Finite Group Databasebeta

← #14453767

Subgroups — #14453767

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
1#11754382C211yesmaximal, characteristic
2#67×Dic10C211yesmaximal, characteristic, complemented
3C22×#6658C211yesmaximal, characteristic, complemented
4C2×#91263C211yesmaximal, characteristic, complemented
5#11750832C211yesmaximal, characteristic, complemented
6C5×#4730C211yesmaximal, characteristic, complemented
7C3×#65028C211yesmaximal, characteristic, complemented
8#11748560C211yesmaximal, characteristic, complemented
9#11748152C211yesmaximal, characteristic, complemented
10#11748132C211yesmaximal, characteristic, complemented
11#11748034C211yesmaximal, characteristic, complemented
12#11747949C211yesmaximal, characteristic, complemented
13#11747841C211yesmaximal, characteristic, complemented
14#11747791C211yesmaximal, characteristic, complemented
15#11747743C211yesmaximal, characteristic, complemented
16#10611226—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C2×#6769C2211yescharacteristic
20C2×D3×Dic10C2211yescharacteristic, complemented
21#91813C2211yescharacteristic
22C2×#6706C2211yescharacteristic
23C2×#6706C2211yescharacteristic
24C4×C5×#67C2211yescharacteristic
25C22×C5×C3⋊C8C2211yescharacteristic
26C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
27C3×#4070C2211yescharacteristic
28C2×C3×Dic20C2211yescharacteristic, complemented
29C2×C3×Dic20C2211yescharacteristic, complemented
30#91574—21no—
31#91573—21no—
32#91561—21no—
33Dic5×#67—21no—
34#91460C2211yescharacteristic
35#91433—21no—
36#91428C2211yescharacteristic
37#91420—21no—
38#91410—21no—
39#91389C2211yescharacteristic, complemented
40#91374C2211yescharacteristic
41#91369C2211yescharacteristic, complemented
42Dic3×Dic10C2211yescharacteristic, complemented
43#91327—21no—
44C2×#6662C2211yescharacteristic, complemented
45C2×#6658—24no—
46C2×#6658C2211yescharacteristic
47C2×#6658C2211yescharacteristic
48C2×#6658C2211yescharacteristic
49C2×#6658C2211yescharacteristic
50#91263—24no—
51C3×C5×C22⋊C8C2211yescharacteristic
52#91105C2211yescharacteristic
53#91105C2211yescharacteristic
54C5×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C5×#815C2211yescharacteristic, complemented
56C5×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#3948C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59#90990C2211yescharacteristic, complemented
60#90974C2211yescharacteristic, complemented
61#90971C2211yescharacteristic, complemented
62#80204—51nomaximal, Hall
63C2×#4055—31no—
64C22×#677—31no—
65#65884—31no—
66D4×Dic10—31no—
67C5×#435—31no—
68#65423—31no—
69#65405—31no—
70#65134—31no—
71#65130—31no—
72#65028D311yescharacteristic, complemented
73#65027—31no—
74#65022—31no—
75#65020—31no—
76#65004—31no—
77#64999—31no—
78C23×D15—21no—
79C22×C3×C4×C5C2311yescharacteristic
80C2×D60—22no—
81C2×D60—21no—
82C2×D60—41no—
83C2×D60C2311yescharacteristic
84C2×D60C2311yescharacteristic
85C2×Dic30C2311yescharacteristic
86C2×C5×#67D411yescharacteristic
87C2×C4×C5×D3C2311yescharacteristic
88C22×C3×Dic5—21no—
89C2×C3×Dic10—22no—
90C2×C3×Dic10—21no—
91C2×C3×Dic10—41no—
92C2×C3×Dic10C2311yescharacteristic
93C2×C3×Dic10C2311yescharacteristic
94C2×C3×Dic10C2311yescharacteristic
95C2×#1204—21no—
96C2×#1203—21no—
97C2×#1203—21no—
98C2×#1200—21no—
99C2×#1200—21no—
100C2×D3×Dic5—21no—
101#6769—22no—
102#6769—41no—
103D3×Dic10—22no—
104D3×Dic10—41no—
105C2×C3×C5×C8C2311yescharacteristic
106C2×C3×C5×C8C2311yescharacteristic
107#6719—21no—
108C4⋊Dic15C2311yescharacteristic
109#6712—21no—
110#6706—22no—
111#6706—41no—
112C5×#217D411yescharacteristic
113C5×(C2×D3)⋊C4D411yescharacteristic
114C5×Dic3⋊C4D411yescharacteristic
115C4×C5×Dic3C2311yescharacteristic
116C2×C5×C3⋊C8—22no—
117C2×C5×C3⋊C8C2311yescharacteristic
118C2×C5×C3⋊C8C2311yescharacteristic
119C5×ΓL(1,𝔽25)—22no—
120C3×C22⋊Dic5—21no—
121C3×C4⋊Dic5C2311yescharacteristic
122C3×#683—21no—
123C3×Dic20—22no—
124C3×Dic20—41no—
125Dic3⋊Dic5—21no—
126Dic3⋊Dic5—21no—
127#6669—21no—
128#6668—21no—
129#6667—21no—
130#6667—21no—
131#6667—21no—
132#6667—21no—
133(C2×D3)⋊Dic5—21no—
134Dic3×Dic5—21no—
135#6662—22no—
136#6658—22no—
137#6658—22no—
138#6658—22no—
139#6658D414yescomplemented
140Q8×#67—51no—
141C22×#215—51no—
142C2×#918—51no—
143#5630—51no—
144C3×#451—51no—
145#5190—51no—
146#5187—51no—
147#5185—51no—
148#5051—51no—
149#4818—51no—
150#4817—51no—
151#4812—51no—
152#4806—51no—
153#4731—51no—
154#4730D511yescharacteristic, complemented
155C2×#709—31no—
156C22×D20—31no—
157C22×Dic10—31no—
158C22×Dic10C2×D311yescharacteristic
159C2×C5×M16—31no—
160C22×C5×C8—31no—
161C4×C5×D4—31no—
162#4083—61no—
163D4×Dic5—61no—
164#4076—31no—
165#4070—31no—
166#4070—31no—
167#4070C2×D311yescharacteristic
168#4055—64no—
169C2×Dic20—31no—
170C2×Dic20C2×D311yescharacteristic, complemented
171C2×Dic20C2×D311yescharacteristic, complemented
172C2×#677—31no—
173C2×#677—31no—
174C2×#677—31no—
175C2×#677—31no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—64no—
179#4040—61no—
180#4034—61no—
181#4030—61no—
182D5×C22⋊C4—61no—
183#4024—61no—
184#4024—61no—
185#4021—31no—
186C4×D20—31no—
187#4015—31no—
188C4×Dic10—31no—
189C5×C4⋊C8—31no—
190C5×C22⋊C8—31no—
191C5×C22⋊C8C2×D311yescharacteristic
192C5×#97—31no—
193#3953—31no—
194#3953—31no—
195#3950—31no—
196#3948—31no—
197#3948—31no—
198#3948C2×D311yescharacteristic, complemented
199#3948C2×D311yescharacteristic, complemented
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—42no—
205C22×D15—42no—
206C22×D15—81no—
207C22×C5×D3C2×D411yescharacteristic
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5C2×D411yescharacteristic
211C2×C3×C4×C5C2411yescharacteristic
212C2×Dic15—21no—
213C2×Dic15—21no—
214D60—21no—
215D60—21no—
216D60—21no—
217D60—42no—
218D60C2×D412yes—
219Dic30—21no—
220Dic30—21no—
221C5×#67—22no—
222C2×C5×Dic3C2×D411yescharacteristic
223C2×C5×Dic3C2×D411yescharacteristic
224C2×C5×Dic3C2×D411yescharacteristic
225C4×C5×D3—21no—
226C4×C5×D3—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—42no—
232C3×Dic10—21no—
233C3×Dic10—21no—
234C3×Dic10—21no—
235C3×Dic10—21no—
236C3×Dic10—21no—
237C3×Dic10—42no—
238C3×Dic10C2×D412yes—
239#1204—42no—
240#1203—42no—
241#1203—81no—
242#1200—42no—
243#1200—81no—
244D3×Dic5—42no—
245C3×C5×C8—21no—
246C3×C5×C8—21no—
247C5×C3⋊C8—21no—
248C5×C3⋊C8C2×D412yes—
249C22×C3×Q8—51no—
250C2×#239—51no—
251C2×D3×Q8—51no—
252C22×D12—51no—
253C2×C3×Q16—51no—
254C2×C3×Q16—51no—
255C3×C22⋊Q8—51no—
256#947—51no—
257#946—51no—
258#946—101no—
259Q8×Dic3—51no—
260#944—51no—
261#944—101no—
262C2×#216—51no—
263C2×#215—51no—
264C2×#215—51no—
265C2×#215—51no—
266C2×#215—51no—
267C2×#215—104no—
268C4×#67—101no—
269C4×#67C2×D511yescharacteristic
270#924—51no—
271#924—101no—
272C22×C3⋊C8C2×D511yescharacteristic
273#918—104no—
274C2×#204—51no—
275C2×#204—51no—
276C2×ΓL(1,𝔽25)C2×D511yescharacteristic, complemented
277#895—51no—
278#895—101no—
279#894—101no—
280#893—51no—
281#882—101no—
282D3×C22⋊C4—101no—
283C3×#103—51no—
284C3×#103—51no—
285C3×C22⋊C8C2×D511yescharacteristic
286#835—51no—
287#821—51no—
288#821—51no—
289(C2×D3)⋊C8C2×D511yescharacteristic, complemented
290#815C2×D511yescharacteristic, complemented
291Dic3⋊C8C2×D511yescharacteristic, complemented
292#810—51no—
293#807—51no—
294C23×D5—61no—
295C2×C5×D4—31no—
296C22×C4×C5—31no—
297C22×C4×C5C22×D311yescharacteristic
298C2×C22⋊D5—61no—
299C2×C22⋊D5—61no—
300C22×Dic5—21no—
301C22×Dic5—61no—
302#709—62no—
303#709—121no—
304C2×D20—31no—
305C2×D20—31no—
306C2×D20—62no—
307C2×D20—61no—
308C2×D20—121no—
309C2×C4×D5—61no—
310C2×C4×D5—61no—
311C2×Dic10—22no—
312C2×Dic10—21no—
313C2×Dic10—31no—
314C2×Dic10—41no—
315C2×Dic10—62no—
316C2×Dic10—61no—
317C2×Dic10—121no—
318C2×Dic10C22×D311yescharacteristic
319C2×Dic10C22×D311yescharacteristic
320C2×Dic10C22×D311yescharacteristic
321C5×M16—62no—
322C2×C5×C8—31no—
323C2×C5×C8—31no—
324C2×C5×C8—62no—
325C2×C5×C8C22×D311yescharacteristic
326C2×C5×C8C22×D311yescharacteristic
327C5×C4⋊C4—31no—
328C5×C22⋊C4—31no—
329C5×C22⋊C4—31no—
330C42×C5—31no—
331C22⋊Dic5—21no—
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334#685—61no—
335#685—61no—
336#685—61no—
337#685—61no—
338C4⋊Dic5—31no—
339C4⋊Dic5—61no—
340C4⋊Dic5—61no—
341C4⋊Dic5C22×D311yescharacteristic
342#683—21no—
343#683—61no—
344#683—61no—
345#683—61no—
346C4×Dic5—61no—
347Dic20—22no—
348Dic20—41no—
349Dic20—62no—
350#677—34no—
351#677—62no—
352#677—62no—
353#677—62no—
354#677—62no—
355#677—121no—
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—151no—
359#546—151no—
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—51no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435—31no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5#13712yescomplemented
374C22×C3×C5C22×D411yescharacteristic
375C2×D15—22no—
376C2×D15—41no—
377C2×D15—41no—
378C2×D15—41no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—84no—
382C2×C5×D3—21no—
383C2×C5×D3—21no—
384C2×C5×D3—21no—
385C3×C4×C5—21no—
386C3×C4×C5C22×D411yescharacteristic
387C3×C4×C5H(5,𝔽2)11yescharacteristic
388Dic15—41no—
389Dic15—41no—
390C3×Dic5—22no—
391C3×Dic5—41no—
392C3×Dic5—41no—
393C3×Dic5—41no—
394C5×Dic3—21no—
395C5×Dic3—21no—
396C5×Dic3—21no—
397C23×D3—101no—
398C2×C3×Q8—51no—
399C2×C3×Q8—51no—
400C2×C3×Q8—51no—
401C2×C3×Q8—102no—
402C2×C3×Q8—101no—
403C2×C3×Q8—201no—
404C22×C3×C4—101no—
405C22×C3×C4C22×D511yescharacteristic
406C2×#67D2011yescharacteristic
407#239—102no—
408#239—201no—
409D3×Q8—102no—
410D3×Q8—201no—
411C2×D12—51no—
412C2×D12—51no—
413C2×D12—102no—
414C2×D12—101no—
415C2×D12—101no—
416C2×D12—101no—
417C2×D12—201no—
418C2×C4×D3—101no—
419C2×C4×D3—101no—
420C2×C4×D3—101no—
421C2×C4×D3C22×D511yescharacteristic
422C2×Dic6—51no—
423C2×Dic6—101no—
424C3×Q16—102no—
425C3×Q16—201no—
426C2×C3×C8C22×D511yescharacteristic
427C2×C3×C8C22×D511yescharacteristic
428C3×C4⋊C4—51no—
429C3×C4⋊C4—101no—
430C3×C22⋊C4—101no—
431#217—101no—
432#217D2011yescharacteristic
433#216—102no—
434#215—54no—
435#215—102no—
436#215—102no—
437#215—102no—
438(C2×D3)⋊C4—101no—
439(C2×D3)⋊C4—101no—
440(C2×D3)⋊C4—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4D2011yescharacteristic
444C4⋊Dic3—51no—
445C4⋊Dic3—101no—
446Dic3⋊C4—101no—
447Dic3⋊C4—101no—
448Dic3⋊C4—101no—
449Dic3⋊C4—101no—
450Dic3⋊C4D2011yescharacteristic
451C4×Dic3—101no—
452C4×Dic3C22×D511yescharacteristic
453C2×C3⋊C8—22no—
454C2×C3⋊C8C22×D511yescharacteristic
455C2×C3⋊C8C22×D511yescharacteristic
456#204—102no—
457#204—201no—
458ΓL(1,𝔽25)—22no—
459C23×C5—31no—
460C23×C5D3×D411yescharacteristic
461C22×D5—61no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—241no—
466C5×D4—62no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—31no—
470C2×C4×C5—31no—
471C2×C4×C5—31no—
472C2×C4×C5—61no—
473C2×C4×C5—61no—
474C2×C4×C5D3×D411yescharacteristic
475C2×C4×C5C23×D311yescharacteristic
476C22⋊D5—122no—
477C22⋊D5—241no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—21no—
481C2×Dic5—21no—
482C2×Dic5—42no—
483C2×Dic5—61no—
484C2×Dic5—61no—
485C2×Dic5—122no—
486D20—32no—
487D20—61no—
488D20—61no—
489D20—61no—
490D20—122no—
491C4×D5—122no—
492C4×D5—241no—
493Dic10—21no—
494Dic10—21no—
495Dic10—21no—
496Dic10—21no—
497Dic10—21no—
498Dic10—42no—
499Dic10—61no—
500Dic10—61no—
501Dic10—122no—
502Dic10D3×D412yes—
503C5×C8—21no—
504C5×C8—21no—
505C5×C8—32no—
506C5×C8—61no—
507C2×#41—151no—
508C22×Q8—51no—
509C22×Q8—151no—
510C22×D4—151no—
511#137—304no—
512C2×Q16—51no—
513C2×Q16—51no—
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—31no—
523C22×C8—31no—
524C4⋊Q8—151no—
525C4⋊Q8—301no—
526#124—151no—
527#123—301no—
528C22⋊Q8—51no—
529C22⋊Q8—151no—
530C22⋊Q8—151no—
531C22⋊Q8—301no—
532C22⋊Q8—301no—
533#121—151no—
534#121—301no—
535#120—301no—
536C4×Q8—151no—
537C4×D4—31no—
538C4×D4—151no—
539C4×D4—301no—
540C2×C22⋊C4—301no—
541#107—151no—
542C4⋊C8—31no—
543#103—51no—
544#103—51no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—31no—
550C22⋊C8D3×D511yescharacteristic
551#97—31no—
552C2×C3×C5—22no—
553C2×C3×C5D4211yescharacteristic
554C2×C3×C5C2×#13711yescharacteristic
555C2×C3×C5#57711yescharacteristic
556D15—42no—
557D15—81no—
558C5×D3—41no—
559C23×C3C2×D2011yescharacteristic
560C22×D3—101no—
561C22×D3—101no—
562C22×D3—202no—
563C22×D3—202no—
564C22×D3—401no—
565C22×D3C2×D2011yescharacteristic
566C3×Q8—52no—
567C3×Q8—101no—
568C3×Q8—101no—
569C3×Q8—101no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—202no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—101no—
576C2×C3×C4—101no—
577C2×C3×C4—101no—
578C2×C3×C4—101no—
579C2×C3×C4—202no—
580C2×C3×C4C2×D2011yescharacteristic
581C2×C3×C4C23×D511yescharacteristic
582#67—22no—
583C2×Dic3—101no—
584C2×Dic3—101no—
585C2×Dic3C2×D2011yescharacteristic
586C2×Dic3C2×D2011yescharacteristic
587C2×Dic3C2×D2011yescharacteristic
588D12—52no—
589D12—101no—
590D12—101no—
591D12—101no—
592D12—202no—
593D12—202no—
594D12—401no—
595C4×D3—21no—
596C4×D3—21no—
597C4×D3—202no—
598C4×D3—202no—
599C4×D3—401no—
600Dic6—101no—
601Dic6—101no—
602Dic6—202no—
603C3×C8—21no—
604C3×C8—21no—
605C3⋊C8—21no—
606C3⋊C8D4×D512yes—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—61no—
610C22×C5—61no—
611C22×C5—61no—
612C22×C5#91812yescomplemented
613C22×C5C2×D3×D411yescharacteristic
614C2×D5—62no—
615C2×D5—121no—
616C2×D5—121no—
617C2×D5—121no—
618C2×D5—121no—
619C2×D5—121no—
620C2×D5—244no—
621C4×C5—21no—
622C4×C5—61no—
623C4×C5—61no—
624C4×C5—61no—
625C4×C5C2×D3×D411yescharacteristic
626C4×C5#100411yescharacteristic
627Dic5—22no—
628Dic5—41no—
629Dic5—41no—
630Dic5—41no—
631Dic5—121no—
632Dic5—121no—
633C24—301no—
634#41—302no—
635#41—601no—
636C2×Q8—51no—
637C2×Q8—51no—
638C2×Q8—51no—
639C2×Q8—102no—
640C2×Q8—101no—
641C2×Q8—151no—
642C2×Q8—201no—
643C2×Q8—301no—
644C2×Q8—302no—
645C2×Q8—601no—
646C2×D4—31no—
647C2×D4—151no—
648C2×D4—151no—
649C2×D4—302no—
650C2×D4—301no—
651C2×D4—301no—
652C2×D4—301no—
653C2×D4—601no—
654C22×C4—31no—
655C22×C4—101no—
656C22×C4—301no—
657C22×C4—301no—
658C22×C4—301no—
659C22×C4C2×D3×D511yescharacteristic
660Q16—102no—
661Q16—201no—
662Q16—302no—
663SD16—154no—
664SD16—302no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—62no—
670C2×C8—31no—
671C2×C8—31no—
672C2×C8—62no—
673C2×C8C2×D3×D511yescharacteristic
674C2×C8C2×D3×D511yescharacteristic
675C4⋊C4—31no—
676C4⋊C4—51no—
677C4⋊C4—101no—
678C4⋊C4—151no—
679C4⋊C4—301no—
680C4⋊C4—301no—
681C4⋊C4—301no—
682C4⋊C4—301no—
683C4⋊C4—301no—
684C22⋊C4—31no—
685C22⋊C4—31no—
686C22⋊C4—101no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C42—31no—
694C42—301no—
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3#405512yescomplemented
699C22×C3C22×D2011yescharacteristic
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—102no—
704C2×D3—201no—
705C2×D3—201no—
706C2×D3—201no—
707C2×D3—201no—
708C2×D3—201no—
709C2×D3—404no—
710C3×C4—21no—
711C3×C4—102no—
712C3×C4—201no—
713C3×C4—201no—
714C3×C4—201no—
715C3×C4C2×D4×D511yescharacteristic
716C3×C4#414911yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—121no—
724C2×C5#559011yescharacteristic
725C2×C5C2×#91811yescharacteristic
726C2×C5#577811yescharacteristic
727D5—122no—
728D5—241no—
729C23—31no—
730C23—301no—
731C23—301no—
732C23—602no—
733C23—602no—
734C23—1201no—
735C23D3×D2011yescharacteristic
736Q8—52no—
737Q8—101no—
738Q8—101no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—202no—
743Q8—301no—
744Q8—301no—
745Q8—602no—
746D4—62no—
747D4—152no—
748D4—301no—
749D4—301no—
750D4—301no—
751D4—602no—
752D4—602no—
753D4—1201no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—202no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—602no—
769C2×C4—602no—
770C2×C4—1201no—
771C2×C4D3×D2011yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—21no—
774C8—21no—
775C8—32no—
776C8—61no—
777C2×C3—22no—
778C2×C3D4×D2011yescharacteristic
779C2×C3C2×#405511yescharacteristic
780C2×C3#6608511yescharacteristic
781D3—41no—
782D3—202no—
783D3—401no—
784C5#8020411yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—302no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22#9126312yescomplemented
798C22C2×D3×D2011yescharacteristic
799C4—21no—
800C4—61no—
801C4—61no—
802C4—61no—
803C4—102no—
804C4—201no—
805C4—201no—
806C4—201no—
807C4—601no—
808C4—601no—
809C4D3×D4×D511yescharacteristic
810C4#9202611yescharacteristic
811C3#1061122611yescharacteristic, complemented, Sylow
812C2—22no—
813C2—121no—
814C2—602no—
815C2—1201no—
816C2#1175323511yescharacteristic
817C2C2×#9126311yescharacteristic
818C2#1175403211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11754382C2
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #67×Dic10C2semidirect
3. C22×#6658C2semidirect
4. C2×#91263C2semidirect
5. #11750832C2semidirect
6. C5×#4730C2semidirect
7. C3×#65028C2semidirect
8. #11748560C2semidirect
9. #11748152C2semidirect
10. #11748132C2semidirect
11. #11748034C2semidirect
12. #11747949C2semidirect
13. #11747841C2semidirect
14. #11747791C2semidirect
15. #11747743C2semidirect
20. C2×D3×Dic10C22semidirect
26. C2×C5×ΓL(1,𝔽25)C22semidirect
28. C2×C3×Dic20C22semidirect
29. C2×C3×Dic20C22semidirect
39. #91389C22semidirect
41. #91369C22semidirect
42. Dic3×Dic10C22semidirect
44. C2×#6662C22semidirect
54. C5×(C2×D3)⋊C8C22semidirect
55. C5×#815C22semidirect
56. C5×Dic3⋊C8C22semidirect
57. C3×#3948C22semidirect
58. C3×#3948C22semidirect
59. #90990C22semidirect
60. #90974C22semidirect
61. #90971C22semidirect
72. #65028D3semidirect
139. #6658D4semidirect
154. #4730D5semidirect
170. C2×Dic20C2×D3semidirect
171. C2×Dic20C2×D3semidirect
198. #3948C2×D3semidirect
199. #3948C2×D3semidirect
276. C2×ΓL(1,𝔽25)C2×D5semidirect
289. (C2×D3)⋊C8C2×D5semidirect
290. #815C2×D5semidirect
291. Dic3⋊C8C2×D5semidirect
373. C22×C3×C5#137semidirect
612. C22×C5#918semidirect
695. C3×C5#3266semidirect
698. C22×C3#4055semidirect
784. C5#80204semidirect
797. C22#91263semidirect
811. C3#10611226semidirect

Maximal subgroups

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

subgroupindex
#117543822
#67×Dic102
C22×#66582
C2×#912632
#117508322
C5×#47302
C3×#650282
#117485602
#117481522
#117481322
#117480342
#117479492
#117478412
#117477912
#117477432
#106112263
#802045