Finite Group Databasebeta

← #14458274

Subgroups — #14458274

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
1D4×#1220C211yesmaximal, characteristic, complemented
2#11756370C211yesmaximal, characteristic, complemented
3C3×C5×#447C211yesmaximal, characteristic, complemented
4C2×#91116C211yesmaximal, characteristic, complemented
5#11751258C211yesmaximal, characteristic, complemented
6#11751257C211yesmaximal, characteristic, complemented
7#11751251C211yesmaximal, characteristic, complemented
8D8×Dic15C211yesmaximal, characteristic, complemented
9#11751139C211yesmaximal, characteristic, complemented
10#11750875C211yesmaximal, characteristic, complemented
11D15×#102C211yesmaximal, characteristic, complemented
12#11750861C211yesmaximal, characteristic, complemented
13#11750860C211yesmaximal, characteristic, complemented
14#11750837C211yesmaximal, characteristic, complemented
15#11750826C211yesmaximal, characteristic, complemented
16#10611745—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×#1220—21no—
19C2×#6819—21no—
20C2×D4×D15C2211yescharacteristic
21C2×C3×C5×D8C2211yescharacteristic
22C2×C3×C5×D8C2211yescharacteristic, complemented
23C3×C5×#121C2211yescharacteristic, complemented
24#91842—21no—
25#91829C2211yescharacteristic
26#91828—21no—
27#91827C2211yescharacteristic
28#91827C2211yescharacteristic, complemented
29#91826—21no—
30#91824—21no—
31D4×Dic15C2211yescharacteristic
32D4×Dic15C2211yescharacteristic, complemented
33C2×#6715C2211yescharacteristic, complemented
34#91819C2211yescharacteristic
35C4×#1220C2211yescharacteristic
36C2×C4⋊Dic15C2211yescharacteristic, complemented
37C22×C3⋊#168C2211yescharacteristic, complemented
38C2×C8×D15C2211yescharacteristic, complemented
39C4⋊C4×D15C2211yescharacteristic, complemented
40#91777C2211yescharacteristic, complemented
41#91772—21no—
42#91767—21no—
43C3×C5×#102C2211yescharacteristic
44C3×C5×#102C2211yescharacteristic, complemented
45C3×C5×C22⋊C8C2211yescharacteristic, complemented
46#91116C2211yescharacteristic
47#91116C2211yescharacteristic
48#91116C2211yescharacteristic, complemented
49#91116C2211yescharacteristic, complemented
50#91116C2211yescharacteristic, complemented
51#91105C2211yescharacteristic, complemented
52#91105C2211yescharacteristic, complemented
53#91104C2211yescharacteristic, complemented
54#91102C2211yescharacteristic, complemented
55#91102C2211yescharacteristic, complemented
56#91098C2211yescharacteristic, complemented
57C8×Dic15C2211yescharacteristic, complemented
58#91093C2211yescharacteristic, complemented
59#91091C2211yescharacteristic, complemented
60#80014—51nomaximal, Hall
61D4×C22⋊D5—31no—
62#65945—31no—
63C5×#447D311yescharacteristic, complemented
64C2×#3964—31no—
65#65446—31no—
66#65445—31no—
67#65439—31no—
68D8×Dic5—31no—
69#65327—31no—
70#65063—31no—
71D5×#102—31no—
72#65049—31no—
73#65048—31no—
74#65025—31no—
75#65014—31no—
76C24×C3×C5—21no—
77C23×D15—21no—
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4—41no—
82C2×C3×C5×D4C2311yescharacteristic
83C2×C3×C5×D4C2311yescharacteristic
84C2×C3×C5×D4C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—21no—
87C2×#1220—21no—
88C2×#1220—21no—
89C2×#1220—21no—
90C2×#1220—21no—
91C2×#1220—21no—
92C2×#1220—44no—
93C2×#1220D411yescharacteristic
94C22×Dic15—21no—
95C22×Dic15—21no—
96C22×Dic15—21no—
97#6819—44no—
98D4×D15—22no—
99D4×D15—41no—
100C2×D60C2311yescharacteristic
101C2×C4×D15—21no—
102C2×C4×D15C2311yescharacteristic
103C2×Dic30—21no—
104C3×C5×D8—22no—
105C3×C5×D8—41no—
106C2×C3×C5×C8C2311yescharacteristic
107C2×C3×C5×C8C2311yescharacteristic
108C3×C5×C4⋊C4C2311yescharacteristic
109C3×C5×C22⋊C4—21no—
110#6719—21no—
111#6719—21no—
112#6719—21no—
113#6719—21no—
114#6719D411yescharacteristic
115#6715—41no—
116#6714—21no—
117#6714D411yescharacteristic
118C4⋊Dic15—21no—
119C4⋊Dic15C2311yescharacteristic
120C4⋊Dic15C2311yescharacteristic
121C4⋊Dic15C2311yescharacteristic
122#6712—21no—
123#6712—21no—
124#6712D411yescharacteristic
125C4×Dic15C2311yescharacteristic
126C2×C3⋊#168—41no—
127C2×C3⋊#168C2311yescharacteristic
128C2×C3⋊#168C2311yescharacteristic
129C8×D15—41no—
130D4×#67—51no—
131#5611—51no—
132C3×#447D511yescharacteristic, complemented
133C2×#832—51no—
134#5157—51no—
135#5156—51no—
136#5150—51no—
137Dic3×D8—51no—
138#5038—51no—
139#4774—51no—
140D3×#102—51no—
141#4760—51no—
142#4759—51no—
143#4736—51no—
144#67⋊C8—51no—
145C22×C5×D4C2×D311yescharacteristic
146C22×C22⋊D5—61no—
147C2×#711—61no—
148C2×D4×D5—31no—
149C2×C5×D8C2×D311yescharacteristic
150C2×C5×D8C2×D311yescharacteristic, complemented
151C5×#121C2×D311yescharacteristic, complemented
152#4099—61no—
153#4086—31no—
154#4085—61no—
155#4084—31no—
156#4084—31no—
157#4083—61no—
158#4081—61no—
159D4×Dic5—31no—
160D4×Dic5—31no—
161C2×#686—31no—
162#4076—31no—
163C4×C22⋊D5—31no—
164C2×C4⋊Dic5—31no—
165C22×#168—31no—
166C2×C8×D5—31no—
167D5×C4⋊C4—31no—
168#4034—31no—
169#4029—61no—
170#4024—61no—
171C5×#102C2×D311yescharacteristic
172C5×#102C2×D311yescharacteristic, complemented
173C5×C22⋊C8C2×D311yescharacteristic, complemented
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964—31no—
178#3964—31no—
179#3953—31no—
180#3953—31no—
181#3952—31no—
182#3950—31no—
183#3950—31no—
184#3946—31no—
185C8×Dic5—31no—
186#3941—31no—
187#3939—31no—
188#3294—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—42no—
193C23×C3×C5—42no—
194C23×C3×C5—81no—
195C23×C3×C5C2×D411yescharacteristic
196C22×D15—21no—
197C22×D15—42no—
198C22×D15—42no—
199C22×D15—81no—
200C22×D15C2×D411yescharacteristic
201C3×C5×D4—21no—
202C3×C5×D4—21no—
203C3×C5×D4—21no—
204C3×C5×D4—21no—
205C3×C5×D4—21no—
206C3×C5×D4—42no—
207C3×C5×D4—42no—
208C3×C5×D4#4112yescomplemented
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5C2×D411yescharacteristic
213C2×C3×C4×C5C2411yescharacteristic
214#1220—42no—
215#1220—42no—
216#1220—42no—
217#1220—42no—
218#1220—42no—
219#1220—81no—
220#1220D814yescomplemented
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—42no—
225C2×Dic15—42no—
226C2×Dic15—42no—
227C2×Dic15C2×D411yescharacteristic
228C2×Dic15C2×D411yescharacteristic
229C2×Dic15C2×D411yescharacteristic
230D60—21no—
231D60—21no—
232C4×D15—21no—
233C4×D15—21no—
234C4×D15—42no—
235Dic30—42no—
236C3×C5×C8—21no—
237C3×C5×C8—21no—
238C3⋊#168—21no—
239C3⋊#168—21no—
240C22×C3×D4C2×D511yescharacteristic
241C22×#67—101no—
242C2×#237—101no—
243C2×D3×D4—51no—
244C2×C3×D8C2×D511yescharacteristic
245C2×C3×D8C2×D511yescharacteristic, complemented
246C3×#121C2×D511yescharacteristic, complemented
247#953—101no—
248#940—51no—
249#939—101no—
250#938—51no—
251#938—51no—
252#937—101no—
253#935—101no—
254D4×Dic3—51no—
255D4×Dic3—51no—
256C2×#213—51no—
257#930—51no—
258C4×#67—51no—
259C2×C4⋊Dic3—51no—
260C22×C3⋊C8—51no—
261C2×D3×C8—51no—
262D3×C4⋊C4—51no—
263#888—51no—
264#883—101no—
265#878—101no—
266C3×#102C2×D511yescharacteristic
267C3×#102C2×D511yescharacteristic, complemented
268C3×C22⋊C8C2×D511yescharacteristic, complemented
269#832—51no—
270#832—51no—
271#832—51no—
272#832—51no—
273#832—51no—
274#821—51no—
275#821—51no—
276(C2×D3)⋊C8—51no—
277#818—51no—
278#818—51no—
279Dic3⋊C8—51no—
280C8×Dic3—51no—
281#809—51no—
282#807—51no—
283C24×C5—21no—
284C23×D5—61no—
285C2×C5×D4—22no—
286C2×C5×D4—21no—
287C2×C5×D4—21no—
288C2×C5×D4—41no—
289C2×C5×D4C22×D311yescharacteristic
290C2×C5×D4C22×D311yescharacteristic
291C2×C5×D4C22×D311yescharacteristic
292C22×C4×C5C22×D311yescharacteristic
293C2×C22⋊D5—31no—
294C2×C22⋊D5—61no—
295C2×C22⋊D5—61no—
296C2×C22⋊D5—61no—
297C2×C22⋊D5—61no—
298C2×C22⋊D5—61no—
299C2×C22⋊D5—61no—
300C2×C22⋊D5—124no—
301C22×Dic5—61no—
302C22×Dic5—61no—
303C22×Dic5—61no—
304#711—124no—
305D4×D5—62no—
306D4×D5—121no—
307C2×D20—31no—
308C2×C4×D5—31no—
309C2×C4×D5—61no—
310C2×Dic10—61no—
311C5×D8—22no—
312C5×D8—41no—
313C2×C5×C8C22×D311yescharacteristic
314C2×C5×C8C22×D311yescharacteristic
315C5×C4⋊C4C22×D311yescharacteristic
316C5×C22⋊C4—21no—
317C22⋊Dic5—31no—
318C22⋊Dic5—61no—
319C22⋊Dic5—61no—
320C22⋊Dic5—61no—
321C22⋊Dic5—61no—
322#686—121no—
323#685—31no—
324#685—61no—
325C4⋊Dic5—31no—
326C4⋊Dic5—31no—
327C4⋊Dic5—31no—
328C4⋊Dic5—61no—
329#683—31no—
330#683—61no—
331#683—61no—
332C4×Dic5—31no—
333C2×#168—31no—
334C2×#168—31no—
335C2×#168—121no—
336C8×D5—121no—
337#547—151no—
338D42—151no—
339#486—151no—
340#480—151no—
341#480—151no—
342#474—151no—
343#466—151no—
344#466—151no—
345#459—151no—
346#447—151no—
347#447D1511yescharacteristic, complemented
348C4×D8—151no—
349C8×D4—151no—
350C2×#102—151no—
351C2×#102—151no—
352C22×C3×C5—21no—
353C22×C3×C5—21no—
354C22×C3×C5—22no—
355C22×C3×C5—41no—
356C22×C3×C5—41no—
357C22×C3×C5—41no—
358C22×C3×C5—41no—
359C22×C3×C5—41no—
360C22×C3×C5—41no—
361C22×C3×C5—41no—
362C22×C3×C5—41no—
363C22×C3×C5—84no—
364C22×C3×C5C2×D812yes—
365C22×C3×C5C22×D411yescharacteristic
366C2×D15—21no—
367C2×D15—21no—
368C2×D15—41no—
369C2×D15—41no—
370C2×D15—41no—
371C2×D15—84no—
372C2×D15C2×D812yes—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5C2×#4111yescharacteristic
376C3×C4×C5H(5,𝔽2)11yescharacteristic
377Dic15—21no—
378Dic15—21no—
379Dic15—41no—
380Dic15—41no—
381Dic15—41no—
382Dic15C2×D812yes—
383C24×C3—21no—
384C23×D3—101no—
385C2×C3×D4—22no—
386C2×C3×D4—21no—
387C2×C3×D4—21no—
388C2×C3×D4—41no—
389C2×C3×D4C22×D511yescharacteristic
390C2×C3×D4C22×D511yescharacteristic
391C2×C3×D4C22×D511yescharacteristic
392C22×C3×C4C22×D511yescharacteristic
393C2×#67—51no—
394C2×#67—101no—
395C2×#67—101no—
396C2×#67—101no—
397C2×#67—101no—
398C2×#67—101no—
399C2×#67—101no—
400C2×#67—204no—
401C22×Dic3—101no—
402C22×Dic3—101no—
403C22×Dic3—101no—
404#237—204no—
405D3×D4—102no—
406D3×D4—201no—
407C2×D12—51no—
408C2×C4×D3—51no—
409C2×C4×D3—101no—
410C2×Dic6—101no—
411C3×D8—22no—
412C3×D8—41no—
413C2×C3×C8C22×D511yescharacteristic
414C2×C3×C8C22×D511yescharacteristic
415C3×C4⋊C4C22×D511yescharacteristic
416C3×C22⋊C4—21no—
417#217—51no—
418#217—101no—
419#217—101no—
420#217—101no—
421#217—101no—
422#213—201no—
423(C2×D3)⋊C4—51no—
424(C2×D3)⋊C4—101no—
425C4⋊Dic3—51no—
426C4⋊Dic3—51no—
427C4⋊Dic3—51no—
428C4⋊Dic3—101no—
429Dic3⋊C4—51no—
430Dic3⋊C4—101no—
431Dic3⋊C4—101no—
432C4×Dic3—51no—
433C2×C3⋊C8—51no—
434C2×C3⋊C8—51no—
435C2×C3⋊C8—201no—
436D3×C8—201no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5—21no—
440C23×C5—42no—
441C23×C5—42no—
442C23×C5—81no—
443C23×C5D3×D411yescharacteristic
444C22×D5—31no—
445C22×D5—61no—
446C22×D5—122no—
447C22×D5—122no—
448C22×D5—241no—
449C5×D4—21no—
450C5×D4—21no—
451C5×D4—21no—
452C5×D4—21no—
453C5×D4—21no—
454C5×D4—42no—
455C5×D4—42no—
456C5×D4#23712yescomplemented
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—21no—
460C2×C4×C5D3×D411yescharacteristic
461C2×C4×C5C23×D311yescharacteristic
462C22⋊D5—34no—
463C22⋊D5—122no—
464C22⋊D5—122no—
465C22⋊D5—122no—
466C22⋊D5—122no—
467C22⋊D5—122no—
468C22⋊D5—241no—
469C2×Dic5—31no—
470C2×Dic5—31no—
471C2×Dic5—31no—
472C2×Dic5—61no—
473C2×Dic5—61no—
474C2×Dic5—61no—
475C2×Dic5—122no—
476C2×Dic5—122no—
477C2×Dic5—122no—
478D20—61no—
479D20—61no—
480C4×D5—61no—
481C4×D5—61no—
482C4×D5—122no—
483Dic10—122no—
484C5×C8—21no—
485C5×C8—21no—
486#168—61no—
487#168—61no—
488C2×#41—301no—
489C22×D4—151no—
490C22×D4—301no—
491C22×D4C2×D1511yescharacteristic
492C2×D8—151no—
493C2×D8C2×D1511yescharacteristic
494C2×D8C2×D1511yescharacteristic, complemented
495C22×C8—151no—
496C22×C8—151no—
497C4⋊Q8—151no—
498#127—151no—
499#123—301no—
500#123—301no—
501C22⋊Q8—301no—
502#121—151no—
503#121—151no—
504#121—151no—
505#121—301no—
506#121C2×D1511yescharacteristic, complemented
507#120—301no—
508#120—301no—
509C4×D4—151no—
510C4×D4—151no—
511C4×D4—151no—
512C2×C4⋊C4—151no—
513C2×C4⋊C4—151no—
514#107—151no—
515#107—151no—
516#107—151no—
517C4⋊C8—151no—
518#102—151no—
519#102—151no—
520#102—151no—
521#102—151no—
522#102—151no—
523#102—151no—
524#102—151no—
525#102—151no—
526#102C2×D1511yescharacteristic
527#102C2×D1511yescharacteristic, complemented
528C22⋊C8—151no—
529C22⋊C8C2×D1511yescharacteristic, complemented
530C4×C8—151no—
531C2×C3×C5—22no—
532C2×C3×C5—42no—
533C2×C3×C5—81no—
534C2×C3×C5—81no—
535C2×C3×C5#54611yescharacteristic
536C2×C3×C5C22×D811yescharacteristic
537C2×C3×C5#57711yescharacteristic
538D15—22no—
539D15—81no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—42no—
544C23×C3—42no—
545C23×C3—81no—
546C23×C3D4×D511yescharacteristic
547C22×D3—51no—
548C22×D3—101no—
549C22×D3—202no—
550C22×D3—202no—
551C22×D3—401no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—42no—
558C3×D4—42no—
559C3×D4#71112yescomplemented
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4D4×D511yescharacteristic
564C2×C3×C4C23×D511yescharacteristic
565#67—54no—
566#67—202no—
567#67—202no—
568#67—202no—
569#67—202no—
570#67—202no—
571#67—401no—
572C2×Dic3—51no—
573C2×Dic3—51no—
574C2×Dic3—51no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—202no—
579C2×Dic3—202no—
580C2×Dic3—202no—
581D12—101no—
582D12—101no—
583C4×D3—101no—
584C4×D3—101no—
585C4×D3—202no—
586Dic6—202no—
587C3×C8—21no—
588C3×C8—21no—
589C3⋊C8—101no—
590C3⋊C8—101no—
591C22×C5—21no—
592C22×C5—21no—
593C22×C5—22no—
594C22×C5—41no—
595C22×C5—41no—
596C22×C5—41no—
597C22×C5—41no—
598C22×C5—41no—
599C22×C5—41no—
600C22×C5—41no—
601C22×C5—41no—
602C22×C5—84no—
603C22×C5D3×D812yes—
604C22×C5C2×D3×D411yescharacteristic
605C2×D5—32no—
606C2×D5—61no—
607C2×D5—61no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—121no—
611C2×D5—244no—
612C4×C5—21no—
613C4×C5—41no—
614C4×C5C2×#23711yescharacteristic
615C4×C5#100411yescharacteristic
616Dic5—32no—
617Dic5—61no—
618Dic5—61no—
619Dic5—121no—
620Dic5—121no—
621Dic5—121no—
622C24—21no—
623C24—301no—
624#41—604no—
625C2×Q8—301no—
626C2×D4—22no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—41no—
630C2×D4—151no—
631C2×D4—151no—
632C2×D4—301no—
633C2×D4—301no—
634C2×D4—301no—
635C2×D4—302no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—301no—
639C2×D4—601no—
640C2×D4—604no—
641C2×D4C22×D1511yescharacteristic
642C2×D4C22×D1511yescharacteristic
643C2×D4C22×D1511yescharacteristic
644C22×C4—151no—
645C22×C4—301no—
646C22×C4—301no—
647C22×C4—301no—
648C22×C4—301no—
649C22×C4C22×D1511yescharacteristic
650D8—22no—
651D8—41no—
652D8—601no—
653C2×C8—151no—
654C2×C8—151no—
655C2×C8—601no—
656C2×C8—601no—
657C2×C8C22×D1511yescharacteristic
658C2×C8C22×D1511yescharacteristic
659C4⋊C4—151no—
660C4⋊C4—151no—
661C4⋊C4—151no—
662C4⋊C4—151no—
663C4⋊C4—301no—
664C4⋊C4—301no—
665C4⋊C4—301no—
666C4⋊C4C22×D1511yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—151no—
669C22⋊C4—151no—
670C22⋊C4—301no—
671C22⋊C4—301no—
672C22⋊C4—301no—
673C22⋊C4—301no—
674C22⋊C4—301no—
675C42—151no—
676C3×C5#329411yescharacteristic, complemented, Hall
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—22no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—84no—
689C22×C3D5×D812yes—
690C22×C3C2×D4×D511yescharacteristic
691C2×D3—52no—
692C2×D3—101no—
693C2×D3—101no—
694C2×D3—201no—
695C2×D3—201no—
696C2×D3—201no—
697C2×D3—404no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4C2×#71111yescharacteristic
701C3×C4#414411yescharacteristic
702Dic3—52no—
703Dic3—101no—
704Dic3—101no—
705Dic3—201no—
706Dic3—201no—
707Dic3—201no—
708C2×C5—22no—
709C2×C5—42no—
710C2×C5—81no—
711C2×C5—81no—
712C2×C5#559111yescharacteristic
713C2×C5C2×D3×D811yescharacteristic
714C2×C5#577511yescharacteristic
715D5—62no—
716D5—241no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—42no—
721C23—42no—
722C23—81no—
723C23—151no—
724C23—301no—
725C23—602no—
726C23—602no—
727C23—1201no—
728C23D4×D1511yescharacteristic
729Q8—602no—
730D4—21no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—42no—
736D4—42no—
737D4—154no—
738D4—301no—
739D4—301no—
740D4—602no—
741D4—602no—
742D4—602no—
743D4—602no—
744D4—602no—
745D4—1201no—
746D4#681912yescomplemented
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—151no—
751C2×C4—151no—
752C2×C4—151no—
753C2×C4—301no—
754C2×C4—301no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—602no—
759C2×C4—602no—
760C2×C4—602no—
761C2×C4—602no—
762C2×C4D4×D1511yescharacteristic
763C2×C4C23×D1511yescharacteristic
764C8—21no—
765C8—21no—
766C8—301no—
767C8—301no—
768C2×C3—22no—
769C2×C3—42no—
770C2×C3—81no—
771C2×C3—81no—
772C2×C3#6592511yescharacteristic
773C2×C3C2×D5×D811yescharacteristic
774C2×C3#6610911yescharacteristic
775D3—102no—
776D3—401no—
777C5#8001411yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—84no—
790C22—152no—
791C22—301no—
792C22—301no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22D8×D1512yes—
798C22C2×D4×D1511yescharacteristic
799C4—21no—
800C4—41no—
801C4—152no—
802C4—301no—
803C4—301no—
804C4—601no—
805C4—601no—
806C4—601no—
807C4C2×#681911yescharacteristic
808C4#9209511yescharacteristic
809C3#1061174511yescharacteristic, complemented, Sylow
810C2—22no—
811C2—42no—
812C2—81no—
813C2—81no—
814C2—302no—
815C2—1201no—
816C2#1175635011yescharacteristic
817C2C2×D8×D1511yescharacteristic
818C2#1175653411yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#447C2
socleC22×C3×C5C22×D4
hypercenter#447D15
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. D4×#1220C2semidirect
2. #11756370C2semidirect
3. C3×C5×#447C2semidirect
4. C2×#91116C2semidirect
5. #11751258C2semidirect
6. #11751257C2semidirect
7. #11751251C2semidirect
8. D8×Dic15C2semidirect
9. #11751139C2semidirect
10. #11750875C2semidirect
11. D15×#102C2semidirect
12. #11750861C2semidirect
13. #11750860C2semidirect
14. #11750837C2semidirect
15. #11750826C2semidirect
22. C2×C3×C5×D8C22semidirect
23. C3×C5×#121C22semidirect
28. #91827C22semidirect
32. D4×Dic15C22semidirect
33. C2×#6715C22semidirect
36. C2×C4⋊Dic15C22semidirect
37. C22×C3⋊#168C22semidirect
38. C2×C8×D15C22semidirect
39. C4⋊C4×D15C22semidirect
40. #91777C22semidirect
44. C3×C5×#102C22semidirect
45. C3×C5×C22⋊C8C22semidirect
48. #91116C22semidirect
49. #91116C22semidirect
50. #91116C22semidirect
51. #91105C22semidirect
52. #91105C22semidirect
53. #91104C22semidirect
54. #91102C22semidirect
55. #91102C22semidirect
56. #91098C22semidirect
57. C8×Dic15C22semidirect
58. #91093C22semidirect
59. #91091C22semidirect
63. C5×#447D3semidirect
132. C3×#447D5semidirect
150. C2×C5×D8C2×D3semidirect
151. C5×#121C2×D3semidirect
172. C5×#102C2×D3semidirect
173. C5×C22⋊C8C2×D3semidirect
208. C3×C5×D4#41semidirect
220. #1220D8semidirect
245. C2×C3×D8C2×D5semidirect
246. C3×#121C2×D5semidirect
267. C3×#102C2×D5semidirect
268. C3×C22⋊C8C2×D5semidirect
347. #447D15semidirect
456. C5×D4#237semidirect
494. C2×D8C2×D15semidirect
506. #121C2×D15semidirect
527. #102C2×D15semidirect
529. C22⋊C8C2×D15semidirect
559. C3×D4#711semidirect
676. C3×C5#3294semidirect
746. D4#6819semidirect
777. C5#80014semidirect
809. C3#10611745semidirect

Maximal subgroups

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

subgroupindex
D4×#12202
#117563702
C3×C5×#4472
C2×#911162
#117512582
#117512572
#117512512
D8×Dic152
#117511392
#117508752
D15×#1022
#117508612
#117508602
#117508372
#117508262
#106117453
#800145