Finite Group Databasebeta

← C2×#10605637 #12266984

Subgroups — C2×#10605637 #12266984

Order 1280.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×C5×#380C211yesmaximal, characteristic, complemented
4C2×#65502C211yesmaximal, characteristic, complemented
5C2×#65281C211yesmaximal, characteristic, complemented
6C2×#65280C211yesmaximal, characteristic, complemented
7C2×#65267C211yesmaximal, characteristic, complemented
8C2×#65249C211yesmaximal, characteristic
9C2×#65250C211yesmaximal, characteristic, complemented
10C2×#65246C211yesmaximal, characteristic, complemented
11C2×#65234C211yesmaximal, characteristic, complemented
12#10605637C2116yesmaximal, direct product factor
13C2×#64954C211yesmaximal, characteristic, complemented
14C2×#64958C211yesmaximal, characteristic, complemented
15C2×#64944C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C2×C4×C22⋊D5—28no—
29C2×C4×C22⋊D5C2218yescomplemented
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4044—28no—
47C2×#4044C2218yescomplemented
48C5×#380C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51#65502C2218yescomplemented
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65281C2218yescomplemented
59#65280C2218yescomplemented
60#65267C2218yescomplemented
61#65250C2218yescomplemented
62#65249C2218yes—
63#65246C2218yescomplemented
64#65234C2218yescomplemented
65#64958C2218yescomplemented
66#64955C2218yescomplemented
67#64954C2218yescomplemented
68#64944C2218yescomplemented
69C2×#2467—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C23×C4×C5—24no—
74C23×C4×C5—24no—
75C23×C4×C5—42no—
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2314yes—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—42no—
89C22×C22⋊D5C2314yes—
90C22×C22⋊D5C2314yes—
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C22×D20—24no—
98C22×D20—42no—
99C22×D20—42no—
100C22×D20C2314yes—
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—42no—
104C22×C4×D5C2314yes—
105C2×C5×C4⋊C4—24no—
106C2×C5×C4⋊C4—42no—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C4⋊C4C2314yes—
109C2×C5×C22⋊C4—42no—
110C2×C5×C22⋊C4—42no—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5C2314yes—
116C2×C22⋊Dic5C2314yes—
117C4×C22⋊D5—232no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—42no—
126C2×#685—42no—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×C4⋊Dic5—24no—
137C2×C4⋊Dic5C2314yes—
138C2×#683—24no—
139C2×#683—42no—
140C2×#683D418yescomplemented
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5—24no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5C2314yes—
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150#4044—232no—
151C5×#95C2314yes—
152C5×#95C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×C4×D4—51no—
161#2467—516no—
162C2×#399—51no—
163C2×#394—51no—
164C2×#394—51no—
165C2×#392—51no—
166C2×#390—51no—
167C2×#388—51no—
168C2×#388—51no—
169C2×#387—51no—
170C2×#387—51no—
171C2×#386—51no—
172C2×#386—51no—
173C2×#380D511yescharacteristic, complemented
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5#4114yes—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5#4114yes—
198C23×D5C2412yes—
199C23×D5C2412yes—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—28no—
217C22×C4×C5—28no—
218C22×C4×C5—44no—
219C22×C4×C5—416no—
220C22×C4×C5C2×D414yes—
221C22×C4×C5#4114yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C2×C22⋊D5—232no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—28no—
231C2×C22⋊D5—28no—
232C2×C22⋊D5—28no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—44no—
235C2×C22⋊D5—416no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5C2×D414yes—
252C22×Dic5C2×D414yes—
253C22×Dic5#4114yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C2×D20—28no—
261C2×D20—44no—
262C2×D20—44no—
263C2×D20—416no—
264C2×C4×D5—28no—
265C2×C4×D5—28no—
266C2×C4×D5—44no—
267C2×C4×D5—416no—
268C5×C4⋊C4—28no—
269C5×C4⋊C4—44no—
270C5×C22⋊C4—44no—
271C5×C22⋊C4—44no—
272C22⋊Dic5—28no—
273C22⋊Dic5—28no—
274#685—28no—
275#685—28no—
276#685—28no—
277#685—28no—
278#685—28no—
279#685—28no—
280#685—28no—
281#685—44no—
282#685—44no—
283C4⋊Dic5—28no—
284#683—28no—
285#683—44no—
286#683C2×D4116yescomplemented
287C4×Dic5—28no—
288C4×Dic5—28no—
289C4×Dic5—44no—
290C23×D4—51no—
291C23×D4—51no—
292C23×D4—51no—
293C24×C4—51no—
294C24×C4C2×D511yescharacteristic
295C2×#126—58no—
296C2×#126—108no—
297C2×C4×D4—58no—
298C2×C4×D4—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4C2×D511yescharacteristic
304C22×C4⋊C4C2×D511yescharacteristic
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4—51no—
315C22×C22⋊C4—51no—
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320C22×C42—51no—
321#399—58no—
322#394—58no—
323#394—58no—
324#392—58no—
325#390—58no—
326#388—58no—
327#388—58no—
328#387—58no—
329#387—58no—
330#386—58no—
331#386—58no—
332#380C2×D518yescomplemented
333C4×C22⋊C4—58no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95C2×D511yescharacteristic
341C2×#95C2×D511yescharacteristic
342C23×C5—28no—
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—44no—
352C23×C5—44no—
353C23×C5—44no—
354C23×C5—44no—
355C23×C5C22×D412yes—
356C23×C5C2×#4112yes—
357C23×C5C2×#4114yes—
358C23×C5C2×#4112yes—
359C23×C5C2×#4112yes—
360C23×C5C2×#4112yes—
361C23×C5H(5,𝔽2)12yes—
362C23×C5H(5,𝔽2)12yes—
363C23×C5C2511yescharacteristic
364C22×D5—28no—
365C22×D5—28no—
366C22×D5—28no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—22no—
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—44no—
381C22×D5—44no—
382C22×D5—44no—
383C22×D5—44no—
384C22×D5—44no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5C2×#4114yes—
392C2×C4×C5—28no—
393C2×C4×C5—28no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—416no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5—44no—
414C2×C4×C5—44no—
415C2×C4×C5C22×D414yes—
416C2×C4×C5C2×#4114yes—
417C22⋊D5—232no—
418C22⋊D5—416no—
419C2×Dic5—28no—
420C2×Dic5—28no—
421C2×Dic5—28no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5C22×D414yes—
441C2×Dic5C22×D414yes—
442C2×Dic5C2×#4114yes—
443D20—416no—
444C4×D5—416no—
445C25—51no—
446C25—51no—
447C25C22×D511yescharacteristic
448C22×D4—54no—
449C22×D4—54no—
450C22×D4—54no—
451C22×D4—104no—
452C22×D4—104no—
453C22×D4—104no—
454C22×D4—104no—
455C22×D4—104no—
456C22×D4—104no—
457C22×D4—202no—
458C22×D4—202no—
459C22×D4—202no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—42no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—54no—
470C23×C4—104no—
471C23×C4—104no—
472C23×C4—202no—
473C23×C4C22×D511yescharacteristic
474C23×C4C22×D511yescharacteristic
475C23×C4C22×D511yescharacteristic
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D514yes—
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480#126—1032no—
481C4×D4—1032no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—58no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—104no—
490C2×C4⋊C4—104no—
491C2×C4⋊C4—202no—
492C2×C4⋊C4C22×D514yes—
493C2×C4⋊C4C22×D514yes—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—54no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—54no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—104no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—104no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4C22×D514yes—
519C2×C22⋊C4C22×D514yes—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—54no—
523C2×C42—104no—
524C2×C42—104no—
525C2×C42—202no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95C22×D514yes—
533#95C22×D514yes—
534C22×C5—24no—
535C22×C5—24no—
536C22×C5—24no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—416no—
542C22×C5#52514yes—
543C22×C5#52914yes—
544C22×C5#53814yes—
545C22×C5#54614yes—
546C22×C5#55014yes—
547C22×C5#55114yes—
548C22×C5#55314yes—
549C22×C5C23×D411yescharacteristic
550C22×C5C22×#4111yescharacteristic
551C22×C5C22×#4111yescharacteristic
552C22×C5C22×#4111yescharacteristic
553C22×C5C22×#4111yescharacteristic
554C22×C5C2×H(5,𝔽2)11yescharacteristic
555C22×C5C2×H(5,𝔽2)11yescharacteristic
556C2×D5—24no—
557C2×D5—24no—
558C2×D5—24no—
559C2×D5—42no—
560C2×D5—42no—
561C2×D5—42no—
562C2×D5—42no—
563C2×D5—416no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—88no—
572C4×C5—24no—
573C4×C5—24no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5—42no—
577C4×C5—42no—
578Dic5—24no—
579Dic5—24no—
580Dic5—24no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—54no—
591C24—52no—
592C24—52no—
593C24—102no—
594C24—102no—
595C24—102no—
596C24—102no—
597C24—102no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24#71314yes—
607C24C23×D512yes—
608C24C23×D511yescharacteristic
609C2×D4—108no—
610C2×D4—108no—
611C2×D4—108no—
612C2×D4—108no—
613C2×D4—1032no—
614C2×D4—108no—
615C2×D4—108no—
616C2×D4—204no—
617C2×D4—204no—
618C2×D4—2016no—
619C2×D4—204no—
620C2×D4—2016no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—44no—
640C22×C4—416no—
641C22×C4—54no—
642C22×C4—54no—
643C22×C4—54no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—108no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—108no—
667C22×C4—204no—
668C22×C4—2016no—
669C22×C4#70914yes—
670C22×C4D4×D514yes—
671C22×C4C23×D512yes—
672C22×C4C23×D512yes—
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C4⋊C4—28no—
678C4⋊C4—44no—
679C4⋊C4—516no—
680C4⋊C4—108no—
681C4⋊C4—108no—
682C4⋊C4—204no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—204no—
695C22⋊C4—204no—
696C42—108no—
697C42—108no—
698C42—204no—
699C2×C5—44no—
700C2×C5#246718yescomplemented
701C2×C5C2×#52511yescharacteristic
702C2×C5C2×#52911yescharacteristic
703C2×C5C2×#53811yescharacteristic
704C2×C5C2×#54611yescharacteristic
705C2×C5C2×#55011yescharacteristic
706C2×C5C2×#55111yescharacteristic
707C2×C5C2×#55311yescharacteristic
708D5—44no—
709D5—82no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—54no—
724C23—108no—
725C23—108no—
726C23—108no—
727C23—102no—
728C23—102no—
729C23—102no—
730C23—102no—
731C23—102no—
732C23—102no—
733C23—102no—
734C23—102no—
735C23—102no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—204no—
741C23—204no—
742C23—204no—
743C23—204no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23—204no—
750C23—204no—
751C23C2×#70912yes—
752C23C2×D4×D512yes—
753C23#414412yes—
754C23#414412yes—
755C23C2×#71314yes—
756C23C2×#71312yes—
757C23D5×#4112yes—
758C23D5×#4112yes—
759C23C24×D511yescharacteristic
760D4—1032no—
761D4—2016no—
762D4—2016no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—54no—
787C2×C4—54no—
788C2×C4—54no—
789C2×C4—108no—
790C2×C4—108no—
791C2×C4—108no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—2016no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4C2×#70914yes—
812C2×C4C2×D4×D514yes—
813C5C2×#246711yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—416no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—104no—
823C22—104no—
824C22—104no—
825C22—202no—
826C22—202no—
827C22—2016no—
828C22—202no—
829C22—202no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—202no—
834C22—202no—
835C22—202no—
836C22—202no—
837C22—408no—
838C22#6582414yes—
839C22#6584814yes—
840C22#6586214yes—
841C22#6593314yes—
842C22#6594714yes—
843C22#6596114yes—
844C22#6597114yes—
845C22C22×#70911yescharacteristic
846C22C22×D4×D511yescharacteristic
847C22C2×#414411yescharacteristic
848C22C2×#414411yescharacteristic
849C22C22×#71311yescharacteristic
850C22C2×D5×#4111yescharacteristic
851C22C2×D5×#4111yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—104no—
859C4—104no—
860C4—104no—
861C4—202no—
862C4—202no—
863C4—202no—
864C2—44no—
865C2—204no—
866C2—402no—
867C2#1060563718yesdirect product factor
868C2C2×#6582411yescharacteristic
869C2C2×#6584811yescharacteristic
870C2C2×#6586211yescharacteristic
871C2C2×#6593311yescharacteristic
872C2C2×#6594711yescharacteristic
873C2C2×#6596111yescharacteristic
874C2C2×#6597111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#380C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC2×#380D5
hypocenterC5C2×#2467
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D5C2semidirect
2. C22×#4044C2semidirect
3. C2×C5×#380C2semidirect
4. C2×#65502C2semidirect
5. C2×#65281C2semidirect
6. C2×#65280C2semidirect
7. C2×#65267C2semidirect
9. C2×#65250C2semidirect
10. C2×#65246C2semidirect
11. C2×#65234C2semidirect
12. #10605637C2direct (N × H)
13. C2×#64954C2semidirect
14. C2×#64958C2semidirect
15. C2×#64944C2semidirect
16. C2×#64955C2semidirect
29. C2×C4×C22⋊D5C22semidirect
47. C2×#4044C22semidirect
48. C5×#380C22semidirect
51. #65502C22semidirect
58. #65281C22semidirect
59. #65280C22semidirect
60. #65267C22semidirect
61. #65250C22semidirect
63. #65246C22semidirect
64. #65234C22semidirect
65. #64958C22semidirect
66. #64955C22semidirect
67. #64954C22semidirect
68. #64944C22semidirect
140. C2×#683D4semidirect
173. C2×#380D5semidirect
286. #683C2×D4semidirect
332. #380C2×D5semidirect
700. C2×C5#2467semidirect
813. C5C2×#2467semidirect
867. C2#10605637direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C22×#40442
C2×C5×#3802
C2×#655022
C2×#652812
C2×#652802
C2×#652672
C2×#652492
C2×#652502
C2×#652462
C2×#652342
#106056372
C2×#649542
C2×#649582
C2×#649442
C2×#649552
C2×#24675