Finite Group Databasebeta

← C2×#10606628 #12267036

Subgroups — C2×#10606628 #12267036

Order 1280.

3546 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4084C211yesmaximal, characteristic
2C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic, complemented
4C2×#65511C211yesmaximal, characteristic, complemented
5C2×#65500C211yesmaximal, characteristic, complemented
6C2×#65245C211yesmaximal, characteristic, complemented
7C2×#65245C211yesmaximal, characteristic, complemented
8C2×#65245C211yesmaximal, characteristic, complemented
9C2×#65242C211yesmaximal, characteristic, complemented
10C2×#65241C211yesmaximal, characteristic, complemented
11C2×#65240C211yesmaximal, characteristic, complemented
12#10606628C2116yesmaximal, direct product factor
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×D5×#95C211yesmaximal, characteristic, complemented
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64944C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C22⋊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
33C2×#4084—28no—
34C2×#4084C2218yes—
35C2×C4×C22⋊D5—28no—
36C2×C4×C22⋊D5C2218yescomplemented
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C5×#386C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47#65511C2218yescomplemented
48#65500C2218yescomplemented
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59#65245C2218yescomplemented
60#65245C2218yescomplemented
61#65245C2218yescomplemented
62#65242C2218yescomplemented
63#65241C2218yescomplemented
64#65240C2218yescomplemented
65#64957C2218yescomplemented
66D5×#95C2218yescomplemented
67#64949C2218yescomplemented
68#64944C2218yescomplemented
69C2×#2444—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—42no—
76C22×C5×D4C2314yes—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—42no—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2314yes—
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5D418yes—
92C22×C22⋊D5C2314yes—
93C22×C22⋊D5C2314yes—
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—42no—
107C22×C4×D5—42no—
108C22×C4×D5—42no—
109C22×C4×D5—42no—
110C22×C4×D5C2314yes—
111C22×C4×D5C2314yes—
112C22×C4×D5C2314yes—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4—42no—
115C2×C5×C22⋊C4—42no—
116C2×C5×C22⋊C4C2314yes—
117C2×C5×C22⋊C4C2314yes—
118C2×C5×C22⋊C4C2314yes—
119C2×C22⋊Dic5—24no—
120C2×C22⋊Dic5—24no—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5—42no—
123C2×C22⋊Dic5—42no—
124C2×C22⋊Dic5—42no—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131#4084—232no—
132C4×C22⋊D5—232no—
133C2×#685—24no—
134C2×#685—24no—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×C4⋊Dic5—24no—
138C2×C4⋊Dic5—42no—
139C2×C4⋊Dic5C2314yes—
140C2×C4⋊Dic5C2314yes—
141C2×#683—24no—
142C2×#683—24no—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×C4×Dic5—24no—
146C2×C4×Dic5C2314yes—
147C5×#95C2314yes—
148C5×#95C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#121—51no—
160C22×C4×D4—51no—
161#2444—516no—
162C2×#400—51no—
163C2×#397—51no—
164C2×#397—51no—
165C2×#394—51no—
166C2×#388—51no—
167C2×#387—51no—
168C2×#386—51no—
169C2×#386—51no—
170C2×#386—51no—
171C2×#386D511yescharacteristic, complemented
172C2×#385—51no—
173C2×#381—51no—
174C22×#95—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×C5C2×D414yes—
189C24×C5C2412yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5C2×D414yes—
197C23×D5#4114yes—
198C23×D5#4114yes—
199C23×D5C2412yes—
200C2×C5×D4—28no—
201C2×C5×D4—28no—
202C2×C5×D4—44no—
203C2×C5×D4—416no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—28no—
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—22no—
217C22×C4×C5—22no—
218C22×C4×C5—28no—
219C22×C4×C5—44no—
220C22×C4×C5—416no—
221C22×C4×C5#4114yes—
222C22×C4×C5#4114yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C2×C22⋊D5—232no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—28no—
231C2×C22⋊D5—28no—
232C2×C22⋊D5—28no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—416no—
235C2×C22⋊D5C2×D4116yes—
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×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5C2×D414yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C2×C4×D5—28no—
265C2×C4×D5—28no—
266C2×C4×D5—28no—
267C2×C4×D5—28no—
268C2×C4×D5—28no—
269C2×C4×D5—44no—
270C2×C4×D5—44no—
271C2×C4×D5—44no—
272C2×C4×D5—44no—
273C2×C4×D5—416no—
274C2×C4×D5—416no—
275C2×C4×D5—416no—
276C5×C22⋊C4—28no—
277C5×C22⋊C4—44no—
278C5×C22⋊C4—44no—
279C22⋊Dic5—28no—
280C22⋊Dic5—28no—
281C22⋊Dic5—28no—
282C22⋊Dic5—44no—
283C22⋊Dic5—44no—
284C22⋊Dic5—44no—
285#685—28no—
286#685—28no—
287C4⋊Dic5—28no—
288C4⋊Dic5—44no—
289#683—28no—
290#683—28no—
291C4×Dic5—28no—
292C23×D4—51no—
293C23×D4—51no—
294C23×D4C2×D511yescharacteristic
295C24×C4—51no—
296C24×C4—51no—
297C24×C4—51no—
298C24×C4C2×D511yescharacteristic
299C2×#121—58no—
300C2×#121—108no—
301C2×C4×D4—58no—
302C2×C4×D4—108no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊C4—51no—
306C22×C4⋊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⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319#400—58no—
320#397—58no—
321#397—58no—
322#394—58no—
323#388—58no—
324#387—58no—
325#386—58no—
326#386—58no—
327#386—58no—
328#386C2×D518yescomplemented
329#385—58no—
330#381—58no—
331C2×#95—51no—
332C2×#95—51no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—58no—
342C2×#95C2×D511yescharacteristic
343C2×#95C2×D511yescharacteristic
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—28no—
347C23×C5—22no—
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—44no—
361C23×C5—44no—
362C23×C5—44no—
363C23×C5—44no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5C22×D414yes—
372C23×C5C22×D412yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5C2×#4112yes—
377C23×C5H(5,𝔽2)12yes—
378C23×C5H(5,𝔽2)12yes—
379C23×C5C2511yescharacteristic
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—28no—
383C22×D5—28no—
384C22×D5—28no—
385C22×D5—28no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5#123116yes—
391C22×D5C22×D414yes—
392C22×D5C2×#4114yes—
393C22×D5C2×#4114yes—
394C5×D4—416no—
395C2×C4×C5—28no—
396C2×C4×C5—28no—
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—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—416no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5—44no—
414C2×C4×C5C2×#4114yes—
415C2×C4×C5C2×#4114yes—
416C22⋊D5—232no—
417C22⋊D5—416no—
418C2×Dic5—28no—
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—22no—
438C2×Dic5—22no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5—44no—
444C2×Dic5—44no—
445C2×Dic5C22×D414yes—
446C4×D5—416no—
447C4×D5—416no—
448C4×D5—416no—
449C25—51no—
450C25C22×D511yescharacteristic
451C25C22×D511yescharacteristic
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—42no—
455C22×D4—58no—
456C22×D4—54no—
457C22×D4—54no—
458C22×D4—104no—
459C22×D4—104no—
460C22×D4—104no—
461C22×D4—104no—
462C22×D4—104no—
463C22×D4C22×D514yes—
464C23×C4—24no—
465C23×C4—24no—
466C23×C4—42no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—51no—
474C23×C4—54no—
475C23×C4—54no—
476C23×C4—54no—
477C23×C4—104no—
478C23×C4—104no—
479C23×C4—104no—
480C23×C4—104no—
481C23×C4—104no—
482C23×C4—202no—
483C23×C4—202no—
484C23×C4—202no—
485C23×C4—202no—
486C23×C4C22×D511yescharacteristic
487C23×C4C22×D511yescharacteristic
488C23×C4C22×D511yescharacteristic
489C23×C4C22×D514yes—
490C23×C4C22×D511yescharacteristic
491C23×C4C22×D511yescharacteristic
492#121—1032no—
493C4×D4—1032no—
494C2×C4⋊C4—54no—
495C2×C4⋊C4—54no—
496C2×C4⋊C4—54no—
497C2×C4⋊C4—54no—
498C2×C4⋊C4—104no—
499C2×C4⋊C4—104no—
500C2×C4⋊C4—104no—
501C2×C4⋊C4—202no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
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—54no—
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⋊C4—202no—
521C2×C22⋊C4C22×D514yes—
522C2×C22⋊C4C22×D514yes—
523C2×C22⋊C4C22×D514yes—
524C2×C42—54no—
525C2×C42—104no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95—54no—
534#95—54no—
535#95—54no—
536#95C22×D514yes—
537#95C22×D514yes—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—416no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—42no—
553C22×C5—88no—
554C22×C5C2×#12314yes—
555C22×C5#52914yes—
556C22×C5#53814yes—
557C22×C5#54614yes—
558C22×C5#54614yes—
559C22×C5#55314yes—
560C22×C5#55314yes—
561C22×C5C23×D411yescharacteristic
562C22×C5C22×#4111yescharacteristic
563C22×C5C22×#4111yescharacteristic
564C22×C5C22×#4111yescharacteristic
565C22×C5C22×#4111yescharacteristic
566C22×C5C2×H(5,𝔽2)11yescharacteristic
567C22×C5C2×H(5,𝔽2)11yescharacteristic
568C2×D5—24no—
569C2×D5—24no—
570C2×D5—24no—
571C2×D5—24no—
572C2×D5—232no—
573C2×D5—24no—
574C2×D5—24no—
575C2×D5C2×#12318yes—
576C4×C5—24no—
577C4×C5—24no—
578C4×C5—42no—
579C4×C5—42no—
580C4×C5—42no—
581Dic5—24no—
582Dic5—42no—
583Dic5—42no—
584Dic5—42no—
585Dic5—42no—
586Dic5—42no—
587Dic5—42no—
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—54no—
602C24—54no—
603C24—54no—
604C24—52no—
605C24—102no—
606C24—102no—
607C24—102no—
608C24—102no—
609C24D4×D514yes—
610C24C23×D512yes—
611C24C23×D512yes—
612C24C23×D511yescharacteristic
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—44no—
616C2×D4—416no—
617C2×D4—516no—
618C2×D4—1032no—
619C2×D4—108no—
620C2×D4—108no—
621C2×D4—108no—
622C2×D4—108no—
623C2×D4—108no—
624C2×D4—2016no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—28no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—28no—
640C22×C4—44no—
641C22×C4—416no—
642C22×C4—54no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—108no—
651C22×C4—108no—
652C22×C4—108no—
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—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—108no—
674C22×C4—108no—
675C22×C4—204no—
676C22×C4—204no—
677C22×C4—204no—
678C22×C4—204no—
679C22×C4—2016no—
680C22×C4—2016no—
681C22×C4—2016no—
682C22×C4#70914yes—
683C22×C4#71114yes—
684C22×C4C23×D512yes—
685C22×C4C23×D512yes—
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C4⋊C4—108no—
690C4⋊C4—108no—
691C4⋊C4—108no—
692C4⋊C4—204no—
693C22⋊C4—28no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—108no—
697C22⋊C4—108no—
698C22⋊C4—108no—
699C22⋊C4—108no—
700C22⋊C4—108no—
701C22⋊C4—204no—
702C22⋊C4—204no—
703C22⋊C4—204no—
704C42—108no—
705C2×C5—44no—
706C2×C5—82no—
707C2×C5#244418yescomplemented
708C2×C5C22×#12311yescharacteristic
709C2×C5C2×#52911yescharacteristic
710C2×C5C2×#53811yescharacteristic
711C2×C5C2×#54611yescharacteristic
712C2×C5C2×#54611yescharacteristic
713C2×C5C2×#55311yescharacteristic
714C2×C5C2×#55311yescharacteristic
715D5—28no—
716C23—28no—
717C23—28no—
718C23—28no—
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—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—516no—
744C23—54no—
745C23—54no—
746C23—54no—
747C23—108no—
748C23—108no—
749C23—108no—
750C23—108no—
751C23—108no—
752C23—108no—
753C23—102no—
754C23—102no—
755C23—102no—
756C23—102no—
757C23C2×#70912yes—
758C23C2×D4×D514yes—
759C23C2×D4×D512yes—
760C23C2×#71112yes—
761C23#414412yes—
762C23#414412yes—
763C23D5×#4112yes—
764C23D5×#4112yes—
765C23C24×D511yescharacteristic
766D4—416no—
767D4—1032no—
768D4—2016no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—416no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—54no—
789C2×C4—108no—
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—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—2016no—
811C2×C4—2016no—
812C2×C4—2016no—
813C2×C4—204no—
814C2×C4—204no—
815C2×C4—204no—
816C2×C4—204no—
817C2×C4—204no—
818C2×C4—204no—
819C2×C4C2×#70914yes—
820C2×C4C2×#71114yes—
821C5C2×#244411yescharacteristic, complemented, Sylow
822C22—24no—
823C22—24no—
824C22—24no—
825C22—416no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—58no—
838C22—88no—
839C22—1032no—
840C22—104no—
841C22—104no—
842C22—104no—
843C22—104no—
844C22—104no—
845C22—104no—
846C22#6582414yes—
847C22#6589114yes—
848C22#6589214yes—
849C22#6592514yes—
850C22#6594714yes—
851C22#6594814yes—
852C22D5×#12314yes—
853C22C22×#70911yescharacteristic
854C22C22×D4×D511yescharacteristic
855C22C22×#71111yescharacteristic
856C22C2×#414411yescharacteristic
857C22C2×#414411yescharacteristic
858C22C2×D5×#4111yescharacteristic
859C22C2×D5×#4111yescharacteristic
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—104no—
866C4—202no—
867C4—202no—
868C4—202no—
869C4—202no—
870C4—202no—
871C4—202no—
872C2—44no—
873C2—82no—
874C2—108no—
875C2#1060662818yesdirect product factor
876C2C2×#6582411yescharacteristic
877C2C2×#6589111yescharacteristic
878C2C2×#6589211yescharacteristic
879C2C2×#6592511yescharacteristic
880C2C2×#6594711yescharacteristic
881C2C2×#6594811yescharacteristic
882C2C2×D5×#12311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC22×#4084C2
hypercenterC2×#386D5
hypocenterC5C2×#2444
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D5C2semidirect
3. C2×C5×#386C2semidirect
4. C2×#65511C2semidirect
5. C2×#65500C2semidirect
6. C2×#65245C2semidirect
7. C2×#65245C2semidirect
8. C2×#65245C2semidirect
9. C2×#65242C2semidirect
10. C2×#65241C2semidirect
11. C2×#65240C2semidirect
12. #10606628C2direct (N × H)
13. C2×#64957C2semidirect
14. C2×D5×#95C2semidirect
15. C2×#64949C2semidirect
16. C2×#64944C2semidirect
36. C2×C4×C22⋊D5C22semidirect
44. C5×#386C22semidirect
47. #65511C22semidirect
48. #65500C22semidirect
59. #65245C22semidirect
60. #65245C22semidirect
61. #65245C22semidirect
62. #65242C22semidirect
63. #65241C22semidirect
64. #65240C22semidirect
65. #64957C22semidirect
66. D5×#95C22semidirect
67. #64949C22semidirect
68. #64944C22semidirect
171. C2×#386D5semidirect
328. #386C2×D5semidirect
707. C2×C5#2444semidirect
821. C5C2×#2444semidirect
875. C2#10606628direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40842
C22×C4×C22⋊D52
C2×C5×#3862
C2×#655112
C2×#655002
C2×#652452
C2×#652422
C2×#652412
C2×#652402
#106066282
C2×#649572
C2×D5×#952
C2×#649492
C2×#649442
C2×#24445