Finite Group Databasebeta

← C2×#10615370 #12979049

Subgroups — C2×#10615370 #12979049

Order 1280.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic, complemented
2C2×#65919C211yesmaximal, characteristic, complemented
3#10615370C2116yesmaximal, direct product factor
4C2×#65376C211yesmaximal, characteristic, complemented
5C2×#65378C211yesmaximal, characteristic, complemented
6C2×#65352C211yesmaximal, characteristic, complemented
7C2×#65355C211yesmaximal, characteristic, complemented
8C2×#65356C211yesmaximal, characteristic, complemented
9C2×#65357C211yesmaximal, characteristic, complemented
10C2×#65313C211yesmaximal, characteristic, complemented
11C2×#65305C211yesmaximal, characteristic, complemented
12C2×#65305C211yesmaximal, characteristic, complemented
13C2×#65304C211yesmaximal, characteristic
14C2×#65303C211yesmaximal, characteristic, complemented
15C2×#65307C211yesmaximal, characteristic, complemented
16C2×C4×#686C211yesmaximal, characteristic, complemented
17C5×#554—24no—
18C5×#554C2218yescomplemented
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#125C2211yescharacteristic
21C2×C5×#125C2211yescharacteristic
22C2×C5×C22⋊Q8—21no—
23C2×C5×C22⋊Q8—21no—
24C2×C5×C22⋊Q8—21no—
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C22×C5×C4⋊C4—21no—
30C2×#4093—21no—
31C22×#687C2211yescharacteristic
32C22×#686C2211yescharacteristic
33C22×#686C2211yescharacteristic
34#65919—24no—
35#65919C2218yescomplemented
36C2×#4040—21no—
37C2×#4040—21no—
38C2×#4039—21no—
39C2×#4021C2211yescharacteristic
40C2×#4021C2211yescharacteristic
41C2×#4020C2211yescharacteristic
42C2×C4×D20C2211yescharacteristic
43C2×C4×D20C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C2×#3964C2211yescharacteristic
46#65378C2218yescomplemented
47#65376C2218yescomplemented
48#65357C2218yescomplemented
49#65356C2218yescomplemented
50#65355C2218yescomplemented
51#65352C2218yescomplemented
52#65313C2218yescomplemented
53#65307C2218yescomplemented
54#65305C2218yescomplemented
55#65305C2218yescomplemented
56#65304C2218yes—
57#65303C2218yescomplemented
58C4×#686C2218yescomplemented
59C2×#3942C2211yescharacteristic
60C2×#3942C2211yescharacteristic
61C2×#3942C2211yescharacteristic
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3941C2211yescharacteristic
66C2×#3941C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×C4⋊#168C2211yescharacteristic
72C2×C4⋊#168C2211yescharacteristic
73C2×C4⋊#168C2211yescharacteristic
74C2×#3935C2211yescharacteristic
75C2×#3935C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3370—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8D411yescharacteristic
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5—21no—
82C23×C4×C5—21no—
83C23×C4×C5—21no—
84C22×D20—21no—
85C22×D20—21no—
86C22×D20C2311yescharacteristic
87C22×D20C2311yescharacteristic
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×Dic10C2311yescharacteristic
91C5×C4⋊Q8—22no—
92C5×C4⋊Q8C2314yes—
93C5×#125—22no—
94C5×#125—22no—
95C5×#125C2314yes—
96C5×#125C2314yes—
97C5×C22⋊Q8—28no—
98C5×C22⋊Q8—28no—
99C5×C22⋊Q8—28no—
100C4×C5×Q8D414yes—
101C4×C5×Q8C2314yes—
102C4×C5×D4—22no—
103C4×C5×D4—22no—
104C4×C5×D4—22no—
105C4×C5×D4C2314yes—
106C4×C5×D4C2314yes—
107C4×C5×D4C2314yes—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4—28no—
114C2×C5×C4⋊C4D411yescharacteristic
115C2×C5×C4⋊C4D411yescharacteristic
116C2×C5×C4⋊C4D411yescharacteristic
117C2×C5×C4⋊C4C2311yescharacteristic
118C2×C5×C4⋊C4C2311yescharacteristic
119C2×C5×C4⋊C4C2311yescharacteristic
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C42×C5C2311yescharacteristic
124C2×C42×C5C2311yescharacteristic
125C2×C42×C5C2311yescharacteristic
126#4093—28no—
127C2×#687—24no—
128C2×#687C2314yes—
129C2×#686—24no—
130C2×#686—24no—
131C2×#686C2314yes—
132C2×#686C2314yes—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685—21no—
138C2×#685—21no—
139C2×C4⋊Dic5C2311yescharacteristic
140C2×#683—21no—
141C2×C4×Dic5—21no—
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C22×#168C2311yescharacteristic
146#4040—28no—
147#4040—28no—
148#4039—28no—
149#4021—22no—
150#4021—22no—
151#4021C2314yes—
152#4021C2314yes—
153#4020—22no—
154#4020C2314yes—
155C4×D20—22no—
156C4×D20—22no—
157C4×D20C2314yes—
158C4×D20C2314yes—
159C4×Dic10—22no—
160C4×Dic10C2314yes—
161#3964C2314yes—
162#3942C2314yes—
163#3942C2314yes—
164#3942C2314yes—
165#3941C2314yes—
166#3941C2314yes—
167#3941C2314yes—
168#3941C2314yes—
169#3941C2314yes—
170#3941C2314yes—
171#3940C2314yes—
172#3939C2314yes—
173#3939C2314yes—
174C4⋊#168C2314yes—
175C4⋊#168C2314yes—
176C4⋊#168C2314yes—
177#3935C2314yes—
178#3935C2314yes—
179C4×#168C2314yes—
180C2×#559—51no—
181C2×#554D511yescharacteristic, complemented
182#3370—516no—
183C2×#490—51no—
184C2×#489—51no—
185C2×#488—51no—
186C2×#479—51no—
187C2×#478—51no—
188C2×#474—51no—
189C2×#463—51no—
190C2×#463—51no—
191C2×#459—51no—
192C2×#446—51no—
193C2×#442—51no—
194C2×#440—51no—
195C2×C4×D8—51no—
196C24×C5—21no—
197C23×D5—21no—
198C23×D5—21no—
199C2×C5×Q8—24no—
200C2×C5×Q8—42no—
201C2×C5×Q8—82no—
202C2×C5×Q8C2×D414yes—
203C2×C5×D4—21no—
204C2×C5×D4—22no—
205C2×C5×D4#4114yes—
206C2×C5×D4C2412yes—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—24no—
211C22×C4×C5—24no—
212C22×C4×C5—24no—
213C22×C4×C5—44no—
214C22×C4×C5—82no—
215C22×C4×C5—82no—
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2411yescharacteristic
223C22×Dic5—21no—
224C22×Dic5—21no—
225C2×D20—22no—
226C2×D20—22no—
227C2×D20—22no—
228C2×D20—22no—
229C2×D20—24no—
230C2×D20—21no—
231C2×D20—21no—
232C2×D20—24no—
233C2×D20—44no—
234C2×D20—82no—
235C2×D20C2412yes—
236C2×D20C2412yes—
237C2×C4×D5—24no—
238C2×C4×D5—24no—
239C2×C4×D5—82no—
240C2×C4×D5—82no—
241C2×Dic10—22no—
242C2×Dic10—22no—
243C2×Dic10—21no—
244C2×Dic10C2412yes—
245C5×C4⋊C4—24no—
246C5×C4⋊C4—24no—
247C5×C4⋊C4—24no—
248C5×C4⋊C4—24no—
249C5×C4⋊C4—24no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4C2×D414yes—
254C5×C4⋊C4C2×D414yes—
255C5×C4⋊C4C2×D414yes—
256C5×C4⋊C4C2412yes—
257C5×C4⋊C4C2412yes—
258C5×C4⋊C4C2412yes—
259C5×C22⋊C4—24no—
260C5×C22⋊C4—24no—
261C5×C22⋊C4—24no—
262C42×C5C2×D412yes—
263C42×C5C2×D412yes—
264C42×C5C2×D412yes—
265C42×C5C2412yes—
266C42×C5C2412yes—
267C42×C5C2412yes—
268#687—28no—
269#686—28no—
270#686—28no—
271#685—24no—
272#685—24no—
273#685—24no—
274#685—24no—
275#685—24no—
276#685—24no—
277C4⋊Dic5—21no—
278C4⋊Dic5C2412yes—
279#683—24no—
280C4×Dic5—24no—
281C2×#168—22no—
282C2×#168—22no—
283C2×#168—22no—
284C2×#168—22no—
285C2×#168C2412yes—
286C2×#168C2412yes—
287C2×#168C2412yes—
288C2×#168C2412yes—
289C22×SD16—51no—
290C22×D8—51no—
291C22×D8—51no—
292#559—58no—
293#559—104no—
294#554—24no—
295#554C2×D518yescomplemented
296C2×C4⋊Q8C2×D511yescharacteristic
297C2×#127—51no—
298C2×#125C2×D511yescharacteristic
299C2×#125C2×D511yescharacteristic
300C2×#124—51no—
301C2×#124—51no—
302C2×#124—101no—
303C2×#123—101no—
304C2×#123—101no—
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8—21no—
307C2×C22⋊Q8—21no—
308C2×C4×Q8—51no—
309C2×C4×Q8C2×D511yescharacteristic
310C2×C4×D4—51no—
311C2×C4×D4—51no—
312C2×C4×D4—101no—
313C2×C4×D4C2×D511yescharacteristic
314C2×C4×D4C2×D511yescharacteristic
315C2×C4×D4C2×D511yescharacteristic
316C22×C4⋊C4—21no—
317#490—58no—
318#489—58no—
319#488—58no—
320#479—58no—
321#478—58no—
322#474—58no—
323#463—58no—
324#463—58no—
325#459—58no—
326#446—58no—
327#442—58no—
328#440—58no—
329C4×D8—58no—
330C2×#107—51no—
331C2×#107—51no—
332C2×#106—51no—
333C2×C4⋊C8—51no—
334C2×C4⋊C8—51no—
335C2×C4⋊C8—51no—
336C2×#103—51no—
337C2×#103—51no—
338C2×#103—51no—
339C2×#102—51no—
340C2×#102—51no—
341C2×#102—51no—
342C2×#102—51no—
343C2×#102—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#97—51no—
347C2×#97—51no—
348C2×C4×C8—51no—
349C23×C5—24no—
350C23×C5—22no—
351C23×C5—42no—
352C23×C5—42no—
353C23×C5C22×D411yescharacteristic
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—42no—
357C22×D5—42no—
358C22×D5—42no—
359C22×D5—42no—
360C22×D5—42no—
361C22×D5—42no—
362C5×Q8—44no—
363C5×Q8—84no—
364C5×D4—24no—
365C5×D4—22no—
366C5×D4C2×#4114yes—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
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—48no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—84no—
381C2×C4×C5—84no—
382C2×C4×C5C22×D412yes—
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×C52−1+412yes—
391C2×C4×C5C2511yescharacteristic
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396D20—22no—
397D20—22no—
398D20—22no—
399D20—22no—
400D20—48no—
401D20—42no—
402D20—42no—
403D20—84no—
404C4×D5—84no—
405C4×D5—84no—
406Dic10—22no—
407Dic10—22no—
408Dic10—42no—
409#168—22no—
410#168—22no—
411#168—22no—
412#168—22no—
413C22×Q8—21no—
414C22×Q8—51no—
415C22×Q8C22⋊D511yescharacteristic
416C22×D4—51no—
417C22×D4—51no—
418C22×D4—101no—
419C22×D4—101no—
420C22×D4C22×D511yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—101no—
425C23×C4—101no—
426C2×SD16—54no—
427C2×SD16—104no—
428C2×D8—54no—
429C2×D8—54no—
430C2×D8—104no—
431C2×D8—104no—
432C22×C8—51no—
433C22×C8—51no—
434C22×C8—51no—
435C22×C8—51no—
436C4⋊Q8—22no—
437C4⋊Q8C22×D514yes—
438#127—54no—
439#127—102no—
440#125—22no—
441#125—22no—
442#125C22×D514yes—
443#125C22×D514yes—
444#124—54no—
445#124—54no—
446#124—108no—
447#124—102no—
448#124—102no—
449#123—108no—
450#123—108no—
451C22⋊Q8—28no—
452C22⋊Q8—28no—
453C22⋊Q8—28no—
454C4×Q8—54no—
455C4×Q8—102no—
456C4×Q8C22⋊D514yes—
457C4×Q8C22×D514yes—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—54no—
462C4×D4—54no—
463C4×D4—108no—
464C4×D4—102no—
465C4×D4—102no—
466C4×D4C22×D514yes—
467C4×D4C22×D514yes—
468C4×D4C22×D514yes—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—28no—
475C2×C4⋊C4—51no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4C22⋊D511yescharacteristic
478C2×C4⋊C4C22⋊D511yescharacteristic
479C2×C4⋊C4C22⋊D511yescharacteristic
480C2×C4⋊C4C22×D511yescharacteristic
481C2×C4⋊C4C22×D511yescharacteristic
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—101no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C42—101no—
493C2×C42C22×D511yescharacteristic
494C2×C42C22×D511yescharacteristic
495C2×C42C22×D511yescharacteristic
496#107—54no—
497#107—54no—
498#106—54no—
499C4⋊C8—54no—
500C4⋊C8—54no—
501C4⋊C8—54no—
502#103—54no—
503#103—54no—
504#103—54no—
505#102—54no—
506#102—54no—
507#102—54no—
508#102—54no—
509#102—54no—
510#102—54no—
511#102—54no—
512#97—54no—
513#97—54no—
514C4×C8—54no—
515C22×C5—24no—
516C22×C5—48no—
517C22×C5—42no—
518C22×C5—42no—
519C22×C5#54812yes—
520C22×C5#57512yes—
521C22×C5#57612yes—
522C22×C5C23×D411yescharacteristic
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—42no—
528C2×D5—42no—
529C2×D5—84no—
530C2×D5—84no—
531C4×C5—22no—
532C4×C5—22no—
533C4×C5—22no—
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—22no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5#54812yes—
541C4×C5C22×#4111yescharacteristic
542C4×C5C2×2−1+411yescharacteristic
543Dic5—42no—
544Dic5—42no—
545C24—21no—
546C24—101no—
547C24—101no—
548C2×Q8—24no—
549C2×Q8—42no—
550C2×Q8—52no—
551C2×Q8—82no—
552C2×Q8—101no—
553C2×Q8—102no—
554C2×Q8—102no—
555C2×Q8C2×C22⋊D514yes—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—52no—
559C2×D4—52no—
560C2×D4—102no—
561C2×D4—102no—
562C2×D4—102no—
563C2×D4—102no—
564C2×D4—104no—
565C2×D4—101no—
566C2×D4—101no—
567C2×D4—104no—
568C2×D4—204no—
569C2×D4—402no—
570C2×D4#71314yes—
571C2×D4C23×D512yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—104no—
584C22×C4—104no—
585C22×C4—402no—
586C22×C4—402no—
587C22×C4C2×C22⋊D511yescharacteristic
588C22×C4C2×C22⋊D511yescharacteristic
589C22×C4C2×C22⋊D511yescharacteristic
590C22×C4C2×C22⋊D511yescharacteristic
591C22×C4C2×C22⋊D511yescharacteristic
592C22×C4C2×C22⋊D511yescharacteristic
593C22×C4C23×D511yescharacteristic
594SD16—108no—
595D8—108no—
596D8—108no—
597C2×C8—52no—
598C2×C8—52no—
599C2×C8—52no—
600C2×C8—52no—
601C2×C8—102no—
602C2×C8—102no—
603C2×C8—102no—
604C2×C8—102no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—52no—
614C4⋊C4—101no—
615C4⋊C4—104no—
616C4⋊C4C2×C22⋊D514yes—
617C4⋊C4C2×C22⋊D514yes—
618C4⋊C4C2×C22⋊D514yes—
619C4⋊C4C23×D512yes—
620C4⋊C4C23×D512yes—
621C4⋊C4C23×D512yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—104no—
626C22⋊C4—104no—
627C22⋊C4—104no—
628C22⋊C4—104no—
629C22⋊C4—104no—
630C22⋊C4—104no—
631C42—104no—
632C42C2×C22⋊D512yes—
633C42C2×C22⋊D512yes—
634C42C2×C22⋊D512yes—
635C42C23×D512yes—
636C42C23×D512yes—
637C42C23×D512yes—
638C2×C5—44no—
639C2×C5#337014yescomplemented
640C2×C5C2×#54811yescharacteristic
641C2×C5C2×#57511yescharacteristic
642C2×C5C2×#57611yescharacteristic
643D5—82no—
644D5—82no—
645C23—24no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—102no—
650C23—102no—
651C23—202no—
652C23—202no—
653C23—202no—
654C23—202no—
655C23—202no—
656C23—202no—
657C23C22×C22⋊D511yescharacteristic
658Q8—44no—
659Q8—84no—
660Q8—102no—
661Q8—102no—
662Q8—202no—
663D4—24no—
664D4—22no—
665D4—102no—
666D4—102no—
667D4—102no—
668D4—102no—
669D4—208no—
670D4—202no—
671D4—202no—
672D4—404no—
673D4C2×#71314yes—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—84no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—202no—
692C2×C4—202no—
693C2×C4—404no—
694C2×C4—404no—
695C2×C4C2×#71312yes—
696C2×C4#414712yes—
697C2×C4C22×C22⋊D512yes—
698C2×C4C22×C22⋊D512yes—
699C2×C4C22×C22⋊D512yes—
700C2×C4C22×C22⋊D512yes—
701C2×C4C22×C22⋊D512yes—
702C2×C4C22×C22⋊D512yes—
703C2×C4C22×C22⋊D511yescharacteristic
704C2×C4C24×D511yescharacteristic
705C8—102no—
706C8—102no—
707C8—102no—
708C8—102no—
709C5C2×#337011yescharacteristic, complemented, Sylow
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—202no—
715C22—202no—
716C22—202no—
717C22—202no—
718C22—202no—
719C22—202no—
720C22—404no—
721C22—404no—
722C22#6615112yes—
723C22#6615612yes—
724C22#6616912yes—
725C22C23×C22⋊D511yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—202no—
736C4—202no—
737C4#6615112yes—
738C4C22×#71311yescharacteristic
739C4C2×#414711yescharacteristic
740C2—44no—
741C2—402no—
742C2—402no—
743C2#1061537014yesdirect product factor
744C2C2×#6615111yescharacteristic
745C2C2×#6615611yescharacteristic
746C2C2×#6616911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#554C2
socleC23×C5C22×D4
prime radicalC2×#65304C2
hypercenterC2×#554D5
hypocenterC5C2×#3370
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C5×#554C2semidirect
2. C2×#65919C2semidirect
3. #10615370C2direct (N × H)
4. C2×#65376C2semidirect
5. C2×#65378C2semidirect
6. C2×#65352C2semidirect
7. C2×#65355C2semidirect
8. C2×#65356C2semidirect
9. C2×#65357C2semidirect
10. C2×#65313C2semidirect
11. C2×#65305C2semidirect
12. C2×#65305C2semidirect
14. C2×#65303C2semidirect
15. C2×#65307C2semidirect
16. C2×C4×#686C2semidirect
18. C5×#554C22semidirect
35. #65919C22semidirect
46. #65378C22semidirect
47. #65376C22semidirect
48. #65357C22semidirect
49. #65356C22semidirect
50. #65355C22semidirect
51. #65352C22semidirect
52. #65313C22semidirect
53. #65307C22semidirect
54. #65305C22semidirect
55. #65305C22semidirect
57. #65303C22semidirect
58. C4×#686C22semidirect
181. C2×#554D5semidirect
295. #554C2×D5semidirect
639. C2×C5#3370semidirect
709. C5C2×#3370semidirect
743. C2#10615370direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
C2×#659192
#106153702
C2×#653762
C2×#653782
C2×#653522
C2×#653552
C2×#653562
C2×#653572
C2×#653132
C2×#653052
C2×#653042
C2×#653032
C2×#653072
C2×C4×#6862
C2×#33705