Finite Group Databasebeta

← #14436329

Subgroups — #14436329

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756571C211yesmaximal, characteristic, complemented
2#11756362C211yesmaximal, characteristic
3C3×C5×#448C211yesmaximal, characteristic
4#11751329C211yesmaximal, characteristic, complemented
5#11751267C211yesmaximal, characteristic, complemented
6#11751267C211yesmaximal, characteristic, complemented
7#11751265C211yesmaximal, characteristic, complemented
8SD16×Dic15C211yesmaximal, characteristic, complemented
9#11751136C211yesmaximal, characteristic
10#11750894C211yesmaximal, characteristic, complemented
11#11750892C211yesmaximal, characteristic, complemented
12#11750891C211yesmaximal, characteristic, complemented
13#11750890C211yesmaximal, characteristic, complemented
14#11750824C211yesmaximal, characteristic, complemented
15#11750821C211yesmaximal, characteristic, complemented
16#10611763—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C2×C3×C5×SD16C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21Q8×Dic15—21no—
22Q8×Dic15—21no—
23Q8×Dic15C2211yescharacteristic
24Q8×Dic15C2211yescharacteristic
25Q8×Dic15C2211yescharacteristic
26Q8×Dic15C2211yescharacteristic
27C2×#6718C2211yescharacteristic
28C2×#6718C2211yescharacteristic
29#91825—21no—
30#91825C2211yescharacteristic
31#91824—21no—
32D4×Dic15C2211yescharacteristic
33#91815—21no—
34#91815—21no—
35#91815C2211yescharacteristic
36#91815C2211yescharacteristic
37#91813C2211yescharacteristic
38#91777C2211yescharacteristic
39#91776C2211yescharacteristic
40#91768—21no—
41#91767—21no—
42C3×C5×#103C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C5×C22⋊C8C2211yescharacteristic
45#91119C2211yescharacteristic
46#91119C2211yescharacteristic
47#91116C2211yescharacteristic
48#91116C2211yescharacteristic
49#91114C2211yescharacteristic
50#91102C2211yescharacteristic
51#91101C2211yescharacteristic
52#91100C2211yescharacteristic
53#91100C2211yescharacteristic
54#91099C2211yescharacteristic
55#91098C2211yescharacteristic
56#91098C2211yescharacteristic
57C8×Dic15C2211yescharacteristic
58#91092C2211yescharacteristic
59#91091C2211yescharacteristic
60#80032—51nomaximal, Hall
61#66146—31no—
62#65937—31no—
63C5×#448D311yescharacteristic
64#65517—31no—
65#65455—31no—
66#65455—31no—
67#65453—31no—
68SD16×Dic5—31no—
69#65324—31no—
70#65083—31no—
71#65080—31no—
72#65079—31no—
73#65078—31no—
74#65012—31no—
75#65009—31no—
76C2×C3×C5×Q8—22no—
77C2×C3×C5×Q8—22no—
78C2×C3×C5×Q8—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5C2311yescharacteristic
85C22×Dic15—21no—
86C2×Dic30—21no—
87C2×Dic30C2311yescharacteristic
88C3×C5×SD16—22no—
89C3×C5×SD16—22no—
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C5×C4⋊C4C2311yescharacteristic
93C3×C5×C22⋊C4—21no—
94#6719—21no—
95#6719—21no—
96#6719—21no—
97#6719—21no—
98#6719—21no—
99#6719D411yescharacteristic
100#6719D411yescharacteristic
101#6718—22no—
102#6718—22no—
103C4⋊Dic15—21no—
104C4⋊Dic15—21no—
105C4⋊Dic15—21no—
106C4⋊Dic15—21no—
107C4⋊Dic15D411yescharacteristic
108C4⋊Dic15D411yescharacteristic
109C4⋊Dic15C2311yescharacteristic
110C4⋊Dic15C2311yescharacteristic
111C4⋊Dic15C2311yescharacteristic
112#6712—21no—
113#6712—21no—
114#6712—21no—
115C4×Dic15—21no—
116C4×Dic15—21no—
117C4×Dic15—21no—
118C4×Dic15—21no—
119C4×Dic15—21no—
120C4×Dic15—21no—
121C4×Dic15C2311yescharacteristic
122C4×Dic15C2311yescharacteristic
123C2×C3⋊#168C2311yescharacteristic
124C2×C3⋊#168C2311yescharacteristic
125#5812—51no—
126#5603—51no—
127C3×#448D511yescharacteristic
128#5228—51no—
129#5166—51no—
130#5166—51no—
131#5164—51no—
132Dic3×SD16—51no—
133#5035—51no—
134#4793—51no—
135#4791—51no—
136#4790—51no—
137#4789—51no—
138#4723—51no—
139#4720—51no—
140C22×C5×Q8C2×D311yescharacteristic
141C2×C5×SD16C2×D311yescharacteristic
142C2×C5×SD16C2×D311yescharacteristic
143C5×#121C2×D311yescharacteristic
144Q8×Dic5—31no—
145Q8×Dic5—31no—
146Q8×Dic5—31no—
147Q8×Dic5—31no—
148Q8×Dic5—61no—
149Q8×Dic5—61no—
150C2×#689—31no—
151C2×#689—31no—
152#4082—31no—
153#4082—61no—
154#4081—61no—
155D4×Dic5—31no—
156#4072—31no—
157#4072—31no—
158#4072—61no—
159#4072—61no—
160#4070—31no—
161#4034—31no—
162#4033—31no—
163#4025—61no—
164#4024—61no—
165C5×#103C2×D311yescharacteristic
166C5×#103C2×D311yescharacteristic
167C5×C22⋊C8C2×D311yescharacteristic
168#3967—31no—
169#3967—31no—
170#3964—31no—
171#3964—31no—
172C22⋊#168—31no—
173#3950—31no—
174#3949—31no—
175#3948—31no—
176#3948—31no—
177#3947—31no—
178#3946—31no—
179#3946—31no—
180C8×Dic5—31no—
181#3940—31no—
182#3939—31no—
183#3121—151noSylow
184C23×C3×C5—21no—
185C23×C3×C5C2×D411yescharacteristic
186C3×C5×Q8—24no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8#4112yes—
190C3×C5×Q8#4112yes—
191C3×C5×D4—21no—
192C3×C5×D4—21no—
193C3×C5×D4—81no—
194C2×C3×C4×C5—24no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—81no—
207C2×Dic15C2×D411yescharacteristic
208C2×Dic15C2×D411yescharacteristic
209C2×Dic15C2×D411yescharacteristic
210C2×Dic15C2×D411yescharacteristic
211Dic30—21no—
212Dic30—21no—
213Dic30—81no—
214C3×C5×C8—21no—
215C3×C5×C8—21no—
216C3⋊#168—21no—
217C3⋊#168—21no—
218C22×C3×Q8C2×D511yescharacteristic
219C2×C3×SD16C2×D511yescharacteristic
220C2×C3×SD16C2×D511yescharacteristic
221C3×#121C2×D511yescharacteristic
222Q8×Dic3—51no—
223Q8×Dic3—51no—
224Q8×Dic3—51no—
225Q8×Dic3—51no—
226Q8×Dic3—101no—
227Q8×Dic3—101no—
228C2×#216—51no—
229C2×#216—51no—
230#936—51no—
231#936—101no—
232#935—101no—
233D4×Dic3—51no—
234#926—51no—
235#926—51no—
236#926—101no—
237#926—101no—
238#924—51no—
239#888—51no—
240#887—51no—
241#879—101no—
242#878—101no—
243C3×#103C2×D511yescharacteristic
244C3×#103C2×D511yescharacteristic
245C3×C22⋊C8C2×D511yescharacteristic
246#835—51no—
247#835—51no—
248#832—51no—
249#832—51no—
250#830—51no—
251#818—51no—
252#817—51no—
253#816—51no—
254#816—51no—
255#815—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258C8×Dic3—51no—
259#808—51no—
260#807—51no—
261C2×C5×Q8—22no—
262C2×C5×Q8—22no—
263C2×C5×Q8—21no—
264C2×C5×Q8C22×D311yescharacteristic
265C2×C5×Q8C22×D311yescharacteristic
266C2×C5×D4—21no—
267C2×C5×D4C22×D311yescharacteristic
268C22×C4×C5—21no—
269C22×C4×C5C22×D311yescharacteristic
270C22×Dic5—61no—
271C2×Dic10—31no—
272C2×Dic10—61no—
273C5×SD16—22no—
274C5×SD16—22no—
275C2×C5×C8C22×D311yescharacteristic
276C2×C5×C8C22×D311yescharacteristic
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—21no—
279C22⋊Dic5—31no—
280C22⋊Dic5—31no—
281C22⋊Dic5—61no—
282C22⋊Dic5—61no—
283C22⋊Dic5—61no—
284C22⋊Dic5—61no—
285C22⋊Dic5—61no—
286#689—62no—
287#689—62no—
288C4⋊Dic5—31no—
289C4⋊Dic5—31no—
290C4⋊Dic5—31no—
291C4⋊Dic5—31no—
292C4⋊Dic5—31no—
293C4⋊Dic5—61no—
294C4⋊Dic5—61no—
295C4⋊Dic5—61no—
296C4⋊Dic5—61no—
297#683—61no—
298#683—61no—
299#683—61no—
300C4×Dic5—31no—
301C4×Dic5—31no—
302C4×Dic5—61no—
303C4×Dic5—61no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C4×Dic5—61no—
307C4×Dic5—61no—
308C2×#168—31no—
309C2×#168—31no—
310#542—151no—
311#519—151no—
312#485—151no—
313#482—151no—
314#477—151no—
315#475—151no—
316#464—151no—
317#464—151no—
318#451—151no—
319#448D1511yescharacteristic
320#441—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5—41no—
329C22×C3×C5—41no—
330C22×C3×C5—41no—
331C22×C3×C5C22×D411yescharacteristic
332C3×C4×C5—22no—
333C3×C4×C5—22no—
334C3×C4×C5—21no—
335C3×C4×C5—41no—
336C3×C4×C5C2×#4111yescharacteristic
337C3×C4×C5C2×#4111yescharacteristic
338Dic15—21no—
339Dic15—21no—
340Dic15—21no—
341Dic15—21no—
342Dic15—41no—
343Dic15—41no—
344Dic15—41no—
345Dic15—41no—
346C2×C3×Q8—22no—
347C2×C3×Q8—22no—
348C2×C3×Q8—21no—
349C2×C3×Q8C22×D511yescharacteristic
350C2×C3×Q8C22×D511yescharacteristic
351C2×C3×D4—21no—
352C2×C3×D4C22×D511yescharacteristic
353C22×C3×C4—21no—
354C22×C3×C4C22×D511yescharacteristic
355C22×Dic3—101no—
356C2×Dic6—51no—
357C2×Dic6—101no—
358C3×SD16—22no—
359C3×SD16—22no—
360C2×C3×C8C22×D511yescharacteristic
361C2×C3×C8C22×D511yescharacteristic
362C3×C4⋊C4C22×D511yescharacteristic
363C3×C22⋊C4—21no—
364#217—51no—
365#217—51no—
366#217—101no—
367#217—101no—
368#217—101no—
369#217—101no—
370#217—101no—
371#216—102no—
372#216—102no—
373C4⋊Dic3—51no—
374C4⋊Dic3—51no—
375C4⋊Dic3—51no—
376C4⋊Dic3—51no—
377C4⋊Dic3—51no—
378C4⋊Dic3—101no—
379C4⋊Dic3—101no—
380C4⋊Dic3—101no—
381C4⋊Dic3—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385C4×Dic3—51no—
386C4×Dic3—51no—
387C4×Dic3—101no—
388C4×Dic3—101no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C4×Dic3—101no—
392C4×Dic3—101no—
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395C23×C5—21no—
396C23×C5D3×D411yescharacteristic
397C5×Q8—24no—
398C5×Q8—21no—
399C5×Q8—21no—
400C5×Q8#23712yes—
401C5×Q8#23712yes—
402C5×D4—21no—
403C5×D4—21no—
404C5×D4—81no—
405C2×C4×C5—24no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5D3×D411yescharacteristic
412C2×C4×C5C23×D311yescharacteristic
413C2×Dic5—31no—
414C2×Dic5—31no—
415C2×Dic5—31no—
416C2×Dic5—31no—
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421C2×Dic5—241no—
422Dic10—61no—
423Dic10—61no—
424Dic10—241no—
425C5×C8—21no—
426C5×C8—21no—
427#168—61no—
428#168—61no—
429C22×Q8C2×D1511yescharacteristic
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16C2×D1511yescharacteristic
433C2×SD16C2×D1511yescharacteristic
434C4⋊Q8—151no—
435#126—301no—
436#124—151no—
437#124—301no—
438#123—301no—
439C22⋊Q8—151no—
440C22⋊Q8—301no—
441#121C2×D1511yescharacteristic
442C4×Q8—151no—
443C4×Q8—151no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×Q8—151no—
447C4×Q8—301no—
448C4×Q8—301no—
449C4×D4—151no—
450#117—151no—
451#117—151no—
452#117—301no—
453#117—301no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460#103—151no—
461#103—151no—
462#103—151no—
463#103—151no—
464#103C2×D1511yescharacteristic
465#103C2×D1511yescharacteristic
466#102—151no—
467#102—151no—
468C22⋊C8—151no—
469C22⋊C8C2×D1511yescharacteristic
470#97—151no—
471C4×C8—151no—
472C2×C3×C5—41no—
473C2×C3×C5—81no—
474C2×C3×C5#52511yescharacteristic
475C2×C3×C5#57711yescharacteristic
476C2×C3×C5#57811yescharacteristic
477C23×C3—21no—
478C23×C3D4×D511yescharacteristic
479C3×Q8—24no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8#71112yes—
483C3×Q8#71112yes—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—81no—
487C2×C3×C4—24no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4D4×D511yescharacteristic
494C2×C3×C4C23×D511yescharacteristic
495C2×Dic3—51no—
496C2×Dic3—51no—
497C2×Dic3—51no—
498C2×Dic3—51no—
499C2×Dic3—101no—
500C2×Dic3—101no—
501C2×Dic3—101no—
502C2×Dic3—101no—
503C2×Dic3—401no—
504Dic6—101no—
505Dic6—101no—
506Dic6—401no—
507C3×C8—21no—
508C3×C8—21no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5—41no—
515C22×C5—41no—
516C22×C5—41no—
517C22×C5C2×D3×D411yescharacteristic
518C4×C5—22no—
519C4×C5—22no—
520C4×C5—21no—
521C4×C5—41no—
522C4×C5C2×#23711yescharacteristic
523C4×C5C2×#23711yescharacteristic
524Dic5—61no—
525Dic5—61no—
526Dic5—61no—
527Dic5—61no—
528Dic5—121no—
529Dic5—121no—
530Dic5—121no—
531Dic5—121no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—21no—
535C2×Q8—151no—
536C2×Q8—301no—
537C2×Q8C22×D1511yescharacteristic
538C2×Q8C22×D1511yescharacteristic
539C2×D4—21no—
540C2×D4C22×D1511yescharacteristic
541C22×C4—21no—
542C22×C4—301no—
543C22×C4C22×D1511yescharacteristic
544Q16—302no—
545Q16—302no—
546SD16—22no—
547SD16—22no—
548C2×C8—151no—
549C2×C8—151no—
550C2×C8C22×D1511yescharacteristic
551C2×C8C22×D1511yescharacteristic
552C4⋊C4—151no—
553C4⋊C4—151no—
554C4⋊C4—151no—
555C4⋊C4—151no—
556C4⋊C4—151no—
557C4⋊C4—301no—
558C4⋊C4—301no—
559C4⋊C4—301no—
560C4⋊C4—301no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4C22×D1511yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—151no—
567C22⋊C4—151no—
568C22⋊C4—301no—
569C22⋊C4—301no—
570C22⋊C4—301no—
571C22⋊C4—301no—
572C22⋊C4—301no—
573C42—151no—
574C42—151no—
575C42—301no—
576C42—301no—
577C42—301no—
578C42—301no—
579C42—301no—
580C42—301no—
581C3×C5#312111yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3C2×D4×D511yescharacteristic
589C3×C4—22no—
590C3×C4—22no—
591C3×C4—21no—
592C3×C4—41no—
593C3×C4C2×#71111yescharacteristic
594C3×C4C2×#71111yescharacteristic
595Dic3—101no—
596Dic3—101no—
597Dic3—101no—
598Dic3—101no—
599Dic3—201no—
600Dic3—201no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5—81no—
605C2×C5#558611yescharacteristic
606C2×C5#576211yescharacteristic
607C2×C5#577911yescharacteristic
608C23—21no—
609C23D4×D1511yescharacteristic
610Q8—24no—
611Q8—21no—
612Q8—21no—
613Q8—301no—
614Q8—301no—
615Q8—1201no—
616Q8#681912yes—
617Q8#681912yes—
618D4—21no—
619D4—21no—
620D4—81no—
621C2×C4—24no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—151no—
628C2×C4—151no—
629C2×C4—151no—
630C2×C4—151no—
631C2×C4—301no—
632C2×C4—301no—
633C2×C4—301no—
634C2×C4—301no—
635C2×C4—1201no—
636C2×C4D4×D1511yescharacteristic
637C2×C4C23×D1511yescharacteristic
638C8—21no—
639C8—21no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3—81no—
644C2×C3#6592011yescharacteristic
645C2×C3#6609611yescharacteristic
646C2×C3#6611311yescharacteristic
647C5#8003211yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22C2×D4×D1511yescharacteristic
655C4—22no—
656C4—22no—
657C4—21no—
658C4—41no—
659C4—301no—
660C4—301no—
661C4—301no—
662C4—301no—
663C4—601no—
664C4—601no—
665C4—601no—
666C4—601no—
667C4C2×#681911yescharacteristic
668C4C2×#681911yescharacteristic
669C3#1061176311yescharacteristic, complemented, Sylow
670C2—41no—
671C2—81no—
672C2#1175634511yescharacteristic
673C2#1175652111yescharacteristic
674C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#448C2
socleC22×C3×C5C22×D4
prime radicalC3×C5×#121C22
hypercenter#448D15
hypocenterC3×C5#3121
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #11756571C2semidirect
4. #11751329C2semidirect
5. #11751267C2semidirect
6. #11751267C2semidirect
7. #11751265C2semidirect
8. SD16×Dic15C2semidirect
10. #11750894C2semidirect
11. #11750892C2semidirect
12. #11750891C2semidirect
13. #11750890C2semidirect
14. #11750824C2semidirect
15. #11750821C2semidirect
581. C3×C5#3121semidirect
647. C5#80032semidirect
669. C3#10611763semidirect

Maximal subgroups

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

subgroupindex
#117565712
#117563622
C3×C5×#4482
#117513292
#117512672
#117512652
SD16×Dic152
#117511362
#117508942
#117508922
#117508912
#117508902
#117508242
#117508212
#106117633
#800325