Finite Group Databasebeta

← C5×#33553 #11956273

Subgroups — C5×#33553 #11956273

Order 1280.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3537C211yesmaximal, characteristic, complemented
2C5×#3027C211yesmaximal, characteristic, complemented
3C5×#3025C211yesmaximal, characteristic, complemented
4C5×#3021C211yesmaximal, characteristic, complemented
5C5×#2200C214yesmaximal, complemented
6C5×#2196C214yesmaximal, complemented
7C5×#2128C211yesmaximal, characteristic, complemented
8C5×#2122C211yesmaximal, characteristic, complemented
9C5×#2120C211yesmaximal, characteristic, complemented
10C5×#585C2211yescharacteristic, complemented
11C2×C5×AGL(1,ℤ/8)—21no—
12C5×#560—21no—
13C5×#560C2212yescomplemented
14C5×#553—21no—
15C5×#553—21no—
16C5×D42—21no—
17C5×D42—21no—
18C5×D42—21no—
19C5×D42C2212yescomplemented
20C5×#540—21no—
21C5×#538—22no—
22C5×#535—21no—
23C5×#535C2211yescharacteristic
24C5×#535C2211yescharacteristic
25C5×#534—22no—
26C5×#525—21no—
27C5×#525C2211yescharacteristic
28C2×C5×#121—21no—
29C5×#458—21no—
30C5×#458C2212yescomplemented
31C5×B(4,𝔽2)—21no—
32C5×B(4,𝔽2)—22no—
33C5×B(4,𝔽2)C2212yescomplemented
34C5×B(4,𝔽2)C2214yescomplemented
35C5×#454—22no—
36C5×#453C2214yescomplemented
37C5×#421—21no—
38C5×#413C2211yescharacteristic, complemented
39C5×#410—21no—
40C5×#410—21no—
41C5×#410C2211yescharacteristic, complemented
42C5×#410C2211yescharacteristic, complemented
43C5×#353C2214yescomplemented
44C5×#352C2212yescomplemented
45C5×AΣL(1,𝔽16)C2212yescomplemented
46C5×AΣL(1,𝔽16)C2214yescomplemented
47#33553C511yesmaximal, 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×D4—21no—
60C22×C5×D4—22no—
61C22×C5×D4—22no—
62C22×C5×D4—22no—
63C22×C5×D4D411yescharacteristic, complemented
64C22×C5×D4D411yescharacteristic, complemented
65C23×C4×C5D411yescharacteristic, complemented
66C5×AGL(1,ℤ/8)—24no—
67C5×AGL(1,ℤ/8)—42no—
68C2×C5×SD16—41no—
69C2×C5×D8—41no—
70C2×C5×M16—21no—
71C5×#127—21no—
72C5×#127—21no—
73C5×#127—41no—
74C5×#127C2312yes—
75C5×#126—22no—
76C5×#126—22no—
77C5×#125—21no—
78C5×#124—21no—
79C5×#124—41no—
80C5×#124D412yescomplemented
81C5×#123—22no—
82C5×#123—22no—
83C5×#123—22no—
84C5×#123—22no—
85C5×#123—22no—
86C5×#123D411yescharacteristic, complemented
87C5×#123C2311yescharacteristic
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—41no—
90C5×#121—22no—
91C5×#121—21no—
92C5×#121—21no—
93C5×#121—22no—
94C5×#121—22no—
95C5×#121—21no—
96C5×#121—22no—
97C5×#121—21no—
98C5×#121—21no—
99C5×#121—22no—
100C5×#121—21no—
101C5×#121—21no—
102C5×#121—22no—
103C5×#121—22no—
104C5×#121—22no—
105C5×#121—42no—
106C5×#121—41no—
107C5×#120—22no—
108C5×#120—22no—
109C5×#120—22no—
110C5×#120—21no—
111C5×#120—21no—
112C5×#120—22no—
113C5×#120—22no—
114C5×#120—24no—
115C5×#120D411yescharacteristic, complemented
116C5×#120D412yescomplemented
117C5×#120C2311yescharacteristic
118C5×#120C2312yes—
119C4×C5×D4—22no—
120C4×C5×D4—21no—
121C4×C5×D4—21no—
122C4×C5×D4—21no—
123C4×C5×D4—21no—
124C4×C5×D4—22no—
125C4×C5×D4—42no—
126C5×#117—21no—
127C5×#117—21no—
128C5×#117D411yescharacteristic, complemented
129C5×#117D411yescharacteristic, complemented
130C5×#117D411yescharacteristic, complemented
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—24no—
139C5×#99—22no—
140C5×#99—22no—
141C5×#99C2312yes—
142C5×#99C2312yes—
143#3537C2×C511yescharacteristic, complemented
144#3027C2×C511yescharacteristic, complemented
145#3025C2×C511yescharacteristic, complemented
146#3021C2×C511yescharacteristic, complemented
147#2200C2×C514yescomplemented
148#2196C2×C514yescomplemented
149#2128C2×C511yescharacteristic, complemented
150#2122C2×C511yescharacteristic, complemented
151#2120C2×C511yescharacteristic, complemented
152C24×C5—22no—
153C24×C5—21no—
154C24×C5C2×D411yescharacteristic
155C24×C5C2×D412yes—
156C5×#41—22no—
157C5×#41—22no—
158C5×#41—41no—
159C5×#41—41no—
160C5×#41—42no—
161C5×#41—41no—
162C5×#41—41no—
163C5×#41—41no—
164C5×#41—41no—
165C5×#41—41no—
166C5×#41—42no—
167C5×#41—42no—
168C5×#41—42no—
169C5×#41—41no—
170C5×#41—41no—
171C5×#41—41no—
172C2×C5×Q8—21no—
173C2×C5×Q8—21no—
174C2×C5×Q8—21no—
175C2×C5×Q8—42no—
176C2×C5×Q8C2×D411yescharacteristic
177C2×C5×D4—21no—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4—21no—
181C2×C5×D4—21no—
182C2×C5×D4—21no—
183C2×C5×D4—21no—
184C2×C5×D4—22no—
185C2×C5×D4—22no—
186C2×C5×D4—22no—
187C2×C5×D4—22no—
188C2×C5×D4—22no—
189C2×C5×D4—22no—
190C2×C5×D4—22no—
191C2×C5×D4—22no—
192C2×C5×D4—22no—
193C2×C5×D4—21no—
194C2×C5×D4—21no—
195C2×C5×D4—21no—
196C2×C5×D4—41no—
197C2×C5×D4—41no—
198C2×C5×D4—41no—
199C2×C5×D4—41no—
200C2×C5×D4—42no—
201C2×C5×D4—42no—
202C2×C5×D4—42no—
203C2×C5×D4—41no—
204C2×C5×D4—42no—
205C2×C5×D4—44no—
206C2×C5×D4—81no—
207C2×C5×D4—81no—
208C2×C5×D4—84no—
209C2×C5×D4—84no—
210C2×C5×D4—84no—
211C2×C5×D4C2×D411yescharacteristic
212C2×C5×D4C2×D411yescharacteristic
213C2×C5×D4C2×D412yes—
214C2×C5×D4C2411yescharacteristic
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—41no—
223C22×C4×C5—41no—
224C22×C4×C5—41no—
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C5×SD16—44no—
230C5×D8—44no—
231C5×M16—22no—
232C5×M16—41no—
233C2×C5×C8—41no—
234C5×C4⋊C4—22no—
235C5×C4⋊C4—22no—
236C5×C4⋊C4—22no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—41no—
243C5×C4⋊C4—41no—
244C5×C4⋊C4—42no—
245C5×C22⋊C4—22no—
246C5×C22⋊C4—22no—
247C5×C22⋊C4—22no—
248C5×C22⋊C4—22no—
249C5×C22⋊C4—21no—
250C5×C22⋊C4—21no—
251C5×C22⋊C4—21no—
252C5×C22⋊C4—22no—
253C5×C22⋊C4—22no—
254C5×C22⋊C4—21no—
255C5×C22⋊C4—22no—
256C5×C22⋊C4—21no—
257C5×C22⋊C4—22no—
258C5×C22⋊C4—22no—
259C5×C22⋊C4—22no—
260C5×C22⋊C4—42no—
261C5×C22⋊C4—44no—
262C5×C22⋊C4—42no—
263C5×C22⋊C4C2×D412yes—
264C5×C22⋊C4C2×D411yescharacteristic
265C5×C22⋊C4C2×D411yescharacteristic
266C42×C5—21no—
267C42×C5—21no—
268C42×C5—41no—
269C42×C5—41no—
270C42×C5C2×D412yes—
271#585C22×C511yescharacteristic, complemented
272C2×AGL(1,ℤ/8)—21no—
273#560—21no—
274#560C22×C512yescomplemented
275#553—21no—
276#553—21no—
277D42—21no—
278D42—21no—
279D42—21no—
280D42C22×C512yescomplemented
281#540—21no—
282#538—22no—
283#535—21no—
284#535C22×C511yescharacteristic
285#535C22×C511yescharacteristic
286#534—22no—
287#525—21no—
288#525C22×C511yescharacteristic
289C2×#121—21no—
290#458—21no—
291#458C22×C512yescomplemented
292B(4,𝔽2)—21no—
293B(4,𝔽2)—22no—
294B(4,𝔽2)C22×C512yescomplemented
295B(4,𝔽2)C22×C514yescomplemented
296#454—22no—
297#453C22×C514yescomplemented
298#421—21no—
299#413C22×C511yescharacteristic, complemented
300#410—21no—
301#410—21no—
302#410C22×C511yescharacteristic, complemented
303#410C22×C511yescharacteristic, complemented
304#353C22×C514yescomplemented
305#352C22×C512yescomplemented
306AΣL(1,𝔽16)C22×C512yescomplemented
307AΣL(1,𝔽16)C22×C514yescomplemented
308C23×C5—21no—
309C23×C5—22no—
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—41no—
314C23×C5—42no—
315C23×C5—41no—
316C23×C5—44no—
317C23×C5—42no—
318C23×C5—81no—
319C23×C5—82no—
320C23×C5—82no—
321C23×C5—82no—
322C23×C5—82no—
323C23×C5#12011yescharacteristic
324C23×C5C22×D411yescharacteristic
325C23×C5C22×D411yescharacteristic
326C5×Q8—22no—
327C5×Q8—41no—
328C5×Q8—41no—
329C5×Q8—41no—
330C5×Q8—41no—
331C5×D4—22no—
332C5×D4—41no—
333C5×D4—41no—
334C5×D4—41no—
335C5×D4—42no—
336C5×D4—41no—
337C5×D4—41no—
338C5×D4—42no—
339C5×D4—42no—
340C5×D4—42no—
341C5×D4—42no—
342C5×D4—44no—
343C5×D4—44no—
344C5×D4—42no—
345C5×D4—42no—
346C5×D4—41no—
347C5×D4—41no—
348C5×D4—41no—
349C5×D4—41no—
350C5×D4—41no—
351C5×D4—81no—
352C5×D4—82no—
353C5×D4—82no—
354C5×D4—82no—
355C5×D4—82no—
356C5×D4—82no—
357C5×D4—82no—
358C5×D4—82no—
359C5×D4—84no—
360C5×D4—164no—
361C2×C4×C5—21no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—21no—
365C2×C4×C5—21no—
366C2×C4×C5—21no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—21no—
371C2×C4×C5—21no—
372C2×C4×C5—22no—
373C2×C4×C5—21no—
374C2×C4×C5—42no—
375C2×C4×C5—42no—
376C2×C4×C5—42no—
377C2×C4×C5—41no—
378C2×C4×C5—42no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—81no—
385C2×C4×C5—82no—
386C2×C4×C5—82no—
387C2×C4×C5—82no—
388C2×C4×C5#12011yescharacteristic
389C2×C4×C5#12011yescharacteristic
390C2×C4×C5#12011yescharacteristic
391C2×C4×C5C22×D411yescharacteristic
392C5×C8—42no—
3932−1+4—21no—
3942−1+4—41no—
395H(5,𝔽2)—21no—
396H(5,𝔽2)—21no—
397H(5,𝔽2)—41no—
398H(5,𝔽2)C23×C512yes—
399C2×#41—21no—
400C2×#41—21no—
401C2×#41—21no—
402C2×#41—42no—
403C2×#41C23×C511yescharacteristic
404C22×D4—21no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—22no—
408C22×D4C5×D411yescharacteristic, complemented
409C22×D4C5×D411yescharacteristic, complemented
410C23×C4C5×D411yescharacteristic, complemented
411AGL(1,ℤ/8)—24no—
412AGL(1,ℤ/8)—42no—
413C2×SD16—41no—
414C2×D8—41no—
415C2×M16—21no—
416#127—21no—
417#127—21no—
418#127—41no—
419#127C23×C512yes—
420#126—22no—
421#126—22no—
422#125—21no—
423#124—21no—
424#124—41no—
425#124C5×D412yescomplemented
426#123—22no—
427#123—22no—
428#123—22no—
429#123—22no—
430#123—22no—
431#123C5×D411yescharacteristic, complemented
432#123C23×C511yescharacteristic
433C22⋊Q8—21no—
434C22⋊Q8—41no—
435#121—22no—
436#121—21no—
437#121—21no—
438#121—22no—
439#121—22no—
440#121—21no—
441#121—22no—
442#121—21no—
443#121—21no—
444#121—22no—
445#121—21no—
446#121—21no—
447#121—22no—
448#121—22no—
449#121—22no—
450#121—42no—
451#121—41no—
452#120—22no—
453#120—22no—
454#120—22no—
455#120—21no—
456#120—21no—
457#120—22no—
458#120—22no—
459#120—24no—
460#120C5×D411yescharacteristic, complemented
461#120C5×D412yescomplemented
462#120C23×C511yescharacteristic
463#120C23×C512yes—
464C4×D4—22no—
465C4×D4—21no—
466C4×D4—21no—
467C4×D4—21no—
468C4×D4—21no—
469C4×D4—22no—
470C4×D4—42no—
471#117—21no—
472#117—21no—
473#117C5×D411yescharacteristic, complemented
474#117C5×D411yescharacteristic, complemented
475#117C5×D411yescharacteristic, complemented
476C2×C4⋊C4—21no—
477C2×C22⋊C4—22no—
478#104—24no—
479#101—21no—
480#100C23×C512yes—
481#99—21no—
482#99—21no—
483#99—24no—
484#99—22no—
485#99—22no—
486#99C23×C512yes—
487#99C23×C512yes—
488C22×C5—22no—
489C22×C5—21no—
490C22×C5—21no—
491C22×C5—21no—
492C22×C5—41no—
493C22×C5—41no—
494C22×C5—41no—
495C22×C5—41no—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—41no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—81no—
506C22×C5—82no—
507C22×C5—82no—
508C22×C5—84no—
509C22×C5—161no—
510C22×C5—164no—
511C22×C5—162no—
512C22×C5C2×#12011yescharacteristic
513C4×C5—21no—
514C4×C5—21no—
515C4×C5—21no—
516C4×C5—42no—
517C4×C5—41no—
518C4×C5—41no—
519C4×C5—42no—
520C4×C5—42no—
521C4×C5—41no—
522C4×C5—82no—
523C4×C5—82no—
524C4×C5B(4,𝔽2)11yescharacteristic
525C4×C5B(4,𝔽2)11yescharacteristic
526C24—22no—
527C24—21no—
528C24C2×C5×D411yescharacteristic
529C24C2×C5×D412yes—
530#41—22no—
531#41—22no—
532#41—41no—
533#41—41no—
534#41—42no—
535#41—41no—
536#41—41no—
537#41—41no—
538#41—41no—
539#41—41no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—41no—
544#41—41no—
545#41—41no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—42no—
550C2×Q8C2×C5×D411yescharacteristic
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—41no—
578C2×D4—42no—
579C2×D4—44no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4—84no—
583C2×D4—84no—
584C2×D4—84no—
585C2×D4C2×C5×D411yescharacteristic
586C2×D4C2×C5×D411yescharacteristic
587C2×D4C2×C5×D412yes—
588C2×D4C24×C511yescharacteristic
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4C2×C5×D411yescharacteristic
600C22×C4C2×C5×D411yescharacteristic
601C22×C4C2×C5×D411yescharacteristic
602C22×C4C2×C5×D411yescharacteristic
603SD16—44no—
604D8—44no—
605M16—22no—
606M16—41no—
607C2×C8—41no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—42no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—21no—
629C22⋊C4—22no—
630C22⋊C4—21no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—42no—
635C22⋊C4—44no—
636C22⋊C4—42no—
637C22⋊C4C2×C5×D412yes—
638C22⋊C4C2×C5×D411yescharacteristic
639C22⋊C4C2×C5×D411yescharacteristic
640C42—21no—
641C42—21no—
642C42—41no—
643C42—41no—
644C42C2×C5×D412yes—
645C2×C5—21no—
646C2×C5—41no—
647C2×C5—41no—
648C2×C5—42no—
649C2×C5—41no—
650C2×C5—82no—
651C2×C5—82no—
652C2×C5—82no—
653C2×C5C2×B(4,𝔽2)11yescharacteristic
654C23—21no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—41no—
660C23—42no—
661C23—41no—
662C23—44no—
663C23—42no—
664C23—81no—
665C23—82no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23C5×#12011yescharacteristic
670C23C22×C5×D411yescharacteristic
671C23C22×C5×D411yescharacteristic
672Q8—22no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677D4—22no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—42no—
682D4—41no—
683D4—41no—
684D4—42no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—81no—
698D4—82no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—84no—
706D4—164no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—81no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4C5×#12011yescharacteristic
735C2×C4C5×#12011yescharacteristic
736C2×C4C5×#12011yescharacteristic
737C2×C4C22×C5×D411yescharacteristic
738C8—42no—
739C5#3355311yescharacteristic, direct product factor, Sylow
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×C5×#12011yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4C5×B(4,𝔽2)11yescharacteristic
777C4C5×B(4,𝔽2)11yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×C5×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C5C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C5
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×#3537C2semidirect
2. C5×#3027C2semidirect
3. C5×#3025C2semidirect
4. C5×#3021C2semidirect
5. C5×#2200C2semidirect
6. C5×#2196C2semidirect
7. C5×#2128C2semidirect
8. C5×#2122C2semidirect
9. C5×#2120C2semidirect
10. C5×#585C22semidirect
13. C5×#560C22semidirect
19. C5×D42C22semidirect
30. C5×#458C22semidirect
33. C5×B(4,𝔽2)C22semidirect
34. C5×B(4,𝔽2)C22semidirect
36. C5×#453C22semidirect
38. C5×#413C22semidirect
41. C5×#410C22semidirect
42. C5×#410C22semidirect
43. C5×#353C22semidirect
44. C5×#352C22semidirect
45. C5×AΣL(1,𝔽16)C22semidirect
46. C5×AΣL(1,𝔽16)C22semidirect
47. #33553C5direct (N × H)
63. C22×C5×D4D4semidirect
64. C22×C5×D4D4semidirect
65. C23×C4×C5D4semidirect
80. C5×#124D4semidirect
86. C5×#123D4semidirect
115. C5×#120D4semidirect
116. C5×#120D4semidirect
128. C5×#117D4semidirect
129. C5×#117D4semidirect
130. C5×#117D4semidirect
143. #3537C2×C5semidirect
144. #3027C2×C5semidirect
145. #3025C2×C5semidirect
146. #3021C2×C5semidirect
147. #2200C2×C5semidirect
148. #2196C2×C5semidirect
149. #2128C2×C5semidirect
150. #2122C2×C5semidirect
151. #2120C2×C5semidirect
271. #585C22×C5semidirect
274. #560C22×C5semidirect
280. D42C22×C5semidirect
291. #458C22×C5semidirect
294. B(4,𝔽2)C22×C5semidirect
295. B(4,𝔽2)C22×C5semidirect
297. #453C22×C5semidirect
299. #413C22×C5semidirect
302. #410C22×C5semidirect
303. #410C22×C5semidirect
304. #353C22×C5semidirect
305. #352C22×C5semidirect
306. AΣL(1,𝔽16)C22×C5semidirect
307. AΣL(1,𝔽16)C22×C5semidirect
408. C22×D4C5×D4semidirect
409. C22×D4C5×D4semidirect
410. C23×C4C5×D4semidirect
425. #124C5×D4semidirect
431. #123C5×D4semidirect
460. #120C5×D4semidirect
461. #120C5×D4semidirect
473. #117C5×D4semidirect
474. #117C5×D4semidirect
475. #117C5×D4semidirect
739. C5#33553direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35372
C5×#30272
C5×#30252
C5×#30212
C5×#22002
C5×#21962
C5×#21282
C5×#21222
C5×#21202
#335535