Finite Group Databasebeta

← #14436165

Subgroups — #14436165

Order 1920.

744 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
1C3×#65880C211yesmaximal, characteristic
2#11752509C211yesmaximal, characteristic, complemented
3#11751110C211yesmaximal, characteristic, complemented
4C5×#5019C211yesmaximal, characteristic, complemented
5#11749047C211yesmaximal, characteristic
6#11749047C211yesmaximal, characteristic
7#11749001C211yesmaximal, characteristic, complemented
8Dic5×#214C211yesmaximal, characteristic, complemented
9#11747340C211yesmaximal, characteristic, complemented
10#11747338C211yesmaximal, characteristic, complemented
11#11747263C211yesmaximal, characteristic, complemented
12#11747262C211yesmaximal, characteristic, complemented
13#11747094C211yesmaximal, characteristic, complemented
14#11746944C211yesmaximal, characteristic, complemented
15#11746873C211yesmaximal, characteristic, complemented
16#10612143—31nomaximal, Hall
17C2×C3×#711C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic
19#91759C2211yescharacteristic
20C2×C5×#214C2211yescharacteristic
21C2×C5×#214C2211yescharacteristic
22C5×#869C2211yescharacteristic
23C3×D4×Dic5C2211yescharacteristic
24C3×C4×C22⋊D5—21no—
25C2×C3×#683—21no—
26C3×D5×C4⋊C4C2211yescharacteristic
27C3×#4033C2211yescharacteristic
28C3×#4027—21no—
29C3×#4023—21no—
30C3×#4018C2211yescharacteristic
31C3×C4×Dic10C2211yescharacteristic
32#91361—21no—
33#91361—21no—
34#91359C2211yescharacteristic
35#91359C2211yescharacteristic
36#91336—21no—
37#91336—21no—
38Dic5×Dic6C2211yescharacteristic
39Dic5×Dic6C2211yescharacteristic
40C2×#6661C2211yescharacteristic
41C2×#6661C2211yescharacteristic
42#91116C2211yescharacteristic
43#91116C2211yescharacteristic
44#91092C2211yescharacteristic
45#91091C2211yescharacteristic
46C4⋊(C3⋊#168)C2211yescharacteristic
47C5×#810C2211yescharacteristic
48C5×#810C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90990C2211yescharacteristic
51#90987C2211yescharacteristic
52#90972C2211yescharacteristic
53#90972C2211yescharacteristic
54#90971C2211yescharacteristic
55#90971C2211yescharacteristic
56#90955C2211yescharacteristic
57#90955C2211yescharacteristic
58#90952C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#82575—51nomaximal, Hall
61#66065—31no—
62#65880D311yescharacteristic
63C5×#461—31no—
64#65462—31no—
65#65462—31no—
66#65453—31no—
67SD16×Dic5—31no—
68#65379—31no—
69#65298—31no—
70#65129—31no—
71#65118—31no—
72#65098—31no—
73#65094—31no—
74#65079—31no—
75#65078—31no—
76C2×C3×C5×D4C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C2×C5×Dic6C2311yescharacteristic
79C2×C5×Dic6C2311yescharacteristic
80C2×C3×C22⋊D5—21no—
81C22×C3×Dic5—21no—
82C22×C3×Dic5—21no—
83C3×#711—22no—
84C3×#711—22no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5C2311yescharacteristic
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C5×C22⋊C4—21no—
90C3×C42×C5C2311yescharacteristic
91C4⋊Dic15C2311yescharacteristic
92C4⋊Dic15C2311yescharacteristic
93#6712—21no—
94#6712—21no—
95C2×C3⋊#168C2311yescharacteristic
96C2×C3⋊#168C2311yescharacteristic
97C5×#214—22no—
98C5×#214—22no—
99C5×C4⋊Dic3—21no—
100C5×C4⋊Dic3—21no—
101C2×C5×C3⋊C8C2311yescharacteristic
102C2×C5×C3⋊C8C2311yescharacteristic
103C3×C22⋊Dic5—21no—
104C3×#685D411yescharacteristic
105C3×#685D411yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C3×#683—21no—
110C3×#683D411yescharacteristic
111C3×#683D411yescharacteristic
112C3×C4×Dic5—21no—
113C3×C4×Dic5—21no—
114C3×C4×Dic5C2311yescharacteristic
115Dic3⋊Dic5—21no—
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6669—21no—
119#6665—21no—
120#6665—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#6661—22no—
124#6661—22no—
125C3×#520—51no—
126#5518—51no—
127#5239—51no—
128#5239—51no—
129#5031—51no—
130#5030—51no—
131C4×#216—51no—
132#5022—51no—
133#5019D511yescharacteristic, complemented
134#5018—51no—
135C4×#214—51no—
136#5009—51no—
137#5000—51no—
138#4971—51no—
139#4970—51no—
140C2×#711C2×D311yescharacteristic
141C2×C5×SD16—31no—
142C2×C5×SD16—31no—
143C5×C4⋊Q8—31no—
144C4×C5×D4C2×D311yescharacteristic
145#4092—31no—
146#4092—31no—
147Q8×Dic5—31no—
148Q8×Dic5—31no—
149C2×#689—31no—
150C2×#689—31no—
151D4×Dic5C2×D311yescharacteristic
152C4×C22⋊D5—21no—
153C2×#683—21no—
154#4044—61no—
155#4044—61no—
156D5×C4⋊C4C2×D311yescharacteristic
157#4035—61no—
158#4035—61no—
159#4033C2×D311yescharacteristic
160#4027—21no—
161#4023—21no—
162#4018C2×D311yescharacteristic
163#4016—31no—
164C4×Dic10C2×D311yescharacteristic
165C5×C4⋊C8—31no—
166C5×#103—31no—
167C5×#103—31no—
168#3967—31no—
169#3967—31no—
170#3964—31no—
171#3964—31no—
172#3952—31no—
173#3952—31no—
174#3950—31no—
175#3949—31no—
176#3948—31no—
177#3948—31no—
178#3947—31no—
179C8×Dic5—31no—
180#3940—31no—
181#3939—31no—
182C4⋊#168—31no—
183#3120—151noSylow
184C23×C3×C5—21no—
185C22×C3×D5C2×D411yescharacteristic
186C3×C5×D4—21no—
187C3×C5×D4#4112yes—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—81no—
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C5×Dic6—21no—
198C5×Dic6—21no—
199C5×Dic6—21no—
200C5×Dic6—21no—
201C3×C22⋊D5—24no—
202C2×C3×Dic5—24no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—81no—
206C2×C3×Dic5C2×D411yescharacteristic
207C2×C3×Dic5C2×D411yescharacteristic
208C2×C3×Dic5C2×D411yescharacteristic
209C3×C4×D5—21no—
210C3×C4×D5—21no—
211C3×C4×D5—81no—
212C3×Dic10—21no—
213C3×Dic10#4112yes—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C5×C3⋊C8—21no—
217C5×C3⋊C8—21no—
218C2×C3×#41—51no—
219C3×C4×Q8—51no—
220C3×C4×Q8—51no—
221C3×C4×D4—51no—
222C3×C4×D4—101no—
223C3×C4×D4—101no—
224C3×C4×D4C2×D511yescharacteristic
225C3×#117—51no—
226C3×#117—101no—
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—101no—
229C2×#216—51no—
230C2×#216—51no—
231C2×#214C2×D511yescharacteristic
232C2×#214C2×D511yescharacteristic
233#924—51no—
234#924—51no—
235#889—101no—
236#889—101no—
237#879—101no—
238#879—101no—
239#870—51no—
240#869C2×D511yescharacteristic
241C4×Dic6—51no—
242C4×Dic6—51no—
243#835—51no—
244#835—51no—
245#832—51no—
246#832—51no—
247#830—51no—
248#830—51no—
249#810—51no—
250#810—51no—
251#810C2×D511yescharacteristic
252#810C2×D511yescharacteristic
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)C2×D511yescharacteristic
259#803—51no—
260C4×C3⋊C8—51no—
261C2×C5×Q8—31no—
262C2×C5×Q8—31no—
263C2×C5×D4C22×D311yescharacteristic
264C22×C4×C5—21no—
265C2×C22⋊D5—21no—
266C22×Dic5—21no—
267C22×Dic5—21no—
268#711—22no—
269#711—22no—
270C2×C4×D5—21no—
271C2×C4×D5C22×D311yescharacteristic
272C2×Dic10C22×D311yescharacteristic
273C5×SD16—62no—
274C5×SD16—62no—
275C2×C5×C8—31no—
276C2×C5×C8—31no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4C22×D311yescharacteristic
280C5×C22⋊C4—21no—
281C42×C5C22×D311yescharacteristic
282C22⋊Dic5—21no—
283#689—62no—
284#689—62no—
285#685—61no—
286#685—61no—
287#685#6711yescharacteristic
288#685#6711yescharacteristic
289C4⋊Dic5—31no—
290C4⋊Dic5—31no—
291C4⋊Dic5—61no—
292C4⋊Dic5—61no—
293C4⋊Dic5C22×D311yescharacteristic
294#683—21no—
295#683—21no—
296#683—21no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683#6711yescharacteristic
302#683#6711yescharacteristic
303C4×Dic5—21no—
304C4×Dic5—21no—
305C4×Dic5—61no—
306C4×Dic5—61no—
307C4×Dic5C22×D311yescharacteristic
308C2×#168—31no—
309C2×#168—31no—
310#541—151no—
311#520—51no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—31no—
318#452—151no—
319#452—151no—
320#441—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5—22no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C3×D5—21no—
330C2×C3×D5—21no—
331C2×C3×D5—21no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—41no—
335C3×C4×C5C2×#4111yescharacteristic
336C3×C4×C5C2×#4111yescharacteristic
337Dic15—41no—
338Dic15—41no—
339C3×Dic5—22no—
340C3×Dic5—21no—
341C3×Dic5—21no—
342C3×Dic5—21no—
343C3×Dic5—41no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C3×#41—102no—
347C3×#41—102no—
348C2×C3×Q8—51no—
349C2×C3×D4—101no—
350C2×C3×D4C22×D511yescharacteristic
351C22×C3×C4—21no—
352C22×C3×C4—51no—
353C22×C3×C4—101no—
354C22×C3×C4—101no—
355C22×C3×C4—101no—
356C2×Dic6C22×D511yescharacteristic
357C2×Dic6C22×D511yescharacteristic
358C3×C4⋊C4—51no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4—101no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4C22×D511yescharacteristic
365C3×C22⋊C4—21no—
366C3×C22⋊C4—51no—
367C3×C22⋊C4—51no—
368C3×C22⋊C4—101no—
369C3×C42—51no—
370C3×C42—101no—
371C3×C42—101no—
372C3×C42C22×D511yescharacteristic
373#217—101no—
374#217—101no—
375#216—102no—
376#216—102no—
377#214—22no—
378#214—22no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3—51no—
382C4⋊Dic3—51no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387Dic3⋊C4—101no—
388Dic3⋊C4—101no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C2×C3⋊C8—51no—
392C2×C3⋊C8—51no—
393C2×C3⋊C8C22×D511yescharacteristic
394C2×C3⋊C8C22×D511yescharacteristic
395C23×C5—21no—
396C22×D5C2×#6711yescharacteristic
397C5×Q8—61no—
398C5×Q8—61no—
399C5×Q8—61no—
400C5×Q8—61no—
401C5×D4—21no—
402C5×D4#23512yes—
403C2×C4×C5—21no—
404C2×C4×C5—61no—
405C2×C4×C5—61no—
406C2×C4×C5—81no—
407C2×C4×C5C2×#6711yescharacteristic
408C2×C4×C5C2×#6711yescharacteristic
409C2×C4×C5C23×D311yescharacteristic
410C22⋊D5—24no—
411C2×Dic5—24no—
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—81no—
417C2×Dic5C2×#6711yescharacteristic
418C2×Dic5C2×#6711yescharacteristic
419C2×Dic5C2×#6711yescharacteristic
420C4×D5—21no—
421C4×D5—21no—
422C4×D5—81no—
423Dic10—21no—
424Dic10#23512yes—
425C5×C8—61no—
426C5×C8—61no—
427#168—61no—
428#168—61no—
429C2×#41—51no—
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16—31no—
433C2×SD16—31no—
434C4⋊Q8—31no—
435#126—301no—
436#126—301no—
437#125—151no—
438#125—301no—
439#125—301no—
440C22⋊Q8—151no—
441C22⋊Q8—151no—
442C4×Q8—51no—
443C4×Q8—51no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—51no—
447C4×D4—101no—
448C4×D4—101no—
449C4×D4D3×D511yescharacteristic
450#117—51no—
451#117—101no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—101no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—31no—
459C4⋊C8—151no—
460#103—31no—
461#103—31no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—151no—
467#102—151no—
468C22⋊C8—151no—
469C22⋊C8—151no—
470#97—151no—
471C4×C8—151no—
472C2×C3×C5—42no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C3×D5—41no—
477C23×C3—21no—
478C23×C3—51no—
479C3×Q8—52no—
480C3×Q8—101no—
481C3×D4—21no—
482C3×D4—104no—
483C3×D4#71112yes—
484C2×C3×C4—21no—
485C2×C3×C4—51no—
486C2×C3×C4—51no—
487C2×C3×C4—51no—
488C2×C3×C4—81no—
489C2×C3×C4—104no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4—101no—
494C2×C3×C4—401no—
495C2×C3×C4—401no—
496C2×C3×C4D4×D511yescharacteristic
497C2×C3×C4D4×D511yescharacteristic
498C2×C3×C4C23×D511yescharacteristic
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—101no—
502C2×Dic3—101no—
503Dic6—21no—
504Dic6—21no—
505Dic6—21no—
506Dic6—21no—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—22no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5C22×#6711yescharacteristic
515C2×D5—21no—
516C2×D5—21no—
517C2×D5—21no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—41no—
521C4×C5—121no—
522C4×C5—121no—
523C4×C5C2×#23511yescharacteristic
524C4×C5C2×#23511yescharacteristic
525Dic5—22no—
526Dic5—21no—
527Dic5—21no—
528Dic5—21no—
529Dic5—41no—
530Dic5—121no—
531Dic5—121no—
532#41—102no—
533#41—102no—
534C2×Q8—31no—
535C2×Q8—31no—
536C2×Q8—51no—
537C2×D4—101no—
538C2×D4C2×D3×D511yescharacteristic
539C22×C4—21no—
540C22×C4—51no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—101no—
544Q16—302no—
545Q16—302no—
546SD16—62no—
547SD16—62no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—51no—
553C4⋊C4—51no—
554C4⋊C4—51no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—101no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—151no—
561C4⋊C4—151no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4C2×D3×D511yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—51no—
571C22⋊C4—51no—
572C22⋊C4—101no—
573C22⋊C4—301no—
574C22⋊C4—301no—
575C42—51no—
576C42—101no—
577C42—101no—
578C42—301no—
579C42—301no—
580C42C2×D3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—22no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—101no—
586C22×C3—101no—
587C22×C3—101no—
588C22×C3C2×D4×D511yescharacteristic
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—41no—
592C3×C4—101no—
593C3×C4—101no—
594C3×C4—101no—
595C3×C4—102no—
596C3×C4—201no—
597C3×C4C2×#71111yescharacteristic
598C3×C4D5×#4111yescharacteristic
599Dic3—41no—
600Dic3—41no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—42no—
604C2×C5#579111yescharacteristic
605C2×C5#583611yescharacteristic
606C2×C5#583811yescharacteristic
607D5—41no—
608C23—21no—
609C23—51no—
610Q8—52no—
611Q8—61no—
612Q8—61no—
613Q8—61no—
614Q8—61no—
615Q8—101no—
616D4—21no—
617D4—104no—
618D4#677212yes—
619C2×C4—21no—
620C2×C4—51no—
621C2×C4—51no—
622C2×C4—51no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—81no—
626C2×C4—104no—
627C2×C4—101no—
628C2×C4—101no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—301no—
632C2×C4—301no—
633C2×C4—401no—
634C2×C4—401no—
635C2×C4D5×#6711yescharacteristic
636C2×C4D5×#6711yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—61no—
639C8—61no—
640C8—301no—
641C8—301no—
642C2×C3—42no—
643C2×C3—201no—
644C2×C3#6594011yescharacteristic
645C2×C3#6609611yescharacteristic
646C2×C3#6611311yescharacteristic
647C5#8257511yescharacteristic, complemented, Sylow
648C22—22no—
649C22—41no—
650C22—41no—
651C22—101no—
652C22—101no—
653C22—101no—
654C22C2×D5×#6711yescharacteristic
655C4—21no—
656C4—21no—
657C4—41no—
658C4—101no—
659C4—102no—
660C4—101no—
661C4—101no—
662C4—121no—
663C4—121no—
664C4—201no—
665C4—601no—
666C4—601no—
667C4C2×#677211yescharacteristic
668C4D5×#23511yescharacteristic
669C3#1061214311yescharacteristic, complemented, Sylow
670C2—42no—
671C2—201no—
672C2#1175452611yescharacteristic
673C2#1175470711yescharacteristic
674C2#1175533611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#711C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752509C2semidirect
3. #11751110C2semidirect
4. C5×#5019C2semidirect
7. #11749001C2semidirect
8. Dic5×#214C2semidirect
9. #11747340C2semidirect
10. #11747338C2semidirect
11. #11747263C2semidirect
12. #11747262C2semidirect
13. #11747094C2semidirect
14. #11746944C2semidirect
15. #11746873C2semidirect
133. #5019D5semidirect
581. C3×C5#3120semidirect
647. C5#82575semidirect
669. C3#10612143semidirect

Maximal subgroups

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

subgroupindex
C3×#658802
#117525092
#117511102
C5×#50192
#117490472
#117490012
Dic5×#2142
#117473402
#117473382
#117472632
#117472622
#117470942
#117469442
#117468732
#106121433
#825755