Finite Group Databasebeta

← #14453743

Subgroups — #14453743

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
1C2×#91831C211yesmaximal, characteristic, complemented
2C3×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×D5×#215C211yesmaximal, characteristic, complemented
4#11754665C211yesmaximal, characteristic
5C5×#5227C211yesmaximal, characteristic, complemented
6#11749397C211yesmaximal, characteristic, complemented
7#11749312C211yesmaximal, characteristic, complemented
8#11749311C211yesmaximal, characteristic, complemented
9#11749292C211yesmaximal, characteristic, complemented
10#11749291C211yesmaximal, characteristic, complemented
11#11749225C211yesmaximal, characteristic, complemented
12#11749222C211yesmaximal, characteristic, complemented
13#11748552C211yesmaximal, characteristic, complemented
14#11748548C211yesmaximal, characteristic, complemented
15#11748494C211yesmaximal, characteristic, complemented
16#10611792—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×#6817C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic
20C2×D5×D12C2211yescharacteristic
21C2×#6718C2211yescharacteristic, complemented
22C2×#6718C2211yescharacteristic, complemented
23#91831—24no—
24C2×#6717C2211yescharacteristic
25C2×#6717C2211yescharacteristic
26C2×#6710C2211yescharacteristic, complemented
27C2×C5×#215C2211yescharacteristic
28C2×C5×#215C2211yescharacteristic
29C5×#930C2211yescharacteristic
30C3×#4092—21no—
31C3×#4092C2211yescharacteristic
32C3×Q8×Dic5C2211yescharacteristic, complemented
33C3×#4090—21no—
34C3×#4090C2211yescharacteristic, complemented
35C3×C4×C22⋊D5—21no—
36C3×C4×C22⋊D5C2211yescharacteristic
37C3×#4070—21no—
38C3×#4070C2211yescharacteristic, complemented
39#91577—21no—
40#91557—21no—
41D5×#215—24no—
42#91473—21no—
43#91418C2211yescharacteristic
44#91373C2211yescharacteristic
45#91360C2211yescharacteristic
46#91355—21no—
47C2×#6662C2211yescharacteristic, complemented
48C2×#6658C2211yescharacteristic
49C2×#6656C2211yescharacteristic
50C2×D5×C3⋊C8C2211yescharacteristic
51C5×#835C2211yescharacteristic, complemented
52C5×#835C2211yescharacteristic, complemented
53C5×#830C2211yescharacteristic, complemented
54#90989C2211yescharacteristic, complemented
55#90982C2211yescharacteristic, complemented
56#90974C2211yescharacteristic, complemented
57#90970C2211yescharacteristic, complemented
58#90968C2211yescharacteristic
59#90966C2211yescharacteristic
60#90955C2211yescharacteristic
61#90952C2211yescharacteristic, complemented
62#83559—51nomaximal, Hall
63Q8×C22⋊D5D311yescharacteristic, complemented
64C2×#4088—31no—
65C2×D5×SD16—31no—
66#65946—31no—
67C5×#448—31no—
68#65458—31no—
69#65456—31no—
70#65455—31no—
71#65331—31no—
72#65107—31no—
73#65106—31no—
74#65102—31no—
75#65097—31no—
76#65022—31no—
77#65017—31no—
78C22×D3×D5—21no—
79C2×C3×C5×Q8—21no—
80C2×C3×C5×Q8—22no—
81C2×C3×C5×Q8—41no—
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×Q8C2311yescharacteristic
84C22×C3×C4×C5—21no—
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—21no—
87#6817—22no—
88#6817—41no—
89C2×D60C2311yescharacteristic
90C2×C4×D15—21no—
91C2×Dic30C2311yescharacteristic
92C2×C5×#67—21no—
93C2×C5×D12C2311yescharacteristic
94C2×C3×C22⋊D5D411yescharacteristic
95C3×Q8×D5—22no—
96C3×Q8×D5—41no—
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5C2311yescharacteristic
99C2×C3×Dic10—21no—
100C2×C3×Dic10C2311yescharacteristic
101C2×#1203—21no—
102C2×#1200—21no—
103D5×D12—22no—
104D5×D12—41no—
105#6718—22no—
106#6718—22no—
107#6717—22no—
108#6717D414yescomplemented
109#6710—22no—
110C2×C3⋊#168C2311yescharacteristic
111C2×C3⋊#168C2311yescharacteristic
112C5×#215—22no—
113C5×#215—41no—
114C5×(C2×D3)⋊C4—21no—
115C5×C4⋊Dic3C2311yescharacteristic
116C2×C5×C3⋊C8C2311yescharacteristic
117C2×C5×C3⋊C8C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×C22⋊Dic5D411yescharacteristic
120C3×#685—21no—
121C3×#685D411yescharacteristic
122C3×C4⋊Dic5—21no—
123C3×C4⋊Dic5C2311yescharacteristic
124C3×#683—21no—
125C3×#683—21no—
126C3×#683—21no—
127C3×#683—21no—
128C3×#683D411yescharacteristic
129C3×C4×Dic5—21no—
130C3×C4×Dic5C2311yescharacteristic
131Dic3⋊Dic5—21no—
132#6667—21no—
133(C2×D3)⋊Dic5—21no—
134(C2×D3)⋊Dic5—21no—
135#6665—21no—
136#6662—41no—
137#6658—22no—
138#6656—22no—
139D5×C3⋊C8—22no—
140C3×D4×Q8—51no—
141C2×#942—51no—
142C22×#215—51no—
143#5550—51no—
144#5228—51no—
145#5227D511yescharacteristic, complemented
146#5086—51no—
147#5083—51no—
148#5051—51no—
149#5049—51no—
150#5047—51no—
151#5046—51no—
152#5028—51no—
153#5026—51no—
154#5011—51no—
155C22×C5×Q8C2×D311yescharacteristic, complemented
156C2×Q8×D5C2×D311yescharacteristic
157C2×D4×D5—31no—
158C2×#709—31no—
159C2×C5×SD16—31no—
160C2×C5×SD16—31no—
161C5×#121—31no—
162#4092—21no—
163#4092C2×D311yescharacteristic
164Q8×Dic5C2×D311yescharacteristic, complemented
165#4090—21no—
166#4090C2×D311yescharacteristic, complemented
167C2×#689—31no—
168C2×#689—31no—
169#4088—64no—
170C2×#688—31no—
171C2×#688—31no—
172#4084—61no—
173#4083—61no—
174#4082—31no—
175C2×#687—31no—
176C4×C22⋊D5—21no—
177C4×C22⋊D5C2×D311yescharacteristic
178#4070—21no—
179#4070C2×D311yescharacteristic, complemented
180C2×#681—31no—
181D5×SD16—64no—
182C2×Dic20—31no—
183C2×#677—31no—
184C2×C8×D5—31no—
185#4043—31no—
186#4039—31no—
187#4029—61no—
188D5×C22⋊C4—61no—
189C5×#103—31no—
190C5×#103—31no—
191C5×C22⋊C8—31no—
192#3964—31no—
193#3953—31no—
194#3952—31no—
195#3948—31no—
196#3947—31no—
197#3946—31no—
198#3942—31no—
199#3939—31no—
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C22×D15—21no—
203C22×C5×D3—21no—
204C22×C3×D5C2×D411yescharacteristic
205C2×D3×D5—42no—
206C2×D3×D5—42no—
207C2×D3×D5—81no—
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—42no—
212C3×C5×Q8C2×D412yes—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—42no—
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2411yescharacteristic
220#1220—42no—
221C2×Dic15—21no—
222D60—21no—
223D60C2×D412yes—
224C4×D15—42no—
225Dic30—21no—
226Dic30—21no—
227C5×#67—81no—
228C2×C5×Dic3—21no—
229C5×D12—21no—
230C5×D12—21no—
231C3×C22⋊D5—22no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5C2×D411yescharacteristic
235C2×C3×Dic5C2×D411yescharacteristic
236C2×C3×Dic5C2×D411yescharacteristic
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239C3×C4×D5—42no—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—42no—
243#1203—42no—
244#1200—81no—
245C3⋊#168—21no—
246C3⋊#168C2×D412yes—
247C5×C3⋊C8—21no—
248C5×C3⋊C8—21no—
249C22×C3×Q8—51no—
250C22×C3×Q8C2×D511yescharacteristic, complemented
251C2×#235—51no—
252C22×D12—51no—
253C3×C4⋊Q8—51no—
254C3×C4⋊Q8—101no—
255C3×C22⋊Q8—51no—
256C3×C22⋊Q8—51no—
257C3×C22⋊Q8—101no—
258C3×C22⋊Q8—101no—
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#930C2×D511yescharacteristic
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#835C2×D511yescharacteristic, complemented
285#835C2×D511yescharacteristic, complemented
286#830—51no—
287#830C2×D511yescharacteristic, complemented
288#810—51no—
289#809—51no—
290#809—51no—
291#807—51no—
292C4⋊(C3⋊C8)—51no—
293#803—51no—
294C23×D5—61no—
295C2×C5×Q8—21no—
296C2×C5×Q8—22no—
297C2×C5×Q8—41no—
298C2×C5×Q8C22×D311yescharacteristic
299C2×C5×Q8C22×D311yescharacteristic
300C2×C5×D4—31no—
301C2×C5×D4—61no—
302C22×C4×C5—21no—
303C22×C4×C5C22×D311yescharacteristic
304C2×C22⋊D5—61no—
305C2×C22⋊D5—61no—
306C2×C22⋊D5#6711yescharacteristic
307Q8×D5—22no—
308Q8×D5—41no—
309D4×D5—62no—
310D4×D5—121no—
311#709—62no—
312#709—121no—
313C2×D20—31no—
314C2×C4×D5—21no—
315C2×C4×D5—61no—
316C2×C4×D5—61no—
317C2×C4×D5C22×D311yescharacteristic
318C2×Dic10—21no—
319C2×Dic10—31no—
320C2×Dic10C22×D311yescharacteristic
321C5×SD16—62no—
322C5×SD16—121no—
323C2×C5×C8—31no—
324C2×C5×C8—31no—
325C5×C4⋊C4—31no—
326C5×C22⋊C4—61no—
327C22⋊Dic5—21no—
328C22⋊Dic5—61no—
329C22⋊Dic5—61no—
330C22⋊Dic5#6711yescharacteristic
331#689—62no—
332#689—62no—
333#688—34no—
334#688—62no—
335#687—62no—
336#685—21no—
337#685—61no—
338#685—61no—
339#685#6711yescharacteristic
340C4⋊Dic5—21no—
341C4⋊Dic5—61no—
342C4⋊Dic5C22×D311yescharacteristic
343#683—21no—
344#683—21no—
345#683—21no—
346#683—21no—
347#683#6711yescharacteristic
348C4×Dic5—21no—
349C4×Dic5C22×D311yescharacteristic
350#681—62no—
351C2×#168—31no—
352C2×#168—31no—
353Dic20—121no—
354#677—62no—
355C8×D5—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—151no—
368#448—31no—
369#440—151no—
370#435—151no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5C22×D411yescharacteristic
375C2×D15—22no—
376C2×D15—41no—
377C2×D15—41no—
378C2×C5×D3—41no—
379C2×C5×D3—41no—
380C2×C5×D3—41no—
381C2×C3×D5—21no—
382C2×C3×D5—21no—
383C2×C3×D5#13712yescomplemented
384D3×D5—84no—
385C3×C4×C5—22no—
386C3×C4×C5—21no—
387C3×C4×C5—41no—
388C3×C4×C5C22×D411yescharacteristic
389C3×C4×C5H(5,𝔽2)11yescharacteristic
390Dic15—41no—
391C3×Dic5—21no—
392C3×Dic5—21no—
393C3×Dic5—21no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C5×Dic3—41no—
397C23×D3—101no—
398C2×C3×Q8—21no—
399C2×C3×Q8—22no—
400C2×C3×Q8—41no—
401C2×C3×Q8—51no—
402C2×C3×Q8—101no—
403C2×C3×Q8—102no—
404C2×C3×Q8—201no—
405C2×C3×Q8C22×D511yescharacteristic
406C2×C3×Q8C22×D511yescharacteristic
407C2×C3×D4—51no—
408C22×C3×C4—21no—
409C22×C3×C4—51no—
410C22×C3×C4—101no—
411C22×C3×C4C22×D511yescharacteristic
412C2×#67—21no—
413C2×#67—101no—
414#235—102no—
415#235—201no—
416C2×D12—51no—
417C2×D12—102no—
418C2×D12—101no—
419C2×D12—201no—
420C2×D12C22×D511yescharacteristic
421C2×C4×D3—101no—
422C2×C4×D3—101no—
423C2×Dic6—51no—
424C3×C4⋊C4—51no—
425C3×C4⋊C4—51no—
426C3×C4⋊C4—101no—
427C3×C4⋊C4—101no—
428C3×C4⋊C4—101no—
429C3×C4⋊C4—101no—
430C3×C4⋊C4—101no—
431C3×C22⋊C4—51no—
432C3×C22⋊C4—51no—
433C3×C22⋊C4—101no—
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—21no—
448(C2×D3)⋊C4—101no—
449(C2×D3)⋊C4—101no—
450(C2×D3)⋊C4—101no—
451C4⋊Dic3C22×D511yescharacteristic
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×C5C2×#6711yescharacteristic
461C22×D5—61no—
462C22×D5—122no—
463C22×D5—122no—
464C22×D5—241no—
465C22×D5C2×#6711yescharacteristic
466C5×Q8—21no—
467C5×Q8—21no—
468C5×Q8—21no—
469C5×Q8—42no—
470C5×Q8D3×D412yes—
471C5×D4—61no—
472C5×D4—61no—
473C5×D4—241no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—42no—
479C2×C4×C5—61no—
480C2×C4×C5C2×#6711yescharacteristic
481C2×C4×C5C23×D311yescharacteristic
482C22⋊D5—22no—
483C22⋊D5—122no—
484C22⋊D5—122no—
485C2×Dic5—21no—
486C2×Dic5—21no—
487C2×Dic5—61no—
488C2×Dic5C2×#6711yescharacteristic
489C2×Dic5C2×#6711yescharacteristic
490C2×Dic5C2×#6711yescharacteristic
491D20—32no—
492D20—61no—
493C4×D5—21no—
494C4×D5—21no—
495C4×D5—42no—
496C4×D5—122no—
497C4×D5—241no—
498Dic10—21no—
499Dic10—21no—
500Dic10—42no—
501Dic10—61no—
502Dic10—61no—
503C5×C8—61no—
504C5×C8—61no—
505#168—32no—
506#168—61no—
507C2×#41—151no—
508C22×Q8—51no—
509C22×Q8D3×D511yescharacteristic, complemented
510C22×D4—151no—
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—51no—
530C22⋊Q8—101no—
531C22⋊Q8—101no—
532C22⋊Q8—151no—
533#121—31no—
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—31no—
544#103—31no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—31no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—41no—
553C2×C3×C5D4211yescharacteristic
554C2×C3×C5C2×#13711yescharacteristic
555C2×C3×C5#57711yescharacteristic
556D15—42no—
557C3×D5—22no—
558C5×D3—81no—
559C23×C3—51no—
560C23×C3D4×D511yescharacteristic
561C22×D3—21no—
562C22×D3—101no—
563C22×D3—202no—
564C22×D3—202no—
565C22×D3—401no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—42no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—202no—
573C3×Q8D4×D512yes—
574C3×D4—102no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—42no—
580C2×C3×C4—51no—
581C2×C3×C4—51no—
582C2×C3×C4—51no—
583C2×C3×C4—101no—
584C2×C3×C4—101no—
585C2×C3×C4—101no—
586C2×C3×C4—101no—
587C2×C3×C4—202no—
588C2×C3×C4D4×D511yescharacteristic
589C2×C3×C4C23×D511yescharacteristic
590#67—81no—
591#67—202no—
592C2×Dic3—21no—
593C2×Dic3—101no—
594D12—21no—
595D12—21no—
596D12—52no—
597D12—101no—
598D12—202no—
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—21no—
610C22×C5—121no—
611C22×C5—121no—
612C22×C5—121no—
613C22×C5C22×#6711yescharacteristic
614C2×D5—21no—
615C2×D5—21no—
616C2×D5—62no—
617C2×D5—121no—
618C2×D5—121no—
619C2×D5—244no—
620C2×D5#94212yescomplemented
621C4×C5—22no—
622C4×C5—21no—
623C4×C5—41no—
624C4×C5—121no—
625C4×C5C2×D3×D411yescharacteristic
626C4×C5#100411yescharacteristic
627Dic5—21no—
628Dic5—21no—
629Dic5—21no—
630Dic5—41no—
631Dic5—41no—
632Dic5—121no—
633C24—301no—
634#41—302no—
635#41—601no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—41no—
639C2×Q8—51no—
640C2×Q8—101no—
641C2×Q8—102no—
642C2×Q8—151no—
643C2×Q8—201no—
644C2×Q8C2×D3×D511yescharacteristic
645C2×Q8C2×D3×D511yescharacteristic
646C2×D4—31no—
647C2×D4—51no—
648C2×D4—61no—
649C2×D4—151no—
650C2×D4—301no—
651C2×D4—302no—
652C2×D4—301no—
653C2×D4—601no—
654C22×C4—21no—
655C22×C4—51no—
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—31no—
676C4⋊C4—51no—
677C4⋊C4—51no—
678C4⋊C4—101no—
679C4⋊C4—101no—
680C4⋊C4—101no—
681C4⋊C4—101no—
682C4⋊C4—101no—
683C4⋊C4—301no—
684C22⋊C4—51no—
685C22⋊C4—51no—
686C22⋊C4—61no—
687C22⋊C4—101no—
688C22⋊C4—101no—
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—21no—
699C22×C3—52no—
700C22×C3—101no—
701C22×C3—101no—
702C22×C3C2×D4×D511yescharacteristic
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—102no—
707C2×D3—201no—
708C2×D3—201no—
709C2×D3—404no—
710C3×C4—21no—
711C3×C4—22no—
712C3×C4—41no—
713C3×C4—101no—
714C3×C4—101no—
715C3×C4—101no—
716C3×C4—201no—
717C3×C4—201no—
718C3×C4C2×D4×D511yescharacteristic
719C3×C4#414411yescharacteristic
720Dic3—41no—
721Dic3—201no—
722C2×C5—41no—
723C2×C5—241no—
724C2×C5D4×#6711yescharacteristic
725C2×C5C2×#94211yescharacteristic
726C2×C5#583711yescharacteristic
727D5—22no—
728D5—122no—
729C23—51no—
730C23—61no—
731C23—301no—
732C23—602no—
733C23—602no—
734C23—1201no—
735C23D5×#6711yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—42no—
740Q8—101no—
741Q8—101no—
742Q8—202no—
743Q8—301no—
744Q8—301no—
745Q8#679012yes—
746D4—61no—
747D4—61no—
748D4—102no—
749D4—152no—
750D4—241no—
751D4—301no—
752D4—602no—
753D4—602no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—42no—
759C2×C4—51no—
760C2×C4—51no—
761C2×C4—51no—
762C2×C4—61no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—202no—
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—41no—
778C2×C3—102no—
779C2×C3#6592411yescharacteristic
780C2×C3#6609611yescharacteristic
781C2×C3D5×#13711yescharacteristic
782D3—81no—
783D3—202no—
784C5#8355911yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—52no—
789C22—101no—
790C22—101no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—302no—
795C22—601no—
796C22—601no—
797C22—1204no—
798C22C2×D5×#6711yescharacteristic
799C4—21no—
800C4—22no—
801C4—41no—
802C4—101no—
803C4—101no—
804C4—101no—
805C4—121no—
806C4—201no—
807C4—201no—
808C4—601no—
809C4C2×#679011yescharacteristic
810C4#9204911yescharacteristic
811C3#1061179211yescharacteristic, complemented, Sylow
812C2—41no—
813C2—102no—
814C2—241no—
815C2—602no—
816C2D5×#94211yescharacteristic
817C2#1175508511yescharacteristic
818C2#1175543711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11754665C2
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. C2×#91831C2semidirect
2. C3×Q8×C22⋊D5C2semidirect
3. C2×D5×#215C2semidirect
5. C5×#5227C2semidirect
6. #11749397C2semidirect
7. #11749312C2semidirect
8. #11749311C2semidirect
9. #11749292C2semidirect
10. #11749291C2semidirect
11. #11749225C2semidirect
12. #11749222C2semidirect
13. #11748552C2semidirect
14. #11748548C2semidirect
15. #11748494C2semidirect
17. C22×C3×C5×Q8C22semidirect
21. C2×#6718C22semidirect
22. C2×#6718C22semidirect
26. C2×#6710C22semidirect
32. C3×Q8×Dic5C22semidirect
34. C3×#4090C22semidirect
38. C3×#4070C22semidirect
47. C2×#6662C22semidirect
51. C5×#835C22semidirect
52. C5×#835C22semidirect
53. C5×#830C22semidirect
54. #90989C22semidirect
55. #90982C22semidirect
56. #90974C22semidirect
57. #90970C22semidirect
61. #90952C22semidirect
63. Q8×C22⋊D5D3semidirect
108. #6717D4semidirect
145. #5227D5semidirect
155. C22×C5×Q8C2×D3semidirect
164. Q8×Dic5C2×D3semidirect
166. #4090C2×D3semidirect
179. #4070C2×D3semidirect
250. C22×C3×Q8C2×D5semidirect
284. #835C2×D5semidirect
285. #835C2×D5semidirect
287. #830C2×D5semidirect
383. C2×C3×D5#137semidirect
509. C22×Q8D3×D5semidirect
620. C2×D5#942semidirect
695. C3×C5#3266semidirect
784. C5#83559semidirect
811. C3#10611792semidirect

Maximal subgroups

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

subgroupindex
C2×#918312
C3×Q8×C22⋊D52
C2×D5×#2152
#117546652
C5×#52272
#117493972
#117493122
#117493112
#117492922
#117492912
#117492252
#117492222
#117485522
#117485482
#117484942
#106117923
#835595