Finite Group Databasebeta

← #14453198

Subgroups — #14453198

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
1C3×C5×#546C211yesmaximal, characteristic, complemented
2C2×#91838C211yesmaximal, characteristic, complemented
3C22×#6715C211yesmaximal, characteristic, complemented
4D4×D60C211yesmaximal, characteristic, complemented
5#11751339C211yesmaximal, characteristic, complemented
6#11751318C211yesmaximal, characteristic, complemented
7#11751159C211yesmaximal, characteristic, complemented
8#11751158C211yesmaximal, characteristic, complemented
9#11751149C211yesmaximal, characteristic, complemented
10#11751147C211yesmaximal, characteristic, complemented
11#11751140C211yesmaximal, characteristic, complemented
12#11751137C211yesmaximal, characteristic, complemented
13#11751116C211yesmaximal, characteristic, complemented
14#11751115C211yesmaximal, characteristic, complemented
15#11751112C211yesmaximal, characteristic, complemented
16#10615233—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×D4C2211yescharacteristic, complemented
19C2×D4×D15—21no—
20C22×D60C2211yescharacteristic
21C22×D60C2211yescharacteristic, complemented
22C3×C5×#124C2211yescharacteristic, complemented
23C3×C5×#123—21no—
24C3×C5×C22⋊Q8C2211yescharacteristic, complemented
25C3×C5×#121—21no—
26C3×C5×#121C2211yescharacteristic, complemented
27C3×C5×#120—21no—
28C3×C4×C5×D4C2211yescharacteristic
29C3×C4×C5×D4C2211yescharacteristic, complemented
30C2×C3×C5×C22⋊C4—21no—
31#91838—24no—
32C2×#6717C2211yescharacteristic, complemented
33C2×#6717C2211yescharacteristic, complemented
34C2×#6717C2211yescharacteristic, complemented
35C2×#6715—24no—
36C2×#6715C2211yescharacteristic
37C2×#6715C2211yescharacteristic
38C2×#6715C2211yescharacteristic, complemented
39C2×#6715C2211yescharacteristic, complemented
40C2×#6715C2211yescharacteristic, complemented
41C2×#6715C2211yescharacteristic, complemented
42#91819C2211yescharacteristic
43#91819C2211yescharacteristic, complemented
44C2×#6710C2211yescharacteristic, complemented
45C22×C3⋊#168C2211yescharacteristic, complemented
46#91784—21no—
47#91771—21no—
48#91771—21no—
49#91763C2211yescharacteristic, complemented
50C4×D60C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55#91114C2211yescharacteristic, complemented
56#91093C2211yescharacteristic, complemented
57#91093C2211yescharacteristic, complemented
58#91093C2211yescharacteristic, complemented
59#91092C2211yescharacteristic, complemented
60C4⋊(C3⋊#168)C2211yescharacteristic, complemented
61#91087C2211yescharacteristic, complemented
62#83502—51nomaximal, Hall
63C5×#546D311yescharacteristic, complemented
64C2×#4095—31no—
65C22×#686—31no—
66D4×D20—31no—
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—
78C24×C3×C5—21no—
79C23×D15—21no—
80C23×D15—21no—
81C3×C5×#41—22no—
82C3×C5×#41—41no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×D4—22no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4—41no—
89C2×C3×C5×D4D411yescharacteristic
90C2×C3×C5×D4C2311yescharacteristic
91C2×C3×C5×D4C2311yescharacteristic
92C22×C3×C4×C5—21no—
93C22×C3×C4×C5—21no—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C2×#1220—21no—
97C2×#1220—21no—
98D4×D15—44no—
99C2×D60—22no—
100C2×D60—22no—
101C2×D60—21no—
102C2×D60—21no—
103C2×D60—21no—
104C2×D60—21no—
105C2×D60—41no—
106C2×D60—41no—
107C2×D60C2311yescharacteristic
108C2×D60C2311yescharacteristic
109C2×D60C2311yescharacteristic
110C2×C4×D15—21no—
111C3×C5×C4⋊C4—21no—
112C3×C5×C4⋊C4D411yescharacteristic
113C3×C5×C4⋊C4C2311yescharacteristic
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4—21no—
116C3×C5×C22⋊C4—21no—
117C3×C5×C22⋊C4—21no—
118C3×C5×C22⋊C4—21no—
119C3×C5×C22⋊C4D411yescharacteristic
120C3×C5×C22⋊C4D411yescharacteristic
121C3×C42×C5C2311yescharacteristic
122#6717—22no—
123#6717—22no—
124#6717—41no—
125#6715—22no—
126#6715—22no—
127#6715—22no—
128#6715—22no—
129#6715—41no—
130#6715D414yescomplemented
131#6714—21no—
132#6714—21no—
133#6714—21no—
134C4⋊Dic15C2311yescharacteristic
135#6710—22no—
136C2×C3⋊#168—22no—
137C2×C3⋊#168C2311yescharacteristic
138C2×C3⋊#168C2311yescharacteristic
139C2×C3⋊#168C2311yescharacteristic
140C2×C3⋊#168C2311yescharacteristic
141C3×#546D511yescharacteristic, complemented
142C2×#949—51no—
143C22×#213—51no—
144D4×D12—51no—
145#5238—51no—
146#5217—51no—
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—
156C2×C5×#41C2×D311yescharacteristic, complemented
157C22×C5×D4C2×D311yescharacteristic, complemented
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20—31no—
161C5×#124C2×D311yescharacteristic, complemented
162C5×#123—21no—
163C5×C22⋊Q8C2×D311yescharacteristic, complemented
164C5×#121—21no—
165C5×#121C2×D311yescharacteristic, complemented
166C5×#120—21no—
167C4×C5×D4C2×D311yescharacteristic
168C4×C5×D4C2×D311yescharacteristic, complemented
169C2×C5×C22⋊C4—21no—
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#4076—31no—
182#4076—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4041—61no—
186#4028—61no—
187#4028—61no—
188#4020—31no—
189C4×D20—31no—
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×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—42no—
205C23×C3×C5—42no—
206C23×C3×C5—81no—
207C23×C3×C5C2×D411yescharacteristic
208C23×C3×C5C2×D411yescharacteristic
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—42no—
213C22×D15—42no—
214C22×D15—42no—
215C22×D15—42no—
216C22×D15—81no—
217C22×D15—81no—
218C3×C5×Q8—21no—
219C3×C5×Q8—21no—
220C3×C5×D4—22no—
221C3×C5×D4—21no—
222C3×C5×D4—21no—
223C3×C5×D4—21no—
224C3×C5×D4—42no—
225C3×C5×D4—42no—
226C3×C5×D4—81no—
227C3×C5×D4C2×D412yescomplemented
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—42no—
235C2×C3×C4×C5—81no—
236C2×C3×C4×C5C2×D411yescharacteristic
237C2×C3×C4×C5C2×D411yescharacteristic
238C2×C3×C4×C5C2×D411yescharacteristic
239C2×C3×C4×C5C2×D411yescharacteristic
240C2×C3×C4×C5C2411yescharacteristic
241#1220—42no—
242#1220—42no—
243C2×Dic15—21no—
244D60—21no—
245D60—21no—
246D60—21no—
247D60—21no—
248D60—21no—
249D60—42no—
250D60—42no—
251D60—42no—
252D60—81no—
253D60C2×D412yes—
254C4×D15—42no—
255C3⋊#168—21no—
256C3⋊#168—21no—
257C3⋊#168—21no—
258C3⋊#168C2×D412yescomplemented
259C2×C3×#41C2×D511yescharacteristic, complemented
260C22×C3×D4C2×D511yescharacteristic, complemented
261C2×D3×D4—101no—
262C22×D12—51no—
263C22×D12—51no—
264C3×#124C2×D511yescharacteristic, complemented
265C3×#123—21no—
266C3×C22⋊Q8C2×D511yescharacteristic, complemented
267C3×#121—21no—
268C3×#121C2×D511yescharacteristic, complemented
269C3×#120—21no—
270C3×C4×D4C2×D511yescharacteristic
271C3×C4×D4C2×D511yescharacteristic, complemented
272C2×C3×C22⋊C4—21no—
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—51no—
282C2×#213—51no—
283C2×#213—104no—
284#930—51no—
285#930—51no—
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#832—51no—
295#832—51no—
296#830—51no—
297#830—51no—
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—
307C5×#41—22no—
308C5×#41—41no—
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—22no—
311C2×C5×D4—21no—
312C2×C5×D4—21no—
313C2×C5×D4—21no—
314C2×C5×D4—41no—
315C2×C5×D4#6711yescharacteristic
316C2×C5×D4C22×D311yescharacteristic
317C2×C5×D4C22×D311yescharacteristic
318C22×C4×C5—21no—
319C22×C4×C5—21no—
320C22×C4×C5C22×D311yescharacteristic
321C22×C4×C5C22×D311yescharacteristic
322C2×C22⋊D5—61no—
323C2×C22⋊D5—61no—
324D4×D5—124no—
325C2×D20—31no—
326C2×D20—31no—
327C2×D20—31no—
328C2×D20—62no—
329C2×D20—62no—
330C2×D20—61no—
331C2×D20—61no—
332C2×D20—61no—
333C2×D20—61no—
334C2×D20—121no—
335C2×D20—121no—
336C2×C4×D5—61no—
337C5×C4⋊C4—21no—
338C5×C4⋊C4#6711yescharacteristic
339C5×C4⋊C4C22×D311yescharacteristic
340C5×C22⋊C4—21no—
341C5×C22⋊C4—21no—
342C5×C22⋊C4—21no—
343C5×C22⋊C4—21no—
344C5×C22⋊C4—21no—
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—61no—
358#685—61no—
359#685—61no—
360C4⋊Dic5—31no—
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#546D1511yescharacteristic, complemented
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—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—22no—
386C22×C3×C5—21no—
387C22×C3×C5—21no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5—41no—
392C22×C3×C5—41no—
393C22×C3×C5—84no—
394C22×C3×C5AGL(1,ℤ/8)12yescomplemented
395C22×C3×C5C22×D411yescharacteristic
396C2×D15—22no—
397C2×D15—41no—
398C2×D15—41no—
399C2×D15—41no—
400C2×D15—41no—
401C2×D15—41no—
402C2×D15—41no—
403C2×D15—41no—
404C2×D15—41no—
405C2×D15—84no—
406C2×D15—84no—
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—21no—
410C3×C4×C5—21no—
411C3×C4×C5—41no—
412C3×C4×C5—41no—
413C3×C4×C5C22×D411yescharacteristic
414C3×C4×C5H(5,𝔽2)11yescharacteristic
415Dic15—41no—
416C24×C3—21no—
417C23×D3—101no—
418C23×D3—101no—
419C3×#41—22no—
420C3×#41—41no—
421C2×C3×Q8C22×D511yescharacteristic
422C2×C3×D4—22no—
423C2×C3×D4—21no—
424C2×C3×D4—21no—
425C2×C3×D4—21no—
426C2×C3×D4—41no—
427C2×C3×D4C22⋊D511yescharacteristic
428C2×C3×D4C22×D511yescharacteristic
429C2×C3×D4C22×D511yescharacteristic
430C22×C3×C4—21no—
431C22×C3×C4—21no—
432C22×C3×C4C22×D511yescharacteristic
433C22×C3×C4C22×D511yescharacteristic
434C2×#67—101no—
435C2×#67—101no—
436D3×D4—204no—
437C2×D12—51no—
438C2×D12—51no—
439C2×D12—51no—
440C2×D12—102no—
441C2×D12—102no—
442C2×D12—101no—
443C2×D12—101no—
444C2×D12—101no—
445C2×D12—101no—
446C2×D12—201no—
447C2×D12—201no—
448C2×C4×D3—101no—
449C3×C4⋊C4—21no—
450C3×C4⋊C4C22⋊D511yescharacteristic
451C3×C4⋊C4C22×D511yescharacteristic
452C3×C22⋊C4—21no—
453C3×C22⋊C4—21no—
454C3×C22⋊C4—21no—
455C3×C22⋊C4—21no—
456C3×C22⋊C4—21no—
457C3×C22⋊C4C22⋊D511yescharacteristic
458C3×C22⋊C4C22⋊D511yescharacteristic
459C3×C42C22×D511yescharacteristic
460#215—102no—
461#215—102no—
462#215—201no—
463#213—54no—
464#213—102no—
465#213—102no—
466#213—102no—
467#213—102no—
468#213—201no—
469(C2×D3)⋊C4—101no—
470(C2×D3)⋊C4—101no—
471(C2×D3)⋊C4—101no—
472C4⋊Dic3—51no—
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—21no—
480C23×C5—21no—
481C23×C5—42no—
482C23×C5—42no—
483C23×C5—81no—
484C23×C5C2×#6711yescharacteristic
485C23×C5C2×#6711yescharacteristic
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—122no—
490C22×D5—122no—
491C22×D5—122no—
492C22×D5—122no—
493C22×D5—241no—
494C22×D5—241no—
495C5×Q8—21no—
496C5×Q8—21no—
497C5×D4—22no—
498C5×D4—21no—
499C5×D4—21no—
500C5×D4—21no—
501C5×D4—42no—
502C5×D4—42no—
503C5×D4—81no—
504C5×D4D3×D412yescomplemented
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—42no—
512C2×C4×C5—81no—
513C2×C4×C5C2×#6711yescharacteristic
514C2×C4×C5C2×#6711yescharacteristic
515C2×C4×C5C2×#6711yescharacteristic
516C2×C4×C5C2×#6711yescharacteristic
517C2×C4×C5C23×D311yescharacteristic
518C22⋊D5—122no—
519C22⋊D5—122no—
520C2×Dic5—61no—
521D20—32no—
522D20—61no—
523D20—61no—
524D20—61no—
525D20—61no—
526D20—61no—
527D20—122no—
528D20—122no—
529D20—122no—
530D20—241no—
531C4×D5—122no—
532#168—32no—
533#168—61no—
534#168—61no—
535#168—61no—
536C2×#41C2×D1511yescharacteristic, complemented
537C22×D4—151no—
538C22×D4—151no—
539C22×D4—301no—
540C22×D4C2×D1511yescharacteristic, complemented
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—151no—
555#124C2×D1511yescharacteristic, complemented
556#123—21no—
557C22⋊Q8C2×D1511yescharacteristic, complemented
558#121—21no—
559#121—151no—
560#121—151no—
561#121—301no—
562#121C2×D1511yescharacteristic, complemented
563#120—21no—
564#120—301no—
565#120—301no—
566C4×D4—151no—
567C4×D4C2×D1511yescharacteristic
568C4×D4C2×D1511yescharacteristic, complemented
569C2×C22⋊C4—21no—
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×C5—42no—
584C2×C3×C5—81no—
585C2×C3×C5D4211yescharacteristic
586C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
587C2×C3×C5#57611yescharacteristic
588D15—42no—
589D15—81no—
590D15—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—81no—
596C23×C3C2×C22⋊D511yescharacteristic
597C23×C3C2×C22⋊D511yescharacteristic
598C22×D3—101no—
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—21no—
608C3×Q8—21no—
609C3×D4—22no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—42no—
614C3×D4—42no—
615C3×D4—81no—
616C3×D4D4×D512yescomplemented
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—42no—
624C2×C3×C4—81no—
625C2×C3×C4C2×C22⋊D511yescharacteristic
626C2×C3×C4C2×C22⋊D511yescharacteristic
627C2×C3×C4C2×C22⋊D511yescharacteristic
628C2×C3×C4C2×C22⋊D511yescharacteristic
629C2×C3×C4C23×D511yescharacteristic
630#67—202no—
631#67—202no—
632C2×Dic3—101no—
633D12—52no—
634D12—101no—
635D12—101no—
636D12—101no—
637D12—101no—
638D12—101no—
639D12—202no—
640D12—202no—
641D12—202no—
642D12—401no—
643C4×D3—202no—
644C3⋊C8—52no—
645C3⋊C8—101no—
646C3⋊C8—101no—
647C3⋊C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—22no—
652C22×C5—21no—
653C22×C5—21no—
654C22×C5—41no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5—41no—
658C22×C5—41no—
659C22×C5—84no—
660C22×C5#94912yescomplemented
661C22×C5C22×#6711yescharacteristic
662C2×D5—62no—
663C2×D5—121no—
664C2×D5—121no—
665C2×D5—121no—
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—21no—
675C4×C5—21no—
676C4×C5—21no—
677C4×C5—41no—
678C4×C5—41no—
679C4×C5C2×D3×D411yescharacteristic
680C4×C5#100411yescharacteristic
681Dic5—121no—
682C24—21no—
683C24—301no—
684C24—301no—
685#41—22no—
686#41—41no—
687C2×Q8C22×D1511yescharacteristic
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—41no—
693C2×D4—151no—
694C2×D4—151no—
695C2×D4—151no—
696C2×D4—302no—
697C2×D4—302no—
698C2×D4—301no—
699C2×D4—301no—
700C2×D4—301no—
701C2×D4—301no—
702C2×D4—301no—
703C2×D4—301no—
704C2×D4—601no—
705C2×D4—601no—
706C2×D4—604no—
707C2×D4#122011yescharacteristic
708C2×D4C22×D1511yescharacteristic
709C2×D4C22×D1511yescharacteristic
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—301no—
713C22×C4C22×D1511yescharacteristic
714C22×C4C22×D1511yescharacteristic
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—21no—
731C4⋊C4—151no—
732C4⋊C4#122011yescharacteristic
733C4⋊C4C22×D1511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—301no—
740C22⋊C4—301no—
741C22⋊C4—301no—
742C22⋊C4#122011yescharacteristic
743C22⋊C4#122011yescharacteristic
744C42C22×D1511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—22no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—84no—
758C22×C3#409512yescomplemented
759C22×C3C22×C22⋊D511yescharacteristic
760C2×D3—102no—
761C2×D3—201no—
762C2×D3—201no—
763C2×D3—201no—
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—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4C2×D4×D511yescharacteristic
778C3×C4#414411yescharacteristic
779Dic3—201no—
780C2×C5—22no—
781C2×C5—41no—
782C2×C5—42no—
783C2×C5—81no—
784C2×C5D4×#6711yescharacteristic
785C2×C5C2×#94911yescharacteristic
786C2×C5#583511yescharacteristic
787D5—122no—
788D5—241no—
789D5—241no—
790C23—21no—
791C23—21no—
792C23—42no—
793C23—42no—
794C23—81no—
795C23—301no—
796C23—301no—
797C23—301no—
798C23—602no—
799C23—602no—
800C23—602no—
801C23—602no—
802C23—1201no—
803C23—1201no—
804C23C2×#122011yescharacteristic
805C23C2×#122011yescharacteristic
806Q8—21no—
807Q8—21no—
808D4—22no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—42no—
813D4—42no—
814D4—81no—
815D4—152no—
816D4—301no—
817D4—301no—
818D4—301no—
819D4—301no—
820D4—301no—
821D4—602no—
822D4—602no—
823D4—602no—
824D4—602no—
825D4—602no—
826D4—1201no—
827D4D4×D1512yescomplemented
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—42no—
835C2×C4—81no—
836C2×C4—301no—
837C2×C4—602no—
838C2×C4C2×#122011yescharacteristic
839C2×C4C2×#122011yescharacteristic
840C2×C4C2×#122011yescharacteristic
841C2×C4C2×#122011yescharacteristic
842C2×C4C23×D1511yescharacteristic
843C8—152no—
844C8—301no—
845C8—301no—
846C8—301no—
847C2×C3—22no—
848C2×C3—41no—
849C2×C3—42no—
850C2×C3—81no—
851C2×C3D4×C22⋊D511yescharacteristic
852C2×C3C2×#409511yescharacteristic
853C2×C3#6616911yescharacteristic
854D3—202no—
855D3—401no—
856D3—401no—
857C5#8350211yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—21no—
861C22—22no—
862C22—21no—
863C22—21no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—84no—
870C22—302no—
871C22—601no—
872C22—601no—
873C22—601no—
874C22—601no—
875C22—601no—
876C22—601no—
877C22—601no—
878C22—601no—
879C22—1204no—
880C22—1204no—
881C22#9183812yescomplemented
882C22C22×#122011yescharacteristic
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—41no—
888C4—41no—
889C4—601no—
890C4C2×D4×D1511yescharacteristic
891C4#9209511yescharacteristic
892C3#1061523311yescharacteristic, complemented, Sylow
893C2—22no—
894C2—41no—
895C2—42no—
896C2—81no—
897C2—602no—
898C2—1201no—
899C2—1201no—
900C2D4×#122011yescharacteristic
901C2C2×#9183811yescharacteristic
902C2#1175659411yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#546C2
socleC22×C3×C5C22×D4
hypercenter#546D15
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C3×C5×#546C2semidirect
2. C2×#91838C2semidirect
3. C22×#6715C2semidirect
4. D4×D60C2semidirect
5. #11751339C2semidirect
6. #11751318C2semidirect
7. #11751159C2semidirect
8. #11751158C2semidirect
9. #11751149C2semidirect
10. #11751147C2semidirect
11. #11751140C2semidirect
12. #11751137C2semidirect
13. #11751116C2semidirect
14. #11751115C2semidirect
15. #11751112C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×D4C22semidirect
21. C22×D60C22semidirect
22. C3×C5×#124C22semidirect
24. C3×C5×C22⋊Q8C22semidirect
26. C3×C5×#121C22semidirect
29. C3×C4×C5×D4C22semidirect
32. C2×#6717C22semidirect
33. C2×#6717C22semidirect
34. C2×#6717C22semidirect
38. C2×#6715C22semidirect
39. C2×#6715C22semidirect
40. C2×#6715C22semidirect
41. C2×#6715C22semidirect
43. #91819C22semidirect
44. C2×#6710C22semidirect
45. C22×C3⋊#168C22semidirect
49. #91763C22semidirect
50. C4×D60C22semidirect
51. #91119C22semidirect
52. #91116C22semidirect
53. #91116C22semidirect
54. #91114C22semidirect
55. #91114C22semidirect
56. #91093C22semidirect
57. #91093C22semidirect
58. #91093C22semidirect
59. #91092C22semidirect
60. C4⋊(C3⋊#168)C22semidirect
61. #91087C22semidirect
63. C5×#546D3semidirect
130. #6715D4semidirect
141. C3×#546D5semidirect
156. C2×C5×#41C2×D3semidirect
157. C22×C5×D4C2×D3semidirect
161. C5×#124C2×D3semidirect
163. C5×C22⋊Q8C2×D3semidirect
165. C5×#121C2×D3semidirect
168. C4×C5×D4C2×D3semidirect
227. C3×C5×D4C2×D4semidirect
258. C3⋊#168C2×D4semidirect
259. C2×C3×#41C2×D5semidirect
260. C22×C3×D4C2×D5semidirect
264. C3×#124C2×D5semidirect
266. C3×C22⋊Q8C2×D5semidirect
268. C3×#121C2×D5semidirect
271. C3×C4×D4C2×D5semidirect
369. #546D15semidirect
394. C22×C3×C5AGL(1,ℤ/8)semidirect
504. C5×D4D3×D4semidirect
536. C2×#41C2×D15semidirect
540. C22×D4C2×D15semidirect
555. #124C2×D15semidirect
557. C22⋊Q8C2×D15semidirect
562. #121C2×D15semidirect
568. C4×D4C2×D15semidirect
616. C3×D4D4×D5semidirect
660. C22×C5#949semidirect
745. C3×C5#3264semidirect
758. C22×C3#4095semidirect
827. D4D4×D15semidirect
857. C5#83502semidirect
881. C22#91838semidirect
892. C3#10615233semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5462
C2×#918382
C22×#67152
D4×D602
#117513392
#117513182
#117511592
#117511582
#117511492
#117511472
#117511402
#117511372
#117511162
#117511152
#117511122
#106152333
#835025