Finite Group Databasebeta

← C2×#10615355 #12977841

Subgroups — C2×#10615355 #12977841

Order 1280.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic
2C2×#65875C211yesmaximal, characteristic
3#10615355C2116yesmaximal, direct product factor
4C2×#65383C211yesmaximal, characteristic, complemented
5C2×#65369C211yesmaximal, characteristic, complemented
6C2×#65341C211yesmaximal, characteristic, complemented
7C2×#65340C211yesmaximal, characteristic, complemented
8C2×#65334C211yesmaximal, characteristic, complemented
9C2×#65332C211yesmaximal, characteristic, complemented
10C2×#65311C211yesmaximal, characteristic, complemented
11C2×#65319C211yesmaximal, characteristic, complemented
12C2×#65300C211yesmaximal, characteristic
13C2×#65259C211yesmaximal, characteristic, complemented
14C2×#65260C211yesmaximal, characteristic, complemented
15C2×#65253C211yesmaximal, characteristic, complemented
16C22×#3940C211yesmaximal, characteristic, complemented
17C5×#554—24no—
18C5×#554C2218yes—
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#125—21no—
21C2×C5×C22⋊Q8—21no—
22C2×C5×C22⋊Q8—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×D4—21no—
27C2×C4×C5×D4C2211yescharacteristic
28C22×C5×C4⋊C4C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C22×#689C2211yescharacteristic
31C2×#4081—21no—
32C2×#4072C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C2×#4070C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65875—24no—
39#65875C2218yes—
40C2×#4035—21no—
41C2×#4025—21no—
42C2×#4023—21no—
43C2×#4016C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C2×#3967C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65383C2218yescomplemented
51#65369C2218yescomplemented
52#65341C2218yescomplemented
53#65340C2218yescomplemented
54#65334C2218yescomplemented
55#65332C2218yescomplemented
56#65319C2218yescomplemented
57#65311C2218yescomplemented
58#65300C2218yes—
59#65260C2218yescomplemented
60#65259C2218yescomplemented
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64#65253C2218yescomplemented
65C2×#3940C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3940C2218yescomplemented
72C2×#3939C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3344—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4D411yescharacteristic
81C23×C4×C5—21no—
82C23×C4×C5—21no—
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×Dic5—21no—
86C22×Dic10C2311yescharacteristic
87C5×C4⋊Q8—22no—
88C5×C4⋊Q8C2314yes—
89C5×#125—28no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8—28no—
93C5×C22⋊Q8—28no—
94C5×C22⋊Q8C2314yes—
95C5×C22⋊Q8C2314yes—
96C4×C5×Q8—22no—
97C4×C5×Q8C2314yes—
98C4×C5×D4—28no—
99C4×C5×D4D414yes—
100C4×C5×D4C2314yes—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4D411yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2314yes—
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4D411yescharacteristic
118C2×C5×C22⋊C4D411yescharacteristic
119C2×C42×C5—21no—
120C2×C42×C5C2311yescharacteristic
121C2×C22⋊Dic5—21no—
122C2×C22⋊Dic5—21no—
123C2×C22⋊Dic5—21no—
124C2×#689—24no—
125C2×#689C2314yes—
126#4081—28no—
127#4072—22no—
128#4072C2314yes—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—22no—
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2314yes—
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×C4×Dic5—21no—
145C2×C4×Dic5—21no—
146C2×#681—24no—
147C2×#681C2314yes—
148C22×#168—24no—
149C22×#168C2314yes—
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154#4035—28no—
155#4025—28no—
156#4023—28no—
157#4016—22no—
158#4016C2314yes—
159C4×Dic10—22no—
160C4×Dic10C2314yes—
161#3967C2314yes—
162#3967C2314yes—
163#3967C2314yes—
164C22⋊#168C2314yes—
165C22⋊#168C2314yes—
166#3942C2314yes—
167#3942C2314yes—
168#3942C2314yes—
169#3940C2314yes—
170#3940C2314yes—
171#3940C2314yes—
172#3940C2314yes—
173#3940C2314yes—
174#3940C2314yes—
175#3939C2314yes—
176#3939C2314yes—
177#3939C2314yes—
178C4⋊#168C2314yes—
179#3935C2314yes—
180C2×#554D511yescharacteristic
181C2×#552—51no—
182#3344—516no—
183C2×#501—51no—
184C2×#484—51no—
185C2×#485—51no—
186C2×#483—51no—
187C2×#483—51no—
188C2×#479—51no—
189C2×#475—51no—
190C2×#470—51no—
191C2×#467—51no—
192C2×#441—51no—
193C2×#435—51no—
194C2×#428—51no—
195C22×#106—51no—
196C24×C5C2×D411yescharacteristic
197C24×C5C2×D411yescharacteristic
198C2×C5×Q8—21no—
199C2×C5×Q8—24no—
200C2×C5×Q8—22no—
201C2×C5×Q8—22no—
202C2×C5×Q8—82no—
203C2×C5×Q8C2412yes—
204C2×C5×D4—24no—
205C2×C5×D4C2×D414yes—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—24no—
215C22×C4×C5—24no—
216C22×C4×C5—82no—
217C22×C4×C5—82no—
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D412yes—
223C22×C4×C5C2×D412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2411yescharacteristic
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—24no—
232C22×Dic5—44no—
233C2×Dic10—22no—
234C2×Dic10—22no—
235C2×Dic10—21no—
236C2×Dic10C2412yes—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—24no—
239C5×C4⋊C4—24no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—24no—
243C5×C4⋊C4—24no—
244C5×C4⋊C4—24no—
245C5×C4⋊C4—24no—
246C5×C4⋊C4C2×D414yes—
247C5×C4⋊C4C2412yes—
248C5×C4⋊C4C2412yes—
249C5×C4⋊C4C2412yes—
250C5×C22⋊C4—24no—
251C5×C22⋊C4—24no—
252C5×C22⋊C4C2×D414yes—
253C5×C22⋊C4C2×D414yes—
254C42×C5—24no—
255C42×C5C2×D412yes—
256C42×C5C2412yes—
257C22⋊Dic5—24no—
258C22⋊Dic5—24no—
259C22⋊Dic5—24no—
260#689—28no—
261C4⋊Dic5—21no—
262C4⋊Dic5—21no—
263C4⋊Dic5—21no—
264C4⋊Dic5—24no—
265C4⋊Dic5C2412yes—
266C4⋊Dic5C2412yes—
267C4⋊Dic5C2412yes—
268#683—24no—
269#683—24no—
270#683—24no—
271#683—24no—
272#683—24no—
273C4×Dic5—24no—
274C4×Dic5—24no—
275#681—28no—
276C2×#168—22no—
277C2×#168—22no—
278C2×#168—22no—
279C2×#168—28no—
280C2×#168#4114yes—
281C2×#168C2412yes—
282C2×#168C2412yes—
283C2×#168C2412yes—
284C2×#168C2412yes—
285C22×Q16—51no—
286C22×M16—51no—
287C23×C8—51no—
288#554—24no—
289#554C2×D518yes—
290#552—58no—
291#552—104no—
292C2×C4⋊Q8C2×D511yescharacteristic
293C2×#126—101no—
294C2×#125—21no—
295C2×#125—51no—
296C2×#125—101no—
297C2×#123—101no—
298C2×C22⋊Q8—21no—
299C2×C22⋊Q8—21no—
300C2×C22⋊Q8—51no—
301C2×C22⋊Q8—51no—
302C2×C22⋊Q8C2×D511yescharacteristic
303C2×C22⋊Q8C2×D511yescharacteristic
304C2×C4×Q8—51no—
305C2×C4×Q8C2×D511yescharacteristic
306C2×C4×D4—21no—
307C2×C4×D4C2×D511yescharacteristic
308C2×#117—51no—
309C2×#117—101no—
310C22×C4⋊C4—51no—
311C22×C4⋊C4C2×D511yescharacteristic
312C22×C4⋊C4C2×D511yescharacteristic
313#501—58no—
314#485—58no—
315#484—58no—
316#483—58no—
317#483—58no—
318#479—58no—
319#475—58no—
320#470—58no—
321#467—58no—
322#441—58no—
323#435—58no—
324#428—58no—
325C2×#107—51no—
326C2×#107—51no—
327C2×#107—51no—
328C2×#106—51no—
329C2×#106—51no—
330C2×#106—51no—
331C2×#106—51no—
332C2×#106—58no—
333C2×#106—51no—
334C2×#106—51no—
335C2×C4⋊C8—51no—
336C2×#103—51no—
337C2×#103—51no—
338C2×#103—51no—
339C2×#103—51no—
340C2×#103—51no—
341C2×#103—51no—
342C2×C22⋊C8—51no—
343C2×C22⋊C8—51no—
344C2×#97—51no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5#13714yes—
351C23×C5C22×D412yes—
352C23×C5C22×D412yes—
353C23×C5C22×D411yescharacteristic
354C5×Q8—22no—
355C5×Q8—22no—
356C5×Q8—42no—
357C5×Q8—84no—
358C5×D4—28no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—24no—
364C2×C4×C5—24no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
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—42no—
374C2×C4×C5—42no—
375C2×C4×C5—42no—
376C2×C4×C5—42no—
377C2×C4×C5—84no—
378C2×C4×C5—84no—
379C2×C4×C5C22×D412yes—
380C2×C4×C5C22×D412yes—
381C2×C4×C5C22×D412yes—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D411yescharacteristic
384C2×C4×C5C2×#4112yes—
385C2×C4×C52−1+412yes—
386C2×C4×C5C2511yescharacteristic
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—42no—
392C2×Dic5—48no—
393C2×Dic5—42no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396Dic10—22no—
397Dic10—22no—
398Dic10—42no—
399#168—22no—
400#168—22no—
401#168—22no—
402#168C2×#4114yes—
403C22×Q8—21no—
404C22×Q8—51no—
405C22×Q8C22×D511yescharacteristic
406C22×D4C22⋊D511yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—101no—
410C23×C4C22×D511yescharacteristic
411C23×C4C22×D511yescharacteristic
412C2×Q16—54no—
413C2×Q16—104no—
414C2×M16—54no—
415C2×M16—104no—
416C22×C8—51no—
417C22×C8—51no—
418C22×C8—54no—
419C22×C8—51no—
420C22×C8—51no—
421C22×C8—104no—
422C4⋊Q8—22no—
423C4⋊Q8C22×D514yes—
424#126—108no—
425#125—28no—
426#125—54no—
427#125—108no—
428#125—102no—
429#123—108no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8—28no—
433C22⋊Q8—28no—
434C22⋊Q8—54no—
435C22⋊Q8—54no—
436C22⋊Q8—102no—
437C22⋊Q8—102no—
438C22⋊Q8C22×D514yes—
439C22⋊Q8C22×D514yes—
440C4×Q8—22no—
441C4×Q8—54no—
442C4×Q8—102no—
443C4×Q8C22×D514yes—
444C4×D4—28no—
445C4×D4C22⋊D514yes—
446C4×D4C22×D514yes—
447#117—54no—
448#117—102no—
449#117—108no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—51no—
459C2×C4⋊C4—51no—
460C2×C4⋊C4—54no—
461C2×C4⋊C4—51no—
462C2×C4⋊C4—101no—
463C2×C4⋊C4—102no—
464C2×C4⋊C4—101no—
465C2×C4⋊C4—101no—
466C2×C4⋊C4—101no—
467C2×C4⋊C4—101no—
468C2×C4⋊C4—101no—
469C2×C4⋊C4C22⋊D511yescharacteristic
470C2×C4⋊C4C22×D511yescharacteristic
471C2×C4⋊C4C22×D511yescharacteristic
472C2×C4⋊C4C22×D511yescharacteristic
473C2×C4⋊C4C22×D514yes—
474C2×C4⋊C4C22×D514yes—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—101no—
478C2×C22⋊C4—101no—
479C2×C22⋊C4—101no—
480C2×C22⋊C4C22⋊D511yescharacteristic
481C2×C22⋊C4C22⋊D511yescharacteristic
482C2×C42—21no—
483C2×C42—101no—
484C2×C42—101no—
485C2×C42C22×D511yescharacteristic
486#107—54no—
487#107—54no—
488#107—54no—
489#106—54no—
490#106—54no—
491#106—54no—
492#106—54no—
493#106—54no—
494#106—54no—
495C4⋊C8—54no—
496#103—54no—
497#103—54no—
498#103—54no—
499#103—54no—
500#103—54no—
501#103—54no—
502C22⋊C8—54no—
503C22⋊C8—54no—
504#97—54no—
505C22×C5—28no—
506C22×C5—22no—
507C22×C5—22no—
508C22×C5—22no—
509C22×C5—22no—
510C22×C5—22no—
511C22×C5—44no—
512C22×C5#54712yes—
513C22×C5C2×#13714yes—
514C22×C5C2×#13712yes—
515C22×C5#57712yes—
516C22×C5C23×D411yescharacteristic
517C4×C5—22no—
518C4×C5—22no—
519C4×C5—22no—
520C4×C5—22no—
521C4×C5—42no—
522C4×C5—42no—
523C4×C5—42no—
524C4×C5—42no—
525C4×C5#54712yes—
526C4×C5C22×#4111yescharacteristic
527C4×C5C2×2−1+411yescharacteristic
528Dic5—42no—
529Dic5—42no—
530Dic5—42no—
531Dic5—42no—
532C24C2×C22⋊D511yescharacteristic
533C24C2×C22⋊D511yescharacteristic
534C2×Q8—21no—
535C2×Q8—24no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—52no—
539C2×Q8—82no—
540C2×Q8—101no—
541C2×Q8—102no—
542C2×Q8—102no—
543C2×Q8C23×D512yes—
544C2×D4—24no—
545C2×D4C2×C22⋊D514yes—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—82no—
557C22×C4—82no—
558C22×C4—104no—
559C22×C4—101no—
560C22×C4—101no—
561C22×C4—101no—
562C22×C4—101no—
563C22×C4—204no—
564C22×C4C2×C22⋊D512yes—
565C22×C4C2×C22⋊D512yes—
566C22×C4C2×C22⋊D511yescharacteristic
567C22×C4C2×C22⋊D511yescharacteristic
568C22×C4C2×C22⋊D511yescharacteristic
569C22×C4C2×C22⋊D511yescharacteristic
570C22×C4C23×D512yes—
571C22×C4C23×D512yes—
572C22×C4C23×D511yescharacteristic
573Q16—108no—
574M16—108no—
575C2×C8—54no—
576C2×C8—52no—
577C2×C8—52no—
578C2×C8—52no—
579C2×C8—52no—
580C2×C8—108no—
581C2×C8—102no—
582C2×C8—102no—
583C2×C8—102no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—52no—
594C4⋊C4—52no—
595C4⋊C4—52no—
596C4⋊C4—101no—
597C4⋊C4—101no—
598C4⋊C4—104no—
599C4⋊C4—101no—
600C4⋊C4—104no—
601C4⋊C4—104no—
602C4⋊C4—104no—
603C4⋊C4—104no—
604C4⋊C4—104no—
605C4⋊C4C2×C22⋊D514yes—
606C4⋊C4C23×D512yes—
607C4⋊C4C23×D512yes—
608C4⋊C4C23×D512yes—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—104no—
612C22⋊C4—104no—
613C22⋊C4—104no—
614C22⋊C4C2×C22⋊D514yes—
615C22⋊C4C2×C22⋊D514yes—
616C42—24no—
617C42—104no—
618C42—104no—
619C42C2×C22⋊D512yes—
620C42C23×D512yes—
621C2×C5—24no—
622C2×C5—42no—
623C2×C5#334414yescomplemented
624C2×C5C2×#54711yescharacteristic
625C2×C5C22×#13711yescharacteristic
626C2×C5C2×#57711yescharacteristic
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23#408814yes—
633C23C22×C22⋊D512yes—
634C23C22×C22⋊D512yes—
635C23C22×C22⋊D511yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—42no—
639Q8—84no—
640Q8—102no—
641Q8—102no—
642Q8—202no—
643D4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—84no—
664C2×C4—102no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—102no—
668C2×C4—208no—
669C2×C4—202no—
670C2×C4—202no—
671C2×C4—202no—
672C2×C4—202no—
673C2×C4D5×#4112yes—
674C2×C4#415012yes—
675C2×C4C22×C22⋊D512yes—
676C2×C4C22×C22⋊D512yes—
677C2×C4C22×C22⋊D512yes—
678C2×C4C22×C22⋊D512yes—
679C2×C4C22×C22⋊D511yescharacteristic
680C2×C4C24×D511yescharacteristic
681C8—54no—
682C8—102no—
683C8—102no—
684C8—102no—
685C5C2×#334411yescharacteristic, complemented, Sylow
686C22—22no—
687C22—22no—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22C2×#408814yes—
694C22C2×#408812yes—
695C22#6615812yes—
696C22#6617012yes—
697C22C23×C22⋊D511yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—202no—
707C4—202no—
708C4—202no—
709C4—202no—
710C4#6615812yes—
711C4C2×D5×#4111yescharacteristic
712C4C2×#415011yescharacteristic
713C2—24no—
714C2—42no—
715C2#1061535514yesdirect product factor
716C2C22×#408811yescharacteristic
717C2C2×#6615811yescharacteristic
718C2C2×#6617011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#554C2
socleC23×C5C22×D4
prime radicalC22×C5×D4D4
hypercenterC2×#554D5
hypocenterC5C2×#3344
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
3. #10615355C2direct (N × H)
4. C2×#65383C2semidirect
5. C2×#65369C2semidirect
6. C2×#65341C2semidirect
7. C2×#65340C2semidirect
8. C2×#65334C2semidirect
9. C2×#65332C2semidirect
10. C2×#65311C2semidirect
11. C2×#65319C2semidirect
13. C2×#65259C2semidirect
14. C2×#65260C2semidirect
15. C2×#65253C2semidirect
16. C22×#3940C2semidirect
50. #65383C22semidirect
51. #65369C22semidirect
52. #65341C22semidirect
53. #65340C22semidirect
54. #65334C22semidirect
55. #65332C22semidirect
56. #65319C22semidirect
57. #65311C22semidirect
59. #65260C22semidirect
60. #65259C22semidirect
64. #65253C22semidirect
71. C2×#3940C22semidirect
623. C2×C5#3344semidirect
685. C5C2×#3344semidirect
715. C2#10615355direct (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×#658752
#106153552
C2×#653832
C2×#653692
C2×#653412
C2×#653402
C2×#653342
C2×#653322
C2×#653112
C2×#653192
C2×#653002
C2×#652592
C2×#652602
C2×#652532
C22×#39402
C2×#33445