Finite Group Databasebeta

← #14453453

Subgroups — #14453453

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#548C211yesmaximal, characteristic, complemented
2C2×#91838C211yesmaximal, characteristic, complemented
3C22×#6717C211yesmaximal, characteristic, complemented
4D4×D60C211yesmaximal, characteristic, complemented
5#11751339C211yesmaximal, characteristic, complemented
6#11751328C211yesmaximal, characteristic, complemented
7#11751159C211yesmaximal, characteristic, complemented
8#11751158C211yesmaximal, characteristic, complemented
9#11751150C211yesmaximal, characteristic, complemented
10#11751147C211yesmaximal, characteristic, complemented
11#11751139C211yesmaximal, characteristic, complemented
12#11751137C211yesmaximal, characteristic, complemented
13#11751128C211yesmaximal, characteristic, complemented
14#11751127C211yesmaximal, characteristic, complemented
15#11751112C211yesmaximal, characteristic, complemented
16#10615273—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C2×D4×D15—21no—
20C22×D60C2211yescharacteristic
21C22×D60C2211yescharacteristic
22C3×C5×#124—21no—
23C3×C5×#124C2211yescharacteristic, complemented
24C3×C5×C22⋊Q8—21no—
25C3×C5×C22⋊Q8C2211yescharacteristic, complemented
26C3×C5×#121—21no—
27C3×C5×#121C2211yescharacteristic, complemented
28C3×C4×C5×Q8C2211yescharacteristic, complemented
29C3×C4×C5×D4—21no—
30C3×C4×C5×D4C2211yescharacteristic
31#91838—24no—
32C2×#6717—24no—
33C2×#6717C2211yescharacteristic
34C2×#6717C2211yescharacteristic
35C2×#6717C2211yescharacteristic, complemented
36C2×#6717C2211yescharacteristic, complemented
37C2×#6717C2211yescharacteristic, complemented
38C2×#6717C2211yescharacteristic, complemented
39C2×#6715C2211yescharacteristic
40C2×#6715C2211yescharacteristic, complemented
41C2×#6715C2211yescharacteristic, complemented
42#91819C2211yescharacteristic
43#91819C2211yescharacteristic
44C2×#6710C2211yescharacteristic, complemented
45C22×C3⋊#168C2211yescharacteristic, complemented
46#91784—21no—
47#91771—21no—
48#91771—21no—
49#91763C2211yescharacteristic
50C4×D60C2211yescharacteristic
51#91119C2211yescharacteristic, complemented
52#91119C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55#91114C2211yescharacteristic, complemented
56#91093C2211yescharacteristic
57#91093C2211yescharacteristic, complemented
58#91093C2211yescharacteristic, complemented
59#91091C2211yescharacteristic, complemented
60C4⋊(C3⋊#168)C2211yescharacteristic, complemented
61#91087C2211yescharacteristic, complemented
62#83542—51nomaximal, Hall
63C5×#548D311yescharacteristic, complemented
64C2×#4095—31no—
65C22×#688—31no—
66D4×D20—31no—
67#65527—31no—
68#65516—31no—
69#65347—31no—
70#65346—31no—
71#65338—31no—
72#65335—31no—
73#65327—31no—
74#65325—31no—
75#65316—31no—
76#65315—31no—
77#65300—31no—
78C23×D15—21no—
79C23×D15—21no—
80C3×C5×#41—22no—
81C3×C5×#41—41no—
82C2×C3×C5×Q8—21no—
83C2×C3×C5×Q8—22no—
84C2×C3×C5×Q8—41no—
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×Q8C2311yescharacteristic
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4—21no—
89C2×C3×C5×D4D411yescharacteristic
90C2×C3×C5×D4C2311yescharacteristic
91C22×C3×C4×C5—21no—
92C22×C3×C4×C5—21no—
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C2×#1220—21no—
96C2×#1220—21no—
97D4×D15—44no—
98C2×D60—22no—
99C2×D60—22no—
100C2×D60—21no—
101C2×D60—21no—
102C2×D60—21no—
103C2×D60—21no—
104C2×D60—41no—
105C2×D60—41no—
106C2×D60C2311yescharacteristic
107C2×D60C2311yescharacteristic
108C2×D60C2311yescharacteristic
109C2×C4×D15—21no—
110C3×C5×C4⋊C4—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⋊C4D411yescharacteristic
119C3×C5×C22⋊C4D411yescharacteristic
120C3×C42×C5—21no—
121C3×C42×C5C2311yescharacteristic
122#6717—22no—
123#6717—22no—
124#6717—22no—
125#6717—22no—
126#6717—41no—
127#6717D414yescomplemented
128#6715—22no—
129#6715—22no—
130#6715—41no—
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×#548D511yescharacteristic, complemented
142C2×#949—51no—
143C22×#215—51no—
144D4×D12—51no—
145#5238—51no—
146#5227—51no—
147#5058—51no—
148#5057—51no—
149#5049—51no—
150#5046—51no—
151#5038—51no—
152#5036—51no—
153#5027—51no—
154#5026—51no—
155#5011—51no—
156C2×C5×#41C2×D311yescharacteristic, complemented
157C22×C5×Q8C2×D311yescharacteristic, complemented
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20—31no—
161C5×#124—21no—
162C5×#124C2×D311yescharacteristic, complemented
163C5×C22⋊Q8—21no—
164C5×C22⋊Q8C2×D311yescharacteristic, complemented
165C5×#121—21no—
166C5×#121C2×D311yescharacteristic, complemented
167C4×C5×Q8C2×D311yescharacteristic, complemented
168C4×C5×D4—21no—
169C4×C5×D4C2×D311yescharacteristic
170#4095—64no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—31no—
176C2×#688—31no—
177C2×#688—64no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
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#3967—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3941—31no—
196#3941—31no—
197#3941—31no—
198#3939—31no—
199C4⋊#168—31no—
200#3935—31no—
201#3265—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C23×C3×C5C2×D411yescharacteristic
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—42no—
209C22×D15—42no—
210C22×D15—42no—
211C22×D15—42no—
212C22×D15—81no—
213C22×D15—81no—
214C3×C5×Q8—21no—
215C3×C5×Q8—21no—
216C3×C5×Q8—21no—
217C3×C5×Q8—42no—
218C3×C5×Q8C2×D412yescomplemented
219C3×C5×D4—22no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C3×C5×D4—42no—
223C3×C5×D4—42no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—42no—
232C2×C3×C4×C5—42no—
233C2×C3×C4×C5C2×D411yescharacteristic
234C2×C3×C4×C5C2×D411yescharacteristic
235C2×C3×C4×C5C2×D411yescharacteristic
236C2×C3×C4×C5C2×D411yescharacteristic
237C2×C3×C4×C5C2411yescharacteristic
238#1220—42no—
239#1220—42no—
240C2×Dic15—21no—
241D60—21no—
242D60—21no—
243D60—21no—
244D60—21no—
245D60—21no—
246D60—42no—
247D60—42no—
248D60—42no—
249D60—81no—
250D60C2×D412yes—
251C4×D15—42no—
252C3⋊#168—21no—
253C3⋊#168—21no—
254C3⋊#168—21no—
255C3⋊#168C2×D412yescomplemented
256C2×C3×#41C2×D511yescharacteristic, complemented
257C22×C3×Q8C2×D511yescharacteristic, complemented
258C2×D3×D4—101no—
259C22×D12—51no—
260C22×D12—51no—
261C3×#124—21no—
262C3×#124C2×D511yescharacteristic, complemented
263C3×C22⋊Q8—21no—
264C3×C22⋊Q8C2×D511yescharacteristic, complemented
265C3×#121—21no—
266C3×#121C2×D511yescharacteristic, complemented
267C3×C4×Q8C2×D511yescharacteristic, complemented
268C3×C4×D4—21no—
269C3×C4×D4C2×D511yescharacteristic
270#949—104no—
271C2×#215—51no—
272C2×#215—51no—
273C2×#215—51no—
274C2×#215—51no—
275C2×#215—51no—
276C2×#215—51no—
277C2×#215—104no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281#930—51no—
282#930—51no—
283C2×#208—51no—
284C22×C3⋊C8—51no—
285#895—101no—
286#882—101no—
287#882—101no—
288#874—51no—
289C4×D12—51no—
290#835—51no—
291#835—51no—
292#832—51no—
293#830—51no—
294#830—51no—
295#809—51no—
296#809—51no—
297#809—51no—
298#807—51no—
299C4⋊(C3⋊C8)—51no—
300#803—51no—
301C23×D5—61no—
302C23×D5—61no—
303C5×#41—22no—
304C5×#41—41no—
305C2×C5×Q8—21no—
306C2×C5×Q8—22no—
307C2×C5×Q8—41no—
308C2×C5×Q8C22×D311yescharacteristic
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—21no—
311C2×C5×D4—21no—
312C2×C5×D4#6711yescharacteristic
313C2×C5×D4C22×D311yescharacteristic
314C22×C4×C5—21no—
315C22×C4×C5—21no—
316C22×C4×C5C22×D311yescharacteristic
317C22×C4×C5C22×D311yescharacteristic
318C2×C22⋊D5—61no—
319C2×C22⋊D5—61no—
320D4×D5—124no—
321C2×D20—31no—
322C2×D20—31no—
323C2×D20—31no—
324C2×D20—62no—
325C2×D20—62no—
326C2×D20—61no—
327C2×D20—61no—
328C2×D20—61no—
329C2×D20—61no—
330C2×D20—121no—
331C2×D20—121no—
332C2×C4×D5—61no—
333C5×C4⋊C4—21no—
334C5×C4⋊C4—21no—
335C5×C4⋊C4#6711yescharacteristic
336C5×C4⋊C4C22×D311yescharacteristic
337C5×C22⋊C4—21no—
338C5×C22⋊C4—21no—
339C5×C22⋊C4—21no—
340C5×C22⋊C4—21no—
341C5×C22⋊C4#6711yescharacteristic
342C5×C22⋊C4#6711yescharacteristic
343C42×C5—21no—
344C42×C5C22×D311yescharacteristic
345#688—34no—
346#688—62no—
347#688—62no—
348#688—62no—
349#688—62no—
350#688—121no—
351#686—62no—
352#686—62no—
353#686—121no—
354#685—61no—
355#685—61no—
356#685—61no—
357C4⋊Dic5—31no—
358#681—62no—
359C2×#168—31no—
360C2×#168—31no—
361C2×#168—31no—
362C2×#168—31no—
363C2×#168—62no—
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548D1511yescharacteristic, complemented
367D42—151no—
368#496—151no—
369#468—151no—
370#466—151no—
371#463—151no—
372#460—151no—
373#450—151no—
374#449—151no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5AGL(1,ℤ/8)12yescomplemented
388C22×C3×C5C22×D411yescharacteristic
389C2×D15—22no—
390C2×D15—41no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15—41no—
396C2×D15—41no—
397C2×D15—41no—
398C2×D15—84no—
399C2×D15—84no—
400C3×C4×C5—21no—
401C3×C4×C5—21no—
402C3×C4×C5—22no—
403C3×C4×C5—21no—
404C3×C4×C5—21no—
405C3×C4×C5—41no—
406C3×C4×C5—41no—
407C3×C4×C5C22×D411yescharacteristic
408C3×C4×C5H(5,𝔽2)11yescharacteristic
409Dic15—41no—
410C23×D3—101no—
411C23×D3—101no—
412C3×#41—22no—
413C3×#41—41no—
414C2×C3×Q8—21no—
415C2×C3×Q8—22no—
416C2×C3×Q8—41no—
417C2×C3×Q8C22×D511yescharacteristic
418C2×C3×Q8C22×D511yescharacteristic
419C2×C3×D4—21no—
420C2×C3×D4—21no—
421C2×C3×D4C22⋊D511yescharacteristic
422C2×C3×D4C22×D511yescharacteristic
423C22×C3×C4—21no—
424C22×C3×C4—21no—
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—101no—
428C2×#67—101no—
429D3×D4—204no—
430C2×D12—51no—
431C2×D12—51no—
432C2×D12—51no—
433C2×D12—102no—
434C2×D12—102no—
435C2×D12—101no—
436C2×D12—101no—
437C2×D12—101no—
438C2×D12—101no—
439C2×D12—201no—
440C2×D12—201no—
441C2×C4×D3—101no—
442C3×C4⋊C4—21no—
443C3×C4⋊C4—21no—
444C3×C4⋊C4C22⋊D511yescharacteristic
445C3×C4⋊C4C22×D511yescharacteristic
446C3×C22⋊C4—21no—
447C3×C22⋊C4—21no—
448C3×C22⋊C4—21no—
449C3×C22⋊C4—21no—
450C3×C22⋊C4C22⋊D511yescharacteristic
451C3×C22⋊C4C22⋊D511yescharacteristic
452C3×C42—21no—
453C3×C42C22×D511yescharacteristic
454#215—54no—
455#215—102no—
456#215—102no—
457#215—102no—
458#215—102no—
459#215—201no—
460#213—102no—
461#213—102no—
462#213—201no—
463(C2×D3)⋊C4—101no—
464(C2×D3)⋊C4—101no—
465(C2×D3)⋊C4—101no—
466C4⋊Dic3—51no—
467#208—102no—
468C2×C3⋊C8—51no—
469C2×C3⋊C8—51no—
470C2×C3⋊C8—51no—
471C2×C3⋊C8—51no—
472C2×C3⋊C8—102no—
473C23×C5—21no—
474C23×C5C2×#6711yescharacteristic
475C23×C5C2×#6711yescharacteristic
476C22×D5—61no—
477C22×D5—61no—
478C22×D5—61no—
479C22×D5—122no—
480C22×D5—122no—
481C22×D5—122no—
482C22×D5—122no—
483C22×D5—241no—
484C22×D5—241no—
485C5×Q8—21no—
486C5×Q8—21no—
487C5×Q8—21no—
488C5×Q8—42no—
489C5×Q8D3×D412yescomplemented
490C5×D4—22no—
491C5×D4—21no—
492C5×D4—21no—
493C5×D4—42no—
494C5×D4—42no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—42no—
503C2×C4×C5—42no—
504C2×C4×C5C2×#6711yescharacteristic
505C2×C4×C5C2×#6711yescharacteristic
506C2×C4×C5C2×#6711yescharacteristic
507C2×C4×C5C2×#6711yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—122no—
510C22⋊D5—122no—
511C2×Dic5—61no—
512D20—32no—
513D20—61no—
514D20—61no—
515D20—61no—
516D20—61no—
517D20—61no—
518D20—122no—
519D20—122no—
520D20—122no—
521D20—241no—
522C4×D5—122no—
523#168—32no—
524#168—61no—
525#168—61no—
526#168—61no—
527C2×#41C2×D1511yescharacteristic, complemented
528C22×Q8C2×D1511yescharacteristic, complemented
529C22×D4—151no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—151no—
534C2×SD16—151no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—151no—
544C22×C8—151no—
545#127—151no—
546#124—21no—
547#124C2×D1511yescharacteristic, complemented
548C22⋊Q8—21no—
549C22⋊Q8C2×D1511yescharacteristic, complemented
550#121—21no—
551#121—151no—
552#121—151no—
553#121—301no—
554#121C2×D1511yescharacteristic, complemented
555#120—301no—
556#120—301no—
557C4×Q8C2×D1511yescharacteristic, complemented
558C4×D4—21no—
559C4×D4—151no—
560C4×D4C2×D1511yescharacteristic
561#107—151no—
562C4⋊C8—151no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—22no—
573C2×C3×C5—41no—
574C2×C3×C5—81no—
575C2×C3×C5D4211yescharacteristic
576C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
577C2×C3×C5#57711yescharacteristic
578D15—42no—
579D15—81no—
580D15—81no—
581C23×C3—21no—
582C23×C3C2×C22⋊D511yescharacteristic
583C23×C3C2×C22⋊D511yescharacteristic
584C22×D3—101no—
585C22×D3—101no—
586C22×D3—101no—
587C22×D3—202no—
588C22×D3—202no—
589C22×D3—202no—
590C22×D3—202no—
591C22×D3—401no—
592C22×D3—401no—
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—21no—
596C3×Q8—42no—
597C3×Q8D4×D512yescomplemented
598C3×D4—22no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—42no—
602C3×D4—42no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—42no—
611C2×C3×C4—42no—
612C2×C3×C4C2×C22⋊D511yescharacteristic
613C2×C3×C4C2×C22⋊D511yescharacteristic
614C2×C3×C4C2×C22⋊D511yescharacteristic
615C2×C3×C4C2×C22⋊D511yescharacteristic
616C2×C3×C4C23×D511yescharacteristic
617#67—202no—
618#67—202no—
619C2×Dic3—101no—
620D12—52no—
621D12—101no—
622D12—101no—
623D12—101no—
624D12—101no—
625D12—101no—
626D12—202no—
627D12—202no—
628D12—202no—
629D12—401no—
630C4×D3—202no—
631C3⋊C8—52no—
632C3⋊C8—101no—
633C3⋊C8—101no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5#94912yescomplemented
644C22×C5C22×#6711yescharacteristic
645C2×D5—62no—
646C2×D5—121no—
647C2×D5—121no—
648C2×D5—121no—
649C2×D5—121no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—244no—
655C2×D5—244no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—22no—
659C4×C5—21no—
660C4×C5—21no—
661C4×C5—41no—
662C4×C5—41no—
663C4×C5C2×D3×D411yescharacteristic
664C4×C5#100411yescharacteristic
665Dic5—121no—
666C24—301no—
667C24—301no—
668#41—22no—
669#41—41no—
670C2×Q8—21no—
671C2×Q8—22no—
672C2×Q8—41no—
673C2×Q8C22×D1511yescharacteristic
674C2×Q8C22×D1511yescharacteristic
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—151no—
678C2×D4—151no—
679C2×D4—151no—
680C2×D4—302no—
681C2×D4—302no—
682C2×D4—301no—
683C2×D4—301no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—301no—
688C2×D4—601no—
689C2×D4—601no—
690C2×D4—604no—
691C2×D4#122011yescharacteristic
692C2×D4C22×D1511yescharacteristic
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—301no—
696C22×C4C22×D1511yescharacteristic
697C22×C4C22×D1511yescharacteristic
698SD16—154no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—151no—
709C2×C8—151no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—151no—
716C4⋊C4#122011yescharacteristic
717C4⋊C4C22×D1511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—301no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4#122011yescharacteristic
726C22⋊C4#122011yescharacteristic
727C42—21no—
728C42C22×D1511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3#409512yescomplemented
739C22×C3C22×C22⋊D511yescharacteristic
740C2×D3—102no—
741C2×D3—201no—
742C2×D3—201no—
743C2×D3—201no—
744C2×D3—201no—
745C2×D3—201no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—404no—
750C2×D3—404no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—22no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4C2×D4×D511yescharacteristic
759C3×C4#414411yescharacteristic
760Dic3—201no—
761C2×C5—22no—
762C2×C5—41no—
763C2×C5—81no—
764C2×C5D4×#6711yescharacteristic
765C2×C5C2×#94911yescharacteristic
766C2×C5#583711yescharacteristic
767D5—122no—
768D5—241no—
769D5—241no—
770C23—21no—
771C23—301no—
772C23—301no—
773C23—301no—
774C23—602no—
775C23—602no—
776C23—602no—
777C23—602no—
778C23—1201no—
779C23—1201no—
780C23C2×#122011yescharacteristic
781C23C2×#122011yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—21no—
785Q8—42no—
786Q8D4×D1512yescomplemented
787D4—22no—
788D4—21no—
789D4—21no—
790D4—42no—
791D4—42no—
792D4—152no—
793D4—301no—
794D4—301no—
795D4—301no—
796D4—301no—
797D4—301no—
798D4—602no—
799D4—602no—
800D4—602no—
801D4—602no—
802D4—602no—
803D4—1201no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—301no—
814C2×C4—602no—
815C2×C4C2×#122011yescharacteristic
816C2×C4C2×#122011yescharacteristic
817C2×C4C2×#122011yescharacteristic
818C2×C4C2×#122011yescharacteristic
819C2×C4C23×D1511yescharacteristic
820C8—152no—
821C8—301no—
822C8—301no—
823C8—301no—
824C2×C3—22no—
825C2×C3—41no—
826C2×C3—81no—
827C2×C3D4×C22⋊D511yescharacteristic
828C2×C3C2×#409511yescharacteristic
829C2×C3#6617111yescharacteristic
830D3—202no—
831D3—401no—
832D3—401no—
833C5#8354211yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—302no—
843C22—601no—
844C22—601no—
845C22—601no—
846C22—601no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—1204no—
852C22—1204no—
853C22#9183812yescomplemented
854C22C22×#122011yescharacteristic
855C4—21no—
856C4—21no—
857C4—22no—
858C4—21no—
859C4—21no—
860C4—41no—
861C4—41no—
862C4—601no—
863C4C2×D4×D1511yescharacteristic
864C4#9209511yescharacteristic
865C3#1061527311yescharacteristic, complemented, Sylow
866C2—22no—
867C2—41no—
868C2—81no—
869C2—602no—
870C2—1201no—
871C2—1201no—
872C2D4×#122011yescharacteristic
873C2C2×#9183811yescharacteristic
874C2#1175659611yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#548C2
socleC22×C3×C5C22×D4
hypercenter#548D15
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C3×C5×#548C2semidirect
2. C2×#91838C2semidirect
3. C22×#6717C2semidirect
4. D4×D60C2semidirect
5. #11751339C2semidirect
6. #11751328C2semidirect
7. #11751159C2semidirect
8. #11751158C2semidirect
9. #11751150C2semidirect
10. #11751147C2semidirect
11. #11751139C2semidirect
12. #11751137C2semidirect
13. #11751128C2semidirect
14. #11751127C2semidirect
15. #11751112C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×Q8C22semidirect
23. C3×C5×#124C22semidirect
25. C3×C5×C22⋊Q8C22semidirect
27. C3×C5×#121C22semidirect
28. C3×C4×C5×Q8C22semidirect
35. C2×#6717C22semidirect
36. C2×#6717C22semidirect
37. C2×#6717C22semidirect
38. C2×#6717C22semidirect
40. C2×#6715C22semidirect
41. C2×#6715C22semidirect
44. C2×#6710C22semidirect
45. C22×C3⋊#168C22semidirect
51. #91119C22semidirect
52. #91119C22semidirect
53. #91116C22semidirect
54. #91114C22semidirect
55. #91114C22semidirect
57. #91093C22semidirect
58. #91093C22semidirect
59. #91091C22semidirect
60. C4⋊(C3⋊#168)C22semidirect
61. #91087C22semidirect
63. C5×#548D3semidirect
127. #6717D4semidirect
141. C3×#548D5semidirect
156. C2×C5×#41C2×D3semidirect
157. C22×C5×Q8C2×D3semidirect
162. C5×#124C2×D3semidirect
164. C5×C22⋊Q8C2×D3semidirect
166. C5×#121C2×D3semidirect
167. C4×C5×Q8C2×D3semidirect
218. C3×C5×Q8C2×D4semidirect
255. C3⋊#168C2×D4semidirect
256. C2×C3×#41C2×D5semidirect
257. C22×C3×Q8C2×D5semidirect
262. C3×#124C2×D5semidirect
264. C3×C22⋊Q8C2×D5semidirect
266. C3×#121C2×D5semidirect
267. C3×C4×Q8C2×D5semidirect
366. #548D15semidirect
387. C22×C3×C5AGL(1,ℤ/8)semidirect
489. C5×Q8D3×D4semidirect
527. C2×#41C2×D15semidirect
528. C22×Q8C2×D15semidirect
547. #124C2×D15semidirect
549. C22⋊Q8C2×D15semidirect
554. #121C2×D15semidirect
557. C4×Q8C2×D15semidirect
597. C3×Q8D4×D5semidirect
643. C22×C5#949semidirect
729. C3×C5#3265semidirect
738. C22×C3#4095semidirect
786. Q8D4×D15semidirect
833. C5#83542semidirect
853. C22#91838semidirect
865. C3#10615273semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5482
C2×#918382
C22×#67172
D4×D602
#117513392
#117513282
#117511592
#117511582
#117511502
#117511472
#117511392
#117511372
#117511282
#117511272
#117511122
#106152733
#835425