Finite Group Databasebeta

← #14425491

Subgroups — #14425491

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
1C5×#5964C211yesmaximal, characteristic, complemented
2C2×#91838C211yesmaximal, characteristic, complemented
3#11754610C211yesmaximal, characteristic, complemented
4C2×#91305C211yesmaximal, characteristic, complemented
5C3×#65525C211yesmaximal, characteristic, complemented
6#11749459C214yesmaximal, complemented
7#11749420C214yesmaximal, complemented
8#11748425C211yesmaximal, characteristic, complemented
9#11748355C211yesmaximal, characteristic, complemented
10#10615853—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C22×D60C2211yescharacteristic, complemented
13C5×#1010—21no—
14C5×#1010C2212yescomplemented
15C5×#1009—21no—
16C5×#1009C2212yescomplemented
17C5×D3×#41—22no—
18C5×D3×#41—22no—
19C5×#1007—21no—
20C5×#1004—21no—
21C5×#1004—22no—
22C2×C5×#235—22no—
23C2×C5×#235C2211yescharacteristic
24C2×C5×#235C2211yescharacteristic
25#91838—22no—
26#91838C2214yescomplemented
27C2×#6717—21no—
28C2×#6715—21no—
29C2×#6710C2211yescharacteristic, complemented
30C3×#4072C2211yescharacteristic, complemented
31C2×C3×#681C2211yescharacteristic, complemented
32#91573—22no—
33#91460—22no—
34#91451C2212yescomplemented
35#91375C2212yescomplemented
36C2×#6660—21no—
37#91305—22no—
38#91305C2214yescomplemented
39C2×#6654—21no—
40C3×#3969C2214yescomplemented
41#90979C2214yescomplemented
42#90962C2212yescomplemented
43#90959C2212yescomplemented
44#78994—51nomaximal, Hall
45C5×#585—31no—
46#66164—31no—
47C2×#4095—31no—
48C2×#4095—31no—
49#65534—34no—
50#65530—34no—
51#65526—31no—
52#65525—31no—
53#65525D311yescharacteristic, complemented
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×C5×#67—24no—
71C2×C5×#67—21no—
72C2×C5×#67D412yes—
73C5×#239—22no—
74C5×#239—22no—
75C5×D3×Q8—22no—
76C5×D3×Q8—22no—
77C5×#237—24no—
78C5×#237—22no—
79C5×#237—22no—
80C5×#237—24no—
81C5×D3×D4—24no—
82C5×D3×D4—22no—
83C5×D3×D4—24no—
84C5×D3×D4—22no—
85C5×#235—24no—
86C5×#235—24no—
87C5×#235—21no—
88C5×#235—21no—
89C5×#235—21no—
90C5×#235—21no—
91C5×#235—21no—
92C5×#235—21no—
93C5×#235—22no—
94C5×#235—22no—
95C5×#235D412yescomplemented
96C5×#235C2312yes—
97C2×C5×D12—22no—
98C2×C5×D12D411yescharacteristic, complemented
99C2×C5×D12C2311yescharacteristic
100C2×C4×C5×D3—24no—
101C2×C4×C5×D3—21no—
102C2×C4×C5×D3D412yes—
103C2×C5×Dic6—22no—
104C2×C5×Dic6D411yescharacteristic, complemented
105C2×C5×Dic6C2311yescharacteristic
106C2×#1203—24no—
107#6717—24no—
108#6715—24no—
109#6710—21no—
110#6710C2312yes—
111C2×C3⋊#168—21no—
112C3×C22⋊Dic5—21no—
113C3×C4⋊Dic5—21no—
114C3×C4×Dic5C2312yes—
115C3×#681—21no—
116C3×#681C2312yes—
117C2×C3×#168—21no—
118#6667—24no—
119#6660—24no—
120#6654—24no—
121#5964D511yescharacteristic, complemented
122C2×#949—51no—
123C2×#908—51no—
124#5525—51no—
125C3×#421—51no—
126#5132—51no—
127#5005—51no—
128#4827—54no—
129#4822—54no—
130C5×2−1+4—32no—
131C5×2−1+4—61no—
132C5×2−1+4—61no—
133C5×H(5,𝔽2)—32no—
134C5×H(5,𝔽2)—62no—
135C5×H(5,𝔽2)—61no—
136C5×H(5,𝔽2)—61no—
137C2×C5×#41—31no—
138C2×C5×#41—31no—
139C2×C5×#41—62no—
140C2×C5×#41—62no—
141C2×C5×#41—62no—
142C2×C5×#41C2×D311yescharacteristic
143C22×D20—31no—
144#4095—34no—
145#4095—34no—
146#4095—62no—
147#4095—62no—
148#4093—32no—
149C2×#688—61no—
150C2×#688—61no—
151#4086—32no—
152#4083—62no—
153C2×#686—61no—
154C2×#686—61no—
155#4076—62no—
156#4072C2×D311yescharacteristic, complemented
157C2×#681—31no—
158C2×#681C2×D311yescharacteristic, complemented
159#3969—34no—
160#3969C2×D314yescomplemented
161#3968—32no—
162#3965—32no—
163#3021—151noSylow
164C23×C3×C5—21no—
165C23×C3×C5C2×D411yescharacteristic
166C22×D15—22no—
167C22×D15—41no—
168C22×D15—41no—
169C22×D15—82no—
170C22×C5×D3—24no—
171C22×C5×D3—21no—
172C22×C5×D3C2×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—
192C5×#67—24no—
193C5×#67—24no—
194C5×#67—22no—
195C5×#67—22no—
196C5×#67—22no—
197C5×#67—22no—
198C2×C5×Dic3—24no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3C2×D412yes—
201C5×D12—24no—
202C5×D12—21no—
203C5×D12—21no—
204C5×D12—21no—
205C5×D12C2×D412yes—
206C4×C5×D3—24no—
207C4×C5×D3—24no—
208C4×C5×D3—22no—
209C4×C5×D3—22no—
210C4×C5×D3—22no—
211C4×C5×D3—22no—
212C5×Dic6—24no—
213C5×Dic6—21no—
214C5×Dic6—21no—
215C5×Dic6—21no—
216C5×Dic6C2×D412yes—
217C2×C3×Dic5—22no—
218#1203—84no—
219C3⋊#168—22no—
220C3×#168—22no—
221C2×C3×#41C2×D511yescharacteristic
222#1010—21no—
223#1010C2×D512yescomplemented
224#1009—21no—
225#1009C2×D512yescomplemented
226D3×#41—22no—
227D3×#41—22no—
228#1007—21no—
229#1004—21no—
230#1004—22no—
231C2×#235—22no—
232C2×#235C2×D511yescharacteristic
233C2×#235C2×D511yescharacteristic
234C22×D12—51no—
235C2×C3×M16—51no—
236C3×#117—51no—
237#949—54no—
238#949—102no—
239C2×#215—101no—
240C2×#213—101no—
241C2×#208—51no—
242#908—54no—
243#908—102no—
244C2×D24—101no—
245C2×#204—101no—
246#895—102no—
247#882—102no—
248#875—52no—
249#874—52no—
250C3×#104—54no—
251#824—52no—
252#823—52no—
253#805—54no—
254C23×D5—61no—
255C5×#41—21no—
256C5×#41—21no—
257C5×#41—32no—
258C5×#41—32no—
259C5×#41—62no—
260C5×#41—62no—
261C5×#41—64no—
262C5×#41—64no—
263C5×#41—64no—
264C5×#41—64no—
265C5×#41—62no—
266C5×#41—62no—
267C5×#41—62no—
268C5×#41—62no—
269C5×#41—61no—
270C5×#41—61no—
271C5×#41—61no—
272C5×#41—61no—
273C5×#41—61no—
274C5×#41—61no—
275C5×#41D1212yescomplemented
276C5×#41C22×D312yes—
277C2×C5×Q8—31no—
278C2×C5×Q8—31no—
279C2×C5×Q8—62no—
280C2×C5×Q8—62no—
281C2×C5×Q8—62no—
282C2×C5×Q8D1211yescharacteristic, complemented
283C2×C5×D4—21no—
284C2×C5×D4—32no—
285C2×C5×D4—31no—
286C2×C5×D4—31no—
287C2×C5×D4—62no—
288C2×C5×D4—64no—
289C2×C5×D4—64no—
290C2×C5×D4—62no—
291C2×C5×D4—64no—
292C2×C5×D4—61no—
293C2×C5×D4—62no—
294C2×C5×D4D1211yescharacteristic, complemented
295C22×C4×C5—21no—
296C22×C4×C5—32no—
297C22×C4×C5—64no—
298C22×C4×C5—61no—
299C22×C4×C5C22×D311yescharacteristic
300C2×C22⋊D5—64no—
301C2×D20—32no—
302C2×D20—61no—
303C2×D20—61no—
304C2×D20—61no—
305C2×D20—61no—
306C2×D20—61no—
307C22⋊Dic5—21no—
308#688—64no—
309#688—64no—
310#686—64no—
311#686—64no—
312#685—64no—
313C4⋊Dic5—21no—
314C4×Dic5C22×D312yes—
315#681—21no—
316#681—32no—
317#681—61no—
318#681C22×D312yes—
319C2×#168—21no—
320C2×#168—61no—
321#585—31no—
322C2×AGL(1,ℤ/8)—151no—
323C2×AGL(1,ℤ/8)—151no—
324#535—151no—
325#454—154no—
326#453—154no—
327#421—51no—
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×C5×D3—22no—
341C2×C5×D3—22no—
342C2×C5×D3—42no—
343C2×C5×D3—81no—
344C2×C5×D3—84no—
345C3×C4×C5—22no—
346C3×C4×C5#12011yescharacteristic
347C3×C4×C5#12011yescharacteristic
348C3×C4×C5C22×D411yescharacteristic
349C3×C4×C5C22×D411yescharacteristic
350C3×Dic5—42no—
351C5×Dic3—22no—
352C5×Dic3—22no—
353C23×D3—101no—
354C3×#41—21no—
355C3×#41—21no—
356C3×#41C22⋊D512yescomplemented
357C3×#41C22×D512yes—
358C2×C3×Q8C22⋊D511yescharacteristic, complemented
359C2×C3×D4—21no—
360C2×C3×D4C22⋊D511yescharacteristic, complemented
361C22×C3×C4—21no—
362C22×C3×C4C22×D511yescharacteristic
363C2×#67—24no—
364C2×#67—21no—
365C2×#67C22⋊D512yes—
366#239—22no—
367#239—22no—
368D3×Q8—22no—
369D3×Q8—22no—
370#237—24no—
371#237—22no—
372#237—22no—
373#237—24no—
374D3×D4—24no—
375D3×D4—22no—
376D3×D4—24no—
377D3×D4—22no—
378#235—24no—
379#235—24no—
380#235—21no—
381#235—21no—
382#235—21no—
383#235—21no—
384#235—21no—
385#235—21no—
386#235—22no—
387#235—22no—
388#235C22⋊D512yescomplemented
389#235C22×D512yes—
390C2×D12—22no—
391C2×D12—52no—
392C2×D12—101no—
393C2×D12—101no—
394C2×D12—101no—
395C2×D12—101no—
396C2×D12—101no—
397C2×D12—104no—
398C2×D12C22⋊D511yescharacteristic, complemented
399C2×D12C22×D511yescharacteristic
400C2×C4×D3—24no—
401C2×C4×D3—21no—
402C2×C4×D3C22⋊D512yes—
403C2×Dic6—22no—
404C2×Dic6C22⋊D511yescharacteristic, complemented
405C2×Dic6C22×D511yescharacteristic
406C3×M16—52no—
407C3×M16—101no—
408C2×C3×C8—101no—
409C3×C4⋊C4—101no—
410C3×C22⋊C4—101no—
411C3×C42—52no—
412#215—104no—
413#213—104no—
414(C2×D3)⋊C4—104no—
415#208—52no—
416#208—101no—
417C2×C3⋊C8—101no—
418D24—104no—
419#204—104no—
420C23×C5—21no—
421C23×C5—32no—
422C23×C5—64no—
423C23×C5—61no—
424C23×C5D3×D411yescharacteristic
425C22×D5—62no—
426C22×D5—121no—
427C22×D5—121no—
428C22×D5—242no—
429C5×Q8—21no—
430C5×Q8—32no—
431C5×Q8—64no—
432C5×Q8—61no—
433C5×Q8—61no—
434C5×Q8—61no—
435C5×Q8C2×D1212yes—
436C5×D4—22no—
437C5×D4—22no—
438C5×D4—21no—
439C5×D4—32no—
440C5×D4—64no—
441C5×D4—64no—
442C5×D4—64no—
443C5×D4—62no—
444C5×D4—62no—
445C5×D4—62no—
446C5×D4—62no—
447C5×D4—61no—
448C5×D4—61no—
449C5×D4—61no—
450C5×D4C2×D1212yes—
451C2×C4×C5—21no—
452C2×C4×C5—22no—
453C2×C4×C5—22no—
454C2×C4×C5—32no—
455C2×C4×C5—64no—
456C2×C4×C5—64no—
457C2×C4×C5—64no—
458C2×C4×C5—61no—
459C2×C4×C5—62no—
460C2×C4×C5—62no—
461C2×C4×C5—62no—
462C2×C4×C5—62no—
463C2×C4×C5C2×D1211yescharacteristic
464C2×C4×C5C2×D1211yescharacteristic
465C2×C4×C5D3×D411yescharacteristic
466C2×C4×C5D3×D411yescharacteristic
467C2×C4×C5D3×D411yescharacteristic
468C2×C4×C5C23×D311yescharacteristic
469C22⋊D5—244no—
470C2×Dic5—22no—
471D20—62no—
472D20—62no—
473D20—121no—
474D20—121no—
475#168—22no—
476#168—62no—
4772−1+4—32no—
4782−1+4—61no—
4792−1+4—61no—
480H(5,𝔽2)—32no—
481H(5,𝔽2)—62no—
482H(5,𝔽2)—61no—
483H(5,𝔽2)—61no—
484C2×#41—31no—
485C2×#41—31no—
486C2×#41—62no—
487C2×#41—62no—
488C2×#41—62no—
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—51no—
500C2×M16—151no—
501#127—152no—
502#124—152no—
503#121—302no—
504#120—302no—
505#117—51no—
506#104—54no—
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—
516C5×D3—42no—
517C5×D3—42no—
518C23×C3—21no—
519C23×C3C2×C22⋊D511yescharacteristic
520C22×D3—24no—
521C22×D3—21no—
522C22×D3—102no—
523C22×D3—201no—
524C22×D3—201no—
525C22×D3—402no—
526C22×D3C2×C22⋊D512yes—
527C3×Q8—21no—
528C3×Q8C2×C22⋊D512yes—
529C3×D4—22no—
530C3×D4—22no—
531C3×D4—21no—
532C3×D4C2×C22⋊D512yes—
533C2×C3×C4—21no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—102no—
537C2×C3×C4C2×C22⋊D511yescharacteristic
538C2×C3×C4C2×C22⋊D511yescharacteristic
539C2×C3×C4C2×C22⋊D511yescharacteristic
540C2×C3×C4C2×C22⋊D511yescharacteristic
541C2×C3×C4C2×C22⋊D511yescharacteristic
542C2×C3×C4C23×D511yescharacteristic
543#67—24no—
544#67—24no—
545#67—22no—
546#67—22no—
547#67—22no—
548#67—22no—
549C2×Dic3—24no—
550C2×Dic3—21no—
551C2×Dic3C2×C22⋊D512yes—
552D12—24no—
553D12—21no—
554D12—21no—
555D12—21no—
556D12—102no—
557D12—102no—
558D12—201no—
559D12—201no—
560D12—404no—
561D12C2×C22⋊D512yes—
562C4×D3—24no—
563C4×D3—24no—
564C4×D3—22no—
565C4×D3—22no—
566C4×D3—22no—
567C4×D3—22no—
568Dic6—24no—
569Dic6—21no—
570Dic6—21no—
571Dic6—21no—
572Dic6C2×C22⋊D512yes—
573C3×C8—102no—
574C3⋊C8—102no—
575C22×C5—22no—
576C22×C5—41no—
577C22×C5—62no—
578C22×C5—62no—
579C22×C5—81no—
580C22×C5—122no—
581C22×C5—241no—
582C22×C5—244no—
583C22×C5#88211yescharacteristic
584C22×C5#88211yescharacteristic
585C22×C5C2×D3×D411yescharacteristic
586C2×D5—124no—
587C2×D5—122no—
588C2×D5—242no—
589C2×D5—242no—
590C4×C5—22no—
591C4×C5—62no—
592C4×C5—62no—
593C4×C5#88211yescharacteristic
594C4×C5#88211yescharacteristic
595C4×C5C22×D1211yescharacteristic
596C4×C5C2×D3×D411yescharacteristic
597Dic5—42no—
598C24—301no—
599#41—21no—
600#41—21no—
601#41—32no—
602#41—32no—
603#41—62no—
604#41—62no—
605#41—64no—
606#41—64no—
607#41—64no—
608#41—64no—
609#41—62no—
610#41—62no—
611#41—62no—
612#41—62no—
613#41—61no—
614#41—61no—
615#41—61no—
616#41—61no—
617#41—61no—
618#41—61no—
619#41#120312yescomplemented
620#41C2×D3×D512yes—
621C2×Q8—31no—
622C2×Q8—31no—
623C2×Q8—62no—
624C2×Q8—62no—
625C2×Q8—62no—
626C2×Q8#120311yescharacteristic, complemented
627C2×D4—21no—
628C2×D4—32no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—62no—
632C2×D4—64no—
633C2×D4—64no—
634C2×D4—62no—
635C2×D4—64no—
636C2×D4—61no—
637C2×D4—62no—
638C2×D4—152no—
639C2×D4—304no—
640C2×D4—301no—
641C2×D4—301no—
642C2×D4—301no—
643C2×D4—301no—
644C2×D4—301no—
645C2×D4#120311yescharacteristic, complemented
646C22×C4—21no—
647C22×C4—32no—
648C22×C4—64no—
649C22×C4—61no—
650C22×C4C2×D3×D511yescharacteristic
651SD16—304no—
652SD16—304no—
653D8—304no—
654D8—304no—
655M16—52no—
656M16—101no—
657M16—152no—
658M16—301no—
659C2×C8—101no—
660C2×C8—301no—
661C4⋊C4—101no—
662C22⋊C4—101no—
663C22⋊C4—304no—
664C42—52no—
665C3×C5#302111yescharacteristic, complemented, Hall
666C22×C3—22no—
667C22×C3—41no—
668C22×C3—81no—
669C22×C3#409911yescharacteristic
670C22×C3#409911yescharacteristic
671C22×C3C22×C22⋊D511yescharacteristic
672C2×D3—22no—
673C2×D3—22no—
674C2×D3—42no—
675C2×D3—81no—
676C2×D3—84no—
677C2×D3—204no—
678C2×D3—202no—
679C2×D3—402no—
680C2×D3—402no—
681C3×C4—22no—
682C3×C4—202no—
683C3×C4#409911yescharacteristic
684C3×C4#409911yescharacteristic
685C3×C4C22×C22⋊D511yescharacteristic
686C3×C4C22×C22⋊D511yescharacteristic
687Dic3—22no—
688Dic3—22no—
689C2×C5—21no—
690C2×C5—21no—
691C2×C5—21no—
692C2×C5—42no—
693C2×C5—122no—
694C2×C5—122no—
695C2×C5C2×#88211yescharacteristic
696D5—242no—
697C23—21no—
698C23—32no—
699C23—64no—
700C23—61no—
701C23—302no—
702C23—601no—
703C23—601no—
704C23—1202no—
705C23D3×C22⋊D511yescharacteristic
706Q8—21no—
707Q8—32no—
708Q8—64no—
709Q8—61no—
710Q8—61no—
711Q8—61no—
712Q8C2×#120312yes—
713D4—22no—
714D4—22no—
715D4—21no—
716D4—32no—
717D4—64no—
718D4—64no—
719D4—64no—
720D4—62no—
721D4—62no—
722D4—62no—
723D4—62no—
724D4—61no—
725D4—61no—
726D4—61no—
727D4—302no—
728D4—302no—
729D4—601no—
730D4—601no—
731D4—1204no—
732D4C2×#120312yes—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—32no—
737C2×C4—64no—
738C2×C4—64no—
739C2×C4—64no—
740C2×C4—61no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—102no—
746C2×C4C2×#120311yescharacteristic
747C2×C4C2×#120311yescharacteristic
748C2×C4D3×C22⋊D511yescharacteristic
749C2×C4D3×C22⋊D511yescharacteristic
750C2×C4D3×C22⋊D511yescharacteristic
751C2×C4C22×D3×D511yescharacteristic
752C8—102no—
753C8—302no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3C2×#409911yescharacteristic
759D3—42no—
760D3—42no—
761D3—402no—
762C5#7899411yescharacteristic, complemented, Sylow
763C22—22no—
764C22—41no—
765C22—62no—
766C22—62no—
767C22—81no—
768C22—122no—
769C22—241no—
770C22—244no—
771C22—604no—
772C22—602no—
773C22—1202no—
774C22—1202no—
775C22#9157011yescharacteristic
776C22#9157011yescharacteristic
777C22C2×D3×C22⋊D511yescharacteristic
778C4—22no—
779C4—62no—
780C4—62no—
781C4—202no—
782C4#9157011yescharacteristic
783C4#9157011yescharacteristic
784C4C22×#120311yescharacteristic
785C4C2×D3×C22⋊D511yescharacteristic
786C3#1061585311yescharacteristic, complemented, Sylow
787C2—21no—
788C2—21no—
789C2—21no—
790C2—42no—
791C2—122no—
792C2—122no—
793C2—1202no—
794C2C2×#9157011yescharacteristic
subgroupG/H
centerC2C2×#91570
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. C5×#5964C2semidirect
2. C2×#91838C2semidirect
3. #11754610C2semidirect
4. C2×#91305C2semidirect
5. C3×#65525C2semidirect
6. #11749459C2semidirect
7. #11749420C2semidirect
8. #11748425C2semidirect
9. #11748355C2semidirect
12. C22×D60C22semidirect
14. C5×#1010C22semidirect
16. C5×#1009C22semidirect
26. #91838C22semidirect
29. C2×#6710C22semidirect
30. C3×#4072C22semidirect
31. C2×C3×#681C22semidirect
34. #91451C22semidirect
35. #91375C22semidirect
38. #91305C22semidirect
40. C3×#3969C22semidirect
41. #90979C22semidirect
42. #90962C22semidirect
43. #90959C22semidirect
53. #65525D3semidirect
57. C3×C5×#41D4semidirect
59. C2×C3×C5×Q8D4semidirect
61. C2×C3×C5×D4D4semidirect
95. C5×#235D4semidirect
98. C2×C5×D12D4semidirect
104. C2×C5×Dic6D4semidirect
121. #5964D5semidirect
156. #4072C2×D3semidirect
158. C2×#681C2×D3semidirect
160. #3969C2×D3semidirect
223. #1010C2×D5semidirect
225. #1009C2×D5semidirect
275. C5×#41D12semidirect
282. C2×C5×Q8D12semidirect
294. C2×C5×D4D12semidirect
356. C3×#41C22⋊D5semidirect
358. C2×C3×Q8C22⋊D5semidirect
360. C2×C3×D4C22⋊D5semidirect
388. #235C22⋊D5semidirect
398. C2×D12C22⋊D5semidirect
404. C2×Dic6C22⋊D5semidirect
619. #41#1203semidirect
626. C2×Q8#1203semidirect
645. C2×D4#1203semidirect
665. C3×C5#3021semidirect
762. C5#78994semidirect
786. C3#10615853semidirect

Maximal subgroups

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

subgroupindex
C5×#59642
C2×#918382
#117546102
C2×#913052
C3×#655252
#117494592
#117494202
#117484252
#117483552
#106158533
#789945