Finite Group Databasebeta

← C2×#10614498 #12267161

Subgroups — C2×#10614498 #12267161

Order 1280.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#4093C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×#4040C211yesmaximal, characteristic, complemented
5C2×#65518C211yesmaximal, characteristic, complemented
6C2×#65502C211yesmaximal, characteristic, complemented
7#10614498C2116yesmaximal, direct product factor
8C2×#65283C211yesmaximal, characteristic, complemented
9C2×#65278C211yesmaximal, characteristic, complemented
10C2×#65279C211yesmaximal, characteristic, complemented
11C2×#65279C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
13C2×#65249C211yesmaximal, characteristic
14C2×#65250C211yesmaximal, characteristic, complemented
15C2×#65246C211yesmaximal, characteristic, complemented
16C2×#65234C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×D20C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C2×C5×C22⋊Q8—28no—
24C2×C5×C22⋊Q8C2218yescomplemented
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×#4093—28no—
33C2×#4093C2218yescomplemented
34C2×C4×C22⋊D5—28no—
35C2×C4×C22⋊D5C2218yescomplemented
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C22×#685C2211yescharacteristic
44C22×#685C2211yescharacteristic
45C22×C4⋊Dic5C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C22×C4×Dic5C2211yescharacteristic
51C22×C4×Dic5C2211yescharacteristic
52C2×#4040—28no—
53C2×#4040C2218yescomplemented
54#65518C2218yescomplemented
55#65502C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65283C2218yescomplemented
63#65279C2218yescomplemented
64#65279C2218yescomplemented
65#65278C2218yescomplemented
66C4⋊C4×Dic5C2218yescomplemented
67#65250C2218yescomplemented
68#65249C2218yes—
69#65246C2218yescomplemented
70#65234C2218yescomplemented
71C2×#2461—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×Q8—24no—
76C22×C5×Q8—24no—
77C22×C5×Q8—42no—
78C22×C5×Q8C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—42no—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2314yes—
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—24no—
93C22×C22⋊D5—24no—
94C22×C22⋊D5—42no—
95C22×C22⋊D5C2314yes—
96C22×C22⋊D5C2314yes—
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C22×D20—24no—
104C22×D20—24no—
105C22×D20—42no—
106C22×D20C2314yes—
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—42no—
110C22×C4×D5C2314yes—
111C5×C22⋊Q8—232no—
112C2×C5×C4⋊C4—24no—
113C2×C5×C4⋊C4—24no—
114C2×C5×C4⋊C4D418yescomplemented
115C2×C5×C4⋊C4C2314yes—
116C2×C5×C4⋊C4C2314yes—
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C22⋊C4—24no—
119C2×C5×C22⋊C4—24no—
120C2×C5×C22⋊C4C2314yes—
121C2×C5×C22⋊C4C2314yes—
122C2×C22⋊Dic5—24no—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126#4093—232no—
127C4×C22⋊D5—232no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685—24no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685D418yescomplemented
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×#685C2314yes—
145C2×#685C2314yes—
146C2×C4⋊Dic5—24no—
147C2×C4⋊Dic5C2314yes—
148C2×#683—24no—
149C2×#683—24no—
150C2×#683—42no—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×C4×Dic5—24no—
155C2×C4×Dic5—24no—
156C2×C4×Dic5—24no—
157C2×C4×Dic5C2314yes—
158C2×C4×Dic5C2314yes—
159C2×C4×Dic5C2314yes—
160#4040—232no—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#124—51no—
168C22×#123—51no—
169C22×C22⋊Q8D511yescharacteristic, complemented
170C22×C4×D4—51no—
171#2461—516no—
172C2×#396—51no—
173C2×#395—51no—
174C2×#394—51no—
175C2×#392—51no—
176C2×#390—51no—
177C2×#388—51no—
178C2×#388—51no—
179C2×#388—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×C4×C4⋊C4—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5#4114yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5C2×D414yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C2×C5×Q8—28no—
209C2×C5×Q8—28no—
210C2×C5×Q8—44no—
211C2×C5×Q8—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—22no—
226C22×C4×C5—28no—
227C22×C4×C5—28no—
228C22×C4×C5—44no—
229C22×C4×C5—416no—
230C22×C4×C5C2×D414yes—
231C22×C4×C5C2×D414yes—
232C22×C4×C5C2×D414yes—
233C22×C4×C5C2×D414yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
238C22×C4×C5C2412yes—
239C22×C4×C5C2412yes—
240C2×C22⋊D5—232no—
241C2×C22⋊D5—28no—
242C2×C22⋊D5—28no—
243C2×C22⋊D5—28no—
244C2×C22⋊D5—28no—
245C2×C22⋊D5—28no—
246C2×C22⋊D5—44no—
247C2×C22⋊D5—416no—
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—22no—
262C22×Dic5—22no—
263C22×Dic5C2×D414yes—
264C22×Dic5#4114yes—
265C22×Dic5#4114yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C2×D20—28no—
273C2×D20—28no—
274C2×D20—44no—
275C2×D20—416no—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—44no—
279C2×C4×D5—416no—
280C5×C4⋊C4—28no—
281C5×C4⋊C4—28no—
282C5×C4⋊C4C2×D4116yescomplemented
283C5×C22⋊C4—28no—
284C5×C22⋊C4—28no—
285C22⋊Dic5—28no—
286C22⋊Dic5—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685C2×D4116yescomplemented
296C4⋊Dic5—28no—
297#683—28no—
298#683—28no—
299#683—44no—
300C4×Dic5—28no—
301C4×Dic5—28no—
302C4×Dic5—28no—
303C23×Q8C2×D511yescharacteristic
304C23×D4—51no—
305C23×D4—51no—
306C23×D4—51no—
307C24×C4—51no—
308C24×C4C2×D511yescharacteristic
309C2×#124—58no—
310C2×#124—108no—
311C2×#123—58no—
312C2×#123—108no—
313C2×C22⋊Q8—28no—
314C2×C22⋊Q8C2×D518yescomplemented
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⋊C4C2×D511yescharacteristic
322C22×C4⋊C4C2×D511yescharacteristic
323C22×C4⋊C4C2×D511yescharacteristic
324C22×C22⋊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⋊C4—51no—
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C42—51no—
338C22×C42—51no—
339C22×C42—51no—
340#396—58no—
341#395—58no—
342#394—58no—
343#392—58no—
344#390—58no—
345#388—58no—
346#388—58no—
347#388—58no—
348#386—58no—
349#385—58no—
350C4×C4⋊C4—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95—51no—
357C23×C5—28no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5C22×D412yes—
371C23×C5C22×D412yes—
372C23×C5C2×#4114yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C52−1+412yes—
378C23×C5C2511yescharacteristic
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—44no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5C22×D414yes—
407C5×Q8—416no—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
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—22no—
426C2×C4×C5—416no—
427C2×C4×C5—44no—
428C2×C4×C5—44no—
429C2×C4×C5C22×D414yes—
430C2×C4×C5C22×D414yes—
431C2×C4×C5C22×D414yes—
432C2×C4×C5C22×D414yes—
433C22⋊D5—232no—
434C22⋊D5—416no—
435C2×Dic5—28no—
436C2×Dic5—28no—
437C2×Dic5—28no—
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—44no—
454C2×Dic5—44no—
455C2×Dic5—44no—
456C2×Dic5C22×D414yes—
457C2×Dic5C2×#4114yes—
458C2×Dic5C2×#4114yes—
459D20—416no—
460C4×D5—416no—
461C25—51no—
462C25—51no—
463C25C22×D511yescharacteristic
464C22×Q8—24no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8C22×D514yes—
468C22×D4—54no—
469C22×D4—54no—
470C22×D4—54no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—202no—
479C22×D4—202no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—42no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—54no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—202no—
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D514yes—
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500#124—1032no—
501#123—1032no—
502C22⋊Q8—232no—
503C4×D4—1032no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—104no—
511C2×C4⋊C4—104no—
512C2×C4⋊C4—104no—
513C2×C4⋊C4—202no—
514C2×C4⋊C4C22⋊D518yescomplemented
515C2×C4⋊C4C22×D514yes—
516C2×C4⋊C4C22×D514yes—
517C2×C4⋊C4C22×D514yes—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—58no—
521C2×C22⋊C4—54no—
522C2×C22⋊C4—54no—
523C2×C22⋊C4—54no—
524C2×C22⋊C4—54no—
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—104no—
533C2×C22⋊C4—104no—
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⋊C4C22×D514yes—
543C2×C22⋊C4C22×D514yes—
544C2×C42—54no—
545C2×C42—54no—
546C2×C42—54no—
547C2×C42—104no—
548C2×C42—104no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556C22×C5—24no—
557C22×C5—24no—
558C22×C5—24no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—416no—
564C22×C5#52514yes—
565C22×C5#53214yes—
566C22×C5#54214yes—
567C22×C5D4214yes—
568C22×C5#54714yes—
569C22×C5#54814yes—
570C22×C5#55114yes—
571C22×C5C23×D411yescharacteristic
572C22×C5C23×D411yescharacteristic
573C22×C5C22×#4111yescharacteristic
574C22×C5C22×#4111yescharacteristic
575C22×C5C22×#4111yescharacteristic
576C22×C5C2×H(5,𝔽2)11yescharacteristic
577C22×C5C2×2−1+411yescharacteristic
578C2×D5—24no—
579C2×D5—24no—
580C2×D5—24no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—416no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—88no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600Dic5—24no—
601Dic5—24no—
602Dic5—24no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—54no—
613C24—52no—
614C24—52no—
615C24—102no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24#71314yes—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×Q8—28no—
632C2×Q8—28no—
633C2×Q8—44no—
634C2×Q8—416no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—1032no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—204no—
644C2×D4—2016no—
645C2×D4—204no—
646C2×D4—2016no—
647C22×C4—22no—
648C22×C4—22no—
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—28no—
662C22×C4—28no—
663C22×C4—44no—
664C22×C4—416no—
665C22×C4—54no—
666C22×C4—54no—
667C22×C4—54no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—108no—
675C22×C4—102no—
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—102no—
690C22×C4—108no—
691C22×C4—204no—
692C22×C4—2016no—
693C22×C4D4×D514yes—
694C22×C4C2×C22⋊D514yes—
695C22×C4C2×C22⋊D514yes—
696C22×C4C2×C22⋊D514yes—
697C22×C4C23×D512yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—204no—
709C4⋊C4C2×C22⋊D5116yescomplemented
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—516no—
713C22⋊C4—108no—
714C22⋊C4—108no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C42—108no—
724C42—108no—
725C42—108no—
726C2×C5—44no—
727C2×C5#246118yescomplemented
728C2×C5C2×#52511yescharacteristic
729C2×C5C2×#53211yescharacteristic
730C2×C5C2×#54211yescharacteristic
731C2×C5C2×D4211yescharacteristic
732C2×C5C2×#54711yescharacteristic
733C2×C5C2×#54811yescharacteristic
734C2×C5C2×#55111yescharacteristic
735D5—44no—
736D5—82no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—54no—
751C23—108no—
752C23—108no—
753C23—108no—
754C23—102no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—204no—
768C23—204no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23C2×D4×D512yes—
779C23#414412yes—
780C23C2×#71314yes—
781C23C2×#71312yes—
782C23#414712yes—
783C23D5×#4112yes—
784C23D5×#4112yes—
785C23C22×C22⋊D512yes—
786C23C24×D511yescharacteristic
787Q8—416no—
788D4—1032no—
789D4—2016no—
790D4—2016no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
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—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—2016no—
834C2×C4—204no—
835C2×C4—204no—
836C2×C4—204no—
837C2×C4C2×D4×D514yes—
838C2×C4C22×C22⋊D514yes—
839C2×C4C22×C22⋊D514yes—
840C2×C4C22×C22⋊D514yes—
841C5C2×#246111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—416no—
850C22—104no—
851C22—104no—
852C22—104no—
853C22—202no—
854C22—202no—
855C22—202no—
856C22—202no—
857C22—2016no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—408no—
866C22#6596114yes—
867C22#6596514yes—
868C22#6597114yes—
869C22#6597414yes—
870C22D4×C22⋊D514yes—
871C22#6615114yes—
872C22#6616614yes—
873C22C22×D4×D511yescharacteristic
874C22C2×#414411yescharacteristic
875C22C22×#71311yescharacteristic
876C22C2×#414711yescharacteristic
877C22C2×D5×#4111yescharacteristic
878C22C2×D5×#4111yescharacteristic
879C22C23×C22⋊D511yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—104no—
887C4—104no—
888C4—104no—
889C4—202no—
890C4—202no—
891C4—202no—
892C2—44no—
893C2—204no—
894C2—402no—
895C2#1061449818yesdirect product factor
896C2C2×#6596111yescharacteristic
897C2C2×#6597411yescharacteristic
898C2C2×#6596511yescharacteristic
899C2C2×#6597111yescharacteristic
900C2C2×D4×C22⋊D511yescharacteristic
901C2C2×#6615111yescharacteristic
902C2C2×#6616611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×C22⋊Q8C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC22×C22⋊Q8D5
hypocenterC5C2×#2461
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C5×C22⋊Q8C2semidirect
2. C22×#4093C2semidirect
3. C22×C4×C22⋊D5C2semidirect
4. C22×#4040C2semidirect
5. C2×#65518C2semidirect
6. C2×#65502C2semidirect
7. #10614498C2direct (N × H)
8. C2×#65283C2semidirect
9. C2×#65278C2semidirect
10. C2×#65279C2semidirect
11. C2×#65279C2semidirect
12. C2×C4⋊C4×Dic5C2semidirect
14. C2×#65250C2semidirect
15. C2×#65246C2semidirect
16. C2×#65234C2semidirect
24. C2×C5×C22⋊Q8C22semidirect
33. C2×#4093C22semidirect
35. C2×C4×C22⋊D5C22semidirect
53. C2×#4040C22semidirect
54. #65518C22semidirect
55. #65502C22semidirect
62. #65283C22semidirect
63. #65279C22semidirect
64. #65279C22semidirect
65. #65278C22semidirect
66. C4⋊C4×Dic5C22semidirect
67. #65250C22semidirect
69. #65246C22semidirect
70. #65234C22semidirect
114. C2×C5×C4⋊C4D4semidirect
136. C2×#685D4semidirect
169. C22×C22⋊Q8D5semidirect
282. C5×C4⋊C4C2×D4semidirect
295. #685C2×D4semidirect
314. C2×C22⋊Q8C2×D5semidirect
514. C2×C4⋊C4C22⋊D5semidirect
709. C4⋊C4C2×C22⋊D5semidirect
727. C2×C5#2461semidirect
841. C5C2×#2461semidirect
895. C2#10614498direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
C22×#40932
C22×C4×C22⋊D52
C22×#40402
C2×#655182
C2×#655022
#106144982
C2×#652832
C2×#652782
C2×#652792
C2×C4⋊C4×Dic52
C2×#652492
C2×#652502
C2×#652462
C2×#652342
C2×#24615