Finite Group Databasebeta

← C53×#63045 #27270557

Subgroups — C53×#63045 #27270557

Order 13568.

7484 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3558C2112yesmaximal, complemented
2C53×#3558C216yesmaximal, complemented
3C53×#3549C213yesmaximal, complemented
4C53×#3545C216yesmaximal, complemented
5C53×#3540C216yesmaximal, complemented
6C53×#3532C2112yesmaximal, complemented
7C53×#3529C211yesmaximal, characteristic, complemented
8C2×C53×H(3,𝔽4)C212yesmaximal, complemented
9C53×#3514C216yesmaximal, complemented
10C53×#3500C213yesmaximal, complemented
11C53×#3484C216yesmaximal, complemented
12C2×2−1+4×C53C2211yescharacteristic, complemented
13C2×H(5,𝔽2)×C53C2213yescomplemented
14C23×D4×C53C2212yescomplemented
15C53×#563C2213yescomplemented
16C53×#562C2216yescomplemented
17C53×#562C22112yescomplemented
18C53×H(3,𝔽4)C2211yescharacteristic, complemented
19C53×H(3,𝔽4)C22112yescomplemented
20C53×H(3,𝔽4)C2216yescomplemented
21C53×H(3,𝔽4)C22112yescomplemented
22C53×H(3,𝔽4)C2216yescomplemented
23C53×#560C2216yescomplemented
24C53×#560C22112yescomplemented
25C53×#559C2216yescomplemented
26C53×#559C22112yescomplemented
27C53×#556C2216yescomplemented
28C53×#555C22112yescomplemented
29C53×#555C2216yescomplemented
30C53×#551C22112yescomplemented
31C53×#551C22124yescomplemented
32D4×Q8×C53C2212yescomplemented
33C53×#548C22112yescomplemented
34C53×#548C22112yescomplemented
35C53×#546C22112yescomplemented
36C53×#546C22112yescomplemented
37C53×#546C22124yescomplemented
38C53×#546C22112yescomplemented
39C53×#546C22124yescomplemented
40C53×#546C22124yescomplemented
41D42×C53C2216yescomplemented
42D42×C53C22124yescomplemented
43D42×C53C2216yescomplemented
44D42×C53C22112yescomplemented
45C53×#542C22112yescomplemented
46C53×#542C22124yescomplemented
47C53×#538C22124yescomplemented
48C53×#538C22124yescomplemented
49C53×#538C22124yescomplemented
50C53×#538C22112yescomplemented
51C53×#536C2213yescomplemented
52C53×#536C2216yescomplemented
53C53×#535C2216yescomplemented
54C53×#535C2216yescomplemented
55C53×#535C2216yescomplemented
56C53×#535C22124yescomplemented
57C53×#535C2213yescomplemented
58C53×#534C22112yescomplemented
59C53×#534C22112yescomplemented
60C53×#534C22112yescomplemented
61C53×#532C2213yescomplemented
62C53×#532C2216yescomplemented
63C53×#532C2216yescomplemented
64C53×#529C2216yescomplemented
65C53×#529C22112yescomplemented
66C2×#124×C53C2216yescomplemented
67C2×#124×C53C22112yescomplemented
68C2×#124×C53C2213yescomplemented
69C53×#525C2216yescomplemented
70C53×#525C2216yescomplemented
71C2×#120×C53C22112yescomplemented
72C2×#120×C53C22112yescomplemented
73C53×#518C2216yescomplemented
74C4×#41×C53C2213yescomplemented
75C25×C53C2314yescomplemented
762−1+4×C53—44no—
77H(5,𝔽2)×C53—412no—
78C2×#41×C53C2313yes—
79C2×#41×C53C2313yes—
80C2×#41×C53C2316yes—
81C2×#41×C53C2316yes—
82C2×#41×C53C2311yescharacteristic, complemented
83C2×#41×C53C2316yescomplemented
84C2×#41×C53C23112yescomplemented
85C22×Q8×C53C2312yescomplemented
86C22×Q8×C53C2313yescomplemented
87C22×Q8×C53C2314yescomplemented
88C22×D4×C53—48no—
89C22×D4×C53C2316yes—
90C22×D4×C53C2316yes—
91C22×D4×C53C23112yes—
92C22×D4×C53C2313yes—
93C22×D4×C53C23112yes—
94C22×D4×C53C23112yescomplemented
95C22×D4×C53C2316yescomplemented
96C22×D4×C53C23124yescomplemented
97C23×C4×C53C2312yescomplemented
98C4⋊Q8×C53C2316yescomplemented
99C4⋊Q8×C53C2313yescomplemented
100C4⋊Q8×C53C2316yescomplemented
101#127×C53C2316yes—
102#127×C53C2313yes—
103#127×C53C23112yes—
104#127×C53C2316yescomplemented
105#126×C53C23124yescomplemented
106#126×C53C23112yescomplemented
107#126×C53C23124yescomplemented
108#125×C53C2316yescomplemented
109#124×C53C2316yes—
110#124×C53C2313yes—
111#124×C53C2316yes—
112#124×C53C23112yes—
113#124×C53C2316yescomplemented
114#124×C53C23112yescomplemented
115#124×C53C2316yescomplemented
116#124×C53C2316yescomplemented
117#124×C53C23112yescomplemented
118#124×C53C23124yescomplemented
119#124×C53C23112yescomplemented
120#124×C53C23124yescomplemented
121#124×C53C23124yescomplemented
122#124×C53C2313yescomplemented
123#124×C53C23124yescomplemented
124#124×C53C23112yescomplemented
125#123×C53C2316yes—
126#123×C53C23112yescomplemented
127#123×C53C2316yescomplemented
128#123×C53C23124yescomplemented
129#123×C53C23112yescomplemented
130#123×C53C23124yescomplemented
131#123×C53C23124yescomplemented
132#123×C53C23124yescomplemented
133#123×C53C23112yescomplemented
134C22⋊Q8×C53C23112yescomplemented
135C22⋊Q8×C53C23112yescomplemented
136C22⋊Q8×C53C23112yescomplemented
137C22⋊Q8×C53C2316yescomplemented
138C22⋊Q8×C53C23124yescomplemented
139C22⋊Q8×C53C23124yescomplemented
140#121×C53C23112yes—
141#121×C53C23112yes—
142#121×C53C23112yes—
143#121×C53C2316yes—
144#121×C53C23124yes—
145#121×C53C23112yescomplemented
146#121×C53C23124yescomplemented
147#121×C53C23112yescomplemented
148#121×C53C23112yescomplemented
149#121×C53C23124yescomplemented
150#121×C53C23124yescomplemented
151#121×C53C23124yescomplemented
152#121×C53C23124yescomplemented
153#120×C53C2316yes—
154#120×C53C23112yes—
155#120×C53C23124yes—
156#120×C53C23124yes—
157#120×C53C2316yescomplemented
158#120×C53C23112yescomplemented
159#120×C53C23112yescomplemented
160#120×C53C23112yescomplemented
161#120×C53C23112yescomplemented
162#120×C53C23124yescomplemented
163#120×C53C23124yescomplemented
164#120×C53C23124yescomplemented
165#120×C53C23112yescomplemented
166C4×Q8×C53C2316yescomplemented
167C4×Q8×C53C2312yescomplemented
168C4×Q8×C53C23112yescomplemented
169C4×D4×C53C2316yes—
170C4×D4×C53C2316yes—
171C4×D4×C53C23112yescomplemented
172C4×D4×C53C23124yescomplemented
173C4×D4×C53C23112yescomplemented
174C4×D4×C53C23112yescomplemented
175C4×D4×C53C23124yescomplemented
176C4×D4×C53C23112yescomplemented
177C4×D4×C53C23112yescomplemented
178C4×D4×C53C23124yescomplemented
179#117×C53C2316yescomplemented
180#117×C53C2313yescomplemented
181#117×C53C2316yescomplemented
182#117×C53C2316yescomplemented
183#117×C53C23124yescomplemented
184C2×C22⋊C4×C53C23112yescomplemented
185C2×C22⋊C4×C53C23112yescomplemented
186C2×C22⋊C4×C53C23124yescomplemented
187C2×C22⋊C4×C53C23124yescomplemented
188C2×C22⋊C4×C53C23112yescomplemented
189C2×C42×C53C2316yescomplemented
190C2×C42×C53C2313yescomplemented
191C24×C53—48no—
192C24×C53—88no—
193C24×C53C24112yes—
194C24×C53C24112yes—
195C24×C53C2416yes—
196C24×C53C2412yes—
197#41×C53—212no—
198#41×C53—46no—
199#41×C53—42no—
200#41×C53—412no—
201#41×C53—412no—
202#41×C53—412no—
203#41×C53—812no—
204C2×Q8×C53—44no—
205C2×Q8×C53—46no—
206C2×Q8×C53—84no—
207C2×Q8×C53C2413yes—
208C2×Q8×C53C2412yes—
209C2×Q8×C53C24112yes—
210C2×Q8×C53C2416yes—
211C2×Q8×C53C2413yes—
212C2×Q8×C53C2411yescharacteristic
213C2×D4×C53—224no—
214C2×D4×C53—412no—
215C2×D4×C53—46no—
216C2×D4×C53—412no—
217C2×D4×C53—424no—
218C2×D4×C53—424no—
219C2×D4×C53—812no—
220C2×D4×C53—824no—
221C2×D4×C53C24112yes—
222C2×D4×C53C2416yes—
223C2×D4×C53C2416yes—
224C2×D4×C53C2416yes—
225C2×D4×C53C24124yes—
226C2×D4×C53C24112yes—
227C2×D4×C53C24112yes—
228C2×D4×C53C24124yes—
229C2×D4×C53C24112yes—
230C2×D4×C53C2413yes—
231C2×D4×C53C24112yes—
232C2×D4×C53C2416yes—
233C2×D4×C53C2413yes—
234C2×D4×C53C2416yes—
235C2×D4×C53C24112yes—
236C2×D4×C53C2411yescharacteristic
237C22×C4×C53—44no—
238C22×C4×C53C2416yes—
239C22×C4×C53C2413yes—
240C22×C4×C53C2416yes—
241C22×C4×C53C24112yes—
242C22×C4×C53C2416yes—
243C22×C4×C53C24124yes—
244C22×C4×C53C2416yes—
245C22×C4×C53C24112yes—
246C22×C4×C53C2416yes—
247C4⋊C4×C53C2416yes—
248C4⋊C4×C53C24112yes—
249C4⋊C4×C53C24112yes—
250C4⋊C4×C53C24112yes—
251C4⋊C4×C53C24112yes—
252C4⋊C4×C53C2416yes—
253C4⋊C4×C53C24124yes—
254C4⋊C4×C53C2416yes—
255C22⋊C4×C53C24112yes—
256C22⋊C4×C53C24112yes—
257C22⋊C4×C53C2416yes—
258C22⋊C4×C53C2416yes—
259C22⋊C4×C53C24112yes—
260C22⋊C4×C53C24124yes—
261C22⋊C4×C53C24112yes—
262C22⋊C4×C53C24124yes—
263C22⋊C4×C53C24124yes—
264C22⋊C4×C53C24124yes—
265C22⋊C4×C53C24124yes—
266C22⋊C4×C53C24124yes—
267C22⋊C4×C53C2416yes—
268C22⋊C4×C53C24112yes—
269C42×C53C2413yes—
270C42×C53C2416yes—
271C42×C53C2416yes—
272C42×C53C2413yes—
273C42×C53C24112yes—
274C42×C53C24112yes—
275C23×C53—224no—
276C23×C53—42no—
277C23×C53—44no—
278C23×C53—412no—
279C23×C53—424no—
280C23×C53—424no—
281C23×C53—46no—
282C23×C53—412no—
283C23×C53—832no—
284C23×C53C2513yes—
285C23×C53C25112yes—
286C23×C53C2516yes—
287C23×C53C2512yes—
288Q8×C53—26no—
289Q8×C53—41no—
290Q8×C53—46no—
291Q8×C53—42no—
292Q8×C53—412no—
293Q8×C53—43no—
294D4×C53—224no—
295D4×C53—212no—
296D4×C53—212no—
297D4×C53—412no—
298D4×C53—43no—
299D4×C53—46no—
300D4×C53—46no—
301D4×C53—412no—
302D4×C53—412no—
303D4×C53—412no—
304D4×C53—424no—
305D4×C53—46no—
306D4×C53—424no—
307D4×C53—412no—
308D4×C53—43no—
309D4×C53H(5,𝔽2)14yes—
310C2×C4×C53—212no—
311C2×C4×C53—212no—
312C2×C4×C53—26no—
313C2×C4×C53—46no—
314C2×C4×C53—412no—
315C2×C4×C53—412no—
316C2×C4×C53—424no—
317C2×C4×C53—46no—
318C2×C4×C53—46no—
319C2×C4×C53C2516yes—
320C2×C4×C53C2516yes—
321C2×C4×C53C2516yes—
322C2×C4×C53C2513yes—
323C2×C4×C53C25112yes—
324C2×C4×C53C2516yes—
325C2×C4×C53C2511yescharacteristic
326#63045C5311yesmaximal, characteristic, direct product factor, Sylow
327C22×C53—24no—
328C22×C53—23no—
329C22×C53—26no—
330C22×C53—212no—
331C22×C53—26no—
332C22×C53—224no—
333C22×C53—212no—
334C22×C53—48no—
335C22×C53—824no—
336C22×C53—824no—
337C22×C53—166no—
338C22×C53C2×H(5,𝔽2)14yes—
339C22×C53C2611yescharacteristic
340C4×C53—23no—
341C4×C53—26no—
342C4×C53—26no—
343C4×C53—26no—
344C4×C53—212no—
345C4×C53—26no—
346C4×C53C2×H(5,𝔽2)12yes—
347#3558C2×C53112yescomplemented
348#3558C2×C5316yescomplemented
349#3549C2×C5313yescomplemented
350#3545C2×C5316yescomplemented
351#3540C2×C5316yescomplemented
352#3532C2×C53112yescomplemented
353#3529C2×C5311yescharacteristic, complemented
354C2×H(3,𝔽4)C2×C5312yescomplemented
355#3514C2×C5316yescomplemented
356#3500C2×C5313yescomplemented
357#3484C2×C5316yescomplemented
358C2×C53—24no—
359C2×C53—46no—
360C2×C53—412no—
361C2×C53—43no—
362C2×C53C22×H(5,𝔽2)11yescharacteristic
363C2×C53H(7,𝔽2)12yes—
364C2×2−1+4C22×C5311yescharacteristic, complemented
365C2×H(5,𝔽2)C22×C5313yescomplemented
366C23×D4C22×C5312yescomplemented
367#563C22×C5313yescomplemented
368#562C22×C5316yescomplemented
369#562C22×C53112yescomplemented
370H(3,𝔽4)C22×C5311yescharacteristic, complemented
371H(3,𝔽4)C22×C53112yescomplemented
372H(3,𝔽4)C22×C5316yescomplemented
373H(3,𝔽4)C22×C53112yescomplemented
374H(3,𝔽4)C22×C5316yescomplemented
375#560C22×C5316yescomplemented
376#560C22×C53112yescomplemented
377#559C22×C5316yescomplemented
378#559C22×C53112yescomplemented
379#556C22×C5316yescomplemented
380#555C22×C53112yescomplemented
381#555C22×C5316yescomplemented
382#551C22×C53112yescomplemented
383#551C22×C53124yescomplemented
384D4×Q8C22×C5312yescomplemented
385#548C22×C53112yescomplemented
386#548C22×C53112yescomplemented
387#546C22×C53112yescomplemented
388#546C22×C53112yescomplemented
389#546C22×C53124yescomplemented
390#546C22×C53112yescomplemented
391#546C22×C53124yescomplemented
392#546C22×C53124yescomplemented
393D42C22×C5316yescomplemented
394D42C22×C53124yescomplemented
395D42C22×C5316yescomplemented
396D42C22×C53112yescomplemented
397#542C22×C53112yescomplemented
398#542C22×C53124yescomplemented
399#538C22×C53124yescomplemented
400#538C22×C53124yescomplemented
401#538C22×C53124yescomplemented
402#538C22×C53112yescomplemented
403#536C22×C5313yescomplemented
404#536C22×C5316yescomplemented
405#535C22×C5316yescomplemented
406#535C22×C5316yescomplemented
407#535C22×C5316yescomplemented
408#535C22×C53124yescomplemented
409#535C22×C5313yescomplemented
410#534C22×C53112yescomplemented
411#534C22×C53112yescomplemented
412#534C22×C53112yescomplemented
413#532C22×C5313yescomplemented
414#532C22×C5316yescomplemented
415#532C22×C5316yescomplemented
416#529C22×C5316yescomplemented
417#529C22×C53112yescomplemented
418C2×#124C22×C5316yescomplemented
419C2×#124C22×C53112yescomplemented
420C2×#124C22×C5313yescomplemented
421#525C22×C5316yescomplemented
422#525C22×C5316yescomplemented
423C2×#120C22×C53112yescomplemented
424C2×#120C22×C53112yescomplemented
425#518C22×C5316yescomplemented
426C4×#41C22×C5313yescomplemented
427C53#6304511yescharacteristic, direct product factor, Sylow
428C25C23×C5314yescomplemented
4292−1+4—44no—
430H(5,𝔽2)—412no—
431C2×#41C23×C5313yes—
432C2×#41C23×C5313yes—
433C2×#41C23×C5316yes—
434C2×#41C23×C5316yes—
435C2×#41C23×C5311yescharacteristic, complemented
436C2×#41C23×C5316yescomplemented
437C2×#41C23×C53112yescomplemented
438C22×Q8C23×C5312yescomplemented
439C22×Q8C23×C5313yescomplemented
440C22×Q8C23×C5314yescomplemented
441C22×D4—48no—
442C22×D4C23×C5316yes—
443C22×D4C23×C5316yes—
444C22×D4C23×C53112yes—
445C22×D4C23×C5313yes—
446C22×D4C23×C53112yes—
447C22×D4C23×C53112yescomplemented
448C22×D4C23×C5316yescomplemented
449C22×D4C23×C53124yescomplemented
450C23×C4C23×C5312yescomplemented
451C4⋊Q8C23×C5316yescomplemented
452C4⋊Q8C23×C5313yescomplemented
453C4⋊Q8C23×C5316yescomplemented
454#127C23×C5316yes—
455#127C23×C5313yes—
456#127C23×C53112yes—
457#127C23×C5316yescomplemented
458#126C23×C53124yescomplemented
459#126C23×C53112yescomplemented
460#126C23×C53124yescomplemented
461#125C23×C5316yescomplemented
462#124C23×C5316yes—
463#124C23×C5313yes—
464#124C23×C5316yes—
465#124C23×C53112yes—
466#124C23×C5316yescomplemented
467#124C23×C53112yescomplemented
468#124C23×C5316yescomplemented
469#124C23×C5316yescomplemented
470#124C23×C53112yescomplemented
471#124C23×C53124yescomplemented
472#124C23×C53112yescomplemented
473#124C23×C53124yescomplemented
474#124C23×C53124yescomplemented
475#124C23×C5313yescomplemented
476#124C23×C53124yescomplemented
477#124C23×C53112yescomplemented
478#123C23×C5316yes—
479#123C23×C53112yescomplemented
480#123C23×C5316yescomplemented
481#123C23×C53124yescomplemented
482#123C23×C53112yescomplemented
483#123C23×C53124yescomplemented
484#123C23×C53124yescomplemented
485#123C23×C53124yescomplemented
486#123C23×C53112yescomplemented
487C22⋊Q8C23×C53112yescomplemented
488C22⋊Q8C23×C53112yescomplemented
489C22⋊Q8C23×C53112yescomplemented
490C22⋊Q8C23×C5316yescomplemented
491C22⋊Q8C23×C53124yescomplemented
492C22⋊Q8C23×C53124yescomplemented
493#121C23×C53112yes—
494#121C23×C53112yes—
495#121C23×C53112yes—
496#121C23×C5316yes—
497#121C23×C53124yes—
498#121C23×C53112yescomplemented
499#121C23×C53124yescomplemented
500#121C23×C53112yescomplemented
501#121C23×C53112yescomplemented
502#121C23×C53124yescomplemented
503#121C23×C53124yescomplemented
504#121C23×C53124yescomplemented
505#121C23×C53124yescomplemented
506#120C23×C5316yes—
507#120C23×C53112yes—
508#120C23×C53124yes—
509#120C23×C53124yes—
510#120C23×C5316yescomplemented
511#120C23×C53112yescomplemented
512#120C23×C53112yescomplemented
513#120C23×C53112yescomplemented
514#120C23×C53112yescomplemented
515#120C23×C53124yescomplemented
516#120C23×C53124yescomplemented
517#120C23×C53124yescomplemented
518#120C23×C53112yescomplemented
519C4×Q8C23×C5316yescomplemented
520C4×Q8C23×C5312yescomplemented
521C4×Q8C23×C53112yescomplemented
522C4×D4C23×C5316yes—
523C4×D4C23×C5316yes—
524C4×D4C23×C53112yescomplemented
525C4×D4C23×C53124yescomplemented
526C4×D4C23×C53112yescomplemented
527C4×D4C23×C53112yescomplemented
528C4×D4C23×C53124yescomplemented
529C4×D4C23×C53112yescomplemented
530C4×D4C23×C53112yescomplemented
531C4×D4C23×C53124yescomplemented
532#117C23×C5316yescomplemented
533#117C23×C5313yescomplemented
534#117C23×C5316yescomplemented
535#117C23×C5316yescomplemented
536#117C23×C53124yescomplemented
537C2×C22⋊C4C23×C53112yescomplemented
538C2×C22⋊C4C23×C53112yescomplemented
539C2×C22⋊C4C23×C53124yescomplemented
540C2×C22⋊C4C23×C53124yescomplemented
541C2×C22⋊C4C23×C53112yescomplemented
542C2×C42C23×C5316yescomplemented
543C2×C42C23×C5313yescomplemented
544C24—48no—
545C24—88no—
546C24C24×C53112yes—
547C24C24×C53112yes—
548C24C24×C5316yes—
549C24C24×C5312yes—
550#41—212no—
551#41—46no—
552#41—42no—
553#41—412no—
554#41—412no—
555#41—412no—
556#41—812no—
557C2×Q8—44no—
558C2×Q8—46no—
559C2×Q8—84no—
560C2×Q8C24×C5313yes—
561C2×Q8C24×C5312yes—
562C2×Q8C24×C53112yes—
563C2×Q8C24×C5316yes—
564C2×Q8C24×C5313yes—
565C2×Q8C24×C5311yescharacteristic
566C2×D4—224no—
567C2×D4—412no—
568C2×D4—46no—
569C2×D4—412no—
570C2×D4—424no—
571C2×D4—424no—
572C2×D4—812no—
573C2×D4—824no—
574C2×D4C24×C53112yes—
575C2×D4C24×C5316yes—
576C2×D4C24×C5316yes—
577C2×D4C24×C5316yes—
578C2×D4C24×C53124yes—
579C2×D4C24×C53112yes—
580C2×D4C24×C53112yes—
581C2×D4C24×C53124yes—
582C2×D4C24×C53112yes—
583C2×D4C24×C5313yes—
584C2×D4C24×C53112yes—
585C2×D4C24×C5316yes—
586C2×D4C24×C5313yes—
587C2×D4C24×C5316yes—
588C2×D4C24×C53112yes—
589C2×D4C24×C5311yescharacteristic
590C22×C4—44no—
591C22×C4C24×C5316yes—
592C22×C4C24×C5313yes—
593C22×C4C24×C5316yes—
594C22×C4C24×C53112yes—
595C22×C4C24×C5316yes—
596C22×C4C24×C53124yes—
597C22×C4C24×C5316yes—
598C22×C4C24×C53112yes—
599C22×C4C24×C5316yes—
600C4⋊C4C24×C5316yes—
601C4⋊C4C24×C53112yes—
602C4⋊C4C24×C53112yes—
603C4⋊C4C24×C53112yes—
604C4⋊C4C24×C53112yes—
605C4⋊C4C24×C5316yes—
606C4⋊C4C24×C53124yes—
607C4⋊C4C24×C5316yes—
608C22⋊C4C24×C53112yes—
609C22⋊C4C24×C53112yes—
610C22⋊C4C24×C5316yes—
611C22⋊C4C24×C5316yes—
612C22⋊C4C24×C53112yes—
613C22⋊C4C24×C53124yes—
614C22⋊C4C24×C53112yes—
615C22⋊C4C24×C53124yes—
616C22⋊C4C24×C53124yes—
617C22⋊C4C24×C53124yes—
618C22⋊C4C24×C53124yes—
619C22⋊C4C24×C53124yes—
620C22⋊C4C24×C5316yes—
621C22⋊C4C24×C53112yes—
622C42C24×C5313yes—
623C42C24×C5316yes—
624C42C24×C5316yes—
625C42C24×C5313yes—
626C42C24×C53112yes—
627C42C24×C53112yes—
628C23—224no—
629C23—42no—
630C23—44no—
631C23—412no—
632C23—424no—
633C23—424no—
634C23—46no—
635C23—412no—
636C23—832no—
637C23C25×C5316yes—
638C23C25×C53112yes—
639C23C25×C5313yes—
640C23C25×C5312yes—
641Q8—26no—
642Q8—41no—
643Q8—46no—
644Q8—42no—
645Q8—412no—
646Q8—43no—
647D4—224no—
648D4—212no—
649D4—212no—
650D4—412no—
651D4—43no—
652D4—46no—
653D4—46no—
654D4—412no—
655D4—412no—
656D4—412no—
657D4—424no—
658D4—46no—
659D4—424no—
660D4—412no—
661D4—43no—
662D4H(5,𝔽2)×C5314yes—
663C2×C4—212no—
664C2×C4—212no—
665C2×C4—26no—
666C2×C4—46no—
667C2×C4—412no—
668C2×C4—412no—
669C2×C4—424no—
670C2×C4—46no—
671C2×C4—46no—
672C2×C4C25×C5316yes—
673C2×C4C25×C53112yes—
674C2×C4C25×C5313yes—
675C2×C4C25×C5316yes—
676C2×C4C25×C5316yes—
677C2×C4C25×C5316yes—
678C2×C4C25×C5311yescharacteristic
679C22—24no—
680C22—23no—
681C22—26no—
682C22—212no—
683C22—26no—
684C22—224no—
685C22—212no—
686C22—48no—
687C22—824no—
688C22—824no—
689C22—166no—
690C22C2×H(5,𝔽2)×C5314yes—
691C22C26×C5311yescharacteristic
692C4—23no—
693C4—26no—
694C4—26no—
695C4—26no—
696C4—212no—
697C4—26no—
698C4C2×H(5,𝔽2)×C5312yes—
699C2—24no—
700C2—46no—
701C2—412no—
702C2—43no—
703C2C22×H(5,𝔽2)×C5311yescharacteristic
704C2C53×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C53C26
commutator, Frattini, cosocleC22C26×C53
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3558C2semidirect
2. C53×#3558C2semidirect
3. C53×#3549C2semidirect
4. C53×#3545C2semidirect
5. C53×#3540C2semidirect
6. C53×#3532C2semidirect
7. C53×#3529C2semidirect
8. C2×C53×H(3,𝔽4)C2semidirect
9. C53×#3514C2semidirect
10. C53×#3500C2semidirect
11. C53×#3484C2semidirect
12. C2×2−1+4×C53C22semidirect
13. C2×H(5,𝔽2)×C53C22semidirect
14. C23×D4×C53C22semidirect
15. C53×#563C22semidirect
16. C53×#562C22semidirect
17. C53×#562C22semidirect
18. C53×H(3,𝔽4)C22semidirect
19. C53×H(3,𝔽4)C22semidirect
20. C53×H(3,𝔽4)C22semidirect
21. C53×H(3,𝔽4)C22semidirect
22. C53×H(3,𝔽4)C22semidirect
23. C53×#560C22semidirect
24. C53×#560C22semidirect
25. C53×#559C22semidirect
26. C53×#559C22semidirect
27. C53×#556C22semidirect
28. C53×#555C22semidirect
29. C53×#555C22semidirect
30. C53×#551C22semidirect
31. C53×#551C22semidirect
32. D4×Q8×C53C22semidirect
33. C53×#548C22semidirect
34. C53×#548C22semidirect
35. C53×#546C22semidirect
36. C53×#546C22semidirect
37. C53×#546C22semidirect
38. C53×#546C22semidirect
39. C53×#546C22semidirect
40. C53×#546C22semidirect
41. D42×C53C22semidirect
42. D42×C53C22semidirect
43. D42×C53C22semidirect
44. D42×C53C22semidirect
45. C53×#542C22semidirect
46. C53×#542C22semidirect
47. C53×#538C22semidirect
48. C53×#538C22semidirect
49. C53×#538C22semidirect
50. C53×#538C22semidirect
51. C53×#536C22semidirect
52. C53×#536C22semidirect
53. C53×#535C22semidirect
54. C53×#535C22semidirect
55. C53×#535C22semidirect
56. C53×#535C22semidirect
57. C53×#535C22semidirect
58. C53×#534C22semidirect
59. C53×#534C22semidirect
60. C53×#534C22semidirect
61. C53×#532C22semidirect
62. C53×#532C22semidirect
63. C53×#532C22semidirect
64. C53×#529C22semidirect
65. C53×#529C22semidirect
66. C2×#124×C53C22semidirect
67. C2×#124×C53C22semidirect
68. C2×#124×C53C22semidirect
69. C53×#525C22semidirect
70. C53×#525C22semidirect
71. C2×#120×C53C22semidirect
72. C2×#120×C53C22semidirect
73. C53×#518C22semidirect
74. C4×#41×C53C22semidirect
75. C25×C53C23semidirect
82. C2×#41×C53C23semidirect
83. C2×#41×C53C23semidirect
84. C2×#41×C53C23semidirect
85. C22×Q8×C53C23semidirect
86. C22×Q8×C53C23semidirect
87. C22×Q8×C53C23semidirect
94. C22×D4×C53C23semidirect
95. C22×D4×C53C23semidirect
96. C22×D4×C53C23semidirect
97. C23×C4×C53C23semidirect
98. C4⋊Q8×C53C23semidirect
99. C4⋊Q8×C53C23semidirect
100. C4⋊Q8×C53C23semidirect
104. #127×C53C23semidirect
105. #126×C53C23semidirect
106. #126×C53C23semidirect
107. #126×C53C23semidirect
108. #125×C53C23semidirect
113. #124×C53C23semidirect
114. #124×C53C23semidirect
115. #124×C53C23semidirect
116. #124×C53C23semidirect
117. #124×C53C23semidirect
118. #124×C53C23semidirect
119. #124×C53C23semidirect
120. #124×C53C23semidirect
121. #124×C53C23semidirect
122. #124×C53C23semidirect
123. #124×C53C23semidirect
124. #124×C53C23semidirect
126. #123×C53C23semidirect
127. #123×C53C23semidirect
128. #123×C53C23semidirect
129. #123×C53C23semidirect
130. #123×C53C23semidirect
131. #123×C53C23semidirect
132. #123×C53C23semidirect
133. #123×C53C23semidirect
134. C22⋊Q8×C53C23semidirect
135. C22⋊Q8×C53C23semidirect
136. C22⋊Q8×C53C23semidirect
137. C22⋊Q8×C53C23semidirect
138. C22⋊Q8×C53C23semidirect
139. C22⋊Q8×C53C23semidirect
145. #121×C53C23semidirect
146. #121×C53C23semidirect
147. #121×C53C23semidirect
148. #121×C53C23semidirect
149. #121×C53C23semidirect
150. #121×C53C23semidirect
151. #121×C53C23semidirect
152. #121×C53C23semidirect
157. #120×C53C23semidirect
158. #120×C53C23semidirect
159. #120×C53C23semidirect
160. #120×C53C23semidirect
161. #120×C53C23semidirect
162. #120×C53C23semidirect
163. #120×C53C23semidirect
164. #120×C53C23semidirect
165. #120×C53C23semidirect
166. C4×Q8×C53C23semidirect
167. C4×Q8×C53C23semidirect
168. C4×Q8×C53C23semidirect
171. C4×D4×C53C23semidirect
172. C4×D4×C53C23semidirect
173. C4×D4×C53C23semidirect
174. C4×D4×C53C23semidirect
175. C4×D4×C53C23semidirect
176. C4×D4×C53C23semidirect
177. C4×D4×C53C23semidirect
178. C4×D4×C53C23semidirect
179. #117×C53C23semidirect
180. #117×C53C23semidirect
181. #117×C53C23semidirect
182. #117×C53C23semidirect
183. #117×C53C23semidirect
184. C2×C22⋊C4×C53C23semidirect
185. C2×C22⋊C4×C53C23semidirect
186. C2×C22⋊C4×C53C23semidirect
187. C2×C22⋊C4×C53C23semidirect
188. C2×C22⋊C4×C53C23semidirect
189. C2×C42×C53C23semidirect
190. C2×C42×C53C23semidirect
326. #63045C53direct (N × H)
347. #3558C2×C53semidirect
348. #3558C2×C53semidirect
349. #3549C2×C53semidirect
350. #3545C2×C53semidirect
351. #3540C2×C53semidirect
352. #3532C2×C53semidirect
353. #3529C2×C53semidirect
354. C2×H(3,𝔽4)C2×C53semidirect
355. #3514C2×C53semidirect
356. #3500C2×C53semidirect
357. #3484C2×C53semidirect
364. C2×2−1+4C22×C53semidirect
365. C2×H(5,𝔽2)C22×C53semidirect
366. C23×D4C22×C53semidirect
367. #563C22×C53semidirect
368. #562C22×C53semidirect
369. #562C22×C53semidirect
370. H(3,𝔽4)C22×C53semidirect
371. H(3,𝔽4)C22×C53semidirect
372. H(3,𝔽4)C22×C53semidirect
373. H(3,𝔽4)C22×C53semidirect
374. H(3,𝔽4)C22×C53semidirect
375. #560C22×C53semidirect
376. #560C22×C53semidirect
377. #559C22×C53semidirect
378. #559C22×C53semidirect
379. #556C22×C53semidirect
380. #555C22×C53semidirect
381. #555C22×C53semidirect
382. #551C22×C53semidirect
383. #551C22×C53semidirect
384. D4×Q8C22×C53semidirect
385. #548C22×C53semidirect
386. #548C22×C53semidirect
387. #546C22×C53semidirect
388. #546C22×C53semidirect
389. #546C22×C53semidirect
390. #546C22×C53semidirect
391. #546C22×C53semidirect
392. #546C22×C53semidirect
393. D42C22×C53semidirect
394. D42C22×C53semidirect
395. D42C22×C53semidirect
396. D42C22×C53semidirect
397. #542C22×C53semidirect
398. #542C22×C53semidirect
399. #538C22×C53semidirect
400. #538C22×C53semidirect
401. #538C22×C53semidirect
402. #538C22×C53semidirect
403. #536C22×C53semidirect
404. #536C22×C53semidirect
405. #535C22×C53semidirect
406. #535C22×C53semidirect
407. #535C22×C53semidirect
408. #535C22×C53semidirect
409. #535C22×C53semidirect
410. #534C22×C53semidirect
411. #534C22×C53semidirect
412. #534C22×C53semidirect
413. #532C22×C53semidirect
414. #532C22×C53semidirect
415. #532C22×C53semidirect
416. #529C22×C53semidirect
417. #529C22×C53semidirect
418. C2×#124C22×C53semidirect
419. C2×#124C22×C53semidirect
420. C2×#124C22×C53semidirect
421. #525C22×C53semidirect
422. #525C22×C53semidirect
423. C2×#120C22×C53semidirect
424. C2×#120C22×C53semidirect
425. #518C22×C53semidirect
426. C4×#41C22×C53semidirect
427. C53#63045direct (N × H)
428. C25C23×C53semidirect
435. C2×#41C23×C53semidirect
436. C2×#41C23×C53semidirect
437. C2×#41C23×C53semidirect
438. C22×Q8C23×C53semidirect
439. C22×Q8C23×C53semidirect
440. C22×Q8C23×C53semidirect
447. C22×D4C23×C53semidirect
448. C22×D4C23×C53semidirect
449. C22×D4C23×C53semidirect
450. C23×C4C23×C53semidirect
451. C4⋊Q8C23×C53semidirect
452. C4⋊Q8C23×C53semidirect
453. C4⋊Q8C23×C53semidirect
457. #127C23×C53semidirect
458. #126C23×C53semidirect
459. #126C23×C53semidirect
460. #126C23×C53semidirect
461. #125C23×C53semidirect
466. #124C23×C53semidirect
467. #124C23×C53semidirect
468. #124C23×C53semidirect
469. #124C23×C53semidirect
470. #124C23×C53semidirect
471. #124C23×C53semidirect
472. #124C23×C53semidirect
473. #124C23×C53semidirect
474. #124C23×C53semidirect
475. #124C23×C53semidirect
476. #124C23×C53semidirect
477. #124C23×C53semidirect
479. #123C23×C53semidirect
480. #123C23×C53semidirect
481. #123C23×C53semidirect
482. #123C23×C53semidirect
483. #123C23×C53semidirect
484. #123C23×C53semidirect
485. #123C23×C53semidirect
486. #123C23×C53semidirect
487. C22⋊Q8C23×C53semidirect
488. C22⋊Q8C23×C53semidirect
489. C22⋊Q8C23×C53semidirect
490. C22⋊Q8C23×C53semidirect
491. C22⋊Q8C23×C53semidirect
492. C22⋊Q8C23×C53semidirect
498. #121C23×C53semidirect
499. #121C23×C53semidirect
500. #121C23×C53semidirect
501. #121C23×C53semidirect
502. #121C23×C53semidirect
503. #121C23×C53semidirect
504. #121C23×C53semidirect
505. #121C23×C53semidirect
510. #120C23×C53semidirect
511. #120C23×C53semidirect
512. #120C23×C53semidirect
513. #120C23×C53semidirect
514. #120C23×C53semidirect
515. #120C23×C53semidirect
516. #120C23×C53semidirect
517. #120C23×C53semidirect
518. #120C23×C53semidirect
519. C4×Q8C23×C53semidirect
520. C4×Q8C23×C53semidirect
521. C4×Q8C23×C53semidirect
524. C4×D4C23×C53semidirect
525. C4×D4C23×C53semidirect
526. C4×D4C23×C53semidirect
527. C4×D4C23×C53semidirect
528. C4×D4C23×C53semidirect
529. C4×D4C23×C53semidirect
530. C4×D4C23×C53semidirect
531. C4×D4C23×C53semidirect
532. #117C23×C53semidirect
533. #117C23×C53semidirect
534. #117C23×C53semidirect
535. #117C23×C53semidirect
536. #117C23×C53semidirect
537. C2×C22⋊C4C23×C53semidirect
538. C2×C22⋊C4C23×C53semidirect
539. C2×C22⋊C4C23×C53semidirect
540. C2×C22⋊C4C23×C53semidirect
541. C2×C22⋊C4C23×C53semidirect
542. C2×C42C23×C53semidirect
543. C2×C42C23×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35582
C53×#35492
C53×#35452
C53×#35402
C53×#35322
C53×#35292
C2×C53×H(3,𝔽4)2
C53×#35142
C53×#35002
C53×#34842
#6304553