Finite Group Databasebeta

← C5×#11113 #11933833

Subgroups — C5×#11113 #11933833

Order 1280.

1006 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#428C211yesmaximal, characteristic, complemented
2C22×C5×#104C211yesmaximal, characteristic
3C2×C5×#417C211yesmaximal, characteristic
4C5×#2311C211yesmaximal, characteristic
5C2×C5×#343C211yesmaximal, characteristic, complemented
6C2×C5×#339C211yesmaximal, characteristic, complemented
7C5×C4⋊#95C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C22×C5×M16C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C2×C5×#117C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C42×C5C2211yescharacteristic
15C5×#428—22no—
16C5×#428—22no—
17C2×C5×#107—21no—
18C2×C5×#106—21no—
19C2×C5×#104—22no—
20C2×C5×#104—22no—
21C2×C5×#104C414yescomplemented
22C5×#417—22no—
23C5×#417—22no—
24C2×C5×#103—21no—
25C2×C5×#102—21no—
26C5×#391—21no—
27C5×#390—21no—
28C5×#386—22no—
29C5×#380—21no—
30C5×#380—21no—
31C2×C5×#95—22no—
32C5×#343—22no—
33C5×#339—22no—
34#11113C511yesmaximal, characteristic, direct product factor, Sylow
35C2×C5×#41—21no—
36C2×C5×#41—21no—
37C2×C5×#41—21no—
38C2×C5×#41—21no—
39C2×C5×#41—21no—
40C2×C5×#41—21no—
41C2×C5×#41—21no—
42C2×C5×#41—21no—
43C2×C5×#41—21no—
44C2×C5×#41—21no—
45C2×C5×#41C2×C412yes—
46C2×C5×#41Q812yes—
47C22×C5×Q8D411yescharacteristic
48C22×C5×D4—21no—
49C22×C5×D4D411yescharacteristic
50C23×C4×C5—21no—
51C23×C4×C5—21no—
52C23×C4×C5—21no—
53C23×C4×C5D412yes—
54C23×C4×C5C2311yescharacteristic
55C2×C5×M16—21no—
56C2×C5×M16—21no—
57C2×C5×M16—21no—
58C2×C5×M16—21no—
59C2×C5×M16—21no—
60C2×C5×M16—21no—
61C2×C5×M16—21no—
62C2×C5×M16—21no—
63C2×C5×M16C2×C412yes—
64C2×C5×M16D412yes—
65C2×C5×M16D412yes—
66C2×C5×M16D412yes—
67C22×C5×C8—21no—
68C22×C5×C8—21no—
69C5×#117—21no—
70C5×#117—21no—
71C5×#117—21no—
72C5×#117—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4D411yescharacteristic
85C2×C5×C4⋊C4D411yescharacteristic
86C2×C5×C4⋊C4D412yes—
87C2×C5×C22⋊C4—21no—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—22no—
90C2×C42×C5—21no—
91C2×C42×C5—21no—
92C2×C42×C5—21no—
93C2×C42×C5—21no—
94C2×C42×C5—21no—
95C2×C42×C5—21no—
96C2×C42×C5C2×C412yes—
97C5×#107—24no—
98C5×#106—24no—
99C5×#104—28no—
100C5×#103—24no—
101C5×#102—24no—
102C5×#95—22no—
103C5×#95—22no—
104C5×#95—44no—
105C2×#428C2×C511yescharacteristic, complemented
106C22×#104C2×C511yescharacteristic
107C2×#417C2×C511yescharacteristic
108#2311C2×C511yescharacteristic
109C2×#343C2×C511yescharacteristic, complemented
110C2×#339C2×C511yescharacteristic, complemented
111C4⋊#95C2×C511yescharacteristic, complemented
112C24×C5—21no—
113C24×C5C2×D411yescharacteristic
114C5×#41—22no—
115C5×#41—22no—
116C5×#41—22no—
117C5×#41—22no—
118C5×#41—22no—
119C5×#41—22no—
120C5×#41—22no—
121C5×#41—22no—
122C5×#41—41no—
123C5×#41—41no—
124C5×#41—41no—
125C5×#41—41no—
126C5×#41—41no—
127C5×#41—41no—
128C5×#41—41no—
129C5×#41—41no—
130C2×C5×Q8—21no—
131C2×C5×Q8—21no—
132C2×C5×Q8—21no—
133C2×C5×Q8—21no—
134C2×C5×Q8—21no—
135C2×C5×Q8C4⋊C412yes—
136C2×C5×D4—22no—
137C2×C5×D4—22no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—41no—
144C2×C5×D4—41no—
145C2×C5×D4—41no—
146C2×C5×D4—41no—
147C2×C5×D4C4⋊C412yes—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—21no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—41no—
161C22×C4×C5—41no—
162C22×C4×C5—41no—
163C22×C4×C5—41no—
164C22×C4×C5—41no—
165C22×C4×C5—41no—
166C22×C4×C5—41no—
167C22×C4×C5—41no—
168C22×C4×C5—42no—
169C22×C4×C5—42no—
170C22×C4×C5—42no—
171C22×C4×C5—42no—
172C22×C4×C5—41no—
173C22×C4×C5—41no—
174C22×C4×C5C22×C411yescharacteristic
175C22×C4×C5C2×D411yescharacteristic
176C22×C4×C5C2×D411yescharacteristic
177C22×C4×C5C2×D411yescharacteristic
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×Q811yescharacteristic
182C22×C4×C5#4111yescharacteristic
183C22×C4×C5#4111yescharacteristic
184C22×C4×C5#4111yescharacteristic
185C22×C4×C5#4111yescharacteristic
186C22×C4×C5#4111yescharacteristic
187C22×C4×C5#4111yescharacteristic
188C5×M16—22no—
189C5×M16—22no—
190C5×M16—22no—
191C5×M16—22no—
192C5×M16—22no—
193C5×M16—41no—
194C5×M16—41no—
195C5×M16C22⋊C414yescomplemented
196C2×C5×C8—22no—
197C2×C5×C8—22no—
198C2×C5×C8—22no—
199C2×C5×C8—22no—
200C2×C5×C8—41no—
201C2×C5×C8—41no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—41no—
209C5×C4⋊C4—41no—
210C5×C4⋊C4—41no—
211C5×C4⋊C4—41no—
212C5×C4⋊C4—41no—
213C5×C4⋊C4—41no—
214C5×C22⋊C4—41no—
215C5×C22⋊C4—41no—
216C5×C22⋊C4—82no—
217C5×C22⋊C4—82no—
218C42×C5—22no—
219C42×C5—22no—
220C42×C5—41no—
221C42×C5—41no—
222C42×C5—41no—
223C42×C5—41no—
224C22×#41C22×C511yescharacteristic
225C22×M16C22×C511yescharacteristic
226C22×M16C22×C511yescharacteristic
227C2×#117C22×C511yescharacteristic
228C22×C4⋊C4C22×C511yescharacteristic
229C22×C4⋊C4C22×C511yescharacteristic
230C22×C42C22×C511yescharacteristic
231#428—22no—
232#428—22no—
233C2×#107—21no—
234C2×#106—21no—
235C2×#104—22no—
236C2×#104—22no—
237C2×#104C4×C514yescomplemented
238#417—22no—
239#417—22no—
240C2×#103—21no—
241C2×#102—21no—
242#391—21no—
243#390—21no—
244#386—22no—
245#380—21no—
246#380—21no—
247C2×#95—22no—
248#343—22no—
249#339—22no—
250C23×C5—21no—
251C23×C5—21no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—22no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5C4×D411yescharacteristic
262C23×C5#12011yescharacteristic
263C23×C5#12111yescharacteristic
264C23×C5#12111yescharacteristic
265C23×C5C22⋊Q811yescharacteristic
266C23×C5#12311yescharacteristic
267C23×C5#12711yescharacteristic
268C5×Q8—22no—
269C5×Q8—22no—
270C5×Q8—41no—
271C5×Q8—41no—
272C5×D4—22no—
273C5×D4—22no—
274C5×D4—42no—
275C5×D4—42no—
276C5×D4—42no—
277C5×D4—42no—
278C5×D4—41no—
279C5×D4—41no—
280C2×C4×C5—24no—
281C2×C4×C5—22no—
282C2×C4×C5—42no—
283C2×C4×C5—42no—
284C2×C4×C5—42no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—42no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—42no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5—42no—
294C2×C4×C5—44no—
295C2×C4×C5—44no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5—41no—
301C2×C4×C5—42no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—42no—
305C2×C4×C5—41no—
306C2×C4×C5—82no—
307C2×C4×C5—81no—
308C2×C4×C5—81no—
309C2×C4×C5—82no—
310C2×C4×C5C2×C22⋊C411yescharacteristic
311C2×C4×C5C2×C4⋊C411yescharacteristic
312C2×C4×C5#11711yescharacteristic
313C2×C4×C5C4×D411yescharacteristic
314C2×C4×C5C4×D411yescharacteristic
315C2×C4×C5C4×D411yescharacteristic
316C2×C4×C5#12011yescharacteristic
317C2×C4×C5#12011yescharacteristic
318C2×C4×C5#12111yescharacteristic
319C2×C4×C5#12111yescharacteristic
320C2×C4×C5#12111yescharacteristic
321C2×C4×C5#12111yescharacteristic
322C2×C4×C5#12111yescharacteristic
323C2×C4×C5#12111yescharacteristic
324C2×C4×C5C22⋊Q811yescharacteristic
325C2×C4×C5C22⋊Q811yescharacteristic
326C2×C4×C5C22⋊Q811yescharacteristic
327C2×C4×C5C22⋊Q811yescharacteristic
328C2×C4×C5C22⋊Q811yescharacteristic
329C2×C4×C5#12311yescharacteristic
330C2×C4×C5#12311yescharacteristic
331C2×C4×C5#12311yescharacteristic
332C2×C4×C5#12311yescharacteristic
333C2×C4×C5#12411yescharacteristic
334C2×C4×C5#12411yescharacteristic
335C2×C4×C5#12411yescharacteristic
336C2×C4×C5#12611yescharacteristic
337C2×C4×C5#12611yescharacteristic
338C5×C8—24no—
339C5×C8—42no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41C2×C4×C512yes—
351C2×#41C5×Q812yes—
352C22×Q8C5×D411yescharacteristic
353C22×D4—21no—
354C22×D4C5×D411yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4C5×D412yes—
359C23×C4C23×C511yescharacteristic
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16C2×C4×C512yes—
369C2×M16C5×D412yes—
370C2×M16C5×D412yes—
371C2×M16C5×D412yes—
372C22×C8—21no—
373C22×C8—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C5×D412yes—
390C2×C4⋊C4C5×D411yescharacteristic
391C2×C4⋊C4C5×D411yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C2×C4×C512yes—
402#107—24no—
403#106—24no—
404#104—28no—
405#103—24no—
406#102—24no—
407#95—22no—
408#95—22no—
409#95—44no—
410C22×C5—21no—
411C22×C5—21no—
412C22×C5—21no—
413C22×C5—21no—
414C22×C5—21no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—42no—
423C22×C5—42no—
424C22×C5—42no—
425C22×C5—81no—
426C22×C5—81no—
427C22×C5—81no—
428C22×C5—81no—
429C22×C5#38511yescharacteristic
430C22×C5#38811yescharacteristic
431C22×C5#39011yescharacteristic
432C22×C5#39211yescharacteristic
433C22×C5#39411yescharacteristic
434C22×C5#39611yescharacteristic
435C22×C5#39911yescharacteristic
436C22×C5#45311yescharacteristic
437C22×C5#45411yescharacteristic
438C22×C5#45511yescharacteristic
439C22×C5#45611yescharacteristic
440C4×C5—44no—
441C4×C5—42no—
442C4×C5—81no—
443C4×C5—82no—
444C4×C5—81no—
445C4×C5—82no—
446C4×C5#38011yescharacteristic
447C4×C5#38511yescharacteristic
448C4×C5#38611yescharacteristic
449C4×C5#38811yescharacteristic
450C4×C5#39311yescharacteristic
451C4×C5#39411yescharacteristic
452C4×C5#39611yescharacteristic
453C4×C5#39711yescharacteristic
454C24—21no—
455C24C2×C5×D411yescharacteristic
456#41—22no—
457#41—22no—
458#41—22no—
459#41—22no—
460#41—22no—
461#41—22no—
462#41—22no—
463#41—22no—
464#41—41no—
465#41—41no—
466#41—41no—
467#41—41no—
468#41—41no—
469#41—41no—
470#41—41no—
471#41—41no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C5×C4⋊C412yes—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4C5×C4⋊C412yes—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4C22×C4×C511yescharacteristic
517C22×C4C2×C5×D411yescharacteristic
518C22×C4C2×C5×D411yescharacteristic
519C22×C4C2×C5×D411yescharacteristic
520C22×C4C2×C5×D411yescharacteristic
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×Q811yescharacteristic
524C22×C4C5×#4111yescharacteristic
525C22×C4C5×#4111yescharacteristic
526C22×C4C5×#4111yescharacteristic
527C22×C4C5×#4111yescharacteristic
528C22×C4C5×#4111yescharacteristic
529C22×C4C5×#4111yescharacteristic
530M16—22no—
531M16—22no—
532M16—22no—
533M16—22no—
534M16—22no—
535M16—41no—
536M16—41no—
537M16C5×C22⋊C414yescomplemented
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—41no—
543C2×C8—41no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—82no—
559C22⋊C4—82no—
560C42—22no—
561C42—22no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C2×C5—21no—
567C2×C5—21no—
568C2×C5—21no—
569C2×C5—21no—
570C2×C5—82no—
571C2×C5#143911yescharacteristic
572C2×C5#185911yescharacteristic
573C2×C5#186011yescharacteristic
574C2×C5#200611yescharacteristic
575C2×C5#200711yescharacteristic
576C2×C5#203711yescharacteristic
577C2×C5#203811yescharacteristic
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—22no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23C4×C5×D411yescharacteristic
590C23C5×#12011yescharacteristic
591C23C5×#12111yescharacteristic
592C23C5×#12111yescharacteristic
593C23C5×C22⋊Q811yescharacteristic
594C23C5×#12311yescharacteristic
595C23C5×#12711yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600D4—22no—
601D4—22no—
602D4—42no—
603D4—42no—
604D4—42no—
605D4—42no—
606D4—41no—
607D4—41no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—82no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—82no—
638C2×C4C2×C5×C22⋊C411yescharacteristic
639C2×C4C2×C5×C4⋊C411yescharacteristic
640C2×C4C5×#11711yescharacteristic
641C2×C4C4×C5×D411yescharacteristic
642C2×C4C4×C5×D411yescharacteristic
643C2×C4C4×C5×D411yescharacteristic
644C2×C4C5×#12011yescharacteristic
645C2×C4C5×#12011yescharacteristic
646C2×C4C5×#12111yescharacteristic
647C2×C4C5×#12111yescharacteristic
648C2×C4C5×#12111yescharacteristic
649C2×C4C5×#12111yescharacteristic
650C2×C4C5×#12111yescharacteristic
651C2×C4C5×#12111yescharacteristic
652C2×C4C5×C22⋊Q811yescharacteristic
653C2×C4C5×C22⋊Q811yescharacteristic
654C2×C4C5×C22⋊Q811yescharacteristic
655C2×C4C5×C22⋊Q811yescharacteristic
656C2×C4C5×C22⋊Q811yescharacteristic
657C2×C4C5×#12311yescharacteristic
658C2×C4C5×#12311yescharacteristic
659C2×C4C5×#12311yescharacteristic
660C2×C4C5×#12311yescharacteristic
661C2×C4C5×#12411yescharacteristic
662C2×C4C5×#12411yescharacteristic
663C2×C4C5×#12411yescharacteristic
664C2×C4C5×#12611yescharacteristic
665C2×C4C5×#12611yescharacteristic
666C8—24no—
667C8—42no—
668C5#1111311yescharacteristic, direct product factor, Sylow
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22C5×#38511yescharacteristic
689C22C5×#38811yescharacteristic
690C22C5×#39011yescharacteristic
691C22C5×#39211yescharacteristic
692C22C5×#39411yescharacteristic
693C22C5×#39611yescharacteristic
694C22C5×#39911yescharacteristic
695C22C5×#45311yescharacteristic
696C22C5×#45411yescharacteristic
697C22C5×#45511yescharacteristic
698C22C5×#45611yescharacteristic
699C4—44no—
700C4—42no—
701C4—82no—
702C4—82no—
703C4—81no—
704C4—81no—
705C4C5×#38011yescharacteristic
706C4C5×#38511yescharacteristic
707C4C5×#38611yescharacteristic
708C4C5×#38811yescharacteristic
709C4C5×#39311yescharacteristic
710C4C5×#39411yescharacteristic
711C4C5×#39611yescharacteristic
712C4C5×#39711yescharacteristic
713C2—21no—
714C2—21no—
715C2—21no—
716C2—21no—
717C2—82no—
718C2C5×#143911yescharacteristic
719C2C5×#185911yescharacteristic
720C2C5×#186011yescharacteristic
721C2C5×#200611yescharacteristic
722C2C5×#200711yescharacteristic
723C2C5×#203711yescharacteristic
724C2C5×#203811yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC22×C5×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#428C2semidirect
5. C2×C5×#343C2semidirect
6. C2×C5×#339C2semidirect
7. C5×C4⋊#95C2semidirect
21. C2×C5×#104C4semidirect
34. #11113C5direct (N × H)
105. C2×#428C2×C5semidirect
109. C2×#343C2×C5semidirect
110. C2×#339C2×C5semidirect
111. C4⋊#95C2×C5semidirect
195. C5×M16C22⋊C4semidirect
237. C2×#104C4×C5semidirect
537. M16C5×C22⋊C4semidirect
668. C5#11113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4282
C22×C5×#1042
C2×C5×#4172
C5×#23112
C2×C5×#3432
C2×C5×#3392
C5×C4⋊#952
#111135