Finite Group Databasebeta

← C2×#10606456 #12267872

Subgroups — C2×#10606456 #12267872

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×#4072C211yesmaximal, characteristic, complemented
2C22×#4032C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic, complemented
4C2×#65512C211yesmaximal, characteristic
5C2×#65509C211yesmaximal, characteristic, complemented
6C2×#65502C211yesmaximal, characteristic, complemented
7C2×#65238C211yesmaximal, characteristic, complemented
8C2×#65237C211yesmaximal, characteristic, complemented
9C2×#65246C211yesmaximal, characteristic, complemented
10C2×#65246C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12#10606456C2116yesmaximal, direct product factor
13C2×#64963C211yesmaximal, characteristic, complemented
14C2×#64958C211yesmaximal, characteristic, complemented
15C2×#64944C211yesmaximal, characteristic, complemented
16C2×#64942C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C2×#4072—28no—
36C2×#4072C2218yescomplemented
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4032—28no—
47C2×#4032C2218yescomplemented
48C5×#386C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51#65512C2218yes—
52#65509C2218yescomplemented
53#65502C2218yescomplemented
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60#65246C2218yescomplemented
61#65246C2218yescomplemented
62#65238C2218yescomplemented
63#65237C2218yescomplemented
64C22⋊C4×Dic5C2218yescomplemented
65#64963C2218yescomplemented
66#64958C2218yescomplemented
67#64944C2218yescomplemented
68#64942C2218yescomplemented
69C2×#2471—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—24no—
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—42no—
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×Dic5C2314yes—
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C2×C5×C22⋊C4—24no—
106C2×C5×C22⋊C4—24no—
107C2×C5×C22⋊C4—42no—
108C2×C5×C22⋊C4C2314yes—
109C2×C5×C22⋊C4C2314yes—
110C2×C5×C22⋊C4C2314yes—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—42no—
115C2×C22⋊Dic5—42no—
116C2×C22⋊Dic5C2314yes—
117C2×C22⋊Dic5C2314yes—
118C2×C22⋊Dic5C2314yes—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—42no—
125C2×#685—42no—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131#4072—232no—
132C2×C4⋊Dic5—24no—
133C2×C4⋊Dic5—24no—
134C2×C4⋊Dic5D418yescomplemented
135C2×C4⋊Dic5C2314yes—
136C2×C4⋊Dic5C2314yes—
137C2×C4⋊Dic5C2314yes—
138C2×#683—24no—
139C2×#683—42no—
140C2×#683—42no—
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#4032—232no—
151C5×#95C2314yes—
152C5×#95C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#123—51no—
160C22×#117—51no—
161#2471—516no—
162C2×#399—51no—
163C2×#397—51no—
164C2×#396—51no—
165C2×#392—51no—
166C2×#390—51no—
167C2×#390—51no—
168C2×#388—51no—
169C2×#387—51no—
170C2×#387—51no—
171C2×#386—51no—
172C2×#386—51no—
173C2×#386D511yescharacteristic, complemented
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#4114yes—
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—22no—
199C23×D5C2412yes—
200C2×C5×D4—28no—
201C2×C5×D4—28no—
202C2×C5×D4—44no—
203C2×C5×D4—416no—
204C22×C4×C5—232no—
205C22×C4×C5—22no—
206C22×C4×C5—28no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—28no—
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—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5C2×D414yes—
222C22×C4×C5#4114yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C2×C22⋊D5—28no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—28no—
231C2×C22⋊D5—28no—
232C2×C22⋊D5—44no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—416no—
235C2×C22⋊D5—416no—
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—28no—
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—28no—
256C22×Dic5—44no—
257C22×Dic5—416no—
258C22×Dic5C2×D414yes—
259C22×Dic5C2×D414yes—
260C22×Dic5#4114yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C5×C22⋊C4—28no—
269C5×C22⋊C4—28no—
270C5×C22⋊C4—44no—
271C22⋊Dic5—28no—
272C22⋊Dic5—28no—
273C22⋊Dic5—28no—
274C22⋊Dic5—44no—
275C22⋊Dic5—44no—
276#685—28no—
277#685—28no—
278#685—28no—
279#685—44no—
280#685—44no—
281C4⋊Dic5—28no—
282C4⋊Dic5—28no—
283C4⋊Dic5C2×D4116yescomplemented
284#683—28no—
285#683—44no—
286#683—44no—
287C4×Dic5—28no—
288C4×Dic5—28no—
289C4×Dic5—44no—
290C23×D4—51no—
291C23×D4—51no—
292C23×D4C2×D511yescharacteristic
293C24×C4—51no—
294C24×C4C2×D511yescharacteristic
295C2×#123—58no—
296C2×#123—108no—
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⋊C4—51no—
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⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320C22×C42—51no—
321#399—58no—
322#397—58no—
323#396—58no—
324#392—58no—
325#390—58no—
326#390—58no—
327#388—58no—
328#387—58no—
329#387—58no—
330#386—58no—
331#386—58no—
332#386C2×D518yescomplemented
333C4×C22⋊C4—58no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95C2×D511yescharacteristic
341C2×#95C2×D511yescharacteristic
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—44no—
361C23×C5—44no—
362C23×C5—44no—
363C23×C5—44no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5C22×D412yes—
369C23×C5C2×#4114yes—
370C23×C5C2×#4112yes—
371C23×C5C2×#4114yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5H(5,𝔽2)12yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C5C2511yescharacteristic
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5—44no—
392C5×D4—416no—
393C2×C4×C5—232no—
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—44no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5C22×D414yes—
413C2×C4×C5C2×#4114yes—
414C22⋊D5—416no—
415C22⋊D5—416no—
416C2×Dic5—28no—
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—416no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5C22×D414yes—
443C2×Dic5C22×D414yes—
444C2×Dic5C2×#4114yes—
445C25—51no—
446C25C22×D511yescharacteristic
447C25C22×D511yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—42no—
451C22×D4—54no—
452C22×D4—54no—
453C22×D4—104no—
454C22×D4—104no—
455C22×D4—104no—
456C22×D4—104no—
457C22×D4—202no—
458C22×D4—202no—
459C22×D4C22×D514yes—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—54no—
471C23×C4—104no—
472C23×C4—104no—
473C23×C4—202no—
474C23×C4C22×D514yes—
475C23×C4C22×D511yescharacteristic
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480#123—1032no—
481#117—1032no—
482C2×C4⋊C4—58no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—54no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—104no—
490C2×C4⋊C4—104no—
491C2×C4⋊C4—104no—
492C2×C4⋊C4—202no—
493C2×C4⋊C4—202no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—42no—
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—54no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
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⋊C4C22×D514yes—
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#95C22×D514yes—
533#95C22×D514yes—
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#52514yes—
551C22×C5#52914yes—
552C22×C5#54014yes—
553C22×C5#54614yes—
554C22×C5#55014yes—
555C22×C5#55114yes—
556C22×C5#55114yes—
557C22×C5C23×D411yescharacteristic
558C22×C5C22×#4111yescharacteristic
559C22×C5C22×#4111yescharacteristic
560C22×C5C22×#4111yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C2×H(5,𝔽2)11yescharacteristic
563C22×C5C2×H(5,𝔽2)11yescharacteristic
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—88no—
572C4×C5—24no—
573C4×C5—24no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5—42no—
577Dic5—24no—
578Dic5—24no—
579Dic5—24no—
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—52no—
597C24—102no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24#70914yes—
605C24#71114yes—
606C24C23×D512yes—
607C24C23×D512yes—
608C24C23×D511yescharacteristic
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—44no—
612C2×D4—416no—
613C2×D4—108no—
614C2×D4—108no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—204no—
618C2×D4—204no—
619C2×D4—2016no—
620C2×D4—2016no—
621C22×C4—232no—
622C22×C4—22no—
623C22×C4—28no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—28no—
628C22×C4—28no—
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—54no—
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—102no—
650C22×C4—102no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—108no—
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—204no—
669C22×C4—2016no—
670C22×C4D4×D514yes—
671C22×C4#71114yes—
672C22×C4C23×D512yes—
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C4⋊C4—516no—
678C4⋊C4—108no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—204no—
682C4⋊C4—204no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—44no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—204no—
693C22⋊C4—204no—
694C22⋊C4—204no—
695C22⋊C4—204no—
696C42—108no—
697C42—108no—
698C42—204no—
699C2×C5—44no—
700C2×C5—44no—
701C2×C5#247118yescomplemented
702C2×C5C2×#52511yescharacteristic
703C2×C5C2×#52911yescharacteristic
704C2×C5C2×#54011yescharacteristic
705C2×C5C2×#54611yescharacteristic
706C2×C5C2×#55011yescharacteristic
707C2×C5C2×#55111yescharacteristic
708C2×C5C2×#55111yescharacteristic
709D5—82no—
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—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23—102no—
743C23—204no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23—204no—
750C23C2×#70914yes—
751C23C2×#70912yes—
752C23C2×D4×D512yes—
753C23C2×#71114yes—
754C23C2×#71112yes—
755C23C2×#71112yes—
756C23#414412yes—
757C23D5×#4112yes—
758C23#414912yes—
759C23C24×D511yescharacteristic
760D4—416no—
761D4—2016no—
762D4—2016no—
763C2×C4—232no—
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—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—54no—
783C2×C4—54no—
784C2×C4—54no—
785C2×C4—108no—
786C2×C4—108no—
787C2×C4—108no—
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—102no—
805C2×C4—102no—
806C2×C4—2016no—
807C2×C4—204no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4C2×D4×D514yes—
812C2×C4C2×#71114yes—
813C5C2×#247111yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—416no—
824C22—416no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—202no—
834C22—202no—
835C22—202no—
836C22—202no—
837C22—408no—
838C22#6582914yes—
839C22#6587214yes—
840C22#6588414yes—
841C22#6592014yes—
842C22#6593314yes—
843C22#6595314yes—
844C22#6599214yes—
845C22C22×#70911yescharacteristic
846C22C22×D4×D511yescharacteristic
847C22C22×#71111yescharacteristic
848C22C22×#71111yescharacteristic
849C22C2×#414411yescharacteristic
850C22C2×D5×#4111yescharacteristic
851C22C2×#414911yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—104no—
858C4—104no—
859C4—104no—
860C4—202no—
861C4—202no—
862C4—202no—
863C4—202no—
864C2—44no—
865C2—44no—
866C2—402no—
867C2#1060645618yesdirect product factor
868C2C2×#6582911yescharacteristic
869C2C2×#6587211yescharacteristic
870C2C2×#6588411yescharacteristic
871C2C2×#6592011yescharacteristic
872C2C2×#6595311yescharacteristic
873C2C2×#6593311yescharacteristic
874C2C2×#6599211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#386D5
hypocenterC5C2×#2471
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#4072C2semidirect
2. C22×#4032C2semidirect
3. C2×C5×#386C2semidirect
5. C2×#65509C2semidirect
6. C2×#65502C2semidirect
7. C2×#65238C2semidirect
8. C2×#65237C2semidirect
9. C2×#65246C2semidirect
10. C2×#65246C2semidirect
11. C2×C22⋊C4×Dic5C2semidirect
12. #10606456C2direct (N × H)
13. C2×#64963C2semidirect
14. C2×#64958C2semidirect
15. C2×#64944C2semidirect
16. C2×#64942C2semidirect
36. C2×#4072C22semidirect
47. C2×#4032C22semidirect
48. C5×#386C22semidirect
52. #65509C22semidirect
53. #65502C22semidirect
60. #65246C22semidirect
61. #65246C22semidirect
62. #65238C22semidirect
63. #65237C22semidirect
64. C22⋊C4×Dic5C22semidirect
65. #64963C22semidirect
66. #64958C22semidirect
67. #64944C22semidirect
68. #64942C22semidirect
134. C2×C4⋊Dic5D4semidirect
173. C2×#386D5semidirect
283. C4⋊Dic5C2×D4semidirect
332. #386C2×D5semidirect
701. C2×C5#2471semidirect
813. C5C2×#2471semidirect
867. C2#10606456direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40722
C22×#40322
C2×C5×#3862
C2×#655122
C2×#655092
C2×#655022
C2×#652382
C2×#652372
C2×#652462
C2×C22⋊C4×Dic52
#106064562
C2×#649632
C2×#649582
C2×#649442
C2×#649422
C2×#24715