Finite Group Databasebeta

← #14453783

Subgroups — #14453783

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65966C211yesmaximal, characteristic, complemented
2C2×#91513C211yesmaximal, characteristic, complemented
3#11754540C211yesmaximal, characteristic
4C22×#6656C211yesmaximal, characteristic, complemented
5#11751152C211yesmaximal, characteristic, complemented
6C5×#5046C211yesmaximal, characteristic, complemented
7#11749312C211yesmaximal, characteristic, complemented
8#11749267C211yesmaximal, characteristic, complemented
9#11749220C211yesmaximal, characteristic, complemented
10#11748556C211yesmaximal, characteristic, complemented
11#11748507C211yesmaximal, characteristic, complemented
12#11747511C211yesmaximal, characteristic, complemented
13#11747370C211yesmaximal, characteristic, complemented
14#11747311C211yesmaximal, characteristic, complemented
15#11747217C211yesmaximal, characteristic, complemented
16#10611900—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic, complemented
19C22×C3×Dic10C2211yescharacteristic
20C2×#6772C2211yescharacteristic
21C3×C5×C22⋊Q8C2211yescharacteristic
22C2×#6718C2211yescharacteristic, complemented
23#91813C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic
25C2×C5×#215C2211yescharacteristic
26C2×C5×#215C2211yescharacteristic
27C3×#4090C2211yescharacteristic, complemented
28C3×C4×C22⋊D5C2211yescharacteristic
29C3×#4043C2211yescharacteristic, complemented
30C3×#4042—21no—
31C3×#4034—21no—
32C3×#4033C2211yescharacteristic, complemented
33C3×#4027—21no—
34C3×#4024—21no—
35#91568—21no—
36D3×C22⋊Dic5—21no—
37#91513—24no—
38#91453—21no—
39#91449C2211yescharacteristic
40#91423—21no—
41Dic5×D12C2211yescharacteristic
42#91373C2211yescharacteristic
43C2×#6662C2211yescharacteristic, complemented
44C2×#6662C2211yescharacteristic, complemented
45C2×#6656—24no—
46C2×#6656C2211yescharacteristic
47C2×#6656C2211yescharacteristic
48C2×#6656C2211yescharacteristic
49C2×#6656C2211yescharacteristic
50C2×#6649C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91094C2211yescharacteristic, complemented
53#91091C2211yescharacteristic, complemented
54C5×#830C2211yescharacteristic
55C5×#809C2211yescharacteristic
56C5×#809C2211yescharacteristic
57#90982C2211yescharacteristic, complemented
58#90971C2211yescharacteristic, complemented
59#90971C2211yescharacteristic, complemented
60#90955C2211yescharacteristic, complemented
61#90952C2211yescharacteristic, complemented
62#83559—51nomaximal, Hall
63#66140—31no—
64C22×#687—31no—
65C2×#4061—31no—
66#65966D311yescharacteristic, complemented
67C5×#450—31no—
68#65459—31no—
69#65456—31no—
70#65451—31no—
71#65340—31no—
72#65072—31no—
73#65069—31no—
74#65056—31no—
75#65046—31no—
76#65028—31no—
77#65019—31no—
78C23×C5×D3—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×Dic30C2311yescharacteristic
82C2×C5×D12—22no—
83C2×C5×D12—21no—
84C2×C5×D12—41no—
85C2×C5×D12C2311yescharacteristic
86C2×C5×D12C2311yescharacteristic
87C2×C3×C22⋊D5D411yescharacteristic
88C22×C3×Dic5—21no—
89C3×Q8×D5—22no—
90C3×Q8×D5—41no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×Dic10—22no—
94C2×C3×Dic10—21no—
95C2×C3×Dic10—21no—
96C2×C3×Dic10—41no—
97C2×C3×Dic10C2311yescharacteristic
98C2×C3×Dic10C2311yescharacteristic
99C2×#1201—21no—
100C2×#1201—21no—
101C2×D3×Dic5—21no—
102C2×D3×Dic5—21no—
103#6772—22no—
104#6772—41no—
105C3×C5×C4⋊C4—21no—
106C3×C5×C4⋊C4C2311yescharacteristic
107C3×C5×C22⋊C4—21no—
108#6719—21no—
109#6718—22no—
110C4⋊Dic15C2311yescharacteristic
111#6712—21no—
112C2×C3⋊#168—22no—
113C2×C3⋊#168C2311yescharacteristic
114C2×C3⋊#168C2311yescharacteristic
115C5×#215—22no—
116C5×#215—41no—
117C2×C5×C3⋊C8C2311yescharacteristic
118C2×C5×C3⋊C8C2311yescharacteristic
119C3×C22⋊Dic5D411yescharacteristic
120C3×#685—21no—
121C3×#685D411yescharacteristic
122C3×C4⋊Dic5—21no—
123C3×#683—21no—
124C3×#683—21no—
125C3×#683—21no—
126C3×#683D411yescharacteristic
127C3×C4×Dic5—21no—
128C3×C4×Dic5C2311yescharacteristic
129(C2×D3)⋊Dic5—21no—
130(C2×D3)⋊Dic5—21no—
131(C2×D3)⋊Dic5—21no—
132(C2×D3)⋊Dic5—21no—
133#6662—22no—
134#6662—41no—
135#6656—22no—
136#6656—22no—
137#6656—22no—
138#6656D414yescomplemented
139#6649—22no—
140C3×D4×Q8—51no—
141C2×#942—51no—
142C22×#215—51no—
143#5550—51no—
144#5228—51no—
145#5227—51no—
146#5086—51no—
147#5083—51no—
148#5051—51no—
149#5049—51no—
150#5047—51no—
151#5046D511yescharacteristic, complemented
152#5028—51no—
153#5026—51no—
154#5011—51no—
155C22×C5×D4—31no—
156C2×Q8×D5C2×D311yescharacteristic, complemented
157C2×#711—31no—
158C22×Dic10C2×D311yescharacteristic
159C2×C5×SD16—31no—
160C2×C5×SD16—31no—
161C5×C22⋊Q8C2×D311yescharacteristic
162#4099—61no—
163C2×C22⋊Dic5—61no—
164#4090C2×D311yescharacteristic, complemented
165C2×#689—31no—
166#4085—61no—
167#4084—31no—
168#4082—31no—
169#4081—61no—
170D4×Dic5—31no—
171C2×#687—31no—
172C2×#687—31no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—64no—
176C4×C22⋊D5C2×D311yescharacteristic
177#4070—31no—
178C22×#168—31no—
179#4061—64no—
180C2×Dic20—31no—
181C2×Dic20—31no—
182C2×#676—31no—
183#4043C2×D311yescharacteristic, complemented
184#4042—21no—
185#4034—21no—
186#4033C2×D311yescharacteristic, complemented
187#4027—21no—
188#4024—21no—
189C5×#102—31no—
190C5×#102—31no—
191C5×C22⋊C8—31no—
192#3967—31no—
193#3952—31no—
194#3948—31no—
195#3948—31no—
196#3947—31no—
197#3946—31no—
198#3942—31no—
199#3939—31no—
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C22×C5×D3—21no—
203C22×C5×D3—21no—
204C22×C5×D3—42no—
205C22×C5×D3—42no—
206C22×C5×D3—81no—
207C22×C3×D5C2×D411yescharacteristic
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2411yescharacteristic
216C2×Dic15—21no—
217C2×Dic15—21no—
218Dic30—21no—
219Dic30—21no—
220C5×D12—21no—
221C5×D12—21no—
222C5×D12—21no—
223C5×D12—42no—
224C5×D12C2×D412yes—
225C3×C22⋊D5—22no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—42no—
229C2×C3×Dic5C2×D411yescharacteristic
230C2×C3×Dic5C2×D411yescharacteristic
231C2×C3×Dic5C2×D411yescharacteristic
232C3×C4×D5—21no—
233C3×C4×D5—21no—
234C3×C4×D5—42no—
235C3×Dic10—21no—
236C3×Dic10—21no—
237C3×Dic10—21no—
238C3×Dic10—42no—
239C3×Dic10—42no—
240C3×Dic10C2×D412yes—
241#1201—42no—
242#1201—81no—
243D3×Dic5—42no—
244D3×Dic5—81no—
245C3⋊#168—21no—
246C3⋊#168C2×D412yes—
247C5×C3⋊C8—21no—
248C5×C3⋊C8—21no—
249C22×C3×Q8—51no—
250C22×C3×Q8—51no—
251C2×#235—51no—
252C22×D12C2×D511yescharacteristic
253C3×C4⋊Q8—51no—
254C3×C4⋊Q8—101no—
255C3×C22⋊Q8—51no—
256C3×C22⋊Q8—101no—
257C3×C22⋊Q8—101no—
258C3×C22⋊Q8C2×D511yescharacteristic
259C3×C4×Q8—51no—
260C3×C4×D4—51no—
261C3×C4×D4—101no—
262C2×#216—51no—
263C2×#216—51no—
264C2×#216—51no—
265#942—104no—
266C2×#215—51no—
267C2×#215—51no—
268C2×#215—51no—
269C2×#215—51no—
270C2×#215—104no—
271C2×#215C2×D511yescharacteristic
272C2×#215C2×D511yescharacteristic
273#937—101no—
274#930—51no—
275#924—51no—
276C2×#208—51no—
277C22×C3⋊C8—51no—
278#894—101no—
279#884—101no—
280D3×C22⋊C4—101no—
281#875—51no—
282C4×D12—51no—
283#835—51no—
284#835—51no—
285#835—51no—
286#830—51no—
287#830C2×D511yescharacteristic
288#810—51no—
289#809C2×D511yescharacteristic
290#809C2×D511yescharacteristic
291#807—51no—
292C4⋊(C3⋊C8)—51no—
293#803—51no—
294C24×C5—61no—
295C2×C5×Q8C22×D311yescharacteristic
296C2×C5×D4—31no—
297C2×C5×D4—31no—
298C2×C5×D4—62no—
299C2×C5×D4—61no—
300C2×C5×D4—121no—
301C22×C4×C5C22×D311yescharacteristic
302C2×C22⋊D5—61no—
303C2×C22⋊D5—61no—
304C2×C22⋊D5#6711yescharacteristic
305C22×Dic5—21no—
306C22×Dic5—61no—
307C22×Dic5—61no—
308Q8×D5—22no—
309Q8×D5—41no—
310#711—62no—
311#711—121no—
312C2×C4×D5—21no—
313C2×C4×D5C22×D311yescharacteristic
314C2×Dic10—22no—
315C2×Dic10—21no—
316C2×Dic10—21no—
317C2×Dic10—31no—
318C2×Dic10—41no—
319C2×Dic10C22×D311yescharacteristic
320C2×Dic10C22×D311yescharacteristic
321C5×SD16—62no—
322C5×SD16—121no—
323C2×C5×C8—31no—
324C2×C5×C8—31no—
325C5×C4⋊C4—21no—
326C5×C4⋊C4C22×D311yescharacteristic
327C5×C22⋊C4—21no—
328C22⋊Dic5—61no—
329C22⋊Dic5—61no—
330C22⋊Dic5—61no—
331C22⋊Dic5—61no—
332C22⋊Dic5—61no—
333C22⋊Dic5#6711yescharacteristic
334#689—62no—
335#687—34no—
336#687—62no—
337#687—62no—
338#687—62no—
339#685—21no—
340#685#6711yescharacteristic
341C4⋊Dic5—21no—
342C4⋊Dic5—31no—
343#683—21no—
344#683—21no—
345#683—21no—
346#683—61no—
347#683#6711yescharacteristic
348C4×Dic5—21no—
349C4×Dic5C22×D311yescharacteristic
350C2×#168—31no—
351C2×#168—31no—
352C2×#168—62no—
353Dic20—62no—
354Dic20—121no—
355#676—62no—
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—51no—
359#546—151no—
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—31no—
368#448—151no—
369#440—151no—
370#435—151no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5#13712yescomplemented
374C22×C3×C5C22×D411yescharacteristic
375C2×C5×D3—22no—
376C2×C5×D3—41no—
377C2×C5×D3—41no—
378C2×C5×D3—41no—
379C2×C5×D3—41no—
380C2×C5×D3—41no—
381C2×C5×D3—84no—
382C2×C3×D5—21no—
383C2×C3×D5—21no—
384C2×C3×D5—21no—
385C3×C4×C5—21no—
386C3×C4×C5—41no—
387C3×C4×C5—41no—
388C3×C4×C5C22×D411yescharacteristic
389C3×C4×C5H(5,𝔽2)11yescharacteristic
390Dic15—41no—
391Dic15—41no—
392C3×Dic5—21no—
393C3×Dic5—22no—
394C3×Dic5—21no—
395C3×Dic5—21no—
396C3×Dic5—41no—
397C23×D3—21no—
398C2×C3×Q8—51no—
399C2×C3×Q8—51no—
400C2×C3×Q8—101no—
401C2×C3×Q8—102no—
402C2×C3×Q8—101no—
403C2×C3×Q8—102no—
404C2×C3×Q8—201no—
405C2×C3×Q8—201no—
406C2×C3×Q8C22×D511yescharacteristic
407C2×C3×D4—51no—
408C22×C3×C4—51no—
409C22×C3×C4—101no—
410C22×C3×C4—101no—
411C22×C3×C4C22×D511yescharacteristic
412C2×#67—101no—
413C2×#67—101no—
414#235—102no—
415#235—201no—
416C2×D12—22no—
417C2×D12—21no—
418C2×D12—41no—
419C2×D12C22×D511yescharacteristic
420C2×D12C22×D511yescharacteristic
421C2×C4×D3—101no—
422C2×C4×D3—101no—
423C2×Dic6—51no—
424C3×C4⋊C4—21no—
425C3×C4⋊C4—51no—
426C3×C4⋊C4—101no—
427C3×C4⋊C4—101no—
428C3×C4⋊C4—101no—
429C3×C4⋊C4—101no—
430C3×C4⋊C4C22×D511yescharacteristic
431C3×C22⋊C4—21no—
432C3×C22⋊C4—51no—
433C3×C22⋊C4—51no—
434C3×C22⋊C4—101no—
435C3×C42—51no—
436C3×C42—101no—
437#217—101no—
438#216—102no—
439#216—102no—
440#216—201no—
441#215—22no—
442#215—41no—
443#215—54no—
444#215—102no—
445#215—102no—
446#215—102no—
447(C2×D3)⋊C4—101no—
448(C2×D3)⋊C4—101no—
449(C2×D3)⋊C4—101no—
450(C2×D3)⋊C4—101no—
451C4⋊Dic3—51no—
452Dic3⋊C4—101no—
453#208—102no—
454C2×C3⋊C8—51no—
455C2×C3⋊C8—51no—
456C2×C3⋊C8—102no—
457C2×C3⋊C8C22×D511yescharacteristic
458C2×C3⋊C8C22×D511yescharacteristic
459C23×C5—61no—
460C23×C5—61no—
461C23×C5—122no—
462C23×C5—122no—
463C23×C5—241no—
464C23×C5C2×#6711yescharacteristic
465C22×D5C2×#6711yescharacteristic
466C5×Q8—21no—
467C5×Q8—21no—
468C5×D4—32no—
469C5×D4—61no—
470C5×D4—61no—
471C5×D4—61no—
472C5×D4—122no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5C2×#6711yescharacteristic
478C2×C4×C5C23×D311yescharacteristic
479C22⋊D5—22no—
480C22⋊D5—122no—
481C22⋊D5—241no—
482C2×Dic5—21no—
483C2×Dic5—21no—
484C2×Dic5—42no—
485C2×Dic5—61no—
486C2×Dic5—61no—
487C2×Dic5—122no—
488C2×Dic5—241no—
489C2×Dic5C2×#6711yescharacteristic
490C2×Dic5C2×#6711yescharacteristic
491C2×Dic5C2×#6711yescharacteristic
492C4×D5—21no—
493C4×D5—21no—
494C4×D5—42no—
495Dic10—21no—
496Dic10—21no—
497Dic10—21no—
498Dic10—42no—
499Dic10—42no—
500Dic10—61no—
501Dic10—61no—
502Dic10D3×D412yes—
503C5×C8—61no—
504C5×C8—61no—
505#168—32no—
506#168—61no—
507C2×#41—151no—
508C22×Q8—51no—
509C22×Q8—51no—
510C22×D4—31no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—31no—
516C2×SD16—31no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—151no—
523C22×C8—151no—
524C4⋊Q8—51no—
525C4⋊Q8—101no—
526#124—151no—
527#123—301no—
528C22⋊Q8—51no—
529C22⋊Q8—101no—
530C22⋊Q8—101no—
531C22⋊Q8—151no—
532C22⋊Q8D3×D511yescharacteristic
533#121—151no—
534#121—301no—
535#120—301no—
536C4×Q8—51no—
537C4×D4—51no—
538C4×D4—101no—
539C4×D4—151no—
540C2×C22⋊C4—301no—
541#107—151no—
542C4⋊C8—151no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—31no—
548#102—31no—
549C22⋊C8—31no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—22no—
553C2×C3×C5D4211yescharacteristic
554C2×C3×C5C2×#13711yescharacteristic
555C2×C3×C5#57711yescharacteristic
556C3×D5—41no—
557C5×D3—42no—
558C5×D3—81no—
559C23×C3—51no—
560C23×C3D4×D511yescharacteristic
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—42no—
564C22×D3—42no—
565C22×D3—81no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—52no—
569C3×Q8—101no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—202no—
573C3×Q8—202no—
574C3×D4—102no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—51no—
580C2×C3×C4—51no—
581C2×C3×C4—51no—
582C2×C3×C4—101no—
583C2×C3×C4—101no—
584C2×C3×C4—101no—
585C2×C3×C4—101no—
586C2×C3×C4—202no—
587C2×C3×C4—202no—
588C2×C3×C4D4×D511yescharacteristic
589C2×C3×C4C23×D511yescharacteristic
590#67—202no—
591#67—401no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594D12—21no—
595D12—21no—
596D12—21no—
597D12—42no—
598D12D4×D512yes—
599C4×D3—202no—
600C4×D3—401no—
601Dic6—101no—
602Dic6—101no—
603C3⋊C8—21no—
604C3⋊C8—21no—
605C3⋊C8—52no—
606C3⋊C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—62no—
610C22×C5—121no—
611C22×C5—121no—
612C22×C5—121no—
613C22×C5—121no—
614C22×C5—121no—
615C22×C5—244no—
616C22×C5#94212yescomplemented
617C22×C5C22×#6711yescharacteristic
618C2×D5—21no—
619C2×D5—21no—
620C2×D5—21no—
621C4×C5—21no—
622C4×C5—41no—
623C4×C5—41no—
624C4×C5C2×D3×D411yescharacteristic
625C4×C5#100411yescharacteristic
626Dic5—22no—
627Dic5—21no—
628Dic5—21no—
629Dic5—21no—
630Dic5—41no—
631Dic5—121no—
632Dic5—121no—
633C24—61no—
634#41—302no—
635#41—601no—
636C2×Q8—51no—
637C2×Q8—51no—
638C2×Q8—101no—
639C2×Q8—102no—
640C2×Q8—101no—
641C2×Q8—102no—
642C2×Q8—151no—
643C2×Q8—201no—
644C2×Q8—201no—
645C2×Q8C2×D3×D511yescharacteristic
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—51no—
649C2×D4—62no—
650C2×D4—61no—
651C2×D4—121no—
652C2×D4—301no—
653C2×D4—301no—
654C22×C4—51no—
655C22×C4—101no—
656C22×C4—101no—
657C22×C4—301no—
658C22×C4—301no—
659C22×C4C2×D3×D511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—62no—
664SD16—121no—
665SD16—154no—
666SD16—302no—
667SD16—302no—
668SD16—302no—
669M16—302no—
670C2×C8—31no—
671C2×C8—31no—
672C2×C8—151no—
673C2×C8—151no—
674C2×C8—302no—
675C4⋊C4—21no—
676C4⋊C4—51no—
677C4⋊C4—101no—
678C4⋊C4—101no—
679C4⋊C4—101no—
680C4⋊C4—101no—
681C4⋊C4—151no—
682C4⋊C4—301no—
683C4⋊C4C2×D3×D511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—51no—
686C22⋊C4—51no—
687C22⋊C4—101no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C42—51no—
694C42—101no—
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—101no—
699C22×C3—101no—
700C22×C3—101no—
701C22×C3#406112yescomplemented
702C22×C3C2×D4×D511yescharacteristic
703C2×D3—22no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—84no—
710C3×C4—21no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—101no—
714C3×C4—101no—
715C3×C4—101no—
716C3×C4—102no—
717C3×C4—201no—
718C3×C4C2×D4×D511yescharacteristic
719C3×C4#414411yescharacteristic
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—122no—
724C2×C5—241no—
725C2×C5D4×#6711yescharacteristic
726C2×C5C2×#94211yescharacteristic
727C2×C5#583711yescharacteristic
728D5—41no—
729C23—51no—
730C23—61no—
731C23—61no—
732C23—122no—
733C23—122no—
734C23—241no—
735C23D5×#6711yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—52no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—202no—
743Q8—202no—
744Q8—301no—
745Q8—301no—
746D4—32no—
747D4—61no—
748D4—61no—
749D4—61no—
750D4—102no—
751D4—122no—
752D4—602no—
753D4—1201no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—51no—
759C2×C4—51no—
760C2×C4—51no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—202no—
766C2×C4—202no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—602no—
770C2×C4—1201no—
771C2×C4D5×#6711yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—61no—
774C8—61no—
775C8—152no—
776C8—301no—
777C2×C3—22no—
778C2×C3—201no—
779C2×C3#6592411yescharacteristic
780C2×C3C2×#406111yescharacteristic
781C2×C3#6610911yescharacteristic
782D3—42no—
783D3—81no—
784C5#8355911yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—62no—
788C22—101no—
789C22—101no—
790C22—101no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—244no—
797C22#9151312yescomplemented
798C22C2×D5×#6711yescharacteristic
799C4—21no—
800C4—41no—
801C4—41no—
802C4—101no—
803C4—102no—
804C4—101no—
805C4—101no—
806C4—201no—
807C4—601no—
808C4—601no—
809C4D3×D4×D511yescharacteristic
810C4#9202511yescharacteristic
811C3#1061190011yescharacteristic, complemented, Sylow
812C2—22no—
813C2—122no—
814C2—201no—
815C2—241no—
816C2#1175503111yescharacteristic
817C2C2×#9151311yescharacteristic
818C2#1175531711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11754540C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#65966C2semidirect
2. C2×#91513C2semidirect
4. C22×#6656C2semidirect
5. #11751152C2semidirect
6. C5×#5046C2semidirect
7. #11749312C2semidirect
8. #11749267C2semidirect
9. #11749220C2semidirect
10. #11748556C2semidirect
11. #11748507C2semidirect
12. #11747511C2semidirect
13. #11747370C2semidirect
14. #11747311C2semidirect
15. #11747217C2semidirect
18. C2×C3×Q8×D5C22semidirect
22. C2×#6718C22semidirect
27. C3×#4090C22semidirect
29. C3×#4043C22semidirect
32. C3×#4033C22semidirect
43. C2×#6662C22semidirect
44. C2×#6662C22semidirect
50. C2×#6649C22semidirect
51. #91119C22semidirect
52. #91094C22semidirect
53. #91091C22semidirect
57. #90982C22semidirect
58. #90971C22semidirect
59. #90971C22semidirect
60. #90955C22semidirect
61. #90952C22semidirect
66. #65966D3semidirect
138. #6656D4semidirect
151. #5046D5semidirect
156. C2×Q8×D5C2×D3semidirect
164. #4090C2×D3semidirect
183. #4043C2×D3semidirect
186. #4033C2×D3semidirect
373. C22×C3×C5#137semidirect
616. C22×C5#942semidirect
695. C3×C5#3266semidirect
701. C22×C3#4061semidirect
784. C5#83559semidirect
797. C22#91513semidirect
811. C3#10611900semidirect

Maximal subgroups

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

subgroupindex
C3×#659662
C2×#915132
#117545402
C22×#66562
#117511522
C5×#50462
#117493122
#117492672
#117492202
#117485562
#117485072
#117475112
#117473702
#117473112
#117472172
#106119003
#835595