect
56. C13×#542C22semidirect
57. C13×#542C22semidirect
58. C13×#542C22semidirect
59. C13×#542C22semidirect
60. C13×#542C22semidirect
61. C13×#542C22semidirect
62. C13×#542C22semidirect
63. C13×#538C22semidirect
64. C13×#538C22semidirect
65. C13×#538C22semidirect
66. C13×#538C22semidirect
67. C13×#538C22semidirect
68. C13×#538C22semidirect
69. C13×#538C22semidirect
70. C13×#536C22semidirect
71. C13×#536C22semidirect
73. C13×#535C22semidirect
74. C13×#534C22semidirect
75. C13×#534C22semidirect
76. C13×#533C22semidirect
77. C13×#532C22semidirect
78. C13×#529C22semidirect
79. C13×#529C22semidirect
80. C13×#529C22semidirect
81. C13×#529C22semidirect
82. C13×#529C22semidirect
83. C2×C13×#124C22semidirect
84. C2×C13×#124C22semidirect
85. C2×C13×#124C22semidirect
86. C13×#525C22semidirect
87. C13×#525C22semidirect
88. C2×C13×#120C22semidirect
89. C2×C13×#120C22semidirect
90. C13×#519C22semidirect
91. C13×#518C22semidirect
92. C13×#518C22semidirect
93. C4×C13×#41C22semidirect
94. C22×C13×C22⋊C4C22semidirect
99. C2×C13×#41C23semidirect
102. C22×Q8×C13C23semidirect
107. C22×D4×C13C23semidirect
108. C23×C4×C13C23semidirect
109. C13×C4⋊Q8C23semidirect
110. C13×C4⋊Q8C23semidirect
111. C13×C4⋊Q8C23semidirect
112. C13×C4⋊Q8C23semidirect
115. C13×#126C23semidirect
116. C13×#126C23semidirect
117. C13×#126C23semidirect
118. C13×#126C23semidirect
119. C13×#126C23semidirect
120. C13×#126C23semidirect
121. C13×#126C23semidirect
122. C13×#126C23semidirect
123. C13×#126C23semidirect
124. C13×#125C23semidirect
125. C13×#125C23semidirect
140. C13×#124C23semidirect
141. C13×#124C23semidirect
142. C13×#124C23semidirect
143. C13×#124C23semidirect
144. C13×#124C23semidirect
145. C13×#124C23semidirect
146. C13×#124C23semidirect
147. C13×#124C23semidirect
148. C13×#124C23semidirect
155. C13×#123C23semidirect
156. C13×#123C23semidirect
157. C13×#123C23semidirect
158. C13×#123C23semidirect
159. C13×#123C23semidirect
160. C13×#123C23semidirect
161. C13×#123C23semidirect
162. C13×#123C23semidirect
163. C13×#123C23semidirect
166. C13×C22⋊Q8C23semidirect
167. C13×C22⋊Q8C23semidirect
168. C13×C22⋊Q8C23semidirect
169. C13×C22⋊Q8C23semidirect
170. C13×C22⋊Q8C23semidirect
171. C13×C22⋊Q8C23semidirect
172. C13×C22⋊Q8C23semidirect
173. C13×C22⋊Q8C23semidirect
174. C13×C22⋊Q8C23semidirect
175. C13×C22⋊Q8C23semidirect
176. C13×C22⋊Q8C23semidirect
177. C13×C22⋊Q8C23semidirect
178. C13×C22⋊Q8C23semidirect
191. C13×#121C23semidirect
192. C13×#121C23semidirect
193. C13×#121C23semidirect
194. C13×#121C23semidirect
206. C13×#120C23semidirect
207. C13×#120C23semidirect
208. C13×#120C23semidirect
209. C4×Q8×C13C23semidirect
210. C4×Q8×C13C23semidirect
211. C4×Q8×C13C23semidirect
212. C4×Q8×C13C23semidirect
213. C4×Q8×C13C23semidirect
214. C4×Q8×C13C23semidirect
215. C4×Q8×C13C23semidirect
225. C4×D4×C13C23semidirect
226. C4×D4×C13C23semidirect
227. C4×D4×C13C23semidirect
228. C4×D4×C13C23semidirect
229. C4×D4×C13C23semidirect
230. C4×D4×C13C23semidirect
231. C4×D4×C13C23semidirect
232. C4×D4×C13C23semidirect
236. C13×#117C23semidirect
237. C13×#117C23semidirect
238. C13×#117C23semidirect
239. C13×#117C23semidirect
240. C13×#117C23semidirect
241. C13×#117C23semidirect
247. C2×C13×C22⋊C4C23semidirect
248. C2×C13×C22⋊C4C23semidirect
249. C2×C13×C22⋊C4C23semidirect
250. C2×C13×C22⋊C4C23semidirect
252. C2×C42×C13C23semidirect
253. #63046C13direct (N × H)
351. #3568C2×C13semidirect
352. #3561C2×C13semidirect
353. #3558C2×C13semidirect
354. #3545C2×C13semidirect
355. #3545C2×C13semidirect
356. #3540C2×C13semidirect
357. #3532C2×C13semidirect
358. #3529C2×C13semidirect
359. C2×H(3,𝔽4)C2×C13semidirect
360. #3514C2×C13semidirect
361. #3510C2×C13semidirect
362. #3490C2×C13semidirect
415. #563C22×C13semidirect
416. #563C22×C13semidirect
417. #563C22×C13semidirect
418. #562C22×C13semidirect
419. #562C22×C13semidirect
420. #562C22×C13semidirect
421. H(3,𝔽4)C22×C13semidirect
422. H(3,𝔽4)C22×C13semidirect
423. H(3,𝔽4)C22×C13semidirect
424. H(3,𝔽4)C22×C13semidirect
425. H(3,𝔽4)C22×C13semidirect
426. H(3,𝔽4)C22×C13semidirect
427. #560C22×C13semidirect
428. #560C22×C13semidirect
429. #559C22×C13semidirect
430. #559C22×C13semidirect
431. #556C22×C13semidirect
432. #556C22×C13semidirect
433. #556C22×C13semidirect
434. #555C22×C13semidirect
435. #555C22×C13semidirect
436. #551C22×C13semidirect
437. #551C22×C13semidirect
438. #551C22×C13semidirect
439. #551C22×C13semidirect
440. #551C22×C13semidirect
441. #551C22×C13semidirect
442. #551C22×C13semidirect
443. #551C22×C13semidirect
444. D4×Q8C22×C13semidirect
445. #548C22×C13semidirect
446. #548C22×C13semidirect
447. #548C22×C13semidirect
448. #546C22×C13semidirect
449. #546C22×C13semidirect
450. #546C22×C13semidirect
451. #546C22×C13semidirect
452. #546C22×C13semidirect
453. #546C22×C13semidirect
454. #546C22×C13semidirect
455. D42C22×C13semidirect
456. D42C22×C13semidirect
457. #543C22×C13semidirect
458. #542C22×C13semidirect
459. #542C22×C13semidirect
460. #542C22×C13semidirect
461. #542C22×C13semidirect
462. #542C22×C13semidirect
463. #542C22×C13semidirect
464. #542C22×C13semidirect
465. #538C22×C13semidirect
466. #538C22×C13semidirect
467. #538C22×C13semidirect
468. #538C22×C13semidirect
469. #538C22×C13semidirect
470. #538C22×C13semidirect
471. #538C22×C13semidirect
472. #536C22×C13semidirect
473. #536C22×C13semidirect
475. #535C22×C13semidirect
476. #534C22×C13semidirect
477. #534C22×C13semidirect
478. #533C22×C13semidirect
479. #532C22×C13semidirect
480. #529C22×C13semidirect
481. #529C22×C13semidirect
482. #529C22×C13semidirect
483. #529C22×C13semidirect
484. #529C22×C13semidirect
485. C2×#124C22×C13semidirect
486. C2×#124C22×C13semidirect
487. C2×#124C22×C13semidirect
488. #525C22×C13semidirect
489. #525C22×C13semidirect
490. C2×#120C22×C13semidirect
491. C2×#120C22×C13semidirect
492. #519C22×C13semidirect
493. #518C22×C13semidirect
494. #518C22×C13semidirect
495. C4×#41C22×C13semidirect
496. C22×C22⋊C4C22×C13semidirect
523. C2×#41C23×C13semidirect
526. C22×Q8C23×C13semidirect
531. C22×D4C23×C13semidirect
532. C23×C4C23×C13semidirect
533. C4⋊Q8C23×C13semidirect
534. C4⋊Q8C23×C13semidirect
535. C4⋊Q8C23×C13semidirect
536. C4⋊Q8C23×C13semidirect
539. #126C23×C13semidirect
540. #126C23×C13semidirect
541. #126C23×C13semidirect
542. #126C23×C13semidirect
543. #126C23×C13semidirect
544. #126C23×C13semidirect
545. #126C23×C13semidirect
546. #126C23×C13semidirect
547. #126C23×C13semidirect
548. #125C23×C13semidirect
549. #125C23×C13semidirect
564. #124C23×C13semidirect
565. #124C23×C13semidirect
566. #124C23×C13semidirect
567. #124C23×C13semidirect
568. #124C23×C13semidirect
569. #124C23×C13semidirect
570. #124C23×C13semidirect
571. #124C23×C13semidirect
572. #124C23×C13semidirect
579. #123C23×C13semidirect
580. #123C23×C13semidirect
581. #123C23×C13semidirect
582. #123C23×C13semidirect
583. #123C23×C13semidirect
584. #123C23×C13semidirect
585. #123C23×C13semidirect
586. #123C23×C13semidirect
587. #123C23×C13semidirect
590. C22⋊Q8C23×C13semidirect
591. C22⋊Q8C23×C13semidirect
592. C22⋊Q8C23×C13semidirect
593. C22⋊Q8C23×C13semidirect
594. C22⋊Q8C23×C13semidirect
595. C22⋊Q8C23×C13semidirect
596. C22⋊Q8C23×C13semidirect
597. C22⋊Q8C23×C13semidirect
598. C22⋊Q8C23×C13semidirect
599. C22⋊Q8C23×C13semidirect
600. C22⋊Q8C23×C13semidirect
601. C22⋊Q8C23×C13semidirect
602. C22⋊Q8C23×C13semidirect
615. #121C23×C13semidirect
616. #121C23×C13semidirect
617. #121C23×C13semidirect
618. #121C23×C13semidirect
630. #120C23×C13semidirect
631. #120C23×C13semidirect
632. #120C23×C13semidirect
633. C4×Q8C23×C13semidirect
634. C4×Q8C23×C13semidirect
635. C4×Q8C23×C13semidirect
636. C4×Q8C23×C13semidirect
637. C4×Q8C23×C13semidirect
638. C4×Q8C23×C13semidirect
639. C4×Q8C23×C13semidirect
649. C4×D4C23×C13semidirect
650. C4×D4C23×C13semidirect
651. C4×D4C23×C13semidirect
652. C4×D4C23×C13semidirect
653. C4×D4C23×C13semidirect
654. C4×D4C23×C13semidirect
655. C4×D4C23×C13semidirect
656. C4×D4C23×C13semidirect
660. #117C23×C13semidirect
661. #117C23×C13semidirect
662. #117C23×C13semidirect
663. #117C23×C13semidirect
664. #117C23×C13semidirect
665. #117C23×C13semidirect
671. C2×C22⋊C4C23×C13semidirect
672. C2×C22⋊C4C23×C13semidirect
673. C2×C22⋊C4C23×C13semidirect
674. C2×C22⋊C4C23×C13semidirect
676. C2×C42C23×C13semidirect
780. C13#63046direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35682
C13×#35612
C13×#35582
C13×#35452
C13×#35402
C13×#35322
C13×#35292
C2×C13×H(3,𝔽4)2
C13×#35142
C13×#35102
C13×#34902
#6304613