Finite Group Databasebeta

← C5×#11089 #11933809

Subgroups — C5×#11089 #11933809

Order 1280.

1154 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#99C211yesmaximal, characteristic
2C22×C5×#99C211yesmaximal, characteristic
3C22×C5×#99C211yesmaximal, characteristic
4C5×#2315C211yesmaximal, characteristic, complemented
5C2×C5×#342C211yesmaximal, characteristic, complemented
6C2×C5×#342C211yesmaximal, characteristic, complemented
7C2×C5×#342C211yesmaximal, characteristic, complemented
8C23×C5×D4C2211yescharacteristic
9C22×C5×C22⋊C4C2211yescharacteristic
10C22×C5×C22⋊C4C2211yescharacteristic
11C22×C5×C22⋊C4C2211yescharacteristic
12C22×C5×C22⋊C4C2211yescharacteristic
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C5×C22⋊C4C2211yescharacteristic
15C2×C5×#99—22no—
16C2×C5×#99—22no—
17C2×C5×#99—22no—
18C2×C5×#99—22no—
19C2×C5×#99—22no—
20C2×C5×#99—22no—
21C2×C5×#99—22no—
22C2×C5×#99—22no—
23C2×C5×#99C414yescomplemented
24C5×#385—22no—
25C5×#385—22no—
26C5×#380—22no—
27C5×#342—22no—
28C5×#342—22no—
29C5×#342—22no—
30#11089C511yesmaximal, characteristic, direct product factor, Sylow
31C25×C5Q811yescharacteristic
32C25×C5C2311yescharacteristic
33C22×C5×D4—21no—
34C22×C5×D4—21no—
35C22×C5×D4—21no—
36C22×C5×D4—21no—
37C22×C5×D4—21no—
38C22×C5×D4—21no—
39C22×C5×D4—21no—
40C22×C5×D4—21no—
41C22×C5×D4—21no—
42C22×C5×D4—21no—
43C22×C5×D4—21no—
44C22×C5×D4—21no—
45C22×C5×D4C2×C412yes—
46C22×C5×D4D412yes—
47C23×C4×C5—21no—
48C23×C4×C5—21no—
49C23×C4×C5—21no—
50C23×C4×C5—21no—
51C23×C4×C5—21no—
52C23×C4×C5—21no—
53C23×C4×C5Q811yescharacteristic
54C2×C5×C4⋊C4—24no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4—21no—
65C2×C5×C22⋊C4—21no—
66C2×C5×C22⋊C4—21no—
67C2×C5×C22⋊C4—21no—
68C2×C5×C22⋊C4—21no—
69C2×C5×C22⋊C4—21no—
70C2×C5×C22⋊C4—21no—
71C2×C5×C22⋊C4—21no—
72C2×C5×C22⋊C4—21no—
73C2×C5×C22⋊C4—21no—
74C2×C5×C22⋊C4—21no—
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4—21no—
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4—21no—
82C2×C5×C22⋊C4—21no—
83C2×C5×C22⋊C4C2×C412yes—
84C2×C5×C22⋊C4C2×C412yes—
85C2×C5×C22⋊C4D412yes—
86C2×C5×C22⋊C4D412yes—
87C2×C5×C22⋊C4D412yes—
88C2×C5×C22⋊C4D412yes—
89C2×C5×C22⋊C4D412yes—
90C2×C5×C22⋊C4D412yes—
91C5×#99—28no—
92C5×#99—28no—
93C5×#99—28no—
94C5×#95—24no—
95C22×#99C2×C511yescharacteristic
96C22×#99C2×C511yescharacteristic
97C22×#99C2×C511yescharacteristic
98#2315C2×C511yescharacteristic, complemented
99C2×#342C2×C511yescharacteristic, complemented
100C2×#342C2×C511yescharacteristic, complemented
101C2×#342C2×C511yescharacteristic, complemented
102C24×C5—21no—
103C24×C5—21no—
104C24×C5—21no—
105C24×C5—21no—
106C24×C5—21no—
107C24×C5—21no—
108C24×C5—82no—
109C24×C5—82no—
110C24×C5C4⋊C412yescomplemented
111C24×C5C22×C411yescharacteristic
112C24×C5C2×D411yescharacteristic
113C24×C5C2×D411yescharacteristic
114C24×C5C2×D411yescharacteristic
115C24×C5C2×D411yescharacteristic
116C24×C5C2×D411yescharacteristic
117C24×C5C2×D411yescharacteristic
118C24×C5C2×D411yescharacteristic
119C24×C5C2×Q811yescharacteristic
120C24×C5#4111yescharacteristic
121C24×C5#4111yescharacteristic
122C24×C5#4111yescharacteristic
123C24×C5#4111yescharacteristic
124C24×C5#4111yescharacteristic
125C24×C5#4111yescharacteristic
126C2×C5×D4—22no—
127C2×C5×D4—22no—
128C2×C5×D4—22no—
129C2×C5×D4—22no—
130C2×C5×D4—22no—
131C2×C5×D4—22no—
132C2×C5×D4—22no—
133C2×C5×D4—22no—
134C2×C5×D4—22no—
135C2×C5×D4—22no—
136C2×C5×D4—22no—
137C2×C5×D4—22no—
138C2×C5×D4—41no—
139C2×C5×D4—41no—
140C2×C5×D4—41no—
141C2×C5×D4—41no—
142C2×C5×D4—41no—
143C2×C5×D4—41no—
144C2×C5×D4—41no—
145C2×C5×D4—41no—
146C2×C5×D4—41no—
147C2×C5×D4—41no—
148C2×C5×D4—41no—
149C2×C5×D4—41no—
150C2×C5×D4—41no—
151C2×C5×D4—41no—
152C2×C5×D4—41no—
153C2×C5×D4—41no—
154C22×C4×C5—22no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—41no—
169C22×C4×C5—41no—
170C22×C4×C5—41no—
171C22×C4×C5—41no—
172C22×C4×C5—41no—
173C22×C4×C5—41no—
174C22×C4×C5—41no—
175C22×C4×C5—41no—
176C22×C4×C5—41no—
177C22×C4×C5—41no—
178C22×C4×C5—82no—
179C22×C4×C5—82no—
180C22×C4×C5—82no—
181C22×C4×C5—82no—
182C22×C4×C5—82no—
183C22×C4×C5—82no—
184C22×C4×C5C4⋊C412yescomplemented
185C5×C4⋊C4—84no—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—22no—
192C5×C22⋊C4—22no—
193C5×C22⋊C4—22no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—22no—
196C5×C22⋊C4—22no—
197C5×C22⋊C4—22no—
198C5×C22⋊C4—22no—
199C5×C22⋊C4—41no—
200C5×C22⋊C4—41no—
201C5×C22⋊C4—41no—
202C5×C22⋊C4—41no—
203C5×C22⋊C4—41no—
204C5×C22⋊C4—41no—
205C5×C22⋊C4—41no—
206C5×C22⋊C4—41no—
207C5×C22⋊C4—41no—
208C5×C22⋊C4—41no—
209C5×C22⋊C4C22⋊C414yes—
210C23×D4C22×C511yescharacteristic
211C22×C22⋊C4C22×C511yescharacteristic
212C22×C22⋊C4C22×C511yescharacteristic
213C22×C22⋊C4C22×C511yescharacteristic
214C22×C22⋊C4C22×C511yescharacteristic
215C22×C22⋊C4C22×C511yescharacteristic
216C22×C22⋊C4C22×C511yescharacteristic
217C2×#99—22no—
218C2×#99—22no—
219C2×#99—22no—
220C2×#99—22no—
221C2×#99—22no—
222C2×#99—22no—
223C2×#99—22no—
224C2×#99—22no—
225C2×#99C4×C514yescomplemented
226#385—22no—
227#385—22no—
228#380—22no—
229#342—22no—
230#342—22no—
231#342—22no—
232C23×C5—22no—
233C23×C5—22no—
234C23×C5—22no—
235C23×C5—42no—
236C23×C5—42no—
237C23×C5—42no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5—41no—
243C23×C5—41no—
244C23×C5—41no—
245C23×C5—41no—
246C23×C5—82no—
247C23×C5—82no—
248C23×C5—82no—
249C23×C5—81no—
250C23×C5—81no—
251C23×C5—81no—
252C23×C5—81no—
253C23×C5—81no—
254C23×C5—81no—
255C23×C5—81no—
256C23×C5—81no—
257C23×C5—82no—
258C23×C5—82no—
259C23×C5—82no—
260C23×C5—82no—
261C23×C5C2×C22⋊C411yescharacteristic
262C23×C5C2×C4⋊C411yescharacteristic
263C23×C5#11711yescharacteristic
264C23×C5C4×D411yescharacteristic
265C23×C5C4×D411yescharacteristic
266C23×C5C4×D411yescharacteristic
267C23×C5C4×D411yescharacteristic
268C23×C5#12011yescharacteristic
269C23×C5#12011yescharacteristic
270C23×C5#12011yescharacteristic
271C23×C5#12111yescharacteristic
272C23×C5#12111yescharacteristic
273C23×C5#12111yescharacteristic
274C23×C5#12111yescharacteristic
275C23×C5#12111yescharacteristic
276C23×C5#12111yescharacteristic
277C23×C5#12111yescharacteristic
278C23×C5#12111yescharacteristic
279C23×C5C22⋊Q811yescharacteristic
280C23×C5C22⋊Q811yescharacteristic
281C23×C5C22⋊Q811yescharacteristic
282C23×C5C22⋊Q811yescharacteristic
283C23×C5C22⋊Q811yescharacteristic
284C23×C5C22⋊Q811yescharacteristic
285C23×C5#12311yescharacteristic
286C23×C5#12311yescharacteristic
287C23×C5#12311yescharacteristic
288C23×C5#12311yescharacteristic
289C23×C5#12311yescharacteristic
290C23×C5#12411yescharacteristic
291C23×C5#12411yescharacteristic
292C23×C5#12411yescharacteristic
293C23×C5#12611yescharacteristic
294C23×C5#12611yescharacteristic
295C23×C5#12711yescharacteristic
296C5×D4—42no—
297C5×D4—42no—
298C5×D4—42no—
299C5×D4—42no—
300C5×D4—42no—
301C5×D4—42no—
302C5×D4—42no—
303C5×D4—42no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—24no—
308C2×C4×C5—44no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—44no—
314C2×C4×C5—44no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—82no—
321C2×C4×C5—82no—
322C2×C4×C5—82no—
323C2×C4×C5—82no—
324C2×C4×C5—82no—
325C2×C4×C5—82no—
326C2×C4×C5—82no—
327C2×C4×C5—82no—
328C2×C4×C5—82no—
329C2×C4×C5—82no—
330C2×C4×C5—82no—
331C2×C4×C5—82no—
332C2×C4×C5—82no—
333C2×C4×C5—82no—
334C2×C4×C5—82no—
335C25C5×Q811yescharacteristic
336C25C23×C511yescharacteristic
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4C2×C4×C512yes—
350C22×D4C5×D412yes—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4C5×Q811yescharacteristic
358C2×C4⋊C4—24no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4C2×C4×C512yes—
388C2×C22⋊C4C2×C4×C512yes—
389C2×C22⋊C4C5×D412yes—
390C2×C22⋊C4C5×D412yes—
391C2×C22⋊C4C5×D412yes—
392C2×C22⋊C4C5×D412yes—
393C2×C22⋊C4C5×D412yes—
394C2×C22⋊C4C5×D412yes—
395#99—28no—
396#99—28no—
397#99—28no—
398#95—24no—
399C22×C5—22no—
400C22×C5—22no—
401C22×C5—22no—
402C22×C5—22no—
403C22×C5—22no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—41no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—41no—
415C22×C5—41no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5—41no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—42no—
435C22×C5—82no—
436C22×C5—82no—
437C22×C5—82no—
438C22×C5—82no—
439C22×C5—82no—
440C22×C5—82no—
441C22×C5—82no—
442C22×C5#38011yescharacteristic
443C22×C5#38511yescharacteristic
444C22×C5#38511yescharacteristic
445C22×C5#38611yescharacteristic
446C22×C5#38811yescharacteristic
447C22×C5#38811yescharacteristic
448C22×C5#39011yescharacteristic
449C22×C5#39211yescharacteristic
450C22×C5#39311yescharacteristic
451C22×C5#39411yescharacteristic
452C22×C5#39411yescharacteristic
453C22×C5#39611yescharacteristic
454C22×C5#39611yescharacteristic
455C22×C5#39711yescharacteristic
456C22×C5#39911yescharacteristic
457C4×C5—44no—
458C4×C5—42no—
459C4×C5—82no—
460C4×C5—82no—
461C4×C5—82no—
462C4×C5—82no—
463C4×C5—82no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—82no—
471C24—82no—
472C24C5×C4⋊C412yescomplemented
473C24C22×C4×C511yescharacteristic
474C24C2×C5×D411yescharacteristic
475C24C2×C5×D411yescharacteristic
476C24C2×C5×D411yescharacteristic
477C24C2×C5×D411yescharacteristic
478C24C2×C5×D411yescharacteristic
479C24C2×C5×D411yescharacteristic
480C24C2×C5×D411yescharacteristic
481C24C2×C5×Q811yescharacteristic
482C24C5×#4111yescharacteristic
483C24C5×#4111yescharacteristic
484C24C5×#4111yescharacteristic
485C24C5×#4111yescharacteristic
486C24C5×#4111yescharacteristic
487C24C5×#4111yescharacteristic
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—82no—
544C22×C4—82no—
545C22×C4—82no—
546C22×C4C5×C4⋊C412yescomplemented
547C4⋊C4—84no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4C5×C22⋊C414yes—
572C2×C5—21no—
573C2×C5—21no—
574C2×C5—21no—
575C2×C5—21no—
576C2×C5—21no—
577C2×C5—21no—
578C2×C5—21no—
579C2×C5—21no—
580C2×C5—21no—
581C2×C5—21no—
582C2×C5—21no—
583C2×C5—21no—
584C2×C5—21no—
585C2×C5—21no—
586C2×C5—82no—
587C2×C5#143911yescharacteristic
588C2×C5#203212yes—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—82no—
604C23—82no—
605C23—82no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—82no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23C2×C5×C22⋊C411yescharacteristic
619C23C2×C5×C4⋊C411yescharacteristic
620C23C5×#11711yescharacteristic
621C23C4×C5×D411yescharacteristic
622C23C4×C5×D411yescharacteristic
623C23C4×C5×D411yescharacteristic
624C23C4×C5×D411yescharacteristic
625C23C5×#12011yescharacteristic
626C23C5×#12011yescharacteristic
627C23C5×#12011yescharacteristic
628C23C5×#12111yescharacteristic
629C23C5×#12111yescharacteristic
630C23C5×#12111yescharacteristic
631C23C5×#12111yescharacteristic
632C23C5×#12111yescharacteristic
633C23C5×#12111yescharacteristic
634C23C5×#12111yescharacteristic
635C23C5×#12111yescharacteristic
636C23C5×C22⋊Q811yescharacteristic
637C23C5×C22⋊Q811yescharacteristic
638C23C5×C22⋊Q811yescharacteristic
639C23C5×C22⋊Q811yescharacteristic
640C23C5×C22⋊Q811yescharacteristic
641C23C5×C22⋊Q811yescharacteristic
642C23C5×#12311yescharacteristic
643C23C5×#12311yescharacteristic
644C23C5×#12311yescharacteristic
645C23C5×#12311yescharacteristic
646C23C5×#12311yescharacteristic
647C23C5×#12411yescharacteristic
648C23C5×#12411yescharacteristic
649C23C5×#12411yescharacteristic
650C23C5×#12611yescharacteristic
651C23C5×#12611yescharacteristic
652C23C5×#12711yescharacteristic
653D4—42no—
654D4—42no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—44no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4—82no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4—82no—
691C2×C4—82no—
692C5#1108911yescharacteristic, direct product factor, Sylow
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22C5×#38011yescharacteristic
737C22C5×#38511yescharacteristic
738C22C5×#38511yescharacteristic
739C22C5×#38611yescharacteristic
740C22C5×#38811yescharacteristic
741C22C5×#38811yescharacteristic
742C22C5×#39011yescharacteristic
743C22C5×#39211yescharacteristic
744C22C5×#39311yescharacteristic
745C22C5×#39411yescharacteristic
746C22C5×#39411yescharacteristic
747C22C5×#39611yescharacteristic
748C22C5×#39611yescharacteristic
749C22C5×#39711yescharacteristic
750C22C5×#39911yescharacteristic
751C4—44no—
752C4—42no—
753C4—82no—
754C4—82no—
755C4—82no—
756C4—82no—
757C4—82no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—82no—
773C2C5×#143911yescharacteristic
774C2C5×#203212yes—
subgroupG/H
center, socleC22×C5#393
commutatorC24C22×C4×C5
Frattini, cosocleC25C23×C5
prime radicalC23×C5×D4C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#2315C2semidirect
5. C2×C5×#342C2semidirect
6. C2×C5×#342C2semidirect
7. C2×C5×#342C2semidirect
23. C2×C5×#99C4semidirect
30. #11089C5direct (N × H)
98. #2315C2×C5semidirect
99. C2×#342C2×C5semidirect
100. C2×#342C2×C5semidirect
101. C2×#342C2×C5semidirect
110. C24×C5C4⋊C4semidirect
184. C22×C4×C5C4⋊C4semidirect
225. C2×#99C4×C5semidirect
472. C24C5×C4⋊C4semidirect
546. C22×C4C5×C4⋊C4semidirect
692. C5#11089direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#992
C5×#23152
C2×C5×#3422
#110895