Finite Group Databasebeta

← #14424602

Subgroups — #14424602

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×#92004C211yesmaximal, characteristic
2C22×C3×Dic20C211yesmaximal, characteristic, complemented
3#11754255C211yesmaximal, characteristic, complemented
4C2×#91315C211yesmaximal, characteristic, complemented
5#11751214C211yesmaximal, characteristic, complemented
6C5×#5110C211yesmaximal, characteristic, complemented
7#11748400C211yesmaximal, characteristic, complemented
8#11748152C214yesmaximal, complemented
9#11748125C214yesmaximal, complemented
10#10610410—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×#6782—22no—
16C2×D15⋊Q8—21no—
17C2×#6769C2212yes—
18#92004—24no—
19#92004—24no—
20C2×#6768—21no—
21C2×D3×Dic10C2212yes—
22C22×C3×C5×C8C2211yescharacteristic
23#91815C2211yescharacteristic
24C2×C5×#208C2211yescharacteristic
25C2×C3×Dic20—24no—
26C2×C3×Dic20C2214yes—
27#91539—22no—
28#91385—21no—
29#91370—21no—
30#91369C2214yes—
31C2×#6662C2212yes—
32#91315—24no—
33C2×#6658C2212yes—
34#91105C2212yes—
35#91100C2212yes—
36C5×(C2×D3)⋊C8C2214yes—
37#90971C2214yes—
38#83884—51nomaximal, Hall
39C2×#4150—31no—
40#66159—31no—
41C2×#4055—31no—
42C22×Dic20D311yescharacteristic, complemented
43C5×#408—31no—
44#65409—31no—
45#65402—31no—
46#65028—34no—
47#65022—34no—
48C22×C3×C4×C5C2311yescharacteristic
49C2×#1220—21no—
50#6817—22no—
51#6817D414yes—
52C2×D60C2311yescharacteristic
53C2×C4×D15—21no—
54C2×Dic30C2311yescharacteristic
55C2×C5×#67D412yes—
56C5×#235—22no—
57C5×#235—22no—
58C2×C5×D12D411yescharacteristic
59C2×C4×C5×D3C2312yes—
60C2×C5×Dic6D411yescharacteristic
61C22×C3×Dic5—21no—
62C22×C3×Dic5—21no—
63C2×C3×Dic10—21no—
64C2×C3×Dic10—22no—
65C2×C3×Dic10—22no—
66C2×C3×Dic10—22no—
67C2×C3×Dic10—21no—
68C2×C3×Dic10D414yes—
69C2×C3×Dic10C2312yes—
70C2×C3×Dic10C2312yes—
71C2×#1204—22no—
72C2×#1203—22no—
73C2×#1200—22no—
74#6782—216no—
75C2×D3×Dic5—22no—
76D15⋊Q8—28no—
77#6769—24no—
78#6769—24no—
79#6768—28no—
80D3×Dic10—24no—
81D3×Dic10—24no—
82C2×C3×C5×C8—22no—
83C2×C3×C5×C8C2312yes—
84#6719—21no—
85C4⋊Dic15C2312yes—
86C4×Dic15—21no—
87C5×#208—22no—
88C2×C5×C3⋊C8C2312yes—
89C3×Dic20—28no—
90#6669—24no—
91(C2×D3)⋊Dic5—24no—
92#6662—24no—
93#6658—24no—
94C2×#1007—51no—
95C22×C3×Q16—51no—
96#5816—51no—
97C2×#942—51no—
98#5225—51no—
99#5187—54no—
100#5186—54no—
101#5113—51no—
102#5110D511yescharacteristic, complemented
103C2×C5×#41—31no—
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—61no—
107C2×#711—61no—
108C2×#711—62no—
109C2×#709—31no—
110C2×#709—32no—
111C22×Dic10—32no—
112C22×Dic10C2×D311yescharacteristic
113C22×Dic10C2×D311yescharacteristic
114C2×C5×M16—31no—
115C22×C5×C8C2×D311yescharacteristic
116#4090—61no—
117#4082—61no—
118#4081—62no—
119#4072—31no—
120#4070—34no—
121#4055—64no—
122C2×Dic20—24no—
123C2×Dic20—32no—
124C2×Dic20C2×D314yes—
125C2×#677—32no—
126C5×C22⋊C8—34no—
127#3953—32no—
128#3948—34no—
129#3948—32no—
130#3011—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15—21no—
133C22×C5×D3C2×D412yes—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2411yescharacteristic
138#1220—24no—
139C2×Dic15—21no—
140C2×Dic15—22no—
141D60—21no—
142D60C2×D412yes—
143C4×D15—24no—
144Dic30—21no—
145Dic30C2×D412yes—
146C5×#67—24no—
147C2×C5×Dic3C2×D412yes—
148C5×D12—22no—
149C4×C5×D3—22no—
150C4×C5×D3—22no—
151C5×Dic6—22no—
152C2×C3×Dic5—24no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—42no—
156C3×Dic10—24no—
157C3×Dic10—22no—
158C3×Dic10—22no—
159C3×Dic10—22no—
160C3×Dic10—42no—
161C3×Dic10C2×D414yes—
162#1204—28no—
163#1203—28no—
164#1200—28no—
165D3×Dic5—28no—
166C3×C5×C8—22no—
167C5×C3⋊C8—22no—
168C22×C3×Q8—51no—
169C22×C3×Q8—51no—
170#1007—104no—
171#1007—104no—
172C2×#239—52no—
173C2×#239—101no—
174C2×D3×Q8—52no—
175C2×D3×Q8—101no—
176C2×#235—51no—
177C2×#235—102no—
178C2×#235C2×D511yescharacteristic
179C2×C3×Q16—54no—
180C2×C3×Q16—104no—
181C22×C3×C8C2×D511yescharacteristic
182#947—101no—
183#946—54no—
184#944—101no—
185C2×#216—52no—
186#942—104no—
187C2×#215—52no—
188#929—102no—
189#926—51no—
190C2×#208C2×D511yescharacteristic
191#835—54no—
192#821—52no—
193(C2×D3)⋊C8C2×D514yes—
194#816—52no—
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—62no—
203C2×C22⋊D5—61no—
204C22×Dic5—21no—
205C22×Dic5—21no—
206C22×Dic5—62no—
207Q8×D5—68no—
208#711—68no—
209#711—616no—
210#709—34no—
211#709—64no—
212#709—62no—
213#709—64no—
214C2×D20—31no—
215C2×C4×D5—62no—
216C2×C4×D5—61no—
217C2×Dic10—21no—
218C2×Dic10—22no—
219C2×Dic10—22no—
220C2×Dic10—22no—
221C2×Dic10—21no—
222C2×Dic10—31no—
223C2×Dic10—64no—
224C2×Dic10—62no—
225C2×Dic10—64no—
226C2×Dic10#6714yes—
227C2×Dic10C22×D312yes—
228C2×Dic10C22×D312yes—
229C5×M16—62no—
230C2×C5×C8—22no—
231C2×C5×C8—32no—
232C2×C5×C8C22×D312yes—
233C22⋊Dic5—64no—
234C22⋊Dic5—61no—
235C4⋊Dic5—32no—
236#683—64no—
237C4×Dic5—61no—
238Dic20—28no—
239Dic20—64no—
240#677—64no—
241C2×2−1+4—151no—
242C2×#137—151no—
243C22×Q16—51no—
244#536—151no—
245#452—154no—
246#451—154no—
247#419—151no—
248#416—151no—
249#408—31no—
250C22×C3×C5—22no—
251C22×C3×C5#12012yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×D15—22no—
254C2×D15—42no—
255C2×C5×D3—22no—
256C2×C5×D3—24no—
257C3×C4×C5#12012yes—
258C3×C4×C5C22×D411yescharacteristic
259C3×C4×C5C22×D411yescharacteristic
260Dic15—22no—
261Dic15—42no—
262C3×Dic5—24no—
263C3×Dic5—42no—
264C5×Dic3—22no—
265C2×C3×Q8—54no—
266C2×C3×Q8—52no—
267C2×C3×Q8—52no—
268C2×C3×Q8—101no—
269C2×C3×Q8—101no—
270C2×C3×Q8—102no—
271C2×C3×Q8—102no—
272C2×C3×Q8—102no—
273C22×C3×C4—101no—
274C22×C3×C4—101no—
275C22×C3×C4C22×D511yescharacteristic
276C2×#67—101no—
277C2×#67D2012yes—
278#239—104no—
279#239—104no—
280#239—108no—
281D3×Q8—108no—
282D3×Q8—104no—
283D3×Q8—104no—
284#235—22no—
285#235—22no—
286#235—54no—
287#235—1016no—
288#235—102no—
289C2×D12—51no—
290C2×D12—102no—
291C2×D12D2011yescharacteristic
292C2×C4×D3—102no—
293C2×C4×D3—101no—
294C2×C4×D3—102no—
295C2×C4×D3C22×D512yes—
296C2×Dic6—51no—
297C2×Dic6—102no—
298C2×Dic6D2011yescharacteristic
299C3×Q16—108no—
300C2×C3×C8—22no—
301C2×C3×C8C22×D512yes—
302#217—101no—
303#216—104no—
304#215—104no—
305(C2×D3)⋊C4—104no—
306C4⋊Dic3—52no—
307Dic3⋊C4—104no—
308C4×Dic3—101no—
309#208—22no—
310C2×C3⋊C8C22×D512yes—
311C23×C5—32no—
312C23×C5D3×D411yescharacteristic
313C22×D5—61no—
314C5×Q8—62no—
315C5×D4—64no—
316C5×D4—62no—
317C2×C4×C5—32no—
318C2×C4×C5—62no—
319C2×C4×C5—62no—
320C2×C4×C5D3×D411yescharacteristic
321C2×C4×C5D3×D412yes—
322C2×C4×C5C2×#6712yes—
323C2×C4×C5C23×D311yescharacteristic
324C22⋊D5—68no—
325C22⋊D5—64no—
326C2×Dic5—24no—
327C2×Dic5—22no—
328C2×Dic5—22no—
329C2×Dic5—42no—
330C2×Dic5—68no—
331C2×Dic5—61no—
332C2×Dic5—62no—
333D20—32no—
334D20—61no—
335C4×D5—68no—
336C4×D5—64no—
337Dic10—24no—
338Dic10—22no—
339Dic10—22no—
340Dic10—22no—
341Dic10—32no—
342Dic10—42no—
343Dic10—68no—
344Dic10—61no—
345Dic10C2×#6714yes—
346C5×C8—22no—
347C5×C8—62no—
3482−1+4—304no—
3492−1+4—304no—
350C2×#41—31no—
351C2×#41—152no—
352C2×#41—151no—
353C2×#41—302no—
354C2×#41—301no—
355C22×Q8—51no—
356C22×Q8—51no—
357C22×Q8—152no—
358C22×Q8—301no—
359#137—304no—
360C2×Q16—54no—
361C2×Q16—104no—
362C2×Q16—152no—
363C2×SD16—152no—
364C2×M16—31no—
365C22×C8D3×D511yescharacteristic
366C4⋊Q8—301no—
367#124—301no—
368#123—302no—
369C22⋊Q8—154no—
370#117—151no—
371#103—154no—
372#103—152no—
373#102—152no—
374C22⋊C8—34no—
375C2×C3×C5—22no—
376C2×C3×C5C2×#12011yescharacteristic
377C2×C3×C5#57812yes—
378D15—42no—
379C5×D3—42no—
380C23×C3C2×D2011yescharacteristic
381C22×D3—101no—
382C22×D3C2×D2012yes—
383C3×Q8—54no—
384C3×Q8—102no—
385C3×Q8—104no—
386C3×Q8—102no—
387C3×Q8—102no—
388C3×Q8—202no—
389C2×C3×C4—102no—
390C2×C3×C4—104no—
391C2×C3×C4—102no—
392C2×C3×C4—202no—
393C2×C3×C4C2×D2011yescharacteristic
394C2×C3×C4D4×D512yes—
395C2×C3×C4D4×D512yes—
396C2×C3×C4C23×D511yescharacteristic
397#67—24no—
398#67—104no—
399C2×Dic3—101no—
400C2×Dic3—102no—
401C2×Dic3C2×D2012yes—
402D12—22no—
403D12—52no—
404D12—108no—
405D12—101no—
406C4×D3—22no—
407C4×D3—22no—
408C4×D3—108no—
409C4×D3—108no—
410C4×D3—104no—
411Dic6—22no—
412Dic6—52no—
413Dic6—108no—
414Dic6—101no—
415C3×C8—22no—
416C3⋊C8—22no—
417C22×C5—22no—
418C22×C5—64no—
419C22×C5—62no—
420C22×C5#93712yes—
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—62no—
423C2×D5—122no—
424C4×C5—62no—
425C4×C5#93712yes—
426C4×C5C2×D3×D411yescharacteristic
427C4×C5C22×#6711yescharacteristic
428Dic5—24no—
429Dic5—42no—
430Dic5—62no—
431Dic5—122no—
432#41—62no—
433#41—62no—
434#41—154no—
435#41—304no—
436#41—304no—
437#41—3016no—
438#41—308no—
439#41—302no—
440C2×Q8—31no—
441C2×Q8—54no—
442C2×Q8—52no—
443C2×Q8—52no—
444C2×Q8—101no—
445C2×Q8—101no—
446C2×Q8—102no—
447C2×Q8—102no—
448C2×Q8—102no—
449C2×Q8—151no—
450C2×Q8—302no—
451C2×Q8—304no—
452C2×Q8—304no—
453C2×Q8—308no—
454C2×D4—32no—
455C2×D4—31no—
456C2×D4—151no—
457C2×D4—302no—
458C2×D4—301no—
459C22×C4—32no—
460C22×C4—101no—
461C22×C4—101no—
462C22×C4—302no—
463C22×C4—302no—
464C22×C4—301no—
465C22×C4C2×D3×D511yescharacteristic
466Q16—108no—
467Q16—304no—
468SD16—304no—
469M16—62no—
470C2×C8—22no—
471C2×C8—32no—
472C2×C8C2×D3×D512yes—
473C4⋊C4—152no—
474C4⋊C4—304no—
475C22⋊C4—304no—
476C22⋊C4—301no—
477C42—301no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3#402812yes—
481C22×C3C22×D2011yescharacteristic
482C2×D3—22no—
483C2×D3—24no—
484C2×D3—102no—
485C2×D3—202no—
486C3×C4—104no—
487C3×C4—202no—
488C3×C4#402812yes—
489C3×C4C2×D4×D511yescharacteristic
490C3×C4C2×D4×D511yescharacteristic
491Dic3—22no—
492Dic3—102no—
493Dic3—202no—
494C2×C5—22no—
495C2×C5—122no—
496C2×C5#576612yes—
497C2×C5C2×#93711yescharacteristic
498D5—122no—
499C23—32no—
500C23—301no—
501C23D3×D2011yescharacteristic
502Q8—54no—
503Q8—62no—
504Q8—104no—
505Q8—102no—
506Q8—102no—
507Q8—102no—
508Q8—152no—
509Q8—202no—
510Q8—308no—
511Q8—301no—
512D4—64no—
513D4—62no—
514D4—152no—
515D4—308no—
516D4—304no—
517D4—301no—
518C2×C4—32no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—104no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—202no—
525C2×C4—308no—
526C2×C4—308no—
527C2×C4—301no—
528C2×C4—304no—
529C2×C4—302no—
530C2×C4D3×D2011yescharacteristic
531C2×C4#677712yes—
532C2×C4D5×#6712yes—
533C2×C4C22×D3×D511yescharacteristic
534C8—22no—
535C8—62no—
536C2×C3—22no—
537C2×C3C2×#402811yescharacteristic
538C2×C3#6608712yes—
539D3—42no—
540D3—202no—
541C5#8388411yescharacteristic, complemented, Sylow
542C22—22no—
543C22—64no—
544C22—62no—
545C22—302no—
546C22—602no—
547C22#9147412yes—
548C22C2×D3×D2011yescharacteristic
549C4—62no—
550C4—104no—
551C4—202no—
552C4—302no—
553C4—602no—
554C4#9147412yes—
555C4C2×#677711yescharacteristic
556C4C2×D5×#6711yescharacteristic
557C3#1061041011yescharacteristic, complemented, Sylow
558C2—22no—
559C2—122no—
560C2—602no—
561C2#1175399112yes—
562C2C2×#9147411yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#92004C2
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×C3×Dic20C2semidirect
3. #11754255C2semidirect
4. C2×#91315C2semidirect
5. #11751214C2semidirect
6. C5×#5110C2semidirect
7. #11748400C2semidirect
8. #11748152C2semidirect
9. #11748125C2semidirect
42. C22×Dic20D3semidirect
102. #5110D5semidirect
478. C3×C5#3011semidirect
541. C5#83884semidirect
557. C3#10610410semidirect

Maximal subgroups

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

subgroupindex
C2×#920042
C22×C3×Dic202
#117542552
C2×#913152
#117512142
C5×#51102
#117484002
#117481522
#117481252
#106104103
#838845