Finite Group Databasebeta

← C2×#10613904 #12266782

Subgroups — C2×#10613904 #12266782

Order 1280.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#4070C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D5C211yesmaximal, characteristic
4C22×#4042C211yesmaximal, characteristic, complemented
5C2×#65502C211yesmaximal, characteristic
6C2×#65502C211yesmaximal, characteristic
7C2×#65499C211yesmaximal, characteristic, complemented
8C2×#65499C211yesmaximal, characteristic, complemented
9C2×#65281C211yesmaximal, characteristic, complemented
10C2×#65283C211yesmaximal, characteristic, complemented
11C2×#65278C211yesmaximal, characteristic, complemented
12#10613904C2116yesmaximal, direct product factor
13C2×#65269C211yesmaximal, characteristic, complemented
14C2×#65268C211yesmaximal, characteristic, complemented
15C2×#65261C211yesmaximal, characteristic, complemented
16C2×#65270C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C4⋊C4—28no—
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic
28C22×C5×C4⋊C4C2218yescomplemented
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×C4×C22⋊D5—28no—
33C2×C4×C22⋊D5C2218yes—
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C2×#4070—28no—
41C2×#4070C2218yescomplemented
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4042—28no—
51C2×#4042C2218yescomplemented
52#65502C2218yes—
53#65502C2218yes—
54#65499C2218yescomplemented
55#65499C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63C2×#3963C2211yescharacteristic
64#65283C2218yescomplemented
65#65281C2218yescomplemented
66#65278C2218yescomplemented
67#65270C2218yescomplemented
68#65269C2218yescomplemented
69#65268C2218yescomplemented
70#65261C2218yescomplemented
71C2×#2449—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C23×C4×C5—24no—
75C23×C4×C5—24no—
76C23×C4×C5—24no—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—42no—
82C23×C4×C5—42no—
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2314yes—
86C23×C4×C5C2314yes—
87C23×C4×C5C2314yes—
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C22×C22⋊D5—24no—
93C22×C22⋊D5—24no—
94C22×C22⋊D5Q818yescomplemented
95C22×C22⋊D5C2314yes—
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—42no—
106C22×C4×D5C2314yes—
107C22×Dic10—24no—
108C22×Dic10—24no—
109C22×Dic10—42no—
110C22×Dic10C2314yes—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4—24no—
113C2×C5×C4⋊C4—24no—
114C2×C5×C4⋊C4—232no—
115C2×C5×C4⋊C4D418yescomplemented
116C2×C5×C4⋊C4C2314yes—
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C4⋊C4C2314yes—
119C2×C5×C4⋊C4C2314yes—
120C2×C22⋊Dic5—24no—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5D418yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C4×C22⋊D5—232no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—42no—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×C4⋊Dic5—24no—
138C2×C4⋊Dic5C2314yes—
139#4070—232no—
140C2×#683—24no—
141C2×#683—24no—
142C2×#683—24no—
143C2×#683—24no—
144C2×#683—24no—
145C2×#683—24no—
146C2×#683—42no—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×C4×Dic5—24no—
155C2×C4×Dic5C2314yes—
156#4042—232no—
157#3963C2314yes—
158#3963C2314yes—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165C22×C22⋊Q8—51no—
166C22×C22⋊Q8—51no—
167C22×C4×D4—51no—
168C23×C4⋊C4D511yescharacteristic, complemented
169#2449—516no—
170C2×#399—51no—
171C2×#398—51no—
172C2×#396—51no—
173C2×#395—51no—
174C2×#389—51no—
175C2×#387—51no—
176C2×#386—51no—
177C2×#386—51no—
178C2×#385—51no—
179C2×#385—51no—
180C2×#385—51no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5C2×D414yes—
186C24×C5C2×Q814yes—
187C24×C5#4114yes—
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—232no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—28no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—28no—
209C22×C4×C5—28no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—28no—
215C22×C4×C5—28no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—28no—
219C22×C4×C5—28no—
220C22×C4×C5—44no—
221C22×C4×C5—44no—
222C22×C4×C5—416no—
223C22×C4×C5—416no—
224C22×C4×C5C2×D414yes—
225C22×C4×C5C2×D414yes—
226C22×C4×C5C2×D414yes—
227C22×C4×C5#4114yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C2×C22⋊D5—232no—
235C2×C22⋊D5—28no—
236C2×C22⋊D5—28no—
237C2×C22⋊D5C2×Q8116yescomplemented
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×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5C2×D414yes—
257C22×Dic5C2×D414yes—
258C22×Dic5C2×Q814yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C2×C4×D5—28no—
267C2×C4×D5—28no—
268C2×C4×D5—44no—
269C2×C4×D5—416no—
270C2×Dic10—28no—
271C2×Dic10—28no—
272C2×Dic10—44no—
273C2×Dic10—416no—
274C5×C4⋊C4—28no—
275C5×C4⋊C4—28no—
276C5×C4⋊C4—28no—
277C5×C4⋊C4C2×D4116yescomplemented
278C22⋊Dic5—28no—
279C22⋊Dic5—28no—
280C22⋊Dic5C2×D4116yes—
281#685—28no—
282#685—28no—
283#685—28no—
284#685—28no—
285#685—44no—
286C4⋊Dic5—28no—
287#683—28no—
288#683—28no—
289#683—28no—
290#683—28no—
291#683—28no—
292#683—28no—
293#683—44no—
294C4×Dic5—28no—
295C23×Q8—51no—
296C23×D4—51no—
297C24×C4—51no—
298C24×C4C2×D511yescharacteristic
299C24×C4C2×D511yescharacteristic
300C24×C4C2×D511yescharacteristic
301C2×C22⋊Q8—58no—
302C2×C22⋊Q8—58no—
303C2×C22⋊Q8—108no—
304C2×C22⋊Q8—108no—
305C2×C4×D4—58no—
306C2×C4×D4—108no—
307C22×C4⋊C4—28no—
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×C4⋊C4C2×D511yescharacteristic
320C22×C4⋊C4C2×D518yescomplemented
321C22×C22⋊C4—51no—
322C22×C22⋊C4—51no—
323C22×C22⋊C4—51no—
324C22×C22⋊C4—51no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C42—51no—
330#399—58no—
331#398—58no—
332#396—58no—
333#395—58no—
334#389—58no—
335#387—58no—
336#386—58no—
337#386—58no—
338#385—58no—
339#385—58no—
340#385—58no—
341C2×#95—51no—
342C2×#95—51no—
343C2×#95—51no—
344C2×#95—51no—
345C2×#95—51no—
346C2×#95—51no—
347C2×#95—51no—
348C2×#95—51no—
349C23×C5—28no—
350C23×C5—28no—
351C23×C5—28no—
352C23×C5—28no—
353C23×C5—28no—
354C23×C5—28no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5C22⋊Q8116yescomplemented
360C23×C5C22×D414yes—
361C23×C5C22×D412yes—
362C23×C5C22×D412yes—
363C23×C5C22×Q814yes—
364C23×C5C22×Q812yes—
365C23×C5C2×#4114yes—
366C23×C5C2×#4112yes—
367C23×C5C2×#4112yes—
368C23×C5H(5,𝔽2)12yes—
369C23×C52−1+412yes—
370C23×C5C2511yescharacteristic
371C22×D5—28no—
372C22×D5—28no—
373C22×D5—28no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—44no—
381C22×D5—44no—
382C22×D5—44no—
383C22×D5—44no—
384C22×D5C22×Q814yes—
385C2×C4×C5—232no—
386C2×C4×C5—28no—
387C2×C4×C5—28no—
388C2×C4×C5—28no—
389C2×C4×C5—28no—
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—22no—
404C2×C4×C5—416no—
405C2×C4×C5—416no—
406C2×C4×C5—44no—
407C2×C4×C5—44no—
408C2×C4×C5C22×D414yes—
409C2×C4×C5C22×D414yes—
410C2×C4×C5C22×D414yes—
411C2×C4×C5C2×#4114yes—
412C22⋊D5—232no—
413C2×Dic5—28no—
414C2×Dic5—28no—
415C2×Dic5—28no—
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—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—44no—
435C2×Dic5—44no—
436C2×Dic5—44no—
437C2×Dic5—44no—
438C2×Dic5C22×D414yes—
439C2×Dic5C22×D414yes—
440C2×Dic5C22×Q814yes—
441C4×D5—416no—
442Dic10—416no—
443C25—51no—
444C25C22×D511yescharacteristic
445C22×Q8—54no—
446C22×Q8—104no—
447C22×Q8—104no—
448C22×Q8—202no—
449C22×D4—58no—
450C22×D4—54no—
451C22×D4—104no—
452C22×D4—104no—
453C23×C4—24no—
454C23×C4—24no—
455C23×C4—24no—
456C23×C4—24no—
457C23×C4—24no—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—54no—
470C23×C4—104no—
471C23×C4—104no—
472C23×C4—202no—
473C23×C4C22×D514yes—
474C23×C4C22×D511yescharacteristic
475C23×C4C22×D511yescharacteristic
476C23×C4C22×D514yes—
477C23×C4C22×D514yes—
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C22⋊Q8—1032no—
483C22⋊Q8—1032no—
484C4×D4—1032no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—232no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—54no—
493C2×C4⋊C4—54no—
494C2×C4⋊C4—54no—
495C2×C4⋊C4—54no—
496C2×C4⋊C4—54no—
497C2×C4⋊C4—104no—
498C2×C4⋊C4—104no—
499C2×C4⋊C4—104no—
500C2×C4⋊C4—104no—
501C2×C4⋊C4—104no—
502C2×C4⋊C4—104no—
503C2×C4⋊C4—104no—
504C2×C4⋊C4—202no—
505C2×C4⋊C4C22⋊D518yescomplemented
506C2×C4⋊C4C22×D514yes—
507C2×C4⋊C4C22×D514yes—
508C2×C4⋊C4C22×D514yes—
509C2×C4⋊C4C22×D514yes—
510C2×C22⋊C4—58no—
511C2×C22⋊C4—54no—
512C2×C22⋊C4—54no—
513C2×C22⋊C4—54no—
514C2×C22⋊C4—54no—
515C2×C22⋊C4—54no—
516C2×C22⋊C4—54no—
517C2×C22⋊C4—54no—
518C2×C22⋊C4—54no—
519C2×C22⋊C4—104no—
520C2×C22⋊C4—104no—
521C2×C22⋊C4—104no—
522C2×C22⋊C4—104no—
523C2×C22⋊C4—104no—
524C2×C22⋊C4—104no—
525C2×C22⋊C4—202no—
526C2×C42—54no—
527C2×C42—104no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95—54no—
534#95—54no—
535#95—54no—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—24no—
542C22×C5—232no—
543C22×C5C2×C22⋊Q814yes—
544C22×C5C2×C22⋊Q818yescomplemented
545C22×C5#52514yes—
546C22×C5#53914yes—
547C22×C5D4214yes—
548C22×C5#54714yes—
549C22×C5D4×Q814yes—
550C22×C5#55414yes—
551C22×C5C23×D411yescharacteristic
552C22×C5C23×D411yescharacteristic
553C22×C5C23×Q811yescharacteristic
554C22×C5C22×#4111yescharacteristic
555C22×C5C22×#4111yescharacteristic
556C22×C5C2×H(5,𝔽2)11yescharacteristic
557C22×C5C2×2−1+411yescharacteristic
558C2×D5—24no—
559C2×D5—24no—
560C2×D5—24no—
561C2×D5—42no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—416no—
566C4×C5—24no—
567C4×C5—24no—
568C4×C5—24no—
569C4×C5—24no—
570C4×C5—42no—
571C4×C5—42no—
572Dic5—24no—
573Dic5—24no—
574Dic5—24no—
575Dic5—42no—
576Dic5—42no—
577Dic5—42no—
578Dic5—42no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—54no—
584C24—52no—
585C24—102no—
586C24—102no—
587C24—102no—
588C24—102no—
589C24—102no—
590C24—102no—
591C24#70914yes—
592C24D4×D514yes—
593C24Q8×D514yes—
594C24C23×D512yes—
595C24C23×D511yescharacteristic
596C2×Q8—108no—
597C2×Q8—108no—
598C2×Q8—204no—
599C2×Q8—2016no—
600C2×D4—516no—
601C2×D4—108no—
602C2×D4—108no—
603C2×D4—1032no—
604C22×C4—232no—
605C22×C4—28no—
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—28no—
615C22×C4—28no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—28no—
625C22×C4—28no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—416no—
629C22×C4—416no—
630C22×C4—54no—
631C22×C4—54no—
632C22×C4—54no—
633C22×C4—52no—
634C22×C4—52no—
635C22×C4—52no—
636C22×C4—52no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—108no—
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—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—108no—
660C22×C4—204no—
661C22×C4—2016no—
662C22×C4#70914yes—
663C22×C4C2×C22⋊D514yes—
664C22×C4C2×C22⋊D514yes—
665C22×C4C2×C22⋊D514yes—
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C22×C4C23×D512yes—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—28no—
675C4⋊C4—108no—
676C4⋊C4—108no—
677C4⋊C4—108no—
678C4⋊C4—108no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—108no—
682C4⋊C4—204no—
683C4⋊C4C2×C22⋊D5116yescomplemented
684C22⋊C4—516no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—204no—
692C42—108no—
693C2×C5—28no—
694C2×C5#244918yescomplemented
695C2×C5C22×C22⋊Q811yescharacteristic
696C2×C5C2×#52511yescharacteristic
697C2×C5C2×#53911yescharacteristic
698C2×C5C2×D4211yescharacteristic
699C2×C5C2×#54711yescharacteristic
700C2×C5C2×D4×Q811yescharacteristic
701C2×C5C2×#55411yescharacteristic
702D5—44no—
703C23—28no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
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—
727C23#4042116yescomplemented
728C23C2×#70914yes—
729C23C2×#70912yes—
730C23C2×#70912yes—
731C23C2×D4×D514yes—
732C23C2×D4×D512yes—
733C23#414412yes—
734C23C2×Q8×D514yes—
735C23C2×Q8×D512yes—
736C23#414712yes—
737C23C22×C22⋊D512yes—
738C23C24×D511yescharacteristic
739Q8—2016no—
740D4—1032no—
741C2×C4—232no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
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—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—416no—
761C2×C4—416no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—54no—
765C2×C4—54no—
766C2×C4—54no—
767C2×C4—108no—
768C2×C4—108no—
769C2×C4—108no—
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—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—2016no—
789C2×C4—204no—
790C2×C4—204no—
791C2×C4—204no—
792C2×C4—204no—
793C2×C4C2×#70914yes—
794C2×C4C22×C22⋊D514yes—
795C2×C4C22×C22⋊D514yes—
796C2×C4C22×C22⋊D514yes—
797C5C2×#244911yescharacteristic, complemented, Sylow
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—232no—
804C22—24no—
805C22—104no—
806C22—104no—
807C22—104no—
808C22—202no—
809C22—202no—
810C22—202no—
811C22—2016no—
812C22—202no—
813C22#6584114yes—
814C22C2×#404214yes—
815C22C2×#404218yescomplemented
816C22#6584514yes—
817C22#6584914yes—
818C22#6612514yes—
819C22D4×C22⋊D514yes—
820C22Q8×C22⋊D514yes—
821C22C22×#70911yescharacteristic
822C22C22×#70911yescharacteristic
823C22C22×D4×D511yescharacteristic
824C22C2×#414411yescharacteristic
825C22C22×Q8×D511yescharacteristic
826C22C2×#414711yescharacteristic
827C22C23×C22⋊D511yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—42no—
833C4—42no—
834C4—104no—
835C4—104no—
836C4—104no—
837C4—202no—
838C4—202no—
839C4—202no—
840C4—202no—
841C2—28no—
842C2—204no—
843C2#1061390418yesdirect product factor
844C2C2×#6584511yescharacteristic
845C2C22×#404211yescharacteristic
846C2C2×#6584911yescharacteristic
847C2C2×#6584111yescharacteristic
848C2C2×#6612511yescharacteristic
849C2C2×D4×C22⋊D511yescharacteristic
850C2C2×Q8×C22⋊D511yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC23×C5×C4⋊C4C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC23×C4⋊C4D5
hypocenterC5C2×#2449
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C5×C4⋊C4C2semidirect
2. C22×#4070C2semidirect
4. C22×#4042C2semidirect
7. C2×#65499C2semidirect
8. C2×#65499C2semidirect
9. C2×#65281C2semidirect
10. C2×#65283C2semidirect
11. C2×#65278C2semidirect
12. #10613904C2direct (N × H)
13. C2×#65269C2semidirect
14. C2×#65268C2semidirect
15. C2×#65261C2semidirect
16. C2×#65270C2semidirect
28. C22×C5×C4⋊C4C22semidirect
41. C2×#4070C22semidirect
51. C2×#4042C22semidirect
54. #65499C22semidirect
55. #65499C22semidirect
64. #65283C22semidirect
65. #65281C22semidirect
66. #65278C22semidirect
67. #65270C22semidirect
68. #65269C22semidirect
69. #65268C22semidirect
70. #65261C22semidirect
94. C22×C22⋊D5Q8semidirect
115. C2×C5×C4⋊C4D4semidirect
168. C23×C4⋊C4D5semidirect
237. C2×C22⋊D5C2×Q8semidirect
277. C5×C4⋊C4C2×D4semidirect
320. C22×C4⋊C4C2×D5semidirect
359. C23×C5C22⋊Q8semidirect
505. C2×C4⋊C4C22⋊D5semidirect
544. C22×C5C2×C22⋊Q8semidirect
683. C4⋊C4C2×C22⋊D5semidirect
694. C2×C5#2449semidirect
727. C23#4042semidirect
797. C5C2×#2449semidirect
815. C22C2×#4042semidirect
843. C2#10613904direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C4⋊C42
C22×#40702
C22×C4×C22⋊D52
C22×#40422
C2×#655022
C2×#654992
C2×#652812
C2×#652832
C2×#652782
#106139042
C2×#652692
C2×#652682
C2×#652612
C2×#652702
C2×#24495