Finite Group Databasebeta

← #14436117

Subgroups — #14436117

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#11754513C211yesmaximal, characteristic
3#11751145C211yesmaximal, characteristic, complemented
4C5×#5047C211yesmaximal, characteristic
5#11749247C211yesmaximal, characteristic, complemented
6#11749245C211yesmaximal, characteristic, complemented
7#11749220C211yesmaximal, characteristic, complemented
8Dic5×#215C211yesmaximal, characteristic, complemented
9#11748538C211yesmaximal, characteristic
10#11748445C211yesmaximal, characteristic, complemented
11#11748319C211yesmaximal, characteristic, complemented
12#11747289C211yesmaximal, characteristic, complemented
13#11747263C211yesmaximal, characteristic, complemented
14#11747241C211yesmaximal, characteristic, complemented
15#11747217C211yesmaximal, characteristic, complemented
16#10611947—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
18C3×C5×C22⋊Q8C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C5×#216C2211yescharacteristic
21C2×C5×#215C2211yescharacteristic
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#67⋊Dic5—21no—
33#67⋊Dic5—21no—
34D3×C4⋊Dic5—21no—
35Dic5×D12C2211yescharacteristic
36Dic5×D12C2211yescharacteristic
37#91338—21no—
38Dic5×Dic6C2211yescharacteristic
39Dic5×Dic6C2211yescharacteristic
40C2×#6661C2211yescharacteristic
41C2×#6656C2211yescharacteristic
42#91119C2211yescharacteristic
43#91119C2211yescharacteristic
44#91114C2211yescharacteristic
45#91091C2211yescharacteristic
46#91091C2211yescharacteristic
47C5×#830C2211yescharacteristic
48C5×#810C2211yescharacteristic
49C5×#809C2211yescharacteristic
50#90987C2211yescharacteristic
51#90987C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90972C2211yescharacteristic
55#90971C2211yescharacteristic
56#90971C2211yescharacteristic
57#90966C2211yescharacteristic
58#90952C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#83446—51nomaximal, Hall
61#66161—31no—
62#65959D311yescharacteristic, complemented
63C5×#452—31no—
64#65528—31no—
65#65473—31no—
66#65471—31no—
67#65451—31no—
68SD16×Dic5—31no—
69#65333—31no—
70#65088—31no—
71#65079—31no—
72#65052—31no—
73#65046—31no—
74#65010—31no—
75#65009—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15—21no—
79C2×C5×#67—21no—
80C5×#235—22no—
81C5×#235—22no—
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C5×Dic6C2311yescharacteristic
85C2×C3×Dic10C2311yescharacteristic
86C2×D3×Dic5—21no—
87C2×D3×Dic5—21no—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91C4⋊Dic15—21no—
92C4⋊Dic15C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C2×C3⋊#168C2311yescharacteristic
96C5×#216—22no—
97C5×#215—22no—
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
117Dic3⋊Dic5—21no—
118Dic3⋊Dic5—21no—
119(C2×D3)⋊Dic5—21no—
120(C2×D3)⋊Dic5—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#6661—22no—
124#6656—22no—
125C3×#541—51no—
126#5523—51no—
127#5090—51no—
128#5083—51no—
129#5066—51no—
130#5063—51no—
131#5047—51no—
132#5047D511yescharacteristic
133#5044—51no—
134#5043—51no—
135#5030—51no—
136C4×#216—51no—
137#5026—51no—
138C4×#215—51no—
139#5000—51no—
140C2×C5×#41—31no—
141C2×C5×Q16—31no—
142C2×C5×SD16—31no—
143C5×C22⋊Q8C2×D311yescharacteristic
144Q8×Dic5—31no—
145Q8×Dic5—31no—
146Q8×Dic5C2×D311yescharacteristic
147#4090C2×D311yescharacteristic
148C2×#689—31no—
149D4×Dic5—31no—
150D4×Dic5—31no—
151D4×Dic5—61no—
152D4×Dic5—61no—
153C2×#687—31no—
154#4072—61no—
155#4072C2×D311yescharacteristic
156C2×C4⋊Dic5—31no—
157C2×C4⋊Dic5—61no—
158#4070C2×D311yescharacteristic
159#4036—21no—
160#4036C2×D311yescharacteristic
161#4035—21no—
162#4033C2×D311yescharacteristic
163#4025—21no—
164#4025—21no—
165C5×#103—31no—
166C5×#102—31no—
167C5×C22⋊C8—31no—
168#3967—31no—
169#3967—31no—
170#3967—31no—
171#3964—31no—
172C22⋊#168—31no—
173#3949—31no—
174#3949—31no—
175#3948—31no—
176#3948—31no—
177#3947—31no—
178#3946—31no—
179#3946—31no—
180C8×Dic5—31no—
181#3939—31no—
182#3939—31no—
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C5×D3—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
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—81no—
197C5×#67—24no—
198C2×C5×Dic3—21no—
199C5×D12—21no—
200C5×D12#4112yes—
201C4×C5×D3—24no—
202C5×Dic6—21no—
203C5×Dic6#4112yes—
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—
212D3×Dic5—81no—
213D3×Dic5—81no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C5×C3⋊C8—21no—
217C5×C3⋊C8—21no—
218C2×#235C2×D511yescharacteristic
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×#216C2×D511yescharacteristic
232C2×#215—51no—
233C2×#215C2×D511yescharacteristic
234C2×C4⋊Dic3—51no—
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#835—51no—
246#835—51no—
247#830—51no—
248#830C2×D511yescharacteristic
249#810—51no—
250#810C2×D511yescharacteristic
251#809—51no—
252#809C2×D511yescharacteristic
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)—51no—
259#803—51no—
260C4×C3⋊C8—51no—
261C5×#41—62no—
262C5×#41—62no—
263C2×C5×Q8—31no—
264C2×C5×Q8C22×D311yescharacteristic
265C2×C5×D4—31no—
266C2×C5×D4—61no—
267C22×C4×C5—61no—
268C22×C4×C5C22×D311yescharacteristic
269C22×Dic5—61no—
270C22×Dic5—61no—
271C22×Dic5—61no—
272C2×Dic10C22×D311yescharacteristic
273C5×Q16—62no—
274C5×SD16—62no—
275C2×C5×C8—31no—
276C2×C5×C8—31no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4C22×D311yescharacteristic
279C5×C22⋊C4—21no—
280C22⋊Dic5—21no—
281C22⋊Dic5—61no—
282C22⋊Dic5—61no—
283C22⋊Dic5#6711yescharacteristic
284C22⋊Dic5#6711yescharacteristic
285#689—62no—
286#687—62no—
287C4⋊Dic5—21no—
288C4⋊Dic5—21no—
289C4⋊Dic5—31no—
290C4⋊Dic5—31no—
291C4⋊Dic5—61no—
292C4⋊Dic5—61no—
293C4⋊Dic5—61no—
294C4⋊Dic5#6711yescharacteristic
295C4⋊Dic5#6711yescharacteristic
296C4⋊Dic5C22×D311yescharacteristic
297#683—21no—
298#683—21no—
299#683—21no—
300#683—21no—
301#683—21no—
302C4×Dic5—21no—
303C4×Dic5—21no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C4×Dic5C22×D311yescharacteristic
307C4×Dic5C22×D311yescharacteristic
308C2×#168—31no—
309C2×#168—31no—
310#541—51no—
311#520—151no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—31no—
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×C5×D3—22no—
330C2×C5×D3—41no—
331C2×C5×D3—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—21no—
340C3×Dic5—21no—
341C3×Dic5—21no—
342C3×Dic5—21no—
343C3×Dic5—41no—
344C3×Dic5—41no—
345C5×Dic3—22no—
346C2×C3×Q8—51no—
347C2×C3×Q8C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C2×#67—21no—
350C22×Dic3—101no—
351#235—22no—
352#235—22no—
353C2×D12C22×D511yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—101no—
356C2×C4×D3—101no—
357C2×Dic6C22×D511yescharacteristic
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—22no—
379#216—102no—
380#215—22no—
381#215—102no—
382(C2×D3)⋊C4—101no—
383(C2×D3)⋊C4—101no—
384C4⋊Dic3—51no—
385C4⋊Dic3—51no—
386C4⋊Dic3—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—61no—
396C23×C5C2×#6711yescharacteristic
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—32no—
400C5×Q8—61no—
401C5×D4—32no—
402C5×D4—64no—
403C5×D4—61no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—64no—
409C2×C4×C5—61no—
410C2×C4×C5C2×#6711yescharacteristic
411C2×C4×C5C23×D311yescharacteristic
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—241no—
417C2×Dic5—241no—
418C2×Dic5—241no—
419C2×Dic5C2×#6711yescharacteristic
420C2×Dic5C2×#6711yescharacteristic
421C2×Dic5C2×#6711yescharacteristic
422C2×Dic5C2×#6711yescharacteristic
423Dic10—21no—
424Dic10—21no—
425C5×C8—61no—
426C5×C8—61no—
427#168—61no—
428#168—61no—
429C2×#41—31no—
430C2×Q16—31no—
431C2×Q16—151no—
432C2×SD16—31no—
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—151no—
453C2×C4⋊C4—301no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460#103—31no—
461#103—151no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—31no—
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
476C5×D3—42no—
477C23×C3D4×D511yescharacteristic
478C22×D3—21no—
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—24no—
496C2×Dic3—21no—
497C2×Dic3—101no—
498C2×Dic3—101no—
499C2×Dic3—401no—
500D12—21no—
501D12#71112yes—
502C4×D3—24no—
503C4×D3—401no—
504C4×D3—401no—
505Dic6—21no—
506Dic6#71112yes—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5—62no—
515C22×C5—121no—
516C22×C5—121no—
517C22×C5C22×#6711yescharacteristic
518C4×C5—21no—
519C4×C5—41no—
520C4×C5—41no—
521C4×C5—62no—
522C4×C5D3×#4111yescharacteristic
523C4×C5D3×#4111yescharacteristic
524Dic5—21no—
525Dic5—21no—
526Dic5—21no—
527Dic5—21no—
528Dic5—41no—
529Dic5—41no—
530Dic5—121no—
531Dic5—121no—
532#41—62no—
533#41—62no—
534C2×Q8—31no—
535C2×Q8—51no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—31no—
538C2×D4—61no—
539C22×C4—61no—
540C22×C4—301no—
541C22×C4—301no—
542C22×C4—301no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—62no—
545Q16—302no—
546SD16—62no—
547SD16—302no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—21no—
553C4⋊C4—51no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—101no—
557C4⋊C4—101no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—101no—
561C4⋊C4—101no—
562C4⋊C4—101no—
563C4⋊C4—151no—
564C4⋊C4—151no—
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—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—22no—
587C2×D3—41no—
588C2×D3—41no—
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×C4C2×#71111yescharacteristic
599C3×C4C2×#71111yescharacteristic
600Dic3—22no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5—122no—
605C2×C5#582811yescharacteristic
606C2×C5#583711yescharacteristic
607C2×C5#583811yescharacteristic
608C23—61no—
609C23D5×#6711yescharacteristic
610Q8—21no—
611Q8—21no—
612Q8—32no—
613Q8—61no—
614Q8—101no—
615Q8—101no—
616D4—32no—
617D4—64no—
618D4—61no—
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—64no—
628C2×C4—61no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—301no—
632C2×C4—301no—
633C2×C4—1201no—
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#6592011yescharacteristic
644C2×C3#6610411yescharacteristic
645C2×C3#6611311yescharacteristic
646D3—42no—
647C5#8344611yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—62no—
652C22—121no—
653C22—121no—
654C22C2×D5×#6711yescharacteristic
655C4—21no—
656C4—41no—
657C4—41no—
658C4—62no—
659C4—101no—
660C4—101no—
661C4—101no—
662C4—101no—
663C4—201no—
664C4—201no—
665C4—601no—
666C4—601no—
667C4D3×#71111yescharacteristic
668C4D3×#71111yescharacteristic
669C3#1061194711yescharacteristic, complemented, Sylow
670C2—41no—
671C2—122no—
672C2#1175479511yescharacteristic
673C2#1175510211yescharacteristic
674C2#1175531911yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
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
3. #11751145C2semidirect
5. #11749247C2semidirect
6. #11749245C2semidirect
7. #11749220C2semidirect
8. Dic5×#215C2semidirect
10. #11748445C2semidirect
11. #11748319C2semidirect
12. #11747289C2semidirect
13. #11747263C2semidirect
14. #11747241C2semidirect
15. #11747217C2semidirect
62. #65959D3semidirect
581. C3×C5#3120semidirect
647. C5#83446semidirect
669. C3#10611947semidirect

Maximal subgroups

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

subgroupindex
C3×#659592
#117545132
#117511452
C5×#50472
#117492472
#117492452
#117492202
Dic5×#2152
#117485382
#117484452
#117483192
#117472892
#117472632
#117472412
#117472172
#106119473
#834465