Finite Group Databasebeta

← C2×#10608849 #12267035

Subgroups — C2×#10608849 #12267035

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×#4027C211yesmaximal, characteristic, complemented
3C2×C5×#394C211yesmaximal, characteristic, complemented
4C2×#65509C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65270C211yesmaximal, characteristic, complemented
7C2×#65245C211yesmaximal, characteristic, complemented
8C2×#65245C211yesmaximal, characteristic, complemented
9C2×#65245C211yesmaximal, characteristic, complemented
10C2×#65241C211yesmaximal, characteristic, complemented
11C2×#65241C211yesmaximal, characteristic, complemented
12C2×#65234C211yesmaximal, characteristic, complemented
13C2×#65232C211yesmaximal, characteristic, complemented
14#10608849C2116yesmaximal, direct product factor
15C2×D5×#95C211yesmaximal, characteristic, complemented
16C2×#64949C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C2×#4084—28no—
35C2×#4084C2218yes—
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4027—28no—
43C2×#4027C2218yescomplemented
44C5×#394C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46#65509C2218yescomplemented
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65278C2218yescomplemented
59#65270C2218yescomplemented
60#65245C2218yescomplemented
61#65245C2218yescomplemented
62#65245C2218yescomplemented
63#65241C2218yescomplemented
64#65241C2218yescomplemented
65#65234C2218yescomplemented
66#65232C2218yescomplemented
67D5×#95C2218yescomplemented
68#64949C2218yescomplemented
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×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5D418yes—
88C22×C22⋊D5C2314yes—
89C22×C22⋊D5C2314yes—
90C23×Dic5—24no—
91C23×Dic5—24no—
92C23×Dic5—42no—
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2314yes—
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×C4⋊C4—24no—
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C22⋊C4—24no—
116C2×C5×C22⋊C4—42no—
117C2×C5×C22⋊C4—42no—
118C2×C5×C22⋊C4—42no—
119C2×C5×C22⋊C4C2314yes—
120C2×C5×C22⋊C4C2314yes—
121C2×C5×C22⋊C4C2314yes—
122C2×C5×C22⋊C4C2314yes—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5—24no—
126C2×C22⋊Dic5—42no—
127C2×C22⋊Dic5—42no—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132C2×C22⋊Dic5C2314yes—
133#4084—232no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×C4⋊Dic5—24no—
139C2×C4⋊Dic5C2314yes—
140C2×#683—24no—
141C2×#683—42no—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5C2314yes—
146#4027—232no—
147C5×#95C2314yes—
148#3963C2314yes—
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×#394D511yescharacteristic, complemented
166C2×#388—51no—
167C2×#387—51no—
168C2×#386—51no—
169C2×#386—51no—
170C2×#386—51no—
171C2×#386—51no—
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—22no—
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#4114yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C2×C22⋊D5—232no—
225C2×C22⋊D5—28no—
226C2×C22⋊D5—28no—
227C2×C22⋊D5—28no—
228C2×C22⋊D5—28no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—416no—
231C2×C22⋊D5C2×D4116yes—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—28no—
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—28no—
253C22×Dic5—44no—
254C22×Dic5—416no—
255C22×Dic5C2×D414yes—
256C22×Dic5#4114yes—
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×C4⋊C4—28no—
277C5×C22⋊C4—28no—
278C5×C22⋊C4—44no—
279C5×C22⋊C4—44no—
280C5×C22⋊C4—44no—
281C22⋊Dic5—28no—
282C22⋊Dic5—28no—
283C22⋊Dic5—28no—
284C22⋊Dic5—44no—
285C22⋊Dic5—44no—
286#685—28no—
287#685—28no—
288C4⋊Dic5—28no—
289#683—28no—
290#683—44no—
291C4×Dic5—28no—
292C23×D4—51no—
293C23×D4—51no—
294C23×D4C2×D511yescharacteristic
295C24×C4—51no—
296C24×C4—51no—
297C24×C4—51no—
298C24×C4—51no—
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⋊C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
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#394C2×D518yescomplemented
323#388—58no—
324#387—58no—
325#386—58no—
326#386—58no—
327#386—58no—
328#386—58no—
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—51no—
342C2×#95—58no—
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—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—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5—44no—
414C2×C4×C5C2×#4114yes—
415C22⋊D5—232no—
416C22⋊D5—416no—
417C2×Dic5—28no—
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—416no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5—44no—
444C2×Dic5C22×D414yes—
445C2×Dic5C2×#4114yes—
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—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—54no—
472C23×C4—54no—
473C23×C4—54no—
474C23×C4—54no—
475C23×C4—104no—
476C23×C4—104no—
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×C4—202no—
487C23×C4C22×D511yescharacteristic
488C23×C4C22×D511yescharacteristic
489C23×C4C22×D511yescharacteristic
490C23×C4C22×D511yescharacteristic
491C23×C4C22×D511yescharacteristic
492#121—1032no—
493C4×D4—1032no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—54no—
496C2×C4⋊C4—54no—
497C2×C4⋊C4—54no—
498C2×C4⋊C4—104no—
499C2×C4⋊C4—104no—
500C2×C4⋊C4—202no—
501C2×C4⋊C4C22×D514yes—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
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⋊C4C22×D514yes—
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#95—54no—
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—42no—
578C4×C5—42no—
579C4×C5—42no—
580C4×C5—42no—
581Dic5—24no—
582Dic5—24no—
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—22no—
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—54no—
640C22×C4—54no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—108no—
649C22×C4—108no—
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—108no—
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—204no—
675C22×C4—204no—
676C22×C4—204no—
677C22×C4—204no—
678C22×C4—2016no—
679C22×C4—2016no—
680C22×C4—2016no—
681C22×C4—204no—
682C22×C4—2016no—
683C22×C4#71114yes—
684C22×C4C23×D512yes—
685C22×C4C23×D512yes—
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C4⋊C4—28no—
690C4⋊C4—108no—
691C4⋊C4—108no—
692C4⋊C4—204no—
693C22⋊C4—28no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—108no—
698C22⋊C4—108no—
699C22⋊C4—108no—
700C22⋊C4—108no—
701C22⋊C4—108no—
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×D4×D514yes—
758C23C2×D4×D512yes—
759C23C2×#71112yes—
760C23#414412yes—
761C23#414412yes—
762C23D5×#4112yes—
763C23D5×#4112yes—
764C23D5×#4112yes—
765C23C24×D511yescharacteristic
766D4—416no—
767D4—1032no—
768D4—2016no—
769C2×C4—28no—
770C2×C4—22no—
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—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—54no—
789C2×C4—54no—
790C2×C4—108no—
791C2×C4—108no—
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—102no—
811C2×C4—2016no—
812C2×C4—2016no—
813C2×C4—2016no—
814C2×C4—2016no—
815C2×C4—204no—
816C2×C4—204no—
817C2×C4—204no—
818C2×C4—204no—
819C2×C4—204no—
820C2×C4C2×#71114yes—
821C5C2×#244411yescharacteristic, complemented, Sylow
822C22—24no—
823C22—24no—
824C22—24no—
825C22—42no—
826C22—42no—
827C22—416no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—58no—
838C22—88no—
839C22—104no—
840C22—104no—
841C22—1032no—
842C22—104no—
843C22—104no—
844C22—104no—
845C22—104no—
846C22#6592514yes—
847C22#6594414yes—
848C22#6594714yes—
849C22#6594814yes—
850C22D5×#12314yes—
851C22#6599514yes—
852C22#6601414yes—
853C22C22×D4×D511yescharacteristic
854C22C22×#71111yescharacteristic
855C22C2×#414411yescharacteristic
856C22C2×#414411yescharacteristic
857C22C2×D5×#4111yescharacteristic
858C22C2×D5×#4111yescharacteristic
859C22C2×D5×#4111yescharacteristic
860C4—24no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—104no—
866C4—104no—
867C4—202no—
868C4—202no—
869C4—202no—
870C4—202no—
871C4—202no—
872C2—44no—
873C2—82no—
874C2—108no—
875C2#1060884918yesdirect product factor
876C2C2×#6592511yescharacteristic
877C2C2×#6594711yescharacteristic
878C2C2×#6594411yescharacteristic
879C2C2×#6594811yescharacteristic
880C2C2×#6599511yescharacteristic
881C2C2×D5×#12311yescharacteristic
882C2C2×#6601411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#394C2
socleC24×C5C24
prime radicalC22×#4084C2
hypercenterC2×#394D5
hypocenterC5C2×#2444
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#4027C2semidirect
3. C2×C5×#394C2semidirect
4. C2×#65509C2semidirect
5. C2×#65278C2semidirect
6. C2×#65270C2semidirect
7. C2×#65245C2semidirect
8. C2×#65245C2semidirect
9. C2×#65245C2semidirect
10. C2×#65241C2semidirect
11. C2×#65241C2semidirect
12. C2×#65234C2semidirect
13. C2×#65232C2semidirect
14. #10608849C2direct (N × H)
15. C2×D5×#95C2semidirect
16. C2×#64949C2semidirect
43. C2×#4027C22semidirect
44. C5×#394C22semidirect
46. #65509C22semidirect
58. #65278C22semidirect
59. #65270C22semidirect
60. #65245C22semidirect
61. #65245C22semidirect
62. #65245C22semidirect
63. #65241C22semidirect
64. #65241C22semidirect
65. #65234C22semidirect
66. #65232C22semidirect
67. D5×#95C22semidirect
68. #64949C22semidirect
165. C2×#394D5semidirect
322. #394C2×D5semidirect
707. C2×C5#2444semidirect
821. C5C2×#2444semidirect
875. C2#10608849direct (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×#40272
C2×C5×#3942
C2×#655092
C2×#652782
C2×#652702
C2×#652452
C2×#652412
C2×#652342
C2×#652322
#106088492
C2×D5×#952
C2×#649492
C2×#24445