Finite Group Databasebeta

← #14329883

Subgroups — #14329883

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91778C211yesmaximal, characteristic
2C3×C5×#387C211yesmaximal, characteristic
3#11751077C211yesmaximal, characteristic
4C4⋊C4×Dic15C211yesmaximal, characteristic
5#11751073C211yesmaximal, characteristic
6C4×#6712C211yesmaximal, characteristic
7C4×#6712C211yesmaximal, characteristic
8#11750755C211yesmaximal, characteristic
9#11750753C211yesmaximal, characteristic
10#11750753C211yesmaximal, characteristic
11#11750750C211yesmaximal, characteristic
12#11750750C211yesmaximal, characteristic
13#11750750C211yesmaximal, characteristic
14#11750748C211yesmaximal, characteristic
15#11750748C211yesmaximal, characteristic
16#10606699—31nomaximal, Hall
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C42×C5C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C2×#6712C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×C4×Dic15C2211yescharacteristic
33C2×C4×Dic15C2211yescharacteristic
34C2×C4×Dic15C2211yescharacteristic
35C2×C4×Dic15C2211yescharacteristic
36C2×C4×Dic15C2211yescharacteristic
37C2×C4×Dic15C2211yescharacteristic
38C2×C4×Dic15C2211yescharacteristic
39C2×C4×Dic15C2211yescharacteristic
40#91778C418yescomplemented
41C3×C5×#95C2211yescharacteristic
42C3×C5×#95C2211yescharacteristic
43C3×C5×#95C2211yescharacteristic
44C3×C5×#95C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#74968—51nomaximal, Hall
54C2×#4035—31no—
55C5×#387D311yescharacteristic
56C4⋊C4×Dic5—31no—
57#65262—31no—
58#65261—31no—
59C4×#683—31no—
60C4×#683—31no—
61#64943—31no—
62#64941—31no—
63#64941—31no—
64#64938—31no—
65#64938—31no—
66#64938—31no—
67#64936—31no—
68#64936—31no—
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C3×C5×C4⋊C4—41no—
85C3×C5×C4⋊C4C2×C414yes—
86C3×C42×C5—41no—
87C4⋊Dic15—22no—
88C4⋊Dic15C2×C414yes—
89#6712—22no—
90#6712—22no—
91#6712—22no—
92#6712—22no—
93#6712—41no—
94#6712C2×C414yes—
95#6712C2×C414yes—
96#6712C2×C414yes—
97#6712C2×C414yes—
98#6712Q814yes—
99C4×Dic15—22no—
100C4×Dic15—22no—
101C4×Dic15—22no—
102C4×Dic15—22no—
103C4×Dic15—41no—
104C4×Dic15—41no—
105C4×Dic15—41no—
106C4×Dic15C2×C414yes—
107C2×#889—51no—
108C3×#387D511yescharacteristic
109#4976—51no—
110Dic3×C4⋊C4—51no—
111#4972—51no—
112C4×Dic3⋊C4—51no—
113C4×Dic3⋊C4—51no—
114#4654—51no—
115#4652—51no—
116#4652—51no—
117#4649—51no—
118#4649—51no—
119#4649—51no—
120#4647—51no—
121#4647—51no—
122C2×C5×C4⋊C4C2×D311yescharacteristic
123C2×C5×C4⋊C4C2×D311yescharacteristic
124C2×C42×C5C2×D311yescharacteristic
125C2×C4⋊Dic5—31no—
126C2×C4⋊Dic5—31no—
127C2×#683—31no—
128C2×#683—31no—
129C2×#683—31no—
130C2×#683—31no—
131C2×#683—31no—
132C2×#683—31no—
133C2×#683—31no—
134C2×#683—31no—
135C2×#683—31no—
136C2×#683—31no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145#4035—38no—
146C5×#95C2×D311yescharacteristic
147C5×#95C2×D311yescharacteristic
148C5×#95C2×D311yescharacteristic
149C5×#95C2×D311yescharacteristic
150#3963—31no—
151#3963—31no—
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#2370—151noSylow
159C23×C3×C5C2411yescharacteristic
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5—21no—
163C2×C3×C4×C5—21no—
164C2×C3×C4×C5—21no—
165C2×C3×C4×C5—21no—
166C2×C3×C4×C5—21no—
167C2×C3×C4×C5—21no—
168C2×C3×C4×C5—21no—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5C22×C412yes—
178C2×C3×C4×C5C22×C412yes—
179C2×C3×C4×C5C22×C412yes—
180C2×C3×C4×C5C2×Q812yes—
181C2×Dic15—21no—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15C22×C412yes—
197C2×Dic15C22×C412yes—
198C2×Dic15C22×C412yes—
199C2×Dic15C22×C412yes—
200C2×Dic15C2×Q812yes—
201C2×Dic15C2×Q812yes—
202C2×Dic15#4112yes—
203C2×Dic15#4112yes—
204C2×Dic15#4112yes—
205C2×C3×C4⋊C4C2×D511yescharacteristic
206C2×C3×C4⋊C4C2×D511yescharacteristic
207C2×C3×C42C2×D511yescharacteristic
208C2×C4⋊Dic3—51no—
209C2×C4⋊Dic3—51no—
210C2×Dic3⋊C4—51no—
211C2×Dic3⋊C4—51no—
212C2×Dic3⋊C4—51no—
213C2×Dic3⋊C4—51no—
214C2×Dic3⋊C4—51no—
215C2×Dic3⋊C4—51no—
216C2×Dic3⋊C4—51no—
217C2×Dic3⋊C4—51no—
218C2×Dic3⋊C4—51no—
219C2×Dic3⋊C4—51no—
220C2×C4×Dic3—51no—
221C2×C4×Dic3—51no—
222C2×C4×Dic3—51no—
223C2×C4×Dic3—51no—
224C2×C4×Dic3—51no—
225C2×C4×Dic3—51no—
226C2×C4×Dic3—51no—
227C2×C4×Dic3—51no—
228#889—58no—
229C3×#95C2×D511yescharacteristic
230C3×#95C2×D511yescharacteristic
231C3×#95C2×D511yescharacteristic
232C3×#95C2×D511yescharacteristic
233C3⋊#95—51no—
234C3⋊#95—51no—
235C3⋊#95—51no—
236C3⋊#95—51no—
237C3⋊#95—51no—
238C3⋊#95—51no—
239C3⋊#95—51no—
240C3⋊#95—51no—
241C22×C4×C5C22×D311yescharacteristic
242C22×C4×C5C22×D311yescharacteristic
243C22×C4×C5C22×D311yescharacteristic
244C22×C4×C5C22×D311yescharacteristic
245C22×C4×C5C22×D311yescharacteristic
246C22×C4×C5C22×D311yescharacteristic
247C22×C4×C5C22×D311yescharacteristic
248C22×Dic5—31no—
249C22×Dic5—31no—
250C22×Dic5—31no—
251C22×Dic5—31no—
252C22×Dic5—31no—
253C22×Dic5—31no—
254C22×Dic5—31no—
255C22×Dic5—31no—
256C5×C4⋊C4—41no—
257C5×C4⋊C4C4×D314yes—
258C42×C5—41no—
259C4⋊Dic5—34no—
260C4⋊Dic5—62no—
261#683—34no—
262#683—34no—
263#683—34no—
264#683—34no—
265#683—34no—
266#683—62no—
267#683—62no—
268#683—62no—
269#683—62no—
270#683—121no—
271C4×Dic5—34no—
272C4×Dic5—62no—
273C4×Dic5—62no—
274C4×Dic5—62no—
275C4×Dic5—62no—
276C4×Dic5—121no—
277C4×Dic5—121no—
278C4×Dic5—121no—
279C2×#125—151no—
280#389—151no—
281#389—151no—
282#389—151no—
283#389—151no—
284#387—151no—
285#387—151no—
286#387—151no—
287#387D1511yescharacteristic
288C4×C4⋊C4—151no—
289C4×C4⋊C4—151no—
290C4×C4⋊C4—151no—
291C4×C4⋊C4—151no—
292C4×C4⋊C4—151no—
293C4×C4⋊C4—151no—
294C22×C3×C5C23×C411yescharacteristic
295C22×C3×C5C22×Q811yescharacteristic
296C22×C3×C5C2×#4111yescharacteristic
297C22×C3×C5C2×#4111yescharacteristic
298C22×C3×C5C2×#4111yescharacteristic
299C22×C3×C5H(5,𝔽2)11yescharacteristic
300C22×C3×C52−1+411yescharacteristic
301C3×C4×C5—22no—
302C3×C4×C5—22no—
303C3×C4×C5—22no—
304C3×C4×C5—22no—
305C3×C4×C5—41no—
306C3×C4×C5—41no—
307C3×C4×C5—41no—
308Dic15—22no—
309Dic15—22no—
310Dic15—22no—
311Dic15—22no—
312Dic15—22no—
313Dic15—22no—
314Dic15—41no—
315Dic15C4×Q814yes—
316C22×C3×C4C22×D511yescharacteristic
317C22×C3×C4C22×D511yescharacteristic
318C22×C3×C4C22×D511yescharacteristic
319C22×C3×C4C22×D511yescharacteristic
320C22×C3×C4C22×D511yescharacteristic
321C22×C3×C4C22×D511yescharacteristic
322C22×C3×C4C22×D511yescharacteristic
323C22×Dic3—51no—
324C22×Dic3—51no—
325C22×Dic3—51no—
326C22×Dic3—51no—
327C22×Dic3—51no—
328C22×Dic3—51no—
329C22×Dic3—51no—
330C22×Dic3—51no—
331C3×C4⋊C4—41no—
332C3×C4⋊C4C4×D514yes—
333C3×C42—41no—
334C4⋊Dic3—54no—
335C4⋊Dic3—102no—
336Dic3⋊C4—54no—
337Dic3⋊C4—54no—
338Dic3⋊C4—54no—
339Dic3⋊C4—54no—
340Dic3⋊C4—54no—
341Dic3⋊C4—102no—
342Dic3⋊C4—102no—
343Dic3⋊C4—102no—
344Dic3⋊C4—102no—
345Dic3⋊C4—201no—
346C4×Dic3—54no—
347C4×Dic3—102no—
348C4×Dic3—102no—
349C4×Dic3—102no—
350C4×Dic3—102no—
351C4×Dic3—201no—
352C4×Dic3—201no—
353C4×Dic3—201no—
354C23×C5C23×D311yescharacteristic
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—21no—
361C2×C4×C5—21no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—21no—
365C2×C4×C5—21no—
366C2×C4×C5—21no—
367C2×C4×C5—21no—
368C2×C4×C5—21no—
369C2×C4×C5—21no—
370C2×C4×C5—21no—
371C2×C4×C5—21no—
372C2×C4×C5C2×C4×D312yes—
373C2×C4×C5C2×C4×D312yes—
374C2×C4×C5C2×C4×D312yes—
375C2×C4×C5D3×Q812yes—
376C2×Dic5—32no—
377C2×Dic5—32no—
378C2×Dic5—32no—
379C2×Dic5—32no—
380C2×Dic5—32no—
381C2×Dic5—32no—
382C2×Dic5—32no—
383C2×Dic5—32no—
384C2×Dic5—32no—
385C2×Dic5—61no—
386C2×Dic5—61no—
387C2×Dic5—61no—
388C2×Dic5—61no—
389C2×Dic5—61no—
390C2×Dic5—61no—
391C2×Dic5—61no—
392C2×Dic5—61no—
393C2×Dic5—61no—
394C2×Dic5—61no—
395C2×Dic5—61no—
396C2×Dic5—61no—
397C2×Dic5—61no—
398C2×Dic5—61no—
399C2×Dic5—61no—
400#125—158no—
401C2×C4⋊C4—151no—
402C2×C4⋊C4—151no—
403C2×C4⋊C4—151no—
404C2×C4⋊C4—151no—
405C2×C4⋊C4—151no—
406C2×C4⋊C4—151no—
407C2×C4⋊C4—151no—
408C2×C4⋊C4—151no—
409C2×C4⋊C4—151no—
410C2×C4⋊C4—151no—
411C2×C4⋊C4—151no—
412C2×C4⋊C4—151no—
413C2×C4⋊C4C2×D1511yescharacteristic
414C2×C4⋊C4C2×D1511yescharacteristic
415C2×C42—151no—
416C2×C42—151no—
417C2×C42—151no—
418C2×C42—151no—
419C2×C42—151no—
420C2×C42—151no—
421C2×C42—151no—
422C2×C42—151no—
423C2×C42C2×D1511yescharacteristic
424#95—151no—
425#95—151no—
426#95—151no—
427#95—151no—
428#95—151no—
429#95—151no—
430#95—151no—
431#95—151no—
432#95C2×D1511yescharacteristic
433#95C2×D1511yescharacteristic
434#95C2×D1511yescharacteristic
435#95C2×D1511yescharacteristic
436C2×C3×C5C2×C4×Q811yescharacteristic
437C2×C3×C5C4×#4111yescharacteristic
438C2×C3×C5#52011yescharacteristic
439C2×C3×C5#55211yescharacteristic
440C2×C3×C5#55311yescharacteristic
441C2×C3×C5#55411yescharacteristic
442C2×C3×C5#55711yescharacteristic
443C23×C3C23×D511yescharacteristic
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4C2×C4×D512yes—
462C2×C3×C4C2×C4×D512yes—
463C2×C3×C4C2×C4×D512yes—
464C2×C3×C4Q8×D512yes—
465C2×Dic3—52no—
466C2×Dic3—52no—
467C2×Dic3—52no—
468C2×Dic3—52no—
469C2×Dic3—52no—
470C2×Dic3—52no—
471C2×Dic3—52no—
472C2×Dic3—52no—
473C2×Dic3—52no—
474C2×Dic3—101no—
475C2×Dic3—101no—
476C2×Dic3—101no—
477C2×Dic3—101no—
478C2×Dic3—101no—
479C2×Dic3—101no—
480C2×Dic3—101no—
481C2×Dic3—101no—
482C2×Dic3—101no—
483C2×Dic3—101no—
484C2×Dic3—101no—
485C2×Dic3—101no—
486C2×Dic3—101no—
487C2×Dic3—101no—
488C2×Dic3—101no—
489C22×C5C22×C4×D311yescharacteristic
490C22×C5#100411yescharacteristic
491C22×C5C2×D3×Q811yescharacteristic
492C22×C5D3×#4111yescharacteristic
493C22×C5D3×#4111yescharacteristic
494C22×C5D3×#4111yescharacteristic
495C22×C5#101011yescharacteristic
496C4×C5—22no—
497C4×C5—22no—
498C4×C5—22no—
499C4×C5—22no—
500C4×C5—41no—
501C4×C5—41no—
502C4×C5—41no—
503Dic5—34no—
504Dic5—62no—
505Dic5—62no—
506Dic5—62no—
507Dic5—62no—
508Dic5—62no—
509Dic5—62no—
510Dic5—121no—
511C22×C4—151no—
512C22×C4—151no—
513C22×C4—151no—
514C22×C4—151no—
515C22×C4—151no—
516C22×C4—151no—
517C22×C4—151no—
518C22×C4—151no—
519C22×C4C22×D1511yescharacteristic
520C22×C4C22×D1511yescharacteristic
521C22×C4C22×D1511yescharacteristic
522C22×C4C22×D1511yescharacteristic
523C22×C4C22×D1511yescharacteristic
524C22×C4C22×D1511yescharacteristic
525C22×C4C22×D1511yescharacteristic
526C4⋊C4—41no—
527C4⋊C4—154no—
528C4⋊C4—154no—
529C4⋊C4—154no—
530C4⋊C4—154no—
531C4⋊C4—154no—
532C4⋊C4—154no—
533C4⋊C4—302no—
534C4⋊C4—302no—
535C4⋊C4—302no—
536C4⋊C4—302no—
537C4⋊C4—302no—
538C4⋊C4—601no—
539C4⋊C4C4×D1514yes—
540C42—41no—
541C42—154no—
542C42—302no—
543C42—302no—
544C42—302no—
545C42—302no—
546C42—601no—
547C42—601no—
548C42—601no—
549C3×C5#237011yescharacteristic, complemented, Hall
550C22×C3C22×C4×D511yescharacteristic
551C22×C3#414411yescharacteristic
552C22×C3C2×Q8×D511yescharacteristic
553C22×C3D5×#4111yescharacteristic
554C22×C3D5×#4111yescharacteristic
555C22×C3D5×#4111yescharacteristic
556C22×C3#415011yescharacteristic
557C3×C4—22no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—41no—
562C3×C4—41no—
563C3×C4—41no—
564Dic3—54no—
565Dic3—102no—
566Dic3—102no—
567Dic3—102no—
568Dic3—102no—
569Dic3—102no—
570Dic3—102no—
571Dic3—201no—
572C2×C5#552211yescharacteristic
573C2×C5#554611yescharacteristic
574C2×C5C4×D3×Q811yescharacteristic
575C2×C5#563611yescharacteristic
576C2×C5#566111yescharacteristic
577C2×C5#568511yescharacteristic
578C2×C5#570811yescharacteristic
579C23C23×D1511yescharacteristic
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—152no—
598C2×C4—152no—
599C2×C4—152no—
600C2×C4—152no—
601C2×C4—152no—
602C2×C4—152no—
603C2×C4—152no—
604C2×C4—152no—
605C2×C4—152no—
606C2×C4—301no—
607C2×C4—301no—
608C2×C4—301no—
609C2×C4—301no—
610C2×C4—301no—
611C2×C4—301no—
612C2×C4—301no—
613C2×C4—301no—
614C2×C4—301no—
615C2×C4—301no—
616C2×C4—301no—
617C2×C4—301no—
618C2×C4—301no—
619C2×C4—301no—
620C2×C4—301no—
621C2×C4C2×C4×D1512yes—
622C2×C4C2×C4×D1512yes—
623C2×C4C2×C4×D1512yes—
624C2×C4Q8×D1512yes—
625C2×C3#6585611yescharacteristic
626C2×C3#6588011yescharacteristic
627C2×C3C4×Q8×D511yescharacteristic
628C2×C3#6597011yescharacteristic
629C2×C3#6599511yescharacteristic
630C2×C3#6601911yescharacteristic
631C2×C3#6604211yescharacteristic
632C5#7496811yescharacteristic, complemented, Sylow
633C22C22×C4×D1511yescharacteristic
634C22#9209511yescharacteristic
635C22C2×Q8×D1511yescharacteristic
636C22#41×D1511yescharacteristic
637C22#41×D1511yescharacteristic
638C22#41×D1511yescharacteristic
639C22#9210111yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—154no—
648C4—302no—
649C4—302no—
650C4—302no—
651C4—302no—
652C4—302no—
653C4—302no—
654C4—601no—
655C3#1060669911yescharacteristic, complemented, Sylow
656C2#1175628111yescharacteristic
657C2#1175630511yescharacteristic
658C2C4×Q8×D1511yescharacteristic
659C2#1175639511yescharacteristic
660C2#1175642011yescharacteristic
661C2#1175644411yescharacteristic
662C2#1175646711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#387C2
socle, prime radical, cosocleC23×C3×C5C24
hypercenter#387D15
hypocenterC3×C5#2370
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
40. #91778C4semidirect
549. C3×C5#2370semidirect
632. C5#74968semidirect
655. C3#10606699semidirect

Maximal subgroups

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

subgroupindex
C2×#917782
C3×C5×#3872
#117510772
C4⋊C4×Dic152
#117510732
C4×#67122
#117507552
#117507532
#117507502
#117507482
#106066993
#749685