Finite Group Databasebeta

← C2×#10611453 #12967336

Subgroups — C2×#10611453 #12967336

Order 1280.

2138 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65912C211yesmaximal, characteristic
2C2×C4×Q8×D5C211yesmaximal, characteristic
3C2×C4×C5×Q16C211yesmaximal, characteristic, complemented
4C2×#65475C211yesmaximal, characteristic
5C2×#65471C211yesmaximal, characteristic, complemented
6C2×C4×#689C211yesmaximal, characteristic, complemented
7C2×C4×#689C211yesmaximal, characteristic, complemented
8#10611453C2116yesmaximal, direct product factor
9C2×#65164C211yesmaximal, characteristic, complemented
10C2×#65173C211yesmaximal, characteristic
11C2×#65082C211yesmaximal, characteristic, complemented
12C2×#65098C211yesmaximal, characteristic
13C2×#65097C211yesmaximal, characteristic
14C2×#65083C211yesmaximal, characteristic, complemented
15C2×C4×Dic20C211yesmaximal, characteristic, complemented
16C2×#64974C211yesmaximal, characteristic
17C22×Q8×D5C2211yescharacteristic
18C22×C5×Q16C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×#4092C2211yescharacteristic
22C2×Q8×Dic5C2211yescharacteristic
23C2×#4090C2211yescharacteristic
24C22×#689C2211yescharacteristic
25C22×#689C2211yescharacteristic
26C22×Dic20C2211yescharacteristic
27#65912—24no—
28#65912C2218yes—
29C4×Q8×D5—24no—
30C4×Q8×D5C2218yes—
31C2×#4043C2211yescharacteristic
32C2×#4042—21no—
33C2×D5×C4⋊C4—21no—
34C2×D5×C4⋊C4C2211yescharacteristic
35C2×#4035—21no—
36C2×#4034C2211yescharacteristic
37C2×#4033—21no—
38C2×#4033C2211yescharacteristic
39C2×#4018—21no—
40C2×C42×D5—21no—
41C2×C42×D5C2211yescharacteristic
42C2×C4×Dic10—21no—
43C2×C4×Dic10—21no—
44C2×C4×Dic10C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic
46C4×C5×Q16C2218yescomplemented
47C2×C5×#107C2211yescharacteristic
48C2×C5×#103C2211yescharacteristic
49C2×C5×#103C2211yescharacteristic
50C2×C4×C5×C8C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53#65475C2218yes—
54#65471C2218yescomplemented
55C2×#3952C2211yescharacteristic
56C2×#3952C2211yescharacteristic
57C2×#3950C2211yescharacteristic
58C2×#3948C2211yescharacteristic
59C2×#3948C2211yescharacteristic
60C2×#3946C2211yescharacteristic
61C2×#3946C2211yescharacteristic
62C4×#689C2218yescomplemented
63C4×#689C2218yescomplemented
64C2×#3942C2211yescharacteristic
65C2×#3942C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67C2×#3939C2211yescharacteristic
68C2×C4×#168C2211yescharacteristic
69#65173C2218yes—
70#65164C2218yescomplemented
71#65098C2218yes—
72#65097C2218yes—
73#65083C2218yescomplemented
74#65082C2218yescomplemented
75C4×Dic20C2218yescomplemented
76#64974C2218yes—
77C2×#3104—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C2×Q8×D5—24no—
81C2×Q8×D5—22no—
82C2×Q8×D5—24no—
83C2×Q8×D5C2314yes—
84C22×C4×D5—21no—
85C22×C4×D5—21no—
86C22×C4×D5D411yescharacteristic
87C22×C4×D5D411yescharacteristic
88C22×C4×D5C2311yescharacteristic
89C22×Dic10—21no—
90C22×Dic10—21no—
91C22×Dic10C2311yescharacteristic
92C22×Dic10C2311yescharacteristic
93C2×C5×Q16—24no—
94C2×C5×Q16C2314yes—
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C4×C5×Q8—22no—
98C4×C5×Q8—22no—
99C4×C5×Q8C2314yes—
100C4×C5×Q8C2314yes—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C42×C5—21no—
106C2×C42×C5—21no—
107C2×C42×C5C2311yescharacteristic
108#4092—22no—
109#4092C2314yes—
110Q8×Dic5—22no—
111Q8×Dic5C2314yes—
112#4090—22no—
113#4090C2314yes—
114C2×#689—24no—
115C2×#689—24no—
116C2×#689C2314yes—
117C2×#689C2314yes—
118C2×#685—21no—
119C2×#685—21no—
120C2×C4⋊Dic5—21no—
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5C2311yescharacteristic
123C2×C4⋊Dic5C2311yescharacteristic
124C2×#683—21no—
125C2×#683—21no—
126C2×#683—21no—
127C2×#683—21no—
128C2×#683—21no—
129C2×#683—21no—
130C2×#683—21no—
131C2×#683—21no—
132C2×C4×Dic5—21no—
133C2×C4×Dic5—21no—
134C2×C4×Dic5—21no—
135C2×C4×Dic5—21no—
136C2×C4×Dic5D411yescharacteristic
137C2×C4×Dic5D411yescharacteristic
138C2×C4×Dic5C2311yescharacteristic
139C22×#168C2311yescharacteristic
140C22×#168C2311yescharacteristic
141C2×Dic20—24no—
142C2×Dic20C2314yes—
143#4043—22no—
144#4043C2314yes—
145#4042—28no—
146D5×C4⋊C4—28no—
147D5×C4⋊C4—22no—
148D5×C4⋊C4C2314yes—
149#4035—28no—
150#4034—22no—
151#4034C2314yes—
152#4033—28no—
153#4033—22no—
154#4033C2314yes—
155#4018—28no—
156C42×D5—28no—
157C42×D5D414yes—
158C42×D5C2314yes—
159C4×Dic10—22no—
160C4×Dic10—22no—
161C4×Dic10—28no—
162C4×Dic10—28no—
163C4×Dic10C2314yes—
164C4×Dic10C2314yes—
165C5×#107C2314yes—
166C5×#103C2314yes—
167C5×#103C2314yes—
168C4×C5×C8C2314yes—
169#3967C2314yes—
170#3967C2314yes—
171#3952C2314yes—
172#3952C2314yes—
173#3950C2314yes—
174#3948C2314yes—
175#3948C2314yes—
176#3946C2314yes—
177#3946C2314yes—
178#3942C2314yes—
179#3942C2314yes—
180#3939C2314yes—
181#3939C2314yes—
182C4×#168C2314yes—
183C2×#533—51no—
184C22×C4×Q8—51no—
185#3104—516no—
186C2×#484—51no—
187C2×#484—51no—
188C2×#477—51no—
189C2×#477—51no—
190C2×#462—51no—
191C2×#462—51no—
192C2×#451—51no—
193C2×#451—51no—
194C2×C4×Q16—51no—
195C2×C4×Q16—51no—
196C2×C4×Q16—51no—
197C2×C4×Q16D511yescharacteristic, complemented
198C2×#431—51no—
199C23×D5C2×D411yescharacteristic
200C2×C5×Q8—21no—
201C2×C5×Q8—21no—
202C2×C5×Q8—22no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
205C2×C5×Q8#4114yes—
206C2×C5×Q8C2412yes—
207C2×C5×Q8C2412yes—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2411yescharacteristic
215C22×Dic5—21no—
216C22×Dic5—21no—
217C22×Dic5—21no—
218C22×Dic5—21no—
219C22×Dic5C2×D411yescharacteristic
220C22×Dic5C2×D411yescharacteristic
221C22×Dic5C2×D411yescharacteristic
222Q8×D5—216no—
223Q8×D5—28no—
224Q8×D5—28no—
225C2×C4×D5—28no—
226C2×C4×D5—24no—
227C2×C4×D5—22no—
228C2×C4×D5—22no—
229C2×C4×D5—24no—
230C2×C4×D5—42no—
231C2×C4×D5—44no—
232C2×C4×D5Q1618yescomplemented
233C2×C4×D5C2×D412yes—
234C2×C4×D5C2×D414yes—
235C2×C4×D5C2×D414yes—
236C2×C4×D5C2412yes—
237C2×Dic10—28no—
238C2×Dic10—21no—
239C2×Dic10—22no—
240C2×Dic10—24no—
241C2×Dic10—22no—
242C2×Dic10—22no—
243C2×Dic10—21no—
244C2×Dic10—24no—
245C2×Dic10—44no—
246C2×Dic10#4114yes—
247C2×Dic10C2412yes—
248C2×Dic10C2412yes—
249C5×Q16—28no—
250C2×C5×C8—22no—
251C2×C5×C8—22no—
252C2×C5×C8C2412yes—
253C2×C5×C8C2412yes—
254C5×C4⋊C4—24no—
255C5×C4⋊C4—24no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4C2412yes—
259C5×C4⋊C4C2412yes—
260C42×C5—24no—
261C42×C5—24no—
262C42×C5C2×D412yes—
263C42×C5C2412yes—
264#689—28no—
265#689—28no—
266#685—24no—
267#685—24no—
268C4⋊Dic5—21no—
269C4⋊Dic5—21no—
270C4⋊Dic5—24no—
271C4⋊Dic5—24no—
272C4⋊Dic5C2412yes—
273C4⋊Dic5C2412yes—
274#683—24no—
275#683—24no—
276#683—24no—
277#683—24no—
278#683—24no—
279#683—24no—
280#683—24no—
281#683—24no—
282C4×Dic5—24no—
283C4×Dic5—24no—
284C4×Dic5—24no—
285C4×Dic5—24no—
286C4×Dic5C2×D414yes—
287C4×Dic5C2×D412yes—
288C4×Dic5C2×D414yes—
289C4×Dic5C2412yes—
290C2×#168—22no—
291C2×#168—22no—
292C2×#168C2412yes—
293C2×#168C2412yes—
294Dic20—28no—
295C23×Q8—51no—
296C22×Q16—51no—
297C22×Q16—51no—
298C22×Q16—51no—
299C22×Q16C2×D511yescharacteristic
300#533—58no—
301#533—104no—
302C2×C4⋊Q8—51no—
303C2×C4⋊Q8—51no—
304C2×#125—101no—
305C2×C22⋊Q8—51no—
306C2×C22⋊Q8—51no—
307C2×C22⋊Q8—101no—
308C2×C4×Q8—51no—
309C2×C4×Q8—58no—
310C2×C4×Q8—51no—
311C2×C4×Q8—51no—
312C2×C4×Q8—51no—
313C2×C4×Q8—101no—
314C2×C4×Q8—101no—
315C2×C4×Q8—101no—
316C2×C4×Q8—104no—
317C2×C4×Q8C2×D511yescharacteristic
318C2×C4×Q8C2×D511yescharacteristic
319C2×#117—101no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—101no—
322C22×C42—51no—
323C22×C42—101no—
324#484—58no—
325#484—58no—
326#477—58no—
327#477—58no—
328#462—58no—
329#462—58no—
330#451—58no—
331#451—58no—
332C4×Q16—58no—
333C4×Q16—58no—
334C4×Q16—58no—
335C4×Q16C2×D518yescomplemented
336#431—58no—
337C2×#107—51no—
338C2×#107—51no—
339C2×#107—51no—
340C2×#107C2×D511yescharacteristic
341C2×C4⋊C8—51no—
342C2×C4⋊C8—51no—
343C2×#103—51no—
344C2×#103—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103—51no—
349C2×#103C2×D511yescharacteristic
350C2×#103C2×D511yescharacteristic
351C2×C22⋊C8—51no—
352C2×C22⋊C8—51no—
353C2×C4×C8—51no—
354C2×C4×C8C2×D511yescharacteristic
355C23×C5C22×D411yescharacteristic
356C22×D5—22no—
357C22×D5—22no—
358C22×D5C2×Q1614yes—
359C22×D5C22×D412yes—
360C5×Q8—24no—
361C5×Q8—22no—
362C5×Q8—22no—
363C5×Q8—22no—
364C5×Q8—42no—
365C5×Q8C2×#4114yes—
366C2×C4×C5—24no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—42no—
373C2×C4×C5—42no—
374C2×C4×C5—42no—
375C2×C4×C5C2×Q1614yes—
376C2×C4×C5C22×D412yes—
377C2×C4×C5C22×D411yescharacteristic
378C2×C4×C5C22×D412yes—
379C2×C4×C5C2×#4112yes—
380C2×C4×C5C2×#4112yes—
381C2×C4×C5C2511yescharacteristic
382C2×Dic5—22no—
383C2×Dic5—24no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5—42no—
392C2×Dic5C2×Q1614yes—
393C2×Dic5C22×D412yes—
394C2×Dic5C22×D412yes—
395C2×Dic5C22×D412yes—
396C4×D5—216no—
397C4×D5—24no—
398C4×D5—22no—
399C4×D5—22no—
400C4×D5—44no—
401C4×D5—48no—
402C4×D5C2×Q16116yescomplemented
403Dic10—216no—
404Dic10—24no—
405Dic10—22no—
406Dic10—22no—
407Dic10—22no—
408Dic10—48no—
409Dic10—42no—
410Dic10C2×#4114yes—
411C5×C8—22no—
412C5×C8—22no—
413#168—22no—
414#168—22no—
415C22×Q8—54no—
416C22×Q8—51no—
417C22×Q8—51no—
418C22×Q8—101no—
419C22×Q8—101no—
420C22×Q8—102no—
421C22×Q8—104no—
422C22×Q8—104no—
423C22×Q8C22×D511yescharacteristic
424C22×Q8C22×D511yescharacteristic
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—101no—
429C23×C4—101no—
430C2×Q16—24no—
431C2×Q16—54no—
432C2×Q16—54no—
433C2×Q16—54no—
434C2×Q16—104no—
435C2×Q16—104no—
436C2×Q16—104no—
437C2×Q16C22×D514yes—
438C22×C8—51no—
439C22×C8—51no—
440C22×C8C22×D511yescharacteristic
441C22×C8C22×D511yescharacteristic
442C4⋊Q8—54no—
443C4⋊Q8—54no—
444C4⋊Q8—102no—
445C4⋊Q8—102no—
446#125—108no—
447C22⋊Q8—54no—
448C22⋊Q8—54no—
449C22⋊Q8—102no—
450C22⋊Q8—108no—
451C22⋊Q8—102no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—54no—
455C4×Q8—54no—
456C4×Q8—54no—
457C4×Q8—54no—
458C4×Q8—108no—
459C4×Q8—108no—
460C4×Q8—108no—
461C4×Q8—102no—
462C4×Q8—102no—
463C4×Q8—102no—
464C4×Q8—102no—
465C4×Q8C22×D514yes—
466C4×Q8C22×D514yes—
467#117—108no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—51no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—54no—
473C2×C4⋊C4—102no—
474C2×C4⋊C4—108no—
475C2×C4⋊C4—101no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4—101no—
478C2×C4⋊C4—101no—
479C2×C4⋊C4—101no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4—101no—
482C2×C4⋊C4—101no—
483C2×C4⋊C4—101no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4C22×D511yescharacteristic
486C2×C4⋊C4C22×D511yescharacteristic
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—51no—
492C2×C42—51no—
493C2×C42—51no—
494C2×C42—54no—
495C2×C42—54no—
496C2×C42—108no—
497C2×C42—101no—
498C2×C42—101no—
499C2×C42—101no—
500C2×C42—101no—
501C2×C42C22×D511yescharacteristic
502#107—54no—
503#107—54no—
504#107—54no—
505#107C22×D514yes—
506C4⋊C8—54no—
507C4⋊C8—54no—
508#103—54no—
509#103—54no—
510#103—54no—
511#103—54no—
512#103—54no—
513#103—54no—
514#103C22×D514yes—
515#103C22×D514yes—
516C22⋊C8—54no—
517C22⋊C8—54no—
518C4×C8—54no—
519C4×C8C22×D514yes—
520C22×C5#52512yes—
521C22×C5C22×Q1612yes—
522C22×C5#57512yes—
523C22×C5C23×D411yescharacteristic
524C2×D5—28no—
525C2×D5—22no—
526C2×D5—22no—
527C2×D5C22×Q1614yes—
528C4×C5—24no—
529C4×C5—22no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5#52512yes—
534C4×C5C22×Q1614yes—
535C4×C5C22×#4111yescharacteristic
536C4×C5C22×#4111yescharacteristic
537Dic5—22no—
538Dic5—24no—
539Dic5—22no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543Dic5C22×Q1614yes—
544C24—51no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—54no—
551C2×Q8—52no—
552C2×Q8—52no—
553C2×Q8—104no—
554C2×Q8—104no—
555C2×Q8—108no—
556C2×Q8—108no—
557C2×Q8—1016no—
558C2×Q8—108no—
559C2×Q8—102no—
560C2×Q8—101no—
561C2×Q8—101no—
562C2×Q8—102no—
563C2×Q8—102no—
564C2×Q8—204no—
565C2×Q8#70914yes—
566C2×Q8C23×D512yes—
567C2×Q8C23×D512yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—51no—
573C22×C4—54no—
574C22×C4—58no—
575C22×C4—51no—
576C22×C4—51no—
577C22×C4—52no—
578C22×C4—52no—
579C22×C4—54no—
580C22×C4—104no—
581C22×C4—108no—
582C22×C4—104no—
583C22×C4—101no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—101no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—202no—
590C22×C4—204no—
591C22×C4D4×D511yescharacteristic
592C22×C4D4×D511yescharacteristic
593C22×C4C23×D511yescharacteristic
594Q16—28no—
595Q16—108no—
596Q16—108no—
597Q16—108no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—52no—
601C2×C8—52no—
602C2×C8—102no—
603C2×C8—102no—
604C2×C8C23×D512yes—
605C2×C8C23×D512yes—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—52no—
611C4⋊C4—52no—
612C4⋊C4—104no—
613C4⋊C4—104no—
614C4⋊C4—104no—
615C4⋊C4—104no—
616C4⋊C4—104no—
617C4⋊C4—104no—
618C4⋊C4—104no—
619C4⋊C4—104no—
620C4⋊C4—101no—
621C4⋊C4—101no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4C23×D512yes—
625C4⋊C4C23×D512yes—
626C22⋊C4—104no—
627C22⋊C4—104no—
628C42—24no—
629C42—24no—
630C42—54no—
631C42—54no—
632C42—52no—
633C42—52no—
634C42—104no—
635C42—104no—
636C42—104no—
637C42—104no—
638C42D4×D512yes—
639C42C23×D512yes—
640C2×C5#310414yescomplemented
641C2×C5C2×#52511yescharacteristic
642C2×C5C23×Q1611yescharacteristic
643C2×C5C2×#57511yescharacteristic
644D5—24no—
645C23—54no—
646C23—52no—
647C23—102no—
648C23—102no—
649C23C2×D4×D511yescharacteristic
650Q8—24no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—54no—
656Q8—1016no—
657Q8—104no—
658Q8—102no—
659Q8—102no—
660Q8—102no—
661Q8—208no—
662Q8—202no—
663Q8C2×#70914yes—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—54no—
674C2×C4—52no—
675C2×C4—516no—
676C2×C4—52no—
677C2×C4—52no—
678C2×C4—1016no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—104no—
682C2×C4—102no—
683C2×C4—104no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—204no—
690C2×C4—208no—
691C2×C4—202no—
692C2×C4—202no—
693C2×C4—202no—
694C2×C4D5×Q1614yes—
695C2×C4C2×#70912yes—
696C2×C4C2×D4×D512yes—
697C2×C4C2×D4×D512yes—
698C2×C4C2×D4×D511yescharacteristic
699C2×C4D5×#4112yes—
700C2×C4C24×D511yescharacteristic
701C8—22no—
702C8—22no—
703C8—102no—
704C8—102no—
705C5C2×#310411yescharacteristic, complemented, Sylow
706C22—54no—
707C22—102no—
708C22—102no—
709C22—108no—
710C22#6588112yes—
711C22C2×D5×Q1612yes—
712C22#6610212yes—
713C22C22×D4×D511yescharacteristic
714C4—24no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—54no—
720C4—102no—
721C4—104no—
722C4—102no—
723C4—202no—
724C4—202no—
725C4—202no—
726C4#6588112yes—
727C4C2×D5×Q1614yes—
728C4C22×#70911yescharacteristic
729C4C2×D5×#4111yescharacteristic
730C2—104no—
731C2#1061145314yesdirect product factor
732C2C2×#6588111yescharacteristic
733C2C22×D5×Q1611yescharacteristic
734C2C2×#6610211yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C4×C5×Q16C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×C4×Q16D5
hypocenterC5C2×#3104
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×C4×C5×Q16C2semidirect
5. C2×#65471C2semidirect
6. C2×C4×#689C2semidirect
7. C2×C4×#689C2semidirect
8. #10611453C2direct (N × H)
9. C2×#65164C2semidirect
11. C2×#65082C2semidirect
14. C2×#65083C2semidirect
15. C2×C4×Dic20C2semidirect
46. C4×C5×Q16C22semidirect
54. #65471C22semidirect
62. C4×#689C22semidirect
63. C4×#689C22semidirect
70. #65164C22semidirect
73. #65083C22semidirect
74. #65082C22semidirect
75. C4×Dic20C22semidirect
197. C2×C4×Q16D5semidirect
232. C2×C4×D5Q16semidirect
335. C4×Q16C2×D5semidirect
402. C4×D5C2×Q16semidirect
640. C2×C5#3104semidirect
705. C5C2×#3104semidirect
731. C2#10611453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659122
C2×C4×Q8×D52
C2×C4×C5×Q162
C2×#654752
C2×#654712
C2×C4×#6892
#106114532
C2×#651642
C2×#651732
C2×#650822
C2×#650982
C2×#650972
C2×#650832
C2×C4×Dic202
C2×#649742
C2×#31045