Finite Group Databasebeta

← C2×#10609242 #12268909

Subgroups — C2×#10609242 #12268909

Order 1280.

2442 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#397C211yesmaximal, characteristic, complemented
2C2×#65276C211yesmaximal, characteristic, complemented
3C2×#65270C211yesmaximal, characteristic, complemented
4C2×#65245C211yesmaximal, characteristic
5C2×#65250C211yesmaximal, characteristic
6C2×#65246C211yesmaximal, characteristic
7C2×#65234C211yesmaximal, characteristic, complemented
8C2×#65234C211yesmaximal, characteristic, complemented
9C2×#65240C211yesmaximal, characteristic, complemented
10#10609242C2116yesmaximal, direct product factor
11C2×#64964C211yesmaximal, characteristic, complemented
12C2×#64946C211yesmaximal, characteristic, complemented
13C2×#64958C211yesmaximal, characteristic, complemented
14C2×#64942C211yesmaximal, characteristic, complemented
15C2×#64955C211yesmaximal, characteristic, complemented
16C2×#64937C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C5×#397C2218yescomplemented
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65276C2218yescomplemented
54#65270C2218yescomplemented
55#65250C2218yes—
56#65246C2218yes—
57#65245C2218yes—
58#65240C2218yescomplemented
59#65234C2218yescomplemented
60#65234C2218yescomplemented
61#64964C2218yescomplemented
62#64958C2218yescomplemented
63#64955C2218yescomplemented
64#64946C2218yescomplemented
65#64942C2218yescomplemented
66#64937C2218yescomplemented
67C2×#2531—51nomaximal, Sylow
68C25×C5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C22×C22⋊D5—24no—
77C22×C22⋊D5—24no—
78C22×C22⋊D5—42no—
79C22×C22⋊D5C2314yes—
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C22×C4×D5—24no—
88C22×C4×D5—24no—
89C22×C4×D5—42no—
90C22×C4×D5C2314yes—
91C2×C5×C4⋊C4—24no—
92C2×C5×C4⋊C4C2314yes—
93C2×C5×C22⋊C4—24no—
94C2×C5×C22⋊C4—42no—
95C2×C5×C22⋊C4—42no—
96C2×C5×C22⋊C4C2314yes—
97C2×C5×C22⋊C4C2314yes—
98C2×C5×C22⋊C4C2314yes—
99C2×C22⋊Dic5—24no—
100C2×C22⋊Dic5—24no—
101C2×C22⋊Dic5—42no—
102C2×C22⋊Dic5C2314yes—
103C2×C22⋊Dic5C2314yes—
104C2×C22⋊Dic5C2314yes—
105C2×#685—24no—
106C2×#685—24no—
107C2×#685—24no—
108C2×#685—42no—
109C2×#685—42no—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×C4⋊Dic5—24no—
116C2×C4⋊Dic5—42no—
117C2×C4⋊Dic5C2314yes—
118C2×C4⋊Dic5C2314yes—
119C2×#683—42no—
120C2×#683—42no—
121C2×#683—42no—
122C2×#683C2314yes—
123C2×#683C2314yes—
124C2×#683C2314yes—
125C2×C4×Dic5—24no—
126C2×C4×Dic5—24no—
127C2×C4×Dic5—24no—
128C2×C4×Dic5—42no—
129C2×C4×Dic5C2314yes—
130C2×C4×Dic5C2314yes—
131C2×C4×Dic5C2314yes—
132C2×C4×Dic5C2314yes—
133C5×#95C2314yes—
134C5×#95C2314yes—
135C5×#95C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2531—516no—
146C2×#398—51no—
147C2×#397—51no—
148C2×#397D511yescharacteristic, complemented
149C2×#394—51no—
150C2×#390—51no—
151C2×#388—51no—
152C2×#388—51no—
153C2×#388—51no—
154C2×#388—51no—
155C2×#387—51no—
156C2×#387—51no—
157C2×#386—51no—
158C2×#380—51no—
159C2×C4×C22⋊C4—51no—
160C2×#376—51no—
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5—22no—
166C24×C5—22no—
167C24×C5—22no—
168C24×C5C2412yes—
169C24×C5C2411yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5#4114yes—
177C23×D5C2412yes—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5#4114yes—
196C22×C4×C5C2412yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C2×C22⋊D5—28no—
203C2×C22⋊D5—28no—
204C2×C22⋊D5—44no—
205C2×C22⋊D5—416no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5#4114yes—
225C22×Dic5#4114yes—
226C22×Dic5#4114yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C2×C4×D5—28no—
235C2×C4×D5—28no—
236C2×C4×D5—44no—
237C2×C4×D5—416no—
238C5×C4⋊C4—28no—
239C5×C22⋊C4—28no—
240C5×C22⋊C4—44no—
241C5×C22⋊C4—44no—
242C22⋊Dic5—28no—
243C22⋊Dic5—28no—
244C22⋊Dic5—44no—
245#685—28no—
246#685—28no—
247#685—28no—
248#685—44no—
249#685—44no—
250C4⋊Dic5—28no—
251C4⋊Dic5—44no—
252#683—44no—
253#683—44no—
254#683—44no—
255C4×Dic5—28no—
256C4×Dic5—28no—
257C4×Dic5—28no—
258C4×Dic5—44no—
259C23×D4—51no—
260C24×C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4C2×D511yescharacteristic
267C22×C22⋊C4—51no—
268C22×C22⋊C4—51no—
269C22×C22⋊C4—51no—
270C22×C22⋊C4—51no—
271C22×C22⋊C4—51no—
272C22×C22⋊C4—51no—
273C22×C22⋊C4—51no—
274C22×C22⋊C4—51no—
275C22×C22⋊C4C2×D511yescharacteristic
276C22×C22⋊C4C2×D511yescharacteristic
277C22×C22⋊C4C2×D511yescharacteristic
278C22×C42—51no—
279C22×C42—51no—
280C22×C42—51no—
281C22×C42—51no—
282#398—58no—
283#397—58no—
284#397C2×D518yescomplemented
285#394—58no—
286#390—58no—
287#388—58no—
288#388—58no—
289#388—58no—
290#388—58no—
291#387—58no—
292#387—58no—
293#386—58no—
294#380—58no—
295C4×C22⋊C4—58no—
296#376—58no—
297C2×#95—51no—
298C2×#95—51no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95—51no—
306C2×#95C2×D511yescharacteristic
307C2×#95C2×D511yescharacteristic
308C2×#95C2×D511yescharacteristic
309C23×C5—22no—
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—44no—
317C23×C5—44no—
318C23×C5—44no—
319C23×C5—44no—
320C23×C5—44no—
321C23×C5—44no—
322C23×C5—44no—
323C23×C5C2×#4112yes—
324C23×C5C2×#4112yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C5C2511yescharacteristic
331C22×D5—28no—
332C22×D5—28no—
333C22×D5—28no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—22no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5C2×#4114yes—
345C2×C4×C5—28no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—44no—
364C2×C4×C5—44no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5C2×#4114yes—
369C22⋊D5—416no—
370C2×Dic5—28no—
371C2×Dic5—28no—
372C2×Dic5—28no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—44no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5C2×#4114yes—
396C2×Dic5C2×#4114yes—
397C2×Dic5C2×#4114yes—
398C4×D5—416no—
399C25—51no—
400C25C22×D511yescharacteristic
401C22×D4—54no—
402C22×D4—104no—
403C22×D4—104no—
404C22×D4—202no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—54no—
413C23×C4—104no—
414C23×C4—104no—
415C23×C4—202no—
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C2×C4⋊C4—24no—
423C2×C4⋊C4—54no—
424C2×C4⋊C4—54no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—202no—
430C2×C4⋊C4—202no—
431C2×C4⋊C4—202no—
432C2×C4⋊C4—202no—
433C2×C4⋊C4C22×D514yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—54no—
438C2×C22⋊C4—54no—
439C2×C22⋊C4—54no—
440C2×C22⋊C4—54no—
441C2×C22⋊C4—54no—
442C2×C22⋊C4—54no—
443C2×C22⋊C4—54no—
444C2×C22⋊C4—54no—
445C2×C22⋊C4—104no—
446C2×C22⋊C4—104no—
447C2×C22⋊C4—104no—
448C2×C22⋊C4—104no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—202no—
451C2×C22⋊C4—202no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4C22×D514yes—
454C2×C22⋊C4C22×D514yes—
455C2×C22⋊C4C22×D514yes—
456C2×C42—54no—
457C2×C42—54no—
458C2×C42—54no—
459C2×C42—54no—
460C2×C42—104no—
461C2×C42—104no—
462C2×C42—104no—
463C2×C42—202no—
464#95—54no—
465#95—54no—
466#95—54no—
467#95—54no—
468#95—54no—
469#95—54no—
470#95—54no—
471#95—54no—
472#95—54no—
473#95C22×D514yes—
474#95C22×D514yes—
475#95C22×D514yes—
476C22×C5—42no—
477C22×C5—42no—
478C22×C5—42no—
479C22×C5—42no—
480C22×C5—42no—
481C22×C5—42no—
482C22×C5—42no—
483C22×C5—88no—
484C22×C5#52914yes—
485C22×C5#52914yes—
486C22×C5#54014yes—
487C22×C5#55114yes—
488C22×C5#55114yes—
489C22×C5#55314yes—
490C22×C5#55514yes—
491C22×C5C22×#4111yescharacteristic
492C22×C5C22×#4111yescharacteristic
493C22×C5C22×#4111yescharacteristic
494C22×C5C22×#4111yescharacteristic
495C22×C5C22×#4111yescharacteristic
496C22×C5C2×H(5,𝔽2)11yescharacteristic
497C22×C5C2×H(5,𝔽2)11yescharacteristic
498C2×D5—24no—
499C2×D5—24no—
500C2×D5—24no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—416no—
506C4×C5—24no—
507C4×C5—42no—
508C4×C5—42no—
509C4×C5—42no—
510C4×C5—42no—
511C4×C5—42no—
512Dic5—24no—
513Dic5—24no—
514Dic5—24no—
515Dic5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—54no—
527C24—52no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24C23×D512yes—
535C24C23×D511yescharacteristic
536C2×D4—108no—
537C2×D4—108no—
538C2×D4—204no—
539C2×D4—2016no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
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—54no—
558C22×C4—54no—
559C22×C4—54no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—108no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—108no—
587C22×C4—204no—
588C22×C4—2016no—
589C22×C4#71114yes—
590C22×C4C23×D512yes—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D512yes—
594C22×C4C23×D512yes—
595C22×C4C23×D512yes—
596C4⋊C4—28no—
597C4⋊C4—108no—
598C4⋊C4—204no—
599C4⋊C4—204no—
600C4⋊C4—204no—
601C4⋊C4—204no—
602C22⋊C4—28no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—108no—
606C22⋊C4—108no—
607C22⋊C4—108no—
608C22⋊C4—108no—
609C22⋊C4—108no—
610C22⋊C4—204no—
611C22⋊C4—204no—
612C22⋊C4—204no—
613C42—108no—
614C42—108no—
615C42—108no—
616C42—204no—
617C2×C5—82no—
618C2×C5#253118yescomplemented
619C2×C5C2×#52911yescharacteristic
620C2×C5C2×#52911yescharacteristic
621C2×C5C2×#54011yescharacteristic
622C2×C5C2×#55111yescharacteristic
623C2×C5C2×#55111yescharacteristic
624C2×C5C2×#55311yescharacteristic
625C2×C5C2×#55511yescharacteristic
626D5—44no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—54no—
642C23—108no—
643C23—108no—
644C23—102no—
645C23—102no—
646C23—102no—
647C23—102no—
648C23—102no—
649C23—102no—
650C23—108no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23—204no—
655C23C2×#71112yes—
656C23#414412yes—
657C23D5×#4112yes—
658C23D5×#4112yes—
659C23D5×#4112yes—
660C23D5×#4112yes—
661C23#414912yes—
662C23C24×D511yescharacteristic
663D4—2016no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—54no—
688C2×C4—54no—
689C2×C4—54no—
690C2×C4—108no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—108no—
698C2×C4—108no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—2016no—
712C2×C4—204no—
713C2×C4—204no—
714C2×C4—204no—
715C2×C4—204no—
716C2×C4C2×#71114yes—
717C5C2×#253111yescharacteristic, complemented, Sylow
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—88no—
726C22—104no—
727C22—104no—
728C22—104no—
729C22—202no—
730C22—202no—
731C22—2016no—
732C22—202no—
733C22—202no—
734C22#6595014yes—
735C22#6599214yes—
736C22#6599514yes—
737C22#6599714yes—
738C22#6601414yes—
739C22#6603914yes—
740C22#6604014yes—
741C22C22×#71111yescharacteristic
742C22C2×#414411yescharacteristic
743C22C2×D5×#4111yescharacteristic
744C22C2×D5×#4111yescharacteristic
745C22C2×D5×#4111yescharacteristic
746C22C2×D5×#4111yescharacteristic
747C22C2×#414911yescharacteristic
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—104no—
755C4—104no—
756C4—104no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4—202no—
761C2—82no—
762C2—204no—
763C2#1060924218yesdirect product factor
764C2C2×#6595011yescharacteristic
765C2C2×#6599711yescharacteristic
766C2C2×#6599511yescharacteristic
767C2C2×#6599211yescharacteristic
768C2C2×#6601411yescharacteristic
769C2C2×#6604011yescharacteristic
770C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#397C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#397D5
hypocenterC5C2×#2531
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×C5×#397C2semidirect
2. C2×#65276C2semidirect
3. C2×#65270C2semidirect
7. C2×#65234C2semidirect
8. C2×#65234C2semidirect
9. C2×#65240C2semidirect
10. #10609242C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64946C2semidirect
13. C2×#64958C2semidirect
14. C2×#64942C2semidirect
15. C2×#64955C2semidirect
16. C2×#64937C2semidirect
40. C5×#397C22semidirect
53. #65276C22semidirect
54. #65270C22semidirect
58. #65240C22semidirect
59. #65234C22semidirect
60. #65234C22semidirect
61. #64964C22semidirect
62. #64958C22semidirect
63. #64955C22semidirect
64. #64946C22semidirect
65. #64942C22semidirect
66. #64937C22semidirect
148. C2×#397D5semidirect
284. #397C2×D5semidirect
618. C2×C5#2531semidirect
717. C5C2×#2531semidirect
763. C2#10609242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3972
C2×#652762
C2×#652702
C2×#652452
C2×#652502
C2×#652462
C2×#652342
C2×#652402
#106092422
C2×#649642
C2×#649462
C2×#649582
C2×#649422
C2×#649552
C2×#649372
C2×#25315