Finite Group Databasebeta

← #14453291

Subgroups — #14453291

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×C5×#213C211yesmaximal, characteristic, complemented
2C3×D4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×#91489C211yesmaximal, characteristic, complemented
4#11754540C211yesmaximal, characteristic, complemented
5#11751319C211yesmaximal, characteristic, complemented
6#11749159C211yesmaximal, characteristic, complemented
7#11749066C211yesmaximal, characteristic, complemented
8#11749065C211yesmaximal, characteristic, complemented
9#11749025C211yesmaximal, characteristic, complemented
10#11749021C211yesmaximal, characteristic, complemented
11#11748977C211yesmaximal, characteristic, complemented
12#11748974C211yesmaximal, characteristic, complemented
13#11748539C211yesmaximal, characteristic, complemented
14#11748516C211yesmaximal, characteristic, complemented
15#11748503C211yesmaximal, characteristic, complemented
16#10615568—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic, complemented
19C22×C3×C22⋊D5—21no—
20C2×C3×D4×D5C2211yescharacteristic, complemented
21C2×#6772C2211yescharacteristic, complemented
22C2×#6716C2211yescharacteristic, complemented
23C2×#6716C2211yescharacteristic, complemented
24#91813C2211yescharacteristic, complemented
25C2×C5×#213—24no—
26C2×C5×#213C2211yescharacteristic
27C2×C5×#213C2211yescharacteristic
28C2×C5×#213C2211yescharacteristic, complemented
29C2×C5×#213C2211yescharacteristic, complemented
30C22×C5×C3⋊C8C2211yescharacteristic, complemented
31C3×#4099—21no—
32C3×#4086C2211yescharacteristic, complemented
33C3×#4085—21no—
34C3×#4084C2211yescharacteristic, complemented
35C3×#4083—21no—
36C3×D4×Dic5C2211yescharacteristic, complemented
37C3×#4076C2211yescharacteristic
38C3×C4×C22⋊D5C2211yescharacteristic
39#91568—21no—
40D3×C22⋊Dic5—21no—
41#91489—24no—
42#91453—21no—
43#91449C2211yescharacteristic, complemented
44#91423—21no—
45Dic5×D12C2211yescharacteristic, complemented
46#91373C2211yescharacteristic, complemented
47C2×#6657C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic, complemented
49C2×#6652C2211yescharacteristic, complemented
50C2×#6649C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53#91114C2211yescharacteristic, complemented
54#90987C2211yescharacteristic, complemented
55#90982C2211yescharacteristic, complemented
56#90974C2211yescharacteristic, complemented
57#90966C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59#90965C2211yescharacteristic, complemented
60#90955C2211yescharacteristic, complemented
61#90952C2211yescharacteristic, complemented
62#83488—51nomaximal, Hall
63C22×C5×D8—31no—
64#66140—31no—
65D4×C22⋊D5D311yescharacteristic, complemented
66C2×#4057—31no—
67#65507—31no—
68#65506—31no—
69#65448—31no—
70#65447—31no—
71#65445—31no—
72#65443—31no—
73#65442—31no—
74#65441—31no—
75#65439—31no—
76#65403—31no—
77#65400—31no—
78C24×C3×C5—21no—
79C23×C5×D3—21no—
80C23×C3×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×Dic30C2311yescharacteristic
88C2×C5×D12—22no—
89C2×C5×D12—21no—
90C2×C5×D12—41no—
91C2×C5×D12C2311yescharacteristic
92C2×C5×D12C2311yescharacteristic
93C2×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5—21no—
97C2×C3×C22⋊D5—21no—
98C2×C3×C22⋊D5—44no—
99C2×C3×C22⋊D5D411yescharacteristic
100C22×C3×Dic5—21no—
101C3×D4×D5—22no—
102C3×D4×D5—41no—
103C2×C3×D20C2311yescharacteristic
104C2×C3×C4×D5C2311yescharacteristic
105C2×#1201—21no—
106C2×#1201—21no—
107C2×D3×Dic5—21no—
108C2×D3×Dic5—21no—
109#6772—22no—
110#6772—41no—
111#6719—21no—
112#6716—22no—
113#6716—41no—
114C4⋊Dic15C2311yescharacteristic
115#6712—21no—
116C2×C3⋊#168C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C5×#213—22no—
119C5×#213—22no—
120C5×#213—22no—
121C5×#213D414yescomplemented
122C2×C5×C3⋊C8—22no—
123C2×C5×C3⋊C8C2311yescharacteristic
124C2×C5×C3⋊C8C2311yescharacteristic
125C3×C22⋊Dic5—21no—
126C3×C22⋊Dic5—21no—
127C3×C22⋊Dic5D411yescharacteristic
128C3×#685—21no—
129C3×#685D411yescharacteristic
130C3×C4⋊Dic5C2311yescharacteristic
131C3×#683D411yescharacteristic
132C3×C4×Dic5C2311yescharacteristic
133(C2×D3)⋊Dic5—21no—
134(C2×D3)⋊Dic5—21no—
135(C2×D3)⋊Dic5—21no—
136(C2×D3)⋊Dic5—21no—
137#6657—22no—
138#6652—22no—
139#6652—41no—
140#6649—22no—
141C3×D42—51no—
142C2×#932—51no—
143C22×#213D511yescharacteristic, complemented
144#5550—51no—
145#5218—51no—
146#5217—51no—
147#5074—51no—
148#5072—51no—
149#5041—51no—
150#5039—51no—
151#5037—51no—
152#5036—51no—
153#5016—51no—
154#5014—51no—
155#5011—51no—
156C22×C5×D4—31no—
157C22×C5×D4C2×D311yescharacteristic
158C22×C22⋊D5—21no—
159C2×#711—31no—
160C2×D4×D5C2×D311yescharacteristic, complemented
161C2×C5×D8—31no—
162C2×C5×D8—31no—
163C2×C5×D8—31no—
164C2×C5×D8—31no—
165C2×C5×D8—64no—
166C22×C5×C8—31no—
167#4099—21no—
168#4099—61no—
169C2×C22⋊Dic5—61no—
170#4086C2×D311yescharacteristic, complemented
171#4085—21no—
172#4085—61no—
173#4084—31no—
174#4084C2×D311yescharacteristic, complemented
175#4083—21no—
176#4082—31no—
177#4081—61no—
178D4×Dic5—31no—
179D4×Dic5C2×D311yescharacteristic, complemented
180C2×#687—31no—
181C2×#687—31no—
182C2×#686—31no—
183C2×#686—31no—
184#4076C2×D311yescharacteristic
185C4×C22⋊D5C2×D311yescharacteristic
186#4070—31no—
187#4057—64no—
188C2×#677—31no—
189C2×#676—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193#3964—31no—
194C22⋊#168—31no—
195#3953—31no—
196#3952—31no—
197#3949—31no—
198#3948—31no—
199#3947—31no—
200#3946—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×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—42no—
211C22×C5×D3—42no—
212C22×C5×D3—81no—
213C22×C3×D5—21no—
214C22×C3×D5—42no—
215C22×C3×D5—42no—
216C22×C3×D5—81no—
217C22×C3×D5C2×D411yescharacteristic
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—42no—
222C3×C5×D4C2×D412yes—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5C2×D411yescharacteristic
226C2×C3×C4×C5C2411yescharacteristic
227C2×Dic15—21no—
228C2×Dic15—21no—
229Dic30—21no—
230Dic30—21no—
231C5×D12—21no—
232C5×D12—21no—
233C5×D12—21no—
234C5×D12—42no—
235C5×D12C2×D412yescomplemented
236C3×C22⋊D5—22no—
237C3×C22⋊D5—42no—
238C3×C22⋊D5—42no—
239C3×C22⋊D5—42no—
240C3×C22⋊D5—42no—
241C3×C22⋊D5—81no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—42no—
244C2×C3×Dic5C2×D411yescharacteristic
245C2×C3×Dic5C2×D411yescharacteristic
246C2×C3×Dic5C2×D411yescharacteristic
247C3×D20—21no—
248C3×D20—21no—
249C3×C4×D5—21no—
250C3×C4×D5—21no—
251#1201—42no—
252#1201—81no—
253D3×Dic5—42no—
254D3×Dic5—81no—
255C3⋊#168—21no—
256C3⋊#168—21no—
257C5×C3⋊C8—21no—
258C5×C3⋊C8C2×D412yescomplemented
259C22×C3×D4—51no—
260C22×C3×D4—101no—
261C22×C3×D4C2×D511yescharacteristic
262C2×#235—51no—
263C22×D12C2×D511yescharacteristic, complemented
264C3×#127—51no—
265C3×#121—51no—
266C3×#121—51no—
267C3×#121—101no—
268C3×#120—101no—
269C3×#120—101no—
270C3×C4×D4—51no—
271C3×C4×D4—51no—
272#937—101no—
273C2×#214—51no—
274C2×#214—51no—
275C2×#214—51no—
276#932—104no—
277C2×#213—24no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213C2×D511yescharacteristic
281C2×#213C2×D511yescharacteristic
282C2×#213C2×D511yescharacteristic, complemented
283C2×#213C2×D511yescharacteristic, complemented
284#930—51no—
285#924—51no—
286C2×#208—51no—
287C22×C3⋊C8C2×D511yescharacteristic, complemented
288#894—101no—
289#884—101no—
290D3×C22⋊C4—101no—
291#875—51no—
292C4×D12—51no—
293#832—51no—
294#832—51no—
295#832—51no—
296#830—51no—
297#830—51no—
298#810—51no—
299#809—51no—
300#809—51no—
301#808—51no—
302C4⋊(C3⋊C8)—51no—
303#803—51no—
304C24×C5—21no—
305C24×C5—61no—
306C23×D5—21no—
307C2×C5×D4—22no—
308C2×C5×D4—21no—
309C2×C5×D4—31no—
310C2×C5×D4—31no—
311C2×C5×D4—41no—
312C2×C5×D4—62no—
313C2×C5×D4—61no—
314C2×C5×D4—121no—
315C2×C5×D4C22×D311yescharacteristic
316C2×C5×D4C22×D311yescharacteristic
317C22×C4×C5C22×D311yescharacteristic
318C2×C22⋊D5—21no—
319C2×C22⋊D5—21no—
320C2×C22⋊D5—21no—
321C2×C22⋊D5—21no—
322C2×C22⋊D5—21no—
323C2×C22⋊D5—44no—
324C2×C22⋊D5—61no—
325C2×C22⋊D5—61no—
326C2×C22⋊D5#6711yescharacteristic
327C22×Dic5—21no—
328C22×Dic5—61no—
329C22×Dic5—61no—
330#711—62no—
331#711—121no—
332D4×D5—22no—
333D4×D5—41no—
334C2×D20C22×D311yescharacteristic
335C2×C4×D5C22×D311yescharacteristic
336C2×Dic10—31no—
337C5×D8—34no—
338C5×D8—62no—
339C5×D8—62no—
340C5×D8—62no—
341C2×C5×C8—31no—
342C2×C5×C8—31no—
343C2×C5×C8—62no—
344C22⋊Dic5—21no—
345C22⋊Dic5—21no—
346C22⋊Dic5—61no—
347C22⋊Dic5—61no—
348C22⋊Dic5—61no—
349C22⋊Dic5—61no—
350C22⋊Dic5—61no—
351C22⋊Dic5#6711yescharacteristic
352#687—62no—
353#687—121no—
354#686—62no—
355#686—121no—
356#685—21no—
357#685#6711yescharacteristic
358C4⋊Dic5—31no—
359C4⋊Dic5C22×D311yescharacteristic
360#683—61no—
361#683#6711yescharacteristic
362C4×Dic5C22×D311yescharacteristic
363C2×#168—31no—
364C2×#168—31no—
365#677—62no—
366#676—62no—
367C2×AGL(1,ℤ/8)—151no—
368C22×D8—31no—
369#546—151no—
370D42—51no—
371#496—151no—
372#469—151no—
373#465—151no—
374#463—151no—
375#459—151no—
376#450—151no—
377#449—151no—
378#447—151no—
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×C5×D3—22no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C2×C5×D3—41no—
399C2×C5×D3—84no—
400C2×C3×D5—21no—
401C2×C3×D5—21no—
402C2×C3×D5—21no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
406C2×C3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5C22×D411yescharacteristic
409C3×C4×C5H(5,𝔽2)11yescharacteristic
410Dic15—41no—
411Dic15—41no—
412C3×Dic5—21no—
413C3×Dic5—21no—
414C3×Dic5—21no—
415C3×Dic5—41no—
416C24×C3—21no—
417C24×C3—101no—
418C23×D3—21no—
419C2×C3×D4—22no—
420C2×C3×D4—21no—
421C2×C3×D4—41no—
422C2×C3×D4—51no—
423C2×C3×D4—51no—
424C2×C3×D4—101no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4—102no—
428C2×C3×D4—101no—
429C2×C3×D4—101no—
430C2×C3×D4—201no—
431C2×C3×D4—204no—
432C2×C3×D4C22×D511yescharacteristic
433C2×C3×D4C22×D511yescharacteristic
434C22×C3×C4—51no—
435C22×C3×C4—101no—
436C22×C3×C4C22×D511yescharacteristic
437C2×#67—101no—
438C2×#67—101no—
439#235—102no—
440#235—201no—
441C2×D12—22no—
442C2×D12—21no—
443C2×D12—41no—
444C2×D12C22×D511yescharacteristic
445C2×D12C22×D511yescharacteristic
446C2×C4×D3—101no—
447C2×C4×D3—101no—
448C2×Dic6—51no—
449C3×C4⋊C4—51no—
450C3×C4⋊C4—51no—
451C3×C22⋊C4—51no—
452C3×C22⋊C4—51no—
453C3×C22⋊C4—101no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
456C3×C42—51no—
457#217—101no—
458#214—102no—
459#214—102no—
460#214—201no—
461#213—22no—
462#213—22no—
463#213—22no—
464#213—102no—
465#213—201no—
466#213C22⋊D514yescomplemented
467(C2×D3)⋊C4—101no—
468(C2×D3)⋊C4—101no—
469(C2×D3)⋊C4—101no—
470(C2×D3)⋊C4—101no—
471C4⋊Dic3—51no—
472Dic3⋊C4—101no—
473#208—102no—
474C2×C3⋊C8—22no—
475C2×C3⋊C8—51no—
476C2×C3⋊C8—51no—
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—61no—
485C23×C5—81no—
486C23×C5—122no—
487C23×C5—122no—
488C23×C5—241no—
489C23×C5C2×#6711yescharacteristic
490C22×D5—21no—
491C22×D5—42no—
492C22×D5—42no—
493C22×D5—81no—
494C22×D5C2×#6711yescharacteristic
495C5×D4—21no—
496C5×D4—21no—
497C5×D4—21no—
498C5×D4—32no—
499C5×D4—42no—
500C5×D4—61no—
501C5×D4—61no—
502C5×D4—61no—
503C5×D4—122no—
504C5×D4D3×D412yes—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5C2×#6711yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—22no—
510C22⋊D5—42no—
511C22⋊D5—42no—
512C22⋊D5—42no—
513C22⋊D5—42no—
514C22⋊D5—81no—
515C22⋊D5—122no—
516C22⋊D5—241no—
517C2×Dic5—21no—
518C2×Dic5—42no—
519C2×Dic5—61no—
520C2×Dic5—61no—
521C2×Dic5—122no—
522C2×Dic5—241no—
523C2×Dic5C2×#6711yescharacteristic
524C2×Dic5C2×#6711yescharacteristic
525C2×Dic5C2×#6711yescharacteristic
526D20—21no—
527D20—21no—
528C4×D5—21no—
529C4×D5—21no—
530Dic10—61no—
531Dic10—61no—
532C5×C8—32no—
533C5×C8—61no—
534#168—61no—
535#168—61no—
536C2×#41—151no—
537C22×D4—31no—
538C22×D4—51no—
539C22×D4—101no—
540C22×D4D3×D511yescharacteristic
541AGL(1,ℤ/8)—304no—
542C2×SD16—151no—
543C2×SD16—151no—
544C2×SD16—151no—
545C2×D8—31no—
546C2×D8—31no—
547C2×D8—31no—
548C2×D8—31no—
549C2×D8—64no—
550C2×D8—151no—
551C2×D8—151no—
552C2×M16—151no—
553C22×C8—31no—
554#127—51no—
555#124—151no—
556#123—301no—
557C22⋊Q8—151no—
558#121—51no—
559#121—51no—
560#121—101no—
561#121—151no—
562#121—301no—
563#120—101no—
564#120—101no—
565#120—301no—
566C4×D4—51no—
567C4×D4—51no—
568C4×D4—151no—
569C2×C22⋊C4—301no—
570#106—151no—
571C4⋊C8—151no—
572#103—151no—
573#102—151no—
574#102—151no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—151no—
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
587C3×D5—41no—
588C3×D5—81no—
589C5×D3—42no—
590C5×D3—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—51no—
596C23×C3—81no—
597C23×C3—101no—
598C23×C3—202no—
599C23×C3—202no—
600C23×C3—401no—
601C23×C3D4×D511yescharacteristic
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—42no—
605C22×D3—42no—
606C22×D3—81no—
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—42no—
611C3×D4—102no—
612C3×D4—101no—
613C3×D4—101no—
614C3×D4—202no—
615C3×D4—202no—
616C3×D4—202no—
617C3×D4—202no—
618C3×D4—401no—
619C3×D4C2×C22⋊D512yes—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—51no—
623C2×C3×C4—51no—
624C2×C3×C4—51no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—101no—
628C2×C3×C4—202no—
629C2×C3×C4D4×D511yescharacteristic
630C2×C3×C4C23×D511yescharacteristic
631#67—202no—
632#67—401no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635D12—21no—
636D12—21no—
637D12—21no—
638D12—42no—
639D12C2×C22⋊D512yescomplemented
640C4×D3—202no—
641C4×D3—401no—
642Dic6—101no—
643Dic6—101no—
644C3⋊C8—21no—
645C3⋊C8—101no—
646C3⋊C8—101no—
647C3⋊C8C2×C22⋊D512yescomplemented
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—62no—
657C22×C5—84no—
658C22×C5—121no—
659C22×C5—121no—
660C22×C5—121no—
661C22×C5—121no—
662C22×C5—121no—
663C22×C5—244no—
664C22×C5#93212yescomplemented
665C22×C5C22×#6711yescharacteristic
666C2×D5—21no—
667C2×D5—21no—
668C2×D5—21no—
669C2×D5—41no—
670C2×D5—41no—
671C2×D5—41no—
672C2×D5—84no—
673C4×C5—21no—
674C4×C5C2×D3×D411yescharacteristic
675C4×C5#100411yescharacteristic
676Dic5—21no—
677Dic5—21no—
678Dic5—21no—
679Dic5—41no—
680Dic5—121no—
681Dic5—121no—
682C24—21no—
683C24—61no—
684C24—101no—
685#41—302no—
686#41—601no—
687C2×Q8—151no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—41no—
693C2×D4—51no—
694C2×D4—51no—
695C2×D4—62no—
696C2×D4—61no—
697C2×D4—101no—
698C2×D4—101no—
699C2×D4—101no—
700C2×D4—102no—
701C2×D4—101no—
702C2×D4—101no—
703C2×D4—121no—
704C2×D4—201no—
705C2×D4—204no—
706C2×D4—301no—
707C2×D4—301no—
708C2×D4C2×D3×D511yescharacteristic
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—51no—
711C22×C4—101no—
712C22×C4—301no—
713C22×C4—301no—
714C22×C4C2×D3×D511yescharacteristic
715SD16—302no—
716SD16—302no—
717SD16—601no—
718D8—34no—
719D8—62no—
720D8—62no—
721D8—62no—
722D8—302no—
723D8—601no—
724M16—302no—
725C2×C8—31no—
726C2×C8—31no—
727C2×C8—62no—
728C2×C8—151no—
729C2×C8—151no—
730C4⋊C4—51no—
731C4⋊C4—51no—
732C4⋊C4—151no—
733C4⋊C4—301no—
734C22⋊C4—51no—
735C22⋊C4—51no—
736C22⋊C4—101no—
737C22⋊C4—101no—
738C22⋊C4—101no—
739C22⋊C4—301no—
740C22⋊C4—301no—
741C22⋊C4—301no—
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—201no—
759C22×C3—201no—
760C22×C3—201no—
761C22×C3—404no—
762C22×C3#405712yescomplemented
763C22×C3C2×D4×D511yescharacteristic
764C2×D3—22no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—84no—
771C3×C4—21no—
772C3×C4—101no—
773C3×C4—101no—
774C3×C4—101no—
775C3×C4—201no—
776C3×C4#414411yescharacteristic
777C3×C4C22×C22⋊D511yescharacteristic
778Dic3—201no—
779Dic3—201no—
780C2×C5—22no—
781C2×C5—42no—
782C2×C5—81no—
783C2×C5—122no—
784C2×C5—241no—
785C2×C5C2×#93211yescharacteristic
786C2×C5D4×#6711yescharacteristic
787C2×C5#583511yescharacteristic
788D5—41no—
789D5—81no—
790C23—21no—
791C23—21no—
792C23—42no—
793C23—42no—
794C23—51no—
795C23—61no—
796C23—61no—
797C23—81no—
798C23—101no—
799C23—122no—
800C23—122no—
801C23—202no—
802C23—202no—
803C23—241no—
804C23—401no—
805C23D5×#6711yescharacteristic
806Q8—301no—
807Q8—301no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—32no—
812D4—42no—
813D4—61no—
814D4—61no—
815D4—61no—
816D4—102no—
817D4—101no—
818D4—101no—
819D4—122no—
820D4—202no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—401no—
825D4—602no—
826D4—1201no—
827D4D3×C22⋊D512yes—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—51no—
831C2×C4—51no—
832C2×C4—51no—
833C2×C4—101no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—202no—
837C2×C4—301no—
838C2×C4—301no—
839C2×C4—602no—
840C2×C4—1201no—
841C2×C4D5×#6711yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—32no—
844C8—61no—
845C8—301no—
846C8—301no—
847C2×C3—22no—
848C2×C3—42no—
849C2×C3—81no—
850C2×C3—201no—
851C2×C3—401no—
852C2×C3C2×#405711yescharacteristic
853C2×C3#6609111yescharacteristic
854C2×C3D4×C22⋊D511yescharacteristic
855D3—42no—
856D3—81no—
857C5#8348811yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—22no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—62no—
867C22—84no—
868C22—101no—
869C22—101no—
870C22—101no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—201no—
877C22—201no—
878C22—201no—
879C22—244no—
880C22—404no—
881C22#9148912yescomplemented
882C22C2×D5×#6711yescharacteristic
883C4—21no—
884C4—101no—
885C4—101no—
886C4—101no—
887C4—201no—
888C4—601no—
889C4—601no—
890C4C2×D3×C22⋊D511yescharacteristic
891C4#9204911yescharacteristic
892C3#1061556811yescharacteristic, complemented, Sylow
893C2—22no—
894C2—42no—
895C2—81no—
896C2—122no—
897C2—201no—
898C2—241no—
899C2—401no—
900C2#1175469111yescharacteristic
901C2C2×#9148911yescharacteristic
902C2#67×C22⋊D511yescharacteristic
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×C5×#213C2semidirect
2. C3×D4×C22⋊D5C2semidirect
3. C2×#91489C2semidirect
4. #11754540C2semidirect
5. #11751319C2semidirect
6. #11749159C2semidirect
7. #11749066C2semidirect
8. #11749065C2semidirect
9. #11749025C2semidirect
10. #11749021C2semidirect
11. #11748977C2semidirect
12. #11748974C2semidirect
13. #11748539C2semidirect
14. #11748516C2semidirect
15. #11748503C2semidirect
18. C22×C5×D12C22semidirect
20. C2×C3×D4×D5C22semidirect
21. C2×#6772C22semidirect
22. C2×#6716C22semidirect
23. C2×#6716C22semidirect
24. #91813C22semidirect
28. C2×C5×#213C22semidirect
29. C2×C5×#213C22semidirect
30. C22×C5×C3⋊C8C22semidirect
32. C3×#4086C22semidirect
34. C3×#4084C22semidirect
36. C3×D4×Dic5C22semidirect
43. #91449C22semidirect
45. Dic5×D12C22semidirect
46. #91373C22semidirect
47. C2×#6657C22semidirect
48. C2×#6652C22semidirect
49. C2×#6652C22semidirect
50. C2×#6649C22semidirect
51. #91116C22semidirect
52. #91116C22semidirect
53. #91114C22semidirect
54. #90987C22semidirect
55. #90982C22semidirect
56. #90974C22semidirect
57. #90966C22semidirect
58. #90966C22semidirect
59. #90965C22semidirect
60. #90955C22semidirect
61. #90952C22semidirect
65. D4×C22⋊D5D3semidirect
121. C5×#213D4semidirect
143. C22×#213D5semidirect
160. C2×D4×D5C2×D3semidirect
170. #4086C2×D3semidirect
174. #4084C2×D3semidirect
179. D4×Dic5C2×D3semidirect
235. C5×D12C2×D4semidirect
258. C5×C3⋊C8C2×D4semidirect
263. C22×D12C2×D5semidirect
282. C2×#213C2×D5semidirect
283. C2×#213C2×D5semidirect
287. C22×C3⋊C8C2×D5semidirect
391. C22×C3×C5AGL(1,ℤ/8)semidirect
466. #213C22⋊D5semidirect
639. D12C2×C22⋊D5semidirect
647. C3⋊C8C2×C22⋊D5semidirect
664. C22×C5#932semidirect
745. C3×C5#3264semidirect
762. C22×C3#4057semidirect
857. C5#83488semidirect
881. C22#91489semidirect
892. C3#10615568semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2132
C3×D4×C22⋊D52
C2×#914892
#117545402
#117513192
#117491592
#117490662
#117490652
#117490252
#117490212
#117489772
#117489742
#117485392
#117485162
#117485032
#106155683
#834885