Finite Group Databasebeta

← C3×C4×#4054 #14416668

Subgroups — C3×C4×#4054 #14416668

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4054C211yesmaximal, characteristic
2C3×C4×#709C211yesmaximal, characteristic, complemented
3C2×C3×C4×D20C211yesmaximal, characteristic, complemented
4C3×C4×C5×M16C211yesmaximal, characteristic, complemented
5C3×#65422C211yesmaximal, characteristic, complemented
6C3×#65420C211yesmaximal, characteristic, complemented
7C3×#65410C211yesmaximal, characteristic, complemented
8C3×#65000C212yesmaximal, complemented
9C3×#64999C212yesmaximal, complemented
10C3×C4×D40C212yesmaximal, complemented
11C3×C4×#677C212yesmaximal, complemented
12C4×#4054C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×#709C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5—21no—
16C2×C3×C5×M16C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18C2×C3×C42×C5C2211yescharacteristic
19C3×C4×C22⋊D5—21no—
20C3×C4×C22⋊D5—21no—
21C2×C3×#685—21no—
22C3×#4072C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C3×#4054C418yesdirect product factor
25C2×C3×D40C2212yes—
26C2×C3×#677C2212yes—
27C3×C4×D20—21no—
28C3×C4×D20—21no—
29C3×C4×D20C2212yes—
30C3×C4×D20C2212yes—
31C3×C4×D20C2211yescharacteristic, complemented
32C3×C4×D20C2211yescharacteristic, complemented
33C3×#4018—21no—
34C3×C42×D5—21no—
35C3×C4×Dic10C2211yescharacteristic, complemented
36C3×C4×Dic10C2211yescharacteristic, complemented
37C3×C5×#97C2212yescomplemented
38C3×C4×C5×C8C2212yescomplemented
39C3×#3953C2212yes—
40C3×#3953C2212yes—
41C3×#3953C2212yescomplemented
42C3×#3950C2212yescomplemented
43C3×#3949C2212yescomplemented
44C3×#3948C2212yescomplemented
45C3×C4×AGL(1,ℤ/8)—51nomaximal, Hall
46C2×#4054C2×C311yescharacteristic
47C4×#709C2×C311yescharacteristic, complemented
48C2×C4×D20C2×C311yescharacteristic, complemented
49C4×C5×M16C2×C311yescharacteristic, complemented
50#65422C2×C311yescharacteristic, complemented
51#65420C2×C311yescharacteristic, complemented
52#65410C2×C311yescharacteristic, complemented
53#65000C2×C312yescomplemented
54#64999C2×C312yescomplemented
55C4×D40C2×C312yescomplemented
56C4×#677C2×C312yescomplemented
57C23×C3×D5—21no—
58C22×C3×C4×C5D411yescharacteristic
59C22×C3×C4×C5D411yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C2×C3×C22⋊D5—21no—
62C22×C3×Dic5—21no—
63C3×#709—22no—
64C3×#709C2×C414yescomplemented
65C2×C3×D20—21no—
66C2×C3×D20—22no—
67C2×C3×D20C2×C414yescomplemented
68C2×C3×D20C2312yes—
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5—21no—
75C2×C3×C4×D5—44no—
76C2×C3×Dic10C2311yescharacteristic
77C3×C5×M16—22no—
78C3×C5×M16C2×C414yescomplemented
79C2×C3×C5×C8C2312yes—
80C2×C3×C5×C8C2312yes—
81C3×C42×C5D411yescharacteristic
82C3×C42×C5D411yescharacteristic
83C3×C42×C5C2311yescharacteristic
84C3×C42×C5C2311yescharacteristic
85C3×C22⋊Dic5—21no—
86C3×#685—21no—
87C3×#685—21no—
88C3×#685—22no—
89C3×#685—22no—
90C3×C4⋊Dic5—21no—
91C3×C4⋊Dic5C2312yes—
92C3×C4⋊Dic5C2311yescharacteristic
93C3×C4⋊Dic5C2311yescharacteristic
94C3×#683—21no—
95C3×#683—21no—
96C3×C4×Dic5—21no—
97C3×C4×Dic5—21no—
98C3×C4×Dic5—21no—
99C3×D40C2×C418yescomplemented
100C3×#677C2×C418yescomplemented
101C2×C3×AGL(1,ℤ/8)—51no—
102C3×C4×#41—51no—
103C2×C3×C4×D4—51no—
104C3×#442—52no—
105C3×#440—52no—
106C3×C4×SD16—52no—
107C3×C4×D8—52no—
108C3×#428—51no—
109C3×#418—51no—
110C3×#417—51no—
111C3×C4×M16D511yescharacteristic, complemented
112C2×#709C22×C311yescharacteristic
113C22×D20C22×C311yescharacteristic
114C22×C4×D5—21no—
115C2×C5×M16C22×C311yescharacteristic
116C2×C5×M16C22×C311yescharacteristic
117C2×C42×C5C22×C311yescharacteristic
118C4×C22⋊D5—21no—
119C4×C22⋊D5—21no—
120C2×#685—21no—
121#4072C22×C311yescharacteristic
122C2×C4⋊Dic5C22×C311yescharacteristic
123#4054C3×C418yesdirect product factor
124C2×D40C22×C312yes—
125C2×#677C22×C312yes—
126C4×D20—21no—
127C4×D20—21no—
128C4×D20C22×C312yes—
129C4×D20C22×C312yes—
130C4×D20C22×C311yescharacteristic, complemented
131C4×D20C22×C311yescharacteristic, complemented
132#4018—21no—
133C42×D5—21no—
134C4×Dic10C22×C311yescharacteristic, complemented
135C4×Dic10C22×C311yescharacteristic, complemented
136C5×#97C22×C312yescomplemented
137C4×C5×C8C22×C312yescomplemented
138#3953C22×C312yes—
139#3953C22×C312yes—
140#3953C22×C312yescomplemented
141#3950C22×C312yescomplemented
142#3949C22×C312yescomplemented
143#3948C22×C312yescomplemented
144C4×AGL(1,ℤ/8)—51noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×C3×D5—24no—
147C22×C3×D5—21no—
148C22×C3×D5—22no—
149C22×C3×D5—42no—
150C22×C3×D5—42no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—41no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D411yescharacteristic
159C2×C3×C4×C5#4112yes—
160C2×C3×C4×C5C2411yescharacteristic
161C3×C22⋊D5—24no—
162C2×C3×Dic5—21no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—42no—
167C3×D20—24no—
168C3×D20—22no—
169C3×D20—21no—
170C3×D20C22×C414yes—
171C3×D20C22×C412yescomplemented
172C3×C4×D5—24no—
173C3×C4×D5—42no—
174C3×C4×D5—44no—
175C3×C4×D5—42no—
176C3×C4×D5—44no—
177C3×Dic10—21no—
178C3×Dic10C22×C412yescomplemented
179C3×C5×C8—22no—
180C3×C5×C8C22×C414yescomplemented
181C2×C3×#41—51no—
182C22×C3×D4—51no—
183C23×C3×C4—101no—
184C3×AGL(1,ℤ/8)—58no—
185C2×C3×SD16—52no—
186C2×C3×D8—52no—
187C2×C3×M16C2×D511yescharacteristic
188C2×C3×M16C2×D511yescharacteristic
189C3×C4×Q8—51no—
190C3×C4×Q8—51no—
191C3×C4×D4—51no—
192C3×C4×D4—52no—
193C3×C4×D4—52no—
194C3×C4×D4—51no—
195C3×C4×D4—101no—
196C3×C4×D4—101no—
197C3×C4×D4—101no—
198C3×C4×D4—101no—
199C3×#117—51no—
200C3×#117—101no—
201C2×C3×C4⋊C4—51no—
202C2×C3×C22⋊C4—101no—
203C2×C3×C42—101no—
204C2×C3×C42C2×D511yescharacteristic
205C3×#107—52no—
206C3×#106—52no—
207C3×#103—52no—
208C3×#102—52no—
209C3×#102—52no—
210C3×#102—52no—
211C3×#97C2×D512yescomplemented
212C3×C4×C8C2×D512yescomplemented
213C23×D5—21no—
214C22×C4×C5C3×D411yescharacteristic
215C22×C4×C5C3×D411yescharacteristic
216C22×C4×C5C23×C311yescharacteristic
217C2×C22⋊D5—21no—
218C22×Dic5—21no—
219#709—22no—
220#709C2×C3×C414yescomplemented
221C2×D20—21no—
222C2×D20—22no—
223C2×D20C2×C3×C414yescomplemented
224C2×D20C23×C312yes—
225C2×D20C23×C311yescharacteristic
226C2×C4×D5—21no—
227C2×C4×D5—22no—
228C2×C4×D5—22no—
229C2×C4×D5—21no—
230C2×C4×D5—21no—
231C2×C4×D5—44no—
232C2×Dic10C23×C311yescharacteristic
233C5×M16—22no—
234C5×M16C2×C3×C414yescomplemented
235C2×C5×C8C23×C312yes—
236C2×C5×C8C23×C312yes—
237C42×C5C3×D411yescharacteristic
238C42×C5C3×D411yescharacteristic
239C42×C5C23×C311yescharacteristic
240C42×C5C23×C311yescharacteristic
241C22⋊Dic5—21no—
242#685—21no—
243#685—21no—
244#685—22no—
245#685—22no—
246C4⋊Dic5—21no—
247C4⋊Dic5C23×C312yes—
248C4⋊Dic5C23×C311yescharacteristic
249C4⋊Dic5C23×C311yescharacteristic
250#683—21no—
251#683—21no—
252C4×Dic5—21no—
253C4×Dic5—21no—
254C4×Dic5—21no—
255D40C2×C3×C418yescomplemented
256#677C2×C3×C418yescomplemented
257C2×AGL(1,ℤ/8)—51no—
258C4×#41—51no—
259C2×C4×D4—51no—
260#442—52no—
261#440—52no—
262C4×SD16—52no—
263C4×D8—52no—
264#428—51no—
265#418—51no—
266#417—51no—
267C4×M16C3×D511yescharacteristic, complemented
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5C4×D412yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×C3×D5—22no—
273C2×C3×D5—24no—
274C2×C3×D5—48no—
275C2×C3×D5—42no—
276C2×C3×D5—41no—
277C2×C3×D5—41no—
278C2×C3×D5—42no—
279C3×C4×C5—21no—
280C3×C4×C5—21no—
281C3×C4×C5—21no—
282C3×C4×C5C4×D412yes—
283C3×C4×C5AGL(1,ℤ/8)12yescomplemented
284C3×C4×C5C23×C411yescharacteristic
285C3×C4×C5C2×#4111yescharacteristic
286C3×Dic5—22no—
287C3×Dic5—42no—
288C3×Dic5—41no—
289C3×Dic5—41no—
290C24×C3—101no—
291C3×#41—54no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—54no—
295C2×C3×D4—51no—
296C2×C3×D4—52no—
297C2×C3×D4—101no—
298C2×C3×D4—101no—
299C2×C3×D4—102no—
300C22×C3×C4—101no—
301C22×C3×C4—101no—
302C22×C3×C4—101no—
303C22×C3×C4—102no—
304C22×C3×C4—101no—
305C22×C3×C4—102no—
306C22×C3×C4—204no—
307C22×C3×C4D2011yescharacteristic
308C22×C3×C4D2011yescharacteristic
309C22×C3×C4C22×D511yescharacteristic
310C3×SD16—58no—
311C3×D8—58no—
312C3×M16—22no—
313C3×M16C4×D514yescomplemented
314C2×C3×C8C22×D512yes—
315C2×C3×C8C22×D512yes—
316C3×C4⋊C4—51no—
317C3×C4⋊C4—51no—
318C3×C4⋊C4—52no—
319C3×C4⋊C4—101no—
320C3×C4⋊C4—101no—
321C3×C4⋊C4—101no—
322C3×C22⋊C4—101no—
323C3×C22⋊C4—102no—
324C3×C22⋊C4—102no—
325C3×C22⋊C4—101no—
326C3×C22⋊C4—101no—
327C3×C42—101no—
328C3×C42—101no—
329C3×C42—101no—
330C3×C42D2011yescharacteristic
331C3×C42D2011yescharacteristic
332C3×C42C22×D511yescharacteristic
333C3×C42C22×D511yescharacteristic
334C23×C5C2×C3×D411yescharacteristic
335C22×D5—24no—
336C22×D5—21no—
337C22×D5—22no—
338C22×D5—42no—
339C22×D5—42no—
340C2×C4×C5—22no—
341C2×C4×C5—41no—
342C2×C4×C5C22×C3×C412yes—
343C2×C4×C5C2×C3×D411yescharacteristic
344C2×C4×C5C2×C3×D411yescharacteristic
345C2×C4×C5C2×C3×D411yescharacteristic
346C2×C4×C5C2×C3×D411yescharacteristic
347C2×C4×C5C2×C3×D411yescharacteristic
348C2×C4×C5C3×#4112yes—
349C2×C4×C5C24×C311yescharacteristic
350C22⋊D5—24no—
351C2×Dic5—21no—
352C2×Dic5—21no—
353C2×Dic5—21no—
354C2×Dic5—22no—
355C2×Dic5—42no—
356D20—24no—
357D20—22no—
358D20—21no—
359D20C22×C3×C414yes—
360D20C22×C3×C412yescomplemented
361C4×D5—24no—
362C4×D5—42no—
363C4×D5—44no—
364C4×D5—42no—
365C4×D5—44no—
366Dic10—21no—
367Dic10C22×C3×C412yescomplemented
368C5×C8—22no—
369C5×C8C22×C3×C414yescomplemented
370C2×#41—51no—
371C22×D4—51no—
372C23×C4—101no—
373AGL(1,ℤ/8)—58no—
374C2×SD16—52no—
375C2×D8—52no—
376C2×M16C2×C3×D511yescharacteristic
377C2×M16C2×C3×D511yescharacteristic
378C4×Q8—51no—
379C4×Q8—51no—
380C4×D4—52no—
381C4×D4—52no—
382C4×D4—51no—
383C4×D4—51no—
384C4×D4—101no—
385C4×D4—101no—
386C4×D4—101no—
387C4×D4—101no—
388#117—51no—
389#117—101no—
390C2×C4⋊C4—51no—
391C2×C22⋊C4—101no—
392C2×C42—101no—
393C2×C42C2×C3×D511yescharacteristic
394#107—52no—
395#106—52no—
396#103—52no—
397#102—52no—
398#102—52no—
399#102—52no—
400#97C2×C3×D512yescomplemented
401C4×C8C2×C3×D512yescomplemented
402C2×C3×C5—22no—
403C2×C3×C5C2×C4×D411yescharacteristic
404C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C3×C5#57511yescharacteristic
406C3×D5—42no—
407C3×D5—44no—
408C23×C3—101no—
409C23×C3—102no—
410C23×C3—104no—
411C23×C3—202no—
412C23×C3—202no—
413C23×C3C2×D2011yescharacteristic
414C3×Q8—52no—
415C3×Q8—101no—
416C3×D4—54no—
417C3×D4—52no—
418C3×D4—104no—
419C3×D4—102no—
420C3×D4—101no—
421C3×D4—104no—
422C2×C3×C4—22no—
423C2×C3×C4—41no—
424C2×C3×C4—101no—
425C2×C3×C4—104no—
426C2×C3×C4—101no—
427C2×C3×C4—101no—
428C2×C3×C4—102no—
429C2×C3×C4—202no—
430C2×C3×C4—204no—
431C2×C3×C4—202no—
432C2×C3×C4—202no—
433C2×C3×C4—204no—
434C2×C3×C4C2×C4×D512yes—
435C2×C3×C4C2×D2011yescharacteristic
436C2×C3×C4C2×D2011yescharacteristic
437C2×C3×C4C2×D2011yescharacteristic
438C2×C3×C4C2×D2011yescharacteristic
439C2×C3×C4C2×D2011yescharacteristic
440C2×C3×C4#70912yes—
441C2×C3×C4C23×D511yescharacteristic
442C3×C8—22no—
443C3×C8C2×C4×D514yescomplemented
444C22×C5—21no—
445C22×C5—21no—
446C22×C5C3×C4×D412yes—
447C22×C5C22×C3×D411yescharacteristic
448C2×D5—22no—
449C2×D5—24no—
450C2×D5—48no—
451C2×D5—42no—
452C2×D5—41no—
453C2×D5—41no—
454C2×D5—42no—
455C4×C5—21no—
456C4×C5—21no—
457C4×C5—21no—
458C4×C5C3×C4×D412yes—
459C4×C5C3×AGL(1,ℤ/8)12yescomplemented
460C4×C5C23×C3×C411yescharacteristic
461C4×C5C2×C3×#4111yescharacteristic
462Dic5—22no—
463Dic5—42no—
464Dic5—41no—
465Dic5—41no—
466C24—101no—
467#41—54no—
468#41—102no—
469C2×Q8—51no—
470C2×D4—54no—
471C2×D4—51no—
472C2×D4—52no—
473C2×D4—101no—
474C2×D4—101no—
475C2×D4—102no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4—204no—
483C22×C4C3×D2011yescharacteristic
484C22×C4C3×D2011yescharacteristic
485C22×C4C22×C3×D511yescharacteristic
486SD16—58no—
487D8—58no—
488M16—22no—
489M16C3×C4×D514yescomplemented
490C2×C8C22×C3×D512yes—
491C2×C8C22×C3×D512yes—
492C4⋊C4—51no—
493C4⋊C4—51no—
494C4⋊C4—52no—
495C4⋊C4—101no—
496C4⋊C4—101no—
497C4⋊C4—101no—
498C22⋊C4—101no—
499C22⋊C4—102no—
500C22⋊C4—102no—
501C22⋊C4—101no—
502C22⋊C4—101no—
503C42—101no—
504C42—101no—
505C42—101no—
506C42C3×D2011yescharacteristic
507C42C3×D2011yescharacteristic
508C42C22×C3×D511yescharacteristic
509C42C22×C3×D511yescharacteristic
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—102no—
514C22×C3—104no—
515C22×C3—208no—
516C22×C3—202no—
517C22×C3—201no—
518C22×C3—201no—
519C22×C3—202no—
520C22×C3C4×D2012yes—
521C22×C3C22×D2011yescharacteristic
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—102no—
526C3×C4—201no—
527C3×C4—202no—
528C3×C4—201no—
529C3×C4C4×D2012yes—
530C3×C4#405412yesdirect product factor
531C3×C4C22×C4×D511yescharacteristic
532C3×C4C2×#70911yescharacteristic
533C2×C5—22no—
534C2×C5C2×C3×C4×D411yescharacteristic
535C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
536C2×C5C3×#57511yescharacteristic
537D5—44no—
538D5—42no—
539C23—101no—
540C23—102no—
541C23—104no—
542C23—202no—
543C23—202no—
544C23C2×C3×D2011yescharacteristic
545Q8—52no—
546Q8—101no—
547D4—52no—
548D4—54no—
549D4—104no—
550D4—102no—
551D4—101no—
552D4—104no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—101no—
556C2×C4—104no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—102no—
560C2×C4—204no—
561C2×C4—202no—
562C2×C4—202no—
563C2×C4—204no—
564C2×C4—202no—
565C2×C4C2×C3×C4×D512yes—
566C2×C4C2×C3×D2011yescharacteristic
567C2×C4C2×C3×D2011yescharacteristic
568C2×C4C2×C3×D2011yescharacteristic
569C2×C4C2×C3×D2011yescharacteristic
570C2×C4C2×C3×D2011yescharacteristic
571C2×C4C3×#70912yes—
572C2×C4C23×C3×D511yescharacteristic
573C8—22no—
574C8C2×C3×C4×D514yescomplemented
575C2×C3—22no—
576C2×C3—204no—
577C2×C3—202no—
578C2×C3C2×C4×D2011yescharacteristic
579C2×C3C2×#405411yescharacteristic
580C2×C3#6608211yescharacteristic
581C5C3×C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—102no—
585C22—104no—
586C22—208no—
587C22—202no—
588C22—201no—
589C22—201no—
590C22—202no—
591C22C3×C4×D2012yes—
592C22C22×C3×D2011yescharacteristic
593C4—21no—
594C4—21no—
595C4—21no—
596C4—102no—
597C4—202no—
598C4—201no—
599C4—201no—
600C4C3×C4×D2012yes—
601C4C3×#405412yesdirect product factor
602C4C22×C3×C4×D511yescharacteristic
603C4C2×C3×#70911yescharacteristic
604C3C4×#405411yescharacteristic, direct product factor, Sylow
605C2—22no—
606C2—204no—
607C2—202no—
608C2C2×C3×C4×D2011yescharacteristic
609C2C2×C3×#405411yescharacteristic
610C2C3×#6608211yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D20
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C4×C5×M16C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4054C2
cosocleC2×C4×C5C24×C3
hypercenterC3×C4×M16D5
hypocenterC5C3×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×M16

Complements

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

NH ≅ G/Ntype
2. C3×C4×#709C2semidirect
3. C2×C3×C4×D20C2semidirect
4. C3×C4×C5×M16C2semidirect
5. C3×#65422C2semidirect
6. C3×#65420C2semidirect
7. C3×#65410C2semidirect
8. C3×#65000C2semidirect
9. C3×#64999C2semidirect
10. C3×C4×D40C2semidirect
11. C3×C4×#677C2semidirect
12. C4×#4054C3direct (N × H)
24. C3×#4054C4direct (N × H)
31. C3×C4×D20C22semidirect
32. C3×C4×D20C22semidirect
35. C3×C4×Dic10C22semidirect
36. C3×C4×Dic10C22semidirect
37. C3×C5×#97C22semidirect
38. C3×C4×C5×C8C22semidirect
41. C3×#3953C22semidirect
42. C3×#3950C22semidirect
43. C3×#3949C22semidirect
44. C3×#3948C22semidirect
47. C4×#709C2×C3semidirect
48. C2×C4×D20C2×C3semidirect
49. C4×C5×M16C2×C3semidirect
50. #65422C2×C3semidirect
51. #65420C2×C3semidirect
52. #65410C2×C3semidirect
53. #65000C2×C3semidirect
54. #64999C2×C3semidirect
55. C4×D40C2×C3semidirect
56. C4×#677C2×C3semidirect
64. C3×#709C2×C4semidirect
67. C2×C3×D20C2×C4semidirect
78. C3×C5×M16C2×C4semidirect
99. C3×D40C2×C4semidirect
100. C3×#677C2×C4semidirect
111. C3×C4×M16D5semidirect
123. #4054C3×C4direct (N × H)
130. C4×D20C22×C3semidirect
131. C4×D20C22×C3semidirect
134. C4×Dic10C22×C3semidirect
135. C4×Dic10C22×C3semidirect
136. C5×#97C22×C3semidirect
137. C4×C5×C8C22×C3semidirect
140. #3953C22×C3semidirect
141. #3950C22×C3semidirect
142. #3949C22×C3semidirect
143. #3948C22×C3semidirect
171. C3×D20C22×C4semidirect
178. C3×Dic10C22×C4semidirect
180. C3×C5×C8C22×C4semidirect
211. C3×#97C2×D5semidirect
212. C3×C4×C8C2×D5semidirect
220. #709C2×C3×C4semidirect
223. C2×D20C2×C3×C4semidirect
234. C5×M16C2×C3×C4semidirect
255. D40C2×C3×C4semidirect
256. #677C2×C3×C4semidirect
267. C4×M16C3×D5semidirect
283. C3×C4×C5AGL(1,ℤ/8)semidirect
313. C3×M16C4×D5semidirect
360. D20C22×C3×C4semidirect
367. Dic10C22×C3×C4semidirect
369. C5×C8C22×C3×C4semidirect
400. #97C2×C3×D5semidirect
401. C4×C8C2×C3×D5semidirect
443. C3×C8C2×C4×D5semidirect
459. C4×C5C3×AGL(1,ℤ/8)semidirect
489. M16C3×C4×D5semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
530. C3×C4#4054direct (N × H)
574. C8C2×C3×C4×D5semidirect
581. C5C3×C4×AGL(1,ℤ/8)semidirect
601. C4C3×#4054direct (N × H)
604. C3C4×#4054direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40542
C3×C4×#7092
C2×C3×C4×D202
C3×C4×C5×M162
C3×#654222
C3×#654202
C3×#654102
C3×#650002
C3×#649992
C3×C4×D402
C3×C4×#6772
C4×#40543
C3×C4×AGL(1,ℤ/8)5