Finite Group Databasebeta

← C2×#10606428 #12267441

Subgroups — C2×#10606428 #12267441

Order 1280.

3894 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
2C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C22×#4031C211yesmaximal, characteristic, complemented
4C22×#4024C211yesmaximal, characteristic, complemented
5C2×C5×#386C211yesmaximal, characteristic, complemented
6C2×#65511C211yesmaximal, characteristic, complemented
7C2×#65501C211yesmaximal, characteristic, complemented
8C2×#65245C211yesmaximal, characteristic, complemented
9C2×#65241C211yesmaximal, characteristic, complemented
10C2×#65250C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12#10606428C2116yesmaximal, direct product factor
13C2×#64956C211yesmaximal, characteristic, complemented
14C2×#64963C211yesmaximal, characteristic, complemented
15C2×#64935C211yesmaximal, characteristic, complemented
16C2×#64936C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×Dic10C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×#4085—28no—
33C2×#4085C2218yes—
34C2×C4×C22⋊D5—28no—
35C2×C4×C22⋊D5C2218yescomplemented
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4031—28no—
49C2×#4031C2218yescomplemented
50C2×#4024—28no—
51C2×#4024C2218yescomplemented
52C5×#386C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55#65511C2218yescomplemented
56#65501C2218yescomplemented
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63#65250C2218yescomplemented
64#65245C2218yescomplemented
65#65241C2218yescomplemented
66C22⋊C4×Dic5C2218yescomplemented
67#64963C2218yescomplemented
68#64956C2218yescomplemented
69#64936C2218yescomplemented
70#64935C2218yescomplemented
71C2×#2427—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—42no—
78C22×C5×D4C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—42no—
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×Dic5C2314yes—
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2311yescharacteristic
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—42no—
110C22×C4×D5C2314yes—
111C22×Dic10—24no—
112C22×Dic10—24no—
113C22×Dic10—24no—
114C22×Dic10C2314yes—
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—24no—
125C2×C22⋊Dic5—24no—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131#4085—232no—
132C4×C22⋊D5—232no—
133C2×#685—24no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685—24no—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×C4⋊Dic5—24no—
142C2×C4⋊Dic5—42no—
143C2×C4⋊Dic5C2314yes—
144C2×C4⋊Dic5C2314yes—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—42no—
148C2×#683D418yescomplemented
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×C4×Dic5—24no—
154C2×C4×Dic5—24no—
155C2×C4×Dic5C2314yes—
156C2×C4×Dic5C2314yes—
157#4031—232no—
158#4024—232no—
159C5×#95C2314yes—
160C5×#95C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#124—51no—
168C22×C22⋊Q8—51no—
169C22×#121—51no—
170C22×C4×D4—51no—
171#2427—516no—
172C2×#397—51no—
173C2×#397—51no—
174C2×#394—51no—
175C2×#394—51no—
176C2×#391—51no—
177C2×#389—51no—
178C2×#386—51no—
179C2×#386D511yescharacteristic, complemented
180C2×#380—51no—
181C2×#380—51no—
182C2×C4×C22⋊C4—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×C5—22no—
195C24×C5C2×D414yes—
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—44no—
211C2×C5×D4—416no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—28no—
226C22×C4×C5—28no—
227C22×C4×C5—44no—
228C22×C4×C5—416no—
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—28no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—232no—
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—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—28no—
262C22×Dic5—28no—
263C22×Dic5—28no—
264C22×Dic5—416no—
265C22×Dic5C2×D414yes—
266C22×Dic5C2×D414yes—
267C22×Dic5C2×D414yes—
268C22×Dic5#4114yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2412yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—44no—
279C2×C4×D5—416no—
280C2×Dic10—28no—
281C2×Dic10—28no—
282C2×Dic10—28no—
283C2×Dic10—416no—
284C5×C22⋊C4—28no—
285C5×C22⋊C4—28no—
286C5×C22⋊C4—28no—
287C22⋊Dic5—28no—
288C22⋊Dic5—28no—
289C22⋊Dic5—28no—
290C22⋊Dic5—28no—
291C22⋊Dic5—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685—28no—
296C4⋊Dic5—28no—
297C4⋊Dic5—44no—
298#683—28no—
299#683—28no—
300#683—44no—
301#683C2×D4116yescomplemented
302C4×Dic5—28no—
303C4×Dic5—28no—
304C23×Q8—51no—
305C23×D4—51no—
306C23×D4—51no—
307C23×D4C2×D511yescharacteristic
308C24×C4—51no—
309C24×C4—51no—
310C24×C4C2×D511yescharacteristic
311C2×#124—58no—
312C2×#124—108no—
313C2×C22⋊Q8—58no—
314C2×C22⋊Q8—108no—
315C2×#121—58no—
316C2×#121—108no—
317C2×C4×D4—58no—
318C2×C4×D4—108no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4—51no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C42—51no—
338C22×C42—51no—
339#397—58no—
340#397—58no—
341#394—58no—
342#394—58no—
343#391—58no—
344#389—58no—
345#386—58no—
346#386C2×D518yescomplemented
347#380—58no—
348#380—58no—
349C4×C22⋊C4—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—22no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5—44no—
383C23×C5—44no—
384C23×C5C22×D414yes—
385C23×C5C22×D412yes—
386C23×C5C22×D412yes—
387C23×C5C2×#4114yes—
388C23×C5C2×#4112yes—
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—28no—
410C2×C4×C5—28no—
411C2×C4×C5—22no—
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—416no—
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—22no—
434C2×Dic5—22no—
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—44no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5—416no—
456C2×Dic5#121116yes—
457C2×Dic5C22×D414yes—
458C2×Dic5C22×D414yes—
459C2×Dic5C22×D414yes—
460C2×Dic5C2×#4114yes—
461C4×D5—416no—
462Dic10—416no—
463C25—51no—
464C25C22×D511yescharacteristic
465C25C22×D511yescharacteristic
466C22×Q8—54no—
467C22×Q8—104no—
468C22×Q8—104no—
469C22×Q8—104no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—42no—
473C22×D4—58no—
474C22×D4—54no—
475C22×D4—54no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—104no—
479C22×D4—104no—
480C22×D4—202no—
481C22×D4C22×D514yes—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—42no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—54no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—51no—
491C23×C4—51no—
492C23×C4—51no—
493C23×C4—54no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—104no—
498C23×C4—104no—
499C23×C4—202no—
500C23×C4C22×D511yescharacteristic
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D514yes—
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#124—1032no—
507C22⋊Q8—1032no—
508#121—1032no—
509C4×D4—1032no—
510C2×C4⋊C4—58no—
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—104no—
518C2×C4⋊C4—104no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—202no—
521C2×C4⋊C4—202no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
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⋊C4C22×D514yes—
544C2×C22⋊C4C22×D514yes—
545C2×C22⋊C4C22×D514yes—
546C2×C42—54no—
547C2×C42—54no—
548C2×C42—104no—
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—24no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—416no—
567C22×C5—416no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—42no—
574C22×C5C2×#12114yes—
575C22×C5#52914yes—
576C22×C5#54214yes—
577C22×C5#54614yes—
578C22×C5#54614yes—
579C22×C5#54714yes—
580C22×C5#54814yes—
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—416no—
593C2×D5—42no—
594C2×D5—42no—
595C2×D5—42no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601Dic5—24no—
602Dic5—42no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5C2×#12118yes—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—54no—
621C24—52no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24#70914yes—
629C24D4×D514yes—
630C24C23×D512yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×Q8—108no—
634C2×Q8—108no—
635C2×Q8—108no—
636C2×Q8—2016no—
637C2×D4—28no—
638C2×D4—28no—
639C2×D4—44no—
640C2×D4—416no—
641C2×D4—516no—
642C2×D4—108no—
643C2×D4—1032no—
644C2×D4—108no—
645C2×D4—108no—
646C2×D4—108no—
647C2×D4—204no—
648C2×D4—2016no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
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—28no—
663C22×C4—28no—
664C22×C4—44no—
665C22×C4—416no—
666C22×C4—54no—
667C22×C4—54no—
668C22×C4—54no—
669C22×C4—52no—
670C22×C4—54no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—52no—
675C22×C4—52no—
676C22×C4—52no—
677C22×C4—108no—
678C22×C4—108no—
679C22×C4—108no—
680C22×C4—108no—
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—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—102no—
694C22×C4—102no—
695C22×C4—102no—
696C22×C4—102no—
697C22×C4—102no—
698C22×C4—108no—
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—204no—
714C4⋊C4—204no—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—108no—
727C42—108no—
728C42—108no—
729C2×C5—44no—
730C2×C5—44no—
731C2×C5#242718yescomplemented
732C2×C5C22×#12111yescharacteristic
733C2×C5C2×#52911yescharacteristic
734C2×C5C2×#54211yescharacteristic
735C2×C5C2×#54611yescharacteristic
736C2×C5C2×#54611yescharacteristic
737C2×C5C2×#54711yescharacteristic
738C2×C5C2×#54811yescharacteristic
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—22no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—54no—
767C23—108no—
768C23—108no—
769C23—108no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—102no—
774C23—102no—
775C23—102no—
776C23—204no—
777C23—204no—
778C23—204no—
779C23—204no—
780C23C2×#70914yes—
781C23C2×#70912yes—
782C23C2×D4×D514yes—
783C23C2×D4×D512yes—
784C23C2×D4×D512yes—
785C23C2×#71112yes—
786C23#414412yes—
787C23D5×#4112yes—
788C23#415012yes—
789C23C24×D511yescharacteristic
790Q8—2016no—
791D4—416no—
792D4—1032no—
793D4—2016no—
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—416no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—516no—
814C2×C4—54no—
815C2×C4—54no—
816C2×C4—54no—
817C2×C4—54no—
818C2×C4—108no—
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—204no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4—204no—
843C2×C4C2×D4×D514yes—
844C2×C4C2×#71114yes—
845C5C2×#242711yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—104no—
863C22—104no—
864C22—104no—
865C22—202no—
866C22—202no—
867C22—202no—
868C22—2016no—
869C22—202no—
870C22#6582414yes—
871C22#6587214yes—
872C22#6588614yes—
873C22#6592514yes—
874C22D5×#12114yes—
875C22#6594514yes—
876C22#6599614yes—
877C22C22×#70911yescharacteristic
878C22C22×D4×D511yescharacteristic
879C22C22×D4×D511yescharacteristic
880C22C22×#71111yescharacteristic
881C22C2×#414411yescharacteristic
882C22C2×D5×#4111yescharacteristic
883C22C2×#415011yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—58no—
890C4—104no—
891C4—202no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—44no—
897C2—44no—
898C2—204no—
899C2#1060642818yesdirect product factor
900C2C2×#6582411yescharacteristic
901C2C2×#6587211yescharacteristic
902C2C2×#6588611yescharacteristic
903C2C2×#6592511yescharacteristic
904C2C2×#6594511yescharacteristic
905C2C2×D5×#12111yescharacteristic
906C2C2×#6599611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC2×#386D5
hypocenterC5C2×#2427
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D5C2semidirect
3. C22×#4031C2semidirect
4. C22×#4024C2semidirect
5. C2×C5×#386C2semidirect
6. C2×#65511C2semidirect
7. C2×#65501C2semidirect
8. C2×#65245C2semidirect
9. C2×#65241C2semidirect
10. C2×#65250C2semidirect
11. C2×C22⋊C4×Dic5C2semidirect
12. #10606428C2direct (N × H)
13. C2×#64956C2semidirect
14. C2×#64963C2semidirect
15. C2×#64935C2semidirect
16. C2×#64936C2semidirect
35. C2×C4×C22⋊D5C22semidirect
49. C2×#4031C22semidirect
51. C2×#4024C22semidirect
52. C5×#386C22semidirect
55. #65511C22semidirect
56. #65501C22semidirect
63. #65250C22semidirect
64. #65245C22semidirect
65. #65241C22semidirect
66. C22⋊C4×Dic5C22semidirect
67. #64963C22semidirect
68. #64956C22semidirect
69. #64936C22semidirect
70. #64935C22semidirect
148. C2×#683D4semidirect
179. C2×#386D5semidirect
301. #683C2×D4semidirect
346. #386C2×D5semidirect
731. C2×C5#2427semidirect
845. C5C2×#2427semidirect
899. C2#10606428direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40852
C22×C4×C22⋊D52
C22×#40312
C22×#40242
C2×C5×#3862
C2×#655112
C2×#655012
C2×#652452
C2×#652412
C2×#652502
C2×C22⋊C4×Dic52
#106064282
C2×#649562
C2×#649632
C2×#649352
C2×#649362
C2×#24275