Finite Group Databasebeta

← #14453684

Subgroups — #14453684

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
1Q8×#1220C211yesmaximal, characteristic, complemented
2C22×#6717C211yesmaximal, characteristic, complemented
3C2×#91807C211yesmaximal, characteristic, complemented
4#11756389C211yesmaximal, characteristic
5C3×C5×#451C211yesmaximal, characteristic, complemented
6#11751291C211yesmaximal, characteristic, complemented
7#11751288C211yesmaximal, characteristic, complemented
8#11751286C211yesmaximal, characteristic, complemented
9#11751152C211yesmaximal, characteristic, complemented
10#11750919C211yesmaximal, characteristic, complemented
11#11750918C211yesmaximal, characteristic, complemented
12#11750913C211yesmaximal, characteristic, complemented
13#11750907C211yesmaximal, characteristic, complemented
14#11750832C211yesmaximal, characteristic, complemented
15#11750831C211yesmaximal, characteristic, complemented
16#10611935—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C2×#6821C2211yescharacteristic
19C2×Q8×D15C2211yescharacteristic, complemented
20C22×D60C2211yescharacteristic
21C2×C3×C5×Q16C2211yescharacteristic, complemented
22C2×C3×C5×Q16C2211yescharacteristic, complemented
23C3×C5×C22⋊Q8C2211yescharacteristic
24#91836C2211yescharacteristic
25#91835—21no—
26#91835C2211yescharacteristic, complemented
27Q8×Dic15C2211yescharacteristic, complemented
28#91833—21no—
29#91833C2211yescharacteristic, complemented
30C2×#6718C2211yescharacteristic, complemented
31C2×#6717—24no—
32C2×#6717C2211yescharacteristic
33C2×#6717C2211yescharacteristic
34C2×#6717C2211yescharacteristic
35C2×#6717C2211yescharacteristic
36C4×#1220—21no—
37C4×#1220C2211yescharacteristic
38#91813—21no—
39#91813C2211yescharacteristic
40C22×C3⋊#168C2211yescharacteristic
41#91807—24no—
42C2×#6706C2211yescharacteristic
43C2×#6706C2211yescharacteristic
44C2×#6705C2211yescharacteristic, complemented
45#91784—21no—
46#91784C2211yescharacteristic
47#91783—21no—
48#91782C2211yescharacteristic
49#91771—21no—
50C22⋊C4×D15—21no—
51C3×C5×#103C2211yescharacteristic, complemented
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×C22⋊C8C2211yescharacteristic
54#91119C2211yescharacteristic, complemented
55#91105C2211yescharacteristic
56#91105C2211yescharacteristic
57#91104C2211yescharacteristic, complemented
58#91099C2211yescharacteristic, complemented
59#91098C2211yescharacteristic, complemented
60#91094C2211yescharacteristic, complemented
61#91091C2211yescharacteristic, complemented
62#80204—51nomaximal, Hall
63Q8×C22⋊D5—31no—
64C22×#688—31no—
65C2×#4064—31no—
66#65964—31no—
67C5×#451D311yescharacteristic, complemented
68#65479—31no—
69#65476—31no—
70#65474—31no—
71#65340—31no—
72#65107—31no—
73#65106—31no—
74#65101—31no—
75#65095—31no—
76#65020—31no—
77#65019—31no—
78C23×D15—21no—
79C2×C3×C5×Q8—21no—
80C2×C3×C5×Q8—22no—
81C2×C3×C5×Q8—41no—
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×Q8C2311yescharacteristic
85C22×C3×C4×C5—21no—
86C22×C3×C4×C5C2311yescharacteristic
87C2×#1220D411yescharacteristic
88#6821—22no—
89#6821—41no—
90Q8×D15—22no—
91Q8×D15—41no—
92C2×D60—22no—
93C2×D60—21no—
94C2×D60—21no—
95C2×D60—21no—
96C2×D60—41no—
97C2×D60C2311yescharacteristic
98C2×D60C2311yescharacteristic
99C2×C4×D15—21no—
100C2×C4×D15—21no—
101C2×C4×D15—21no—
102C2×C4×D15C2311yescharacteristic
103C2×Dic30—21no—
104C2×Dic30C2311yescharacteristic
105C3×C5×Q16—22no—
106C3×C5×Q16—41no—
107C2×C3×C5×C8C2311yescharacteristic
108C2×C3×C5×C8C2311yescharacteristic
109C3×C5×C4⋊C4—21no—
110C3×C5×C4⋊C4C2311yescharacteristic
111C3×C5×C22⋊C4—21no—
112#6719—21no—
113#6719D411yescharacteristic
114#6718—22no—
115#6717—22no—
116#6717—22no—
117#6717—22no—
118#6717D414yescomplemented
119#6714—21no—
120#6714—21no—
121#6714—21no—
122#6714—21no—
123#6714—21no—
124#6714D411yescharacteristic
125C4⋊Dic15—21no—
126C4⋊Dic15C2311yescharacteristic
127#6712—21no—
128#6712—21no—
129#6712—21no—
130#6712—21no—
131#6712D411yescharacteristic
132C4×Dic15—21no—
133C4×Dic15C2311yescharacteristic
134C2×C3⋊#168—22no—
135C2×C3⋊#168C2311yescharacteristic
136C2×C3⋊#168C2311yescharacteristic
137#6706—22no—
138#6706—41no—
139#6705—22no—
140Q8×#67—51no—
141C22×#215—51no—
142C2×#918—51no—
143#5630—51no—
144C3×#451D511yescharacteristic, complemented
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#4730—51no—
155C22×C5×Q8C2×D311yescharacteristic
156C2×#713—31no—
157C2×Q8×D5—31no—
158C22×D20—31no—
159C2×C5×Q16C2×D311yescharacteristic, complemented
160C2×C5×Q16C2×D311yescharacteristic, complemented
161C5×C22⋊Q8C2×D311yescharacteristic
162#4093—31no—
163#4092—31no—
164#4092—61no—
165Q8×Dic5—31no—
166#4090—31no—
167#4090—61no—
168C2×#689—31no—
169C2×#688—31no—
170C2×#688—31no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688—64no—
174C4×C22⋊D5—31no—
175C4×C22⋊D5—61no—
176#4070—31no—
177#4070—61no—
178C22×#168—31no—
179#4064—64no—
180C2×#677—31no—
181C2×#677—31no—
182C2×#676—31no—
183#4041—31no—
184#4041—61no—
185#4040—61no—
186#4039—31no—
187#4028—61no—
188D5×C22⋊C4—61no—
189C5×#103C2×D311yescharacteristic, complemented
190C5×#103C2×D311yescharacteristic, complemented
191C5×C22⋊C8C2×D311yescharacteristic
192#3967—31no—
193#3953—31no—
194#3953—31no—
195#3952—31no—
196#3947—31no—
197#3946—31no—
198#3942—31no—
199#3939—31no—
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—42no—
205C22×D15—42no—
206C22×D15—81no—
207C22×D15C2×D411yescharacteristic
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C3×C5×Q8—42no—
214C3×C5×Q8C2×D412yes—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—42no—
222C2×C3×C4×C5C2×D411yescharacteristic
223C2×C3×C4×C5C2411yescharacteristic
224#1220—22no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15C2×D411yescharacteristic
228C2×Dic15C2×D411yescharacteristic
229C2×Dic15C2×D411yescharacteristic
230D60—21no—
231D60—21no—
232D60—21no—
233D60—42no—
234D60—42no—
235D60—81no—
236D60C2×D412yes—
237C4×D15—21no—
238C4×D15—21no—
239C4×D15—42no—
240C4×D15—42no—
241C4×D15—81no—
242Dic30—21no—
243Dic30—21no—
244Dic30—42no—
245C3×C5×C8—21no—
246C3×C5×C8—21no—
247C3⋊#168—21no—
248C3⋊#168C2×D412yes—
249C22×C3×Q8C2×D511yescharacteristic
250C2×#239—51no—
251C2×D3×Q8—51no—
252C22×D12—51no—
253C2×C3×Q16C2×D511yescharacteristic, complemented
254C2×C3×Q16C2×D511yescharacteristic, complemented
255C3×C22⋊Q8C2×D511yescharacteristic
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—51no—
269C4×#67—101no—
270#924—51no—
271#924—101no—
272C22×C3⋊C8—51no—
273#918—104no—
274C2×#204—51no—
275C2×#204—51no—
276C2×ΓL(1,𝔽25)—51no—
277#895—51no—
278#895—101no—
279#894—101no—
280#893—51no—
281#882—101no—
282D3×C22⋊C4—101no—
283C3×#103C2×D511yescharacteristic, complemented
284C3×#103C2×D511yescharacteristic, complemented
285C3×C22⋊C8C2×D511yescharacteristic
286#835—51no—
287#821—51no—
288#821—51no—
289(C2×D3)⋊C8—51no—
290#815—51no—
291Dic3⋊C8—51no—
292#810—51no—
293#807—51no—
294C23×D5—61no—
295C2×C5×Q8—21no—
296C2×C5×Q8—22no—
297C2×C5×Q8—41no—
298C2×C5×Q8C22×D311yescharacteristic
299C2×C5×Q8C22×D311yescharacteristic
300C2×C5×Q8C22×D311yescharacteristic
301C22×C4×C5—21no—
302C22×C4×C5C22×D311yescharacteristic
303C2×C22⋊D5—31no—
304#713—62no—
305#713—121no—
306Q8×D5—62no—
307Q8×D5—121no—
308C2×D20—31no—
309C2×D20—31no—
310C2×D20—62no—
311C2×D20—61no—
312C2×D20—61no—
313C2×D20—61no—
314C2×D20—121no—
315C2×C4×D5—31no—
316C2×C4×D5—61no—
317C2×C4×D5—61no—
318C2×C4×D5—61no—
319C2×Dic10—31no—
320C2×Dic10—61no—
321C5×Q16—22no—
322C5×Q16—41no—
323C2×C5×C8C22×D311yescharacteristic
324C2×C5×C8C22×D311yescharacteristic
325C5×C4⋊C4—21no—
326C5×C4⋊C4C22×D311yescharacteristic
327C5×C22⋊C4—21no—
328C22⋊Dic5—31no—
329C22⋊Dic5—61no—
330#689—62no—
331#688—34no—
332#688—62no—
333#688—62no—
334#688—62no—
335#685—31no—
336#685—61no—
337#685—61no—
338#685—61no—
339#685—61no—
340#685—61no—
341C4⋊Dic5—31no—
342C4⋊Dic5—61no—
343#683—31no—
344#683—61no—
345#683—61no—
346#683—61no—
347#683—61no—
348C4×Dic5—31no—
349C4×Dic5—61no—
350C2×#168—31no—
351C2×#168—31no—
352C2×#168—62no—
353#677—62no—
354#677—121no—
355#676—62no—
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#451D1511yescharacteristic, complemented
367#450—151no—
368#448—151no—
369#440—151no—
370#435—151no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5#13712yescomplemented
374C22×C3×C5C22×D411yescharacteristic
375C2×D15—21no—
376C2×D15—22no—
377C2×D15—21no—
378C2×D15—21no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—41no—
384C2×D15—84no—
385C3×C4×C5—22no—
386C3×C4×C5—21no—
387C3×C4×C5—41no—
388C3×C4×C5—41no—
389C3×C4×C5—41no—
390C3×C4×C5C22×D411yescharacteristic
391C3×C4×C5H(5,𝔽2)11yescharacteristic
392Dic15—21no—
393Dic15—21no—
394Dic15—21no—
395Dic15—41no—
396Dic15—41no—
397C23×D3—101no—
398C2×C3×Q8—21no—
399C2×C3×Q8—22no—
400C2×C3×Q8—41no—
401C2×C3×Q8C22×D511yescharacteristic
402C2×C3×Q8C22×D511yescharacteristic
403C2×C3×Q8C22×D511yescharacteristic
404C22×C3×C4—21no—
405C22×C3×C4C22×D511yescharacteristic
406C2×#67—51no—
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—51no—
419C2×C4×D3—101no—
420C2×C4×D3—101no—
421C2×C4×D3—101no—
422C2×Dic6—51no—
423C2×Dic6—101no—
424C3×Q16—22no—
425C3×Q16—41no—
426C2×C3×C8C22×D511yescharacteristic
427C2×C3×C8C22×D511yescharacteristic
428C3×C4⋊C4—21no—
429C3×C4⋊C4C22×D511yescharacteristic
430C3×C22⋊C4—21no—
431#217—51no—
432#217—101no—
433#216—102no—
434#215—54no—
435#215—102no—
436#215—102no—
437#215—102no—
438(C2×D3)⋊C4—51no—
439(C2×D3)⋊C4—101no—
440(C2×D3)⋊C4—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444C4⋊Dic3—51no—
445C4⋊Dic3—101no—
446Dic3⋊C4—51no—
447Dic3⋊C4—101no—
448Dic3⋊C4—101no—
449Dic3⋊C4—101no—
450Dic3⋊C4—101no—
451C4×Dic3—51no—
452C4×Dic3—101no—
453C2×C3⋊C8—51no—
454C2×C3⋊C8—51no—
455C2×C3⋊C8—102no—
456#204—102no—
457#204—201no—
458ΓL(1,𝔽25)—102no—
459C23×C5D3×D411yescharacteristic
460C22×D5—31no—
461C22×D5—61no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—241no—
466C5×Q8—21no—
467C5×Q8—21no—
468C5×Q8—21no—
469C5×Q8—21no—
470C5×Q8—21no—
471C5×Q8—42no—
472C5×Q8D3×D412yes—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—42no—
480C2×C4×C5D3×D411yescharacteristic
481C2×C4×C5C23×D311yescharacteristic
482C22⋊D5—62no—
483C2×Dic5—31no—
484C2×Dic5—31no—
485C2×Dic5—31no—
486C2×Dic5—61no—
487C2×Dic5—61no—
488D20—32no—
489D20—61no—
490D20—61no—
491D20—61no—
492D20—122no—
493D20—122no—
494D20—241no—
495C4×D5—61no—
496C4×D5—61no—
497C4×D5—122no—
498C4×D5—122no—
499C4×D5—241no—
500Dic10—61no—
501Dic10—61no—
502Dic10—122no—
503C5×C8—21no—
504C5×C8—21no—
505#168—32no—
506#168—61no—
507C2×#41—151no—
508C22×Q8—151no—
509C22×Q8C2×D1511yescharacteristic
510C22×D4—151no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16C2×D1511yescharacteristic, complemented
514C2×Q16C2×D1511yescharacteristic, complemented
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—151no—
523C22×C8—151no—
524C4⋊Q8—151no—
525C4⋊Q8—301no—
526#124—151no—
527#123—301no—
528C22⋊Q8—151no—
529C22⋊Q8—151no—
530C22⋊Q8—301no—
531C22⋊Q8—301no—
532C22⋊Q8C2×D1511yescharacteristic
533#121—151no—
534#121—301no—
535#120—301no—
536C4×Q8—151no—
537C4×D4—151no—
538C4×D4—151no—
539C4×D4—301no—
540C2×C22⋊C4—301no—
541#107—151no—
542C4⋊C8—151no—
543#103—151no—
544#103—151no—
545#103C2×D1511yescharacteristic, complemented
546#103C2×D1511yescharacteristic, complemented
547#102—151no—
548#102—151no—
549C22⋊C8—151no—
550C22⋊C8C2×D1511yescharacteristic
551#97—151no—
552C2×C3×C5—22no—
553C2×C3×C5D4211yescharacteristic
554C2×C3×C5C2×#13711yescharacteristic
555C2×C3×C5#57711yescharacteristic
556D15—41no—
557D15—42no—
558D15—81no—
559C23×C3D4×D511yescharacteristic
560C22×D3—51no—
561C22×D3—101no—
562C22×D3—101no—
563C22×D3—202no—
564C22×D3—202no—
565C22×D3—401no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—42no—
572C3×Q8D4×D512yes—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—42no—
580C2×C3×C4D4×D511yescharacteristic
581C2×C3×C4C23×D511yescharacteristic
582#67—102no—
583C2×Dic3—51no—
584C2×Dic3—51no—
585C2×Dic3—51no—
586C2×Dic3—101no—
587C2×Dic3—101no—
588D12—52no—
589D12—101no—
590D12—101no—
591D12—101no—
592D12—202no—
593D12—202no—
594D12—401no—
595C4×D3—101no—
596C4×D3—101no—
597C4×D3—202no—
598C4×D3—202no—
599C4×D3—401no—
600Dic6—101no—
601Dic6—101no—
602Dic6—202no—
603C3×C8—21no—
604C3×C8—21no—
605C3⋊C8—52no—
606C3⋊C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5#91812yescomplemented
610C22×C5C2×D3×D411yescharacteristic
611C2×D5—61no—
612C2×D5—61no—
613C2×D5—61no—
614C2×D5—62no—
615C2×D5—121no—
616C2×D5—121no—
617C2×D5—121no—
618C2×D5—121no—
619C2×D5—121no—
620C2×D5—244no—
621C4×C5—22no—
622C4×C5—21no—
623C4×C5—41no—
624C4×C5—41no—
625C4×C5—41no—
626C4×C5C2×D3×D411yescharacteristic
627C4×C5#100411yescharacteristic
628Dic5—61no—
629Dic5—61no—
630Dic5—61no—
631Dic5—121no—
632Dic5—121no—
633C24—301no—
634#41—302no—
635#41—601no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—41no—
639C2×Q8—151no—
640C2×Q8—301no—
641C2×Q8—302no—
642C2×Q8—601no—
643C2×Q8C22×D1511yescharacteristic
644C2×Q8C22×D1511yescharacteristic
645C2×Q8C22×D1511yescharacteristic
646C2×D4—151no—
647C2×D4—151no—
648C2×D4—151no—
649C2×D4—302no—
650C2×D4—301no—
651C2×D4—301no—
652C2×D4—301no—
653C2×D4—601no—
654C22×C4—21no—
655C22×C4—151no—
656C22×C4—301no—
657C22×C4—301no—
658C22×C4—301no—
659C22×C4C22×D1511yescharacteristic
660Q16—22no—
661Q16—41no—
662Q16—302no—
663SD16—154no—
664SD16—302no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—302no—
670C2×C8—151no—
671C2×C8—151no—
672C2×C8—302no—
673C2×C8C22×D1511yescharacteristic
674C2×C8C22×D1511yescharacteristic
675C4⋊C4—21no—
676C4⋊C4—151no—
677C4⋊C4—151no—
678C4⋊C4—301no—
679C4⋊C4—301no—
680C4⋊C4—301no—
681C4⋊C4—301no—
682C4⋊C4—301no—
683C4⋊C4C22×D1511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—151no—
686C22⋊C4—151no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C42—151no—
694C42—301no—
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3#406412yescomplemented
699C22×C3C2×D4×D511yescharacteristic
700C2×D3—101no—
701C2×D3—101no—
702C2×D3—101no—
703C2×D3—102no—
704C2×D3—201no—
705C2×D3—201no—
706C2×D3—201no—
707C2×D3—201no—
708C2×D3—201no—
709C2×D3—404no—
710C3×C4—22no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4C2×D4×D511yescharacteristic
716C3×C4#414411yescharacteristic
717Dic3—101no—
718Dic3—101no—
719Dic3—101no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5#559011yescharacteristic
724C2×C5C2×#91811yescharacteristic
725C2×C5#577811yescharacteristic
726D5—121no—
727D5—122no—
728D5—241no—
729C23—151no—
730C23—301no—
731C23—301no—
732C23—602no—
733C23—602no—
734C23—1201no—
735C23D4×D1511yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—21no—
740Q8—21no—
741Q8—42no—
742Q8—301no—
743Q8—301no—
744Q8—602no—
745Q8D4×D1512yes—
746D4—152no—
747D4—302no—
748D4—301no—
749D4—301no—
750D4—301no—
751D4—602no—
752D4—602no—
753D4—1201no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—42no—
761C2×C4—151no—
762C2×C4—151no—
763C2×C4—151no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—602no—
769C2×C4—602no—
770C2×C4—1201no—
771C2×C4D4×D1511yescharacteristic
772C2×C4C23×D1511yescharacteristic
773C8—21no—
774C8—21no—
775C8—152no—
776C8—301no—
777C2×C3—22no—
778C2×C3#6592411yescharacteristic
779C2×C3C2×#406411yescharacteristic
780C2×C3#6611211yescharacteristic
781D3—201no—
782D3—202no—
783D3—401no—
784C5#8020411yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—301no—
788C22—302no—
789C22—301no—
790C22—301no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22#9180712yescomplemented
798C22C2×D4×D1511yescharacteristic
799C4—21no—
800C4—22no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—301no—
805C4—301no—
806C4—301no—
807C4—601no—
808C4—601no—
809C4C2×D4×D1511yescharacteristic
810C4#9209511yescharacteristic
811C3#1061193511yescharacteristic, complemented, Sylow
812C2—22no—
813C2—601no—
814C2—602no—
815C2—1201no—
816C2#1175634911yescharacteristic
817C2C2×#9180711yescharacteristic
818C2#1175653711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#451C2
socleC22×C3×C5C22×D4
prime radical#11756389C2
hypercenter#451D15
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. Q8×#1220C2semidirect
2. C22×#6717C2semidirect
3. C2×#91807C2semidirect
5. C3×C5×#451C2semidirect
6. #11751291C2semidirect
7. #11751288C2semidirect
8. #11751286C2semidirect
9. #11751152C2semidirect
10. #11750919C2semidirect
11. #11750918C2semidirect
12. #11750913C2semidirect
13. #11750907C2semidirect
14. #11750832C2semidirect
15. #11750831C2semidirect
19. C2×Q8×D15C22semidirect
21. C2×C3×C5×Q16C22semidirect
22. C2×C3×C5×Q16C22semidirect
26. #91835C22semidirect
27. Q8×Dic15C22semidirect
29. #91833C22semidirect
30. C2×#6718C22semidirect
44. C2×#6705C22semidirect
51. C3×C5×#103C22semidirect
52. C3×C5×#103C22semidirect
54. #91119C22semidirect
57. #91104C22semidirect
58. #91099C22semidirect
59. #91098C22semidirect
60. #91094C22semidirect
61. #91091C22semidirect
67. C5×#451D3semidirect
118. #6717D4semidirect
144. C3×#451D5semidirect
159. C2×C5×Q16C2×D3semidirect
160. C2×C5×Q16C2×D3semidirect
189. C5×#103C2×D3semidirect
190. C5×#103C2×D3semidirect
253. C2×C3×Q16C2×D5semidirect
254. C2×C3×Q16C2×D5semidirect
283. C3×#103C2×D5semidirect
284. C3×#103C2×D5semidirect
366. #451D15semidirect
373. C22×C3×C5#137semidirect
513. C2×Q16C2×D15semidirect
514. C2×Q16C2×D15semidirect
545. #103C2×D15semidirect
546. #103C2×D15semidirect
609. C22×C5#918semidirect
695. C3×C5#3266semidirect
698. C22×C3#4064semidirect
784. C5#80204semidirect
797. C22#91807semidirect
811. C3#10611935semidirect

Maximal subgroups

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

subgroupindex
Q8×#12202
C22×#67172
C2×#918072
#117563892
C3×C5×#4512
#117512912
#117512882
#117512862
#117511522
#117509192
#117509182
#117509132
#117509072
#117508322
#117508312
#106119353
#802045