Finite Group Databasebeta

← C5×#10998 #11933718

Subgroups — C5×#10998 #11933718

Order 1280.

1350 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
1C2×C5×#536C211yesmaximal, characteristic
2C22×C5×#104C211yesmaximal, characteristic
3C2×C5×#417C211yesmaximal, characteristic
4C22×C5×#101C211yesmaximal, characteristic, complemented
5C2×C5×#391C211yesmaximal, characteristic, complemented
6C5×#1736C211yesmaximal, characteristic, complemented
7C2×C5×#339C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C23×C5×Q8C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C22×C5×M16C2211yescharacteristic
12C5×#536—22no—
13C5×#536—22no—
14C5×#536—22no—
15C5×#536C414yescomplemented
16C2×C5×C4⋊Q8—21no—
17C2×C5×#124—21no—
18C2×C5×#123—22no—
19C2×C5×C22⋊Q8—22no—
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C42×C5C2211yescharacteristic
23C2×C5×#104—22no—
24C2×C5×#104—22no—
25C2×C5×#104—22no—
26C5×#417—22no—
27C5×#417—22no—
28C2×C5×#103—21no—
29C2×C5×#102—21no—
30C2×C5×#101—22no—
31C2×C5×#101—22no—
32C2×C5×#101—22no—
33C5×#391—22no—
34C5×#391—22no—
35C2×C5×#95—22no—
36C5×#340—22no—
37C5×#339—22no—
38#10998C511yesmaximal, 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×Q8—21no—
63C22×C5×Q8C2×C412yes—
64C22×C5×Q8D411yescharacteristic
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
73C2×C5×M16—21no—
74C2×C5×M16—21no—
75C2×C5×M16—21no—
76C2×C5×M16—21no—
77C2×C5×M16—21no—
78C2×C5×M16—21no—
79C2×C5×M16—21no—
80C2×C5×M16—21no—
81C2×C5×M16—21no—
82C2×C5×M16—21no—
83C2×C5×M16D412yes—
84C2×C5×M16D412yes—
85C22×C5×C8—21no—
86C22×C5×C8—21no—
87C5×C4⋊Q8—24no—
88C5×C4⋊Q8—24no—
89C5×#124—24no—
90C5×#124—24no—
91C5×#123—28no—
92C5×#123—28no—
93C5×C22⋊Q8—28no—
94C5×C22⋊Q8—28no—
95C5×#117—21no—
96C5×#117—21no—
97C5×#117C2×C412yes—
98C5×#117D412yes—
99C2×C5×C4⋊C4—24no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4D412yes—
106C2×C5×C4⋊C4D412yes—
107C2×C5×C22⋊C4—24no—
108C2×C5×C22⋊C4—21no—
109C2×C42×C5—21no—
110C2×C42×C5—21no—
111C2×C42×C5—21no—
112C2×C42×C5—21no—
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5D412yes—
116C5×#104—28no—
117C5×#103—24no—
118C5×#102—24no—
119C5×#101—28no—
120C5×#95—28no—
121C2×#536C2×C511yescharacteristic
122C22×#104C2×C511yescharacteristic
123C2×#417C2×C511yescharacteristic
124C22×#101C2×C511yescharacteristic, complemented
125C2×#391C2×C511yescharacteristic, complemented
126#1736C2×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—22no—
150C2×C5×Q8—22no—
151C2×C5×Q8—22no—
152C2×C5×Q8—22no—
153C2×C5×Q8—22no—
154C2×C5×Q8—21no—
155C2×C5×Q8—22no—
156C2×C5×Q8—22no—
157C2×C5×Q8—22no—
158C2×C5×Q8—22no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—41no—
164C2×C5×Q8—41no—
165C2×C5×Q8—41no—
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×Q8—41no—
179C2×C5×Q8C22⋊C412yes—
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—22no—
197C22×C4×C5—22no—
198C22×C4×C5—21no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—42no—
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—44no—
213C22×C4×C5—41no—
214C22×C4×C5—41no—
215C22×C4×C5C22⋊C414yes—
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×M16—22no—
231C5×M16—22no—
232C5×M16—22no—
233C5×M16—22no—
234C5×M16—41no—
235C5×M16—41no—
236C5×M16—41no—
237C5×M16—41no—
238C2×C5×C8—22no—
239C2×C5×C8—22no—
240C2×C5×C8—41no—
241C2×C5×C8—41no—
242C2×C5×C8—41no—
243C2×C5×C8—41no—
244C5×C4⋊C4—216no—
245C5×C4⋊C4—22no—
246C5×C4⋊C4—22no—
247C5×C4⋊C4—22no—
248C5×C4⋊C4—41no—
249C5×C4⋊C4—41no—
250C5×C4⋊C4C22⋊C414yes—
251C5×C22⋊C4—216no—
252C5×C22⋊C4—22no—
253C5×C22⋊C4—22no—
254C42×C5—22no—
255C42×C5—22no—
256C42×C5—22no—
257C42×C5—22no—
258C42×C5—41no—
259C42×C5—41no—
260C22×#41C22×C511yescharacteristic
261C23×Q8C22×C511yescharacteristic
262C22×M16C22×C511yescharacteristic
263C22×M16C22×C511yescharacteristic
264#536—22no—
265#536—22no—
266#536—22no—
267#536C4×C514yescomplemented
268C2×C4⋊Q8—21no—
269C2×#124—21no—
270C2×#123—22no—
271C2×C22⋊Q8—22no—
272C2×#117C22×C511yescharacteristic
273C22×C4⋊C4C22×C511yescharacteristic
274C22×C42C22×C511yescharacteristic
275C2×#104—22no—
276C2×#104—22no—
277C2×#104—22no—
278#417—22no—
279#417—22no—
280C2×#103—21no—
281C2×#102—21no—
282C2×#101—22no—
283C2×#101—22no—
284C2×#101—22no—
285#391—22no—
286#391—22no—
287C2×#95—22no—
288#340—22no—
289#339—22no—
290C23×C5—22no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—42no—
296C23×C5—42no—
297C23×C5C2×C22⋊C411yescharacteristic
298C23×C5#12011yescharacteristic
299C23×C5#12011yescharacteristic
300C23×C5#12011yescharacteristic
301C23×C5#12111yescharacteristic
302C23×C5#12111yescharacteristic
303C23×C5#12311yescharacteristic
304C5×Q8—22no—
305C5×Q8—22no—
306C5×Q8—42no—
307C5×Q8—42no—
308C5×Q8—42no—
309C5×Q8—42no—
310C5×Q8—42no—
311C5×Q8—42no—
312C5×Q8—41no—
313C5×Q8—42no—
314C5×Q8—42no—
315C5×Q8—41no—
316C5×D4—22no—
317C5×D4—22no—
318C5×D4—42no—
319C5×D4—42no—
320C5×D4—42no—
321C5×D4—42no—
322C5×D4—41no—
323C5×D4—41no—
324C2×C4×C5—24no—
325C2×C4×C5—24no—
326C2×C4×C5—24no—
327C2×C4×C5—22no—
328C2×C4×C5—24no—
329C2×C4×C5—24no—
330C2×C4×C5—44no—
331C2×C4×C5—42no—
332C2×C4×C5—44no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5—42no—
336C2×C4×C5—41no—
337C2×C4×C5—42no—
338C2×C4×C5—42no—
339C2×C4×C5—41no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5—42no—
344C2×C4×C5—42no—
345C2×C4×C5—42no—
346C2×C4×C5—44no—
347C2×C4×C5—42no—
348C2×C4×C5—82no—
349C2×C4×C5—82no—
350C2×C4×C5C2×C22⋊C411yescharacteristic
351C2×C4×C5C2×C22⋊C411yescharacteristic
352C2×C4×C5C4×D411yescharacteristic
353C2×C4×C5C4×D411yescharacteristic
354C2×C4×C5C4×D411yescharacteristic
355C2×C4×C5C4×D411yescharacteristic
356C2×C4×C5#12011yescharacteristic
357C2×C4×C5#12011yescharacteristic
358C2×C4×C5#12011yescharacteristic
359C2×C4×C5#12011yescharacteristic
360C2×C4×C5#12011yescharacteristic
361C2×C4×C5#12111yescharacteristic
362C2×C4×C5#12111yescharacteristic
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#12311yescharacteristic
372C2×C4×C5#12311yescharacteristic
373C2×C4×C5#12311yescharacteristic
374C2×C4×C5#12411yescharacteristic
375C2×C4×C5#12411yescharacteristic
376C2×C4×C5#12711yescharacteristic
377C2×C4×C5#12711yescharacteristic
378C5×C8—42no—
379C5×C8—42no—
380C2×#41—21no—
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×#41C2×C4×C512yes—
391C2×#41C5×D412yes—
392C22×Q8—21no—
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×D4—21no—
408C22×D4C5×D411yescharacteristic
409C23×C4—21no—
410C23×C4—21no—
411C23×C4—21no—
412C23×C4C5×D412yes—
413C23×C4C23×C511yescharacteristic
414C2×M16—21no—
415C2×M16—21no—
416C2×M16—21no—
417C2×M16—21no—
418C2×M16—21no—
419C2×M16—21no—
420C2×M16—21no—
421C2×M16—21no—
422C2×M16—21no—
423C2×M16—21no—
424C2×M16C5×D412yes—
425C2×M16C5×D412yes—
426C22×C8—21no—
427C22×C8—21no—
428C4⋊Q8—24no—
429C4⋊Q8—24no—
430#124—24no—
431#124—24no—
432#123—28no—
433#123—28no—
434C22⋊Q8—28no—
435C22⋊Q8—28no—
436#117—21no—
437#117—21no—
438#117C2×C4×C512yes—
439#117C5×D412yes—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C5×D412yes—
447C2×C4⋊C4C5×D412yes—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42C5×D412yes—
457#104—28no—
458#103—24no—
459#102—24no—
460#101—28no—
461#95—28no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—21no—
465C22×C5—21no—
466C22×C5—21no—
467C22×C5—21no—
468C22×C5—22no—
469C22×C5—22no—
470C22×C5—44no—
471C22×C5—42no—
472C22×C5—81no—
473C22×C5—81no—
474C22×C5—82no—
475C22×C5#37911yescharacteristic
476C22×C5#38611yescharacteristic
477C22×C5#38611yescharacteristic
478C22×C5#39211yescharacteristic
479C22×C5#39211yescharacteristic
480C22×C5#39411yescharacteristic
481C22×C5#39411yescharacteristic
482C22×C5#45412yes—
483C22×C5#45612yes—
484C4×C5—44no—
485C4×C5—44no—
486C4×C5—44no—
487C4×C5—42no—
488C4×C5—82no—
489C4×C5#38611yescharacteristic
490C4×C5#38611yescharacteristic
491C4×C5#39011yescharacteristic
492C4×C5#39011yescharacteristic
493C4×C5#39211yescharacteristic
494C4×C5#39211yescharacteristic
495C4×C5#39411yescharacteristic
496C4×C5#39411yescharacteristic
497C24—21no—
498C24C2×C5×D411yescharacteristic
499#41—22no—
500#41—22no—
501#41—22no—
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—22no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—41no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—21no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
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×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4C5×C22⋊C412yes—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
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—44no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4C5×C22⋊C414yes—
585C22×C4C22×C4×C511yescharacteristic
586C22×C4C2×C5×D411yescharacteristic
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×C4C5×#4111yescharacteristic
596C22×C4C5×#4111yescharacteristic
597C22×C4C5×#4111yescharacteristic
598C22×C4C5×#4111yescharacteristic
599M16—22no—
600M16—22no—
601M16—22no—
602M16—22no—
603M16—41no—
604M16—41no—
605M16—41no—
606M16—41no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C4⋊C4—216no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4C5×C22⋊C414yes—
620C22⋊C4—216no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—41no—
628C42—41no—
629C2×C5—21no—
630C2×C5—21no—
631C2×C5—21no—
632C2×C5—21no—
633C2×C5—82no—
634C2×C5#143811yescharacteristic
635C2×C5#179312yes—
636C2×C5#200311yescharacteristic
637C2×C5#200511yescharacteristic
638C2×C5#203812yes—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23C2×C5×C22⋊C411yescharacteristic
647C23C5×#12011yescharacteristic
648C23C5×#12011yescharacteristic
649C23C5×#12011yescharacteristic
650C23C5×#12111yescharacteristic
651C23C5×#12111yescharacteristic
652C23C5×#12311yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—41no—
662Q8—42no—
663Q8—42no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—42no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—41no—
672D4—41no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4C2×C5×C22⋊C411yescharacteristic
700C2×C4C2×C5×C22⋊C411yescharacteristic
701C2×C4C4×C5×D411yescharacteristic
702C2×C4C4×C5×D411yescharacteristic
703C2×C4C4×C5×D411yescharacteristic
704C2×C4C4×C5×D411yescharacteristic
705C2×C4C5×#12011yescharacteristic
706C2×C4C5×#12011yescharacteristic
707C2×C4C5×#12011yescharacteristic
708C2×C4C5×#12011yescharacteristic
709C2×C4C5×#12011yescharacteristic
710C2×C4C5×#12111yescharacteristic
711C2×C4C5×#12111yescharacteristic
712C2×C4C5×#12111yescharacteristic
713C2×C4C5×#12111yescharacteristic
714C2×C4C5×#12111yescharacteristic
715C2×C4C5×#12111yescharacteristic
716C2×C4C5×#12111yescharacteristic
717C2×C4C5×#12111yescharacteristic
718C2×C4C5×#12111yescharacteristic
719C2×C4C5×#12111yescharacteristic
720C2×C4C5×#12311yescharacteristic
721C2×C4C5×#12311yescharacteristic
722C2×C4C5×#12311yescharacteristic
723C2×C4C5×#12411yescharacteristic
724C2×C4C5×#12411yescharacteristic
725C2×C4C5×#12711yescharacteristic
726C2×C4C5×#12711yescharacteristic
727C8—42no—
728C8—42no—
729C5#1099811yescharacteristic, direct product factor, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—44no—
739C22—42no—
740C22—82no—
741C22—81no—
742C22—81no—
743C22C5×#37911yescharacteristic
744C22C5×#38611yescharacteristic
745C22C5×#38611yescharacteristic
746C22C5×#39211yescharacteristic
747C22C5×#39211yescharacteristic
748C22C5×#39411yescharacteristic
749C22C5×#39411yescharacteristic
750C22C5×#45412yes—
751C22C5×#45612yes—
752C4—44no—
753C4—44no—
754C4—44no—
755C4—42no—
756C4—82no—
757C4C5×#38611yescharacteristic
758C4C5×#38611yescharacteristic
759C4C5×#39011yescharacteristic
760C4C5×#39011yescharacteristic
761C4C5×#39211yescharacteristic
762C4C5×#39211yescharacteristic
763C4C5×#39411yescharacteristic
764C4C5×#39411yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—82no—
770C2C5×#143811yescharacteristic
771C2C5×#179312yes—
772C2C5×#200311yescharacteristic
773C2C5×#200511yescharacteristic
774C2C5×#203812yes—
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
4. C22×C5×#101C2semidirect
5. C2×C5×#391C2semidirect
6. C5×#1736C2semidirect
7. C2×C5×#339C2semidirect
15. C5×#536C4semidirect
38. #10998C5direct (N × H)
124. C22×#101C2×C5semidirect
125. C2×#391C2×C5semidirect
126. #1736C2×C5semidirect
127. C2×#339C2×C5semidirect
267. #536C4×C5semidirect
729. C5#10998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5362
C22×C5×#1042
C2×C5×#4172
C22×C5×#1012
C2×C5×#3912
C5×#17362
C2×C5×#3392
#109985