Finite Group Databasebeta

← #14300331

Subgroups — #14300331

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#11756245C211yesmaximal, characteristic
2C3×#65235C211yesmaximal, characteristic, complemented
3#11749509C211yesmaximal, characteristic, complemented
4#11749494C211yesmaximal, characteristic
5C2×#90997C211yesmaximal, characteristic
6C5×#4526C211yesmaximal, characteristic, complemented
7#11746020C211yesmaximal, characteristic, complemented
8#10599754—31nomaximal, Hall
9C22×#1220C2211yescharacteristic
10C23×C3×Dic5C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C4×#1220—21no—
14C4×#1220—21no—
15#91770—21no—
16#91770—21no—
17C22⋊C4×D15—21no—
18#91766—21no—
19C2×C5×#217C2211yescharacteristic
20C2×C5×#217C2211yescharacteristic
21C2×C3×C22⋊Dic5C2211yescharacteristic
22C2×C3×#683—21no—
23C2×Dic3⋊Dic5—21no—
24C2×#6667—21no—
25C3×#3963—21no—
26#90997C414yescomplemented
27#90994—21no—
28#90994—21no—
29#69595—51nomaximal, Hall
30#65820—31no—
31#65247—31no—
32C2×#3938—31no—
33#65239—31no—
34#65235D311yescharacteristic, complemented
35C5×#342—31no—
36#64747—31no—
37C24×C3×C5C2311yescharacteristic
38C23×D15D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5D411yescharacteristic
41C2×#1220—21no—
42C2×#1220—21no—
43C2×#1220—21no—
44C2×#1220—21no—
45C2×#1220C2×C412yes—
46C2×#1220Q812yes—
47C22×Dic15D411yescharacteristic
48C22×Dic15D411yescharacteristic
49C22×Dic15D411yescharacteristic
50C2×C4×D15—21no—
51C2×C4×D15—21no—
52C22×C5×Dic3—21no—
53C22×C5×Dic3—21no—
54C22×C3×Dic5—21no—
55C22×C3×Dic5—21no—
56C22×C3×Dic5—21no—
57C22×C3×Dic5—21no—
58C22×C3×Dic5—42no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61#6719—21no—
62#6719—21no—
63#6714—21no—
64#6714—21no—
65#6712—21no—
66#6712—21no—
67C4×Dic15—21no—
68C4×Dic15—21no—
69C5×#217—21no—
70C5×#217—21no—
71C5×#217—21no—
72C5×#217C2×C412yescomplemented
73C3×C22⋊Dic5—21no—
74C3×C22⋊Dic5C2×C412yescomplemented
75C3×#683—42no—
76Dic3⋊Dic5—42no—
77#6667—42no—
78#5486—51no—
79C3×#385—51no—
80#5213—51no—
81#5210—51no—
82C2×#806—51no—
83#4527—51no—
84#4526D511yescharacteristic, complemented
85C22×C22⋊D5—31no—
86C23×Dic5C2×D311yescharacteristic
87C2×C5×C22⋊C4—31no—
88C2×C5×C22⋊C4—31no—
89C2×C5×C22⋊C4C2×D311yescharacteristic
90C2×C22⋊Dic5—31no—
91C2×C22⋊Dic5C2×D311yescharacteristic
92C4×C22⋊D5—61no—
93C4×C22⋊D5—61no—
94C2×#685—61no—
95C2×C4⋊Dic5—61no—
96C2×#683—21no—
97#4027—61no—
98#4027—61no—
99D5×C22⋊C4—61no—
100#4023—61no—
101#3963—21no—
102#3963—61no—
103#3963—61no—
104#3938—34no—
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×D15—21no—
116C22×D15—21no—
117C22×D15—41no—
118C22×D15—41no—
119C22×D15C4⋊C412yescomplemented
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5—41no—
123C2×C3×C4×C5—41no—
124#1220—22no—
125#1220—22no—
126#1220—22no—
127#1220—22no—
128C2×Dic15—21no—
129C2×Dic15—21no—
130C2×Dic15—21no—
131C2×Dic15—21no—
132C2×Dic15—41no—
133C2×Dic15—41no—
134C2×Dic15C4⋊C412yescomplemented
135C4×D15—81no—
136C4×D15—81no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—41no—
139C2×C5×Dic3—41no—
140C2×C5×Dic3—41no—
141C2×C5×Dic3—41no—
142C2×C5×Dic3—41no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—41no—
148C2×C3×Dic5—41no—
149C2×C3×Dic5—41no—
150C2×C3×Dic5—41no—
151C2×C3×Dic5—41no—
152C2×C3×Dic5—41no—
153C23×C3×C4—51no—
154C22×#67—51no—
155C2×C3×C4⋊C4—101no—
156C2×C3×C22⋊C4—51no—
157C2×C3×C22⋊C4C2×D511yescharacteristic
158C2×#217—51no—
159C2×#217C2×D511yescharacteristic
160C2×#217C2×D511yescharacteristic
161C4×#67—101no—
162C4×#67—101no—
163C2×(C2×D3)⋊C4—101no—
164C2×Dic3⋊C4—101no—
165#67⋊C4—101no—
166#67⋊C4—101no—
167D3×C22⋊C4—101no—
168#877—101no—
169C3×#95—101no—
170C3⋊#95—101no—
171C3⋊#95—101no—
172#806—54no—
173C24×C5C22×D311yescharacteristic
174C23×D5—31no—
175C22×C4×C5—61no—
176C22×C4×C5—61no—
177C22×C4×C5#6711yescharacteristic
178C22×C4×C5#6711yescharacteristic
179C2×C22⋊D5—32no—
180C2×C22⋊D5—32no—
181C2×C22⋊D5—61no—
182C2×C22⋊D5—61no—
183C2×C22⋊D5—61no—
184C2×C22⋊D5—61no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—21no—
189C22×Dic5—31no—
190C22×Dic5—31no—
191C22×Dic5—31no—
192C22×Dic5—42no—
193C2×C4×D5—61no—
194C2×C4×D5—61no—
195C5×C22⋊C4—21no—
196C5×C22⋊C4—21no—
197C5×C22⋊C4—32no—
198C5×C22⋊C4—61no—
199C5×C22⋊C4—61no—
200C5×C22⋊C4—61no—
201C22⋊Dic5—21no—
202C22⋊Dic5—61no—
203C22⋊Dic5—61no—
204C22⋊Dic5C4×D312yescomplemented
205#685—61no—
206#685—61no—
207#685—122no—
208C4⋊Dic5—122no—
209#683—42no—
210#683—61no—
211#683—61no—
212C4×Dic5—61no—
213C4×Dic5—61no—
214#518—151no—
215C2×#99—151no—
216#386—151no—
217#385—51no—
218#385—151no—
219#342—31no—
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×D15—22no—
239C2×D15—41no—
240C2×D15—41no—
241C2×D15—42no—
242C2×D15—81no—
243C3×C4×C5—41no—
244C3×C4×C5—41no—
245Dic15—22no—
246Dic15—41no—
247Dic15—41no—
248C3×Dic5—42no—
249C3×Dic5—42no—
250C5×Dic3—42no—
251C5×Dic3—81no—
252C24×C3C22×D511yescharacteristic
253C23×D3—51no—
254C22×C3×C4—101no—
255C22×C3×C4—101no—
256C22×C3×C4—101no—
257C22×C3×C4—101no—
258C22×C3×C4—202no—
259C22×C3×C4D2011yescharacteristic
260C22×C3×C4D2011yescharacteristic
261C2×#67—52no—
262C2×#67—52no—
263C2×#67—101no—
264C2×#67—101no—
265C2×#67—101no—
266C2×#67—101no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—51no—
270C22×Dic3—51no—
271C22×Dic3—51no—
272C2×C4×D3—101no—
273C2×C4×D3—101no—
274C3×C4⋊C4—202no—
275C3×C22⋊C4—21no—
276C3×C22⋊C4—21no—
277C3×C22⋊C4—52no—
278C3×C22⋊C4—101no—
279#217—21no—
280#217—21no—
281#217—21no—
282#217—101no—
283#217—101no—
284#217C4×D512yescomplemented
285(C2×D3)⋊C4—101no—
286(C2×D3)⋊C4—101no—
287(C2×D3)⋊C4—202no—
288Dic3⋊C4—101no—
289Dic3⋊C4—101no—
290Dic3⋊C4—202no—
291C4×Dic3—101no—
292C4×Dic3—101no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5C2×C4×D311yescharacteristic
296C23×C5#23511yescharacteristic
297C23×C5D3×D411yescharacteristic
298C23×C5D3×D411yescharacteristic
299C23×C5D3×Q811yescharacteristic
300C23×C5#23911yescharacteristic
301C23×C5C2×#6711yescharacteristic
302C22×D5—32no—
303C22×D5—61no—
304C22×D5—61no—
305C22×D5—121no—
306C22×D5—121no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—62no—
312C2×C4×C5—121no—
313C2×C4×C5—121no—
314C2×C4×C5—121no—
315C2×C4×C5—121no—
316C2×C4×C5—121no—
317C22⋊D5—62no—
318C22⋊D5—62no—
319C22⋊D5—62no—
320C22⋊D5—62no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—32no—
326C2×Dic5—41no—
327C2×Dic5—41no—
328C2×Dic5—41no—
329C2×Dic5—41no—
330C2×Dic5—41no—
331C2×Dic5—41no—
332C2×Dic5—61no—
333C2×Dic5—61no—
334C2×Dic5—61no—
335C2×Dic5—61no—
336C2×Dic5—121no—
337C2×Dic5—121no—
338C4×D5—241no—
339C4×D5—241no—
340C22×D4—151no—
341C23×C4—51no—
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—31no—
351C2×C22⋊C4—51no—
352C2×C22⋊C4—151no—
353C2×C22⋊C4—301no—
354C2×C22⋊C4—301no—
355C2×C22⋊C4D3×D511yescharacteristic
356#99—154no—
357#95—101no—
358#95—301no—
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
369D15—42no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3C2×C4×D511yescharacteristic
373C23×C3C2×D2011yescharacteristic
374C23×C3#70911yescharacteristic
375C23×C3D4×D511yescharacteristic
376C23×C3D4×D511yescharacteristic
377C23×C3#71111yescharacteristic
378C23×C3Q8×D511yescharacteristic
379C22×D3—52no—
380C22×D3—101no—
381C22×D3—101no—
382C22×D3—201no—
383C22×D3—201no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4—201no—
393C2×C3×C4—201no—
394C2×C3×C4—201no—
395C2×C3×C4—201no—
396C2×C3×C4—201no—
397C2×C3×C4—201no—
398#67—102no—
399#67—102no—
400#67—102no—
401#67—102no—
402C2×Dic3—22no—
403C2×Dic3—41no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406C2×Dic3—41no—
407C2×Dic3—41no—
408C2×Dic3—52no—
409C2×Dic3—101no—
410C2×Dic3—101no—
411C2×Dic3—101no—
412C2×Dic3—101no—
413C2×Dic3—201no—
414C2×Dic3—201no—
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×C5D3×C4⋊C411yescharacteristic
428C22×C5#89311yescharacteristic
429C22×C5#89411yescharacteristic
430C22×C5#89611yescharacteristic
431C22×C5C4×#6711yescharacteristic
432C22×C5#93711yescharacteristic
433C22×C5#94611yescharacteristic
434C2×D5—62no—
435C2×D5—121no—
436C2×D5—121no—
437C2×D5—122no—
438C2×D5—241no—
439C4×C5—41no—
440C4×C5—41no—
441C4×C5—122no—
442C4×C5—241no—
443Dic5—42no—
444Dic5—42no—
445Dic5—62no—
446Dic5—121no—
447Dic5—121no—
448C24—151no—
449C24C2×D3×D511yescharacteristic
450C2×D4—152no—
451C2×D4—152no—
452C2×D4—301no—
453C2×D4—301no—
454C2×D4—301no—
455C2×D4—301no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—101no—
459C22×C4—101no—
460C22×C4—101no—
461C22×C4—101no—
462C22×C4—151no—
463C22×C4—151no—
464C22×C4—151no—
465C22×C4—202no—
466C22×C4—301no—
467C22×C4—301no—
468C22×C4#120211yescharacteristic
469C22×C4#120211yescharacteristic
470C4⋊C4—202no—
471C4⋊C4—301no—
472C4⋊C4—301no—
473C4⋊C4—602no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—32no—
477C22⋊C4—52no—
478C22⋊C4—61no—
479C22⋊C4—61no—
480C22⋊C4—61no—
481C22⋊C4—101no—
482C22⋊C4—301no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C22⋊C4—301no—
486C22⋊C4—602no—
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×C3C4×D2011yescharacteristic
501C22×C3#402711yescharacteristic
502C22×C3#402811yescharacteristic
503C22×C3#402911yescharacteristic
504C22×C3D5×C4⋊C411yescharacteristic
505C22×C3#404211yescharacteristic
506C22×C3#404311yescharacteristic
507C2×D3—102no—
508C2×D3—201no—
509C2×D3—201no—
510C2×D3—202no—
511C2×D3—401no—
512C3×C4—41no—
513C3×C4—41no—
514C3×C4—202no—
515C3×C4—202no—
516Dic3—42no—
517Dic3—81no—
518Dic3—102no—
519Dic3—201no—
520Dic3—201no—
521C2×C5—21no—
522C2×C5—21no—
523C2×C5—21no—
524C2×C5—21no—
525C2×C5—21no—
526C2×C5—21no—
527C2×C5#498911yescharacteristic
528C2×C5#503211yescharacteristic
529C2×C5#505311yescharacteristic
530D5—122no—
531C23—41no—
532C23—41no—
533C23—152no—
534C23—301no—
535C23—301no—
536C23—601no—
537C23—601no—
538C23#676811yescharacteristic
539C23D15⋊Q811yescharacteristic
540C23#677111yescharacteristic
541C23C4×D3×D511yescharacteristic
542C23C2×#120211yescharacteristic
543C23#679011yescharacteristic
544C23#679011yescharacteristic
545D4—302no—
546D4—302no—
547D4—302no—
548D4—302no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—62no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—121no—
559C2×C4—121no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—121no—
563C2×C4—152no—
564C2×C4—201no—
565C2×C4—201no—
566C2×C4—201no—
567C2×C4—201no—
568C2×C4—201no—
569C2×C4—201no—
570C2×C4—301no—
571C2×C4—301no—
572C2×C4—301no—
573C2×C4—301no—
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#6495711yescharacteristic
585C2×C3#6503011yescharacteristic
586C2×C3#6503111yescharacteristic
587D3—202no—
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—302no—
600C22—602no—
601C22—601no—
602C22—601no—
603C22—1201no—
604C22#9135511yescharacteristic
605C22#9137711yescharacteristic
606C22#9139011yescharacteristic
607C22#9140411yescharacteristic
608C22#9140611yescharacteristic
609C22C4×#120211yescharacteristic
610C22#9157211yescharacteristic
611C4—41no—
612C4—41no—
613C4—122no—
614C4—202no—
615C4—202no—
616C4—241no—
617C4—302no—
618C4—601no—
619C4—601no—
620C3#1059975411yescharacteristic, complemented, Sylow
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—602no—
628C2#1174872911yescharacteristic
629C2#1174917911yescharacteristic
630C2#1174918511yescharacteristic
subgroupG/H
centerC22#91572
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
prime radicalC22×#1220C22
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1867
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#65235C2semidirect
3. #11749509C2semidirect
6. C5×#4526C2semidirect
7. #11746020C2semidirect
26. #90997C4semidirect
34. #65235D3semidirect
72. C5×#217C2×C4semidirect
74. C3×C22⋊Dic5C2×C4semidirect
84. #4526D5semidirect
119. C22×D15C4⋊C4semidirect
134. C2×Dic15C4⋊C4semidirect
204. C22⋊Dic5C4×D3semidirect
284. #217C4×D5semidirect
489. C3×C5#1867semidirect
588. C5#69595semidirect
620. C3#10599754semidirect

Maximal subgroups

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

subgroupindex
#117562452
C3×#652352
#117495092
#117494942
C2×#909972
C5×#45262
#117460202
#105997543
#695955