Finite Group Databasebeta

← C2×#10613224 #12967368

Subgroups — C2×#10613224 #12967368

Order 1280.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65956C211yesmaximal, characteristic, complemented
2C2×#65856C211yesmaximal, characteristic
3C2×C5×#485C211yesmaximal, characteristic, complemented
4C2×#65336C211yesmaximal, characteristic
5C2×#65285C211yesmaximal, characteristic, complemented
6#10613224C2116yesmaximal, direct product factor
7C2×#65179C211yesmaximal, characteristic, complemented
8C2×#65162C211yesmaximal, characteristic, complemented
9C2×#65143C211yesmaximal, characteristic, complemented
10C2×#65141C211yesmaximal, characteristic, complemented
11C2×#65082C211yesmaximal, characteristic, complemented
12C2×#65107C211yesmaximal, characteristic, complemented
13C2×#65079C211yesmaximal, characteristic, complemented
14C2×#65077C211yesmaximal, characteristic, complemented
15C2×#65022C211yesmaximal, characteristic
16C2×#65007C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C2×Q8×Dic5C2211yescharacteristic
21C2×#4090C2211yescharacteristic
22C22×#689C2211yescharacteristic
23C22×#688C2211yescharacteristic
24C2×#4070C2211yescharacteristic
25C22×C4×Dic5C2211yescharacteristic
26C22×Dic20C2211yescharacteristic
27C22×#677C2211yescharacteristic
28#65956—24no—
29#65956C2218yescomplemented
30#65856—24no—
31#65856C2218yes—
32C2×#4039C2211yescharacteristic
33C2×#4039C2211yescharacteristic
34C2×#4035—21no—
35C2×#4034C2211yescharacteristic
36C2×#4033—21no—
37C2×#4033C2211yescharacteristic
38C2×#4033C2211yescharacteristic
39C2×#4033C2211yescharacteristic
40C2×#4027—21no—
41C2×#4027—21no—
42C2×#4024—21no—
43C2×#4023—21no—
44C2×#4018—21no—
45C2×C42×D5—21no—
46C5×#485C2218yescomplemented
47C2×C5×#107C2211yescharacteristic
48C2×C5×#106C2211yescharacteristic
49C2×C5×#103C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×C5×C22⋊C8C2211yescharacteristic
52C2×C22⋊#168C2211yescharacteristic
53C2×#3953C2211yescharacteristic
54C2×#3948C2211yescharacteristic
55C2×#3946C2211yescharacteristic
56C2×#3946C2211yescharacteristic
57C2×C8×Dic5C2211yescharacteristic
58C2×C8×Dic5C2211yescharacteristic
59#65336C2218yes—
60#65285C2218yescomplemented
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67#65179C2218yescomplemented
68#65162C2218yescomplemented
69#65143C2218yescomplemented
70#65141C2218yescomplemented
71#65107C2218yescomplemented
72#65082C2218yescomplemented
73#65079C2218yescomplemented
74#65077C2218yescomplemented
75#65022C2218yes—
76#65007C2218yescomplemented
77C2×#3107—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5—21no—
81C23×Dic5D411yescharacteristic
82C23×Dic5D411yescharacteristic
83C2×#709—22no—
84C2×#709—24no—
85C2×#709—24no—
86C2×#709C2314yes—
87C22×D20C2311yescharacteristic
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×Dic10—21no—
92C22×Dic10C2311yescharacteristic
93C22×Dic10C2311yescharacteristic
94C22×C5×C8C2311yescharacteristic
95C22×C5×C8C2311yescharacteristic
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8C2314yes—
98C5×#117—22no—
99C5×#117C2314yes—
100C2×C5×C4⋊C4—21no—
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—
108Q8×Dic5—22no—
109Q8×Dic5C2314yes—
110#4090—22no—
111#4090C2314yes—
112C2×#689—24no—
113C2×#689C2314yes—
114C2×#688—24no—
115C2×#688C2314yes—
116C2×#685—21no—
117C2×#685—21no—
118C2×C4⋊Dic5—21no—
119C2×C4⋊Dic5C2311yescharacteristic
120#4070—22no—
121#4070C2314yes—
122C2×#683—21no—
123C2×#683—21no—
124C2×#683—21no—
125C2×#683—21no—
126C2×#683—21no—
127C2×#683—21no—
128C2×#683—21no—
129C2×C4×Dic5—21no—
130C2×C4×Dic5—21no—
131C2×C4×Dic5—21no—
132C2×C4×Dic5—21no—
133C2×C4×Dic5D411yescharacteristic
134C2×C4×Dic5D411yescharacteristic
135C2×C4×Dic5D414yes—
136C2×C4×Dic5C2311yescharacteristic
137C2×C4×Dic5C2311yescharacteristic
138C2×C4×Dic5C2314yes—
139C22×#168C2311yescharacteristic
140C22×#168C2311yescharacteristic
141C2×Dic20—24no—
142C2×Dic20C2314yes—
143C2×#677—24no—
144C2×#677C2314yes—
145#4039—22no—
146#4039—22no—
147#4039C2314yes—
148#4039C2314yes—
149#4035—28no—
150#4034—22no—
151#4034C2314yes—
152#4033—28no—
153#4033—22no—
154#4033—22no—
155#4033—22no—
156#4033C2314yes—
157#4033C2314yes—
158#4033C2314yes—
159#4027—28no—
160#4027—28no—
161#4024—28no—
162#4023—28no—
163#4018—28no—
164C42×D5—28no—
165C5×#107C2314yes—
166C5×#106C2314yes—
167C5×#103C2314yes—
168C5×#103C2314yes—
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×#533—51no—
184C2×C4×#41—51no—
185#3107—516no—
186C2×#485—51no—
187C2×#485D511yescharacteristic, complemented
188C2×#475—51no—
189C2×#474—51no—
190C2×#462—51no—
191C2×#461—51no—
192C2×#452—51no—
193C2×#452—51no—
194C2×C4×Q16—51no—
195C2×C4×Q16—51no—
196C2×C4×SD16—51no—
197C2×C4×SD16—51no—
198C2×#431—51no—
199C24×C5C2×D411yescharacteristic
200C23×D5—21no—
201C2×C5×Q8—21no—
202C2×C5×Q8—22no—
203C2×C5×Q8—22no—
204C2×C5×Q8C2412yes—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D412yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2411yescharacteristic
215C2×C22⋊D5—28no—
216C2×C22⋊D5—24no—
217C22×Dic5—21no—
218C22×Dic5—24no—
219C22×Dic5—24no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5C2×D414yes—
223C22×Dic5C2×D414yes—
224C22×Dic5C2×D411yescharacteristic
225C22×Dic5C2×D411yescharacteristic
226C22×Dic5C2×D411yescharacteristic
227C22×Dic5C2×D411yescharacteristic
228#709—216no—
229#709—28no—
230#709—28no—
231C2×D20—21no—
232C2×D20—22no—
233C2×D20#4114yes—
234C2×D20C2412yes—
235C2×C4×D5—28no—
236C2×C4×D5—24no—
237C2×C4×D5—24no—
238C2×C4×D5—24no—
239C2×C4×D5—44no—
240C2×C4×D5—44no—
241C2×Dic10—21no—
242C2×Dic10—22no—
243C2×Dic10—22no—
244C2×Dic10—22no—
245C2×Dic10—21no—
246C2×Dic10—24no—
247C2×Dic10—44no—
248C2×Dic10#4114yes—
249C2×Dic10C2412yes—
250C2×Dic10C2412yes—
251C2×C5×C8—22no—
252C2×C5×C8—22no—
253C2×C5×C8C2412yes—
254C2×C5×C8C2412yes—
255C5×C4⋊C4—24no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C4⋊C4C2412yes—
262C5×C22⋊C4—24no—
263C5×C22⋊C4—24no—
264C42×C5—24no—
265C22⋊Dic5—24no—
266#689—28no—
267#688—28no—
268#685—24no—
269#685—24no—
270C4⋊Dic5—21no—
271C4⋊Dic5—24no—
272C4⋊Dic5C2412yes—
273#683—24no—
274#683—24no—
275#683—24no—
276#683—24no—
277#683—24no—
278#683—24no—
279#683—24no—
280C4×Dic5—24no—
281C4×Dic5—24no—
282C4×Dic5—24no—
283C4×Dic5—24no—
284C4×Dic5C2×D414yes—
285C4×Dic5C2×D414yes—
286C4×Dic5C2×D412yes—
287C4×Dic5C2×D412yes—
288C4×Dic5C2412yes—
289C4×Dic5C2412yes—
290C2×#168—22no—
291C2×#168—22no—
292C2×#168C2412yes—
293C2×#168C2412yes—
294Dic20—28no—
295#677—28no—
296C22×#41—51no—
297C22×Q16—51no—
298C22×Q16—51no—
299C22×SD16—51no—
300C22×SD16—51no—
301#533—58no—
302#533—104no—
303C2×C4⋊Q8—51no—
304C2×C4⋊Q8—51no—
305C2×#125—101no—
306C2×C22⋊Q8—51no—
307C2×C22⋊Q8—101no—
308C2×C22⋊Q8C2×D511yescharacteristic
309C4×#41—58no—
310C4×#41—104no—
311C2×C4×Q8—51no—
312C2×C4×Q8—51no—
313C2×C4×Q8—51no—
314C2×C4×Q8—51no—
315C2×C4×Q8—101no—
316C2×C4×D4—51no—
317C2×C4×D4—51no—
318C2×C4×D4—101no—
319C2×C4×D4—101no—
320C2×#117—101no—
321C2×#117—101no—
322C2×#117C2×D511yescharacteristic
323C22×C42—51no—
324C22×C42—101no—
325#485—58no—
326#485C2×D518yescomplemented
327#475—58no—
328#474—58no—
329#462—58no—
330#461—58no—
331#452—58no—
332#452—58no—
333C4×Q16—58no—
334C4×Q16—58no—
335C4×SD16—58no—
336C4×SD16—58no—
337#431—58no—
338C2×#107—51no—
339C2×#107C2×D511yescharacteristic
340C2×#106—51no—
341C2×#106C2×D511yescharacteristic
342C2×C4⋊C8—51no—
343C2×C4⋊C8—51no—
344C2×#103—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103C2×D511yescharacteristic
349C2×#103C2×D511yescharacteristic
350C2×#102—51no—
351C2×#102—51no—
352C2×C22⋊C8—51no—
353C2×C22⋊C8C2×D511yescharacteristic
354C2×C4×C8—51no—
355C2×C4×C8—51no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5C22×D412yes—
360C23×C5C22×D411yescharacteristic
361C22×D5—24no—
362C22×D5—22no—
363C22×D5—42no—
364C22×D5—42no—
365C5×Q8—22no—
366C5×Q8—22no—
367C5×Q8—42no—
368C2×C4×C5—22no—
369C2×C4×C5—24no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—42no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5C22×D412yes—
381C2×C4×C5C22×D411yescharacteristic
382C2×C4×C5C2×#4112yes—
383C2×C4×C5C2×#4112yes—
384C2×C4×C5C2511yescharacteristic
385C22⋊D5—216no—
386C2×Dic5—24no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—28no—
391C2×Dic5—28no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396C2×Dic5#13514yes—
397C2×Dic5#13714yes—
398C2×Dic5C22×D412yes—
399C2×Dic5C22×D412yes—
400C2×Dic5C22×D412yes—
401C2×Dic5C22×D412yes—
402D20—24no—
403D20—22no—
404D20C2×#4114yes—
405C4×D5—216no—
406C4×D5—48no—
407C4×D5—48no—
408Dic10—24no—
409Dic10—22no—
410Dic10—22no—
411Dic10—22no—
412Dic10—42no—
413Dic10—48no—
414Dic10C2×#4114yes—
415C5×C8—22no—
416C5×C8—22no—
417#168—22no—
418#168—22no—
419C2×#41—54no—
420C2×#41—104no—
421C2×#41—104no—
422C2×#41—102no—
423C22×Q8—51no—
424C22×Q8—51no—
425C22×Q8—101no—
426C22×Q8C22×D511yescharacteristic
427C22×D4—51no—
428C22×D4—101no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—101no—
432C23×C4—101no—
433C23×C4—101no—
434C23×C4C22×D511yescharacteristic
435C2×Q16—54no—
436C2×Q16—54no—
437C2×Q16—104no—
438C2×Q16—104no—
439C2×SD16—54no—
440C2×SD16—54no—
441C2×SD16—104no—
442C2×SD16—104no—
443C22×C8—51no—
444C22×C8—51no—
445C22×C8C22×D511yescharacteristic
446C22×C8C22×D511yescharacteristic
447C4⋊Q8—54no—
448C4⋊Q8—54no—
449C4⋊Q8—102no—
450C4⋊Q8—102no—
451#125—108no—
452C22⋊Q8—22no—
453C22⋊Q8—54no—
454C22⋊Q8—108no—
455C22⋊Q8—102no—
456C22⋊Q8C22×D514yes—
457C4×Q8—54no—
458C4×Q8—54no—
459C4×Q8—54no—
460C4×Q8—54no—
461C4×Q8—102no—
462C4×Q8—102no—
463C4×Q8—102no—
464C4×Q8—108no—
465C4×Q8—102no—
466C4×D4—54no—
467C4×D4—54no—
468C4×D4—102no—
469C4×D4—102no—
470C4×D4—108no—
471C4×D4—108no—
472#117—22no—
473#117—108no—
474#117—108no—
475#117C22×D514yes—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—51no—
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⋊C4—101no—
486C2×C4⋊C4C22×D511yescharacteristic
487C2×C4⋊C4C22×D511yescharacteristic
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493C2×C22⋊C4—101no—
494C2×C42—21no—
495C2×C42—51no—
496C2×C42—51no—
497C2×C42—54no—
498C2×C42—51no—
499C2×C42—51no—
500C2×C42—54no—
501C2×C42—108no—
502C2×C42—101no—
503C2×C42—101no—
504C2×C42—101no—
505C2×C42—101no—
506#107—54no—
507#107C22×D514yes—
508#106—54no—
509#106C22×D514yes—
510C4⋊C8—54no—
511C4⋊C8—54no—
512#103—54no—
513#103—54no—
514#103—54no—
515#103—54no—
516#103C22×D514yes—
517#103C22×D514yes—
518#102—54no—
519#102—54no—
520C22⋊C8—54no—
521C22⋊C8C22×D514yes—
522C4×C8—54no—
523C4×C8—54no—
524C22×C5—22no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5—44no—
528C22×C5#52512yes—
529C22×C5C2×#13512yes—
530C22×C5C2×#13712yes—
531C22×C5C23×D411yescharacteristic
532C2×D5—24no—
533C2×D5—48no—
534C2×D5—42no—
535C2×D5—42no—
536C4×C5—22no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5—42no—
541C4×C5#52512yes—
542C4×C5C22×#4111yescharacteristic
543C4×C5C22×#4111yescharacteristic
544Dic5—24no—
545Dic5—22no—
546Dic5—22no—
547Dic5—42no—
548Dic5—42no—
549Dic5C2×#13514yes—
550Dic5C2×#13714yes—
551C24—101no—
552C24D4×D511yescharacteristic
553#41—108no—
554#41—108no—
555#41—1016no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—54no—
560C2×Q8—52no—
561C2×Q8—52no—
562C2×Q8—104no—
563C2×Q8—101no—
564C2×Q8—101no—
565C2×Q8—102no—
566C2×Q8—102no—
567C2×Q8—102no—
568C2×Q8—204no—
569C2×Q8C23×D512yes—
570C2×D4—54no—
571C2×D4—52no—
572C2×D4—108no—
573C2×D4—104no—
574C2×D4—101no—
575C2×D4—102no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—51no—
583C22×C4—51no—
584C22×C4—54no—
585C22×C4—54no—
586C22×C4—51no—
587C22×C4—51no—
588C22×C4—104no—
589C22×C4—104no—
590C22×C4—108no—
591C22×C4—104no—
592C22×C4—104no—
593C22×C4—101no—
594C22×C4—104no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—204no—
598C22×C4—204no—
599C22×C4D4×D512yes—
600C22×C4D4×D511yescharacteristic
601C22×C4C23×D512yes—
602C22×C4C23×D511yescharacteristic
603Q16—108no—
604Q16—108no—
605SD16—108no—
606SD16—108no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—52no—
610C2×C8—52no—
611C2×C8—102no—
612C2×C8—102no—
613C2×C8C23×D512yes—
614C2×C8C23×D512yes—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—52no—
620C4⋊C4—104no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4—104no—
627C4⋊C4—101no—
628C4⋊C4—104no—
629C4⋊C4C23×D512yes—
630C4⋊C4C23×D512yes—
631C4⋊C4C23×D512yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—104no—
635C22⋊C4—104no—
636C22⋊C4—104no—
637C42—24no—
638C42—54no—
639C42—54no—
640C42—52no—
641C42—52no—
642C42—52no—
643C42—52no—
644C42—104no—
645C42—104no—
646C42—104no—
647C42—104no—
648C2×C5—42no—
649C2×C5#310714yescomplemented
650C2×C5C2×#52511yescharacteristic
651C2×C5C22×#13511yescharacteristic
652C2×C5C22×#13711yescharacteristic
653D5—44no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—104no—
658C23—102no—
659C23—202no—
660C23—202no—
661C23C2×D4×D512yes—
662C23C2×D4×D511yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—42no—
666Q8—54no—
667Q8—104no—
668Q8—102no—
669Q8—102no—
670Q8—102no—
671Q8—208no—
672Q8—202no—
673D4—54no—
674D4—1016no—
675D4—104no—
676D4—102no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—54no—
690C2×C4—54no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—52no—
694C2×C4—52no—
695C2×C4—1016no—
696C2×C4—108no—
697C2×C4—108no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—104no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—208no—
705C2×C4—208no—
706C2×C4—202no—
707C2×C4—202no—
708C2×C4C2×D4×D512yes—
709C2×C4C2×D4×D511yescharacteristic
710C2×C4D5×#4112yes—
711C2×C4D5×#4112yes—
712C2×C4C24×D511yescharacteristic
713C8—22no—
714C8—22no—
715C8—102no—
716C8—102no—
717C5C2×#310711yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—104no—
723C22—202no—
724C22—202no—
725C22—208no—
726C22#6599012yes—
727C22D5×#13512yes—
728C22D5×#13712yes—
729C22C22×D4×D511yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—54no—
736C4—54no—
737C4—104no—
738C4—102no—
739C4—102no—
740C4—202no—
741C4—202no—
742C4#6599012yes—
743C4C2×D5×#4111yescharacteristic
744C4C2×D5×#4111yescharacteristic
745C2—42no—
746C2—204no—
747C2#1061322414yesdirect product factor
748C2C2×#6599011yescharacteristic
749C2C2×D5×#13511yescharacteristic
750C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#485C2
socleC23×C5C22×D4
prime radicalC22×#709C22
hypercenterC2×#485D5
hypocenterC5C2×#3107
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#65956C2semidirect
3. C2×C5×#485C2semidirect
5. C2×#65285C2semidirect
6. #10613224C2direct (N × H)
7. C2×#65179C2semidirect
8. C2×#65162C2semidirect
9. C2×#65143C2semidirect
10. C2×#65141C2semidirect
11. C2×#65082C2semidirect
12. C2×#65107C2semidirect
13. C2×#65079C2semidirect
14. C2×#65077C2semidirect
16. C2×#65007C2semidirect
29. #65956C22semidirect
46. C5×#485C22semidirect
60. #65285C22semidirect
67. #65179C22semidirect
68. #65162C22semidirect
69. #65143C22semidirect
70. #65141C22semidirect
71. #65107C22semidirect
72. #65082C22semidirect
73. #65079C22semidirect
74. #65077C22semidirect
76. #65007C22semidirect
187. C2×#485D5semidirect
326. #485C2×D5semidirect
649. C2×C5#3107semidirect
717. C5C2×#3107semidirect
747. C2#10613224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659562
C2×#658562
C2×C5×#4852
C2×#653362
C2×#652852
#106132242
C2×#651792
C2×#651622
C2×#651432
C2×#651412
C2×#650822
C2×#651072
C2×#650792
C2×#650772
C2×#650222
C2×#650072
C2×#31075