Finite Group Databasebeta

← #14296871

Subgroups — #14296871

Order 1920.

1224 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6782C211yesmaximal, characteristic
2C2×#91090C211yesmaximal, characteristic, complemented
3C2×C5×#806C211yesmaximal, characteristic, complemented
4C3×#65232C211yesmaximal, characteristic, complemented
5C2×#90997C211yesmaximal, characteristic, complemented
6C2×#90996C211yesmaximal, characteristic, complemented
7#11749471C211yesmaximal, characteristic, complemented
8#10600820—31nomaximal, Hall
9C22×#1220C2211yescharacteristic
10C22×C5×#67C2211yescharacteristic
11C23×C3×Dic5C2211yescharacteristic
12C22×#1204C411yescharacteristic, complemented
13C22×#1203C411yescharacteristic, complemented
14C22×#1200C411yescharacteristic, complemented
15C2×#6782—22no—
16C2×#6782—22no—
17C2×#6782—22no—
18C2×#6782—22no—
19C2×#6782—22no—
20C2×#6782—22no—
21C22×D3×Dic5C411yescharacteristic, complemented
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26#91090—22no—
27C5×#806—22no—
28C3×#3963—22no—
29#90997—22no—
30#90996—22no—
31#90994—22no—
32#69537—51nomaximal, Hall
33C22×#711—31no—
34C2×C5×#99—31no—
35C2×#3966—31no—
36C2×#3938—31no—
37C2×#3938—31no—
38#65232—31no—
39#65232D311yescharacteristic, complemented
40C24×C3×C5C2311yescharacteristic
41C23×D15C2×C411yescharacteristic
42C23×C5×D3C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C2×#1220—21no—
45C2×#1220—21no—
46C2×#1220—21no—
47C2×#1220—21no—
48C2×#1220D412yes—
49C2×#1220D412yes—
50C22×Dic15—21no—
51C22×Dic15C2×C411yescharacteristic
52C2×C5×#67—21no—
53C2×C5×#67—21no—
54C2×C5×#67—21no—
55C2×C5×#67—21no—
56C2×C5×#67D412yes—
57C2×C5×#67D412yes—
58C22×C5×Dic3—21no—
59C22×C5×Dic3C2×C411yescharacteristic
60C22×C3×Dic5—21no—
61C22×C3×Dic5—21no—
62C22×C3×Dic5—21no—
63C22×C3×Dic5—21no—
64C22×C3×Dic5—21no—
65C22×C3×Dic5C2×C411yescharacteristic
66C22×C3×Dic5C2×C411yescharacteristic
67C22×C3×Dic5D412yes—
68C22×C3×Dic5D412yes—
69C2×#1204—22no—
70C2×#1204—22no—
71C2×#1204—22no—
72C2×#1203—22no—
73C2×#1203—22no—
74C2×#1203—22no—
75C2×#1200—22no—
76C2×#1200—22no—
77C2×#1200—22no—
78#6782—28no—
79#6782—28no—
80#6782—28no—
81#6782—28no—
82C2×D3×Dic5—22no—
83C2×D3×Dic5—22no—
84C2×D3×Dic5—22no—
85C3×C5×C22⋊C4—21no—
86C3×C5×C22⋊C4—21no—
87#6719—21no—
88#6719—21no—
89C5×#217—21no—
90C5×#217—21no—
91C3×C22⋊Dic5—21no—
92C3×C22⋊Dic5—21no—
93C22×#235—51no—
94C3×#381—51no—
95#5211—51no—
96C2×#806—51no—
97C2×#806—51no—
98C2×#806—51no—
99C2×#806D511yescharacteristic, complemented
100C22×C5×D4—31no—
101C22×C22⋊D5—31no—
102C22×C22⋊D5—31no—
103C23×Dic5—31no—
104C23×Dic5C2×D311yescharacteristic
105C2×#711—62no—
106C2×#711—62no—
107C2×#711—62no—
108C2×#711—62no—
109C2×#711—62no—
110C2×#711—62no—
111C22×C4×D5—31no—
112C22×Dic10—31no—
113C2×C5×C22⋊C4—31no—
114C2×C5×C22⋊C4C2×D311yescharacteristic
115C2×C22⋊Dic5—31no—
116C2×C22⋊Dic5C2×D311yescharacteristic
117C5×#99—62no—
118#3966—62no—
119#3963—22no—
120#3963—62no—
121#3938—62no—
122#3938—62no—
123#1782—151noSylow
124C23×C3×C5—42no—
125C23×C3×C5C22×C411yescharacteristic
126C23×C3×C5C2×D411yescharacteristic
127C23×C3×C5C2×D411yescharacteristic
128C23×C3×C5C2×D411yescharacteristic
129C23×C3×C5C2×D411yescharacteristic
130C23×C3×C5C2×D411yescharacteristic
131C23×C3×C5C2×D411yescharacteristic
132C22×D15—21no—
133C22×D15—21no—
134C22×D15—42no—
135C22×D15C22⋊C412yes—
136C22×C5×D3—21no—
137C22×C5×D3—21no—
138C22×C5×D3—42no—
139C22×C5×D3C22⋊C412yes—
140C2×C3×C4×C5—42no—
141C2×C3×C4×C5—41no—
142#1220—22no—
143#1220—22no—
144#1220—22no—
145#1220—22no—
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15—42no—
149C2×Dic15—41no—
150C2×Dic15C22⋊C412yes—
151C5×#67—22no—
152C5×#67—22no—
153C5×#67—22no—
154C5×#67—22no—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—42no—
158C2×C5×Dic3—41no—
159C2×C5×Dic3C22⋊C412yes—
160C2×C3×Dic5—21no—
161C2×C3×Dic5—21no—
162C2×C3×Dic5—21no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—42no—
169C2×C3×Dic5—41no—
170C2×C3×Dic5C22⋊C412yes—
171C2×C3×Dic5C22⋊C412yes—
172#1204—28no—
173#1203—28no—
174#1200—28no—
175D3×Dic5—28no—
176C23×C3×C4—51no—
177C22×#67—51no—
178C22×#67C2×D511yescharacteristic
179C2×#235—102no—
180C2×#235—102no—
181C2×#235—102no—
182C2×#235—102no—
183C2×#235—102no—
184C2×#235—102no—
185C22×D12—51no—
186C22×C4×D3—51no—
187C22×C4×D3—51no—
188C22×Dic6—51no—
189C2×C3×C22⋊C4—51no—
190C2×C3×C22⋊C4C2×D511yescharacteristic
191C2×#217—51no—
192C2×#217C2×D511yescharacteristic
193C3×#95—102no—
194C3⋊#95—102no—
195#806—22no—
196#806—102no—
197#806—102no—
198#806—102no—
199C24×C5—31no—
200C24×C5C22×D311yescharacteristic
201C23×D5—31no—
202C2×C5×D4—32no—
203C2×C5×D4—32no—
204C2×C5×D4—61no—
205C2×C5×D4—61no—
206C2×C5×D4—61no—
207C2×C5×D4—61no—
208C22×C4×C5—21no—
209C22×C4×C5—31no—
210C22×C4×C5—61no—
211C2×C22⋊D5—32no—
212C2×C22⋊D5—32no—
213C2×C22⋊D5—62no—
214C2×C22⋊D5—62no—
215C2×C22⋊D5—61no—
216C2×C22⋊D5—61no—
217C2×C22⋊D5—61no—
218C2×C22⋊D5—61no—
219C2×C22⋊D5—62no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—31no—
226C22×Dic5—62no—
227C22×Dic5—62no—
228C22×Dic5—62no—
229C22×Dic5—61no—
230C22×Dic5C4×D311yescharacteristic
231C22×Dic5C4×D311yescharacteristic
232C22×Dic5D1212yes—
233C22×Dic5#6712yes—
234#711—68no—
235#711—68no—
236#711—68no—
237#711—68no—
238C2×C4×D5—62no—
239C2×C4×D5—62no—
240C2×C4×D5—62no—
241C2×Dic10—62no—
242C2×Dic10—62no—
243C2×Dic10—62no—
244C5×C22⋊C4—21no—
245C5×C22⋊C4—21no—
246C5×C22⋊C4—61no—
247C5×C22⋊C4—61no—
248C22⋊Dic5—21no—
249C22⋊Dic5—21no—
250C22⋊Dic5—61no—
251C22⋊Dic5—61no—
252C22×#41—151no—
253C2×#99—31no—
254C2×#99—151no—
255C2×#99—151no—
256C2×#99—151no—
257#381—51no—
258#381—151no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—22no—
262C22×C3×C5—41no—
263C22×C3×C5—41no—
264C22×C3×C5—41no—
265C22×C3×C5—41no—
266C22×C3×C5C2×C22⋊C411yescharacteristic
267C22×C3×C5C2×C22⋊C411yescharacteristic
268C22×C3×C5C2×C22⋊C411yescharacteristic
269C22×C3×C5#12011yescharacteristic
270C22×C3×C5#12011yescharacteristic
271C22×C3×C5#12011yescharacteristic
272C22×C3×C5#12011yescharacteristic
273C2×D15—22no—
274C2×D15—42no—
275C2×D15—42no—
276C2×D15—42no—
277C2×C5×D3—22no—
278C2×C5×D3—42no—
279C2×C5×D3—42no—
280C2×C5×D3—42no—
281C3×C4×C5—81no—
282Dic15—22no—
283Dic15—81no—
284C3×Dic5—22no—
285C3×Dic5—22no—
286C3×Dic5—81no—
287C5×Dic3—22no—
288C5×Dic3—81no—
289C24×C3C22×D511yescharacteristic
290C23×D3—51no—
291C23×D3C4×D511yescharacteristic
292C22×C3×C4—21no—
293C22×C3×C4—51no—
294C22×C3×C4—51no—
295C22×C3×C4—52no—
296C22×C3×C4—52no—
297C22×C3×C4—101no—
298C22×C3×C4—101no—
299C22×C3×C4—101no—
300C22×C3×C4—101no—
301C22×C3×C4—101no—
302C2×#67—21no—
303C2×#67—21no—
304C2×#67—21no—
305C2×#67—21no—
306C2×#67—52no—
307C2×#67—52no—
308C2×#67—101no—
309C2×#67—101no—
310C2×#67—101no—
311C2×#67—101no—
312C2×#67D2012yes—
313C2×#67C22⋊D512yes—
314C22×Dic3—21no—
315C22×Dic3—51no—
316C22×Dic3—101no—
317C22×Dic3C4×D511yescharacteristic
318#235—108no—
319#235—108no—
320#235—108no—
321#235—108no—
322C2×D12—102no—
323C2×D12—102no—
324C2×D12—102no—
325C2×C4×D3—102no—
326C2×C4×D3—102no—
327C2×C4×D3—102no—
328C2×C4×D3—102no—
329C2×C4×D3—102no—
330C2×C4×D3—102no—
331C2×Dic6—102no—
332C2×Dic6—102no—
333C2×Dic6—102no—
334C3×C22⋊C4—21no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—101no—
337C3×C22⋊C4—101no—
338#217—21no—
339#217—21no—
340#217—101no—
341#217—101no—
342C23×C5—32no—
343C23×C5—42no—
344C23×C5—61no—
345C23×C5—61no—
346C23×C5—122no—
347C23×C5C2×C4×D311yescharacteristic
348C23×C5C2×D1211yescharacteristic
349C23×C5D3×D411yescharacteristic
350C23×C5D3×D411yescharacteristic
351C23×C5D3×D411yescharacteristic
352C23×C5D3×D411yescharacteristic
353C23×C5C2×#6711yescharacteristic
354C22×D5—32no—
355C22×D5—61no—
356C22×D5—61no—
357C22×D5—122no—
358C5×D4—62no—
359C5×D4—62no—
360C5×D4—62no—
361C5×D4—62no—
362C2×C4×C5—32no—
363C2×C4×C5—42no—
364C2×C4×C5—41no—
365C2×C4×C5—61no—
366C2×C4×C5—61no—
367C2×C4×C5—122no—
368C2×C4×C5—121no—
369C22⋊D5—68no—
370C22⋊D5—62no—
371C22⋊D5—62no—
372C22⋊D5—62no—
373C22⋊D5—62no—
374C2×Dic5—21no—
375C2×Dic5—21no—
376C2×Dic5—21no—
377C2×Dic5—21no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—32no—
383C2×Dic5—42no—
384C2×Dic5—41no—
385C2×Dic5—68no—
386C2×Dic5—61no—
387C2×Dic5—61no—
388C2×Dic5—122no—
389C2×Dic5—121no—
390C2×Dic5(C2×D3)⋊C412yes—
391C2×Dic5(C2×D3)⋊C412yes—
392C4×D5—68no—
393Dic10—68no—
394C2×#41—302no—
395C2×#41—302no—
396C2×#41—302no—
397C2×#41—302no—
398C2×#41—302no—
399C2×#41—302no—
400C22×Q8—151no—
401C22×D4—31no—
402C22×D4—151no—
403C22×D4—151no—
404C23×C4—51no—
405C23×C4—151no—
406C23×C4—151no—
407C2×C22⋊C4—31no—
408C2×C22⋊C4—51no—
409C2×C22⋊C4—151no—
410C2×C22⋊C4D3×D511yescharacteristic
411#99—62no—
412#99—302no—
413#99—302no—
414#99—302no—
415#95—102no—
416#95—302no—
417C2×C3×C5—21no—
418C2×C3×C5—21no—
419C2×C3×C5—21no—
420C2×C3×C5—21no—
421C2×C3×C5—21no—
422C2×C3×C5—21no—
423C2×C3×C5#37911yescharacteristic
424C2×C3×C5#41012yes—
425D15—42no—
426C5×D3—42no—
427C23×C3—42no—
428C23×C3C2×C4×D511yescharacteristic
429C23×C3C2×D2011yescharacteristic
430C23×C3D4×D511yescharacteristic
431C23×C3D4×D511yescharacteristic
432C23×C3D4×D511yescharacteristic
433C23×C3D4×D511yescharacteristic
434C23×C3C2×C22⋊D511yescharacteristic
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—42no—
438C22×D3—52no—
439C22×D3—101no—
440C22×D3—101no—
441C22×D3—202no—
442C22×D3#68512yes—
443C2×C3×C4—42no—
444C2×C3×C4—41no—
445C2×C3×C4—52no—
446C2×C3×C4—52no—
447C2×C3×C4—101no—
448C2×C3×C4—101no—
449C2×C3×C4—102no—
450C2×C3×C4—102no—
451C2×C3×C4—101no—
452C2×C3×C4—101no—
453C2×C3×C4—102no—
454C2×C3×C4—102no—
455C2×C3×C4—202no—
456C2×C3×C4—201no—
457#67—22no—
458#67—22no—
459#67—22no—
460#67—22no—
461#67—102no—
462#67—102no—
463#67—102no—
464#67—102no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—42no—
468C2×Dic3—41no—
469C2×Dic3—52no—
470C2×Dic3—101no—
471C2×Dic3—101no—
472C2×Dic3—202no—
473C2×Dic3—201no—
474C2×Dic3#68512yes—
475D12—108no—
476C4×D3—108no—
477C4×D3—108no—
478Dic6—108no—
479C22×C5—22no—
480C22×C5—22no—
481C22×C5—22no—
482C22×C5—41no—
483C22×C5—41no—
484C22×C5—41no—
485C22×C5—41no—
486C22×C5—62no—
487C22×C5—122no—
488C22×C5—122no—
489C22×C5—122no—
490C22×C5D3×C22⋊C411yescharacteristic
491C22×C5D3×C22⋊C411yescharacteristic
492C22×C5#88211yescharacteristic
493C22×C5#88211yescharacteristic
494C22×C5C2×(C2×D3)⋊C411yescharacteristic
495C22×C5#93711yescharacteristic
496C22×C5#93711yescharacteristic
497C2×D5—62no—
498C2×D5—122no—
499C2×D5—122no—
500C2×D5—122no—
501C4×C5—62no—
502C4×C5—81no—
503C4×C5—241no—
504Dic5—22no—
505Dic5—22no—
506Dic5—62no—
507Dic5—81no—
508Dic5—241no—
509C24—31no—
510C24—151no—
511C24C2×D3×D511yescharacteristic
512#41—308no—
513#41—308no—
514#41—308no—
515#41—308no—
516C2×Q8—302no—
517C2×Q8—302no—
518C2×Q8—302no—
519C2×D4—32no—
520C2×D4—32no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—152no—
526C2×D4—152no—
527C2×D4—302no—
528C2×D4—302no—
529C2×D4—302no—
530C2×D4—301no—
531C2×D4—301no—
532C2×D4—301no—
533C2×D4—301no—
534C22×C4—21no—
535C22×C4—31no—
536C22×C4—51no—
537C22×C4—51no—
538C22×C4—52no—
539C22×C4—52no—
540C22×C4—61no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—101no—
544C22×C4—101no—
545C22×C4—101no—
546C22×C4—151no—
547C22×C4—302no—
548C22×C4—302no—
549C22×C4—302no—
550C22×C4—302no—
551C22×C4—302no—
552C22×C4—302no—
553C22×C4—301no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—61no—
557C22⋊C4—61no—
558C22⋊C4—101no—
559C22⋊C4—101no—
560C22⋊C4—301no—
561C22⋊C4—301no—
562C3×C5#178211yescharacteristic, complemented, Hall
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3D5×C22⋊C411yescharacteristic
571C22×C3D5×C22⋊C411yescharacteristic
572C22×C3#402811yescharacteristic
573C22×C3#402811yescharacteristic
574C22×C3C2×#68511yescharacteristic
575C22×C3#408311yescharacteristic
576C22×C3#408311yescharacteristic
577C2×D3—22no—
578C2×D3—42no—
579C2×D3—42no—
580C2×D3—42no—
581C2×D3—102no—
582C2×D3—202no—
583C2×D3—202no—
584C2×D3—202no—
585C3×C4—81no—
586C3×C4—102no—
587C3×C4—102no—
588C3×C4—401no—
589Dic3—22no—
590Dic3—81no—
591Dic3—102no—
592Dic3—401no—
593C2×C5—21no—
594C2×C5—21no—
595C2×C5—21no—
596C2×C5—21no—
597C2×C5—21no—
598C2×C5—21no—
599C2×C5—122no—
600C2×C5#495511yescharacteristic
601C2×C5#500612yes—
602D5—122no—
603C23—32no—
604C23—42no—
605C23—61no—
606C23—61no—
607C23—122no—
608C23—152no—
609C23—301no—
610C23—301no—
611C23—602no—
612C23C4×D3×D511yescharacteristic
613C23D5×D1211yescharacteristic
614C23D3×D2011yescharacteristic
615C23#677711yescharacteristic
616C23D5×#6711yescharacteristic
617C23D3×C22⋊D511yescharacteristic
618C23#679011yescharacteristic
619Q8—308no—
620D4—62no—
621D4—62no—
622D4—62no—
623D4—62no—
624D4—308no—
625D4—302no—
626D4—302no—
627D4—302no—
628D4—302no—
629C2×C4—32no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—52no—
633C2×C4—52no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—101no—
637C2×C4—101no—
638C2×C4—101no—
639C2×C4—101no—
640C2×C4—102no—
641C2×C4—102no—
642C2×C4—102no—
643C2×C4—102no—
644C2×C4—122no—
645C2×C4—121no—
646C2×C4—152no—
647C2×C4—202no—
648C2×C4—201no—
649C2×C4—308no—
650C2×C4—308no—
651C2×C4—301no—
652C2×C4—301no—
653C2×C4—602no—
654C2×C4—601no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3#6502912yes—
662C2×C3#6524411yescharacteristic
663D3—42no—
664D3—202no—
665C5#6953711yescharacteristic, complemented, Sylow
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—62no—
674C22—122no—
675C22—122no—
676C22—122no—
677C22—302no—
678C22—602no—
679C22—602no—
680C22—602no—
681C22D5×(C2×D3)⋊C411yescharacteristic
682C22D3×#68511yescharacteristic
683C22#9147311yescharacteristic
684C22#9147411yescharacteristic
685C22#9147511yescharacteristic
686C22#9147611yescharacteristic
687C22#9157711yescharacteristic
688C4—62no—
689C4—81no—
690C4—102no—
691C4—102no—
692C4—241no—
693C4—302no—
694C4—401no—
695C4—1201no—
696C3#1060082011yescharacteristic, complemented, Sylow
697C2—21no—
698C2—21no—
699C2—21no—
700C2—21no—
701C2—21no—
702C2—21no—
703C2—122no—
704C2—602no—
705C2#1174712912yes—
706C2#1174894011yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6782C2
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1782
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. C2×#91090C2semidirect
3. C2×C5×#806C2semidirect
4. C3×#65232C2semidirect
5. C2×#90997C2semidirect
6. C2×#90996C2semidirect
7. #11749471C2semidirect
12. C22×#1204C4semidirect
13. C22×#1203C4semidirect
14. C22×#1200C4semidirect
21. C22×D3×Dic5C4semidirect
39. #65232D3semidirect
99. C2×#806D5semidirect
562. C3×C5#1782semidirect
665. C5#69537semidirect
696. C3#10600820semidirect

Maximal subgroups

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

subgroupindex
C22×#67822
C2×#910902
C2×C5×#8062
C3×#652322
C2×#909972
C2×#909962
#117494712
#106008203
#695375