Finite Group Databasebeta

← #14453248

Subgroups — #14453248

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6715C211yesmaximal, characteristic, complemented
2C3×#66140C211yesmaximal, characteristic, complemented
3C2×#91478C211yesmaximal, characteristic, complemented
4#11754647C211yesmaximal, characteristic, complemented
5C5×#5217C211yesmaximal, characteristic, complemented
6#11749151C211yesmaximal, characteristic, complemented
7#11749094C211yesmaximal, characteristic, complemented
8#11749092C211yesmaximal, characteristic, complemented
9#11749027C211yesmaximal, characteristic, complemented
10#11749026C211yesmaximal, characteristic, complemented
11#11748980C211yesmaximal, characteristic, complemented
12#11748979C211yesmaximal, characteristic, complemented
13#11748551C211yesmaximal, characteristic, complemented
14#11748547C211yesmaximal, characteristic, complemented
15#11748507C211yesmaximal, characteristic, complemented
16#10611753—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic, complemented
18C22×D60C2211yescharacteristic
19C2×C3×#711C2211yescharacteristic, complemented
20C2×#6790—21no—
21C2×D5×D12C2211yescharacteristic, complemented
22C2×#6715—24no—
23C2×#6715C2211yescharacteristic
24C2×#6715C2211yescharacteristic
25C2×#6715C2211yescharacteristic, complemented
26C2×#6715C2211yescharacteristic, complemented
27C22×C3⋊#168C2211yescharacteristic, complemented
28C2×C5×#213C2211yescharacteristic, complemented
29C2×C5×#213C2211yescharacteristic, complemented
30C5×#930C2211yescharacteristic
31C3×#4099—21no—
32C2×C3×C22⋊Dic5—21no—
33C3×#4085—21no—
34C3×#4084C2211yescharacteristic, complemented
35C3×#4082C2211yescharacteristic, complemented
36C3×#4081—21no—
37C3×D4×Dic5C2211yescharacteristic, complemented
38C3×C4×C22⋊D5C2211yescharacteristic
39C3×#4070C2211yescharacteristic, complemented
40#91573—21no—
41#91478—24no—
42#91476—21no—
43#91451C2211yescharacteristic, complemented
44#91450C2211yescharacteristic, complemented
45#91420—21no—
46#91418C2211yescharacteristic, complemented
47C2×#6658C2211yescharacteristic, complemented
48C2×#6658C2211yescharacteristic, complemented
49C2×#6656C2211yescharacteristic, complemented
50C2×#6649C2211yescharacteristic, complemented
51C5×#832C2211yescharacteristic, complemented
52C5×#832C2211yescharacteristic, complemented
53C5×#830C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90982C2211yescharacteristic, complemented
56#90970C2211yescharacteristic, complemented
57#90968C2211yescharacteristic, complemented
58#90968C2211yescharacteristic, complemented
59#90966C2211yescharacteristic, complemented
60#90955C2211yescharacteristic, complemented
61#90952C2211yescharacteristic, complemented
62#83502—51nomaximal, Hall
63#66140D311yescharacteristic, complemented
64C22×#686—31no—
65C2×#4057—31no—
66#65943—31no—
67C5×#447—31no—
68#65445—31no—
69#65443—31no—
70#65439—31no—
71#65330—31no—
72#65076—31no—
73#65074—31no—
74#65071—31no—
75#65070—31no—
76#65020—31no—
77#65019—31no—
78C24×C3×C5—21no—
79C23×D15—21no—
80C22×D3×D5—21no—
81C2×C3×C5×D4—22no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—41no—
84C2×C3×C5×D4C2311yescharacteristic
85C2×C3×C5×D4C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C2×D60—22no—
88C2×D60—21no—
89C2×D60—41no—
90C2×D60C2311yescharacteristic
91C2×D60C2311yescharacteristic
92C2×C5×#67—21no—
93C2×C5×D12C2311yescharacteristic
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5D411yescharacteristic
97C22×C3×Dic5—21no—
98C22×C3×Dic5—21no—
99C3×#711—22no—
100C3×#711—41no—
101C2×C3×C4×D5C2311yescharacteristic
102C2×C3×Dic10C2311yescharacteristic
103#6790—44no—
104C2×#1203—21no—
105C2×#1203—21no—
106C2×#1203—21no—
107C2×#1202—21no—
108C2×#1200—21no—
109D5×D12—22no—
110D5×D12—41no—
111#6715—22no—
112#6715—22no—
113#6715—22no—
114#6715D414yescomplemented
115C2×C3⋊#168—22no—
116C2×C3⋊#168C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C5×#213—22no—
119C5×#213—41no—
120C5×(C2×D3)⋊C4—21no—
121C5×C4⋊Dic3C2311yescharacteristic
122C2×C5×C3⋊C8C2311yescharacteristic
123C2×C5×C3⋊C8C2311yescharacteristic
124C3×C22⋊Dic5—21no—
125C3×C22⋊Dic5—21no—
126C3×C22⋊Dic5—21no—
127C3×C22⋊Dic5—21no—
128C3×C22⋊Dic5—21no—
129C3×C22⋊Dic5D411yescharacteristic
130C3×#685D411yescharacteristic
131C3×C4⋊Dic5C2311yescharacteristic
132C3×#683—21no—
133C3×#683D411yescharacteristic
134C3×C4×Dic5C2311yescharacteristic
135#6667—21no—
136#6667—21no—
137#6658—22no—
138#6658—41no—
139#6656—22no—
140#6649—22no—
141C3×#546—51no—
142C2×#949—51no—
143C22×#213—51no—
144D4×D12—51no—
145#5238—51no—
146#5217D511yescharacteristic, complemented
147#5058—51no—
148#5057—51no—
149#5048—51no—
150#5046—51no—
151#5039—51no—
152#5036—51no—
153#5015—51no—
154#5014—51no—
155#5011—51no—
156C22×C5×D4C2×D311yescharacteristic, complemented
157C2×#711C2×D311yescharacteristic, complemented
158C2×D4×D5—31no—
159C2×D4×D5—61no—
160C22×D20—31no—
161C2×C5×D8—31no—
162C2×C5×D8—31no—
163C5×#121—31no—
164#4099—21no—
165C2×C22⋊Dic5—21no—
166#4086—31no—
167#4085—21no—
168#4084C2×D311yescharacteristic, complemented
169#4083—61no—
170#4082C2×D311yescharacteristic, complemented
171#4081—21no—
172D4×Dic5C2×D311yescharacteristic, complemented
173C2×#687—31no—
174C2×#686—31no—
175C2×#686—31no—
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—64no—
179C4×C22⋊D5C2×D311yescharacteristic
180#4070C2×D311yescharacteristic, complemented
181C22×#168—31no—
182#4057—64no—
183C2×#677—31no—
184C2×#677—31no—
185C2×#676—31no—
186#4041—31no—
187#4039—31no—
188#4030—61no—
189#4028—61no—
190C5×#102—31no—
191C5×#102—31no—
192C5×C22⋊C8—31no—
193#3964—31no—
194#3953—31no—
195#3953—31no—
196#3952—31no—
197#3947—31no—
198#3946—31no—
199#3942—31no—
200#3940—31no—
201#3264—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—42no—
205C23×C3×C5—42no—
206C23×C3×C5—81no—
207C23×C3×C5C2×D411yescharacteristic
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—42no—
211C22×D15—42no—
212C22×D15—81no—
213C22×C5×D3—21no—
214C22×C3×D5C2×D411yescharacteristic
215C2×D3×D5—42no—
216C2×D3×D5—42no—
217C2×D3×D5—81no—
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—42no—
222C3×C5×D4C2×D412yescomplemented
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5C2×D411yescharacteristic
226C2×C3×C4×C5C2411yescharacteristic
227D60—21no—
228D60—21no—
229D60—21no—
230D60—42no—
231D60C2×D412yes—
232C5×#67—42no—
233C2×C5×Dic3—21no—
234C5×D12—21no—
235C5×D12—21no—
236C3×C22⋊D5—22no—
237C3×C22⋊D5—42no—
238C3×C22⋊D5—81no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—42no—
242C2×C3×Dic5—81no—
243C2×C3×Dic5C2×D411yescharacteristic
244C2×C3×Dic5C2×D411yescharacteristic
245C2×C3×Dic5C2×D411yescharacteristic
246C3×C4×D5—21no—
247C3×C4×D5—21no—
248C3×Dic10—21no—
249C3×Dic10—21no—
250#1203—42no—
251#1203—42no—
252#1203—81no—
253#1202—42no—
254#1200—42no—
255C3⋊#168—21no—
256C3⋊#168C2×D412yescomplemented
257C5×C3⋊C8—21no—
258C5×C3⋊C8—21no—
259C2×C3×#41—51no—
260C22×C3×D4C2×D511yescharacteristic, complemented
261C2×D3×D4—101no—
262C22×D12—51no—
263C22×D12—51no—
264C3×#124—51no—
265C3×#123—101no—
266C3×C22⋊Q8—51no—
267C3×#121—51no—
268C3×#121—101no—
269C3×#120—101no—
270C3×C4×D4—51no—
271C3×C4×D4—51no—
272C2×C3×C22⋊C4—101no—
273#949—104no—
274C2×#215—51no—
275C2×#215—51no—
276C2×#215—51no—
277C2×#213—51no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281C2×#213—104no—
282C2×#213C2×D511yescharacteristic, complemented
283C2×#213C2×D511yescharacteristic, complemented
284#930—51no—
285#930C2×D511yescharacteristic
286C2×#208—51no—
287C22×C3⋊C8—51no—
288#895—101no—
289#882—101no—
290#882—101no—
291#874—51no—
292C4×D12—51no—
293#835—51no—
294#832C2×D511yescharacteristic, complemented
295#832C2×D511yescharacteristic, complemented
296#830—51no—
297#830C2×D511yescharacteristic, complemented
298#809—51no—
299#809—51no—
300#809—51no—
301#808—51no—
302C4⋊(C3⋊C8)—51no—
303#803—51no—
304C24×C5—21no—
305C23×D5—61no—
306C23×D5—61no—
307C2×C5×D4—22no—
308C2×C5×D4—21no—
309C2×C5×D4—31no—
310C2×C5×D4—41no—
311C2×C5×D4—61no—
312C2×C5×D4C22×D311yescharacteristic
313C2×C5×D4C22×D311yescharacteristic
314C22×C4×C5C22×D311yescharacteristic
315C2×C22⋊D5—21no—
316C2×C22⋊D5—21no—
317C2×C22⋊D5—61no—
318C2×C22⋊D5—61no—
319C2×C22⋊D5—61no—
320C2×C22⋊D5#6711yescharacteristic
321C22×Dic5—21no—
322C22×Dic5—21no—
323#711—22no—
324#711—41no—
325D4×D5—62no—
326D4×D5—121no—
327D4×D5—124no—
328C2×D20—31no—
329C2×D20—31no—
330C2×D20—62no—
331C2×D20—61no—
332C2×D20—61no—
333C2×D20—121no—
334C2×C4×D5—61no—
335C2×C4×D5C22×D311yescharacteristic
336C2×Dic10C22×D311yescharacteristic
337C5×D8—62no—
338C5×D8—121no—
339C2×C5×C8—31no—
340C2×C5×C8—31no—
341C5×C4⋊C4—31no—
342C5×C22⋊C4—61no—
343C22⋊Dic5—21no—
344C22⋊Dic5—21no—
345C22⋊Dic5—21no—
346C22⋊Dic5—21no—
347C22⋊Dic5—21no—
348C22⋊Dic5#6711yescharacteristic
349#687—62no—
350#686—34no—
351#686—62no—
352#686—62no—
353#686—62no—
354#685—61no—
355#685—61no—
356#685#6711yescharacteristic
357C4⋊Dic5C22×D311yescharacteristic
358#683—21no—
359#683#6711yescharacteristic
360C4×Dic5C22×D311yescharacteristic
361C2×#168—31no—
362C2×#168—31no—
363C2×#168—62no—
364#677—62no—
365#677—121no—
366#676—62no—
367C2×AGL(1,ℤ/8)—151no—
368C22×D8—151no—
369#546—51no—
370D42—151no—
371#496—151no—
372#469—151no—
373#465—151no—
374#463—151no—
375#459—151no—
376#450—151no—
377#449—151no—
378#447—31no—
379#447—151no—
380#442—151no—
381#435—151no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5—22no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—84no—
391C22×C3×C5AGL(1,ℤ/8)12yescomplemented
392C22×C3×C5C22×D411yescharacteristic
393C2×D15—22no—
394C2×D15—41no—
395C2×D15—41no—
396C2×D15—41no—
397C2×D15—41no—
398C2×D15—41no—
399C2×D15—84no—
400C2×C5×D3—41no—
401C2×C5×D3—41no—
402C2×C5×D3—41no—
403C2×C3×D5—21no—
404C2×C3×D5—21no—
405C2×C3×D5—21no—
406D3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5C22×D411yescharacteristic
409C3×C4×C5H(5,𝔽2)11yescharacteristic
410C3×Dic5—21no—
411C3×Dic5—21no—
412C3×Dic5—21no—
413C3×Dic5—41no—
414C3×Dic5—41no—
415C5×Dic3—41no—
416C24×C3—21no—
417C23×D3—101no—
418C23×D3—101no—
419C3×#41—102no—
420C3×#41—201no—
421C2×C3×Q8—51no—
422C2×C3×D4—22no—
423C2×C3×D4—21no—
424C2×C3×D4—41no—
425C2×C3×D4—51no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4C22×D511yescharacteristic
429C2×C3×D4C22×D511yescharacteristic
430C22×C3×C4—51no—
431C22×C3×C4—101no—
432C22×C3×C4—101no—
433C22×C3×C4C22×D511yescharacteristic
434C2×#67—21no—
435C2×#67—101no—
436D3×D4—204no—
437C2×D12—51no—
438C2×D12—51no—
439C2×D12—102no—
440C2×D12—102no—
441C2×D12—101no—
442C2×D12—101no—
443C2×D12—101no—
444C2×D12—101no—
445C2×D12—201no—
446C2×D12—201no—
447C2×D12C22×D511yescharacteristic
448C2×C4×D3—101no—
449C3×C4⋊C4—51no—
450C3×C4⋊C4—51no—
451C3×C4⋊C4—101no—
452C3×C22⋊C4—51no—
453C3×C22⋊C4—51no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C42—51no—
460#215—102no—
461#215—102no—
462#215—201no—
463#213—22no—
464#213—41no—
465#213—54no—
466#213—102no—
467#213—102no—
468#213—102no—
469(C2×D3)⋊C4—21no—
470(C2×D3)⋊C4—101no—
471(C2×D3)⋊C4—101no—
472C4⋊Dic3C22×D511yescharacteristic
473#208—102no—
474C2×C3⋊C8—51no—
475C2×C3⋊C8—51no—
476C2×C3⋊C8—102no—
477C2×C3⋊C8C22×D511yescharacteristic
478C2×C3⋊C8C22×D511yescharacteristic
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—42no—
482C23×C5—42no—
483C23×C5—61no—
484C23×C5—81no—
485C23×C5C2×#6711yescharacteristic
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—122no—
489C22×D5—122no—
490C22×D5—122no—
491C22×D5—122no—
492C22×D5—241no—
493C22×D5—241no—
494C22×D5C2×#6711yescharacteristic
495C5×D4—21no—
496C5×D4—21no—
497C5×D4—21no—
498C5×D4—42no—
499C5×D4—61no—
500C5×D4—61no—
501C5×D4—122no—
502C5×D4D3×D412yescomplemented
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—61no—
506C2×C4×C5C2×#6711yescharacteristic
507C2×C4×C5C23×D311yescharacteristic
508C22⋊D5—22no—
509C22⋊D5—42no—
510C22⋊D5—81no—
511C22⋊D5—122no—
512C22⋊D5—122no—
513C22⋊D5—241no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—42no—
517C2×Dic5—81no—
518C2×Dic5C2×#6711yescharacteristic
519C2×Dic5C2×#6711yescharacteristic
520C2×Dic5C2×#6711yescharacteristic
521D20—32no—
522D20—61no—
523D20—61no—
524D20—61no—
525D20—122no—
526D20—122no—
527C4×D5—21no—
528C4×D5—21no—
529C4×D5—122no—
530Dic10—21no—
531Dic10—21no—
532C5×C8—61no—
533C5×C8—61no—
534#168—32no—
535#168—61no—
536C2×#41—51no—
537C22×D4—151no—
538C22×D4—151no—
539C22×D4—301no—
540C22×D4D3×D511yescharacteristic, complemented
541AGL(1,ℤ/8)—304no—
542C2×SD16—151no—
543C2×SD16—151no—
544C2×SD16—151no—
545C2×D8—31no—
546C2×D8—31no—
547C2×D8—151no—
548C2×D8—151no—
549C2×D8—151no—
550C2×D8—151no—
551C2×D8—304no—
552C2×M16—151no—
553C22×C8—151no—
554#127—151no—
555#124—51no—
556#123—101no—
557C22⋊Q8—51no—
558#121—31no—
559#121—51no—
560#121—101no—
561#121—151no—
562#121—301no—
563#120—101no—
564#120—301no—
565#120—301no—
566C4×D4—51no—
567C4×D4—51no—
568C4×D4—151no—
569C2×C22⋊C4—101no—
570#106—151no—
571C4⋊C8—151no—
572#103—151no—
573#102—31no—
574#102—31no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—31no—
579C22⋊C8—151no—
580#97—151no—
581C2×C3×C5—22no—
582C2×C3×C5—42no—
583C2×C3×C5—81no—
584C2×C3×C5D4211yescharacteristic
585C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
586C2×C3×C5#57611yescharacteristic
587D15—42no—
588D15—81no—
589C3×D5—41no—
590C5×D3—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—51no—
596C23×C3—81no—
597C23×C3D4×D511yescharacteristic
598C22×D3—21no—
599C22×D3—101no—
600C22×D3—101no—
601C22×D3—202no—
602C22×D3—202no—
603C22×D3—202no—
604C22×D3—202no—
605C22×D3—401no—
606C22×D3—401no—
607C3×Q8—101no—
608C3×Q8—101no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—42no—
613C3×D4—102no—
614C3×D4—202no—
615C3×D4—401no—
616C3×D4D4×D512yescomplemented
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—51no—
620C2×C3×C4—51no—
621C2×C3×C4—51no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—202no—
627C2×C3×C4—401no—
628C2×C3×C4D4×D511yescharacteristic
629C2×C3×C4C23×D511yescharacteristic
630#67—42no—
631#67—202no—
632C2×Dic3—21no—
633D12—21no—
634D12—21no—
635D12—52no—
636D12—101no—
637D12—101no—
638D12—101no—
639D12—202no—
640D12—202no—
641D12—202no—
642D12—401no—
643C4×D3—202no—
644C3⋊C8—21no—
645C3⋊C8—21no—
646C3⋊C8—52no—
647C3⋊C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—22no—
651C22×C5—41no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5—41no—
655C22×C5—41no—
656C22×C5—84no—
657C22×C5—121no—
658C22×C5—121no—
659C22×C5—121no—
660C22×C5#94912yescomplemented
661C22×C5C22×#6711yescharacteristic
662C2×D5—21no—
663C2×D5—21no—
664C2×D5—21no—
665C2×D5—62no—
666C2×D5—121no—
667C2×D5—121no—
668C2×D5—121no—
669C2×D5—121no—
670C2×D5—121no—
671C2×D5—244no—
672C2×D5—244no—
673C4×C5—21no—
674C4×C5—121no—
675C4×C5C2×D3×D411yescharacteristic
676C4×C5#100411yescharacteristic
677Dic5—21no—
678Dic5—21no—
679Dic5—21no—
680Dic5—41no—
681Dic5—41no—
682C24—21no—
683C24—301no—
684C24—301no—
685#41—102no—
686#41—201no—
687C2×Q8—51no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—31no—
691C2×D4—41no—
692C2×D4—51no—
693C2×D4—61no—
694C2×D4—101no—
695C2×D4—101no—
696C2×D4—151no—
697C2×D4—151no—
698C2×D4—302no—
699C2×D4—301no—
700C2×D4—301no—
701C2×D4—301no—
702C2×D4—301no—
703C2×D4—302no—
704C2×D4—301no—
705C2×D4—601no—
706C2×D4—601no—
707C2×D4—604no—
708C2×D4C2×D3×D511yescharacteristic
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—51no—
711C22×C4—101no—
712C22×C4—101no—
713C22×C4—301no—
714C22×C4C2×D3×D511yescharacteristic
715SD16—302no—
716SD16—302no—
717SD16—601no—
718D8—62no—
719D8—121no—
720D8—154no—
721D8—302no—
722D8—302no—
723D8—302no—
724M16—302no—
725C2×C8—31no—
726C2×C8—31no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—31no—
731C4⋊C4—51no—
732C4⋊C4—51no—
733C4⋊C4—101no—
734C22⋊C4—51no—
735C22⋊C4—51no—
736C22⋊C4—61no—
737C22⋊C4—101no—
738C22⋊C4—101no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—101no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42—51no—
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—22no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—84no—
755C22×C3—101no—
756C22×C3—101no—
757C22×C3—101no—
758C22×C3#405712yescomplemented
759C22×C3C2×D4×D511yescharacteristic
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—102no—
764C2×D3—201no—
765C2×D3—201no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3—201no—
769C2×D3—404no—
770C2×D3—404no—
771C3×C4—21no—
772C3×C4—101no—
773C3×C4—101no—
774C3×C4—101no—
775C3×C4—201no—
776C3×C4—201no—
777C3×C4C2×D4×D511yescharacteristic
778C3×C4#414411yescharacteristic
779Dic3—41no—
780C2×C5—22no—
781C2×C5—42no—
782C2×C5—81no—
783C2×C5—241no—
784C2×C5D4×#6711yescharacteristic
785C2×C5C2×#94911yescharacteristic
786C2×C5#583511yescharacteristic
787D5—41no—
788D5—122no—
789D5—241no—
790C23—21no—
791C23—21no—
792C23—42no—
793C23—42no—
794C23—51no—
795C23—61no—
796C23—81no—
797C23—301no—
798C23—301no—
799C23—602no—
800C23—602no—
801C23—602no—
802C23—602no—
803C23—1201no—
804C23—1201no—
805C23D5×#6711yescharacteristic
806Q8—101no—
807Q8—101no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—42no—
812D4—61no—
813D4—61no—
814D4—102no—
815D4—122no—
816D4—152no—
817D4—202no—
818D4—301no—
819D4—301no—
820D4—301no—
821D4—401no—
822D4—602no—
823D4—602no—
824D4—602no—
825D4—602no—
826D4—1201no—
827D4#679012yescomplemented
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—51no—
831C2×C4—51no—
832C2×C4—51no—
833C2×C4—61no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—202no—
839C2×C4—401no—
840C2×C4—602no—
841C2×C4D5×#6711yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—61no—
844C8—61no—
845C8—152no—
846C8—301no—
847C2×C3—22no—
848C2×C3—42no—
849C2×C3—81no—
850C2×C3—201no—
851C2×C3#6592411yescharacteristic
852C2×C3C2×#405711yescharacteristic
853C2×C3#6610811yescharacteristic
854D3—81no—
855D3—202no—
856D3—401no—
857C5#8350211yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—22no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—84no—
867C22—101no—
868C22—101no—
869C22—101no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—302no—
874C22—601no—
875C22—601no—
876C22—601no—
877C22—601no—
878C22—601no—
879C22—1204no—
880C22—1204no—
881C22#9147812yescomplemented
882C22C2×D5×#6711yescharacteristic
883C4—21no—
884C4—101no—
885C4—101no—
886C4—101no—
887C4—121no—
888C4—201no—
889C4—201no—
890C4C2×#679011yescharacteristic
891C4#9204911yescharacteristic
892C3#1061175311yescharacteristic, complemented, Sylow
893C2—22no—
894C2—42no—
895C2—81no—
896C2—201no—
897C2—241no—
898C2—602no—
899C2—1201no—
900C2C2×#9147811yescharacteristic
901C2#1175469211yescharacteristic
902C2#1175543711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6715C2semidirect
2. C3×#66140C2semidirect
3. C2×#91478C2semidirect
4. #11754647C2semidirect
5. C5×#5217C2semidirect
6. #11749151C2semidirect
7. #11749094C2semidirect
8. #11749092C2semidirect
9. #11749027C2semidirect
10. #11749026C2semidirect
11. #11748980C2semidirect
12. #11748979C2semidirect
13. #11748551C2semidirect
14. #11748547C2semidirect
15. #11748507C2semidirect
17. C22×C3×C5×D4C22semidirect
19. C2×C3×#711C22semidirect
21. C2×D5×D12C22semidirect
25. C2×#6715C22semidirect
26. C2×#6715C22semidirect
27. C22×C3⋊#168C22semidirect
28. C2×C5×#213C22semidirect
29. C2×C5×#213C22semidirect
34. C3×#4084C22semidirect
35. C3×#4082C22semidirect
37. C3×D4×Dic5C22semidirect
39. C3×#4070C22semidirect
43. #91451C22semidirect
44. #91450C22semidirect
46. #91418C22semidirect
47. C2×#6658C22semidirect
48. C2×#6658C22semidirect
49. C2×#6656C22semidirect
50. C2×#6649C22semidirect
51. C5×#832C22semidirect
52. C5×#832C22semidirect
53. C5×#830C22semidirect
54. #90986C22semidirect
55. #90982C22semidirect
56. #90970C22semidirect
57. #90968C22semidirect
58. #90968C22semidirect
59. #90966C22semidirect
60. #90955C22semidirect
61. #90952C22semidirect
63. #66140D3semidirect
114. #6715D4semidirect
146. #5217D5semidirect
156. C22×C5×D4C2×D3semidirect
157. C2×#711C2×D3semidirect
168. #4084C2×D3semidirect
170. #4082C2×D3semidirect
172. D4×Dic5C2×D3semidirect
180. #4070C2×D3semidirect
222. C3×C5×D4C2×D4semidirect
256. C3⋊#168C2×D4semidirect
260. C22×C3×D4C2×D5semidirect
282. C2×#213C2×D5semidirect
283. C2×#213C2×D5semidirect
294. #832C2×D5semidirect
295. #832C2×D5semidirect
297. #830C2×D5semidirect
391. C22×C3×C5AGL(1,ℤ/8)semidirect
502. C5×D4D3×D4semidirect
540. C22×D4D3×D5semidirect
616. C3×D4D4×D5semidirect
660. C22×C5#949semidirect
745. C3×C5#3264semidirect
758. C22×C3#4057semidirect
827. D4#6790semidirect
857. C5#83502semidirect
881. C22#91478semidirect
892. C3#10611753semidirect

Maximal subgroups

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

subgroupindex
C22×#67152
C3×#661402
C2×#914782
#117546472
C5×#52172
#117491512
#117490942
#117490922
#117490272
#117490262
#117489802
#117489792
#117485512
#117485472
#117485072
#106117533
#835025