Finite Group Databasebeta

← C2×#10615335 #12976012

Subgroups — C2×#10615335 #12976012

Order 1280.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#552C211yesmaximal, characteristic, complemented
2C2×#65887C211yesmaximal, characteristic
3#10615335C2116yesmaximal, direct product factor
4C2×#65352C211yesmaximal, characteristic, complemented
5C2×#65356C211yesmaximal, characteristic, complemented
6C2×#65336C211yesmaximal, characteristic, complemented
7C2×#65336C211yesmaximal, characteristic, complemented
8C2×#65338C211yesmaximal, characteristic, complemented
9C2×#65337C211yesmaximal, characteristic, complemented
10C2×#65316C211yesmaximal, characteristic, complemented
11C2×#65319C211yesmaximal, characteristic, complemented
12C2×#65300C211yesmaximal, characteristic, complemented
13C2×#65292C211yesmaximal, characteristic, complemented
14C2×#65291C211yesmaximal, characteristic, complemented
15C2×#65257C211yesmaximal, characteristic, complemented
16C2×#65255C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C5×#552—24no—
20C5×#552C2218yescomplemented
21C2×C5×#126—21no—
22C2×C5×#125—21no—
23C2×C5×#125C2211yescharacteristic
24C2×C5×#123—21no—
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117—21no—
30C2×C5×#117C2211yescharacteristic
31C22×C5×C4⋊C4C2211yescharacteristic
32C22×#689C2211yescharacteristic
33C22×#688C2211yescharacteristic
34C22×#688C2211yescharacteristic
35C2×#4086—21no—
36C2×#4076C2211yescharacteristic
37C2×#4076C2211yescharacteristic
38C22×#681C2211yescharacteristic
39C23×#168C2211yescharacteristic
40#65887—24no—
41#65887C2218yes—
42C2×#4039—21no—
43C2×#4030—21no—
44C2×#4030—21no—
45C2×#4020C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65356C2218yescomplemented
51#65352C2218yescomplemented
52#65338C2218yescomplemented
53#65337C2218yescomplemented
54#65336C2218yescomplemented
55#65336C2218yescomplemented
56#65319C2218yescomplemented
57#65316C2218yescomplemented
58#65300C2218yescomplemented
59#65292C2218yescomplemented
60#65291C2218yescomplemented
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64#65257C2218yescomplemented
65#65255C2218yescomplemented
66C2×#3941C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3941C2211yescharacteristic
70C2×#3941C2211yescharacteristic
71C2×#3941C2211yescharacteristic
72C2×#3940C2211yescharacteristic
73C2×#3940C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3317—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4D411yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×C22⋊D5—21no—
87C2×#709—22no—
88C2×#709—22no—
89C2×#709—24no—
90C2×#709—24no—
91C2×#709—42no—
92C2×#709—42no—
93C2×#709C2314yes—
94C2×#709C2314yes—
95C22×D20—21no—
96C22×D20—21no—
97C22×D20C2311yescharacteristic
98C22×D20C2311yescharacteristic
99C22×C4×D5—21no—
100C22×C4×D5—21no—
101C22×Dic10C2311yescharacteristic
102C5×#126—28no—
103C5×#125—28no—
104C5×#125—22no—
105C5×#125C2314yes—
106C5×#123—28no—
107C5×C22⋊Q8—22no—
108C5×C22⋊Q8—22no—
109C5×C22⋊Q8C2314yes—
110C5×C22⋊Q8C2314yes—
111C4×C5×Q8—22no—
112C4×C5×Q8C2314yes—
113C4×C5×D4D414yes—
114C4×C5×D4C2314yes—
115C5×#117—22no—
116C5×#117—28no—
117C5×#117C2314yes—
118C2×C5×C4⋊C4—21no—
119C2×C5×C4⋊C4—22no—
120C2×C5×C4⋊C4—21no—
121C2×C5×C4⋊C4—21no—
122C2×C5×C4⋊C4—21no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4D411yescharacteristic
126C2×C5×C4⋊C4C2311yescharacteristic
127C2×C5×C4⋊C4C2311yescharacteristic
128C2×C5×C4⋊C4C2314yes—
129C2×C5×C4⋊C4C2311yescharacteristic
130C2×C5×C22⋊C4—21no—
131C2×C5×C22⋊C4—21no—
132C2×C5×C22⋊C4—21no—
133C2×C5×C22⋊C4D411yescharacteristic
134C2×C5×C22⋊C4D411yescharacteristic
135C2×C42×C5—21no—
136C2×C42×C5—21no—
137C2×C42×C5C2311yescharacteristic
138C2×#689—24no—
139C2×#689C2314yes—
140C2×#688—42no—
141C2×#688—42no—
142C2×#688C2314yes—
143C2×#688C2314yes—
144#4086—28no—
145#4076—22no—
146#4076—22no—
147#4076C2314yes—
148#4076C2314yes—
149C2×#685—21no—
150C2×#685—21no—
151C2×C4⋊Dic5C2311yescharacteristic
152C2×#683—21no—
153C2×C4×Dic5—21no—
154C2×#681—42no—
155C2×#681C2314yes—
156C22×#168—42no—
157C22×#168C2311yescharacteristic
158C22×#168C2311yescharacteristic
159C22×#168C2311yescharacteristic
160C22×#168C2311yescharacteristic
161C22×#168C2314yes—
162#4039—28no—
163#4030—28no—
164#4030—28no—
165#4020—22no—
166#4020C2314yes—
167C4×Dic10—22no—
168C4×Dic10C2314yes—
169#3967C2314yes—
170C22⋊#168C2314yes—
171C22⋊#168C2314yes—
172#3942C2314yes—
173#3942C2314yes—
174#3942C2314yes—
175#3941C2314yes—
176#3941C2314yes—
177#3941C2314yes—
178#3941C2314yes—
179#3941C2314yes—
180#3941C2314yes—
181#3940C2314yes—
182#3940C2314yes—
183#3939C2314yes—
184C4⋊#168C2314yes—
185#3935C2314yes—
186C2×#552D511yescharacteristic, complemented
187C2×#550—51no—
188#3317—516no—
189C2×#490—51no—
190C2×#481—51no—
191C2×#482—51no—
192C2×#479—51no—
193C2×#468—51no—
194C2×#465—51no—
195C2×#460—51no—
196C2×#452—51no—
197C2×#452—51no—
198C2×#441—51no—
199C2×#435—51no—
200C2×#417—51no—
201C2×#416—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5—21no—
206C2×C5×Q8—21no—
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×Q8C2412yes—
210C2×C5×D4—42no—
211C2×C5×D4C2×D414yes—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—24no—
221C22×C4×C5—44no—
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2411yescharacteristic
231C2×C22⋊D5—24no—
232C2×C22⋊D5—24no—
233C2×C22⋊D5—24no—
234C2×C22⋊D5—24no—
235C2×C22⋊D5—44no—
236C2×C22⋊D5—44no—
237C2×C22⋊D5—82no—
238C2×C22⋊D5—82no—
239C22×Dic5—21no—
240C22×Dic5—21no—
241#709—28no—
242#709—28no—
243#709—44no—
244#709—44no—
245#709—48no—
246#709—48no—
247C2×D20—22no—
248C2×D20—22no—
249C2×D20—22no—
250C2×D20—22no—
251C2×D20—24no—
252C2×D20—21no—
253C2×D20—21no—
254C2×D20—24no—
255C2×D20—44no—
256C2×D20—82no—
257C2×D20C2412yes—
258C2×D20C2412yes—
259C2×C4×D5—24no—
260C2×C4×D5—24no—
261C2×C4×D5—44no—
262C2×C4×D5—44no—
263C2×Dic10—21no—
264C2×Dic10—22no—
265C2×Dic10#4114yes—
266C2×Dic10C2412yes—
267C5×C4⋊C4—21no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—24no—
270C5×C4⋊C4—24no—
271C5×C4⋊C4—24no—
272C5×C4⋊C4—24no—
273C5×C4⋊C4—24no—
274C5×C4⋊C4—24no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4C2×D414yes—
277C5×C4⋊C4C2412yes—
278C5×C4⋊C4C2412yes—
279C5×C4⋊C4C2412yes—
280C5×C22⋊C4—24no—
281C5×C22⋊C4—24no—
282C5×C22⋊C4—24no—
283C5×C22⋊C4C2×D414yes—
284C5×C22⋊C4C2×D414yes—
285C42×C5—24no—
286C42×C5—24no—
287C42×C5C2×D412yes—
288C42×C5C2412yes—
289#689—28no—
290#688—44no—
291#688—44no—
292#685—24no—
293#685—24no—
294C4⋊Dic5—21no—
295C4⋊Dic5C2412yes—
296#683—24no—
297C4×Dic5—24no—
298#681—44no—
299C2×#168—22no—
300C2×#168—22no—
301C2×#168—22no—
302C2×#168—22no—
303C2×#168—44no—
304C2×#168C2412yes—
305C2×#168C2412yes—
306C2×#168C2412yes—
307C2×#168C2412yes—
308C22×#41—51no—
309C22×#41—51no—
310C22×Q16—51no—
311C22×SD16—51no—
312C22×SD16—51no—
313C22×M16—51no—
314C23×C8—51no—
315#552—24no—
316#552C2×D518yescomplemented
317#550—58no—
318#550—104no—
319C2×#127—51no—
320C2×#127—101no—
321C2×#126—21no—
322C2×#125—21no—
323C2×#125C2×D511yescharacteristic
324C2×#123—21no—
325C2×C22⋊Q8C2×D511yescharacteristic
326C2×C22⋊Q8C2×D511yescharacteristic
327C2×#121—51no—
328C2×#121—51no—
329C2×#121—101no—
330C2×#121—101no—
331C2×C4×Q8—51no—
332C2×C4×Q8C2×D511yescharacteristic
333C2×C4×D4—101no—
334C2×C4×D4C2×D511yescharacteristic
335C2×#117—21no—
336C2×#117C2×D511yescharacteristic
337C22×C4⋊C4C2×D511yescharacteristic
338#490—58no—
339#482—58no—
340#481—58no—
341#479—58no—
342#468—58no—
343#465—58no—
344#460—58no—
345#452—58no—
346#452—58no—
347#441—58no—
348#435—58no—
349C2×#107—51no—
350C2×#106—51no—
351C2×#106—51no—
352C2×C4⋊C8—51no—
353#417—58no—
354#416—58no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×C22⋊C8—51no—
366C2×C22⋊C8—51no—
367C2×#97—51no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5C22×D412yes—
375C23×C5C22×D412yes—
376C23×C5C22×D411yescharacteristic
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—42no—
380C22×D5—42no—
381C22×D5—42no—
382C22×D5—42no—
383C22×D5—42no—
384C22×D5—42no—
385C5×Q8—22no—
386C5×Q8—22no—
387C5×Q8—42no—
388C5×D4—44no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—24no—
394C2×C4×C5—24no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—48no—
404C2×C4×C5—42no—
405C2×C4×C5—42no—
406C2×C4×C5—42no—
407C2×C4×C5—42no—
408C2×C4×C5C22×D412yes—
409C2×C4×C5C22×D412yes—
410C2×C4×C5C22×D412yes—
411C2×C4×C5C22×D412yes—
412C2×C4×C5C22×D411yescharacteristic
413C2×C4×C5C2×#4112yes—
414C2×C4×C5H(5,𝔽2)12yes—
415C2×C4×C5C2511yescharacteristic
416C22⋊D5—48no—
417C22⋊D5—48no—
418C22⋊D5—84no—
419C22⋊D5—84no—
420C2×Dic5—24no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—42no—
424D20—22no—
425D20—22no—
426D20—22no—
427D20—22no—
428D20—48no—
429D20—42no—
430D20—42no—
431D20—84no—
432C4×D5—48no—
433C4×D5—48no—
434Dic10—24no—
435Dic10—22no—
436Dic10C2×#4114yes—
437#168—22no—
438#168—22no—
439#168—22no—
440#168—22no—
441C2×#41—54no—
442C2×#41—54no—
443C2×#41—104no—
444C2×#41—104no—
445C2×#41—102no—
446C2×#41—102no—
447C2×#41—202no—
448C2×#41—202no—
449C22×Q8—51no—
450C22×Q8C22×D511yescharacteristic
451C22×D4—51no—
452C22×D4—51no—
453C22×D4—101no—
454C22×D4—101no—
455C22×D4—101no—
456C22×D4—101no—
457C22×D4—101no—
458C22×D4—101no—
459C22×D4C22⋊D511yescharacteristic
460C23×C4—21no—
461C23×C4—101no—
462C23×C4—101no—
463C23×C4C22×D511yescharacteristic
464C23×C4C22×D511yescharacteristic
465C2×Q16—54no—
466C2×Q16—104no—
467C2×SD16—54no—
468C2×SD16—54no—
469C2×SD16—202no—
470C2×SD16—202no—
471C2×M16—54no—
472C2×M16—202no—
473C22×C8—51no—
474C22×C8—51no—
475C22×C8—51no—
476C22×C8—51no—
477C22×C8—54no—
478C22×C8—202no—
479#127—54no—
480#127—108no—
481#127—102no—
482#126—28no—
483#125—28no—
484#125—22no—
485#125C22×D514yes—
486#123—28no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8C22×D514yes—
490C22⋊Q8C22×D514yes—
491#121—54no—
492#121—54no—
493#121—102no—
494#121—102no—
495#121—108no—
496#121—108no—
497C4×Q8—22no—
498C4×Q8—54no—
499C4×Q8—102no—
500C4×Q8C22×D514yes—
501C4×D4—108no—
502C4×D4C22⋊D514yes—
503C4×D4C22×D514yes—
504#117—22no—
505#117—28no—
506#117C22×D514yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—51no—
515C2×C4⋊C4—101no—
516C2×C4⋊C4C22⋊D511yescharacteristic
517C2×C4⋊C4C22×D511yescharacteristic
518C2×C4⋊C4C22×D511yescharacteristic
519C2×C4⋊C4C22×D514yes—
520C2×C4⋊C4C22×D511yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—101no—
525C2×C22⋊C4—101no—
526C2×C22⋊C4C22⋊D511yescharacteristic
527C2×C22⋊C4C22⋊D511yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—101no—
531C2×C42C22×D511yescharacteristic
532#107—54no—
533#106—54no—
534#106—54no—
535C4⋊C8—54no—
536#103—54no—
537#103—54no—
538#103—54no—
539#103—54no—
540#102—54no—
541#102—54no—
542#102—54no—
543#102—54no—
544#102—54no—
545#102—54no—
546C22⋊C8—54no—
547C22⋊C8—54no—
548#97—54no—
549C22×C5—22no—
550C22×C5—22no—
551C22×C5—22no—
552C22×C5—22no—
553C22×C5—22no—
554C22×C5—22no—
555C22×C5—44no—
556C22×C5—44no—
557C22×C5#54612yes—
558C22×C5#57512yes—
559C22×C5#57712yes—
560C22×C5C23×D411yescharacteristic
561C2×D5—42no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—84no—
568C2×D5—84no—
569C4×C5—22no—
570C4×C5—22no—
571C4×C5—22no—
572C4×C5—22no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5—42no—
577C4×C5#54612yes—
578C4×C5C22×#4111yescharacteristic
579C4×C5C2×H(5,𝔽2)11yescharacteristic
580Dic5—24no—
581Dic5—42no—
582C24—101no—
583C24—101no—
584C24C2×C22⋊D511yescharacteristic
585C24C2×C22⋊D511yescharacteristic
586#41—108no—
587#41—108no—
588#41—204no—
589#41—204no—
590#41—208no—
591#41—208no—
592C2×Q8—21no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—54no—
596C2×Q8—52no—
597C2×Q8—102no—
598C2×Q8—101no—
599C2×Q8C23×D512yes—
600C2×D4—42no—
601C2×D4—52no—
602C2×D4—52no—
603C2×D4—104no—
604C2×D4—104no—
605C2×D4—104no—
606C2×D4—104no—
607C2×D4—102no—
608C2×D4—102no—
609C2×D4—102no—
610C2×D4—102no—
611C2×D4—104no—
612C2×D4—101no—
613C2×D4—101no—
614C2×D4—104no—
615C2×D4—204no—
616C2×D4—204no—
617C2×D4—204no—
618C2×D4—402no—
619C2×D4—402no—
620C2×D4—402no—
621C2×D4C2×C22⋊D514yes—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—24no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—44no—
632C22×C4—101no—
633C22×C4—101no—
634C22×C4—104no—
635C22×C4—104no—
636C22×C4—204no—
637C22×C4—204no—
638C22×C4C2×C22⋊D512yes—
639C22×C4C2×C22⋊D512yes—
640C22×C4C2×C22⋊D511yescharacteristic
641C22×C4C2×C22⋊D511yescharacteristic
642C22×C4C2×C22⋊D511yescharacteristic
643C22×C4C2×C22⋊D511yescharacteristic
644C22×C4C23×D512yes—
645C22×C4C23×D512yes—
646C22×C4C23×D511yescharacteristic
647Q16—108no—
648SD16—204no—
649SD16—204no—
650M16—204no—
651C2×C8—52no—
652C2×C8—52no—
653C2×C8—52no—
654C2×C8—52no—
655C2×C8—102no—
656C2×C8—102no—
657C2×C8—102no—
658C2×C8—102no—
659C2×C8—204no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—21no—
669C4⋊C4—52no—
670C4⋊C4—101no—
671C4⋊C4—104no—
672C4⋊C4C2×C22⋊D514yes—
673C4⋊C4C23×D512yes—
674C4⋊C4C23×D512yes—
675C4⋊C4C23×D512yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—104no—
680C22⋊C4—104no—
681C22⋊C4C2×C22⋊D514yes—
682C22⋊C4C2×C22⋊D514yes—
683C42—24no—
684C42—24no—
685C42—104no—
686C42C2×C22⋊D512yes—
687C42C23×D512yes—
688C2×C5—42no—
689C2×C5—42no—
690C2×C5#331714yescomplemented
691C2×C5C2×#54611yescharacteristic
692C2×C5C2×#57511yescharacteristic
693C2×C5C2×#57711yescharacteristic
694D5—82no—
695D5—82no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—102no—
703C23—102no—
704C23—202no—
705C23—202no—
706C23—202no—
707C23—202no—
708C23—202no—
709C23—202no—
710C23C22×C22⋊D512yes—
711C23C22×C22⋊D512yes—
712C23C22×C22⋊D511yescharacteristic
713Q8—22no—
714Q8—22no—
715Q8—42no—
716Q8—54no—
717Q8—104no—
718Q8—102no—
719D4—44no—
720D4—102no—
721D4—102no—
722D4—102no—
723D4—102no—
724D4—208no—
725D4—208no—
726D4—208no—
727D4—202no—
728D4—202no—
729D4—404no—
730D4—404no—
731D4—404no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—104no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—208no—
755C2×C4—208no—
756C2×C4—202no—
757C2×C4D5×#4112yes—
758C2×C4#414912yes—
759C2×C4C22×C22⋊D512yes—
760C2×C4C22×C22⋊D512yes—
761C2×C4C22×C22⋊D512yes—
762C2×C4C22×C22⋊D512yes—
763C2×C4C22×C22⋊D511yescharacteristic
764C2×C4C24×D511yescharacteristic
765C8—102no—
766C8—102no—
767C8—102no—
768C8—102no—
769C5C2×#331711yescharacteristic, complemented, Sylow
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—202no—
779C22—202no—
780C22—202no—
781C22—202no—
782C22—202no—
783C22—202no—
784C22—404no—
785C22—404no—
786C22#6615612yes—
787C22#6616312yes—
788C22#6617112yes—
789C22C23×C22⋊D511yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—104no—
799C4—202no—
800C4#6616312yes—
801C4C2×D5×#4111yescharacteristic
802C4C2×#414911yescharacteristic
803C2—42no—
804C2—42no—
805C2—402no—
806C2—402no—
807C2#1061533514yesdirect product factor
808C2C2×#6615611yescharacteristic
809C2C2×#6616311yescharacteristic
810C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#552C2
socleC23×C5C22×D4
prime radicalC2×#65887C2
hypercenterC2×#552D5
hypocenterC5C2×#3317
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×C5×#552C2semidirect
3. #10615335C2direct (N × H)
4. C2×#65352C2semidirect
5. C2×#65356C2semidirect
6. C2×#65336C2semidirect
7. C2×#65336C2semidirect
8. C2×#65338C2semidirect
9. C2×#65337C2semidirect
10. C2×#65316C2semidirect
11. C2×#65319C2semidirect
12. C2×#65300C2semidirect
13. C2×#65292C2semidirect
14. C2×#65291C2semidirect
15. C2×#65257C2semidirect
16. C2×#65255C2semidirect
20. C5×#552C22semidirect
50. #65356C22semidirect
51. #65352C22semidirect
52. #65338C22semidirect
53. #65337C22semidirect
54. #65336C22semidirect
55. #65336C22semidirect
56. #65319C22semidirect
57. #65316C22semidirect
58. #65300C22semidirect
59. #65292C22semidirect
60. #65291C22semidirect
64. #65257C22semidirect
65. #65255C22semidirect
186. C2×#552D5semidirect
316. #552C2×D5semidirect
690. C2×C5#3317semidirect
769. C5C2×#3317semidirect
807. C2#10615335direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5522
C2×#658872
#106153352
C2×#653522
C2×#653562
C2×#653362
C2×#653382
C2×#653372
C2×#653162
C2×#653192
C2×#653002
C2×#652922
C2×#652912
C2×#652572
C2×#652552
C2×#33175