Finite Group Databasebeta

← C2×#10612103 #12978994

Subgroups — C2×#10612103 #12978994

Order 1280.

2122 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66052C211yesmaximal, characteristic
2C2×#65903C211yesmaximal, characteristic, complemented
3C2×C5×#460C211yesmaximal, characteristic, complemented
4C2×#65452C211yesmaximal, characteristic, complemented
5C2×#65452C211yesmaximal, characteristic, complemented
6C2×#65453C211yesmaximal, characteristic, complemented
7C2×SD16×Dic5C211yesmaximal, characteristic, complemented
8C2×#65360C211yesmaximal, characteristic, complemented
9C2×#65315C211yesmaximal, characteristic, complemented
10#10612103C2116yesmaximal, direct product factor
11C2×#65136C211yesmaximal, characteristic, complemented
12C2×#65117C211yesmaximal, characteristic, complemented
13C2×#65053C211yesmaximal, characteristic, complemented
14C2×#65049C211yesmaximal, characteristic, complemented
15C2×#65052C211yesmaximal, characteristic, complemented
16C2×#65048C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C22×C5×SD16C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic
20C2×C5×#127C2211yescharacteristic
21C2×C4×C5×Q8C2211yescharacteristic
22C2×Q8×Dic5C2211yescharacteristic
23C2×Q8×Dic5C2211yescharacteristic
24C22×#688C2211yescharacteristic
25C2×#4086C2211yescharacteristic
26C2×#4086C2211yescharacteristic
27C2×#4085—21no—
28C2×#4085—21no—
29C2×#4084—21no—
30C2×D4×Dic5C2211yescharacteristic
31C2×D4×Dic5C2211yescharacteristic
32#66052—24no—
33#66052C2218yes—
34#65903—24no—
35#65903C2218yescomplemented
36C2×#4036—21no—
37C2×#4036C2211yescharacteristic
38C2×#4034—21no—
39C2×#4034C2211yescharacteristic
40C2×C4×D20C2211yescharacteristic
41C2×#4016—21no—
42C2×#4016C2211yescharacteristic
43C2×C4×Dic10—21no—
44C2×C4×Dic10C2211yescharacteristic
45C5×#460C2218yescomplemented
46C2×C5×C4⋊C8C2211yescharacteristic
47C2×C5×#102C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54#65453C2218yescomplemented
55#65452C2218yescomplemented
56#65452C2218yescomplemented
57SD16×Dic5C2218yescomplemented
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3950C2211yescharacteristic
61C2×#3949C2211yescharacteristic
62C2×#3947C2211yescharacteristic
63C2×#3946C2211yescharacteristic
64C2×#3946C2211yescharacteristic
65C2×C8×Dic5C2211yescharacteristic
66#65360C2218yescomplemented
67#65315C2218yescomplemented
68C2×#3941C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3935C2211yescharacteristic
71#65136C2218yescomplemented
72#65117C2218yescomplemented
73#65053C2218yescomplemented
74#65052C2218yescomplemented
75#65049C2218yescomplemented
76#65048C2218yescomplemented
77C2×#3368—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4—21no—
80C22×C5×D4—21no—
81C22×C5×D4C2311yescharacteristic
82C22×C5×D4C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×C22⋊D5—21no—
87C23×Dic5—21no—
88C23×Dic5—21no—
89C2×#711—28no—
90C2×#711—48no—
91C22×D20C2311yescharacteristic
92C22×C4×D5—21no—
93C22×Dic10—21no—
94C22×Dic10D411yescharacteristic
95C2×C5×SD16—24no—
96C2×C5×SD16—24no—
97C2×C5×SD16C2314yes—
98C2×C5×SD16C2314yes—
99C22×C5×C8C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C5×#127—22no—
102C5×#127C2314yes—
103C4×C5×Q8—22no—
104C4×C5×Q8C2314yes—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C42×C5—21no—
108C2×C42×C5C2311yescharacteristic
109C2×C22⋊Dic5—21no—
110C2×C22⋊Dic5—21no—
111Q8×Dic5—22no—
112Q8×Dic5—22no—
113Q8×Dic5C2314yes—
114Q8×Dic5C2314yes—
115C2×#688—24no—
116C2×#688C2314yes—
117#4086—22no—
118#4086—22no—
119#4086C2314yes—
120#4086C2314yes—
121#4085—28no—
122#4085—28no—
123#4084—28no—
124D4×Dic5—22no—
125D4×Dic5—22no—
126D4×Dic5C2314yes—
127D4×Dic5C2314yes—
128C2×#685—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—21no—
131C2×C4⋊Dic5—21no—
132C2×C4⋊Dic5D411yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136C2×#683—21no—
137C2×#683—21no—
138C2×#683—21no—
139C2×#683—21no—
140C2×#683D411yescharacteristic
141C2×#683D411yescharacteristic
142C2×C4×Dic5—21no—
143C2×C4×Dic5—21no—
144C2×C4×Dic5C2311yescharacteristic
145C2×C4×Dic5C2311yescharacteristic
146C22×#168C2311yescharacteristic
147C22×#168C2311yescharacteristic
148#4036—28no—
149#4036—22no—
150#4036C2314yes—
151#4034—28no—
152#4034—22no—
153#4034C2314yes—
154C4×D20—22no—
155C4×D20C2314yes—
156#4016—22no—
157#4016—28no—
158#4016C2314yes—
159C4×Dic10—28no—
160C4×Dic10D414yes—
161C4×Dic10C2314yes—
162C5×C4⋊C8C2314yes—
163C5×#102C2314yes—
164C5×#102C2314yes—
165#3967C2314yes—
166#3964C2314yes—
167#3964C2314yes—
168#3964C2314yes—
169#3964C2314yes—
170#3953C2314yes—
171#3953C2314yes—
172#3950C2314yes—
173#3949C2314yes—
174#3947C2314yes—
175#3946C2314yes—
176#3946C2314yes—
177C8×Dic5C2314yes—
178#3941C2314yes—
179#3939C2314yes—
180#3935C2314yes—
181C2×#557—51no—
182C2×#550—51no—
183#3368—516no—
184C2×#490—51no—
185C2×#490—51no—
186C2×#486—51no—
187C2×#478—51no—
188C2×#478—51no—
189C2×#474—51no—
190C2×#460—51no—
191C2×#460—51no—
192C2×#460D511yescharacteristic, complemented
193C2×#446—51no—
194C2×#440—51no—
195C2×#440—51no—
196C2×C4×SD16—51no—
197C24×C5—21no—
198C24×C5—21no—
199C23×D5—21no—
200C2×C5×Q8—21no—
201C2×C5×Q8—22no—
202C2×C5×Q8#4114yescomplemented
203C2×C5×Q8C2412yes—
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—24no—
207C2×C5×D4—24no—
208C2×C5×D4—22no—
209C2×C5×D4—22no—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4—44no—
213C2×C5×D4—82no—
214C2×C5×D4C2412yes—
215C2×C5×D4C2412yes—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2411yescharacteristic
221C2×C22⋊D5—24no—
222C2×C22⋊D5—24no—
223C2×C22⋊D5—24no—
224C2×C22⋊D5—24no—
225C2×C22⋊D5—44no—
226C2×C22⋊D5—44no—
227C2×C22⋊D5—82no—
228C2×C22⋊D5—82no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—24no—
233C22×Dic5—24no—
234C22×Dic5—44no—
235C22×Dic5—44no—
236C22×Dic5C2×D411yescharacteristic
237C22×Dic5C2×D411yescharacteristic
238C22×Dic5C2×D411yescharacteristic
239C22×Dic5C2×D411yescharacteristic
240#711—432no—
241C2×D20—22no—
242C2×D20—22no—
243C2×D20—21no—
244C2×D20C2412yes—
245C2×C4×D5—24no—
246C2×C4×D5—44no—
247C2×Dic10—24no—
248C2×Dic10—24no—
249C2×Dic10—44no—
250C2×Dic10C2×D414yes—
251C5×SD16—28no—
252C5×SD16—28no—
253C2×C5×C8—22no—
254C2×C5×C8—22no—
255C2×C5×C8C2412yes—
256C2×C5×C8C2412yes—
257C5×C4⋊C4—24no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4C2412yes—
260C42×C5—24no—
261C42×C5C2×D412yes—
262C42×C5C2412yes—
263C22⋊Dic5—24no—
264C22⋊Dic5—24no—
265#688—28no—
266#685—24no—
267C4⋊Dic5—21no—
268C4⋊Dic5—21no—
269C4⋊Dic5—21no—
270C4⋊Dic5—24no—
271C4⋊Dic5—24no—
272C4⋊Dic5—24no—
273C4⋊Dic5C2×D414yes—
274C4⋊Dic5C2412yes—
275C4⋊Dic5C2412yes—
276C4⋊Dic5C2412yes—
277#683—24no—
278#683—24no—
279#683—24no—
280#683—24no—
281#683C2×D414yes—
282#683C2×D414yes—
283C4×Dic5—24no—
284C4×Dic5—24no—
285C4×Dic5C2×D412yes—
286C4×Dic5C2×D412yes—
287C4×Dic5C2412yes—
288C4×Dic5C2412yes—
289C2×#168—22no—
290C2×#168—22no—
291C2×#168C2412yes—
292C2×#168C2412yes—
293C22×#41—101no—
294C22×SD16—51no—
295C22×SD16C2×D511yescharacteristic
296C22×SD16C2×D511yescharacteristic
297#557—58no—
298#557—104no—
299#550—58no—
300#550—104no—
301C2×C4⋊Q8—51no—
302C2×C4⋊Q8—101no—
303C2×#127—51no—
304C2×#127—51no—
305C2×#127C2×D511yescharacteristic
306C2×#125—51no—
307C2×#125—51no—
308C2×#125—101no—
309C2×#125—101no—
310C2×#121—101no—
311C2×#121—101no—
312C2×#121—101no—
313C2×C4×Q8—51no—
314C2×C4×Q8—51no—
315C2×C4×Q8—51no—
316C2×C4×Q8—101no—
317C2×C4×Q8C2×D511yescharacteristic
318C2×C4×D4—51no—
319C2×C4×D4—51no—
320C2×C4×D4—51no—
321#490—58no—
322#490—58no—
323#486—58no—
324#478—58no—
325#478—58no—
326#474—58no—
327#460—58no—
328#460—58no—
329#460C2×D518yescomplemented
330#446—58no—
331#440—58no—
332#440—58no—
333C4×SD16—58no—
334C2×#107—51no—
335C2×#107—51no—
336C2×#106—51no—
337C2×C4⋊C8—51no—
338C2×C4⋊C8—51no—
339C2×C4⋊C8C2×D511yescharacteristic
340C2×#103—51no—
341C2×#102—51no—
342C2×#102—51no—
343C2×#102—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102C2×D511yescharacteristic
349C2×#102C2×D511yescharacteristic
350C2×#97—51no—
351C2×#97—51no—
352C2×C4×C8—51no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—42no—
356C23×C5—42no—
357C23×C5—42no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—42no—
364C22×D5—42no—
365C22×D5—42no—
366C5×Q8—24no—
367C5×Q8—22no—
368C5×Q8C2×#4114yescomplemented
369C5×D4—22no—
370C5×D4—22no—
371C5×D4—22no—
372C5×D4—22no—
373C5×D4—48no—
374C5×D4—42no—
375C5×D4—42no—
376C5×D4—84no—
377C2×C4×C5—24no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—42no—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D411yescharacteristic
386C2×C4×C5C2×#4112yes—
387C2×C4×C52−1+412yes—
388C2×C4×C5C2511yescharacteristic
389C22⋊D5—48no—
390C22⋊D5—48no—
391C22⋊D5—84no—
392C22⋊D5—84no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—48no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5—42no—
403C2×Dic5—48no—
404C2×Dic5AGL(1,ℤ/8)14yes—
405C2×Dic5C22×D412yes—
406C2×Dic5C22×D412yes—
407C2×Dic5C22×D412yes—
408C2×Dic5C22×D412yes—
409D20—22no—
410D20—22no—
411D20—42no—
412C4×D5—48no—
413Dic10—28no—
414Dic10—48no—
415C5×C8—22no—
416C5×C8—22no—
417#168—22no—
418#168—22no—
419C2×#41—108no—
420C2×#41—208no—
421C22×Q8—51no—
422C22×Q8—101no—
423C22×Q8C22×D511yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—51no—
427C22×D4—101no—
428C22×D4—101no—
429C22×D4—101no—
430C22×D4—101no—
431C22×D4C22×D511yescharacteristic
432C22×D4C22×D511yescharacteristic
433C23×C4—101no—
434C23×C4—101no—
435C23×C4—101no—
436C2×SD16—24no—
437C2×SD16—24no—
438C2×SD16—54no—
439C2×SD16—104no—
440C2×SD16C22×D514yes—
441C2×SD16C22×D514yes—
442C22×C8—51no—
443C22×C8—51no—
444C22×C8C22×D511yescharacteristic
445C22×C8C22×D511yescharacteristic
446C4⋊Q8—54no—
447C4⋊Q8—102no—
448C4⋊Q8—108no—
449#127—22no—
450#127—54no—
451#127—54no—
452#127—102no—
453#127—102no—
454#127C22×D514yes—
455#125—54no—
456#125—54no—
457#125—108no—
458#125—102no—
459#125—108no—
460#125—102no—
461#121—108no—
462#121—108no—
463#121—108no—
464C4×Q8—22no—
465C4×Q8—54no—
466C4×Q8—54no—
467C4×Q8—54no—
468C4×Q8—54no—
469C4×Q8—108no—
470C4×Q8—102no—
471C4×Q8—102no—
472C4×Q8C22×D514yes—
473C4×D4—54no—
474C4×D4—54no—
475C4×D4—54no—
476C4×D4—102no—
477C4×D4—102no—
478C4×D4—102no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—51no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4—101no—
491C2×C4⋊C4—101no—
492C2×C4⋊C4—101no—
493C2×C4⋊C4C22×D511yescharacteristic
494C2×C22⋊C4—101no—
495C2×C22⋊C4—101no—
496C2×C22⋊C4—101no—
497C2×C42—21no—
498C2×C42—51no—
499C2×C42—51no—
500C2×C42—101no—
501C2×C42—101no—
502C2×C42C22×D511yescharacteristic
503#107—54no—
504#107—54no—
505#106—54no—
506C4⋊C8—54no—
507C4⋊C8—54no—
508C4⋊C8C22×D514yes—
509#103—54no—
510#102—54no—
511#102—54no—
512#102—54no—
513#102—54no—
514#102—54no—
515#102—54no—
516#102—54no—
517#102C22×D514yes—
518#102C22×D514yes—
519#97—54no—
520#97—54no—
521C4×C8—54no—
522C22×C5—42no—
523C22×C5—42no—
524C22×C5—42no—
525C22×C5—42no—
526C22×C5—42no—
527C22×C5—42no—
528C22×C5—84no—
529C22×C5—84no—
530C22×C5#54812yes—
531C22×C5C2×AGL(1,ℤ/8)12yes—
532C22×C5#57712yes—
533C22×C5C23×D411yescharacteristic
534C2×D5—42no—
535C2×D5—42no—
536C2×D5—42no—
537C2×D5—84no—
538C4×C5—24no—
539C4×C5—22no—
540C4×C5—22no—
541C4×C5—42no—
542C4×C5#54812yes—
543C4×C5C22×#4111yescharacteristic
544C4×C5C2×2−1+411yescharacteristic
545Dic5—22no—
546Dic5—22no—
547Dic5—22no—
548Dic5—42no—
549Dic5—42no—
550Dic5—42no—
551Dic5C2×AGL(1,ℤ/8)14yes—
552C24—21no—
553C24—21no—
554C24—101no—
555#41—2032no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—54no—
559C2×Q8—104no—
560C2×Q8—104no—
561C2×Q8—204no—
562C2×Q8#71114yescomplemented
563C2×Q8C23×D512yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—44no—
573C2×D4—52no—
574C2×D4—82no—
575C2×D4—104no—
576C2×D4—104no—
577C2×D4—104no—
578C2×D4—104no—
579C2×D4—101no—
580C2×D4—102no—
581C2×D4—102no—
582C2×D4—204no—
583C2×D4—204no—
584C2×D4—402no—
585C2×D4—402no—
586C2×D4C23×D512yes—
587C2×D4C23×D512yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—51no—
591C22×C4—51no—
592C22×C4—51no—
593C22×C4—51no—
594C22×C4—104no—
595C22×C4—104no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—104no—
600C22×C4—204no—
601C22×C4—204no—
602C22×C4—204no—
603C22×C4D4×D511yescharacteristic
604C22×C4D4×D511yescharacteristic
605C22×C4C23×D511yescharacteristic
606SD16—28no—
607SD16—28no—
608SD16—108no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—52no—
612C2×C8—52no—
613C2×C8—102no—
614C2×C8—102no—
615C2×C8C23×D512yes—
616C2×C8C23×D512yes—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—54no—
620C4⋊C4—54no—
621C4⋊C4—54no—
622C4⋊C4—52no—
623C4⋊C4—52no—
624C4⋊C4—52no—
625C4⋊C4—104no—
626C4⋊C4—104no—
627C4⋊C4—104no—
628C4⋊C4—104no—
629C4⋊C4—104no—
630C4⋊C4—101no—
631C4⋊C4—101no—
632C4⋊C4—101no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4C23×D512yes—
636C22⋊C4—104no—
637C22⋊C4—104no—
638C22⋊C4—104no—
639C42—24no—
640C42—52no—
641C42—52no—
642C42—52no—
643C42—52no—
644C42—104no—
645C42—104no—
646C42D4×D512yes—
647C42C23×D512yes—
648C2×C5—82no—
649C2×C5—82no—
650C2×C5#336814yescomplemented
651C2×C5C2×#54811yescharacteristic
652C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
653C2×C5C2×#57711yescharacteristic
654D5—82no—
655C23—22no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—102no—
664C23—202no—
665C23—202no—
666C23—202no—
667C23C2×D4×D511yescharacteristic
668Q8—24no—
669Q8—22no—
670Q8—108no—
671Q8—208no—
672Q8C2×#71114yescomplemented
673D4—22no—
674D4—22no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—42no—
680D4—84no—
681D4—102no—
682D4—102no—
683D4—208no—
684D4—208no—
685D4—202no—
686D4—404no—
687D4—404no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—54no—
695C2×C4—52no—
696C2×C4—52no—
697C2×C4—52no—
698C2×C4—52no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—208no—
706C2×C4—208no—
707C2×C4—208no—
708C2×C4—202no—
709C2×C4—202no—
710C2×C4—202no—
711C2×C4C2×D4×D512yes—
712C2×C4C2×D4×D512yes—
713C2×C4C2×D4×D511yescharacteristic
714C2×C4C2×#71112yes—
715C2×C4#415012yes—
716C2×C4C24×D511yescharacteristic
717C8—22no—
718C8—22no—
719C8—102no—
720C8—102no—
721C5C2×#336811yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—404no—
734C22#6593212yes—
735C22#6609612yes—
736C22D5×AGL(1,ℤ/8)12yes—
737C22C22×D4×D511yescharacteristic
738C4—22no—
739C4—22no—
740C4—24no—
741C4—42no—
742C4—54no—
743C4—102no—
744C4—102no—
745C4—102no—
746C4—202no—
747C4—202no—
748C4—202no—
749C4#6593212yes—
750C4C22×#71111yescharacteristic
751C4C2×#415011yescharacteristic
752C2—82no—
753C2—82no—
754C2—402no—
755C2#1061210314yesdirect product factor
756C2C2×#6593211yescharacteristic
757C2C2×#6609611yescharacteristic
758C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#460C2
socleC23×C5C22×D4
prime radicalC2×#66052C2
hypercenterC2×#460D5
hypocenterC5C2×#3368
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. C2×#65903C2semidirect
3. C2×C5×#460C2semidirect
4. C2×#65452C2semidirect
5. C2×#65452C2semidirect
6. C2×#65453C2semidirect
7. C2×SD16×Dic5C2semidirect
8. C2×#65360C2semidirect
9. C2×#65315C2semidirect
10. #10612103C2direct (N × H)
11. C2×#65136C2semidirect
12. C2×#65117C2semidirect
13. C2×#65053C2semidirect
14. C2×#65049C2semidirect
15. C2×#65052C2semidirect
16. C2×#65048C2semidirect
35. #65903C22semidirect
45. C5×#460C22semidirect
54. #65453C22semidirect
55. #65452C22semidirect
56. #65452C22semidirect
57. SD16×Dic5C22semidirect
66. #65360C22semidirect
67. #65315C22semidirect
71. #65136C22semidirect
72. #65117C22semidirect
73. #65053C22semidirect
74. #65052C22semidirect
75. #65049C22semidirect
76. #65048C22semidirect
192. C2×#460D5semidirect
202. C2×C5×Q8#41semidirect
329. #460C2×D5semidirect
368. C5×Q8C2×#41semidirect
562. C2×Q8#711semidirect
650. C2×C5#3368semidirect
672. Q8C2×#711semidirect
721. C5C2×#3368semidirect
755. C2#10612103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660522
C2×#659032
C2×C5×#4602
C2×#654522
C2×#654532
C2×SD16×Dic52
C2×#653602
C2×#653152
#106121032
C2×#651362
C2×#651172
C2×#650532
C2×#650492
C2×#650522
C2×#650482
C2×#33685