Finite Group Databasebeta

← #12272258

Subgroups — #12272258

Order 1280.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65894C212yesmaximal, complemented
2C42×C5×D4C211yesmaximal, characteristic, complemented
3#10614138C212yesmaximal, complemented
4#10614134C211yesmaximal, characteristic, complemented
5#10614083C211yesmaximal, characteristic, complemented
6#10613812C211yesmaximal, characteristic, complemented
7#10613811C211yesmaximal, characteristic, complemented
8C4×#4076C211yesmaximal, characteristic, complemented
9C2×#65228C211yesmaximal, characteristic, complemented
10#10605547C212yesmaximal, complemented
11#10605534C212yesmaximal, complemented
12#10605511C211yesmaximal, characteristic, complemented
13#10605423C211yesmaximal, characteristic, complemented
14#10605342C212yesmaximal, complemented
15#10605331C212yesmaximal, complemented
16#10605325C212yesmaximal, complemented
17#10605318C211yesmaximal, characteristic, complemented
18#10605300C212yesmaximal, complemented
19#10605238C211yesmaximal, characteristic, complemented
20#10605224C211yesmaximal, characteristic, complemented
21#10605218C211yesmaximal, characteristic, complemented
22#10605045C211yesmaximal, characteristic, complemented
23#10605044C211yesmaximal, characteristic, complemented
24C23×D20C2211yescharacteristic
25C2×C4×C5×D4C2211yescharacteristic
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C22×C42×C5C2211yescharacteristic, complemented
30C2×#4085C2212yes—
31C2×#4083C2212yes—
32C2×#4076C2211yescharacteristic
33C2×#4076C2211yescharacteristic
34C2×#4076C2211yescharacteristic
35C2×#4076C2212yescomplemented
36C2×#4076C2212yescomplemented
37C2×#4076C2211yescharacteristic, complemented
38C2×#4075C2212yescomplemented
39C2×C4×C22⋊D5C2212yes—
40C22×#685C2212yes—
41C22×#685C2212yes—
42C22×C4⋊Dic5C2211yescharacteristic
43#65894—216no—
44C2×#4044C2212yescomplemented
45C2×#4040C2212yescomplemented
46C2×#4031C2212yescomplemented
47C2×#4030C2212yescomplemented
48C2×#4028C2212yes—
49C2×#4028C2212yes—
50C2×#4024C2212yes—
51C2×#4022C2212yescomplemented
52C2×#4021C2212yescomplemented
53C2×#4021C2212yescomplemented
54C2×#4020C2211yescharacteristic
55C2×#4020C2211yescharacteristic
56C2×C4×D20C2211yescharacteristic, complemented
57C2×#4015C2211yescharacteristic, complemented
58C4×C5×C4⋊C4C2211yescharacteristic, complemented
59C4×C5×C4⋊C4C2211yescharacteristic, complemented
60C4×C5×C4⋊C4C2211yescharacteristic, complemented
61C4×C5×C22⋊C4C2211yescharacteristic
62C4×C5×C22⋊C4C2211yescharacteristic
63C4×C5×C22⋊C4C2211yescharacteristic
64C4×C5×C22⋊C4C2211yescharacteristic, complemented
65C4×C5×C22⋊C4C2211yescharacteristic, complemented
66C4×C5×C22⋊C4C2211yescharacteristic, complemented
67C43×C5C2211yescharacteristic, complemented
68#65502C2212yes—
69#65502C2212yescomplemented
70#65501C2211yescharacteristic
71#65501C2211yescharacteristic, complemented
72#65283C2212yescomplemented
73#65283C2212yescomplemented
74#65280C2212yes—
75#65280C2212yescomplemented
76#65250C2212yescomplemented
77#65250C2212yescomplemented
78#65249C2212yes—
79#65249C2212yescomplemented
80#65247C2212yes—
81#65244C2212yes—
82#65239C2212yes—
83#65229C2212yescomplemented
84#65229C2212yescomplemented
85#65229C2212yescomplemented
86#65229C2212yescomplemented
87#65229C2212yescomplemented
88#65229C2212yescomplemented
89#65228C2211yescharacteristic
90#65228C2211yescharacteristic
91#65228C2212yes—
92#65228C2212yes—
93#65228C2211yescharacteristic
94#65228C2211yescharacteristic
95#65228C2211yescharacteristic
96#65228C2211yescharacteristic
97#65228C2211yescharacteristic
98#65228C2211yescharacteristic
99#65228C2212yescomplemented
100#65228C2212yescomplemented
101#65228C2211yescharacteristic, complemented
102#65228C2212yescomplemented
103#65228C2211yescharacteristic, complemented
104#65228C2212yescomplemented
105C4×#685C2212yescomplemented
106#65224C2211yescharacteristic, complemented
107C4×C4⋊Dic5C2211yescharacteristic, complemented
108#65217C2211yescharacteristic, complemented
109#65217C2211yescharacteristic, complemented
110#65217C2211yescharacteristic, complemented
111#65217C2211yescharacteristic, complemented
112#64963C2212yescomplemented
113#64962C2212yescomplemented
114#64961C2212yescomplemented
115#64961C2212yescomplemented
116#64960C2212yes—
117#64960C2212yes—
118#64959C2212yescomplemented
119#64959C2212yescomplemented
120#64954C2212yescomplemented
121#64954C2212yescomplemented
122#64950C2212yescomplemented
123#64945C2212yescomplemented
124#35007—51nomaximal, Sylow
125C24×D5C2312yes—
126C22×C5×D4C2311yescharacteristic
127C23×C4×C5C2311yescharacteristic
128C23×C4×C5C2311yescharacteristic
129C23×C4×C5C2311yescharacteristic
130C23×C4×C5C2311yescharacteristic
131C23×C4×C5C2311yescharacteristic
132C23×C4×C5C2311yescharacteristic
133C22×C22⋊D5C2312yes—
134C22×C22⋊D5C2312yes—
135C22×C22⋊D5C2312yes—
136C22×C22⋊D5C2312yes—
137C23×Dic5C2312yes—
138C22×D20—24no—
139C22×D20—42no—
140C22×D20—42no—
141C22×D20C2311yescharacteristic
142C22×D20C2311yescharacteristic
143C22×D20C2311yescharacteristic
144C22×D20C2312yes—
145C22×D20C2312yes—
146C22×D20C2312yes—
147C22×D20C2312yes—
148C22×D20C2312yes—
149C22×C4×D5C2312yes—
150C22×Dic10C2312yes—
151C4×C5×D4—24no—
152C4×C5×D4—24no—
153C4×C5×D4D418yescomplemented
154C2×C5×C4⋊C4C2311yescharacteristic
155C2×C5×C4⋊C4C2311yescharacteristic
156C2×C5×C4⋊C4C2311yescharacteristic
157C2×C5×C22⋊C4C2311yescharacteristic
158C2×C5×C22⋊C4C2311yescharacteristic
159C2×C5×C22⋊C4C2311yescharacteristic
160C2×C5×C22⋊C4C2311yescharacteristic
161C2×C5×C22⋊C4C2311yescharacteristic
162C2×C5×C22⋊C4C2311yescharacteristic
163C2×C42×C5—42no—
164C2×C42×C5—42no—
165C2×C42×C5C2311yescharacteristic
166C2×C42×C5C2311yescharacteristic
167C2×C42×C5C2311yescharacteristic
168C2×C42×C5C2311yescharacteristic
169C2×C42×C5C2311yescharacteristic
170C2×C42×C5C2311yescharacteristic
171C2×C42×C5C2311yescharacteristic
172C2×C42×C5C2311yescharacteristic
173C2×C42×C5C2311yescharacteristic
174C2×C42×C5C2311yescharacteristic
175C2×C42×C5C2311yescharacteristic
176C2×C42×C5C2311yescharacteristic
177C2×C42×C5C2311yescharacteristic
178C2×C22⋊Dic5C2312yes—
179C2×C22⋊Dic5C2312yes—
180#4085—28no—
181#4083—28no—
182#4076—28no—
183#4076—24no—
184#4076—42no—
185#4076—42no—
186#4076—42no—
187#4076—44no—
188#4075—28no—
189C4×C22⋊D5—28no—
190C2×#685—28no—
191C2×#685—44no—
192C2×#685C2312yes—
193C2×#685C2312yes—
194C2×#685C2312yes—
195C2×#685C2312yes—
196C2×#685C2312yes—
197C2×#685C2312yes—
198C2×#685C2312yes—
199C2×#685C2312yes—
200C2×#685C2312yes—
201C2×#685C2312yes—
202C2×#685C2312yes—
203C2×#685C2312yes—
204C2×#685C2312yes—
205C2×#685C2312yes—
206C2×#685C2312yes—
207C2×#685C2312yes—
208C2×#685C2312yes—
209C2×#685C2312yes—
210C2×#685C2312yes—
211C2×#685C2312yes—
212C2×#685C2312yes—
213C2×#685C2312yes—
214C2×#685C2312yes—
215C2×#685C2312yes—
216C2×#685C2312yes—
217C2×C4⋊Dic5—42no—
218C2×C4⋊Dic5C2311yescharacteristic
219C2×C4⋊Dic5C2311yescharacteristic
220C2×C4⋊Dic5C2311yescharacteristic
221C2×C4⋊Dic5C2312yes—
222C2×C4⋊Dic5C2311yescharacteristic
223C2×C4⋊Dic5C2311yescharacteristic
224C2×C4⋊Dic5C2312yes—
225C2×C4⋊Dic5C2312yes—
226C2×C4⋊Dic5C2312yes—
227C2×#683C2312yes—
228C2×#683C2312yes—
229C2×#683C2312yes—
230C2×#683C2312yes—
231C2×C4×Dic5C2312yes—
232#4044—28no—
233#4040—28no—
234#4031—28no—
235#4030—28no—
236#4028—28no—
237#4028—28no—
238#4024—28no—
239#4022—28no—
240#4021—28no—
241#4021—44no—
242#4020—42no—
243#4020—42no—
244C4×D20—42no—
245#4015—42no—
246C5×#95C2311yescharacteristic
247C5×#95C2311yescharacteristic
248C5×#95C2311yescharacteristic
249C5×#95C2311yescharacteristic
250C5×#95C2311yescharacteristic
251C5×#95C2311yescharacteristic
252#3963C2312yes—
253#3963C2312yes—
254#3963C2312yes—
255#3963C2312yes—
256#3963C2312yes—
257#3963C2312yes—
258#3963C2312yes—
259C2×#538—52no—
260#2860—51no—
261#2858—51no—
262#2856—51no—
263#2854—51no—
264#2662—52no—
265#2661—52no—
266#2555—52no—
267#2554—52no—
268#2512—51no—
269#2491—51no—
270#2472—52no—
271#2445—51no—
272#2440—51no—
273#2433—51no—
274#2428—51no—
275#2424—52no—
276#2416—51no—
277#2408—51no—
278#2321—52no—
279C4×#121—51no—
280C2×#390—51no—
281C42×D4D511yescharacteristic, complemented
282C24×C5C2411yescharacteristic
283C24×C5C2411yescharacteristic
284C23×D5—24no—
285C23×D5—24no—
286C23×D5—24no—
287C23×D5—42no—
288C23×D5—42no—
289C23×D5—42no—
290C23×D5—42no—
291C23×D5C2412yes—
292C23×D5C2412yes—
293C23×D5C2412yes—
294C2×C5×D4—22no—
295C2×C5×D4—22no—
296C2×C5×D4C2×D414yes—
297C22×C4×C5—22no—
298C22×C4×C5—22no—
299C22×C4×C5—22no—
300C22×C4×C5—22no—
301C22×C4×C5—22no—
302C22×C4×C5—22no—
303C22×C4×C5—22no—
304C22×C4×C5—22no—
305C22×C4×C5—22no—
306C22×C4×C5—41no—
307C22×C4×C5—41no—
308C22×C4×C5—41no—
309C22×C4×C5—41no—
310C22×C4×C5—41no—
311C22×C4×C5—41no—
312C22×C4×C5C2×D414yes—
313C22×C4×C5C2×D414yescomplemented
314C22×C4×C5#4114yes—
315C22×C4×C5C2411yescharacteristic
316C22×C4×C5C2411yescharacteristic
317C22×C4×C5C2411yescharacteristic
318C22×C4×C5C2411yescharacteristic
319C22×C4×C5C2411yescharacteristic
320C22×C4×C5C2411yescharacteristic
321C22×C4×C5C2411yescharacteristic
322C22×C4×C5C2411yescharacteristic
323C22×C4×C5C2411yescharacteristic
324C22×C4×C5C2411yescharacteristic
325C22×C4×C5C2411yescharacteristic
326C22×C4×C5C2411yescharacteristic
327C22×C4×C5C2411yescharacteristic
328C2×C22⋊D5—24no—
329C2×C22⋊D5—24no—
330C2×C22⋊D5—24no—
331C2×C22⋊D5—24no—
332C2×C22⋊D5—24no—
333C2×C22⋊D5—24no—
334C2×C22⋊D5—42no—
335C2×C22⋊D5—42no—
336C2×C22⋊D5—42no—
337C2×C22⋊D5—42no—
338C2×C22⋊D5—42no—
339C2×C22⋊D5—42no—
340C22×Dic5—24no—
341C22×Dic5—42no—
342C22×Dic5—42no—
343C22×Dic5C2412yes—
344C22×Dic5C2412yes—
345C22×Dic5C2412yes—
346C22×Dic5C2412yes—
347C22×Dic5C2412yes—
348C2×D20—24no—
349C2×D20—22no—
350C2×D20—22no—
351C2×D20—22no—
352C2×D20—22no—
353C2×D20—22no—
354C2×D20—22no—
355C2×D20—22no—
356C2×D20—22no—
357C2×D20—22no—
358C2×D20—24no—
359C2×D20—24no—
360C2×D20—24no—
361C2×D20—24no—
362C2×D20—42no—
363C2×D20—42no—
364C2×D20—416no—
365C2×D20—42no—
366C2×D20—42no—
367C2×D20—42no—
368C2×D20—42no—
369C2×D20—42no—
370C2×D20—42no—
371C2×D20—42no—
372C2×D20—42no—
373C2×C4×D5—24no—
374C2×C4×D5—42no—
375C2×C4×D5—42no—
376C2×Dic10—24no—
377C2×Dic10—42no—
378C2×Dic10—42no—
379C5×C4⋊C4—22no—
380C5×C4⋊C4—22no—
381C5×C4⋊C4C2×D414yescomplemented
382C5×C22⋊C4—22no—
383C5×C22⋊C4—22no—
384C5×C22⋊C4—22no—
385C5×C22⋊C4C2×D414yes—
386C5×C22⋊C4C2×D414yescomplemented
387C5×C22⋊C4#4114yes—
388C42×C5—22no—
389C42×C5—22no—
390C42×C5—22no—
391C42×C5—22no—
392C42×C5—22no—
393C42×C5—22no—
394C42×C5—22no—
395C42×C5—41no—
396C42×C5—41no—
397C42×C5—41no—
398C42×C5—41no—
399C42×C5—41no—
400C42×C5C2×D414yescomplemented
401C22⋊Dic5—24no—
402C22⋊Dic5—24no—
403#685—24no—
404#685—24no—
405#685—24no—
406#685—24no—
407#685—24no—
408#685—24no—
409#685—24no—
410#685—24no—
411#685—24no—
412#685—24no—
413#685—24no—
414#685—24no—
415#685—24no—
416#685—24no—
417#685—24no—
418#685—24no—
419#685—42no—
420#685—42no—
421#685—42no—
422#685—42no—
423#685—42no—
424#685—42no—
425#685—42no—
426#685—42no—
427#685—42no—
428C4⋊Dic5—24no—
429C4⋊Dic5—22no—
430C4⋊Dic5—22no—
431C4⋊Dic5—22no—
432C4⋊Dic5—22no—
433C4⋊Dic5—22no—
434C4⋊Dic5—42no—
435C4⋊Dic5—42no—
436C4⋊Dic5—42no—
437#683—24no—
438#683—24no—
439#683—24no—
440#683—24no—
441C4×Dic5—24no—
442C23×D4—51no—
443#538—1016no—
444C2×C4⋊Q8—51no—
445C2×#127—51no—
446C2×#127—51no—
447C2×#126—52no—
448C2×#126—52no—
449C2×#124—52no—
450C2×#124—52no—
451C2×#124—52no—
452C2×#123—52no—
453C2×#123—52no—
454C2×C22⋊Q8—52no—
455C2×#121—52no—
456C2×#121—52no—
457C2×#121—51no—
458C2×#121—51no—
459C2×#121—51no—
460C2×#121—51no—
461C2×#121—52no—
462C2×#121—52no—
463C2×#120—52no—
464C2×#120—52no—
465C2×#120—52no—
466C2×C4×D4—52no—
467C2×C4×D4—51no—
468C2×C4×D4C2×D511yescharacteristic
469C2×C4×D4C2×D511yescharacteristic
470C2×C4×D4C2×D511yescharacteristic
471C22×C4⋊C4—51no—
472C22×C22⋊C4—52no—
473C22×C22⋊C4—52no—
474C22×C42C2×D511yescharacteristic
475C22×C42C2×D511yescharacteristic, complemented
476#398—52no—
477#397—52no—
478#396—52no—
479#396—52no—
480#395—52no—
481#394—52no—
482#394—52no—
483#394—52no—
484#394—52no—
485#394—52no—
486#394—52no—
487#393—52no—
488#392—52no—
489#392—52no—
490#392—52no—
491#392—52no—
492#390—52no—
493#390—52no—
494#390—51no—
495#390—51no—
496#390—51no—
497#390—51no—
498#390—52no—
499#390—51no—
500#390—51no—
501#390—52no—
502#390—51no—
503#390—51no—
504#390—52no—
505#390—51no—
506#390—51no—
507#390—52no—
508#389—51no—
509#389—51no—
510#389—51no—
511#389—51no—
512#388—52no—
513#388—52no—
514#388—52no—
515#388—52no—
516#388—52no—
517#388—52no—
518#388—52no—
519#388—52no—
520#386—52no—
521#386—52no—
522#386—52no—
523#386—52no—
524#386—52no—
525#385—52no—
526#384—51no—
527#380—51no—
528#380—51no—
529#379—52no—
530C4×C4⋊C4—51no—
531C4×C4⋊C4C2×D511yescharacteristic, complemented
532C4×C4⋊C4C2×D511yescharacteristic, complemented
533C4×C4⋊C4C2×D511yescharacteristic, complemented
534C4×C22⋊C4—52no—
535C4×C22⋊C4C2×D511yescharacteristic
536C4×C22⋊C4C2×D511yescharacteristic
537C4×C22⋊C4C2×D511yescharacteristic
538C4×C22⋊C4C2×D511yescharacteristic, complemented
539C4×C22⋊C4C2×D511yescharacteristic, complemented
540C4×C22⋊C4C2×D511yescharacteristic, complemented
541C43C2×D511yescharacteristic, complemented
542C23×C5—21no—
543C23×C5—21no—
544C23×C5—21no—
545C23×C5—21no—
546C23×C5—21no—
547C23×C5—21no—
548C23×C5—21no—
549C23×C5—21no—
550C23×C5—21no—
551C23×C5—21no—
552C23×C5C22×D412yes—
553C23×C5C22×D412yes—
554C23×C5C2×#4112yes—
555C23×C5C2×#4112yes—
556C23×C5C2511yescharacteristic
557C22×D5—22no—
558C22×D5—22no—
559C22×D5—22no—
560C22×D5—22no—
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—22no—
569C22×D5—22no—
570C22×D5—22no—
571C22×D5—22no—
572C22×D5—22no—
573C22×D5—22no—
574C22×D5—22no—
575C22×D5—22no—
576C22×D5—22no—
577C22×D5—22no—
578C22×D5—48no—
579C22×D5—48no—
580C22×D5—48no—
581C22×D5—84no—
582C22×D5—84no—
583C22×D5—84no—
584C22×D5—84no—
585C5×D4—28no—
586C2×C4×C5—21no—
587C2×C4×C5—21no—
588C2×C4×C5—21no—
589C2×C4×C5—21no—
590C2×C4×C5—21no—
591C2×C4×C5—21no—
592C2×C4×C5—21no—
593C2×C4×C5—21no—
594C2×C4×C5—21no—
595C2×C4×C5—21no—
596C2×C4×C5—21no—
597C2×C4×C5—21no—
598C2×C4×C5—21no—
599C2×C4×C5—21no—
600C2×C4×C5—21no—
601C2×C4×C5—21no—
602C2×C4×C5—21no—
603C2×C4×C5—21no—
604C2×C4×C5—28no—
605C2×C4×C5—21no—
606C2×C4×C5—21no—
607C2×C4×C5—21no—
608C2×C4×C5—21no—
609C2×C4×C5—21no—
610C2×C4×C5—21no—
611C2×C4×C5—21no—
612C2×C4×C5—21no—
613C2×C4×C5—21no—
614C2×C4×C5—44no—
615C2×C4×C5—44no—
616C2×C4×C5—44no—
617C2×C4×C5—44no—
618C2×C4×C5—44no—
619C2×C4×C5C22×D412yes—
620C2×C4×C5C22×D412yes—
621C2×C4×C5C22×D412yes—
622C2×C4×C5C22×D412yes—
623C2×C4×C5C22×D412yes—
624C2×C4×C5C2×#4112yes—
625C2×C4×C5C2×#4112yes—
626C2×C4×C5C2×#4112yes—
627C2×C4×C5C2×#4112yes—
628C2×C4×C5H(5,𝔽2)12yes—
629C2×C4×C5H(5,𝔽2)12yes—
630C2×C4×C5H(5,𝔽2)12yes—
631C22⋊D5—48no—
632C22⋊D5—84no—
633C22⋊D5—84no—
634C22⋊D5—84no—
635C2×Dic5—22no—
636C2×Dic5—22no—
637C2×Dic5—22no—
638C2×Dic5—22no—
639C2×Dic5—22no—
640C2×Dic5—22no—
641C2×Dic5—22no—
642C2×Dic5—22no—
643C2×Dic5—22no—
644C2×Dic5—22no—
645C2×Dic5—22no—
646C2×Dic5—22no—
647C2×Dic5—22no—
648C2×Dic5—22no—
649C2×Dic5—22no—
650C2×Dic5—84no—
651D20—48no—
652D20—44no—
653D20—44no—
654D20—44no—
655D20—84no—
656D20—84no—
657D20—84no—
658D20—84no—
659C4×D5—84no—
660Dic10—84no—
661C25—52no—
662C22×Q8—52no—
663C22×D4—52no—
664C22×D4—52no—
665C22×D4—52no—
666C22×D4—52no—
667C22×D4—51no—
668C22×D4—51no—
669C22×D4—51no—
670C22×D4—52no—
671C22×D4—52no—
672C22×D4—52no—
673C22×D4—52no—
674C22×D4—52no—
675C22×D4—104no—
676C22×D4—202no—
677C22×D4—202no—
678C22×D4C22×D511yescharacteristic
679C23×C4—52no—
680C23×C4—52no—
681C23×C4C22×D511yescharacteristic
682C23×C4C22×D511yescharacteristic
683C23×C4C22×D511yescharacteristic
684C23×C4C22×D511yescharacteristic
685C23×C4C22×D511yescharacteristic
686C23×C4C22×D511yescharacteristic
687C4⋊Q8—202no—
688#127—202no—
689#127—202no—
690#126—108no—
691#126—108no—
692#124—108no—
693#124—108no—
694#124—204no—
695#123—108no—
696#123—108no—
697C22⋊Q8—108no—
698#121—108no—
699#121—108no—
700#121—104no—
701#121—108no—
702#121—204no—
703#121—202no—
704#121—202no—
705#121—202no—
706#120—108no—
707#120—108no—
708#120—108no—
709C4×D4—24no—
710C4×D4—24no—
711C4×D4—108no—
712C4×D4—202no—
713C4×D4D2018yescomplemented
714C2×C4⋊C4—51no—
715C2×C4⋊C4—51no—
716C2×C4⋊C4—51no—
717C2×C4⋊C4—52no—
718C2×C4⋊C4—52no—
719C2×C4⋊C4—52no—
720C2×C4⋊C4—52no—
721C2×C4⋊C4—51no—
722C2×C4⋊C4—51no—
723C2×C4⋊C4—52no—
724C2×C4⋊C4—52no—
725C2×C4⋊C4—52no—
726C2×C4⋊C4—52no—
727C2×C4⋊C4—202no—
728C2×C4⋊C4C22×D511yescharacteristic
729C2×C4⋊C4C22×D511yescharacteristic
730C2×C4⋊C4C22×D511yescharacteristic
731C2×C22⋊C4—52no—
732C2×C22⋊C4—52no—
733C2×C22⋊C4—52no—
734C2×C22⋊C4—52no—
735C2×C22⋊C4—52no—
736C2×C22⋊C4—52no—
737C2×C22⋊C4—52no—
738C2×C22⋊C4—52no—
739C2×C22⋊C4—52no—
740C2×C22⋊C4—52no—
741C2×C22⋊C4—52no—
742C2×C22⋊C4—52no—
743C2×C22⋊C4—52no—
744C2×C22⋊C4—52no—
745C2×C22⋊C4—52no—
746C2×C22⋊C4—52no—
747C2×C22⋊C4—52no—
748C2×C22⋊C4—52no—
749C2×C22⋊C4—52no—
750C2×C22⋊C4—52no—
751C2×C22⋊C4—52no—
752C2×C22⋊C4—52no—
753C2×C22⋊C4—52no—
754C2×C22⋊C4—52no—
755C2×C22⋊C4—52no—
756C2×C22⋊C4—52no—
757C2×C22⋊C4—52no—
758C2×C22⋊C4—108no—
759C2×C22⋊C4—204no—
760C2×C22⋊C4C22×D511yescharacteristic
761C2×C22⋊C4C22×D511yescharacteristic
762C2×C22⋊C4C22×D511yescharacteristic
763C2×C22⋊C4C22×D511yescharacteristic
764C2×C22⋊C4C22×D511yescharacteristic
765C2×C22⋊C4C22×D511yescharacteristic
766C2×C42—42no—
767C2×C42—42no—
768C2×C42—52no—
769C2×C42C22×D511yescharacteristic
770C2×C42C22×D511yescharacteristic
771C2×C42C22×D511yescharacteristic
772C2×C42C22×D511yescharacteristic
773C2×C42C22×D511yescharacteristic
774C2×C42C22×D511yescharacteristic
775C2×C42C22×D511yescharacteristic
776C2×C42C22×D511yescharacteristic
777C2×C42C22×D511yescharacteristic
778C2×C42C22×D511yescharacteristic
779C2×C42C22×D511yescharacteristic
780C2×C42C22×D511yescharacteristic
781C2×C42C22×D511yescharacteristic
782#95—52no—
783#95—52no—
784#95—52no—
785#95—52no—
786#95—52no—
787#95—52no—
788#95—52no—
789#95C22×D511yescharacteristic
790#95C22×D511yescharacteristic
791#95C22×D511yescharacteristic
792#95C22×D511yescharacteristic
793#95C22×D511yescharacteristic
794#95C22×D511yescharacteristic
795C22×C5—22no—
796C22×C5—22no—
797C22×C5—22no—
798C22×C5—22no—
799C22×C5—22no—
800C22×C5—22no—
801C22×C5—22no—
802C22×C5—22no—
803C22×C5—22no—
804C22×C5—41no—
805C22×C5—41no—
806C22×C5—41no—
807C22×C5—41no—
808C22×C5#53214yes—
809C22×C5C23×D411yescharacteristic
810C22×C5C22×#4111yescharacteristic
811C22×C5C22×#4111yescharacteristic
812C22×C5C2×H(5,𝔽2)11yescharacteristic
813C22×C5C2×H(5,𝔽2)11yescharacteristic
814C22×C5C2×H(5,𝔽2)11yescharacteristic
815C22×C5#58511yescharacteristic
816C2×D5—42no—
817C2×D5—42no—
818C2×D5—42no—
819C2×D5—42no—
820C2×D5—42no—
821C2×D5—42no—
822C2×D5—42no—
823C2×D5—42no—
824C2×D5—42no—
825C2×D5—42no—
826C2×D5—42no—
827C2×D5—42no—
828C2×D5—42no—
829C2×D5—42no—
830C2×D5—42no—
831C2×D5—42no—
832C2×D5—42no—
833C2×D5—42no—
834C2×D5—42no—
835C2×D5—42no—
836C2×D5—42no—
837C2×D5—816no—
838C4×C5—22no—
839C4×C5—22no—
840C4×C5—22no—
841C4×C5—22no—
842C4×C5—22no—
843C4×C5—22no—
844C4×C5—22no—
845C4×C5—22no—
846C4×C5—22no—
847C4×C5—41no—
848C4×C5—41no—
849C4×C5—41no—
850C4×C5#53814yescomplemented
851Dic5—42no—
852Dic5—42no—
853Dic5—42no—
854Dic5—42no—
855Dic5—42no—
856C24—52no—
857C24—52no—
858C24—52no—
859C24—104no—
860C24—104no—
861C24—104no—
862C24—202no—
863C24—202no—
864C24—202no—
865C24—202no—
866C24C23×D511yescharacteristic
867C24C23×D511yescharacteristic
868C2×Q8—104no—
869C2×Q8—202no—
870C2×Q8—202no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—104no—
874C2×D4—104no—
875C2×D4—104no—
876C2×D4—104no—
877C2×D4—104no—
878C2×D4—104no—
879C2×D4—104no—
880C2×D4—104no—
881C2×D4—102no—
882C2×D4—104no—
883C2×D4—102no—
884C2×D4—102no—
885C2×D4—104no—
886C2×D4—104no—
887C2×D4—102no—
888C2×D4—102no—
889C2×D4—102no—
890C2×D4—102no—
891C2×D4—102no—
892C2×D4—102no—
893C2×D4—202no—
894C2×D4—202no—
895C2×D4—2016no—
896C2×D4—202no—
897C2×D4—202no—
898C2×D4—202no—
899C2×D4—202no—
900C2×D4—202no—
901C2×D4—202no—
902C2×D4—202no—
903C2×D4—202no—
904C2×D4—202no—
905C2×D4—202no—
906C2×D4—202no—
907C2×D4—202no—
908C2×D4—202no—
909C2×D4—202no—
910C2×D4C2×D2014yes—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—52no—
927C22×C4—52no—
928C22×C4—52no—
929C22×C4—52no—
930C22×C4—52no—
931C22×C4—104no—
932C22×C4—104no—
933C22×C4—202no—
934C22×C4—202no—
935C22×C4—202no—
936C22×C4—202no—
937C22×C4C2×D2014yes—
938C22×C4C2×D2014yescomplemented
939C22×C4#70914yes—
940C22×C4C23×D511yescharacteristic
941C22×C4C23×D511yescharacteristic
942C22×C4C23×D511yescharacteristic
943C22×C4C23×D511yescharacteristic
944C22×C4C23×D511yescharacteristic
945C22×C4C23×D511yescharacteristic
946C22×C4C23×D511yescharacteristic
947C22×C4C23×D511yescharacteristic
948C22×C4C23×D511yescharacteristic
949C22×C4C23×D511yescharacteristic
950C22×C4C23×D511yescharacteristic
951C22×C4C23×D511yescharacteristic
952C22×C4C23×D511yescharacteristic
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—104no—
956C4⋊C4—104no—
957C4⋊C4—104no—
958C4⋊C4—104no—
959C4⋊C4—104no—
960C4⋊C4—102no—
961C4⋊C4—102no—
962C4⋊C4—102no—
963C4⋊C4—102no—
964C4⋊C4—102no—
965C4⋊C4—202no—
966C4⋊C4—202no—
967C4⋊C4—202no—
968C4⋊C4C2×D2014yescomplemented
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—104no—
973C22⋊C4—104no—
974C22⋊C4—104no—
975C22⋊C4—104no—
976C22⋊C4—104no—
977C22⋊C4—104no—
978C22⋊C4—104no—
979C22⋊C4—104no—
980C22⋊C4—104no—
981C22⋊C4—104no—
982C22⋊C4—104no—
983C22⋊C4—104no—
984C22⋊C4—104no—
985C22⋊C4—104no—
986C22⋊C4—104no—
987C22⋊C4—104no—
988C22⋊C4—104no—
989C22⋊C4—104no—
990C22⋊C4—202no—
991C22⋊C4—202no—
992C22⋊C4—202no—
993C22⋊C4—202no—
994C22⋊C4—202no—
995C22⋊C4—202no—
996C22⋊C4—202no—
997C22⋊C4—202no—
998C22⋊C4—202no—
999C22⋊C4C2×D2014yes—
1000C22⋊C4C2×D2014yescomplemented
1001C22⋊C4#70914yes—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C42—22no—
1006C42—22no—
1007C42—22no—
1008C42—22no—
1009C42—41no—
1010C42—41no—
1011C42—41no—
1012C42—41no—
1013C42—41no—
1014C42—104no—
1015C42C2×D2014yescomplemented
1016C2×C5—24no—
1017C2×C5—42no—
1018C2×C5C2×#53211yescharacteristic
1019C2×C5C2×#53811yescharacteristic
1020C2×C5#346011yescharacteristic
1021C2×C5#349611yescharacteristic
1022C2×C5#349811yescharacteristic
1023C2×C5#351411yescharacteristic
1024C2×C5#351911yescharacteristic
1025D5—82no—
1026D5—82no—
1027D5—82no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—102no—
1039C23—102no—
1040C23—102no—
1041C23—102no—
1042C23—102no—
1043C23—102no—
1044C23—102no—
1045C23—102no—
1046C23—102no—
1047C23—102no—
1048C23—102no—
1049C23—102no—
1050C23—102no—
1051C23—102no—
1052C23—102no—
1053C23—102no—
1054C23—102no—
1055C23—102no—
1056C23—102no—
1057C23—102no—
1058C23—102no—
1059C23—208no—
1060C23—208no—
1061C23—208no—
1062C23—404no—
1063C23—404no—
1064C23—404no—
1065C23—404no—
1066C23C22×D2012yes—
1067C23C22×D2012yes—
1068C23C2×#70912yes—
1069C23C2×#70912yes—
1070C23C24×D511yescharacteristic
1071Q8—404no—
1072D4—28no—
1073D4—208no—
1074D4—208no—
1075D4—204no—
1076D4—204no—
1077D4—204no—
1078D4—404no—
1079D4—404no—
1080D4—404no—
1081D4—404no—
1082D4—404no—
1083D4—404no—
1084D4—404no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—28no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—44no—
1118C2×C4—102no—
1119C2×C4—102no—
1120C2×C4—102no—
1121C2×C4—102no—
1122C2×C4—102no—
1123C2×C4—102no—
1124C2×C4—102no—
1125C2×C4—102no—
1126C2×C4—102no—
1127C2×C4—102no—
1128C2×C4—102no—
1129C2×C4—102no—
1130C2×C4—102no—
1131C2×C4—102no—
1132C2×C4—102no—
1133C2×C4—404no—
1134C2×C4—404no—
1135C2×C4C22×D2012yes—
1136C2×C4C22×D2012yes—
1137C2×C4C22×D2012yes—
1138C2×C4C22×D2012yes—
1139C2×C4C22×D2012yes—
1140C2×C4C2×#70912yes—
1141C2×C4C2×#70912yes—
1142C2×C4C2×#70912yes—
1143C2×C4C2×#70912yes—
1144C2×C4#414412yes—
1145C2×C4#414912yes—
1146C2×C4#414912yes—
1147C5#3500711yescharacteristic, complemented, Sylow
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—202no—
1162C22—202no—
1163C22—202no—
1164C22—202no—
1165C22—202no—
1166C22—202no—
1167C22—202no—
1168C22—202no—
1169C22—202no—
1170C22—202no—
1171C22—202no—
1172C22—202no—
1173C22—202no—
1174C22—202no—
1175C22—202no—
1176C22—202no—
1177C22—202no—
1178C22—202no—
1179C22—202no—
1180C22—202no—
1181C22—202no—
1182C22—4016no—
1183C22#6581114yes—
1184C22C23×D2011yescharacteristic
1185C22C22×#70911yescharacteristic
1186C22C22×#70911yescharacteristic
1187C22C2×#414411yescharacteristic
1188C22C2×#414911yescharacteristic
1189C22C2×#414911yescharacteristic
1190C22#6628311yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—22no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—202no—
1204C4—202no—
1205C4—202no—
1206C4—202no—
1207C4—202no—
1208C4#6589414yescomplemented
1209C2—24no—
1210C2—42no—
1211C2—402no—
1212C2—402no—
1213C2—402no—
1214C2C2×#6581111yescharacteristic
1215C2C2×#6589411yescharacteristic
1216C2#1061768711yescharacteristic
1217C2#1061769111yescharacteristic
1218C2#1061773911yescharacteristic
1219C2#1061774711yescharacteristic
1220C2#1061775311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC42×C5×D4C2
hypercenterC42×D4D5
hypocenterC5#35007
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
1. C2×#65894C2semidirect
2. C42×C5×D4C2semidirect
3. #10614138C2semidirect
4. #10614134C2semidirect
5. #10614083C2semidirect
6. #10613812C2semidirect
7. #10613811C2semidirect
8. C4×#4076C2semidirect
9. C2×#65228C2semidirect
10. #10605547C2semidirect
11. #10605534C2semidirect
12. #10605511C2semidirect
13. #10605423C2semidirect
14. #10605342C2semidirect
15. #10605331C2semidirect
16. #10605325C2semidirect
17. #10605318C2semidirect
18. #10605300C2semidirect
19. #10605238C2semidirect
20. #10605224C2semidirect
21. #10605218C2semidirect
22. #10605045C2semidirect
23. #10605044C2semidirect
29. C22×C42×C5C22semidirect
35. C2×#4076C22semidirect
36. C2×#4076C22semidirect
37. C2×#4076C22semidirect
38. C2×#4075C22semidirect
44. C2×#4044C22semidirect
45. C2×#4040C22semidirect
46. C2×#4031C22semidirect
47. C2×#4030C22semidirect
51. C2×#4022C22semidirect
52. C2×#4021C22semidirect
53. C2×#4021C22semidirect
56. C2×C4×D20C22semidirect
57. C2×#4015C22semidirect
58. C4×C5×C4⋊C4C22semidirect
59. C4×C5×C4⋊C4C22semidirect
60. C4×C5×C4⋊C4C22semidirect
64. C4×C5×C22⋊C4C22semidirect
65. C4×C5×C22⋊C4C22semidirect
66. C4×C5×C22⋊C4C22semidirect
67. C43×C5C22semidirect
69. #65502C22semidirect
71. #65501C22semidirect
72. #65283C22semidirect
73. #65283C22semidirect
75. #65280C22semidirect
76. #65250C22semidirect
77. #65250C22semidirect
79. #65249C22semidirect
83. #65229C22semidirect
84. #65229C22semidirect
85. #65229C22semidirect
86. #65229C22semidirect
87. #65229C22semidirect
88. #65229C22semidirect
99. #65228C22semidirect
100. #65228C22semidirect
101. #65228C22semidirect
102. #65228C22semidirect
103. #65228C22semidirect
104. #65228C22semidirect
105. C4×#685C22semidirect
106. #65224C22semidirect
107. C4×C4⋊Dic5C22semidirect
108. #65217C22semidirect
109. #65217C22semidirect
110. #65217C22semidirect
111. #65217C22semidirect
112. #64963C22semidirect
113. #64962C22semidirect
114. #64961C22semidirect
115. #64961C22semidirect
118. #64959C22semidirect
119. #64959C22semidirect
120. #64954C22semidirect
121. #64954C22semidirect
122. #64950C22semidirect
123. #64945C22semidirect
153. C4×C5×D4D4semidirect
281. C42×D4D5semidirect
313. C22×C4×C5C2×D4semidirect
381. C5×C4⋊C4C2×D4semidirect
386. C5×C22⋊C4C2×D4semidirect
400. C42×C5C2×D4semidirect
475. C22×C42C2×D5semidirect
531. C4×C4⋊C4C2×D5semidirect
532. C4×C4⋊C4C2×D5semidirect
533. C4×C4⋊C4C2×D5semidirect
538. C4×C22⋊C4C2×D5semidirect
539. C4×C22⋊C4C2×D5semidirect
540. C4×C22⋊C4C2×D5semidirect
541. C43C2×D5semidirect
713. C4×D4D20semidirect
850. C4×C5#538semidirect
938. C22×C4C2×D20semidirect
968. C4⋊C4C2×D20semidirect
1000. C22⋊C4C2×D20semidirect
1015. C42C2×D20semidirect
1147. C5#35007semidirect
1208. C4#65894semidirect

Maximal subgroups

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

subgroupindex
C2×#658942
C42×C5×D42
#106141382
#106141342
#106140832
#106138122
#106138112
C4×#40762
C2×#652282
#106055472
#106055342
#106055112
#106054232
#106053422
#106053312
#106053252
#106053182
#106053002
#106052382
#106052242
#106052182
#106050452
#106050442
#350075