Finite Group Databasebeta

← C2×#10615189 #12969162

Subgroups — C2×#10615189 #12969162

Order 1280.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#542C211yesmaximal, characteristic
2C2×#65852C211yesmaximal, characteristic, complemented
3#10615189C2116yesmaximal, direct product factor
4C2×#65369C211yesmaximal, characteristic, complemented
5C2×#65382C211yesmaximal, characteristic, complemented
6C2×#65349C211yesmaximal, characteristic, complemented
7C2×#65345C211yesmaximal, characteristic, complemented
8C2×#65341C211yesmaximal, characteristic, complemented
9C2×#65340C211yesmaximal, characteristic, complemented
10C2×#65331C211yesmaximal, characteristic
11C2×#65330C211yesmaximal, characteristic
12C2×#65319C211yesmaximal, characteristic, complemented
13C2×C4×#689C211yesmaximal, characteristic, complemented
14C2×C4×#687C211yesmaximal, characteristic, complemented
15C2×#65307C211yesmaximal, characteristic, complemented
16C2×#65286C211yesmaximal, characteristic, complemented
17C5×#542—24no—
18C5×#542C2218yes—
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#126—21no—
21C2×C5×#124—21no—
22C2×C5×#124C2211yescharacteristic
23C2×C5×#123—21no—
24C2×C5×C22⋊Q8—21no—
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×#121C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×#689C2211yescharacteristic
31C22×#689C2211yescharacteristic
32C22×#687C2211yescharacteristic
33C22×#687C2211yescharacteristic
34C2×#4070C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65852—24no—
39#65852C2218yescomplemented
40C2×#4035—21no—
41C2×#4035—21no—
42C2×#4025—21no—
43C2×#4025—21no—
44C2×#4016C2211yescharacteristic
45C2×#4015C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C2×C4×Dic10C2211yescharacteristic
48C2×#3967C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52#65382C2218yescomplemented
53#65369C2218yescomplemented
54#65349C2218yescomplemented
55#65345C2218yescomplemented
56#65341C2218yescomplemented
57#65340C2218yescomplemented
58#65331C2218yes—
59#65330C2218yes—
60#65319C2218yescomplemented
61C4×#689C2218yescomplemented
62#65307C2218yescomplemented
63C4×#687C2218yescomplemented
64#65286C2218yescomplemented
65C2×#3942C2211yescharacteristic
66C2×#3942C2211yescharacteristic
67C2×#3942C2211yescharacteristic
68C2×#3942C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×#3935C2211yescharacteristic
74C2×#3935C2211yescharacteristic
75C2×C4×#168C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3178—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4—21no—
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C23×C4×C5C2311yescharacteristic
84C22×Dic10C2311yescharacteristic
85C22×Dic10C2311yescharacteristic
86C5×C4⋊Q8—22no—
87C5×C4⋊Q8C2314yes—
88C5×#126—28no—
89C5×#124—28no—
90C5×#124—22no—
91C5×#124C2314yes—
92C5×#123—28no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—28no—
95C5×C22⋊Q8C2314yes—
96C5×#121—22no—
97C5×#121C2314yes—
98C4×C5×Q8—22no—
99C4×C5×Q8C2314yes—
100C4×C5×D4—22no—
101C4×C5×D4C2314yes—
102C5×#117D414yes—
103C5×#117C2314yes—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4D411yescharacteristic
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4D411yescharacteristic
117C2×C5×C22⋊C4D411yescharacteristic
118C2×C42×C5—21no—
119C2×C42×C5C2311yescharacteristic
120C2×C42×C5C2311yescharacteristic
121C2×C22⋊Dic5—21no—
122C2×C22⋊Dic5—21no—
123C2×#689—24no—
124C2×#689—24no—
125C2×#689C2314yes—
126C2×#689C2314yes—
127C2×#687—24no—
128C2×#687—24no—
129C2×#687C2314yes—
130C2×#687C2314yes—
131C2×C4⋊Dic5—21no—
132C2×C4⋊Dic5—21no—
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135#4070—22no—
136#4070—22no—
137#4070C2314yes—
138#4070C2314yes—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×#683—21no—
144C2×#683—21no—
145C2×C4×Dic5—21no—
146C2×C4×Dic5—21no—
147C2×#681—24no—
148C2×#681C2314yes—
149C22×#168—24no—
150C22×#168C2314yes—
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155#4035—28no—
156#4035—28no—
157#4025—28no—
158#4025—28no—
159#4016—22no—
160#4016C2314yes—
161#4015—22no—
162#4015C2314yes—
163C4×Dic10—22no—
164C4×Dic10—22no—
165C4×Dic10C2314yes—
166C4×Dic10C2314yes—
167#3967C2314yes—
168#3967C2314yes—
169#3964C2314yes—
170#3964C2314yes—
171#3942C2314yes—
172#3942C2314yes—
173#3942C2314yes—
174#3942C2314yes—
175#3940C2314yes—
176#3940C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179#3935C2314yes—
180#3935C2314yes—
181C4×#168C2314yes—
182C4×#168C2314yes—
183C2×#542D511yescharacteristic
184C2×#541—51no—
185#3178—516no—
186C2×#501—51no—
187C2×#497—51no—
188C2×#488—51no—
189C2×#487—51no—
190C2×#470—51no—
191C2×#468—51no—
192C2×#467—51no—
193C2×#465—51no—
194C2×#441—51no—
195C2×#440—51no—
196C2×C4×Q16—51no—
197C2×C4×SD16—51no—
198C2×#405—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C2×C5×Q8—21no—
202C2×C5×Q8—24no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
205C2×C5×Q8—82no—
206C2×C5×Q8C2412yes—
207C2×C5×D4—24no—
208C2×C5×D4—21no—
209C2×C5×D4—22no—
210C2×C5×D4—22no—
211C2×C5×D4—82no—
212C2×C5×D4C2412yes—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—24no—
219C22×C4×C5—82no—
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2411yescharacteristic
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C2×Dic10—22no—
233C2×Dic10—22no—
234C2×Dic10—22no—
235C2×Dic10—22no—
236C2×Dic10—21no—
237C2×Dic10—21no—
238C2×Dic10C2412yes—
239C2×Dic10C2412yes—
240C5×C4⋊C4—24no—
241C5×C4⋊C4—24no—
242C5×C4⋊C4—24no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—21no—
245C5×C4⋊C4C2×D414yes—
246C5×C4⋊C4C2×D414yes—
247C5×C4⋊C4C2412yes—
248C5×C4⋊C4C2412yes—
249C5×C22⋊C4—24no—
250C5×C22⋊C4—24no—
251C5×C22⋊C4—24no—
252C5×C22⋊C4—24no—
253C5×C22⋊C4—24no—
254C5×C22⋊C4C2×D414yes—
255C5×C22⋊C4C2×D414yes—
256C42×C5—24no—
257C42×C5C2×D412yes—
258C42×C5C2×D412yes—
259C42×C5C2412yes—
260C42×C5C2412yes—
261C22⋊Dic5—24no—
262C22⋊Dic5—24no—
263#689—28no—
264#689—28no—
265#687—28no—
266#687—28no—
267C4⋊Dic5—21no—
268C4⋊Dic5—21no—
269C4⋊Dic5—24no—
270C4⋊Dic5—24no—
271C4⋊Dic5C2412yes—
272C4⋊Dic5C2412yes—
273#683—24no—
274#683—24no—
275#683—24no—
276#683—24no—
277#683—24no—
278#683—24no—
279C4×Dic5—24no—
280C4×Dic5—24no—
281#681—28no—
282C2×#168—22no—
283C2×#168—22no—
284C2×#168—28no—
285C2×#168#4114yes—
286C2×#168#4114yes—
287C2×#168C2412yes—
288C2×#168C2412yes—
289C2×#168C2412yes—
290C2×#168C2412yes—
291C22×Q16—51no—
292C22×Q16—51no—
293C22×SD16—51no—
294C22×SD16—51no—
295C22×M16—51no—
296C23×C8—51no—
297#542—24no—
298#542C2×D518yes—
299#541—58no—
300#541—104no—
301C2×C4⋊Q8—51no—
302C2×C4⋊Q8C2×D511yescharacteristic
303C2×#126—21no—
304C2×#126—101no—
305C2×#126—101no—
306C2×#125—51no—
307C2×#125—101no—
308C2×#125—101no—
309C2×#124—21no—
310C2×#124C2×D511yescharacteristic
311C2×#123—21no—
312C2×C22⋊Q8—21no—
313C2×C22⋊Q8—51no—
314C2×C22⋊Q8—51no—
315C2×C22⋊Q8C2×D511yescharacteristic
316C2×#121C2×D511yescharacteristic
317C2×C4×Q8—51no—
318C2×C4×Q8—51no—
319C2×C4×Q8C2×D511yescharacteristic
320C2×C4×D4C2×D511yescharacteristic
321C2×#117C2×D511yescharacteristic
322#501—58no—
323#497—58no—
324#488—58no—
325#487—58no—
326#470—58no—
327#468—58no—
328#467—58no—
329#465—58no—
330#441—58no—
331#440—58no—
332C4×Q16—58no—
333C4×SD16—58no—
334C2×#107—51no—
335C2×#107—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×#103—51no—
339C2×#103—51no—
340C2×#103—51no—
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#102—51no—
345C2×#102—51no—
346#405—58no—
347C2×#97—51no—
348C2×#97—51no—
349C2×C4×C8—51no—
350C2×C4×C8—51no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—42no—
356C23×C5—42no—
357C23×C5—42no—
358C23×C5C22×D412yes—
359C23×C5C22×D411yescharacteristic
360C5×Q8—22no—
361C5×Q8—22no—
362C5×Q8—42no—
363C5×Q8—84no—
364C5×D4—22no—
365C5×D4—22no—
366C5×D4—42no—
367C5×D4—84no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—24no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—42no—
382C2×C4×C5—84no—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D412yes—
388C2×C4×C5C22×D411yescharacteristic
389C2×C4×C5C2×#4112yes—
390C2×C4×C5C2×#4112yes—
391C2×C4×C5C2511yescharacteristic
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400Dic10—22no—
401Dic10—22no—
402Dic10—22no—
403Dic10—22no—
404Dic10—42no—
405Dic10—42no—
406#168—22no—
407#168—22no—
408#168C2×#4114yes—
409#168C2×#4114yes—
410C22×Q8—21no—
411C22×Q8—51no—
412C22×Q8—51no—
413C22×Q8C22×D511yescharacteristic
414C22×D4—21no—
415C22×D4C22×D511yescharacteristic
416C23×C4—21no—
417C23×C4C22×D511yescharacteristic
418C2×Q16—54no—
419C2×Q16—54no—
420C2×Q16—104no—
421C2×Q16—104no—
422C2×SD16—54no—
423C2×SD16—54no—
424C2×SD16—104no—
425C2×SD16—104no—
426C2×M16—54no—
427C2×M16—104no—
428C22×C8—51no—
429C22×C8—51no—
430C22×C8—51no—
431C22×C8—54no—
432C22×C8—51no—
433C22×C8—104no—
434C4⋊Q8—22no—
435C4⋊Q8—54no—
436C4⋊Q8—102no—
437C4⋊Q8C22×D514yes—
438#126—28no—
439#126—108no—
440#126—108no—
441#125—54no—
442#125—108no—
443#125—108no—
444#125—102no—
445#124—28no—
446#124—22no—
447#124C22×D514yes—
448#123—28no—
449C22⋊Q8—22no—
450C22⋊Q8—28no—
451C22⋊Q8—54no—
452C22⋊Q8—54no—
453C22⋊Q8—102no—
454C22⋊Q8—102no—
455C22⋊Q8C22×D514yes—
456#121—22no—
457#121C22×D514yes—
458C4×Q8—22no—
459C4×Q8—54no—
460C4×Q8—54no—
461C4×Q8—102no—
462C4×Q8—102no—
463C4×Q8C22×D514yes—
464C4×D4—22no—
465C4×D4C22×D514yes—
466#117C22⋊D514yes—
467#117C22×D514yes—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—101no—
474C2×C4⋊C4—101no—
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⋊C4C22⋊D511yescharacteristic
482C2×C4⋊C4C22⋊D511yescharacteristic
483C2×C4⋊C4C22×D511yescharacteristic
484C2×C4⋊C4C22×D511yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4C22⋊D511yescharacteristic
493C2×C22⋊C4C22⋊D511yescharacteristic
494C2×C42—21no—
495C2×C42—101no—
496C2×C42—101no—
497C2×C42C22×D511yescharacteristic
498C2×C42C22×D511yescharacteristic
499#107—54no—
500#107—54no—
501#106—54no—
502#106—54no—
503#103—54no—
504#103—54no—
505#103—54no—
506#103—54no—
507#103—54no—
508#103—54no—
509#102—54no—
510#102—54no—
511#97—54no—
512#97—54no—
513C4×C8—54no—
514C4×C8—54no—
515C22×C5—22no—
516C22×C5—22no—
517C22×C5—22no—
518C22×C5—44no—
519C22×C5—42no—
520C22×C5—42no—
521C22×C5—42no—
522C22×C5—84no—
523C22×C5#53212yes—
524C22×C5#57712yes—
525C22×C5#57812yes—
526C22×C5C23×D411yescharacteristic
527C4×C5—22no—
528C4×C5—22no—
529C4×C5—22no—
530C4×C5—22no—
531C4×C5—22no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5#53212yes—
536C4×C5C22×#4111yescharacteristic
537C4×C5C22×#4111yescharacteristic
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542C24—21no—
543C24C2×C22⋊D511yescharacteristic
544C2×Q8—21no—
545C2×Q8—24no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—52no—
549C2×Q8—52no—
550C2×Q8—82no—
551C2×Q8—101no—
552C2×Q8—101no—
553C2×Q8—102no—
554C2×Q8—102no—
555C2×Q8—102no—
556C2×Q8—102no—
557C2×Q8C23×D512yes—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—82no—
563C2×D4C23×D512yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—82no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4C2×C22⋊D512yes—
576C22×C4C2×C22⋊D511yescharacteristic
577C22×C4C2×C22⋊D511yescharacteristic
578C22×C4C2×C22⋊D511yescharacteristic
579C22×C4C2×C22⋊D511yescharacteristic
580C22×C4C2×C22⋊D511yescharacteristic
581C22×C4C23×D512yes—
582C22×C4C23×D511yescharacteristic
583Q16—108no—
584Q16—108no—
585SD16—108no—
586SD16—108no—
587M16—108no—
588C2×C8—54no—
589C2×C8—54no—
590C2×C8—52no—
591C2×C8—52no—
592C2×C8—52no—
593C2×C8—52no—
594C2×C8—108no—
595C2×C8—102no—
596C2×C8—102no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—52no—
603C4⋊C4—52no—
604C4⋊C4—101no—
605C4⋊C4—101no—
606C4⋊C4—104no—
607C4⋊C4—104no—
608C4⋊C4—104no—
609C4⋊C4—104no—
610C4⋊C4—104no—
611C4⋊C4—104no—
612C4⋊C4—104no—
613C4⋊C4—104no—
614C4⋊C4C2×C22⋊D514yes—
615C4⋊C4C2×C22⋊D514yes—
616C4⋊C4C23×D512yes—
617C4⋊C4C23×D512yes—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—104no—
624C22⋊C4—104no—
625C22⋊C4C2×C22⋊D514yes—
626C22⋊C4C2×C22⋊D514yes—
627C42—24no—
628C42—104no—
629C42—104no—
630C42C2×C22⋊D512yes—
631C42C2×C22⋊D512yes—
632C42C23×D512yes—
633C42C23×D512yes—
634C2×C5—42no—
635C2×C5—82no—
636C2×C5#317814yescomplemented
637C2×C5C2×#53211yescharacteristic
638C2×C5C2×#57711yescharacteristic
639C2×C5C2×#57811yescharacteristic
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×C22⋊D512yes—
648C23C22×C22⋊D511yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652Q8—84no—
653Q8—102no—
654Q8—102no—
655Q8—102no—
656Q8—102no—
657Q8—202no—
658Q8—202no—
659D4—22no—
660D4—22no—
661D4—42no—
662D4—84no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—84no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—202no—
683C2×C4—202no—
684C2×C4—202no—
685C2×C4—202no—
686C2×C4D5×#4112yes—
687C2×C4D5×#4112yes—
688C2×C4C22×C22⋊D512yes—
689C2×C4C22×C22⋊D512yes—
690C2×C4C22×C22⋊D512yes—
691C2×C4C22×C22⋊D512yes—
692C2×C4C22×C22⋊D512yes—
693C2×C4C22×C22⋊D511yescharacteristic
694C2×C4C24×D511yescharacteristic
695C8—54no—
696C8—54no—
697C8—102no—
698C8—102no—
699C5C2×#317811yescharacteristic, complemented, Sylow
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#6616612yes—
709C22#6617012yes—
710C22#6617212yes—
711C22C23×C22⋊D511yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—202no—
721C4—202no—
722C4—202no—
723C4—202no—
724C4#6616612yes—
725C4C2×D5×#4111yescharacteristic
726C4C2×D5×#4111yescharacteristic
727C2—42no—
728C2—82no—
729C2#1061518914yesdirect product factor
730C2C2×#6616611yescharacteristic
731C2C2×#6617011yescharacteristic
732C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#542C2
socleC23×C5C22×D4
prime radicalC2×C5×#121C22
hypercenterC2×#542D5
hypocenterC5C2×#3178
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
2. C2×#65852C2semidirect
3. #10615189C2direct (N × H)
4. C2×#65369C2semidirect
5. C2×#65382C2semidirect
6. C2×#65349C2semidirect
7. C2×#65345C2semidirect
8. C2×#65341C2semidirect
9. C2×#65340C2semidirect
12. C2×#65319C2semidirect
13. C2×C4×#689C2semidirect
14. C2×C4×#687C2semidirect
15. C2×#65307C2semidirect
16. C2×#65286C2semidirect
39. #65852C22semidirect
52. #65382C22semidirect
53. #65369C22semidirect
54. #65349C22semidirect
55. #65345C22semidirect
56. #65341C22semidirect
57. #65340C22semidirect
60. #65319C22semidirect
61. C4×#689C22semidirect
62. #65307C22semidirect
63. C4×#687C22semidirect
64. #65286C22semidirect
636. C2×C5#3178semidirect
699. C5C2×#3178semidirect
729. C2#10615189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5422
C2×#658522
#106151892
C2×#653692
C2×#653822
C2×#653492
C2×#653452
C2×#653412
C2×#653402
C2×#653312
C2×#653302
C2×#653192
C2×C4×#6892
C2×C4×#6872
C2×#653072
C2×#652862
C2×#31785