Finite Group Databasebeta

← #14436134

Subgroups — #14436134

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×#65959C211yesmaximal, characteristic, complemented
2#11754506C211yesmaximal, characteristic
3#11751148C211yesmaximal, characteristic
4C5×#5043C211yesmaximal, characteristic, complemented
5#11749246C211yesmaximal, characteristic, complemented
6#11749244C211yesmaximal, characteristic, complemented
7#11749225C211yesmaximal, characteristic, complemented
8#11749222C211yesmaximal, characteristic, complemented
9#11748552C211yesmaximal, characteristic
10#11748461C211yesmaximal, characteristic, complemented
11#11748319C211yesmaximal, characteristic, complemented
12#11747286C211yesmaximal, characteristic, complemented
13#11747269C211yesmaximal, characteristic, complemented
14#11747244C211yesmaximal, characteristic, complemented
15#11747225C211yesmaximal, characteristic, complemented
16#10613147—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C3×C5×C22⋊Q8C2211yescharacteristic
19C2×#6718C2211yescharacteristic
20C2×#6717C2211yescharacteristic
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C3×#4090C2211yescharacteristic
24C3×#4072C2211yescharacteristic
25C3×#4070C2211yescharacteristic
26C3×#4036—21no—
27C3×#4036C2211yescharacteristic
28C3×#4035—21no—
29C3×#4033C2211yescharacteristic
30C3×#4025—21no—
31C3×#4025—21no—
32#91556—21no—
33#91556—21no—
34#91437—21no—
35#91418C2211yescharacteristic
36#91418C2211yescharacteristic
37#91347—21no—
38#91333C2211yescharacteristic
39#91333C2211yescharacteristic
40C2×#6662C2211yescharacteristic
41C2×#6658C2211yescharacteristic
42#91114C2211yescharacteristic
43#91094C2211yescharacteristic
44#91093C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#835C2211yescharacteristic
47C5×#830C2211yescharacteristic
48C5×#808C2211yescharacteristic
49C5×#808C2211yescharacteristic
50#90989C2211yescharacteristic
51#90989C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90974C2211yescharacteristic
55#90970C2211yescharacteristic
56#90970C2211yescharacteristic
57#90968C2211yescharacteristic
58#90952C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#83446—51nomaximal, Hall
61#65959D311yescharacteristic, complemented
62#65838—31no—
63C5×#483—31no—
64#65336—31no—
65#65259—31no—
66#65160—31no—
67#65146—31no—
68#65142—31no—
69#65141—31no—
70#65107—31no—
71#65106—31no—
72#65082—31no—
73#65079—31no—
74#65022—31no—
75#65009—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—21no—
79#6817—22no—
80#6817—22no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×Dic30C2311yescharacteristic
84C22×C5×Dic3—21no—
85C2×C3×Dic10C2311yescharacteristic
86C2×#1200—21no—
87C2×#1200—21no—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91#6718—22no—
92#6717—22no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×C4⋊Dic3—21no—
96C5×C4⋊Dic3C2311yescharacteristic
97C5×C4⋊Dic3C2311yescharacteristic
98C2×C5×C3⋊C8C2311yescharacteristic
99C2×C5×C3⋊C8C2311yescharacteristic
100C3×C22⋊Dic5—21no—
101C3×C22⋊Dic5D411yescharacteristic
102C3×C22⋊Dic5D411yescharacteristic
103C3×C4⋊Dic5—21no—
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5D411yescharacteristic
106C3×C4⋊Dic5D411yescharacteristic
107C3×C4⋊Dic5C2311yescharacteristic
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×#683—21no—
112C3×#683—21no—
113C3×C4×Dic5—21no—
114C3×C4×Dic5—21no—
115C3×C4×Dic5C2311yescharacteristic
116C3×C4×Dic5C2311yescharacteristic
117#6669—21no—
118#6669—21no—
119#6667—21no—
120#6667—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#6662—22no—
124#6658—22no—
125C3×#541—51no—
126#5523—51no—
127#5090—51no—
128#5083—51no—
129#5066—51no—
130#5063—51no—
131#5047—51no—
132#5047—51no—
133#5044—51no—
134#5043D511yescharacteristic, complemented
135#5030—51no—
136C4×#216—51no—
137#5026—51no—
138C4×#215—51no—
139#5000—51no—
140C2×#709—31no—
141C5×C22⋊Q8C2×D311yescharacteristic
142C2×C5×C4⋊C4—31no—
143Q8×Dic5C2×D311yescharacteristic
144#4090C2×D311yescharacteristic
145C2×#689—31no—
146C2×#688—31no—
147C4×C22⋊D5—61no—
148C4×C22⋊D5—61no—
149#4072C2×D311yescharacteristic
150#4070C2×D311yescharacteristic
151C2×Dic20—31no—
152C2×#677—31no—
153#4039—31no—
154#4039—31no—
155#4038—61no—
156D5×C4⋊C4—61no—
157#4036—21no—
158#4036C2×D311yescharacteristic
159#4035—21no—
160#4033—31no—
161#4033—31no—
162#4033C2×D311yescharacteristic
163#4025—21no—
164#4025—21no—
165C5×#106—31no—
166C5×#106—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#3939—31no—
182#3939—31no—
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×D15—21no—
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2411yescharacteristic
194#1220—24no—
195C2×Dic15—21no—
196D60—21no—
197D60#4112yes—
198C4×D15—24no—
199Dic30—21no—
200Dic30#4112yes—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—81no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5C2×D411yescharacteristic
207C2×C3×Dic5C2×D411yescharacteristic
208C2×C3×Dic5C2×D411yescharacteristic
209C2×C3×Dic5C2×D411yescharacteristic
210C3×Dic10—21no—
211C3×Dic10—21no—
212#1200—81no—
213#1200—81no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C5×C3⋊C8—21no—
217C5×C3⋊C8—21no—
218C2×#235—51no—
219C3×C4⋊Q8—51no—
220C3×#126—101no—
221C3×#126—101no—
222C3×#125—51no—
223C3×#125—101no—
224C3×#125—101no—
225C3×C22⋊Q8—51no—
226C3×C22⋊Q8C2×D511yescharacteristic
227C3×C4×Q8—51no—
228C3×C4×Q8—51no—
229C3×#117—51no—
230C2×#216—51no—
231C2×#216—51no—
232C2×#215—51no—
233C2×#215—51no—
234C2×C4⋊Dic3C2×D511yescharacteristic
235#892—101no—
236D3×C4⋊C4—101no—
237#67⋊C4—101no—
238#67⋊C4—101no—
239C4×D12—51no—
240C4×D12—51no—
241C4×Dic6—51no—
242C4×Dic6—51no—
243#835—51no—
244#835—51no—
245#835C2×D511yescharacteristic
246#835C2×D511yescharacteristic
247#830—51no—
248#830C2×D511yescharacteristic
249#810—51no—
250#810—51no—
251#809—51no—
252#809—51no—
253#808C2×D511yescharacteristic
254#808C2×D511yescharacteristic
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)—51no—
259#803—51no—
260C4×C3⋊C8—51no—
261C2×C5×Q8C22×D311yescharacteristic
262C22×C4×C5—61no—
263C22×C4×C5C22×D311yescharacteristic
264C2×C22⋊D5—61no—
265#709—62no—
266#709—62no—
267C2×D20—31no—
268C2×C4×D5—61no—
269C2×C4×D5—61no—
270C2×C4×D5—61no—
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—31no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4C22×D311yescharacteristic
280C5×C22⋊C4—21no—
281C22⋊Dic5—21no—
282C22⋊Dic5#6711yescharacteristic
283C22⋊Dic5#6711yescharacteristic
284#689—62no—
285#688—62no—
286#685—61no—
287#685—61no—
288C4⋊Dic5—21no—
289C4⋊Dic5—21no—
290C4⋊Dic5#6711yescharacteristic
291C4⋊Dic5#6711yescharacteristic
292C4⋊Dic5C22×D311yescharacteristic
293#683—21no—
294#683—21no—
295#683—21no—
296#683—21no—
297#683—21no—
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—51no—
311#520—151no—
312#484—151no—
313#483—31no—
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×D15—22no—
330C2×D15—41no—
331C2×D15—41no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5—41no—
335C3×C4×C5C2×#4111yescharacteristic
336C3×C4×C5C2×#4111yescharacteristic
337Dic15—22no—
338C3×Dic5—21no—
339C3×Dic5—21no—
340C3×Dic5—21no—
341C3×Dic5—21no—
342C3×Dic5—41no—
343C3×Dic5—41no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C2×C3×Q8—51no—
347C2×C3×Q8C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C2×#67—101no—
350C22×Dic3—21no—
351#235—102no—
352#235—102no—
353C2×D12—51no—
354C2×C4×D3—101no—
355C2×C4×D3—101no—
356C2×C4×D3—101no—
357C2×Dic6—51no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4—51no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4—101no—
365C3×C4⋊C4—101no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4—101no—
368C3×C4⋊C4—101no—
369C3×C4⋊C4C22×D511yescharacteristic
370C3×C22⋊C4—21no—
371C3×C22⋊C4—51no—
372C3×C22⋊C4—51no—
373C3×C22⋊C4—101no—
374C3×C42—51no—
375C3×C42—51no—
376C3×C42—101no—
377C3×C42—101no—
378#216—102no—
379#216—102no—
380#215—102no—
381#215—102no—
382(C2×D3)⋊C4—101no—
383(C2×D3)⋊C4—101no—
384C4⋊Dic3—21no—
385C4⋊Dic3C22×D511yescharacteristic
386C4⋊Dic3C22×D511yescharacteristic
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—61no—
397C5×Q8—21no—
398C5×Q8—21no—
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—241no—
406C2×C4×C5C2×#6711yescharacteristic
407C2×C4×C5C23×D311yescharacteristic
408C22⋊D5—64no—
409C2×Dic5—21no—
410C2×Dic5—21no—
411C2×Dic5—61no—
412C2×Dic5C2×#6711yescharacteristic
413C2×Dic5C2×#6711yescharacteristic
414C2×Dic5C2×#6711yescharacteristic
415C2×Dic5C2×#6711yescharacteristic
416D20—32no—
417D20—61no—
418C4×D5—64no—
419C4×D5—241no—
420C4×D5—241no—
421Dic10—21no—
422Dic10—21no—
423Dic10—32no—
424Dic10—61no—
425C5×C8—61no—
426C5×C8—61no—
427#168—61no—
428#168—61no—
429C2×#41—151no—
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16—151no—
433C2×SD16—151no—
434C4⋊Q8—51no—
435#126—101no—
436#126—101no—
437#125—51no—
438#125—101no—
439#125—101no—
440C22⋊Q8—51no—
441C22⋊Q8D3×D511yescharacteristic
442C4×Q8—51no—
443C4×Q8—51no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—301no—
449C4×D4—301no—
450#117—51no—
451#117—301no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—301no—
454#107—151no—
455#107—151no—
456#106—31no—
457#106—31no—
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
476D15—42no—
477C23×C3D4×D511yescharacteristic
478C22×D3—101no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—101no—
482C3×Q8—101no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—51no—
488C2×C3×C4—51no—
489C2×C3×C4—51no—
490C2×C3×C4—51no—
491C2×C3×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4D4×D511yescharacteristic
494C2×C3×C4C23×D511yescharacteristic
495#67—104no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—81no—
499C2×Dic3—101no—
500D12—52no—
501D12—101no—
502C4×D3—104no—
503C4×D3—401no—
504C4×D3—401no—
505Dic6—52no—
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—62no—
516C2×D5—121no—
517C2×D5—121no—
518C4×C5—21no—
519C4×C5—41no—
520C4×C5—41no—
521C4×C5—121no—
522C4×C5—121no—
523C4×C5D3×#4111yescharacteristic
524C4×C5D3×#4111yescharacteristic
525Dic5—21no—
526Dic5—21no—
527Dic5—21no—
528Dic5—21no—
529Dic5—41no—
530Dic5—41no—
531Dic5—62no—
532#41—302no—
533#41—302no—
534C2×Q8—51no—
535C2×Q8—151no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—151no—
538C2×D4—301no—
539C22×C4—61no—
540C22×C4—301no—
541C22×C4—301no—
542C22×C4—301no—
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—31no—
555C4⋊C4—51no—
556C4⋊C4—51no—
557C4⋊C4—51no—
558C4⋊C4—61no—
559C4⋊C4—101no—
560C4⋊C4—101no—
561C4⋊C4—101no—
562C4⋊C4—101no—
563C4⋊C4—101no—
564C4⋊C4—101no—
565C4⋊C4—101no—
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—51no—
577C42—101no—
578C42—101no—
579C42—301no—
580C42—301no—
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3C2×D4×D511yescharacteristic
586C2×D3—102no—
587C2×D3—201no—
588C2×D3—201no—
589C3×C4—21no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—101no—
593C3×C4—101no—
594C3×C4—101no—
595C3×C4—101no—
596C3×C4—201no—
597C3×C4—201no—
598C3×C4D5×#4111yescharacteristic
599C3×C4D5×#4111yescharacteristic
600Dic3—41no—
601Dic3—41no—
602Dic3—102no—
603C2×C5—41no—
604C2×C5#582811yescharacteristic
605C2×C5#583711yescharacteristic
606C2×C5#583811yescharacteristic
607D5—122no—
608C23—301no—
609C23D5×#6711yescharacteristic
610Q8—21no—
611Q8—21no—
612Q8—101no—
613Q8—101no—
614Q8—152no—
615Q8—301no—
616D4—152no—
617D4—304no—
618D4—301no—
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—101no—
630C2×C4—101no—
631C2×C4—241no—
632C2×C4—304no—
633C2×C4—301no—
634C2×C4—1201no—
635C2×C4—1201no—
636C2×C4D5×#6711yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—61no—
639C8—61no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3#6599011yescharacteristic
644C2×C3#6609611yescharacteristic
645C2×C3#6611311yescharacteristic
646D3—202no—
647C5#8344611yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—302no—
652C22—601no—
653C22—601no—
654C22C2×D5×#6711yescharacteristic
655C4—21no—
656C4—41no—
657C4—41no—
658C4—101no—
659C4—101no—
660C4—101no—
661C4—101no—
662C4—121no—
663C4—121no—
664C4—201no—
665C4—201no—
666C4—302no—
667C4#9202411yescharacteristic
668C4#9202411yescharacteristic
669C3#1061314711yescharacteristic, complemented, Sylow
670C2—41no—
671C2—602no—
672C2#1175480011yescharacteristic
673C2#1175508511yescharacteristic
674C2#1175533611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#65959C2semidirect
4. C5×#5043C2semidirect
5. #11749246C2semidirect
6. #11749244C2semidirect
7. #11749225C2semidirect
8. #11749222C2semidirect
10. #11748461C2semidirect
11. #11748319C2semidirect
12. #11747286C2semidirect
13. #11747269C2semidirect
14. #11747244C2semidirect
15. #11747225C2semidirect
61. #65959D3semidirect
134. #5043D5semidirect
581. C3×C5#3120semidirect
647. C5#83446semidirect
669. C3#10613147semidirect

Maximal subgroups

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

subgroupindex
C3×#659592
#117545062
#117511482
C5×#50432
#117492462
#117492442
#117492252
#117492222
#117485522
#117484612
#117483192
#117472862
#117472692
#117472442
#117472252
#106131473
#834465