Finite Group Databasebeta

← C2×#10613843 #12266906

Subgroups — C2×#10613843 #12266906

Order 1280.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C22⋊C4C211yesmaximal, characteristic
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×#65536C211yesmaximal, characteristic
4C2×#65536C211yesmaximal, characteristic
5C2×#65499C211yesmaximal, characteristic, complemented
6C2×#65499C211yesmaximal, characteristic, complemented
7C2×#65501C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
9#10613843C2116yesmaximal, direct product factor
10C2×#65242C211yesmaximal, characteristic, complemented
11C2×#65241C211yesmaximal, characteristic, complemented
12C2×#65241C211yesmaximal, characteristic, complemented
13C2×#65237C211yesmaximal, characteristic, complemented
14C2×#65234C211yesmaximal, characteristic, complemented
15C2×#65233C211yesmaximal, characteristic, complemented
16C2×#65240C211yesmaximal, characteristic, complemented
17C26×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C22×C5×C22⋊C4—28no—
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2218yes—
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C22×C22⋊Dic5C2211yescharacteristic
36C22×C22⋊Dic5C2211yescharacteristic
37C22×C22⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic, complemented
39C22×C4⋊Dic5C2211yescharacteristic, complemented
40C22×#683C2211yescharacteristic, complemented
41C22×#683C2211yescharacteristic, complemented
42C22×#683C2211yescharacteristic, complemented
43C22×#683C2211yescharacteristic, complemented
44C22×C4×Dic5C2211yescharacteristic, complemented
45C22×C4×Dic5C2211yescharacteristic, complemented
46C2×#4025—28no—
47C2×#4025C2218yescomplemented
48#65536C2218yes—
49#65536C2218yes—
50#65501C2218yescomplemented
51#65499C2218yescomplemented
52#65499C2218yescomplemented
53C4×C22⋊Dic5C2218yescomplemented
54C2×#3963C2211yescharacteristic, complemented
55C2×#3963C2211yescharacteristic, complemented
56C2×#3963C2211yescharacteristic, complemented
57C2×#3963C2211yescharacteristic, complemented
58C2×#3963C2211yescharacteristic, complemented
59C2×#3963C2211yescharacteristic, complemented
60C2×#3963C2211yescharacteristic, complemented
61C2×#3963C2211yescharacteristic, complemented
62#65242C2218yescomplemented
63#65241C2218yescomplemented
64#65241C2218yescomplemented
65#65240C2218yescomplemented
66#65237C2218yescomplemented
67#65234C2218yescomplemented
68#65233C2218yescomplemented
69C2×#2480—51nomaximal, Sylow
70C25×C5—24no—
71C25×C5—24no—
72C25×C5—24no—
73C25×C5—24no—
74C25×C5—24no—
75C25×C5—42no—
76C25×C5—42no—
77C25×C5C2311yescharacteristic
78C25×C5C2311yescharacteristic
79C25×C5C2314yes—
80C25×C5C2311yescharacteristic
81C23×C4×C5—24no—
82C23×C4×C5—24no—
83C23×C4×C5—24no—
84C23×C4×C5—24no—
85C23×C4×C5—42no—
86C23×C4×C5—42no—
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2314yes—
90C23×C4×C5C2314yes—
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C2×C5×C22⋊C4—24no—
102C2×C5×C22⋊C4—24no—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4—232no—
105C2×C5×C22⋊C4D418yes—
106C2×C5×C22⋊C4C2314yes—
107C2×C5×C22⋊C4C2314yes—
108C2×C5×C22⋊C4C2314yes—
109C2×C5×C22⋊C4C2314yes—
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—24no—
118C2×C22⋊Dic5—42no—
119C2×C22⋊Dic5—42no—
120C2×C22⋊Dic5—42no—
121C2×C22⋊Dic5—42no—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132C2×C22⋊Dic5C2314yes—
133C2×C22⋊Dic5C2314yes—
134C2×C4⋊Dic5—24no—
135C2×C4⋊Dic5—42no—
136C2×C4⋊Dic5C2314yescomplemented
137C2×C4⋊Dic5C2314yescomplemented
138C2×#683—24no—
139C2×#683—24no—
140C2×#683—42no—
141C2×#683—42no—
142C2×#683C2314yescomplemented
143C2×#683C2314yescomplemented
144C2×#683C2314yescomplemented
145C2×#683C2314yescomplemented
146C2×C4×Dic5—24no—
147C2×C4×Dic5—42no—
148C2×C4×Dic5C2314yescomplemented
149C2×C4×Dic5C2314yescomplemented
150#4025—232no—
151#3963C2314yescomplemented
152#3963C2314yescomplemented
153#3963C2314yescomplemented
154#3963C2314yescomplemented
155#3963C2314yescomplemented
156#3963C2314yescomplemented
157#3963C2314yescomplemented
158#3963C2314yescomplemented
159C22×#126—51no—
160C23×C22⋊C4D511yescharacteristic
161#2480—516no—
162C2×#397—51no—
163C2×#397—51no—
164C2×#397—51no—
165C2×#396—51no—
166C2×#388—51no—
167C2×#388—51no—
168C2×#388—51no—
169C2×#385—51no—
170C2×#385—51no—
171C2×#380—51no—
172C2×#379—51no—
173C2×#379—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—232no—
180C24×C5—28no—
181C24×C5—22no—
182C24×C5—28no—
183C24×C5—28no—
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×C5—28no—
196C24×C5—28no—
197C24×C5—44no—
198C24×C5—44no—
199C24×C5—416no—
200C24×C5—416no—
201C24×C5—416no—
202C24×C5—416no—
203C24×C5—416no—
204C24×C5—416no—
205C24×C5C2×D414yes—
206C24×C5#4114yes—
207C24×C5#4114yes—
208C24×C5#4114yes—
209C24×C5#4114yes—
210C24×C5C2412yes—
211C24×C5C2412yes—
212C24×C5C2412yes—
213C24×C5C2411yescharacteristic
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—28no—
221C22×C4×C5—28no—
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—44no—
230C22×C4×C5—416no—
231C22×C4×C5—416no—
232C22×C4×C5C2×D414yes—
233C22×C4×C5C2×D414yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
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×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C5×C22⋊C4—28no—
271C5×C22⋊C4—28no—
272C5×C22⋊C4—28no—
273C5×C22⋊C4C2×D4116yes—
274C22⋊Dic5—28no—
275C22⋊Dic5—28no—
276C22⋊Dic5—28no—
277C22⋊Dic5—28no—
278C22⋊Dic5—28no—
279C22⋊Dic5—28no—
280C22⋊Dic5—28no—
281C22⋊Dic5—28no—
282C22⋊Dic5—44no—
283C22⋊Dic5—44no—
284C22⋊Dic5—44no—
285C22⋊Dic5—44no—
286C4⋊Dic5—28no—
287C4⋊Dic5—44no—
288#683—28no—
289#683—28no—
290#683—44no—
291#683—44no—
292C4×Dic5—28no—
293C4×Dic5—44no—
294C26C2×D511yescharacteristic
295C24×C4C2×D511yescharacteristic
296C24×C4C2×D511yescharacteristic
297C2×#126—58no—
298C2×#126—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C22⋊C4—28no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4—51no—
315C22×C22⋊C4—51no—
316C22×C22⋊C4—51no—
317C22×C22⋊C4—51no—
318C22×C22⋊C4C2×D511yescharacteristic
319C22×C22⋊C4C2×D511yescharacteristic
320C22×C22⋊C4C2×D518yes—
321C22×C22⋊C4C2×D511yescharacteristic
322C22×C22⋊C4C2×D511yescharacteristic
323C22×C42—51no—
324C22×C42—51no—
325#397—58no—
326#397—58no—
327#397—58no—
328#396—58no—
329#388—58no—
330#388—58no—
331#388—58no—
332#385—58no—
333#385—58no—
334#380—58no—
335#379—58no—
336#379—58no—
337C4×C22⋊C4—58no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—51no—
342C2×#95—51no—
343C2×#95—51no—
344C2×#95—51no—
345C2×#95—51no—
346C23×C5—28no—
347C23×C5—28no—
348C23×C5—28no—
349C23×C5—28no—
350C23×C5—28no—
351C23×C5—28no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—232no—
357C23×C5—28no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—28no—
362C23×C5—28no—
363C23×C5—22no—
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—416no—
376C23×C5—416no—
377C23×C5—416no—
378C23×C5—416no—
379C23×C5—416no—
380C23×C5—4128no—
381C23×C5—44no—
382C23×C5—44no—
383C23×C5—416no—
384C23×C5—44no—
385C23×C5—44no—
386C23×C5—44no—
387C23×C5—44no—
388C23×C5—44no—
389C23×C5—44no—
390C23×C5#126116yescomplemented
391C23×C5C22×D414yes—
392C23×C5C22×D412yes—
393C23×C5C2×#4114yes—
394C23×C5C2×#4114yes—
395C23×C5C2×#4112yes—
396C23×C5C2×#4112yes—
397C23×C5C2×#4114yes—
398C23×C5C2×#4114yes—
399C23×C5C2×#4112yes—
400C23×C5C2×#4112yes—
401C23×C5H(5,𝔽2)12yes—
402C23×C5H(5,𝔽2)12yes—
403C23×C5C2511yescharacteristic
404C2×C4×C5—28no—
405C2×C4×C5—28no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—416no—
417C2×C4×C5—416no—
418C2×C4×C5—44no—
419C2×C4×C5—44no—
420C2×C4×C5C22×D414yes—
421C2×C4×C5C22×D414yes—
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—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—44no—
447C2×Dic5—44no—
448C2×Dic5—44no—
449C2×Dic5—44no—
450C2×Dic5—44no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C25—24no—
455C25—24no—
456C25—24no—
457C25—24no—
458C25—24no—
459C25—42no—
460C25—42no—
461C25C22×D511yescharacteristic
462C25C22×D511yescharacteristic
463C25C22×D514yes—
464C25C22×D511yescharacteristic
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—24no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—51no—
474C23×C4—51no—
475C23×C4—51no—
476C23×C4—51no—
477C23×C4—51no—
478C23×C4—51no—
479C23×C4C22×D511yescharacteristic
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D514yes—
482C23×C4C22×D514yes—
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485#126—1032no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—104no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4—202no—
496C2×C4⋊C4—202no—
497C2×C4⋊C4—202no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—232no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
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—54no—
513C2×C22⋊C4—54no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—104no—
516C2×C22⋊C4—104no—
517C2×C22⋊C4—104no—
518C2×C22⋊C4—104no—
519C2×C22⋊C4—104no—
520C2×C22⋊C4—104no—
521C2×C22⋊C4—104no—
522C2×C22⋊C4—202no—
523C2×C22⋊C4—202no—
524C2×C22⋊C4—202no—
525C2×C22⋊C4—202no—
526C2×C22⋊C4C22⋊D518yes—
527C2×C22⋊C4C22×D514yes—
528C2×C22⋊C4C22×D514yes—
529C2×C22⋊C4C22×D514yes—
530C2×C22⋊C4C22×D514yes—
531C2×C42—54no—
532C2×C42—54no—
533C2×C42—104no—
534C2×C42—202no—
535#95—54no—
536#95—54no—
537#95—54no—
538#95—54no—
539#95—54no—
540#95—54no—
541#95—54no—
542#95—54no—
543C22×C5—24no—
544C22×C5—24no—
545C22×C5—24no—
546C22×C5—24no—
547C22×C5—24no—
548C22×C5—24no—
549C22×C5—232no—
550C22×C5—24no—
551C22×C5—24no—
552C22×C5—24no—
553C22×C5—24no—
554C22×C5—24no—
555C22×C5—24no—
556C22×C5—464no—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—416no—
566C22×C5—416no—
567C22×C5#52514yes—
568C22×C5C2×#12614yes—
569C22×C5C2×#12618yescomplemented
570C22×C5#53814yes—
571C22×C5#54614yes—
572C22×C5#54614yes—
573C22×C5#55114yes—
574C22×C5#55114yes—
575C22×C5C23×D411yescharacteristic
576C22×C5C22×#4111yescharacteristic
577C22×C5C22×#4111yescharacteristic
578C22×C5C22×#4111yescharacteristic
579C22×C5C22×#4111yescharacteristic
580C22×C5C2×H(5,𝔽2)11yescharacteristic
581C22×C5C2×H(5,𝔽2)11yescharacteristic
582C4×C5—24no—
583C4×C5—24no—
584C4×C5—42no—
585C4×C5—42no—
586Dic5—42no—
587Dic5—42no—
588Dic5—42no—
589Dic5—42no—
590Dic5—42no—
591Dic5—42no—
592Dic5—42no—
593Dic5—42no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—232no—
599C24—28no—
600C24—28no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—28no—
613C24—22no—
614C24—28no—
615C24—28no—
616C24—44no—
617C24—44no—
618C24—416no—
619C24—416no—
620C24—416no—
621C24—416no—
622C24—416no—
623C24—416no—
624C24#70914yes—
625C24#70914yes—
626C24#71114yes—
627C24#71114yes—
628C24C2×C22⋊D514yes—
629C24C23×D512yes—
630C24C23×D512yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—416no—
650C22×C4—416no—
651C22×C4—52no—
652C22×C4—52no—
653C22×C4—52no—
654C22×C4—52no—
655C22×C4—52no—
656C22×C4—52no—
657C22×C4—52no—
658C22×C4—52no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—102no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—102no—
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×C4C2×C22⋊D514yes—
684C22×C4C2×C22⋊D514yes—
685C22×C4C23×D512yes—
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C4⋊C4—108no—
690C4⋊C4—108no—
691C4⋊C4—108no—
692C4⋊C4—204no—
693C4⋊C4—204no—
694C4⋊C4—204no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—108no—
699C22⋊C4—108no—
700C22⋊C4—108no—
701C22⋊C4—108no—
702C22⋊C4—108no—
703C22⋊C4—108no—
704C22⋊C4—108no—
705C22⋊C4—108no—
706C22⋊C4—204no—
707C22⋊C4—204no—
708C22⋊C4—204no—
709C22⋊C4—204no—
710C22⋊C4C2×C22⋊D5116yes—
711C42—108no—
712C42—204no—
713C2×C5—28no—
714C2×C5—44no—
715C2×C5—44no—
716C2×C5#248018yescomplemented
717C2×C5C2×#52511yescharacteristic
718C2×C5C22×#12611yescharacteristic
719C2×C5C2×#53811yescharacteristic
720C2×C5C2×#54611yescharacteristic
721C2×C5C2×#54611yescharacteristic
722C2×C5C2×#55111yescharacteristic
723C2×C5C2×#55111yescharacteristic
724C23—28no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—232no—
735C23—28no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—416no—
754C23—416no—
755C23—416no—
756C23—416no—
757C23—4128no—
758C23—416no—
759C23—44no—
760C23—44no—
761C23—416no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23#4025116yescomplemented
769C23C2×#70914yes—
770C23C2×#70914yes—
771C23C2×#70912yes—
772C23C2×#70912yes—
773C23C2×#71114yes—
774C23C2×#71114yes—
775C23C2×#71112yes—
776C23C2×#71112yes—
777C23#414412yes—
778C23#414412yes—
779C23C22×C22⋊D514yes—
780C23C22×C22⋊D512yes—
781C23C24×D511yescharacteristic
782C2×C4—28no—
783C2×C4—28no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—416no—
795C2×C4—416no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—102no—
811C2×C4—102no—
812C2×C4—102no—
813C2×C4—102no—
814C2×C4—102no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—204no—
823C2×C4—204no—
824C2×C4—204no—
825C2×C4—204no—
826C2×C4—204no—
827C2×C4—204no—
828C2×C4—204no—
829C2×C4—204no—
830C2×C4C22×C22⋊D514yes—
831C2×C4C22×C22⋊D514yes—
832C5C2×#248011yescharacteristic, complemented, Sylow
833C22—232no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—464no—
847C22—416no—
848C22—416no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22C2×#402514yes—
858C22C2×#402518yescomplemented
859C22#6582814yes—
860C22#6582914yes—
861C22#6582914yes—
862C22#6612514yes—
863C22#6614014yes—
864C22#6614014yes—
865C22C22×#70911yescharacteristic
866C22C22×#70911yescharacteristic
867C22C22×#71111yescharacteristic
868C22C22×#71111yescharacteristic
869C22C2×#414411yescharacteristic
870C22C2×#414411yescharacteristic
871C22C23×C22⋊D511yescharacteristic
872C4—24no—
873C4—24no—
874C4—42no—
875C4—42no—
876C4—202no—
877C4—202no—
878C4—202no—
879C4—202no—
880C4—202no—
881C4—202no—
882C4—202no—
883C4—202no—
884C2—28no—
885C2—44no—
886C2—44no—
887C2#1061384318yesdirect product factor
888C2C22×#402511yescharacteristic
889C2C2×#6582911yescharacteristic
890C2C2×#6582911yescharacteristic
891C2C2×#6582811yescharacteristic
892C2C2×#6612511yescharacteristic
893C2C2×#6614011yescharacteristic
894C2C2×#6614011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC23×C5×C22⋊C4C2
socleC24×C5C24
prime radicalC26×C5C22
hypercenterC23×C22⋊C4D5
hypocenterC5C2×#2480
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#4025C2semidirect
5. C2×#65499C2semidirect
6. C2×#65499C2semidirect
7. C2×#65501C2semidirect
8. C2×C4×C22⋊Dic5C2semidirect
9. #10613843C2direct (N × H)
10. C2×#65242C2semidirect
11. C2×#65241C2semidirect
12. C2×#65241C2semidirect
13. C2×#65237C2semidirect
14. C2×#65234C2semidirect
15. C2×#65233C2semidirect
16. C2×#65240C2semidirect
38. C22×C4⋊Dic5C22semidirect
39. C22×C4⋊Dic5C22semidirect
40. C22×#683C22semidirect
41. C22×#683C22semidirect
42. C22×#683C22semidirect
43. C22×#683C22semidirect
44. C22×C4×Dic5C22semidirect
45. C22×C4×Dic5C22semidirect
47. C2×#4025C22semidirect
50. #65501C22semidirect
51. #65499C22semidirect
52. #65499C22semidirect
53. C4×C22⋊Dic5C22semidirect
54. C2×#3963C22semidirect
55. C2×#3963C22semidirect
56. C2×#3963C22semidirect
57. C2×#3963C22semidirect
58. C2×#3963C22semidirect
59. C2×#3963C22semidirect
60. C2×#3963C22semidirect
61. C2×#3963C22semidirect
62. #65242C22semidirect
63. #65241C22semidirect
64. #65241C22semidirect
65. #65240C22semidirect
66. #65237C22semidirect
67. #65234C22semidirect
68. #65233C22semidirect
136. C2×C4⋊Dic5C23semidirect
137. C2×C4⋊Dic5C23semidirect
142. C2×#683C23semidirect
143. C2×#683C23semidirect
144. C2×#683C23semidirect
145. C2×#683C23semidirect
148. C2×C4×Dic5C23semidirect
149. C2×C4×Dic5C23semidirect
151. #3963C23semidirect
152. #3963C23semidirect
153. #3963C23semidirect
154. #3963C23semidirect
155. #3963C23semidirect
156. #3963C23semidirect
157. #3963C23semidirect
158. #3963C23semidirect
390. C23×C5#126semidirect
569. C22×C5C2×#126semidirect
716. C2×C5#2480semidirect
768. C23#4025semidirect
832. C5C2×#2480semidirect
858. C22C2×#4025semidirect
887. C2#10613843direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C22⋊C42
C22×#40252
C2×#655362
C2×#654992
C2×#655012
C2×C4×C22⋊Dic52
#106138432
C2×#652422
C2×#652412
C2×#652372
C2×#652342
C2×#652332
C2×#652402
C2×#24805