Finite Group Databasebeta

← C2×#10606678 #12258041

Subgroups — C2×#10606678 #12258041

Order 1280.

3198 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic
2C22×#4038C211yesmaximal, characteristic
3C22×C4×Dic10C211yesmaximal, characteristic, complemented
4C2×C5×#387C211yesmaximal, characteristic, complemented
5C2×#65274C211yesmaximal, characteristic, complemented
6C2×#65267C211yesmaximal, characteristic, complemented
7C2×#65229C211yesmaximal, characteristic
8#10606678C2116yesmaximal, direct product factor
9C2×#64956C211yesmaximal, characteristic
10C2×#64935C211yesmaximal, characteristic, complemented
11C2×#64936C211yesmaximal, characteristic, complemented
12C2×#64936C211yesmaximal, characteristic, complemented
13C2×#64959C211yesmaximal, characteristic
14C2×#64959C211yesmaximal, characteristic
15C2×#64958C211yesmaximal, characteristic
16C2×#64938C211yesmaximal, characteristic, complemented
17C23×C4×D5C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×#685C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4042C4116yescomplemented
43C2×#4042C2218yes—
44C2×#4038—28no—
45C2×#4038C2218yes—
46C2×C4×Dic10—28no—
47C2×C4×Dic10C2218yescomplemented
48C5×#387C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59#65274C2218yescomplemented
60#65267C2218yescomplemented
61#65229C2218yes—
62#64959C2218yes—
63#64959C2218yes—
64#64958C2218yes—
65#64956C2218yes—
66#64938C2218yescomplemented
67#64936C2218yescomplemented
68#64936C2218yescomplemented
69#64935C2218yescomplemented
70C2×#2323—51nomaximal, Sylow
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C22×C4×D5—24no—
87C22×C4×D5—24no—
88C22×C4×D5C2×C418yes—
89C22×C4×D5C2314yes—
90C22×Dic10—24no—
91C22×Dic10—24no—
92C22×Dic10C2×C418yes—
93C22×Dic10C2314yes—
94C2×C5×C4⋊C4—24no—
95C2×C5×C4⋊C4C2×C418yes—
96C2×C5×C4⋊C4C2314yes—
97C2×C5×C4⋊C4C2314yes—
98C2×C42×C5—24no—
99C2×C42×C5C2314yes—
100C2×#685—24no—
101C2×#685—24no—
102C2×#685—42no—
103C2×#685—42no—
104C2×#685C2×C418yes—
105C2×#685C2×C418yes—
106C2×#685C2314yes—
107C2×#685C2314yes—
108C2×#685C2314yes—
109C2×#685C2314yes—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×C4⋊Dic5—24no—
113C2×C4⋊Dic5—24no—
114C2×C4⋊Dic5—42no—
115C2×C4⋊Dic5C2314yes—
116C2×C4⋊Dic5C2314yes—
117C2×C4⋊Dic5C2314yes—
118C2×#683—24no—
119C2×#683—24no—
120C2×#683—24no—
121C2×#683—42no—
122C2×#683C2×C418yes—
123C2×#683C2×C418yes—
124C2×#683C2314yes—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×C4×Dic5—24no—
131C2×C4×Dic5—24no—
132C2×C4×Dic5—42no—
133C2×C4×Dic5—42no—
134C2×C4×Dic5D418yes—
135C2×C4×Dic5C2314yes—
136C2×C4×Dic5C2314yes—
137C2×C4×Dic5C2314yes—
138C2×C4×Dic5C2314yes—
139C2×C4×Dic5C2314yes—
140#4042C2×C4164yescomplemented
141#4038—232no—
142C4×Dic10—232no—
143C5×#95C2314yes—
144C5×#95C2314yes—
145C5×#95C2314yes—
146C5×#95C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×C22⋊Q8—51no—
154C22×C4×Q8—51no—
155C22×#117—51no—
156#2323—516no—
157C2×#391—51no—
158C2×#389—51no—
159C2×#389—51no—
160C2×#389—51no—
161C2×#388—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#387—51no—
166C2×#387D511yescharacteristic, complemented
167C2×#380—51no—
168C2×C4×C4⋊C4—51no—
169C24×C5C2411yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5C22×C414yes—
177C23×D5C2412yes—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5C22×C414yes—
196C22×C4×C5C22×C414yes—
197C22×C4×C5C22×C414yes—
198C22×C4×C5C2×D414yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5C22×C414yes—
222C22×Dic5C22×C414yes—
223C22×Dic5C22×C414yes—
224C22×Dic5C2×D414yes—
225C22×Dic5C2×D414yes—
226C22×Dic5#4114yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C2×C4×D5—232no—
235C2×C4×D5—28no—
236C2×C4×D5—28no—
237C2×C4×D5C22×C4116yes—
238C2×Dic10—232no—
239C2×Dic10—28no—
240C2×Dic10—28no—
241C2×Dic10C22×C4116yes—
242C5×C4⋊C4—28no—
243C5×C4⋊C4C22×C4116yes—
244C42×C5—28no—
245#685—28no—
246#685—28no—
247#685—44no—
248#685—44no—
249#685C22×C4116yes—
250#685C22×C4116yes—
251C4⋊Dic5—28no—
252C4⋊Dic5—28no—
253C4⋊Dic5—44no—
254#683—28no—
255#683—28no—
256#683—28no—
257#683—44no—
258#683C22×C4116yes—
259#683C22×C4116yes—
260C4×Dic5—28no—
261C4×Dic5—28no—
262C4×Dic5—44no—
263C4×Dic5—44no—
264C4×Dic5C2×D4116yes—
265C23×Q8—51no—
266C24×C4—51no—
267C2×C22⋊Q8—516no—
268C2×C22⋊Q8—58no—
269C2×C4×Q8—58no—
270C2×C4×Q8—108no—
271C2×#117—58no—
272C2×#117—108no—
273C22×C4⋊C4—51no—
274C22×C4⋊C4—51no—
275C22×C4⋊C4—51no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4C2×D511yescharacteristic
283C22×C4⋊C4C2×D511yescharacteristic
284C22×C22⋊C4—51no—
285C22×C22⋊C4—51no—
286C22×C22⋊C4—51no—
287C22×C22⋊C4—51no—
288C22×C22⋊C4—51no—
289C22×C22⋊C4—51no—
290C22×C42—51no—
291C22×C42—51no—
292C22×C42—51no—
293C22×C42—51no—
294C22×C42—51no—
295C22×C42C2×D511yescharacteristic
296#391—58no—
297#389—58no—
298#389—58no—
299#389—58no—
300#388—58no—
301#388—58no—
302#388—58no—
303#388—58no—
304#387—58no—
305#387C2×D518yescomplemented
306#380—58no—
307C4×C4⋊C4—58no—
308C2×#95—51no—
309C2×#95—51no—
310C2×#95—51no—
311C2×#95—51no—
312C2×#95—51no—
313C2×#95—51no—
314C2×#95C2×D511yescharacteristic
315C2×#95C2×D511yescharacteristic
316C2×#95C2×D511yescharacteristic
317C2×#95C2×D511yescharacteristic
318C23×C5C23×C412yes—
319C23×C5C22×D412yes—
320C23×C5C2×#4112yes—
321C23×C5H(5,𝔽2)12yes—
322C23×C52−1+412yes—
323C23×C52−1+412yes—
324C23×C52−1+412yes—
325C23×C5C2511yescharacteristic
326C22×D5—28no—
327C22×D5—28no—
328C22×D5—28no—
329C22×D5—22no—
330C22×D5—22no—
331C22×D5—22no—
332C22×D5—22no—
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—44no—
336C22×D5—44no—
337C22×D5—44no—
338C22×D5—44no—
339C22×D5C23×C414yes—
340C2×C4×C5—28no—
341C2×C4×C5—28no—
342C2×C4×C5—28no—
343C2×C4×C5—28no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—44no—
362C2×C4×C5—44no—
363C2×C4×C5—44no—
364C2×C4×C5C23×C414yes—
365C2×C4×C5C23×C414yes—
366C2×C4×C5C23×C414yes—
367C2×C4×C5C22×D414yes—
368C2×Dic5—28no—
369C2×Dic5—28no—
370C2×Dic5—28no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—44no—
387C2×Dic5—44no—
388C2×Dic5—44no—
389C2×Dic5C4×D4116yes—
390C2×Dic5C23×C414yes—
391C2×Dic5C23×C414yes—
392C2×Dic5C23×C414yes—
393C2×Dic5C22×D414yes—
394C2×Dic5C22×D414yes—
395C2×Dic5C2×#4114yes—
396C4×D5—232no—
397Dic10—232no—
398C25—51no—
399C22×Q8—58no—
400C22×Q8—54no—
401C22×Q8—104no—
402C22×Q8—104no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—58no—
408C23×C4—54no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—104no—
413C23×C4—104no—
414C23×C4C22×D511yescharacteristic
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C22⋊Q8—564no—
422C4×Q8—1032no—
423#117—1032no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—58no—
426C2×C4⋊C4—58no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—54no—
429C2×C4⋊C4—54no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—54no—
433C2×C4⋊C4—54no—
434C2×C4⋊C4—54no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—104no—
437C2×C4⋊C4—104no—
438C2×C4⋊C4—104no—
439C2×C4⋊C4—104no—
440C2×C4⋊C4—104no—
441C2×C4⋊C4—202no—
442C2×C4⋊C4—202no—
443C2×C4⋊C4C4×D518yes—
444C2×C4⋊C4C22×D514yes—
445C2×C4⋊C4C22×D514yes—
446C2×C22⋊C4—58no—
447C2×C22⋊C4—58no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—54no—
451C2×C22⋊C4—54no—
452C2×C22⋊C4—54no—
453C2×C22⋊C4—54no—
454C2×C22⋊C4—104no—
455C2×C22⋊C4—104no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4—202no—
458C2×C42—24no—
459C2×C42—58no—
460C2×C42—54no—
461C2×C42—54no—
462C2×C42—54no—
463C2×C42—54no—
464C2×C42—54no—
465C2×C42—104no—
466C2×C42—104no—
467C2×C42—202no—
468C2×C42—202no—
469C2×C42C22×D514yes—
470#95—54no—
471#95—54no—
472#95—54no—
473#95—54no—
474#95—54no—
475#95—54no—
476#95C22×D514yes—
477#95C22×D514yes—
478#95C22×D514yes—
479#95C22×D514yes—
480C22×C5C2×C4×D414yes—
481C22×C5#51914yes—
482C22×C5#52014yes—
483C22×C5#53614yes—
484C22×C5#53714yes—
485C22×C5#54114yes—
486C22×C5#54214yes—
487C22×C5C24×C411yescharacteristic
488C22×C5C23×D411yescharacteristic
489C22×C5C22×#4111yescharacteristic
490C22×C5C2×H(5,𝔽2)11yescharacteristic
491C22×C5C2×2−1+411yescharacteristic
492C22×C5C2×2−1+411yescharacteristic
493C22×C5C2×2−1+411yescharacteristic
494C2×D5—24no—
495C2×D5—24no—
496C2×D5—24no—
497C2×D5—416no—
498C2×D5—42no—
499C2×D5—42no—
500C2×D5—42no—
501C2×D5—42no—
502C4×C5—24no—
503C4×C5—24no—
504C4×C5—24no—
505C4×C5—24no—
506C4×C5—42no—
507C4×C5—42no—
508C4×C5—42no—
509Dic5—24no—
510Dic5—24no—
511Dic5—24no—
512Dic5—42no—
513Dic5—42no—
514Dic5—42no—
515Dic5C2×C4×D418yes—
516C24—54no—
517C24—52no—
518C24—102no—
519C24—102no—
520C24—102no—
521C24—102no—
522C24—102no—
523C24—102no—
524C24C23×D511yescharacteristic
525C2×Q8—516no—
526C2×Q8—108no—
527C2×Q8—1032no—
528C2×Q8—108no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—54no—
547C22×C4—54no—
548C22×C4—54no—
549C22×C4—52no—
550C22×C4—54no—
551C22×C4—54no—
552C22×C4—54no—
553C22×C4—52no—
554C22×C4—52no—
555C22×C4—52no—
556C22×C4—516no—
557C22×C4—52no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—108no—
561C22×C4—1032no—
562C22×C4—108no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4C2×C4×D514yes—
579C22×C4C2×C4×D514yes—
580C22×C4C2×C4×D514yes—
581C22×C4D4×D514yes—
582C22×C4C23×D512yes—
583C22×C4C23×D512yes—
584C22×C4C23×D512yes—
585C22×C4C23×D512yes—
586C22×C4C23×D512yes—
587C22×C4C23×D512yes—
588C22×C4C23×D512yes—
589C4⋊C4—28no—
590C4⋊C4—516no—
591C4⋊C4—516no—
592C4⋊C4—108no—
593C4⋊C4—108no—
594C4⋊C4—108no—
595C4⋊C4—108no—
596C4⋊C4—108no—
597C4⋊C4—204no—
598C4⋊C4—204no—
599C4⋊C4C2×C4×D5116yes—
600C22⋊C4—516no—
601C22⋊C4—516no—
602C22⋊C4—108no—
603C22⋊C4—108no—
604C22⋊C4—204no—
605C22⋊C4—204no—
606C42—28no—
607C42—516no—
608C42—108no—
609C42—108no—
610C42—204no—
611C42—204no—
612C2×C5#232318yescomplemented
613C2×C5C22×C4×D411yescharacteristic
614C2×C5C2×#51911yescharacteristic
615C2×C5C2×#52011yescharacteristic
616C2×C5C2×#53611yescharacteristic
617C2×C5C2×#53711yescharacteristic
618C2×C5C2×#54111yescharacteristic
619C2×C5C2×#54211yescharacteristic
620D5—44no—
621C23—54no—
622C23—108no—
623C23—108no—
624C23—108no—
625C23—102no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—204no—
632C23—204no—
633C23—204no—
634C23—204no—
635C23C22×C4×D512yes—
636C23C2×D4×D512yes—
637C23#414712yes—
638C23D5×#4112yes—
639C23#414912yes—
640C23#415012yes—
641C23#415012yes—
642C23C24×D511yescharacteristic
643Q8—1032no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—516no—
669C2×C4—54no—
670C2×C4—54no—
671C2×C4—54no—
672C2×C4—54no—
673C2×C4—54no—
674C2×C4—54no—
675C2×C4—1032no—
676C2×C4—108no—
677C2×C4—108no—
678C2×C4—108no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—204no—
695C2×C4—204no—
696C2×C4—204no—
697C2×C4C22×C4×D514yes—
698C2×C4C22×C4×D514yes—
699C2×C4C22×C4×D514yes—
700C2×C4C2×D4×D514yes—
701C5C2×#232311yescharacteristic, complemented, Sylow
702C22—104no—
703C22—104no—
704C22—104no—
705C22—202no—
706C22—202no—
707C22—2016no—
708C22—202no—
709C22—202no—
710C22#6585714yes—
711C22C4×D4×D514yes—
712C22#6590614yes—
713C22#6596314yes—
714C22#6598214yes—
715C22#6603014yes—
716C22#6604414yes—
717C22C23×C4×D511yescharacteristic
718C22C22×D4×D511yescharacteristic
719C22C2×#414711yescharacteristic
720C22C2×D5×#4111yescharacteristic
721C22C2×#414911yescharacteristic
722C22C2×#415011yescharacteristic
723C22C2×#415011yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—58no—
732C4—104no—
733C4—104no—
734C4—104no—
735C4—202no—
736C4—202no—
737C4—202no—
738C2—204no—
739C2#1060667818yesdirect product factor
740C2C2×#6585711yescharacteristic
741C2C2×C4×D4×D511yescharacteristic
742C2C2×#6590611yescharacteristic
743C2C2×#6596311yescharacteristic
744C2C2×#6598211yescharacteristic
745C2C2×#6603011yescharacteristic
746C2C2×#6604411yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC24×D5C23
cosocleC23×C5C25
hypercenterC2×#387D5
hypocenterC5C2×#2323
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C22×C4×Dic10C2semidirect
4. C2×C5×#387C2semidirect
5. C2×#65274C2semidirect
6. C2×#65267C2semidirect
8. #10606678C2direct (N × H)
10. C2×#64935C2semidirect
11. C2×#64936C2semidirect
12. C2×#64936C2semidirect
16. C2×#64938C2semidirect
42. C2×#4042C4semidirect
47. C2×C4×Dic10C22semidirect
48. C5×#387C22semidirect
59. #65274C22semidirect
60. #65267C22semidirect
66. #64938C22semidirect
67. #64936C22semidirect
68. #64936C22semidirect
69. #64935C22semidirect
140. #4042C2×C4semidirect
166. C2×#387D5semidirect
305. #387C2×D5semidirect
612. C2×C5#2323semidirect
701. C5C2×#2323semidirect
739. C2#10606678direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40422
C22×#40382
C22×C4×Dic102
C2×C5×#3872
C2×#652742
C2×#652672
C2×#652292
#106066782
C2×#649562
C2×#649352
C2×#649362
C2×#649592
C2×#649582
C2×#649382
C2×#23235