Finite Group Databasebeta

← C2×#10614497 #12267205

Subgroups — C2×#10614497 #12267205

Order 1280.

3614 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#4090C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D5C211yesmaximal, characteristic
4C22×#4042C211yesmaximal, characteristic, complemented
5C2×#65520C211yesmaximal, characteristic, complemented
6C2×#65499C211yesmaximal, characteristic, complemented
7#10614497C2116yesmaximal, direct product factor
8C2×#65283C211yesmaximal, characteristic, complemented
9C2×#65278C211yesmaximal, characteristic, complemented
10C2×#65261C211yesmaximal, characteristic, complemented
11C2×#65261C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
13C2×#65237C211yesmaximal, characteristic, complemented
14C2×#65236C211yesmaximal, characteristic, complemented
15C2×#65246C211yesmaximal, characteristic
16C2×#65246C211yesmaximal, characteristic
17C23×C5×Q8C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×Dic10C2211yescharacteristic
22C2×C5×C22⋊Q8—28no—
23C2×C5×C22⋊Q8C2218yescomplemented
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×#4090—28no—
33C2×#4090C2218yescomplemented
34C2×C4×C22⋊D5—28no—
35C2×C4×C22⋊D5C2218yes—
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C22×C4×Dic5C2211yescharacteristic
51C22×C4×Dic5C2211yescharacteristic
52C2×#4042—28no—
53C2×#4042C2218yescomplemented
54#65520C2218yescomplemented
55#65499C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65283C2218yescomplemented
63#65278C2218yescomplemented
64C4⋊C4×Dic5C2218yescomplemented
65#65261C2218yescomplemented
66#65261C2218yescomplemented
67#65246C2218yes—
68#65246C2218yes—
69#65237C2218yescomplemented
70#65236C2218yescomplemented
71C2×#2452—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C22×C5×Q8—24no—
75C22×C5×Q8—24no—
76C22×C5×Q8—42no—
77C22×C5×Q8C2314yes—
78C23×C4×C5—24no—
79C23×C4×C5—24no—
80C23×C4×C5—42no—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2314yes—
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5Q818yescomplemented
91C22×C22⋊D5C2314yes—
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—42no—
102C22×C4×D5C2314yes—
103C22×Dic10—24no—
104C22×Dic10—24no—
105C22×Dic10—42no—
106C22×Dic10C2314yes—
107C5×C22⋊Q8—232no—
108C2×C5×C4⋊C4—24no—
109C2×C5×C4⋊C4—24no—
110C2×C5×C4⋊C4D418yescomplemented
111C2×C5×C4⋊C4C2314yes—
112C2×C5×C4⋊C4C2314yes—
113C2×C5×C4⋊C4C2314yes—
114C2×C5×C22⋊C4—24no—
115C2×C5×C22⋊C4—24no—
116C2×C5×C22⋊C4C2314yes—
117C2×C5×C22⋊C4C2314yes—
118C2×C22⋊Dic5—24no—
119C2×C22⋊Dic5—24no—
120C2×C22⋊Dic5—42no—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124#4090—232no—
125C4×C22⋊D5—232no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—42no—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×C4⋊Dic5—24no—
137C2×C4⋊Dic5C2314yes—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683—24no—
141C2×#683—24no—
142C2×#683—24no—
143C2×#683—24no—
144C2×#683D418yes—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×C4×Dic5—24no—
153C2×C4×Dic5—24no—
154C2×C4×Dic5—24no—
155C2×C4×Dic5C2314yes—
156C2×C4×Dic5C2314yes—
157C2×C4×Dic5C2314yes—
158#4042—232no—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165C22×C4⋊Q8—51no—
166C22×C22⋊Q8—51no—
167C22×C22⋊Q8D511yescharacteristic, complemented
168C22×C4×D4—51no—
169#2452—516no—
170C2×#396—51no—
171C2×#396—51no—
172C2×#393—51no—
173C2×#393—51no—
174C2×#390—51no—
175C2×#390—51no—
176C2×#389—51no—
177C2×#389—51no—
178C2×#385—51no—
179C2×#385—51no—
180C2×C4×C4⋊C4—51no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5C2×Q814yes—
188C24×C5C2412yes—
189C24×C5C2411yescharacteristic
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5C2×Q814yes—
197C23×D5C2412yes—
198C2×C5×Q8—28no—
199C2×C5×Q8—28no—
200C2×C5×Q8—44no—
201C2×C5×Q8—416no—
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×C5C2×D414yes—
222C22×C4×C5C2×D414yes—
223C22×C4×C5C2×D414yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C2×C22⋊D5—232no—
231C2×C22⋊D5—28no—
232C2×C22⋊D5—28no—
233C2×C22⋊D5C2×Q8116yescomplemented
234C22×Dic5—22no—
235C22×Dic5—22no—
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×Dic5C2×D414yes—
251C22×Dic5C2×D414yes—
252C22×Dic5C2×Q814yes—
253C22×Dic5#4114yes—
254C22×Dic5#4114yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C2×C4×D5—28no—
263C2×C4×D5—28no—
264C2×C4×D5—44no—
265C2×C4×D5—416no—
266C2×Dic10—28no—
267C2×Dic10—28no—
268C2×Dic10—44no—
269C2×Dic10—416no—
270C5×C4⋊C4—28no—
271C5×C4⋊C4—28no—
272C5×C4⋊C4C2×D4116yescomplemented
273C5×C22⋊C4—28no—
274C5×C22⋊C4—28no—
275C22⋊Dic5—28no—
276C22⋊Dic5—28no—
277C22⋊Dic5—44no—
278#685—28no—
279#685—28no—
280#685—28no—
281#685—28no—
282#685—44no—
283C4⋊Dic5—28no—
284#683—28no—
285#683—28no—
286#683—28no—
287#683—28no—
288#683—28no—
289#683—28no—
290#683C2×D4116yes—
291C4×Dic5—28no—
292C4×Dic5—28no—
293C4×Dic5—28no—
294C23×Q8—51no—
295C23×Q8C2×D511yescharacteristic
296C23×D4—51no—
297C24×C4—51no—
298C24×C4C2×D511yescharacteristic
299C2×C4⋊Q8—58no—
300C2×C4⋊Q8—108no—
301C2×C22⋊Q8—28no—
302C2×C22⋊Q8—58no—
303C2×C22⋊Q8—108no—
304C2×C22⋊Q8C2×D518yescomplemented
305C2×C4×D4—58no—
306C2×C4×D4—108no—
307C22×C4⋊C4—51no—
308C22×C4⋊C4—51no—
309C22×C4⋊C4—51no—
310C22×C4⋊C4—51no—
311C22×C4⋊C4—51no—
312C22×C4⋊C4—51no—
313C22×C4⋊C4—51no—
314C22×C4⋊C4—51no—
315C22×C4⋊C4C2×D511yescharacteristic
316C22×C4⋊C4C2×D511yescharacteristic
317C22×C4⋊C4C2×D511yescharacteristic
318C22×C22⋊C4—51no—
319C22×C22⋊C4—51no—
320C22×C22⋊C4—51no—
321C22×C22⋊C4—51no—
322C22×C22⋊C4—51no—
323C22×C22⋊C4—51no—
324C22×C22⋊C4—51no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4C2×D511yescharacteristic
327C22×C22⋊C4C2×D511yescharacteristic
328C22×C42—51no—
329C22×C42—51no—
330C22×C42—51no—
331#396—58no—
332#396—58no—
333#393—58no—
334#393—58no—
335#390—58no—
336#390—58no—
337#389—58no—
338#389—58no—
339#385—58no—
340#385—58no—
341C4×C4⋊C4—58no—
342C2×#95—51no—
343C2×#95—51no—
344C2×#95—51no—
345C2×#95—51no—
346C2×#95—51no—
347C2×#95—51no—
348C23×C5—28no—
349C23×C5—28no—
350C23×C5—28no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—44no—
358C23×C5—44no—
359C23×C5—44no—
360C23×C5—44no—
361C23×C5C22×D412yes—
362C23×C5C22×D412yes—
363C23×C5C22×Q814yes—
364C23×C5C22×Q812yes—
365C23×C5C2×#4112yes—
366C23×C5C2×#4112yes—
367C23×C5H(5,𝔽2)12yes—
368C23×C52−1+412yes—
369C23×C5C2511yescharacteristic
370C22×D5—28no—
371C22×D5—28no—
372C22×D5—28no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—44no—
380C22×D5—44no—
381C22×D5—44no—
382C22×D5—44no—
383C22×D5C22×Q814yes—
384C5×Q8—416no—
385C2×C4×C5—28no—
386C2×C4×C5—28no—
387C2×C4×C5—28no—
388C2×C4×C5—28no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
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—416no—
404C2×C4×C5—44no—
405C2×C4×C5—44no—
406C2×C4×C5C22×D414yes—
407C2×C4×C5C22×D414yes—
408C2×C4×C5C22×D414yes—
409C2×C4×C5C22×D414yes—
410C22⋊D5—232no—
411C2×Dic5—28no—
412C2×Dic5—28no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—44no—
430C2×Dic5—44no—
431C2×Dic5—44no—
432C2×Dic5—44no—
433C2×Dic5C22⋊Q8116yescomplemented
434C2×Dic5C22×D414yes—
435C2×Dic5C22×D414yes—
436C2×Dic5C22×Q814yes—
437C2×Dic5C2×#4114yes—
438C2×Dic5C2×#4114yes—
439C4×D5—416no—
440Dic10—416no—
441C25—51no—
442C25C22×D511yescharacteristic
443C22×Q8—24no—
444C22×Q8—24no—
445C22×Q8—42no—
446C22×Q8—54no—
447C22×Q8—104no—
448C22×Q8—104no—
449C22×Q8—202no—
450C22×Q8C22×D514yes—
451C22×D4—58no—
452C22×D4—54no—
453C22×D4—104no—
454C22×D4—104no—
455C23×C4—24no—
456C23×C4—24no—
457C23×C4—42no—
458C23×C4—51no—
459C23×C4—51no—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—54no—
466C23×C4—104no—
467C23×C4—104no—
468C23×C4—202no—
469C23×C4C22×D511yescharacteristic
470C23×C4C22×D511yescharacteristic
471C23×C4C22×D514yes—
472C23×C4C22×D511yescharacteristic
473C23×C4C22×D511yescharacteristic
474C23×C4C22×D511yescharacteristic
475C23×C4C22×D511yescharacteristic
476C4⋊Q8—1032no—
477C22⋊Q8—232no—
478C22⋊Q8—1032no—
479C4×D4—1032no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—58no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—54no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—104no—
492C2×C4⋊C4—104no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4—104no—
496C2×C4⋊C4—104no—
497C2×C4⋊C4—104no—
498C2×C4⋊C4C22⋊D518yescomplemented
499C2×C4⋊C4C22×D514yes—
500C2×C4⋊C4C22×D514yes—
501C2×C4⋊C4C22×D514yes—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—54no—
508C2×C22⋊C4—54no—
509C2×C22⋊C4—54no—
510C2×C22⋊C4—54no—
511C2×C22⋊C4—54no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—104no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—104no—
516C2×C22⋊C4—104no—
517C2×C22⋊C4—104no—
518C2×C22⋊C4—202no—
519C2×C22⋊C4—202no—
520C2×C22⋊C4C22×D514yes—
521C2×C22⋊C4C22×D514yes—
522C2×C42—54no—
523C2×C42—54no—
524C2×C42—54no—
525C2×C42—104no—
526C2×C42—104no—
527C2×C42—104no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95—54no—
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×C5C2×C22⋊Q814yes—
543C22×C5#53214yes—
544C22×C5#54214yes—
545C22×C5D4214yes—
546C22×C5#54814yes—
547C22×C5D4×Q814yes—
548C22×C5#55414yes—
549C22×C5C23×D411yescharacteristic
550C22×C5C23×D411yescharacteristic
551C22×C5C23×Q811yescharacteristic
552C22×C5C22×#4111yescharacteristic
553C22×C5C22×#4111yescharacteristic
554C22×C5C2×H(5,𝔽2)11yescharacteristic
555C22×C5C2×2−1+411yescharacteristic
556C2×D5—24no—
557C2×D5—24no—
558C2×D5—24no—
559C2×D5—42no—
560C2×D5—42no—
561C2×D5—42no—
562C2×D5—42no—
563C2×D5—416no—
564C4×C5—24no—
565C4×C5—24no—
566C4×C5—24no—
567C4×C5—24no—
568C4×C5—42no—
569C4×C5—42no—
570Dic5—24no—
571Dic5—24no—
572Dic5—42no—
573Dic5—42no—
574Dic5—42no—
575Dic5—42no—
576Dic5C2×C22⋊Q818yescomplemented
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—54no—
584C24—52no—
585C24—102no—
586C24—102no—
587C24—102no—
588C24—102no—
589C24—102no—
590C24—102no—
591C24Q8×D514yes—
592C24C23×D512yes—
593C24C23×D511yescharacteristic
594C2×Q8—28no—
595C2×Q8—28no—
596C2×Q8—44no—
597C2×Q8—416no—
598C2×Q8—108no—
599C2×Q8—108no—
600C2×Q8—204no—
601C2×Q8—2016no—
602C2×D4—516no—
603C2×D4—108no—
604C2×D4—1032no—
605C2×D4—108no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—44no—
623C22×C4—416no—
624C22×C4—54no—
625C22×C4—54no—
626C22×C4—54no—
627C22×C4—52no—
628C22×C4—54no—
629C22×C4—54no—
630C22×C4—52no—
631C22×C4—52no—
632C22×C4—52no—
633C22×C4—52no—
634C22×C4—52no—
635C22×C4—52no—
636C22×C4—108no—
637C22×C4—102no—
638C22×C4—102no—
639C22×C4—102no—
640C22×C4—102no—
641C22×C4—102no—
642C22×C4—102no—
643C22×C4—102no—
644C22×C4—102no—
645C22×C4—102no—
646C22×C4—102no—
647C22×C4—102no—
648C22×C4—102no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—108no—
654C22×C4—204no—
655C22×C4—2016no—
656C22×C4D4×D514yes—
657C22×C4C2×C22⋊D514yes—
658C22×C4C2×C22⋊D514yes—
659C22×C4C2×C22⋊D514yes—
660C22×C4C23×D512yes—
661C22×C4C23×D512yes—
662C22×C4C23×D512yes—
663C22×C4C23×D512yes—
664C22×C4C23×D512yes—
665C22×C4C23×D512yes—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—516no—
669C4⋊C4—108no—
670C4⋊C4—108no—
671C4⋊C4—108no—
672C4⋊C4—108no—
673C4⋊C4—108no—
674C4⋊C4—108no—
675C4⋊C4—108no—
676C4⋊C4C2×C22⋊D5116yescomplemented
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—108no—
680C22⋊C4—108no—
681C22⋊C4—108no—
682C22⋊C4—108no—
683C22⋊C4—108no—
684C22⋊C4—108no—
685C22⋊C4—204no—
686C22⋊C4—204no—
687C42—108no—
688C42—108no—
689C42—108no—
690C2×C5—44no—
691C2×C5#245218yescomplemented
692C2×C5C22×C22⋊Q811yescharacteristic
693C2×C5C2×#53211yescharacteristic
694C2×C5C2×#54211yescharacteristic
695C2×C5C2×D4211yescharacteristic
696C2×C5C2×#54811yescharacteristic
697C2×C5C2×D4×Q811yescharacteristic
698C2×C5C2×#55411yescharacteristic
699D5—44no—
700C23—28no—
701C23—28no—
702C23—28no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—54no—
714C23—108no—
715C23—108no—
716C23—108no—
717C23—102no—
718C23—102no—
719C23—102no—
720C23—102no—
721C23—102no—
722C23—102no—
723C23—204no—
724C23—204no—
725C23—204no—
726C23—204no—
727C23C2×D4×D512yes—
728C23#414412yes—
729C23C2×Q8×D514yes—
730C23C2×Q8×D512yes—
731C23#414712yes—
732C23D5×#4112yes—
733C23D5×#4112yes—
734C23C22×C22⋊D512yes—
735C23C24×D511yescharacteristic
736Q8—416no—
737Q8—2016no—
738D4—1032no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—416no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—516no—
761C2×C4—54no—
762C2×C4—54no—
763C2×C4—54no—
764C2×C4—54no—
765C2×C4—54no—
766C2×C4—108no—
767C2×C4—108no—
768C2×C4—102no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—2016no—
785C2×C4—204no—
786C2×C4—204no—
787C2×C4—204no—
788C2×C4—204no—
789C2×C4C2×D4×D514yes—
790C2×C4C22×C22⋊D514yes—
791C2×C4C22×C22⋊D514yes—
792C2×C4C22×C22⋊D514yes—
793C5C2×#245211yescharacteristic, complemented, Sylow
794C22—24no—
795C22—24no—
796C22—24no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—416no—
802C22—104no—
803C22—104no—
804C22—104no—
805C22—202no—
806C22—202no—
807C22—202no—
808C22—202no—
809C22—2016no—
810C22D5×C22⋊Q814yes—
811C22#6596714yes—
812C22#6597014yes—
813C22#6597414yes—
814C22D4×C22⋊D514yes—
815C22Q8×C22⋊D514yes—
816C22#6616614yes—
817C22C22×D4×D511yescharacteristic
818C22C2×#414411yescharacteristic
819C22C22×Q8×D511yescharacteristic
820C22C2×#414711yescharacteristic
821C22C2×D5×#4111yescharacteristic
822C22C2×D5×#4111yescharacteristic
823C22C23×C22⋊D511yescharacteristic
824C4—24no—
825C4—24no—
826C4—24no—
827C4—24no—
828C4—42no—
829C4—42no—
830C4—58no—
831C4—104no—
832C4—104no—
833C4—202no—
834C4—202no—
835C4—202no—
836C4—202no—
837C2—44no—
838C2—204no—
839C2#1061449718yesdirect product factor
840C2C2×#6597411yescharacteristic
841C2C2×#6597011yescharacteristic
842C2C2×D5×C22⋊Q811yescharacteristic
843C2C2×#6596711yescharacteristic
844C2C2×D4×C22⋊D511yescharacteristic
845C2C2×Q8×C22⋊D511yescharacteristic
846C2C2×#6616611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×C22⋊Q8C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC22×C22⋊Q8D5
hypocenterC5C2×#2452
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×#4090C2semidirect
4. C22×#4042C2semidirect
5. C2×#65520C2semidirect
6. C2×#65499C2semidirect
7. #10614497C2direct (N × H)
8. C2×#65283C2semidirect
9. C2×#65278C2semidirect
10. C2×#65261C2semidirect
11. C2×#65261C2semidirect
12. C2×C4⋊C4×Dic5C2semidirect
13. C2×#65237C2semidirect
14. C2×#65236C2semidirect
23. C2×C5×C22⋊Q8C22semidirect
33. C2×#4090C22semidirect
53. C2×#4042C22semidirect
54. #65520C22semidirect
55. #65499C22semidirect
62. #65283C22semidirect
63. #65278C22semidirect
64. C4⋊C4×Dic5C22semidirect
65. #65261C22semidirect
66. #65261C22semidirect
69. #65237C22semidirect
70. #65236C22semidirect
90. C22×C22⋊D5Q8semidirect
110. C2×C5×C4⋊C4D4semidirect
167. C22×C22⋊Q8D5semidirect
233. C2×C22⋊D5C2×Q8semidirect
272. C5×C4⋊C4C2×D4semidirect
304. C2×C22⋊Q8C2×D5semidirect
433. C2×Dic5C22⋊Q8semidirect
498. C2×C4⋊C4C22⋊D5semidirect
576. Dic5C2×C22⋊Q8semidirect
676. C4⋊C4C2×C22⋊D5semidirect
691. C2×C5#2452semidirect
793. C5C2×#2452semidirect
839. C2#10614497direct (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×#40902
C22×C4×C22⋊D52
C22×#40422
C2×#655202
C2×#654992
#106144972
C2×#652832
C2×#652782
C2×#652612
C2×C4⋊C4×Dic52
C2×#652372
C2×#652362
C2×#652462
C2×#24525