Finite Group Databasebeta

← #14453438

Subgroups — #14453438

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×D42C211yesmaximal, characteristic, complemented
2C22×#6716C211yesmaximal, characteristic, complemented
3C2×#91821C211yesmaximal, characteristic, complemented
4#11756311C211yesmaximal, characteristic, complemented
5#11751319C211yesmaximal, characteristic, complemented
6#11751318C211yesmaximal, characteristic, complemented
7#11751176C211yesmaximal, characteristic, complemented
8#11751175C211yesmaximal, characteristic, complemented
9#11751143C211yesmaximal, characteristic, complemented
10#11751141C211yesmaximal, characteristic, complemented
11#11751139C211yesmaximal, characteristic, complemented
12#11751138C211yesmaximal, characteristic, complemented
13#11751119C211yesmaximal, characteristic, complemented
14#11751117C211yesmaximal, characteristic, complemented
15#11751112C211yesmaximal, characteristic, complemented
16#10615222—31nomaximal, Hall
17C22×C3×C5×D4—21no—
18C22×C3×C5×D4C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C2×#6817C2211yescharacteristic, complemented
21C22×Dic30C2211yescharacteristic, complemented
22C3×C5×#127C2211yescharacteristic
23C3×C5×#121—21no—
24C3×C5×#121C2211yescharacteristic
25C3×C5×#121C2211yescharacteristic
26C3×C5×#120—21no—
27C3×C5×#120—21no—
28C3×C4×C5×D4C2211yescharacteristic
29C3×C4×C5×D4C2211yescharacteristic
30#91828—21no—
31C2×#6716—24no—
32C2×#6716C2211yescharacteristic
33C2×#6716C2211yescharacteristic
34C2×#6716C2211yescharacteristic, complemented
35C2×#6716C2211yescharacteristic, complemented
36C2×#6716C2211yescharacteristic, complemented
37C2×#6716C2211yescharacteristic, complemented
38#91821—24no—
39C2×#6715C2211yescharacteristic
40C2×#6715C2211yescharacteristic, complemented
41C2×#6715C2211yescharacteristic, complemented
42#91819C2211yescharacteristic, complemented
43#91813C2211yescharacteristic, complemented
44C2×#6710C2211yescharacteristic, complemented
45C22×C3⋊#168C2211yescharacteristic, complemented
46#91785—21no—
47#91774—21no—
48#91770—21no—
49#91764C2211yescharacteristic, complemented
50C4×Dic30C2211yescharacteristic, complemented
51#91116C2211yescharacteristic
52#91116C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55#91114C2211yescharacteristic, complemented
56#91094C2211yescharacteristic, complemented
57#91094C2211yescharacteristic, complemented
58#91093C2211yescharacteristic, complemented
59#91091C2211yescharacteristic, complemented
60C4⋊(C3⋊#168)C2211yescharacteristic, complemented
61#91087C2211yescharacteristic, complemented
62#83491—51nomaximal, Hall
63C5×D42D311yescharacteristic, complemented
64C22×#687—31no—
65C2×#4078—31no—
66#65886—31no—
67#65507—31no—
68#65506—31no—
69#65364—31no—
70#65363—31no—
71#65331—31no—
72#65329—31no—
73#65327—31no—
74#65326—31no—
75#65307—31no—
76#65305—31no—
77#65300—31no—
78C24×C3×C5—21no—
79C24×C3×C5—21no—
80C2×C3×C5×D4—22no—
81C2×C3×C5×D4—22no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4—41no—
89C2×C3×C5×D4—41no—
90C2×C3×C5×D4—44no—
91C2×C3×C5×D4D411yescharacteristic
92C2×C3×C5×D4C2311yescharacteristic
93C2×C3×C5×D4C2311yescharacteristic
94C2×C3×C5×D4C2311yescharacteristic
95C22×C3×C4×C5—21no—
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C2×#1220—21no—
99C2×#1220—21no—
100C22×Dic15—21no—
101#6817—22no—
102#6817—41no—
103C2×D60C2311yescharacteristic
104C2×C4×D15—21no—
105C2×Dic30—22no—
106C2×Dic30—21no—
107C2×Dic30—41no—
108C2×Dic30C2311yescharacteristic
109C2×Dic30C2311yescharacteristic
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113C3×C5×C22⋊C4—21no—
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4D411yescharacteristic
116C3×C5×C22⋊C4D411yescharacteristic
117C3×C42×C5C2311yescharacteristic
118#6719—21no—
119#6716—22no—
120#6716—22no—
121#6716—22no—
122#6716—22no—
123#6716—41no—
124#6716D414yescomplemented
125#6715—22no—
126#6715—22no—
127#6715—41no—
128#6714—21no—
129#6714—21no—
130#6714—21no—
131C4⋊Dic15C2311yescharacteristic
132#6712—21no—
133#6712—21no—
134C4×Dic15—21no—
135#6710—22no—
136C2×C3⋊#168—22no—
137C2×C3⋊#168C2311yescharacteristic
138C2×C3⋊#168C2311yescharacteristic
139C2×C3⋊#168C2311yescharacteristic
140C2×C3⋊#168C2311yescharacteristic
141C3×D42D511yescharacteristic, complemented
142C22×#214—51no—
143C2×#932—51no—
144#5552—51no—
145#5218—51no—
146#5217—51no—
147#5075—51no—
148#5074—51no—
149#5042—51no—
150#5040—51no—
151#5038—51no—
152#5037—51no—
153#5018—51no—
154#5016—51no—
155#5011—51no—
156C22×C5×D4—21no—
157C22×C5×D4C2×D311yescharacteristic
158C22×C5×D4C2×D311yescharacteristic
159C2×#709—31no—
160C22×Dic10—31no—
161C5×#127C2×D311yescharacteristic
162C5×#121—21no—
163C5×#121C2×D311yescharacteristic
164C5×#121C2×D311yescharacteristic
165C5×#120—21no—
166C5×#120—21no—
167C4×C5×D4C2×D311yescharacteristic
168C4×C5×D4C2×D311yescharacteristic
169#4085—61no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#687—31no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#687—64no—
177#4078—64no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
181#4076—31no—
182#4070—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4042—61no—
186#4031—61no—
187#4027—61no—
188#4021—31no—
189C4×Dic10—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3942—31no—
196#3942—31no—
197#3941—31no—
198#3939—31no—
199C4⋊#168—31no—
200#3935—31no—
201#3265—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5—42no—
206C23×C3×C5—42no—
207C23×C3×C5—42no—
208C23×C3×C5—42no—
209C23×C3×C5—81no—
210C23×C3×C5—81no—
211C23×C3×C5C2×D411yescharacteristic
212C23×C3×C5C2×D411yescharacteristic
213C22×D15—21no—
214C3×C5×D4—22no—
215C3×C5×D4—21no—
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—42no—
221C3×C5×D4—42no—
222C3×C5×D4—42no—
223C3×C5×D4—42no—
224C3×C5×D4—42no—
225C3×C5×D4—81no—
226C3×C5×D4C2×D412yes—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—42no—
233C2×C3×C4×C5C2×D411yescharacteristic
234C2×C3×C4×C5C2×D411yescharacteristic
235C2×C3×C4×C5C2×D411yescharacteristic
236C2×C3×C4×C5C2×D411yescharacteristic
237C2×C3×C4×C5C2411yescharacteristic
238#1220—42no—
239#1220—42no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—42no—
244D60—21no—
245D60—21no—
246C4×D15—42no—
247Dic30—21no—
248Dic30—21no—
249Dic30—21no—
250Dic30—42no—
251Dic30C2×D412yescomplemented
252C3⋊#168—21no—
253C3⋊#168—21no—
254C3⋊#168—21no—
255C3⋊#168C2×D412yescomplemented
256C22×C3×D4—21no—
257C22×C3×D4C2×D511yescharacteristic
258C22×C3×D4C2×D511yescharacteristic
259C2×#235—51no—
260C22×Dic6—51no—
261C3×#127C2×D511yescharacteristic
262C3×#121—21no—
263C3×#121C2×D511yescharacteristic
264C3×#121C2×D511yescharacteristic
265C3×#120—21no—
266C3×#120—21no—
267C3×C4×D4C2×D511yescharacteristic
268C3×C4×D4C2×D511yescharacteristic
269#939—101no—
270C2×#214—51no—
271C2×#214—51no—
272C2×#214—51no—
273C2×#214—51no—
274C2×#214—51no—
275C2×#214—51no—
276C2×#214—104no—
277#932—104no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281#930—51no—
282#924—51no—
283C2×#208—51no—
284C22×C3⋊C8—51no—
285#896—101no—
286#885—101no—
287#67⋊C4—101no—
288#875—51no—
289C4×Dic6—51no—
290#832—51no—
291#832—51no—
292#832—51no—
293#830—51no—
294#830—51no—
295#810—51no—
296#810—51no—
297#809—51no—
298#807—51no—
299C4⋊(C3⋊C8)—51no—
300#803—51no—
301C24×C5—21no—
302C24×C5—21no—
303C2×C5×D4—22no—
304C2×C5×D4—22no—
305C2×C5×D4—21no—
306C2×C5×D4—21no—
307C2×C5×D4—21no—
308C2×C5×D4—21no—
309C2×C5×D4—21no—
310C2×C5×D4—21no—
311C2×C5×D4—41no—
312C2×C5×D4—41no—
313C2×C5×D4—44no—
314C2×C5×D4#6711yescharacteristic
315C2×C5×D4C22×D311yescharacteristic
316C2×C5×D4C22×D311yescharacteristic
317C2×C5×D4C22×D311yescharacteristic
318C22×C4×C5—21no—
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D311yescharacteristic
321C2×C22⋊D5—61no—
322C2×C22⋊D5—61no—
323C22×Dic5—61no—
324#709—62no—
325#709—121no—
326C2×D20—31no—
327C2×C4×D5—61no—
328C2×Dic10—31no—
329C2×Dic10—31no—
330C2×Dic10—62no—
331C2×Dic10—61no—
332C2×Dic10—121no—
333C5×C4⋊C4#6711yescharacteristic
334C5×C4⋊C4C22×D311yescharacteristic
335C5×C22⋊C4—21no—
336C5×C22⋊C4—21no—
337C5×C22⋊C4—21no—
338C5×C22⋊C4#6711yescharacteristic
339C5×C22⋊C4#6711yescharacteristic
340C42×C5C22×D311yescharacteristic
341C22⋊Dic5—61no—
342#687—34no—
343#687—62no—
344#687—62no—
345#687—62no—
346#687—62no—
347#687—121no—
348#686—62no—
349#686—62no—
350#686—121no—
351#685—61no—
352#685—61no—
353#685—61no—
354C4⋊Dic5—31no—
355#683—61no—
356#683—61no—
357C4×Dic5—61no—
358#681—62no—
359C2×#168—31no—
360C2×#168—31no—
361C2×#168—31no—
362C2×#168—31no—
363C2×#168—62no—
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—151no—
367D42D1511yescharacteristic, complemented
368#496—151no—
369#468—151no—
370#466—151no—
371#463—151no—
372#460—151no—
373#450—151no—
374#449—151no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—22no—
383C22×C3×C5—21no—
384C22×C3×C5—21no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5—41no—
392C22×C3×C5—41no—
393C22×C3×C5—84no—
394C22×C3×C5—84no—
395C22×C3×C5AGL(1,ℤ/8)12yescomplemented
396C22×C3×C5C22×D411yescharacteristic
397C2×D15—41no—
398C2×D15—41no—
399C2×D15—41no—
400C3×C4×C5—21no—
401C3×C4×C5—21no—
402C3×C4×C5—21no—
403C3×C4×C5—21no—
404C3×C4×C5—41no—
405C3×C4×C5C22×D411yescharacteristic
406C3×C4×C5H(5,𝔽2)11yescharacteristic
407Dic15—22no—
408Dic15—41no—
409Dic15—41no—
410C24×C3—21no—
411C24×C3—21no—
412C2×C3×D4—22no—
413C2×C3×D4—22no—
414C2×C3×D4—21no—
415C2×C3×D4—21no—
416C2×C3×D4—21no—
417C2×C3×D4—21no—
418C2×C3×D4—21no—
419C2×C3×D4—21no—
420C2×C3×D4—41no—
421C2×C3×D4—41no—
422C2×C3×D4—44no—
423C2×C3×D4C22⋊D511yescharacteristic
424C2×C3×D4C22×D511yescharacteristic
425C2×C3×D4C22×D511yescharacteristic
426C2×C3×D4C22×D511yescharacteristic
427C22×C3×C4—21no—
428C22×C3×C4C22×D511yescharacteristic
429C22×C3×C4C22×D511yescharacteristic
430C2×#67—101no—
431C2×#67—101no—
432C22×Dic3—101no—
433#235—102no—
434#235—201no—
435C2×D12—51no—
436C2×C4×D3—101no—
437C2×Dic6—51no—
438C2×Dic6—51no—
439C2×Dic6—102no—
440C2×Dic6—101no—
441C2×Dic6—201no—
442C3×C4⋊C4C22⋊D511yescharacteristic
443C3×C4⋊C4C22×D511yescharacteristic
444C3×C22⋊C4—21no—
445C3×C22⋊C4—21no—
446C3×C22⋊C4—21no—
447C3×C22⋊C4C22⋊D511yescharacteristic
448C3×C22⋊C4C22⋊D511yescharacteristic
449C3×C42C22×D511yescharacteristic
450#217—101no—
451#214—54no—
452#214—102no—
453#214—102no—
454#214—102no—
455#214—102no—
456#214—201no—
457#213—102no—
458#213—102no—
459#213—201no—
460(C2×D3)⋊C4—101no—
461(C2×D3)⋊C4—101no—
462(C2×D3)⋊C4—101no—
463C4⋊Dic3—51no—
464Dic3⋊C4—101no—
465Dic3⋊C4—101no—
466C4×Dic3—101no—
467#208—102no—
468C2×C3⋊C8—51no—
469C2×C3⋊C8—51no—
470C2×C3⋊C8—51no—
471C2×C3⋊C8—51no—
472C2×C3⋊C8—102no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—42no—
477C23×C5—42no—
478C23×C5—42no—
479C23×C5—42no—
480C23×C5—81no—
481C23×C5—81no—
482C23×C5C2×#6711yescharacteristic
483C23×C5C2×#6711yescharacteristic
484C22×D5—61no—
485C5×D4—22no—
486C5×D4—21no—
487C5×D4—21no—
488C5×D4—21no—
489C5×D4—21no—
490C5×D4—21no—
491C5×D4—42no—
492C5×D4—42no—
493C5×D4—42no—
494C5×D4—42no—
495C5×D4—42no—
496C5×D4—81no—
497C5×D4D3×D412yes—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—42no—
504C2×C4×C5C2×#6711yescharacteristic
505C2×C4×C5C2×#6711yescharacteristic
506C2×C4×C5C2×#6711yescharacteristic
507C2×C4×C5C2×#6711yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—122no—
510C22⋊D5—122no—
511C2×Dic5—61no—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—122no—
515D20—61no—
516D20—61no—
517C4×D5—122no—
518Dic10—32no—
519Dic10—61no—
520Dic10—61no—
521Dic10—61no—
522Dic10—122no—
523#168—32no—
524#168—61no—
525#168—61no—
526#168—61no—
527C2×#41—151no—
528C22×Q8—151no—
529C22×D4—21no—
530C22×D4C2×D1511yescharacteristic
531C22×D4C2×D1511yescharacteristic
532AGL(1,ℤ/8)—304no—
533C2×SD16—151no—
534C2×SD16—151no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—151no—
544C22×C8—151no—
545#127C2×D1511yescharacteristic
546#124—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—21no—
551#121—151no—
552#121—301no—
553#121C2×D1511yescharacteristic
554#121C2×D1511yescharacteristic
555#120—21no—
556#120—21no—
557C4×Q8—151no—
558C4×D4—301no—
559C4×D4C2×D1511yescharacteristic
560C4×D4C2×D1511yescharacteristic
561#107—151no—
562C4⋊C8—151no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—22no—
573C2×C3×C5—41no—
574C2×C3×C5—42no—
575C2×C3×C5—81no—
576C2×C3×C5—81no—
577C2×C3×C5D4211yescharacteristic
578C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
579C2×C3×C5#57711yescharacteristic
580D15—81no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3—42no—
587C23×C3—42no—
588C23×C3—81no—
589C23×C3—81no—
590C23×C3C2×C22⋊D511yescharacteristic
591C23×C3C2×C22⋊D511yescharacteristic
592C22×D3—101no—
593C3×D4—22no—
594C3×D4—21no—
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—21no—
598C3×D4—21no—
599C3×D4—42no—
600C3×D4—42no—
601C3×D4—42no—
602C3×D4—42no—
603C3×D4—42no—
604C3×D4—81no—
605C3×D4D4×D512yes—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—42no—
612C2×C3×C4C2×C22⋊D511yescharacteristic
613C2×C3×C4C2×C22⋊D511yescharacteristic
614C2×C3×C4C2×C22⋊D511yescharacteristic
615C2×C3×C4C2×C22⋊D511yescharacteristic
616C2×C3×C4C23×D511yescharacteristic
617#67—202no—
618#67—202no—
619C2×Dic3—101no—
620C2×Dic3—101no—
621C2×Dic3—101no—
622C2×Dic3—202no—
623D12—101no—
624D12—101no—
625C4×D3—202no—
626Dic6—52no—
627Dic6—101no—
628Dic6—101no—
629Dic6—101no—
630Dic6—202no—
631C3⋊C8—52no—
632C3⋊C8—101no—
633C3⋊C8—101no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—21no—
639C22×C5—22no—
640C22×C5—21no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—41no—
644C22×C5—41no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—41no—
649C22×C5—84no—
650C22×C5—84no—
651C22×C5#93212yescomplemented
652C22×C5C22×#6711yescharacteristic
653C2×D5—121no—
654C2×D5—121no—
655C2×D5—121no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—21no—
660C4×C5—41no—
661C4×C5C2×D3×D411yescharacteristic
662C4×C5#100411yescharacteristic
663Dic5—62no—
664Dic5—121no—
665Dic5—121no—
666C24—21no—
667C24—21no—
668#41—302no—
669#41—601no—
670C2×Q8—151no—
671C2×Q8—151no—
672C2×Q8—302no—
673C2×Q8—301no—
674C2×Q8—601no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—41no—
684C2×D4—41no—
685C2×D4—44no—
686C2×D4—151no—
687C2×D4—301no—
688C2×D4—301no—
689C2×D4#122011yescharacteristic
690C2×D4C22×D1511yescharacteristic
691C2×D4C22×D1511yescharacteristic
692C2×D4C22×D1511yescharacteristic
693C22×C4—21no—
694C22×C4—301no—
695C22×C4—301no—
696C22×C4C22×D1511yescharacteristic
697C22×C4C22×D1511yescharacteristic
698SD16—154no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—151no—
709C2×C8—151no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—151no—
714C4⋊C4—301no—
715C4⋊C4—301no—
716C4⋊C4#122011yescharacteristic
717C4⋊C4C22×D1511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—301no—
722C22⋊C4—301no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4#122011yescharacteristic
726C22⋊C4#122011yescharacteristic
727C42—301no—
728C42C22×D1511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—22no—
735C22×C3—21no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—84no—
745C22×C3—84no—
746C22×C3#407812yescomplemented
747C22×C3C22×C22⋊D511yescharacteristic
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—201no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—41no—
756C3×C4C2×D4×D511yescharacteristic
757C3×C4#414411yescharacteristic
758Dic3—102no—
759Dic3—201no—
760Dic3—201no—
761C2×C5—22no—
762C2×C5—41no—
763C2×C5—42no—
764C2×C5—81no—
765C2×C5—81no—
766C2×C5C2×#93211yescharacteristic
767C2×C5D4×#6711yescharacteristic
768C2×C5#583611yescharacteristic
769D5—241no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—81no—
778C23—81no—
779C23—301no—
780C23C2×#122011yescharacteristic
781C23C2×#122011yescharacteristic
782Q8—152no—
783Q8—301no—
784Q8—301no—
785Q8—301no—
786Q8—602no—
787D4—22no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—42no—
797D4—42no—
798D4—81no—
799D4—301no—
800D4—301no—
801D4—602no—
802D4—602no—
803D4D4×D1512yes—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—42no—
810C2×C4—301no—
811C2×C4—301no—
812C2×C4—301no—
813C2×C4—602no—
814C2×C4—602no—
815C2×C4C2×#122011yescharacteristic
816C2×C4C2×#122011yescharacteristic
817C2×C4C2×#122011yescharacteristic
818C2×C4C2×#122011yescharacteristic
819C2×C4C23×D1511yescharacteristic
820C8—152no—
821C8—301no—
822C8—301no—
823C8—301no—
824C2×C3—22no—
825C2×C3—41no—
826C2×C3—42no—
827C2×C3—81no—
828C2×C3—81no—
829C2×C3C2×#407811yescharacteristic
830C2×C3D4×C22⋊D511yescharacteristic
831C2×C3#6617011yescharacteristic
832D3—401no—
833C5#8349111yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—22no—
839C22—21no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—84no—
849C22—84no—
850C22—601no—
851C22—601no—
852C22—601no—
853C22#9182112yescomplemented
854C22C22×#122011yescharacteristic
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—41no—
860C4—302no—
861C4—601no—
862C4—601no—
863C4C2×D4×D1511yescharacteristic
864C4#9209511yescharacteristic
865C3#1061522211yescharacteristic, complemented, Sylow
866C2—22no—
867C2—41no—
868C2—42no—
869C2—81no—
870C2—81no—
871C2—1201no—
872C2C2×#9182111yescharacteristic
873C2D4×#122011yescharacteristic
874C2#1175659511yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×D42C2
socleC22×C3×C5C22×D4
hypercenterD42D15
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C3×C5×D42C2semidirect
2. C22×#6716C2semidirect
3. C2×#91821C2semidirect
4. #11756311C2semidirect
5. #11751319C2semidirect
6. #11751318C2semidirect
7. #11751176C2semidirect
8. #11751175C2semidirect
9. #11751143C2semidirect
10. #11751141C2semidirect
11. #11751139C2semidirect
12. #11751138C2semidirect
13. #11751119C2semidirect
14. #11751117C2semidirect
15. #11751112C2semidirect
20. C2×#6817C22semidirect
21. C22×Dic30C22semidirect
34. C2×#6716C22semidirect
35. C2×#6716C22semidirect
36. C2×#6716C22semidirect
37. C2×#6716C22semidirect
40. C2×#6715C22semidirect
41. C2×#6715C22semidirect
42. #91819C22semidirect
43. #91813C22semidirect
44. C2×#6710C22semidirect
45. C22×C3⋊#168C22semidirect
49. #91764C22semidirect
50. C4×Dic30C22semidirect
52. #91116C22semidirect
53. #91116C22semidirect
54. #91114C22semidirect
55. #91114C22semidirect
56. #91094C22semidirect
57. #91094C22semidirect
58. #91093C22semidirect
59. #91091C22semidirect
60. C4⋊(C3⋊#168)C22semidirect
61. #91087C22semidirect
63. C5×D42D3semidirect
124. #6716D4semidirect
141. C3×D42D5semidirect
251. Dic30C2×D4semidirect
255. C3⋊#168C2×D4semidirect
367. D42D15semidirect
395. C22×C3×C5AGL(1,ℤ/8)semidirect
651. C22×C5#932semidirect
729. C3×C5#3265semidirect
746. C22×C3#4078semidirect
833. C5#83491semidirect
853. C22#91821semidirect
865. C3#10615222semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D422
C22×#67162
C2×#918212
#117563112
#117513192
#117513182
#117511762
#117511752
#117511432
#117511412
#117511392
#117511382
#117511192
#117511172
#117511122
#106152223
#834915