Finite Group Databasebeta

← C2×#10608823 #12305498

Subgroups — C2×#10608823 #12305498

Order 1280.

2218 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×#394C211yesmaximal, characteristic
2C2×#65511C211yesmaximal, characteristic
3C2×#65509C211yesmaximal, characteristic
4C2×#65272C211yesmaximal, characteristic, complemented
5C2×#65269C211yesmaximal, characteristic, complemented
6C2×#65238C211yesmaximal, characteristic, complemented
7C2×#65242C211yesmaximal, characteristic, complemented
8C2×#65241C211yesmaximal, characteristic, complemented
9C2×#65241C211yesmaximal, characteristic, complemented
10C2×#65237C211yesmaximal, characteristic, complemented
11C2×#65237C211yesmaximal, characteristic, complemented
12C2×#65239C211yesmaximal, characteristic, complemented
13C2×#65235C211yesmaximal, characteristic, complemented
14#10608823C2116yesmaximal, direct product factor
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64949C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C5×#394C2218yes—
41C2×C5×#95C2211yescharacteristic
42#65511C2218yes—
43#65509C2218yes—
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55#65272C2218yescomplemented
56#65269C2218yescomplemented
57#65242C2218yescomplemented
58#65241C2218yescomplemented
59#65241C2218yescomplemented
60#65239C2218yescomplemented
61#65238C2218yescomplemented
62#65237C2218yescomplemented
63#65237C2218yescomplemented
64#65235C2218yescomplemented
65#64949C2218yescomplemented
66#64949C2218yescomplemented
67C2×#2827—51nomaximal, Sylow
68C25×C5C2311yescharacteristic
69C25×C5C2311yescharacteristic
70C22×C5×D4—24no—
71C22×C5×D4—42no—
72C22×C5×D4—42no—
73C22×C5×D4C2314yes—
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×Dic5—42no—
80C23×Dic5—42no—
81C23×Dic5—42no—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2314yes—
91C2×C5×C4⋊C4—42no—
92C2×C5×C4⋊C4C2314yes—
93C2×C5×C22⋊C4—24no—
94C2×C5×C22⋊C4—42no—
95C2×C5×C22⋊C4—42no—
96C2×C5×C22⋊C4—42no—
97C2×C5×C22⋊C4C2314yes—
98C2×C5×C22⋊C4C2314yes—
99C2×C5×C22⋊C4C2314yes—
100C2×C5×C22⋊C4C2314yes—
101C2×C22⋊Dic5—24no—
102C2×C22⋊Dic5—42no—
103C2×C22⋊Dic5—42no—
104C2×C22⋊Dic5—42no—
105C2×C22⋊Dic5—42no—
106C2×C22⋊Dic5—42no—
107C2×C22⋊Dic5—42no—
108C2×C22⋊Dic5C2314yes—
109C2×C22⋊Dic5C2314yes—
110C2×C22⋊Dic5C2314yes—
111C2×C22⋊Dic5C2314yes—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×C22⋊Dic5C2314yes—
115C2×C4⋊Dic5—42no—
116C2×C4⋊Dic5—42no—
117C2×C4⋊Dic5—42no—
118C2×C4⋊Dic5C2314yes—
119C2×C4⋊Dic5C2314yes—
120C2×C4⋊Dic5C2314yes—
121C2×#683—42no—
122C2×#683—42no—
123C2×#683—42no—
124C2×#683—42no—
125C2×#683—42no—
126C2×#683—42no—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C5×#95C2314yes—
134#3963C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2827—516no—
146C2×#400—51no—
147C2×#400—51no—
148C2×#399—51no—
149C2×#398—51no—
150C2×#398—51no—
151C2×#397—51no—
152C2×#397—51no—
153C2×#397—51no—
154C2×#396—51no—
155C2×#396—51no—
156C2×#394—51no—
157C2×#394D511yescharacteristic
158C2×#386—51no—
159C2×#385—51no—
160C2×#385—51no—
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5—22no—
166C24×C5—22no—
167C24×C5—22no—
168C24×C5—22no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5#4114yes—
175C24×C5C2412yes—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C2×C5×D4—28no—
179C2×C5×D4—44no—
180C2×C5×D4—44no—
181C2×C5×D4—416no—
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—22no—
196C22×C4×C5—22no—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
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—22no—
225C22×Dic5—22no—
226C22×Dic5—44no—
227C22×Dic5—44no—
228C22×Dic5—44no—
229C22×Dic5—416no—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C5×C4⋊C4—44no—
239C5×C22⋊C4—28no—
240C5×C22⋊C4—44no—
241C5×C22⋊C4—44no—
242C5×C22⋊C4—44no—
243C22⋊Dic5—28no—
244C22⋊Dic5—44no—
245C22⋊Dic5—44no—
246C22⋊Dic5—44no—
247C22⋊Dic5—44no—
248C22⋊Dic5—44no—
249C22⋊Dic5—44no—
250C4⋊Dic5—44no—
251C4⋊Dic5—44no—
252C4⋊Dic5—44no—
253#683—44no—
254#683—44no—
255#683—44no—
256#683—44no—
257#683—44no—
258#683—44no—
259C23×D4C2×D511yescharacteristic
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⋊C4—51no—
267C22×C4⋊C4—51no—
268C22×C4⋊C4—51no—
269C22×C4⋊C4—51no—
270C22×C4⋊C4C2×D511yescharacteristic
271C22×C22⋊C4—51no—
272C22×C22⋊C4—51no—
273C22×C22⋊C4—51no—
274C22×C22⋊C4—51no—
275C22×C22⋊C4—51no—
276C22×C22⋊C4—51no—
277C22×C22⋊C4—51no—
278C22×C22⋊C4C2×D511yescharacteristic
279C22×C22⋊C4C2×D511yescharacteristic
280C22×C22⋊C4C2×D511yescharacteristic
281C22×C22⋊C4C2×D511yescharacteristic
282#400—58no—
283#400—58no—
284#399—58no—
285#398—58no—
286#398—58no—
287#397—58no—
288#397—58no—
289#397—58no—
290#396—58no—
291#396—58no—
292#394—58no—
293#394C2×D518yes—
294#386—58no—
295#385—58no—
296#385—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×#95—51no—
307C2×#95—51no—
308C2×#95C2×D511yescharacteristic
309C23×C5—28no—
310C23×C5—28no—
311C23×C5—28no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—44no—
326C23×C5—44no—
327C23×C5—44no—
328C23×C5—44no—
329C23×C5—44no—
330C23×C5—44no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5C2×#4114yes—
337C23×C5C2×#4112yes—
338C23×C5H(5,𝔽2)12yes—
339C23×C5H(5,𝔽2)12yes—
340C23×C5H(5,𝔽2)12yes—
341C23×C5H(5,𝔽2)12yes—
342C23×C52−1+412yes—
343C23×C52−1+412yes—
344C23×C5C2511yescharacteristic
345C5×D4—416no—
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—44no—
362C2×C4×C5—44no—
363C2×C4×C5—44no—
364C2×C4×C5—44no—
365C2×C4×C5—44no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
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—416no—
391C2×Dic5—44no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C2×Dic5—44no—
398C2×Dic5—44no—
399C25C22×D511yescharacteristic
400C25C22×D511yescharacteristic
401C22×D4—24no—
402C22×D4—42no—
403C22×D4—42no—
404C22×D4C22×D514yes—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—54no—
414C23×C4—202no—
415C23×C4—202no—
416C23×C4—202no—
417C23×C4C22×D511yescharacteristic
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C2×C4⋊C4—42no—
423C2×C4⋊C4—54no—
424C2×C4⋊C4—54no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—54no—
429C2×C4⋊C4—54no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—202no—
433C2×C4⋊C4—202no—
434C2×C4⋊C4—202no—
435C2×C4⋊C4—202no—
436C2×C4⋊C4—202no—
437C2×C4⋊C4—202no—
438C2×C4⋊C4—202no—
439C2×C4⋊C4—202no—
440C2×C4⋊C4—202no—
441C2×C4⋊C4C22×D514yes—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—54no—
447C2×C22⋊C4—54no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—54no—
451C2×C22⋊C4—54no—
452C2×C22⋊C4—54no—
453C2×C22⋊C4—104no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4—202no—
458C2×C22⋊C4—202no—
459C2×C22⋊C4—202no—
460C2×C22⋊C4C22×D514yes—
461C2×C22⋊C4C22×D514yes—
462C2×C22⋊C4C22×D514yes—
463C2×C22⋊C4C22×D514yes—
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#95—54no—
474#95—54no—
475#95C22×D514yes—
476C22×C5—24no—
477C22×C5—24no—
478C22×C5—24no—
479C22×C5—416no—
480C22×C5—42no—
481C22×C5—42no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5—42no—
487C22×C5—42no—
488C22×C5—42no—
489C22×C5—42no—
490C22×C5—42no—
491C22×C5—88no—
492C22×C5#53814yes—
493C22×C5#53914yes—
494C22×C5#53914yes—
495C22×C5#56014yes—
496C22×C5#56214yes—
497C22×C5#56214yes—
498C22×C5#56314yes—
499C22×C5C22×#4111yescharacteristic
500C22×C5C2×H(5,𝔽2)11yescharacteristic
501C22×C5C2×H(5,𝔽2)11yescharacteristic
502C22×C5C2×H(5,𝔽2)11yescharacteristic
503C22×C5C2×H(5,𝔽2)11yescharacteristic
504C22×C5C2×2−1+411yescharacteristic
505C22×C5C2×2−1+411yescharacteristic
506C4×C5—42no—
507C4×C5—42no—
508C4×C5—42no—
509C4×C5—42no—
510C4×C5—42no—
511Dic5—42no—
512Dic5—42no—
513Dic5—42no—
514Dic5—42no—
515Dic5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24#71114yes—
533C24C23×D512yes—
534C24C23×D512yes—
535C24C23×D511yescharacteristic
536C2×D4—28no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—416no—
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—52no—
556C22×C4—52no—
557C22×C4—52no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
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—102no—
587C22×C4—204no—
588C22×C4—204no—
589C22×C4—204no—
590C22×C4—2016no—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D512yes—
594C22×C4C23×D512yes—
595C22×C4C23×D512yes—
596C4⋊C4—44no—
597C4⋊C4—204no—
598C4⋊C4—204no—
599C4⋊C4—204no—
600C4⋊C4—204no—
601C4⋊C4—204no—
602C4⋊C4—204no—
603C4⋊C4—204no—
604C4⋊C4—204no—
605C4⋊C4—204no—
606C22⋊C4—28no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—108no—
611C22⋊C4—204no—
612C22⋊C4—204no—
613C22⋊C4—204no—
614C22⋊C4—204no—
615C22⋊C4—204no—
616C22⋊C4—204no—
617C2×C5—44no—
618C2×C5—82no—
619C2×C5#282718yescomplemented
620C2×C5C2×#53811yescharacteristic
621C2×C5C2×#53911yescharacteristic
622C2×C5C2×#53911yescharacteristic
623C2×C5C2×#56011yescharacteristic
624C2×C5C2×#56211yescharacteristic
625C2×C5C2×#56211yescharacteristic
626C2×C5C2×#56311yescharacteristic
627C23—28no—
628C23—28no—
629C23—28no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23C2×#71114yes—
655C23C2×#71112yes—
656C23#414412yes—
657C23#414412yes—
658C23#414412yes—
659C23#414912yes—
660C23#415012yes—
661C23#415012yes—
662C23C24×D511yescharacteristic
663D4—416no—
664C2×C4—22no—
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—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
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—2016no—
709C2×C4—204no—
710C2×C4—204no—
711C2×C4—204no—
712C2×C4—204no—
713C2×C4—204no—
714C2×C4—204no—
715C2×C4—204no—
716C2×C4—204no—
717C5C2×#282711yescharacteristic, complemented, Sylow
718C22—24no—
719C22—24no—
720C22—24no—
721C22—42no—
722C22—42no—
723C22—416no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—88no—
734C22#6592714yes—
735C22#6593614yes—
736C22#6595414yes—
737C22#6595514yes—
738C22#6599914yes—
739C22#6600114yes—
740C22#6600614yes—
741C22C22×#71111yescharacteristic
742C22C2×#414411yescharacteristic
743C22C2×#414411yescharacteristic
744C22C2×#414411yescharacteristic
745C22C2×#414911yescharacteristic
746C22C2×#415011yescharacteristic
747C22C2×#415011yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—202no—
754C4—202no—
755C4—202no—
756C4—202no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4—202no—
761C2—44no—
762C2—82no—
763C2#1060882318yesdirect product factor
764C2C2×#6592711yescharacteristic
765C2C2×#6593611yescharacteristic
766C2C2×#6595411yescharacteristic
767C2C2×#6595511yescharacteristic
768C2C2×#6599911yescharacteristic
769C2C2×#6600111yescharacteristic
770C2C2×#6600611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#394C2
socleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC2×#394D5
hypocenterC5C2×#2827
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
4. C2×#65272C2semidirect
5. C2×#65269C2semidirect
6. C2×#65238C2semidirect
7. C2×#65242C2semidirect
8. C2×#65241C2semidirect
9. C2×#65241C2semidirect
10. C2×#65237C2semidirect
11. C2×#65237C2semidirect
12. C2×#65239C2semidirect
13. C2×#65235C2semidirect
14. #10608823C2direct (N × H)
15. C2×#64949C2semidirect
16. C2×#64949C2semidirect
55. #65272C22semidirect
56. #65269C22semidirect
57. #65242C22semidirect
58. #65241C22semidirect
59. #65241C22semidirect
60. #65239C22semidirect
61. #65238C22semidirect
62. #65237C22semidirect
63. #65237C22semidirect
64. #65235C22semidirect
65. #64949C22semidirect
66. #64949C22semidirect
619. C2×C5#2827semidirect
717. C5C2×#2827semidirect
763. C2#10608823direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3942
C2×#655112
C2×#655092
C2×#652722
C2×#652692
C2×#652382
C2×#652422
C2×#652412
C2×#652372
C2×#652392
C2×#652352
#106088232
C2×#649492
C2×#28275