Finite Group Databasebeta

← #14427865

Subgroups — #14427865

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755070C211yesmaximal, characteristic, complemented
2C2×#91499C211yesmaximal, characteristic, complemented
3C2×D3×C8×D5C211yesmaximal, characteristic, complemented
4#11753886C211yesmaximal, characteristic, complemented
5#11750873C211yesmaximal, characteristic, complemented
6C5×#4775C211yesmaximal, characteristic, complemented
7C3×#65067C211yesmaximal, characteristic, complemented
8#11749119C211yesmaximal, characteristic, complemented
9#11749050C211yesmaximal, characteristic, complemented
10#11748145C211yesmaximal, characteristic, complemented
11#11747947C211yesmaximal, characteristic, complemented
12#11747892C211yesmaximal, characteristic, complemented
13#11747448C211yesmaximal, characteristic, complemented
14#11747445C211yesmaximal, characteristic, complemented
15#11747440C211yesmaximal, characteristic, complemented
16#10612445—31nomaximal, Hall
17C2×#6819C2211yescharacteristic
18C2×C4×D3×D5C2211yescharacteristic
19C2×#6768C2211yescharacteristic
20C2×C8×D15C2211yescharacteristic
21#91781C2211yescharacteristic
22C5×#938C2211yescharacteristic
23C2×C5×#213C2211yescharacteristic, complemented
24C2×C5×D3×C8C2211yescharacteristic
25C5×#895C2211yescharacteristic
26C3×#4084C2211yescharacteristic
27C2×C3×#687C2211yescharacteristic, complemented
28C2×C3×C8×D5C2211yescharacteristic
29C3×#4043C2211yescharacteristic
30#91577—21no—
31#91562—21no—
32#67⋊Dic5—21no—
33#91559—21no—
34#91499—24no—
35#91475—21no—
36#91449C2211yescharacteristic
37#91442—21no—
38#91438—21no—
39#91435—21no—
40#91369C2211yescharacteristic
41#91365C2211yescharacteristic
42#91360C2211yescharacteristic
43#91347C2211yescharacteristic
44C2×#6662C2211yescharacteristic, complemented
45C2×#6659C2211yescharacteristic, complemented
46C2×#6648C2211yescharacteristic
47C2×D3×#168C2211yescharacteristic
48C2×D5×C3⋊C8C2211yescharacteristic
49D3×C8×D5—24no—
50C3×C5×#102C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91100C2211yescharacteristic, complemented
53#91094C2211yescharacteristic, complemented
54C5×#821C2211yescharacteristic, complemented
55C5×#807C2211yescharacteristic, complemented
56C3×#3948C2211yescharacteristic, complemented
57C3×#3940C2211yescharacteristic, complemented
58#90990C2211yescharacteristic, complemented
59#90985C2211yescharacteristic, complemented
60#90970C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62#80656—51nomaximal, Hall
63C2×#4058—31no—
64C22×C8×D5—31no—
65#65940—31no—
66#65940—31no—
67C5×#466—31no—
68#65446—31no—
69#65405—31no—
70#65330—31no—
71#65330—31no—
72#65176—31no—
73#65169—31no—
74#65067—31no—
75#65067D311yescharacteristic, complemented
76#65061—31no—
77#65061—31no—
78C22×D3×D5D411yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C2×#1220—21no—
81C22×Dic15—21no—
82#6819—22no—
83#6819—22no—
84C2×C4×D15C2311yescharacteristic
85C2×Dic30C2311yescharacteristic
86C2×C5×#67—21no—
87C2×C5×D12—21no—
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3C2311yescharacteristic
90C2×C3×C22⋊D5—21no—
91C2×C3×C4×D5C2311yescharacteristic
92C2×C3×Dic10C2311yescharacteristic
93C2×#1203—21no—
94C2×#1201—21no—
95C2×#1200D411yescharacteristic
96C2×D3×Dic5—21no—
97C2×D3×Dic5D411yescharacteristic
98C2×D5×Dic3D411yescharacteristic
99C4×D3×D5—22no—
100C4×D3×D5—22no—
101#6768—22no—
102#6768—22no—
103C2×C3×C5×C8C2311yescharacteristic
104C3×C5×C4⋊C4C2311yescharacteristic
105#6714—21no—
106C4⋊Dic15C2311yescharacteristic
107C4×Dic15—21no—
108C2×C3⋊#168C2311yescharacteristic
109C8×D15—22no—
110C5×#217—21no—
111C5×#213—22no—
112C5×(C2×D3)⋊C4—21no—
113C5×C4⋊Dic3C2311yescharacteristic
114C2×C5×C3⋊C8C2311yescharacteristic
115C5×D3×C8—22no—
116C3×C22⋊Dic5—21no—
117C3×#687—22no—
118C3×#685—21no—
119C3×C4⋊Dic5—21no—
120C3×C4⋊Dic5C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122C3×C8×D5—22no—
123Dic3⋊Dic5—21no—
124#6669—21no—
125#6668—21no—
126#6667—21no—
127(C2×D3)⋊Dic5—21no—
128(C2×D3)⋊Dic5—21no—
129(C2×D3)⋊Dic5—21no—
130#6665—21no—
131Dic3×Dic5—21no—
132#6662—22no—
133#6659—22no—
134#6648D414yescomplemented
135D3×#168—22no—
136D5×C3⋊C8—22no—
137C2×#916—51no—
138C22×D3×C8—51no—
139#5627—51no—
140#5606—51no—
141C3×#465—51no—
142#5171—51no—
143#5114—51no—
144#5051—51no—
145#5038—51no—
146#4864—51no—
147#4860—51no—
148#4813—51no—
149#4804—51no—
150#4775D511yescharacteristic, complemented
151#4772—51no—
152C2×#711—31no—
153C2×#711—31no—
154C22×C4×D5—31no—
155C2×C5×D8—31no—
156C22×C5×C8—31no—
157C5×#121—31no—
158C5×#121—31no—
159#4084—31no—
160#4084C2×D311yescharacteristic
161#4083—61no—
162#4083—61no—
163D4×Dic5—61no—
164D4×Dic5—61no—
165C2×#687—31no—
166C2×#687C2×D311yescharacteristic, complemented
167#4070—31no—
168#4070—31no—
169C22×#168—31no—
170#4058—64no—
171C2×Dic20—31no—
172C2×C8×D5—31no—
173C2×C8×D5—31no—
174C2×C8×D5—31no—
175C2×C8×D5—64no—
176C2×C8×D5C2×D311yescharacteristic
177#4043—31no—
178#4043C2×D311yescharacteristic
179#4038—31no—
180#4038—31no—
181#4029—61no—
182#4029—61no—
183#4027—61no—
184#4027—61no—
185C5×#107—31no—
186C5×#102—31no—
187C5×#102C2×D311yescharacteristic, complemented
188#3964—31no—
189#3964—31no—
190#3950—31no—
191#3948—31no—
192#3948C2×D311yescharacteristic, complemented
193#3942—31no—
194#3942—31no—
195#3940—31no—
196#3940C2×D311yescharacteristic, complemented
197#3050—151noSylow
198C23×C3×C5—21no—
199C22×D15C2×D411yescharacteristic
200C22×C5×D3—21no—
201C22×C5×D3C2×D411yescharacteristic
202C22×C3×D5C2×D411yescharacteristic
203C2×D3×D5—22no—
204C2×D3×D5—22no—
205C2×D3×D5—22no—
206C3×C5×D4—21no—
207C3×C5×D4—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5C2411yescharacteristic
210#1220—42no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—42no—
214C2×Dic15C2×D411yescharacteristic
215C4×D15C2×D412yes—
216C4×D15#4112yes—
217Dic30—21no—
218Dic30—21no—
219C5×#67—42no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3C2×D411yescharacteristic
222C5×D12—21no—
223C5×D12—21no—
224C5×D12—42no—
225C4×C5×D3—21no—
226C4×C5×D3—21no—
227C3×C22⋊D5—42no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5C2×D411yescharacteristic
231C3×C4×D5—21no—
232C3×C4×D5—21no—
233C3×Dic10—21no—
234C3×Dic10—21no—
235#1203—42no—
236#1201—42no—
237#1200—22no—
238D3×Dic5—22no—
239D3×Dic5—42no—
240D5×Dic3—22no—
241C3×C5×C8—21no—
242C3⋊#168—21no—
243C3×#168C2×D412yes—
244C5×C3⋊C8C2×D412yes—
245C2×#239—51no—
246C2×#237—51no—
247C22×C4×D3—51no—
248C2×C3×SD16—51no—
249C22×C3×C8—51no—
250C3×C22⋊Q8—51no—
251C3×#121—51no—
252#946—51no—
253C2×#216—51no—
254#938C2×D511yescharacteristic
255#937—101no—
256D4×Dic3—101no—
257C2×#213C2×D511yescharacteristic, complemented
258#930—51no—
259#924—51no—
260C22×C3⋊C8—51no—
261#916—104no—
262C2×#204—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—51no—
266C2×D3×C8—104no—
267C2×D3×C8C2×D511yescharacteristic
268#897—51no—
269#895C2×D511yescharacteristic
270#894—101no—
271#893—101no—
272#892—51no—
273#892—51no—
274#883—101no—
275#882—101no—
276#67⋊C4—101no—
277#67⋊C4—101no—
278C3×#106—51no—
279C3×#103—51no—
280C3×#102C2×D511yescharacteristic, complemented
281#835—51no—
282#832—51no—
283#821C2×D511yescharacteristic, complemented
284#817—51no—
285#816—51no—
286#810—51no—
287#809—51no—
288#807—51no—
289#807C2×D511yescharacteristic, complemented
290C23×D5—31no—
291C2×C5×D4—31no—
292C2×C5×D4—61no—
293C2×C5×D4—61no—
294C2×C5×D4C22×D311yescharacteristic
295C22×C4×C5—31no—
296C2×C22⋊D5—21no—
297C2×C22⋊D5—61no—
298C2×C22⋊D5—61no—
299C2×C22⋊D5—61no—
300C22×Dic5—31no—
301C22×Dic5—61no—
302C22×Dic5—61no—
303#711—62no—
304#711—62no—
305#711—62no—
306#711—62no—
307C2×C4×D5—31no—
308C2×C4×D5—31no—
309C2×C4×D5—31no—
310C2×C4×D5—62no—
311C2×C4×D5—62no—
312C2×C4×D5C22×D311yescharacteristic
313C2×Dic10—31no—
314C2×Dic10C22×D311yescharacteristic
315C5×D8—62no—
316C2×C5×C8—31no—
317C2×C5×C8—62no—
318C2×C5×C8C22×D311yescharacteristic
319C5×C4⋊C4—31no—
320C5×C4⋊C4C22×D311yescharacteristic
321C5×C22⋊C4—61no—
322C5×C22⋊C4—61no—
323C22⋊Dic5—21no—
324C22⋊Dic5—61no—
325C22⋊Dic5—61no—
326C22⋊Dic5—61no—
327#687—22no—
328#687—62no—
329#685—21no—
330#685—61no—
331#685—61no—
332#685—61no—
333C4⋊Dic5—21no—
334C4⋊Dic5—31no—
335C4⋊Dic5—61no—
336C4⋊Dic5C22×D311yescharacteristic
337#683—61no—
338#683—61no—
339C4×Dic5—61no—
340C4×Dic5—61no—
341C2×#168—31no—
342C2×#168—62no—
343C2×#168C22×D311yescharacteristic
344Dic20—62no—
345C8×D5—22no—
346C8×D5—34no—
347C8×D5—62no—
348C8×D5—62no—
349C2×#135—151no—
350C23×C8—151no—
351#525—151no—
352#525—151no—
353#467—151no—
354#467—151no—
355#466—31no—
356#466—151no—
357#465—51no—
358#465—151no—
359#465—151no—
360#465—151no—
361#427—151no—
362#416—151no—
363#416—151no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5C22×D411yescharacteristic
368C2×D15—21no—
369C2×D15—21no—
370C2×D15#12112yes—
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3—41no—
374C2×C5×D3—41no—
375C2×C5×D3—41no—
376C2×C5×D3#13512yescomplemented
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5#13512yescomplemented
380D3×D5—28no—
381C3×C4×C5—41no—
382C3×C4×C5C22×D411yescharacteristic
383C3×C4×C5C2×#4111yescharacteristic
384Dic15—41no—
385Dic15—41no—
386Dic15#12112yes—
387C3×Dic5—21no—
388C3×Dic5—41no—
389C3×Dic5—41no—
390C5×Dic3—21no—
391C5×Dic3—41no—
392C23×D3—51no—
393C2×C3×Q8—51no—
394C2×C3×D4—101no—
395C2×C3×D4C22×D511yescharacteristic
396C22×C3×C4—51no—
397C2×#67—21no—
398C2×#67—101no—
399C2×#67—101no—
400C22×Dic3—51no—
401C22×Dic3—101no—
402#239—102no—
403#239—102no—
404#237—102no—
405#237—102no—
406C2×D12—21no—
407C2×D12—101no—
408C2×D12C22×D511yescharacteristic
409C2×C4×D3—51no—
410C2×C4×D3—51no—
411C2×C4×D3—51no—
412C2×C4×D3—102no—
413C2×C4×D3—102no—
414C2×C4×D3—101no—
415C2×C4×D3C22×D511yescharacteristic
416C2×Dic6—51no—
417C3×SD16—102no—
418C2×C3×C8—51no—
419C2×C3×C8—102no—
420C2×C3×C8C22×D511yescharacteristic
421C3×C4⋊C4—51no—
422C3×C4⋊C4—101no—
423C3×C4⋊C4C22×D511yescharacteristic
424C3×C22⋊C4—101no—
425C3×C22⋊C4—101no—
426#217—21no—
427#217—101no—
428#216—102no—
429#213—22no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—101no—
432(C2×D3)⋊C4—101no—
433(C2×D3)⋊C4—101no—
434(C2×D3)⋊C4—101no—
435(C2×D3)⋊C4—101no—
436C4⋊Dic3—51no—
437C4⋊Dic3—101no—
438C4⋊Dic3C22×D511yescharacteristic
439Dic3⋊C4—101no—
440Dic3⋊C4—101no—
441C4×Dic3—101no—
442C4×Dic3—101no—
443C2×C3⋊C8—51no—
444C2×C3⋊C8—102no—
445C2×C3⋊C8C22×D511yescharacteristic
446#204—102no—
447D3×C8—22no—
448D3×C8—54no—
449D3×C8—102no—
450D3×C8—102no—
451C23×C5—21no—
452C23×C5—31no—
453C23×C5—61no—
454C22×D5—31no—
455C22×D5—62no—
456C22×D5—62no—
457C22×D5—62no—
458C22×D5D3×D411yescharacteristic
459C5×D4—21no—
460C5×D4—21no—
461C5×D4—61no—
462C5×D4—61no—
463C5×D4—122no—
464C5×D4—122no—
465C2×C4×C5—21no—
466C2×C4×C5—31no—
467C2×C4×C5—61no—
468C2×C4×C5—61no—
469C2×C4×C5—61no—
470C2×C4×C5C23×D311yescharacteristic
471C22⋊D5—42no—
472C22⋊D5—122no—
473C22⋊D5—122no—
474C22⋊D5—122no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—31no—
478C2×Dic5—62no—
479C2×Dic5—61no—
480C2×Dic5—61no—
481C2×Dic5—122no—
482C2×Dic5—122no—
483C2×Dic5D3×D411yescharacteristic
484C4×D5—21no—
485C4×D5—21no—
486C4×D5—32no—
487C4×D5—32no—
488C4×D5—62no—
489C4×D5—62no—
490Dic10—21no—
491Dic10—21no—
492Dic10—61no—
493Dic10—61no—
494C5×C8—21no—
495C5×C8—32no—
496#168—61no—
497#168D3×D412yes—
498C2×#41—151no—
499C2×#41—151no—
500C23×C4—151no—
501#135—304no—
502C2×Q16—151no—
503C2×SD16—51no—
504C2×SD16—151no—
505C2×D8—31no—
506C22×C8—31no—
507C22×C8—51no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—304no—
513#123—301no—
514#123—301no—
515C22⋊Q8—51no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518C22⋊Q8—151no—
519#121—31no—
520#121—31no—
521#121—51no—
522#121—151no—
523#120—301no—
524#120—301no—
525C4×D4—301no—
526C4×D4—301no—
527C4×D4—301no—
528C4×D4—301no—
529#117—151no—
530#117—151no—
531#107—31no—
532#107—151no—
533#106—51no—
534#106—151no—
535#103—51no—
536#103—151no—
537#103—151no—
538#103—151no—
539#102—31no—
540#102—151no—
541#102—151no—
542#102D3×D511yescharacteristic, complemented
543C2×C3×C5—81no—
544C2×C3×C5C2×#12111yescharacteristic
545C2×C3×C5C2×#13511yescharacteristic
546C2×C3×C5C2×#13511yescharacteristic
547D15—22no—
548C3×D5—22no—
549C5×D3—22no—
550C5×D3—81no—
551C23×C3—21no—
552C23×C3—51no—
553C22×D3—21no—
554C22×D3—51no—
555C22×D3—102no—
556C22×D3—102no—
557C22×D3—102no—
558C22×D3D4×D511yescharacteristic
559C3×Q8—101no—
560C3×Q8—101no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—202no—
564C2×C3×C4—21no—
565C2×C3×C4—51no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4C23×D511yescharacteristic
571#67—42no—
572#67—202no—
573#67—202no—
574C2×Dic3—21no—
575C2×Dic3—51no—
576C2×Dic3—102no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—202no—
580C2×Dic3D4×D511yescharacteristic
581D12—21no—
582D12—21no—
583D12—42no—
584D12—202no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—52no—
588C4×D3—52no—
589C4×D3—102no—
590C4×D3—102no—
591C4×D3—202no—
592Dic6—101no—
593Dic6—101no—
594C3×C8—21no—
595C3×C8—52no—
596C3⋊C8—101no—
597C3⋊C8D4×D512yes—
598C22×C5—32no—
599C22×C5—41no—
600C22×C5—41no—
601C22×C5—41no—
602C22×C5—61no—
603C22×C5—61no—
604C22×C5—121no—
605C22×C5—121no—
606C22×C5—121no—
607C22×C5C2×D3×D411yescharacteristic
608C2×D5—21no—
609C2×D5—21no—
610C2×D5—32no—
611C2×D5—68no—
612C2×D5—61no—
613C2×D5—61no—
614C2×D5#91612yescomplemented
615C4×C5—41no—
616C4×C5—61no—
617C4×C5—121no—
618C4×C5C2×D3×D411yescharacteristic
619C4×C5D3×#4111yescharacteristic
620Dic5—21no—
621Dic5—32no—
622Dic5—41no—
623Dic5—41no—
624Dic5—121no—
625Dic5—121no—
626C24—151no—
627#41—302no—
628#41—302no—
629#41—302no—
630#41—302no—
631C2×Q8—51no—
632C2×Q8—151no—
633C2×D4—31no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—101no—
637C2×D4—301no—
638C2×D4—301no—
639C2×D4—301no—
640C2×D4C2×D3×D511yescharacteristic
641C22×C4—31no—
642C22×C4—51no—
643C22×C4—151no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4—151no—
647C22×C4—302no—
648C22×C4—302no—
649C22×C4—301no—
650C22×C4—301no—
651Q16—302no—
652SD16—102no—
653SD16—302no—
654D8—62no—
655C2×C8—31no—
656C2×C8—51no—
657C2×C8—62no—
658C2×C8—102no—
659C2×C8—154no—
660C2×C8—151no—
661C2×C8—302no—
662C2×C8—302no—
663C2×C8—302no—
664C2×C8C2×D3×D511yescharacteristic
665C4⋊C4—31no—
666C4⋊C4—51no—
667C4⋊C4—101no—
668C4⋊C4—151no—
669C4⋊C4—301no—
670C4⋊C4—301no—
671C4⋊C4—301no—
672C4⋊C4C2×D3×D511yescharacteristic
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—101no—
676C22⋊C4—101no—
677C22⋊C4—301no—
678C22⋊C4—301no—
679C22⋊C4—301no—
680C22⋊C4—301no—
681C22⋊C4—301no—
682C22⋊C4—301no—
683C42—301no—
684C42—301no—
685C3×C5#305011yescharacteristic, complemented, Hall
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—52no—
690C22×C3—101no—
691C22×C3—101no—
692C22×C3C2×D4×D511yescharacteristic
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—52no—
699C2×D3—108no—
700C2×D3—101no—
701C2×D3—101no—
702C2×D3#405812yescomplemented
703C3×C4—41no—
704C3×C4—101no—
705C3×C4—201no—
706C3×C4—201no—
707C3×C4C2×D4×D511yescharacteristic
708C3×C4D5×#4111yescharacteristic
709Dic3—21no—
710Dic3—41no—
711Dic3—52no—
712Dic3—201no—
713Dic3—201no—
714C2×C5—62no—
715C2×C5—81no—
716C2×C5—241no—
717C2×C5D3×#12111yescharacteristic
718C2×C5C2×#91611yescharacteristic
719C2×C5D3×#13511yescharacteristic
720D5—22no—
721D5—62no—
722C23—21no—
723C23—31no—
724C23—51no—
725C23—61no—
726C23—151no—
727C23—302no—
728C23—302no—
729C23—302no—
730Q8—101no—
731Q8—101no—
732Q8—301no—
733Q8—301no—
734D4—21no—
735D4—21no—
736D4—61no—
737D4—61no—
738D4—122no—
739D4—122no—
740D4—202no—
741D4—602no—
742D4—602no—
743D4—602no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—51no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—151no—
755C2×C4—152no—
756C2×C4—152no—
757C2×C4—302no—
758C2×C4—302no—
759C2×C4—302no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—602no—
763C2×C4—602no—
764C2×C4C22×D3×D511yescharacteristic
765C8—21no—
766C8—32no—
767C8—52no—
768C8—301no—
769C2×C3—81no—
770C2×C3—102no—
771C2×C3D5×#12111yescharacteristic
772C2×C3C2×#405811yescharacteristic
773C2×C3D5×#13511yescharacteristic
774D3—22no—
775D3—81no—
776D3—102no—
777C5#8065611yescharacteristic, complemented, Sylow
778C22—32no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—52no—
783C22—61no—
784C22—61no—
785C22—101no—
786C22—101no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—152no—
791C22—308no—
792C22—301no—
793C22—301no—
794C22D3×D4×D511yescharacteristic
795C4—41no—
796C4—61no—
797C4—101no—
798C4—121no—
799C4—152no—
800C4—201no—
801C4—201no—
802C4—601no—
803C4—601no—
804C4#9201611yescharacteristic
805C4D3×D4×D511yescharacteristic
806C3#1061244511yescharacteristic, complemented, Sylow
807C2—62no—
808C2—81no—
809C2—102no—
810C2—241no—
811C2—302no—
812C2#1175321911yescharacteristic
813C2D3×#405811yescharacteristic
814C2D5×#91611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
hypercenter#102D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #11755070C2semidirect
2. C2×#91499C2semidirect
3. C2×D3×C8×D5C2semidirect
4. #11753886C2semidirect
5. #11750873C2semidirect
6. C5×#4775C2semidirect
7. C3×#65067C2semidirect
8. #11749119C2semidirect
9. #11749050C2semidirect
10. #11748145C2semidirect
11. #11747947C2semidirect
12. #11747892C2semidirect
13. #11747448C2semidirect
14. #11747445C2semidirect
15. #11747440C2semidirect
23. C2×C5×#213C22semidirect
27. C2×C3×#687C22semidirect
44. C2×#6662C22semidirect
45. C2×#6659C22semidirect
50. C3×C5×#102C22semidirect
51. #91116C22semidirect
52. #91100C22semidirect
53. #91094C22semidirect
54. C5×#821C22semidirect
55. C5×#807C22semidirect
56. C3×#3948C22semidirect
57. C3×#3940C22semidirect
58. #90990C22semidirect
59. #90985C22semidirect
60. #90970C22semidirect
61. #90966C22semidirect
75. #65067D3semidirect
134. #6648D4semidirect
150. #4775D5semidirect
166. C2×#687C2×D3semidirect
187. C5×#102C2×D3semidirect
192. #3948C2×D3semidirect
196. #3940C2×D3semidirect
257. C2×#213C2×D5semidirect
280. C3×#102C2×D5semidirect
283. #821C2×D5semidirect
289. #807C2×D5semidirect
376. C2×C5×D3#135semidirect
379. C2×C3×D5#135semidirect
542. #102D3×D5semidirect
614. C2×D5#916semidirect
685. C3×C5#3050semidirect
702. C2×D3#4058semidirect
777. C5#80656semidirect
806. C3#10612445semidirect

Maximal subgroups

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

subgroupindex
#117550702
C2×#914992
C2×D3×C8×D52
#117538862
#117508732
C5×#47752
C3×#650672
#117491192
#117490502
#117481452
#117479472
#117478922
#117474482
#117474452
#117474402
#106124453
#806565