Finite Group Databasebeta

← #14296926

Subgroups — #14296926

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×Dic6C211yesmaximal, characteristic
2C2×#91108C211yesmaximal, characteristic, complemented
3C2×C5×#824C211yesmaximal, characteristic, complemented
4C3×#65415C211yesmaximal, characteristic
5C2×#90963C211yesmaximal, characteristic, complemented
6C2×#90962C211yesmaximal, characteristic, complemented
7#11748341C211yesmaximal, characteristic
8#10600906—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C22×#1204C412yes—
13C22×D5×Dic3C412yes—
14C2×D5×Dic6—22no—
15C2×D5×Dic6—22no—
16C2×D5×Dic6—22no—
17C2×D5×Dic6—22no—
18C2×D5×Dic6—22no—
19C2×D5×Dic6—22no—
20C2×C3×C5×M16C2211yescharacteristic
21C2×#6710C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C2×C3×#681C2211yescharacteristic
24#91108—22no—
25C5×#824—22no—
26C3×#3952—22no—
27#90963—22no—
28#90962—22no—
29#90955—22no—
30#69990—51nomaximal, Hall
31C22×Q8×D5—31no—
32C2×C5×#101—31no—
33C2×#3968—31no—
34C2×#3956—31no—
35C2×#3956—31no—
36#65415—31no—
37#65415D311yescharacteristic
38C23×C3×D5C2×C411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15C2×C412yes—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×Dic30—21no—
44C2×Dic30—21no—
45C2×Dic30D412yes—
46C2×Dic30D412yes—
47C22×C5×Dic3C2×C412yes—
48C2×C5×Dic6—21no—
49C2×C5×Dic6—21no—
50C2×C5×Dic6—21no—
51C2×C5×Dic6—21no—
52C2×C5×Dic6D412yes—
53C2×C5×Dic6D412yes—
54C22×C3×Dic5C2×C411yescharacteristic
55C2×C3×C4×D5—21no—
56C2×C3×C4×D5—21no—
57C2×C3×C4×D5—21no—
58C2×C3×C4×D5—21no—
59C2×C3×C4×D5D412yes—
60C2×C3×C4×D5D412yes—
61C2×#1204—24no—
62C2×#1204—24no—
63C2×#1204—24no—
64C2×D5×Dic3—24no—
65C2×D5×Dic3—24no—
66C2×D5×Dic3—24no—
67D5×Dic6—28no—
68D5×Dic6—28no—
69D5×Dic6—28no—
70D5×Dic6—28no—
71C3×C5×M16—21no—
72C3×C5×M16—21no—
73C2×C3×C5×C8—21no—
74#6710—21no—
75#6710—21no—
76C2×C3⋊#168—21no—
77C5×#208—21no—
78C5×#208—21no—
79C2×C5×C3⋊C8—21no—
80C3×#681—21no—
81C3×#681—21no—
82C2×C3×#168—21no—
83C23×Dic6—51no—
84C3×#407—51no—
85#5207—51no—
86C2×#824—51no—
87C2×#824—51no—
88C2×#824—51no—
89C2×#824D511yescharacteristic, complemented
90C22×C5×Q8—31no—
91C2×Q8×D5—62no—
92C2×Q8×D5—62no—
93C2×Q8×D5—62no—
94C2×Q8×D5—62no—
95C2×Q8×D5—62no—
96C2×Q8×D5—62no—
97C22×C4×D5—32no—
98C22×C4×D5C2×D311yescharacteristic
99C22×Dic10—31no—
100C22×Dic10—32no—
101C2×C5×M16—31no—
102C2×C5×M16C2×D311yescharacteristic
103C2×#681—31no—
104C2×#681C2×D311yescharacteristic
105C5×#101—62no—
106#3968—62no—
107#3956—62no—
108#3956—62no—
109#3952—22no—
110#3952—62no—
111#1784—151noSylow
112C23×C3×C5C22×C411yescharacteristic
113C22×C3×D5—21no—
114C22×C3×D5—21no—
115C22×C3×D5—24no—
116C22×C3×D5C22⋊C412yes—
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×Dic15—22no—
124C2×Dic15—22no—
125C2×Dic15C22⋊C414yes—
126Dic30—22no—
127Dic30—22no—
128Dic30—22no—
129Dic30—22no—
130C2×C5×Dic3—22no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3C22⋊C414yes—
133C5×Dic6—22no—
134C5×Dic6—22no—
135C5×Dic6—22no—
136C5×Dic6—22no—
137C2×C3×Dic5—21no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5C22⋊C412yes—
140C3×C4×D5—22no—
141C3×C4×D5—22no—
142C3×C4×D5—22no—
143C3×C4×D5—22no—
144#1204—216no—
145D5×Dic3—216no—
146C3×C5×C8—41no—
147C3⋊#168—41no—
148C3×#168—41no—
149C5×C3⋊C8—41no—
150C23×C3×C4—51no—
151C23×Dic3—52no—
152C22×Dic6—51no—
153C22×Dic6—52no—
154C22×Dic6—102no—
155C22×Dic6—102no—
156C22×Dic6—102no—
157C22×Dic6—102no—
158C22×Dic6—102no—
159C22×Dic6—102no—
160C22×Dic6C2×D511yescharacteristic
161C2×C3×M16—51no—
162C2×C3×M16C2×D511yescharacteristic
163C2×#208—51no—
164C2×#208C2×D511yescharacteristic
165C3×C22⋊C8—102no—
166#830—102no—
167#824—22no—
168#824—102no—
169#824—102no—
170#824—102no—
171C23×D5C4×D311yescharacteristic
172C2×C5×Q8—32no—
173C2×C5×Q8—32no—
174C2×C5×Q8—61no—
175C2×C5×Q8—61no—
176C2×C5×Q8—61no—
177C2×C5×Q8—61no—
178C22×C4×C5—32no—
179C22×C4×C5C22×D311yescharacteristic
180C22×Dic5—32no—
181C22×Dic5C4×D311yescharacteristic
182Q8×D5—68no—
183Q8×D5—68no—
184Q8×D5—68no—
185Q8×D5—68no—
186C2×C4×D5—21no—
187C2×C4×D5—21no—
188C2×C4×D5—21no—
189C2×C4×D5—21no—
190C2×C4×D5—64no—
191C2×C4×D5—64no—
192C2×C4×D5—64no—
193C2×C4×D5D1212yes—
194C2×C4×D5#6712yes—
195C2×Dic10—32no—
196C2×Dic10—32no—
197C2×Dic10—64no—
198C2×Dic10—64no—
199C2×Dic10—61no—
200C2×Dic10—61no—
201C2×Dic10—61no—
202C2×Dic10—61no—
203C2×Dic10—64no—
204C5×M16—21no—
205C5×M16—21no—
206C5×M16—61no—
207C5×M16—61no—
208C2×C5×C8—21no—
209C2×C5×C8—61no—
210#681—21no—
211#681—21no—
212#681—61no—
213#681—61no—
214C2×#168—21no—
215C2×#168—61no—
216C23×Q8—151no—
217C2×#101—31no—
218C2×#101—151no—
219C2×#101—151no—
220C2×#101—151no—
221#407—51no—
222#407—151no—
223C22×C3×C5—22no—
224C22×C3×C5C2×C22⋊C411yescharacteristic
225C22×C3×C5C2×C22⋊C411yescharacteristic
226C22×C3×C5C2×C22⋊C411yescharacteristic
227C2×C3×D5—24no—
228C2×C3×D5—24no—
229C2×C3×D5—22no—
230C2×C3×D5—22no—
231C2×C3×D5#10114yescomplemented
232C3×C4×C5#12011yescharacteristic
233C3×C4×C5#12011yescharacteristic
234C3×C4×C5#12011yescharacteristic
235C3×C4×C5#12011yescharacteristic
236Dic15—24no—
237C3×Dic5—22no—
238C5×Dic3—24no—
239C24×C3—51no—
240C22×C3×C4—51no—
241C22×C3×C4—52no—
242C22×C3×C4—52no—
243C22×C3×C4—101no—
244C22×C3×C4—101no—
245C22×C3×C4—101no—
246C22×C3×C4—101no—
247C22×C3×C4C22×D511yescharacteristic
248C22×Dic3—52no—
249C22×Dic3—104no—
250C22×Dic3—104no—
251C22×Dic3—104no—
252C22×Dic3C4×D512yes—
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—52no—
258C2×Dic6—52no—
259C2×Dic6—108no—
260C2×Dic6—108no—
261C2×Dic6—108no—
262C2×Dic6—108no—
263C2×Dic6—104no—
264C2×Dic6—104no—
265C2×Dic6—101no—
266C2×Dic6—101no—
267C2×Dic6—101no—
268C2×Dic6—101no—
269C2×Dic6—104no—
270C2×Dic6D2012yes—
271C2×Dic6C22⋊D512yes—
272C3×M16—21no—
273C3×M16—21no—
274C3×M16—101no—
275C3×M16—101no—
276C2×C3×C8—21no—
277C2×C3×C8—101no—
278#208—21no—
279#208—21no—
280#208—101no—
281#208—101no—
282C2×C3⋊C8—21no—
283C2×C3⋊C8—101no—
284C23×C5C2×C4×D311yescharacteristic
285C22×D5—21no—
286C22×D5—21no—
287C22×D5—24no—
288C22×D5(C2×D3)⋊C412yes—
289C5×Q8—62no—
290C5×Q8—62no—
291C5×Q8—62no—
292C5×Q8—62no—
293C2×C4×C5—34no—
294C2×C4×C5—62no—
295C2×C4×C5—62no—
296C2×C4×C5C2×D1211yescharacteristic
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5D3×D411yescharacteristic
300C2×C4×C5D3×D411yescharacteristic
301C2×C4×C5C2×#6711yescharacteristic
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—34no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5(C2×D3)⋊C412yes—
308C4×D5—22no—
309C4×D5—22no—
310C4×D5—22no—
311C4×D5—22no—
312C4×D5—616no—
313Dic10—616no—
314Dic10—62no—
315Dic10—62no—
316Dic10—62no—
317Dic10—62no—
318C5×C8—41no—
319C5×C8—121no—
320#168—41no—
321#168—121no—
322C22×Q8—31no—
323C22×Q8—152no—
324C22×Q8—151no—
325C22×Q8—302no—
326C22×Q8—302no—
327C22×Q8—302no—
328C22×Q8—302no—
329C22×Q8—302no—
330C22×Q8—302no—
331C23×C4—51no—
332C23×C4—152no—
333C2×M16—31no—
334C2×M16—51no—
335C2×M16—151no—
336C2×M16D3×D511yescharacteristic
337#101—62no—
338#101—302no—
339#101—302no—
340#101—302no—
341C22⋊C8—102no—
342C22⋊C8—302no—
343C2×C3×C5—21no—
344C2×C3×C5—21no—
345C2×C3×C5#37911yescharacteristic
346C2×C3×C5C2×#10112yes—
347C3×D5—24no—
348C23×C3—52no—
349C23×C3—104no—
350C23×C3—101no—
351C23×C3—101no—
352C23×C3C2×C4×D511yescharacteristic
353C2×C3×C4—52no—
354C2×C3×C4—101no—
355C2×C3×C4—101no—
356C2×C3×C4—102no—
357C2×C3×C4—102no—
358C2×C3×C4—102no—
359C2×C3×C4—102no—
360C2×C3×C4C2×D2011yescharacteristic
361C2×C3×C4D4×D511yescharacteristic
362C2×C3×C4D4×D511yescharacteristic
363C2×C3×C4D4×D511yescharacteristic
364C2×C3×C4D4×D511yescharacteristic
365C2×C3×C4C2×C22⋊D511yescharacteristic
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—54no—
369C2×Dic3—1016no—
370C2×Dic3—102no—
371C2×Dic3—102no—
372C2×Dic3#68514yes—
373Dic6—22no—
374Dic6—22no—
375Dic6—22no—
376Dic6—22no—
377Dic6—1016no—
378Dic6—102no—
379Dic6—102no—
380Dic6—102no—
381Dic6—102no—
382C3×C8—41no—
383C3×C8—201no—
384C3⋊C8—41no—
385C3⋊C8—201no—
386C22×C5—22no—
387C22×C5D3×C22⋊C411yescharacteristic
388C22×C5D3×C22⋊C411yescharacteristic
389C22×C5C2×(C2×D3)⋊C411yescharacteristic
390C2×D5—24no—
391C2×D5—24no—
392C2×D5—22no—
393C2×D5—22no—
394C2×D5#82414yescomplemented
395C4×C5—64no—
396C4×C5#88211yescharacteristic
397C4×C5#88211yescharacteristic
398C4×C5#93711yescharacteristic
399C4×C5#93711yescharacteristic
400Dic5—22no—
401Dic5—64no—
402C24—51no—
403C2×Q8—32no—
404C2×Q8—32no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×Q8—61no—
409C2×Q8—152no—
410C2×Q8—152no—
411C2×Q8—304no—
412C2×Q8—304no—
413C2×Q8—304no—
414C2×Q8—308no—
415C2×Q8—308no—
416C2×Q8—308no—
417C2×Q8—308no—
418C2×Q8—301no—
419C2×Q8—301no—
420C2×Q8—301no—
421C2×Q8—301no—
422C22×C4—32no—
423C22×C4—51no—
424C22×C4—52no—
425C22×C4—52no—
426C22×C4—101no—
427C22×C4—101no—
428C22×C4—101no—
429C22×C4—101no—
430C22×C4—152no—
431C22×C4—304no—
432C22×C4—304no—
433C22×C4—304no—
434C22×C4C2×D3×D511yescharacteristic
435M16—21no—
436M16—21no—
437M16—61no—
438M16—61no—
439M16—101no—
440M16—101no—
441M16—301no—
442M16—301no—
443C2×C8—21no—
444C2×C8—61no—
445C2×C8—101no—
446C2×C8—301no—
447C3×C5#178411yescharacteristic, complemented, Hall
448C22×C3—22no—
449C22×C3—54no—
450C22×C3—104no—
451C22×C3—104no—
452C22×C3—102no—
453C22×C3—102no—
454C22×C3D5×C22⋊C411yescharacteristic
455C22×C3D5×C22⋊C411yescharacteristic
456C22×C3C2×#68511yescharacteristic
457C3×C4—102no—
458C3×C4#402811yescharacteristic
459C3×C4#402811yescharacteristic
460C3×C4#408311yescharacteristic
461C3×C4#408311yescharacteristic
462Dic3—24no—
463Dic3—104no—
464C2×C5—21no—
465C2×C5—21no—
466C2×C5#495511yescharacteristic
467C2×C5C2×#82412yes—
468D5—24no—
469C23—52no—
470C23—104no—
471C23—101no—
472C23—101no—
473C23C4×D3×D511yescharacteristic
474Q8—62no—
475Q8—62no—
476Q8—62no—
477Q8—62no—
478Q8—3016no—
479Q8—302no—
480Q8—302no—
481Q8—302no—
482Q8—302no—
483C2×C4—34no—
484C2×C4—52no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—101no—
488C2×C4—101no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—102no—
493C2×C4—154no—
494C2×C4—3016no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4D5×D1211yescharacteristic
498C2×C4D3×D2011yescharacteristic
499C2×C4#677711yescharacteristic
500C2×C4D5×#6711yescharacteristic
501C2×C4D3×C22⋊D511yescharacteristic
502C2×C4#679011yescharacteristic
503C8—41no—
504C8—121no—
505C8—201no—
506C8—601no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—104no—
510C2×C3D5×#10112yes—
511C2×C3#6524411yescharacteristic
512C5#6999011yescharacteristic, complemented, Sylow
513C22—22no—
514C22—54no—
515C22—104no—
516C22—104no—
517C22—102no—
518C22—102no—
519C22D5×(C2×D3)⋊C411yescharacteristic
520C22D3×#68511yescharacteristic
521C22#9147311yescharacteristic
522C4—64no—
523C4—102no—
524C4—304no—
525C4#9147411yescharacteristic
526C4#9147511yescharacteristic
527C4#9147611yescharacteristic
528C4#9157711yescharacteristic
529C3#1060090611yescharacteristic, complemented, Sylow
530C2—21no—
531C2—21no—
532C2—104no—
533C2D5×#82412yes—
534C2#1174894011yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1784
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#91108C2semidirect
3. C2×C5×#824C2semidirect
5. C2×#90963C2semidirect
6. C2×#90962C2semidirect
89. C2×#824D5semidirect
231. C2×C3×D5#101semidirect
394. C2×D5#824semidirect
447. C3×C5#1784semidirect
512. C5#69990semidirect
529. C3#10600906semidirect

Maximal subgroups

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

subgroupindex
C22×D5×Dic62
C2×#911082
C2×C5×#8242
C3×#654152
C2×#909632
C2×#909622
#117483412
#106009063
#699905