Finite Group Databasebeta

← #14424191

Subgroups — #14424191

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
2D3×#4070C211yesmaximal, characteristic, complemented
3C2×#91274C211yesmaximal, characteristic, complemented
4C2×#91263C211yesmaximal, characteristic, complemented
5#11750834C211yesmaximal, characteristic, complemented
6C5×#4726C211yesmaximal, characteristic, complemented
7C3×#65022C211yesmaximal, characteristic, complemented
8#11748552C211yesmaximal, characteristic, complemented
9#11748531C211yesmaximal, characteristic, complemented
10#11748138C211yesmaximal, characteristic, complemented
11#11748133C211yesmaximal, characteristic, complemented
12#11748125C211yesmaximal, characteristic, complemented
13#11748120C211yesmaximal, characteristic, complemented
14#11748110C211yesmaximal, characteristic, complemented
15#11747608C211yesmaximal, characteristic, complemented
16#10610371—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C2×C3×#709C2211yescharacteristic
20C2×D3×C22⋊D5—21no—
21C2×#6779—21no—
22D3×#709—24no—
23D3×#709—24no—
24C2×D3×D20C2211yescharacteristic
25C2×C4×D3×D5—21no—
26C2×#6771—21no—
27C2×#6769C2211yescharacteristic
28C2×D3×Dic10C2211yescharacteristic
29C2×D3×Dic10C2211yescharacteristic, complemented
30C2×#6765C2211yescharacteristic
31#91813C2211yescharacteristic, complemented
32C2×Dic60C2211yescharacteristic, complemented
33C2×#6706C2211yescharacteristic, complemented
34C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
35C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
36C3×#4070C2211yescharacteristic, complemented
37C2×C3×Dic20C2211yescharacteristic, complemented
38C2×C3×#677C2211yescharacteristic, complemented
39#91575—21no—
40D3×C22⋊Dic5—21no—
41D3×C4⋊Dic5C2211yescharacteristic, complemented
42D3×#683—21no—
43#91369C2211yescharacteristic
44#91365C2211yescharacteristic
45#91352—21no—
46C2×#6662C2211yescharacteristic, complemented
47C2×#6662C2211yescharacteristic, complemented
48C2×#6658C2211yescharacteristic, complemented
49C2×#6657C2211yescharacteristic, complemented
50#91274—24no—
51#91263—24no—
52C3×C5×C22⋊C8C2211yescharacteristic, complemented
53#91105C2211yescharacteristic, complemented
54#91100C2211yescharacteristic, complemented
55C5×#830C2211yescharacteristic, complemented
56C5×(C2×D3)⋊C8C2211yescharacteristic
57C5×(C2×D3)⋊C8C2211yescharacteristic
58C3×#3953C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60#90974C2211yescharacteristic, complemented
61#90971C2211yescharacteristic, complemented
62#90968C2211yescharacteristic, complemented
63#90965C2211yescharacteristic, complemented
64#80228—51nomaximal, Hall
65C22×#709—31no—
66C2×#4070—31no—
67C2×#4055—31no—
68C2×#4055—31no—
69C5×#407—31no—
70#65422—31no—
71#65422—31no—
72#65028—31no—
73#65028—31no—
74#65022—31no—
75#65022—31no—
76#65022—31no—
77#65022D311yescharacteristic, complemented
78#65020—31no—
79#65020—31no—
80C23×C5×D3D411yescharacteristic
81C22×D3×D5—21no—
82C22×C3×C4×C5C2311yescharacteristic
83C2×#1220—21no—
84#6817—22no—
85#6817—22no—
86C2×D60C2311yescharacteristic
87C2×C4×D15—21no—
88C2×Dic30C2311yescharacteristic
89C2×Dic30C2311yescharacteristic
90C22×C5×Dic3D411yescharacteristic
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3—22no—
93C2×C4×C5×D3D411yescharacteristic
94C2×C4×C5×D3D411yescharacteristic
95C2×C4×C5×D3C2311yescharacteristic
96C2×C4×C5×D3C2311yescharacteristic
97C2×C3×C22⋊D5—21no—
98C3×#709—22no—
99C3×#709—22no—
100C2×C3×D20C2311yescharacteristic
101C2×C3×C4×D5—21no—
102C2×C3×Dic10C2311yescharacteristic
103C2×C3×Dic10C2311yescharacteristic
104D3×C22⋊D5—28no—
105C2×#1204—21no—
106C2×#1204—21no—
107C2×#1203—21no—
108C2×#1202—21no—
109C2×#1201—21no—
110C2×#1200—21no—
111C2×D3×Dic5—21no—
112C2×D3×Dic5—21no—
113C2×D3×Dic5—21no—
114#6779—28no—
115C2×D5×Dic3—21no—
116D3×D20—22no—
117D3×D20—22no—
118C4×D3×D5—28no—
119#6771—28no—
120#6769—22no—
121#6769D414yes—
122D3×Dic10—22no—
123D3×Dic10—22no—
124D3×Dic10—22no—
125D3×Dic10—22no—
126#6765—22no—
127#6765D414yes—
128C2×C3×C5×C8C2311yescharacteristic
129C2×C3×C5×C8C2311yescharacteristic
130#6719—21no—
131C4⋊Dic15C2311yescharacteristic
132#6712—21no—
133Dic60—22no—
134#6706—22no—
135C2×C5×C3⋊C8C2311yescharacteristic
136C2×C5×C3⋊C8C2311yescharacteristic
137C5×ΓL(1,𝔽25)—22no—
138C5×ΓL(1,𝔽25)—22no—
139C3×C22⋊Dic5—21no—
140C3×C4⋊Dic5C2311yescharacteristic
141C3×#683—21no—
142C3×Dic20—22no—
143C3×#677—22no—
144Dic3⋊Dic5—21no—
145#6669—21no—
146#6668—21no—
147(C2×D3)⋊Dic5—21no—
148(C2×D3)⋊Dic5—21no—
149#6662—22no—
150#6662—22no—
151#6658—22no—
152#6657—22no—
153C2×D3×#41—51no—
154C2×#918—51no—
155C2×#915—51no—
156D3×C22⋊Q8—51no—
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#4726D511yescharacteristic, complemented
168C23×C4×C5—31no—
169C22×C22⋊D5—61no—
170C2×#709—31no—
171C2×#709—31no—
172C2×#709—31no—
173C2×#709—61no—
174C2×#709—64no—
175C2×#709—64no—
176C2×#709—61no—
177C2×#709C2×D311yescharacteristic
178C22×D20—31no—
179C22×C4×D5—61no—
180C22×Dic10—31no—
181C22×Dic10—31no—
182C2×C5×M16—31no—
183C2×C5×M16—31no—
184C2×C22⋊Dic5—61no—
185C2×C4⋊Dic5—31no—
186#4070—31no—
187#4070—31no—
188#4070—31no—
189#4070—61no—
190#4070—61no—
191#4070C2×D311yescharacteristic, complemented
192C2×#683—61no—
193#4055—64no—
194#4055—64no—
195C2×Dic20—31no—
196C2×Dic20—31no—
197C2×Dic20—31no—
198C2×Dic20C2×D311yescharacteristic, complemented
199C2×#677—31no—
200C2×#677—31no—
201C2×#677—31no—
202C2×#677C2×D311yescharacteristic, complemented
203C5×C22⋊C8—31no—
204C5×C22⋊C8—31no—
205C5×C22⋊C8—31no—
206C5×C22⋊C8C2×D311yescharacteristic, complemented
207#3953—31no—
208#3953—31no—
209#3953—31no—
210#3953C2×D311yescharacteristic, complemented
211#3948—31no—
212#3948—31no—
213#3948—31no—
214#3948C2×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—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2411yescharacteristic
231#1220—24no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235D60—21no—
236D60C2×D412yes—
237C4×D15—24no—
238Dic30—21no—
239Dic30—21no—
240Dic30—21no—
241Dic30C2×D412yes—
242C2×C5×Dic3—22no—
243C2×C5×Dic3C2×D411yescharacteristic
244C2×C5×Dic3C2×D411yescharacteristic
245C4×C5×D3—22no—
246C4×C5×D3—21no—
247C4×C5×D3—21no—
248C4×C5×D3—22no—
249C4×C5×D3C2×D412yes—
250C4×C5×D3C2×D412yes—
251C3×C22⋊D5—24no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C3×D20—21no—
256C3×D20C2×D412yes—
257C3×C4×D5—24no—
258C3×Dic10—21no—
259C3×Dic10—21no—
260C3×Dic10—21no—
261C3×Dic10C2×D412yes—
262#1204—24no—
263#1204—42no—
264#1203—24no—
265#1202—24no—
266#1201—24no—
267#1200—24no—
268D3×Dic5—24no—
269D3×Dic5—42no—
270D3×Dic5—42no—
271D5×Dic3—24no—
272C3×C5×C8—21no—
273C3×C5×C8—21no—
274C5×C3⋊C8—21no—
275C5×C3⋊C8—21no—
276C2×C3×#41—51no—
277D3×#41—104no—
278D3×#41—104no—
279C2×#239—51no—
280C2×D3×Q8—51no—
281C2×D3×Q8—51no—
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⋊Q8—51no—
293#946—51no—
294C2×#216—51no—
295C2×#216—51no—
296C2×#215—51no—
297C2×#214—51no—
298#924—51no—
299#918—104no—
300#915—104no—
301C2×Dic12—51no—
302C2×#204—51no—
303C2×ΓL(1,𝔽25)C2×D511yescharacteristic, complemented
304C2×ΓL(1,𝔽25)C2×D511yescharacteristic, complemented
305#897—51no—
306#896—101no—
307D3×C4⋊C4—51no—
308D3×C4⋊C4—101no—
309D3×C22⋊C4—101no—
310#878—101no—
311C3×#103—51no—
312C3×#102—51no—
313C3×C22⋊C8C2×D511yescharacteristic, complemented
314#835—51no—
315#832—51no—
316#830C2×D511yescharacteristic, complemented
317#821—51no—
318(C2×D3)⋊C8C2×D511yescharacteristic
319(C2×D3)⋊C8C2×D511yescharacteristic
320#816—51no—
321#810—51no—
322#809—51no—
323C24×C5—31no—
324C23×D5—61no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×C4×C5—62no—
331C22×C4×C5—62no—
332C22×C4×C5C22×D311yescharacteristic
333C2×C22⋊D5—21no—
334C2×C22⋊D5—61no—
335C2×C22⋊D5—68no—
336C2×C22⋊D5—61no—
337C2×C22⋊D5—61no—
338C22×Dic5—61no—
339C22×Dic5—61no—
340C22×Dic5—61no—
341#709—22no—
342#709—22no—
343#709—34no—
344#709—34no—
345#709—62no—
346#709—62no—
347#709—68no—
348#709—62no—
349#709—62no—
350#709—68no—
351C2×D20—31no—
352C2×D20—62no—
353C2×D20—61no—
354C2×D20—62no—
355C2×D20C22×D311yescharacteristic
356C2×C4×D5—21no—
357C2×C4×D5—68no—
358C2×C4×D5—61no—
359C2×C4×D5—61no—
360C2×C4×D5—61no—
361C2×Dic10—31no—
362C2×Dic10—31no—
363C2×Dic10—62no—
364C2×Dic10—62no—
365C2×Dic10—62no—
366C2×Dic10—61no—
367C2×Dic10—62no—
368C2×Dic10—61no—
369C2×Dic10C22×D311yescharacteristic
370C2×Dic10C22×D311yescharacteristic
371C5×M16—62no—
372C5×M16—62no—
373C2×C5×C8—31no—
374C2×C5×C8—31no—
375C2×C5×C8C22×D311yescharacteristic
376C2×C5×C8C22×D311yescharacteristic
377C22⋊Dic5—21no—
378C22⋊Dic5—61no—
379C22⋊Dic5—61no—
380C22⋊Dic5—61no—
381C4⋊Dic5—31no—
382C4⋊Dic5—61no—
383C4⋊Dic5C22×D311yescharacteristic
384#683—21no—
385#683—61no—
386#683—61no—
387#683—61no—
388Dic20—22no—
389Dic20—62no—
390Dic20—62no—
391Dic20—62no—
392#677—22no—
393#677—62no—
394#677—62no—
395#677—62no—
396C22×#41—151no—
397C2×#137—151no—
398C2×#137—151no—
399C2×C22⋊Q8—151no—
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—31no—
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×C5C22×D411yescharacteristic
431C3×C4×C5C22×D411yescharacteristic
432Dic15—22no—
433Dic15—41no—
434Dic15—41no—
435C3×Dic5—22no—
436C3×Dic5—41no—
437C3×Dic5—41no—
438C5×Dic3—21no—
439C5×Dic3#12012yes—
440C23×D3—101no—
441C23×D3D2011yescharacteristic
442C3×#41—102no—
443C3×#41—102no—
444C2×C3×Q8—51no—
445C2×C3×Q8—51no—
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×Dic3D2011yescharacteristic
455#239—54no—
456#239—102no—
457D3×Q8—102no—
458D3×Q8—102no—
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—108no—
475C2×C4×D3—101no—
476C2×C4×D3—101no—
477C2×C4×D3—101no—
478C2×C4×D3—101no—
479C2×C4×D3—101no—
480C2×C4×D3D2011yescharacteristic
481C2×C4×D3D2011yescharacteristic
482C2×C4×D3C22×D511yescharacteristic
483C2×C4×D3C22×D511yescharacteristic
484C2×Dic6—51no—
485C2×Dic6—51no—
486C2×Dic6—101no—
487C2×Dic6—101no—
488C3×Q16—102no—
489C3×SD16—102no—
490C2×C3×C8C22×D511yescharacteristic
491C2×C3×C8C22×D511yescharacteristic
492C3×C4⋊C4—51no—
493C3×C4⋊C4—101no—
494C3×C22⋊C4—101no—
495#217—101no—
496#216—102no—
497#216—102no—
498#215—102no—
499#214—102no—
500(C2×D3)⋊C4—101no—
501(C2×D3)⋊C4—101no—
502C4⋊Dic3—51no—
503C4⋊Dic3—101no—
504Dic3⋊C4—101no—
505Dic3⋊C4—101no—
506Dic3⋊C4—101no—
507C2×C3⋊C8C22×D511yescharacteristic
508C2×C3⋊C8C22×D511yescharacteristic
509Dic12—102no—
510#204—102no—
511ΓL(1,𝔽25)—22no—
512ΓL(1,𝔽25)—22no—
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—
524C2×C4×C5—21no—
525C2×C4×C5—21no—
526C2×C4×C5—31no—
527C2×C4×C5—32no—
528C2×C4×C5—32no—
529C2×C4×C5—31no—
530C2×C4×C5—62no—
531C2×C4×C5—62no—
532C2×C4×C5—62no—
533C2×C4×C5—61no—
534C2×C4×C5—61no—
535C2×C4×C5D3×D411yescharacteristic
536C2×C4×C5C23×D311yescharacteristic
537C22⋊D5—24no—
538C22⋊D5—64no—
539C22⋊D5—64no—
540C22⋊D5—64no—
541C2×Dic5—21no—
542C2×Dic5—21no—
543C2×Dic5—21no—
544C2×Dic5—64no—
545C2×Dic5—61no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—122no—
549C2×Dic5—122no—
550D20—21no—
551D20—32no—
552D20—64no—
553D20—61no—
554D20D3×D412yes—
555C4×D5—24no—
556C4×D5—64no—
557C4×D5—64no—
558C4×D5—64no—
559Dic10—21no—
560Dic10—21no—
561Dic10—21no—
562Dic10—32no—
563Dic10—64no—
564Dic10—61no—
565Dic10—61no—
566Dic10—61no—
567Dic10—122no—
568Dic10D3×D412yes—
569C5×C8—21no—
570C5×C8—21no—
571C5×C8—61no—
572C5×C8—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—151no—
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—31no—
598C2×M16—31no—
599C22⋊Q8—51no—
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—51no—
609#103—151no—
610#103—151no—
611#103—151no—
612#102—51no—
613#102—151no—
614#102—151no—
615#102—151no—
616C22⋊C8—31no—
617C22⋊C8—31no—
618C22⋊C8—31no—
619C22⋊C8D3×D511yescharacteristic, complemented
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×D2011yescharacteristic
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—41no—
633C22×D3—104no—
634C22×D3—101no—
635C22×D3—202no—
636C22×D3—202no—
637C22×D3C2×D2011yescharacteristic
638C22×D3C2×D2011yescharacteristic
639C3×Q8—52no—
640C3×Q8—101no—
641C3×Q8—101no—
642C3×Q8—101no—
643C3×D4—52no—
644C3×D4—104no—
645C3×D4—101no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—104no—
649C2×C3×C4—101no—
650C2×C3×C4—101no—
651C2×C3×C4—101no—
652C2×C3×C4C2×D2011yescharacteristic
653C2×C3×C4C23×D511yescharacteristic
654#67—104no—
655#67—104no—
656#67—104no—
657C2×Dic3—22no—
658C2×Dic3—101no—
659C2×Dic3—104no—
660C2×Dic3—101no—
661C2×Dic3—101no—
662C2×Dic3C2×D2011yescharacteristic
663C2×Dic3C2×D2011yescharacteristic
664D12—52no—
665D12—104no—
666D12—101no—
667C4×D3—22no—
668C4×D3—21no—
669C4×D3—21no—
670C4×D3—22no—
671C4×D3—104no—
672C4×D3—104no—
673C4×D3—104no—
674C4×D3—202no—
675C4×D3—202no—
676C4×D3D4×D512yes—
677C4×D3D4×D512yes—
678Dic6—52no—
679Dic6—104no—
680Dic6—101no—
681Dic6—101no—
682Dic6—101no—
683Dic6—202no—
684C3×C8—21no—
685C3×C8—21no—
686C3⋊C8—21no—
687C3⋊C8—21no—
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—61no—
709C4×C5C2×D3×D411yescharacteristic
710C4×C5C2×D3×D411yescharacteristic
711Dic5—22no—
712Dic5—41no—
713Dic5—41no—
714Dic5—62no—
715Dic5—121no—
716Dic5—121no—
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—51no—
730C2×Q8—51no—
731C2×Q8—151no—
732C2×Q8—151no—
733C2×Q8—301no—
734C2×Q8—301no—
735C2×Q8—302no—
736C2×Q8—302no—
737C2×Q8—302no—
738C2×Q8—302no—
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—101no—
757C22×C4—301no—
758C22×C4—301no—
759C22×C4—308no—
760C22×C4—301no—
761C22×C4—301no—
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—62no—
774M16—62no—
775C2×C8—31no—
776C2×C8—31no—
777C2×C8C2×D3×D511yescharacteristic
778C2×C8C2×D3×D511yescharacteristic
779C4⋊C4—51no—
780C4⋊C4—101no—
781C4⋊C4—151no—
782C4⋊C4—301no—
783C4⋊C4—301no—
784C4⋊C4—301no—
785C4⋊C4—301no—
786C22⋊C4—101no—
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—102no—
795C22×C3—201no—
796C22×C3—201no—
797C22×C3C22×D2011yescharacteristic
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#402812yes—
808C2×D3#405512yescomplemented
809C3×C4—21no—
810C3×C4—102no—
811C3×C4—201no—
812C3×C4—201no—
813C3×C4C2×D4×D511yescharacteristic
814C3×C4C2×D4×D511yescharacteristic
815Dic3—21no—
816Dic3—102no—
817Dic3—201no—
818Dic3—201no—
819Dic3#402812yes—
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×D2011yescharacteristic
839Q8—52no—
840Q8—101no—
841Q8—101no—
842Q8—101no—
843Q8—152no—
844Q8—304no—
845Q8—301no—
846Q8—301no—
847Q8—301no—
848Q8—602no—
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—31no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—31no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—104no—
870C2×C4—101no—
871C2×C4—101no—
872C2×C4—101no—
873C2×C4—304no—
874C2×C4—304no—
875C2×C4—304no—
876C2×C4—304no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—602no—
881C2×C4—602no—
882C2×C4D3×D2011yescharacteristic
883C2×C4C22×D3×D511yescharacteristic
884C8—21no—
885C8—21no—
886C8—61no—
887C8—61no—
888C2×C3—41no—
889C2×C3—202no—
890C2×C3C2×#402811yescharacteristic
891C2×C3C2×#405511yescharacteristic
892C2×C3#6608211yescharacteristic
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×D2011yescharacteristic
915C4—21no—
916C4—32no—
917C4—61no—
918C4—102no—
919C4—201no—
920C4—201no—
921C4—302no—
922C4—601no—
923C4—601no—
924C4D3×D4×D511yescharacteristic
925C4D3×D4×D511yescharacteristic
926C3#1061037111yescharacteristic, complemented, Sylow
927C2—41no—
928C2—62no—
929C2—62no—
930C2—202no—
931C2—602no—
932C2D3×#402811yescharacteristic
933C2#1175396911yescharacteristic
934C2D3×#405511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×#709C2
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. D3×#4070C2semidirect
3. C2×#91274C2semidirect
4. C2×#91263C2semidirect
5. #11750834C2semidirect
6. C5×#4726C2semidirect
7. C3×#65022C2semidirect
8. #11748552C2semidirect
9. #11748531C2semidirect
10. #11748138C2semidirect
11. #11748133C2semidirect
12. #11748125C2semidirect
13. #11748120C2semidirect
14. #11748110C2semidirect
15. #11747608C2semidirect
29. C2×D3×Dic10C22semidirect
31. #91813C22semidirect
32. C2×Dic60C22semidirect
33. C2×#6706C22semidirect
34. C2×C5×ΓL(1,𝔽25)C22semidirect
35. C2×C5×ΓL(1,𝔽25)C22semidirect
36. C3×#4070C22semidirect
37. C2×C3×Dic20C22semidirect
38. C2×C3×#677C22semidirect
41. D3×C4⋊Dic5C22semidirect
46. C2×#6662C22semidirect
47. C2×#6662C22semidirect
48. C2×#6658C22semidirect
49. C2×#6657C22semidirect
52. C3×C5×C22⋊C8C22semidirect
53. #91105C22semidirect
54. #91100C22semidirect
55. C5×#830C22semidirect
58. C3×#3953C22semidirect
59. C3×#3948C22semidirect
60. #90974C22semidirect
61. #90971C22semidirect
62. #90968C22semidirect
63. #90965C22semidirect
77. #65022D3semidirect
167. #4726D5semidirect
191. #4070C2×D3semidirect
198. C2×Dic20C2×D3semidirect
202. C2×#677C2×D3semidirect
206. C5×C22⋊C8C2×D3semidirect
210. #3953C2×D3semidirect
214. #3948C2×D3semidirect
303. C2×ΓL(1,𝔽25)C2×D5semidirect
304. C2×ΓL(1,𝔽25)C2×D5semidirect
313. C3×C22⋊C8C2×D5semidirect
316. #830C2×D5semidirect
424. C2×C5×D3#137semidirect
619. C22⋊C8D3×D5semidirect
790. C3×C5#3007semidirect
808. C2×D3#4055semidirect
896. C5#80228semidirect
926. C3#10610371semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7092
D3×#40702
C2×#912742
C2×#912632
#117508342
C5×#47262
C3×#650222
#117485522
#117485312
#117481382
#117481332
#117481252
#117481202
#117481102
#117476082
#106103713
#802285