Finite Group Databasebeta

← C53×#33553 #27241065

Subgroups — C53×#33553 #27241065

Order 13568.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3537C211yesmaximal, characteristic, complemented
2C53×#3027C211yesmaximal, characteristic, complemented
3C53×#3025C211yesmaximal, characteristic, complemented
4C53×#3021C211yesmaximal, characteristic, complemented
5C53×#2200C214yesmaximal, complemented
6C53×#2196C214yesmaximal, complemented
7C53×#2128C211yesmaximal, characteristic, complemented
8C53×#2122C211yesmaximal, characteristic, complemented
9C53×#2120C211yesmaximal, characteristic, complemented
10C53×#585C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C53—21no—
12C53×#560—21no—
13C53×#560C2212yescomplemented
14C53×#553—21no—
15C53×#553—21no—
16D42×C53—21no—
17D42×C53—21no—
18D42×C53—21no—
19D42×C53C2212yescomplemented
20C53×#540—21no—
21C53×#538—22no—
22C53×#535—21no—
23C53×#535C2211yescharacteristic
24C53×#535C2211yescharacteristic
25C53×#534—22no—
26C53×#525—21no—
27C53×#525C2211yescharacteristic
28C2×#121×C53—21no—
29C53×#458—21no—
30C53×#458C2212yescomplemented
31C53×B(4,𝔽2)—21no—
32C53×B(4,𝔽2)—22no—
33C53×B(4,𝔽2)C2212yescomplemented
34C53×B(4,𝔽2)C2214yescomplemented
35C53×#454—22no—
36C53×#453C2214yescomplemented
37C53×#421—21no—
38C53×#413C2211yescharacteristic, complemented
39C53×#410—21no—
40C53×#410—21no—
41C53×#410C2211yescharacteristic, complemented
42C53×#410C2211yescharacteristic, complemented
43C53×#353C2214yescomplemented
44C53×#352C2212yescomplemented
45C53×AΣL(1,𝔽16)C2212yescomplemented
46C53×AΣL(1,𝔽16)C2214yescomplemented
472−1+4×C53—21no—
482−1+4×C53—41no—
49H(5,𝔽2)×C53—21no—
50H(5,𝔽2)×C53—21no—
51H(5,𝔽2)×C53—41no—
52H(5,𝔽2)×C53C2312yes—
53C2×#41×C53—21no—
54C2×#41×C53—21no—
55C2×#41×C53—21no—
56C2×#41×C53—42no—
57C2×#41×C53C2311yescharacteristic
58C22×D4×C53—21no—
59C22×D4×C53—22no—
60C22×D4×C53—22no—
61C22×D4×C53—22no—
62C22×D4×C53D411yescharacteristic, complemented
63C22×D4×C53D411yescharacteristic, complemented
64C23×C4×C53D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C53—24no—
66AGL(1,ℤ/8)×C53—42no—
67C2×SD16×C53—41no—
68C2×D8×C53—41no—
69C2×M16×C53—21no—
70#127×C53—21no—
71#127×C53—21no—
72#127×C53—41no—
73#127×C53C2312yes—
74#126×C53—22no—
75#126×C53—22no—
76#125×C53—21no—
77#124×C53—21no—
78#124×C53—41no—
79#124×C53D412yescomplemented
80#123×C53—22no—
81#123×C53—22no—
82#123×C53—22no—
83#123×C53—22no—
84#123×C53—22no—
85#123×C53D411yescharacteristic, complemented
86#123×C53C2311yescharacteristic
87C22⋊Q8×C53—21no—
88C22⋊Q8×C53—41no—
89#121×C53—22no—
90#121×C53—21no—
91#121×C53—21no—
92#121×C53—22no—
93#121×C53—22no—
94#121×C53—22no—
95#121×C53—22no—
96#121×C53—22no—
97#121×C53—21no—
98#121×C53—22no—
99#121×C53—21no—
100#121×C53—21no—
101#121×C53—22no—
102#121×C53—21no—
103#121×C53—21no—
104#121×C53—42no—
105#121×C53—41no—
106#120×C53—22no—
107#120×C53—22no—
108#120×C53—22no—
109#120×C53—21no—
110#120×C53—21no—
111#120×C53—22no—
112#120×C53—22no—
113#120×C53—24no—
114#120×C53D411yescharacteristic, complemented
115#120×C53D412yescomplemented
116#120×C53C2311yescharacteristic
117#120×C53C2312yes—
118C4×D4×C53—22no—
119C4×D4×C53—21no—
120C4×D4×C53—21no—
121C4×D4×C53—22no—
122C4×D4×C53—21no—
123C4×D4×C53—21no—
124C4×D4×C53—42no—
125#117×C53—21no—
126#117×C53—21no—
127#117×C53D411yescharacteristic, complemented
128#117×C53D411yescharacteristic, complemented
129#117×C53D411yescharacteristic, complemented
130C2×C4⋊C4×C53—21no—
131C2×C22⋊C4×C53—22no—
132#104×C53—24no—
133#101×C53—21no—
134#100×C53C2312yes—
135#99×C53—24no—
136#99×C53—22no—
137#99×C53—22no—
138#99×C53—21no—
139#99×C53—21no—
140#99×C53C2312yes—
141#99×C53C2312yes—
142C24×C53—22no—
143C24×C53—21no—
144C24×C53C2×D411yescharacteristic
145C24×C53C2×D412yes—
146#41×C53—22no—
147#41×C53—22no—
148#41×C53—41no—
149#41×C53—41no—
150#41×C53—42no—
151#41×C53—41no—
152#41×C53—41no—
153#41×C53—41no—
154#41×C53—41no—
155#41×C53—41no—
156#41×C53—42no—
157#41×C53—42no—
158#41×C53—42no—
159#41×C53—41no—
160#41×C53—41no—
161#41×C53—41no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—42no—
166C2×Q8×C53C2×D411yescharacteristic
167C2×D4×C53—21no—
168C2×D4×C53—22no—
169C2×D4×C53—22no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53—22no—
174C2×D4×C53—22no—
175C2×D4×C53—21no—
176C2×D4×C53—22no—
177C2×D4×C53—22no—
178C2×D4×C53—22no—
179C2×D4×C53—22no—
180C2×D4×C53—22no—
181C2×D4×C53—22no—
182C2×D4×C53—22no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—41no—
187C2×D4×C53—41no—
188C2×D4×C53—41no—
189C2×D4×C53—41no—
190C2×D4×C53—42no—
191C2×D4×C53—42no—
192C2×D4×C53—42no—
193C2×D4×C53—41no—
194C2×D4×C53—42no—
195C2×D4×C53—44no—
196C2×D4×C53—81no—
197C2×D4×C53—81no—
198C2×D4×C53—84no—
199C2×D4×C53—84no—
200C2×D4×C53—84no—
201C2×D4×C53C2×D411yescharacteristic
202C2×D4×C53C2×D411yescharacteristic
203C2×D4×C53C2×D412yes—
204C2×D4×C53C2411yescharacteristic
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—22no—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—41no—
213C22×C4×C53—41no—
214C22×C4×C53—41no—
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219SD16×C53—44no—
220D8×C53—44no—
221M16×C53—22no—
222M16×C53—41no—
223C2×C8×C53—41no—
224C4⋊C4×C53—22no—
225C4⋊C4×C53—22no—
226C4⋊C4×C53—22no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53—41no—
233C4⋊C4×C53—41no—
234C4⋊C4×C53—42no—
235C22⋊C4×C53—22no—
236C22⋊C4×C53—22no—
237C22⋊C4×C53—22no—
238C22⋊C4×C53—22no—
239C22⋊C4×C53—21no—
240C22⋊C4×C53—21no—
241C22⋊C4×C53—21no—
242C22⋊C4×C53—22no—
243C22⋊C4×C53—22no—
244C22⋊C4×C53—21no—
245C22⋊C4×C53—22no—
246C22⋊C4×C53—21no—
247C22⋊C4×C53—22no—
248C22⋊C4×C53—22no—
249C22⋊C4×C53—22no—
250C22⋊C4×C53—42no—
251C22⋊C4×C53—44no—
252C22⋊C4×C53—42no—
253C22⋊C4×C53C2×D412yes—
254C22⋊C4×C53C2×D411yescharacteristic
255C22⋊C4×C53C2×D411yescharacteristic
256C42×C53—21no—
257C42×C53—21no—
258C42×C53—41no—
259C42×C53—41no—
260C42×C53C2×D412yes—
261C23×C53—21no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—41no—
267C23×C53—42no—
268C23×C53—41no—
269C23×C53—44no—
270C23×C53—42no—
271C23×C53—81no—
272C23×C53—82no—
273C23×C53—82no—
274C23×C53—82no—
275C23×C53—82no—
276C23×C53#12011yescharacteristic
277C23×C53C22×D411yescharacteristic
278C23×C53C22×D411yescharacteristic
279Q8×C53—22no—
280Q8×C53—41no—
281Q8×C53—41no—
282Q8×C53—41no—
283Q8×C53—41no—
284D4×C53—22no—
285D4×C53—41no—
286D4×C53—41no—
287D4×C53—41no—
288D4×C53—42no—
289D4×C53—41no—
290D4×C53—41no—
291D4×C53—42no—
292D4×C53—42no—
293D4×C53—42no—
294D4×C53—42no—
295D4×C53—44no—
296D4×C53—44no—
297D4×C53—42no—
298D4×C53—42no—
299D4×C53—41no—
300D4×C53—41no—
301D4×C53—41no—
302D4×C53—41no—
303D4×C53—41no—
304D4×C53—81no—
305D4×C53—82no—
306D4×C53—82no—
307D4×C53—82no—
308D4×C53—82no—
309D4×C53—82no—
310D4×C53—82no—
311D4×C53—82no—
312D4×C53—84no—
313D4×C53—164no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—21no—
323C2×C4×C53—22no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—22no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53—42no—
330C2×C4×C53—41no—
331C2×C4×C53—42no—
332C2×C4×C53—41no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—42no—
336C2×C4×C53—42no—
337C2×C4×C53—81no—
338C2×C4×C53—82no—
339C2×C4×C53—82no—
340C2×C4×C53—82no—
341C2×C4×C53#12011yescharacteristic
342C2×C4×C53#12011yescharacteristic
343C2×C4×C53#12011yescharacteristic
344C2×C4×C53C22×D411yescharacteristic
345C8×C53—42no—
346#33553C5311yesmaximal, characteristic, direct product factor, Sylow
347C22×C53—22no—
348C22×C53—21no—
349C22×C53—21no—
350C22×C53—21no—
351C22×C53—41no—
352C22×C53—41no—
353C22×C53—41no—
354C22×C53—41no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—41no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—81no—
365C22×C53—82no—
366C22×C53—82no—
367C22×C53—84no—
368C22×C53—161no—
369C22×C53—164no—
370C22×C53—162no—
371C22×C53C2×#12011yescharacteristic
372C4×C53—21no—
373C4×C53—21no—
374C4×C53—21no—
375C4×C53—42no—
376C4×C53—41no—
377C4×C53—41no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53—41no—
381C4×C53—82no—
382C4×C53—82no—
383C4×C53B(4,𝔽2)11yescharacteristic
384C4×C53B(4,𝔽2)11yescharacteristic
385#3537C2×C5311yescharacteristic, complemented
386#3027C2×C5311yescharacteristic, complemented
387#3025C2×C5311yescharacteristic, complemented
388#3021C2×C5311yescharacteristic, complemented
389#2200C2×C5314yescomplemented
390#2196C2×C5314yescomplemented
391#2128C2×C5311yescharacteristic, complemented
392#2122C2×C5311yescharacteristic, complemented
393#2120C2×C5311yescharacteristic, complemented
394C2×C53—21no—
395C2×C53—41no—
396C2×C53—41no—
397C2×C53—42no—
398C2×C53—41no—
399C2×C53—82no—
400C2×C53—82no—
401C2×C53—82no—
402C2×C53C2×B(4,𝔽2)11yescharacteristic
403#585C22×C5311yescharacteristic, complemented
404C2×AGL(1,ℤ/8)—21no—
405#560—21no—
406#560C22×C5312yescomplemented
407#553—21no—
408#553—21no—
409D42—21no—
410D42—21no—
411D42—21no—
412D42C22×C5312yescomplemented
413#540—21no—
414#538—22no—
415#535—21no—
416#535C22×C5311yescharacteristic
417#535C22×C5311yescharacteristic
418#534—22no—
419#525—21no—
420#525C22×C5311yescharacteristic
421C2×#121—21no—
422#458—21no—
423#458C22×C5312yescomplemented
424B(4,𝔽2)—21no—
425B(4,𝔽2)—22no—
426B(4,𝔽2)C22×C5312yescomplemented
427B(4,𝔽2)C22×C5314yescomplemented
428#454—22no—
429#453C22×C5314yescomplemented
430#421—21no—
431#413C22×C5311yescharacteristic, complemented
432#410—21no—
433#410—21no—
434#410C22×C5311yescharacteristic, complemented
435#410C22×C5311yescharacteristic, complemented
436#353C22×C5314yescomplemented
437#352C22×C5312yescomplemented
438AΣL(1,𝔽16)C22×C5312yescomplemented
439AΣL(1,𝔽16)C22×C5314yescomplemented
440C53#3355311yescharacteristic, direct product factor, Sylow
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C5312yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C5311yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C5311yescharacteristic, complemented
457C22×D4D4×C5311yescharacteristic, complemented
458C23×C4D4×C5311yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C5312yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C5312yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C5311yescharacteristic, complemented
480#123C23×C5311yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C5311yescharacteristic, complemented
509#120D4×C5312yescomplemented
510#120C23×C5311yescharacteristic
511#120C23×C5312yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C5311yescharacteristic, complemented
522#117D4×C5311yescharacteristic, complemented
523#117D4×C5311yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C5312yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C5312yes—
535#99C23×C5312yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C5311yescharacteristic
539C24C2×D4×C5312yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C5311yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C5311yescharacteristic
596C2×D4C2×D4×C5311yescharacteristic
597C2×D4C2×D4×C5312yes—
598C2×D4C24×C5311yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C5311yescharacteristic
610C22×C4C2×D4×C5311yescharacteristic
611C22×C4C2×D4×C5311yescharacteristic
612C22×C4C2×D4×C5311yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C5312yes—
648C22⋊C4C2×D4×C5311yescharacteristic
649C22⋊C4C2×D4×C5311yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C5312yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C5311yescharacteristic
671C23C22×D4×C5311yescharacteristic
672C23C22×D4×C5311yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C5311yescharacteristic
736C2×C4#120×C5311yescharacteristic
737C2×C4#120×C5311yescharacteristic
738C2×C4C22×D4×C5311yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C5311yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4C53×B(4,𝔽2)11yescharacteristic
777C4C53×B(4,𝔽2)11yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×C53×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C53C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C53
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C53 ◁ C2×C4×C53 ◁ C2×#41×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3537C2semidirect
2. C53×#3027C2semidirect
3. C53×#3025C2semidirect
4. C53×#3021C2semidirect
5. C53×#2200C2semidirect
6. C53×#2196C2semidirect
7. C53×#2128C2semidirect
8. C53×#2122C2semidirect
9. C53×#2120C2semidirect
10. C53×#585C22semidirect
13. C53×#560C22semidirect
19. D42×C53C22semidirect
30. C53×#458C22semidirect
33. C53×B(4,𝔽2)C22semidirect
34. C53×B(4,𝔽2)C22semidirect
36. C53×#453C22semidirect
38. C53×#413C22semidirect
41. C53×#410C22semidirect
42. C53×#410C22semidirect
43. C53×#353C22semidirect
44. C53×#352C22semidirect
45. C53×AΣL(1,𝔽16)C22semidirect
46. C53×AΣL(1,𝔽16)C22semidirect
62. C22×D4×C53D4semidirect
63. C22×D4×C53D4semidirect
64. C23×C4×C53D4semidirect
79. #124×C53D4semidirect
85. #123×C53D4semidirect
114. #120×C53D4semidirect
115. #120×C53D4semidirect
127. #117×C53D4semidirect
128. #117×C53D4semidirect
129. #117×C53D4semidirect
346. #33553C53direct (N × H)
385. #3537C2×C53semidirect
386. #3027C2×C53semidirect
387. #3025C2×C53semidirect
388. #3021C2×C53semidirect
389. #2200C2×C53semidirect
390. #2196C2×C53semidirect
391. #2128C2×C53semidirect
392. #2122C2×C53semidirect
393. #2120C2×C53semidirect
403. #585C22×C53semidirect
406. #560C22×C53semidirect
412. D42C22×C53semidirect
423. #458C22×C53semidirect
426. B(4,𝔽2)C22×C53semidirect
427. B(4,𝔽2)C22×C53semidirect
429. #453C22×C53semidirect
431. #413C22×C53semidirect
434. #410C22×C53semidirect
435. #410C22×C53semidirect
436. #353C22×C53semidirect
437. #352C22×C53semidirect
438. AΣL(1,𝔽16)C22×C53semidirect
439. AΣL(1,𝔽16)C22×C53semidirect
440. C53#33553direct (N × H)
456. C22×D4D4×C53semidirect
457. C22×D4D4×C53semidirect
458. C23×C4D4×C53semidirect
473. #124D4×C53semidirect
479. #123D4×C53semidirect
508. #120D4×C53semidirect
509. #120D4×C53semidirect
521. #117D4×C53semidirect
522. #117D4×C53semidirect
523. #117D4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35372
C53×#30272
C53×#30252
C53×#30212
C53×#22002
C53×#21962
C53×#21282
C53×#21222
C53×#21202
#3355353