Finite Group Databasebeta

← #14430832

Subgroups — #14430832

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754922C211yesmaximal, characteristic
2#11753388C211yesmaximal, characteristic, complemented
3#11750871C211yesmaximal, characteristic
4C5×#4761C211yesmaximal, characteristic, complemented
5C3×#65048C211yesmaximal, characteristic, complemented
6#11749087C211yesmaximal, characteristic, complemented
7#11749083C211yesmaximal, characteristic, complemented
8#11748957C211yesmaximal, characteristic
9#11747801C211yesmaximal, characteristic, complemented
10#11747773C211yesmaximal, characteristic, complemented
11#11747664C211yesmaximal, characteristic, complemented
12#11747640C211yesmaximal, characteristic, complemented
13#11747439C211yesmaximal, characteristic, complemented
14#11747246C211yesmaximal, characteristic, complemented
15#11747240C211yesmaximal, characteristic, complemented
16#10612793—31nomaximal, Hall
17C2×D4×D15C2211yescharacteristic
18C2×#6705C2211yescharacteristic
19#91781C2211yescharacteristic
20C5×D4×Dic3C2211yescharacteristic
21C5×#888C2211yescharacteristic, complemented
22C3×D4×Dic5C2211yescharacteristic
23C3×#4034C2211yescharacteristic, complemented
24#91561—21no—
25#91556—21no—
26#91552—21no—
27C2×#6667—21no—
28#91437C2211yescharacteristic
29#91428C2211yescharacteristic
30#91424—21no—
31#91418C2211yescharacteristic
32#91411—21no—
33#91388C2211yescharacteristic, complemented
34#91386C2211yescharacteristic
35#91385—21no—
36#91382—21no—
37#91381C2211yescharacteristic, complemented
38#91347C2211yescharacteristic
39C2×#6648C2211yescharacteristic
40C3×C5×#102C2211yescharacteristic
41#91116C2211yescharacteristic
42#91105C2211yescharacteristic
43#91093C2211yescharacteristic
44C5×#832C2211yescharacteristic
45C5×#817C2211yescharacteristic, complemented
46C5×Dic3⋊C8C2211yescharacteristic, complemented
47C5×#808C2211yescharacteristic, complemented
48C3×#3964C2211yescharacteristic
49C3×#3950C2211yescharacteristic, complemented
50C3×#3946C2211yescharacteristic, complemented
51C3×#3939C2211yescharacteristic, complemented
52#90989C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90987C2211yescharacteristic, complemented
55#90986C2211yescharacteristic, complemented
56Dic3⋊#168C2211yescharacteristic, complemented
57#90982C2211yescharacteristic, complemented
58#90969C2211yescharacteristic
59#90968C2211yescharacteristic
60#80967—51nomaximal, Hall
61#66063—31no—
62#65879—31no—
63C5×#476—31no—
64#65376—31no—
65#65298—31no—
66#65160—31no—
67#65159—31no—
68#65150—31no—
69#65149—31no—
70#65136—31no—
71#65128—31no—
72#65059—31no—
73D5×#102—31no—
74#65052—31no—
75#65048D311yescharacteristic, complemented
76C23×D15—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C2×#1220—21no—
79D4×D15—22no—
80D4×D15Q814yescomplemented
81C2×D60C2311yescharacteristic
82C2×C4×D15C2311yescharacteristic
83C22×C5×Dic3—21no—
84C2×C5×Dic6—21no—
85C22×C3×Dic5—21no—
86C2×C3×Dic10—21no—
87C2×#1200—21no—
88C2×#1200—21no—
89C2×#1200—21no—
90C2×C3×C5×C8C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92#6714—21no—
93C4⋊Dic15C2311yescharacteristic
94C4×Dic15—21no—
95C2×C3⋊#168C2311yescharacteristic
96#6705—22no—
97C5×#217—21no—
98C5×C4⋊Dic3C2311yescharacteristic
99C5×C4⋊Dic3C2311yescharacteristic
100C5×Dic3⋊C4—21no—
101C4×C5×Dic3C2311yescharacteristic
102C2×C5×C3⋊C8C2311yescharacteristic
103C3×C22⋊Dic5—21no—
104C3×C4⋊Dic5C2311yescharacteristic
105C3×C4⋊Dic5C2311yescharacteristic
106C3×#683—21no—
107C3×C4×Dic5C2311yescharacteristic
108C2×C3×#168C2311yescharacteristic
109Dic3⋊Dic5—21no—
110#6669—21no—
111#6669—21no—
112#6669—21no—
113#6669D411yescharacteristic
114#6669D411yescharacteristic
115#6668—21no—
116#6667—21no—
117#6667—21no—
118#6667—21no—
119#6667D411yescharacteristic
120#6667D411yescharacteristic
121Dic3×Dic5—21no—
122#6648—22no—
123#5729—51no—
124#5545—51no—
125C3×#474—51no—
126#5084—51no—
127#5009—51no—
128#4891—51no—
129#4890—51no—
130#4881—51no—
131#4880—51no—
132#4847—51no—
133#4839—51no—
134#4770—51no—
135D3×#102—51no—
136#4766—51no—
137#4761D511yescharacteristic, complemented
138C2×D4×D5—31no—
139C5×C4⋊Q8—31no—
140C4×C5×D4—31no—
141#4092—61no—
142#4090—61no—
143D4×Dic5C2×D311yescharacteristic
144C4×C22⋊D5—61no—
145C2×#685—61no—
146C2×#676—31no—
147C2×C8×D5—31no—
148#4042—61no—
149#4039—31no—
150#4038—31no—
151#4038—31no—
152D5×C4⋊C4—31no—
153#4036—31no—
154#4035—61no—
155#4034C2×D311yescharacteristic, complemented
156#4027—61no—
157D5×C22⋊C4—61no—
158C4×D20—31no—
159#4018—31no—
160#4016—31no—
161C5×#106—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#102—31no—
165C5×#102C2×D311yescharacteristic
166#3964—31no—
167#3964C2×D311yescharacteristic
168#3953—31no—
169#3953—31no—
170#3950C2×D311yescharacteristic, complemented
171#3949—31no—
172#3946—31no—
173#3946C2×D311yescharacteristic, complemented
174#3941—31no—
175#3941—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179#3939C2×D311yescharacteristic, complemented
180C4⋊#168—31no—
181#3081—151noSylow
182C23×C3×C5—21no—
183C22×D15—21no—
184C22×D15—24no—
185C22×D15—81no—
186C22×D15—81no—
187C22×D15C2×D411yescharacteristic
188C3×C5×D4—21no—
189C3×C5×D4C2×Q812yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5C2411yescharacteristic
192#1220—24no—
193C2×Dic15—21no—
194C2×Dic15C2×D411yescharacteristic
195D60—21no—
196D60C2×Q812yes—
197C4×D15C2×Q812yes—
198C4×D15#4112yes—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—81no—
202C2×C5×Dic3C2×D411yescharacteristic
203C2×C5×Dic3C2×D411yescharacteristic
204C5×Dic6—81no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—81no—
208C2×C3×Dic5C2×D411yescharacteristic
209C2×C3×Dic5C2×D411yescharacteristic
210C3×Dic10—81no—
211#1200—81no—
212#1200—81no—
213#1200—81no—
214C3×C5×C8—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C5×C3⋊C8—21no—
218C2×D3×D4—51no—
219C3×C4⋊Q8—51no—
220C3×C4×D4—51no—
221#946—101no—
222#944—101no—
223D4×Dic3C2×D511yescharacteristic
224C4×#67—101no—
225C2×(C2×D3)⋊C4—101no—
226C2×ΓL(1,𝔽25)—51no—
227C2×D3×C8—51no—
228#896—101no—
229#893—51no—
230#892—51no—
231#892—51no—
232D3×C4⋊C4—51no—
233#890—51no—
234#889—101no—
235#888C2×D511yescharacteristic, complemented
236#67⋊C4—101no—
237D3×C22⋊C4—101no—
238C4×D12—51no—
239#872—51no—
240#870—51no—
241C3×#107—51no—
242C3×#107—51no—
243C3×C4⋊C8—51no—
244C3×#102—51no—
245C3×#102C2×D511yescharacteristic
246#832—51no—
247#832C2×D511yescharacteristic
248#821—51no—
249#821—51no—
250#818—51no—
251#817C2×D511yescharacteristic, complemented
252Dic3⋊C8—51no—
253Dic3⋊C8C2×D511yescharacteristic, complemented
254#809—51no—
255#809—51no—
256#808—51no—
257#808—51no—
258#808C2×D511yescharacteristic, complemented
259#807—51no—
260C4⋊(C3⋊C8)—51no—
261C23×D5—61no—
262C2×C5×Q8—61no—
263C2×C5×D4C22×D311yescharacteristic
264C22×C4×C5—61no—
265C2×C22⋊D5—61no—
266C22×Dic5—21no—
267D4×D5—34no—
268D4×D5—62no—
269C2×D20—31no—
270C2×C4×D5—31no—
271C2×C4×D5—61no—
272C2×C4×D5—61no—
273C2×C4×D5—61no—
274C2×Dic10—21no—
275C2×C5×C8—31no—
276C2×C5×C8C22×D311yescharacteristic
277C5×C4⋊C4—31no—
278C5×C4⋊C4—31no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4C22×D311yescharacteristic
281C5×C22⋊C4—61no—
282C42×C5—31no—
283C22⋊Dic5—21no—
284#685—31no—
285#685—31no—
286#685—61no—
287#685—61no—
288#685—61no—
289#685—61no—
290C4⋊Dic5—31no—
291C4⋊Dic5—61no—
292C4⋊Dic5C22×D311yescharacteristic
293C4⋊Dic5C22×D311yescharacteristic
294#683—21no—
295#683—31no—
296#683—31no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301C4×Dic5—61no—
302C4×Dic5—61no—
303C4×Dic5C22×D311yescharacteristic
304C2×#168—31no—
305C2×#168C22×D311yescharacteristic
306#676—62no—
307C8×D5—62no—
308#544—151no—
309#518—151no—
310#478—151no—
311#478—151no—
312#478—151no—
313#478—151no—
314#476—31no—
315#476—151no—
316#474—51no—
317#474—151no—
318#428—151no—
319#427—151no—
320#424—151no—
321#418—151no—
322C2×#102—151no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—41no—
326C22×C3×C5C22×D411yescharacteristic
327C2×D15—21no—
328C2×D15—21no—
329C2×D15—22no—
330C2×D15—41no—
331C2×D15—41no—
332C2×D15—84no—
333C2×D15C22⋊Q812yes—
334C3×C4×C5—41no—
335C3×C4×C5C22×Q811yescharacteristic
336C3×C4×C5C2×#4111yescharacteristic
337Dic15—41no—
338Dic15C22⋊Q812yes—
339C3×Dic5—21no—
340C3×Dic5—21no—
341C3×Dic5—41no—
342C3×Dic5—41no—
343C5×Dic3—21no—
344C5×Dic3—21no—
345C5×Dic3—41no—
346C5×Dic3—41no—
347C23×D3—101no—
348C2×C3×Q8—101no—
349C2×C3×D4C22×D511yescharacteristic
350C22×C3×C4—101no—
351C2×#67—101no—
352C22×Dic3—21no—
353D3×D4—54no—
354D3×D4—102no—
355C2×D12—51no—
356C2×C4×D3—51no—
357C2×C4×D3—101no—
358C2×C4×D3—101no—
359C2×C4×D3—101no—
360C2×Dic6—21no—
361C2×C3×C8—51no—
362C2×C3×C8C22×D511yescharacteristic
363C3×C4⋊C4—51no—
364C3×C4⋊C4—51no—
365C3×C4⋊C4—101no—
366C3×C4⋊C4C22×D511yescharacteristic
367C3×C22⋊C4—101no—
368C3×C42—51no—
369#217—21no—
370(C2×D3)⋊C4—51no—
371(C2×D3)⋊C4—51no—
372(C2×D3)⋊C4—101no—
373(C2×D3)⋊C4—101no—
374(C2×D3)⋊C4—101no—
375(C2×D3)⋊C4—101no—
376C4⋊Dic3—51no—
377C4⋊Dic3—101no—
378C4⋊Dic3C22×D511yescharacteristic
379C4⋊Dic3C22×D511yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—51no—
382Dic3⋊C4—51no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387C4×Dic3—101no—
388C4×Dic3—101no—
389C4×Dic3C22×D511yescharacteristic
390C2×C3⋊C8—51no—
391C2×C3⋊C8C22×D511yescharacteristic
392ΓL(1,𝔽25)—102no—
393D3×C8—102no—
394C23×C5—21no—
395C22×D5—31no—
396C22×D5—64no—
397C22×D5—61no—
398C22×D5—241no—
399C22×D5—241no—
400C5×Q8—241no—
401C5×D4—21no—
402C5×D4D3×Q812yes—
403C2×C4×C5—21no—
404C2×C4×C5—31no—
405C2×C4×C5—31no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—241no—
409C2×C4×C5C23×D311yescharacteristic
410C22⋊D5—64no—
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5—31no—
414C2×Dic5—61no—
415C2×Dic5—81no—
416C2×Dic5D3×D411yescharacteristic
417C2×Dic5D3×D411yescharacteristic
418D20—32no—
419D20—61no—
420C4×D5—32no—
421C4×D5—32no—
422C4×D5—241no—
423C4×D5—241no—
424C4×D5—241no—
425Dic10—81no—
426C5×C8—21no—
427C5×C8—61no—
428#168—21no—
429#168—61no—
430C22×D4—151no—
431C2×M16—151no—
432C22×C8—151no—
433C4⋊Q8—31no—
434C4⋊Q8—51no—
435C4⋊Q8—301no—
436#125—151no—
437#125—151no—
438#125—301no—
439C22⋊Q8—301no—
440C22⋊Q8—301no—
441C4×D4—31no—
442C4×D4—51no—
443C4×D4—151no—
444C4×D4—151no—
445C4×D4—301no—
446C4×D4—301no—
447#117—151no—
448#117—151no—
449#117—151no—
450C2×C4⋊C4—151no—
451C2×C22⋊C4—301no—
452C2×C22⋊C4—301no—
453#107—51no—
454#107—51no—
455#107—151no—
456#107—151no—
457#106—31no—
458#106—31no—
459#106—151no—
460#106—151no—
461C4⋊C8—31no—
462C4⋊C8—51no—
463C4⋊C8—151no—
464C4⋊C8—151no—
465#102—31no—
466#102—51no—
467#102—151no—
468#102—151no—
469#102—151no—
470#102—151no—
471#102—151no—
472#102D3×D511yescharacteristic
473C2×C3×C5—42no—
474C2×C3×C5C2×C22⋊Q811yescharacteristic
475C2×C3×C5#57611yescharacteristic
476C2×C3×C5#57711yescharacteristic
477D15—22no—
478D15—42no—
479C23×C3—21no—
480C22×D3—51no—
481C22×D3—104no—
482C22×D3—101no—
483C22×D3—401no—
484C22×D3—401no—
485C3×Q8—401no—
486C3×D4—21no—
487C3×D4Q8×D512yes—
488C2×C3×C4—21no—
489C2×C3×C4—51no—
490C2×C3×C4—51no—
491C2×C3×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4—401no—
494C2×C3×C4C23×D511yescharacteristic
495#67—104no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—51no—
499C2×Dic3—81no—
500C2×Dic3—101no—
501C2×Dic3D4×D511yescharacteristic
502C2×Dic3D4×D511yescharacteristic
503D12—52no—
504D12—101no—
505C4×D3—52no—
506C4×D3—52no—
507C4×D3—401no—
508C4×D3—401no—
509C4×D3—401no—
510Dic6—81no—
511C3×C8—21no—
512C3×C8—101no—
513C3⋊C8—21no—
514C3⋊C8—101no—
515C22×C5—22no—
516C22×C5—41no—
517C22×C5—41no—
518C22×C5C2×D3×D411yescharacteristic
519C2×D5—32no—
520C2×D5—61no—
521C2×D5—61no—
522C2×D5—62no—
523C2×D5—121no—
524C2×D5—121no—
525C2×D5—244no—
526C4×C5—41no—
527C4×C5—61no—
528C4×C5—61no—
529C4×C5—121no—
530C4×C5—121no—
531C4×C5C2×D3×Q811yescharacteristic
532C4×C5D3×#4111yescharacteristic
533Dic5—21no—
534Dic5—21no—
535Dic5—32no—
536Dic5—41no—
537Dic5—41no—
538Dic5—121no—
539C24—301no—
540C2×Q8—61no—
541C2×Q8—101no—
542C2×D4—154no—
543C2×D4—151no—
544C2×D4—302no—
545C2×D4—301no—
546C2×D4C2×D3×D511yescharacteristic
547C22×C4—61no—
548C22×C4—101no—
549C22×C4—151no—
550C22×C4—301no—
551C22×C4—301no—
552C22×C4—301no—
553M16—302no—
554C2×C8—31no—
555C2×C8—51no—
556C2×C8—151no—
557C2×C8—302no—
558C2×C8C2×D3×D511yescharacteristic
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—51no—
562C4⋊C4—51no—
563C4⋊C4—61no—
564C4⋊C4—101no—
565C4⋊C4—151no—
566C4⋊C4—151no—
567C4⋊C4—151no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4—301no—
573C4⋊C4C2×D3×D511yescharacteristic
574C22⋊C4—61no—
575C22⋊C4—101no—
576C22⋊C4—151no—
577C22⋊C4—151no—
578C22⋊C4—301no—
579C22⋊C4—301no—
580C22⋊C4—301no—
581C22⋊C4—301no—
582C42—31no—
583C42—51no—
584C42—301no—
585C42—301no—
586C3×C5#308111yescharacteristic, complemented, Hall
587C22×C3—22no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3C2×D4×D511yescharacteristic
591C2×D3—52no—
592C2×D3—101no—
593C2×D3—101no—
594C2×D3—102no—
595C2×D3—201no—
596C2×D3—201no—
597C2×D3—404no—
598C3×C4—41no—
599C3×C4—101no—
600C3×C4—101no—
601C3×C4—201no—
602C3×C4—201no—
603C3×C4C2×Q8×D511yescharacteristic
604C3×C4D5×#4111yescharacteristic
605Dic3—21no—
606Dic3—21no—
607Dic3—41no—
608Dic3—41no—
609Dic3—52no—
610Dic3—201no—
611C2×C5—42no—
612C2×C5D3×C22⋊Q811yescharacteristic
613C2×C5#575711yescharacteristic
614C2×C5#577811yescharacteristic
615D5—62no—
616D5—122no—
617C23—21no—
618C23—151no—
619C23—304no—
620C23—301no—
621C23—1201no—
622C23—1201no—
623Q8—241no—
624Q8—401no—
625D4—21no—
626D4—152no—
627D4—304no—
628D4—301no—
629D4D15⋊Q812yes—
630C2×C4—21no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—51no—
634C2×C4—51no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—101no—
638C2×C4—101no—
639C2×C4—151no—
640C2×C4—152no—
641C2×C4—152no—
642C2×C4—241no—
643C2×C4—301no—
644C2×C4—401no—
645C2×C4—1201no—
646C2×C4—1201no—
647C2×C4—1201no—
648C2×C4C22×D3×D511yescharacteristic
649C8—21no—
650C8—61no—
651C8—101no—
652C8—301no—
653C2×C3—42no—
654C2×C3D5×C22⋊Q811yescharacteristic
655C2×C3#6609611yescharacteristic
656C2×C3#6610811yescharacteristic
657D3—102no—
658D3—202no—
659C5#8096711yescharacteristic, complemented, Sylow
660C22—22no—
661C22—41no—
662C22—41no—
663C22—152no—
664C22—301no—
665C22—301no—
666C22—302no—
667C22—601no—
668C22—601no—
669C22—1204no—
670C22D3×D4×D511yescharacteristic
671C4—41no—
672C4—61no—
673C4—61no—
674C4—101no—
675C4—101no—
676C4—121no—
677C4—121no—
678C4—152no—
679C4—201no—
680C4—201no—
681C4—601no—
682C4C2×D15⋊Q811yescharacteristic
683C4#9202411yescharacteristic
684C3#1061279311yescharacteristic, complemented, Sylow
685C2—42no—
686C2—302no—
687C2—602no—
688C2#1175285011yescharacteristic
689C2#1175405511yescharacteristic
690C2#1175408511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×D4×D15C22
hypercenter#102D3×D5
hypocenterC3×C5#3081
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
2. #11753388C2semidirect
4. C5×#4761C2semidirect
5. C3×#65048C2semidirect
6. #11749087C2semidirect
7. #11749083C2semidirect
9. #11747801C2semidirect
10. #11747773C2semidirect
11. #11747664C2semidirect
12. #11747640C2semidirect
13. #11747439C2semidirect
14. #11747246C2semidirect
15. #11747240C2semidirect
21. C5×#888C22semidirect
23. C3×#4034C22semidirect
33. #91388C22semidirect
37. #91381C22semidirect
45. C5×#817C22semidirect
46. C5×Dic3⋊C8C22semidirect
47. C5×#808C22semidirect
49. C3×#3950C22semidirect
50. C3×#3946C22semidirect
51. C3×#3939C22semidirect
52. #90989C22semidirect
53. #90988C22semidirect
54. #90987C22semidirect
55. #90986C22semidirect
56. Dic3⋊#168C22semidirect
57. #90982C22semidirect
75. #65048D3semidirect
80. D4×D15Q8semidirect
137. #4761D5semidirect
155. #4034C2×D3semidirect
170. #3950C2×D3semidirect
173. #3946C2×D3semidirect
179. #3939C2×D3semidirect
235. #888C2×D5semidirect
251. #817C2×D5semidirect
253. Dic3⋊C8C2×D5semidirect
258. #808C2×D5semidirect
586. C3×C5#3081semidirect
659. C5#80967semidirect
684. C3#10612793semidirect

Maximal subgroups

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

subgroupindex
#117549222
#117533882
#117508712
C5×#47612
C3×#650482
#117490872
#117490832
#117489572
#117478012
#117477732
#117476642
#117476402
#117474392
#117472462
#117472402
#106127933
#809675