Finite Group Databasebeta

← #14424359

Subgroups — #14424359

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1009C211yesmaximal, characteristic
2C2×#91510C211yesmaximal, characteristic, complemented
3C2×D3×#687C211yesmaximal, characteristic, complemented
4#11754348C211yesmaximal, characteristic, complemented
5#11751340C211yesmaximal, characteristic, complemented
6C3×#65528C211yesmaximal, characteristic, complemented
7#11749305C211yesmaximal, characteristic, complemented
8#11749300C211yesmaximal, characteristic, complemented
9#11749211C211yesmaximal, characteristic, complemented
10#11749058C211yesmaximal, characteristic, complemented
11#11749056C211yesmaximal, characteristic, complemented
12#11748967C211yesmaximal, characteristic, complemented
13#11748543C211yesmaximal, characteristic, complemented
14#11748537C211yesmaximal, characteristic, complemented
15#11748490C211yesmaximal, characteristic, complemented
16#10615836—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C5×#1009—24no—
19C5×#1009—24no—
20C2×C5×#239C2211yescharacteristic
21C2×C5×#239C2211yescharacteristic
22C2×C5×D3×D4—21no—
23C2×C5×D3×D4—21no—
24C2×C5×D3×D4C2211yescharacteristic
25C2×C5×D3×D4C2211yescharacteristic
26C2×C5×#235—21no—
27C2×C5×#235C2211yescharacteristic
28C22×C5×D12—21no—
29C22×C5×D12C2211yescharacteristic
30C2×D3×Dic10C2211yescharacteristic, complemented
31C2×#6718C2211yescharacteristic, complemented
32C2×#6716C2211yescharacteristic, complemented
33#91813C2211yescharacteristic, complemented
34C2×C3×#689C2211yescharacteristic, complemented
35C2×C3×#687C2211yescharacteristic, complemented
36C3×#4070C2211yescharacteristic, complemented
37#91555—21no—
38#91525—21no—
39#91510—24no—
40D3×#687—24no—
41#91423—21no—
42#91369C2211yescharacteristic, complemented
43#91365C2211yescharacteristic, complemented
44#91338C2211yescharacteristic, complemented
45#91329—21no—
46C2×#6659C2211yescharacteristic, complemented
47C2×#6659C2211yescharacteristic, complemented
48C2×#6656C2211yescharacteristic, complemented
49C2×#6656C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51C2×D3×#168C2211yescharacteristic, complemented
52#91119C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55C3×#3967C2211yescharacteristic, complemented
56C3×#3964C2211yescharacteristic, complemented
57C3×C22⋊#168C2211yescharacteristic, complemented
58#90967C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60#90966C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62(C2×D3)⋊#168C2211yescharacteristic, complemented
63(C2×D3)⋊#168C2211yescharacteristic, complemented
64#80229—51nomaximal, Hall
65C2×C5×H(5,𝔽2)—31no—
66#66159—31no—
67C2×#4097—31no—
68C22×#687—31no—
69#65528—31no—
70#65528—31no—
71#65528—31no—
72#65528D311yescharacteristic, complemented
73#65523—31no—
74#65522—31no—
75#65507—31no—
76#65507—31no—
77#65507—31no—
78#65507—31no—
79#65504—31no—
80C23×C5×D3—21no—
81C23×C5×D3—21no—
82C23×C5×D3—21no—
83C3×C5×#41—22no—
84C3×C5×#41—22no—
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4C2311yescharacteristic
88C22×C3×C4×C5—21no—
89C22×C3×C4×C5C2311yescharacteristic
90C2×Dic30C2311yescharacteristic
91C2×C5×#67—21no—
92C2×C5×#67—21no—
93C2×C5×#67D411yescharacteristic
94C2×C5×#67D411yescharacteristic
95C5×#239—22no—
96C5×#239—22no—
97C5×#239—22no—
98C5×#239D414yes—
99C5×D3×D4—28no—
100C5×D3×D4—28no—
101C5×D3×D4—22no—
102C5×D3×D4—22no—
103C5×D3×D4—22no—
104C5×D3×D4D414yes—
105C5×#235—28no—
106C5×#235—22no—
107C5×#235—22no—
108C2×C5×D12—28no—
109C2×C5×D12—21no—
110C2×C5×D12—21no—
111C2×C5×D12—21no—
112C2×C5×D12—22no—
113C2×C5×D12—22no—
114C2×C5×D12D411yescharacteristic
115C2×C5×D12C2311yescharacteristic
116C2×C5×D12C2311yescharacteristic
117C2×C4×C5×D3—21no—
118C2×C4×C5×D3—21no—
119C2×C4×C5×D3C2311yescharacteristic
120C2×C4×C5×D3C2311yescharacteristic
121C2×C5×Dic6D411yescharacteristic
122C2×C3×Dic10C2311yescharacteristic
123C2×#1204—21no—
124C2×D3×Dic5—21no—
125D3×Dic10—22no—
126D3×Dic10—22no—
127#6719—21no—
128#6718—22no—
129#6716—22no—
130C4⋊Dic15C2311yescharacteristic
131#6712—21no—
132C2×C3⋊#168C2311yescharacteristic
133C2×C3⋊#168C2311yescharacteristic
134C3×C22⋊Dic5—21no—
135C3×#689—22no—
136C3×#687—22no—
137C3×C4⋊Dic5C2311yescharacteristic
138C3×#683—21no—
139C2×C3×#168C2311yescharacteristic
140C2×C3×#168C2311yescharacteristic
141#6669—21no—
142#6668—21no—
143(C2×D3)⋊Dic5—21no—
144(C2×D3)⋊Dic5—21no—
145(C2×D3)⋊Dic5—21no—
146Dic3×Dic5—21no—
147#6659—22no—
148#6659—22no—
149#6656—22no—
150#6656—22no—
151#6650—22no—
152D3×#168—22no—
153C2×#1009D511yescharacteristic
154C2×#918—51no—
155C2×D3×SD16—51no—
156#5628—51no—
157C3×#452—51no—
158#5239—51no—
159#5187—51no—
160#5169—51no—
161#5046—51no—
162#4808—51no—
163#4804—51no—
164#4776—51no—
165#4770—51no—
166#4731—51no—
167#4727—51no—
168C5×H(5,𝔽2)—64no—
169C5×H(5,𝔽2)—64no—
170C2×C5×#41—31no—
171C2×C5×#41—31no—
172C2×C5×#41—31no—
173C2×C5×#41—61no—
174C2×C5×#41C2×D311yescharacteristic
175C22×C5×D4—31no—
176C22×C5×D4—31no—
177C22×C5×D4—31no—
178C22×C5×D4—61no—
179C22×C5×D4—61no—
180C22×C5×D4—61no—
181C22×Dic10—31no—
182#4097—64no—
183#4090—61no—
184C2×#689—31no—
185C2×#689C2×D311yescharacteristic, complemented
186#4082—61no—
187#4081—61no—
188#4081—61no—
189C2×#687—31no—
190C2×#687—31no—
191C2×#687—31no—
192C2×#687—31no—
193C2×#687—31no—
194C2×#687—64no—
195C2×#687C2×D311yescharacteristic, complemented
196#4072—31no—
197#4070—31no—
198#4070—31no—
199#4070—31no—
200#4070C2×D311yescharacteristic, complemented
201C2×#681—31no—
202C22×#168—31no—
203#3967—31no—
204#3967C2×D311yescharacteristic, complemented
205#3964—31no—
206#3964—31no—
207#3964—31no—
208#3964—31no—
209#3964—31no—
210#3964C2×D311yescharacteristic, complemented
211C22⋊#168—31no—
212C22⋊#168—31no—
213C22⋊#168—31no—
214C22⋊#168C2×D311yescharacteristic, complemented
215#3009—151noSylow
216C23×C3×C5—21no—
217C23×C3×C5C2×D411yescharacteristic
218C22×C5×D3—21no—
219C22×C5×D3—21no—
220C22×C5×D3—24no—
221C22×C5×D3—24no—
222C22×C5×D3—24no—
223C22×C5×D3—81no—
224C22×C5×D3—81no—
225C22×C5×D3—81no—
226C22×C5×D3—81no—
227C22×C5×D3—81no—
228C22×C5×D3—81no—
229C22×C5×D3C2×D411yescharacteristic
230C22×C5×D3C2×D411yescharacteristic
231C3×C5×Q8—21no—
232C3×C5×Q8C2×D412yes—
233C3×C5×D4—24no—
234C3×C5×D4—21no—
235C3×C5×D4C2×D412yes—
236C2×C3×C4×C5—24no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5—21no—
239C2×C3×C4×C5—21no—
240C2×C3×C4×C5C2×D411yescharacteristic
241C2×C3×C4×C5C2411yescharacteristic
242C2×Dic15—21no—
243C2×Dic15—21no—
244Dic30—21no—
245Dic30—21no—
246C5×#67—24no—
247C5×#67—22no—
248C5×#67—22no—
249C5×#67—24no—
250C2×C5×Dic3C2×D411yescharacteristic
251C2×C5×Dic3C2×D411yescharacteristic
252C5×D12—24no—
253C5×D12—24no—
254C5×D12—22no—
255C5×D12—24no—
256C5×D12—21no—
257C5×D12—21no—
258C5×D12C2×D412yes—
259C5×D12C2×D412yes—
260C4×C5×D3—24no—
261C4×C5×D3—21no—
262C4×C5×D3—21no—
263C4×C5×D3—24no—
264C4×C5×D3C2×D412yes—
265C4×C5×D3C2×D412yes—
266C5×Dic6—22no—
267C2×C3×Dic5—21no—
268C2×C3×Dic5—21no—
269C3×Dic10—21no—
270C3×Dic10—21no—
271#1204—42no—
272D3×Dic5—42no—
273C3⋊#168—21no—
274C3⋊#168—21no—
275C3×#168—21no—
276C3×#168—21no—
277C2×C3×#41C2×D511yescharacteristic
278#1009—24no—
279#1009—24no—
280C2×#239C2×D511yescharacteristic
281C2×#239C2×D511yescharacteristic
282C2×D3×Q8—51no—
283C2×D3×D4—21no—
284C2×D3×D4—21no—
285C2×D3×D4C2×D511yescharacteristic
286C2×D3×D4C2×D511yescharacteristic
287C2×#235—21no—
288C2×#235C2×D511yescharacteristic
289C22×D12—21no—
290C22×D12C2×D511yescharacteristic
291C2×C3×Q16—51no—
292C2×C3×SD16—51no—
293C3×C22⋊Q8—51no—
294#946—51no—
295C2×#216—51no—
296C2×#215—51no—
297C2×#215—51no—
298C2×#214—51no—
299#924—51no—
300#918—104no—
301D3×SD16—104no—
302C2×#204—51no—
303C2×#204—51no—
304C2×ΓL(1,𝔽25)—51no—
305C2×D3×C8—51no—
306#897—51no—
307#894—101no—
308#892—51no—
309#888—101no—
310#885—101no—
311#883—101no—
312C3×#103—51no—
313C3×#102—51no—
314C3×C22⋊C8—51no—
315#835—51no—
316#832—51no—
317#830—51no—
318#821—51no—
319#821—51no—
320(C2×D3)⋊C8—51no—
321(C2×D3)⋊C8—51no—
322#809—51no—
323#809—51no—
324C24×C5—61no—
325C24×C5—61no—
326C24×C5—61no—
327C5×#41—22no—
328C5×#41—22no—
329C5×#41—34no—
330C5×#41—62no—
331C5×#41—62no—
332C5×#41—68no—
333C5×#41—62no—
334C5×#41—62no—
335C5×#41—62no—
336C2×C5×Q8—31no—
337C2×C5×Q8C22×D311yescharacteristic
338C2×C5×D4—21no—
339C2×C5×D4—34no—
340C2×C5×D4—31no—
341C2×C5×D4—31no—
342C2×C5×D4—31no—
343C2×C5×D4—31no—
344C2×C5×D4—31no—
345C2×C5×D4—62no—
346C2×C5×D4—62no—
347C2×C5×D4—61no—
348C2×C5×D4—61no—
349C2×C5×D4—68no—
350C2×C5×D4—62no—
351C2×C5×D4—61no—
352C2×C5×D4—61no—
353C2×C5×D4—62no—
354C2×C5×D4—68no—
355C2×C5×D4—68no—
356C2×C5×D4—62no—
357C2×C5×D4—61no—
358C2×C5×D4C22×D311yescharacteristic
359C22×C4×C5—21no—
360C22×C4×C5—31no—
361C22×C4×C5—31no—
362C22×C4×C5—61no—
363C22×C4×C5—61no—
364C22×C4×C5C22×D311yescharacteristic
365C22×Dic5—61no—
366C2×Dic10—31no—
367C2×Dic10—62no—
368C2×Dic10—62no—
369C2×Dic10—61no—
370C2×Dic10C22×D311yescharacteristic
371C22⋊Dic5—21no—
372C22⋊Dic5—61no—
373C22⋊Dic5—61no—
374C22⋊Dic5—61no—
375C22⋊Dic5—61no—
376#689—22no—
377#689—62no—
378#687—22no—
379#687—62no—
380#687—62no—
381#687—62no—
382#687—62no—
383#687—62no—
384C4⋊Dic5—31no—
385C4⋊Dic5C22×D311yescharacteristic
386#683—21no—
387#683—61no—
388#683—61no—
389#683—61no—
390C4×Dic5—61no—
391#681—62no—
392C2×#168—31no—
393C2×#168—31no—
394C2×#168—62no—
395C2×#168C22×D311yescharacteristic
396C2×#168C22×D311yescharacteristic
397C2×H(5,𝔽2)—31no—
398C2×#137—151no—
399C22×SD16—151no—
400#536—151no—
401#452—51no—
402#452—151no—
403#452—151no—
404#452—151no—
405#450—151no—
406#450—151no—
407#450—151no—
408#450—151no—
409#418—151no—
410#416—151no—
411#408—151no—
412C22×C3×C5—21no—
413C22×C3×C5—22no—
414C22×C3×C5—21no—
415C22×C3×C5—21no—
416C22×C3×C5—41no—
417C22×C3×C5—41no—
418C22×C3×C5C22×D411yescharacteristic
419C2×C5×D3—21no—
420C2×C5×D3—21no—
421C2×C5×D3—21no—
422C2×C5×D3—22no—
423C2×C5×D3—22no—
424C2×C5×D3—21no—
425C2×C5×D3—21no—
426C2×C5×D3—41no—
427C2×C5×D3—41no—
428C2×C5×D3—41no—
429C2×C5×D3—41no—
430C2×C5×D3—84no—
431C2×C5×D3—84no—
432C2×C5×D3—84no—
433C2×C5×D3#12012yes—
434C3×C4×C5—21no—
435C3×C4×C5—22no—
436C3×C4×C5C22×D411yescharacteristic
437C3×C4×C5C22×D411yescharacteristic
438Dic15—41no—
439Dic15—41no—
440C3×Dic5—41no—
441C3×Dic5—41no—
442C5×Dic3—21no—
443C5×Dic3#12012yes—
444C23×D3—21no—
445C23×D3—21no—
446C23×D3—21no—
447C3×#41—22no—
448C3×#41—22no—
449C2×C3×Q8—51no—
450C2×C3×Q8C22×D511yescharacteristic
451C2×C3×D4—21no—
452C2×C3×D4C22×D511yescharacteristic
453C22×C3×C4—21no—
454C22×C3×C4C22×D511yescharacteristic
455C2×#67—21no—
456C2×#67—21no—
457C2×#67C22⋊D511yescharacteristic
458C2×#67C22⋊D511yescharacteristic
459#239—22no—
460#239—22no—
461#239—22no—
462#239C22⋊D514yes—
463D3×Q8—102no—
464D3×Q8—102no—
465D3×D4—28no—
466D3×D4—28no—
467D3×D4—22no—
468D3×D4—22no—
469D3×D4—22no—
470D3×D4C22⋊D514yes—
471#235—28no—
472#235—22no—
473#235—22no—
474C2×D12—28no—
475C2×D12—21no—
476C2×D12—21no—
477C2×D12—21no—
478C2×D12—22no—
479C2×D12—22no—
480C2×D12C22⋊D511yescharacteristic
481C2×D12C22×D511yescharacteristic
482C2×D12C22×D511yescharacteristic
483C2×C4×D3—21no—
484C2×C4×D3—21no—
485C2×C4×D3—101no—
486C2×C4×D3C22×D511yescharacteristic
487C2×C4×D3C22×D511yescharacteristic
488C2×Dic6—51no—
489C2×Dic6—101no—
490C2×Dic6C22⋊D511yescharacteristic
491C3×Q16—102no—
492C3×SD16—102no—
493C2×C3×C8—51no—
494C2×C3×C8—51no—
495C3×C4⋊C4—51no—
496C3×C4⋊C4—101no—
497C3×C22⋊C4—101no—
498#217—101no—
499#216—102no—
500#215—102no—
501#215—102no—
502#214—102no—
503(C2×D3)⋊C4—101no—
504(C2×D3)⋊C4—101no—
505(C2×D3)⋊C4—101no—
506C4⋊Dic3—51no—
507C4⋊Dic3—101no—
508Dic3⋊C4—101no—
509Dic3⋊C4—101no—
510C4×Dic3—101no—
511C2×C3⋊C8—51no—
512C2×C3⋊C8—51no—
513#204—102no—
514#204—102no—
515ΓL(1,𝔽25)—102no—
516D3×C8—102no—
517C23×C5—21no—
518C23×C5—31no—
519C23×C5—31no—
520C23×C5—64no—
521C23×C5—64no—
522C23×C5—64no—
523C23×C5—61no—
524C23×C5—61no—
525C23×C5—241no—
526C23×C5—241no—
527C23×C5—241no—
528C23×C5—241no—
529C23×C5—241no—
530C23×C5—241no—
531C23×C5D3×D411yescharacteristic
532C5×Q8—21no—
533C5×Q8—62no—
534C5×Q8D3×D412yes—
535C5×D4—24no—
536C5×D4—21no—
537C5×D4—32no—
538C5×D4—32no—
539C5×D4—62no—
540C5×D4—64no—
541C5×D4—64no—
542C5×D4—64no—
543C5×D4—62no—
544C5×D4—64no—
545C5×D4—62no—
546C5×D4—64no—
547C5×D4—61no—
548C5×D4—61no—
549C5×D4D3×D412yes—
550C2×C4×C5—24no—
551C2×C4×C5—21no—
552C2×C4×C5—21no—
553C2×C4×C5—21no—
554C2×C4×C5—31no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—31no—
558C2×C4×C5—64no—
559C2×C4×C5—64no—
560C2×C4×C5—61no—
561C2×C4×C5—61no—
562C2×C4×C5D3×D411yescharacteristic
563C2×C4×C5C23×D311yescharacteristic
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5—122no—
569Dic10—21no—
570Dic10—21no—
571Dic10—61no—
572Dic10—61no—
573Dic10—122no—
574#168—21no—
575#168—21no—
576#168—61no—
577#168—61no—
578H(5,𝔽2)—64no—
579H(5,𝔽2)—64no—
580C2×#41—31no—
581C2×#41—31no—
582C2×#41—31no—
583C2×#41—61no—
584C2×#41D3×D511yescharacteristic
585C22×Q8—151no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—31no—
589C22×D4—61no—
590C22×D4—61no—
591C22×D4—61no—
592#137—304no—
593C2×Q16—51no—
594C2×Q16—151no—
595C2×SD16—51no—
596C2×SD16—151no—
597C2×SD16—151no—
598C2×SD16—151no—
599C2×SD16—151no—
600C2×SD16—151no—
601C2×SD16—304no—
602C2×M16—151no—
603C22×C8—151no—
604C4⋊Q8—301no—
605#124—301no—
606#123—301no—
607#123—301no—
608C22⋊Q8—51no—
609C22⋊Q8—151no—
610C22⋊Q8—151no—
611C22⋊Q8—151no—
612#117—151no—
613#103—51no—
614#103—151no—
615#102—51no—
616#102—151no—
617#102—151no—
618#102—151no—
619#102—151no—
620#102—151no—
621C22⋊C8—51no—
622C22⋊C8—151no—
623C22⋊C8—151no—
624C22⋊C8—151no—
625C2×C3×C5—41no—
626C2×C3×C5—42no—
627C2×C3×C5C2×#12011yescharacteristic
628C2×C3×C5#57711yescharacteristic
629C2×C3×C5#57711yescharacteristic
630C5×D3—22no—
631C5×D3—41no—
632C5×D3—42no—
633C5×D3—42no—
634C23×C3—21no—
635C23×C3C2×C22⋊D511yescharacteristic
636C22×D3—21no—
637C22×D3—21no—
638C22×D3—24no—
639C22×D3—24no—
640C22×D3—24no—
641C22×D3—81no—
642C22×D3—81no—
643C22×D3—81no—
644C22×D3—81no—
645C22×D3—81no—
646C22×D3—81no—
647C22×D3C2×C22⋊D511yescharacteristic
648C22×D3C2×C22⋊D511yescharacteristic
649C3×Q8—21no—
650C3×Q8—101no—
651C3×Q8—101no—
652C3×Q8C2×C22⋊D512yes—
653C3×D4—24no—
654C3×D4—21no—
655C3×D4C2×C22⋊D512yes—
656C2×C3×C4—24no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—101no—
661C2×C3×C4—101no—
662C2×C3×C4C2×C22⋊D511yescharacteristic
663C2×C3×C4C23×D511yescharacteristic
664#67—24no—
665#67—22no—
666#67—22no—
667#67—24no—
668C2×Dic3—101no—
669C2×Dic3—101no—
670C2×Dic3C2×C22⋊D511yescharacteristic
671C2×Dic3C2×C22⋊D511yescharacteristic
672D12—24no—
673D12—24no—
674D12—22no—
675D12—24no—
676D12—21no—
677D12—21no—
678D12C2×C22⋊D512yes—
679D12C2×C22⋊D512yes—
680C4×D3—24no—
681C4×D3—21no—
682C4×D3—21no—
683C4×D3—24no—
684C4×D3—202no—
685C4×D3C2×C22⋊D512yes—
686C4×D3C2×C22⋊D512yes—
687Dic6—22no—
688Dic6—101no—
689Dic6—101no—
690Dic6—202no—
691C3×C8—101no—
692C3×C8—101no—
693C3⋊C8—101no—
694C3⋊C8—101no—
695C22×C5—21no—
696C22×C5—21no—
697C22×C5—21no—
698C22×C5—22no—
699C22×C5—32no—
700C22×C5—41no—
701C22×C5—41no—
702C22×C5—61no—
703C22×C5—61no—
704C22×C5—61no—
705C22×C5—61no—
706C22×C5—62no—
707C22×C5—62no—
708C22×C5—61no—
709C22×C5—121no—
710C22×C5—121no—
711C22×C5—121no—
712C22×C5—121no—
713C22×C5—244no—
714C22×C5—244no—
715C22×C5—244no—
716C22×C5C2×D3×D411yescharacteristic
717C4×C5—21no—
718C4×C5—22no—
719C4×C5—32no—
720C4×C5—61no—
721C4×C5C2×D3×D411yescharacteristic
722C4×C5C2×D3×D411yescharacteristic
723Dic5—41no—
724Dic5—41no—
725Dic5—121no—
726Dic5—121no—
727C24—61no—
728C24—61no—
729C24—61no—
730#41—22no—
731#41—22no—
732#41—34no—
733#41—62no—
734#41—62no—
735#41—68no—
736#41—62no—
737#41—62no—
738#41—62no—
739C2×Q8—31no—
740C2×Q8—51no—
741C2×Q8—151no—
742C2×Q8—301no—
743C2×Q8—302no—
744C2×Q8—302no—
745C2×Q8C2×D3×D511yescharacteristic
746C2×D4—21no—
747C2×D4—34no—
748C2×D4—31no—
749C2×D4—31no—
750C2×D4—31no—
751C2×D4—31no—
752C2×D4—31no—
753C2×D4—62no—
754C2×D4—62no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—68no—
758C2×D4—62no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4—62no—
762C2×D4—68no—
763C2×D4—68no—
764C2×D4—62no—
765C2×D4—61no—
766C2×D4C2×D3×D511yescharacteristic
767C22×C4—21no—
768C22×C4—31no—
769C22×C4—31no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—301no—
773C22×C4C2×D3×D511yescharacteristic
774Q16—102no—
775Q16—302no—
776SD16—102no—
777SD16—302no—
778SD16—302no—
779SD16—302no—
780SD16—302no—
781SD16—302no—
782M16—302no—
783C2×C8—51no—
784C2×C8—51no—
785C2×C8—151no—
786C2×C8—151no—
787C2×C8—302no—
788C4⋊C4—51no—
789C4⋊C4—101no—
790C4⋊C4—151no—
791C4⋊C4—301no—
792C4⋊C4—301no—
793C4⋊C4—301no—
794C22⋊C4—101no—
795C22⋊C4—301no—
796C22⋊C4—301no—
797C22⋊C4—301no—
798C22⋊C4—301no—
799C42—301no—
800C3×C5#300911yescharacteristic, complemented, Hall
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—22no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3C22×C22⋊D511yescharacteristic
808C2×D3—21no—
809C2×D3—21no—
810C2×D3—21no—
811C2×D3—21no—
812C2×D3—21no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—84no—
820C2×D3—84no—
821C2×D3—84no—
822C2×D3#409912yes—
823C3×C4—21no—
824C3×C4—22no—
825C3×C4—201no—
826C3×C4—201no—
827C3×C4C22×C22⋊D511yescharacteristic
828C3×C4C22×C22⋊D511yescharacteristic
829Dic3—21no—
830Dic3—201no—
831Dic3—201no—
832Dic3#409912yes—
833C2×C5—41no—
834C2×C5—42no—
835C2×C5—62no—
836C2×C5—121no—
837C2×C5—122no—
838C2×C5—122no—
839C2×C5D3×#12011yescharacteristic
840C2×C5#577011yescharacteristic
841C2×C5#577811yescharacteristic
842C23—21no—
843C23—31no—
844C23—31no—
845C23—64no—
846C23—64no—
847C23—64no—
848C23—61no—
849C23—61no—
850C23—241no—
851C23—241no—
852C23—241no—
853C23—241no—
854C23—241no—
855C23—241no—
856C23D3×C22⋊D511yescharacteristic
857Q8—21no—
858Q8—62no—
859Q8—101no—
860Q8—101no—
861Q8—301no—
862Q8—301no—
863Q8—602no—
864Q8D3×C22⋊D512yes—
865D4—24no—
866D4—21no—
867D4—32no—
868D4—32no—
869D4—62no—
870D4—64no—
871D4—64no—
872D4—64no—
873D4—62no—
874D4—64no—
875D4—62no—
876D4—64no—
877D4—61no—
878D4—61no—
879D4D3×C22⋊D512yes—
880C2×C4—24no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—31no—
885C2×C4—32no—
886C2×C4—32no—
887C2×C4—31no—
888C2×C4—64no—
889C2×C4—64no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—101no—
893C2×C4—101no—
894C2×C4—301no—
895C2×C4—301no—
896C2×C4—602no—
897C2×C4D3×C22⋊D511yescharacteristic
898C2×C4C22×D3×D511yescharacteristic
899C8—101no—
900C8—101no—
901C8—301no—
902C8—301no—
903C2×C3—41no—
904C2×C3—42no—
905C2×C3#6617011yescharacteristic
906C2×C3#6617011yescharacteristic
907C2×C3C2×#409911yescharacteristic
908D3—22no—
909D3—41no—
910D3—42no—
911D3—42no—
912C5#8022911yescharacteristic, complemented, Sylow
913C22—21no—
914C22—21no—
915C22—21no—
916C22—22no—
917C22—32no—
918C22—41no—
919C22—41no—
920C22—61no—
921C22—61no—
922C22—61no—
923C22—61no—
924C22—62no—
925C22—62no—
926C22—61no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—244no—
932C22—244no—
933C22—244no—
934C22C2×D3×C22⋊D511yescharacteristic
935C4—21no—
936C4—22no—
937C4—32no—
938C4—61no—
939C4—201no—
940C4—201no—
941C4—601no—
942C4—601no—
943C4C2×D3×C22⋊D511yescharacteristic
944C4C2×D3×C22⋊D511yescharacteristic
945C3#1061583611yescharacteristic, complemented, Sylow
946C2—41no—
947C2—42no—
948C2—62no—
949C2—121no—
950C2—122no—
951C2—122no—
952C2#1175534011yescharacteristic
953C2#1175534711yescharacteristic
954C2D3×#409911yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#1009C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3009
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91510C2semidirect
3. C2×D3×#687C2semidirect
4. #11754348C2semidirect
5. #11751340C2semidirect
6. C3×#65528C2semidirect
7. #11749305C2semidirect
8. #11749300C2semidirect
9. #11749211C2semidirect
10. #11749058C2semidirect
11. #11749056C2semidirect
12. #11748967C2semidirect
13. #11748543C2semidirect
14. #11748537C2semidirect
15. #11748490C2semidirect
30. C2×D3×Dic10C22semidirect
31. C2×#6718C22semidirect
32. C2×#6716C22semidirect
33. #91813C22semidirect
34. C2×C3×#689C22semidirect
35. C2×C3×#687C22semidirect
36. C3×#4070C22semidirect
42. #91369C22semidirect
43. #91365C22semidirect
44. #91338C22semidirect
46. C2×#6659C22semidirect
47. C2×#6659C22semidirect
48. C2×#6656C22semidirect
49. C2×#6656C22semidirect
50. C2×#6650C22semidirect
51. C2×D3×#168C22semidirect
52. #91119C22semidirect
53. #91116C22semidirect
54. #91114C22semidirect
55. C3×#3967C22semidirect
56. C3×#3964C22semidirect
57. C3×C22⋊#168C22semidirect
58. #90967C22semidirect
59. #90967C22semidirect
60. #90966C22semidirect
61. #90966C22semidirect
62. (C2×D3)⋊#168C22semidirect
63. (C2×D3)⋊#168C22semidirect
72. #65528D3semidirect
185. C2×#689C2×D3semidirect
195. C2×#687C2×D3semidirect
200. #4070C2×D3semidirect
204. #3967C2×D3semidirect
210. #3964C2×D3semidirect
214. C22⋊#168C2×D3semidirect
800. C3×C5#3009semidirect
912. C5#80229semidirect
945. C3#10615836semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10092
C2×#915102
C2×D3×#6872
#117543482
#117513402
C3×#655282
#117493052
#117493002
#117492112
#117490582
#117490562
#117489672
#117485432
#117485372
#117484902
#106158363
#802295