Finite Group Databasebeta

← #14424186

Subgroups — #14424186

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C2×#91508C211yesmaximal, characteristic, complemented
3C2×#91484C211yesmaximal, characteristic, complemented
4D5×#924C211yesmaximal, characteristic, complemented
5#11751340C211yesmaximal, characteristic, complemented
6C5×#5239C211yesmaximal, characteristic, complemented
7#11749291C211yesmaximal, characteristic, complemented
8#11749290C211yesmaximal, characteristic, complemented
9#11749198C211yesmaximal, characteristic, complemented
10#11749045C211yesmaximal, characteristic, complemented
11#11749044C211yesmaximal, characteristic, complemented
12#11748951C211yesmaximal, characteristic, complemented
13#11748531C211yesmaximal, characteristic, complemented
14#11748528C211yesmaximal, characteristic, complemented
15#11748499C211yesmaximal, characteristic, complemented
16#10611959—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C3×D5×#41—24no—
19C3×D5×#41—24no—
20C2×C3×#713C2211yescharacteristic
21C2×C3×Q8×D5C2211yescharacteristic
22C2×C3×#711—21no—
23C2×C3×#711C2211yescharacteristic
24C2×C3×D4×D5—21no—
25C2×C3×D4×D5C2211yescharacteristic
26C2×C3×#709—21no—
27C2×C3×#709C2211yescharacteristic
28C22×C3×C4×D5—21no—
29C22×C3×C4×D5C2211yescharacteristic
30C2×D5×Dic6C2211yescharacteristic, complemented
31C2×#6718C2211yescharacteristic, complemented
32C2×#6716C2211yescharacteristic, complemented
33#91813C2211yescharacteristic, complemented
34C2×C5×#216C2211yescharacteristic, complemented
35C2×C5×#214C2211yescharacteristic, complemented
36C5×#924C2211yescharacteristic, complemented
37#91574—21no—
38D5×#217—21no—
39#91508—24no—
40#91484—24no—
41D5×C4⋊Dic3C2211yescharacteristic, complemented
42D5×Dic3⋊C4—21no—
43#91360C2211yescharacteristic
44#91359C2211yescharacteristic
45#91349—21no—
46C2×#6662C2211yescharacteristic, complemented
47C2×#6661C2211yescharacteristic, complemented
48C2×#6657C2211yescharacteristic, complemented
49C2×#6655C2211yescharacteristic, complemented
50C2×#6649C2211yescharacteristic, complemented
51C2×#6649C2211yescharacteristic, complemented
52#91119C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55C5×#835C2211yescharacteristic, complemented
56C5×#832C2211yescharacteristic, complemented
57C5×#830C2211yescharacteristic, complemented
58#90971C2211yescharacteristic, complemented
59#90970C2211yescharacteristic, complemented
60#90965C2211yescharacteristic, complemented
61#90964C2211yescharacteristic, complemented
62#90955C2211yescharacteristic
63#90955C2211yescharacteristic
64#84084—51nomaximal, Hall
65C2×D5×#41D311yescharacteristic
66C2×#4064—31no—
67C2×#4061—31no—
68D5×C22⋊Q8—31no—
69C5×#452—31no—
70#65528—31no—
71#65475—31no—
72#65458—31no—
73#65336—31no—
74#65097—31no—
75#65092—31no—
76#65065—31no—
77#65060—31no—
78#65022—31no—
79#65015—31no—
80C23×C3×D5—21no—
81C23×C3×D5D411yescharacteristic
82C3×C5×#41—22no—
83C3×C5×#41—22no—
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4C2311yescharacteristic
87C22×C3×C4×C5—21no—
88C22×C3×C4×C5C2311yescharacteristic
89C2×Dic30C2311yescharacteristic
90C2×C5×Dic6C2311yescharacteristic
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C22×C3×Dic5—21no—
95C22×C3×Dic5D411yescharacteristic
96C3×#713—22no—
97C3×#713D414yes—
98C3×Q8×D5—22no—
99C3×Q8×D5—22no—
100C3×#711—28no—
101C3×#711—22no—
102C3×#711D414yes—
103C3×D4×D5—28no—
104C3×D4×D5—22no—
105C3×D4×D5—22no—
106C3×#709—28no—
107C3×#709—22no—
108C3×#709—22no—
109C2×C3×D20—21no—
110C2×C3×D20C2311yescharacteristic
111C2×C3×C4×D5—28no—
112C2×C3×C4×D5—21no—
113C2×C3×C4×D5—21no—
114C2×C3×C4×D5—21no—
115C2×C3×C4×D5—22no—
116C2×C3×C4×D5—22no—
117C2×C3×C4×D5D411yescharacteristic
118C2×C3×C4×D5D411yescharacteristic
119C2×C3×C4×D5C2311yescharacteristic
120C2×C3×C4×D5C2311yescharacteristic
121C2×C3×Dic10—21no—
122C2×C3×Dic10C2311yescharacteristic
123C2×#1204—21no—
124C2×D5×Dic3—21no—
125C2×D5×Dic3—21no—
126D5×Dic6—22no—
127D5×Dic6—22no—
128#6719—21no—
129#6718—22no—
130#6716—22no—
131C4⋊Dic15C2311yescharacteristic
132#6712—21no—
133C2×C3⋊#168C2311yescharacteristic
134C2×C3⋊#168C2311yescharacteristic
135C5×#217—21no—
136C5×#216—22no—
137C5×#214—22no—
138C5×C4⋊Dic3C2311yescharacteristic
139C5×Dic3⋊C4—21no—
140C2×C5×C3⋊C8C2311yescharacteristic
141C2×C5×C3⋊C8C2311yescharacteristic
142Dic3⋊Dic5—21no—
143#6669—21no—
144#6668—21no—
145#6665—21no—
146#6665—21no—
147#6662—22no—
148#6661—22no—
149#6657—22no—
150#6655—22no—
151#6649—22no—
152#6649—22no—
153C22×C3×#41—51no—
154C2×#951—51no—
155C2×#951—51no—
156C2×#924—51no—
157#5239—51no—
158#5239—51no—
159#5239—51no—
160#5239D511yescharacteristic, complemented
161#5232—51no—
162#5232—51no—
163#5228—51no—
164#5228—51no—
165#5218—51no—
166#5218—51no—
167#5207—51no—
168C2×C5×#41C2×D311yescharacteristic
169D5×#41—24no—
170D5×#41—24no—
171C2×#713C2×D311yescharacteristic
172C2×Q8×D5—31no—
173C2×Q8×D5C2×D311yescharacteristic
174C2×#711—21no—
175C2×#711C2×D311yescharacteristic
176C2×D4×D5—21no—
177C2×D4×D5C2×D311yescharacteristic
178C2×#709—21no—
179C2×#709C2×D311yescharacteristic
180C22×C4×D5—21no—
181C22×C4×D5C2×D311yescharacteristic
182C2×C5×Q16—31no—
183C2×C5×SD16—31no—
184C5×C22⋊Q8—31no—
185#4092—31no—
186C2×#689—31no—
187C2×#689—31no—
188C2×#688—31no—
189C2×#687—31no—
190#4070—31no—
191#4064—64no—
192#4061—64no—
193C2×Dic20—31no—
194C2×#677—31no—
195C2×#676—31no—
196C2×#676—31no—
197#4043—31no—
198#4042—61no—
199D5×C4⋊C4—31no—
200D5×C4⋊C4—61no—
201D5×C22⋊C4—61no—
202#4024—61no—
203C5×#103—31no—
204C5×#102—31no—
205C5×C22⋊C8—31no—
206#3967—31no—
207#3964—31no—
208C22⋊#168—31no—
209#3953—31no—
210#3952—31no—
211#3952—31no—
212#3948—31no—
213#3942—31no—
214#3941—31no—
215#3007—151noSylow
216C23×C3×C5—21no—
217C23×C3×C5C2×D411yescharacteristic
218C22×C3×D5—24no—
219C22×C3×D5—21no—
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5—41no—
223C22×C3×D5—42no—
224C22×C3×D5—42no—
225C22×C3×D5C2×D411yescharacteristic
226C22×C3×D5C2×D411yescharacteristic
227C3×C5×Q8—21no—
228C3×C5×Q8C2×D412yes—
229C3×C5×D4—24no—
230C3×C5×D4—21no—
231C3×C5×D4C2×D412yes—
232C2×C3×C4×C5—24no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5C2×D411yescharacteristic
237C2×C3×C4×C5C2411yescharacteristic
238C2×Dic15—21no—
239C2×Dic15—21no—
240Dic30—21no—
241Dic30—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C5×Dic6—21no—
245C5×Dic6—21no—
246C3×C22⋊D5—24no—
247C3×C22⋊D5—24no—
248C3×C22⋊D5—24no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—22no—
251C2×C3×Dic5—24no—
252C2×C3×Dic5C2×D411yescharacteristic
253C2×C3×Dic5C2×D411yescharacteristic
254C3×D20—24no—
255C3×D20—21no—
256C3×D20C2×D412yes—
257C3×C4×D5—24no—
258C3×C4×D5—24no—
259C3×C4×D5—22no—
260C3×C4×D5—21no—
261C3×C4×D5—21no—
262C3×C4×D5—22no—
263C3×C4×D5—24no—
264C3×C4×D5C2×D412yes—
265C3×C4×D5C2×D412yes—
266C3×Dic10—24no—
267C3×Dic10—21no—
268C3×Dic10C2×D412yes—
269#1204—42no—
270D5×Dic3—42no—
271D5×Dic3—42no—
272C3⋊#168—21no—
273C3⋊#168—21no—
274C5×C3⋊C8—21no—
275C5×C3⋊C8—21no—
276C2×C3×#41—51no—
277C2×C3×#41—51no—
278C2×C3×#41—51no—
279C2×C3×#41—101no—
280C2×C3×#41—101no—
281C2×C3×#41—104no—
282C2×C3×#41—104no—
283C2×C3×#41C2×D511yescharacteristic
284C22×C3×Q8—51no—
285C22×C3×D4—51no—
286C22×C3×D4—101no—
287C23×C3×C4—51no—
288C23×C3×C4—101no—
289C22×Dic6—51no—
290C2×#217—101no—
291#951—104no—
292#951—104no—
293C2×#216—51no—
294C2×#216—51no—
295C2×#216—51no—
296C2×#216C2×D511yescharacteristic, complemented
297C2×#214—51no—
298C2×#214—51no—
299C2×#214—51no—
300C2×#214C2×D511yescharacteristic, complemented
301C2×C4⋊Dic3—51no—
302#924—51no—
303#924—51no—
304#924—51no—
305#924—101no—
306#924—101no—
307#924C2×D511yescharacteristic, complemented
308C2×Dic3⋊C4—101no—
309C2×#208—51no—
310C2×#208—51no—
311#835—51no—
312#835—51no—
313#835—51no—
314#835C2×D511yescharacteristic, complemented
315#832—51no—
316#832—51no—
317#832—51no—
318#832C2×D511yescharacteristic, complemented
319#830—51no—
320#830—51no—
321#830—51no—
322#830C2×D511yescharacteristic, complemented
323C23×D5—21no—
324C23×D5#6711yescharacteristic
325C5×#41—22no—
326C5×#41—22no—
327C2×C5×Q8—31no—
328C2×C5×Q8C22×D311yescharacteristic
329C2×C5×D4—21no—
330C2×C5×D4C22×D311yescharacteristic
331C22×C4×C5—21no—
332C22×C4×C5C22×D311yescharacteristic
333C2×C22⋊D5—21no—
334C2×C22⋊D5—21no—
335C2×C22⋊D5—21no—
336C22×Dic5—21no—
337C22×Dic5#6711yescharacteristic
338#713—22no—
339#713#6714yes—
340Q8×D5—22no—
341Q8×D5—22no—
342Q8×D5—62no—
343Q8×D5—62no—
344#711—28no—
345#711—22no—
346#711#6714yes—
347D4×D5—28no—
348D4×D5—22no—
349D4×D5—22no—
350#709—28no—
351#709—22no—
352#709—22no—
353C2×D20—21no—
354C2×D20C22×D311yescharacteristic
355C2×C4×D5—28no—
356C2×C4×D5—21no—
357C2×C4×D5—21no—
358C2×C4×D5—21no—
359C2×C4×D5—22no—
360C2×C4×D5—22no—
361C2×C4×D5—61no—
362C2×C4×D5—61no—
363C2×C4×D5#6711yescharacteristic
364C2×C4×D5#6711yescharacteristic
365C2×C4×D5C22×D311yescharacteristic
366C2×C4×D5C22×D311yescharacteristic
367C2×Dic10—21no—
368C2×Dic10—31no—
369C2×Dic10—61no—
370C2×Dic10C22×D311yescharacteristic
371C5×Q16—62no—
372C5×SD16—62no—
373C2×C5×C8—31no—
374C2×C5×C8—31no—
375C5×C4⋊C4—31no—
376C5×C4⋊C4—61no—
377C5×C22⋊C4—61no—
378C22⋊Dic5—61no—
379#689—62no—
380#689—62no—
381#688—62no—
382#687—62no—
383#685—61no—
384#685—61no—
385C4⋊Dic5—31no—
386C4⋊Dic5—61no—
387#683—61no—
388#683—61no—
389#683—61no—
390C2×#168—31no—
391C2×#168—31no—
392Dic20—62no—
393#677—62no—
394#676—62no—
395#676—62no—
396C22×#41—51no—
397C2×#137—151no—
398C2×#137—151no—
399C2×C22⋊Q8—151no—
400#452—31no—
401#452—151no—
402#452—151no—
403#452—151no—
404#451—151no—
405#451—151no—
406#450—151no—
407#450—151no—
408#417—151no—
409#417—151no—
410#407—151no—
411C22×C3×C5—21no—
412C22×C3×C5—22no—
413C22×C3×C5—21no—
414C22×C3×C5—21no—
415C22×C3×C5—41no—
416C22×C3×C5—41no—
417C22×C3×C5C22×D411yescharacteristic
418C2×C3×D5—21no—
419C2×C3×D5—21no—
420C2×C3×D5—21no—
421C2×C3×D5—21no—
422C2×C3×D5—22no—
423C2×C3×D5—44no—
424C2×C3×D5—48no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5#12012yes—
428C2×C3×D5#13712yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—21no—
431C3×C4×C5C22×D411yescharacteristic
432C3×C4×C5C22×D411yescharacteristic
433Dic15—41no—
434Dic15—41no—
435C3×Dic5—21no—
436C3×Dic5—22no—
437C3×Dic5#12012yes—
438C5×Dic3—41no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3—101no—
442C3×#41—22no—
443C3×#41—22no—
444C3×#41—54no—
445C3×#41—54no—
446C3×#41—102no—
447C3×#41—102no—
448C3×#41—108no—
449C3×#41—102no—
450C3×#41—102no—
451C3×#41—108no—
452C2×C3×Q8—51no—
453C2×C3×Q8—101no—
454C2×C3×Q8—102no—
455C2×C3×Q8—102no—
456C2×C3×Q8C22×D511yescharacteristic
457C2×C3×D4—21no—
458C2×C3×D4—51no—
459C2×C3×D4—101no—
460C2×C3×D4—101no—
461C2×C3×D4—102no—
462C2×C3×D4—108no—
463C2×C3×D4—101no—
464C2×C3×D4—101no—
465C2×C3×D4—102no—
466C2×C3×D4C22×D511yescharacteristic
467C22×C3×C4—21no—
468C22×C3×C4—51no—
469C22×C3×C4—51no—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—51no—
473C22×C3×C4—102no—
474C22×C3×C4—102no—
475C22×C3×C4—101no—
476C22×C3×C4—101no—
477C22×C3×C4—108no—
478C22×C3×C4—101no—
479C22×C3×C4—101no—
480C22×C3×C4C22×D511yescharacteristic
481C22×Dic3—101no—
482C22×Dic3—101no—
483C2×Dic6—51no—
484C2×Dic6—102no—
485C2×Dic6—102no—
486C2×Dic6—101no—
487C2×Dic6C22×D511yescharacteristic
488#217—21no—
489#217—101no—
490#217—101no—
491#217—101no—
492#216—22no—
493#216—102no—
494#216—102no—
495#216—102no—
496#214—22no—
497#214—102no—
498#214—102no—
499#214—102no—
500C4⋊Dic3—51no—
501C4⋊Dic3—101no—
502C4⋊Dic3C22×D511yescharacteristic
503Dic3⋊C4—21no—
504Dic3⋊C4—101no—
505Dic3⋊C4—101no—
506Dic3⋊C4—101no—
507#208—102no—
508#208—102no—
509C2×C3⋊C8—51no—
510C2×C3⋊C8—51no—
511C2×C3⋊C8C22×D511yescharacteristic
512C2×C3⋊C8C22×D511yescharacteristic
513C23×C5—21no—
514C23×C5C2×#6711yescharacteristic
515C22×D5—24no—
516C22×D5—21no—
517C22×D5—22no—
518C22×D5—22no—
519C22×D5—41no—
520C22×D5—42no—
521C22×D5—42no—
522C22×D5C2×#6711yescharacteristic
523C22×D5C2×#6711yescharacteristic
524C5×Q8—21no—
525C5×Q8—61no—
526C5×Q8—61no—
527C5×Q8C2×#6712yes—
528C5×D4—24no—
529C5×D4—21no—
530C5×D4C2×#6712yes—
531C2×C4×C5—24no—
532C2×C4×C5—21no—
533C2×C4×C5—21no—
534C2×C4×C5—21no—
535C2×C4×C5—61no—
536C2×C4×C5—61no—
537C2×C4×C5C2×#6711yescharacteristic
538C2×C4×C5C23×D311yescharacteristic
539C22⋊D5—24no—
540C22⋊D5—24no—
541C22⋊D5—24no—
542C2×Dic5—21no—
543C2×Dic5—22no—
544C2×Dic5—24no—
545C2×Dic5—61no—
546C2×Dic5—61no—
547C2×Dic5C2×#6711yescharacteristic
548C2×Dic5C2×#6711yescharacteristic
549D20—24no—
550D20—21no—
551D20C2×#6712yes—
552C4×D5—24no—
553C4×D5—24no—
554C4×D5—22no—
555C4×D5—21no—
556C4×D5—21no—
557C4×D5—22no—
558C4×D5—24no—
559C4×D5—122no—
560C4×D5—122no—
561C4×D5C2×#6712yes—
562C4×D5C2×#6712yes—
563Dic10—24no—
564Dic10—21no—
565Dic10—61no—
566Dic10—61no—
567Dic10—122no—
568Dic10C2×#6712yes—
569C5×C8—61no—
570C5×C8—61no—
571#168—61no—
572#168—61no—
573C2×#41—51no—
574C2×#41—51no—
575C2×#41—51no—
576C2×#41—101no—
577C2×#41—101no—
578C2×#41—104no—
579C2×#41—104no—
580C2×#41D3×D511yescharacteristic
581C22×Q8—51no—
582C22×Q8—151no—
583C22×D4—51no—
584C22×D4—101no—
585C23×C4—51no—
586C23×C4—101no—
587#137—304no—
588#137—304no—
589C2×Q16—31no—
590C2×Q16—151no—
591C2×Q16—151no—
592C2×Q16—151no—
593C2×SD16—31no—
594C2×SD16—151no—
595C2×SD16—151no—
596C2×SD16—151no—
597C2×M16—151no—
598C2×M16—151no—
599C22⋊Q8—31no—
600C22⋊Q8—151no—
601C22⋊Q8—151no—
602C22⋊Q8—151no—
603C22⋊Q8—301no—
604C22⋊Q8—301no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—301no—
607C2×C22⋊C4—301no—
608#103—31no—
609#103—151no—
610#103—151no—
611#103—151no—
612#102—31no—
613#102—151no—
614#102—151no—
615#102—151no—
616C22⋊C8—31no—
617C22⋊C8—151no—
618C22⋊C8—151no—
619C22⋊C8—151no—
620C2×C3×C5—41no—
621C2×C3×C5—42no—
622C2×C3×C5C2×#12011yescharacteristic
623C2×C3×C5C2×#13711yescharacteristic
624C2×C3×C5#57511yescharacteristic
625C3×D5—22no—
626C3×D5—22no—
627C3×D5—42no—
628C23×C3—21no—
629C23×C3—51no—
630C23×C3—51no—
631C23×C3—102no—
632C23×C3—102no—
633C23×C3—104no—
634C23×C3—101no—
635C23×C3—201no—
636C23×C3—202no—
637C23×C3—202no—
638C23×C3D4×D511yescharacteristic
639C3×Q8—21no—
640C3×Q8—52no—
641C3×Q8—104no—
642C3×Q8—101no—
643C3×Q8D4×D512yes—
644C3×D4—24no—
645C3×D4—21no—
646C3×D4—52no—
647C3×D4—104no—
648C3×D4—104no—
649C3×D4—104no—
650C3×D4—104no—
651C3×D4—101no—
652C3×D4D4×D512yes—
653C2×C3×C4—24no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—51no—
658C2×C3×C4—52no—
659C2×C3×C4—52no—
660C2×C3×C4—51no—
661C2×C3×C4—102no—
662C2×C3×C4—104no—
663C2×C3×C4—102no—
664C2×C3×C4—104no—
665C2×C3×C4—104no—
666C2×C3×C4—102no—
667C2×C3×C4—104no—
668C2×C3×C4—101no—
669C2×C3×C4—101no—
670C2×C3×C4—101no—
671C2×C3×C4D4×D511yescharacteristic
672C2×C3×C4C23×D511yescharacteristic
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—101no—
676C2×Dic3—101no—
677C2×Dic3—202no—
678C2×Dic3—202no—
679Dic6—21no—
680Dic6—21no—
681Dic6—101no—
682Dic6—101no—
683Dic6—202no—
684C3⋊C8—21no—
685C3⋊C8—21no—
686C3⋊C8—101no—
687C3⋊C8—101no—
688C22×C5—21no—
689C22×C5—21no—
690C22×C5—21no—
691C22×C5—22no—
692C22×C5—41no—
693C22×C5—41no—
694C22×C5C22×#6711yescharacteristic
695C2×D5—21no—
696C2×D5—21no—
697C2×D5—21no—
698C2×D5—21no—
699C2×D5—22no—
700C2×D5—44no—
701C2×D5—48no—
702C2×D5—41no—
703C2×D5—41no—
704C2×D5#95112yescomplemented
705C2×D5#95312yes—
706C4×C5—22no—
707C4×C5—21no—
708C4×C5—121no—
709C4×C5—121no—
710C4×C5C22×#6711yescharacteristic
711C4×C5C22×#6711yescharacteristic
712Dic5—21no—
713Dic5—22no—
714Dic5—121no—
715Dic5—121no—
716Dic5#95312yes—
717C24—51no—
718C24—101no—
719#41—22no—
720#41—22no—
721#41—54no—
722#41—54no—
723#41—102no—
724#41—102no—
725#41—108no—
726#41—102no—
727#41—102no—
728#41—108no—
729C2×Q8—31no—
730C2×Q8—51no—
731C2×Q8—101no—
732C2×Q8—102no—
733C2×Q8—102no—
734C2×Q8—151no—
735C2×Q8—301no—
736C2×Q8—302no—
737C2×Q8—302no—
738C2×Q8C2×D3×D511yescharacteristic
739C2×D4—21no—
740C2×D4—51no—
741C2×D4—101no—
742C2×D4—101no—
743C2×D4—102no—
744C2×D4—108no—
745C2×D4—101no—
746C2×D4—101no—
747C2×D4—102no—
748C2×D4C2×D3×D511yescharacteristic
749C22×C4—21no—
750C22×C4—51no—
751C22×C4—51no—
752C22×C4—51no—
753C22×C4—51no—
754C22×C4—51no—
755C22×C4—102no—
756C22×C4—102no—
757C22×C4—101no—
758C22×C4—101no—
759C22×C4—108no—
760C22×C4—101no—
761C22×C4—101no—
762C22×C4—301no—
763C22×C4—301no—
764C22×C4C2×D3×D511yescharacteristic
765Q16—62no—
766Q16—302no—
767Q16—302no—
768Q16—302no—
769SD16—62no—
770SD16—302no—
771SD16—302no—
772SD16—302no—
773M16—302no—
774M16—302no—
775C2×C8—31no—
776C2×C8—31no—
777C2×C8—151no—
778C2×C8—151no—
779C4⋊C4—31no—
780C4⋊C4—61no—
781C4⋊C4—151no—
782C4⋊C4—301no—
783C4⋊C4—301no—
784C4⋊C4—301no—
785C4⋊C4—301no—
786C22⋊C4—61no—
787C22⋊C4—301no—
788C22⋊C4—301no—
789C22⋊C4—301no—
790C3×C5#300711yescharacteristic, complemented, Hall
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—22no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—52no—
798C22×C3—52no—
799C22×C3—101no—
800C22×C3—101no—
801C22×C3—101no—
802C22×C3—101no—
803C22×C3—102no—
804C22×C3—204no—
805C22×C3—208no—
806C22×C3—201no—
807C22×C3—201no—
808C22×C3C2×D4×D511yescharacteristic
809C3×C4—21no—
810C3×C4—22no—
811C3×C4—52no—
812C3×C4—101no—
813C3×C4—102no—
814C3×C4C2×D4×D511yescharacteristic
815C3×C4C2×D4×D511yescharacteristic
816Dic3—41no—
817Dic3—41no—
818Dic3—201no—
819Dic3—201no—
820C2×C5—41no—
821C2×C5—42no—
822C2×C5#582211yescharacteristic
823C2×C5C2×#95111yescharacteristic
824C2×C5C2×#95311yescharacteristic
825D5—22no—
826D5—22no—
827D5—42no—
828C23—21no—
829C23—51no—
830C23—51no—
831C23—102no—
832C23—102no—
833C23—104no—
834C23—101no—
835C23—201no—
836C23—202no—
837C23—202no—
838C23D5×#6711yescharacteristic
839Q8—21no—
840Q8—52no—
841Q8—61no—
842Q8—61no—
843Q8—104no—
844Q8—101no—
845Q8—301no—
846Q8—301no—
847Q8—602no—
848Q8D5×#6712yes—
849D4—24no—
850D4—21no—
851D4—52no—
852D4—104no—
853D4—104no—
854D4—104no—
855D4—104no—
856D4—101no—
857D4D5×#6712yes—
858C2×C4—24no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—51no—
863C2×C4—52no—
864C2×C4—52no—
865C2×C4—51no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—102no—
869C2×C4—104no—
870C2×C4—102no—
871C2×C4—104no—
872C2×C4—104no—
873C2×C4—102no—
874C2×C4—104no—
875C2×C4—101no—
876C2×C4—101no—
877C2×C4—101no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—602no—
881C2×C4—602no—
882C2×C4D5×#6711yescharacteristic
883C2×C4C22×D3×D511yescharacteristic
884C8—61no—
885C8—61no—
886C8—301no—
887C8—301no—
888C2×C3—41no—
889C2×C3—42no—
890C2×C3—102no—
891C2×C3—102no—
892C2×C3—202no—
893C2×C3D5×#12011yescharacteristic
894C2×C3#6610211yescharacteristic
895C2×C3D5×#13711yescharacteristic
896C5#8408411yescharacteristic, complemented, Sylow
897C22—21no—
898C22—21no—
899C22—21no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—52no—
904C22—52no—
905C22—101no—
906C22—101no—
907C22—101no—
908C22—101no—
909C22—102no—
910C22—204no—
911C22—208no—
912C22—201no—
913C22—201no—
914C22C2×D5×#6711yescharacteristic
915C4—21no—
916C4—22no—
917C4—52no—
918C4—101no—
919C4—102no—
920C4—121no—
921C4—121no—
922C4—601no—
923C4—601no—
924C4C2×D5×#6711yescharacteristic
925C4C2×D5×#6711yescharacteristic
926C3#1061195911yescharacteristic, complemented, Sylow
927C2—41no—
928C2—42no—
929C2—102no—
930C2—102no—
931C2—202no—
932C2#1175531511yescharacteristic
933C2D5×#95111yescharacteristic
934C2D5×#95311yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D5×#41C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3007
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×#91508C2semidirect
3. C2×#91484C2semidirect
4. D5×#924C2semidirect
5. #11751340C2semidirect
6. C5×#5239C2semidirect
7. #11749291C2semidirect
8. #11749290C2semidirect
9. #11749198C2semidirect
10. #11749045C2semidirect
11. #11749044C2semidirect
12. #11748951C2semidirect
13. #11748531C2semidirect
14. #11748528C2semidirect
15. #11748499C2semidirect
30. C2×D5×Dic6C22semidirect
31. C2×#6718C22semidirect
32. C2×#6716C22semidirect
33. #91813C22semidirect
34. C2×C5×#216C22semidirect
35. C2×C5×#214C22semidirect
36. C5×#924C22semidirect
41. D5×C4⋊Dic3C22semidirect
46. C2×#6662C22semidirect
47. C2×#6661C22semidirect
48. C2×#6657C22semidirect
49. C2×#6655C22semidirect
50. C2×#6649C22semidirect
51. C2×#6649C22semidirect
52. #91119C22semidirect
53. #91116C22semidirect
54. #91114C22semidirect
55. C5×#835C22semidirect
56. C5×#832C22semidirect
57. C5×#830C22semidirect
58. #90971C22semidirect
59. #90970C22semidirect
60. #90965C22semidirect
61. #90964C22semidirect
160. #5239D5semidirect
296. C2×#216C2×D5semidirect
300. C2×#214C2×D5semidirect
307. #924C2×D5semidirect
314. #835C2×D5semidirect
318. #832C2×D5semidirect
322. #830C2×D5semidirect
428. C2×C3×D5#137semidirect
704. C2×D5#951semidirect
790. C3×C5#3007semidirect
896. C5#84084semidirect
926. C3#10611959semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C2×#915082
C2×#914842
D5×#9242
#117513402
C5×#52392
#117492912
#117492902
#117491982
#117490452
#117490442
#117489512
#117485312
#117485282
#117484992
#106119593
#840845