Finite Group Databasebeta

← #14424185

Subgroups — #14424185

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×D3×#709C211yesmaximal, characteristic
2C5×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×#91520C211yesmaximal, characteristic, complemented
4C2×#91518C211yesmaximal, characteristic, complemented
5#11751148C211yesmaximal, characteristic, complemented
6C3×#65336C211yesmaximal, characteristic, complemented
7#11749401C211yesmaximal, characteristic, complemented
8#11749398C211yesmaximal, characteristic, complemented
9#11748566C211yesmaximal, characteristic, complemented
10#11748528C211yesmaximal, characteristic, complemented
11#11748505C211yesmaximal, characteristic, complemented
12#11747505C211yesmaximal, characteristic, complemented
13#11747503C211yesmaximal, characteristic, complemented
14#11747495C211yesmaximal, characteristic, complemented
15#11747483C211yesmaximal, characteristic, complemented
16#10614466—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic, complemented
19C22×C4×C5×D3C2211yescharacteristic
20C2×C3×#709C2211yescharacteristic
21C2×D3×C22⋊D5—21no—
22C2×#6779—21no—
23D3×#709—24no—
24D3×#709—24no—
25C2×D3×D20C2211yescharacteristic
26C2×C4×D3×D5—21no—
27C2×#6771—21no—
28C2×#6769C2211yescharacteristic
29C2×D3×Dic10C2211yescharacteristic
30C2×#6765C2211yescharacteristic
31C3×C5×C22⋊Q8C2211yescharacteristic, complemented
32C2×#6718C2211yescharacteristic, complemented
33C2×#6717C2211yescharacteristic, complemented
34C5×#946C2211yescharacteristic
35C5×#924C2211yescharacteristic, complemented
36C5×#897C2211yescharacteristic
37C5×#896—21no—
38C5×D3×C4⋊C4—21no—
39C5×D3×C4⋊C4C2211yescharacteristic, complemented
40C5×D3×C22⋊C4—21no—
41C5×#878—21no—
42C2×C3×#689C2211yescharacteristic, complemented
43C2×C3×#688C2211yescharacteristic, complemented
44#91520—24no—
45#91518—24no—
46C2×#6663C2211yescharacteristic, complemented
47C2×#6661C2211yescharacteristic, complemented
48C2×#6660C2211yescharacteristic, complemented
49C2×#6655C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51C2×#6650C2211yescharacteristic, complemented
52#91114C2211yescharacteristic, complemented
53#91094C2211yescharacteristic, complemented
54#91093C2211yescharacteristic, complemented
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic, complemented
58#90975C2211yescharacteristic, complemented
59#90970C2211yescharacteristic, complemented
60#90969C2211yescharacteristic, complemented
61#90964C2211yescharacteristic, complemented
62(C2×D3)⋊#168C2211yescharacteristic
63(C2×D3)⋊#168C2211yescharacteristic
64#80228—51nomaximal, Hall
65C22×#709—31no—
66C2×C5×C22⋊Q8—31no—
67C2×#4088—31no—
68C2×#4088—31no—
69#65496—31no—
70#65339—31no—
71#65339—31no—
72#65336—31no—
73#65336—31no—
74#65336—31no—
75#65336D311yescharacteristic, complemented
76#65335—31no—
77#65335—31no—
78#65255—31no—
79#65255—31no—
80C23×C5×D3D411yescharacteristic
81C22×D3×D5—21no—
82C2×C3×C5×Q8C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×#1220—21no—
85#6817—22no—
86#6817—22no—
87C2×D60C2311yescharacteristic
88C2×C4×D15—21no—
89C2×Dic30C2311yescharacteristic
90C22×C5×Dic3D411yescharacteristic
91C5×D3×Q8—22no—
92C5×D3×Q8—22no—
93C2×C4×C5×D3—22no—
94C2×C4×C5×D3—22no—
95C2×C4×C5×D3—21no—
96C2×C4×C5×D3—21no—
97C2×C4×C5×D3D411yescharacteristic
98C2×C4×C5×D3D411yescharacteristic
99C2×C4×C5×D3C2311yescharacteristic
100C2×C4×C5×D3C2311yescharacteristic
101C2×C5×Dic6—21no—
102C2×C5×Dic6C2311yescharacteristic
103C2×C3×C22⋊D5—21no—
104C3×#709—22no—
105C3×#709—22no—
106C2×C3×D20C2311yescharacteristic
107C2×C3×C4×D5—21no—
108C2×C3×Dic10C2311yescharacteristic
109D3×C22⋊D5—28no—
110C2×#1204—21no—
111C2×#1203—21no—
112C2×#1202—21no—
113C2×#1201—21no—
114C2×#1200—21no—
115C2×D3×Dic5—21no—
116#6779—28no—
117C2×D5×Dic3—21no—
118D3×D20—22no—
119D3×D20—22no—
120C4×D3×D5—28no—
121#6771—28no—
122#6769—22no—
123#6769D414yes—
124D3×Dic10—22no—
125D3×Dic10—22no—
126#6765—22no—
127#6765D414yes—
128C3×C5×C4⋊C4—21no—
129C3×C5×C4⋊C4C2311yescharacteristic
130C3×C5×C22⋊C4—21no—
131#6718—22no—
132#6717—22no—
133C2×C3⋊#168C2311yescharacteristic
134C2×C3⋊#168C2311yescharacteristic
135C5×#217—21no—
136C5×(C2×D3)⋊C4—21no—
137C5×(C2×D3)⋊C4—21no—
138C5×C4⋊Dic3—21no—
139C5×C4⋊Dic3C2311yescharacteristic
140C5×Dic3⋊C4—21no—
141C5×Dic3⋊C4—21no—
142C5×Dic3⋊C4—21no—
143C3×#689—22no—
144C3×#688—22no—
145C2×C3×#168C2311yescharacteristic
146C2×C3×#168C2311yescharacteristic
147#6663—22no—
148#6661—22no—
149#6660—22no—
150#6655—22no—
151#6650—22no—
152#6650—22no—
153C2×D3×#41—51no—
154C2×#918—51no—
155C2×#915—51no—
156D3×C22⋊Q8D511yescharacteristic, complemented
157C3×#452—51no—
158#5239—51no—
159#5186—51no—
160#5169—51no—
161#5047—51no—
162#4809—51no—
163#4803—51no—
164#4776—51no—
165#4771—51no—
166#4733—51no—
167#4726—51no—
168C22×C5×Q8—31no—
169C23×C4×C5—31no—
170C22×C22⋊D5—61no—
171C2×#709—31no—
172C2×#709—31no—
173C2×#709—31no—
174C2×#709—61no—
175C2×#709—64no—
176C2×#709—64no—
177C2×#709—61no—
178C2×#709C2×D311yescharacteristic
179C22×D20—31no—
180C22×C4×D5—61no—
181C22×Dic10—31no—
182C5×C22⋊Q8—31no—
183C5×C22⋊Q8—31no—
184C5×C22⋊Q8—31no—
185C5×C22⋊Q8—61no—
186C5×C22⋊Q8—61no—
187C5×C22⋊Q8C2×D311yescharacteristic, complemented
188C2×C5×C4⋊C4—31no—
189C2×C5×C4⋊C4—61no—
190C2×C5×C22⋊C4—61no—
191C2×#689—31no—
192C2×#689—31no—
193C2×#689—31no—
194C2×#689C2×D311yescharacteristic, complemented
195#4088—64no—
196#4088—64no—
197C2×#688—31no—
198C2×#688—31no—
199C2×#688—31no—
200C2×#688C2×D311yescharacteristic, complemented
201C2×#681—31no—
202C2×#681—31no—
203C22⋊#168—31no—
204C22⋊#168—31no—
205C22⋊#168—31no—
206C22⋊#168C2×D311yescharacteristic, complemented
207#3942—31no—
208#3942—31no—
209#3942—31no—
210#3942C2×D311yescharacteristic, complemented
211#3941—31no—
212#3941—31no—
213#3941—31no—
214#3941C2×D311yescharacteristic, complemented
215#3007—151noSylow
216C23×C3×C5C2×D411yescharacteristic
217C22×D15—21no—
218C22×C5×D3—22no—
219C22×C5×D3—22no—
220C22×C5×D3—41no—
221C22×C5×D3C2×D411yescharacteristic
222C22×C5×D3C2×D411yescharacteristic
223C22×C3×D5—21no—
224C2×D3×D5—24no—
225C2×D3×D5—42no—
226C2×D3×D5—42no—
227C3×C5×Q8—21no—
228C3×C5×Q8—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5C2×D411yescharacteristic
234C2×C3×C4×C5C2411yescharacteristic
235#1220—24no—
236C2×Dic15—21no—
237D60—21no—
238D60C2×D412yes—
239C4×D15—24no—
240Dic30—21no—
241Dic30C2×D412yes—
242C2×C5×Dic3—22no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3C2×D411yescharacteristic
246C2×C5×Dic3C2×D411yescharacteristic
247C4×C5×D3—22no—
248C4×C5×D3—21no—
249C4×C5×D3—21no—
250C4×C5×D3—22no—
251C4×C5×D3—42no—
252C4×C5×D3—42no—
253C4×C5×D3C2×D412yes—
254C4×C5×D3C2×D412yes—
255C5×Dic6—21no—
256C5×Dic6—21no—
257C5×Dic6—42no—
258C3×C22⋊D5—24no—
259C2×C3×Dic5—21no—
260C3×D20—21no—
261C3×D20C2×D412yes—
262C3×C4×D5—24no—
263C3×Dic10—21no—
264C3×Dic10C2×D412yes—
265#1204—24no—
266#1203—24no—
267#1202—24no—
268#1201—24no—
269#1200—24no—
270D3×Dic5—24no—
271D5×Dic3—24no—
272C3⋊#168—21no—
273C3⋊#168—21no—
274C3×#168—21no—
275C3×#168—21no—
276C2×C3×#41—51no—
277D3×#41—104no—
278D3×#41—104no—
279C2×#239—51no—
280C2×D3×Q8—51no—
281C2×D3×Q8C2×D511yescharacteristic, complemented
282C2×#237—51no—
283C2×#237—101no—
284C2×D3×D4—51no—
285C2×D3×D4—101no—
286C2×#235—51no—
287C2×#235—101no—
288C22×C4×D3—101no—
289C22×C4×D3C2×D511yescharacteristic
290C2×C3×Q16—51no—
291C2×C3×SD16—51no—
292C3×C22⋊Q8C2×D511yescharacteristic, complemented
293#946C2×D511yescharacteristic
294C2×#216—51no—
295C2×#216—51no—
296C2×#215—51no—
297C2×#214—51no—
298#924C2×D511yescharacteristic, complemented
299#918—104no—
300#915—104no—
301C2×Dic12—51no—
302C2×#204—51no—
303C2×ΓL(1,𝔽25)—51no—
304C2×ΓL(1,𝔽25)—51no—
305#897C2×D511yescharacteristic
306#896—21no—
307D3×C4⋊C4—21no—
308D3×C4⋊C4C2×D511yescharacteristic, complemented
309D3×C22⋊C4—21no—
310#878—21no—
311C3×#103—51no—
312C3×#102—51no—
313C3×C22⋊C8—51no—
314#835—51no—
315#832—51no—
316#830—51no—
317#821—51no—
318(C2×D3)⋊C8—51no—
319(C2×D3)⋊C8—51no—
320#816—51no—
321#810—51no—
322#809—51no—
323C24×C5—31no—
324C23×D5—61no—
325C2×C5×Q8—31no—
326C2×C5×Q8—61no—
327C2×C5×Q8—62no—
328C2×C5×Q8—62no—
329C2×C5×Q8C22×D311yescharacteristic
330C22×C4×C5—31no—
331C22×C4×C5—31no—
332C22×C4×C5—31no—
333C22×C4×C5—31no—
334C22×C4×C5—31no—
335C22×C4×C5—62no—
336C22×C4×C5—62no—
337C22×C4×C5—61no—
338C22×C4×C5—61no—
339C22×C4×C5C22×D311yescharacteristic
340C2×C22⋊D5—21no—
341C2×C22⋊D5—61no—
342C2×C22⋊D5—68no—
343C2×C22⋊D5—61no—
344C2×C22⋊D5—61no—
345C22×Dic5—61no—
346#709—22no—
347#709—22no—
348#709—34no—
349#709—34no—
350#709—62no—
351#709—62no—
352#709—68no—
353#709—62no—
354#709—62no—
355#709—68no—
356C2×D20—31no—
357C2×D20—62no—
358C2×D20—61no—
359C2×D20—62no—
360C2×D20C22×D311yescharacteristic
361C2×C4×D5—21no—
362C2×C4×D5—68no—
363C2×C4×D5—61no—
364C2×C4×D5—61no—
365C2×C4×D5—61no—
366C2×Dic10—31no—
367C2×Dic10—62no—
368C2×Dic10—61no—
369C2×Dic10—62no—
370C2×Dic10C22×D311yescharacteristic
371C5×C4⋊C4—21no—
372C5×C4⋊C4—31no—
373C5×C4⋊C4—61no—
374C5×C4⋊C4—61no—
375C5×C4⋊C4—61no—
376C5×C4⋊C4—61no—
377C5×C4⋊C4C22×D311yescharacteristic
378C5×C22⋊C4—21no—
379C5×C22⋊C4—61no—
380C5×C22⋊C4—61no—
381C5×C22⋊C4—61no—
382#689—22no—
383#689—62no—
384#689—62no—
385#689—62no—
386#688—22no—
387#688—62no—
388#688—62no—
389#688—62no—
390#681—62no—
391#681—62no—
392C2×#168—31no—
393C2×#168—31no—
394C2×#168C22×D311yescharacteristic
395C2×#168C22×D311yescharacteristic
396C22×#41—151no—
397C2×#137—151no—
398C2×#137—151no—
399C2×C22⋊Q8—31no—
400#452—51no—
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—21no—
413C22×C3×C5—21no—
414C22×C3×C5C22×D411yescharacteristic
415C2×D15—22no—
416C2×D15—41no—
417C2×D15—41no—
418C2×C5×D3—21no—
419C2×C5×D3—21no—
420C2×C5×D3—21no—
421C2×C5×D3—21no—
422C2×C5×D3—44no—
423C2×C5×D3#12012yes—
424C2×C5×D3#13712yescomplemented
425C2×C3×D5—22no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428D3×D5—48no—
429C3×C4×C5—21no—
430C3×C4×C5—41no—
431C3×C4×C5—41no—
432C3×C4×C5C22×D411yescharacteristic
433C3×C4×C5C22×D411yescharacteristic
434Dic15—22no—
435C3×Dic5—22no—
436C5×Dic3—21no—
437C5×Dic3—41no—
438C5×Dic3—41no—
439C5×Dic3#12012yes—
440C23×D3—101no—
441C23×D3C22⋊D511yescharacteristic
442C3×#41—102no—
443C3×#41—102no—
444C2×C3×Q8—51no—
445C2×C3×Q8C22×D511yescharacteristic
446C2×C3×D4—51no—
447C2×C3×D4—101no—
448C22×C3×C4—101no—
449C22×C3×C4C22×D511yescharacteristic
450C2×#67—101no—
451C2×#67—101no—
452C2×#67—101no—
453C22×Dic3—101no—
454C22×Dic3C22⋊D511yescharacteristic
455#239—54no—
456#239—102no—
457D3×Q8—22no—
458D3×Q8—22no—
459D3×Q8—102no—
460D3×Q8—102no—
461#237—54no—
462#237—108no—
463#237—102no—
464D3×D4—102no—
465D3×D4—102no—
466D3×D4—108no—
467#235—102no—
468#235—108no—
469#235—102no—
470C2×D12—51no—
471C2×D12—101no—
472C2×C4×D3—22no—
473C2×C4×D3—22no—
474C2×C4×D3—21no—
475C2×C4×D3—21no—
476C2×C4×D3—108no—
477C2×C4×D3—101no—
478C2×C4×D3—101no—
479C2×C4×D3—101no—
480C2×C4×D3C22⋊D511yescharacteristic
481C2×C4×D3C22⋊D511yescharacteristic
482C2×C4×D3C22×D511yescharacteristic
483C2×C4×D3C22×D511yescharacteristic
484C2×Dic6—21no—
485C2×Dic6—51no—
486C2×Dic6—101no—
487C2×Dic6C22×D511yescharacteristic
488C3×Q16—102no—
489C3×SD16—102no—
490C2×C3×C8—51no—
491C2×C3×C8—51no—
492C3×C4⋊C4—21no—
493C3×C4⋊C4C22×D511yescharacteristic
494C3×C22⋊C4—21no—
495#217—21no—
496#216—102no—
497#216—102no—
498#215—102no—
499#214—102no—
500(C2×D3)⋊C4—21no—
501(C2×D3)⋊C4—21no—
502C4⋊Dic3—21no—
503C4⋊Dic3C22×D511yescharacteristic
504Dic3⋊C4—21no—
505Dic3⋊C4—21no—
506Dic3⋊C4—21no—
507C2×C3⋊C8—51no—
508C2×C3⋊C8—51no—
509Dic12—102no—
510#204—102no—
511ΓL(1,𝔽25)—102no—
512ΓL(1,𝔽25)—102no—
513C23×C5—31no—
514C23×C5—31no—
515C23×C5—62no—
516C23×C5—62no—
517C23×C5—121no—
518C23×C5D3×D411yescharacteristic
519C22×D5—21no—
520C22×D5—64no—
521C22×D5—61no—
522C22×D5—122no—
523C22×D5—122no—
524C5×Q8—21no—
525C5×Q8—21no—
526C5×Q8—61no—
527C5×Q8—61no—
528C5×Q8—122no—
529C2×C4×C5—21no—
530C2×C4×C5—21no—
531C2×C4×C5—21no—
532C2×C4×C5—21no—
533C2×C4×C5—31no—
534C2×C4×C5—32no—
535C2×C4×C5—32no—
536C2×C4×C5—31no—
537C2×C4×C5—62no—
538C2×C4×C5—62no—
539C2×C4×C5—62no—
540C2×C4×C5—61no—
541C2×C4×C5—61no—
542C2×C4×C5—61no—
543C2×C4×C5—61no—
544C2×C4×C5—122no—
545C2×C4×C5—122no—
546C2×C4×C5D3×D411yescharacteristic
547C2×C4×C5C23×D311yescharacteristic
548C22⋊D5—24no—
549C22⋊D5—64no—
550C22⋊D5—64no—
551C22⋊D5—64no—
552C2×Dic5—21no—
553C2×Dic5—64no—
554C2×Dic5—61no—
555D20—21no—
556D20—32no—
557D20—64no—
558D20—61no—
559D20D3×D412yes—
560C4×D5—24no—
561C4×D5—64no—
562C4×D5—64no—
563C4×D5—64no—
564Dic10—21no—
565Dic10—32no—
566Dic10—64no—
567Dic10—61no—
568Dic10D3×D412yes—
569#168—21no—
570#168—21no—
571#168—61no—
572#168—61no—
573C2×#41—51no—
574C2×#41—151no—
575C2×#41—151no—
576C2×#41—151no—
577C2×#41—301no—
578C2×#41—301no—
579C2×#41—304no—
580C2×#41—304no—
581C22×Q8—31no—
582C22×Q8—151no—
583C22×D4—151no—
584C22×D4—301no—
585C23×C4—31no—
586C23×C4—301no—
587#137—304no—
588#137—304no—
589C2×Q16—51no—
590C2×Q16—151no—
591C2×Q16—151no—
592C2×Q16—151no—
593C2×SD16—51no—
594C2×SD16—151no—
595C2×SD16—151no—
596C2×SD16—151no—
597C2×M16—151no—
598C2×M16—151no—
599C22⋊Q8—31no—
600C22⋊Q8—31no—
601C22⋊Q8—31no—
602C22⋊Q8—61no—
603C22⋊Q8—61no—
604C22⋊Q8D3×D511yescharacteristic, complemented
605C2×C4⋊C4—31no—
606C2×C4⋊C4—61no—
607C2×C22⋊C4—61no—
608#103—51no—
609#103—151no—
610#103—151no—
611#103—151no—
612#102—51no—
613#102—151no—
614#102—151no—
615#102—151no—
616C22⋊C8—51no—
617C22⋊C8—151no—
618C22⋊C8—151no—
619C22⋊C8—151no—
620C2×C3×C5—41no—
621C2×C3×C5C2×#12011yescharacteristic
622C2×C3×C5C2×#13711yescharacteristic
623C2×C3×C5#57511yescharacteristic
624D15—42no—
625C3×D5—42no—
626C5×D3—22no—
627C5×D3—22no—
628C23×C3—101no—
629C23×C3C2×C22⋊D511yescharacteristic
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—41no—
633C22×D3—104no—
634C22×D3—101no—
635C22×D3—202no—
636C22×D3—202no—
637C22×D3C2×C22⋊D511yescharacteristic
638C22×D3C2×C22⋊D511yescharacteristic
639C3×Q8—21no—
640C3×Q8—21no—
641C3×Q8—52no—
642C3×Q8—101no—
643C3×D4—52no—
644C3×D4—104no—
645C3×D4—101no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—104no—
651C2×C3×C4—101no—
652C2×C3×C4C2×C22⋊D511yescharacteristic
653C2×C3×C4C23×D511yescharacteristic
654#67—104no—
655#67—104no—
656#67—104no—
657C2×Dic3—22no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—101no—
661C2×Dic3—104no—
662C2×Dic3C2×C22⋊D511yescharacteristic
663C2×Dic3C2×C22⋊D511yescharacteristic
664D12—52no—
665D12—104no—
666D12—101no—
667C4×D3—22no—
668C4×D3—21no—
669C4×D3—21no—
670C4×D3—22no—
671C4×D3—42no—
672C4×D3—42no—
673C4×D3—104no—
674C4×D3—104no—
675C4×D3—104no—
676C4×D3D4×D512yes—
677C4×D3D4×D512yes—
678Dic6—21no—
679Dic6—21no—
680Dic6—42no—
681Dic6—52no—
682Dic6—104no—
683Dic6—101no—
684C3×C8—101no—
685C3×C8—101no—
686C3⋊C8—101no—
687C3⋊C8—101no—
688C22×C5—21no—
689C22×C5—21no—
690C22×C5—21no—
691C22×C5—32no—
692C22×C5—32no—
693C22×C5—61no—
694C22×C5—61no—
695C22×C5—61no—
696C22×C5—61no—
697C22×C5—124no—
698C22×C5C2×D3×D411yescharacteristic
699C2×D5—22no—
700C2×D5—41no—
701C2×D5—41no—
702C2×D5—62no—
703C2×D5—128no—
704C2×D5—121no—
705C2×D5—121no—
706C4×C5—21no—
707C4×C5—32no—
708C4×C5—41no—
709C4×C5—41no—
710C4×C5—61no—
711C4×C5—121no—
712C4×C5—121no—
713C4×C5C2×D3×D411yescharacteristic
714C4×C5C2×D3×D411yescharacteristic
715Dic5—22no—
716Dic5—62no—
717C24—31no—
718C24—301no—
719#41—102no—
720#41—102no—
721#41—154no—
722#41—154no—
723#41—302no—
724#41—302no—
725#41—302no—
726#41—302no—
727#41—308no—
728#41—308no—
729C2×Q8—31no—
730C2×Q8—51no—
731C2×Q8—61no—
732C2×Q8—62no—
733C2×Q8—62no—
734C2×Q8—151no—
735C2×Q8—301no—
736C2×Q8—302no—
737C2×Q8—302no—
738C2×Q8C2×D3×D511yescharacteristic
739C2×D4—51no—
740C2×D4—101no—
741C2×D4—151no—
742C2×D4—301no—
743C2×D4—302no—
744C2×D4—302no—
745C2×D4—301no—
746C2×D4—308no—
747C2×D4—301no—
748C2×D4—301no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—62no—
755C22×C4—62no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—101no—
759C22×C4—301no—
760C22×C4—301no—
761C22×C4—308no—
762C22×C4—301no—
763C22×C4—301no—
764C22×C4C2×D3×D511yescharacteristic
765Q16—102no—
766Q16—302no—
767Q16—302no—
768Q16—302no—
769SD16—102no—
770SD16—302no—
771SD16—302no—
772SD16—302no—
773M16—302no—
774M16—302no—
775C2×C8—51no—
776C2×C8—51no—
777C2×C8—151no—
778C2×C8—151no—
779C4⋊C4—21no—
780C4⋊C4—31no—
781C4⋊C4—61no—
782C4⋊C4—61no—
783C4⋊C4—61no—
784C4⋊C4—61no—
785C4⋊C4C2×D3×D511yescharacteristic
786C22⋊C4—21no—
787C22⋊C4—61no—
788C22⋊C4—61no—
789C22⋊C4—61no—
790C3×C5#300711yescharacteristic, complemented, Hall
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—102no—
795C22×C3—201no—
796C22×C3—201no—
797C22×C3C22×C22⋊D511yescharacteristic
798C2×D3—21no—
799C2×D3—21no—
800C2×D3—21no—
801C2×D3—21no—
802C2×D3—44no—
803C2×D3—102no—
804C2×D3—208no—
805C2×D3—201no—
806C2×D3—201no—
807C2×D3#408312yes—
808C2×D3#408812yescomplemented
809C3×C4—21no—
810C3×C4—41no—
811C3×C4—41no—
812C3×C4—102no—
813C3×C4C2×D4×D511yescharacteristic
814C3×C4C2×D4×D511yescharacteristic
815Dic3—21no—
816Dic3—41no—
817Dic3—41no—
818Dic3—102no—
819Dic3#408312yes—
820C2×C5—41no—
821C2×C5—62no—
822C2×C5—62no—
823C2×C5D3×#12011yescharacteristic
824C2×C5#576811yescharacteristic
825C2×C5D3×#13711yescharacteristic
826D5—42no—
827D5—122no—
828C23—31no—
829C23—31no—
830C23—62no—
831C23—62no—
832C23—101no—
833C23—121no—
834C23—304no—
835C23—301no—
836C23—602no—
837C23—602no—
838C23D3×C22⋊D511yescharacteristic
839Q8—21no—
840Q8—21no—
841Q8—52no—
842Q8—61no—
843Q8—61no—
844Q8—101no—
845Q8—122no—
846Q8—152no—
847Q8—304no—
848Q8—301no—
849D4—52no—
850D4—104no—
851D4—101no—
852D4—152no—
853D4—304no—
854D4—304no—
855D4—304no—
856D4—304no—
857D4—301no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—31no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—31no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—104no—
874C2×C4—101no—
875C2×C4—122no—
876C2×C4—122no—
877C2×C4—304no—
878C2×C4—304no—
879C2×C4—304no—
880C2×C4—304no—
881C2×C4—301no—
882C2×C4D3×C22⋊D511yescharacteristic
883C2×C4C22×D3×D511yescharacteristic
884C8—101no—
885C8—101no—
886C8—301no—
887C8—301no—
888C2×C3—41no—
889C2×C3—202no—
890C2×C3C2×#408311yescharacteristic
891C2×C3C2×#408811yescharacteristic
892C2×C3#6615611yescharacteristic
893D3—22no—
894D3—22no—
895D3—202no—
896C5#8022811yescharacteristic, complemented, Sylow
897C22—21no—
898C22—21no—
899C22—21no—
900C22—32no—
901C22—32no—
902C22—61no—
903C22—61no—
904C22—61no—
905C22—61no—
906C22—102no—
907C22—124no—
908C22—201no—
909C22—201no—
910C22—302no—
911C22—608no—
912C22—601no—
913C22—601no—
914C22C2×D3×C22⋊D511yescharacteristic
915C4—21no—
916C4—32no—
917C4—41no—
918C4—41no—
919C4—61no—
920C4—102no—
921C4—121no—
922C4—121no—
923C4—302no—
924C4D3×D4×D511yescharacteristic
925C4D3×D4×D511yescharacteristic
926C3#1061446611yescharacteristic, complemented, Sylow
927C2—41no—
928C2—62no—
929C2—62no—
930C2—202no—
931C2—602no—
932C2D3×#408311yescharacteristic
933C2D3×#408811yescharacteristic
934C2#1175532211yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×#709C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3007
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
2. C5×D3×C22⋊Q8C2semidirect
3. C2×#91520C2semidirect
4. C2×#91518C2semidirect
5. #11751148C2semidirect
6. C3×#65336C2semidirect
7. #11749401C2semidirect
8. #11749398C2semidirect
9. #11748566C2semidirect
10. #11748528C2semidirect
11. #11748505C2semidirect
12. #11747505C2semidirect
13. #11747503C2semidirect
14. #11747495C2semidirect
15. #11747483C2semidirect
18. C2×C5×D3×Q8C22semidirect
31. C3×C5×C22⋊Q8C22semidirect
32. C2×#6718C22semidirect
33. C2×#6717C22semidirect
35. C5×#924C22semidirect
39. C5×D3×C4⋊C4C22semidirect
42. C2×C3×#689C22semidirect
43. C2×C3×#688C22semidirect
46. C2×#6663C22semidirect
47. C2×#6661C22semidirect
48. C2×#6660C22semidirect
49. C2×#6655C22semidirect
50. C2×#6650C22semidirect
51. C2×#6650C22semidirect
52. #91114C22semidirect
53. #91094C22semidirect
54. #91093C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3942C22semidirect
57. C3×#3941C22semidirect
58. #90975C22semidirect
59. #90970C22semidirect
60. #90969C22semidirect
61. #90964C22semidirect
75. #65336D3semidirect
156. D3×C22⋊Q8D5semidirect
187. C5×C22⋊Q8C2×D3semidirect
194. C2×#689C2×D3semidirect
200. C2×#688C2×D3semidirect
206. C22⋊#168C2×D3semidirect
210. #3942C2×D3semidirect
214. #3941C2×D3semidirect
281. C2×D3×Q8C2×D5semidirect
292. C3×C22⋊Q8C2×D5semidirect
298. #924C2×D5semidirect
308. D3×C4⋊C4C2×D5semidirect
424. C2×C5×D3#137semidirect
604. C22⋊Q8D3×D5semidirect
790. C3×C5#3007semidirect
808. C2×D3#4088semidirect
896. C5#80228semidirect
926. C3#10614466semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7092
C5×D3×C22⋊Q82
C2×#915202
C2×#915182
#117511482
C3×#653362
#117494012
#117493982
#117485662
#117485282
#117485052
#117475052
#117475032
#117474952
#117474832
#106144663
#802285