Finite Group Databasebeta

← #14416267

Subgroups — #14416267

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
1C2×#91839C211yesmaximal, characteristic
2C5×Dic3×#41C211yesmaximal, characteristic, complemented
3#11754436C211yesmaximal, characteristic, complemented
4C3×#65522C211yesmaximal, characteristic, complemented
5#11749257C212yesmaximal, complemented
6#11749232C212yesmaximal, complemented
7#11749011C212yesmaximal, complemented
8#11748986C212yesmaximal, complemented
9#11748469C211yesmaximal, characteristic, complemented
10#11748393C211yesmaximal, characteristic, complemented
11C2×Dic3×#168C211yesmaximal, characteristic, complemented
12C4×#4096—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15#91839C418yescomplemented
16C2×#6718C2211yescharacteristic
17C2×#6717C2211yescharacteristic
18C2×#6716C2211yescharacteristic
19C2×#6715C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C5×Q8×Dic3C2212yes—
22C5×D4×Dic3—22no—
23C5×D4×Dic3C2212yes—
24C5×#926—21no—
25C5×#926C2211yescharacteristic
26C2×C4×C5×Dic3—21no—
27C2×C4×C5×Dic3C2211yescharacteristic
28C3×#4072C2211yescharacteristic
29C22×C3×#168C2211yescharacteristic
30#91556—22no—
31#91428C2212yes—
32C4×#1200—21no—
33#91386—21no—
34#91340C2212yes—
35C3×#3967C2212yes—
36C3×#3964C2212yes—
37#90989C2212yes—
38#90986C2212yes—
39#90975C2212yes—
40#90969C2212yes—
41Dic3×#168C2212yes—
42Dic3×#168C2212yes—
43#78818—51nomaximal, Hall
44C4×C5×#41—31no—
45C2×#4096—31no—
46C4×#709—31no—
47#65522D311yescharacteristic, complemented
48C4×#689—32no—
49C4×#688—32no—
50C4×#687—32no—
51C4×#686—32no—
52#65291—31no—
53#65287—31no—
54C2×C4×#168—31no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yescomplemented
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63#6817—22no—
64#6817C2×C414yescomplemented
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C22×C5×Dic3—22no—
69C22×C5×Dic3D412yes—
70C2×#1200—22no—
71#6718C2×C414yescomplemented
72#6717C2×C414yescomplemented
73#6716C2×C414yescomplemented
74#6715C2×C414yescomplemented
75C2×C3⋊#168C2×C414yescomplemented
76C2×C3⋊#168C2311yescharacteristic
77C2×C3⋊#168C2311yescharacteristic
78C5×#217—21no—
79C5×#217—22no—
80C5×C4⋊Dic3—22no—
81C5×C4⋊Dic3C2312yes—
82C4×C5×Dic3—21no—
83C4×C5×Dic3—22no—
84C4×C5×Dic3D411yescharacteristic
85C4×C5×Dic3D411yescharacteristic
86C4×C5×Dic3C2312yes—
87C3×C22⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×C4×Dic5—21no—
90C2×C3×#168—22no—
91C2×C3×#168C2312yes—
92#6669—22no—
93#6667—22no—
94Dic3×Dic5—22no—
95Dic3×#41D511yescharacteristic, complemented
96C2×#950—51no—
97#5522—51no—
98C3×#416—51no—
99#5113—51no—
100C2×C8×Dic3—51no—
101#4998—51no—
102#4790—52no—
103#4788—52no—
104#4758—52no—
105#4756—52no—
106C2×C5×#41C2×D311yescharacteristic
107C2×#709—31no—
108C4×C5×Q8—32no—
109C4×C5×D4—32no—
110C4×C5×D4—62no—
111C5×#117—31no—
112C5×#117—61no—
113C2×C42×C5—31no—
114C2×C42×C5—61no—
115#4096—38no—
116C2×#689—31no—
117C2×#688—31no—
118C2×#687—31no—
119C2×#686—31no—
120C4×C22⋊D5—62no—
121#4072C2×D311yescharacteristic
122C22×#168—31no—
123C22×#168C2×D311yescharacteristic
124C4×D20—32no—
125#4018—61no—
126C42×D5—61no—
127C4×Dic10—32no—
128#3967C2×D312yes—
129#3964C2×D312yes—
130#3942—32no—
131#3941—32no—
132#3940—32no—
133#3939—32no—
134C4×#168—32no—
135C4×#168—32no—
136C4×#135—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C22×D15—21no—
140C3×C5×Q8—21no—
141C3×C5×Q8C22×C412yes—
142C3×C5×D4—24no—
143C3×C5×D4—21no—
144C3×C5×D4C22×C412yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—24no—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5#4112yes—
150C2×C3×C4×C5C2411yescharacteristic
151#1220—24no—
152C2×Dic15—21no—
153D60—21no—
154D60C22×C412yes—
155C4×D15—24no—
156Dic30—21no—
157Dic30C22×C412yes—
158C2×C5×Dic3—24no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—44no—
161C2×C5×Dic3C2×D412yes—
162C2×C5×Dic3C2×D412yes—
163C2×C3×Dic5—22no—
164#1200—44no—
165C3⋊#168C22×C412yes—
166C3⋊#168C22×C412yes—
167C3×#168—22no—
168C2×C3×#41C2×D511yescharacteristic
169C2×#235—51no—
170C22×C3×C8—51no—
171C3×#117—51no—
172#950—58no—
173Q8×Dic3C2×D512yes—
174C2×#216—51no—
175C2×#215—51no—
176D4×Dic3—22no—
177D4×Dic3C2×D512yes—
178C2×#214—51no—
179C2×#213—51no—
180#926—21no—
181#926C2×D511yescharacteristic
182C2×C4×Dic3—21no—
183C2×C4×Dic3C2×D511yescharacteristic
184C22×C3⋊C8—51no—
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×Dic3—52no—
195C8×Dic3—52no—
196#808—52no—
197#807—52no—
198C5×#41—22no—
199C5×#41C4×D314yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5—32no—
205C22×C4×C5—62no—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—61no—
208#709—34no—
209#709—62no—
210C2×D20—31no—
211C2×C4×D5—61no—
212C2×C4×D5—62no—
213C2×Dic10—31no—
214C5×C4⋊C4—32no—
215C5×C4⋊C4—62no—
216C5×C22⋊C4—62no—
217C5×C22⋊C4—61no—
218C42×C5—31no—
219C42×C5—31no—
220C42×C5—32no—
221C42×C5—62no—
222C42×C5—61no—
223C22⋊Dic5—21no—
224#689—34no—
225#688—34no—
226#687—34no—
227#686—34no—
228#685—62no—
229C4⋊Dic5C22×D312yes—
230#683—62no—
231C4×Dic5—21no—
232C4×Dic5—62no—
233C2×#168—22no—
234C2×#168—34no—
235C2×#168—31no—
236C2×#168—31no—
237C2×#168C22×D312yes—
238C2×#135—151no—
239C4×#41—31no—
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—151no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5—42no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—22no—
255C2×D15—42no—
256C3×C4×C5—22no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—22no—
261C3×Dic5—42no—
262C5×Dic3—22no—
263C5×Dic3—42no—
264C5×Dic3#13514yescomplemented
265C3×#41—22no—
266C3×#41C4×D514yescomplemented
267C2×C3×Q8C22×D511yescharacteristic
268C2×C3×D4—21no—
269C2×C3×D4C22×D511yescharacteristic
270C22×C3×C4—21no—
271C22×C3×C4C22×D511yescharacteristic
272C2×#67—101no—
273C22×Dic3—22no—
274C22×Dic3C22⋊D512yes—
275#235—54no—
276#235—102no—
277C2×D12—51no—
278C2×C4×D3—101no—
279C2×C4×D3—102no—
280C2×Dic6—51no—
281C2×C3×C8—52no—
282C2×C3×C8—102no—
283C3×C4⋊C4—52no—
284C3×C22⋊C4—101no—
285C3×C42—101no—
286#217—21no—
287#217—22no—
288#216—54no—
289#215—54no—
290#214—54no—
291#213—54no—
292(C2×D3)⋊C4—102no—
293C4⋊Dic3—22no—
294C4⋊Dic3C22×D512yes—
295Dic3⋊C4—102no—
296C4×Dic3—21no—
297C4×Dic3—22no—
298C4×Dic3—102no—
299C4×Dic3C22⋊D511yescharacteristic
300C4×Dic3C22⋊D511yescharacteristic
301C4×Dic3C22×D512yes—
302C2×C3⋊C8—54no—
303C2×C3⋊C8—51no—
304C2×C3⋊C8—51no—
305C23×C5—21no—
306C23×C5D3×D411yescharacteristic
307C22×D5—61no—
308C5×Q8—21no—
309C5×Q8C2×C4×D312yes—
310C5×D4—24no—
311C5×D4—21no—
312C5×D4C2×C4×D312yes—
313C2×C4×C5—21no—
314C2×C4×C5—24no—
315C2×C4×C5—32no—
316C2×C4×C5—32no—
317C2×C4×C5—64no—
318C2×C4×C5—62no—
319C2×C4×C5—124no—
320C2×C4×C5C2×C4×D312yes—
321C2×C4×C5D3×D411yescharacteristic
322C2×C4×C5#23712yes—
323C2×C4×C5C23×D311yescharacteristic
324C22⋊D5—64no—
325C2×Dic5—22no—
326C2×Dic5—61no—
327D20—32no—
328D20—61no—
329C4×D5—64no—
330C4×D5—124no—
331Dic10—32no—
332Dic10—61no—
333#168—22no—
334#168—32no—
335#168—32no—
336C2×#41—151no—
337C2×#41D3×D511yescharacteristic
338#135—158no—
339C2×Q16—151no—
340C2×SD16—151no—
341C2×SD16—151no—
342C2×D8—151no—
343C22×C8—51no—
344C22×C8—151no—
345C4×Q8—32no—
346C4×Q8—152no—
347C4×D4—32no—
348C4×D4—62no—
349C4×D4—152no—
350C4×D4—302no—
351#117—31no—
352#117—51no—
353#117—61no—
354#117—301no—
355C2×C42—31no—
356C2×C42—61no—
357C2×C42—301no—
358#107—152no—
359#106—152no—
360#103—52no—
361#103—152no—
362#102—52no—
363#102—152no—
364C4×C8—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5C2×#13512yes—
370D15—42no—
371C23×C3—21no—
372C23×C3C2×C22⋊D511yescharacteristic
373C22×D3—101no—
374C3×Q8—21no—
375C3×Q8C2×C4×D512yes—
376C3×D4—24no—
377C3×D4—21no—
378C3×D4C2×C4×D512yes—
379C2×C3×C4—21no—
380C2×C3×C4—24no—
381C2×C3×C4—102no—
382C2×C3×C4C2×C4×D512yes—
383C2×C3×C4#70912yes—
384C2×C3×C4C2×C22⋊D511yescharacteristic
385C2×C3×C4C23×D511yescharacteristic
386#67—104no—
387C2×Dic3—24no—
388C2×Dic3—22no—
389C2×Dic3—44no—
390C2×Dic3—101no—
391C2×Dic3C2×C22⋊D512yes—
392C2×Dic3C2×C22⋊D512yes—
393D12—52no—
394D12—101no—
395C4×D3—104no—
396C4×D3—204no—
397Dic6—52no—
398Dic6—101no—
399C3×C8—102no—
400C3⋊C8—52no—
401C3⋊C8—52no—
402C22×C5—22no—
403C22×C5—22no—
404C22×C5—42no—
405C22×C5#67⋊C412yes—
406C22×C5C2×D3×D411yescharacteristic
407C2×D5—62no—
408C2×D5—122no—
409C4×C5—22no—
410C4×C5—34no—
411C4×C5—62no—
412C4×C5—122no—
413C4×C5#67⋊C412yes—
414C4×C5C22×C4×D311yescharacteristic
415C4×C5C2×#23711yescharacteristic
416Dic5—42no—
417Dic5—62no—
418#41—22no—
419#41—154no—
420#41—302no—
421#41#120014yescomplemented
422C2×Q8—151no—
423C2×Q8C2×D3×D511yescharacteristic
424C2×D4—21no—
425C2×D4—151no—
426C2×D4—301no—
427C2×D4C2×D3×D511yescharacteristic
428C22×C4—21no—
429C22×C4—32no—
430C22×C4—62no—
431C22×C4—302no—
432C22×C4—301no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—154no—
435SD16—154no—
436SD16—154no—
437D8—154no—
438C2×C8—52no—
439C2×C8—102no—
440C2×C8—154no—
441C2×C8—151no—
442C2×C8—151no—
443C4⋊C4—32no—
444C4⋊C4—52no—
445C4⋊C4—62no—
446C4⋊C4—302no—
447C22⋊C4—62no—
448C22⋊C4—61no—
449C22⋊C4—101no—
450C22⋊C4—302no—
451C42—31no—
452C42—31no—
453C42—32no—
454C42—62no—
455C42—61no—
456C42—101no—
457C42—302no—
458C3×C5C4×#13511yescharacteristic, complemented, Hall
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—42no—
462C22×C3C4×C22⋊D512yes—
463C22×C3C22×C22⋊D511yescharacteristic
464C2×D3—102no—
465C2×D3—202no—
466C3×C4—22no—
467C3×C4—202no—
468C3×C4C4×C22⋊D512yes—
469C3×C4C22×C4×D511yescharacteristic
470C3×C4C2×#70911yescharacteristic
471Dic3—22no—
472Dic3—42no—
473Dic3—102no—
474Dic3#409614yescomplemented
475C2×C5—22no—
476C2×C5—42no—
477C2×C5C2×#67⋊C411yescharacteristic
478C2×C5D3×#13512yes—
479D5—122no—
480C23—21no—
481C23—301no—
482C23D3×C22⋊D511yescharacteristic
483Q8—21no—
484Q8—152no—
485Q8—301no—
486Q8C2×#120012yes—
487D4—24no—
488D4—21no—
489D4—152no—
490D4—304no—
491D4—301no—
492D4C2×#120012yes—
493C2×C4—21no—
494C2×C4—24no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—64no—
498C2×C4—62no—
499C2×C4—102no—
500C2×C4—124no—
501C2×C4—301no—
502C2×C4—304no—
503C2×C4—604no—
504C2×C4#677912yes—
505C2×C4C2×#120012yes—
506C2×C4D3×C22⋊D511yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—102no—
509C8—152no—
510C8—152no—
511C2×C3—22no—
512C2×C3—42no—
513C2×C3C2×C4×C22⋊D511yescharacteristic
514C2×C3C2×#409612yes—
515D3—202no—
516C5#7881811yescharacteristic, complemented, Sylow
517C22—22no—
518C22—22no—
519C22—42no—
520C22—302no—
521C22—602no—
522C22#9155612yes—
523C22C2×D3×C22⋊D511yescharacteristic
524C4—22no—
525C4—34no—
526C4—62no—
527C4—122no—
528C4—202no—
529C4—302no—
530C4#9155612yes—
531C4C2×#677911yescharacteristic
532C4C22×#120011yescharacteristic
533C3C4×#409611yescharacteristic, complemented, Sylow
534C2—22no—
535C2—42no—
536C2—602no—
537C2D3×#409612yes—
538C2C2×#9155611yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×#91839C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C5×Dic3×#41C2semidirect
3. #11754436C2semidirect
4. C3×#65522C2semidirect
5. #11749257C2semidirect
6. #11749232C2semidirect
7. #11749011C2semidirect
8. #11748986C2semidirect
9. #11748469C2semidirect
10. #11748393C2semidirect
11. C2×Dic3×#168C2semidirect
15. #91839C4semidirect
47. #65522D3semidirect
56. C3×C5×#41C2×C4semidirect
64. #6817C2×C4semidirect
71. #6718C2×C4semidirect
72. #6717C2×C4semidirect
73. #6716C2×C4semidirect
74. #6715C2×C4semidirect
75. C2×C3⋊#168C2×C4semidirect
95. Dic3×#41D5semidirect
199. C5×#41C4×D3semidirect
264. C5×Dic3#135semidirect
266. C3×#41C4×D5semidirect
421. #41#1200semidirect
458. C3×C5C4×#135semidirect
474. Dic3#4096semidirect
516. C5#78818semidirect
533. C3C4×#4096semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C5×Dic3×#412
#117544362
C3×#655222
#117492572
#117492322
#117490112
#117489862
#117484692
#117483932
C2×Dic3×#1682
C4×#40963
#788185