Finite Group Databasebeta

← C2×#10613079 #12967310

Subgroups — C2×#10613079 #12967310

Order 1280.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65934C211yesmaximal, characteristic, complemented
2C2×#65856C211yesmaximal, characteristic, complemented
3C2×C5×#482C211yesmaximal, characteristic, complemented
4C2×#65326C211yesmaximal, characteristic
5C2×#65285C211yesmaximal, characteristic, complemented
6#10613079C2116yesmaximal, direct product factor
7C2×#65180C211yesmaximal, characteristic, complemented
8C2×#65162C211yesmaximal, characteristic, complemented
9C2×#65146C211yesmaximal, characteristic, complemented
10C2×#65141C211yesmaximal, characteristic, complemented
11C2×#65056C211yesmaximal, characteristic, complemented
12C2×#65076C211yesmaximal, characteristic, complemented
13C2×#65047C211yesmaximal, characteristic, complemented
14C2×#65045C211yesmaximal, characteristic, complemented
15C2×#65022C211yesmaximal, characteristic, complemented
16C2×#65007C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C2×C5×#121C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C2×#4082C2211yescharacteristic
21C2×#4081—21no—
22C2×D4×Dic5—21no—
23C2×D4×Dic5C2211yescharacteristic
24C22×#687C2211yescharacteristic
25C22×#686C2211yescharacteristic
26C2×#4070C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C22×Dic20C2211yescharacteristic
29C22×#677C2211yescharacteristic
30#65934—24no—
31#65934C2218yescomplemented
32#65856—24no—
33#65856C2218yescomplemented
34C2×#4039C2211yescharacteristic
35C2×#4039C2211yescharacteristic
36C2×#4036C2211yescharacteristic
37C2×#4033C2211yescharacteristic
38C2×#4033C2211yescharacteristic
39C2×#4033C2211yescharacteristic
40C2×#4027—21no—
41C2×#4027—21no—
42C2×#4025—21no—
43C2×#4023—21no—
44C2×#4018—21no—
45C2×C42×D5—21no—
46C5×#482C2218yescomplemented
47C2×C5×#107C2211yescharacteristic
48C2×C5×#106C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×#102C2211yescharacteristic
51C2×C5×C22⋊C8C2211yescharacteristic
52C2×C22⋊#168C2211yescharacteristic
53C2×#3953C2211yescharacteristic
54C2×#3948C2211yescharacteristic
55C2×#3946C2211yescharacteristic
56C2×#3946C2211yescharacteristic
57C2×C8×Dic5C2211yescharacteristic
58C2×C8×Dic5C2211yescharacteristic
59#65326C2218yes—
60#65285C2218yescomplemented
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67#65180C2218yescomplemented
68#65162C2218yescomplemented
69#65146C2218yescomplemented
70#65141C2218yescomplemented
71#65076C2218yescomplemented
72#65056C2218yescomplemented
73#65047C2218yescomplemented
74#65045C2218yescomplemented
75#65022C2218yescomplemented
76#65007C2218yescomplemented
77C2×#3102—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C23×Dic5—21no—
83C23×Dic5D411yescharacteristic
84C23×Dic5D411yescharacteristic
85C2×#709—22no—
86C2×#709—24no—
87C2×#709—24no—
88C2×#709C2314yes—
89C22×D20C2311yescharacteristic
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×Dic10C2311yescharacteristic
94C22×Dic10C2311yescharacteristic
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C5×#121—22no—
98C5×#121C2314yes—
99C5×#117—22no—
100C5×#117C2314yes—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C42×C5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5—21no—
109C2×C22⋊Dic5—21no—
110C2×C22⋊Dic5—21no—
111#4082—22no—
112#4082C2314yes—
113#4081—28no—
114D4×Dic5—28no—
115D4×Dic5—22no—
116D4×Dic5C2314yes—
117C2×#687—24no—
118C2×#687C2314yes—
119C2×#686—24no—
120C2×#686C2314yes—
121C2×#685—21no—
122C2×#685—21no—
123C2×C4⋊Dic5—21no—
124C2×C4⋊Dic5C2311yescharacteristic
125#4070—22no—
126#4070C2314yes—
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×Dic5D411yescharacteristic
136C2×C4×Dic5D411yescharacteristic
137C2×C4×Dic5D414yes—
138C2×C4×Dic5C2311yescharacteristic
139C2×C4×Dic5C2311yescharacteristic
140C2×C4×Dic5C2314yes—
141C22×#168C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C2×Dic20—24no—
144C2×Dic20C2314yes—
145C2×#677—24no—
146C2×#677C2314yes—
147#4039—22no—
148#4039—22no—
149#4039C2314yes—
150#4039C2314yes—
151#4036—22no—
152#4036C2314yes—
153#4033—22no—
154#4033—22no—
155#4033—22no—
156#4033C2314yes—
157#4033C2314yes—
158#4033C2314yes—
159#4027—28no—
160#4027—28no—
161#4025—28no—
162#4023—28no—
163#4018—28no—
164C42×D5—28no—
165C5×#107C2314yes—
166C5×#106C2314yes—
167C5×#102C2314yes—
168C5×#102C2314yes—
169C5×C22⋊C8C2314yes—
170C22⋊#168C2314yes—
171#3953C2314yes—
172#3948C2314yes—
173#3946C2314yes—
174#3946C2314yes—
175C8×Dic5C2314yes—
176C8×Dic5C2314yes—
177#3942C2314yes—
178#3942C2314yes—
179#3942C2314yes—
180#3941C2314yes—
181#3940C2314yes—
182#3939C2314yes—
183C2×#529—51no—
184C2×C4×#41—51no—
185#3102—516no—
186C2×#485—51no—
187C2×#482D511yescharacteristic, complemented
188C2×#479—51no—
189C2×#478—51no—
190C2×#464—51no—
191C2×#463—51no—
192C2×#452—51no—
193C2×#449—51no—
194C2×C4×Q16—51no—
195C2×C4×SD16—51no—
196C2×C4×SD16—51no—
197C2×C4×D8—51no—
198C2×#431—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C23×D5—21no—
202C2×C5×D4—24no—
203C2×C5×D4—21no—
204C2×C5×D4—22no—
205C2×C5×D4—22no—
206C2×C5×D4—44no—
207C2×C5×D4C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D412yes—
215C22×C4×C5C2412yes—
216C22×C4×C5C2411yescharacteristic
217C2×C22⋊D5—28no—
218C2×C22⋊D5—24no—
219C22×Dic5—21no—
220C22×Dic5—24no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—24no—
224C22×Dic5—42no—
225C22×Dic5—44no—
226C22×Dic5C2×D411yescharacteristic
227C22×Dic5C2×D411yescharacteristic
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D414yes—
230C22×Dic5C2×D414yes—
231C22×Dic5C2×D411yescharacteristic
232#709—216no—
233#709—28no—
234#709—28no—
235C2×D20—21no—
236C2×D20—22no—
237C2×D20#4114yes—
238C2×D20C2412yes—
239C2×C4×D5—28no—
240C2×C4×D5—24no—
241C2×C4×D5—24no—
242C2×C4×D5—24no—
243C2×C4×D5—44no—
244C2×C4×D5—44no—
245C2×Dic10—21no—
246C2×Dic10—22no—
247C2×Dic10—22no—
248C2×Dic10—22no—
249C2×Dic10—21no—
250C2×Dic10#4114yes—
251C2×Dic10C2412yes—
252C2×Dic10C2412yes—
253C2×C5×C8—22no—
254C2×C5×C8—22no—
255C2×C5×C8C2412yes—
256C2×C5×C8C2412yes—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4C2412yes—
261C5×C4⋊C4C2412yes—
262C5×C4⋊C4C2412yes—
263C5×C22⋊C4—24no—
264C5×C22⋊C4—24no—
265C42×C5—24no—
266C22⋊Dic5—24no—
267C22⋊Dic5—24no—
268C22⋊Dic5—24no—
269C22⋊Dic5—24no—
270#687—28no—
271#686—28no—
272#685—24no—
273#685—24no—
274C4⋊Dic5—21no—
275C4⋊Dic5—24no—
276C4⋊Dic5C2412yes—
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×Dic5C2×D414yes—
286C4×Dic5C2×D414yes—
287C4×Dic5C2×D412yes—
288C4×Dic5C2×D412yes—
289C4×Dic5C2412yes—
290C4×Dic5C2412yes—
291C2×#168—22no—
292C2×#168—22no—
293C2×#168C2412yes—
294C2×#168C2412yes—
295Dic20—28no—
296#677—28no—
297C22×#41—51no—
298C22×Q16—51no—
299C22×SD16—51no—
300C22×SD16—51no—
301C22×D8—51no—
302#529—58no—
303#529—104no—
304C2×#126—101no—
305C2×#125—51no—
306C2×#124—51no—
307C2×#123—101no—
308C2×C22⋊Q8—51no—
309C2×#121C2×D511yescharacteristic
310C4×#41—58no—
311C4×#41—104no—
312C2×C4×Q8—51no—
313C2×C4×Q8—51no—
314C2×C4×Q8—51no—
315C2×C4×D4—51no—
316C2×C4×D4—51no—
317C2×C4×D4—51no—
318C2×C4×D4—101no—
319C2×C4×D4—101no—
320C2×C4×D4—101no—
321C2×#117—101no—
322C2×#117—101no—
323C2×#117C2×D511yescharacteristic
324C22×C42—51no—
325C22×C42—101no—
326#485—58no—
327#482C2×D518yescomplemented
328#479—58no—
329#478—58no—
330#464—58no—
331#463—58no—
332#452—58no—
333#449—58no—
334C4×Q16—58no—
335C4×SD16—58no—
336C4×SD16—58no—
337C4×D8—58no—
338#431—58no—
339C2×#107—51no—
340C2×#107C2×D511yescharacteristic
341C2×#106—51no—
342C2×#106C2×D511yescharacteristic
343C2×C4⋊C8—51no—
344C2×C4⋊C8—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103—51no—
349C2×#102—51no—
350C2×#102—51no—
351C2×#102C2×D511yescharacteristic
352C2×#102C2×D511yescharacteristic
353C2×C22⋊C8—51no—
354C2×C22⋊C8C2×D511yescharacteristic
355C2×C4×C8—51no—
356C2×C4×C8—51no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—42no—
362C23×C5—42no—
363C23×C5—42no—
364C23×C5C22×D412yes—
365C23×C5C22×D411yescharacteristic
366C22×D5—24no—
367C22×D5—22no—
368C22×D5—42no—
369C22×D5—42no—
370C5×D4—22no—
371C5×D4—22no—
372C5×D4—48no—
373C5×D4—42no—
374C2×C4×C5—22no—
375C2×C4×C5—24no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—42no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D411yescharacteristic
386C2×C4×C5C2×#4112yes—
387C2×C4×C5C2×#4112yes—
388C2×C4×C5C2511yescharacteristic
389C22⋊D5—216no—
390C2×Dic5—24no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—28no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—44no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—48no—
402C2×Dic5#13514yes—
403C2×Dic5C22×D412yes—
404C2×Dic5C22×D412yes—
405C2×Dic5C22×D412yes—
406C2×Dic5C22×D412yes—
407D20—24no—
408D20—22no—
409D20C2×#4114yes—
410C4×D5—216no—
411C4×D5—48no—
412C4×D5—48no—
413Dic10—24no—
414Dic10—22no—
415Dic10—22no—
416Dic10—22no—
417Dic10—42no—
418Dic10C2×#4114yes—
419C5×C8—22no—
420C5×C8—22no—
421#168—22no—
422#168—22no—
423C2×#41—54no—
424C2×#41—104no—
425C2×#41—104no—
426C2×#41—102no—
427C22×Q8—51no—
428C22×Q8—51no—
429C22×D4—21no—
430C22×D4—51no—
431C22×D4—101no—
432C22×D4C22×D511yescharacteristic
433C23×C4—51no—
434C23×C4—51no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4—101no—
438C23×C4—101no—
439C23×C4C22×D511yescharacteristic
440C2×Q16—54no—
441C2×Q16—104no—
442C2×SD16—54no—
443C2×SD16—54no—
444C2×SD16—104no—
445C2×SD16—104no—
446C2×D8—54no—
447C2×D8—104no—
448C22×C8—51no—
449C22×C8—51no—
450C22×C8C22×D511yescharacteristic
451C22×C8C22×D511yescharacteristic
452#126—108no—
453#125—54no—
454#125—102no—
455#124—54no—
456#124—102no—
457#123—108no—
458C22⋊Q8—54no—
459C22⋊Q8—102no—
460#121—22no—
461#121C22×D514yes—
462C4×Q8—54no—
463C4×Q8—54no—
464C4×Q8—54no—
465C4×Q8—102no—
466C4×Q8—102no—
467C4×Q8—102no—
468C4×D4—54no—
469C4×D4—54no—
470C4×D4—54no—
471C4×D4—102no—
472C4×D4—102no—
473C4×D4—102no—
474C4×D4—108no—
475C4×D4—108no—
476C4×D4—108no—
477#117—22no—
478#117—108no—
479#117—108no—
480#117C22×D514yes—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—101no—
483C2×C4⋊C4—101no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—101no—
494C2×C22⋊C4—101no—
495C2×C22⋊C4—101no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C42—21no—
500C2×C42—51no—
501C2×C42—51no—
502C2×C42—54no—
503C2×C42—51no—
504C2×C42—51no—
505C2×C42—54no—
506C2×C42—108no—
507C2×C42—101no—
508C2×C42—101no—
509C2×C42—101no—
510#107—54no—
511#107C22×D514yes—
512#106—54no—
513#106C22×D514yes—
514C4⋊C8—54no—
515C4⋊C8—54no—
516#103—54no—
517#103—54no—
518#103—54no—
519#103—54no—
520#102—54no—
521#102—54no—
522#102C22×D514yes—
523#102C22×D514yes—
524C22⋊C8—54no—
525C22⋊C8C22×D514yes—
526C4×C8—54no—
527C4×C8—54no—
528C22×C5—22no—
529C22×C5—22no—
530C22×C5—22no—
531C22×C5—44no—
532C22×C5—42no—
533C22×C5—42no—
534C22×C5—42no—
535C22×C5—84no—
536C22×C5#52512yes—
537C22×C5C2×#13512yes—
538C22×C5#57512yes—
539C22×C5C23×D411yescharacteristic
540C2×D5—24no—
541C2×D5—48no—
542C2×D5—42no—
543C2×D5—42no—
544C4×C5—22no—
545C4×C5—42no—
546C4×C5—42no—
547C4×C5—42no—
548C4×C5#52512yes—
549C4×C5C22×#4111yescharacteristic
550C4×C5C22×#4111yescharacteristic
551Dic5—24no—
552Dic5—22no—
553Dic5—22no—
554Dic5—22no—
555Dic5—42no—
556Dic5—42no—
557Dic5C2×#13514yes—
558C24—21no—
559C24—101no—
560C24D4×D511yescharacteristic
561#41—108no—
562#41—108no—
563#41—1016no—
564C2×Q8—54no—
565C2×Q8—52no—
566C2×Q8—52no—
567C2×Q8—101no—
568C2×Q8—101no—
569C2×Q8—102no—
570C2×Q8—102no—
571C2×Q8—102no—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—44no—
577C2×D4—54no—
578C2×D4—52no—
579C2×D4—108no—
580C2×D4—104no—
581C2×D4—101no—
582C2×D4—102no—
583C2×D4C23×D512yes—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—51no—
590C22×C4—54no—
591C22×C4—51no—
592C22×C4—51no—
593C22×C4—51no—
594C22×C4—54no—
595C22×C4—104no—
596C22×C4—104no—
597C22×C4—108no—
598C22×C4—104no—
599C22×C4—104no—
600C22×C4—101no—
601C22×C4—104no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—204no—
605C22×C4—204no—
606C22×C4—204no—
607C22×C4—202no—
608C22×C4D4×D512yes—
609C22×C4D4×D511yescharacteristic
610C22×C4C23×D512yes—
611C22×C4C23×D511yescharacteristic
612Q16—108no—
613SD16—108no—
614SD16—108no—
615D8—108no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—52no—
619C2×C8—52no—
620C2×C8—102no—
621C2×C8—102no—
622C2×C8C23×D512yes—
623C2×C8C23×D512yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—52no—
628C4⋊C4—104no—
629C4⋊C4—104no—
630C4⋊C4—104no—
631C4⋊C4—104no—
632C4⋊C4—104no—
633C4⋊C4—101no—
634C4⋊C4—104no—
635C4⋊C4C23×D512yes—
636C4⋊C4C23×D512yes—
637C4⋊C4C23×D512yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—104no—
641C22⋊C4—104no—
642C22⋊C4—104no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C42—24no—
647C42—54no—
648C42—54no—
649C42—52no—
650C42—52no—
651C42—52no—
652C42—52no—
653C42—104no—
654C42—104no—
655C42—104no—
656C2×C5—42no—
657C2×C5—82no—
658C2×C5#310214yescomplemented
659C2×C5C2×#52511yescharacteristic
660C2×C5C22×#13511yescharacteristic
661C2×C5C2×#57511yescharacteristic
662D5—44no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—104no—
671C23—102no—
672C23—202no—
673C23—202no—
674C23C2×D4×D512yes—
675C23C2×D4×D511yescharacteristic
676Q8—54no—
677Q8—104no—
678Q8—102no—
679Q8—102no—
680Q8—102no—
681Q8—202no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—42no—
686D4—54no—
687D4—1016no—
688D4—104no—
689D4—102no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—54no—
701C2×C4—52no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—52no—
705C2×C4—1016no—
706C2×C4—108no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—104no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—208no—
715C2×C4—208no—
716C2×C4—208no—
717C2×C4—204no—
718C2×C4—202no—
719C2×C4—202no—
720C2×C4C2×D4×D512yes—
721C2×C4C2×D4×D511yescharacteristic
722C2×C4D5×#4112yes—
723C2×C4D5×#4112yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—22no—
727C8—102no—
728C8—102no—
729C5C2×#310211yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—104no—
739C22—208no—
740C22—202no—
741C22—202no—
742C22#6599012yes—
743C22D5×#13512yes—
744C22#6610712yes—
745C22C22×D4×D511yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—54no—
751C4—104no—
752C4—102no—
753C4—102no—
754C4—102no—
755C4—202no—
756C4—202no—
757C4#6599012yes—
758C4C2×D5×#4111yescharacteristic
759C4C2×D5×#4111yescharacteristic
760C2—42no—
761C2—82no—
762C2—204no—
763C2#1061307914yesdirect product factor
764C2C2×#6599011yescharacteristic
765C2C2×D5×#13511yescharacteristic
766C2C2×#6610711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#482C2
socleC23×C5C22×D4
prime radicalC2×#65326C2
hypercenterC2×#482D5
hypocenterC5C2×#3102
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#65934C2semidirect
2. C2×#65856C2semidirect
3. C2×C5×#482C2semidirect
5. C2×#65285C2semidirect
6. #10613079C2direct (N × H)
7. C2×#65180C2semidirect
8. C2×#65162C2semidirect
9. C2×#65146C2semidirect
10. C2×#65141C2semidirect
11. C2×#65056C2semidirect
12. C2×#65076C2semidirect
13. C2×#65047C2semidirect
14. C2×#65045C2semidirect
15. C2×#65022C2semidirect
16. C2×#65007C2semidirect
31. #65934C22semidirect
33. #65856C22semidirect
46. C5×#482C22semidirect
60. #65285C22semidirect
67. #65180C22semidirect
68. #65162C22semidirect
69. #65146C22semidirect
70. #65141C22semidirect
71. #65076C22semidirect
72. #65056C22semidirect
73. #65047C22semidirect
74. #65045C22semidirect
75. #65022C22semidirect
76. #65007C22semidirect
187. C2×#482D5semidirect
327. #482C2×D5semidirect
658. C2×C5#3102semidirect
729. C5C2×#3102semidirect
763. C2#10613079direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659342
C2×#658562
C2×C5×#4822
C2×#653262
C2×#652852
#106130792
C2×#651802
C2×#651622
C2×#651462
C2×#651412
C2×#650562
C2×#650762
C2×#650472
C2×#650452
C2×#650222
C2×#650072
C2×#31025