Finite Group Databasebeta

← C4×C5×GL(2,ℤ/4) #14511222

Subgroups — C4×C5×GL(2,ℤ/4) #14511222

Order 1920.

994 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×A4C211yesmaximal, characteristic, complemented
2C2×C5×GL(2,ℤ/4)C211yesmaximal, characteristic
3C2×C4×C5×S4C211yesmaximal, characteristic, complemented
4C5×#5432C211yesmaximal, characteristic, complemented
5C5×(C2×S4)⋊C4C211yesmaximal, characteristic, complemented
6C5×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic, complemented
7C4×C5×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
8C4×C5×#120—31nomaximal, Hall
9C23×C5×A4C2211yescharacteristic
10C22×C5×S4C2211yescharacteristic
11C2×C4×C5×A4—22no—
12C2×C4×C5×A4C2211yescharacteristic
13C2×C4×C5×A4C2211yescharacteristic
14C5×GL(2,ℤ/4)C414yesdirect product factor
15C2×C5×SL(2,ℤ/4)C2211yescharacteristic
16C2×C5×SL(2,ℤ/4)C2211yescharacteristic
17C2×C5×SL(2,ℤ/4)C2211yescharacteristic
18C4×C5×S4—22no—
19C4×C5×#67—41nomaximal
20C4×GL(2,ℤ/4)C511yesmaximal, characteristic, direct product factor, Hall
21C24×C4×C5D311yescharacteristic, complemented
22C2×C5×#120—31no—
23C2×C4×C5×D4—31no—
24C2×C4×C5×D4—31no—
25C2×C4×C5×D4—31no—
26C5×#386—31no—
27C5×#386—31no—
28C5×#386—31no—
29C5×#385—31no—
30C5×#385—31no—
31C5×#385—31no—
32C5×#379—31no—
33C4×C5×C22⋊C4—31no—
34C4×C5×C22⋊C4—31no—
35C4×C5×C22⋊C4—31no—
36C22×C5×A4—21no—
37C22×C5×A4—21no—
38C22×C5×A4C2×C412yescomplemented
39C22×C5×A4C2311yescharacteristic
40C2×C5×S4—21no—
41C2×C5×S4—21no—
42C2×C5×S4C2×C412yescomplemented
43C22×C3×C4×C5—41no—
44C2×C5×#67—41no—
45C2×C4×C5×D3—41no—
46C4×C5×A4—21no—
47C4×C5×A4D412yescomplemented
48C5×SL(2,ℤ/4)—21no—
49C5×SL(2,ℤ/4)—21no—
50C5×SL(2,ℤ/4)C2×C412yescomplemented
51C5×#217—41no—
52C5×(C2×D3)⋊C4—41no—
53C5×Dic3⋊C4—41no—
54C4×C5×Dic3—41no—
55C22×C4×A4C2×C511yescharacteristic, complemented
56C2×GL(2,ℤ/4)C2×C511yescharacteristic
57C2×C4×S4C2×C511yescharacteristic, complemented
58#5432C2×C511yescharacteristic, complemented
59(C2×S4)⋊C4C2×C511yescharacteristic, complemented
60SL(2,ℤ/4)⋊C4C2×C511yescharacteristic, complemented
61C4×SL(2,ℤ/4)C2×C511yescharacteristic, complemented
62C25×C5C2×D311yescharacteristic
63C22×C5×D4—31no—
64C22×C5×D4—31no—
65C22×C5×D4—31no—
66C23×C4×C5—22no—
67C23×C4×C5—31no—
68C23×C4×C5—31no—
69C23×C4×C5—31no—
70C23×C4×C5—31no—
71C23×C4×C5—31no—
72C23×C4×C5—62no—
73C23×C4×C5C2×D311yescharacteristic
74C23×C4×C5C2×D311yescharacteristic
75C5×#120—34no—
76C5×#120—34no—
77C4×C5×D4—62no—
78C4×C5×D4—64no—
79C4×C5×D4—61no—
80C4×C5×D4—61no—
81C4×C5×D4—61no—
82C4×C5×D4—62no—
83C4×C5×D4—61no—
84C2×C5×C4⋊C4—31no—
85C2×C5×C4⋊C4—31no—
86C2×C5×C4⋊C4—31no—
87C2×C5×C22⋊C4—31no—
88C2×C5×C22⋊C4—31no—
89C2×C5×C22⋊C4—31no—
90C2×C5×C22⋊C4—31no—
91C2×C5×C22⋊C4—31no—
92C2×C5×C22⋊C4—31no—
93C2×C5×C22⋊C4—31no—
94C2×C5×C22⋊C4—31no—
95C2×C5×C22⋊C4—31no—
96C2×C5×C22⋊C4—31no—
97C2×C5×C22⋊C4—31no—
98C2×C5×C22⋊C4—31no—
99C2×C42×C5—31no—
100C2×C42×C5—31no—
101C2×C42×C5—31no—
102C5×#95—31no—
103C5×#95—31no—
104C5×#95—31no—
105C5×#95—31no—
106C5×#95—31no—
107C5×#95—31no—
108C4×#120—31noSylow
109C23×C3×C5—41no—
110C22×C5×D3—41no—
111C2×C5×A4—22no—
112C2×C5×A4C22×C411yescharacteristic
113C2×C5×A4C2×D411yescharacteristic
114C2×C5×A4#4111yescharacteristic
115C5×S4—22no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—82no—
119C5×#67—44no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C4×C5×D3—82no—
124C23×A4C22×C511yescharacteristic
125C22×S4C22×C511yescharacteristic
126C2×C4×A4—22no—
127C2×C4×A4C22×C511yescharacteristic
128C2×C4×A4C22×C511yescharacteristic
129GL(2,ℤ/4)C4×C514yesdirect product factor
130C2×SL(2,ℤ/4)C22×C511yescharacteristic
131C2×SL(2,ℤ/4)C22×C511yescharacteristic
132C2×SL(2,ℤ/4)C22×C511yescharacteristic
133C4×S4—22no—
134C4×#67—41no—
135C24×C5—21no—
136C24×C5—21no—
137C24×C5—31no—
138C24×C5—31no—
139C24×C5—32no—
140C24×C5—31no—
141C24×C5—61no—
142C24×C5—61no—
143C24×C5C4×D312yescomplemented
144C24×C5C22×D311yescharacteristic
145C2×C5×D4—34no—
146C2×C5×D4—32no—
147C2×C5×D4—34no—
148C2×C5×D4—32no—
149C2×C5×D4—61no—
150C2×C5×D4—62no—
151C2×C5×D4—61no—
152C2×C5×D4—61no—
153C2×C5×D4—62no—
154C2×C5×D4—62no—
155C2×C5×D4—61no—
156C2×C5×D4—61no—
157C2×C5×D4—61no—
158C22×C4×C5—21no—
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—32no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5—31no—
166C22×C4×C5—34no—
167C22×C4×C5—31no—
168C22×C4×C5—31no—
169C22×C4×C5—31no—
170C22×C4×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—31no—
173C22×C4×C5—31no—
174C22×C4×C5—31no—
175C22×C4×C5—62no—
176C22×C4×C5—62no—
177C22×C4×C5—61no—
178C22×C4×C5—61no—
179C22×C4×C5—62no—
180C22×C4×C5—62no—
181C22×C4×C5—62no—
182C22×C4×C5—62no—
183C22×C4×C5—61no—
184C22×C4×C5—62no—
185C22×C4×C5—62no—
186C22×C4×C5—62no—
187C22×C4×C5—61no—
188C22×C4×C5#6712yescomplemented
189C22×C4×C5S411yescharacteristic, complemented
190C5×C4⋊C4—62no—
191C5×C4⋊C4—62no—
192C5×C4⋊C4—61no—
193C5×C4⋊C4—61no—
194C5×C22⋊C4—34no—
195C5×C22⋊C4—32no—
196C5×C22⋊C4—34no—
197C5×C22⋊C4—32no—
198C5×C22⋊C4—62no—
199C5×C22⋊C4—62no—
200C5×C22⋊C4—61no—
201C5×C22⋊C4—61no—
202C5×C22⋊C4—62no—
203C5×C22⋊C4—62no—
204C5×C22⋊C4—61no—
205C5×C22⋊C4—62no—
206C5×C22⋊C4—61no—
207C5×C22⋊C4—61no—
208C5×C22⋊C4—61no—
209C5×C22⋊C4—61no—
210C5×C22⋊C4—61no—
211C42×C5—61no—
212C42×C5—62no—
213C42×C5—62no—
214C42×C5—61no—
215C24×C4C5×D311yescharacteristic, complemented
216C2×#120—31no—
217C2×C4×D4—31no—
218C2×C4×D4—31no—
219C2×C4×D4—31no—
220#386—31no—
221#386—31no—
222#386—31no—
223#385—31no—
224#385—31no—
225#385—31no—
226#379—31no—
227C4×C22⋊C4—31no—
228C4×C22⋊C4—31no—
229C4×C22⋊C4—31no—
230C22×C3×C5—42no—
231C22×C3×C5—41no—
232C22×C3×C5—81no—
233C22×C3×C5—81no—
234C2×C5×D3—42no—
235C2×C5×D3—81no—
236C2×C5×D3—81no—
237C5×A4C4×D411yescharacteristic, complemented
238C3×C4×C5—42no—
239C3×C4×C5—81no—
240C5×Dic3—42no—
241C5×Dic3—81no—
242C5×Dic3—81no—
243C22×A4—21no—
244C22×A4—21no—
245C22×A4C2×C4×C512yescomplemented
246C22×A4C23×C511yescharacteristic
247C2×S4—21no—
248C2×S4—21no—
249C2×S4C2×C4×C512yescomplemented
250C22×C3×C4—41no—
251C2×#67—41no—
252C2×C4×D3—41no—
253C4×A4—21no—
254C4×A4C5×D412yescomplemented
255SL(2,ℤ/4)—21no—
256SL(2,ℤ/4)—21no—
257SL(2,ℤ/4)C2×C4×C512yescomplemented
258#217—41no—
259(C2×D3)⋊C4—41no—
260Dic3⋊C4—41no—
261C4×Dic3—41no—
262C23×C5—22no—
263C23×C5—31no—
264C23×C5—32no—
265C23×C5—31no—
266C23×C5—31no—
267C23×C5—31no—
268C23×C5—32no—
269C23×C5—32no—
270C23×C5—32no—
271C23×C5—32no—
272C23×C5—31no—
273C23×C5—32no—
274C23×C5—61no—
275C23×C5—61no—
276C23×C5—61no—
277C23×C5—61no—
278C23×C5—62no—
279C23×C5—61no—
280C23×C5—61no—
281C23×C5—62no—
282C23×C5—62no—
283C23×C5—61no—
284C23×C5—64no—
285C23×C5—61no—
286C23×C5—61no—
287C23×C5—61no—
288C23×C5—61no—
289C23×C5—61no—
290C23×C5—61no—
291C23×C5C2×C4×D311yescharacteristic
292C23×C5#23511yescharacteristic
293C23×C5C2×#6711yescharacteristic
294C23×C5C2×S411yescharacteristic
295C5×D4—62no—
296C5×D4—62no—
297C5×D4—62no—
298C5×D4—68no—
299C5×D4—64no—
300C5×D4—62no—
301C5×D4—64no—
302C2×C4×C5—22no—
303C2×C4×C5—31no—
304C2×C4×C5—32no—
305C2×C4×C5—32no—
306C2×C4×C5—32no—
307C2×C4×C5—32no—
308C2×C4×C5—32no—
309C2×C4×C5—32no—
310C2×C4×C5—32no—
311C2×C4×C5—31no—
312C2×C4×C5—62no—
313C2×C4×C5—61no—
314C2×C4×C5—61no—
315C2×C4×C5—61no—
316C2×C4×C5—62no—
317C2×C4×C5—64no—
318C2×C4×C5—61no—
319C2×C4×C5—61no—
320C2×C4×C5—61no—
321C2×C4×C5—61no—
322C2×C4×C5—61no—
323C2×C4×C5—61no—
324C2×C4×C5—62no—
325C2×C4×C5—61no—
326C2×C4×C5—61no—
327C2×C4×C5—61no—
328C2×C4×C5—61no—
329C2×C4×C5—61no—
330C2×C4×C5—61no—
331C2×C4×C5—61no—
332C2×C4×C5—61no—
333C2×C4×C5—61no—
334C2×C4×C5—61no—
335C2×C4×C5—61no—
336C2×C4×C5—61no—
337C2×C4×C5—61no—
338C2×C4×C5—122no—
339C2×C4×C5—122no—
340C2×C4×C5C2×S411yescharacteristic
341C2×C4×C5C2×S411yescharacteristic
342C25C2×C5×D311yescharacteristic
343C22×D4—31no—
344C22×D4—31no—
345C22×D4—31no—
346C23×C4—22no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—62no—
353C23×C4C2×C5×D311yescharacteristic
354C23×C4C2×C5×D311yescharacteristic
355#120—34no—
356#120—34no—
357C4×D4—62no—
358C4×D4—64no—
359C4×D4—61no—
360C4×D4—61no—
361C4×D4—61no—
362C4×D4—62no—
363C4×D4—61no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—31no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—31no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—31no—
382#95—31no—
383#95—31no—
384#95—31no—
385#95—31no—
386#95—31no—
387#95—31no—
388C2×C3×C5—41no—
389C2×C3×C5—41no—
390C2×C3×C5—41no—
391C2×C3×C5—82no—
392C5×D3—82no—
393C23×C3—41no—
394C22×D3—41no—
395C2×A4—22no—
396C2×A4C22×C4×C511yescharacteristic
397C2×A4C2×C5×D411yescharacteristic
398C2×A4C5×#4111yescharacteristic
399S4—22no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—82no—
403#67—44no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406C2×Dic3—41no—
407C4×D3—82no—
408C22×C5—21no—
409C22×C5—21no—
410C22×C5—31no—
411C22×C5—31no—
412C22×C5—31no—
413C22×C5—31no—
414C22×C5—31no—
415C22×C5—31no—
416C22×C5—31no—
417C22×C5—31no—
418C22×C5—31no—
419C22×C5—34no—
420C22×C5—32no—
421C22×C5—62no—
422C22×C5—62no—
423C22×C5—62no—
424C22×C5—62no—
425C22×C5—61no—
426C22×C5—62no—
427C22×C5—62no—
428C22×C5—62no—
429C22×C5—62no—
430C22×C5—62no—
431C22×C5—61no—
432C22×C5—61no—
433C22×C5—62no—
434C22×C5—121no—
435C22×C5—121no—
436C22×C5—121no—
437C22×C5—121no—
438C22×C5C4×#6711yescharacteristic, complemented
439C22×C5C4×S412yescomplemented
440C22×C5C22×S411yescharacteristic
441C4×C5—21no—
442C4×C5—32no—
443C4×C5—62no—
444C4×C5—62no—
445C4×C5—62no—
446C4×C5—61no—
447C4×C5—121no—
448C4×C5—121no—
449C4×C5—121no—
450C4×C5—121no—
451C4×C5GL(2,ℤ/4)12yesdirect product factor
452C24—21no—
453C24—21no—
454C24—31no—
455C24—31no—
456C24—32no—
457C24—31no—
458C24—61no—
459C24—61no—
460C24C4×C5×D312yescomplemented
461C24C22×C5×D311yescharacteristic
462C2×D4—34no—
463C2×D4—32no—
464C2×D4—34no—
465C2×D4—32no—
466C2×D4—61no—
467C2×D4—62no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4—62no—
471C2×D4—62no—
472C2×D4—61no—
473C2×D4—61no—
474C2×D4—61no—
475C22×C4—21no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—32no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—34no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—31no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4—31no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—61no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—61no—
505C22×C4C5×#6712yescomplemented
506C22×C4C5×S411yescharacteristic, complemented
507C4⋊C4—62no—
508C4⋊C4—62no—
509C4⋊C4—61no—
510C4⋊C4—61no—
511C22⋊C4—34no—
512C22⋊C4—32no—
513C22⋊C4—34no—
514C22⋊C4—32no—
515C22⋊C4—62no—
516C22⋊C4—62no—
517C22⋊C4—61no—
518C22⋊C4—61no—
519C22⋊C4—62no—
520C22⋊C4—61no—
521C22⋊C4—61no—
522C22⋊C4—62no—
523C22⋊C4—62no—
524C22⋊C4—61no—
525C22⋊C4—61no—
526C22⋊C4—61no—
527C22⋊C4—61no—
528C42—61no—
529C42—62no—
530C42—62no—
531C42—61no—
532C3×C5—41noHall
533C22×C3—42no—
534C22×C3—41no—
535C22×C3—81no—
536C22×C3—81no—
537C2×D3—42no—
538C2×D3—81no—
539C2×D3—81no—
540A4C4×C5×D411yescharacteristic, complemented
541C3×C4—42no—
542C3×C4—81no—
543Dic3—42no—
544Dic3—81no—
545Dic3—81no—
546C2×C5—22no—
547C2×C5—31no—
548C2×C5—31no—
549C2×C5—31no—
550C2×C5—31no—
551C2×C5—62no—
552C2×C5—122no—
553C2×C5C2×C4×S411yescharacteristic
554C2×C5#591211yescharacteristic
555C2×C5C2×GL(2,ℤ/4)11yescharacteristic
556C23—22no—
557C23—31no—
558C23—32no—
559C23—31no—
560C23—31no—
561C23—31no—
562C23—32no—
563C23—32no—
564C23—32no—
565C23—32no—
566C23—31no—
567C23—32no—
568C23—61no—
569C23—61no—
570C23—61no—
571C23—61no—
572C23—62no—
573C23—61no—
574C23—61no—
575C23—62no—
576C23—62no—
577C23—61no—
578C23—64no—
579C23—61no—
580C23—61no—
581C23—61no—
582C23—61no—
583C23—61no—
584C23—61no—
585C23C2×C4×C5×D311yescharacteristic
586C23C5×#23511yescharacteristic
587C23C2×C5×#6711yescharacteristic
588C23C2×C5×S411yescharacteristic
589D4—62no—
590D4—62no—
591D4—62no—
592D4—68no—
593D4—64no—
594D4—64no—
595D4—62no—
596C2×C4—22no—
597C2×C4—31no—
598C2×C4—32no—
599C2×C4—32no—
600C2×C4—32no—
601C2×C4—32no—
602C2×C4—32no—
603C2×C4—32no—
604C2×C4—32no—
605C2×C4—31no—
606C2×C4—62no—
607C2×C4—61no—
608C2×C4—61no—
609C2×C4—61no—
610C2×C4—62no—
611C2×C4—64no—
612C2×C4—61no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—61no—
616C2×C4—61no—
617C2×C4—61no—
618C2×C4—62no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—122no—
633C2×C4—122no—
634C2×C4C2×C5×S411yescharacteristic
635C2×C4C2×C5×S411yescharacteristic
636C2×C3—41no—
637C2×C3—41no—
638C2×C3—41no—
639C2×C3—82no—
640D3—82no—
641C5C4×GL(2,ℤ/4)11yescharacteristic, direct product factor, Sylow
642C22—21no—
643C22—21no—
644C22—31no—
645C22—31no—
646C22—31no—
647C22—31no—
648C22—31no—
649C22—31no—
650C22—31no—
651C22—31no—
652C22—31no—
653C22—34no—
654C22—32no—
655C22—62no—
656C22—62no—
657C22—62no—
658C22—62no—
659C22—61no—
660C22—62no—
661C22—62no—
662C22—62no—
663C22—62no—
664C22—62no—
665C22—61no—
666C22—61no—
667C22—62no—
668C22—121no—
669C22—121no—
670C22—121no—
671C22—121no—
672C22C4×C5×#6711yescharacteristic, complemented
673C22C4×C5×S412yescomplemented
674C22C22×C5×S411yescharacteristic
675C4—21no—
676C4—32no—
677C4—62no—
678C4—62no—
679C4—62no—
680C4—61no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—121no—
685C4C5×GL(2,ℤ/4)12yesdirect product factor
686C3—41noSylow
687C2—22no—
688C2—31no—
689C2—31no—
690C2—31no—
691C2—31no—
692C2—62no—
693C2—122no—
694C2C2×C4×C5×S411yescharacteristic
695C2C5×#591211yescharacteristic
696C2C2×C5×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC2×C4×C5C2×S4
commutatorC2×A4C22×C4×C5
FrattiniC22C22×C5×S4
FittingC24×C4×C5D3
socleC24×C5C22×D3
prime radicalC2×C5×GL(2,ℤ/4)C2
cosocleC22×A4C23×C5
hypercenterC22×C4×C5S4
hypocenterA4C4×C5×D4
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×A4C2semidirect
3. C2×C4×C5×S4C2semidirect
4. C5×#5432C2semidirect
5. C5×(C2×S4)⋊C4C2semidirect
6. C5×SL(2,ℤ/4)⋊C4C2semidirect
7. C4×C5×SL(2,ℤ/4)C2semidirect
14. C5×GL(2,ℤ/4)C4direct (N × H)
20. C4×GL(2,ℤ/4)C5direct (N × H)
21. C24×C4×C5D3semidirect
38. C22×C5×A4C2×C4semidirect
42. C2×C5×S4C2×C4semidirect
47. C4×C5×A4D4semidirect
50. C5×SL(2,ℤ/4)C2×C4semidirect
55. C22×C4×A4C2×C5semidirect
57. C2×C4×S4C2×C5semidirect
58. #5432C2×C5semidirect
59. (C2×S4)⋊C4C2×C5semidirect
60. SL(2,ℤ/4)⋊C4C2×C5semidirect
61. C4×SL(2,ℤ/4)C2×C5semidirect
129. GL(2,ℤ/4)C4×C5direct (N × H)
143. C24×C5C4×D3semidirect
188. C22×C4×C5#67semidirect
189. C22×C4×C5S4semidirect
215. C24×C4C5×D3semidirect
237. C5×A4C4×D4semidirect
245. C22×A4C2×C4×C5semidirect
249. C2×S4C2×C4×C5semidirect
254. C4×A4C5×D4semidirect
257. SL(2,ℤ/4)C2×C4×C5semidirect
438. C22×C5C4×#67semidirect
439. C22×C5C4×S4semidirect
451. C4×C5GL(2,ℤ/4)direct (N × H)
460. C24C4×C5×D3semidirect
505. C22×C4C5×#67semidirect
506. C22×C4C5×S4semidirect
540. A4C4×C5×D4semidirect
641. C5C4×GL(2,ℤ/4)direct (N × H)
672. C22C4×C5×#67semidirect
673. C22C4×C5×S4semidirect
685. C4C5×GL(2,ℤ/4)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×A42
C2×C5×GL(2,ℤ/4)2
C2×C4×C5×S42
C5×#54322
C5×(C2×S4)⋊C42
C5×SL(2,ℤ/4)⋊C42
C4×C5×SL(2,ℤ/4)2
C4×C5×#1203
C4×C5×#674
C4×GL(2,ℤ/4)5