Finite Group Databasebeta

← C5×#11017 #11933737

Subgroups — C5×#11017 #11933737

Order 1280.

1358 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#137C211yesmaximal, characteristic
2C22×C5×#104C211yesmaximal, characteristic
3C2×C5×#419C211yesmaximal, characteristic, complemented
4C5×#2311C211yesmaximal, characteristic
5C2×C5×#391C211yesmaximal, characteristic, complemented
6C2×C5×#343C211yesmaximal, characteristic, complemented
7C2×C5×#339C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C23×C5×Q8C2211yescharacteristic
10C2×C5×#137—22no—
11C2×C5×#137—22no—
12C2×C5×#137—22no—
13C2×C5×#137—22no—
14C2×C5×#137—22no—
15C2×C5×#137C414yescomplemented
16C22×C5×Q16—21no—
17C22×C5×SD16—21no—
18C22×C5×M16C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C42×C5C2211yescharacteristic
23C2×C5×#104—22no—
24C2×C5×#104—22no—
25C2×C5×#104—22no—
26C5×#419—22no—
27C5×#419—22no—
28C2×C5×#103—22no—
29C5×#391—22no—
30C5×#391—21no—
31C5×#391—22no—
32C5×#390—21no—
33C5×#386—22no—
34C5×#380—22no—
35C2×C5×#95—22no—
36C5×#343—22no—
37C5×#339—22no—
38#11017C511yesmaximal, characteristic, direct product factor, Sylow
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×#41—21no—
46C2×C5×#41—21no—
47C2×C5×#41—21no—
48C2×C5×#41—21no—
49C2×C5×#41C2×C412yes—
50C2×C5×#41D412yes—
51C22×C5×Q8—21no—
52C22×C5×Q8—21no—
53C22×C5×Q8—21no—
54C22×C5×Q8—21no—
55C22×C5×Q8—21no—
56C22×C5×Q8—21no—
57C22×C5×Q8—21no—
58C22×C5×Q8—21no—
59C22×C5×Q8—21no—
60C22×C5×Q8—21no—
61C22×C5×Q8—21no—
62C22×C5×Q8C2×C412yes—
63C22×C5×Q8D411yescharacteristic
64C22×C5×Q8D412yes—
65C22×C5×Q8D412yes—
66C22×C5×D4—21no—
67C22×C5×D4D411yescharacteristic
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C23×C4×C5—21no—
71C23×C4×C5D412yes—
72C23×C4×C5C2311yescharacteristic
73C5×#137—28no—
74C5×#137—28no—
75C5×#137—28no—
76C5×#137—28no—
77C2×C5×Q16—24no—
78C2×C5×Q16—24no—
79C2×C5×Q16—24no—
80C2×C5×SD16—24no—
81C2×C5×SD16—24no—
82C2×C5×SD16—24no—
83C2×C5×M16—21no—
84C2×C5×M16—21no—
85C2×C5×M16—21no—
86C2×C5×M16—21no—
87C2×C5×M16—21no—
88C2×C5×M16—21no—
89C2×C5×M16—21no—
90C2×C5×M16—21no—
91C2×C5×M16C2×C412yes—
92C2×C5×M16D412yes—
93C2×C5×M16D412yes—
94C2×C5×M16D412yes—
95C22×C5×C8—21no—
96C22×C5×C8—21no—
97C5×#117—21no—
98C5×#117—21no—
99C5×#117—21no—
100C5×#117—21no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4D412yes—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4—24no—
110C2×C42×C5—21no—
111C2×C42×C5—21no—
112C2×C42×C5—21no—
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5—21no—
116C2×C42×C5D412yes—
117C5×#104—28no—
118C5×#103—28no—
119C5×#95—28no—
120C5×#95—24no—
121C22×#137C2×C511yescharacteristic
122C22×#104C2×C511yescharacteristic
123C2×#419C2×C511yescharacteristic, complemented
124#2311C2×C511yescharacteristic
125C2×#391C2×C511yescharacteristic, complemented
126C2×#343C2×C511yescharacteristic, complemented
127C2×#339C2×C511yescharacteristic, complemented
128C24×C5—21no—
129C24×C5C2×D411yescharacteristic
130C5×#41—22no—
131C5×#41—22no—
132C5×#41—22no—
133C5×#41—22no—
134C5×#41—22no—
135C5×#41—22no—
136C5×#41—22no—
137C5×#41—22no—
138C5×#41—41no—
139C5×#41—41no—
140C5×#41—41no—
141C5×#41—41no—
142C5×#41—41no—
143C5×#41—41no—
144C5×#41—41no—
145C5×#41—41no—
146C2×C5×Q8—22no—
147C2×C5×Q8—22no—
148C2×C5×Q8—22no—
149C2×C5×Q8—21no—
150C2×C5×Q8—22no—
151C2×C5×Q8—22no—
152C2×C5×Q8—22no—
153C2×C5×Q8—22no—
154C2×C5×Q8—22no—
155C2×C5×Q8—22no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—22no—
159C2×C5×Q8—22no—
160C2×C5×Q8—22no—
161C2×C5×Q8—22no—
162C2×C5×Q8—22no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—22no—
166C2×C5×Q8—41no—
167C2×C5×Q8—41no—
168C2×C5×Q8—41no—
169C2×C5×Q8—41no—
170C2×C5×Q8—41no—
171C2×C5×Q8—41no—
172C2×C5×Q8—41no—
173C2×C5×Q8—41no—
174C2×C5×Q8—41no—
175C2×C5×Q8—41no—
176C2×C5×Q8—41no—
177C2×C5×Q8—41no—
178C2×C5×Q8C22⋊C412yes—
179C2×C5×Q8C22⋊C414yescomplemented
180C2×C5×D4—22no—
181C2×C5×D4—22no—
182C2×C5×D4—21no—
183C2×C5×D4—21no—
184C2×C5×D4—21no—
185C2×C5×D4—21no—
186C2×C5×D4—21no—
187C2×C5×D4—41no—
188C2×C5×D4—41no—
189C2×C5×D4—41no—
190C2×C5×D4—41no—
191C2×C5×D4C22⋊C412yes—
192C22×C4×C5—24no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—21no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—42no—
205C22×C4×C5—41no—
206C22×C4×C5—41no—
207C22×C4×C5—41no—
208C22×C4×C5—41no—
209C22×C4×C5—41no—
210C22×C4×C5—41no—
211C22×C4×C5—41no—
212C22×C4×C5—41no—
213C22×C4×C5—41no—
214C22×C4×C5—41no—
215C22×C4×C5—44no—
216C22×C4×C5C22×C411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5#4111yescharacteristic
227C22×C4×C5#4111yescharacteristic
228C22×C4×C5#4111yescharacteristic
229C22×C4×C5#4111yescharacteristic
230C5×Q16—216no—
231C5×SD16—216no—
232C5×M16—22no—
233C5×M16—22no—
234C5×M16—22no—
235C5×M16—22no—
236C5×M16—22no—
237C5×M16—41no—
238C5×M16—41no—
239C5×M16C22⋊C414yescomplemented
240C2×C5×C8—22no—
241C2×C5×C8—22no—
242C2×C5×C8—22no—
243C2×C5×C8—22no—
244C2×C5×C8—41no—
245C2×C5×C8—41no—
246C5×C4⋊C4—22no—
247C5×C4⋊C4—22no—
248C5×C4⋊C4—41no—
249C5×C4⋊C4—41no—
250C5×C4⋊C4—41no—
251C5×C4⋊C4—41no—
252C5×C22⋊C4—41no—
253C5×C22⋊C4—41no—
254C5×C22⋊C4—84no—
255C42×C5—22no—
256C42×C5—22no—
257C42×C5—41no—
258C42×C5—41no—
259C42×C5—41no—
260C42×C5—41no—
261C22×#41C22×C511yescharacteristic
262C23×Q8C22×C511yescharacteristic
263C2×#137—22no—
264C2×#137—22no—
265C2×#137—22no—
266C2×#137—22no—
267C2×#137—22no—
268C2×#137C4×C514yescomplemented
269C22×Q16—21no—
270C22×SD16—21no—
271C22×M16C22×C511yescharacteristic
272C22×M16C22×C511yescharacteristic
273C2×#117C22×C511yescharacteristic
274C22×C4⋊C4C22×C511yescharacteristic
275C22×C42C22×C511yescharacteristic
276C2×#104—22no—
277C2×#104—22no—
278C2×#104—22no—
279#419—22no—
280#419—22no—
281C2×#103—22no—
282#391—21no—
283#391—22no—
284#391—22no—
285#390—21no—
286#386—22no—
287#380—22no—
288C2×#95—22no—
289#343—22no—
290#339—22no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—22no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—42no—
297C23×C5—42no—
298C23×C5C4×D411yescharacteristic
299C23×C5#12011yescharacteristic
300C23×C5#12011yescharacteristic
301C23×C5#12111yescharacteristic
302C23×C5#12111yescharacteristic
303C23×C5#12111yescharacteristic
304C23×C5#12711yescharacteristic
305C5×Q8—24no—
306C5×Q8—22no—
307C5×Q8—24no—
308C5×Q8—22no—
309C5×Q8—42no—
310C5×Q8—42no—
311C5×Q8—42no—
312C5×Q8—42no—
313C5×Q8—42no—
314C5×Q8—42no—
315C5×Q8—41no—
316C5×Q8—41no—
317C5×D4—22no—
318C5×D4—22no—
319C5×D4—42no—
320C5×D4—42no—
321C5×D4—42no—
322C5×D4—42no—
323C5×D4—41no—
324C5×D4—41no—
325C2×C4×C5—24no—
326C2×C4×C5—22no—
327C2×C4×C5—24no—
328C2×C4×C5—44no—
329C2×C4×C5—42no—
330C2×C4×C5—44no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—42no—
339C2×C4×C5—42no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5—42no—
344C2×C4×C5—44no—
345C2×C4×C5—42no—
346C2×C4×C5—42no—
347C2×C4×C5—42no—
348C2×C4×C5—44no—
349C2×C4×C5—42no—
350C2×C4×C5—82no—
351C2×C4×C5C2×C22⋊C411yescharacteristic
352C2×C4×C5C2×C22⋊C411yescharacteristic
353C2×C4×C5C2×C22⋊C411yescharacteristic
354C2×C4×C5C4×D411yescharacteristic
355C2×C4×C5C4×D411yescharacteristic
356C2×C4×C5C4×D411yescharacteristic
357C2×C4×C5#12011yescharacteristic
358C2×C4×C5#12011yescharacteristic
359C2×C4×C5#12011yescharacteristic
360C2×C4×C5#12011yescharacteristic
361C2×C4×C5#12011yescharacteristic
362C2×C4×C5#12011yescharacteristic
363C2×C4×C5#12111yescharacteristic
364C2×C4×C5#12111yescharacteristic
365C2×C4×C5#12111yescharacteristic
366C2×C4×C5#12111yescharacteristic
367C2×C4×C5#12111yescharacteristic
368C2×C4×C5#12111yescharacteristic
369C2×C4×C5#12111yescharacteristic
370C2×C4×C5#12111yescharacteristic
371C2×C4×C5#12111yescharacteristic
372C2×C4×C5#12311yescharacteristic
373C2×C4×C5#12311yescharacteristic
374C2×C4×C5#12311yescharacteristic
375C2×C4×C5#12311yescharacteristic
376C2×C4×C5#12411yescharacteristic
377C2×C4×C5#12411yescharacteristic
378C2×C4×C5#12711yescharacteristic
379C5×C8—24no—
380C5×C8—42no—
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41—21no—
389C2×#41—21no—
390C2×#41—21no—
391C2×#41C2×C4×C512yes—
392C2×#41C5×D412yes—
393C22×Q8—21no—
394C22×Q8—21no—
395C22×Q8—21no—
396C22×Q8—21no—
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8—21no—
400C22×Q8—21no—
401C22×Q8—21no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×Q8C2×C4×C512yes—
405C22×Q8C5×D411yescharacteristic
406C22×Q8C5×D412yes—
407C22×Q8C5×D412yes—
408C22×D4—21no—
409C22×D4C5×D411yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—21no—
413C23×C4C5×D412yes—
414C23×C4C23×C511yescharacteristic
415#137—28no—
416#137—28no—
417#137—28no—
418#137—28no—
419C2×Q16—24no—
420C2×Q16—24no—
421C2×Q16—24no—
422C2×SD16—24no—
423C2×SD16—24no—
424C2×SD16—24no—
425C2×M16—21no—
426C2×M16—21no—
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16—21no—
431C2×M16—21no—
432C2×M16—21no—
433C2×M16C2×C4×C512yes—
434C2×M16C5×D412yes—
435C2×M16C5×D412yes—
436C2×M16C5×D412yes—
437C22×C8—21no—
438C22×C8—21no—
439#117—21no—
440#117—21no—
441#117—21no—
442#117—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C5×D412yes—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—24no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42C5×D412yes—
459#104—28no—
460#103—28no—
461#95—28no—
462#95—24no—
463C22×C5—22no—
464C22×C5—22no—
465C22×C5—21no—
466C22×C5—21no—
467C22×C5—21no—
468C22×C5—21no—
469C22×C5—22no—
470C22×C5—22no—
471C22×C5—44no—
472C22×C5—42no—
473C22×C5—81no—
474C22×C5—81no—
475C22×C5—82no—
476C22×C5#38611yescharacteristic
477C22×C5#38611yescharacteristic
478C22×C5#39011yescharacteristic
479C22×C5#39211yescharacteristic
480C22×C5#39211yescharacteristic
481C22×C5#39211yescharacteristic
482C22×C5#39411yescharacteristic
483C22×C5#45512yes—
484C22×C5#45612yes—
485C4×C5—44no—
486C4×C5—42no—
487C4×C5—44no—
488C4×C5—82no—
489C4×C5—82no—
490C4×C5#37911yescharacteristic
491C4×C5#38611yescharacteristic
492C4×C5#38611yescharacteristic
493C4×C5#39011yescharacteristic
494C4×C5#39211yescharacteristic
495C4×C5#39411yescharacteristic
496C4×C5#39411yescharacteristic
497C4×C5#39411yescharacteristic
498C24—21no—
499C24C2×C5×D411yescharacteristic
500#41—22no—
501#41—22no—
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—22no—
507#41—22no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—41no—
515#41—41no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—21no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—22no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8C5×C22⋊C412yes—
549C2×Q8C5×C22⋊C414yescomplemented
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4C5×C22⋊C412yes—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—42no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—44no—
586C22×C4C22×C4×C511yescharacteristic
587C22×C4C2×C5×D411yescharacteristic
588C22×C4C2×C5×D411yescharacteristic
589C22×C4C2×C5×D411yescharacteristic
590C22×C4C2×C5×D411yescharacteristic
591C22×C4C2×C5×D411yescharacteristic
592C22×C4C2×C5×D411yescharacteristic
593C22×C4C2×C5×D411yescharacteristic
594C22×C4C2×C5×D411yescharacteristic
595C22×C4C2×C5×D411yescharacteristic
596C22×C4C5×#4111yescharacteristic
597C22×C4C5×#4111yescharacteristic
598C22×C4C5×#4111yescharacteristic
599C22×C4C5×#4111yescharacteristic
600Q16—216no—
601SD16—216no—
602M16—22no—
603M16—22no—
604M16—22no—
605M16—22no—
606M16—22no—
607M16—41no—
608M16—41no—
609M16C5×C22⋊C414yescomplemented
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—41no—
615C2×C8—41no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—84no—
625C42—22no—
626C42—22no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C2×C5—21no—
632C2×C5—21no—
633C2×C5—21no—
634C2×C5—21no—
635C2×C5—82no—
636C2×C5#143811yescharacteristic
637C2×C5#188212yes—
638C2×C5#200411yescharacteristic
639C2×C5#200511yescharacteristic
640C2×C5#200712yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23C4×C5×D411yescharacteristic
649C23C5×#12011yescharacteristic
650C23C5×#12011yescharacteristic
651C23C5×#12111yescharacteristic
652C23C5×#12111yescharacteristic
653C23C5×#12111yescharacteristic
654C23C5×#12711yescharacteristic
655Q8—24no—
656Q8—22no—
657Q8—24no—
658Q8—22no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—41no—
666Q8—41no—
667D4—22no—
668D4—22no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—41no—
674D4—41no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—82no—
701C2×C4C2×C5×C22⋊C411yescharacteristic
702C2×C4C2×C5×C22⋊C411yescharacteristic
703C2×C4C2×C5×C22⋊C411yescharacteristic
704C2×C4C4×C5×D411yescharacteristic
705C2×C4C4×C5×D411yescharacteristic
706C2×C4C4×C5×D411yescharacteristic
707C2×C4C5×#12011yescharacteristic
708C2×C4C5×#12011yescharacteristic
709C2×C4C5×#12011yescharacteristic
710C2×C4C5×#12011yescharacteristic
711C2×C4C5×#12011yescharacteristic
712C2×C4C5×#12011yescharacteristic
713C2×C4C5×#12111yescharacteristic
714C2×C4C5×#12111yescharacteristic
715C2×C4C5×#12111yescharacteristic
716C2×C4C5×#12111yescharacteristic
717C2×C4C5×#12111yescharacteristic
718C2×C4C5×#12111yescharacteristic
719C2×C4C5×#12111yescharacteristic
720C2×C4C5×#12111yescharacteristic
721C2×C4C5×#12111yescharacteristic
722C2×C4C5×#12311yescharacteristic
723C2×C4C5×#12311yescharacteristic
724C2×C4C5×#12311yescharacteristic
725C2×C4C5×#12311yescharacteristic
726C2×C4C5×#12411yescharacteristic
727C2×C4C5×#12411yescharacteristic
728C2×C4C5×#12711yescharacteristic
729C8—24no—
730C8—42no—
731C5#1101711yescharacteristic, direct product factor, Sylow
732C22—22no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—22no—
740C22—44no—
741C22—42no—
742C22—81no—
743C22—81no—
744C22—82no—
745C22C5×#38611yescharacteristic
746C22C5×#38611yescharacteristic
747C22C5×#39011yescharacteristic
748C22C5×#39211yescharacteristic
749C22C5×#39211yescharacteristic
750C22C5×#39211yescharacteristic
751C22C5×#39411yescharacteristic
752C22C5×#45512yes—
753C22C5×#45612yes—
754C4—44no—
755C4—42no—
756C4—44no—
757C4—82no—
758C4—82no—
759C4C5×#37911yescharacteristic
760C4C5×#38611yescharacteristic
761C4C5×#38611yescharacteristic
762C4C5×#39011yescharacteristic
763C4C5×#39211yescharacteristic
764C4C5×#39411yescharacteristic
765C4C5×#39411yescharacteristic
766C4C5×#39411yescharacteristic
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—82no—
772C2C5×#143811yescharacteristic
773C2C5×#188212yes—
774C2C5×#200411yescharacteristic
775C2C5×#200511yescharacteristic
776C2C5×#200712yes—
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
3. C2×C5×#419C2semidirect
5. C2×C5×#391C2semidirect
6. C2×C5×#343C2semidirect
7. C2×C5×#339C2semidirect
15. C2×C5×#137C4semidirect
38. #11017C5direct (N × H)
123. C2×#419C2×C5semidirect
125. C2×#391C2×C5semidirect
126. C2×#343C2×C5semidirect
127. C2×#339C2×C5semidirect
179. C2×C5×Q8C22⋊C4semidirect
239. C5×M16C22⋊C4semidirect
268. C2×#137C4×C5semidirect
549. C2×Q8C5×C22⋊C4semidirect
609. M16C5×C22⋊C4semidirect
731. C5#11017direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1372
C22×C5×#1042
C2×C5×#4192
C5×#23112
C2×C5×#3912
C2×C5×#3432
C2×C5×#3392
#110175