Finite Group Databasebeta

← C2×#10606435 #12266760

Subgroups — C2×#10606435 #12266760

Order 1280.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4085C211yesmaximal, characteristic
2C23×C4⋊Dic5C211yesmaximal, characteristic, complemented
3C22×#4029C211yesmaximal, characteristic, complemented
4C22×#4027C211yesmaximal, characteristic, complemented
5C2×C5×#386C211yesmaximal, characteristic, complemented
6C2×#65509C211yesmaximal, characteristic, complemented
7C2×#65502C211yesmaximal, characteristic, complemented
8C2×#65238C211yesmaximal, characteristic, complemented
9C2×#65250C211yesmaximal, characteristic, complemented
10C2×#65240C211yesmaximal, characteristic, complemented
11C2×#65235C211yesmaximal, characteristic, complemented
12#10606435C2116yesmaximal, direct product factor
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64946C211yesmaximal, characteristic, complemented
15C2×#64963C211yesmaximal, characteristic, complemented
16C2×#64943C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C24×Dic5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C2×#4085—28no—
32C2×#4085C2218yes—
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×C4⋊Dic5—28no—
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×C4⋊Dic5C2218yescomplemented
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4029—28no—
49C2×#4029C2218yescomplemented
50C2×#4027—28no—
51C2×#4027C2218yescomplemented
52C5×#386C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55#65509C2218yescomplemented
56#65502C2218yescomplemented
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63#65250C2218yescomplemented
64#65240C2218yescomplemented
65#65238C2218yescomplemented
66#65235C2218yescomplemented
67#64963C2218yescomplemented
68#64957C2218yescomplemented
69#64946C2218yescomplemented
70#64943C2218yescomplemented
71C2×#2443—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—24no—
78C22×C5×D4C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—24no—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2314yes—
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—42no—
93C22×C22⋊D5D418yes—
94C22×C22⋊D5C2314yes—
95C22×C22⋊D5C2314yes—
96C23×Dic5—24no—
97C23×Dic5—24no—
98C23×Dic5—24no—
99C23×Dic5—24no—
100C23×Dic5—42no—
101C23×Dic5—42no—
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2314yes—
107C23×Dic5C2314yes—
108C23×Dic5C2311yescharacteristic
109C23×Dic5C2311yescharacteristic
110C23×Dic5C2311yescharacteristic
111C22×C4×D5—24no—
112C22×C4×D5—24no—
113C22×C4×D5—42no—
114C22×C4×D5C2314yes—
115C2×C5×C22⋊C4—24no—
116C2×C5×C22⋊C4—24no—
117C2×C5×C22⋊C4—24no—
118C2×C5×C22⋊C4C2314yes—
119C2×C5×C22⋊C4C2314yes—
120C2×C5×C22⋊C4C2314yes—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5—24no—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5—42no—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129#4085—232no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685—24no—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×C4⋊Dic5—24no—
139C2×C4⋊Dic5—24no—
140C2×C4⋊Dic5—24no—
141C2×C4⋊Dic5—232no—
142C2×C4⋊Dic5D418yescomplemented
143C2×C4⋊Dic5C2314yes—
144C2×C4⋊Dic5C2314yes—
145C2×C4⋊Dic5C2314yes—
146C2×C4⋊Dic5C2314yes—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683—24no—
150C2×#683—42no—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157#4029—232no—
158#4027—232no—
159C5×#95C2314yes—
160C5×#95C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#121—51no—
169C22×C4×D4—51no—
170C23×C4⋊C4—51no—
171#2443—516no—
172C2×#399—51no—
173C2×#398—51no—
174C2×#397—51no—
175C2×#394—51no—
176C2×#388—51no—
177C2×#387—51no—
178C2×#386—51no—
179C2×#386—51no—
180C2×#386D511yescharacteristic, complemented
181C2×#385—51no—
182C2×#385—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5C2×D414yes—
195C24×C5#4114yes—
196C24×C5#4114yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5—22no—
206C23×D5C2×D414yes—
207C23×D5C2412yes—
208C2×C5×D4—28no—
209C2×C5×D4—28no—
210C2×C5×D4—28no—
211C2×C5×D4—416no—
212C22×C4×C5—232no—
213C22×C4×C5—22no—
214C22×C4×C5—28no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—28no—
219C22×C4×C5—28no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—22no—
229C22×C4×C5C2×D414yes—
230C22×C4×C5#4114yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C2×C22⋊D5—232no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—28no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—44no—
242C2×C22⋊D5—416no—
243C2×C22⋊D5C2×D4116yes—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—28no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—28no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5—28no—
265C22×Dic5—28no—
266C22×Dic5—44no—
267C22×Dic5—44no—
268C22×Dic5—416no—
269C22×Dic5—416no—
270C22×Dic5C2×D414yes—
271C22×Dic5C2×D414yes—
272C22×Dic5C2×D414yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C22×Dic5C2412yes—
277C22×Dic5C2412yes—
278C22×Dic5C2412yes—
279C22×Dic5C2412yes—
280C2×C4×D5—28no—
281C2×C4×D5—28no—
282C2×C4×D5—44no—
283C2×C4×D5—416no—
284C5×C22⋊C4—28no—
285C5×C22⋊C4—28no—
286C5×C22⋊C4—28no—
287C22⋊Dic5—28no—
288C22⋊Dic5—28no—
289C22⋊Dic5—28no—
290C22⋊Dic5—44no—
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295C4⋊Dic5—28no—
296C4⋊Dic5—28no—
297C4⋊Dic5—28no—
298C4⋊Dic5C2×D4116yescomplemented
299#683—28no—
300#683—28no—
301#683—28no—
302#683—44no—
303C4×Dic5—28no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4C2×D511yescharacteristic
307C24×C4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4C2×D511yescharacteristic
311C2×#123—58no—
312C2×#123—108no—
313C2×#121—58no—
314C2×#121—108no—
315C2×C4×D4—58no—
316C2×C4×D4—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4—58no—
325C22×C4⋊C4—51no—
326C22×C4⋊C4—108no—
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4—51no—
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C22⋊C4C2×D511yescharacteristic
338C22×C42—51no—
339#399—58no—
340#398—58no—
341#397—58no—
342#394—58no—
343#388—58no—
344#387—58no—
345#386—58no—
346#386—58no—
347#386C2×D518yescomplemented
348#385—58no—
349#385—58no—
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95C2×D511yescharacteristic
357C2×#95C2×D511yescharacteristic
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—28no—
362C23×C5—28no—
363C23×C5—28no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5#123116yescomplemented
383C23×C5C22×D414yes—
384C23×C5C22×D412yes—
385C23×C5C22×D412yes—
386C23×C5C2×#4114yes—
387C23×C5C2×#4112yes—
388C23×C5C2×#4114yes—
389C23×C5C2×#4112yes—
390C23×C5C2×#4112yes—
391C23×C5H(5,𝔽2)12yes—
392C23×C52−1+412yes—
393C23×C5C2511yescharacteristic
394C22×D5—28no—
395C22×D5—28no—
396C22×D5—28no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—22no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5—44no—
407C22×D5C22×D414yes—
408C5×D4—416no—
409C2×C4×C5—232no—
410C2×C4×C5—28no—
411C2×C4×C5—28no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×C4×C5C22×D414yes—
429C2×C4×C5C2×#4114yes—
430C22⋊D5—232no—
431C22⋊D5—416no—
432C2×Dic5—28no—
433C2×Dic5—28no—
434C2×Dic5—28no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—22no—
453C2×Dic5—416no—
454C2×Dic5—416no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5—44no—
458C2×Dic5—44no—
459C2×Dic5C22×D414yes—
460C2×Dic5C22×D414yes—
461C2×Dic5C22×D414yes—
462C4×D5—416no—
463C25—51no—
464C25C22×D511yescharacteristic
465C25C22×D511yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—58no—
470C22×D4—54no—
471C22×D4—54no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—202no—
477C22×D4C22×D514yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—54no—
489C23×C4—54no—
490C23×C4—54no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—202no—
498C23×C4—202no—
499C23×C4—202no—
500C23×C4C22×D514yes—
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#123—1032no—
507#121—1032no—
508C4×D4—1032no—
509C2×C4⋊C4—58no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—54no—
517C2×C4⋊C4—54no—
518C2×C4⋊C4—1032no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—104no—
521C2×C4⋊C4—104no—
522C2×C4⋊C4—104no—
523C2×C4⋊C4—104no—
524C2×C4⋊C4—104no—
525C2×C4⋊C4—202no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—54no—
535C2×C22⋊C4—54no—
536C2×C22⋊C4—54no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—104no—
542C2×C22⋊C4—104no—
543C2×C22⋊C4—104no—
544C2×C22⋊C4—202no—
545C2×C22⋊C4C22×D514yes—
546C2×C22⋊C4C22×D514yes—
547C2×C22⋊C4C22×D514yes—
548C2×C42—54no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556#95C22×D514yes—
557#95C22×D514yes—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—24no—
562C22×C5—24no—
563C22×C5—232no—
564C22×C5—24no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—88no—
573C22×C5C2×#12314yes—
574C22×C5C2×#12318yescomplemented
575C22×C5#52514yes—
576C22×C5#53914yes—
577C22×C5D4214yes—
578C22×C5#54714yes—
579C22×C5#54814yes—
580C22×C5#55314yes—
581C22×C5C23×D411yescharacteristic
582C22×C5C23×D411yescharacteristic
583C22×C5C22×#4111yescharacteristic
584C22×C5C22×#4111yescharacteristic
585C22×C5C22×#4111yescharacteristic
586C22×C5C2×H(5,𝔽2)11yescharacteristic
587C22×C5C2×2−1+411yescharacteristic
588C2×D5—24no—
589C2×D5—24no—
590C2×D5—24no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C2×D5—416no—
595C2×D5—42no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601Dic5—24no—
602Dic5—24no—
603Dic5—24no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—54no—
620C24—52no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24#70914yes—
628C24D4×D514yes—
629C24#71114yes—
630C24C23×D512yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—28no—
636C2×D4—416no—
637C2×D4—516no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—1032no—
642C2×D4—108no—
643C2×D4—204no—
644C2×D4—2016no—
645C22×C4—232no—
646C22×C4—22no—
647C22×C4—28no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—54no—
663C22×C4—54no—
664C22×C4—54no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—108no—
673C22×C4—108no—
674C22×C4—108no—
675C22×C4—108no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—108no—
690C22×C4—108no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—102no—
694C22×C4—102no—
695C22×C4—102no—
696C22×C4—204no—
697C22×C4—2016no—
698C22×C4—204no—
699C22×C4—204no—
700C22×C4—2016no—
701C22×C4—2016no—
702C22×C4D4×D514yes—
703C22×C4#71114yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—516no—
710C4⋊C4—108no—
711C4⋊C4—108no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4—108no—
715C4⋊C4—108no—
716C4⋊C4—204no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—108no—
727C22⋊C4—204no—
728C42—108no—
729C2×C5—28no—
730C2×C5—82no—
731C2×C5#244318yescomplemented
732C2×C5C22×#12311yescharacteristic
733C2×C5C2×#52511yescharacteristic
734C2×C5C2×#53911yescharacteristic
735C2×C5C2×D4211yescharacteristic
736C2×C5C2×#54711yescharacteristic
737C2×C5C2×#54811yescharacteristic
738C2×C5C2×#55311yescharacteristic
739D5—44no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—54no—
765C23—108no—
766C23—108no—
767C23—108no—
768C23—102no—
769C23—102no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—102no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23#4029116yescomplemented
779C23C2×#70914yes—
780C23C2×#70912yes—
781C23C2×D4×D514yes—
782C23C2×D4×D512yes—
783C23C2×D4×D512yes—
784C23C2×#71114yes—
785C23C2×#71112yes—
786C23C2×#71112yes—
787C23#414912yes—
788C23#415012yes—
789C23C24×D511yescharacteristic
790D4—416no—
791D4—1032no—
792D4—2016no—
793C2×C4—232no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—54no—
813C2×C4—54no—
814C2×C4—54no—
815C2×C4—108no—
816C2×C4—108no—
817C2×C4—108no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—102no—
836C2×C4—2016no—
837C2×C4—2016no—
838C2×C4—2016no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4—204no—
843C2×C4C2×D4×D514yes—
844C2×C4C2×#71114yes—
845C5C2×#244311yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—232no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—88no—
861C22—104no—
862C22—104no—
863C22—104no—
864C22—202no—
865C22—202no—
866C22—202no—
867C22—2016no—
868C22—202no—
869C22C2×#402914yes—
870C22C2×#402918yescomplemented
871C22#6588614yes—
872C22#6589914yes—
873C22#6592014yes—
874C22#6594314yes—
875C22#6594514yes—
876C22#6599914yes—
877C22C22×#70911yescharacteristic
878C22C22×D4×D511yescharacteristic
879C22C22×D4×D511yescharacteristic
880C22C22×#71111yescharacteristic
881C22C22×#71111yescharacteristic
882C22C2×#414911yescharacteristic
883C22C2×#415011yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—104no—
890C4—104no—
891C4—104no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—28no—
897C2—82no—
898C2—204no—
899C2#1060643518yesdirect product factor
900C2C22×#402911yescharacteristic
901C2C2×#6588611yescharacteristic
902C2C2×#6589911yescharacteristic
903C2C2×#6592011yescharacteristic
904C2C2×#6594511yescharacteristic
905C2C2×#6594311yescharacteristic
906C2C2×#6599911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC2×#386D5
hypocenterC5C2×#2443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊Dic5C2semidirect
3. C22×#4029C2semidirect
4. C22×#4027C2semidirect
5. C2×C5×#386C2semidirect
6. C2×#65509C2semidirect
7. C2×#65502C2semidirect
8. C2×#65238C2semidirect
9. C2×#65250C2semidirect
10. C2×#65240C2semidirect
11. C2×#65235C2semidirect
12. #10606435C2direct (N × H)
13. C2×#64957C2semidirect
14. C2×#64946C2semidirect
15. C2×#64963C2semidirect
16. C2×#64943C2semidirect
42. C22×C4⋊Dic5C22semidirect
49. C2×#4029C22semidirect
51. C2×#4027C22semidirect
52. C5×#386C22semidirect
55. #65509C22semidirect
56. #65502C22semidirect
63. #65250C22semidirect
64. #65240C22semidirect
65. #65238C22semidirect
66. #65235C22semidirect
67. #64963C22semidirect
68. #64957C22semidirect
69. #64946C22semidirect
70. #64943C22semidirect
142. C2×C4⋊Dic5D4semidirect
180. C2×#386D5semidirect
298. C4⋊Dic5C2×D4semidirect
347. #386C2×D5semidirect
382. C23×C5#123semidirect
574. C22×C5C2×#123semidirect
731. C2×C5#2443semidirect
778. C23#4029semidirect
845. C5C2×#2443semidirect
870. C22C2×#4029semidirect
899. C2#10606435direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40852
C23×C4⋊Dic52
C22×#40292
C22×#40272
C2×C5×#3862
C2×#655092
C2×#655022
C2×#652382
C2×#652502
C2×#652402
C2×#652352
#106064352
C2×#649572
C2×#649462
C2×#649632
C2×#649432
C2×#24435