Finite Group Databasebeta

← #14436273

Subgroups — #14436273

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×#65838C211yesmaximal, characteristic
2#11754212C211yesmaximal, characteristic, complemented
3#11751072C211yesmaximal, characteristic, complemented
4C5×#4970C211yesmaximal, characteristic, complemented
5#11748531C211yesmaximal, characteristic
6#11748528C211yesmaximal, characteristic
7#11748319C211yesmaximal, characteristic, complemented
8#11747472C211yesmaximal, characteristic, complemented
9#11747414C211yesmaximal, characteristic, complemented
10#11747412C211yesmaximal, characteristic, complemented
11#11747391C211yesmaximal, characteristic, complemented
12#11747389C211yesmaximal, characteristic, complemented
13#11747270C211yesmaximal, characteristic, complemented
14#11747262C211yesmaximal, characteristic, complemented
15#11747261C211yesmaximal, characteristic, complemented
16#10613187—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19#91813C2211yescharacteristic
20C5×#924C2211yescharacteristic
21C3×C4×C22⋊D5—21no—
22C3×C4×C22⋊D5—21no—
23C3×#4072C2211yescharacteristic
24C3×#4039C2211yescharacteristic
25C3×#4039C2211yescharacteristic
26C3×#4038—21no—
27C3×D5×C4⋊C4—21no—
28C3×#4033C2211yescharacteristic
29C3×#4033C2211yescharacteristic
30#91531—21no—
31#91530—21no—
32#91388C2211yescharacteristic
33#91376C2211yescharacteristic
34#91346—21no—
35#91339—21no—
36#91333C2211yescharacteristic
37Dic5×Dic6C2211yescharacteristic
38C2×#6662C2211yescharacteristic
39C2×#6661C2211yescharacteristic
40C2×#6657C2211yescharacteristic
41C2×#6655C2211yescharacteristic
42#91114C2211yescharacteristic
43#91094C2211yescharacteristic
44#91094C2211yescharacteristic
45#91092C2211yescharacteristic
46#91092C2211yescharacteristic
47C5×#830C2211yescharacteristic
48C5×#810C2211yescharacteristic
49C5×#810C2211yescharacteristic
50C5×#807C2211yescharacteristic
51C5×#807C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90971C2211yescharacteristic
55#90970C2211yescharacteristic
56#90965C2211yescharacteristic
57#90964C2211yescharacteristic
58#90952C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#82575—51nomaximal, Hall
61#65959—31no—
62#65838D311yescharacteristic
63C5×#484—31no—
64#65336—31no—
65#65260—31no—
66#65180—31no—
67#65178—31no—
68#65166—31no—
69#65162—31no—
70#65107—31no—
71#65082—31no—
72#65078—31no—
73#65077—31no—
74#65022—31no—
75#65009—31no—
76C22×C3×C4×C5—21no—
77C22×C3×C4×C5C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×Dic6C2311yescharacteristic
80C2×C3×C22⋊D5—21no—
81C3×#709—22no—
82C3×#709—22no—
83C2×C3×D20C2311yescharacteristic
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91#6719—21no—
92C4⋊Dic15C2311yescharacteristic
93#6712—21no—
94C2×C3⋊#168C2311yescharacteristic
95C2×C3⋊#168C2311yescharacteristic
96C5×#217—21no—
97C5×C4⋊Dic3C2311yescharacteristic
98C5×Dic3⋊C4—21no—
99C2×C5×C3⋊C8C2311yescharacteristic
100C2×C5×C3⋊C8C2311yescharacteristic
101C3×C22⋊Dic5D411yescharacteristic
102C3×C22⋊Dic5D411yescharacteristic
103C3×#685—21no—
104C3×#685—21no—
105C3×C4⋊Dic5D411yescharacteristic
106C3×C4⋊Dic5D411yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C3×C4×Dic5—21no—
110C3×C4×Dic5—21no—
111C3×C4×Dic5C2311yescharacteristic
112C3×C4×Dic5C2311yescharacteristic
113Dic3⋊Dic5—21no—
114Dic3⋊Dic5—21no—
115#6669—21no—
116#6669—21no—
117#6668—21no—
118#6668—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121#6662—22no—
122#6661—22no—
123#6657—22no—
124#6655—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#5019—51no—
134#5018—51no—
135C4×#214—51no—
136#5009—51no—
137#5000—51no—
138#4971—51no—
139#4970D511yescharacteristic, complemented
140C2×#709C2×D311yescharacteristic
141C5×C22⋊Q8—31no—
142C2×C5×C4⋊C4C2×D311yescharacteristic
143Q8×Dic5—31no—
144#4090—31no—
145C2×#689—31no—
146C2×#688—31no—
147C4×C22⋊D5—21no—
148C4×C22⋊D5—21no—
149#4072C2×D311yescharacteristic
150#4070—31no—
151C2×Dic20—31no—
152C2×#677—31no—
153#4039C2×D311yescharacteristic
154#4039C2×D311yescharacteristic
155#4038—21no—
156D5×C4⋊C4—21no—
157#4036—31no—
158#4036—61no—
159#4035—61no—
160#4033—31no—
161#4033C2×D311yescharacteristic
162#4033C2×D311yescharacteristic
163#4025—61no—
164#4025—61no—
165C5×#107—31no—
166C5×#107—31no—
167C5×#103—31no—
168C5×#103—31no—
169C5×C22⋊C8—31no—
170C22⋊#168—31no—
171#3953—31no—
172#3948—31no—
173#3947—31no—
174#3946—31no—
175#3946—31no—
176C8×Dic5—31no—
177#3942—31no—
178#3942—31no—
179#3942—31no—
180#3941—31no—
181#3940—31no—
182#3940—31no—
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C3×D5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—81no—
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15—21no—
194C2×Dic15—21no—
195Dic30—21no—
196Dic30—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C5×Dic6—21no—
200C5×Dic6—21no—
201C3×C22⋊D5—24no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C2×C3×Dic5C2×D411yescharacteristic
206C2×C3×Dic5C2×D411yescharacteristic
207C3×D20—21no—
208C3×D20#4112yes—
209C3×C4×D5—24no—
210C3×C4×D5—81no—
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—51no—
223C3×C4×D4—101no—
224C3×C4×D4—101no—
225C3×#117—51no—
226C3×#117—101no—
227C2×C3×C4⋊C4—101no—
228C2×C3×C4⋊C4C2×D511yescharacteristic
229C2×#216—51no—
230C2×#216—51no—
231C2×#214—51no—
232C2×#214—51no—
233#924—51no—
234#924C2×D511yescharacteristic
235#889—101no—
236#889—101no—
237#879—101no—
238#879—101no—
239#870—51no—
240#869—51no—
241C4×Dic6—51no—
242C4×Dic6—51no—
243#835—51no—
244#835—51no—
245#832—51no—
246#832—51no—
247#830—51no—
248#830C2×D511yescharacteristic
249#810—51no—
250#810—51no—
251#810C2×D511yescharacteristic
252#810C2×D511yescharacteristic
253#808—51no—
254#808—51no—
255#807C2×D511yescharacteristic
256#807C2×D511yescharacteristic
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)—51no—
259#803—51no—
260C4×C3⋊C8—51no—
261C2×C5×Q8—31no—
262C22×C4×C5—21no—
263C22×C4×C5C22×D311yescharacteristic
264C2×C22⋊D5—21no—
265#709—22no—
266#709—22no—
267C2×D20C22×D311yescharacteristic
268C2×C4×D5—21no—
269C2×C4×D5—21no—
270C2×C4×D5—21no—
271C2×Dic10—31no—
272C2×Dic10C22×D311yescharacteristic
273C2×C5×C8—31no—
274C2×C5×C8—31no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—31no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4C22×D311yescharacteristic
279C5×C4⋊C4C22×D311yescharacteristic
280C5×C22⋊C4—61no—
281C22⋊Dic5—61no—
282C22⋊Dic5#6711yescharacteristic
283C22⋊Dic5#6711yescharacteristic
284#689—62no—
285#688—62no—
286#685—21no—
287#685—21no—
288C4⋊Dic5—31no—
289C4⋊Dic5—61no—
290C4⋊Dic5—61no—
291C4⋊Dic5#6711yescharacteristic
292C4⋊Dic5#6711yescharacteristic
293#683—21no—
294#683—21no—
295#683—61no—
296#683—61no—
297#683—61no—
298#683—61no—
299#683—61no—
300C4×Dic5—21no—
301C4×Dic5—21no—
302C4×Dic5—61no—
303C4×Dic5—61no—
304C4×Dic5C22×D311yescharacteristic
305C4×Dic5C22×D311yescharacteristic
306C2×#168—31no—
307C2×#168—31no—
308Dic20—62no—
309#677—62no—
310#541—151no—
311#520—51no—
312#484—31no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—151no—
319#452—151no—
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×C5C22×D411yescharacteristic
329C2×C3×D5—22no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
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—21no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C3×#41—102no—
347C3×#41—102no—
348C2×C3×Q8—51no—
349C2×C3×D4—51no—
350C2×C3×D4—101no—
351C22×C3×C4—21no—
352C22×C3×C4—101no—
353C22×C3×C4—101no—
354C22×C3×C4—101no—
355C22×C3×C4C22×D511yescharacteristic
356C2×Dic6—51no—
357C2×Dic6C22×D511yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4—101no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4C22×D511yescharacteristic
364C3×C4⋊C4C22×D511yescharacteristic
365C3×C22⋊C4—51no—
366C3×C22⋊C4—51no—
367C3×C22⋊C4—101no—
368C3×C22⋊C4—101no—
369C3×C42—51no—
370C3×C42—51no—
371C3×C42—101no—
372C3×C42—101no—
373#217—21no—
374#217—101no—
375#216—102no—
376#216—102no—
377#214—102no—
378#214—102no—
379C4⋊Dic3—51no—
380C4⋊Dic3—101no—
381C4⋊Dic3—101no—
382C4⋊Dic3C22×D511yescharacteristic
383Dic3⋊C4—21no—
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×C5C2×#6711yescharacteristic
396C22×D5—21no—
397C5×Q8—61no—
398C5×Q8—61no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—61no—
404C2×C4×C5—61no—
405C2×C4×C5—81no—
406C2×C4×C5C2×#6711yescharacteristic
407C2×C4×C5C23×D311yescharacteristic
408C22⋊D5—24no—
409C2×Dic5—21no—
410C2×Dic5—61no—
411C2×Dic5—61no—
412C2×Dic5C2×#6711yescharacteristic
413C2×Dic5C2×#6711yescharacteristic
414C2×Dic5C2×#6711yescharacteristic
415C2×Dic5C2×#6711yescharacteristic
416D20—21no—
417D20#23512yes—
418C4×D5—24no—
419C4×D5—81no—
420C4×D5—81no—
421Dic10—21no—
422Dic10—61no—
423Dic10—61no—
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—151no—
433C2×SD16—151no—
434C4⋊Q8—151no—
435#126—301no—
436#126—301no—
437#125—151no—
438#125—301no—
439#125—301no—
440C22⋊Q8—31no—
441C22⋊Q8—151no—
442C4×Q8—51no—
443C4×Q8—51no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—51no—
447C4×D4—51no—
448C4×D4—101no—
449C4×D4—101no—
450#117—51no—
451#117—101no—
452C2×C4⋊C4—101no—
453C2×C4⋊C4D3×D511yescharacteristic
454#107—31no—
455#107—31no—
456#106—151no—
457#106—151no—
458C4⋊C8—151no—
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—31no—
469C22⋊C8—151no—
470#97—151no—
471C4×C8—151no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C3×D5—42no—
477C23×C3—101no—
478C23×C3D4×D511yescharacteristic
479C3×Q8—52no—
480C3×Q8—101no—
481C3×D4—52no—
482C3×D4—104no—
483C3×D4—101no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—51no—
489C2×C3×C4—51no—
490C2×C3×C4—51no—
491C2×C3×C4—51no—
492C2×C3×C4—81no—
493C2×C3×C4—104no—
494C2×C3×C4—101no—
495C2×C3×C4—401no—
496C2×C3×C4—401no—
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—101no—
506Dic6—101no—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C22×#6711yescharacteristic
515C2×D5—22no—
516C2×D5—41no—
517C2×D5—41no—
518C4×C5—21no—
519C4×C5—41no—
520C4×C5—41no—
521C4×C5—121no—
522C4×C5—121no—
523C4×C5C2×#23511yescharacteristic
524C4×C5C2×#23511yescharacteristic
525Dic5—22no—
526Dic5—21no—
527Dic5—21no—
528Dic5—21no—
529Dic5—21no—
530Dic5—121no—
531Dic5—121no—
532#41—102no—
533#41—102no—
534C2×Q8—31no—
535C2×Q8—51no—
536C2×Q8—151no—
537C2×D4—51no—
538C2×D4—101no—
539C22×C4—21no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—302no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—21no—
553C4⋊C4—31no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—61no—
557C4⋊C4—101no—
558C4⋊C4—101no—
559C4⋊C4—151no—
560C4⋊C4—301no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4C2×D3×D511yescharacteristic
568C4⋊C4C2×D3×D511yescharacteristic
569C22⋊C4—51no—
570C22⋊C4—51no—
571C22⋊C4—61no—
572C22⋊C4—101no—
573C22⋊C4—101no—
574C22⋊C4—301no—
575C42—51no—
576C42—51no—
577C42—101no—
578C42—101no—
579C42—301no—
580C42—301no—
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—102no—
586C22×C3—201no—
587C22×C3—201no—
588C22×C3C2×D4×D511yescharacteristic
589C3×C4—21no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—101no—
593C3×C4—101no—
594C3×C4—101no—
595C3×C4—101no—
596C3×C4—102no—
597C3×C4D5×#4111yescharacteristic
598C3×C4D5×#4111yescharacteristic
599Dic3—41no—
600Dic3—41no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5#579111yescharacteristic
605C2×C5#583611yescharacteristic
606C2×C5#583811yescharacteristic
607D5—42no—
608C23—101no—
609C23D5×#6711yescharacteristic
610Q8—52no—
611Q8—61no—
612Q8—61no—
613Q8—101no—
614Q8—301no—
615Q8—301no—
616D4—52no—
617D4—104no—
618D4—101no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—51no—
624C2×C4—51no—
625C2×C4—51no—
626C2×C4—51no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—81no—
630C2×C4—104no—
631C2×C4—101no—
632C2×C4—301no—
633C2×C4—301no—
634C2×C4—401no—
635C2×C4—401no—
636C2×C4D5×#6711yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—61no—
639C8—61no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3—202no—
644C2×C3#6599011yescharacteristic
645C2×C3#6610011yescharacteristic
646C2×C3#6610911yescharacteristic
647C5#8257511yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—102no—
652C22—201no—
653C22—201no—
654C22C2×D5×#6711yescharacteristic
655C4—21no—
656C4—41no—
657C4—41no—
658C4—102no—
659C4—101no—
660C4—101no—
661C4—101no—
662C4—101no—
663C4—121no—
664C4—121no—
665C4—601no—
666C4—601no—
667C4D5×#23511yescharacteristic
668C4D5×#23511yescharacteristic
669C3#1061318711yescharacteristic, complemented, Sylow
670C2—41no—
671C2—202no—
672C2#1175431611yescharacteristic
673C2#1175470811yescharacteristic
674C2#1175510111yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11754212C2semidirect
3. #11751072C2semidirect
4. C5×#4970C2semidirect
7. #11748319C2semidirect
8. #11747472C2semidirect
9. #11747414C2semidirect
10. #11747412C2semidirect
11. #11747391C2semidirect
12. #11747389C2semidirect
13. #11747270C2semidirect
14. #11747262C2semidirect
15. #11747261C2semidirect
139. #4970D5semidirect
581. C3×C5#3120semidirect
647. C5#82575semidirect
669. C3#10613187semidirect

Maximal subgroups

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

subgroupindex
C3×#658382
#117542122
#117510722
C5×#49702
#117485312
#117485282
#117483192
#117474722
#117474142
#117474122
#117473912
#117473892
#117472702
#117472622
#117472612
#106131873
#825755