Finite Group Databasebeta

← C2×#10612518 #12969117

Subgroups — C2×#10612518 #12969117

Order 1280.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65977C211yesmaximal, characteristic, complemented
2C2×#65937C211yesmaximal, characteristic, complemented
3C2×C5×#468C211yesmaximal, characteristic, complemented
4C2×#65457C211yesmaximal, characteristic, complemented
5C2×#65453C211yesmaximal, characteristic, complemented
6C2×#65423C211yesmaximal, characteristic, complemented
7C2×#65411C211yesmaximal, characteristic, complemented
8C2×#65340C211yesmaximal, characteristic, complemented
9C2×#65327C211yesmaximal, characteristic
10#10612518C2116yesmaximal, direct product factor
11C2×#65163C211yesmaximal, characteristic, complemented
12C2×#65178C211yesmaximal, characteristic, complemented
13C2×#65084C211yesmaximal, characteristic, complemented
14C2×#65079C211yesmaximal, characteristic, complemented
15C2×#65054C211yesmaximal, characteristic, complemented
16C2×#65045C211yesmaximal, characteristic, complemented
17C22×C5×SD16C2211yescharacteristic
18C22×C5×M16C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×#121C2211yescharacteristic
21C2×#4093C2211yescharacteristic
22C2×Q8×Dic5C2211yescharacteristic
23C22×#689C2211yescharacteristic
24C2×#4082—21no—
25C2×#4082C2211yescharacteristic
26C2×#4081—21no—
27C2×D4×Dic5C2211yescharacteristic
28C22×#686C2211yescharacteristic
29C2×#4076C2211yescharacteristic
30C2×#4072C2211yescharacteristic
31C2×#4070C2211yescharacteristic
32C23×#168C2211yescharacteristic
33C22×#677C2211yescharacteristic
34#65977—24no—
35#65977C2218yescomplemented
36#65937—24no—
37#65937C2218yescomplemented
38C2×#4044—21no—
39C2×#4043—21no—
40C2×#4039C2211yescharacteristic
41C2×#4034C2211yescharacteristic
42C2×#4034C2211yescharacteristic
43C2×#4033C2211yescharacteristic
44C2×#4031—21no—
45C2×#4029—21no—
46C2×#4025—21no—
47C2×#4024—21no—
48C5×#468C2218yescomplemented
49C2×C5×#107C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×C5×#102C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54#65457C2218yescomplemented
55#65453C2218yescomplemented
56#65423C2218yescomplemented
57#65411C2218yescomplemented
58C2×#3953C2211yescharacteristic
59C2×#3950C2211yescharacteristic
60C2×#3948C2211yescharacteristic
61C2×#3947C2211yescharacteristic
62C2×#3947C2211yescharacteristic
63C2×C8×Dic5C2211yescharacteristic
64C2×C8×Dic5C2211yescharacteristic
65#65340C2218yescomplemented
66#65327C2218yes—
67C2×#3942C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71#65178C2218yescomplemented
72#65163C2218yescomplemented
73#65084C2218yescomplemented
74#65079C2218yescomplemented
75#65054C2218yescomplemented
76#65045C2218yescomplemented
77C2×#3175—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C23×Dic5—21no—
84C22×D20C2311yescharacteristic
85C22×C4×D5—21no—
86C22×Dic10—21no—
87C22×Dic10—21no—
88C22×Dic10C2311yescharacteristic
89C2×C5×SD16—24no—
90C2×C5×SD16C2314yes—
91C2×C5×M16—24no—
92C2×C5×M16C2314yes—
93C22×C5×C8C2311yescharacteristic
94C22×C5×C8C2311yescharacteristic
95C5×C22⋊Q8—22no—
96C5×C22⋊Q8C2314yes—
97C5×#121—22no—
98C5×#121C2314yes—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C22⋊Dic5—21no—
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5D411yescharacteristic
109C2×C22⋊Dic5D411yescharacteristic
110#4093—22no—
111#4093C2314yes—
112Q8×Dic5—22no—
113Q8×Dic5C2314yes—
114C2×#689—24no—
115C2×#689C2314yes—
116#4082—28no—
117#4082—22no—
118#4082C2314yes—
119#4081—28no—
120D4×Dic5—22no—
121D4×Dic5C2314yes—
122C2×#686—24no—
123C2×#686C2314yes—
124#4076—22no—
125#4076C2314yes—
126C2×#685—21no—
127C2×#685—21no—
128C2×#685—21no—
129C2×#685—21no—
130#4072D414yes—
131#4072C2314yes—
132C2×C4⋊Dic5—21no—
133C2×C4⋊Dic5D411yescharacteristic
134C2×C4⋊Dic5D411yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136C2×C4⋊Dic5C2311yescharacteristic
137#4070—22no—
138#4070C2314yes—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×C4×Dic5—21no—
144C2×C4×Dic5—21no—
145C2×C4×Dic5C2311yescharacteristic
146C2×C4×Dic5C2311yescharacteristic
147C22×#168—24no—
148C22×#168C2314yes—
149C22×#168C2311yescharacteristic
150C22×#168C2311yescharacteristic
151C2×#677—24no—
152C2×#677C2314yes—
153#4044—28no—
154#4043—28no—
155#4039—22no—
156#4039C2314yes—
157#4034—22no—
158#4034—22no—
159#4034C2314yes—
160#4034C2314yes—
161#4033—22no—
162#4033C2314yes—
163#4031—28no—
164#4029—28no—
165#4025—28no—
166#4024—28no—
167C5×#107C2314yes—
168C5×#103C2314yes—
169C5×#102C2314yes—
170#3967C2314yes—
171#3964C2314yes—
172#3953C2314yes—
173#3950C2314yes—
174#3948C2314yes—
175#3947C2314yes—
176#3947C2314yes—
177C8×Dic5C2314yes—
178C8×Dic5C2314yes—
179#3942C2314yes—
180#3941C2314yes—
181#3939C2314yes—
182#3939C2314yes—
183C2×#542—51no—
184C2×#542—51no—
185#3175—516no—
186C2×#500—51no—
187C2×#495—51no—
188C2×#489—51no—
189C2×#489—51no—
190C2×#468—51no—
191C2×#468D511yescharacteristic, complemented
192C2×#467—51no—
193C2×#466—51no—
194C2×#440—51no—
195C2×#440—51no—
196C2×C4×Q16—51no—
197C2×C4×D8—51no—
198C2×#405—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C23×D5—21no—
202C2×C5×Q8—21no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
205C2×C5×Q8C2412yes—
206C2×C5×D4—24no—
207C2×C5×D4—21no—
208C2×C5×D4—22no—
209C2×C5×D4—22no—
210C2×C5×D4—82no—
211C2×C5×D4C2412yes—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D412yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2411yescharacteristic
221C2×C22⋊D5—24no—
222C2×C22⋊D5—82no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—24no—
227C22×Dic5—82no—
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231C22×Dic5C2×D411yescharacteristic
232C2×D20—22no—
233C2×D20—22no—
234C2×D20—21no—
235C2×D20C2412yes—
236C2×C4×D5—24no—
237C2×C4×D5—82no—
238C2×Dic10—22no—
239C2×Dic10—22no—
240C2×Dic10—21no—
241C2×Dic10—24no—
242C2×Dic10—24no—
243C2×Dic10—82no—
244C2×Dic10—82no—
245C2×Dic10C2412yes—
246C5×SD16—28no—
247C5×M16—28no—
248C2×C5×C8—22no—
249C2×C5×C8#4114yes—
250C2×C5×C8C2412yes—
251C2×C5×C8C2412yes—
252C5×C4⋊C4—24no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4C2412yes—
256C5×C4⋊C4C2412yes—
257C5×C22⋊C4—24no—
258C5×C22⋊C4—24no—
259C22⋊Dic5—24no—
260C22⋊Dic5—24no—
261C22⋊Dic5—24no—
262C22⋊Dic5—24no—
263C22⋊Dic5C2×D414yes—
264C22⋊Dic5C2×D414yes—
265#689—28no—
266#686—28no—
267#685—24no—
268#685—24no—
269#685—24no—
270#685—24no—
271C4⋊Dic5—21no—
272C4⋊Dic5—21no—
273C4⋊Dic5—24no—
274C4⋊Dic5C2×D414yes—
275C4⋊Dic5C2×D414yes—
276C4⋊Dic5C2412yes—
277C4⋊Dic5C2412yes—
278#683—24no—
279#683—24no—
280#683—24no—
281#683—24no—
282C4×Dic5—24no—
283C4×Dic5—24no—
284C4×Dic5C2×D412yes—
285C4×Dic5C2×D412yes—
286C4×Dic5C2412yes—
287C4×Dic5C2412yes—
288C2×#168—22no—
289C2×#168—28no—
290C2×#168#4114yes—
291C2×#168C2412yes—
292C2×#168C2412yes—
293#677—28no—
294C22×Q16—51no—
295C22×SD16—51no—
296C22×SD16C2×D511yescharacteristic
297C22×D8—51no—
298C22×M16C2×D511yescharacteristic
299C23×C8—51no—
300#542—58no—
301#542—58no—
302#542—104no—
303#542—104no—
304C2×C4⋊Q8—51no—
305C2×C4⋊Q8—51no—
306C2×#126—101no—
307C2×#126—101no—
308C2×#124—51no—
309C2×#124—51no—
310C2×#124—101no—
311C2×#124—101no—
312C2×#123—101no—
313C2×#123—101no—
314C2×C22⋊Q8—51no—
315C2×C22⋊Q8—101no—
316C2×C22⋊Q8—101no—
317C2×C22⋊Q8C2×D511yescharacteristic
318C2×#121—51no—
319C2×#121C2×D511yescharacteristic
320C2×C4×Q8—51no—
321C2×C4×Q8—51no—
322C2×C4×D4—51no—
323C2×C4×D4—51no—
324C2×#117—51no—
325#500—58no—
326#495—58no—
327#489—58no—
328#489—58no—
329#468—58no—
330#468C2×D518yescomplemented
331#467—58no—
332#466—58no—
333#440—58no—
334#440—58no—
335C4×Q16—58no—
336C4×D8—58no—
337C2×#107—51no—
338C2×#107—51no—
339C2×#107—51no—
340C2×#107C2×D511yescharacteristic
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#103C2×D511yescharacteristic
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102C2×D511yescharacteristic
349#405—58no—
350C2×#97—51no—
351C2×#97—51no—
352C2×C4×C8—51no—
353C2×C4×C8—51no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5C22×D412yes—
362C23×C5C22×D411yescharacteristic
363C22×D5—22no—
364C22×D5—42no—
365C22×D5—42no—
366C22×D5—42no—
367C5×Q8—22no—
368C5×Q8—22no—
369C5×Q8—42no—
370C5×D4—22no—
371C5×D4—22no—
372C5×D4—42no—
373C5×D4—84no—
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—84no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—42no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400C2×Dic5—84no—
401C2×Dic5C22×D412yes—
402C2×Dic5C22×D412yes—
403C2×Dic5C22×D412yes—
404C2×Dic5C22×D412yes—
405D20—22no—
406D20—22no—
407D20—42no—
408C4×D5—84no—
409Dic10—22no—
410Dic10—22no—
411Dic10—42no—
412Dic10—84no—
413Dic10—84no—
414C5×C8—22no—
415C5×C8C2×#4114yes—
416#168—22no—
417#168C2×#4114yes—
418C22×Q8—51no—
419C22×Q8—101no—
420C22×Q8—101no—
421C22×Q8C22×D511yescharacteristic
422C22×D4—21no—
423C22×D4—51no—
424C22×D4—101no—
425C22×D4C22×D511yescharacteristic
426C23×C4—101no—
427C23×C4—101no—
428C23×C4C22×D511yescharacteristic
429C2×Q16—54no—
430C2×Q16—104no—
431C2×SD16—24no—
432C2×SD16—54no—
433C2×SD16—104no—
434C2×SD16C22×D514yes—
435C2×D8—54no—
436C2×D8—104no—
437C2×M16—24no—
438C2×M16C22×D514yes—
439C22×C8—51no—
440C22×C8—51no—
441C22×C8—54no—
442C22×C8—104no—
443C22×C8C22×D511yescharacteristic
444C22×C8C22×D511yescharacteristic
445C4⋊Q8—54no—
446C4⋊Q8—54no—
447C4⋊Q8—102no—
448C4⋊Q8—102no—
449#126—108no—
450#126—108no—
451#124—54no—
452#124—54no—
453#124—102no—
454#124—102no—
455#124—108no—
456#124—108no—
457#123—108no—
458#123—108no—
459C22⋊Q8—22no—
460C22⋊Q8—54no—
461C22⋊Q8—108no—
462C22⋊Q8—108no—
463C22⋊Q8—102no—
464C22⋊Q8C22×D514yes—
465#121—22no—
466#121—54no—
467#121—102no—
468#121C22×D514yes—
469C4×Q8—54no—
470C4×Q8—54no—
471C4×Q8—102no—
472C4×Q8—102no—
473C4×D4—54no—
474C4×D4—54no—
475C4×D4—102no—
476C4×D4—102no—
477#117—54no—
478#117—54no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—51no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—51no—
495C2×C22⋊C4—101no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4—101no—
502C2×C22⋊C4—101no—
503C2×C42—51no—
504C2×C42—51no—
505C2×C42—101no—
506C2×C42—101no—
507#107—54no—
508#107—54no—
509#107—54no—
510#107C22×D514yes—
511#103—54no—
512#103—54no—
513#103—54no—
514#103C22×D514yes—
515#102—54no—
516#102—54no—
517#102—54no—
518#102C22×D514yes—
519#97—54no—
520#97—54no—
521C4×C8—54no—
522C4×C8—54no—
523C22×C5—22no—
524C22×C5—22no—
525C22×C5—22no—
526C22×C5—44no—
527C22×C5—42no—
528C22×C5—42no—
529C22×C5—42no—
530C22×C5—84no—
531C22×C5#53212yes—
532C22×C5#57612yes—
533C22×C5#57812yes—
534C22×C5C23×D411yescharacteristic
535C2×D5—42no—
536C2×D5—42no—
537C2×D5—42no—
538C2×D5—84no—
539C4×C5—22no—
540C4×C5—42no—
541C4×C5—42no—
542C4×C5—42no—
543C4×C5#53212yes—
544C4×C5C22×#4111yescharacteristic
545C4×C5C22×#4111yescharacteristic
546Dic5—22no—
547Dic5—22no—
548Dic5—22no—
549Dic5—22no—
550Dic5—42no—
551Dic5—42no—
552Dic5—42no—
553C24—21no—
554C24—101no—
555C24D4×D511yescharacteristic
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—52no—
560C2×Q8—104no—
561C2×Q8—104no—
562C2×Q8—101no—
563C2×Q8—102no—
564C2×Q8—102no—
565C2×Q8—402no—
566C2×Q8—402no—
567C2×Q8C23×D512yes—
568C2×D4—24no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—52no—
573C2×D4—82no—
574C2×D4—104no—
575C2×D4—101no—
576C2×D4—102no—
577C2×D4—102no—
578C2×D4—402no—
579C2×D4C23×D512yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—51no—
586C22×C4—51no—
587C22×C4—51no—
588C22×C4—51no—
589C22×C4—104no—
590C22×C4—104no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—402no—
595C22×C4—402no—
596C22×C4D4×D512yes—
597C22×C4D4×D511yescharacteristic
598C22×C4C23×D512yes—
599C22×C4C23×D511yescharacteristic
600Q16—108no—
601SD16—28no—
602SD16—108no—
603D8—108no—
604M16—28no—
605C2×C8—22no—
606C2×C8—54no—
607C2×C8—52no—
608C2×C8—52no—
609C2×C8—108no—
610C2×C8—102no—
611C2×C8#71114yes—
612C2×C8C23×D512yes—
613C2×C8C23×D512yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—54no—
618C4⋊C4—54no—
619C4⋊C4—52no—
620C4⋊C4—52no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—101no—
626C4⋊C4—101no—
627C4⋊C4—104no—
628C4⋊C4C23×D512yes—
629C4⋊C4C23×D512yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—54no—
633C22⋊C4—54no—
634C22⋊C4—104no—
635C22⋊C4—104no—
636C22⋊C4—104no—
637C22⋊C4—104no—
638C22⋊C4—104no—
639C22⋊C4—104no—
640C22⋊C4—104no—
641C22⋊C4—104no—
642C42—52no—
643C42—52no—
644C42—52no—
645C42—52no—
646C42—104no—
647C42—104no—
648C2×C5—42no—
649C2×C5—82no—
650C2×C5#317514yescomplemented
651C2×C5C2×#53211yescharacteristic
652C2×C5C2×#57611yescharacteristic
653C2×C5C2×#57811yescharacteristic
654D5—82no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—102no—
663C23—202no—
664C23—202no—
665C23—202no—
666C23C2×D4×D512yes—
667C23C2×D4×D511yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—102no—
672Q8—102no—
673Q8—202no—
674Q8—404no—
675Q8—404no—
676D4—22no—
677D4—22no—
678D4—42no—
679D4—84no—
680D4—102no—
681D4—102no—
682D4—202no—
683D4—404no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—52no—
695C2×C4—52no—
696C2×C4—52no—
697C2×C4—52no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—202no—
706C2×C4—202no—
707C2×C4—202no—
708C2×C4—404no—
709C2×C4—404no—
710C2×C4C2×D4×D512yes—
711C2×C4C2×D4×D511yescharacteristic
712C2×C4C2×#71112yes—
713C2×C4D5×#4112yes—
714C2×C4C24×D511yescharacteristic
715C8—22no—
716C8—54no—
717C8—102no—
718C8C2×#71114yes—
719C5C2×#317511yescharacteristic, complemented, Sylow
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—404no—
732C22#6593012yes—
733C22#6610812yes—
734C22#6611312yes—
735C22C22×D4×D511yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—102no—
741C4—102no—
742C4—102no—
743C4—102no—
744C4—202no—
745C4—202no—
746C4—202no—
747C4#6593012yes—
748C4C22×#71111yescharacteristic
749C4C2×D5×#4111yescharacteristic
750C2—42no—
751C2—82no—
752C2—402no—
753C2#1061251814yesdirect product factor
754C2C2×#6593011yescharacteristic
755C2C2×#6610811yescharacteristic
756C2C2×#6611311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#468C2
socleC23×C5C22×D4
prime radicalC2×#65327C2
hypercenterC2×#468D5
hypocenterC5C2×#3175
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#65977C2semidirect
2. C2×#65937C2semidirect
3. C2×C5×#468C2semidirect
4. C2×#65457C2semidirect
5. C2×#65453C2semidirect
6. C2×#65423C2semidirect
7. C2×#65411C2semidirect
8. C2×#65340C2semidirect
10. #10612518C2direct (N × H)
11. C2×#65163C2semidirect
12. C2×#65178C2semidirect
13. C2×#65084C2semidirect
14. C2×#65079C2semidirect
15. C2×#65054C2semidirect
16. C2×#65045C2semidirect
35. #65977C22semidirect
37. #65937C22semidirect
48. C5×#468C22semidirect
54. #65457C22semidirect
55. #65453C22semidirect
56. #65423C22semidirect
57. #65411C22semidirect
65. #65340C22semidirect
71. #65178C22semidirect
72. #65163C22semidirect
73. #65084C22semidirect
74. #65079C22semidirect
75. #65054C22semidirect
76. #65045C22semidirect
191. C2×#468D5semidirect
330. #468C2×D5semidirect
650. C2×C5#3175semidirect
719. C5C2×#3175semidirect
753. C2#10612518direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659772
C2×#659372
C2×C5×#4682
C2×#654572
C2×#654532
C2×#654232
C2×#654112
C2×#653402
C2×#653272
#106125182
C2×#651632
C2×#651782
C2×#650842
C2×#650792
C2×#650542
C2×#650452
C2×#31755