Finite Group Databasebeta

← #14416276

Subgroups — #14416276

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754436C211yesmaximal, characteristic, complemented
2Dic3×#709C211yesmaximal, characteristic, complemented
3C2×#91311C211yesmaximal, characteristic
4#11751214C211yesmaximal, characteristic, complemented
5C2×C5×C8×Dic3C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic, complemented
7#11748451C211yesmaximal, characteristic, complemented
8#11747831C212yesmaximal, complemented
9#11747830C212yesmaximal, complemented
10#11747740C212yesmaximal, complemented
11#11747739C212yesmaximal, complemented
12C4×#4050—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16#91815C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20#91556—22no—
21Dic3×C22⋊D5—22no—
22#91428C2212yes—
23Dic3×D20C2212yes—
24C4×#1200—21no—
25C4×D5×Dic3—21no—
26#91386—21no—
27#91357—21no—
28#91340C2212yes—
29Dic3×Dic10C2212yes—
30C2×#6662C2211yescharacteristic
31C2×#6658C2211yescharacteristic
32#91311C418yescomplemented
33C2×#6657C2211yescharacteristic
34C2×#6653C2211yescharacteristic
35#91105C2212yes—
36#91100C2212yes—
37C5×C8×Dic3C2212yes—
38C5×C8×Dic3C2212yes—
39C3×#3953C2212yes—
40C3×#3948C2212yes—
41#90990C2212yes—
42#90987C2212yes—
43#78818—51nomaximal, Hall
44C2×#4050—31no—
45C4×#709—31no—
46C4×#709—31no—
47C2×C4×C5×C8—31no—
48#65402—31no—
49#65402D311yescharacteristic, complemented
50#65395—31no—
51C4×Dic20—32no—
52C4×D40—32no—
53C4×#677—32no—
54C4×#677—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57#6817—22no—
58#6817C2×C414yescomplemented
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30C2311yescharacteristic
62C22×C5×Dic3D412yes—
63C2×C3×C22⋊D5—21no—
64C3×#709—22no—
65C3×#709C2×C414yescomplemented
66C2×C3×D20C2311yescharacteristic
67C2×C3×C4×D5—21no—
68C2×C3×Dic10C2311yescharacteristic
69C2×#1200—22no—
70C2×D5×Dic3—22no—
71C2×C3×C5×C8—22no—
72C2×C3×C5×C8C2312yes—
73#6719—21no—
74C4⋊Dic15C2312yes—
75C4×Dic15—21no—
76C4×C5×Dic3D411yescharacteristic
77C4×C5×Dic3D411yescharacteristic
78C4×C5×Dic3C2312yes—
79C2×C5×C3⋊C8C2×C414yescomplemented
80C2×C5×C3⋊C8C2311yescharacteristic
81C2×C5×C3⋊C8C2311yescharacteristic
82C3×C22⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×C4×Dic5—21no—
85#6669—22no—
86#6668—22no—
87#6667—22no—
88#6665—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91#6662C2×C414yescomplemented
92#6658C2×C414yescomplemented
93#6657C2×C414yescomplemented
94#6653C2×C414yescomplemented
95Dic3×#41—51no—
96C2×#950—51no—
97#5522—51no—
98C3×#416—51no—
99#5113—51no—
100C2×C8×Dic3D511yescharacteristic, complemented
101#4998—51no—
102#4790—52no—
103#4788—52no—
104#4758—52no—
105#4756—52no—
106C2×#709—31no—
107C2×#709C2×D311yescharacteristic
108C22×C5×C8—31no—
109C22×C5×C8C2×D311yescharacteristic
110C2×C42×C5—31no—
111C4×C22⋊D5—62no—
112C4×C22⋊D5—62no—
113#4072—31no—
114#4072C2×D311yescharacteristic
115C2×Dic20—31no—
116#4050—38no—
117C2×D40—31no—
118C2×#677—31no—
119C2×#677—31no—
120C4×D20—32no—
121C4×D20—32no—
122#4018—61no—
123#4018—61no—
124C42×D5—61no—
125C42×D5—61no—
126C4×Dic10—32no—
127C4×Dic10—32no—
128C4×C5×C8—32no—
129C4×C5×C8—32no—
130#3953—32no—
131#3953C2×D312yes—
132#3950—32no—
133#3949—32no—
134#3948—32no—
135#3948C2×D312yes—
136C4×#135—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C22×C3×D5—21no—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5#4112yes—
143C2×C3×C4×C5C2411yescharacteristic
144#1220—24no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147D60—21no—
148D60C22×C412yes—
149C4×D15—24no—
150Dic30—21no—
151Dic30C22×C412yes—
152C2×C5×Dic3—24no—
153C2×C5×Dic3C2×D412yes—
154C2×C5×Dic3C2×D412yes—
155C3×C22⋊D5—24no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C3×D20—21no—
159C3×D20C22×C412yes—
160C3×C4×D5—24no—
161C3×Dic10—21no—
162C3×Dic10C22×C412yes—
163#1200—44no—
164D5×Dic3—44no—
165C3×C5×C8—22no—
166C5×C3⋊C8C22×C412yes—
167C5×C3⋊C8C22×C412yes—
168C2×C3×#41—51no—
169C2×#235—51no—
170C22×C3×C8C2×D511yescharacteristic
171C3×#117—51no—
172#950—58no—
173Q8×Dic3—52no—
174C2×#216—51no—
175C2×#215—51no—
176D4×Dic3—52no—
177D4×Dic3—102no—
178C2×#214—51no—
179C2×#213—51no—
180#926—51no—
181#926—101no—
182C2×C4×Dic3—101no—
183C2×C4×Dic3C2×D511yescharacteristic
184C22×C3⋊C8C2×D511yescharacteristic
185#893—52no—
186#887—52no—
187#67⋊C4—102no—
188#872—101no—
189C42×D3—101no—
190C3×#103—52no—
191C3×#102—52no—
192#821—52no—
193#816—52no—
194C8×Dic3C2×D512yes—
195C8×Dic3C2×D512yes—
196#808—52no—
197#807—52no—
198C22×C4×C5—32no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—21no—
201C2×C22⋊D5—61no—
202#709—22no—
203#709—34no—
204#709—62no—
205#709C4×D314yescomplemented
206C2×D20—31no—
207C2×D20C22×D311yescharacteristic
208C2×C4×D5—21no—
209C2×C4×D5—61no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×Dic10—31no—
213C2×Dic10C22×D311yescharacteristic
214C2×C5×C8—22no—
215C2×C5×C8—34no—
216C2×C5×C8—31no—
217C2×C5×C8—31no—
218C2×C5×C8C22×D312yes—
219C42×C5—31no—
220C42×C5—31no—
221C42×C5—32no—
222C22⋊Dic5—21no—
223C22⋊Dic5—61no—
224#685—62no—
225#685—62no—
226C4⋊Dic5—32no—
227C4⋊Dic5C22×D312yes—
228#683—62no—
229#683—62no—
230C4×Dic5—21no—
231C4×Dic5—62no—
232C4×Dic5—62no—
233C4×Dic5—61no—
234Dic20—34no—
235D40—34no—
236#677—34no—
237#677—34no—
238C2×#135—151no—
239C4×#41—151no—
240C4×#41—151no—
241C4×Q16—152no—
242C4×SD16—152no—
243C4×SD16—152no—
244C4×D8—152no—
245#427—151no—
246#416—51no—
247#416—151no—
248C2×C4×C8—31no—
249C22×C3×C5—22no—
250C22×C3×C5C4×D412yes—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15—22no—
253C2×D15—42no—
254C2×C3×D5—22no—
255C2×C3×D5—42no—
256C3×C4×C5C4×D412yes—
257C3×C4×C5C23×C411yescharacteristic
258C3×C4×C5C2×#4111yescharacteristic
259Dic15—22no—
260Dic15—42no—
261C3×Dic5—22no—
262C3×Dic5—42no—
263C5×Dic3—22no—
264C5×Dic3#13514yescomplemented
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—101no—
273C22×Dic3—102no—
274C22×Dic3D2012yes—
275#235—54no—
276#235—102no—
277C2×D12—51no—
278C2×C4×D3—101no—
279C2×C4×D3—102no—
280C2×Dic6—51no—
281C2×C3×C8—22no—
282C2×C3×C8C22×D512yes—
283C3×C4⋊C4—52no—
284C3×C22⋊C4—101no—
285C3×C42—101no—
286#217—101no—
287#217—102no—
288#216—54no—
289#215—54no—
290#214—54no—
291#213—54no—
292(C2×D3)⋊C4—102no—
293C4⋊Dic3—52no—
294C4⋊Dic3—102no—
295Dic3⋊C4—102no—
296C4×Dic3—101no—
297C4×Dic3—102no—
298C4×Dic3—102no—
299C4×Dic3D2011yescharacteristic
300C4×Dic3D2011yescharacteristic
301C4×Dic3C22×D512yes—
302C2×C3⋊C8C4×D514yescomplemented
303C2×C3⋊C8C22×D511yescharacteristic
304C2×C3⋊C8C22×D511yescharacteristic
305C23×C5D3×D411yescharacteristic
306C22×D5—21no—
307C22×D5—61no—
308C2×C4×C5—32no—
309C2×C4×C5—32no—
310C2×C4×C5—64no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5#23712yes—
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—24no—
316C22⋊D5—64no—
317C2×Dic5—21no—
318C2×Dic5—22no—
319C2×Dic5—61no—
320C2×Dic5—62no—
321D20—21no—
322D20—32no—
323D20—61no—
324D20C2×C4×D312yes—
325C4×D5—24no—
326C4×D5—64no—
327C4×D5—124no—
328C4×D5—124no—
329Dic10—21no—
330Dic10—32no—
331Dic10—61no—
332Dic10C2×C4×D312yes—
333C5×C8—22no—
334C5×C8—32no—
335C5×C8—32no—
336C2×#41—51no—
337C2×#41—151no—
338#135—158no—
339C2×Q16—151no—
340C2×SD16—151no—
341C2×SD16—151no—
342C2×D8—151no—
343C22×C8—31no—
344C22×C8D3×D511yescharacteristic
345C4×Q8—152no—
346C4×Q8—152no—
347C4×D4—152no—
348C4×D4—152no—
349C4×D4—302no—
350C4×D4—302no—
351#117—51no—
352#117—151no—
353#117—301no—
354#117—301no—
355C2×C42—31no—
356C2×C42—301no—
357C2×C42—301no—
358#107—152no—
359#106—152no—
360#103—52no—
361#103—152no—
362#102—52no—
363#102—152no—
364C4×C8—32no—
365C4×C8—32no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5C2×#13512yes—
369D15—42no—
370C3×D5—42no—
371C23×C3—101no—
372C23×C3C2×D2011yescharacteristic
373C22×D3—101no—
374C3×Q8—52no—
375C3×Q8—101no—
376C3×D4—52no—
377C3×D4—104no—
378C3×D4—101no—
379C2×C3×C4—101no—
380C2×C3×C4—104no—
381C2×C3×C4—102no—
382C2×C3×C4C2×C4×D512yes—
383C2×C3×C4C2×D2011yescharacteristic
384C2×C3×C4#70912yes—
385C2×C3×C4C23×D511yescharacteristic
386#67—104no—
387C2×Dic3—24no—
388C2×Dic3—101no—
389C2×Dic3—102no—
390C2×Dic3—204no—
391C2×Dic3C2×D2012yes—
392C2×Dic3C2×D2012yes—
393D12—52no—
394D12—101no—
395C4×D3—104no—
396C4×D3—204no—
397Dic6—52no—
398Dic6—101no—
399C3×C8—22no—
400C3⋊C8C2×C4×D512yes—
401C3⋊C8C2×C4×D512yes—
402C22×C5—22no—
403C22×C5#67⋊C412yes—
404C22×C5C2×D3×D411yescharacteristic
405C2×D5—22no—
406C2×D5—42no—
407C2×D5—62no—
408C2×D5—122no—
409C4×C5—34no—
410C4×C5—62no—
411C4×C5#67⋊C412yes—
412C4×C5C22×C4×D311yescharacteristic
413C4×C5C2×#23711yescharacteristic
414Dic5—22no—
415Dic5—42no—
416Dic5—62no—
417Dic5—122no—
418#41—54no—
419#41—102no—
420#41—154no—
421#41—302no—
422C2×Q8—51no—
423C2×Q8—151no—
424C2×D4—51no—
425C2×D4—101no—
426C2×D4—151no—
427C2×D4—301no—
428C22×C4—32no—
429C22×C4—101no—
430C22×C4—302no—
431C22×C4—302no—
432C22×C4—301no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—154no—
435SD16—154no—
436SD16—154no—
437D8—154no—
438C2×C8—22no—
439C2×C8—34no—
440C2×C8—31no—
441C2×C8—31no—
442C2×C8C2×D3×D512yes—
443C4⋊C4—52no—
444C4⋊C4—152no—
445C4⋊C4—302no—
446C4⋊C4—302no—
447C22⋊C4—101no—
448C22⋊C4—302no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—31no—
452C42—31no—
453C42—32no—
454C42—101no—
455C42—302no—
456C42—302no—
457C42—301no—
458C3×C5C4×#13511yescharacteristic, complemented, Hall
459C22×C3—22no—
460C22×C3—102no—
461C22×C3—202no—
462C22×C3C4×D2012yes—
463C22×C3C22×D2011yescharacteristic
464C2×D3—102no—
465C2×D3—202no—
466C3×C4—102no—
467C3×C4—202no—
468C3×C4C4×D2012yes—
469C3×C4C22×C4×D511yescharacteristic
470C3×C4C2×#70911yescharacteristic
471Dic3—22no—
472Dic3—102no—
473Dic3—202no—
474Dic3#405014yescomplemented
475C2×C5—22no—
476C2×C5C2×#67⋊C411yescharacteristic
477C2×C5D3×#13512yes—
478D5—42no—
479D5—122no—
480C23—101no—
481C23—301no—
482C23D3×D2011yescharacteristic
483Q8—52no—
484Q8—101no—
485Q8—152no—
486Q8—301no—
487D4—52no—
488D4—104no—
489D4—101no—
490D4—152no—
491D4—304no—
492D4—301no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—64no—
496C2×C4—101no—
497C2×C4—104no—
498C2×C4—102no—
499C2×C4—301no—
500C2×C4—304no—
501C2×C4—302no—
502C2×C4—604no—
503C2×C4—604no—
504C2×C4C4×D3×D512yes—
505C2×C4D3×D2011yescharacteristic
506C2×C4#677912yes—
507C2×C4C22×D3×D511yescharacteristic
508C8—22no—
509C8—32no—
510C8—32no—
511C2×C3—22no—
512C2×C3—202no—
513C2×C3C2×C4×D2011yescharacteristic
514C2×C3C2×#405012yes—
515D3—202no—
516C5#7881811yescharacteristic, complemented, Sylow
517C22—22no—
518C22—102no—
519C22—202no—
520C22—302no—
521C22—602no—
522C22#9139512yes—
523C22C2×D3×D2011yescharacteristic
524C4—34no—
525C4—62no—
526C4—102no—
527C4—202no—
528C4—302no—
529C4—602no—
530C4#9139512yes—
531C4C2×C4×D3×D511yescharacteristic
532C4C2×#677911yescharacteristic
533C3C4×#405011yescharacteristic, complemented, Sylow
534C2—22no—
535C2—202no—
536C2—602no—
537C2D3×#405012yes—
538C2C2×#9139511yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91311C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #11754436C2semidirect
2. Dic3×#709C2semidirect
4. #11751214C2semidirect
5. C2×C5×C8×Dic3C2semidirect
6. C3×#65402C2semidirect
7. #11748451C2semidirect
8. #11747831C2semidirect
9. #11747830C2semidirect
10. #11747740C2semidirect
11. #11747739C2semidirect
32. #91311C4semidirect
49. #65402D3semidirect
58. #6817C2×C4semidirect
65. C3×#709C2×C4semidirect
79. C2×C5×C3⋊C8C2×C4semidirect
91. #6662C2×C4semidirect
92. #6658C2×C4semidirect
93. #6657C2×C4semidirect
94. #6653C2×C4semidirect
100. C2×C8×Dic3D5semidirect
205. #709C4×D3semidirect
264. C5×Dic3#135semidirect
302. C2×C3⋊C8C4×D5semidirect
458. C3×C5C4×#135semidirect
474. Dic3#4050semidirect
516. C5#78818semidirect
533. C3C4×#4050semidirect

Maximal subgroups

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

subgroupindex
#117544362
Dic3×#7092
C2×#913112
#117512142
C2×C5×C8×Dic32
C3×#654022
#117484512
#117478312
#117478302
#117477402
#117477392
C4×#40503
#788185