Finite Group Databasebeta

← C2×#10607546 #12305633

Subgroups — C2×#10607546 #12305633

Order 1280.

2238 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×#388C211yesmaximal, characteristic, complemented
2C2×#65282C211yesmaximal, characteristic, complemented
3C2×#65275C211yesmaximal, characteristic, complemented
4C2×#65248C211yesmaximal, characteristic
5C2×#65241C211yesmaximal, characteristic, complemented
6C2×#65250C211yesmaximal, characteristic
7C2×#65250C211yesmaximal, characteristic
8C2×#65236C211yesmaximal, characteristic, complemented
9C2×#65236C211yesmaximal, characteristic, complemented
10C2×#65218C211yesmaximal, characteristic, complemented
11C2×#65229C211yesmaximal, characteristic, complemented
12#10607546C2116yesmaximal, direct product factor
13C2×#64962C211yesmaximal, characteristic, complemented
14C2×#64962C211yesmaximal, characteristic, complemented
15C2×#64947C211yesmaximal, characteristic, complemented
16C2×#64945C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C5×#388C2218yescomplemented
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65282C2218yescomplemented
54#65275C2218yescomplemented
55#65250C2218yes—
56#65250C2218yes—
57#65248C2218yes—
58#65241C2218yescomplemented
59#65236C2218yescomplemented
60#65236C2218yescomplemented
61#65229C2218yescomplemented
62#65218C2218yescomplemented
63#64962C2218yescomplemented
64#64962C2218yescomplemented
65#64947C2218yescomplemented
66#64945C2218yescomplemented
67C2×#2832—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—42no—
77C22×C22⋊D5—42no—
78C22×C22⋊D5—42no—
79C22×C22⋊D5C2314yes—
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C22×Dic10—24no—
88C22×Dic10—42no—
89C22×Dic10—42no—
90C22×Dic10—42no—
91C22×Dic10—42no—
92C22×Dic10—42no—
93C22×Dic10C2314yes—
94C22×Dic10C2314yes—
95C2×C5×C4⋊C4—42no—
96C2×C5×C4⋊C4C2314yes—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4—42no—
99C2×C5×C22⋊C4—42no—
100C2×C5×C22⋊C4C2314yes—
101C2×C5×C22⋊C4C2314yes—
102C2×C5×C22⋊C4C2314yes—
103C2×C42×C5—42no—
104C2×C42×C5C2314yes—
105C2×C22⋊Dic5—42no—
106C2×C22⋊Dic5—42no—
107C2×C22⋊Dic5—42no—
108C2×C22⋊Dic5C2314yes—
109C2×C22⋊Dic5C2314yes—
110C2×C22⋊Dic5C2314yes—
111C2×#685—24no—
112C2×#685—42no—
113C2×#685—42no—
114C2×#685—42no—
115C2×#685—42no—
116C2×#685—42no—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×C4⋊Dic5—42no—
124C2×C4⋊Dic5—42no—
125C2×C4⋊Dic5C2314yes—
126C2×C4⋊Dic5C2314yes—
127C2×#683—42no—
128C2×#683—42no—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C5×#95C2314yes—
132C5×#95C2314yes—
133#3963C2314yes—
134#3963C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2832—516no—
146C2×#400—51no—
147C2×#400—51no—
148C2×#397—51no—
149C2×#397—51no—
150C2×#395—51no—
151C2×#394—51no—
152C2×#394—51no—
153C2×#394—51no—
154C2×#393—51no—
155C2×#393—51no—
156C2×#393—51no—
157C2×#393—51no—
158C2×#391—51no—
159C2×#388—51no—
160C2×#388D511yescharacteristic, complemented
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—22no—
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—44no—
203C2×C22⋊D5—44no—
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—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C2×Dic10—28no—
235C2×Dic10—44no—
236C2×Dic10—44no—
237C2×Dic10—44no—
238C2×Dic10—44no—
239C2×Dic10—44no—
240C2×Dic10—416no—
241C2×Dic10—416no—
242C5×C4⋊C4—44no—
243C5×C22⋊C4—28no—
244C5×C22⋊C4—44no—
245C5×C22⋊C4—44no—
246C42×C5—44no—
247C22⋊Dic5—44no—
248C22⋊Dic5—44no—
249C22⋊Dic5—44no—
250#685—28no—
251#685—44no—
252#685—44no—
253#685—44no—
254#685—44no—
255#685—44no—
256C4⋊Dic5—44no—
257C4⋊Dic5—44no—
258#683—44no—
259#683—44no—
260C23×Q8—51no—
261C23×Q8—51no—
262C23×D4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C4⋊C4C2×D511yescharacteristic
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⋊C4—51no—
276C22×C22⋊C4—51no—
277C22×C22⋊C4C2×D511yescharacteristic
278C22×C22⋊C4C2×D511yescharacteristic
279C22×C22⋊C4C2×D511yescharacteristic
280C22×C42C2×D511yescharacteristic
281#400—58no—
282#400—58no—
283#397—58no—
284#397—58no—
285#395—58no—
286#394—58no—
287#394—58no—
288#394—58no—
289#393—58no—
290#393—58no—
291#393—58no—
292#393—58no—
293#391—58no—
294#388—58no—
295#388C2×D518yescomplemented
296C2×#95—51no—
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
309C2×#95C2×D511yescharacteristic
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—44no—
318C23×C5—44no—
319C23×C5—44no—
320C23×C5—44no—
321C23×C5—44no—
322C23×C5—44no—
323C23×C5—44no—
324C23×C5C2×#4112yes—
325C23×C5H(5,𝔽2)12yes—
326C23×C5H(5,𝔽2)12yes—
327C23×C5H(5,𝔽2)12yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C52−1+412yes—
330C23×C52−1+412yes—
331C23×C5C2511yescharacteristic
332C22×D5—22no—
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—44no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5—44no—
345C22×D5—44no—
346C2×C4×C5—28no—
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—22no—
364C2×C4×C5—44no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5C2×#4114yes—
370C22⋊D5—416no—
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—22no—
391C2×Dic5—22no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C2×Dic5—44no—
398C2×Dic5—44no—
399Dic10—416no—
400Dic10—416no—
401C25—51no—
402C25C22×D511yescharacteristic
403C22×Q8—54no—
404C22×Q8—54no—
405C22×Q8—104no—
406C22×Q8—202no—
407C22×Q8—202no—
408C22×Q8—202no—
409C22×Q8—202no—
410C22×Q8—202no—
411C22×D4—54no—
412C22×D4—202no—
413C22×D4—202no—
414C22×D4—202no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—51no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—51no—
422C23×C4C22×D511yescharacteristic
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C2×C4⋊C4—42no—
429C2×C4⋊C4—54no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—54no—
433C2×C4⋊C4—202no—
434C2×C4⋊C4—202no—
435C2×C4⋊C4—202no—
436C2×C4⋊C4—202no—
437C2×C4⋊C4C22×D514yes—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—54no—
442C2×C22⋊C4—54no—
443C2×C22⋊C4—54no—
444C2×C22⋊C4—54no—
445C2×C22⋊C4—54no—
446C2×C22⋊C4—54no—
447C2×C22⋊C4—54no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—202no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4—202no—
458C2×C22⋊C4—202no—
459C2×C22⋊C4C22×D514yes—
460C2×C22⋊C4C22×D514yes—
461C2×C22⋊C4C22×D514yes—
462C2×C42—42no—
463C2×C42C22×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#95—54no—
476#95C22×D514yes—
477#95C22×D514yes—
478C22×C5—42no—
479C22×C5—42no—
480C22×C5—42no—
481C22×C5—42no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—88no—
486C22×C5#53814yes—
487C22×C5#54214yes—
488C22×C5#54214yes—
489C22×C5H(3,𝔽4)14yes—
490C22×C5#56214yes—
491C22×C5#56214yes—
492C22×C5#56314yes—
493C22×C5C22×#4111yescharacteristic
494C22×C5C2×H(5,𝔽2)11yescharacteristic
495C22×C5C2×H(5,𝔽2)11yescharacteristic
496C22×C5C2×H(5,𝔽2)11yescharacteristic
497C22×C5C2×H(5,𝔽2)11yescharacteristic
498C22×C5C2×2−1+411yescharacteristic
499C22×C5C2×2−1+411yescharacteristic
500C2×D5—42no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—88no—
508C4×C5—24no—
509C4×C5—42no—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—42no—
513C4×C5—42no—
514Dic5—42no—
515Dic5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519Dic5—42no—
520Dic5—42no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—52no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24—102no—
536C24C23×D512yes—
537C24C23×D511yescharacteristic
538C2×Q8—108no—
539C2×Q8—204no—
540C2×Q8—204no—
541C2×Q8—204no—
542C2×Q8—204no—
543C2×Q8—204no—
544C2×Q8—2016no—
545C2×Q8—2016no—
546C2×D4—204no—
547C2×D4—204no—
548C2×D4—204no—
549C2×D4—2016no—
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—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—52no—
568C22×C4—52no—
569C22×C4—52no—
570C22×C4—52no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
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—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4#70914yes—
596C22×C4C23×D512yes—
597C22×C4C23×D512yes—
598C22×C4C23×D512yes—
599C22×C4C23×D512yes—
600C22×C4C23×D512yes—
601C22×C4C23×D512yes—
602C4⋊C4—44no—
603C4⋊C4—204no—
604C4⋊C4—204no—
605C4⋊C4—204no—
606C4⋊C4—204no—
607C22⋊C4—28no—
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—
617C22⋊C4—204no—
618C22⋊C4—204no—
619C42—44no—
620C2×C5—82no—
621C2×C5#283218yescomplemented
622C2×C5C2×#53811yescharacteristic
623C2×C5C2×#54211yescharacteristic
624C2×C5C2×#54211yescharacteristic
625C2×C5C2×H(3,𝔽4)11yescharacteristic
626C2×C5C2×#56211yescharacteristic
627C2×C5C2×#56211yescharacteristic
628C2×C5C2×#56311yescharacteristic
629D5—82no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—102no—
645C23—102no—
646C23—102no—
647C23—102no—
648C23—102no—
649C23—102no—
650C23—102no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23—204no—
655C23—204no—
656C23—204no—
657C23—204no—
658C23C2×#70912yes—
659C23#414412yes—
660C23#414412yes—
661C23#414912yes—
662C23#414912yes—
663C23#415012yes—
664C23#415012yes—
665C23C24×D511yescharacteristic
666Q8—2016no—
667Q8—2016no—
668D4—2016no—
669C2×C4—28no—
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—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
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—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—204no—
714C2×C4—204no—
715C2×C4—204no—
716C2×C4—204no—
717C2×C4—204no—
718C2×C4—204no—
719C2×C4—204no—
720C2×C4C2×#70914yes—
721C5C2×#283211yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—88no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—202no—
734C22—202no—
735C22—202no—
736C22—202no—
737C22—408no—
738C22#6586814yes—
739C22#6589414yes—
740C22#6589514yes—
741C22#6595514yes—
742C22#6600114yes—
743C22#6601714yes—
744C22#6604614yes—
745C22C22×#70911yescharacteristic
746C22C2×#414411yescharacteristic
747C22C2×#414411yescharacteristic
748C22C2×#414911yescharacteristic
749C22C2×#414911yescharacteristic
750C22C2×#415011yescharacteristic
751C22C2×#415011yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—202no—
759C4—202no—
760C4—202no—
761C4—202no—
762C4—202no—
763C4—202no—
764C4—202no—
765C2—82no—
766C2—402no—
767C2#1060754618yesdirect product factor
768C2C2×#6586811yescharacteristic
769C2C2×#6589411yescharacteristic
770C2C2×#6589511yescharacteristic
771C2C2×#6595511yescharacteristic
772C2C2×#6600111yescharacteristic
773C2C2×#6601711yescharacteristic
774C2C2×#6604611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#388D5
hypocenterC5C2×#2832
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×C5×#388C2semidirect
2. C2×#65282C2semidirect
3. C2×#65275C2semidirect
5. C2×#65241C2semidirect
8. C2×#65236C2semidirect
9. C2×#65236C2semidirect
10. C2×#65218C2semidirect
11. C2×#65229C2semidirect
12. #10607546C2direct (N × H)
13. C2×#64962C2semidirect
14. C2×#64962C2semidirect
15. C2×#64947C2semidirect
16. C2×#64945C2semidirect
38. C5×#388C22semidirect
53. #65282C22semidirect
54. #65275C22semidirect
58. #65241C22semidirect
59. #65236C22semidirect
60. #65236C22semidirect
61. #65229C22semidirect
62. #65218C22semidirect
63. #64962C22semidirect
64. #64962C22semidirect
65. #64947C22semidirect
66. #64945C22semidirect
160. C2×#388D5semidirect
295. #388C2×D5semidirect
621. C2×C5#2832semidirect
721. C5C2×#2832semidirect
767. C2#10607546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3882
C2×#652822
C2×#652752
C2×#652482
C2×#652412
C2×#652502
C2×#652362
C2×#652182
C2×#652292
#106075462
C2×#649622
C2×#649472
C2×#649452
C2×#28325