Finite Group Databasebeta

← #14424603

Subgroups — #14424603

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×#92001C211yesmaximal, characteristic
2C22×Dic60C211yesmaximal, characteristic, complemented
3#11754271C211yesmaximal, characteristic, complemented
4C2×#91313C211yesmaximal, characteristic, complemented
5C5×#5110C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic, complemented
7#11748415C211yesmaximal, characteristic, complemented
8#11748162C214yesmaximal, complemented
9#11748133C214yesmaximal, complemented
10#10610410—31nomaximal, Hall
11C22×Dic30C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×#6780—22no—
16C2×#6772—21no—
17C2×D3×Dic10C2212yes—
18#92001—24no—
19#92001—24no—
20C2×#6765C2212yes—
21C2×D5×Dic6—21no—
22C22×C3×C5×C8C2211yescharacteristic
23C2×Dic60—24no—
24C2×Dic60C2214yes—
25C2×C5×#208C2211yescharacteristic
26C3×#4072C2211yescharacteristic
27#91543—22no—
28#91376—21no—
29#91373—21no—
30#91365C2214yes—
31C2×#6662C2212yes—
32#91313—24no—
33C2×#6657C2212yes—
34C5×(C2×D3)⋊C8C2214yes—
35C3×#3953C2212yes—
36C3×#3948C2212yes—
37#90974C2214yes—
38#78837—51nomaximal, Hall
39C2×#4150—31no—
40#66159—31no—
41C2×#4055—31no—
42C22×Dic20—31no—
43C5×#408—31no—
44#65409—31no—
45#65402D311yescharacteristic, complemented
46#65028—34no—
47#65022—34no—
48C22×C3×C4×C5C2311yescharacteristic
49C22×Dic15—21no—
50C22×Dic15—21no—
51C2×Dic30—21no—
52C2×Dic30—22no—
53C2×Dic30—22no—
54C2×Dic30—22no—
55C2×Dic30—21no—
56C2×Dic30D414yes—
57C2×Dic30C2312yes—
58C2×Dic30C2312yes—
59C2×C5×#67D412yes—
60C5×#235—22no—
61C5×#235—22no—
62C2×C5×D12D411yescharacteristic
63C2×C4×C5×D3C2312yes—
64C2×C5×Dic6D411yescharacteristic
65C2×C3×C22⋊D5—21no—
66C3×#709—22no—
67C3×#709D414yes—
68C2×C3×D20C2311yescharacteristic
69C2×C3×C4×D5—21no—
70C2×C3×Dic10C2311yescharacteristic
71C2×#1204—22no—
72C2×#1201—22no—
73C2×D3×Dic5—22no—
74#6780—216no—
75C2×D5×Dic3—22no—
76#6772—28no—
77D3×Dic10—24no—
78D3×Dic10—24no—
79#6765—24no—
80#6765—24no—
81D5×Dic6—28no—
82C2×C3×C5×C8—22no—
83C2×C3×C5×C8C2312yes—
84Dic60—28no—
85C5×#208—22no—
86C2×C5×C3⋊C8C2312yes—
87C3×C22⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×C4×Dic5—21no—
90#6668—24no—
91(C2×D3)⋊Dic5—24no—
92#6662—24no—
93#6657—24no—
94C2×#1010—51no—
95C2×#951—51no—
96C22×Dic12—51no—
97#5526—51no—
98C3×#416—51no—
99#5110D511yescharacteristic, complemented
100#5004—51no—
101#4809—54no—
102#4783—54no—
103C2×C5×#41—31no—
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—61no—
107C2×#711—61no—
108C2×#711—62no—
109C2×#709—32no—
110C2×#709C2×D311yescharacteristic
111C22×Dic10—31no—
112C22×Dic10—31no—
113C22×Dic10—32no—
114C2×C5×M16—31no—
115C22×C5×C8C2×D311yescharacteristic
116#4090—61no—
117#4082—61no—
118#4081—62no—
119#4072C2×D311yescharacteristic
120#4070—34no—
121#4055—64no—
122C2×Dic20—32no—
123C2×Dic20—34no—
124C2×Dic20—64no—
125C2×#677—32no—
126C5×C22⋊C8—34no—
127#3953C2×D312yes—
128#3948—34no—
129#3948C2×D312yes—
130#3011—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×C5×D3C2×D412yes—
133C22×C3×D5—21no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2411yescharacteristic
138C2×Dic15—24no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—42no—
142Dic30—24no—
143Dic30—22no—
144Dic30—22no—
145Dic30—22no—
146Dic30—42no—
147Dic30C2×D414yes—
148C5×#67—24no—
149C2×C5×Dic3C2×D412yes—
150C5×D12—22no—
151C4×C5×D3—22no—
152C4×C5×D3—22no—
153C5×Dic6—22no—
154C3×C22⋊D5—24no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C3×D20—21no—
158C3×D20C2×D412yes—
159C3×C4×D5—24no—
160C3×Dic10—21no—
161C3×Dic10C2×D412yes—
162#1204—28no—
163#1201—28no—
164D3×Dic5—28no—
165D5×Dic3—28no—
166C3×C5×C8—22no—
167C5×C3⋊C8—22no—
168C2×C3×#41—51no—
169#1010—104no—
170#1010—104no—
171C2×D3×Q8—52no—
172C2×#237—52no—
173C2×#237—102no—
174C2×#235—101no—
175C2×#235C2×D511yescharacteristic
176C22×Dic6—51no—
177C22×Dic6—51no—
178C22×Dic6—101no—
179C22×C3×C8C2×D511yescharacteristic
180C3×#117—51no—
181#951—104no—
182C2×#216—52no—
183C2×#214—52no—
184C2×#208C2×D511yescharacteristic
185C2×Dic12—54no—
186C2×Dic12—104no—
187#897—54no—
188#886—102no—
189#875—101no—
190#869—101no—
191C3×#103—52no—
192C3×#102—52no—
193(C2×D3)⋊C8C2×D514yes—
194#810—54no—
195C5×#41—62no—
196C5×#41—62no—
197C2×C5×Q8—31no—
198C2×C5×D4—32no—
199C2×C5×D4—31no—
200C22×C4×C5—32no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—21no—
203C2×C22⋊D5—62no—
204C22×Dic5—62no—
205C22×Dic5—61no—
206C22×Dic5—61no—
207Q8×D5—68no—
208#711—68no—
209#711—616no—
210#709—22no—
211#709—64no—
212#709—64no—
213#709D1214yes—
214C2×D20C22×D311yescharacteristic
215C2×C4×D5—21no—
216C2×C4×D5—62no—
217C2×Dic10—34no—
218C2×Dic10—32no—
219C2×Dic10—32no—
220C2×Dic10—64no—
221C2×Dic10—62no—
222C2×Dic10—62no—
223C2×Dic10—61no—
224C2×Dic10—64no—
225C2×Dic10—62no—
226C2×Dic10—62no—
227C2×Dic10—61no—
228C2×Dic10C22×D311yescharacteristic
229C5×M16—62no—
230C2×C5×C8—22no—
231C2×C5×C8—32no—
232C2×C5×C8C22×D312yes—
233C22⋊Dic5—21no—
234C22⋊Dic5—64no—
235C4⋊Dic5C22×D312yes—
236#683—64no—
237C4×Dic5—21no—
238Dic20—68no—
239Dic20—64no—
240#677—64no—
241C2×2−1+4—151no—
242C2×#137—151no—
243C22×Q16—151no—
244#536—151no—
245#452—154no—
246#451—154no—
247#419—151no—
248#416—51no—
249#408—31no—
250C22×C3×C5—22no—
251C22×C3×C5#12012yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×C5×D3—22no—
254C2×C5×D3—24no—
255C2×C3×D5—22no—
256C2×C3×D5—42no—
257C3×C4×C5#12012yes—
258C3×C4×C5C22×D411yescharacteristic
259C3×C4×C5C22×D411yescharacteristic
260Dic15—24no—
261Dic15—42no—
262C3×Dic5—22no—
263C3×Dic5—42no—
264C5×Dic3—22no—
265C3×#41—54no—
266C3×#41—102no—
267C2×C3×Q8—51no—
268C2×C3×D4—51no—
269C2×C3×D4—101no—
270C22×C3×C4—101no—
271C22×C3×C4C22×D511yescharacteristic
272C2×#67—102no—
273C2×#67D2012yes—
274C22×Dic3—101no—
275C22×Dic3—102no—
276C22×Dic3—101no—
277D3×Q8—104no—
278D3×Q8—104no—
279#237—104no—
280#237—104no—
281#237—1016no—
282#235—22no—
283#235—22no—
284#235—108no—
285C2×D12D2011yescharacteristic
286C2×C4×D3—102no—
287C2×C4×D3C22×D512yes—
288C2×Dic6—54no—
289C2×Dic6—52no—
290C2×Dic6—52no—
291C2×Dic6—108no—
292C2×Dic6—101no—
293C2×Dic6—102no—
294C2×Dic6—102no—
295C2×Dic6—102no—
296C2×Dic6—102no—
297C2×Dic6—101no—
298C2×Dic6D2011yescharacteristic
299C2×C3×C8—22no—
300C2×C3×C8C22×D512yes—
301C3×C4⋊C4—52no—
302C3×C22⋊C4—101no—
303C3×C42—101no—
304#216—104no—
305#214—104no—
306(C2×D3)⋊C4—104no—
307C4⋊Dic3—104no—
308#208—22no—
309C2×C3⋊C8C22×D512yes—
310Dic12—108no—
311C23×C5—32no—
312C23×C5D3×D411yescharacteristic
313C22×D5—21no—
314C5×Q8—62no—
315C5×D4—64no—
316C5×D4—62no—
317C2×C4×C5—32no—
318C2×C4×C5—62no—
319C2×C4×C5—62no—
320C2×C4×C5C2×D1212yes—
321C2×C4×C5D3×D411yescharacteristic
322C2×C4×C5D3×D412yes—
323C2×C4×C5C23×D311yescharacteristic
324C22⋊D5—24no—
325C22⋊D5—68no—
326C2×Dic5—21no—
327C2×Dic5—22no—
328C2×Dic5—68no—
329C2×Dic5—64no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—122no—
333D20—21no—
334D20C2×D1212yes—
335C4×D5—24no—
336C4×D5—68no—
337Dic10—21no—
338Dic10—34no—
339Dic10—68no—
340Dic10—64no—
341Dic10—62no—
342Dic10—62no—
343Dic10—62no—
344Dic10—122no—
345Dic10C2×D1212yes—
346C5×C8—22no—
347C5×C8—62no—
3482−1+4—304no—
3492−1+4—304no—
350C2×#41—31no—
351C2×#41—51no—
352C2×#41—152no—
353C2×#41—301no—
354C2×#41—302no—
355C22×Q8—152no—
356C22×Q8—151no—
357C22×Q8—151no—
358C22×Q8—301no—
359#137—304no—
360C2×Q16—152no—
361C2×Q16—154no—
362C2×Q16—304no—
363C2×SD16—152no—
364C2×M16—31no—
365C22×C8D3×D511yescharacteristic
366C4⋊Q8—301no—
367#124—301no—
368#123—302no—
369C22⋊Q8—154no—
370#117—51no—
371#103—52no—
372#103—154no—
373#102—52no—
374C22⋊C8—34no—
375C2×C3×C5—22no—
376C2×C3×C5C2×#12011yescharacteristic
377C2×C3×C5#57812yes—
378C3×D5—42no—
379C5×D3—42no—
380C23×C3—101no—
381C23×C3C2×D2011yescharacteristic
382C22×D3C2×D2012yes—
383C3×Q8—52no—
384C3×Q8—101no—
385C3×D4—52no—
386C3×D4—104no—
387C3×D4—101no—
388C2×C3×C4—101no—
389C2×C3×C4—104no—
390C2×C3×C4—102no—
391C2×C3×C4C2×D2011yescharacteristic
392C2×C3×C4D4×D512yes—
393C2×C3×C4D4×D512yes—
394C2×C3×C4C23×D511yescharacteristic
395#67—24no—
396#67—108no—
397C2×Dic3—108no—
398C2×Dic3—102no—
399C2×Dic3—104no—
400C2×Dic3—102no—
401C2×Dic3—202no—
402C2×Dic3C2×D2012yes—
403D12—22no—
404C4×D3—22no—
405C4×D3—22no—
406C4×D3—108no—
407Dic6—22no—
408Dic6—54no—
409Dic6—108no—
410Dic6—102no—
411Dic6—104no—
412Dic6—102no—
413Dic6—102no—
414Dic6—202no—
415C3×C8—22no—
416C3⋊C8—22no—
417C22×C5—22no—
418C22×C5—62no—
419C22×C5—64no—
420C22×C5#88212yes—
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—22no—
423C2×D5—42no—
424C4×C5—62no—
425C4×C5#88212yes—
426C4×C5C22×D1211yescharacteristic
427C4×C5C2×D3×D411yescharacteristic
428Dic5—22no—
429Dic5—42no—
430Dic5—64no—
431Dic5—122no—
432#41—54no—
433#41—62no—
434#41—62no—
435#41—102no—
436#41—304no—
437#41—304no—
438#41—308no—
439#41—3016no—
440C2×Q8—31no—
441C2×Q8—51no—
442C2×Q8—154no—
443C2×Q8—152no—
444C2×Q8—152no—
445C2×Q8—302no—
446C2×Q8—304no—
447C2×Q8—304no—
448C2×Q8—308no—
449C2×Q8—302no—
450C2×Q8—301no—
451C2×Q8—301no—
452C2×Q8—302no—
453C2×Q8—302no—
454C2×D4—32no—
455C2×D4—31no—
456C2×D4—51no—
457C2×D4—101no—
458C2×D4—302no—
459C22×C4—32no—
460C22×C4—101no—
461C22×C4—302no—
462C22×C4—302no—
463C22×C4—301no—
464C22×C4—301no—
465C22×C4C2×D3×D511yescharacteristic
466Q16—308no—
467Q16—304no—
468SD16—304no—
469M16—62no—
470C2×C8—22no—
471C2×C8—32no—
472C2×C8C2×D3×D512yes—
473C4⋊C4—52no—
474C4⋊C4—304no—
475C22⋊C4—101no—
476C22⋊C4—304no—
477C42—101no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—102no—
481C22×C3—202no—
482C22×C3#402812yes—
483C22×C3C22×D2011yescharacteristic
484C2×D3—22no—
485C2×D3—24no—
486C3×C4—102no—
487C3×C4—202no—
488C3×C4#402812yes—
489C3×C4C2×D4×D511yescharacteristic
490C3×C4C2×D4×D511yescharacteristic
491Dic3—22no—
492Dic3—104no—
493Dic3—202no—
494C2×C5—22no—
495C2×C5—122no—
496C2×C5C2×#88211yescharacteristic
497C2×C5#577112yes—
498D5—42no—
499C23—32no—
500C23—101no—
501C23D3×D2011yescharacteristic
502Q8—52no—
503Q8—62no—
504Q8—101no—
505Q8—154no—
506Q8—308no—
507Q8—304no—
508Q8—302no—
509Q8—302no—
510Q8—302no—
511Q8—602no—
512D4—52no—
513D4—64no—
514D4—62no—
515D4—104no—
516D4—101no—
517D4—308no—
518C2×C4—32no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—101no—
522C2×C4—104no—
523C2×C4—102no—
524C2×C4—308no—
525C2×C4—308no—
526C2×C4—304no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4—602no—
530C2×C4D5×D1212yes—
531C2×C4D3×D2011yescharacteristic
532C2×C4#679012yes—
533C2×C4C22×D3×D511yescharacteristic
534C8—22no—
535C8—62no—
536C2×C3—22no—
537C2×C3—202no—
538C2×C3C2×#402811yescharacteristic
539C2×C3#6608712yes—
540D3—42no—
541C5#7883711yescharacteristic, complemented, Sylow
542C22—22no—
543C22—64no—
544C22—62no—
545C22—102no—
546C22—202no—
547C22#9147612yes—
548C22C2×D3×D2011yescharacteristic
549C4—62no—
550C4—102no—
551C4—202no—
552C4—304no—
553C4—602no—
554C4#9147612yes—
555C4C2×D5×D1211yescharacteristic
556C4C2×#679011yescharacteristic
557C3#1061041011yescharacteristic, complemented, Sylow
558C2—22no—
559C2—122no—
560C2—202no—
561C2#1175400312yes—
562C2C2×#9147611yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#92001C2
hypercenterC22×C8D3×D5
hypocenterC3×C5#3011
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×Dic60C2semidirect
3. #11754271C2semidirect
4. C2×#91313C2semidirect
5. C5×#5110C2semidirect
6. C3×#65402C2semidirect
7. #11748415C2semidirect
8. #11748162C2semidirect
9. #11748133C2semidirect
45. #65402D3semidirect
99. #5110D5semidirect
478. C3×C5#3011semidirect
541. C5#78837semidirect
557. C3#10610410semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C22×Dic602
#117542712
C2×#913132
C5×#51102
C3×#654022
#117484152
#117481622
#117481332
#106104103
#788375