Finite Group Databasebeta

← #14424461

Subgroups — #14424461

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1007C211yesmaximal, characteristic, complemented
2C2×#91504C211yesmaximal, characteristic, complemented
3C2×D3×#688C211yesmaximal, characteristic, complemented
4#11754655C211yesmaximal, characteristic, complemented
5#11751328C211yesmaximal, characteristic, complemented
6C3×#65516C211yesmaximal, characteristic, complemented
7#11749282C211yesmaximal, characteristic, complemented
8#11749281C211yesmaximal, characteristic, complemented
9#11749279C211yesmaximal, characteristic, complemented
10#11749278C211yesmaximal, characteristic, complemented
11#11749213C211yesmaximal, characteristic, complemented
12#11749211C211yesmaximal, characteristic, complemented
13#11748521C211yesmaximal, characteristic, complemented
14#11748517C211yesmaximal, characteristic, complemented
15#11748490C211yesmaximal, characteristic, complemented
16#10615844—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C5×#1007—24no—
19C5×#1007—24no—
20C2×C5×#239—21no—
21C2×C5×#239C2211yescharacteristic
22C2×C5×#239C2211yescharacteristic, complemented
23C2×C5×D3×Q8—21no—
24C2×C5×D3×Q8C2211yescharacteristic
25C2×C5×D3×Q8C2211yescharacteristic, complemented
26C2×C5×#235—21no—
27C2×C5×#235—21no—
28C2×C5×#235C2211yescharacteristic
29C2×C5×#235C2211yescharacteristic, complemented
30C2×D3×D20C2211yescharacteristic
31C2×#6717C2211yescharacteristic
32C2×#6717C2211yescharacteristic
33#91819C2211yescharacteristic
34C2×C3×#688C2211yescharacteristic
35C2×C3×#688C2211yescharacteristic
36C3×#4076C2211yescharacteristic
37#91577—21no—
38#91567—21no—
39#91504—24no—
40D3×#688—24no—
41#91475—21no—
42#91460C2211yescharacteristic
43#91456C2211yescharacteristic
44#91455—21no—
45#91338C2211yescharacteristic
46C2×#6660C2211yescharacteristic
47C2×#6655C2211yescharacteristic
48C2×#6654C2211yescharacteristic
49C2×#6652C2211yescharacteristic
50C2×#6650C2211yescharacteristic
51C2×D3×#168C2211yescharacteristic
52#91119C2211yescharacteristic, complemented
53#91119C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55C3×#3967C2211yescharacteristic, complemented
56C3×#3967C2211yescharacteristic, complemented
57C3×C22⋊#168C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90972C2211yescharacteristic, complemented
60#90967C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62(C2×D3)⋊#168C2211yescharacteristic, complemented
63(C2×D3)⋊#168C2211yescharacteristic, complemented
64#80041—51nomaximal, Hall
65C2×C5×2−1+4—31no—
66#66164—31no—
67C2×#4095—31no—
68C22×#688—31no—
69#65527—31no—
70#65527—31no—
71#65527—31no—
72#65527—31no—
73#65523—31no—
74#65522—31no—
75#65516—31no—
76#65516—31no—
77#65516—31no—
78#65516D311yescharacteristic, complemented
79#65514—31no—
80C22×D3×D5—21no—
81C2×C3×C5×Q8—22no—
82C2×C3×C5×Q8—22no—
83C2×C3×C5×Q8—21no—
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×Q8C2311yescharacteristic
86C22×C3×C4×C5—21no—
87C22×C3×C4×C5C2311yescharacteristic
88C2×#1220—21no—
89C2×D60C2311yescharacteristic
90C2×C5×#67—21no—
91C2×C5×#67D411yescharacteristic
92C2×C5×#67D411yescharacteristic
93C5×#239—28no—
94C5×#239—22no—
95C5×#239—22no—
96C5×#239—22no—
97C5×#239D414yescomplemented
98C5×D3×Q8—28no—
99C5×D3×Q8—22no—
100C5×D3×Q8—22no—
101C5×D3×Q8—22no—
102C5×D3×Q8D414yescomplemented
103C5×#235—28no—
104C5×#235—28no—
105C5×#235—22no—
106C5×#235—22no—
107C5×#235—22no—
108C5×#235—22no—
109C2×C5×D12—21no—
110C2×C5×D12—21no—
111C2×C5×D12D411yescharacteristic
112C2×C5×D12C2311yescharacteristic
113C2×C4×C5×D3—21no—
114C2×C4×C5×D3—21no—
115C2×C4×C5×D3—21no—
116C2×C4×C5×D3—21no—
117C2×C4×C5×D3—21no—
118C2×C4×C5×D3C2311yescharacteristic
119C2×C4×C5×D3C2311yescharacteristic
120C2×C5×Dic6—21no—
121C2×C5×Dic6—21no—
122C2×C5×Dic6D411yescharacteristic
123C2×C5×Dic6C2311yescharacteristic
124C2×C3×C22⋊D5—21no—
125C2×C3×D20C2311yescharacteristic
126C2×#1203—21no—
127C2×#1202—21no—
128C2×#1201—21no—
129D3×D20—22no—
130D3×D20—22no—
131#6717—22no—
132#6717—22no—
133#6714—21no—
134C4⋊Dic15C2311yescharacteristic
135C2×C3⋊#168C2311yescharacteristic
136C2×C3⋊#168C2311yescharacteristic
137C3×#688—22no—
138C3×#688—22no—
139C3×#685—21no—
140C3×C4⋊Dic5C2311yescharacteristic
141C2×C3×#168C2311yescharacteristic
142C2×C3×#168C2311yescharacteristic
143#6667—21no—
144(C2×D3)⋊Dic5—21no—
145#6665—21no—
146Dic3×Dic5—21no—
147#6660—22no—
148#6655—22no—
149#6654—22no—
150#6652—22no—
151#6650—22no—
152D3×#168—22no—
153C2×#1007D511yescharacteristic, complemented
154C2×#914—51no—
155C2×D3×SD16—51no—
156#5607—51no—
157C3×#448—51no—
158#5227—51no—
159#5172—51no—
160#5170—51no—
161#5037—51no—
162#4810—51no—
163#4806—51no—
164#4804—51no—
165#4802—51no—
166#4734—51no—
167#4727—51no—
168C5×2−1+4—64no—
169C5×2−1+4—64no—
170C2×C5×#41—31no—
171C2×C5×#41—31no—
172C2×C5×#41—31no—
173C2×C5×#41—31no—
174C2×C5×#41—61no—
175C2×C5×#41—61no—
176C2×C5×#41—61no—
177C22×C5×Q8—31no—
178C22×C5×Q8—31no—
179C22×C5×Q8—61no—
180C22×C5×Q8C2×D311yescharacteristic, complemented
181C22×D20—31no—
182#4095—64no—
183#4093—61no—
184C2×#688—31no—
185C2×#688—31no—
186C2×#688—31no—
187C2×#688—31no—
188C2×#688—64no—
189C2×#688C2×D311yescharacteristic
190C2×#688C2×D311yescharacteristic
191#4086—61no—
192#4083—61no—
193#4083—61no—
194C2×#686—31no—
195C2×#686—31no—
196#4076—31no—
197#4076—31no—
198#4076—31no—
199#4076C2×D311yescharacteristic
200#4072—31no—
201C2×#681—31no—
202C22×#168—31no—
203#3967—31no—
204#3967—31no—
205#3967—31no—
206#3967—31no—
207#3967C2×D311yescharacteristic, complemented
208#3967C2×D311yescharacteristic, complemented
209#3964—31no—
210#3964—31no—
211C22⋊#168—31no—
212C22⋊#168—31no—
213C22⋊#168—31no—
214C22⋊#168C2×D311yescharacteristic, complemented
215#3010—151noSylow
216C23×C3×C5C2×D411yescharacteristic
217C22×D15—21no—
218C22×C5×D3—21no—
219C22×C5×D3C2×D411yescharacteristic
220C22×C5×D3C2×D411yescharacteristic
221C22×C3×D5—21no—
222C2×D3×D5—42no—
223C2×D3×D5—81no—
224C2×D3×D5—81no—
225C3×C5×Q8—24no—
226C3×C5×Q8—21no—
227C3×C5×Q8—21no—
228C3×C5×Q8C2×D412yes—
229C3×C5×Q8C2×D412yes—
230C2×C3×C4×C5—24no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5C2×D411yescharacteristic
236C2×C3×C4×C5C2411yescharacteristic
237#1220—81no—
238C2×Dic15—21no—
239D60—21no—
240D60—21no—
241C5×#67—24no—
242C5×#67—22no—
243C5×#67—22no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3C2×D411yescharacteristic
246C2×C5×Dic3C2×D411yescharacteristic
247C5×D12—24no—
248C5×D12—24no—
249C5×D12—22no—
250C5×D12—21no—
251C5×D12C2×D412yes—
252C4×C5×D3—24no—
253C4×C5×D3—24no—
254C4×C5×D3—24no—
255C4×C5×D3—24no—
256C4×C5×D3—21no—
257C4×C5×D3—21no—
258C4×C5×D3—24no—
259C4×C5×D3C2×D412yes—
260C4×C5×D3C2×D412yes—
261C5×Dic6—24no—
262C5×Dic6—21no—
263C5×Dic6—24no—
264C5×Dic6—22no—
265C5×Dic6C2×D412yes—
266C3×C22⋊D5—81no—
267C2×C3×Dic5—21no—
268C3×D20—21no—
269C3×D20—21no—
270#1203—81no—
271#1202—42no—
272#1201—81no—
273C3⋊#168—21no—
274C3⋊#168—21no—
275C3×#168—21no—
276C3×#168—21no—
277C22×C3×Q8C2×D511yescharacteristic, complemented
278#1007—24no—
279#1007—24no—
280C2×#239—21no—
281C2×#239C2×D511yescharacteristic
282C2×#239C2×D511yescharacteristic, complemented
283C2×D3×Q8—21no—
284C2×D3×Q8C2×D511yescharacteristic
285C2×D3×Q8C2×D511yescharacteristic, complemented
286C2×D3×D4—51no—
287C2×#235—21no—
288C2×#235—21no—
289C2×#235C2×D511yescharacteristic
290C2×#235C2×D511yescharacteristic, complemented
291C2×C3×SD16—51no—
292C2×C3×SD16—51no—
293C3×#121—51no—
294C2×#215—51no—
295C2×#215—51no—
296#940—101no—
297#938—51no—
298#937—101no—
299C2×#214—51no—
300C2×#213—51no—
301#930—51no—
302#914—104no—
303D3×SD16—104no—
304C2×D24—51no—
305C2×#204—51no—
306C2×ΓL(1,𝔽25)—51no—
307C2×D3×C8—51no—
308#895—51no—
309#892—51no—
310#885—101no—
311#882—101no—
312C3×#103—51no—
313C3×#103—51no—
314C3×C22⋊C8—51no—
315#835—51no—
316#835—51no—
317#830—51no—
318#821—51no—
319(C2×D3)⋊C8—51no—
320(C2×D3)⋊C8—51no—
321#816—51no—
322#810—51no—
323#809—51no—
324C23×D5—61no—
325C5×#41—34no—
326C5×#41—62no—
327C5×#41—62no—
328C5×#41—62no—
329C5×#41—62no—
330C5×#41—68no—
331C5×#41—68no—
332C5×#41—62no—
333C5×#41—62no—
334C5×#41—68no—
335C5×#41—62no—
336C2×C5×Q8—22no—
337C2×C5×Q8—22no—
338C2×C5×Q8—21no—
339C2×C5×Q8—31no—
340C2×C5×Q8—34no—
341C2×C5×Q8—31no—
342C2×C5×Q8—61no—
343C2×C5×Q8—61no—
344C2×C5×Q8—62no—
345C2×C5×Q8—62no—
346C2×C5×Q8—68no—
347C2×C5×Q8—62no—
348C2×C5×Q8C22×D311yescharacteristic
349C2×C5×Q8C22×D311yescharacteristic
350C2×C5×D4—31no—
351C2×C5×D4—31no—
352C2×C5×D4—31no—
353C2×C5×D4—31no—
354C2×C5×D4—61no—
355C2×C5×D4—61no—
356C2×C5×D4—61no—
357C22×C4×C5—21no—
358C22×C4×C5—31no—
359C22×C4×C5—31no—
360C22×C4×C5—61no—
361C22×C4×C5—61no—
362C22×C4×C5—61no—
363C22×C4×C5—61no—
364C22×C4×C5—61no—
365C22×C4×C5C22×D311yescharacteristic
366C2×C22⋊D5—21no—
367C2×C22⋊D5—61no—
368C2×C22⋊D5—61no—
369C2×C22⋊D5—61no—
370C2×D20—31no—
371C2×D20—62no—
372C2×D20—62no—
373C2×D20—61no—
374C2×D20C22×D311yescharacteristic
375C22⋊Dic5—61no—
376#688—22no—
377#688—22no—
378#688—62no—
379#688—62no—
380#688—62no—
381#688—62no—
382#686—62no—
383#686—62no—
384#685—21no—
385#685—61no—
386#685—61no—
387#685—61no—
388C4⋊Dic5—31no—
389C4⋊Dic5C22×D311yescharacteristic
390C4×Dic5—61no—
391#681—62no—
392C2×#168—31no—
393C2×#168—31no—
394C2×#168—62no—
395C2×#168C22×D311yescharacteristic
396C2×#168C22×D311yescharacteristic
397C2×2−1+4—31no—
398C2×AGL(1,ℤ/8)—151no—
399C22×SD16—151no—
400#535—151no—
401#449—151no—
402#449—151no—
403#449—151no—
404#449—151no—
405#448—51no—
406#448—151no—
407#448—151no—
408#448—151no—
409#419—151no—
410#416—151no—
411#408—151no—
412C22×C3×C5—21no—
413C22×C3×C5—21no—
414C22×C3×C5—21no—
415C22×C3×C5C22×D411yescharacteristic
416C2×D15—41no—
417C2×D15—41no—
418C2×D15—41no—
419C2×C5×D3—21no—
420C2×C5×D3—21no—
421C2×C5×D3—21no—
422C2×C5×D3—22no—
423C2×C5×D3—21no—
424C2×C5×D3—21no—
425C2×C5×D3—41no—
426C2×C5×D3—41no—
427C2×C5×D3#12012yes—
428C2×C3×D5—41no—
429C2×C3×D5—41no—
430C2×C3×D5—41no—
431D3×D5—84no—
432C3×C4×C5—22no—
433C3×C4×C5—22no—
434C3×C4×C5—21no—
435C3×C4×C5C22×D411yescharacteristic
436C3×C4×C5C22×D411yescharacteristic
437Dic15—41no—
438C3×Dic5—41no—
439C5×Dic3—21no—
440C5×Dic3—22no—
441C5×Dic3#12012yes—
442C23×D3—101no—
443C2×C3×Q8—22no—
444C2×C3×Q8—22no—
445C2×C3×Q8—21no—
446C2×C3×Q8C22×D511yescharacteristic
447C2×C3×Q8C22×D511yescharacteristic
448C2×C3×D4—51no—
449C2×C3×D4—101no—
450C22×C3×C4—21no—
451C22×C3×C4C22×D511yescharacteristic
452C2×#67—21no—
453C2×#67—101no—
454C2×#67—101no—
455C2×#67—101no—
456C2×#67C22⋊D511yescharacteristic
457C2×#67C22⋊D511yescharacteristic
458#239—28no—
459#239—22no—
460#239—22no—
461#239—22no—
462#239C22⋊D514yescomplemented
463D3×Q8—28no—
464D3×Q8—22no—
465D3×Q8—22no—
466D3×Q8—22no—
467D3×Q8C22⋊D514yescomplemented
468D3×D4—102no—
469D3×D4—102no—
470#235—28no—
471#235—28no—
472#235—22no—
473#235—22no—
474#235—22no—
475#235—22no—
476C2×D12—21no—
477C2×D12—21no—
478C2×D12—51no—
479C2×D12—101no—
480C2×D12C22⋊D511yescharacteristic
481C2×D12C22×D511yescharacteristic
482C2×C4×D3—21no—
483C2×C4×D3—21no—
484C2×C4×D3—21no—
485C2×C4×D3—21no—
486C2×C4×D3—21no—
487C2×C4×D3C22×D511yescharacteristic
488C2×C4×D3C22×D511yescharacteristic
489C2×Dic6—21no—
490C2×Dic6—21no—
491C2×Dic6C22⋊D511yescharacteristic
492C2×Dic6C22×D511yescharacteristic
493C3×SD16—102no—
494C3×SD16—102no—
495C2×C3×C8—51no—
496C2×C3×C8—51no—
497C3×C4⋊C4—51no—
498C3×C22⋊C4—101no—
499#217—101no—
500#215—102no—
501#215—102no—
502#214—102no—
503#213—102no—
504(C2×D3)⋊C4—101no—
505(C2×D3)⋊C4—101no—
506(C2×D3)⋊C4—101no—
507C4⋊Dic3—51no—
508C4×Dic3—101no—
509C2×C3⋊C8—51no—
510C2×C3⋊C8—51no—
511D24—102no—
512#204—102no—
513ΓL(1,𝔽25)—102no—
514D3×C8—102no—
515C23×C5—31no—
516C23×C5—31no—
517C23×C5—61no—
518C23×C5D3×D411yescharacteristic
519C22×D5—21no—
520C22×D5—61no—
521C22×D5—122no—
522C22×D5—241no—
523C22×D5—241no—
524C5×Q8—24no—
525C5×Q8—21no—
526C5×Q8—21no—
527C5×Q8—32no—
528C5×Q8—64no—
529C5×Q8—62no—
530C5×Q8—64no—
531C5×Q8—61no—
532C5×Q8D3×D412yes—
533C5×Q8D3×D412yes—
534C5×D4—32no—
535C5×D4—62no—
536C5×D4—64no—
537C5×D4—64no—
538C5×D4—62no—
539C5×D4—62no—
540C5×D4—64no—
541C5×D4—61no—
542C2×C4×C5—24no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—31no—
548C2×C4×C5—32no—
549C2×C4×C5—32no—
550C2×C4×C5—31no—
551C2×C4×C5—64no—
552C2×C4×C5—64no—
553C2×C4×C5—64no—
554C2×C4×C5—64no—
555C2×C4×C5—64no—
556C2×C4×C5—61no—
557C2×C4×C5—61no—
558C2×C4×C5—61no—
559C2×C4×C5D3×D411yescharacteristic
560C2×C4×C5C23×D311yescharacteristic
561C22⋊D5—81no—
562C22⋊D5—241no—
563C22⋊D5—241no—
564C22⋊D5—241no—
565C2×Dic5—21no—
566C2×Dic5—61no—
567D20—21no—
568D20—21no—
569D20—61no—
570D20—61no—
571D20—122no—
572#168—21no—
573#168—21no—
574#168—61no—
575#168—61no—
5762−1+4—64no—
5772−1+4—64no—
578C2×#41—31no—
579C2×#41—31no—
580C2×#41—31no—
581C2×#41—31no—
582C2×#41—61no—
583C2×#41—61no—
584C2×#41—61no—
585C22×Q8—31no—
586C22×Q8—31no—
587C22×Q8—61no—
588C22×Q8D3×D511yescharacteristic, complemented
589C22×D4—151no—
590AGL(1,ℤ/8)—304no—
591C2×SD16—51no—
592C2×SD16—51no—
593C2×SD16—151no—
594C2×SD16—151no—
595C2×SD16—151no—
596C2×SD16—151no—
597C2×SD16—304no—
598C2×D8—151no—
599C2×D8—151no—
600C2×M16—151no—
601C22×C8—151no—
602#127—301no—
603#124—301no—
604#121—51no—
605#121—151no—
606#121—151no—
607#121—151no—
608#120—301no—
609#120—301no—
610#117—151no—
611#103—51no—
612#103—51no—
613#103—151no—
614#103—151no—
615#103—151no—
616#103—151no—
617#102—151no—
618#102—151no—
619C22⋊C8—51no—
620C22⋊C8—151no—
621C22⋊C8—151no—
622C22⋊C8—151no—
623C2×C3×C5—41no—
624C2×C3×C5C2×#12011yescharacteristic
625C2×C3×C5#57711yescharacteristic
626C2×C3×C5#57711yescharacteristic
627D15—81no—
628C3×D5—81no—
629C5×D3—22no—
630C5×D3—41no—
631C5×D3—42no—
632C23×C3—101no—
633C23×C3C2×C22⋊D511yescharacteristic
634C22×D3—21no—
635C22×D3—101no—
636C22×D3—202no—
637C22×D3—401no—
638C22×D3—401no—
639C22×D3C2×C22⋊D511yescharacteristic
640C22×D3C2×C22⋊D511yescharacteristic
641C3×Q8—24no—
642C3×Q8—21no—
643C3×Q8—21no—
644C3×Q8C2×C22⋊D512yes—
645C3×Q8C2×C22⋊D512yes—
646C3×D4—101no—
647C3×D4—101no—
648C3×D4—401no—
649C2×C3×C4—24no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—101no—
655C2×C3×C4C2×C22⋊D511yescharacteristic
656C2×C3×C4C23×D511yescharacteristic
657#67—24no—
658#67—22no—
659#67—22no—
660#67—202no—
661#67—401no—
662#67—401no—
663C2×Dic3—21no—
664C2×Dic3—101no—
665C2×Dic3C2×C22⋊D511yescharacteristic
666C2×Dic3C2×C22⋊D511yescharacteristic
667D12—24no—
668D12—24no—
669D12—22no—
670D12—21no—
671D12—101no—
672D12—101no—
673D12—401no—
674D12C2×C22⋊D512yes—
675C4×D3—24no—
676C4×D3—24no—
677C4×D3—24no—
678C4×D3—24no—
679C4×D3—21no—
680C4×D3—21no—
681C4×D3—24no—
682C4×D3C2×C22⋊D512yes—
683C4×D3C2×C22⋊D512yes—
684Dic6—24no—
685Dic6—21no—
686Dic6—24no—
687Dic6—22no—
688Dic6C2×C22⋊D512yes—
689C3×C8—101no—
690C3×C8—101no—
691C3⋊C8—101no—
692C3⋊C8—101no—
693C22×C5—21no—
694C22×C5—21no—
695C22×C5—21no—
696C22×C5—32no—
697C22×C5—61no—
698C22×C5—61no—
699C22×C5—61no—
700C22×C5—61no—
701C22×C5—62no—
702C22×C5—61no—
703C22×C5—121no—
704C22×C5—121no—
705C22×C5C2×D3×D411yescharacteristic
706C2×D5—41no—
707C2×D5—41no—
708C2×D5—41no—
709C2×D5—121no—
710C2×D5—121no—
711C2×D5—121no—
712C2×D5—244no—
713C4×C5—22no—
714C4×C5—22no—
715C4×C5—21no—
716C4×C5—32no—
717C4×C5—61no—
718C4×C5—62no—
719C4×C5C2×D3×D411yescharacteristic
720C4×C5C2×D3×D411yescharacteristic
721Dic5—41no—
722Dic5—121no—
723C24—301no—
724#41—34no—
725#41—62no—
726#41—62no—
727#41—62no—
728#41—62no—
729#41—68no—
730#41—68no—
731#41—62no—
732#41—62no—
733#41—68no—
734#41—62no—
735C2×Q8—22no—
736C2×Q8—22no—
737C2×Q8—21no—
738C2×Q8—31no—
739C2×Q8—34no—
740C2×Q8—31no—
741C2×Q8—61no—
742C2×Q8—61no—
743C2×Q8—62no—
744C2×Q8—62no—
745C2×Q8—68no—
746C2×Q8—62no—
747C2×Q8C2×D3×D511yescharacteristic
748C2×Q8C2×D3×D511yescharacteristic
749C2×D4—31no—
750C2×D4—31no—
751C2×D4—31no—
752C2×D4—31no—
753C2×D4—51no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—101no—
758C2×D4—151no—
759C2×D4—302no—
760C2×D4—302no—
761C2×D4—301no—
762C2×D4—301no—
763C2×D4—301no—
764C2×D4—301no—
765C22×C4—21no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4C2×D3×D511yescharacteristic
774SD16—102no—
775SD16—102no—
776SD16—302no—
777SD16—302no—
778SD16—302no—
779SD16—302no—
780D8—302no—
781D8—302no—
782M16—302no—
783C2×C8—51no—
784C2×C8—51no—
785C2×C8—151no—
786C2×C8—151no—
787C2×C8—302no—
788C4⋊C4—51no—
789C4⋊C4—151no—
790C22⋊C4—101no—
791C22⋊C4—301no—
792C22⋊C4—301no—
793C22⋊C4—301no—
794C22⋊C4—301no—
795C42—301no—
796C3×C5#301011yescharacteristic, complemented, Hall
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—201no—
801C22×C3—201no—
802C22×C3—201no—
803C22×C3C22×C22⋊D511yescharacteristic
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—21no—
807C2×D3—21no—
808C2×D3—21no—
809C2×D3—22no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—201no—
813C2×D3—201no—
814C2×D3—201no—
815C2×D3—404no—
816C2×D3#409912yes—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—21no—
820C3×C4—201no—
821C3×C4C22×C22⋊D511yescharacteristic
822C3×C4C22×C22⋊D511yescharacteristic
823Dic3—21no—
824Dic3—22no—
825Dic3—201no—
826Dic3#409912yes—
827C2×C5—41no—
828C2×C5—62no—
829C2×C5—121no—
830C2×C5—122no—
831C2×C5D3×#12011yescharacteristic
832C2×C5#576211yescharacteristic
833C2×C5#577811yescharacteristic
834D5—81no—
835D5—241no—
836C23—31no—
837C23—31no—
838C23—61no—
839C23—101no—
840C23—301no—
841C23—602no—
842C23—1201no—
843C23—1201no—
844C23D3×C22⋊D511yescharacteristic
845Q8—24no—
846Q8—21no—
847Q8—21no—
848Q8—32no—
849Q8—64no—
850Q8—62no—
851Q8—64no—
852Q8—61no—
853Q8D3×C22⋊D512yes—
854Q8D3×C22⋊D512yes—
855D4—32no—
856D4—62no—
857D4—64no—
858D4—64no—
859D4—62no—
860D4—62no—
861D4—64no—
862D4—61no—
863D4—101no—
864D4—101no—
865D4—301no—
866D4—301no—
867D4—401no—
868D4—602no—
869D4—1201no—
870D4—1201no—
871D4—1201no—
872C2×C4—24no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—31no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—31no—
881C2×C4—64no—
882C2×C4—64no—
883C2×C4—64no—
884C2×C4—64no—
885C2×C4—64no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—101no—
890C2×C4—301no—
891C2×C4D3×C22⋊D511yescharacteristic
892C2×C4C22×D3×D511yescharacteristic
893C8—101no—
894C8—101no—
895C8—301no—
896C8—301no—
897C2×C3—41no—
898C2×C3—401no—
899C2×C3#6617111yescharacteristic
900C2×C3#6617111yescharacteristic
901C2×C3C2×#409911yescharacteristic
902D3—22no—
903D3—41no—
904D3—42no—
905D3—401no—
906C5#8004111yescharacteristic, complemented, Sylow
907C22—21no—
908C22—21no—
909C22—21no—
910C22—32no—
911C22—61no—
912C22—61no—
913C22—61no—
914C22—61no—
915C22—62no—
916C22—61no—
917C22—121no—
918C22—121no—
919C22—201no—
920C22—201no—
921C22—201no—
922C22—601no—
923C22—601no—
924C22—601no—
925C22—1204no—
926C22C2×D3×C22⋊D511yescharacteristic
927C4—22no—
928C4—22no—
929C4—21no—
930C4—32no—
931C4—61no—
932C4—62no—
933C4—201no—
934C4—601no—
935C4C2×D3×C22⋊D511yescharacteristic
936C4C2×D3×C22⋊D511yescharacteristic
937C3#1061584411yescharacteristic, complemented, Sylow
938C2—41no—
939C2—62no—
940C2—121no—
941C2—122no—
942C2—401no—
943C2—1201no—
944C2#1175509111yescharacteristic
945C2#1175509211yescharacteristic
946C2D3×#409911yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1007C2semidirect
2. C2×#91504C2semidirect
3. C2×D3×#688C2semidirect
4. #11754655C2semidirect
5. #11751328C2semidirect
6. C3×#65516C2semidirect
7. #11749282C2semidirect
8. #11749281C2semidirect
9. #11749279C2semidirect
10. #11749278C2semidirect
11. #11749213C2semidirect
12. #11749211C2semidirect
13. #11748521C2semidirect
14. #11748517C2semidirect
15. #11748490C2semidirect
17. C22×C3×C5×Q8C22semidirect
22. C2×C5×#239C22semidirect
25. C2×C5×D3×Q8C22semidirect
29. C2×C5×#235C22semidirect
52. #91119C22semidirect
53. #91119C22semidirect
54. #91114C22semidirect
55. C3×#3967C22semidirect
56. C3×#3967C22semidirect
57. C3×C22⋊#168C22semidirect
58. #90973C22semidirect
59. #90972C22semidirect
60. #90967C22semidirect
61. #90966C22semidirect
62. (C2×D3)⋊#168C22semidirect
63. (C2×D3)⋊#168C22semidirect
78. #65516D3semidirect
97. C5×#239D4semidirect
102. C5×D3×Q8D4semidirect
153. C2×#1007D5semidirect
180. C22×C5×Q8C2×D3semidirect
207. #3967C2×D3semidirect
208. #3967C2×D3semidirect
214. C22⋊#168C2×D3semidirect
277. C22×C3×Q8C2×D5semidirect
282. C2×#239C2×D5semidirect
285. C2×D3×Q8C2×D5semidirect
290. C2×#235C2×D5semidirect
462. #239C22⋊D5semidirect
467. D3×Q8C22⋊D5semidirect
588. C22×Q8D3×D5semidirect
796. C3×C5#3010semidirect
906. C5#80041semidirect
937. C3#10615844semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10072
C2×#915042
C2×D3×#6882
#117546552
#117513282
C3×#655162
#117492822
#117492812
#117492792
#117492782
#117492132
#117492112
#117485212
#117485172
#117484902
#106158443
#800415