Finite Group Databasebeta

← D5×#3209 #12970486

Subgroups — D5×#3209 #12970486

Order 1280.

2134 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#533C211yesmaximal, characteristic
2C2×D5×C4⋊Q8C211yesmaximal, characteristic
3C5×#3209C211yesmaximal, characteristic, complemented
4#10615101C211yesmaximal, characteristic, complemented
5#10614953C211yesmaximal, characteristic, complemented
6#10613533C212yesmaximal, complemented
7D5×#494C212yesmaximal, complemented
8#10613335C212yesmaximal, complemented
9D5×#487C212yesmaximal, complemented
10#10612211C214yesmaximal, complemented
11D5×#462C214yesmaximal, complemented
12D5×#451C214yesmaximal
13#10611909C214yesmaximal, complemented
14#10611044C211yesmaximal, characteristic, complemented
15D5×#431C211yesmaximal, characteristic
16C22×Q8×D5C2212yes—
17C5×#533C2211yescharacteristic
18C2×C5×C4⋊Q8C2211yescharacteristic
19C2×#4090C2212yes—
20C2×D5×Q16C2218yes—
21#66062C2211yescharacteristic
22#66062C2211yescharacteristic
23D5×C4⋊Q8—21no—
24D5×C4⋊Q8—21no—
25D5×C4⋊Q8—21no—
26D5×C4⋊Q8—21no—
27D5×C4⋊Q8C2211yescharacteristic
28D5×C4⋊Q8C2211yescharacteristic
29D5×C4⋊Q8C2212yes—
30D5×C4⋊Q8C2212yes—
31D5×C4⋊Q8C2212yes—
32D5×C4⋊Q8C2212yes—
33#66022—21no—
34D5×#125—21no—
35D5×C22⋊Q8—21no—
36D5×C22⋊Q8C2212yes—
37#65956—21no—
38#65956C2212yes—
39#65912—21no—
40#65912C2212yes—
41C4×Q8×D5—21no—
42C4×Q8×D5C2212yes—
43D5×#117—21no—
44#65851—21no—
45C2×D5×C4⋊C4—21no—
46C2×D5×C4⋊C4—21no—
47C2×#4034—21no—
48C2×#4034—21no—
49C2×C42×D5C2211yescharacteristic
50#65804C2211yescharacteristic
51C2×#4015C2211yescharacteristic
52C5×#494C2212yescomplemented
53C5×#487C2212yescomplemented
54C5×#462C2214yescomplemented
55C5×#451C2214yes—
56C5×#431C2211yescharacteristic
57#65517C2214yes—
58#65475C2218yes—
59#65471C2218yescomplemented
60#65470C2218yescomplemented
61#65382C2212yescomplemented
62#65381C2212yescomplemented
63#65381C2212yescomplemented
64#65379C2214yescomplemented
65#65370C2212yescomplemented
66#65339C2214yes—
67#65320C2214yescomplemented
68#65214C2211yescharacteristic
69#65138C2214yescomplemented
70#65122C2212yes—
71D5×C4⋊C8C2212yes—
72#65097C2218yes—
73D5×#103C2218yes—
74#65082C2218yescomplemented
75#65081C2218yescomplemented
76#65028C2214yes—
77D5×C22⋊C8C2212yes—
78#65007C2212yes—
79#64988C2212yescomplemented
80#64974C2212yes—
81C4×C8×D5C2212yes—
82#64970C2212yescomplemented
83C2×#3209—51nomaximal, Sylow
84C22×C5×Q8C2312yes—
85C2×Q8×D5—22no—
86C2×Q8×D5—22no—
87C2×Q8×D5—21no—
88C2×Q8×D5—48no—
89C2×Q8×D5C2314yes—
90C2×Q8×D5C2312yes—
91C2×Q8×D5C2314yes—
92C22×C4×D5—22no—
93C22×C4×D5D411yescharacteristic
94C22×C4×D5D411yescharacteristic
95C22×C4×D5C2311yescharacteristic
96C22×Dic10—22no—
97C22×Dic10C2312yes—
98C2×C5×Q16C2318yes—
99C5×C4⋊Q8—21no—
100C5×C4⋊Q8—21no—
101C5×C4⋊Q8C2312yes—
102C5×C4⋊Q8C2312yes—
103C5×C4⋊Q8C2311yescharacteristic
104C5×C4⋊Q8C2311yescharacteristic
105C5×#125—21no—
106C5×C22⋊Q8—21no—
107C5×C22⋊Q8C2312yes—
108C4×C5×Q8—21no—
109C4×C5×Q8C2312yes—
110C5×#117—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C42×C5C2311yescharacteristic
114#4092—21no—
115#4092C2312yes—
116Q8×Dic5—21no—
117Q8×Dic5C2312yes—
118#4090—22no—
119#4090—22no—
120#4090—21no—
121#4090C2314yes—
122#4090C2314yes—
123#4090C2312yes—
124C2×#689C2318yes—
125C2×#689C2318yes—
126#4072—21no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—21no—
129#4070—21no—
130#4070C2312yes—
131C2×#683—22no—
132C2×#683—22no—
133C2×C4×Dic5D411yescharacteristic
134C2×C4×Dic5D411yescharacteristic
135C2×C4×Dic5C2311yescharacteristic
136D5×Q16—416no—
137C2×Dic20C2318yes—
138C2×C8×D5C2314yes—
139#4043—21no—
140#4043C2312yes—
141#4042—22no—
142#4042—22no—
143#4038—21no—
144#4038—21no—
145D5×C4⋊C4—22no—
146D5×C4⋊C4—22no—
147D5×C4⋊C4—22no—
148D5×C4⋊C4—22no—
149D5×C4⋊C4—22no—
150D5×C4⋊C4—22no—
151D5×C4⋊C4—22no—
152D5×C4⋊C4—22no—
153D5×C4⋊C4—21no—
154D5×C4⋊C4—21no—
155D5×C4⋊C4—21no—
156D5×C4⋊C4—22no—
157D5×C4⋊C4—22no—
158D5×C4⋊C4C2312yes—
159#4036—21no—
160#4036—21no—
161#4035—22no—
162#4035—22no—
163#4034—22no—
164#4034—22no—
165#4034—22no—
166#4034—22no—
167#4034—22no—
168#4034—22no—
169#4034—22no—
170#4034—22no—
171#4034—21no—
172#4034—21no—
173#4034—21no—
174#4034C2312yes—
175#4033—21no—
176#4033—22no—
177#4033—22no—
178#4033C2312yes—
179D5×C22⋊C4—22no—
180#4024—22no—
181#4024—22no—
182#4023—22no—
183#4018—22no—
184C42×D5—22no—
185C42×D5D411yescharacteristic
186C42×D5D411yescharacteristic
187C42×D5D411yescharacteristic
188C42×D5D411yescharacteristic
189C42×D5C2311yescharacteristic
190C42×D5C2311yescharacteristic
191C42×D5C2311yescharacteristic
192C42×D5C2311yescharacteristic
193#4016—21no—
194#4015—21no—
195#4015—21no—
196#4015C2312yes—
197#4015C2312yes—
198#4015C2311yescharacteristic
199#4015C2311yescharacteristic
200C4×Dic10—21no—
201C4×Dic10—22no—
202C4×Dic10—22no—
203C4×Dic10C2312yes—
204C5×C4⋊C8C2312yes—
205C5×#103C2318yes—
206C5×C22⋊C8C2312yes—
207C4×C5×C8C2312yes—
208#3967C2318yes—
209C22⋊#168C2312yes—
210#3952C2314yes—
211#3948C2318yes—
212#3946C2314yes—
213C8×Dic5C2314yes—
214#3942C2318yes—
215C4⋊#168C2312yes—
216C4×#168C2312yes—
217C2×#533—51no—
218C22×C4⋊Q8—51no—
219#3209—52no—
220#3209—52no—
221#3209—54no—
222#3209—54no—
223#3209—51no—
224#3209—51no—
225#3209—51no—
226#3209D511yescharacteristic, direct product factor
227C2×#494—52no—
228C2×#487—52no—
229C2×#462—54no—
230C2×#451—54no—
231C2×#431—51no—
232C23×D5C2×D411yescharacteristic
233C2×C5×Q8—21no—
234C2×C5×Q8—22no—
235C2×C5×Q8—44no—
236C2×C5×Q8C2412yes—
237C2×C5×Q8C2414yes—
238C22×C4×C5—22no—
239C22×C4×C5C2×D411yescharacteristic
240C22×C4×C5C2×D411yescharacteristic
241C22×C4×C5C2411yescharacteristic
242C22×Dic5—22no—
243C22×Dic5C2×D411yescharacteristic
244C22×Dic5C2×D411yescharacteristic
245C22×Dic5C2×D411yescharacteristic
246Q8×D5—216no—
247Q8×D5—28no—
248Q8×D5—48no—
249Q8×D5—48no—
250Q8×D5—48no—
251Q8×D5—44no—
252C2×C4×D5—24no—
253C2×C4×D5—24no—
254C2×C4×D5—24no—
255C2×C4×D5—24no—
256C2×C4×D5—22no—
257C2×C4×D5—22no—
258C2×C4×D5—48no—
259C2×C4×D5Q1618yescomplemented
260C2×C4×D5C2×D411yescharacteristic
261C2×C4×D5C2×D411yescharacteristic
262C2×C4×D5C2×D411yescharacteristic
263C2×C4×D5C2×D411yescharacteristic
264C2×C4×D5C2×D411yescharacteristic
265C2×C4×D5C2×D411yescharacteristic
266C2×C4×D5C2×D411yescharacteristic
267C2×C4×D5C2×D411yescharacteristic
268C2×C4×D5C2×D411yescharacteristic
269C2×C4×D5C2×D411yescharacteristic
270C2×C4×D5C2411yescharacteristic
271C2×C4×D5C2411yescharacteristic
272C2×Dic10—22no—
273C2×Dic10—21no—
274C2×Dic10—24no—
275C2×Dic10—24no—
276C2×Dic10—22no—
277C2×Dic10—22no—
278C2×Dic10—44no—
279C2×Dic10—48no—
280C2×Dic10C2414yes—
281C2×Dic10C2412yes—
282C5×Q16—48no—
283C2×C5×C8C2414yes—
284C5×C4⋊C4—22no—
285C5×C4⋊C4—22no—
286C5×C4⋊C4—22no—
287C5×C4⋊C4—22no—
288C5×C4⋊C4—21no—
289C5×C4⋊C4—21no—
290C5×C4⋊C4—21no—
291C5×C4⋊C4—22no—
292C5×C4⋊C4—22no—
293C5×C4⋊C4C2412yes—
294C5×C22⋊C4—22no—
295C42×C5—22no—
296C42×C5C2×D411yescharacteristic
297C42×C5C2×D411yescharacteristic
298C42×C5C2411yescharacteristic
299C42×C5C2411yescharacteristic
300C22⋊Dic5—22no—
301#689—48no—
302#689—48no—
303#685—22no—
304#685—22no—
305C4⋊Dic5—21no—
306C4⋊Dic5—22no—
307C4⋊Dic5—22no—
308C4⋊Dic5—22no—
309C4⋊Dic5—22no—
310C4⋊Dic5—21no—
311C4⋊Dic5—21no—
312C4⋊Dic5—22no—
313C4⋊Dic5—22no—
314C4⋊Dic5C2412yes—
315#683—22no—
316#683—22no—
317#683—22no—
318#683—22no—
319#683—22no—
320#683—22no—
321#683—22no—
322#683—22no—
323#683—24no—
324#683—24no—
325#683—24no—
326#683—24no—
327C4×Dic5—22no—
328C4×Dic5—22no—
329C4×Dic5—22no—
330C4×Dic5C2×D411yescharacteristic
331C4×Dic5C2×D411yescharacteristic
332C4×Dic5C2×D411yescharacteristic
333C4×Dic5C2×D411yescharacteristic
334C4×Dic5C2×D411yescharacteristic
335C4×Dic5C2×D411yescharacteristic
336C4×Dic5C2×D411yescharacteristic
337C4×Dic5C2×D411yescharacteristic
338C4×Dic5C2×D411yescharacteristic
339C4×Dic5C2×D411yescharacteristic
340C4×Dic5C2411yescharacteristic
341C4×Dic5C2411yescharacteristic
342C2×#168C2414yes—
343Dic20—48no—
344C8×D5—28no—
345C23×Q8—52no—
346C22×Q16—58no—
347#533—51no—
348#533—51no—
349#533—52no—
350#533—52no—
351#533—51no—
352#533—101no—
353#533—101no—
354#533—101no—
355#533—101no—
356#533C2×D511yescharacteristic
357C2×C4⋊Q8—51no—
358C2×C4⋊Q8—52no—
359C2×C4⋊Q8—52no—
360C2×C4⋊Q8—51no—
361C2×C4⋊Q8—52no—
362C2×C4⋊Q8—52no—
363C2×C4⋊Q8—52no—
364C2×C4⋊Q8—51no—
365C2×C4⋊Q8—101no—
366C2×C4⋊Q8—101no—
367C2×C4⋊Q8—101no—
368C2×C4⋊Q8—101no—
369C2×C4⋊Q8—101no—
370C2×C4⋊Q8—101no—
371C2×C4⋊Q8C2×D511yescharacteristic
372C2×#125—101no—
373C2×C22⋊Q8—52no—
374C2×C22⋊Q8—101no—
375C2×C4×Q8—52no—
376C2×C4×Q8—101no—
377C2×#117—101no—
378C22×C4⋊C4—101no—
379C22×C4⋊C4—101no—
380C22×C42—51no—
381#494—58no—
382#494—52no—
383#494—52no—
384#494—52no—
385#494C2×D512yescomplemented
386#487—52no—
387#487—52no—
388#487—58no—
389#487—52no—
390#487C2×D512yescomplemented
391#462—58no—
392#462—54no—
393#462—54no—
394#462—54no—
395#462—58no—
396#462C2×D514yescomplemented
397#451—54no—
398#451—58no—
399#451—54no—
400#451—58no—
401#451—54no—
402#451C2×D514yes—
403#431—51no—
404#431—52no—
405#431—52no—
406#431—52no—
407#431C2×D511yescharacteristic
408C2×C4⋊C8—52no—
409C2×#103—58no—
410C2×C22⋊C8—52no—
411C2×C4×C8—52no—
412C23×C5C22×D411yescharacteristic
413C22×D5—22no—
414C22×D5—22no—
415C22×D5C2×Q1614yes—
416C22×D5C22×D411yescharacteristic
417C22×D5C22×D411yescharacteristic
418C5×Q8—24no—
419C5×Q8—28no—
420C5×Q8—44no—
421C5×Q8—42no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—24no—
427C2×C4×C5—44no—
428C2×C4×C5C2×Q1614yescomplemented
429C2×C4×C5C22×D411yescharacteristic
430C2×C4×C5C22×D411yescharacteristic
431C2×C4×C5C22×D411yescharacteristic
432C2×C4×C5C22×D411yescharacteristic
433C2×C4×C5C22×D411yescharacteristic
434C2×C4×C5C2511yescharacteristic
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—24no—
440C2×Dic5—44no—
441C2×Dic5C2×Q1614yescomplemented
442C2×Dic5C22×D411yescharacteristic
443C2×Dic5C22×D411yescharacteristic
444C2×Dic5C22×D411yescharacteristic
445C2×Dic5C22×D411yescharacteristic
446C2×Dic5C22×D411yescharacteristic
447C2×Dic5C22×D411yescharacteristic
448C4×D5—22no—
449C4×D5—22no—
450C4×D5—22no—
451C4×D5—22no—
452C4×D5—22no—
453C4×D5—22no—
454C4×D5—48no—
455C4×D5—48no—
456C4×D5—44no—
457C4×D5—44no—
458C4×D5C2×Q1614yes—
459C4×D5C2×Q1614yes—
460C4×D5C2×Q1614yescomplemented
461C4×D5C2×Q1614yescomplemented
462C4×D5#13714yes—
463C4×D5H(5,𝔽2)14yes—
464Dic10—24no—
465Dic10—28no—
466Dic10—48no—
467Dic10—44no—
468Dic10—42no—
469Dic10—48no—
470Dic10—44no—
471Dic10—44no—
472C5×C8—24no—
473#168—24no—
474C22×Q8—52no—
475C22×Q8—54no—
476C22×Q8—54no—
477C22×Q8—52no—
478C22×Q8—102no—
479C22×Q8—101no—
480C22×Q8—102no—
481C22×Q8—102no—
482C22×Q8—208no—
483C22×Q8C22×D512yes—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—102no—
488C2×Q16—58no—
489C2×Q16—58no—
490C2×Q16—58no—
491C2×Q16—2016no—
492C2×Q16C22×D518yes—
493C22×C8—54no—
494C4⋊Q8—21no—
495C4⋊Q8—21no—
496C4⋊Q8—52no—
497C4⋊Q8—54no—
498C4⋊Q8—54no—
499C4⋊Q8—52no—
500C4⋊Q8—51no—
501C4⋊Q8—52no—
502C4⋊Q8—52no—
503C4⋊Q8—51no—
504C4⋊Q8—102no—
505C4⋊Q8—102no—
506C4⋊Q8—102no—
507C4⋊Q8—102no—
508C4⋊Q8—102no—
509C4⋊Q8—102no—
510C4⋊Q8—102no—
511C4⋊Q8—102no—
512C4⋊Q8—101no—
513C4⋊Q8—101no—
514C4⋊Q8—101no—
515C4⋊Q8—102no—
516C4⋊Q8—102no—
517C4⋊Q8—101no—
518C4⋊Q8—101no—
519C4⋊Q8—101no—
520C4⋊Q8C22×D512yes—
521C4⋊Q8C22×D512yes—
522C4⋊Q8C22×D511yescharacteristic
523C4⋊Q8C22×D511yescharacteristic
524#125—21no—
525#125—102no—
526#125—102no—
527#125—101no—
528#125—101no—
529#125—101no—
530C22⋊Q8—21no—
531C22⋊Q8—52no—
532C22⋊Q8—52no—
533C22⋊Q8—52no—
534C22⋊Q8—102no—
535C22⋊Q8—102no—
536C22⋊Q8—102no—
537C22⋊Q8—102no—
538C22⋊Q8—101no—
539C22⋊Q8—101no—
540C22⋊Q8—101no—
541C22⋊Q8C22×D512yes—
542C4×Q8—21no—
543C4×Q8—52no—
544C4×Q8—52no—
545C4×Q8—52no—
546C4×Q8—102no—
547C4×Q8—102no—
548C4×Q8—102no—
549C4×Q8—101no—
550C4×Q8—102no—
551C4×Q8—101no—
552C4×Q8—101no—
553C4×Q8C22×D512yes—
554#117—21no—
555#117—102no—
556#117—102no—
557#117—101no—
558#117—101no—
559#117—101no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—52no—
563C2×C4⋊C4—102no—
564C2×C4⋊C4—102no—
565C2×C4⋊C4—102no—
566C2×C4⋊C4—102no—
567C2×C4⋊C4—102no—
568C2×C4⋊C4—102no—
569C2×C4⋊C4—102no—
570C2×C4⋊C4—102no—
571C2×C4⋊C4—101no—
572C2×C4⋊C4—101no—
573C2×C4⋊C4—102no—
574C2×C4⋊C4—102no—
575C2×C4⋊C4—101no—
576C2×C4⋊C4—102no—
577C2×C4⋊C4—102no—
578C2×C4⋊C4—101no—
579C2×C4⋊C4—101no—
580C2×C22⋊C4—102no—
581C2×C42—51no—
582C2×C42—51no—
583C2×C42—51no—
584C2×C42—51no—
585C2×C42—51no—
586C2×C42—51no—
587C2×C42—51no—
588C2×C42—51no—
589C2×C42—51no—
590C2×C42—51no—
591C2×C42—51no—
592C2×C42—102no—
593C2×C42C22×D511yescharacteristic
594C4⋊C8—54no—
595C4⋊C8—52no—
596C4⋊C8C22×D512yes—
597#103—58no—
598#103—58no—
599#103—58no—
600#103C22×D518yes—
601C22⋊C8—52no—
602C22⋊C8—54no—
603C22⋊C8C22×D512yes—
604C4×C8—54no—
605C4×C8—52no—
606C4×C8C22×D512yes—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5C22×Q1612yes—
610C22×C5C23×D411yescharacteristic
611C2×D5—21no—
612C2×D5—21no—
613C2×D5—28no—
614C2×D5#53512yes—
615C2×D5C22×Q1612yes—
616C2×D5C22×Q1612yes—
617C2×D5C2×#13712yes—
618C4×C5—21no—
619C4×C5—21no—
620C4×C5—44no—
621C4×C5—42no—
622C4×C5—42no—
623C4×C5C22×Q1612yes—
624C4×C5C22×Q1612yes—
625C4×C5C2×#13712yes—
626C4×C5C2×H(5,𝔽2)12yes—
627Dic5—21no—
628Dic5—21no—
629Dic5—44no—
630Dic5—42no—
631Dic5—42no—
632Dic5#53512yes—
633Dic5C22×Q1612yes—
634Dic5C22×Q1612yes—
635Dic5C2×#13712yes—
636C24—51no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—44no—
640C2×Q8—54no—
641C2×Q8—52no—
642C2×Q8—102no—
643C2×Q8—102no—
644C2×Q8—104no—
645C2×Q8—104no—
646C2×Q8—108no—
647C2×Q8—1016no—
648C2×Q8—101no—
649C2×Q8—102no—
650C2×Q8—204no—
651C2×Q8—208no—
652C2×Q8—204no—
653C2×Q8—208no—
654C2×Q8—208no—
655C2×Q8—208no—
656C2×Q8C23×D514yes—
657C2×Q8C23×D512yes—
658C22×C4—22no—
659C22×C4—51no—
660C22×C4—51no—
661C22×C4—51no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—51no—
665C22×C4—51no—
666C22×C4—58no—
667C22×C4—51no—
668C22×C4—51no—
669C22×C4—51no—
670C22×C4—51no—
671C22×C4—51no—
672C22×C4—51no—
673C22×C4—51no—
674C22×C4—51no—
675C22×C4—104no—
676C22×C4—104no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—104no—
680C22×C4—104no—
681C22×C4—102no—
682C22×C4—208no—
683C22×C4D4×D511yescharacteristic
684C22×C4D4×D511yescharacteristic
685C22×C4C23×D511yescharacteristic
686Q16—48no—
687Q16—208no—
688Q16—208no—
689Q16—208no—
690C2×C8—54no—
691C2×C8—108no—
692C2×C8C23×D514yes—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—52no—
703C4⋊C4—102no—
704C4⋊C4—104no—
705C4⋊C4—104no—
706C4⋊C4—104no—
707C4⋊C4—104no—
708C4⋊C4—102no—
709C4⋊C4—102no—
710C4⋊C4—102no—
711C4⋊C4—102no—
712C4⋊C4—102no—
713C4⋊C4—102no—
714C4⋊C4—102no—
715C4⋊C4—102no—
716C4⋊C4—102no—
717C4⋊C4—102no—
718C4⋊C4—102no—
719C4⋊C4—101no—
720C4⋊C4—101no—
721C4⋊C4—102no—
722C4⋊C4—102no—
723C4⋊C4—101no—
724C4⋊C4C23×D512yes—
725C22⋊C4—22no—
726C22⋊C4—102no—
727C22⋊C4—102no—
728C22⋊C4—102no—
729C42—22no—
730C42—51no—
731C42—51no—
732C42—51no—
733C42—51no—
734C42—51no—
735C42—51no—
736C42—51no—
737C42—51no—
738C42—51no—
739C42—51no—
740C42—51no—
741C42—51no—
742C42—102no—
743C42—102no—
744C42—102no—
745C42D4×D511yescharacteristic
746C42D4×D511yescharacteristic
747C42C23×D511yescharacteristic
748C42C23×D511yescharacteristic
749C2×C5—22no—
750C2×C5C2×#53511yescharacteristic
751C2×C5C23×Q1611yescharacteristic
752C2×C5C22×#13711yescharacteristic
753D5—22no—
754D5#320914yesdirect product factor
755C23—51no—
756C23—54no—
757C23—51no—
758C23—102no—
759C23—102no—
760C23C2×D4×D511yescharacteristic
761Q8—24no—
762Q8—28no—
763Q8—44no—
764Q8—42no—
765Q8—104no—
766Q8—108no—
767Q8—204no—
768Q8—208no—
769Q8—204no—
770Q8—204no—
771Q8—208no—
772Q8—202no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—44no—
779C2×C4—54no—
780C2×C4—51no—
781C2×C4—51no—
782C2×C4—51no—
783C2×C4—51no—
784C2×C4—54no—
785C2×C4—54no—
786C2×C4—54no—
787C2×C4—54no—
788C2×C4—54no—
789C2×C4—54no—
790C2×C4—51no—
791C2×C4—51no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—104no—
803C2×C4—208no—
804C2×C4—204no—
805C2×C4—204no—
806C2×C4—208no—
807C2×C4—204no—
808C2×C4D5×Q1614yescomplemented
809C2×C4C2×D4×D511yescharacteristic
810C2×C4C2×D4×D511yescharacteristic
811C2×C4C2×D4×D511yescharacteristic
812C2×C4C2×D4×D511yescharacteristic
813C2×C4C2×D4×D511yescharacteristic
814C2×C4C24×D511yescharacteristic
815C8—24no—
816C8—104no—
817C5C2×#320911yescharacteristic, complemented, Sylow
818C22—21no—
819C22—21no—
820C22—52no—
821C22—52no—
822C22—52no—
823C22—52no—
824C22—108no—
825C22—101no—
826C22—101no—
827C22C2×D5×Q1612yes—
828C22C22×D4×D511yescharacteristic
829C4—21no—
830C4—21no—
831C4—44no—
832C4—42no—
833C4—42no—
834C4—52no—
835C4—52no—
836C4—52no—
837C4—52no—
838C4—101no—
839C4—101no—
840C4—204no—
841C4—202no—
842C4—202no—
843C4C2×D5×Q1612yes—
844C4C2×D5×Q1612yes—
845C4D5×#13712yes—
846C4D5×H(5,𝔽2)12yes—
847C2—22no—
848C2—54no—
849C2—102no—
850C2D5×#53511yescharacteristic
851C2C22×D5×Q1611yescharacteristic
852C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC22C22×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC5×#3209C2
socleC22×C5C23×D4
prime radicalC23×D5C2×D4
hypercenter#3209D5
hypocenterC5C2×#3209
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
3. C5×#3209C2semidirect
4. #10615101C2semidirect
5. #10614953C2semidirect
6. #10613533C2semidirect
7. D5×#494C2semidirect
8. #10613335C2semidirect
9. D5×#487C2semidirect
10. #10612211C2semidirect
11. D5×#462C2semidirect
13. #10611909C2semidirect
14. #10611044C2semidirect
52. C5×#494C22semidirect
53. C5×#487C22semidirect
54. C5×#462C22semidirect
59. #65471C22semidirect
60. #65470C22semidirect
61. #65382C22semidirect
62. #65381C22semidirect
63. #65381C22semidirect
64. #65379C22semidirect
65. #65370C22semidirect
67. #65320C22semidirect
69. #65138C22semidirect
74. #65082C22semidirect
75. #65081C22semidirect
79. #64988C22semidirect
82. #64970C22semidirect
226. #3209D5direct (N × H)
259. C2×C4×D5Q16semidirect
385. #494C2×D5semidirect
390. #487C2×D5semidirect
396. #462C2×D5semidirect
428. C2×C4×C5C2×Q16semidirect
441. C2×Dic5C2×Q16semidirect
460. C4×D5C2×Q16semidirect
461. C4×D5C2×Q16semidirect
754. D5#3209direct (N × H)
808. C2×C4D5×Q16semidirect
817. C5C2×#3209semidirect

Maximal subgroups

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

subgroupindex
D5×#5332
C2×D5×C4⋊Q82
C5×#32092
#106151012
#106149532
#106135332
D5×#4942
#106133352
D5×#4872
#106122112
D5×#4622
D5×#4512
#106119092
#106110442
D5×#4312
C2×#32095