Finite Group Databasebeta

← #14424188

Subgroups — #14424188

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×C5×D3×#41C211yesmaximal, characteristic
2C2×#91510C211yesmaximal, characteristic, complemented
3C2×#91486C211yesmaximal, characteristic, complemented
4D3×#4070C211yesmaximal, characteristic, complemented
5#11751340C211yesmaximal, characteristic, complemented
6C3×#65528C211yesmaximal, characteristic, complemented
7#11749304C211yesmaximal, characteristic, complemented
8#11749302C211yesmaximal, characteristic, complemented
9#11749201C211yesmaximal, characteristic, complemented
10#11749058C211yesmaximal, characteristic, complemented
11#11749056C211yesmaximal, characteristic, complemented
12#11748955C211yesmaximal, characteristic, complemented
13#11748538C211yesmaximal, characteristic, complemented
14#11748505C211yesmaximal, characteristic, complemented
15#11748361C211yesmaximal, characteristic, complemented
16#10615815—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C5×D3×#41—24no—
19C5×D3×#41—24no—
20C2×C5×#239C2211yescharacteristic
21C2×C5×D3×Q8C2211yescharacteristic
22C2×C5×#237—21no—
23C2×C5×#237C2211yescharacteristic
24C2×C5×D3×D4—21no—
25C2×C5×D3×D4C2211yescharacteristic
26C2×C5×#235—21no—
27C2×C5×#235C2211yescharacteristic
28C22×C4×C5×D3—21no—
29C22×C4×C5×D3C2211yescharacteristic
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#91575—21no—
38D3×C22⋊Dic5—21no—
39#91510—24no—
40#91486—24no—
41D3×C4⋊Dic5C2211yescharacteristic, complemented
42D3×#683—21no—
43#91369C2211yescharacteristic
44#91365C2211yescharacteristic
45#91352—21no—
46C2×#6663C2211yescharacteristic, complemented
47C2×#6661C2211yescharacteristic, complemented
48C2×#6659C2211yescharacteristic, complemented
49C2×#6656C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51C2×#6650C2211yescharacteristic, complemented
52#91119C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55C3×#3967C2211yescharacteristic, complemented
56C3×#3964C2211yescharacteristic, complemented
57C3×C22⋊#168C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90972C2211yescharacteristic, complemented
60#90967C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62(C2×D3)⋊#168C2211yescharacteristic
63(C2×D3)⋊#168C2211yescharacteristic
64#80228—51nomaximal, Hall
65C22×C5×#41—31no—
66C2×#4097—31no—
67C2×#4097—31no—
68C2×#4070—31no—
69#65528—31no—
70#65528—31no—
71#65528—31no—
72#65528D311yescharacteristic, complemented
73#65521—31no—
74#65521—31no—
75#65517—31no—
76#65517—31no—
77#65507—31no—
78#65507—31no—
79#65496—31no—
80C23×C5×D3—21no—
81C23×C5×D3D411yescharacteristic
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×#67—21no—
91C2×C5×#67—21no—
92C2×C5×#67—21no—
93C22×C5×Dic3—21no—
94C22×C5×Dic3D411yescharacteristic
95C5×#239—22no—
96C5×#239D414yes—
97C5×D3×Q8—22no—
98C5×D3×Q8—22no—
99C5×#237—28no—
100C5×#237—22no—
101C5×#237D414yes—
102C5×D3×D4—28no—
103C5×D3×D4—22no—
104C5×D3×D4—22no—
105C5×#235—28no—
106C5×#235—22no—
107C5×#235—22no—
108C2×C5×D12—21no—
109C2×C5×D12C2311yescharacteristic
110C2×C4×C5×D3—28no—
111C2×C4×C5×D3—21no—
112C2×C4×C5×D3—21no—
113C2×C4×C5×D3—21no—
114C2×C4×C5×D3—22no—
115C2×C4×C5×D3—22no—
116C2×C4×C5×D3D411yescharacteristic
117C2×C4×C5×D3D411yescharacteristic
118C2×C4×C5×D3C2311yescharacteristic
119C2×C4×C5×D3C2311yescharacteristic
120C2×C5×Dic6—21no—
121C2×C5×Dic6C2311yescharacteristic
122C2×C3×Dic10C2311yescharacteristic
123C2×#1204—21no—
124C2×D3×Dic5—21no—
125C2×D3×Dic5—21no—
126D3×Dic10—22no—
127D3×Dic10—22no—
128#6719—21no—
129#6718—22no—
130#6716—22no—
131C4⋊Dic15C2311yescharacteristic
132#6712—21no—
133C2×C3⋊#168C2311yescharacteristic
134C2×C3⋊#168C2311yescharacteristic
135C3×C22⋊Dic5—21no—
136C3×#689—22no—
137C3×#687—22no—
138C3×C4⋊Dic5C2311yescharacteristic
139C3×#683—21no—
140C2×C3×#168C2311yescharacteristic
141C2×C3×#168C2311yescharacteristic
142Dic3⋊Dic5—21no—
143#6669—21no—
144#6668—21no—
145(C2×D3)⋊Dic5—21no—
146(C2×D3)⋊Dic5—21no—
147#6663—22no—
148#6661—22no—
149#6659—22no—
150#6656—22no—
151#6650—22no—
152#6650—22no—
153C2×D3×#41D511yescharacteristic
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#4726—51no—
168C2×C5×#41—31no—
169C2×C5×#41—31no—
170C2×C5×#41—31no—
171C2×C5×#41—61no—
172C2×C5×#41—61no—
173C2×C5×#41—64no—
174C2×C5×#41—64no—
175C2×C5×#41C2×D311yescharacteristic
176C22×C5×Q8—31no—
177C22×C5×D4—31no—
178C22×C5×D4—61no—
179C23×C4×C5—31no—
180C23×C4×C5—61no—
181C22×Dic10—31no—
182C2×C22⋊Dic5—61no—
183#4097—64no—
184#4097—64no—
185C2×#689—31no—
186C2×#689—31no—
187C2×#689—31no—
188C2×#689C2×D311yescharacteristic, complemented
189C2×#687—31no—
190C2×#687—31no—
191C2×#687—31no—
192C2×#687C2×D311yescharacteristic, complemented
193C2×C4⋊Dic5—31no—
194#4070—31no—
195#4070—31no—
196#4070—31no—
197#4070—61no—
198#4070—61no—
199#4070C2×D311yescharacteristic, complemented
200C2×#683—61no—
201C2×#681—31no—
202C2×#681—31no—
203#3967—31no—
204#3967—31no—
205#3967—31no—
206#3967C2×D311yescharacteristic, complemented
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#3007—151noSylow
216C23×C3×C5—21no—
217C23×C3×C5C2×D411yescharacteristic
218C22×C5×D3—24no—
219C22×C5×D3—21no—
220C22×C5×D3—22no—
221C22×C5×D3—22no—
222C22×C5×D3—41no—
223C22×C5×D3—42no—
224C22×C5×D3—42no—
225C22×C5×D3C2×D411yescharacteristic
226C22×C5×D3C2×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—
242C5×#67—24no—
243C5×#67—24no—
244C5×#67—24no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—24no—
248C2×C5×Dic3C2×D411yescharacteristic
249C2×C5×Dic3C2×D411yescharacteristic
250C5×D12—24no—
251C5×D12—21no—
252C5×D12C2×D412yes—
253C4×C5×D3—24no—
254C4×C5×D3—24no—
255C4×C5×D3—22no—
256C4×C5×D3—21no—
257C4×C5×D3—21no—
258C4×C5×D3—22no—
259C4×C5×D3—24no—
260C4×C5×D3C2×D412yes—
261C4×C5×D3C2×D412yes—
262C5×Dic6—24no—
263C5×Dic6—21no—
264C5×Dic6C2×D412yes—
265C2×C3×Dic5—21no—
266C2×C3×Dic5—21no—
267C3×Dic10—21no—
268C3×Dic10—21no—
269#1204—42no—
270D3×Dic5—42no—
271D3×Dic5—42no—
272C3⋊#168—21no—
273C3⋊#168—21no—
274C3×#168—21no—
275C3×#168—21no—
276C2×C3×#41C2×D511yescharacteristic
277D3×#41—24no—
278D3×#41—24no—
279C2×#239C2×D511yescharacteristic
280C2×D3×Q8—51no—
281C2×D3×Q8C2×D511yescharacteristic
282C2×#237—21no—
283C2×#237C2×D511yescharacteristic
284C2×D3×D4—21no—
285C2×D3×D4C2×D511yescharacteristic
286C2×#235—21no—
287C2×#235C2×D511yescharacteristic
288C22×C4×D3—21no—
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)—51no—
304C2×ΓL(1,𝔽25)—51no—
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⋊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—
324C24×C5—61no—
325C5×#41—22no—
326C5×#41—22no—
327C5×#41—34no—
328C5×#41—34no—
329C5×#41—62no—
330C5×#41—62no—
331C5×#41—68no—
332C5×#41—62no—
333C5×#41—62no—
334C5×#41—68no—
335C2×C5×Q8—31no—
336C2×C5×Q8—61no—
337C2×C5×Q8—62no—
338C2×C5×Q8—62no—
339C2×C5×Q8C22×D311yescharacteristic
340C2×C5×D4—21no—
341C2×C5×D4—31no—
342C2×C5×D4—61no—
343C2×C5×D4—61no—
344C2×C5×D4—62no—
345C2×C5×D4—68no—
346C2×C5×D4—61no—
347C2×C5×D4—61no—
348C2×C5×D4—62no—
349C2×C5×D4C22×D311yescharacteristic
350C22×C4×C5—21no—
351C22×C4×C5—31no—
352C22×C4×C5—31no—
353C22×C4×C5—31no—
354C22×C4×C5—31no—
355C22×C4×C5—31no—
356C22×C4×C5—62no—
357C22×C4×C5—62no—
358C22×C4×C5—61no—
359C22×C4×C5—61no—
360C22×C4×C5—68no—
361C22×C4×C5—61no—
362C22×C4×C5—61no—
363C22×C4×C5C22×D311yescharacteristic
364C22×Dic5—61no—
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—
375#689—22no—
376#689—62no—
377#689—62no—
378#689—62no—
379#687—22no—
380#687—62no—
381#687—62no—
382#687—62no—
383C4⋊Dic5—31no—
384C4⋊Dic5—61no—
385C4⋊Dic5C22×D311yescharacteristic
386#683—21no—
387#683—61no—
388#683—61no—
389#683—61no—
390#681—62no—
391#681—62no—
392C2×#168—31no—
393C2×#168—31no—
394C2×#168C22×D311yescharacteristic
395C2×#168C22×D311yescharacteristic
396C22×#41—31no—
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—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×C5×D3—21no—
419C2×C5×D3—21no—
420C2×C5×D3—21no—
421C2×C5×D3—21no—
422C2×C5×D3—22no—
423C2×C5×D3—44no—
424C2×C5×D3—48no—
425C2×C5×D3—41no—
426C2×C5×D3—41no—
427C2×C5×D3#12012yes—
428C2×C5×D3#13712yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—21no—
431C3×C4×C5C22×D411yescharacteristic
432C3×C4×C5C22×D411yescharacteristic
433Dic15—41no—
434Dic15—41no—
435C3×Dic5—41no—
436C3×Dic5—41no—
437C5×Dic3—21no—
438C5×Dic3—22no—
439C5×Dic3#12012yes—
440C23×D3—21no—
441C23×D3C22⋊D511yescharacteristic
442C3×#41—22no—
443C3×#41—22no—
444C2×C3×Q8—51no—
445C2×C3×Q8C22×D511yescharacteristic
446C2×C3×D4—21no—
447C2×C3×D4C22×D511yescharacteristic
448C22×C3×C4—21no—
449C22×C3×C4C22×D511yescharacteristic
450C2×#67—21no—
451C2×#67—21no—
452C2×#67—21no—
453C22×Dic3—21no—
454C22×Dic3C22⋊D511yescharacteristic
455#239—22no—
456#239C22⋊D514yes—
457D3×Q8—22no—
458D3×Q8—22no—
459D3×Q8—102no—
460D3×Q8—102no—
461#237—28no—
462#237—22no—
463#237C22⋊D514yes—
464D3×D4—28no—
465D3×D4—22no—
466D3×D4—22no—
467#235—28no—
468#235—22no—
469#235—22no—
470C2×D12—21no—
471C2×D12C22×D511yescharacteristic
472C2×C4×D3—28no—
473C2×C4×D3—21no—
474C2×C4×D3—21no—
475C2×C4×D3—21no—
476C2×C4×D3—22no—
477C2×C4×D3—22no—
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—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⋊C8—51no—
508C2×C3⋊C8—51no—
509Dic12—102no—
510#204—102no—
511ΓL(1,𝔽25)—102no—
512ΓL(1,𝔽25)—102no—
513C23×C5—21no—
514C23×C5—31no—
515C23×C5—31no—
516C23×C5—62no—
517C23×C5—62no—
518C23×C5—64no—
519C23×C5—61no—
520C23×C5—121no—
521C23×C5—122no—
522C23×C5—122no—
523C23×C5D3×D411yescharacteristic
524C5×Q8—21no—
525C5×Q8—32no—
526C5×Q8—64no—
527C5×Q8—61no—
528C5×Q8D3×D412yes—
529C5×D4—24no—
530C5×D4—21no—
531C5×D4—32no—
532C5×D4—64no—
533C5×D4—64no—
534C5×D4—64no—
535C5×D4—64no—
536C5×D4—61no—
537C5×D4D3×D412yes—
538C2×C4×C5—24no—
539C2×C4×C5—21no—
540C2×C4×C5—21no—
541C2×C4×C5—21no—
542C2×C4×C5—31no—
543C2×C4×C5—32no—
544C2×C4×C5—32no—
545C2×C4×C5—31no—
546C2×C4×C5—62no—
547C2×C4×C5—64no—
548C2×C4×C5—62no—
549C2×C4×C5—64no—
550C2×C4×C5—64no—
551C2×C4×C5—62no—
552C2×C4×C5—64no—
553C2×C4×C5—61no—
554C2×C4×C5—61no—
555C2×C4×C5—61no—
556C2×C4×C5D3×D411yescharacteristic
557C2×C4×C5C23×D311yescharacteristic
558C2×Dic5—21no—
559C2×Dic5—21no—
560C2×Dic5—61no—
561C2×Dic5—61no—
562C2×Dic5—122no—
563C2×Dic5—122no—
564Dic10—21no—
565Dic10—21no—
566Dic10—61no—
567Dic10—61no—
568Dic10—122no—
569#168—21no—
570#168—21no—
571#168—61no—
572#168—61no—
573C2×#41—31no—
574C2×#41—31no—
575C2×#41—31no—
576C2×#41—61no—
577C2×#41—61no—
578C2×#41—64no—
579C2×#41—64no—
580C2×#41D3×D511yescharacteristic
581C22×Q8—31no—
582C22×Q8—151no—
583C22×D4—31no—
584C22×D4—61no—
585C23×C4—31no—
586C23×C4—61no—
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—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—51no—
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
625C5×D3—22no—
626C5×D3—22no—
627C5×D3—42no—
628C23×C3—21no—
629C23×C3C2×C22⋊D511yescharacteristic
630C22×D3—24no—
631C22×D3—21no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—41no—
635C22×D3—42no—
636C22×D3—42no—
637C22×D3C2×C22⋊D511yescharacteristic
638C22×D3C2×C22⋊D511yescharacteristic
639C3×Q8—21no—
640C3×Q8—101no—
641C3×Q8—101no—
642C3×Q8C2×C22⋊D512yes—
643C3×D4—24no—
644C3×D4—21no—
645C3×D4C2×C22⋊D512yes—
646C2×C3×C4—24no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—101no—
651C2×C3×C4—101no—
652C2×C3×C4C2×C22⋊D511yescharacteristic
653C2×C3×C4C23×D511yescharacteristic
654#67—24no—
655#67—24no—
656#67—24no—
657C2×Dic3—21no—
658C2×Dic3—22no—
659C2×Dic3—24no—
660C2×Dic3—101no—
661C2×Dic3—101no—
662C2×Dic3C2×C22⋊D511yescharacteristic
663C2×Dic3C2×C22⋊D511yescharacteristic
664D12—24no—
665D12—21no—
666D12C2×C22⋊D512yes—
667C4×D3—24no—
668C4×D3—24no—
669C4×D3—22no—
670C4×D3—21no—
671C4×D3—21no—
672C4×D3—22no—
673C4×D3—24no—
674C4×D3—202no—
675C4×D3—202no—
676C4×D3C2×C22⋊D512yes—
677C4×D3C2×C22⋊D512yes—
678Dic6—24no—
679Dic6—21no—
680Dic6—101no—
681Dic6—101no—
682Dic6—202no—
683Dic6C2×C22⋊D512yes—
684C3×C8—101no—
685C3×C8—101no—
686C3⋊C8—101no—
687C3⋊C8—101no—
688C22×C5—21no—
689C22×C5—21no—
690C22×C5—21no—
691C22×C5—22no—
692C22×C5—32no—
693C22×C5—32no—
694C22×C5—41no—
695C22×C5—41no—
696C22×C5—61no—
697C22×C5—61no—
698C22×C5—61no—
699C22×C5—61no—
700C22×C5—62no—
701C22×C5—124no—
702C22×C5—128no—
703C22×C5—121no—
704C22×C5—121no—
705C22×C5C2×D3×D411yescharacteristic
706C4×C5—21no—
707C4×C5—22no—
708C4×C5—32no—
709C4×C5—61no—
710C4×C5—62no—
711C4×C5C2×D3×D411yescharacteristic
712C4×C5C2×D3×D411yescharacteristic
713Dic5—41no—
714Dic5—41no—
715Dic5—121no—
716Dic5—121no—
717C24—31no—
718C24—61no—
719#41—22no—
720#41—22no—
721#41—34no—
722#41—34no—
723#41—62no—
724#41—62no—
725#41—68no—
726#41—62no—
727#41—62no—
728#41—68no—
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—21no—
740C2×D4—31no—
741C2×D4—61no—
742C2×D4—61no—
743C2×D4—62no—
744C2×D4—68no—
745C2×D4—61no—
746C2×D4—61no—
747C2×D4—62no—
748C2×D4C2×D3×D511yescharacteristic
749C22×C4—21no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—62no—
756C22×C4—62no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—68no—
760C22×C4—61no—
761C22×C4—61no—
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—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—22no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3C22×C22⋊D511yescharacteristic
798C2×D3—21no—
799C2×D3—21no—
800C2×D3—21no—
801C2×D3—21no—
802C2×D3—22no—
803C2×D3—44no—
804C2×D3—48no—
805C2×D3—41no—
806C2×D3—41no—
807C2×D3#409712yescomplemented
808C2×D3#409912yes—
809C3×C4—22no—
810C3×C4—21no—
811C3×C4—201no—
812C3×C4—201no—
813C3×C4C22×C22⋊D511yescharacteristic
814C3×C4C22×C22⋊D511yescharacteristic
815Dic3—21no—
816Dic3—22no—
817Dic3—201no—
818Dic3—201no—
819Dic3#409912yes—
820C2×C5—41no—
821C2×C5—42no—
822C2×C5—62no—
823C2×C5—62no—
824C2×C5—122no—
825C2×C5D3×#12011yescharacteristic
826C2×C5#576811yescharacteristic
827C2×C5D3×#13711yescharacteristic
828C23—21no—
829C23—31no—
830C23—31no—
831C23—62no—
832C23—62no—
833C23—64no—
834C23—61no—
835C23—121no—
836C23—122no—
837C23—122no—
838C23D3×C22⋊D511yescharacteristic
839Q8—21no—
840Q8—32no—
841Q8—64no—
842Q8—61no—
843Q8—101no—
844Q8—101no—
845Q8—301no—
846Q8—301no—
847Q8—602no—
848Q8D3×C22⋊D512yes—
849D4—24no—
850D4—21no—
851D4—32no—
852D4—64no—
853D4—64no—
854D4—64no—
855D4—64no—
856D4—61no—
857D4D3×C22⋊D512yes—
858C2×C4—24no—
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—64no—
868C2×C4—62no—
869C2×C4—64no—
870C2×C4—64no—
871C2×C4—62no—
872C2×C4—64no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—101no—
877C2×C4—101no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—602no—
881C2×C4—602no—
882C2×C4D3×C22⋊D511yescharacteristic
883C2×C4C22×D3×D511yescharacteristic
884C8—101no—
885C8—101no—
886C8—301no—
887C8—301no—
888C2×C3—41no—
889C2×C3—42no—
890C2×C3#6615611yescharacteristic
891C2×C3C2×#409711yescharacteristic
892C2×C3C2×#409911yescharacteristic
893D3—22no—
894D3—22no—
895D3—42no—
896C5#8022811yescharacteristic, complemented, Sylow
897C22—21no—
898C22—21no—
899C22—21no—
900C22—22no—
901C22—32no—
902C22—32no—
903C22—41no—
904C22—41no—
905C22—61no—
906C22—61no—
907C22—61no—
908C22—61no—
909C22—62no—
910C22—124no—
911C22—128no—
912C22—121no—
913C22—121no—
914C22C2×D3×C22⋊D511yescharacteristic
915C4—21no—
916C4—22no—
917C4—32no—
918C4—61no—
919C4—62no—
920C4—201no—
921C4—201no—
922C4—601no—
923C4—601no—
924C4C2×D3×C22⋊D511yescharacteristic
925C4C2×D3×C22⋊D511yescharacteristic
926C3#1061581511yescharacteristic, complemented, Sylow
927C2—41no—
928C2—42no—
929C2—62no—
930C2—62no—
931C2—122no—
932C2#1175532211yescharacteristic
933C2D3×#409711yescharacteristic
934C2D3×#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×D3×#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×#91510C2semidirect
3. C2×#91486C2semidirect
4. D3×#4070C2semidirect
5. #11751340C2semidirect
6. C3×#65528C2semidirect
7. #11749304C2semidirect
8. #11749302C2semidirect
9. #11749201C2semidirect
10. #11749058C2semidirect
11. #11749056C2semidirect
12. #11748955C2semidirect
13. #11748538C2semidirect
14. #11748505C2semidirect
15. #11748361C2semidirect
30. C2×D3×Dic10C22semidirect
31. C2×#6718C22semidirect
32. C2×#6716C22semidirect
33. #91813C22semidirect
34. C2×C3×#689C22semidirect
35. C2×C3×#687C22semidirect
36. C3×#4070C22semidirect
41. D3×C4⋊Dic5C22semidirect
46. C2×#6663C22semidirect
47. C2×#6661C22semidirect
48. C2×#6659C22semidirect
49. C2×#6656C22semidirect
50. C2×#6650C22semidirect
51. C2×#6650C22semidirect
52. #91119C22semidirect
53. #91116C22semidirect
54. #91114C22semidirect
55. C3×#3967C22semidirect
56. C3×#3964C22semidirect
57. C3×C22⋊#168C22semidirect
58. #90973C22semidirect
59. #90972C22semidirect
60. #90967C22semidirect
61. #90966C22semidirect
72. #65528D3semidirect
188. C2×#689C2×D3semidirect
192. C2×#687C2×D3semidirect
199. #4070C2×D3semidirect
206. #3967C2×D3semidirect
210. #3964C2×D3semidirect
214. C22⋊#168C2×D3semidirect
428. C2×C5×D3#137semidirect
790. C3×C5#3007semidirect
807. C2×D3#4097semidirect
896. C5#80228semidirect
926. C3#10615815semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×#412
C2×#915102
C2×#914862
D3×#40702
#117513402
C3×#655282
#117493042
#117493022
#117492012
#117490582
#117490562
#117489552
#117485382
#117485052
#117483612
#106158153
#802285