Finite Group Databasebeta

← #14453693

Subgroups — #14453693

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#546C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic, complemented
3C22×#6716C211yesmaximal, characteristic, complemented
4D4×Dic30C211yesmaximal, characteristic, complemented
5#11751340C211yesmaximal, characteristic, complemented
6#11751319C211yesmaximal, characteristic, complemented
7#11751161C211yesmaximal, characteristic, complemented
8#11751155C211yesmaximal, characteristic, complemented
9#11751152C211yesmaximal, characteristic, complemented
10#11751151C211yesmaximal, characteristic, complemented
11#11751143C211yesmaximal, characteristic, complemented
12#11751141C211yesmaximal, characteristic, complemented
13#11751120C211yesmaximal, characteristic, complemented
14#11751119C211yesmaximal, characteristic, complemented
15#11751112C211yesmaximal, characteristic, complemented
16#10615237—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×Dic30C2211yescharacteristic, complemented
21C3×C5×#124C2211yescharacteristic
22C3×C5×#123—21no—
23C3×C5×C22⋊Q8C2211yescharacteristic
24C3×C5×#121—21no—
25C3×C5×#121C2211yescharacteristic
26C3×C5×#120—21no—
27C3×C4×C5×D4C2211yescharacteristic
28C3×C4×C5×D4C2211yescharacteristic
29C2×C3×C5×C22⋊C4—21no—
30#91840—24no—
31C2×#6718C2211yescharacteristic, complemented
32C2×#6718C2211yescharacteristic, complemented
33C2×#6718C2211yescharacteristic, complemented
34D4×Dic15—21no—
35C2×#6716—24no—
36C2×#6716C2211yescharacteristic
37C2×#6716C2211yescharacteristic
38C2×#6716C2211yescharacteristic
39C2×#6716C2211yescharacteristic
40C2×#6716C2211yescharacteristic
41C2×#6716C2211yescharacteristic
42#91813C2211yescharacteristic
43#91813C2211yescharacteristic, complemented
44C2×#6710C2211yescharacteristic, complemented
45C22×C3⋊#168C2211yescharacteristic
46#91777—21no—
47#91767—21no—
48#91767—21no—
49#91758C2211yescharacteristic, complemented
50C4×Dic30C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91116C2211yescharacteristic
53#91116C2211yescharacteristic
54#91114C2211yescharacteristic
55#91114C2211yescharacteristic, complemented
56#91094C2211yescharacteristic, complemented
57#91094C2211yescharacteristic, complemented
58#91094C2211yescharacteristic, complemented
59#91091C2211yescharacteristic, complemented
60C4⋊(C3⋊#168)C2211yescharacteristic, complemented
61#91087C2211yescharacteristic, complemented
62#83506—51nomaximal, Hall
63C5×#546D311yescharacteristic
64C2×#4097—31no—
65C22×#687—31no—
66D4×Dic10—31no—
67#65528—31no—
68#65507—31no—
69#65349—31no—
70#65343—31no—
71#65340—31no—
72#65339—31no—
73#65331—31no—
74#65329—31no—
75#65308—31no—
76#65307—31no—
77#65300—31no—
78C24×C3×C5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4—22no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—41no—
87C2×C3×C5×D4D411yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C2×C3×C5×D4C2311yescharacteristic
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5—21no—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×Dic15—21no—
95C22×Dic15—21no—
96C2×Dic30—22no—
97C2×Dic30—22no—
98C2×Dic30—21no—
99C2×Dic30—21no—
100C2×Dic30—41no—
101C2×Dic30—41no—
102C2×Dic30C2311yescharacteristic
103C2×Dic30C2311yescharacteristic
104C2×Dic30C2311yescharacteristic
105C3×C5×C4⋊C4—21no—
106C3×C5×C4⋊C4D411yescharacteristic
107C3×C5×C4⋊C4C2311yescharacteristic
108C3×C5×C22⋊C4—21no—
109C3×C5×C22⋊C4—21no—
110C3×C5×C22⋊C4—21no—
111C3×C5×C22⋊C4—21no—
112C3×C5×C22⋊C4—21no—
113C3×C5×C22⋊C4D411yescharacteristic
114C3×C5×C22⋊C4D411yescharacteristic
115C3×C42×C5C2311yescharacteristic
116#6719—21no—
117#6719—21no—
118#6718—22no—
119#6718—22no—
120#6718—41no—
121#6716—22no—
122#6716—22no—
123#6716—22no—
124#6716—22no—
125#6716—41no—
126#6716D414yescomplemented
127C4⋊Dic15—21no—
128C4⋊Dic15—21no—
129C4⋊Dic15C2311yescharacteristic
130#6712—21no—
131#6712—21no—
132#6712—21no—
133C4×Dic15—21no—
134#6710—22no—
135C2×C3⋊#168—22no—
136C2×C3⋊#168C2311yescharacteristic
137C2×C3⋊#168C2311yescharacteristic
138C2×C3⋊#168C2311yescharacteristic
139C2×C3⋊#168C2311yescharacteristic
140C3×#546D511yescharacteristic
141C2×#951—51no—
142C22×#214—51no—
143D4×Dic6—51no—
144#5239—51no—
145#5218—51no—
146#5060—51no—
147#5054—51no—
148#5051—51no—
149#5050—51no—
150#5042—51no—
151#5040—51no—
152#5019—51no—
153#5018—51no—
154#5011—51no—
155C2×C5×#41C2×D311yescharacteristic
156C22×C5×D4C2×D311yescharacteristic
157C22×Dic10—31no—
158C22×Dic10—31no—
159C5×#124C2×D311yescharacteristic
160C5×#123—21no—
161C5×C22⋊Q8C2×D311yescharacteristic
162C5×#121—21no—
163C5×#121C2×D311yescharacteristic
164C5×#120—21no—
165C4×C5×D4C2×D311yescharacteristic
166C4×C5×D4C2×D311yescharacteristic
167C2×C5×C22⋊C4—21no—
168#4097—64no—
169C2×#689—31no—
170C2×#689—31no—
171C2×#689—31no—
172D4×Dic5—61no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#687—31no—
177C2×#687—31no—
178C2×#687—31no—
179C2×#687—64no—
180#4070—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168—31no—
184#4034—61no—
185#4024—61no—
186#4024—61no—
187#4015—31no—
188C4×Dic10—31no—
189#3967—31no—
190#3964—31no—
191#3964—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3942—31no—
196#3942—31no—
197#3939—31no—
198C4⋊#168—31no—
199#3935—31no—
200#3266—151noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—42no—
204C23×C3×C5—42no—
205C23×C3×C5—81no—
206C23×C3×C5C2×D411yescharacteristic
207C23×C3×C5C2×D411yescharacteristic
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C3×C5×D4—22no—
211C3×C5×D4—21no—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—42no—
215C3×C5×D4—42no—
216C3×C5×D4—81no—
217C3×C5×D4C2×D412yes—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—42no—
225C2×C3×C4×C5—81no—
226C2×C3×C4×C5C2×D411yescharacteristic
227C2×C3×C4×C5C2×D411yescharacteristic
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2411yescharacteristic
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—42no—
236C2×Dic15—42no—
237Dic30—21no—
238Dic30—21no—
239Dic30—21no—
240Dic30—21no—
241Dic30—21no—
242Dic30—42no—
243Dic30—42no—
244Dic30C2×D412yes—
245C3⋊#168—21no—
246C3⋊#168—21no—
247C3⋊#168—21no—
248C3⋊#168C2×D412yes—
249C2×C3×#41C2×D511yescharacteristic
250C22×C3×D4C2×D511yescharacteristic
251C22×Dic6—51no—
252C22×Dic6—51no—
253C3×#124C2×D511yescharacteristic
254C3×#123—21no—
255C3×C22⋊Q8C2×D511yescharacteristic
256C3×#121—21no—
257C3×#121C2×D511yescharacteristic
258C3×#120—21no—
259C3×C4×D4C2×D511yescharacteristic
260C3×C4×D4C2×D511yescharacteristic
261C2×C3×C22⋊C4—21no—
262#951—104no—
263C2×#216—51no—
264C2×#216—51no—
265C2×#216—51no—
266D4×Dic3—101no—
267C2×#214—51no—
268C2×#214—51no—
269C2×#214—51no—
270C2×#214—51no—
271C2×#214—51no—
272C2×#214—51no—
273C2×#214—104no—
274#924—51no—
275#924—51no—
276C2×#208—51no—
277C22×C3⋊C8—51no—
278#888—101no—
279#878—101no—
280#878—101no—
281#869—51no—
282C4×Dic6—51no—
283#835—51no—
284#832—51no—
285#832—51no—
286#830—51no—
287#830—51no—
288#810—51no—
289#810—51no—
290#810—51no—
291#807—51no—
292C4⋊(C3⋊C8)—51no—
293#803—51no—
294C24×C5—21no—
295C5×#41—22no—
296C5×#41—41no—
297C2×C5×Q8C22×D311yescharacteristic
298C2×C5×D4—22no—
299C2×C5×D4—21no—
300C2×C5×D4—21no—
301C2×C5×D4—21no—
302C2×C5×D4—41no—
303C2×C5×D4#6711yescharacteristic
304C2×C5×D4C22×D311yescharacteristic
305C2×C5×D4C22×D311yescharacteristic
306C22×C4×C5—21no—
307C22×C4×C5—21no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×Dic5—61no—
311C22×Dic5—61no—
312C2×Dic10—31no—
313C2×Dic10—31no—
314C2×Dic10—31no—
315C2×Dic10—62no—
316C2×Dic10—62no—
317C2×Dic10—61no—
318C2×Dic10—61no—
319C2×Dic10—121no—
320C2×Dic10—121no—
321C5×C4⋊C4—21no—
322C5×C4⋊C4#6711yescharacteristic
323C5×C4⋊C4C22×D311yescharacteristic
324C5×C22⋊C4—21no—
325C5×C22⋊C4—21no—
326C5×C22⋊C4—21no—
327C5×C22⋊C4—21no—
328C5×C22⋊C4—21no—
329C5×C22⋊C4#6711yescharacteristic
330C5×C22⋊C4#6711yescharacteristic
331C42×C5C22×D311yescharacteristic
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334#689—62no—
335#689—62no—
336#689—121no—
337#687—34no—
338#687—62no—
339#687—62no—
340#687—62no—
341#687—62no—
342#687—121no—
343C4⋊Dic5—31no—
344C4⋊Dic5—61no—
345C4⋊Dic5—61no—
346#683—61no—
347#683—61no—
348#683—61no—
349C4×Dic5—61no—
350#681—62no—
351C2×#168—31no—
352C2×#168—31no—
353C2×#168—31no—
354C2×#168—31no—
355C2×#168—62no—
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—151no—
359#546D1511yescharacteristic
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435—151no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—22no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—84no—
383C22×C3×C5#13712yescomplemented
384C22×C3×C5C22×D411yescharacteristic
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—21no—
388C3×C4×C5—21no—
389C3×C4×C5—41no—
390C3×C4×C5—41no—
391C3×C4×C5C22×D411yescharacteristic
392C3×C4×C5H(5,𝔽2)11yescharacteristic
393Dic15—22no—
394Dic15—41no—
395Dic15—41no—
396Dic15—41no—
397C24×C3—21no—
398C3×#41—22no—
399C3×#41—41no—
400C2×C3×Q8C22×D511yescharacteristic
401C2×C3×D4—22no—
402C2×C3×D4—21no—
403C2×C3×D4—21no—
404C2×C3×D4—21no—
405C2×C3×D4—41no—
406C2×C3×D4C22⋊D511yescharacteristic
407C2×C3×D4C22×D511yescharacteristic
408C2×C3×D4C22×D511yescharacteristic
409C22×C3×C4—21no—
410C22×C3×C4—21no—
411C22×C3×C4C22×D511yescharacteristic
412C22×C3×C4C22×D511yescharacteristic
413C22×Dic3—101no—
414C22×Dic3—101no—
415C2×Dic6—51no—
416C2×Dic6—51no—
417C2×Dic6—51no—
418C2×Dic6—102no—
419C2×Dic6—102no—
420C2×Dic6—101no—
421C2×Dic6—101no—
422C2×Dic6—201no—
423C2×Dic6—201no—
424C3×C4⋊C4—21no—
425C3×C4⋊C4C22⋊D511yescharacteristic
426C3×C4⋊C4C22×D511yescharacteristic
427C3×C22⋊C4—21no—
428C3×C22⋊C4—21no—
429C3×C22⋊C4—21no—
430C3×C22⋊C4—21no—
431C3×C22⋊C4—21no—
432C3×C22⋊C4C22⋊D511yescharacteristic
433C3×C22⋊C4C22⋊D511yescharacteristic
434C3×C42C22×D511yescharacteristic
435#217—101no—
436#217—101no—
437#216—102no—
438#216—102no—
439#216—201no—
440#214—54no—
441#214—102no—
442#214—102no—
443#214—102no—
444#214—102no—
445#214—201no—
446C4⋊Dic3—51no—
447C4⋊Dic3—101no—
448C4⋊Dic3—101no—
449Dic3⋊C4—101no—
450Dic3⋊C4—101no—
451Dic3⋊C4—101no—
452C4×Dic3—101no—
453#208—102no—
454C2×C3⋊C8—51no—
455C2×C3⋊C8—51no—
456C2×C3⋊C8—51no—
457C2×C3⋊C8—51no—
458C2×C3⋊C8—102no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—42no—
462C23×C5—42no—
463C23×C5—81no—
464C23×C5C2×#6711yescharacteristic
465C23×C5C2×#6711yescharacteristic
466C5×Q8—21no—
467C5×Q8—21no—
468C5×D4—22no—
469C5×D4—21no—
470C5×D4—21no—
471C5×D4—21no—
472C5×D4—42no—
473C5×D4—42no—
474C5×D4—81no—
475C5×D4D3×D412yes—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—42no—
483C2×C4×C5—81no—
484C2×C4×C5C2×#6711yescharacteristic
485C2×C4×C5C2×#6711yescharacteristic
486C2×C4×C5C2×#6711yescharacteristic
487C2×C4×C5C2×#6711yescharacteristic
488C2×C4×C5C23×D311yescharacteristic
489C2×Dic5—61no—
490C2×Dic5—61no—
491C2×Dic5—61no—
492C2×Dic5—61no—
493C2×Dic5—122no—
494C2×Dic5—122no—
495Dic10—32no—
496Dic10—61no—
497Dic10—61no—
498Dic10—61no—
499Dic10—61no—
500Dic10—61no—
501Dic10—122no—
502Dic10—122no—
503#168—32no—
504#168—61no—
505#168—61no—
506#168—61no—
507C2×#41C2×D1511yescharacteristic
508C22×Q8—151no—
509C22×Q8—151no—
510C22×D4C2×D1511yescharacteristic
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—151no—
523C22×C8—151no—
524C4⋊Q8—151no—
525C4⋊Q8—301no—
526#124C2×D1511yescharacteristic
527#123—21no—
528C22⋊Q8—151no—
529C22⋊Q8—151no—
530C22⋊Q8—301no—
531C22⋊Q8—301no—
532C22⋊Q8C2×D1511yescharacteristic
533#121—21no—
534#121C2×D1511yescharacteristic
535#120—21no—
536C4×Q8—151no—
537C4×D4—301no—
538C4×D4C2×D1511yescharacteristic
539C4×D4C2×D1511yescharacteristic
540C2×C22⋊C4—21no—
541#107—151no—
542C4⋊C8—151no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—151no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—22no—
553C2×C3×C5—41no—
554C2×C3×C5—42no—
555C2×C3×C5—81no—
556C2×C3×C5D4211yescharacteristic
557C2×C3×C5C2×#13711yescharacteristic
558C2×C3×C5#57711yescharacteristic
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—81no—
564C23×C3C2×C22⋊D511yescharacteristic
565C23×C3C2×C22⋊D511yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×D4—22no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—42no—
573C3×D4—42no—
574C3×D4—81no—
575C3×D4D4×D512yes—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—42no—
583C2×C3×C4—81no—
584C2×C3×C4C2×C22⋊D511yescharacteristic
585C2×C3×C4C2×C22⋊D511yescharacteristic
586C2×C3×C4C2×C22⋊D511yescharacteristic
587C2×C3×C4C2×C22⋊D511yescharacteristic
588C2×C3×C4C23×D511yescharacteristic
589C2×Dic3—101no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3—101no—
593C2×Dic3—202no—
594C2×Dic3—202no—
595Dic6—52no—
596Dic6—101no—
597Dic6—101no—
598Dic6—101no—
599Dic6—101no—
600Dic6—101no—
601Dic6—202no—
602Dic6—202no—
603C3⋊C8—52no—
604C3⋊C8—101no—
605C3⋊C8—101no—
606C3⋊C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—22no—
611C22×C5—21no—
612C22×C5—21no—
613C22×C5—41no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—84no—
619C22×C5#95112yescomplemented
620C22×C5C22×#6711yescharacteristic
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5—41no—
626C4×C5—41no—
627C4×C5C2×D3×D411yescharacteristic
628C4×C5#100411yescharacteristic
629Dic5—62no—
630Dic5—121no—
631Dic5—121no—
632Dic5—121no—
633C24—21no—
634#41—22no—
635#41—41no—
636C2×Q8—151no—
637C2×Q8—151no—
638C2×Q8—151no—
639C2×Q8—302no—
640C2×Q8—302no—
641C2×Q8—301no—
642C2×Q8—301no—
643C2×Q8—601no—
644C2×Q8—601no—
645C2×Q8C22×D1511yescharacteristic
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—41no—
651C2×D4#122011yescharacteristic
652C2×D4C22×D1511yescharacteristic
653C2×D4C22×D1511yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—301no—
657C22×C4—301no—
658C22×C4C22×D1511yescharacteristic
659C22×C4C22×D1511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—154no—
664SD16—302no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—302no—
670C2×C8—151no—
671C2×C8—151no—
672C2×C8—151no—
673C2×C8—151no—
674C2×C8—302no—
675C4⋊C4—21no—
676C4⋊C4—151no—
677C4⋊C4—301no—
678C4⋊C4—301no—
679C4⋊C4—301no—
680C4⋊C4—301no—
681C4⋊C4—301no—
682C4⋊C4#122011yescharacteristic
683C4⋊C4C22×D1511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4#122011yescharacteristic
692C22⋊C4#122011yescharacteristic
693C42—301no—
694C42C22×D1511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—22no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—84no—
708C22×C3#409712yescomplemented
709C22×C3C22×C22⋊D511yescharacteristic
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4C2×D4×D511yescharacteristic
717C3×C4#414411yescharacteristic
718Dic3—102no—
719Dic3—201no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—41no—
724C2×C5—42no—
725C2×C5—81no—
726C2×C5D4×#6711yescharacteristic
727C2×C5C2×#95111yescharacteristic
728C2×C5#583611yescharacteristic
729C23—21no—
730C23—21no—
731C23—42no—
732C23—42no—
733C23—81no—
734C23C2×#122011yescharacteristic
735C23C2×#122011yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—152no—
739Q8—301no—
740Q8—301no—
741Q8—301no—
742Q8—301no—
743Q8—301no—
744Q8—602no—
745Q8—602no—
746D4—22no—
747D4—21no—
748D4—21no—
749D4—21no—
750D4—42no—
751D4—42no—
752D4—81no—
753D4D4×D1512yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—42no—
761C2×C4—81no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—602no—
767C2×C4—602no—
768C2×C4C2×#122011yescharacteristic
769C2×C4C2×#122011yescharacteristic
770C2×C4C2×#122011yescharacteristic
771C2×C4C2×#122011yescharacteristic
772C2×C4C23×D1511yescharacteristic
773C8—152no—
774C8—301no—
775C8—301no—
776C8—301no—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3—42no—
780C2×C3—81no—
781C2×C3D4×C22⋊D511yescharacteristic
782C2×C3C2×#409711yescharacteristic
783C2×C3#6617011yescharacteristic
784C5#8350611yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—21no—
790C22—21no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—84no—
797C22#9184012yescomplemented
798C22C22×#122011yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—41no—
804C4—41no—
805C4—302no—
806C4—601no—
807C4—601no—
808C4—601no—
809C4C2×D4×D1511yescharacteristic
810C4#9209511yescharacteristic
811C3#1061523711yescharacteristic, complemented, Sylow
812C2—22no—
813C2—41no—
814C2—42no—
815C2—81no—
816C2D4×#122011yescharacteristic
817C2C2×#9184011yescharacteristic
818C2#1175659511yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
Fitting, prime radicalC3×C5×#546C2
socleC22×C3×C5C22×D4
hypercenter#546D15
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
2. C2×#91840C2semidirect
3. C22×#6716C2semidirect
4. D4×Dic30C2semidirect
5. #11751340C2semidirect
6. #11751319C2semidirect
7. #11751161C2semidirect
8. #11751155C2semidirect
9. #11751152C2semidirect
10. #11751151C2semidirect
11. #11751143C2semidirect
12. #11751141C2semidirect
13. #11751120C2semidirect
14. #11751119C2semidirect
15. #11751112C2semidirect
20. C22×Dic30C22semidirect
31. C2×#6718C22semidirect
32. C2×#6718C22semidirect
33. C2×#6718C22semidirect
43. #91813C22semidirect
44. C2×#6710C22semidirect
49. #91758C22semidirect
50. C4×Dic30C22semidirect
51. #91119C22semidirect
55. #91114C22semidirect
56. #91094C22semidirect
57. #91094C22semidirect
58. #91094C22semidirect
59. #91091C22semidirect
60. C4⋊(C3⋊#168)C22semidirect
61. #91087C22semidirect
126. #6716D4semidirect
383. C22×C3×C5#137semidirect
619. C22×C5#951semidirect
695. C3×C5#3266semidirect
708. C22×C3#4097semidirect
784. C5#83506semidirect
797. C22#91840semidirect
811. C3#10615237semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5462
C2×#918402
C22×#67162
D4×Dic302
#117513402
#117513192
#117511612
#117511552
#117511522
#117511512
#117511432
#117511412
#117511202
#117511192
#117511122
#106152373
#835065