Finite Group Databasebeta

← C2×#10617452 #13044766

Subgroups — C2×#10617452 #13044766

Order 1280.

2666 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5⋊#131C211yesmaximal, characteristic, complemented
2C22×#4133C211yesmaximal, characteristic, complemented
3C2×#66111C211yesmaximal, characteristic
4C2×#65795C211yesmaximal, characteristic, complemented
5C2×#65784C211yesmaximal, characteristic, complemented
6#10617452C2116yesmaximal, direct product factor
7C2×#65741C212yesmaximal, complemented
8C2×#65740C212yesmaximal, complemented
9C2×#65737C212yesmaximal, complemented
10C2×#65736C212yesmaximal, complemented
11C2×#65729C211yesmaximal, characteristic, complemented
12C2×#65728C211yesmaximal, characteristic, complemented
13C2×D5×#41C2211yescharacteristic
14C22×#713C2211yescharacteristic
15D5⋊#131—24no—
16D5⋊#131C2218yescomplemented
17C2×#4133—21no—
18C2×#4133—21no—
19C2×#4133—24no—
20C2×#4133C2212yescomplemented
21C2×#4133C2212yescomplemented
22C2×#4133C2218yescomplemented
23C2×#4133C2211yescharacteristic, complemented
24C2×#4133C2211yescharacteristic, complemented
25C2×#4131—21no—
26C2×#4131—21no—
27C2×#4131C2211yescharacteristic, complemented
28C2×#4131C2211yescharacteristic, complemented
29C2×#4130C2211yescharacteristic
30C2×D5⋊M16—21no—
31C2×D5⋊M16C2211yescharacteristic
32C22×#700—21no—
33C22×#700C2211yescharacteristic
34C22×D5⋊C8—21no—
35C22×D5⋊C8—21no—
36C22×D5⋊C8C2211yescharacteristic
37C2×C5×#137C411yescharacteristic, complemented
38C2×#4095C411yescharacteristic, complemented
39C2×#4088C411yescharacteristic, complemented
40#66111C418yescomplemented
41#66111C2218yes—
42C2×#4065C2212yes—
43C2×#4064C412yescomplemented
44C2×#4062C2212yes—
45C2×#4060C412yescomplemented
46C2×#4054C411yescharacteristic, complemented
47C2×D5×M16C2211yescharacteristic
48#65795C2218yescomplemented
49#65784C2218yescomplemented
50C2×#4010C2212yescomplemented
51C2×#4010C2212yescomplemented
52C2×#4010C2212yescomplemented
53C2×#4008C2212yescomplemented
54#65741C22116yescomplemented
55#65740C22116yescomplemented
56#65737C22116yescomplemented
57#65736C22116yescomplemented
58#65729C2218yescomplemented
59#65728C2218yescomplemented
60C2×#3996C2212yescomplemented
61C2×#3995C2212yescomplemented
62C2×#3992C2212yescomplemented
63C2×C8×AGL(1,𝔽5)C2212yescomplemented
64C2×#2955—51nomaximal, Sylow
65C2×C5×#41C2×C411yescharacteristic
66C22×C5×Q8C2×C411yescharacteristic
67D5×#41—22no—
68D5×#41—22no—
69D5×#41C2×C414yes—
70D5×#41C2314yes—
71C2×#713—21no—
72C2×#713—22no—
73C2×#713—21no—
74C2×#713—22no—
75C2×#713C2×C412yes—
76C2×#713C2×C414yes—
77C2×#713C2312yes—
78C2×#713C2311yescharacteristic
79C2×#713C2314yes—
80C2×Q8×D5C2×C411yescharacteristic
81C2×#711—21no—
82C2×#711C2311yescharacteristic
83C2×D4×D5—21no—
84C2×D4×D5C2×C411yescharacteristic
85C2×#709—21no—
86C2×#709C2×C411yescharacteristic
87C22×D20—21no—
88C22×D20C2×C411yescharacteristic
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×C4×D5C2311yescharacteristic
92C2×C22⋊AGL(1,𝔽5)—21no—
93C2×#704—21no—
94C2×#704—21no—
95C2×#704—21no—
96C22×#170—21no—
97C22×#170—21no—
98C22×#170—21no—
99C22×#170D411yescharacteristic
100C22×#170D411yescharacteristic
101#4133—28no—
102#4133—28no—
103#4133—24no—
104#4133—24no—
105#4133—22no—
106#4133—22no—
107#4133C2318yescomplemented
108#4133C2318yescomplemented
109#4133C2314yescomplemented
110#4133C2314yescomplemented
111#4131—28no—
112#4131—28no—
113#4131—22no—
114#4131—22no—
115#4131C2314yescomplemented
116#4131C2314yescomplemented
117#4130—22no—
118#4130C2314yes—
119C2×C4⋊AGL(1,𝔽5)—21no—
120C2×C4×AGL(1,𝔽5)C2312yes—
121D5⋊M16—22no—
122D5⋊M16—28no—
123D5⋊M16C2314yes—
124C2×#700—21no—
125C2×#700—22no—
126C2×#700—22no—
127C2×#700—22no—
128C2×#700—28no—
129C2×#700—21no—
130C2×#700—21no—
131C2×#700C2314yes—
132C2×#700C2311yescharacteristic
133C2×#700C2312yes—
134C2×#700C2311yescharacteristic
135C2×D5⋊C8—21no—
136C2×D5⋊C8—21no—
137C2×D5⋊C8—21no—
138C2×D5⋊C8—22no—
139C2×D5⋊C8—22no—
140C2×D5⋊C8—28no—
141C2×D5⋊C8—28no—
142C2×D5⋊C8D411yescharacteristic
143C2×D5⋊C8D411yescharacteristic
144C2×D5⋊C8D414yes—
145C2×D5⋊C8C2311yescharacteristic
146C2×D5⋊C8C2311yescharacteristic
147C2×D5⋊C8C2314yes—
148C5×#137C2×C418yescomplemented
149C2×C5×Q16C2×C412yes—
150C2×C5×SD16C2×C412yes—
151C2×C5×M16C2×C411yescharacteristic
152#4095C2×C418yescomplemented
153C2×#689C2×C412yes—
154#4088C2×C418yescomplemented
155C2×#688C2×C412yes—
156C2×#688C2×C412yes—
157C2×#686C2×C412yes—
158C2×#681C2×C411yescharacteristic
159#4065C2×C418yes—
160#4065C2318yes—
161#4064C2×C4116yescomplemented
162#4062C2×C418yes—
163#4062C2318yes—
164#4060C2×C4116yescomplemented
165#4054C2×C418yescomplemented
166D5×M16C2×C414yes—
167D5×M16C2314yes—
168C2×D40C2×C412yes—
169C2×#677C2×C412yes—
170C2×#676C2×C412yes—
171C2×C8×D5C2312yes—
172#4010C2318yescomplemented
173#4010C2318yescomplemented
174#4010C2318yescomplemented
175#4008C2318yescomplemented
176#3996C2318yescomplemented
177#3995C2318yescomplemented
178#3992C2318yescomplemented
179C8×AGL(1,𝔽5)C2318yescomplemented
180C2×#575—51no—
181C22×#131—51no—
182C22×#131—51no—
183#2955—516no—
184C2×#444—52no—
185C2×#444—52no—
186C2×#443—52no—
187C2×#443—52no—
188C2×#430—51no—
189C2×#421—51no—
190C2×#421—51no—
191C2×#405—51no—
192C23×D5—21no—
193C23×D5—21no—
194C23×D5#4111yescharacteristic
195C22×AGL(1,𝔽5)—22no—
196C5×#41—22no—
197C5×#41C22×C414yes—
198C2×C5×Q8—21no—
199C2×C5×Q8—22no—
200C2×C5×Q8C22×C412yes—
201C2×C5×Q8C22×C411yescharacteristic
202C2×C5×Q8C22×C414yes—
203C2×C5×D4—21no—
204C2×C5×D4C22×C411yescharacteristic
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5C22×C411yescharacteristic
208C2×C22⋊D5—21no—
209C2×C22⋊D5—21no—
210C2×C22⋊D5—21no—
211C22×Dic5—21no—
212C22×Dic5C2×D411yescharacteristic
213#713—24no—
214#713—24no—
215#713—24no—
216#713—24no—
217#713—22no—
218#713—21no—
219#713—22no—
220#713—24no—
221#713—21no—
222#713C22×C418yes—
223#713C22×C414yes—
224#713C22×C412yes—
225#713C2414yes—
226#713C2412yes—
227Q8×D5—22no—
228Q8×D5C22×C414yes—
229#711—24no—
230#711—24no—
231#711—21no—
232#711—21no—
233#711C22×C412yes—
234#711C2412yes—
235D4×D5—24no—
236D4×D5—24no—
237D4×D5—22no—
238D4×D5C22×C414yes—
239#709—22no—
240#709—24no—
241#709—24no—
242#709C22×C414yes—
243C2×D20—22no—
244C2×D20—24no—
245C2×D20—22no—
246C2×D20—24no—
247C2×D20—21no—
248C2×D20—21no—
249C2×D20—22no—
250C2×D20C22×C412yes—
251C2×D20C22×C414yes—
252C2×D20C22×C411yescharacteristic
253C2×C4×D5—21no—
254C2×C4×D5—21no—
255C2×C4×D5—22no—
256C2×C4×D5—24no—
257C2×C4×D5—21no—
258C2×C4×D5—22no—
259C2×C4×D5—24no—
260C2×C4×D5—24no—
261C2×C4×D5—24no—
262C2×C4×D5C22×C411yescharacteristic
263C2×C4×D5C22×C412yes—
264C2×C4×D5C2×D411yescharacteristic
265C2×C4×D5C2×D412yes—
266C2×C4×D5#4111yescharacteristic
267C2×C4×D5#4112yes—
268C2×C4×D5C2411yescharacteristic
269C2×C4×D5C2412yes—
270C2×Dic10—21no—
271C2×Dic10C22×C411yescharacteristic
272C22⋊AGL(1,𝔽5)—24no—
273#704—24no—
274#704—24no—
275#704—24no—
276C2×#170—22no—
277C2×#170—24no—
278C2×#170—21no—
279C2×#170—21no—
280C2×#170—24no—
281C2×#170—24no—
282C2×#170C2×D411yescharacteristic
283C2×#170C2×D411yescharacteristic
284C2×#170C2×D414yes—
285C2×#170C2×D411yescharacteristic
286C2×#170C2×D411yescharacteristic
287C2×#170C2×D414yes—
288C4⋊AGL(1,𝔽5)—24no—
289C4×AGL(1,𝔽5)—22no—
290C4×AGL(1,𝔽5)C2414yes—
291#700—24no—
292#700—22no—
293#700—21no—
294#700—21no—
295#700—28no—
296#700—28no—
297#700—24no—
298#700—24no—
299#700C2414yes—
300#700C2412yes—
301#700C2412yes—
302D5⋊C8—24no—
303D5⋊C8—24no—
304D5⋊C8—24no—
305D5⋊C8—28no—
306D5⋊C8—28no—
307D5⋊C8C2×D414yes—
308D5⋊C8C2×D414yes—
309D5⋊C8C2×D412yes—
310D5⋊C8C2×D412yes—
311D5⋊C8C2412yes—
312D5⋊C8C2412yes—
313C5×Q16C22×C418yes—
314C5×SD16C22×C418yes—
315C5×M16C22×C414yes—
316C2×C5×C8C22×C412yes—
317#689C22×C418yes—
318#688C22×C418yes—
319#688C22×C418yes—
320#686C22×C418yes—
321#681C22×C414yes—
322C2×#168C22×C412yes—
323D40C22×C418yes—
324#677C22×C418yes—
325#676C22×C418yes—
326C8×D5C22×C414yes—
327C8×D5C2414yes—
328C22×#41—51no—
329C22×#41—51no—
330#575—58no—
331#575—58no—
332C2×#137—51no—
333C2×#137—52no—
334C2×#137AGL(1,𝔽5)11yescharacteristic, complemented
335C2×AGL(1,ℤ/8)—51no—
336C2×AGL(1,ℤ/8)—52no—
337C2×AGL(1,ℤ/8)—51no—
338C2×#135—52no—
339C2×#135—52no—
340C2×#131—51no—
341C2×#131—52no—
342C2×#131—51no—
343C2×#131—51no—
344C2×#131—52no—
345C2×#131—51no—
346C2×#131—58no—
347C2×#131—58no—
348C2×#131—101no—
349C2×#131—101no—
350C2×#131—101no—
351C2×#131—101no—
352C2×#131—104no—
353C2×#131—104no—
354C22×M16—51no—
355C22×M16—51no—
356C22×M16—51no—
357C22×M16—101no—
358C22×M16—101no—
359C23×C8—51no—
360C23×C8—101no—
361C23×C8—101no—
362C2×#117—51no—
363#444—516no—
364#444—516no—
365#443—516no—
366#443—516no—
367#430—58no—
368C2×#108—52no—
369C2×#108—52no—
370#421—58no—
371#421—58no—
372C2×#104—52no—
373C2×#104—52no—
374C2×#104—52no—
375C2×#104—52no—
376#405—58no—
377C2×#97—52no—
378C2×C4×C8—52no—
379C23×C5—21no—
380C23×C5C4×D411yescharacteristic
381C22×D5—24no—
382C22×D5—22no—
383C22×D5—21no—
384C22×D5—24no—
385C22×D5—42no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5C4×D411yescharacteristic
389C22×D5C4×D412yes—
390C22×D5C2×#4111yescharacteristic
391C22×D5C2×#4112yes—
392C2×AGL(1,𝔽5)—24no—
393C2×AGL(1,𝔽5)—44no—
394C5×Q8—21no—
395C5×Q8—22no—
396C5×Q8—24no—
397C5×Q8C23×C412yes—
398C5×Q8C23×C414yes—
399C5×D4—24no—
400C5×D4—21no—
401C5×D4C23×C412yes—
402C2×C4×C5—21no—
403C2×C4×C5—24no—
404C2×C4×C5—22no—
405C2×C4×C5—24no—
406C2×C4×C5C4×D411yescharacteristic
407C2×C4×C5C4×D412yes—
408C2×C4×C5C23×C411yescharacteristic
409C2×C4×C5C23×C412yes—
410C22⋊D5—24no—
411C22⋊D5—22no—
412C22⋊D5—22no—
413C22⋊D5—24no—
414C2×Dic5—21no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5C4×D411yescharacteristic
418C2×Dic5C4×D412yes—
419C2×Dic5C22×D411yescharacteristic
420C2×Dic5C22×D412yes—
421D20—28no—
422D20—24no—
423D20—22no—
424D20—24no—
425D20—22no—
426D20—22no—
427D20—24no—
428D20—21no—
429D20C23×C414yes—
430D20C23×C412yes—
431C4×D5—24no—
432C4×D5—24no—
433C4×D5—22no—
434C4×D5—28no—
435C4×D5—24no—
436C4×D5—22no—
437C4×D5—24no—
438C4×D5C4×D412yes—
439C4×D5C4×D412yes—
440C4×D5C4×D412yes—
441C4×D5C23×C411yescharacteristic
442C4×D5C23×C412yes—
443C4×D5C22×D412yes—
444C4×D5C22×D411yescharacteristic
445C4×D5C2×#4111yescharacteristic
446C4×D5C2×#4112yes—
447C4×D5C2511yescharacteristic
448Dic10—21no—
449Dic10—24no—
450Dic10C23×C412yes—
451#170—24no—
452#170—22no—
453#170—22no—
454#170C22×D412yes—
455#170C22×D412yes—
456#170C22×D412yes—
457#170C22×D412yes—
458C5×C8C23×C414yes—
459#168C23×C414yes—
460C2×#41—54no—
461C2×#41—54no—
462C2×#41—52no—
463C2×#41—54no—
464C2×#41—51no—
465C2×#41—52no—
466C2×#41—54no—
467C2×#41—51no—
468C2×#41—51no—
469C2×#41—101no—
470C2×#41—101no—
471C2×#41—101no—
472C2×#41—102no—
473C2×#41—101no—
474C2×#41—102no—
475C2×#41—102no—
476C2×#41—102no—
477C2×#41C2×AGL(1,𝔽5)11yescharacteristic
478C22×Q8—51no—
479C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
480C22×D4—51no—
481C22×D4—51no—
482C22×D4—101no—
483C22×D4—101no—
484C23×C4—51no—
485C23×C4—101no—
486C23×C4—101no—
487#137—58no—
488#137—516no—
489#137C2×AGL(1,𝔽5)18yescomplemented
490AGL(1,ℤ/8)—58no—
491AGL(1,ℤ/8)—516no—
492AGL(1,ℤ/8)—58no—
493#135—58no—
494#135—58no—
495#135—58no—
496#135—58no—
497C2×Q16—52no—
498C2×Q16C2×AGL(1,𝔽5)12yes—
499C2×SD16—52no—
500C2×SD16—52no—
501C2×SD16—52no—
502C2×SD16C2×AGL(1,𝔽5)12yes—
503C2×D8—52no—
504C2×D8—52no—
505#131—54no—
506#131—54no—
507#131—58no—
508#131—54no—
509#131—58no—
510#131—54no—
511#131—108no—
512#131—108no—
513#131—102no—
514#131—102no—
515#131—108no—
516#131—108no—
517#131—104no—
518#131—104no—
519#131—102no—
520#131—102no—
521C2×M16—51no—
522C2×M16—54no—
523C2×M16—54no—
524C2×M16—52no—
525C2×M16—51no—
526C2×M16—52no—
527C2×M16—51no—
528C2×M16—54no—
529C2×M16—54no—
530C2×M16—102no—
531C2×M16—101no—
532C2×M16—102no—
533C2×M16—101no—
534C2×M16—108no—
535C2×M16—108no—
536C2×M16—101no—
537C2×M16—101no—
538C2×M16—101no—
539C2×M16—102no—
540C2×M16—102no—
541C2×M16—101no—
542C2×M16C2×AGL(1,𝔽5)11yescharacteristic
543C22×C8—51no—
544C22×C8—51no—
545C22×C8—54no—
546C22×C8—51no—
547C22×C8—51no—
548C22×C8—54no—
549C22×C8—51no—
550C22×C8—51no—
551C22×C8—52no—
552C22×C8—101no—
553C22×C8—102no—
554C22×C8—101no—
555C22×C8—102no—
556C22×C8—108no—
557C22×C8—108no—
558C22×C8—101no—
559C22×C8—101no—
560C22×C8—101no—
561C22×C8—101no—
562#117—54no—
563#117—102no—
564C2×C4⋊C4—101no—
565C2×C22⋊C4—101no—
566C2×C42—52no—
567#108—58no—
568#108—58no—
569#104—58no—
570#104—58no—
571#104—58no—
572#104—58no—
573#97—58no—
574C4×C8—58no—
575C22×C5—22no—
576C22×C5—22no—
577C22×C5—42no—
578C22×C5C2×C4×D412yes—
579C22×C5C2×C4×D411yescharacteristic
580C2×D5—22no—
581C2×D5—22no—
582C2×D5—24no—
583C2×D5—22no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—48no—
587C2×D5—48no—
588C2×D5—44no—
589C2×D5—42no—
590C2×D5C2×C4×D412yes—
591C2×D5C2×C4×D411yescharacteristic
592C2×D5C22×#4111yescharacteristic
593AGL(1,𝔽5)—44no—
594C4×C5—22no—
595C4×C5—24no—
596C4×C5C2×C4×D411yescharacteristic
597C4×C5C2×C4×D412yes—
598C4×C5C24×C411yescharacteristic
599Dic5—22no—
600Dic5C2×C4×D412yes—
601Dic5C2×C4×D411yescharacteristic
602Dic5C23×D411yescharacteristic
603C24—51no—
604C24—101no—
605C24—101no—
606#41—22no—
607#41—52no—
608#41—54no—
609#41—52no—
610#41—54no—
611#41—58no—
612#41—52no—
613#41—52no—
614#41—54no—
615#41—104no—
616#41—104no—
617#41—104no—
618#41—101no—
619#41—104no—
620#41—101no—
621#41—104no—
622#41—102no—
623#41—101no—
624#41—102no—
625#41—101no—
626#41—104no—
627#41—104no—
628#41—104no—
629#41—104no—
630#41—102no—
631#41C22×AGL(1,𝔽5)14yes—
632C2×Q8—22no—
633C2×Q8—21no—
634C2×Q8—54no—
635C2×Q8—51no—
636C2×Q8—101no—
637C2×Q8—102no—
638C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
639C2×Q8C22×AGL(1,𝔽5)12yes—
640C2×Q8C22×AGL(1,𝔽5)14yes—
641C2×D4—21no—
642C2×D4—54no—
643C2×D4—52no—
644C2×D4—51no—
645C2×D4—54no—
646C2×D4—104no—
647C2×D4—104no—
648C2×D4—101no—
649C2×D4—102no—
650C2×D4—102no—
651C2×D4—102no—
652C2×D4—101no—
653C2×D4—104no—
654C2×D4—104no—
655C2×D4—101no—
656C2×D4—101no—
657C2×D4—102no—
658C2×D4—101no—
659C2×D4C22×AGL(1,𝔽5)11yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—52no—
665C22×C4—51no—
666C22×C4—52no—
667C22×C4—51no—
668C22×C4—52no—
669C22×C4—51no—
670C22×C4—52no—
671C22×C4—104no—
672C22×C4—101no—
673C22×C4—102no—
674C22×C4—104no—
675C22×C4—104no—
676C22×C4—102no—
677C22×C4—104no—
678C22×C4—101no—
679C22×C4—101no—
680C22×C4—101no—
681C22×C4—102no—
682C22×C4C22×AGL(1,𝔽5)11yescharacteristic
683Q16—58no—
684Q16C22×AGL(1,𝔽5)18yes—
685SD16—58no—
686SD16—58no—
687SD16—58no—
688SD16C22×AGL(1,𝔽5)18yes—
689D8—58no—
690D8—58no—
691M16—54no—
692M16—58no—
693M16—54no—
694M16—52no—
695M16—52no—
696M16—108no—
697M16—104no—
698M16—108no—
699M16—104no—
700M16—104no—
701M16—104no—
702M16—104no—
703M16—102no—
704M16—101no—
705M16—101no—
706M16—104no—
707M16C22×AGL(1,𝔽5)14yes—
708C2×C8—52no—
709C2×C8—52no—
710C2×C8—51no—
711C2×C8—51no—
712C2×C8—51no—
713C2×C8—54no—
714C2×C8—54no—
715C2×C8—51no—
716C2×C8—54no—
717C2×C8—54no—
718C2×C8—52no—
719C2×C8—52no—
720C2×C8—52no—
721C2×C8—54no—
722C2×C8—54no—
723C2×C8—104no—
724C2×C8—108no—
725C2×C8—104no—
726C2×C8—108no—
727C2×C8—104no—
728C2×C8—104no—
729C2×C8—104no—
730C2×C8—104no—
731C2×C8—102no—
732C2×C8—101no—
733C2×C8—101no—
734C2×C8C22×AGL(1,𝔽5)12yes—
735C4⋊C4—104no—
736C22⋊C4—104no—
737C42—54no—
738C42—102no—
739C2×C5—22no—
740C2×C5—42no—
741C2×C5#295512yescomplemented
742C2×C5C22×C4×D411yescharacteristic
743D5—21no—
744D5—22no—
745D5—21no—
746D5—44no—
747D5—42no—
748C23—21no—
749C23—51no—
750C23—51no—
751C23—52no—
752C23—52no—
753C23—104no—
754C23—104no—
755C23—102no—
756C23—101no—
757C23—202no—
758C23—204no—
759C23—204no—
760C23D4×AGL(1,𝔽5)11yescharacteristic
761Q8—24no—
762Q8—22no—
763Q8—21no—
764Q8—52no—
765Q8—104no—
766Q8—101no—
767Q8C23×AGL(1,𝔽5)12yes—
768Q8C23×AGL(1,𝔽5)14yes—
769D4—24no—
770D4—21no—
771D4—54no—
772D4—52no—
773D4—102no—
774D4—102no—
775D4—104no—
776D4—108no—
777D4—104no—
778D4—104no—
779D4—102no—
780D4—102no—
781D4—104no—
782D4—104no—
783D4—101no—
784D4—102no—
785D4C23×AGL(1,𝔽5)12yes—
786C2×C4—24no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—52no—
791C2×C4—52no—
792C2×C4—51no—
793C2×C4—51no—
794C2×C4—51no—
795C2×C4—52no—
796C2×C4—52no—
797C2×C4—51no—
798C2×C4—52no—
799C2×C4—52no—
800C2×C4—52no—
801C2×C4—51no—
802C2×C4—51no—
803C2×C4—52no—
804C2×C4—102no—
805C2×C4—104no—
806C2×C4—102no—
807C2×C4—104no—
808C2×C4—108no—
809C2×C4—104no—
810C2×C4—102no—
811C2×C4—102no—
812C2×C4—101no—
813C2×C4—104no—
814C2×C4—104no—
815C2×C4—204no—
816C2×C4D4×AGL(1,𝔽5)12yes—
817C2×C4D4×AGL(1,𝔽5)11yescharacteristic
818C2×C4C23×AGL(1,𝔽5)12yes—
819C2×C4C23×AGL(1,𝔽5)11yescharacteristic
820C8—52no—
821C8—52no—
822C8—52no—
823C8—52no—
824C8—54no—
825C8—104no—
826C8—102no—
827C8—102no—
828C8C23×AGL(1,𝔽5)14yes—
829C5C2×#295511yescharacteristic, complemented, Sylow
830C22—22no—
831C22—22no—
832C22—42no—
833C22—51no—
834C22—52no—
835C22—51no—
836C22—102no—
837C22—102no—
838C22—104no—
839C22—102no—
840C22—202no—
841C22—202no—
842C22—208no—
843C22—208no—
844C22—204no—
845C22—202no—
846C22C2×D4×AGL(1,𝔽5)12yes—
847C22C2×D4×AGL(1,𝔽5)11yescharacteristic
848C4—22no—
849C4—24no—
850C4—51no—
851C4—51no—
852C4—52no—
853C4—102no—
854C4—204no—
855C4C2×D4×AGL(1,𝔽5)12yes—
856C4C2×D4×AGL(1,𝔽5)11yescharacteristic
857C4C24×AGL(1,𝔽5)11yescharacteristic
858C2—22no—
859C2—42no—
860C2—101no—
861C2—102no—
862C2—101no—
863C2—204no—
864C2—202no—
865C2#1061745212yesdirect product factor
866C2C22×D4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC2×C5×#137C4
socleC22×C5C2×C4×D4
prime radicalC2×#66111C2
cosocleC4×D5C25
hypercenterC2×#137AGL(1,𝔽5)
hypocenterC5C2×#2955
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×D5⋊#131C2semidirect
2. C22×#4133C2semidirect
4. C2×#65795C2semidirect
5. C2×#65784C2semidirect
6. #10617452C2direct (N × H)
7. C2×#65741C2semidirect
8. C2×#65740C2semidirect
9. C2×#65737C2semidirect
10. C2×#65736C2semidirect
11. C2×#65729C2semidirect
12. C2×#65728C2semidirect
16. D5⋊#131C22semidirect
20. C2×#4133C22semidirect
21. C2×#4133C22semidirect
22. C2×#4133C22semidirect
23. C2×#4133C22semidirect
24. C2×#4133C22semidirect
27. C2×#4131C22semidirect
28. C2×#4131C22semidirect
37. C2×C5×#137C4semidirect
38. C2×#4095C4semidirect
39. C2×#4088C4semidirect
40. #66111C4semidirect
43. C2×#4064C4semidirect
45. C2×#4060C4semidirect
46. C2×#4054C4semidirect
48. #65795C22semidirect
49. #65784C22semidirect
50. C2×#4010C22semidirect
51. C2×#4010C22semidirect
52. C2×#4010C22semidirect
53. C2×#4008C22semidirect
54. #65741C22semidirect
55. #65740C22semidirect
56. #65737C22semidirect
57. #65736C22semidirect
58. #65729C22semidirect
59. #65728C22semidirect
60. C2×#3996C22semidirect
61. C2×#3995C22semidirect
62. C2×#3992C22semidirect
63. C2×C8×AGL(1,𝔽5)C22semidirect
107. #4133C23semidirect
108. #4133C23semidirect
109. #4133C23semidirect
110. #4133C23semidirect
115. #4131C23semidirect
116. #4131C23semidirect
148. C5×#137C2×C4semidirect
152. #4095C2×C4semidirect
154. #4088C2×C4semidirect
161. #4064C2×C4semidirect
164. #4060C2×C4semidirect
165. #4054C2×C4semidirect
172. #4010C23semidirect
173. #4010C23semidirect
174. #4010C23semidirect
175. #4008C23semidirect
176. #3996C23semidirect
177. #3995C23semidirect
178. #3992C23semidirect
179. C8×AGL(1,𝔽5)C23semidirect
334. C2×#137AGL(1,𝔽5)semidirect
489. #137C2×AGL(1,𝔽5)semidirect
741. C2×C5#2955semidirect
829. C5C2×#2955semidirect
865. C2#10617452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5⋊#1312
C22×#41332
C2×#661112
C2×#657952
C2×#657842
#106174522
C2×#657412
C2×#657402
C2×#657372
C2×#657362
C2×#657292
C2×#657282
C2×#29555