Finite Group Databasebeta

← C2×#10615341 #12977889

Subgroups — C2×#10615341 #12977889

Order 1280.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#553C211yesmaximal, characteristic, complemented
2C2×#65897C211yesmaximal, characteristic, complemented
3#10615341C2116yesmaximal, direct product factor
4C2×#65355C211yesmaximal, characteristic, complemented
5C2×#65354C211yesmaximal, characteristic, complemented
6C2×#65328C211yesmaximal, characteristic, complemented
7C2×#65327C211yesmaximal, characteristic, complemented
8C2×#65324C211yesmaximal, characteristic, complemented
9C2×#65324C211yesmaximal, characteristic, complemented
10C2×#65300C211yesmaximal, characteristic, complemented
11C2×#65296C211yesmaximal, characteristic, complemented
12C2×#65303C211yesmaximal, characteristic, complemented
13C2×#65292C211yesmaximal, characteristic, complemented
14C2×#65287C211yesmaximal, characteristic, complemented
15C2×#65256C211yesmaximal, characteristic, complemented
16C2×#65253C211yesmaximal, characteristic, complemented
17C5×#553—24no—
18C5×#553C2218yescomplemented
19C2×C5×#126—21no—
20C2×C5×#125C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×#121—21no—
23C2×C5×#121C2211yescharacteristic
24C2×C5×#121C2211yescharacteristic
25C2×C4×C5×D4—21no—
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C2×#4084—21no—
31C22×#686C2211yescharacteristic
32C2×#4076C2211yescharacteristic
33C2×#4076C2211yescharacteristic
34C2×#4072C2211yescharacteristic
35C2×#4072C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65897—24no—
39#65897C2218yescomplemented
40C2×#4038—21no—
41C2×#4031—21no—
42C2×#4031—21no—
43C2×C4×D20C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C2×#3964C2211yescharacteristic
46C2×#3964C2211yescharacteristic
47C2×#3964C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65355C2218yescomplemented
51#65354C2218yescomplemented
52#65328C2218yescomplemented
53#65327C2218yescomplemented
54#65324C2218yescomplemented
55#65324C2218yescomplemented
56#65303C2218yescomplemented
57#65300C2218yescomplemented
58#65296C2218yescomplemented
59#65292C2218yescomplemented
60#65287C2218yescomplemented
61#65256C2218yescomplemented
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65#65253C2218yescomplemented
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3347—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4—21no—
80C22×C5×D4D411yescharacteristic
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C23×C4×C5—21no—
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C22×C22⋊D5—21no—
87C22×C22⋊D5—21no—
88C22×D20C2311yescharacteristic
89C22×C4×D5—21no—
90C22×Dic10—21no—
91C5×#126—28no—
92C5×#125—22no—
93C5×#125C2314yes—
94C5×#123—28no—
95C5×#121—28no—
96C5×#121—22no—
97C5×#121—22no—
98C5×#121C2314yes—
99C5×#121C2314yes—
100C4×C5×D4—28no—
101C4×C5×D4—22no—
102C4×C5×D4D414yes—
103C4×C5×D4C2314yes—
104C4×C5×D4C2314yes—
105C5×#117—22no—
106C5×#117C2314yes—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—22no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4D411yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4D411yescharacteristic
121C2×C5×C22⋊C4D411yescharacteristic
122C2×C42×C5—21no—
123C2×C42×C5C2311yescharacteristic
124C2×C22⋊Dic5—21no—
125C2×C22⋊Dic5—21no—
126#4084—28no—
127C2×#686—24no—
128C2×#686C2314yes—
129#4076—22no—
130#4076—22no—
131#4076C2314yes—
132#4076C2314yes—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685—21no—
136#4072—22no—
137#4072—22no—
138#4072C2314yes—
139#4072C2314yes—
140C2×C4⋊Dic5—21no—
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
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#4038—28no—
155#4031—28no—
156#4031—28no—
157C4×D20—22no—
158C4×D20C2314yes—
159#4015—22no—
160#4015C2314yes—
161#3964C2314yes—
162#3964C2314yes—
163#3964C2314yes—
164C22⋊#168C2314yes—
165C22⋊#168C2314yes—
166#3941C2314yes—
167#3941C2314yes—
168#3941C2314yes—
169#3940C2314yes—
170#3940C2314yes—
171#3940C2314yes—
172#3940C2314yes—
173#3939C2314yes—
174#3939C2314yes—
175#3939C2314yes—
176#3939C2314yes—
177#3939C2314yes—
178C4⋊#168C2314yes—
179#3935C2314yes—
180C2×#555—51no—
181C2×#553D511yescharacteristic, complemented
182#3347—516no—
183C2×#501—51no—
184C2×#482—51no—
185C2×#482—51no—
186C2×#482—51no—
187C2×#480—51no—
188C2×#478—51no—
189C2×#474—51no—
190C2×#469—51no—
191C2×#466—51no—
192C2×#442—51no—
193C2×#435—51no—
194C2×#428—51no—
195C2×#427—51no—
196C24×C5—21no—
197C24×C5C2×D411yescharacteristic
198C24×C5C2×D411yescharacteristic
199C23×D5—21no—
200C2×C5×D4—24no—
201C2×C5×D4—24no—
202C2×C5×D4—21no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—42no—
206C2×C5×D4—44no—
207C2×C5×D4—82no—
208C2×C5×D4C2×D414yes—
209C2×C5×D4C2412yes—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—24no—
218C22×C4×C5—24no—
219C22×C4×C5—82no—
220C22×C4×C5—82no—
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2411yescharacteristic
230C2×C22⋊D5—24no—
231C2×C22⋊D5—24no—
232C2×C22⋊D5—82no—
233C2×C22⋊D5—82no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C2×D20—22no—
238C2×D20—22no—
239C2×D20—21no—
240C2×D20C2412yes—
241C2×C4×D5—24no—
242C2×C4×D5—44no—
243C2×Dic10—24no—
244C2×Dic10—82no—
245C5×C4⋊C4—21no—
246C5×C4⋊C4—21no—
247C5×C4⋊C4—24no—
248C5×C4⋊C4—24no—
249C5×C4⋊C4—24no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4C2×D414yes—
252C5×C4⋊C4C2412yes—
253C5×C4⋊C4C2412yes—
254C5×C4⋊C4C2412yes—
255C5×C22⋊C4—24no—
256C5×C22⋊C4—24no—
257C5×C22⋊C4—24no—
258C5×C22⋊C4—24no—
259C5×C22⋊C4C2×D414yes—
260C5×C22⋊C4C2×D414yes—
261C42×C5—24no—
262C42×C5C2×D412yes—
263C42×C5C2412yes—
264C22⋊Dic5—24no—
265C22⋊Dic5—24no—
266#686—28no—
267#685—24no—
268#685—24no—
269#685—24no—
270C4⋊Dic5—21no—
271C4⋊Dic5—21no—
272C4⋊Dic5—24no—
273C4⋊Dic5—21no—
274C4⋊Dic5C2412yes—
275C4⋊Dic5C2412yes—
276C4⋊Dic5C2412yes—
277C4×Dic5—24no—
278C4×Dic5—24no—
279#681—28no—
280C2×#168—22no—
281C2×#168—22no—
282C2×#168—22no—
283C2×#168—28no—
284C2×#168#4114yes—
285C2×#168C2412yes—
286C2×#168C2412yes—
287C2×#168C2412yes—
288C2×#168C2412yes—
289C22×D8—51no—
290C22×M16—51no—
291C23×C8—51no—
292#555—58no—
293#555—104no—
294#553—24no—
295#553C2×D518yescomplemented
296C2×C4⋊Q8—51no—
297C2×#126—21no—
298C2×#125C2×D511yescharacteristic
299C2×#124—101no—
300C2×#124—101no—
301C2×#123—21no—
302C2×#121—21no—
303C2×#121—51no—
304C2×#121—51no—
305C2×#121—101no—
306C2×#121C2×D511yescharacteristic
307C2×#121C2×D511yescharacteristic
308C2×C4×D4—21no—
309C2×C4×D4—51no—
310C2×C4×D4C2×D511yescharacteristic
311C2×C4×D4C2×D511yescharacteristic
312C2×#117—51no—
313C2×#117—51no—
314C2×#117—101no—
315C2×#117C2×D511yescharacteristic
316C22×C4⋊C4C2×D511yescharacteristic
317#501—58no—
318#482—58no—
319#482—58no—
320#482—58no—
321#480—58no—
322#478—58no—
323#474—58no—
324#469—58no—
325#466—58no—
326#442—58no—
327#435—58no—
328#428—58no—
329#427—58no—
330C2×#107—51no—
331C2×#107—51no—
332C2×#107—51no—
333C2×#107—51no—
334C2×#107—51no—
335C2×#106—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×C4⋊C8—51no—
340C2×#102—51no—
341C2×#102—51no—
342C2×#102—51no—
343C2×#102—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×C22⋊C8—51no—
347C2×C22⋊C8—51no—
348C2×#97—51no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—42no—
357C23×C5—42no—
358C23×C5—42no—
359C23×C5C22×D412yes—
360C23×C5C22×D412yes—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—42no—
364C22×D5—42no—
365C22×D5—42no—
366C5×D4—22no—
367C5×D4—22no—
368C5×D4—44no—
369C5×D4—48no—
370C5×D4—42no—
371C5×D4—84no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—24no—
377C2×C4×C5—24no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—84no—
389C2×C4×C5—84no—
390C2×C4×C5C22×D412yes—
391C2×C4×C5C22×D412yes—
392C2×C4×C5C22×D412yes—
393C2×C4×C5C22×D412yes—
394C2×C4×C5C22×D411yescharacteristic
395C2×C4×C5C2×#4112yes—
396C2×C4×C52−1+412yes—
397C2×C4×C5C2511yescharacteristic
398C22⋊D5—84no—
399C22⋊D5—84no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—42no—
404C2×Dic5—42no—
405C2×Dic5—42no—
406D20—22no—
407D20—22no—
408D20—42no—
409C4×D5—48no—
410Dic10—84no—
411#168—22no—
412#168—22no—
413#168—22no—
414#168C2×#4114yes—
415C22×Q8—101no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—51no—
419C22×D4—101no—
420C22×D4—101no—
421C22×D4C22⋊D511yescharacteristic
422C22×D4C22×D511yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—101no—
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C2×D8—54no—
429C2×D8—104no—
430C2×M16—54no—
431C2×M16—104no—
432C22×C8—51no—
433C22×C8—51no—
434C22×C8—54no—
435C22×C8—51no—
436C22×C8—51no—
437C22×C8—104no—
438C4⋊Q8—54no—
439C4⋊Q8—102no—
440#126—28no—
441#125—22no—
442#125C22×D514yes—
443#124—108no—
444#124—108no—
445#123—28no—
446#121—28no—
447#121—22no—
448#121—22no—
449#121—54no—
450#121—54no—
451#121—108no—
452#121—102no—
453#121—102no—
454#121C22×D514yes—
455#121C22×D514yes—
456C4×D4—28no—
457C4×D4—22no—
458C4×D4—54no—
459C4×D4—102no—
460C4×D4C22⋊D514yes—
461C4×D4C22×D514yes—
462C4×D4C22×D514yes—
463#117—22no—
464#117—54no—
465#117—54no—
466#117—102no—
467#117—102no—
468#117—108no—
469#117C22×D514yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—51no—
475C2×C4⋊C4—51no—
476C2×C4⋊C4—51no—
477C2×C4⋊C4—101no—
478C2×C4⋊C4C22⋊D511yescharacteristic
479C2×C4⋊C4C22×D511yescharacteristic
480C2×C4⋊C4C22×D511yescharacteristic
481C2×C4⋊C4C22×D514yes—
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4—101no—
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
498#107—54no—
499#107—54no—
500#107—54no—
501#107—54no—
502#107—54no—
503#106—54no—
504#106—54no—
505#106—54no—
506#106—54no—
507C4⋊C8—54no—
508#102—54no—
509#102—54no—
510#102—54no—
511#102—54no—
512#102—54no—
513#102—54no—
514C22⋊C8—54no—
515C22⋊C8—54no—
516#97—54no—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—22no—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—44no—
524C22×C5—44no—
525C22×C5—42no—
526C22×C5—42no—
527C22×C5—42no—
528C22×C5—84no—
529C22×C5#54712yes—
530C22×C5#57512yes—
531C22×C5#57612yes—
532C22×C5C23×D411yescharacteristic
533C2×D5—42no—
534C2×D5—42no—
535C2×D5—42no—
536C2×D5—84no—
537C4×C5—22no—
538C4×C5—22no—
539C4×C5—22no—
540C4×C5—22no—
541C4×C5—42no—
542C4×C5—42no—
543C4×C5—42no—
544C4×C5#54712yes—
545C4×C5C22×#4111yescharacteristic
546C4×C5C2×2−1+411yescharacteristic
547Dic5—42no—
548Dic5—42no—
549Dic5—42no—
550C24—21no—
551C24—101no—
552C24C2×C22⋊D511yescharacteristic
553C24C2×C22⋊D511yescharacteristic
554C2×Q8—104no—
555C2×Q8—402no—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—52no—
564C2×D4—82no—
565C2×D4—104no—
566C2×D4—104no—
567C2×D4—102no—
568C2×D4—102no—
569C2×D4—101no—
570C2×D4—402no—
571C2×D4—402no—
572C2×D4C2×C22⋊D514yes—
573C2×D4C23×D512yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4—101no—
588C22×C4—104no—
589C22×C4—204no—
590C22×C4C2×C22⋊D512yes—
591C22×C4C2×C22⋊D512yes—
592C22×C4C2×C22⋊D511yescharacteristic
593C22×C4C2×C22⋊D511yescharacteristic
594C22×C4C2×C22⋊D511yescharacteristic
595C22×C4C2×C22⋊D511yescharacteristic
596C22×C4C23×D512yes—
597C22×C4C23×D512yes—
598C22×C4C23×D511yescharacteristic
599D8—108no—
600M16—108no—
601C2×C8—54no—
602C2×C8—52no—
603C2×C8—52no—
604C2×C8—52no—
605C2×C8—52no—
606C2×C8—108no—
607C2×C8—102no—
608C2×C8—102no—
609C2×C8—102no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—52no—
617C4⋊C4—52no—
618C4⋊C4—52no—
619C4⋊C4—101no—
620C4⋊C4—101no—
621C4⋊C4—101no—
622C4⋊C4—104no—
623C4⋊C4C2×C22⋊D514yes—
624C4⋊C4C23×D512yes—
625C4⋊C4C23×D512yes—
626C4⋊C4C23×D512yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—104no—
632C22⋊C4—104no—
633C22⋊C4—104no—
634C22⋊C4—104no—
635C22⋊C4—104no—
636C22⋊C4C2×C22⋊D514yes—
637C22⋊C4C2×C22⋊D514yes—
638C42—24no—
639C42—104no—
640C42—104no—
641C42C2×C22⋊D512yes—
642C42C23×D512yes—
643C2×C5—42no—
644C2×C5—42no—
645C2×C5—82no—
646C2×C5#334714yescomplemented
647C2×C5C2×#54711yescharacteristic
648C2×C5C2×#57511yescharacteristic
649C2×C5C2×#57611yescharacteristic
650D5—82no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—102no—
662C23—202no—
663C23—202no—
664C23—202no—
665C23C22×C22⋊D512yes—
666C23C22×C22⋊D512yes—
667C23C22×C22⋊D511yescharacteristic
668Q8—404no—
669D4—22no—
670D4—22no—
671D4—44no—
672D4—48no—
673D4—42no—
674D4—84no—
675D4—102no—
676D4—102no—
677D4—202no—
678D4—404no—
679D4—404no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—208no—
702C2×C4—202no—
703C2×C4—202no—
704C2×C4—202no—
705C2×C4D5×#4112yes—
706C2×C4#415012yes—
707C2×C4C22×C22⋊D512yes—
708C2×C4C22×C22⋊D512yes—
709C2×C4C22×C22⋊D512yes—
710C2×C4C22×C22⋊D512yes—
711C2×C4C22×C22⋊D511yescharacteristic
712C2×C4C24×D511yescharacteristic
713C8—54no—
714C8—102no—
715C8—102no—
716C8—102no—
717C5C2×#334711yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—404no—
734C22#6615612yes—
735C22#6615812yes—
736C22#6616912yes—
737C22C23×C22⋊D511yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—202no—
746C4—202no—
747C4—202no—
748C4#6615812yes—
749C4C2×D5×#4111yescharacteristic
750C4C2×#415011yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—402no—
755C2#1061534114yesdirect product factor
756C2C2×#6615611yescharacteristic
757C2C2×#6615811yescharacteristic
758C2C2×#6616911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#553C2
socleC23×C5C22×D4
hypercenterC2×#553D5
hypocenterC5C2×#3347
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×C5×#553C2semidirect
2. C2×#65897C2semidirect
3. #10615341C2direct (N × H)
4. C2×#65355C2semidirect
5. C2×#65354C2semidirect
6. C2×#65328C2semidirect
7. C2×#65327C2semidirect
8. C2×#65324C2semidirect
9. C2×#65324C2semidirect
10. C2×#65300C2semidirect
11. C2×#65296C2semidirect
12. C2×#65303C2semidirect
13. C2×#65292C2semidirect
14. C2×#65287C2semidirect
15. C2×#65256C2semidirect
16. C2×#65253C2semidirect
18. C5×#553C22semidirect
39. #65897C22semidirect
50. #65355C22semidirect
51. #65354C22semidirect
52. #65328C22semidirect
53. #65327C22semidirect
54. #65324C22semidirect
55. #65324C22semidirect
56. #65303C22semidirect
57. #65300C22semidirect
58. #65296C22semidirect
59. #65292C22semidirect
60. #65287C22semidirect
61. #65256C22semidirect
65. #65253C22semidirect
181. C2×#553D5semidirect
295. #553C2×D5semidirect
646. C2×C5#3347semidirect
717. C5C2×#3347semidirect
755. C2#10615341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5532
C2×#658972
#106153412
C2×#653552
C2×#653542
C2×#653282
C2×#653272
C2×#653242
C2×#653002
C2×#652962
C2×#653032
C2×#652922
C2×#652872
C2×#652562
C2×#652532
C2×#33475