Finite Group Databasebeta

← #14453259

Subgroups — #14453259

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
1C5×#5550C211yesmaximal, characteristic, complemented
2C3×D4×D20C211yesmaximal, characteristic, complemented
3C2×#91298C211yesmaximal, characteristic, complemented
4C22×#6652C211yesmaximal, characteristic, complemented
5#11751112C211yesmaximal, characteristic, complemented
6#11748545C211yesmaximal, characteristic, complemented
7#11748527C211yesmaximal, characteristic, complemented
8#11748523C211yesmaximal, characteristic, complemented
9#11748517C211yesmaximal, characteristic, complemented
10#11748516C211yesmaximal, characteristic, complemented
11#11748510C211yesmaximal, characteristic, complemented
12#11747041C211yesmaximal, characteristic, complemented
13#11747033C211yesmaximal, characteristic, complemented
14#11747027C211yesmaximal, characteristic, complemented
15#11747021C211yesmaximal, characteristic, complemented
16#10615233—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic, complemented
18C22×C5×D12C2211yescharacteristic, complemented
19C2×C3×D4×D5—21no—
20C22×C3×D20C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic, complemented
22C3×C4×C5×D4C2211yescharacteristic
23C2×#6710C2211yescharacteristic, complemented
24C22×C3⋊#168C2211yescharacteristic, complemented
25C5×#937—21no—
26C5×#930C2211yescharacteristic, complemented
27C5×#924C2211yescharacteristic, complemented
28C5×#894—21no—
29C5×#884—21no—
30C5×D3×C22⋊C4—21no—
31C5×#875C2211yescharacteristic, complemented
32C4×C5×D12C2211yescharacteristic, complemented
33C3×#4076C2211yescharacteristic
34C3×#4076C2211yescharacteristic, complemented
35C3×#4041—21no—
36C3×#4028—21no—
37C3×#4028—21no—
38C3×#4020C2211yescharacteristic, complemented
39C3×C4×D20C2211yescharacteristic, complemented
40C2×#6655C2211yescharacteristic, complemented
41C2×#6655C2211yescharacteristic, complemented
42C2×#6655C2211yescharacteristic, complemented
43#91298—24no—
44C2×#6652—24no—
45C2×#6652C2211yescharacteristic
46C2×#6652C2211yescharacteristic
47C2×#6652C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic, complemented
49C2×#6652C2211yescharacteristic, complemented
50C2×#6652C2211yescharacteristic, complemented
51#91114C2211yescharacteristic, complemented
52#91114C2211yescharacteristic, complemented
53C4⋊(C3⋊#168)C2211yescharacteristic, complemented
54#91087C2211yescharacteristic, complemented
55#90986C2211yescharacteristic, complemented
56#90972C2211yescharacteristic, complemented
57#90966C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60#90964C2211yescharacteristic, complemented
61#90964C2211yescharacteristic, complemented
62#83488—51nomaximal, Hall
63C5×#546—31no—
64C2×#4095—31no—
65C22×#686—31no—
66D4×D20D311yescharacteristic, complemented
67#65527—31no—
68#65506—31no—
69#65347—31no—
70#65346—31no—
71#65337—31no—
72#65335—31no—
73#65328—31no—
74#65325—31no—
75#65304—31no—
76#65303—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C23×C3×D5—21no—
80C23×C3×D5—21no—
81C2×C3×C5×D4D411yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×C5×#67—21no—
85C2×C5×#67—21no—
86C5×#235—22no—
87C5×#235—41no—
88C2×C5×D12—22no—
89C2×C5×D12—21no—
90C2×C5×D12—41no—
91C2×C5×D12C2311yescharacteristic
92C2×C5×D12C2311yescharacteristic
93C2×C4×C5×D3—21no—
94C2×C4×C5×D3—21no—
95C2×C5×Dic6C2311yescharacteristic
96C2×C3×C22⋊D5—21no—
97C2×C3×C22⋊D5—21no—
98C3×D4×D5—44no—
99C2×C3×D20—22no—
100C2×C3×D20—22no—
101C2×C3×D20—21no—
102C2×C3×D20—21no—
103C2×C3×D20—21no—
104C2×C3×D20—21no—
105C2×C3×D20—41no—
106C2×C3×D20—41no—
107C2×C3×D20C2311yescharacteristic
108C2×C3×D20C2311yescharacteristic
109C2×C3×D20C2311yescharacteristic
110C2×C3×C4×D5—21no—
111C3×C5×C4⋊C4D411yescharacteristic
112C3×C5×C22⋊C4D411yescharacteristic
113C3×C5×C22⋊C4D411yescharacteristic
114C3×C42×C5C2311yescharacteristic
115#6710—22no—
116C2×C3⋊#168—22no—
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C2×C3⋊#168C2311yescharacteristic
120C2×C3⋊#168C2311yescharacteristic
121C5×#217—21no—
122C5×(C2×D3)⋊C4—21no—
123C5×(C2×D3)⋊C4—21no—
124C5×(C2×D3)⋊C4—21no—
125C5×(C2×D3)⋊C4—21no—
126C5×C4⋊Dic3C2311yescharacteristic
127C5×Dic3⋊C4—21no—
128C3×#685—21no—
129C3×#685—21no—
130C3×#685—21no—
131C3×C4⋊Dic5C2311yescharacteristic
132#6655—22no—
133#6655—22no—
134#6655—41no—
135#6652—22no—
136#6652—22no—
137#6652—22no—
138#6652—22no—
139#6652—41no—
140#6652D414yescomplemented
141C3×D42—51no—
142C2×#932—51no—
143C22×#213—51no—
144#5550D511yescharacteristic, complemented
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—
156C2×C5×#41—31no—
157C22×C5×D4—31no—
158C2×D4×D5—21no—
159C22×D20C2×D311yescharacteristic
160C22×D20C2×D311yescharacteristic, complemented
161C5×#124—31no—
162C5×#123—61no—
163C5×C22⋊Q8—31no—
164C5×#121—31no—
165C5×#121—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4C2×D311yescharacteristic
169C2×C5×C22⋊C4—61no—
170#4095—64no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#686—31no—
175C2×#686—31no—
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—64no—
181#4076C2×D311yescharacteristic
182#4076C2×D311yescharacteristic, complemented
183C2×#681—31no—
184C22×#168—31no—
185#4041—21no—
186#4028—21no—
187#4028—21no—
188#4020C2×D311yescharacteristic, complemented
189C4×D20C2×D311yescharacteristic, complemented
190#3967—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3941—31no—
196#3941—31no—
197#3941—31no—
198#3940—31no—
199C4⋊#168—31no—
200#3935—31no—
201#3264—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C23×C3×C5C2×D411yescharacteristic
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—42no—
207C22×C5×D3—42no—
208C22×C5×D3—81no—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—42no—
213C22×C3×D5—42no—
214C22×C3×D5—42no—
215C22×C3×D5—42no—
216C22×C3×D5—81no—
217C22×C3×D5—81no—
218C3×C5×D4—22no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2×D411yescharacteristic
226C2×C3×C4×C5C2×D411yescharacteristic
227C2×C3×C4×C5C2411yescharacteristic
228C5×#67—42no—
229C5×#67—81no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C5×D12—21no—
233C5×D12—21no—
234C5×D12—21no—
235C5×D12—42no—
236C5×D12C2×D412yescomplemented
237C4×C5×D3—42no—
238C4×C5×D3—81no—
239C5×Dic6—21no—
240C5×Dic6—21no—
241C3×C22⋊D5—42no—
242C3×C22⋊D5—42no—
243C2×C3×Dic5—21no—
244C3×D20—21no—
245C3×D20—21no—
246C3×D20—21no—
247C3×D20—21no—
248C3×D20—21no—
249C3×D20—42no—
250C3×D20—42no—
251C3×D20—42no—
252C3×D20—81no—
253C3×D20C2×D412yes—
254C3×C4×D5—42no—
255C3⋊#168—21no—
256C3⋊#168—21no—
257C3⋊#168—21no—
258C3⋊#168C2×D412yescomplemented
259C22×C3×D4—51no—
260C22×C3×D4—51no—
261C22×C3×D4—101no—
262C2×#235C2×D511yescharacteristic, complemented
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×D4C2×D511yescharacteristic
272#937—21no—
273C2×#214—51no—
274C2×#214—51no—
275C2×#214—51no—
276#932—104no—
277C2×#213—51no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281C2×#213—51no—
282C2×#213—51no—
283C2×#213—104no—
284#930C2×D511yescharacteristic, complemented
285#924C2×D511yescharacteristic, complemented
286C2×#208—51no—
287C22×C3⋊C8—51no—
288#894—21no—
289#884—21no—
290D3×C22⋊C4—21no—
291#875C2×D511yescharacteristic, complemented
292C4×D12C2×D511yescharacteristic, complemented
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—61no—
305C23×D5—21no—
306C23×D5—21no—
307C5×#41—62no—
308C5×#41—121no—
309C2×C5×Q8—31no—
310C2×C5×D4—31no—
311C2×C5×D4—31no—
312C2×C5×D4—62no—
313C2×C5×D4—61no—
314C2×C5×D4—61no—
315C2×C5×D4—61no—
316C2×C5×D4—121no—
317C2×C5×D4#6711yescharacteristic
318C22×C4×C5—61no—
319C22×C4×C5—61no—
320C22×C4×C5C22×D311yescharacteristic
321C22×C4×C5C22×D311yescharacteristic
322C2×C22⋊D5—21no—
323C2×C22⋊D5—21no—
324D4×D5—44no—
325C2×D20—22no—
326C2×D20—22no—
327C2×D20—21no—
328C2×D20—21no—
329C2×D20—21no—
330C2×D20—21no—
331C2×D20—41no—
332C2×D20—41no—
333C2×D20C22×D311yescharacteristic
334C2×D20C22×D311yescharacteristic
335C2×D20C22×D311yescharacteristic
336C2×C4×D5—21no—
337C5×C4⋊C4—31no—
338C5×C4⋊C4—61no—
339C5×C4⋊C4#6711yescharacteristic
340C5×C22⋊C4—61no—
341C5×C22⋊C4—61no—
342C5×C22⋊C4—61no—
343C5×C22⋊C4—61no—
344C5×C22⋊C4—61no—
345C5×C22⋊C4#6711yescharacteristic
346C5×C22⋊C4#6711yescharacteristic
347C42×C5C22×D311yescharacteristic
348#688—62no—
349#688—62no—
350#688—121no—
351#686—34no—
352#686—62no—
353#686—62no—
354#686—62no—
355#686—62no—
356#686—121no—
357#685—21no—
358#685—21no—
359#685—21no—
360C4⋊Dic5C22×D311yescharacteristic
361#681—62no—
362C2×#168—31no—
363C2×#168—31no—
364C2×#168—31no—
365C2×#168—31no—
366C2×#168—62no—
367C2×AGL(1,ℤ/8)—151no—
368C22×D8—151no—
369#546—31no—
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—21no—
385C22×C3×C5—21no—
386C22×C3×C5—21no—
387C22×C3×C5AGL(1,ℤ/8)12yescomplemented
388C22×C3×C5C22×D411yescharacteristic
389C2×C5×D3—22no—
390C2×C5×D3—41no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—84no—
396C2×C3×D5—22no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—84no—
406C2×C3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—21no—
410C3×C4×C5—21no—
411C3×C4×C5C22×D411yescharacteristic
412C3×C4×C5H(5,𝔽2)11yescharacteristic
413C3×Dic5—41no—
414C5×Dic3—41no—
415C5×Dic3—41no—
416C24×C3—101no—
417C24×C3—101no—
418C23×D3—21no—
419C2×C3×D4—51no—
420C2×C3×D4—51no—
421C2×C3×D4—51no—
422C2×C3×D4—102no—
423C2×C3×D4—102no—
424C2×C3×D4—101no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—101no—
429C2×C3×D4—101no—
430C2×C3×D4—201no—
431C2×C3×D4—201no—
432C2×C3×D4—204no—
433C2×C3×D4C22⋊D511yescharacteristic
434C22×C3×C4—101no—
435C22×C3×C4C22×D511yescharacteristic
436C22×C3×C4C22×D511yescharacteristic
437C2×#67—21no—
438C2×#67—21no—
439#235—22no—
440#235—41no—
441C2×D12—22no—
442C2×D12—21no—
443C2×D12—41no—
444C2×D12C22×D511yescharacteristic
445C2×D12C22×D511yescharacteristic
446C2×C4×D3—21no—
447C2×C4×D3—21no—
448C2×Dic6C22×D511yescharacteristic
449C3×C4⋊C4—51no—
450C3×C4⋊C4C22⋊D511yescharacteristic
451C3×C22⋊C4—101no—
452C3×C22⋊C4—101no—
453C3×C22⋊C4—101no—
454C3×C22⋊C4C22⋊D511yescharacteristic
455C3×C22⋊C4C22⋊D511yescharacteristic
456C3×C42C22×D511yescharacteristic
457#217—21no—
458#214—102no—
459#214—102no—
460#214—201no—
461#213—54no—
462#213—102no—
463#213—102no—
464#213—102no—
465#213—102no—
466#213—201no—
467(C2×D3)⋊C4—21no—
468(C2×D3)⋊C4—21no—
469(C2×D3)⋊C4—21no—
470(C2×D3)⋊C4—21no—
471C4⋊Dic3C22×D511yescharacteristic
472Dic3⋊C4—21no—
473#208—102no—
474C2×C3⋊C8—51no—
475C2×C3⋊C8—51no—
476C2×C3⋊C8—51no—
477C2×C3⋊C8—51no—
478C2×C3⋊C8—102no—
479C23×C5—61no—
480C23×C5—61no—
481C23×C5—122no—
482C23×C5—122no—
483C23×C5—241no—
484C23×C5C2×#6711yescharacteristic
485C23×C5C2×#6711yescharacteristic
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—21no—
489C22×D5—42no—
490C22×D5—42no—
491C22×D5—42no—
492C22×D5—42no—
493C22×D5—81no—
494C22×D5—81no—
495C5×Q8—61no—
496C5×Q8—61no—
497C5×D4—22no—
498C5×D4—32no—
499C5×D4—61no—
500C5×D4—61no—
501C5×D4—61no—
502C5×D4—122no—
503C5×D4—122no—
504C5×D4—241no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—122no—
512C2×C4×C5—241no—
513C2×C4×C5C2×#6711yescharacteristic
514C2×C4×C5C2×#6711yescharacteristic
515C2×C4×C5C2×#6711yescharacteristic
516C2×C4×C5C2×#6711yescharacteristic
517C2×C4×C5C23×D311yescharacteristic
518C22⋊D5—42no—
519C22⋊D5—42no—
520C2×Dic5—21no—
521D20—21no—
522D20—21no—
523D20—21no—
524D20—21no—
525D20—21no—
526D20—42no—
527D20—42no—
528D20—42no—
529D20—81no—
530D20D3×D412yes—
531C4×D5—42no—
532#168—32no—
533#168—61no—
534#168—61no—
535#168—61no—
536C2×#41—31no—
537C22×D4—31no—
538C22×D4—51no—
539C22×D4—51no—
540C22×D4—101no—
541AGL(1,ℤ/8)—304no—
542C2×SD16—151no—
543C2×SD16—151no—
544C2×SD16—151no—
545C2×D8—151no—
546C2×D8—151no—
547C2×D8—151no—
548C2×D8—151no—
549C2×D8—151no—
550C2×D8—151no—
551C2×D8—304no—
552C2×M16—151no—
553C22×C8—151no—
554#127—51no—
555#124—31no—
556#123—61no—
557C22⋊Q8—31no—
558#121—31no—
559#121—51no—
560#121—51no—
561#121—61no—
562#121—101no—
563#120—61no—
564#120—101no—
565#120—101no—
566C4×D4—31no—
567C4×D4—51no—
568C4×D4D3×D511yescharacteristic
569C2×C22⋊C4—61no—
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—41no—
583C2×C3×C5D4211yescharacteristic
584C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
585C2×C3×C5#57611yescharacteristic
586C3×D5—42no—
587C3×D5—81no—
588C3×D5—81no—
589C5×D3—42no—
590C5×D3—81no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—202no—
595C23×C3—202no—
596C23×C3—202no—
597C23×C3—202no—
598C23×C3—401no—
599C23×C3—401no—
600C23×C3C2×C22⋊D511yescharacteristic
601C23×C3C2×C22⋊D511yescharacteristic
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—42no—
605C22×D3—42no—
606C22×D3—81no—
607C3×D4—22no—
608C3×D4—52no—
609C3×D4—101no—
610C3×D4—101no—
611C3×D4—101no—
612C3×D4—101no—
613C3×D4—101no—
614C3×D4—202no—
615C3×D4—202no—
616C3×D4—202no—
617C3×D4—202no—
618C3×D4—202no—
619C3×D4—401no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—101no—
625C2×C3×C4—202no—
626C2×C3×C4C2×C22⋊D511yescharacteristic
627C2×C3×C4C2×C22⋊D511yescharacteristic
628C2×C3×C4C2×C22⋊D511yescharacteristic
629C2×C3×C4C2×C22⋊D511yescharacteristic
630C2×C3×C4C23×D511yescharacteristic
631#67—42no—
632#67—81no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635D12—21no—
636D12—21no—
637D12—21no—
638D12—42no—
639D12D4×D512yescomplemented
640C4×D3—42no—
641C4×D3—81no—
642Dic6—21no—
643Dic6—21no—
644C3⋊C8—52no—
645C3⋊C8—101no—
646C3⋊C8—101no—
647C3⋊C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—21no—
652C22×C5—21no—
653C22×C5—62no—
654C22×C5—121no—
655C22×C5—121no—
656C22×C5—121no—
657C22×C5—121no—
658C22×C5—121no—
659C22×C5—244no—
660C22×C5#93212yescomplemented
661C22×C5C22×#6711yescharacteristic
662C2×D5—22no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5—41no—
671C2×D5—84no—
672C2×D5—84no—
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—21no—
676C4×C5—21no—
677C4×C5—121no—
678C4×C5—121no—
679C4×C5C2×D3×D411yescharacteristic
680C4×C5#100411yescharacteristic
681Dic5—41no—
682C24—61no—
683C24—101no—
684C24—101no—
685#41—62no—
686#41—121no—
687C2×Q8—31no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—51no—
691C2×D4—51no—
692C2×D4—51no—
693C2×D4—62no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—102no—
698C2×D4—102no—
699C2×D4—101no—
700C2×D4—101no—
701C2×D4—101no—
702C2×D4—101no—
703C2×D4—101no—
704C2×D4—101no—
705C2×D4—121no—
706C2×D4—201no—
707C2×D4—201no—
708C2×D4—204no—
709C2×D4#120111yescharacteristic
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—101no—
713C22×C4C2×D3×D511yescharacteristic
714C22×C4C2×D3×D511yescharacteristic
715SD16—302no—
716SD16—302no—
717SD16—601no—
718D8—154no—
719D8—302no—
720D8—302no—
721D8—302no—
722D8—302no—
723D8—601no—
724M16—302no—
725C2×C8—151no—
726C2×C8—151no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—31no—
731C4⋊C4—51no—
732C4⋊C4—61no—
733C4⋊C4#120111yescharacteristic
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—101no—
742C22⋊C4#120111yescharacteristic
743C22⋊C4#120111yescharacteristic
744C42C2×D3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—102no—
752C22×C3—201no—
753C22×C3—201no—
754C22×C3—201no—
755C22×C3—201no—
756C22×C3—201no—
757C22×C3—201no—
758C22×C3—201no—
759C22×C3—201no—
760C22×C3—404no—
761C22×C3—404no—
762C22×C3#409512yescomplemented
763C22×C3C22×C22⋊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—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—201no—
776C3×C4C2×D4×D511yescharacteristic
777C3×C4#414411yescharacteristic
778Dic3—41no—
779Dic3—41no—
780C2×C5—22no—
781C2×C5—41no—
782C2×C5—122no—
783C2×C5—241no—
784C2×C5C2×#93211yescharacteristic
785C2×C5D4×#6711yescharacteristic
786C2×C5#583511yescharacteristic
787D5—42no—
788D5—81no—
789D5—81no—
790C23—61no—
791C23—61no—
792C23—101no—
793C23—101no—
794C23—101no—
795C23—122no—
796C23—122no—
797C23—202no—
798C23—202no—
799C23—202no—
800C23—202no—
801C23—241no—
802C23—401no—
803C23—401no—
804C23C2×#120111yescharacteristic
805C23C2×#120111yescharacteristic
806Q8—61no—
807Q8—61no—
808D4—22no—
809D4—32no—
810D4—52no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—101no—
815D4—101no—
816D4—101no—
817D4—101no—
818D4—101no—
819D4—122no—
820D4—122no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—202no—
825D4—202no—
826D4—241no—
827D4—401no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—101no—
835C2×C4—122no—
836C2×C4—202no—
837C2×C4—241no—
838C2×C4C2×#120111yescharacteristic
839C2×C4C2×#120111yescharacteristic
840C2×C4C2×#120111yescharacteristic
841C2×C4C2×#120111yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—152no—
844C8—301no—
845C8—301no—
846C8—301no—
847C2×C3—22no—
848C2×C3—41no—
849C2×C3—202no—
850C2×C3—401no—
851C2×C3—401no—
852C2×C3D4×C22⋊D511yescharacteristic
853C2×C3C2×#409511yescharacteristic
854C2×C3#6616911yescharacteristic
855D3—42no—
856D3—81no—
857C5#8348811yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—62no—
864C22—102no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—201no—
871C22—201no—
872C22—201no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—201no—
877C22—201no—
878C22—244no—
879C22—404no—
880C22—404no—
881C22#9129812yescomplemented
882C22C22×#120111yescharacteristic
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—121no—
888C4—121no—
889C4—201no—
890C4D3×D4×D511yescharacteristic
891C4#9202511yescharacteristic
892C3#1061523311yescharacteristic, complemented, Sylow
893C2—22no—
894C2—41no—
895C2—122no—
896C2—202no—
897C2—241no—
898C2—401no—
899C2—401no—
900C2C2×#9129811yescharacteristic
901C2D4×#120111yescharacteristic
902C2#1175530111yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5550C2semidirect
2. C3×D4×D20C2semidirect
3. C2×#91298C2semidirect
4. C22×#6652C2semidirect
5. #11751112C2semidirect
6. #11748545C2semidirect
7. #11748527C2semidirect
8. #11748523C2semidirect
9. #11748517C2semidirect
10. #11748516C2semidirect
11. #11748510C2semidirect
12. #11747041C2semidirect
13. #11747033C2semidirect
14. #11747027C2semidirect
15. #11747021C2semidirect
17. C2×C5×#235C22semidirect
18. C22×C5×D12C22semidirect
21. C22×C3×D20C22semidirect
23. C2×#6710C22semidirect
24. C22×C3⋊#168C22semidirect
26. C5×#930C22semidirect
27. C5×#924C22semidirect
31. C5×#875C22semidirect
32. C4×C5×D12C22semidirect
34. C3×#4076C22semidirect
38. C3×#4020C22semidirect
39. C3×C4×D20C22semidirect
40. C2×#6655C22semidirect
41. C2×#6655C22semidirect
42. C2×#6655C22semidirect
47. C2×#6652C22semidirect
48. C2×#6652C22semidirect
49. C2×#6652C22semidirect
50. C2×#6652C22semidirect
51. #91114C22semidirect
52. #91114C22semidirect
53. C4⋊(C3⋊#168)C22semidirect
54. #91087C22semidirect
55. #90986C22semidirect
56. #90972C22semidirect
57. #90966C22semidirect
58. #90966C22semidirect
59. #90964C22semidirect
60. #90964C22semidirect
61. #90964C22semidirect
66. D4×D20D3semidirect
140. #6652D4semidirect
144. #5550D5semidirect
160. C22×D20C2×D3semidirect
182. #4076C2×D3semidirect
188. #4020C2×D3semidirect
189. C4×D20C2×D3semidirect
236. C5×D12C2×D4semidirect
258. C3⋊#168C2×D4semidirect
262. C2×#235C2×D5semidirect
263. C22×D12C2×D5semidirect
284. #930C2×D5semidirect
285. #924C2×D5semidirect
291. #875C2×D5semidirect
292. C4×D12C2×D5semidirect
387. C22×C3×C5AGL(1,ℤ/8)semidirect
639. D12D4×D5semidirect
660. C22×C5#932semidirect
745. C3×C5#3264semidirect
762. C22×C3#4095semidirect
857. C5#83488semidirect
881. C22#91298semidirect
892. C3#10615233semidirect

Maximal subgroups

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

subgroupindex
C5×#55502
C3×D4×D202
C2×#912982
C22×#66522
#117511122
#117485452
#117485272
#117485232
#117485172
#117485162
#117485102
#117470412
#117470332
#117470272
#117470212
#106152333
#834885