Finite Group Databasebeta

← #14424598

Subgroups — #14424598

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92101C211yesmaximal, characteristic
2C3×#66159C211yesmaximal, characteristic, complemented
3C22×#6662C211yesmaximal, characteristic, complemented
4C2×#91315C211yesmaximal, characteristic, complemented
5C5×#5234C211yesmaximal, characteristic, complemented
6#11748564C214yesmaximal, complemented
7#11748552C214yesmaximal, complemented
8#11748415C211yesmaximal, characteristic, complemented
9#11748411C211yesmaximal, characteristic, complemented
10#10610410—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12#92101—24no—
13#92101—24no—
14C2×Q8×D15—21no—
15C2×#6819—22no—
16C2×#6819—21no—
17C2×#6817C2212yes—
18C2×#6817C2211yescharacteristic
19C22×Dic30C2212yes—
20C22×Dic30C2211yescharacteristic
21C22×C3×Dic10C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4090—21no—
25C3×#4082—21no—
26C3×#4081—22no—
27C3×#4072C2211yescharacteristic
28C3×#4070C2214yes—
29C2×#6662—24no—
30C2×#6662C2212yes—
31C2×#6662C2214yes—
32#91315—24no—
33C2×#6658C2212yes—
34C5×#830C2214yes—
35#90974C2212yes—
36#90974C2214yes—
37#90968C2212yes—
38#83411—51nomaximal, Hall
39C2×#4150—31no—
40#66159D311yescharacteristic, complemented
41C2×#4055—31no—
42C22×Dic20—31no—
43C5×#408—31no—
44#65409—31no—
45#65402—31no—
46#65028—34no—
47#65022—34no—
48C3×C5×#41—22no—
49C3×C5×#41—22no—
50C2×C3×C5×Q8D411yescharacteristic
51C2×C3×C5×D4D412yes—
52C2×C3×C5×D4D411yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—22no—
56C2×#1220—21no—
57C22×Dic15—22no—
58C22×Dic15—21no—
59Q8×D15—28no—
60#6819—216no—
61#6819—28no—
62#6817—22no—
63#6817—24no—
64#6817—24no—
65#6817D414yes—
66C2×D60C2311yescharacteristic
67C2×C4×D15—22no—
68C2×C4×D15—21no—
69C2×Dic30—22no—
70C2×Dic30—21no—
71C2×Dic30—22no—
72C2×Dic30—24no—
73C2×Dic30—24no—
74C2×Dic30D414yes—
75C2×Dic30C2311yescharacteristic
76C2×Dic30C2312yes—
77C22×C3×Dic5—21no—
78C2×C3×Dic10—22no—
79C2×C3×Dic10—22no—
80C2×C3×Dic10—21no—
81C2×C3×Dic10C2312yes—
82C5×#208—22no—
83C2×C5×C3⋊C8—22no—
84C2×C5×C3⋊C8C2312yes—
85C2×C5×C3⋊C8C2312yes—
86C3×C22⋊Dic5—21no—
87C3×C22⋊Dic5—24no—
88C3×C4⋊Dic5C2312yes—
89C3×#683—24no—
90C3×C4×Dic5—21no—
91#6662—24no—
92#6662—28no—
93#6658—24no—
94C2×#1010—51no—
95C3×#536—51no—
96C22×#216—51no—
97C2×#942—51no—
98#5234D511yescharacteristic, complemented
99#5050—54no—
100#5047—54no—
101#5004—51no—
102#5002—51no—
103C2×C5×#41C2×D311yescharacteristic
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—61no—
107C2×#711—62no—
108C2×#711—61no—
109C2×#709—31no—
110C2×#709—32no—
111C22×Dic10—31no—
112C22×Dic10—32no—
113C22×Dic10C2×D311yescharacteristic
114C2×C5×M16—31no—
115C22×C5×C8—31no—
116#4090—21no—
117#4082—21no—
118#4081—22no—
119#4072C2×D311yescharacteristic
120#4070C2×D314yes—
121#4055—64no—
122C2×Dic20—32no—
123C2×Dic20—34no—
124C2×Dic20—64no—
125C2×#677—32no—
126C5×C22⋊C8—34no—
127#3953—32no—
128#3948—32no—
129#3948—34no—
130#3011—151noSylow
131C23×C3×C5C2×D412yes—
132C23×C3×C5C2×D411yescharacteristic
133C22×D15—21no—
134C3×C5×Q8—22no—
135C3×C5×D4—24no—
136C3×C5×D4—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2411yescharacteristic
144#1220—28no—
145#1220—24no—
146C2×Dic15—28no—
147C2×Dic15—24no—
148C2×Dic15—21no—
149C2×Dic15—22no—
150D60—21no—
151D60C2×D412yes—
152C4×D15—28no—
153C4×D15—24no—
154Dic30—28no—
155Dic30—24no—
156Dic30—22no—
157Dic30—21no—
158Dic30C2×D412yes—
159Dic30C2×D414yes—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—42no—
163C3×Dic10—22no—
164C3×Dic10—22no—
165C3×Dic10—42no—
166C5×C3⋊C8—22no—
167C5×C3⋊C8—22no—
168C2×C3×#41C2×D511yescharacteristic
169C22×C3×Q8—51no—
170#1010—104no—
171#1010—104no—
172C2×D3×Q8—101no—
173C2×#237—102no—
174C2×#237—101no—
175C2×#235—51no—
176C2×#235—52no—
177C22×Dic6—51no—
178C22×Dic6—52no—
179C3×C4⋊Q8—101no—
180C3×#124—101no—
181C3×#123—102no—
182C3×C22⋊Q8—54no—
183C3×#117—51no—
184C2×#216—52no—
185C2×#216—54no—
186C2×#216—104no—
187#942—104no—
188C2×#215—52no—
189C2×#208C2×D511yescharacteristic
190C22×C3⋊C8C2×D511yescharacteristic
191#830C2×D514yes—
192#810—52no—
193#810—54no—
194#809—52no—
195C5×#41—22no—
196C5×#41—22no—
197C2×C5×Q8#6711yescharacteristic
198C2×C5×D4#6712yes—
199C2×C5×D4#6711yescharacteristic
200C22×C4×C5C22×D312yes—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—62no—
203C2×C22⋊D5—61no—
204C22×Dic5—21no—
205C22×Dic5—62no—
206C22×Dic5—61no—
207Q8×D5—68no—
208#711—616no—
209#711—68no—
210#709—34no—
211#709—64no—
212#709—64no—
213#709—62no—
214C2×D20—31no—
215C2×C4×D5—62no—
216C2×C4×D5—61no—
217C2×Dic10—22no—
218C2×Dic10—22no—
219C2×Dic10—21no—
220C2×Dic10—34no—
221C2×Dic10—32no—
222C2×Dic10—31no—
223C2×Dic10—64no—
224C2×Dic10—64no—
225C2×Dic10—62no—
226C2×Dic10—62no—
227C2×Dic10—61no—
228C2×Dic10C22×D312yes—
229C5×M16—62no—
230C2×C5×C8—32no—
231C2×C5×C8—32no—
232C2×C5×C8—62no—
233C22⋊Dic5—24no—
234C22⋊Dic5—21no—
235C4⋊Dic5C22×D312yes—
236#683—24no—
237C4×Dic5—21no—
238Dic20—68no—
239Dic20—64no—
240#677—64no—
241C2×2−1+4—151no—
242C2×#137—151no—
243C22×Q16—151no—
244#536—51no—
245#452—154no—
246#451—154no—
247#419—151no—
248#416—151no—
249#408—31no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—24no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—22no—
256C2×D15—42no—
257C3×C4×C5—22no—
258C3×C4×C5#12012yes—
259C3×C4×C5C22×D411yescharacteristic
260C3×C4×C5C22×D411yescharacteristic
261Dic15—22no—
262Dic15—24no—
263C3×Dic5—42no—
264C3×Dic5—42no—
265C3×#41—22no—
266C3×#41—22no—
267C2×C3×Q8—52no—
268C2×C3×Q8—101no—
269C2×C3×Q8—102no—
270C2×C3×Q8—102no—
271C2×C3×Q8D2011yescharacteristic
272C2×C3×D4D2012yes—
273C2×C3×D4D2011yescharacteristic
274C22×C3×C4—101no—
275C22×C3×C4C22×D512yes—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—102no—
278C2×#67—101no—
279C22×Dic3—102no—
280C22×Dic3—101no—
281D3×Q8—108no—
282#237—1016no—
283#237—108no—
284#235—54no—
285#235—104no—
286#235—104no—
287#235—102no—
288C2×D12—51no—
289C2×C4×D3—102no—
290C2×C4×D3—101no—
291C2×Dic6—54no—
292C2×Dic6—52no—
293C2×Dic6—51no—
294C2×Dic6—104no—
295C2×Dic6—104no—
296C2×Dic6—102no—
297C2×Dic6—101no—
298C2×Dic6—102no—
299C3×C4⋊C4—52no—
300C3×C4⋊C4—104no—
301C3×C22⋊C4—101no—
302C3×C22⋊C4—104no—
303C3×C42—101no—
304#216—104no—
305#216—108no—
306#215—104no—
307#208—22no—
308C2×C3⋊C8—22no—
309C2×C3⋊C8C22×D512yes—
310C2×C3⋊C8C22×D512yes—
311C23×C5C2×#6712yes—
312C23×C5C2×#6711yescharacteristic
313C22×D5—61no—
314C5×Q8—22no—
315C5×D4—24no—
316C5×D4—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5D3×D412yes—
320C2×C4×C5D3×D412yes—
321C2×C4×C5C2×#6712yes—
322C2×C4×C5C2×#6711yescharacteristic
323C2×C4×C5C23×D311yescharacteristic
324C22⋊D5—68no—
325C22⋊D5—64no—
326C2×Dic5—22no—
327C2×Dic5—22no—
328C2×Dic5—42no—
329C2×Dic5—68no—
330C2×Dic5—64no—
331C2×Dic5—62no—
332C2×Dic5—61no—
333D20—32no—
334D20—61no—
335C4×D5—68no—
336C4×D5—64no—
337Dic10—22no—
338Dic10—22no—
339Dic10—34no—
340Dic10—32no—
341Dic10—42no—
342Dic10—68no—
343Dic10—64no—
344Dic10—61no—
345Dic10—62no—
346C5×C8—62no—
347C5×C8—62no—
3482−1+4—304no—
3492−1+4—304no—
350C2×#41—151no—
351C2×#41—152no—
352C2×#41—302no—
353C2×#41—301no—
354C2×#41D3×D511yescharacteristic
355C22×Q8—51no—
356C22×Q8—151no—
357C22×Q8—152no—
358C22×Q8—301no—
359#137—304no—
360C2×Q16—154no—
361C2×Q16—152no—
362C2×Q16—304no—
363C2×SD16—152no—
364C2×M16—31no—
365C22×C8—31no—
366C4⋊Q8—101no—
367#124—101no—
368#123—102no—
369C22⋊Q8—54no—
370#117—51no—
371#103—152no—
372#103—154no—
373#102—152no—
374C22⋊C8—34no—
375C2×C3×C5—22no—
376C2×C3×C5—42no—
377C2×C3×C5C2×#12011yescharacteristic
378C2×C3×C5#57812yes—
379D15—42no—
380C23×C3C2×D2012yes—
381C23×C3C2×D2011yescharacteristic
382C22×D3—101no—
383C3×Q8—22no—
384C3×Q8—102no—
385C3×Q8—102no—
386C3×Q8—202no—
387C3×D4—24no—
388C3×D4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—102no—
392C2×C3×C4—102no—
393C2×C3×C4—202no—
394C2×C3×C4C2×D2012yes—
395C2×C3×C4C2×D2011yescharacteristic
396C2×C3×C4D4×D512yes—
397C2×C3×C4D4×D512yes—
398C2×C3×C4C23×D511yescharacteristic
399#67—108no—
400#67—104no—
401C2×Dic3—108no—
402C2×Dic3—102no—
403C2×Dic3—101no—
404C2×Dic3—104no—
405D12—52no—
406D12—101no—
407C4×D3—108no—
408C4×D3—104no—
409Dic6—54no—
410Dic6—52no—
411Dic6—108no—
412Dic6—101no—
413Dic6—102no—
414Dic6—104no—
415C3⋊C8—22no—
416C3⋊C8—22no—
417C22×C5—22no—
418C22×C5—22no—
419C22×C5—24no—
420C22×C5#93712yes—
421C22×C5C22×#6711yescharacteristic
422C2×D5—62no—
423C2×D5—122no—
424C4×C5—22no—
425C4×C5#93712yes—
426C4×C5C2×D3×D411yescharacteristic
427C4×C5C2×D3×D411yescharacteristic
428Dic5—42no—
429Dic5—42no—
430Dic5—64no—
431Dic5—62no—
432#41—22no—
433#41—22no—
434#41—154no—
435#41—304no—
436#41—304no—
437#41—3016no—
438#41—308no—
439#41—302no—
440C2×Q8—52no—
441C2×Q8—101no—
442C2×Q8—102no—
443C2×Q8—102no—
444C2×Q8—154no—
445C2×Q8—152no—
446C2×Q8—151no—
447C2×Q8—304no—
448C2×Q8—304no—
449C2×Q8—308no—
450C2×Q8—302no—
451C2×Q8—301no—
452C2×Q8—302no—
453C2×Q8#120211yescharacteristic
454C2×D4—151no—
455C2×D4—302no—
456C2×D4—301no—
457C2×D4#120212yes—
458C2×D4#120211yescharacteristic
459C22×C4—101no—
460C22×C4—302no—
461C22×C4—301no—
462C22×C4—302no—
463C22×C4—301no—
464C22×C4C2×D3×D512yes—
465C22×C4C2×D3×D511yescharacteristic
466Q16—308no—
467Q16—304no—
468SD16—304no—
469M16—62no—
470C2×C8—32no—
471C2×C8—32no—
472C2×C8—62no—
473C4⋊C4—52no—
474C4⋊C4—104no—
475C22⋊C4—101no—
476C22⋊C4—104no—
477C42—101no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—24no—
482C22×C3#402812yes—
483C22×C3C22×D2011yescharacteristic
484C2×D3—102no—
485C2×D3—202no—
486C3×C4—22no—
487C3×C4—202no—
488C3×C4—202no—
489C3×C4#402812yes—
490C3×C4C2×D4×D511yescharacteristic
491C3×C4C2×D4×D511yescharacteristic
492Dic3—104no—
493Dic3—102no—
494C2×C5—22no—
495C2×C5—42no—
496C2×C5C2×#93711yescharacteristic
497C2×C5#583812yes—
498D5—122no—
499C23—301no—
500C23C2×#120212yes—
501C23C2×#120211yescharacteristic
502Q8—22no—
503Q8—102no—
504Q8—102no—
505Q8—154no—
506Q8—152no—
507Q8—202no—
508Q8—308no—
509Q8—302no—
510Q8—301no—
511Q8—304no—
512D4—24no—
513D4—22no—
514D4—152no—
515D4—308no—
516D4—304no—
517D4—301no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—102no—
521C2×C4—102no—
522C2×C4—202no—
523C2×C4—308no—
524C2×C4—308no—
525C2×C4—302no—
526C2×C4—301no—
527C2×C4—304no—
528C2×C4—304no—
529C2×C4C2×#120212yes—
530C2×C4C2×#120211yescharacteristic
531C2×C4#679012yes—
532C2×C4#679012yes—
533C2×C4C22×D3×D511yescharacteristic
534C8—62no—
535C8—62no—
536C2×C3—22no—
537C2×C3—42no—
538C2×C3C2×#402811yescharacteristic
539C2×C3#6608712yes—
540D3—202no—
541C5#8341111yescharacteristic, complemented, Sylow
542C22—22no—
543C22—24no—
544C22—22no—
545C22—302no—
546C22—602no—
547C22#9157212yes—
548C22C22×#120211yescharacteristic
549C4—22no—
550C4—202no—
551C4—202no—
552C4—304no—
553C4—302no—
554C4#9157212yes—
555C4C2×#679011yescharacteristic
556C4C2×#679011yescharacteristic
557C3#1061041011yescharacteristic, complemented, Sylow
558C2—22no—
559C2—42no—
560C2—602no—
561C2#1175531212yes—
562C2C2×#9157211yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×#92101C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3011
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#66159C2semidirect
3. C22×#6662C2semidirect
4. C2×#91315C2semidirect
5. C5×#5234C2semidirect
6. #11748564C2semidirect
7. #11748552C2semidirect
8. #11748415C2semidirect
9. #11748411C2semidirect
40. #66159D3semidirect
98. #5234D5semidirect
478. C3×C5#3011semidirect
541. C5#83411semidirect
557. C3#10610410semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C3×#661592
C22×#66622
C2×#913152
C5×#52342
#117485642
#117485522
#117484152
#117484112
#106104103
#834115