Finite Group Databasebeta

← C2×#10614391 #12267654

Subgroups — C2×#10614391 #12267654

Order 1280.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#121C211yesmaximal, characteristic
2C22×#4023C211yesmaximal, characteristic, complemented
3C2×#65511C211yesmaximal, characteristic, complemented
4C2×#65511C211yesmaximal, characteristic, complemented
5C2×#65511C211yesmaximal, characteristic, complemented
6C2×#65510C211yesmaximal, characteristic, complemented
7C2×#65509C211yesmaximal, characteristic, complemented
8C2×#65509C211yesmaximal, characteristic, complemented
9C2×#65499C211yesmaximal, characteristic, complemented
10C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
11#10614391C2116yesmaximal, direct product factor
12C2×#65273C211yesmaximal, characteristic, complemented
13C2×#65267C211yesmaximal, characteristic, complemented
14C2×#65234C211yesmaximal, characteristic, complemented
15C2×#65233C211yesmaximal, characteristic, complemented
16C2×#65240C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C23×C5×D4C2211yescharacteristic
20C24×C4×C5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C2×C5×#121—28no—
23C2×C5×#121C2218yes—
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
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
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4023—28no—
47C2×#4023C2218yescomplemented
48#65511C2218yescomplemented
49#65511C2218yescomplemented
50#65511C2218yescomplemented
51#65510C2218yescomplemented
52#65509C2218yescomplemented
53#65509C2218yescomplemented
54#65499C2218yescomplemented
55C4×C22⋊Dic5C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63C2×#3963C2211yescharacteristic
64#65273C2218yescomplemented
65#65267C2218yescomplemented
66#65240C2218yescomplemented
67#65234C2218yescomplemented
68#65233C2218yescomplemented
69C2×#2476—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C25×C5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—24no—
78C22×C5×D4—24no—
79C22×C5×D4—42no—
80C22×C5×D4—42no—
81C22×C5×D4—42no—
82C22×C5×D4C2314yes—
83C22×C5×D4C2314yes—
84C22×C5×D4C2314yes—
85C23×C4×C5—24no—
86C23×C4×C5—24no—
87C23×C4×C5—42no—
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2314yes—
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C23×Dic5—24no—
94C23×Dic5—24no—
95C23×Dic5—24no—
96C23×Dic5C2314yes—
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C5×#121—232no—
106C2×C5×C4⋊C4—24no—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4D418yes—
110C2×C5×C22⋊C4C2314yes—
111C2×C5×C22⋊C4C2314yes—
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⋊Dic5—42no—
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—42no—
135C2×C4⋊Dic5C2314yes—
136C2×#683—24no—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—42no—
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5—24no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5C2314yes—
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150#4023—232no—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#121D511yescharacteristic
160C22×#117—51no—
161#2476—516no—
162C2×#398—51no—
163C2×#394—51no—
164C2×#394—51no—
165C2×#394—51no—
166C2×#390—51no—
167C2×#388—51no—
168C2×#388—51no—
169C2×#388—51no—
170C2×#387—51no—
171C2×#386—51no—
172C2×#386—51no—
173C2×#385—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
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×C5C2×D414yes—
195C24×C5#4114yes—
196C24×C5C2412yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C2×C5×D4—28no—
201C2×C5×D4—28no—
202C2×C5×D4—28no—
203C2×C5×D4—28no—
204C2×C5×D4—28no—
205C2×C5×D4—28no—
206C2×C5×D4—44no—
207C2×C5×D4—44no—
208C2×C5×D4—44no—
209C2×C5×D4—416no—
210C2×C5×D4—416no—
211C2×C5×D4—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—28no—
222C22×C4×C5—28no—
223C22×C4×C5—44no—
224C22×C4×C5—416no—
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×Dic5—232no—
233C22×Dic5—28no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—28no—
239C22×Dic5—28no—
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#4114yes—
259C22×Dic5#4114yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C5×C4⋊C4—28no—
269C5×C22⋊C4—28no—
270C5×C22⋊C4C2×D4116yes—
271C22⋊Dic5—28no—
272C22⋊Dic5—28no—
273C22⋊Dic5—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—28no—
276C22⋊Dic5—28no—
277C22⋊Dic5—44no—
278C22⋊Dic5—44no—
279C22⋊Dic5—44no—
280C22⋊Dic5—44no—
281C22⋊Dic5—44no—
282C4⋊Dic5—44no—
283#683—28no—
284#683—28no—
285#683—28no—
286#683—44no—
287C4×Dic5—28no—
288C4×Dic5—28no—
289C4×Dic5—44no—
290C23×D4C2×D511yescharacteristic
291C23×D4C2×D511yescharacteristic
292C23×D4C2×D511yescharacteristic
293C24×C4—51no—
294C24×C4C2×D511yescharacteristic
295C2×#121—28no—
296C2×#121C2×D518yes—
297C2×#117—58no—
298C2×#117—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4C2×D511yescharacteristic
305C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320C22×C42—51no—
321#398—58no—
322#394—58no—
323#394—58no—
324#394—58no—
325#390—58no—
326#388—58no—
327#388—58no—
328#388—58no—
329#387—58no—
330#386—58no—
331#386—58no—
332#385—58no—
333C4×C22⋊C4—58no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—51no—
342C23×C5—28no—
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—28no—
347C23×C5—28no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5—44no—
372C23×C5—44no—
373C23×C5—44no—
374C23×C5—44no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5C22×D414yes—
383C23×C5C22×D412yes—
384C23×C5C2×#4114yes—
385C23×C5C2×#4112yes—
386C23×C5C2×#4112yes—
387C23×C5C2×#4112yes—
388C23×C5C2×#4112yes—
389C23×C5H(5,𝔽2)12yes—
390C23×C5H(5,𝔽2)12yes—
391C23×C5C2511yescharacteristic
392C5×D4—416no—
393C5×D4—416no—
394C5×D4—416no—
395C2×C4×C5—28no—
396C2×C4×C5—28no—
397C2×C4×C5—28no—
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—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—416no—
408C2×C4×C5—44no—
409C2×C4×C5C22×D414yes—
410C2×C4×C5C22×D414yes—
411C2×C4×C5C2×#4114yes—
412C2×Dic5—232no—
413C2×Dic5—28no—
414C2×Dic5—28no—
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—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5C2×#4114yes—
444C2×Dic5C2×#4114yes—
445C25C22×D511yescharacteristic
446C25C22×D511yescharacteristic
447C25C22×D511yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—42no—
455C22×D4—42no—
456C22×D4—42no—
457C22×D4C22×D514yes—
458C22×D4C22×D514yes—
459C22×D4C22×D514yes—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—42no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—54no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—104no—
473C23×C4—104no—
474C23×C4—104no—
475C23×C4C22×D511yescharacteristic
476C23×C4C22×D514yes—
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480#121—232no—
481#117—1032no—
482C2×C4⋊C4—24no—
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—202no—
492C2×C4⋊C4—202no—
493C2×C4⋊C4C22×D514yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—54no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—54no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—54no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—104no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—202no—
513C2×C22⋊C4—202no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4C22⋊D518yes—
518C2×C22⋊C4C22×D514yes—
519C2×C22⋊C4C22×D514yes—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—54no—
523C2×C42—104no—
524C2×C42—104no—
525C2×C42—202no—
526#95—54no—
527#95—54no—
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—24no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—416no—
549C22×C5—416no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—42no—
553C22×C5—42no—
554C22×C5—42no—
555C22×C5—42no—
556C22×C5—42no—
557C22×C5—88no—
558C22×C5#52514yes—
559C22×C5#52914yes—
560C22×C5#54014yes—
561C22×C5#54614yes—
562C22×C5#54614yes—
563C22×C5#55314yes—
564C22×C5#55514yes—
565C22×C5C23×D411yescharacteristic
566C22×C5C22×#4111yescharacteristic
567C22×C5C22×#4111yescharacteristic
568C22×C5C22×#4111yescharacteristic
569C22×C5C22×#4111yescharacteristic
570C22×C5C2×H(5,𝔽2)11yescharacteristic
571C22×C5C2×H(5,𝔽2)11yescharacteristic
572C4×C5—24no—
573C4×C5—24no—
574C4×C5—24no—
575C4×C5—42no—
576Dic5—24no—
577Dic5—24no—
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24#71114yes—
604C24C2×C22⋊D514yes—
605C24C23×D512yes—
606C24C23×D512yes—
607C24C23×D512yes—
608C24C23×D511yescharacteristic
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—416no—
619C2×D4—416no—
620C2×D4—416no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—44no—
633C22×C4—416no—
634C22×C4—54no—
635C22×C4—54no—
636C22×C4—52no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—52no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—108no—
645C22×C4—108no—
646C22×C4—1032no—
647C22×C4—102no—
648C22×C4—102no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—108no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
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#71114yes—
671C22×C4C2×C22⋊D514yes—
672C22×C4C2×C22⋊D514yes—
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C4⋊C4—28no—
678C4⋊C4—108no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—204no—
682C4⋊C4—204no—
683C22⋊C4—28no—
684C22⋊C4—108no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—204no—
691C22⋊C4—204no—
692C22⋊C4—204no—
693C22⋊C4—204no—
694C22⋊C4—204no—
695C22⋊C4C2×C22⋊D5116yes—
696C42—108no—
697C42—108no—
698C42—204no—
699C2×C5—44no—
700C2×C5—44no—
701C2×C5—82no—
702C2×C5#247618yescomplemented
703C2×C5C2×#52511yescharacteristic
704C2×C5C2×#52911yescharacteristic
705C2×C5C2×#54011yescharacteristic
706C2×C5C2×#54611yescharacteristic
707C2×C5C2×#54611yescharacteristic
708C2×C5C2×#55311yescharacteristic
709C2×C5C2×#55511yescharacteristic
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23C2×#71114yes—
751C23C2×#71112yes—
752C23C2×#71112yes—
753C23#414412yes—
754C23#414412yes—
755C23D5×#4112yes—
756C23D5×#4112yes—
757C23C22×C22⋊D514yes—
758C23C22×C22⋊D512yes—
759C23C24×D511yescharacteristic
760D4—416no—
761D4—416no—
762D4—416no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—416no—
776C2×C4—44no—
777C2×C4—54no—
778C2×C4—54no—
779C2×C4—1032no—
780C2×C4—108no—
781C2×C4—108no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—204no—
805C2×C4—204no—
806C2×C4—204no—
807C2×C4—204no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4C2×#71114yes—
811C2×C4C22×C22⋊D514yes—
812C2×C4C22×C22⋊D514yes—
813C5C2×#247611yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—416no—
822C22—416no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—88no—
838C22#6593414yes—
839C22#6593514yes—
840C22#6594914yes—
841C22#6595014yes—
842C22#6614014yes—
843C22#6614014yes—
844C22#6616214yes—
845C22C22×#71111yescharacteristic
846C22C22×#71111yescharacteristic
847C22C2×#414411yescharacteristic
848C22C2×#414411yescharacteristic
849C22C2×D5×#4111yescharacteristic
850C22C2×D5×#4111yescharacteristic
851C22C23×C22⋊D511yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—104no—
857C4—104no—
858C4—202no—
859C4—202no—
860C4—202no—
861C4—202no—
862C4—202no—
863C4—202no—
864C2—44no—
865C2—44no—
866C2—82no—
867C2#1061439118yesdirect product factor
868C2C2×#6593411yescharacteristic
869C2C2×#6594911yescharacteristic
870C2C2×#6593511yescharacteristic
871C2C2×#6595011yescharacteristic
872C2C2×#6614011yescharacteristic
873C2C2×#6614011yescharacteristic
874C2C2×#6616211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
Fitting, prime radicalC22×C5×#121C2
socleC24×C5C24
hypercenterC22×#121D5
hypocenterC5C2×#2476
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
2. C22×#4023C2semidirect
3. C2×#65511C2semidirect
4. C2×#65511C2semidirect
5. C2×#65511C2semidirect
6. C2×#65510C2semidirect
7. C2×#65509C2semidirect
8. C2×#65509C2semidirect
9. C2×#65499C2semidirect
10. C2×C4×C22⋊Dic5C2semidirect
11. #10614391C2direct (N × H)
12. C2×#65273C2semidirect
13. C2×#65267C2semidirect
14. C2×#65234C2semidirect
15. C2×#65233C2semidirect
16. C2×#65240C2semidirect
47. C2×#4023C22semidirect
48. #65511C22semidirect
49. #65511C22semidirect
50. #65511C22semidirect
51. #65510C22semidirect
52. #65509C22semidirect
53. #65509C22semidirect
54. #65499C22semidirect
55. C4×C22⋊Dic5C22semidirect
64. #65273C22semidirect
65. #65267C22semidirect
66. #65240C22semidirect
67. #65234C22semidirect
68. #65233C22semidirect
702. C2×C5#2476semidirect
813. C5C2×#2476semidirect
867. C2#10614391direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1212
C22×#40232
C2×#655112
C2×#655102
C2×#655092
C2×#654992
C2×C4×C22⋊Dic52
#106143912
C2×#652732
C2×#652672
C2×#652342
C2×#652332
C2×#652402
C2×#24765