Finite Group Databasebeta

← C2×#10609045 #12271067

Subgroups — C2×#10609045 #12271067

Order 1280.

3614 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic, complemented
2C22×#4033C211yesmaximal, characteristic, complemented
3C22×#4024C211yesmaximal, characteristic, complemented
4C22×#4027C211yesmaximal, characteristic
5C2×C5×#396C211yesmaximal, characteristic, complemented
6C2×#65283C211yesmaximal, characteristic, complemented
7C2×#65283C211yesmaximal, characteristic, complemented
8C2×#65261C211yesmaximal, characteristic, complemented
9C2×#65265C211yesmaximal, characteristic, complemented
10C2×#65237C211yesmaximal, characteristic, complemented
11C2×#65246C211yesmaximal, characteristic
12C2×#65246C211yesmaximal, characteristic
13C2×#65231C211yesmaximal, characteristic, complemented
14#10609045C2116yesmaximal, direct product factor
15C2×#64956C211yesmaximal, characteristic, complemented
16C2×#64936C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4042—28no—
49C2×#4042C2218yescomplemented
50C2×#4033—28no—
51C2×#4033C2218yescomplemented
52C2×#4027—28no—
53C2×#4027C2218yes—
54C2×#4024—28no—
55C2×#4024C2218yescomplemented
56C5×#396C2218yescomplemented
57C2×C5×#95C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65283C2218yescomplemented
62#65283C2218yescomplemented
63#65265C2218yescomplemented
64#65261C2218yescomplemented
65#65246C2218yes—
66#65246C2218yes—
67#65237C2218yescomplemented
68#65231C2218yescomplemented
69#64956C2218yescomplemented
70#64936C2218yescomplemented
71C2×#2538—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5—24no—
81C22×C22⋊D5—24no—
82C22×C22⋊D5Q818yescomplemented
83C22×C22⋊D5C2314yes—
84C23×Dic5—24no—
85C23×Dic5—24no—
86C23×Dic5—24no—
87C23×Dic5C2314yes—
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C22×C4×D5—24no—
96C22×C4×D5—24no—
97C22×C4×D5—24no—
98C22×C4×D5C2314yes—
99C22×Dic10—24no—
100C22×Dic10—24no—
101C22×Dic10D418yescomplemented
102C22×Dic10C2314yes—
103C2×C5×C4⋊C4—24no—
104C2×C5×C4⋊C4—24no—
105C2×C5×C4⋊C4—42no—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C4⋊C4C2314yes—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4—42no—
112C2×C5×C22⋊C4C2314yes—
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—42no—
117C2×C22⋊Dic5C2314yes—
118C2×C22⋊Dic5C2314yes—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685—24no—
122C2×#685—42no—
123C2×#685—42no—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×C4⋊Dic5—24no—
130C2×C4⋊Dic5—42no—
131C2×C4⋊Dic5C2314yes—
132C2×C4⋊Dic5C2314yes—
133C2×#683—24no—
134C2×#683—24no—
135C2×#683—24no—
136C2×#683—24no—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683—24no—
141C2×#683—24no—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×C4×Dic5—24no—
152C2×C4×Dic5—24no—
153C2×C4×Dic5D418yes—
154C2×C4×Dic5C2314yes—
155C2×C4×Dic5C2314yes—
156C2×C4×Dic5C2314yes—
157#4042—232no—
158#4033—232no—
159#4027—232no—
160#4024—232no—
161C5×#95C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165C22×C22⋊Q8—51no—
166C22×C22⋊Q8—51no—
167C22×C4×Q8—51no—
168C22×C4×D4—51no—
169#2538—516no—
170C2×#396—51no—
171C2×#396—51no—
172C2×#396—51no—
173C2×#396D511yescharacteristic, complemented
174C2×#390—51no—
175C2×#390—51no—
176C2×#389—51no—
177C2×#389—51no—
178C2×#384—51no—
179C2×#380—51no—
180C2×#380—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—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
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×C5C2×D414yes—
215C22×C4×C5C2×D414yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C2×C22⋊D5—232no—
223C2×C22⋊D5—28no—
224C2×C22⋊D5—28no—
225C2×C22⋊D5C2×Q8116yescomplemented
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—28no—
241C22×Dic5—28no—
242C22×Dic5—28no—
243C22×Dic5—416no—
244C22×Dic5C2×D414yes—
245C22×Dic5C2×D414yes—
246C22×Dic5C2×D414yes—
247C22×Dic5C2×D414yes—
248C22×Dic5C2×Q814yes—
249C22×Dic5#4114yes—
250C22×Dic5#4114yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C2×C4×D5—28no—
259C2×C4×D5—28no—
260C2×C4×D5—28no—
261C2×C4×D5—416no—
262C2×Dic10—232no—
263C2×Dic10—28no—
264C2×Dic10—28no—
265C2×Dic10C2×D4116yescomplemented
266C5×C4⋊C4—28no—
267C5×C4⋊C4—28no—
268C5×C4⋊C4—44no—
269C5×C22⋊C4—28no—
270C5×C22⋊C4—28no—
271C5×C22⋊C4—44no—
272C22⋊Dic5—28no—
273C22⋊Dic5—44no—
274#685—28no—
275#685—28no—
276#685—28no—
277#685—44no—
278#685—44no—
279C4⋊Dic5—28no—
280C4⋊Dic5—44no—
281#683—28no—
282#683—28no—
283#683—28no—
284#683—28no—
285#683—28no—
286#683—28no—
287#683—28no—
288#683—28no—
289#683—28no—
290C4×Dic5—28no—
291C4×Dic5—28no—
292C4×Dic5C2×D4116yes—
293C23×Q8—51no—
294C23×D4—51no—
295C24×C4—51no—
296C24×C4—51no—
297C2×C22⋊Q8—58no—
298C2×C22⋊Q8—58no—
299C2×C22⋊Q8—108no—
300C2×C22⋊Q8—108no—
301C2×C4×Q8—58no—
302C2×C4×Q8—108no—
303C2×C4×D4—58no—
304C2×C4×D4—108no—
305C22×C4⋊C4—51no—
306C22×C4⋊C4—51no—
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⋊C4—51no—
316C22×C4⋊C4C2×D511yescharacteristic
317C22×C4⋊C4C2×D511yescharacteristic
318C22×C4⋊C4C2×D511yescharacteristic
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×C22⋊C4C2×D511yescharacteristic
329C22×C42—51no—
330C22×C42—51no—
331C22×C42—51no—
332#396—58no—
333#396—58no—
334#396—58no—
335#396C2×D518yescomplemented
336#390—58no—
337#390—58no—
338#389—58no—
339#389—58no—
340#384—58no—
341#380—58no—
342#380—58no—
343C2×#95—51no—
344C2×#95—51no—
345C2×#95—51no—
346C2×#95C2×D511yescharacteristic
347C23×C5—28no—
348C23×C5—28no—
349C23×C5—28no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—44no—
357C23×C5—44no—
358C23×C5—44no—
359C23×C5—44no—
360C23×C5C22×D412yes—
361C23×C5C22×D412yes—
362C23×C5C22×Q814yes—
363C23×C5C22×Q812yes—
364C23×C5C2×#4112yes—
365C23×C5C2×#4112yes—
366C23×C5H(5,𝔽2)12yes—
367C23×C52−1+412yes—
368C23×C5C2511yescharacteristic
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—28no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—44no—
379C22×D5—44no—
380C22×D5—44no—
381C22×D5—44no—
382C22×D5C22×Q814yes—
383C2×C4×C5—28no—
384C2×C4×C5—28no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
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—44no—
402C2×C4×C5—44no—
403C2×C4×C5—44no—
404C2×C4×C5—44no—
405C2×C4×C5C22×D414yes—
406C2×C4×C5C22×D414yes—
407C22⋊D5—232no—
408C2×Dic5—28no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
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—44no—
424C2×Dic5—44no—
425C2×Dic5—44no—
426C2×Dic5—44no—
427C2×Dic5—416no—
428C2×Dic5#121116yes—
429C2×Dic5C22⋊Q8116yescomplemented
430C2×Dic5C22×D414yes—
431C2×Dic5C22×D414yes—
432C2×Dic5C22×D414yes—
433C2×Dic5C22×D414yes—
434C2×Dic5C22×Q814yes—
435C2×Dic5C2×#4114yes—
436C2×Dic5C2×#4114yes—
437C4×D5—416no—
438Dic10—232no—
439C25—51no—
440C25C22×D511yescharacteristic
441C22×Q8—58no—
442C22×Q8—54no—
443C22×Q8—104no—
444C22×Q8—104no—
445C22×D4—58no—
446C22×D4—54no—
447C22×D4—104no—
448C22×D4—104no—
449C23×C4—51no—
450C23×C4—51no—
451C23×C4—51no—
452C23×C4—54no—
453C23×C4—51no—
454C23×C4—51no—
455C23×C4—51no—
456C23×C4—51no—
457C23×C4—54no—
458C23×C4—104no—
459C23×C4—104no—
460C23×C4—104no—
461C23×C4—104no—
462C23×C4—104no—
463C23×C4—104no—
464C23×C4C22×D511yescharacteristic
465C23×C4C22×D511yescharacteristic
466C23×C4C22×D511yescharacteristic
467C23×C4C22×D511yescharacteristic
468C23×C4C22×D511yescharacteristic
469C23×C4C22×D511yescharacteristic
470C22⋊Q8—1032no—
471C22⋊Q8—1032no—
472C4×Q8—1032no—
473C4×D4—1032no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—54no—
478C2×C4⋊C4—54no—
479C2×C4⋊C4—54no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—54no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—104no—
489C2×C4⋊C4—104no—
490C2×C4⋊C4—104no—
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⋊C4—202no—
499C2×C4⋊C4C22×D514yes—
500C2×C4⋊C4C22×D514yes—
501C2×C4⋊C4C22×D514yes—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—42no—
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—202no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4—202no—
519C2×C22⋊C4C22×D514yes—
520C2×C22⋊C4C22×D514yes—
521C2×C22⋊C4C22×D514yes—
522C2×C42—58no—
523C2×C42—54no—
524C2×C42—54no—
525C2×C42—54no—
526C2×C42—104no—
527C2×C42—104no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95C22×D514yes—
532C22×C5—24no—
533C22×C5—24no—
534C22×C5—24no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—416no—
540C22×C5C2×#12114yes—
541C22×C5C2×C22⋊Q814yes—
542C22×C5#53714yes—
543C22×C5D4×Q814yes—
544C22×C5#55014yes—
545C22×C5#55414yes—
546C22×C5#55614yes—
547C22×C5C23×D411yescharacteristic
548C22×C5C23×D411yescharacteristic
549C22×C5C23×Q811yescharacteristic
550C22×C5C22×#4111yescharacteristic
551C22×C5C22×#4111yescharacteristic
552C22×C5C2×H(5,𝔽2)11yescharacteristic
553C22×C5C2×2−1+411yescharacteristic
554C2×D5—24no—
555C2×D5—24no—
556C2×D5—24no—
557C2×D5—42no—
558C2×D5—42no—
559C2×D5—42no—
560C2×D5—42no—
561C2×D5—416no—
562C4×C5—24no—
563C4×C5—24no—
564C4×C5—42no—
565C4×C5—42no—
566C4×C5—42no—
567C4×C5—42no—
568Dic5—24no—
569Dic5—42no—
570Dic5—42no—
571Dic5—42no—
572Dic5—42no—
573Dic5C2×#12118yes—
574Dic5C2×C22⋊Q818yescomplemented
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—54no—
582C24—52no—
583C24—102no—
584C24—102no—
585C24—102no—
586C24—102no—
587C24—102no—
588C24—102no—
589C24Q8×D514yes—
590C24C23×D512yes—
591C24C23×D511yescharacteristic
592C2×Q8—516no—
593C2×Q8—108no—
594C2×Q8—1032no—
595C2×Q8—108no—
596C2×D4—516no—
597C2×D4—108no—
598C2×D4—1032no—
599C2×D4—108no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
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—54no—
617C22×C4—54no—
618C22×C4—54no—
619C22×C4—54no—
620C22×C4—54no—
621C22×C4—54no—
622C22×C4—52no—
623C22×C4—52no—
624C22×C4—54no—
625C22×C4—52no—
626C22×C4—52no—
627C22×C4—52no—
628C22×C4—52no—
629C22×C4—52no—
630C22×C4—108no—
631C22×C4—108no—
632C22×C4—108no—
633C22×C4—108no—
634C22×C4—108no—
635C22×C4—108no—
636C22×C4—102no—
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—2016no—
651C22×C4—2016no—
652C22×C4D4×D514yes—
653C22×C4D4×D514yes—
654C22×C4C23×D512yes—
655C22×C4C23×D512yes—
656C22×C4C23×D512yes—
657C22×C4C23×D512yes—
658C22×C4C23×D512yes—
659C22×C4C23×D512yes—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—44no—
663C4⋊C4—108no—
664C4⋊C4—108no—
665C4⋊C4—108no—
666C4⋊C4—108no—
667C4⋊C4—108no—
668C4⋊C4—108no—
669C4⋊C4—108no—
670C4⋊C4—108no—
671C4⋊C4—108no—
672C4⋊C4—108no—
673C4⋊C4—204no—
674C22⋊C4—28no—
675C22⋊C4—28no—
676C22⋊C4—44no—
677C22⋊C4—108no—
678C22⋊C4—108no—
679C22⋊C4—108no—
680C22⋊C4—108no—
681C22⋊C4—204no—
682C22⋊C4—204no—
683C22⋊C4—204no—
684C42—516no—
685C42—108no—
686C42—108no—
687C2×C5—44no—
688C2×C5#253818yescomplemented
689C2×C5C22×#12111yescharacteristic
690C2×C5C22×C22⋊Q811yescharacteristic
691C2×C5C2×#53711yescharacteristic
692C2×C5C2×D4×Q811yescharacteristic
693C2×C5C2×#55011yescharacteristic
694C2×C5C2×#55411yescharacteristic
695C2×C5C2×#55611yescharacteristic
696D5—44no—
697C23—28no—
698C23—28no—
699C23—28no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—54no—
711C23—108no—
712C23—108no—
713C23—108no—
714C23—102no—
715C23—102no—
716C23—102no—
717C23—102no—
718C23—102no—
719C23—102no—
720C23—204no—
721C23—204no—
722C23—204no—
723C23—204no—
724C23C2×D4×D512yes—
725C23C2×D4×D512yes—
726C23#414412yes—
727C23C2×Q8×D514yes—
728C23C2×Q8×D512yes—
729C23D5×#4112yes—
730C23D5×#4112yes—
731C23#415012yes—
732C23C24×D511yescharacteristic
733Q8—1032no—
734D4—1032no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
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—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—516no—
758C2×C4—516no—
759C2×C4—54no—
760C2×C4—54no—
761C2×C4—54no—
762C2×C4—54no—
763C2×C4—54no—
764C2×C4—54no—
765C2×C4—54no—
766C2×C4—108no—
767C2×C4—102no—
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—2016no—
782C2×C4—2016no—
783C2×C4—204no—
784C2×C4—204no—
785C2×C4—204no—
786C2×C4—204no—
787C2×C4C2×D4×D514yes—
788C2×C4C2×D4×D514yes—
789C5C2×#253811yescharacteristic, complemented, Sylow
790C22—24no—
791C22—24no—
792C22—24no—
793C22—416no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—104no—
799C22—104no—
800C22—104no—
801C22—2016no—
802C22—202no—
803C22—202no—
804C22—202no—
805C22—202no—
806C22#6593114yes—
807C22#6593314yes—
808C22D5×#12114yes—
809C22D5×C22⋊Q814yes—
810C22#6596614yes—
811C22#6597014yes—
812C22#6603614yes—
813C22C22×D4×D511yescharacteristic
814C22C22×D4×D511yescharacteristic
815C22C2×#414411yescharacteristic
816C22C22×Q8×D511yescharacteristic
817C22C2×D5×#4111yescharacteristic
818C22C2×D5×#4111yescharacteristic
819C22C2×#415011yescharacteristic
820C4—24no—
821C4—24no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—58no—
827C4—58no—
828C4—104no—
829C4—202no—
830C4—202no—
831C4—202no—
832C4—202no—
833C2—44no—
834C2—204no—
835C2#1060904518yesdirect product factor
836C2C2×#6593111yescharacteristic
837C2C2×#6593311yescharacteristic
838C2C2×D5×#12111yescharacteristic
839C2C2×#6596611yescharacteristic
840C2C2×#6597011yescharacteristic
841C2C2×D5×C22⋊Q811yescharacteristic
842C2C2×#6603611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#396D5
hypocenterC5C2×#2538
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#4042C2semidirect
2. C22×#4033C2semidirect
3. C22×#4024C2semidirect
5. C2×C5×#396C2semidirect
6. C2×#65283C2semidirect
7. C2×#65283C2semidirect
8. C2×#65261C2semidirect
9. C2×#65265C2semidirect
10. C2×#65237C2semidirect
13. C2×#65231C2semidirect
14. #10609045C2direct (N × H)
15. C2×#64956C2semidirect
16. C2×#64936C2semidirect
49. C2×#4042C22semidirect
51. C2×#4033C22semidirect
55. C2×#4024C22semidirect
56. C5×#396C22semidirect
61. #65283C22semidirect
62. #65283C22semidirect
63. #65265C22semidirect
64. #65261C22semidirect
67. #65237C22semidirect
68. #65231C22semidirect
69. #64956C22semidirect
70. #64936C22semidirect
82. C22×C22⋊D5Q8semidirect
101. C22×Dic10D4semidirect
173. C2×#396D5semidirect
225. C2×C22⋊D5C2×Q8semidirect
265. C2×Dic10C2×D4semidirect
335. #396C2×D5semidirect
429. C2×Dic5C22⋊Q8semidirect
574. Dic5C2×C22⋊Q8semidirect
688. C2×C5#2538semidirect
789. C5C2×#2538semidirect
835. C2#10609045direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40422
C22×#40332
C22×#40242
C22×#40272
C2×C5×#3962
C2×#652832
C2×#652612
C2×#652652
C2×#652372
C2×#652462
C2×#652312
#106090452
C2×#649562
C2×#649362
C2×#25385