Finite Group Databasebeta

← #14425490

Subgroups — #14425490

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×C3×#4095C211yesmaximal, characteristic, complemented
3#11754600C211yesmaximal, characteristic, complemented
4C2×#91298C211yesmaximal, characteristic, complemented
5#11751337C211yesmaximal, characteristic, complemented
6#11749458C214yesmaximal, complemented
7#11749419C214yesmaximal, complemented
8#11748424C211yesmaximal, characteristic, complemented
9#11748355C211yesmaximal, characteristic, complemented
10#10615853—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C5×#1010—21no—
13C5×#1010C2212yescomplemented
14C5×#1009—21no—
15C5×#1009C2212yescomplemented
16C5×D3×#41—22no—
17C5×D3×#41—22no—
18C5×#1007—21no—
19C5×#1004—21no—
20C5×#1004—22no—
21C2×C5×#235—22no—
22C2×C5×#235C2211yescharacteristic
23C2×C5×#235C2211yescharacteristic
24C22×C3×D20C2211yescharacteristic, complemented
25#91815C2211yescharacteristic, complemented
26C2×#6710C2211yescharacteristic, complemented
27C3×#4095—22no—
28C3×#4095C2214yescomplemented
29C2×C3×#688—21no—
30C2×C3×#686—21no—
31C2×C3×#681C2211yescharacteristic, complemented
32#91563—22no—
33#91463C2212yescomplemented
34#91456—22no—
35#91368C2212yescomplemented
36C2×#6655—21no—
37#91298—22no—
38#91298C2214yescomplemented
39C2×#6652—21no—
40#91121C2214yescomplemented
41#90978C2214yescomplemented
42#90962C2212yescomplemented
43#90959C2212yescomplemented
44#83957—51nomaximal, Hall
45C5×#585—31no—
46#66164—31no—
47C2×#4095—31no—
48C2×#4095D311yescharacteristic, complemented
49#65534—34no—
50#65530—34no—
51#65526—31no—
52#65525—31no—
53#65525—31no—
54C23×C3×D5—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×C5×#67—24no—
65C2×C5×#67—21no—
66C2×C5×#67D412yes—
67C5×#239—22no—
68C5×#239—22no—
69C5×D3×Q8—22no—
70C5×D3×Q8—22no—
71C5×#237—24no—
72C5×#237—22no—
73C5×#237—22no—
74C5×#237—24no—
75C5×D3×D4—24no—
76C5×D3×D4—22no—
77C5×D3×D4—24no—
78C5×D3×D4—22no—
79C5×#235—24no—
80C5×#235—24no—
81C5×#235—21no—
82C5×#235—21no—
83C5×#235—21no—
84C5×#235—21no—
85C5×#235—21no—
86C5×#235—21no—
87C5×#235—22no—
88C5×#235—22no—
89C5×#235D412yescomplemented
90C5×#235C2312yes—
91C2×C5×D12—22no—
92C2×C5×D12D411yescharacteristic, complemented
93C2×C5×D12C2311yescharacteristic
94C2×C4×C5×D3—24no—
95C2×C4×C5×D3—21no—
96C2×C4×C5×D3D412yes—
97C2×C5×Dic6—22no—
98C2×C5×Dic6D411yescharacteristic, complemented
99C2×C5×Dic6C2311yescharacteristic
100C2×C3×D20—21no—
101C2×C3×D20—21no—
102C2×C3×D20—21no—
103C2×C3×D20—21no—
104C2×C3×D20—21no—
105C2×C3×D20C2312yes—
106C2×#1201—24no—
107#6719—21no—
108C4⋊Dic15—21no—
109C4×Dic15C2312yes—
110#6710—21no—
111#6710C2312yes—
112C2×C3⋊#168—21no—
113C3×#688—24no—
114C3×#686—24no—
115C3×#681—21no—
116C3×#681C2312yes—
117C2×C3×#168—21no—
118#6665—24no—
119#6655—24no—
120#6652—24no—
121#5964D511yescharacteristic, complemented
122C2×C3×AGL(1,ℤ/8)—51no—
123#5805—51no—
124C2×#932—51no—
125#5236—51no—
126#5201—54no—
127#5198—54no—
128#5139—51no—
129#5132—51no—
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×D20C2×D311yescharacteristic, complemented
144#4095—22no—
145#4095—34no—
146#4095—62no—
147#4095C2×D314yescomplemented
148#4093—32no—
149C2×#688—21no—
150C2×#688—61no—
151#4086—32no—
152#4083—62no—
153C2×#686—21no—
154C2×#686—61no—
155#4076—62no—
156#4072—31no—
157C2×#681—31no—
158C2×#681C2×D311yescharacteristic, complemented
159#3969—34no—
160#3969—34no—
161#3968—32no—
162#3965—32no—
163#3021—151noSylow
164C23×C3×C5—21no—
165C23×C3×C5C2×D411yescharacteristic
166C22×C5×D3—24no—
167C22×C5×D3—21no—
168C22×C5×D3C2×D412yes—
169C22×C3×D5—22no—
170C22×C3×D5—41no—
171C22×C3×D5—41no—
172C22×C3×D5—82no—
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
188C2×Dic15—22no—
189C5×#67—24no—
190C5×#67—24no—
191C5×#67—22no—
192C5×#67—22no—
193C5×#67—22no—
194C5×#67—22no—
195C2×C5×Dic3—24no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3C2×D412yes—
198C5×D12—24no—
199C5×D12—21no—
200C5×D12—21no—
201C5×D12—21no—
202C5×D12C2×D412yes—
203C4×C5×D3—24no—
204C4×C5×D3—24no—
205C4×C5×D3—22no—
206C4×C5×D3—22no—
207C4×C5×D3—22no—
208C4×C5×D3—22no—
209C5×Dic6—24no—
210C5×Dic6—21no—
211C5×Dic6—21no—
212C5×Dic6—21no—
213C5×Dic6C2×D412yes—
214C3×D20—22no—
215C3×D20—22no—
216C3×D20—41no—
217C3×D20—41no—
218#1201—84no—
219C3⋊#168—22no—
220C3×#168—22no—
221C2×C3×#41C2×D511yescharacteristic
222C22×C3×D4—51no—
223#1010—21no—
224#1010C2×D512yescomplemented
225#1009—21no—
226#1009C2×D512yescomplemented
227D3×#41—22no—
228D3×#41—22no—
229#1007—21no—
230#1004—21no—
231#1004—22no—
232C2×#235—22no—
233C2×#235C2×D511yescharacteristic
234C2×#235C2×D511yescharacteristic
235C3×AGL(1,ℤ/8)—54no—
236C3×AGL(1,ℤ/8)—102no—
237C2×C3×SD16—101no—
238C2×C3×D8—101no—
239C2×C3×M16—51no—
240#953—102no—
241#940—52no—
242#938—102no—
243#936—52no—
244C2×#214—101no—
245#932—54no—
246#932—102no—
247C2×#213—101no—
248#926—51no—
249C2×#208—51no—
250#837—54no—
251#825—54no—
252#824—52no—
253#823—52no—
254C23×D5—21no—
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×#41#6712yescomplemented
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×Q8#6711yescharacteristic, 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×D4#6711yescharacteristic, 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—21no—
302C2×D20—21no—
303C2×D20—21no—
304C2×D20—21no—
305C2×D20—21no—
306C2×D20C22×D312yes—
307C22⋊Dic5—61no—
308#688—24no—
309#688—64no—
310#686—24no—
311#686—64no—
312#685—64no—
313C4⋊Dic5—61no—
314C4×Dic5—32no—
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)—51no—
323C2×AGL(1,ℤ/8)—151no—
324#535—151no—
325#454—154no—
326#453—154no—
327#421—151no—
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×C5×D3—22no—
337C2×C5×D3—22no—
338C2×C5×D3—42no—
339C2×C5×D3—81no—
340C2×C5×D3—84no—
341C2×C3×D5—44no—
342C2×C3×D5—42no—
343C2×C3×D5—82no—
344C2×C3×D5—82no—
345C3×C4×C5—22no—
346C3×C4×C5#12011yescharacteristic
347C3×C4×C5#12011yescharacteristic
348C3×C4×C5C22×D411yescharacteristic
349C3×C4×C5C22×D411yescharacteristic
350Dic15—42no—
351C5×Dic3—22no—
352C5×Dic3—22no—
353C24×C3—101no—
354C3×#41—21no—
355C3×#41—21no—
356C3×#41C22⋊D512yescomplemented
357C3×#41C22×D512yes—
358C2×C3×Q8C22⋊D511yescharacteristic, complemented
359C2×C3×D4—21no—
360C2×C3×D4—52no—
361C2×C3×D4—101no—
362C2×C3×D4—101no—
363C2×C3×D4—101no—
364C2×C3×D4—101no—
365C2×C3×D4—101no—
366C2×C3×D4C22⋊D511yescharacteristic, complemented
367C22×C3×C4—21no—
368C22×C3×C4C22×D511yescharacteristic
369C2×#67—24no—
370C2×#67—21no—
371C2×#67—104no—
372C2×#67C22⋊D512yes—
373#239—22no—
374#239—22no—
375D3×Q8—22no—
376D3×Q8—22no—
377#237—24no—
378#237—22no—
379#237—22no—
380#237—24no—
381D3×D4—24no—
382D3×D4—22no—
383D3×D4—24no—
384D3×D4—22no—
385#235—24no—
386#235—24no—
387#235—21no—
388#235—21no—
389#235—21no—
390#235—21no—
391#235—21no—
392#235—21no—
393#235—22no—
394#235—22no—
395#235C22⋊D512yescomplemented
396#235C22×D512yes—
397C2×D12—22no—
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×SD16—104no—
407C3×D8—104no—
408C3×M16—52no—
409C3×M16—101no—
410C2×C3×C8—101no—
411#217—101no—
412#217—104no—
413#214—104no—
414#213—104no—
415C4⋊Dic3—101no—
416C4×Dic3—52no—
417#208—52no—
418#208—101no—
419C2×C3⋊C8—101no—
420C23×C5—21no—
421C23×C5—32no—
422C23×C5—64no—
423C23×C5—61no—
424C23×C5D3×D411yescharacteristic
425C22×D5—22no—
426C22×D5—41no—
427C22×D5—41no—
428C22×D5—82no—
429C5×Q8—21no—
430C5×Q8—32no—
431C5×Q8—64no—
432C5×Q8—61no—
433C5×Q8—61no—
434C5×Q8—61no—
435C5×Q8C2×#6712yes—
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×#6712yes—
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×C5D3×D411yescharacteristic
464C2×C4×C5D3×D411yescharacteristic
465C2×C4×C5D3×D411yescharacteristic
466C2×C4×C5C2×#6711yescharacteristic
467C2×C4×C5C2×#6711yescharacteristic
468C2×C4×C5C23×D311yescharacteristic
469C22⋊D5—244no—
470C2×Dic5—62no—
471D20—22no—
472D20—22no—
473D20—41no—
474D20—41no—
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—51no—
491AGL(1,ℤ/8)—54no—
492AGL(1,ℤ/8)—102no—
493AGL(1,ℤ/8)—154no—
494AGL(1,ℤ/8)—302no—
495C2×SD16—101no—
496C2×SD16—301no—
497C2×D8—101no—
498C2×D8—301no—
499C2×M16—51no—
500C2×M16—151no—
501#127—152no—
502#124—152no—
503#121—302no—
504#120—302no—
505#117—151no—
506#104—154no—
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
515C3×D5—82no—
516C5×D3—42no—
517C5×D3—42no—
518C23×C3—21no—
519C23×C3—102no—
520C23×C3—201no—
521C23×C3—201no—
522C23×C3—402no—
523C23×C3C2×C22⋊D511yescharacteristic
524C22×D3—24no—
525C22×D3—21no—
526C22×D3C2×C22⋊D512yes—
527C3×Q8—21no—
528C3×Q8C2×C22⋊D512yes—
529C3×D4—22no—
530C3×D4—22no—
531C3×D4—21no—
532C3×D4—102no—
533C3×D4—102no—
534C3×D4—201no—
535C3×D4—201no—
536C3×D4C2×C22⋊D512yes—
537C2×C3×C4—21no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4C2×C22⋊D511yescharacteristic
541C2×C3×C4C2×C22⋊D511yescharacteristic
542C2×C3×C4C2×C22⋊D511yescharacteristic
543C2×C3×C4C2×C22⋊D511yescharacteristic
544C2×C3×C4C2×C22⋊D511yescharacteristic
545C2×C3×C4C23×D511yescharacteristic
546#67—24no—
547#67—24no—
548#67—22no—
549#67—22no—
550#67—22no—
551#67—22no—
552#67—404no—
553C2×Dic3—24no—
554C2×Dic3—21no—
555C2×Dic3—102no—
556C2×Dic3C2×C22⋊D512yes—
557D12—24no—
558D12—21no—
559D12—21no—
560D12—21no—
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#93711yescharacteristic
584C22×C5#93711yescharacteristic
585C22×C5C2×D3×D411yescharacteristic
586C2×D5—44no—
587C2×D5—42no—
588C2×D5—82no—
589C2×D5—82no—
590C4×C5—22no—
591C4×C5—62no—
592C4×C5—62no—
593C4×C5#93711yescharacteristic
594C4×C5#93711yescharacteristic
595C4×C5C2×D3×D411yescharacteristic
596C4×C5C22×#6711yescharacteristic
597Dic5—122no—
598C24—101no—
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#120112yescomplemented
620#41C2×D3×D512yes—
621C2×Q8—31no—
622C2×Q8—31no—
623C2×Q8—62no—
624C2×Q8—62no—
625C2×Q8—62no—
626C2×Q8#120111yescharacteristic, complemented
627C2×D4—21no—
628C2×D4—32no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—52no—
632C2×D4—62no—
633C2×D4—64no—
634C2×D4—64no—
635C2×D4—62no—
636C2×D4—64no—
637C2×D4—61no—
638C2×D4—62no—
639C2×D4—101no—
640C2×D4—101no—
641C2×D4—101no—
642C2×D4—101no—
643C2×D4—101no—
644C2×D4—304no—
645C2×D4#120111yescharacteristic, complemented
646C22×C4—21no—
647C22×C4—32no—
648C22×C4—64no—
649C22×C4—61no—
650C22×C4C2×D3×D511yescharacteristic
651SD16—104no—
652SD16—304no—
653D8—104no—
654D8—304no—
655M16—52no—
656M16—101no—
657M16—152no—
658M16—301no—
659C2×C8—101no—
660C2×C8—301no—
661C4⋊C4—301no—
662C22⋊C4—304no—
663C22⋊C4—301no—
664C42—152no—
665C3×C5#302111yescharacteristic, complemented, Hall
666C22×C3—22no—
667C22×C3—41no—
668C22×C3—81no—
669C22×C3—204no—
670C22×C3—202no—
671C22×C3—402no—
672C22×C3—402no—
673C22×C3#409911yescharacteristic
674C22×C3#409911yescharacteristic
675C22×C3C22×C22⋊D511yescharacteristic
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—42no—
679C2×D3—81no—
680C2×D3—84no—
681C3×C4—22no—
682C3×C4#409911yescharacteristic
683C3×C4#409911yescharacteristic
684C3×C4C22×C22⋊D511yescharacteristic
685C3×C4C22×C22⋊D511yescharacteristic
686Dic3—22no—
687Dic3—22no—
688Dic3—202no—
689C2×C5—21no—
690C2×C5—21no—
691C2×C5—21no—
692C2×C5—42no—
693C2×C5—122no—
694C2×C5—122no—
695C2×C5C2×#93711yescharacteristic
696D5—82no—
697C23—21no—
698C23—32no—
699C23—64no—
700C23—61no—
701C23—102no—
702C23—201no—
703C23—201no—
704C23—402no—
705C23D3×C22⋊D511yescharacteristic
706Q8—21no—
707Q8—32no—
708Q8—64no—
709Q8—61no—
710Q8—61no—
711Q8—61no—
712Q8C2×#120112yes—
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—102no—
728D4—102no—
729D4—201no—
730D4—201no—
731D4—1204no—
732D4C2×#120112yes—
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—302no—
746C2×C4C2×#120111yescharacteristic
747C2×C4C2×#120111yescharacteristic
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×C3—402no—
759C2×C3C2×#409911yescharacteristic
760D3—42no—
761D3—42no—
762C5#8395711yescharacteristic, complemented, Sylow
763C22—22no—
764C22—41no—
765C22—62no—
766C22—62no—
767C22—81no—
768C22—122no—
769C22—204no—
770C22—202no—
771C22—241no—
772C22—244no—
773C22—402no—
774C22—402no—
775C22#9156811yescharacteristic
776C22#9156811yescharacteristic
777C22C2×D3×C22⋊D511yescharacteristic
778C4—22no—
779C4—62no—
780C4—62no—
781C4—602no—
782C4#9156811yescharacteristic
783C4#9156811yescharacteristic
784C4C22×#120111yescharacteristic
785C4C2×D3×C22⋊D511yescharacteristic
786C3#1061585311yescharacteristic, complemented, Sylow
787C2—21no—
788C2—21no—
789C2—21no—
790C2—42no—
791C2—122no—
792C2—122no—
793C2—402no—
794C2C2×#9156811yescharacteristic
subgroupG/H
centerC2C2×#91568
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×C3×#4095C2semidirect
3. #11754600C2semidirect
4. C2×#91298C2semidirect
5. #11751337C2semidirect
6. #11749458C2semidirect
7. #11749419C2semidirect
8. #11748424C2semidirect
9. #11748355C2semidirect
13. C5×#1010C22semidirect
15. C5×#1009C22semidirect
24. C22×C3×D20C22semidirect
25. #91815C22semidirect
26. C2×#6710C22semidirect
28. C3×#4095C22semidirect
31. C2×C3×#681C22semidirect
33. #91463C22semidirect
35. #91368C22semidirect
38. #91298C22semidirect
40. #91121C22semidirect
41. #90978C22semidirect
42. #90962C22semidirect
43. #90959C22semidirect
48. C2×#4095D3semidirect
57. C3×C5×#41D4semidirect
59. C2×C3×C5×Q8D4semidirect
61. C2×C3×C5×D4D4semidirect
89. C5×#235D4semidirect
92. C2×C5×D12D4semidirect
98. C2×C5×Dic6D4semidirect
121. #5964D5semidirect
143. C22×D20C2×D3semidirect
147. #4095C2×D3semidirect
158. C2×#681C2×D3semidirect
224. #1010C2×D5semidirect
226. #1009C2×D5semidirect
275. C5×#41#67semidirect
282. C2×C5×Q8#67semidirect
294. C2×C5×D4#67semidirect
356. C3×#41C22⋊D5semidirect
358. C2×C3×Q8C22⋊D5semidirect
366. C2×C3×D4C22⋊D5semidirect
395. #235C22⋊D5semidirect
398. C2×D12C22⋊D5semidirect
404. C2×Dic6C22⋊D5semidirect
619. #41#1201semidirect
626. C2×Q8#1201semidirect
645. C2×D4#1201semidirect
665. C3×C5#3021semidirect
762. C5#83957semidirect
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×C3×#40952
#117546002
C2×#912982
#117513372
#117494582
#117494192
#117484242
#117483552
#106158533
#839575