Finite Group Databasebeta

← #14300326

Subgroups — #14300326

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755410C211yesmaximal, characteristic
2#11751311C211yesmaximal, characteristic, complemented
3C5×#5213C211yesmaximal, characteristic
4C3×#65499C211yesmaximal, characteristic, complemented
5C2×#90996C211yesmaximal, characteristic
6#11746020C211yesmaximal, characteristic, complemented
7#11746019C211yesmaximal, characteristic, complemented
8#10600390—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C22×C5×#67C2211yescharacteristic
11C2×#6719C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×#6712—21no—
14C2×C5×#217C2211yescharacteristic
15C2×C5×(C2×D3)⋊C4—21no—
16C2×C3×C22⋊Dic5C2211yescharacteristic
17C2×C3×C22⋊Dic5C2211yescharacteristic
18C2×C3×#683—21no—
19#67⋊Dic5—21no—
20#67⋊Dic5—21no—
21D3×C22⋊Dic5—21no—
22Dic5×#67—21no—
23Dic5×#67—21no—
24#91529—21no—
25#91115—21no—
26C5×C3⋊#95—21no—
27C3×#3963—21no—
28#90996C414yescomplemented
29#69595—51nomaximal, Hall
30#66132—31no—
31C5×#386—31no—
32C2×#3966—31no—
33#65499—31no—
34#65499D311yescharacteristic, complemented
35#64747—31no—
36#64747—31no—
37C24×C3×C5C2311yescharacteristic
38C23×C5×D3D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—42no—
43C22×Dic15—21no—
44C22×Dic15D411yescharacteristic
45C22×Dic15D411yescharacteristic
46C2×C5×#67—21no—
47C2×C5×#67—21no—
48C2×C5×#67—21no—
49C2×C5×#67—21no—
50C2×C5×#67C2×C412yes—
51C2×C5×#67Q812yes—
52C22×C5×Dic3—21no—
53C22×C5×Dic3D411yescharacteristic
54C22×C3×Dic5—21no—
55C22×C3×Dic5D411yescharacteristic
56C22×C3×Dic5D411yescharacteristic
57C2×D3×Dic5—21no—
58C2×D3×Dic5—21no—
59#6719—21no—
60#6719—21no—
61#6719—21no—
62#6719C2×C412yescomplemented
63#6712—42no—
64C5×#217—21no—
65C5×#217—21no—
66C5×(C2×D3)⋊C4—42no—
67C3×C22⋊Dic5—21no—
68C3×C22⋊Dic5—21no—
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5C2×C412yescomplemented
71C3×#683—42no—
72Dic3⋊Dic5—21no—
73Dic3⋊Dic5—21no—
74(C2×D3)⋊Dic5—21no—
75(C2×D3)⋊Dic5—21no—
76Dic3×Dic5—21no—
77Dic3×Dic5—21no—
78#5486—51no—
79C3×#385—51no—
80#5213D511yescharacteristic
81#5210—51no—
82C2×#806—51no—
83#4527—51no—
84#4526—51no—
85C22×C5×D4—31no—
86C23×C4×C5C2×D311yescharacteristic
87C2×C5×C22⋊C4—31no—
88C2×C5×C22⋊C4—61no—
89C2×C22⋊Dic5—31no—
90C2×C22⋊Dic5—31no—
91C2×C22⋊Dic5—61no—
92C2×C22⋊Dic5C2×D311yescharacteristic
93C2×C22⋊Dic5C2×D311yescharacteristic
94D4×Dic5—61no—
95D4×Dic5—61no—
96D4×Dic5—61no—
97D4×Dic5—61no—
98#4072—61no—
99C2×#683—21no—
100C2×#683—61no—
101C5×#95—61no—
102#3966—34no—
103#3963—21no—
104#3963—61no—
105#1867—151noSylow
106C23×C3×C5—41no—
107C23×C3×C5—41no—
108C23×C3×C5C22×C411yescharacteristic
109C23×C3×C5C2×D411yescharacteristic
110C23×C3×C5C2×D411yescharacteristic
111C23×C3×C5C2×D411yescharacteristic
112C23×C3×C5C2×Q811yescharacteristic
113C23×C3×C5#4111yescharacteristic
114C23×C3×C5#4111yescharacteristic
115C22×C5×D3—21no—
116C22×C5×D3—21no—
117C22×C5×D3—41no—
118C22×C5×D3—41no—
119C22×C5×D3C4⋊C412yescomplemented
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5—41no—
127C2×Dic15—22no—
128C2×Dic15—21no—
129C2×Dic15—21no—
130C2×Dic15—41no—
131C2×Dic15—41no—
132C2×Dic15—41no—
133C2×Dic15—41no—
134C5×#67—22no—
135C5×#67—22no—
136C5×#67—22no—
137C5×#67—22no—
138C2×C5×Dic3—21no—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—41no—
141C2×C5×Dic3—41no—
142C2×C5×Dic3—41no—
143C2×C5×Dic3C4⋊C412yescomplemented
144C2×C3×Dic5—22no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—41no—
148C2×C3×Dic5—41no—
149C2×C3×Dic5—41no—
150C2×C3×Dic5—41no—
151D3×Dic5—81no—
152D3×Dic5—81no—
153C23×C3×C4C2×D511yescharacteristic
154C22×#67C2×D511yescharacteristic
155C2×C3×C4⋊C4—101no—
156C2×C3×C22⋊C4—51no—
157C2×C3×C22⋊C4—51no—
158C2×#217—51no—
159C2×#217—51no—
160C2×#217C2×D511yescharacteristic
161C4×#67—101no—
162C4×#67—101no—
163C2×(C2×D3)⋊C4—21no—
164C2×Dic3⋊C4—101no—
165#67⋊C4—101no—
166#67⋊C4—101no—
167D3×C22⋊C4—101no—
168#877—101no—
169C3×#95—101no—
170C3⋊#95—21no—
171C3⋊#95—101no—
172#806—54no—
173C24×C5—31no—
174C24×C5C22×D311yescharacteristic
175C2×C5×D4—32no—
176C2×C5×D4—32no—
177C2×C5×D4—61no—
178C2×C5×D4—61no—
179C2×C5×D4—61no—
180C2×C5×D4—61no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—31no—
185C22×C4×C5—42no—
186C22×C4×C5—61no—
187C22×Dic5—21no—
188C22×Dic5—31no—
189C22×Dic5—31no—
190C22×Dic5—61no—
191C22×Dic5—61no—
192C22×Dic5—61no—
193C22×Dic5#6711yescharacteristic
194C22×Dic5#6711yescharacteristic
195C5×C22⋊C4—61no—
196C5×C22⋊C4—61no—
197C5×C22⋊C4—122no—
198C22⋊Dic5—21no—
199C22⋊Dic5—21no—
200C22⋊Dic5—21no—
201C22⋊Dic5—32no—
202C22⋊Dic5—61no—
203C22⋊Dic5—61no—
204C22⋊Dic5—61no—
205C22⋊Dic5—61no—
206C22⋊Dic5—61no—
207C22⋊Dic5C4×D312yescomplemented
208C4⋊Dic5—61no—
209C4⋊Dic5—61no—
210#683—42no—
211#683—122no—
212C4×Dic5—61no—
213C4×Dic5—61no—
214#518—151no—
215C2×#99—151no—
216#386—31no—
217#385—51no—
218#385—151no—
219#342—151no—
220#342—151no—
221C22×C3×C5—21no—
222C22×C3×C5—21no—
223C22×C3×C5—21no—
224C22×C3×C5—21no—
225C22×C3×C5—21no—
226C22×C3×C5—21no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5—41no—
230C22×C3×C5—41no—
231C22×C3×C5C2×C4⋊C411yescharacteristic
232C22×C3×C5C4×D411yescharacteristic
233C22×C3×C5C4×D411yescharacteristic
234C22×C3×C5#12011yescharacteristic
235C22×C3×C5C22⋊Q811yescharacteristic
236C22×C3×C5C22⋊Q811yescharacteristic
237C22×C3×C5#12311yescharacteristic
238C2×C5×D3—22no—
239C2×C5×D3—41no—
240C2×C5×D3—41no—
241C2×C5×D3—42no—
242C2×C5×D3—81no—
243C3×C4×C5—42no—
244Dic15—42no—
245Dic15—41no—
246Dic15—41no—
247C3×Dic5—42no—
248C3×Dic5—41no—
249C3×Dic5—41no—
250C5×Dic3—22no—
251C5×Dic3—81no—
252C24×C3C22×D511yescharacteristic
253C23×D3C22⋊D511yescharacteristic
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—42no—
258C22×C3×C4—51no—
259C22×C3×C4—51no—
260C22×C3×C4—101no—
261C2×#67—21no—
262C2×#67—21no—
263C2×#67—21no—
264C2×#67—21no—
265C2×#67Dic1012yes—
266C2×#67C4×D512yes—
267C22×Dic3—21no—
268C22×Dic3—51no—
269C22×Dic3—51no—
270C22×Dic3—101no—
271C22×Dic3C22⋊D511yescharacteristic
272C2×C4×D3—101no—
273C2×C4×D3—101no—
274C3×C4⋊C4—202no—
275C3×C22⋊C4—52no—
276C3×C22⋊C4—101no—
277C3×C22⋊C4—101no—
278C3×C22⋊C4—101no—
279#217—21no—
280#217—21no—
281#217—52no—
282#217—101no—
283#217—101no—
284#217—101no—
285(C2×D3)⋊C4—42no—
286(C2×D3)⋊C4—101no—
287(C2×D3)⋊C4—101no—
288Dic3⋊C4—101no—
289Dic3⋊C4—101no—
290Dic3⋊C4—202no—
291C4×Dic3—101no—
292C4×Dic3—101no—
293C23×C5—32no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—61no—
297C23×C5—61no—
298C23×C5—121no—
299C23×C5—121no—
300C23×C5C2×C4×D311yescharacteristic
301C23×C5#23511yescharacteristic
302C23×C5D3×D411yescharacteristic
303C23×C5D3×D411yescharacteristic
304C23×C5D3×Q811yescharacteristic
305C23×C5#23911yescharacteristic
306C23×C5C2×#6711yescharacteristic
307C5×D4—62no—
308C5×D4—62no—
309C5×D4—62no—
310C5×D4—62no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—32no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—61no—
320C2×C4×C5—61no—
321C2×C4×C5—121no—
322C2×C4×C5—121no—
323C2×C4×C5—121no—
324C2×Dic5—22no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—41no—
328C2×Dic5—41no—
329C2×Dic5—41no—
330C2×Dic5—41no—
331C2×Dic5—62no—
332C2×Dic5—61no—
333C2×Dic5—61no—
334C2×Dic5—121no—
335C2×Dic5—121no—
336C2×Dic5—121no—
337C2×Dic5—121no—
338C2×Dic5—241no—
339C2×Dic5—241no—
340C22×D4—31no—
341C23×C4D3×D511yescharacteristic
342C4×D4—301no—
343C4×D4—301no—
344C4×D4—301no—
345C4×D4—301no—
346#117—301no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4—301no—
349C2×C22⋊C4—31no—
350C2×C22⋊C4—51no—
351C2×C22⋊C4—51no—
352C2×C22⋊C4—61no—
353C2×C22⋊C4—151no—
354C2×C22⋊C4—151no—
355C2×C22⋊C4—301no—
356#99—154no—
357#95—61no—
358#95—101no—
359#95—301no—
360C2×C3×C5—21no—
361C2×C3×C5—21no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5—21no—
365C2×C3×C5—21no—
366C2×C3×C5#38511yescharacteristic
367C2×C3×C5B(4,𝔽2)11yescharacteristic
368C2×C3×C5#45811yescharacteristic
369C5×D3—42no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3C2×Dic1011yescharacteristic
373C23×C3C2×C4×D511yescharacteristic
374C23×C3D4×D511yescharacteristic
375C23×C3D4×D511yescharacteristic
376C23×C3#71111yescharacteristic
377C23×C3#71111yescharacteristic
378C23×C3C2×C22⋊D511yescharacteristic
379C22×D3—21no—
380C22×D3—21no—
381C22×D3—41no—
382C22×D3—41no—
383C22×D3#68312yescomplemented
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—102no—
392C2×C3×C4—101no—
393C2×C3×C4—101no—
394C2×C3×C4—201no—
395C2×C3×C4—201no—
396C2×C3×C4—201no—
397C2×C3×C4—201no—
398#67—22no—
399#67—22no—
400#67—22no—
401#67—22no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406C2×Dic3—41no—
407C2×Dic3—102no—
408C2×Dic3—101no—
409C2×Dic3—101no—
410C2×Dic3—201no—
411C2×Dic3—201no—
412C2×Dic3—201no—
413C2×Dic3—201no—
414C2×Dic3#68312yescomplemented
415C4×D3—401no—
416C4×D3—401no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—21no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—62no—
428C22×C5—122no—
429C22×C5—121no—
430C22×C5—121no—
431C22×C5—241no—
432C22×C5D3×C4⋊C411yescharacteristic
433C22×C5#89311yescharacteristic
434C22×C5#89411yescharacteristic
435C22×C5#89611yescharacteristic
436C22×C5C4×#6711yescharacteristic
437C22×C5#93711yescharacteristic
438C22×C5#94611yescharacteristic
439C4×C5—42no—
440C4×C5—62no—
441C4×C5—241no—
442Dic5—42no—
443Dic5—41no—
444Dic5—41no—
445Dic5—122no—
446Dic5—121no—
447Dic5—121no—
448C24—31no—
449C24C2×D3×D511yescharacteristic
450C2×D4—32no—
451C2×D4—32no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4—61no—
455C2×D4—61no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—31no—
460C22×C4—42no—
461C22×C4—51no—
462C22×C4—51no—
463C22×C4—61no—
464C22×C4—101no—
465C22×C4—151no—
466C22×C4—151no—
467C22×C4—301no—
468C22×C4—301no—
469C22×C4—301no—
470C4⋊C4—202no—
471C4⋊C4—301no—
472C4⋊C4—301no—
473C4⋊C4—602no—
474C22⋊C4—52no—
475C22⋊C4—61no—
476C22⋊C4—61no—
477C22⋊C4—101no—
478C22⋊C4—101no—
479C22⋊C4—101no—
480C22⋊C4—122no—
481C22⋊C4—152no—
482C22⋊C4—301no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C22⋊C4—301no—
486C22⋊C4—301no—
487C42—301no—
488C42—301no—
489C3×C5#186711yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3#402411yescharacteristic
501C22×C3#402411yescharacteristic
502C22×C3#402711yescharacteristic
503C22×C3#402711yescharacteristic
504C22×C3C2×#68311yescharacteristic
505C22×C3#408111yescharacteristic
506C22×C3#408311yescharacteristic
507C2×D3—22no—
508C2×D3—41no—
509C2×D3—41no—
510C2×D3—42no—
511C2×D3—81no—
512C3×C4—42no—
513C3×C4—202no—
514C3×C4—201no—
515C3×C4—201no—
516Dic3—22no—
517Dic3—81no—
518Dic3—202no—
519Dic3—201no—
520Dic3—201no—
521C2×C5—21no—
522C2×C5—21no—
523C2×C5—21no—
524C2×C5—21no—
525C2×C5—21no—
526C2×C5—21no—
527C2×C5—122no—
528C2×C5#498911yescharacteristic
529C2×C5#503211yescharacteristic
530C2×C5#505311yescharacteristic
531C23—32no—
532C23—41no—
533C23—41no—
534C23—61no—
535C23—61no—
536C23—121no—
537C23—121no—
538C23D3×Dic1011yescharacteristic
539C23#676811yescharacteristic
540C23#677211yescharacteristic
541C23C4×D3×D511yescharacteristic
542C23D5×#6711yescharacteristic
543C23D3×C22⋊D511yescharacteristic
544C23#679011yescharacteristic
545D4—62no—
546D4—62no—
547D4—62no—
548D4—62no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—32no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—102no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—201no—
566C2×C4—201no—
567C2×C4—201no—
568C2×C4—201no—
569C2×C4—302no—
570C2×C4—301no—
571C2×C4—301no—
572C2×C4—601no—
573C2×C4—601no—
574C2×C4—601no—
575C2×C4—601no—
576C2×C4—1201no—
577C2×C4—1201no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3#6523511yescharacteristic
585C2×C3#6532111yescharacteristic
586C2×C3#6534211yescharacteristic
587D3—42no—
588C5#6959511yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—62no—
600C22—122no—
601C22—121no—
602C22—121no—
603C22—241no—
604C22D3×#68311yescharacteristic
605C22#9140611yescharacteristic
606C22#9141011yescharacteristic
607C22#9142311yescharacteristic
608C22#9143211yescharacteristic
609C22#9144011yescharacteristic
610C22#9157711yescharacteristic
611C4—42no—
612C4—62no—
613C4—202no—
614C4—201no—
615C4—201no—
616C4—241no—
617C4—602no—
618C4—601no—
619C4—601no—
620C3#1060039011yescharacteristic, complemented, Sylow
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—122no—
628C2#1174889211yescharacteristic
629C2#1174893911yescharacteristic
630C2#1174952511yescharacteristic
subgroupG/H
centerC22#91577
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5#120
prime radicalC22×C5×#67C22
cosocleC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1867
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751311C2semidirect
4. C3×#65499C2semidirect
6. #11746020C2semidirect
7. #11746019C2semidirect
28. #90996C4semidirect
34. #65499D3semidirect
62. #6719C2×C4semidirect
70. C3×C22⋊Dic5C2×C4semidirect
119. C22×C5×D3C4⋊C4semidirect
143. C2×C5×Dic3C4⋊C4semidirect
207. C22⋊Dic5C4×D3semidirect
383. C22×D3#683semidirect
414. C2×Dic3#683semidirect
489. C3×C5#1867semidirect
588. C5#69595semidirect
620. C3#10600390semidirect

Maximal subgroups

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

subgroupindex
#117554102
#117513112
C5×#52132
C3×#654992
C2×#909962
#117460202
#117460192
#106003903
#695955