Finite Group Databasebeta

← C5×#33554 #11956274

Subgroups — C5×#33554 #11956274

Order 1280.

1112 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3538C211yesmaximal, characteristic, complemented
2C5×#3028C211yesmaximal, characteristic, complemented
3C5×#3025C211yesmaximal, characteristic
4C5×#3022C211yesmaximal, characteristic, complemented
5C5×#2201C214yesmaximal, complemented
6C5×#2197C214yesmaximal, complemented
7C5×#2129C211yesmaximal, characteristic, complemented
8C5×#2123C211yesmaximal, characteristic, complemented
9C5×#2120C211yesmaximal, characteristic, complemented
10C5×#585C2211yescharacteristic
11C2×C5×#137—21no—
12C5×#563—21no—
13C5×#563C2212yescomplemented
14C5×#552—21no—
15C5×#552—21no—
16C5×#551—21no—
17C5×#551C2212yescomplemented
18C5×D4×Q8—21no—
19C5×D4×Q8—21no—
20C5×#544—22no—
21C5×#541—21no—
22C5×#539—22no—
23C5×#536—21no—
24C5×#536C2211yescharacteristic
25C5×#536C2211yescharacteristic
26C5×#525—21no—
27C5×#525C2211yescharacteristic
28C2×C5×C22⋊Q8—21no—
29C5×#458—21no—
30C5×#458—22no—
31C5×#458C2212yes—
32C5×#458C2214yes—
33C5×B(4,𝔽2)—21no—
34C5×B(4,𝔽2)C2212yes—
35C5×#456—22no—
36C5×#455C2214yes—
37C5×#421—21no—
38C5×#413C2211yescharacteristic
39C5×#410—21no—
40C5×#410—21no—
41C5×#410C2211yescharacteristic
42C5×#410C2211yescharacteristic
43C5×#354C2214yescomplemented
44C5×#352C2212yescomplemented
45C5×#352C2214yescomplemented
46C5×AΣL(1,𝔽16)C2212yescomplemented
47#33554C511yesmaximal, characteristic, direct product factor, Sylow
48C5×2−1+4—21no—
49C5×2−1+4—41no—
50C5×H(5,𝔽2)—21no—
51C5×H(5,𝔽2)—21no—
52C5×H(5,𝔽2)—41no—
53C5×H(5,𝔽2)C2312yes—
54C2×C5×#41—21no—
55C2×C5×#41—21no—
56C2×C5×#41—21no—
57C2×C5×#41—42no—
58C2×C5×#41C2311yescharacteristic
59C22×C5×Q8—21no—
60C22×C5×Q8D411yescharacteristic, complemented
61C22×C5×Q8D411yescharacteristic, complemented
62C23×C4×C5D411yescharacteristic
63C5×#137—24no—
64C5×#137—42no—
65C2×C5×Q16—41no—
66C2×C5×SD16—41no—
67C2×C5×M16—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—22no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8—22no—
72C5×C4⋊Q8—41no—
73C5×C4⋊Q8D412yescomplemented
74C5×#126—22no—
75C5×#126—22no—
76C5×#126—22no—
77C5×#126—22no—
78C5×#125—22no—
79C5×#125—22no—
80C5×#125—21no—
81C5×#125—22no—
82C5×#125—22no—
83C5×#124—21no—
84C5×#124—41no—
85C5×#124C2312yes—
86C5×#123—22no—
87C5×#123—21no—
88C5×#123—21no—
89C5×#123—22no—
90C5×#123—22no—
91C5×#123—24no—
92C5×#123D411yescharacteristic
93C5×#123D412yescomplemented
94C5×#123C2311yescharacteristic
95C5×#123C2312yes—
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8—21no—
98C5×C22⋊Q8—21no—
99C5×C22⋊Q8—22no—
100C5×C22⋊Q8—22no—
101C5×C22⋊Q8—21no—
102C5×C22⋊Q8—22no—
103C5×C22⋊Q8—21no—
104C5×C22⋊Q8—21no—
105C5×C22⋊Q8—22no—
106C5×C22⋊Q8—21no—
107C5×C22⋊Q8—21no—
108C5×C22⋊Q8—22no—
109C5×C22⋊Q8—42no—
110C5×C22⋊Q8—41no—
111C5×#121—21no—
112C5×#121—41no—
113C5×#120—22no—
114C5×#120D411yescharacteristic
115C5×#120C2311yescharacteristic
116C4×C5×Q8—21no—
117C4×C5×Q8—21no—
118C4×C5×D4—22no—
119C4×C5×D4—21no—
120C4×C5×D4—21no—
121C4×C5×D4—22no—
122C4×C5×D4—42no—
123C5×#117—22no—
124C5×#117—22no—
125C5×#117—21no—
126C5×#117—21no—
127C5×#117D411yescharacteristic
128C5×#117D411yescharacteristic, complemented
129C5×#117D411yescharacteristic, complemented
130C2×C5×C4⋊C4—22no—
131C2×C5×C4⋊C4—21no—
132C2×C5×C22⋊C4—22no—
133C5×#104—24no—
134C5×#101—21no—
135C5×#100C2312yes—
136C5×#99—21no—
137C5×#99—21no—
138C5×#99—22no—
139C5×#99—22no—
140C5×#99—24no—
141C5×#99C2312yes—
142C5×#99C2312yes—
143#3538C2×C511yescharacteristic, complemented
144#3028C2×C511yescharacteristic, complemented
145#3025C2×C511yescharacteristic
146#3022C2×C511yescharacteristic, complemented
147#2201C2×C514yescomplemented
148#2197C2×C514yescomplemented
149#2129C2×C511yescharacteristic, complemented
150#2123C2×C511yescharacteristic, complemented
151#2120C2×C511yescharacteristic, complemented
152C24×C5C2×D411yescharacteristic
153C5×#41—22no—
154C5×#41—22no—
155C5×#41—41no—
156C5×#41—41no—
157C5×#41—42no—
158C5×#41—41no—
159C5×#41—41no—
160C5×#41—41no—
161C5×#41—41no—
162C5×#41—41no—
163C5×#41—42no—
164C5×#41—42no—
165C5×#41—42no—
166C5×#41—41no—
167C5×#41—41no—
168C5×#41—41no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8—22no—
172C2×C5×Q8—21no—
173C2×C5×Q8—21no—
174C2×C5×Q8—21no—
175C2×C5×Q8—21no—
176C2×C5×Q8—41no—
177C2×C5×Q8—41no—
178C2×C5×Q8—41no—
179C2×C5×Q8—41no—
180C2×C5×Q8—42no—
181C2×C5×Q8—81no—
182C2×C5×Q8—81no—
183C2×C5×Q8C2×D412yes—
184C2×C5×Q8C2×D411yescharacteristic
185C2×C5×D4—21no—
186C2×C5×D4—21no—
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4—21no—
190C2×C5×D4—22no—
191C2×C5×D4—22no—
192C2×C5×D4—42no—
193C2×C5×D4—42no—
194C2×C5×D4—42no—
195C2×C5×D4—41no—
196C2×C5×D4—42no—
197C2×C5×D4C2×D411yescharacteristic
198C2×C5×D4C2×D411yescharacteristic
199C2×C5×D4C2411yescharacteristic
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—41no—
208C22×C4×C5—41no—
209C22×C4×C5—41no—
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D412yes—
214C22×C4×C5C2×D411yescharacteristic
215C5×Q16—44no—
216C5×SD16—44no—
217C5×M16—22no—
218C5×M16—41no—
219C2×C5×C8—41no—
220C5×C4⋊C4—22no—
221C5×C4⋊C4—22no—
222C5×C4⋊C4—22no—
223C5×C4⋊C4—22no—
224C5×C4⋊C4—22no—
225C5×C4⋊C4—22no—
226C5×C4⋊C4—22no—
227C5×C4⋊C4—22no—
228C5×C4⋊C4—22no—
229C5×C4⋊C4—22no—
230C5×C4⋊C4—22no—
231C5×C4⋊C4—22no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—21no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4—22no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—41no—
239C5×C4⋊C4—41no—
240C5×C4⋊C4—42no—
241C5×C4⋊C4—44no—
242C5×C22⋊C4—22no—
243C5×C22⋊C4—22no—
244C5×C22⋊C4—21no—
245C5×C22⋊C4—21no—
246C5×C22⋊C4—22no—
247C5×C22⋊C4—22no—
248C5×C22⋊C4—22no—
249C5×C22⋊C4—21no—
250C5×C22⋊C4—22no—
251C5×C22⋊C4—21no—
252C5×C22⋊C4—21no—
253C5×C22⋊C4—22no—
254C5×C22⋊C4—22no—
255C5×C22⋊C4—42no—
256C5×C22⋊C4—42no—
257C5×C22⋊C4—44no—
258C5×C22⋊C4C2×D411yescharacteristic
259C5×C22⋊C4C2×D411yescharacteristic
260C5×C22⋊C4C2×D412yes—
261C42×C5—22no—
262C42×C5—22no—
263C42×C5—21no—
264C42×C5—21no—
265C42×C5—41no—
266C42×C5—41no—
267C42×C5C2×D412yes—
268#585C22×C511yescharacteristic
269C2×#137—21no—
270#563—21no—
271#563C22×C512yescomplemented
272#552—21no—
273#552—21no—
274#551—21no—
275#551C22×C512yescomplemented
276D4×Q8—21no—
277D4×Q8—21no—
278#544—22no—
279#541—21no—
280#539—22no—
281#536—21no—
282#536C22×C511yescharacteristic
283#536C22×C511yescharacteristic
284#525—21no—
285#525C22×C511yescharacteristic
286C2×C22⋊Q8—21no—
287#458—21no—
288#458—22no—
289#458C22×C514yes—
290#458C22×C512yes—
291B(4,𝔽2)—21no—
292B(4,𝔽2)C22×C512yes—
293#456—22no—
294#455C22×C514yes—
295#421—21no—
296#413C22×C511yescharacteristic
297#410—21no—
298#410—21no—
299#410C22×C511yescharacteristic
300#410C22×C511yescharacteristic
301#354C22×C514yescomplemented
302#352C22×C512yescomplemented
303#352C22×C514yescomplemented
304AΣL(1,𝔽16)C22×C512yescomplemented
305C23×C5—21no—
306C23×C5—22no—
307C23×C5—22no—
308C23×C5—41no—
309C23×C5—42no—
310C23×C5—41no—
311C23×C5#12011yescharacteristic
312C23×C5C22×D411yescharacteristic
313C23×C5C22×D411yescharacteristic
314C5×Q8—22no—
315C5×Q8—41no—
316C5×Q8—42no—
317C5×Q8—41no—
318C5×Q8—41no—
319C5×Q8—41no—
320C5×Q8—41no—
321C5×Q8—41no—
322C5×Q8—41no—
323C5×Q8—41no—
324C5×Q8—81no—
325C5×Q8—82no—
326C5×D4—22no—
327C5×D4—41no—
328C5×D4—41no—
329C5×D4—41no—
330C5×D4—41no—
331C5×D4—41no—
332C5×D4—42no—
333C5×D4—42no—
334C5×D4—42no—
335C5×D4—42no—
336C5×D4—42no—
337C5×D4—42no—
338C5×D4—41no—
339C5×D4—84no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—21no—
349C2×C4×C5—21no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—21no—
355C2×C4×C5—42no—
356C2×C4×C5—42no—
357C2×C4×C5—42no—
358C2×C4×C5—44no—
359C2×C4×C5—41no—
360C2×C4×C5—42no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—42no—
365C2×C4×C5—42no—
366C2×C4×C5—42no—
367C2×C4×C5—81no—
368C2×C4×C5—81no—
369C2×C4×C5—82no—
370C2×C4×C5#12011yescharacteristic
371C2×C4×C5#12011yescharacteristic
372C2×C4×C5#12011yescharacteristic
373C2×C4×C5C22×D411yescharacteristic
374C5×C8—42no—
3752−1+4—21no—
3762−1+4—41no—
377H(5,𝔽2)—21no—
378H(5,𝔽2)—21no—
379H(5,𝔽2)—41no—
380H(5,𝔽2)C23×C512yes—
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—21no—
384C2×#41—42no—
385C2×#41C23×C511yescharacteristic
386C22×Q8—21no—
387C22×Q8C5×D411yescharacteristic, complemented
388C22×Q8C5×D411yescharacteristic, complemented
389C23×C4C5×D411yescharacteristic
390#137—24no—
391#137—42no—
392C2×Q16—41no—
393C2×SD16—41no—
394C2×M16—21no—
395C4⋊Q8—21no—
396C4⋊Q8—22no—
397C4⋊Q8—21no—
398C4⋊Q8—22no—
399C4⋊Q8—41no—
400C4⋊Q8C5×D412yescomplemented
401#126—22no—
402#126—22no—
403#126—22no—
404#126—22no—
405#125—22no—
406#125—22no—
407#125—21no—
408#125—22no—
409#125—22no—
410#124—21no—
411#124—41no—
412#124C23×C512yes—
413#123—22no—
414#123—21no—
415#123—21no—
416#123—22no—
417#123—22no—
418#123—24no—
419#123C5×D411yescharacteristic
420#123C5×D412yescomplemented
421#123C23×C511yescharacteristic
422#123C23×C512yes—
423C22⋊Q8—22no—
424C22⋊Q8—21no—
425C22⋊Q8—21no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—21no—
429C22⋊Q8—22no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432C22⋊Q8—22no—
433C22⋊Q8—21no—
434C22⋊Q8—21no—
435C22⋊Q8—22no—
436C22⋊Q8—42no—
437C22⋊Q8—41no—
438#121—21no—
439#121—41no—
440#120—22no—
441#120C5×D411yescharacteristic
442#120C23×C511yescharacteristic
443C4×Q8—21no—
444C4×Q8—21no—
445C4×D4—22no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—22no—
449C4×D4—42no—
450#117—22no—
451#117—22no—
452#117—21no—
453#117—21no—
454#117C5×D411yescharacteristic
455#117C5×D411yescharacteristic, complemented
456#117C5×D411yescharacteristic, complemented
457C2×C4⋊C4—22no—
458C2×C4⋊C4—21no—
459C2×C22⋊C4—22no—
460#104—24no—
461#101—21no—
462#100C23×C512yes—
463#99—21no—
464#99—21no—
465#99—22no—
466#99—22no—
467#99—24no—
468#99C23×C512yes—
469#99C23×C512yes—
470C22×C5—22no—
471C22×C5—21no—
472C22×C5—21no—
473C22×C5—21no—
474C22×C5—41no—
475C22×C5—41no—
476C22×C5—41no—
477C22×C5—41no—
478C22×C5—42no—
479C22×C5—41no—
480C22×C5—42no—
481C22×C5—81no—
482C22×C5—82no—
483C22×C5—82no—
484C22×C5—161no—
485C22×C5C2×#12011yescharacteristic
486C4×C5—21no—
487C4×C5—21no—
488C4×C5—21no—
489C4×C5—42no—
490C4×C5—42no—
491C4×C5—41no—
492C4×C5—41no—
493C4×C5—42no—
494C4×C5—41no—
495C4×C5—42no—
496C4×C5—42no—
497C4×C5—82no—
498C4×C5—82no—
499C4×C5B(4,𝔽2)11yescharacteristic
500C4×C5B(4,𝔽2)11yescharacteristic
501C24C2×C5×D411yescharacteristic
502#41—22no—
503#41—22no—
504#41—41no—
505#41—41no—
506#41—42no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—42no—
513#41—42no—
514#41—42no—
515#41—41no—
516#41—41no—
517#41—41no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—22no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—41no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—42no—
530C2×Q8—81no—
531C2×Q8—81no—
532C2×Q8C2×C5×D412yes—
533C2×Q8C2×C5×D411yescharacteristic
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—41no—
545C2×D4—42no—
546C2×D4C2×C5×D411yescharacteristic
547C2×D4C2×C5×D411yescharacteristic
548C2×D4C24×C511yescharacteristic
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4C2×C5×D411yescharacteristic
560C22×C4C2×C5×D411yescharacteristic
561C22×C4C2×C5×D411yescharacteristic
562C22×C4C2×C5×D412yes—
563C22×C4C2×C5×D411yescharacteristic
564Q16—44no—
565SD16—44no—
566M16—22no—
567M16—41no—
568C2×C8—41no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—22no—
586C4⋊C4—21no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—21no—
594C22⋊C4—21no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—21no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—44no—
607C22⋊C4C2×C5×D411yescharacteristic
608C22⋊C4C2×C5×D411yescharacteristic
609C22⋊C4C2×C5×D412yes—
610C42—22no—
611C42—22no—
612C42—21no—
613C42—21no—
614C42—41no—
615C42—41no—
616C42C2×C5×D412yes—
617C2×C5—21no—
618C2×C5—41no—
619C2×C5—41no—
620C2×C5—42no—
621C2×C5—41no—
622C2×C5—82no—
623C2×C5C2×B(4,𝔽2)11yescharacteristic
624C23—21no—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—42no—
629C23—41no—
630C23C5×#12011yescharacteristic
631C23C22×C5×D411yescharacteristic
632C23C22×C5×D411yescharacteristic
633Q8—22no—
634Q8—41no—
635Q8—42no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—81no—
644Q8—82no—
645D4—22no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—42no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—42no—
656D4—42no—
657D4—41no—
658D4—84no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—82no—
689C2×C4C5×#12011yescharacteristic
690C2×C4C5×#12011yescharacteristic
691C2×C4C5×#12011yescharacteristic
692C2×C4C22×C5×D411yescharacteristic
693C8—42no—
694C5#3355411yescharacteristic, direct product factor, Sylow
695C22—22no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—41no—
705C22—42no—
706C22—81no—
707C22—82no—
708C22—82no—
709C22—161no—
710C22C2×C5×#12011yescharacteristic
711C4—21no—
712C4—21no—
713C4—21no—
714C4—42no—
715C4—42no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—41no—
720C4—42no—
721C4—42no—
722C4—82no—
723C4—82no—
724C4C5×B(4,𝔽2)11yescharacteristic
725C4C5×B(4,𝔽2)11yescharacteristic
726C2—21no—
727C2—41no—
728C2—41no—
729C2—42no—
730C2—41no—
731C2—82no—
732C2C2×C5×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C5C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C5
prime radicalC5×#3025C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3538C2semidirect
2. C5×#3028C2semidirect
4. C5×#3022C2semidirect
5. C5×#2201C2semidirect
6. C5×#2197C2semidirect
7. C5×#2129C2semidirect
8. C5×#2123C2semidirect
9. C5×#2120C2semidirect
13. C5×#563C22semidirect
17. C5×#551C22semidirect
43. C5×#354C22semidirect
44. C5×#352C22semidirect
45. C5×#352C22semidirect
46. C5×AΣL(1,𝔽16)C22semidirect
47. #33554C5direct (N × H)
60. C22×C5×Q8D4semidirect
61. C22×C5×Q8D4semidirect
73. C5×C4⋊Q8D4semidirect
93. C5×#123D4semidirect
128. C5×#117D4semidirect
129. C5×#117D4semidirect
143. #3538C2×C5semidirect
144. #3028C2×C5semidirect
146. #3022C2×C5semidirect
147. #2201C2×C5semidirect
148. #2197C2×C5semidirect
149. #2129C2×C5semidirect
150. #2123C2×C5semidirect
151. #2120C2×C5semidirect
271. #563C22×C5semidirect
275. #551C22×C5semidirect
301. #354C22×C5semidirect
302. #352C22×C5semidirect
303. #352C22×C5semidirect
304. AΣL(1,𝔽16)C22×C5semidirect
387. C22×Q8C5×D4semidirect
388. C22×Q8C5×D4semidirect
400. C4⋊Q8C5×D4semidirect
420. #123C5×D4semidirect
455. #117C5×D4semidirect
456. #117C5×D4semidirect
694. C5#33554direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35382
C5×#30282
C5×#30252
C5×#30222
C5×#22012
C5×#21972
C5×#21292
C5×#21232
C5×#21202
#335545