Finite Group Databasebeta

← C2×#10614581 #12267410

Subgroups — C2×#10614581 #12267410

Order 1280.

3438 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#123C211yesmaximal, characteristic, complemented
2C22×#4027C211yesmaximal, characteristic, complemented
3C2×#65512C211yesmaximal, characteristic
4C2×#65509C211yesmaximal, characteristic, complemented
5C2×#65502C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
7#10614581C2116yesmaximal, direct product factor
8C2×#65276C211yesmaximal, characteristic, complemented
9C2×#65271C211yesmaximal, characteristic, complemented
10C2×#65279C211yesmaximal, characteristic, complemented
11C2×#65267C211yesmaximal, characteristic, complemented
12C2×#65248C211yesmaximal, characteristic, complemented
13C2×#65245C211yesmaximal, characteristic, complemented
14C2×#65237C211yesmaximal, characteristic, complemented
15C2×#65240C211yesmaximal, characteristic, complemented
16C2×#65232C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C2×C5×#123—28no—
24C2×C5×#123C2218yescomplemented
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4027—28no—
45C2×#4027C2218yescomplemented
46#65512C2218yes—
47#65509C2218yescomplemented
48#65502C2218yescomplemented
49C4×C22⋊Dic5C2218yescomplemented
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60#65279C2218yescomplemented
61#65276C2218yescomplemented
62#65271C2218yescomplemented
63#65267C2218yescomplemented
64#65248C2218yescomplemented
65#65245C2218yescomplemented
66#65240C2218yescomplemented
67#65237C2218yescomplemented
68#65232C2218yescomplemented
69C2×#2457—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⋊D5—42no—
92C22×C22⋊D5C2314yes—
93C22×C22⋊D5C2314yes—
94C23×Dic5—24no—
95C23×Dic5—24no—
96C23×Dic5—42no—
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2314yes—
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—42no—
108C22×C4×D5C2314yes—
109C5×#123—232no—
110C2×C5×C4⋊C4—24no—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4C2314yes—
113C2×C5×C4⋊C4C2314yes—
114C2×C5×C22⋊C4—24no—
115C2×C5×C22⋊C4—24no—
116C2×C5×C22⋊C4D418yescomplemented
117C2×C5×C22⋊C4C2314yes—
118C2×C5×C22⋊C4C2314yes—
119C2×C5×C22⋊C4C2314yes—
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×#685—24no—
131C2×#685—24no—
132C2×#685—42no—
133C2×#685—42no—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×C4⋊Dic5—42no—
139C2×C4⋊Dic5C2314yes—
140C2×#683—24no—
141C2×#683—24no—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5—42no—
146C2×C4×Dic5C2314yes—
147C2×C4×Dic5C2314yes—
148#4027—232no—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#123D511yescharacteristic, complemented
160C22×C4×D4—51no—
161#2457—516no—
162C2×#400—51no—
163C2×#396—51no—
164C2×#394—51no—
165C2×#392—51no—
166C2×#388—51no—
167C2×#388—51no—
168C2×#387—51no—
169C2×#386—51no—
170C2×#386—51no—
171C2×#386—51no—
172C2×#381—51no—
173C2×#380—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×C5C2×D414yes—
188C24×C5#4114yes—
189C24×C5C2412yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
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—28no—
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×C5C2×D414yes—
222C22×C4×C5C2×D414yes—
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—44no—
235C2×C22⋊D5—416no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—28no—
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—28no—
257C22×Dic5—44no—
258C22×Dic5—416no—
259C22×Dic5#4114yes—
260C22×Dic5#4114yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×C4×D5—28no—
269C2×C4×D5—28no—
270C2×C4×D5—44no—
271C2×C4×D5—416no—
272C5×C4⋊C4—28no—
273C5×C4⋊C4—28no—
274C5×C22⋊C4—28no—
275C5×C22⋊C4—28no—
276C5×C22⋊C4C2×D4116yescomplemented
277C22⋊Dic5—28no—
278C22⋊Dic5—28no—
279C22⋊Dic5—44no—
280C22⋊Dic5—44no—
281C22⋊Dic5—44no—
282#685—28no—
283#685—28no—
284#685—44no—
285#685—44no—
286C4⋊Dic5—44no—
287#683—28no—
288#683—28no—
289C4×Dic5—28no—
290C4×Dic5—44no—
291C23×D4—51no—
292C23×D4—51no—
293C23×D4C2×D511yescharacteristic
294C24×C4—51no—
295C24×C4—51no—
296C24×C4C2×D511yescharacteristic
297C2×#123—28no—
298C2×#123C2×D518yescomplemented
299C2×C4×D4—58no—
300C2×C4×D4—108no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4C2×D511yescharacteristic
305C22×C4⋊C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320#400—58no—
321#396—58no—
322#394—58no—
323#392—58no—
324#388—58no—
325#388—58no—
326#387—58no—
327#386—58no—
328#386—58no—
329#386—58no—
330#381—58no—
331#380—58no—
332C4×C22⋊C4—58no—
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—51no—
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—28no—
347C23×C5—28no—
348C23×C5—28no—
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—44no—
362C23×C5—44no—
363C23×C5—44no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5C22×D414yes—
370C23×C5C22×D412yes—
371C23×C5C2×#4114yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C5H(5,𝔽2)12yes—
378C23×C5C2511yescharacteristic
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5—44no—
392C22×D5C2×#4114yes—
393C5×D4—416no—
394C2×C4×C5—28no—
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—416no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5C22×D414yes—
414C2×C4×C5C22×D414yes—
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×Dic5C2×#4114yes—
445C2×Dic5C2×#4114yes—
446C4×D5—416no—
447C25—51no—
448C25C22×D511yescharacteristic
449C25C22×D511yescharacteristic
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4—54no—
454C22×D4—54no—
455C22×D4—104no—
456C22×D4—104no—
457C22×D4—104no—
458C22×D4—104no—
459C22×D4—104no—
460C22×D4—202no—
461C22×D4C22×D514yes—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—42no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—54no—
473C23×C4—54no—
474C23×C4—104no—
475C23×C4—104no—
476C23×C4—104no—
477C23×C4—104no—
478C23×C4—202no—
479C23×C4—202no—
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D514yes—
484C23×C4C22×D511yescharacteristic
485C23×C4C22×D511yescharacteristic
486#123—232no—
487C4×D4—1032no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—54no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4—202no—
496C2×C4⋊C4C22×D514yes—
497C2×C4⋊C4C22×D514yes—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
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—54no—
507C2×C22⋊C4—54no—
508C2×C22⋊C4—54no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—202no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4C22⋊D518yescomplemented
519C2×C22⋊C4C22×D514yes—
520C2×C22⋊C4C22×D514yes—
521C2×C22⋊C4C22×D514yes—
522C2×C42—54no—
523C2×C42—54no—
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—
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—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—416no—
551C22×C5—416no—
552C22×C5#52514yes—
553C22×C5#52914yes—
554C22×C5#54014yes—
555C22×C5#54614yes—
556C22×C5#54614yes—
557C22×C5#55114yes—
558C22×C5#55314yes—
559C22×C5C23×D411yescharacteristic
560C22×C5C22×#4111yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C22×#4111yescharacteristic
563C22×C5C22×#4111yescharacteristic
564C22×C5C2×H(5,𝔽2)11yescharacteristic
565C22×C5C2×H(5,𝔽2)11yescharacteristic
566C2×D5—24no—
567C2×D5—24no—
568C2×D5—24no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—42no—
572C2×D5—42no—
573C2×D5—416no—
574C4×C5—24no—
575C4×C5—24no—
576C4×C5—42no—
577C4×C5—42no—
578C4×C5—42no—
579Dic5—24no—
580Dic5—24no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584Dic5—42no—
585Dic5—42no—
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—54no—
599C24—52no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24#71114yes—
607C24C2×C22⋊D514yes—
608C24C23×D512yes—
609C24C23×D512yes—
610C24C23×D511yescharacteristic
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—44no—
614C2×D4—416no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—1032no—
618C2×D4—108no—
619C2×D4—108no—
620C2×D4—108no—
621C2×D4—204no—
622C2×D4—2016no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—28no—
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—28no—
638C22×C4—44no—
639C22×C4—416no—
640C22×C4—54no—
641C22×C4—54no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—108no—
650C22×C4—108no—
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—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—108no—
671C22×C4—108no—
672C22×C4—204no—
673C22×C4—2016no—
674C22×C4—204no—
675C22×C4—2016no—
676C22×C4C2×C22⋊D514yes—
677C22×C4C2×C22⋊D514yes—
678C22×C4C23×D512yes—
679C22×C4C23×D512yes—
680C22×C4C23×D512yes—
681C22×C4C23×D512yes—
682C22×C4C23×D512yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—108no—
686C4⋊C4—108no—
687C4⋊C4—204no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—204no—
695C22⋊C4—204no—
696C22⋊C4—204no—
697C22⋊C4—204no—
698C22⋊C4—204no—
699C22⋊C4C2×C22⋊D5116yescomplemented
700C42—108no—
701C42—204no—
702C2×C5—44no—
703C2×C5—44no—
704C2×C5#245718yescomplemented
705C2×C5C2×#52511yescharacteristic
706C2×C5C2×#52911yescharacteristic
707C2×C5C2×#54011yescharacteristic
708C2×C5C2×#54611yescharacteristic
709C2×C5C2×#54611yescharacteristic
710C2×C5C2×#55111yescharacteristic
711C2×C5C2×#55311yescharacteristic
712D5—44no—
713C23—28no—
714C23—28no—
715C23—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—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—54no—
740C23—108no—
741C23—108no—
742C23—108no—
743C23—102no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—204no—
750C23—204no—
751C23—204no—
752C23—204no—
753C23C2×#71114yes—
754C23C2×#71112yes—
755C23#414412yes—
756C23D5×#4112yes—
757C23D5×#4112yes—
758C23D5×#4112yes—
759C23#414912yes—
760C23C22×C22⋊D514yes—
761C23C22×C22⋊D512yes—
762C23C24×D511yescharacteristic
763D4—416no—
764D4—1032no—
765D4—2016no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—22no—
769C2×C4—22no—
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—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—54no—
786C2×C4—54no—
787C2×C4—108no—
788C2×C4—108no—
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—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
808C2×C4—2016no—
809C2×C4—2016no—
810C2×C4—204no—
811C2×C4—204no—
812C2×C4—204no—
813C2×C4—204no—
814C2×C4—204no—
815C2×C4C22×C22⋊D514yes—
816C2×C4C22×C22⋊D514yes—
817C5C2×#245711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—416no—
832C22—416no—
833C22—42no—
834C22—104no—
835C22—104no—
836C22—104no—
837C22—202no—
838C22—202no—
839C22—202no—
840C22—2016no—
841C22—202no—
842C22#6598314yes—
843C22#6599214yes—
844C22#6599514yes—
845C22#6599714yes—
846C22#6614014yes—
847C22#6616214yes—
848C22#6616314yes—
849C22C22×#71111yescharacteristic
850C22C2×#414411yescharacteristic
851C22C2×D5×#4111yescharacteristic
852C22C2×D5×#4111yescharacteristic
853C22C2×D5×#4111yescharacteristic
854C22C2×#414911yescharacteristic
855C22C23×C22⋊D511yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—104no—
862C4—104no—
863C4—202no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C2—44no—
869C2—44no—
870C2—204no—
871C2#1061458118yesdirect product factor
872C2C2×#6598311yescharacteristic
873C2C2×#6599711yescharacteristic
874C2C2×#6599511yescharacteristic
875C2C2×#6599211yescharacteristic
876C2C2×#6614011yescharacteristic
877C2C2×#6616211yescharacteristic
878C2C2×#6616311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#123C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC22×#123D5
hypocenterC5C2×#2457
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C5×#123C2semidirect
2. C22×#4027C2semidirect
4. C2×#65509C2semidirect
5. C2×#65502C2semidirect
6. C2×C4×C22⋊Dic5C2semidirect
7. #10614581C2direct (N × H)
8. C2×#65276C2semidirect
9. C2×#65271C2semidirect
10. C2×#65279C2semidirect
11. C2×#65267C2semidirect
12. C2×#65248C2semidirect
13. C2×#65245C2semidirect
14. C2×#65237C2semidirect
15. C2×#65240C2semidirect
16. C2×#65232C2semidirect
24. C2×C5×#123C22semidirect
45. C2×#4027C22semidirect
47. #65509C22semidirect
48. #65502C22semidirect
49. C4×C22⋊Dic5C22semidirect
60. #65279C22semidirect
61. #65276C22semidirect
62. #65271C22semidirect
63. #65267C22semidirect
64. #65248C22semidirect
65. #65245C22semidirect
66. #65240C22semidirect
67. #65237C22semidirect
68. #65232C22semidirect
116. C2×C5×C22⋊C4D4semidirect
159. C22×#123D5semidirect
276. C5×C22⋊C4C2×D4semidirect
298. C2×#123C2×D5semidirect
518. C2×C22⋊C4C22⋊D5semidirect
699. C22⋊C4C2×C22⋊D5semidirect
704. C2×C5#2457semidirect
817. C5C2×#2457semidirect
871. C2#10614581direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1232
C22×#40272
C2×#655122
C2×#655092
C2×#655022
C2×C4×C22⋊Dic52
#106145812
C2×#652762
C2×#652712
C2×#652792
C2×#652672
C2×#652482
C2×#652452
C2×#652372
C2×#652402
C2×#652322
C2×#24575