Finite Group Databasebeta

← #14425493

Subgroups — #14425493

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66283C211yesmaximal, characteristic, complemented
2C2×#91838C211yesmaximal, characteristic, complemented
3#11754609C211yesmaximal, characteristic, complemented
4C2×#91301C211yesmaximal, characteristic, complemented
5C5×#5236C211yesmaximal, characteristic, complemented
6#11749457C214yesmaximal, complemented
7#11749418C214yesmaximal, complemented
8#11748421C211yesmaximal, characteristic, complemented
9#11748353C211yesmaximal, characteristic, complemented
10#10610725—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C22×D60C2211yescharacteristic, complemented
13C3×#4150—21no—
14C3×#4150C2212yescomplemented
15C3×#4149—21no—
16C3×#4149C2212yescomplemented
17C3×D5×#41—22no—
18C3×D5×#41—22no—
19C3×#4147—21no—
20C3×#4144—21no—
21C3×#4144—22no—
22C2×C3×#709—22no—
23C2×C3×#709C2211yescharacteristic
24C2×C3×#709C2211yescharacteristic
25#91838—22no—
26#91838C2214yescomplemented
27C2×#6717—21no—
28C2×#6715—21no—
29C2×#6710C2211yescharacteristic, complemented
30C5×#926C2211yescharacteristic, complemented
31C2×C5×#208C2211yescharacteristic, complemented
32#91572—22no—
33#91458C2212yescomplemented
34#91450—22no—
35#91374C2212yescomplemented
36C2×#6658—21no—
37#91301—22no—
38#91301C2214yescomplemented
39C2×#6653—21no—
40C5×#837C2214yescomplemented
41#90977C2214yescomplemented
42#90961C2212yescomplemented
43#90958C2212yescomplemented
44#84122—51nomaximal, Hall
45#66283D311yescharacteristic, complemented
46C2×#4095—31no—
47C2×#4054—31no—
48#65859—31no—
49C5×#421—31no—
50#65421—31no—
51#65294—31no—
52#65116—34no—
53#65111—34no—
54C23×D15—21no—
55C3×C5×#41—21no—
56C3×C5×#41—21no—
57C3×C5×#41D412yescomplemented
58C3×C5×#41C2312yes—
59C2×C3×C5×Q8D411yescharacteristic, complemented
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4D411yescharacteristic, complemented
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×D60—21no—
65C2×D60—21no—
66C2×D60—21no—
67C2×D60—21no—
68C2×D60—21no—
69C2×D60C2312yes—
70C2×C3×C22⋊D5—24no—
71C2×C3×C22⋊D5—21no—
72C2×C3×C22⋊D5D412yes—
73C3×#713—22no—
74C3×#713—22no—
75C3×Q8×D5—22no—
76C3×Q8×D5—22no—
77C3×#711—24no—
78C3×#711—22no—
79C3×#711—22no—
80C3×#711—24no—
81C3×D4×D5—24no—
82C3×D4×D5—22no—
83C3×D4×D5—24no—
84C3×D4×D5—22no—
85C3×#709—24no—
86C3×#709—24no—
87C3×#709—21no—
88C3×#709—21no—
89C3×#709—21no—
90C3×#709—21no—
91C3×#709—21no—
92C3×#709—21no—
93C3×#709—22no—
94C3×#709—22no—
95C3×#709D412yescomplemented
96C3×#709C2312yes—
97C2×C3×D20—22no—
98C2×C3×D20D411yescharacteristic, complemented
99C2×C3×D20C2311yescharacteristic
100C2×C3×C4×D5—24no—
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5D412yes—
103C2×C3×Dic10—22no—
104C2×C3×Dic10D411yescharacteristic, complemented
105C2×C3×Dic10C2311yescharacteristic
106C2×#1202—24no—
107#6717—24no—
108#6715—24no—
109#6710—21no—
110#6710C2312yes—
111C2×C3⋊#168—21no—
112C5×#217—21no—
113C5×C4⋊Dic3—21no—
114C4×C5×Dic3C2312yes—
115C5×#208—21no—
116C5×#208C2312yes—
117C2×C5×C3⋊C8—21no—
118#6667—24no—
119#6658—24no—
120#6653—24no—
121C3×#585—51no—
122#5830—51no—
123C2×#949—51no—
124C2×#949—51no—
125#5245—54no—
126#5241—54no—
127#5237—51no—
128#5236—51no—
129#5236D511yescharacteristic, complemented
130C2×C5×#41C2×D311yescharacteristic
131#4150—21no—
132#4150C2×D312yescomplemented
133#4149—21no—
134#4149C2×D312yescomplemented
135D5×#41—22no—
136D5×#41—22no—
137#4147—21no—
138#4144—21no—
139#4144—22no—
140C2×#709—22no—
141C2×#709C2×D311yescharacteristic
142C2×#709C2×D311yescharacteristic
143C22×D20—31no—
144C2×C5×M16—31no—
145C5×#117—31no—
146#4095—34no—
147#4095—62no—
148C2×#688—61no—
149C2×#686—61no—
150C2×#681—31no—
151#4054—34no—
152#4054—62no—
153C2×D40—61no—
154C2×#677—61no—
155#4041—62no—
156#4028—62no—
157#4021—32no—
158#4020—32no—
159C5×#104—34no—
160#3956—32no—
161#3955—32no—
162#3937—34no—
163#3021—151noSylow
164C23×C3×C5—21no—
165C23×C3×C5C2×D411yescharacteristic
166C22×D15—22no—
167C22×D15—41no—
168C22×D15—41no—
169C22×D15—82no—
170C22×C3×D5—24no—
171C22×C3×D5—21no—
172C22×C3×D5C2×D412yes—
173C3×C5×Q8—21no—
174C3×C5×Q8C2×D412yes—
175C3×C5×D4—22no—
176C3×C5×D4—22no—
177C3×C5×D4—21no—
178C3×C5×D4C2×D412yes—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5—22no—
182C2×C3×C4×C5C2×D411yescharacteristic
183C2×C3×C4×C5C2×D411yescharacteristic
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2411yescharacteristic
188D60—22no—
189D60—22no—
190D60—41no—
191D60—41no—
192C2×C5×Dic3—22no—
193C3×C22⋊D5—24no—
194C3×C22⋊D5—24no—
195C3×C22⋊D5—22no—
196C3×C22⋊D5—22no—
197C3×C22⋊D5—22no—
198C3×C22⋊D5—22no—
199C2×C3×Dic5—24no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5C2×D412yes—
202C3×D20—24no—
203C3×D20—21no—
204C3×D20—21no—
205C3×D20—21no—
206C3×D20C2×D412yes—
207C3×C4×D5—24no—
208C3×C4×D5—24no—
209C3×C4×D5—22no—
210C3×C4×D5—22no—
211C3×C4×D5—22no—
212C3×C4×D5—22no—
213C3×Dic10—24no—
214C3×Dic10—21no—
215C3×Dic10—21no—
216C3×Dic10—21no—
217C3×Dic10C2×D412yes—
218#1202—84no—
219C3⋊#168—22no—
220C5×C3⋊C8—22no—
221C3×2−1+4—52no—
222C3×2−1+4—101no—
223C3×2−1+4—101no—
224C3×H(5,𝔽2)—52no—
225C3×H(5,𝔽2)—102no—
226C3×H(5,𝔽2)—101no—
227C3×H(5,𝔽2)—101no—
228C2×C3×#41—51no—
229C2×C3×#41—51no—
230C2×C3×#41—102no—
231C2×C3×#41—102no—
232C2×C3×#41—102no—
233C2×C3×#41C2×D511yescharacteristic
234C22×D12—51no—
235#949—54no—
236#949—54no—
237#949—102no—
238#949—102no—
239#947—52no—
240C2×#215—101no—
241C2×#215—101no—
242#940—52no—
243#937—102no—
244C2×#213—101no—
245C2×#213—101no—
246#930—102no—
247#926C2×D511yescharacteristic, complemented
248C2×#208—51no—
249C2×#208C2×D511yescharacteristic, complemented
250#837—54no—
251#837C2×D514yescomplemented
252#836—52no—
253#833—52no—
254C23×D5—61no—
255C5×#41—21no—
256C5×#41—21no—
257C5×#41#6712yescomplemented
258C5×#41C22×D312yes—
259C2×C5×Q8#6711yescharacteristic, complemented
260C2×C5×D4—21no—
261C2×C5×D4#6711yescharacteristic, complemented
262C22×C4×C5—21no—
263C22×C4×C5C22×D311yescharacteristic
264C2×C22⋊D5—24no—
265C2×C22⋊D5—21no—
266C2×C22⋊D5#6712yes—
267#713—22no—
268#713—22no—
269Q8×D5—22no—
270Q8×D5—22no—
271#711—24no—
272#711—22no—
273#711—22no—
274#711—24no—
275D4×D5—24no—
276D4×D5—22no—
277D4×D5—24no—
278D4×D5—22no—
279#709—24no—
280#709—24no—
281#709—21no—
282#709—21no—
283#709—21no—
284#709—21no—
285#709—21no—
286#709—21no—
287#709—22no—
288#709—22no—
289#709#6712yescomplemented
290#709C22×D312yes—
291C2×D20—22no—
292C2×D20—32no—
293C2×D20—61no—
294C2×D20—61no—
295C2×D20—61no—
296C2×D20—61no—
297C2×D20—61no—
298C2×D20—64no—
299C2×D20#6711yescharacteristic, complemented
300C2×D20C22×D311yescharacteristic
301C2×C4×D5—24no—
302C2×C4×D5—21no—
303C2×C4×D5#6712yes—
304C2×Dic10—22no—
305C2×Dic10#6711yescharacteristic, complemented
306C2×Dic10C22×D311yescharacteristic
307C5×M16—32no—
308C5×M16—61no—
309C2×C5×C8—61no—
310C5×C4⋊C4—61no—
311C5×C22⋊C4—61no—
312C42×C5—32no—
313#688—64no—
314#686—64no—
315#685—64no—
316#681—32no—
317#681—61no—
318C2×#168—61no—
319D40—64no—
320#677—64no—
321#585—51no—
322C2×AGL(1,ℤ/8)—151no—
323C2×AGL(1,ℤ/8)—151no—
324#535—151no—
325#454—154no—
326#453—154no—
327#421—31no—
328#421—151no—
329#413—151no—
330C22×C3×C5—22no—
331C22×C3×C5—41no—
332C22×C3×C5—81no—
333C22×C3×C5#12011yescharacteristic
334C22×C3×C5#12011yescharacteristic
335C22×C3×C5C22×D411yescharacteristic
336C2×D15—44no—
337C2×D15—42no—
338C2×D15—82no—
339C2×D15—82no—
340C2×C3×D5—22no—
341C2×C3×D5—22no—
342C2×C3×D5—42no—
343C2×C3×D5—81no—
344C2×C3×D5—84no—
345C3×C4×C5—22no—
346C3×C4×C5#12011yescharacteristic
347C3×C4×C5#12011yescharacteristic
348C3×C4×C5C22×D411yescharacteristic
349C3×C4×C5C22×D411yescharacteristic
350C3×Dic5—22no—
351C3×Dic5—22no—
352C5×Dic3—42no—
353C23×D3—101no—
354C3×#41—21no—
355C3×#41—21no—
356C3×#41—52no—
357C3×#41—52no—
358C3×#41—102no—
359C3×#41—102no—
360C3×#41—104no—
361C3×#41—104no—
362C3×#41—104no—
363C3×#41—104no—
364C3×#41—102no—
365C3×#41—102no—
366C3×#41—102no—
367C3×#41—102no—
368C3×#41—101no—
369C3×#41—101no—
370C3×#41—101no—
371C3×#41—101no—
372C3×#41—101no—
373C3×#41—101no—
374C3×#41D2012yescomplemented
375C3×#41C22×D512yes—
376C2×C3×Q8—51no—
377C2×C3×Q8—51no—
378C2×C3×Q8—102no—
379C2×C3×Q8—102no—
380C2×C3×Q8—102no—
381C2×C3×Q8D2011yescharacteristic, complemented
382C2×C3×D4—21no—
383C2×C3×D4—52no—
384C2×C3×D4—51no—
385C2×C3×D4—51no—
386C2×C3×D4—102no—
387C2×C3×D4—104no—
388C2×C3×D4—104no—
389C2×C3×D4—102no—
390C2×C3×D4—104no—
391C2×C3×D4—101no—
392C2×C3×D4—102no—
393C2×C3×D4D2011yescharacteristic, complemented
394C22×C3×C4—21no—
395C22×C3×C4—52no—
396C22×C3×C4—104no—
397C22×C3×C4—101no—
398C22×C3×C4C22×D511yescharacteristic
399C2×#67—104no—
400C2×D12—52no—
401C2×D12—101no—
402C2×D12—101no—
403C2×D12—101no—
404C2×D12—101no—
405C2×D12—101no—
406#217—21no—
407#215—104no—
408#215—104no—
409#213—104no—
410#213—104no—
411(C2×D3)⋊C4—104no—
412C4⋊Dic3—21no—
413C4×Dic3C22×D512yes—
414#208—21no—
415#208—52no—
416#208—101no—
417#208C22×D512yes—
418C2×C3⋊C8—21no—
419C2×C3⋊C8—101no—
420C23×C5—21no—
421C23×C5C2×#6711yescharacteristic
422C22×D5—24no—
423C22×D5—21no—
424C22×D5—62no—
425C22×D5—121no—
426C22×D5—121no—
427C22×D5—242no—
428C22×D5C2×#6712yes—
429C5×Q8—21no—
430C5×Q8C2×#6712yes—
431C5×D4—22no—
432C5×D4—22no—
433C5×D4—21no—
434C5×D4C2×#6712yes—
435C2×C4×C5—21no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—62no—
439C2×C4×C5C2×#6711yescharacteristic
440C2×C4×C5C2×#6711yescharacteristic
441C2×C4×C5C2×#6711yescharacteristic
442C2×C4×C5C2×#6711yescharacteristic
443C2×C4×C5C2×#6711yescharacteristic
444C2×C4×C5C23×D311yescharacteristic
445C22⋊D5—24no—
446C22⋊D5—24no—
447C22⋊D5—22no—
448C22⋊D5—22no—
449C22⋊D5—22no—
450C22⋊D5—22no—
451C2×Dic5—24no—
452C2×Dic5—21no—
453C2×Dic5C2×#6712yes—
454D20—24no—
455D20—21no—
456D20—21no—
457D20—21no—
458D20—62no—
459D20—62no—
460D20—121no—
461D20—121no—
462D20—244no—
463D20C2×#6712yes—
464C4×D5—24no—
465C4×D5—24no—
466C4×D5—22no—
467C4×D5—22no—
468C4×D5—22no—
469C4×D5—22no—
470Dic10—24no—
471Dic10—21no—
472Dic10—21no—
473Dic10—21no—
474Dic10C2×#6712yes—
475C5×C8—62no—
476#168—62no—
4772−1+4—52no—
4782−1+4—101no—
4792−1+4—101no—
480H(5,𝔽2)—52no—
481H(5,𝔽2)—102no—
482H(5,𝔽2)—101no—
483H(5,𝔽2)—101no—
484C2×#41—51no—
485C2×#41—51no—
486C2×#41—102no—
487C2×#41—102no—
488C2×#41—102no—
489C2×#41D3×D511yescharacteristic
490C22×D4—151no—
491AGL(1,ℤ/8)—154no—
492AGL(1,ℤ/8)—154no—
493AGL(1,ℤ/8)—302no—
494AGL(1,ℤ/8)—302no—
495C2×SD16—301no—
496C2×SD16—301no—
497C2×D8—301no—
498C2×D8—301no—
499C2×M16—31no—
500C2×M16—151no—
501#127—152no—
502#124—152no—
503#121—302no—
504#120—302no—
505#117—31no—
506#104—34no—
507#104—154no—
508#101—152no—
509#100—152no—
510C2×C3×C5—21no—
511C2×C3×C5—21no—
512C2×C3×C5—21no—
513C2×C3×C5—42no—
514C2×C3×C5C2×#12011yescharacteristic
515D15—82no—
516C3×D5—42no—
517C3×D5—42no—
518C23×C3—21no—
519C23×C3—52no—
520C23×C3—104no—
521C23×C3—101no—
522C23×C3D4×D511yescharacteristic
523C22×D3—102no—
524C22×D3—201no—
525C22×D3—201no—
526C22×D3—402no—
527C3×Q8—21no—
528C3×Q8—52no—
529C3×Q8—104no—
530C3×Q8—101no—
531C3×Q8—101no—
532C3×Q8—101no—
533C3×Q8C2×D2012yes—
534C3×D4—22no—
535C3×D4—22no—
536C3×D4—21no—
537C3×D4—52no—
538C3×D4—104no—
539C3×D4—104no—
540C3×D4—104no—
541C3×D4—102no—
542C3×D4—102no—
543C3×D4—102no—
544C3×D4—102no—
545C3×D4—101no—
546C3×D4—101no—
547C3×D4—101no—
548C3×D4C2×D2012yes—
549C2×C3×C4—21no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—52no—
553C2×C3×C4—104no—
554C2×C3×C4—104no—
555C2×C3×C4—104no—
556C2×C3×C4—101no—
557C2×C3×C4—102no—
558C2×C3×C4—102no—
559C2×C3×C4—102no—
560C2×C3×C4—102no—
561C2×C3×C4C2×D2011yescharacteristic
562C2×C3×C4C2×D2011yescharacteristic
563C2×C3×C4D4×D511yescharacteristic
564C2×C3×C4D4×D511yescharacteristic
565C2×C3×C4D4×D511yescharacteristic
566C2×C3×C4C23×D511yescharacteristic
567#67—404no—
568C2×Dic3—22no—
569D12—102no—
570D12—102no—
571D12—201no—
572D12—201no—
573C3⋊C8—22no—
574C3⋊C8—102no—
575C22×C5—22no—
576C22×C5—41no—
577C22×C5—81no—
578C22×C5#95311yescharacteristic
579C22×C5#95311yescharacteristic
580C22×C5C22×#6711yescharacteristic
581C2×D5—22no—
582C2×D5—22no—
583C2×D5—42no—
584C2×D5—81no—
585C2×D5—84no—
586C2×D5—124no—
587C2×D5—122no—
588C2×D5—242no—
589C2×D5—242no—
590C4×C5—22no—
591C4×C5—122no—
592C4×C5#95311yescharacteristic
593C4×C5#95311yescharacteristic
594C4×C5C22×#6711yescharacteristic
595C4×C5C22×#6711yescharacteristic
596Dic5—22no—
597Dic5—22no—
598C24—301no—
599#41—21no—
600#41—21no—
601#41—52no—
602#41—52no—
603#41—102no—
604#41—102no—
605#41—104no—
606#41—104no—
607#41—104no—
608#41—104no—
609#41—102no—
610#41—102no—
611#41—102no—
612#41—102no—
613#41—101no—
614#41—101no—
615#41—101no—
616#41—101no—
617#41—101no—
618#41—101no—
619#41#120212yescomplemented
620#41C2×D3×D512yes—
621C2×Q8—51no—
622C2×Q8—51no—
623C2×Q8—102no—
624C2×Q8—102no—
625C2×Q8—102no—
626C2×Q8#120211yescharacteristic, complemented
627C2×D4—21no—
628C2×D4—52no—
629C2×D4—51no—
630C2×D4—51no—
631C2×D4—102no—
632C2×D4—104no—
633C2×D4—104no—
634C2×D4—102no—
635C2×D4—104no—
636C2×D4—101no—
637C2×D4—102no—
638C2×D4—152no—
639C2×D4—304no—
640C2×D4—301no—
641C2×D4—301no—
642C2×D4—301no—
643C2×D4—301no—
644C2×D4—301no—
645C2×D4#120211yescharacteristic, complemented
646C22×C4—21no—
647C22×C4—52no—
648C22×C4—104no—
649C22×C4—101no—
650C22×C4C2×D3×D511yescharacteristic
651SD16—304no—
652SD16—304no—
653D8—304no—
654D8—304no—
655M16—32no—
656M16—61no—
657M16—152no—
658M16—301no—
659C2×C8—61no—
660C2×C8—301no—
661C4⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—304no—
664C42—32no—
665C3×C5#302111yescharacteristic, complemented, Hall
666C22×C3—22no—
667C22×C3—41no—
668C22×C3—81no—
669C22×C3—102no—
670C22×C3—102no—
671C22×C3—202no—
672C22×C3—401no—
673C22×C3—404no—
674C22×C3#402811yescharacteristic
675C22×C3#402811yescharacteristic
676C22×C3C2×D4×D511yescharacteristic
677C2×D3—204no—
678C2×D3—202no—
679C2×D3—402no—
680C2×D3—402no—
681C3×C4—22no—
682C3×C4—102no—
683C3×C4—102no—
684C3×C4#402811yescharacteristic
685C3×C4#402811yescharacteristic
686C3×C4C22×D2011yescharacteristic
687C3×C4C2×D4×D511yescharacteristic
688Dic3—42no—
689C2×C5—21no—
690C2×C5—21no—
691C2×C5—21no—
692C2×C5—42no—
693C2×C5C2×#95311yescharacteristic
694D5—42no—
695D5—42no—
696D5—242no—
697C23—21no—
698C23—52no—
699C23—104no—
700C23—101no—
701C23—302no—
702C23—601no—
703C23—601no—
704C23—1202no—
705C23D5×#6711yescharacteristic
706Q8—21no—
707Q8—52no—
708Q8—104no—
709Q8—101no—
710Q8—101no—
711Q8—101no—
712Q8C2×#120212yes—
713D4—22no—
714D4—22no—
715D4—21no—
716D4—52no—
717D4—104no—
718D4—104no—
719D4—104no—
720D4—102no—
721D4—102no—
722D4—102no—
723D4—102no—
724D4—101no—
725D4—101no—
726D4—101no—
727D4—302no—
728D4—302no—
729D4—601no—
730D4—601no—
731D4—1204no—
732D4C2×#120212yes—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—52no—
737C2×C4—62no—
738C2×C4—104no—
739C2×C4—104no—
740C2×C4—104no—
741C2×C4—101no—
742C2×C4—102no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4C2×#120211yescharacteristic
747C2×C4C2×#120211yescharacteristic
748C2×C4D5×#6711yescharacteristic
749C2×C4D5×#6711yescharacteristic
750C2×C4D5×#6711yescharacteristic
751C2×C4C22×D3×D511yescharacteristic
752C8—62no—
753C8—302no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—202no—
759C2×C3—202no—
760C2×C3C2×#402811yescharacteristic
761D3—402no—
762C5#8412211yescharacteristic, complemented, Sylow
763C22—22no—
764C22—41no—
765C22—81no—
766C22—102no—
767C22—102no—
768C22—202no—
769C22—401no—
770C22—404no—
771C22—604no—
772C22—602no—
773C22—1202no—
774C22—1202no—
775C22#9156411yescharacteristic
776C22#9156411yescharacteristic
777C22C2×D5×#6711yescharacteristic
778C4—22no—
779C4—102no—
780C4—102no—
781C4—122no—
782C4#9156411yescharacteristic
783C4#9156411yescharacteristic
784C4C22×#120211yescharacteristic
785C4C2×D5×#6711yescharacteristic
786C3#1061072511yescharacteristic, complemented, Sylow
787C2—21no—
788C2—21no—
789C2—21no—
790C2—42no—
791C2—202no—
792C2—202no—
793C2—1202no—
794C2C2×#9156411yescharacteristic
subgroupG/H
centerC2C2×#91564
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3021
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#66283C2semidirect
2. C2×#91838C2semidirect
3. #11754609C2semidirect
4. C2×#91301C2semidirect
5. C5×#5236C2semidirect
6. #11749457C2semidirect
7. #11749418C2semidirect
8. #11748421C2semidirect
9. #11748353C2semidirect
12. C22×D60C22semidirect
14. C3×#4150C22semidirect
16. C3×#4149C22semidirect
26. #91838C22semidirect
29. C2×#6710C22semidirect
30. C5×#926C22semidirect
31. C2×C5×#208C22semidirect
33. #91458C22semidirect
35. #91374C22semidirect
38. #91301C22semidirect
40. C5×#837C22semidirect
41. #90977C22semidirect
42. #90961C22semidirect
43. #90958C22semidirect
45. #66283D3semidirect
57. C3×C5×#41D4semidirect
59. C2×C3×C5×Q8D4semidirect
61. C2×C3×C5×D4D4semidirect
95. C3×#709D4semidirect
98. C2×C3×D20D4semidirect
104. C2×C3×Dic10D4semidirect
129. #5236D5semidirect
132. #4150C2×D3semidirect
134. #4149C2×D3semidirect
247. #926C2×D5semidirect
249. C2×#208C2×D5semidirect
251. #837C2×D5semidirect
257. C5×#41#67semidirect
259. C2×C5×Q8#67semidirect
261. C2×C5×D4#67semidirect
289. #709#67semidirect
299. C2×D20#67semidirect
305. C2×Dic10#67semidirect
374. C3×#41D20semidirect
381. C2×C3×Q8D20semidirect
393. C2×C3×D4D20semidirect
619. #41#1202semidirect
626. C2×Q8#1202semidirect
645. C2×D4#1202semidirect
665. C3×C5#3021semidirect
762. C5#84122semidirect
786. C3#10610725semidirect

Maximal subgroups

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

subgroupindex
C3×#662832
C2×#918382
#117546092
C2×#913012
C5×#52362
#117494572
#117494182
#117484212
#117483532
#106107253
#841225