Finite Group Databasebeta

← C5×GL(2,ℤ/4)⋊C4 #14511034

Subgroups — C5×GL(2,ℤ/4)⋊C4 #14511034

Order 1920.

914 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C2×C5×GL(2,ℤ/4)C211yesmaximal, characteristic
2C22×C5×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
3C2×C4×C5×S4C211yesmaximal, characteristic, complemented
4C5×A4×C22⋊C4C211yesmaximal, 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
8C5×#2358—31nomaximal, Hall
9C23×C5×A4C2211yescharacteristic
10C22×C5×S4C2211yescharacteristic
11C2×C4×C5×A4C2211yescharacteristic
12C2×C4×C5×A4C2211yescharacteristic
13C5×GL(2,ℤ/4)C414yescomplemented
14C2×C5×SL(2,ℤ/4)—22no—
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—
19C5×#67⋊C4—41nomaximal
20GL(2,ℤ/4)⋊C4C511yesmaximal, characteristic, direct product factor, Hall
21C2×C5×#120—31no—
22C2×C4×C5×D4—31no—
23C2×C4×C5×D4—31no—
24C22×C5×C22⋊C4—31no—
25C22×C5×C22⋊C4D311yescharacteristic, complemented
26C5×#390—31no—
27C5×#388—31no—
28C5×#388—31no—
29C5×#386—31no—
30C5×#386—31no—
31C5×#386—31no—
32C5×#385—31no—
33C5×#385—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
43C2×C5×#67—41no—
44C22×C5×Dic3—41no—
45C2×C4×C5×D3—41no—
46C4×C5×A4—21no—
47C4×C5×A4—21no—
48C5×SL(2,ℤ/4)—21no—
49C5×SL(2,ℤ/4)C2×C412yescomplemented
50C5×SL(2,ℤ/4)D412yescomplemented
51C3×C5×C22⋊C4—41no—
52C5×(C2×D3)⋊C4—41no—
53C5×Dic3⋊C4—41no—
54C4×C5×Dic3—41no—
55C2×GL(2,ℤ/4)C2×C511yescharacteristic
56C22×SL(2,ℤ/4)C2×C511yescharacteristic, complemented
57C2×C4×S4C2×C511yescharacteristic, complemented
58A4×C22⋊C4C2×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—31no—
67C23×C4×C5—31no—
68C23×C4×C5—31no—
69C23×C4×C5C2×D311yescharacteristic
70C23×C4×C5C2×D311yescharacteristic
71C5×#120—34no—
72C5×#120—34no—
73C4×C5×D4—62no—
74C4×C5×D4—62no—
75C4×C5×D4—61no—
76C4×C5×D4—61no—
77C4×C5×D4—61no—
78C4×C5×D4—61no—
79C2×C5×C4⋊C4—31no—
80C2×C5×C4⋊C4—31no—
81C2×C5×C4⋊C4—31no—
82C2×C5×C22⋊C4—31no—
83C2×C5×C22⋊C4—31no—
84C2×C5×C22⋊C4—31no—
85C2×C5×C22⋊C4—31no—
86C2×C5×C22⋊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—62no—
97C2×C5×C22⋊C4—62no—
98C2×C42×C5—31no—
99C2×C42×C5—31no—
100C2×C42×C5—31no—
101C5×#95—31no—
102C5×#95—31no—
103C5×#95—31no—
104C5×#95—31no—
105C5×#95—31no—
106C5×#95—31no—
107#2358—31noSylow
108C23×C3×C5—41no—
109C22×C5×D3—41no—
110C2×C5×A4—22no—
111C2×C5×A4C22×C411yescharacteristic
112C2×C5×A4C2×D411yescharacteristic
113C2×C5×A4#4111yescharacteristic
114C5×S4—22no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C5×#67—44no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—82no—
122C4×C5×D3—82no—
123C23×A4C22×C511yescharacteristic
124C22×S4C22×C511yescharacteristic
125C2×C4×A4C22×C511yescharacteristic
126C2×C4×A4C22×C511yescharacteristic
127GL(2,ℤ/4)C4×C514yescomplemented
128C2×SL(2,ℤ/4)—22no—
129C2×SL(2,ℤ/4)C22×C511yescharacteristic
130C2×SL(2,ℤ/4)C22×C511yescharacteristic
131C2×SL(2,ℤ/4)C22×C511yescharacteristic
132C4×S4—22no—
133#67⋊C4—41no—
134C24×C5—21no—
135C24×C5—21no—
136C24×C5—31no—
137C24×C5—31no—
138C24×C5—32no—
139C24×C5—31no—
140C24×C5—61no—
141C24×C5—61no—
142C24×C5C4×D312yescomplemented
143C24×C5C22×D311yescharacteristic
144C2×C5×D4—32no—
145C2×C5×D4—34no—
146C2×C5×D4—32no—
147C2×C5×D4—34no—
148C2×C5×D4—61no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C2×C5×D4—62no—
152C2×C5×D4—61no—
153C2×C5×D4—61no—
154C2×C5×D4—61no—
155C2×C5×D4—121no—
156C2×C5×D4—121no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5—31no—
166C22×C4×C5—31no—
167C22×C4×C5—31no—
168C22×C4×C5—31no—
169C22×C4×C5—31no—
170C22×C4×C5—62no—
171C22×C4×C5—62no—
172C22×C4×C5—62no—
173C22×C4×C5—61no—
174C22×C4×C5—61no—
175C22×C4×C5—61no—
176C22×C4×C5—61no—
177C22×C4×C5—62no—
178C22×C4×C5—61no—
179C22×C4×C5—61no—
180C22×C4×C5—121no—
181C22×C4×C5—121no—
182C22×C4×C5—121no—
183C5×C4⋊C4—62no—
184C5×C4⋊C4—61no—
185C5×C4⋊C4—61no—
186C5×C4⋊C4—121no—
187C5×C22⋊C4—32no—
188C5×C22⋊C4—32no—
189C5×C22⋊C4—34no—
190C5×C22⋊C4—34no—
191C5×C22⋊C4—32no—
192C5×C22⋊C4—32no—
193C5×C22⋊C4—31no—
194C5×C22⋊C4—31no—
195C5×C22⋊C4—31no—
196C5×C22⋊C4—61no—
197C5×C22⋊C4—62no—
198C5×C22⋊C4—62no—
199C5×C22⋊C4—62no—
200C5×C22⋊C4—61no—
201C5×C22⋊C4—61no—
202C5×C22⋊C4—61no—
203C5×C22⋊C4—61no—
204C5×C22⋊C4—121no—
205C5×C22⋊C4S411yescharacteristic, complemented
206C42×C5—62no—
207C42×C5—61no—
208C42×C5—61no—
209C42×C5—121no—
210C2×#120—31no—
211C2×C4×D4—31no—
212C2×C4×D4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4C5×D311yescharacteristic, complemented
215#390—31no—
216#388—31no—
217#388—31no—
218#386—31no—
219#386—31no—
220#386—31no—
221#385—31no—
222#385—31no—
223C4×C22⋊C4—31no—
224C4×C22⋊C4—31no—
225C22×C3×C5—42no—
226C22×C3×C5—41no—
227C22×C3×C5—81no—
228C22×C3×C5—81no—
229C2×C5×D3—42no—
230C2×C5×D3—81no—
231C2×C5×D3—81no—
232C5×A4C4×D411yescharacteristic, complemented
233C3×C4×C5—81no—
234C3×C4×C5—81no—
235C5×Dic3—42no—
236C5×Dic3—42no—
237C5×Dic3—81no—
238C22×A4—21no—
239C22×A4—21no—
240C22×A4C2×C4×C512yescomplemented
241C22×A4C23×C511yescharacteristic
242C2×S4—21no—
243C2×S4—21no—
244C2×S4C2×C4×C512yescomplemented
245C2×#67—41no—
246C22×Dic3—41no—
247C2×C4×D3—41no—
248C4×A4—21no—
249C4×A4—21no—
250SL(2,ℤ/4)—21no—
251SL(2,ℤ/4)C2×C4×C512yescomplemented
252SL(2,ℤ/4)C5×D412yescomplemented
253C3×C22⋊C4—41no—
254(C2×D3)⋊C4—41no—
255Dic3⋊C4—41no—
256C4×Dic3—41no—
257C23×C5—22no—
258C23×C5—31no—
259C23×C5—31no—
260C23×C5—31no—
261C23×C5—31no—
262C23×C5—32no—
263C23×C5—32no—
264C23×C5—32no—
265C23×C5—31no—
266C23×C5—32no—
267C23×C5—61no—
268C23×C5—61no—
269C23×C5—61no—
270C23×C5—61no—
271C23×C5—61no—
272C23×C5—62no—
273C23×C5—61no—
274C23×C5—61no—
275C23×C5—61no—
276C23×C5—62no—
277C23×C5—62no—
278C23×C5—61no—
279C23×C5—61no—
280C23×C5—61no—
281C23×C5—61no—
282C23×C5—61no—
283C23×C5—61no—
284C23×C5—61no—
285C23×C5—122no—
286C23×C5C2×C4×D311yescharacteristic
287C23×C5D3×D411yescharacteristic
288C23×C5#23711yescharacteristic
289C23×C5C2×S411yescharacteristic
290C5×D4—62no—
291C5×D4—62no—
292C5×D4—62no—
293C5×D4—64no—
294C5×D4—62no—
295C5×D4—64no—
296C5×D4—124no—
297C2×C4×C5—32no—
298C2×C4×C5—32no—
299C2×C4×C5—32no—
300C2×C4×C5—32no—
301C2×C4×C5—32no—
302C2×C4×C5—31no—
303C2×C4×C5—31no—
304C2×C4×C5—61no—
305C2×C4×C5—61no—
306C2×C4×C5—61no—
307C2×C4×C5—61no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C2×C4×C5—61no—
312C2×C4×C5—61no—
313C2×C4×C5—61no—
314C2×C4×C5—61no—
315C2×C4×C5—61no—
316C2×C4×C5—61no—
317C2×C4×C5—61no—
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—61no—
325C2×C4×C5—61no—
326C2×C4×C5—61no—
327C2×C4×C5—61no—
328C2×C4×C5—122no—
329C2×C4×C5—122no—
330C2×C4×C5—122no—
331C2×C4×C5—124no—
332C2×C4×C5—122no—
333C2×C4×C5C2×S411yescharacteristic
334C2×C4×C5C2×S411yescharacteristic
335C25C2×C5×D311yescharacteristic
336C22×D4—31no—
337C22×D4—31no—
338C22×D4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4C2×C5×D311yescharacteristic
343C23×C4C2×C5×D311yescharacteristic
344#120—34no—
345#120—34no—
346C4×D4—62no—
347C4×D4—62no—
348C4×D4—61no—
349C4×D4—61no—
350C4×D4—61no—
351C4×D4—61no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C22⋊C4—31no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4—31no—
358C2×C22⋊C4—31no—
359C2×C22⋊C4—31no—
360C2×C22⋊C4—31no—
361C2×C22⋊C4—31no—
362C2×C22⋊C4—31no—
363C2×C22⋊C4—31no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C42—31no—
372C2×C42—31no—
373C2×C42—31no—
374#95—31no—
375#95—31no—
376#95—31no—
377#95—31no—
378#95—31no—
379#95—31no—
380C2×C3×C5—41no—
381C2×C3×C5—41no—
382C2×C3×C5—41no—
383C2×C3×C5—82no—
384C5×D3—82no—
385C23×C3—41no—
386C22×D3—41no—
387C2×A4—22no—
388C2×A4C22×C4×C511yescharacteristic
389C2×A4C2×C5×D411yescharacteristic
390C2×A4C5×#4111yescharacteristic
391S4—22no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394#67—44no—
395C2×Dic3—41no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—82no—
399C4×D3—82no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5—31no—
403C22×C5—31no—
404C22×C5—31no—
405C22×C5—31no—
406C22×C5—31no—
407C22×C5—31no—
408C22×C5—31no—
409C22×C5—31no—
410C22×C5—31no—
411C22×C5—32no—
412C22×C5—62no—
413C22×C5—62no—
414C22×C5—62no—
415C22×C5—62no—
416C22×C5—61no—
417C22×C5—62no—
418C22×C5—62no—
419C22×C5—62no—
420C22×C5—62no—
421C22×C5—61no—
422C22×C5—61no—
423C22×C5—62no—
424C22×C5—121no—
425C22×C5—121no—
426C22×C5—121no—
427C22×C5—121no—
428C22×C5—121no—
429C22×C5—121no—
430C22×C5#67⋊C411yescharacteristic, complemented
431C22×C5C4×S412yescomplemented
432C22×C5C22×S411yescharacteristic
433C4×C5—21no—
434C4×C5—21no—
435C4×C5—62no—
436C4×C5—62no—
437C4×C5—62no—
438C4×C5—62no—
439C4×C5—62no—
440C4×C5—61no—
441C4×C5—61no—
442C4×C5—121no—
443C4×C5—121no—
444C24—21no—
445C24—21no—
446C24—31no—
447C24—31no—
448C24—32no—
449C24—31no—
450C24—61no—
451C24—61no—
452C24C4×C5×D312yescomplemented
453C24C22×C5×D311yescharacteristic
454C2×D4—32no—
455C2×D4—34no—
456C2×D4—32no—
457C2×D4—34no—
458C2×D4—61no—
459C2×D4—61no—
460C2×D4—61no—
461C2×D4—62no—
462C2×D4—61no—
463C2×D4—61no—
464C2×D4—61no—
465C2×D4—121no—
466C2×D4—121no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—31no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—62no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—62no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—121no—
491C22×C4—121no—
492C22×C4—121no—
493C4⋊C4—62no—
494C4⋊C4—61no—
495C4⋊C4—61no—
496C4⋊C4—121no—
497C22⋊C4—32no—
498C22⋊C4—32no—
499C22⋊C4—34no—
500C22⋊C4—34no—
501C22⋊C4—32no—
502C22⋊C4—32no—
503C22⋊C4—31no—
504C22⋊C4—31no—
505C22⋊C4—31no—
506C22⋊C4—61no—
507C22⋊C4—62no—
508C22⋊C4—62no—
509C22⋊C4—62no—
510C22⋊C4—61no—
511C22⋊C4—61no—
512C22⋊C4—61no—
513C22⋊C4—61no—
514C22⋊C4—121no—
515C22⋊C4C5×S411yescharacteristic, complemented
516C42—62no—
517C42—61no—
518C42—61no—
519C42—121no—
520C3×C5—41noHall
521C22×C3—42no—
522C22×C3—41no—
523C22×C3—81no—
524C22×C3—81no—
525C2×D3—42no—
526C2×D3—81no—
527C2×D3—81no—
528A4C4×C5×D411yescharacteristic, complemented
529C3×C4—81no—
530C3×C4—81no—
531Dic3—42no—
532Dic3—42no—
533Dic3—81no—
534C2×C5—22no—
535C2×C5—31no—
536C2×C5—31no—
537C2×C5—31no—
538C2×C5—31no—
539C2×C5—62no—
540C2×C5—122no—
541C2×C5C2×C4×S411yescharacteristic
542C2×C5D4×S411yescharacteristic
543C2×C5#591411yescharacteristic
544C23—22no—
545C23—31no—
546C23—31no—
547C23—31no—
548C23—31no—
549C23—32no—
550C23—32no—
551C23—32no—
552C23—31no—
553C23—32no—
554C23—61no—
555C23—61no—
556C23—61no—
557C23—61no—
558C23—61no—
559C23—62no—
560C23—61no—
561C23—61no—
562C23—61no—
563C23—62no—
564C23—62no—
565C23—61no—
566C23—61no—
567C23—61no—
568C23—61no—
569C23—61no—
570C23—61no—
571C23—61no—
572C23—122no—
573C23C2×C4×C5×D311yescharacteristic
574C23C5×D3×D411yescharacteristic
575C23C5×#23711yescharacteristic
576C23C2×C5×S411yescharacteristic
577D4—62no—
578D4—62no—
579D4—62no—
580D4—64no—
581D4—64no—
582D4—62no—
583D4—124no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—32no—
587C2×C4—32no—
588C2×C4—32no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—61no—
608C2×C4—61no—
609C2×C4—61no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—122no—
616C2×C4—122no—
617C2×C4—122no—
618C2×C4—124no—
619C2×C4—122no—
620C2×C4C2×C5×S411yescharacteristic
621C2×C4C2×C5×S411yescharacteristic
622C2×C3—41no—
623C2×C3—41no—
624C2×C3—41no—
625C2×C3—82no—
626D3—82no—
627C5GL(2,ℤ/4)⋊C411yescharacteristic, direct product factor, Sylow
628C22—21no—
629C22—21no—
630C22—31no—
631C22—31no—
632C22—31no—
633C22—31no—
634C22—31no—
635C22—31no—
636C22—31no—
637C22—31no—
638C22—31no—
639C22—32no—
640C22—62no—
641C22—62no—
642C22—62no—
643C22—62no—
644C22—61no—
645C22—62no—
646C22—62no—
647C22—62no—
648C22—62no—
649C22—61no—
650C22—61no—
651C22—62no—
652C22—121no—
653C22—121no—
654C22—121no—
655C22—121no—
656C22—121no—
657C22—121no—
658C22C5×#67⋊C411yescharacteristic, complemented
659C22C4×C5×S412yescomplemented
660C22C22×C5×S411yescharacteristic
661C4—21no—
662C4—21no—
663C4—62no—
664C4—62no—
665C4—62no—
666C4—62no—
667C4—61no—
668C4—62no—
669C4—61no—
670C4—121no—
671C4—121no—
672C3—41noSylow
673C2—22no—
674C2—31no—
675C2—31no—
676C2—31no—
677C2—31no—
678C2—62no—
679C2—122no—
680C2C2×C4×C5×S411yescharacteristic
681C2C5×D4×S411yescharacteristic
682C2C5×#591411yescharacteristic
subgroupG/H
centerC22×C5C22×S4
commutatorC2×A4C22×C4×C5
FrattiniC22C22×C5×S4
FittingC22×C5×C22⋊C4D3
socleC24×C5C22×D3
prime radicalC2×C5×GL(2,ℤ/4)C2
cosocleC22×A4C23×C5
hypercenterC5×C22⋊C4S4
hypocenterA4C4×C5×D4
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C22×C5 ◁ C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C5×SL(2,ℤ/4)C2semidirect
3. C2×C4×C5×S4C2semidirect
4. C5×A4×C22⋊C4C2semidirect
5. C5×(C2×S4)⋊C4C2semidirect
6. C5×SL(2,ℤ/4)⋊C4C2semidirect
7. C4×C5×SL(2,ℤ/4)C2semidirect
13. C5×GL(2,ℤ/4)C4semidirect
20. GL(2,ℤ/4)⋊C4C5direct (N × H)
25. C22×C5×C22⋊C4D3semidirect
38. C22×C5×A4C2×C4semidirect
42. C2×C5×S4C2×C4semidirect
49. C5×SL(2,ℤ/4)C2×C4semidirect
50. C5×SL(2,ℤ/4)D4semidirect
56. C22×SL(2,ℤ/4)C2×C5semidirect
57. C2×C4×S4C2×C5semidirect
58. A4×C22⋊C4C2×C5semidirect
59. (C2×S4)⋊C4C2×C5semidirect
60. SL(2,ℤ/4)⋊C4C2×C5semidirect
61. C4×SL(2,ℤ/4)C2×C5semidirect
127. GL(2,ℤ/4)C4×C5semidirect
142. C24×C5C4×D3semidirect
205. C5×C22⋊C4S4semidirect
214. C22×C22⋊C4C5×D3semidirect
232. C5×A4C4×D4semidirect
240. C22×A4C2×C4×C5semidirect
244. C2×S4C2×C4×C5semidirect
251. SL(2,ℤ/4)C2×C4×C5semidirect
252. SL(2,ℤ/4)C5×D4semidirect
430. C22×C5#67⋊C4semidirect
431. C22×C5C4×S4semidirect
452. C24C4×C5×D3semidirect
515. C22⋊C4C5×S4semidirect
528. A4C4×C5×D4semidirect
627. C5GL(2,ℤ/4)⋊C4direct (N × H)
658. C22C5×#67⋊C4semidirect
659. C22C4×C5×S4semidirect

Maximal subgroups

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

subgroupindex
C2×C5×GL(2,ℤ/4)2
C22×C5×SL(2,ℤ/4)2
C2×C4×C5×S42
C5×A4×C22⋊C42
C5×(C2×S4)⋊C42
C5×SL(2,ℤ/4)⋊C42
C4×C5×SL(2,ℤ/4)2
C5×#23583
C5×#67⋊C44
GL(2,ℤ/4)⋊C45