Finite Group Databasebeta

← D3×#65442 #14425949

Subgroups — D3×#65442 #14425949

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×D8C211yesmaximal, characteristic
2D3×#4082C211yesmaximal, characteristic, complemented
3D3×D4×Dic5C211yesmaximal, characteristic, complemented
4C2×D3×#687C211yesmaximal, characteristic, complemented
5#11751254C211yesmaximal, characteristic, complemented
6C3×#65442C211yesmaximal, characteristic, complemented
7#11749082C211yesmaximal, characteristic, complemented
8#11749065C211yesmaximal, characteristic, complemented
9#11748992C211yesmaximal, characteristic, complemented
10#11748978C211yesmaximal, characteristic, complemented
11D3×#3964C211yesmaximal, characteristic, complemented
12#11747787C211yesmaximal, characteristic, complemented
13#11747777C211yesmaximal, characteristic, complemented
14D3×#3948C211yesmaximal, characteristic, complemented
15D3×#3946C211yesmaximal, characteristic, complemented
16C2×#65442—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic
19C22×D3×Dic5—21no—
20C2×D3×Dic10C2211yescharacteristic
21C2×C3×C5×D8C2211yescharacteristic
22#91825C2211yescharacteristic, complemented
23D4×Dic15C2211yescharacteristic, complemented
24C2×#6716C2211yescharacteristic, complemented
25C2×C5×#213C2211yescharacteristic
26C2×C5×#213C2211yescharacteristic
27C5×D3×D8—24no—
28C2×C5×D24C2211yescharacteristic
29C2×C5×D3×C8C2211yescharacteristic
30C3×#4082C2211yescharacteristic, complemented
31C3×D4×Dic5C2211yescharacteristic, complemented
32C2×C3×#687C2211yescharacteristic, complemented
33#67⋊Dic5—21no—
34D3×C22⋊Dic5—21no—
35D3×C22⋊Dic5—21no—
36D3×C22⋊Dic5—21no—
37Dic5×#67—21no—
38#91525—21no—
39#91525—21no—
40D3×#687—24no—
41#91435C2211yescharacteristic, complemented
42D3×C4⋊Dic5C2211yescharacteristic
43Dic5×D12C2211yescharacteristic, complemented
44C4×D3×Dic5C2211yescharacteristic
45#91373C2211yescharacteristic, complemented
46#91370C2211yescharacteristic, complemented
47C2×#6659C2211yescharacteristic, complemented
48C2×#6656C2211yescharacteristic, complemented
49C2×D3×#168C2211yescharacteristic
50#91116C2211yescharacteristic, complemented
51#91100C2211yescharacteristic, complemented
52#91098C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×#3948C2211yescharacteristic, complemented
55C3×#3946C2211yescharacteristic, complemented
56#90983C2211yescharacteristic, complemented
57#90982C2211yescharacteristic, complemented
58#90974C2211yescharacteristic, complemented
59#90971C2211yescharacteristic, complemented
60#90967C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62D3×#463—51nomaximal, Hall
63C22×C5×D8—31no—
64C2×#4082—31no—
65C2×D4×Dic5—31no—
66C22×#687—31no—
67C2×#3964—31no—
68#65442—31no—
69#65442—31no—
70#65442—31no—
71#65442—31no—
72#65442—31no—
73#65442—31no—
74#65442—31no—
75#65442D311yescharacteristic, direct product factor
76C2×#3948—31no—
77C2×#3946—31no—
78C23×C5×D3—21no—
79C23×C5×D3—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C22×Dic15—21no—
83C2×Dic30C2311yescharacteristic
84C2×C5×#67—21no—
85C2×C5×#67—21no—
86C5×D3×D4—22no—
87C5×D3×D4—22no—
88C5×D3×D4—22no—
89C5×D3×D4D414yes—
90C2×C5×D12C2311yescharacteristic
91C2×C5×D12C2311yescharacteristic
92C2×C4×C5×D3C2311yescharacteristic
93C22×C3×Dic5—21no—
94C2×C3×Dic10C2311yescharacteristic
95C2×#1204—21no—
96C2×D3×Dic5—21no—
97C2×D3×Dic5—21no—
98C2×D3×Dic5—21no—
99C2×D3×Dic5—21no—
100C2×D3×Dic5—44no—
101C2×D3×Dic5D411yescharacteristic
102C2×D3×Dic5D411yescharacteristic
103D3×Dic10—22no—
104D3×Dic10—22no—
105C3×C5×D8—22no—
106C2×C3×C5×C8C2311yescharacteristic
107#6719—21no—
108#6719—21no—
109#6719—21no—
110#6716—22no—
111C4⋊Dic15C2311yescharacteristic
112C4×Dic15C2311yescharacteristic
113C2×C3⋊#168C2311yescharacteristic
114C5×#213—22no—
115C5×#213—22no—
116C2×C5×C3⋊C8C2311yescharacteristic
117C5×D24—22no—
118C5×D3×C8—22no—
119C3×C22⋊Dic5—21no—
120C3×C22⋊Dic5—21no—
121C3×C22⋊Dic5—21no—
122C3×#687—22no—
123C3×C4⋊Dic5C2311yescharacteristic
124C3×C4×Dic5C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126Dic3⋊Dic5—21no—
127(C2×D3)⋊Dic5—21no—
128(C2×D3)⋊Dic5—21no—
129(C2×D3)⋊Dic5—21no—
130(C2×D3)⋊Dic5—21no—
131(C2×D3)⋊Dic5—21no—
132(C2×D3)⋊Dic5—21no—
133Dic3×Dic5D411yescharacteristic
134Dic3×Dic5D411yescharacteristic
135#6659—22no—
136#6656—22no—
137D3×#168—22no—
138C2×D3×SD16—51no—
139C2×D3×D8D511yescharacteristic
140D3×#124—51no—
141C4×D3×D4—51no—
142C3×#463—51no—
143#5165—51no—
144#5153—51no—
145#5057—51no—
146#5016—51no—
147#4844—51no—
148D3×C4⋊C8—51no—
149#4819—51no—
150D3×#103—51no—
151#4787—51no—
152D3×#102—51no—
153C22×C5×D4—31no—
154C22×C5×D4—31no—
155C23×Dic5—61no—
156C22×Dic10—31no—
157C2×C5×D8—31no—
158C2×C5×D8—31no—
159C2×C5×D8—31no—
160C2×C5×D8—64no—
161C2×C5×D8C2×D311yescharacteristic
162C22×C5×C8—31no—
163C2×C22⋊Dic5—61no—
164C2×C22⋊Dic5—61no—
165C2×C22⋊Dic5—61no—
166#4082—31no—
167#4082—31no—
168#4082—31no—
169#4082—61no—
170#4082—61no—
171#4082C2×D311yescharacteristic, complemented
172D4×Dic5—31no—
173D4×Dic5—31no—
174D4×Dic5—31no—
175D4×Dic5—61no—
176D4×Dic5—61no—
177D4×Dic5C2×D311yescharacteristic, complemented
178C2×#687—31no—
179C2×#687—31no—
180C2×#687—31no—
181C2×#687—64no—
182C2×#687C2×D311yescharacteristic, complemented
183C2×C4⋊Dic5—31no—
184C2×C4×Dic5—31no—
185C22×#168—31no—
186#3964—31no—
187#3964—31no—
188#3964—31no—
189#3964C2×D311yescharacteristic, complemented
190#3948—31no—
191#3948—31no—
192#3948—31no—
193#3948C2×D311yescharacteristic, complemented
194#3946—31no—
195#3946—31no—
196#3946—31no—
197#3946C2×D311yescharacteristic, complemented
198C2×#463—151noSylow
199C23×C3×C5—21no—
200C23×C3×C5—21no—
201C22×C5×D3—21no—
202C22×C5×D3—24no—
203C22×C5×D3—21no—
204C22×C5×D3—42no—
205C22×C5×D3—42no—
206C22×C5×D3—42no—
207C22×C5×D3—42no—
208C22×C5×D3—42no—
209C22×C5×D3C2×D411yescharacteristic
210C3×C5×D4—21no—
211C3×C5×D4—21no—
212C3×C5×D4—21no—
213C3×C5×D4C2×D412yes—
214C2×C3×C4×C5C2411yescharacteristic
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—42no—
218C2×Dic15C2×D411yescharacteristic
219C2×Dic15C2×D411yescharacteristic
220Dic30—21no—
221Dic30—21no—
222C5×#67—24no—
223C5×#67—42no—
224C2×C5×Dic3C2×D411yescharacteristic
225C5×D12—21no—
226C5×D12—21no—
227C5×D12—21no—
228C5×D12C2×D412yes—
229C4×C5×D3C2×D412yes—
230C4×C5×D3#4112yes—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—42no—
234C2×C3×Dic5C2×D411yescharacteristic
235C2×C3×Dic5C2×D411yescharacteristic
236C3×Dic10—21no—
237C3×Dic10—21no—
238#1204—42no—
239D3×Dic5—22no—
240D3×Dic5—22no—
241D3×Dic5—42no—
242D3×Dic5—42no—
243D3×Dic5—42no—
244D3×Dic5—42no—
245C3×C5×C8—21no—
246C3⋊#168—21no—
247C3×#168—21no—
248C5×C3⋊C8—21no—
249C2×D3×Q8—51no—
250C2×D3×D4C2×D511yescharacteristic
251C2×D3×D4C2×D511yescharacteristic
252C22×C4×D3—101no—
253C2×C3×SD16—51no—
254C2×C3×D8C2×D511yescharacteristic
255C3×#124—51no—
256C3×C4×D4—51no—
257#947—51no—
258C2×#215—51no—
259#936—51no—
260D4×Dic3—51no—
261C2×#214—51no—
262C2×#213C2×D511yescharacteristic
263C2×#213C2×D511yescharacteristic
264C4×#67—101no—
265D3×SD16—104no—
266D3×D8—24no—
267C2×D24C2×D511yescharacteristic
268C2×#204—51no—
269C2×D3×C8—51no—
270C2×D3×C8C2×D511yescharacteristic
271#893—51no—
272D3×C4⋊C4—51no—
273#885—101no—
274#885—101no—
275#67⋊C4—101no—
276D3×C22⋊C4—101no—
277D3×C22⋊C4—101no—
278D3×C22⋊C4—101no—
279#875—51no—
280C4×D12—51no—
281C42×D3—51no—
282C3×C4⋊C8—51no—
283C3×#103—51no—
284C3×#102—51no—
285#835—51no—
286#832—51no—
287#821—51no—
288#816—51no—
289Dic3⋊C8—51no—
290Dic3⋊C8—51no—
291#810—51no—
292#809—51no—
293C4⋊(C3⋊C8)—51no—
294C24×C5—61no—
295C24×C5—61no—
296C2×C5×D4—34no—
297C2×C5×D4—31no—
298C2×C5×D4—31no—
299C2×C5×D4—62no—
300C2×C5×D4—62no—
301C2×C5×D4—62no—
302C2×C5×D4—61no—
303C2×C5×D4—61no—
304C2×C5×D4C22×D311yescharacteristic
305C2×C5×D4C22×D311yescharacteristic
306C22×C4×C5—31no—
307C22×Dic5—21no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—61no—
311C22×Dic5—61no—
312C22×Dic5—61no—
313C22×Dic5—61no—
314C22×Dic5—61no—
315C22×Dic5—124no—
316C2×Dic10—31no—
317C2×Dic10—62no—
318C2×Dic10—62no—
319C2×Dic10—61no—
320C2×Dic10C22×D311yescharacteristic
321C5×D8—22no—
322C5×D8—62no—
323C5×D8—62no—
324C5×D8—62no—
325C2×C5×C8—31no—
326C2×C5×C8—62no—
327C2×C5×C8C22×D311yescharacteristic
328C22⋊Dic5—21no—
329C22⋊Dic5—21no—
330C22⋊Dic5—21no—
331C22⋊Dic5—61no—
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334C22⋊Dic5—61no—
335C22⋊Dic5—61no—
336C22⋊Dic5—61no—
337C22⋊Dic5—61no—
338C22⋊Dic5—61no—
339C22⋊Dic5—61no—
340#687—22no—
341#687—62no—
342#687—62no—
343#687—62no—
344C4⋊Dic5—31no—
345C4⋊Dic5—61no—
346C4⋊Dic5C22×D311yescharacteristic
347C4×Dic5—31no—
348C4×Dic5—31no—
349C4×Dic5—31no—
350C4×Dic5C22×D311yescharacteristic
351C2×#168—31no—
352C2×#168—62no—
353C2×#168C22×D311yescharacteristic
354C22×SD16—151no—
355C22×D8—31no—
356C2×#124—151no—
357C2×C4×D4—151no—
358#463—51no—
359#463—151no—
360#463—151no—
361#463—151no—
362#463—151no—
363#463—151no—
364#463—151no—
365#463—151no—
366C2×C4⋊C8—151no—
367C2×#103—151no—
368C2×#102—151no—
369C22×C3×C5—22no—
370C22×C3×C5—41no—
371C22×C3×C5—41no—
372C22×C3×C5—41no—
373C22×C3×C5—41no—
374C22×C3×C5—41no—
375C22×C3×C5C22×D411yescharacteristic
376C2×C5×D3—22no—
377C2×C5×D3—41no—
378C2×C5×D3—41no—
379C2×C5×D3—48no—
380C2×C5×D3—41no—
381C2×C5×D3—41no—
382C2×C5×D3—41no—
383C2×C5×D3—84no—
384C2×C5×D3#12112yes—
385C2×C5×D3#13512yes—
386C2×C5×D3AGL(1,ℤ/8)12yes—
387C3×C4×C5C22×D411yescharacteristic
388C3×C4×C5C2×#4111yescharacteristic
389Dic15—21no—
390Dic15—21no—
391Dic15—41no—
392Dic15—41no—
393C3×Dic5—21no—
394C3×Dic5—21no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C5×Dic3#12112yes—
398C23×D3—21no—
399C23×D3—21no—
400C2×C3×Q8—51no—
401C2×C3×D4C22×D511yescharacteristic
402C2×C3×D4C22×D511yescharacteristic
403C22×C3×C4—101no—
404C2×#67—21no—
405C2×#67—21no—
406C22×Dic3—101no—
407D3×Q8—102no—
408D3×Q8—102no—
409D3×D4—22no—
410D3×D4—22no—
411D3×D4—22no—
412D3×D4C22⋊D514yes—
413C2×D12C22×D511yescharacteristic
414C2×D12C22×D511yescharacteristic
415C2×C4×D3—51no—
416C2×C4×D3—51no—
417C2×C4×D3—101no—
418C2×C4×D3—101no—
419C2×C4×D3—101no—
420C2×C4×D3—101no—
421C2×C4×D3—204no—
422C2×C4×D3C22×D511yescharacteristic
423C2×Dic6—51no—
424C2×Dic6—101no—
425C3×SD16—102no—
426C3×D8—22no—
427C2×C3×C8—51no—
428C2×C3×C8C22×D511yescharacteristic
429C3×C4⋊C4—51no—
430C3×C22⋊C4—101no—
431C3×C22⋊C4—101no—
432C3×C22⋊C4—101no—
433C3×C42—51no—
434#217—101no—
435#217—101no—
436#217—101no—
437#215—102no—
438#214—102no—
439#213—22no—
440#213—22no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444(C2×D3)⋊C4—101no—
445(C2×D3)⋊C4—101no—
446(C2×D3)⋊C4—101no—
447C4⋊Dic3—51no—
448Dic3⋊C4—101no—
449C4×Dic3—51no—
450C4×Dic3—51no—
451C4×Dic3—51no—
452C2×C3⋊C8—51no—
453C2×C3⋊C8C22×D511yescharacteristic
454D24—22no—
455#204—102no—
456D3×C8—22no—
457D3×C8—102no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—31no—
461C23×C5—64no—
462C23×C5—61no—
463C23×C5—61no—
464C23×C5—122no—
465C23×C5—122no—
466C23×C5—122no—
467C23×C5—122no—
468C23×C5—122no—
469C5×D4—21no—
470C5×D4—21no—
471C5×D4—21no—
472C5×D4—32no—
473C5×D4—64no—
474C5×D4—61no—
475C5×D4—61no—
476C5×D4—61no—
477C5×D4—122no—
478C5×D4D3×D412yes—
479C2×C4×C5—31no—
480C2×C4×C5—32no—
481C2×C4×C5—32no—
482C2×C4×C5C23×D311yescharacteristic
483C2×Dic5—21no—
484C2×Dic5—21no—
485C2×Dic5—31no—
486C2×Dic5—31no—
487C2×Dic5—42no—
488C2×Dic5—62no—
489C2×Dic5—62no—
490C2×Dic5—61no—
491C2×Dic5—61no—
492C2×Dic5—122no—
493C2×Dic5—122no—
494C2×Dic5—122no—
495C2×Dic5—122no—
496C2×Dic5—122no—
497C2×Dic5D3×D411yescharacteristic
498C2×Dic5D3×D411yescharacteristic
499Dic10—21no—
500Dic10—21no—
501Dic10—61no—
502Dic10—61no—
503Dic10—122no—
504C5×C8—21no—
505C5×C8—61no—
506#168—21no—
507#168—61no—
508C22×Q8—151no—
509C22×D4—31no—
510C22×D4—31no—
511C23×C4—301no—
512C2×SD16—51no—
513C2×SD16—151no—
514C2×SD16—151no—
515C2×SD16—151no—
516C2×SD16—304no—
517C2×D8—31no—
518C2×D8—31no—
519C2×D8—31no—
520C2×D8—64no—
521C2×D8D3×D511yescharacteristic
522C22×C8—31no—
523C22×C8—151no—
524#124—51no—
525#124—151no—
526#124—151no—
527#124—151no—
528#124—301no—
529#124—301no—
530C4×D4—51no—
531C4×D4—151no—
532C4×D4—151no—
533C4×D4—151no—
534C4×D4—301no—
535C4×D4—301no—
536C2×C4⋊C4—151no—
537C2×C22⋊C4—301no—
538C2×C22⋊C4—301no—
539C2×C22⋊C4—301no—
540C2×C42—151no—
541C4⋊C8—51no—
542C4⋊C8—151no—
543C4⋊C8—151no—
544C4⋊C8—151no—
545#103—51no—
546#103—151no—
547#103—151no—
548#103—151no—
549#102—51no—
550#102—151no—
551#102—151no—
552#102—151no—
553C2×C3×C5—42no—
554C2×C3×C5—81no—
555C2×C3×C5C2×#12111yescharacteristic
556C2×C3×C5C2×#13511yescharacteristic
557C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
558C5×D3—42no—
559C5×D3—81no—
560C5×D3#46314yescomplemented
561C23×C3—21no—
562C23×C3—21no—
563C22×D3—21no—
564C22×D3—24no—
565C22×D3—21no—
566C22×D3—42no—
567C22×D3—42no—
568C22×D3—42no—
569C22×D3—42no—
570C22×D3—42no—
571C22×D3D4×D511yescharacteristic
572C3×Q8—101no—
573C3×Q8—101no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4C2×C22⋊D512yes—
578C2×C3×C4—51no—
579C2×C3×C4—51no—
580C2×C3×C4—101no—
581C2×C3×C4—101no—
582C2×C3×C4—202no—
583C2×C3×C4C23×D511yescharacteristic
584#67—24no—
585#67—42no—
586C2×Dic3—51no—
587C2×Dic3—51no—
588C2×Dic3—101no—
589C2×Dic3—101no—
590C2×Dic3—202no—
591C2×Dic3D4×D511yescharacteristic
592D12—21no—
593D12—21no—
594D12—21no—
595D12C2×C22⋊D512yes—
596C4×D3—102no—
597C4×D3—102no—
598C4×D3—202no—
599C4×D3—202no—
600C4×D3—202no—
601C4×D3—202no—
602C4×D3#71112yes—
603C4×D3C2×C22⋊D512yes—
604Dic6—101no—
605Dic6—101no—
606Dic6—202no—
607C3×C8—21no—
608C3×C8—101no—
609C3⋊C8—21no—
610C3⋊C8—101no—
611C22×C5—22no—
612C22×C5—32no—
613C22×C5—32no—
614C22×C5—32no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—41no—
620C22×C5—62no—
621C22×C5—128no—
622C22×C5—121no—
623C22×C5—121no—
624C22×C5—121no—
625C22×C5—121no—
626C22×C5—121no—
627C22×C5—244no—
628C22×C5C2×D3×D411yescharacteristic
629C4×C5—32no—
630C4×C5C2×D3×D411yescharacteristic
631C4×C5D3×#4111yescharacteristic
632Dic5—21no—
633Dic5—21no—
634Dic5—41no—
635Dic5—41no—
636Dic5—61no—
637Dic5—61no—
638Dic5—121no—
639Dic5—121no—
640C24—61no—
641C24—61no—
642C2×Q8—51no—
643C2×Q8—151no—
644C2×Q8—301no—
645C2×Q8—302no—
646C2×Q8—302no—
647C2×D4—34no—
648C2×D4—31no—
649C2×D4—31no—
650C2×D4—62no—
651C2×D4—62no—
652C2×D4—62no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4C2×D3×D511yescharacteristic
656C2×D4C2×D3×D511yescharacteristic
657C22×C4—31no—
658C22×C4—101no—
659C22×C4—151no—
660C22×C4—151no—
661C22×C4—301no—
662C22×C4—301no—
663C22×C4—301no—
664C22×C4—301no—
665C22×C4—301no—
666C22×C4—604no—
667SD16—102no—
668SD16—302no—
669SD16—302no—
670SD16—302no—
671D8—22no—
672D8—62no—
673D8—62no—
674D8—62no—
675C2×C8—31no—
676C2×C8—51no—
677C2×C8—62no—
678C2×C8—151no—
679C2×C8—302no—
680C2×C8C2×D3×D511yescharacteristic
681C4⋊C4—51no—
682C4⋊C4—151no—
683C4⋊C4—301no—
684C22⋊C4—101no—
685C22⋊C4—101no—
686C22⋊C4—101no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C22⋊C4—301no—
694C22⋊C4—301no—
695C22⋊C4—301no—
696C42—51no—
697C42—151no—
698C42—151no—
699C42—151no—
700C3×C5C2×#46311yescharacteristic, complemented, Hall
701C22×C3—22no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3C2×D4×D511yescharacteristic
708C2×D3—22no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—48no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—84no—
716C2×D3#405712yes—
717C2×D3#405812yes—
718C2×D3#408512yes—
719C3×C4—101no—
720C3×C4—101no—
721C3×C4—201no—
722C3×C4—201no—
723C3×C4C2×#71111yescharacteristic
724C3×C4C22×C22⋊D511yescharacteristic
725Dic3—101no—
726Dic3—101no—
727Dic3—201no—
728Dic3—201no—
729Dic3#408512yes—
730C2×C5—34no—
731C2×C5—42no—
732C2×C5—81no—
733C2×C5—122no—
734C2×C5—241no—
735C2×C5D3×#12111yescharacteristic
736C2×C5D3×#13511yescharacteristic
737C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
738C23—21no—
739C23—21no—
740C23—31no—
741C23—64no—
742C23—61no—
743C23—61no—
744C23—122no—
745C23—122no—
746C23—122no—
747C23—122no—
748C23—122no—
749Q8—101no—
750Q8—101no—
751Q8—301no—
752Q8—301no—
753Q8—602no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—32no—
758D4—64no—
759D4—61no—
760D4—61no—
761D4—61no—
762D4—122no—
763D4D3×C22⋊D512yes—
764C2×C4—31no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—51no—
768C2×C4—51no—
769C2×C4—101no—
770C2×C4—101no—
771C2×C4—151no—
772C2×C4—151no—
773C2×C4—202no—
774C2×C4—302no—
775C2×C4—302no—
776C2×C4—301no—
777C2×C4—301no—
778C2×C4—602no—
779C2×C4—602no—
780C2×C4—602no—
781C2×C4—602no—
782C2×C4—602no—
783C2×C4C22×D3×D511yescharacteristic
784C8—21no—
785C8—61no—
786C8—101no—
787C8—301no—
788C2×C3—42no—
789C2×C3—81no—
790C2×C3C2×#405711yescharacteristic
791C2×C3C2×#405811yescharacteristic
792C2×C3C2×#408511yescharacteristic
793D3—42no—
794D3—81no—
795D3#6544214yesdirect product factor
796C5D3×#46311yescharacteristic, complemented, Sylow
797C22—22no—
798C22—32no—
799C22—32no—
800C22—32no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—62no—
807C22—128no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—244no—
814C22D3×D4×D511yescharacteristic
815C4—32no—
816C4—101no—
817C4—101no—
818C4—201no—
819C4—201no—
820C4—301no—
821C4—301no—
822C4—601no—
823C4—601no—
824C4D3×#71111yescharacteristic
825C4C2×D3×C22⋊D511yescharacteristic
826C3C2×#6544211yescharacteristic, complemented, Sylow
827C2—34no—
828C2—42no—
829C2—81no—
830C2—122no—
831C2—241no—
832C2D3×#405711yescharacteristic
833C2D3×#405811yescharacteristic
834C2D3×#408511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D3×D8C2
hypercenterC2×D8D3×D5
hypocenterC3×C5C2×#463
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. D3×#4082C2semidirect
3. D3×D4×Dic5C2semidirect
4. C2×D3×#687C2semidirect
5. #11751254C2semidirect
6. C3×#65442C2semidirect
7. #11749082C2semidirect
8. #11749065C2semidirect
9. #11748992C2semidirect
10. #11748978C2semidirect
11. D3×#3964C2semidirect
12. #11747787C2semidirect
13. #11747777C2semidirect
14. D3×#3948C2semidirect
15. D3×#3946C2semidirect
22. #91825C22semidirect
23. D4×Dic15C22semidirect
24. C2×#6716C22semidirect
30. C3×#4082C22semidirect
31. C3×D4×Dic5C22semidirect
32. C2×C3×#687C22semidirect
41. #91435C22semidirect
43. Dic5×D12C22semidirect
45. #91373C22semidirect
46. #91370C22semidirect
47. C2×#6659C22semidirect
48. C2×#6656C22semidirect
50. #91116C22semidirect
51. #91100C22semidirect
52. #91098C22semidirect
53. C3×#3964C22semidirect
54. C3×#3948C22semidirect
55. C3×#3946C22semidirect
56. #90983C22semidirect
57. #90982C22semidirect
58. #90974C22semidirect
59. #90971C22semidirect
60. #90967C22semidirect
61. #90966C22semidirect
75. #65442D3direct (N × H)
171. #4082C2×D3semidirect
177. D4×Dic5C2×D3semidirect
182. C2×#687C2×D3semidirect
189. #3964C2×D3semidirect
193. #3948C2×D3semidirect
197. #3946C2×D3semidirect
560. C5×D3#463semidirect
700. C3×C5C2×#463semidirect
795. D3#65442direct (N × H)
796. C5D3×#463semidirect
826. C3C2×#65442semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×D82
D3×#40822
D3×D4×Dic52
C2×D3×#6872
#117512542
C3×#654422
#117490822
#117490652
#117489922
#117489782
D3×#39642
#117477872
#117477772
D3×#39482
D3×#39462
C2×#654423
D3×#4635