Finite Group Databasebeta

← #14416286

Subgroups — #14416286

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91275C211yesmaximal, characteristic
2#11753408C212yesmaximal, complemented
3#11750973C211yesmaximal, characteristic, complemented
4C5×#4880C211yesmaximal, characteristic, complemented
5C3×#65162C211yesmaximal, characteristic, complemented
6#11747883C211yesmaximal, characteristic, complemented
7#11747766C211yesmaximal, characteristic, complemented
8D3×C8×Dic5C211yesmaximal, characteristic, complemented
9#11747504C212yesmaximal, complemented
10#11747272C212yesmaximal, complemented
11#11747225C212yesmaximal, complemented
12#10610896—31nomaximal, Hall
13C2×#6769C2212yes—
14C2×D120C2211yescharacteristic
15#91782C2212yes—
16C2×C5×D3×C8C2211yescharacteristic
17C5×#892C2212yes—
18C2×C3×Dic20C2211yescharacteristic
19C3×#4033C2212yes—
20#91418C2212yes—
21#91406—22no—
22#91405—22no—
23#91403—22no—
24C4×#1200—22no—
25C4×D3×Dic5C2211yescharacteristic
26#91331C2212yes—
27C2×#6658C2212yes—
28C2×D3×#168C2211yescharacteristic
29#91275C418yescomplemented
30C3×C5×#107C2211yescharacteristic
31C8×Dic15C2211yescharacteristic
32#91093C2212yes—
33C5×#818C2211yescharacteristic
34C5×#808C2212yes—
35C3×C8×Dic5C2211yescharacteristic
36C3×#3942C2212yes—
37#90970C2212yes—
38#90969C2212yes—
39#90951C2211yescharacteristic
40Dic5×C3⋊C8C2211yescharacteristic
41C4×#919—51nomaximal, Hall
42C2×#4050—31no—
43#65856—32no—
44C5×#427—31no—
45C2×C8×Dic5—31no—
46#65291—32no—
47#65162—31no—
48#65162D311yescharacteristic, complemented
49#65161—31no—
50#65161—31no—
51#65141—32no—
52#65141—32no—
53C2×D60C2312yes—
54C2×C4×D15—22no—
55C2×C4×C5×D3C2311yescharacteristic
56C2×C3×Dic10C2312yes—
57C2×#1203—22no—
58C2×#1200—22no—
59C2×#1200—22no—
60C2×D3×Dic5D411yescharacteristic
61C2×D3×Dic5D411yescharacteristic
62#6769—24no—
63#6769C2×C418yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65C3×C5×C4⋊C4C2312yes—
66#6714—22no—
67C4×Dic15C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69D120C2×C414yescomplemented
70C5×(C2×D3)⋊C4—22no—
71C5×C4⋊Dic3C2312yes—
72C4×C5×Dic3—22no—
73C2×C5×C3⋊C8C2311yescharacteristic
74C5×D3×C8C2×C414yescomplemented
75C3×#683—22no—
76C3×C4×Dic5—22no—
77C3×C4×Dic5C2311yescharacteristic
78C2×C3×#168C2311yescharacteristic
79C3×Dic20C2×C414yescomplemented
80#6668—22no—
81#6667—22no—
82Dic3×Dic5—22no—
83Dic3×Dic5D411yescharacteristic
84Dic3×Dic5D411yescharacteristic
85#6658C2×C418yescomplemented
86D3×#168—22no—
87C2×#919—51no—
88C4×#239—52no—
89C3×C4×Q16—51no—
90Dic3×Q16—51no—
91C4×#215—52no—
92#4880D511yescharacteristic, complemented
93#4872—51no—
94#4804—52no—
95#4788—52no—
96C4×D24—51no—
97C4×D3×C8—51no—
98C2×#709—32no—
99C22×C5×C8—31no—
100C5×#117—32no—
101C2×C4×Dic5—31no—
102C22×#168—31no—
103C2×Dic20C2×D311yescharacteristic
104#4050—38no—
105C2×D40—31no—
106C2×#677—32no—
107#4039—32no—
108#4039—32no—
109#4033—32no—
110#4033C2×D312yes—
111#4027—62no—
112#4027—62no—
113#4018—62no—
114C42×D5—62no—
115C5×#107—31no—
116C5×#107C2×D311yescharacteristic
117C5×#106—32no—
118C8×Dic5—31no—
119C8×Dic5—31no—
120C8×Dic5—31no—
121C8×Dic5C2×D311yescharacteristic
122#3942—32no—
123#3942C2×D312yes—
124#3941—32no—
125#3941—32no—
126C4×#135—151noSylow
127C22×D15—22no—
128C22×C5×D3C2×D411yescharacteristic
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15C2×D411yescharacteristic
132C2×Dic15C2×D411yescharacteristic
133D60—22no—
134D60C22×C414yes—
135C4×D15—44no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3C2×D411yescharacteristic
138C4×C5×D3C22×C412yes—
139C4×C5×D3#4112yes—
140C2×C3×Dic5—22no—
141C2×C3×Dic5C2×D411yescharacteristic
142C2×C3×Dic5C2×D411yescharacteristic
143C3×Dic10—22no—
144C3×Dic10C22×C414yes—
145#1203—28no—
146#1200—28no—
147#1200—44no—
148D3×Dic5—22no—
149D3×Dic5—22no—
150C3×C5×C8C22×C412yes—
151C3⋊#168—21no—
152C3×#168—21no—
153C5×C3⋊C8C22×C412yes—
154C2×#239—52no—
155C2×C3×Q16—51no—
156C3×C4×Q8—52no—
157Q8×Dic3—52no—
158C2×#215—52no—
159#919—58no—
160C2×D24—51no—
161C2×D3×C8—51no—
162C2×D3×C8C2×D511yescharacteristic
163#893—52no—
164#893—102no—
165#892—102no—
166#892C2×D512yes—
167C4×D12—52no—
168C4×D12—102no—
169C42×D3—51no—
170C42×D3—102no—
171C3×#107C2×D511yescharacteristic
172C3×#103—52no—
173C3×C4×C8—51no—
174#835—52no—
175#821—52no—
176#818C2×D511yescharacteristic
177C8×Dic3—51no—
178C8×Dic3—51no—
179#809—52no—
180#808C2×D512yes—
181C4×C3⋊C8—51no—
182C22×C4×C5—31no—
183C2×C22⋊D5—62no—
184C22×Dic5—31no—
185C22×Dic5—31no—
186#709—38no—
187#709—64no—
188C2×D20—32no—
189C2×C4×D5—62no—
190C2×C4×D5—62no—
191C2×C4×D5—62no—
192C2×Dic10C22×D312yes—
193C2×C5×C8—31no—
194C2×C5×C8—34no—
195C2×C5×C8C22×D311yescharacteristic
196C5×C4⋊C4—32no—
197C5×C4⋊C4C22×D312yes—
198C5×C22⋊C4—62no—
199C42×C5—62no—
200#685—62no—
201#685—62no—
202#683—22no—
203#683—62no—
204C4×Dic5—22no—
205C4×Dic5—31no—
206C4×Dic5—31no—
207C4×Dic5—31no—
208C4×Dic5—62no—
209C4×Dic5C22×D311yescharacteristic
210C2×#168—31no—
211C2×#168—62no—
212C2×#168C22×D311yescharacteristic
213Dic20C4×D314yescomplemented
214D40—34no—
215#677—38no—
216C2×#135—151no—
217C4×#41—152no—
218C4×Q16—51no—
219C4×Q16—151no—
220C4×SD16—152no—
221C4×SD16—152no—
222C4×D8—151no—
223C4×D8—151no—
224#427—31no—
225#416—152no—
226C2×C4×C8—151no—
227C22×C3×C5C22×D411yescharacteristic
228C2×D15—24no—
229C2×D15—42no—
230C2×D15—42no—
231C2×C5×D3—21no—
232C2×C5×D3—21no—
233C2×C5×D3C4×D412yes—
234C3×C4×C5—42no—
235C3×C4×C5C23×C411yescharacteristic
236C3×C4×C5C2×#4111yescharacteristic
237Dic15—21no—
238Dic15#13512yescomplemented
239C3×Dic5—24no—
240C3×Dic5—21no—
241C3×Dic5#13512yescomplemented
242C5×Dic3—42no—
243C5×Dic3C4×D412yes—
244C2×C3×Q8—52no—
245#239—58no—
246#239—104no—
247C2×D12—52no—
248C2×D12—102no—
249C2×C4×D3—51no—
250C2×C4×D3—51no—
251C2×C4×D3—102no—
252C2×C4×D3—102no—
253C2×C4×D3—102no—
254C2×C4×D3C22×D511yescharacteristic
255C3×Q16—54no—
256C2×C3×C8—51no—
257C2×C3×C8C22×D511yescharacteristic
258C3×C4⋊C4—102no—
259C3×C4⋊C4C22×D512yes—
260C3×C42—51no—
261C3×C42—102no—
262#215—58no—
263(C2×D3)⋊C4—22no—
264(C2×D3)⋊C4—102no—
265(C2×D3)⋊C4—102no—
266C4⋊Dic3—102no—
267C4⋊Dic3C22×D512yes—
268C4×Dic3—22no—
269C4×Dic3—51no—
270C4×Dic3—51no—
271C4×Dic3—51no—
272C4×Dic3—102no—
273C2×C3⋊C8—51no—
274C2×C3⋊C8C22×D511yescharacteristic
275D24—54no—
276D3×C8—102no—
277D3×C8C4×D514yescomplemented
278C23×C5—31no—
279C22×D5—62no—
280C2×C4×C5—22no—
281C2×C4×C5—31no—
282C2×C4×C5—32no—
283C2×C4×C5—32no—
284C2×C4×C5—62no—
285C2×C4×C5C23×D311yescharacteristic
286C22⋊D5—68no—
287C2×Dic5—22no—
288C2×Dic5—31no—
289C2×Dic5—31no—
290C2×Dic5—62no—
291C2×Dic5—62no—
292C2×Dic5D3×D411yescharacteristic
293C2×Dic5D3×D411yescharacteristic
294D20—34no—
295D20—62no—
296C4×D5—68no—
297C4×D5—124no—
298C4×D5—124no—
299Dic10—22no—
300Dic10C2×C4×D314yes—
301C5×C8—32no—
302C5×C8C2×C4×D312yes—
303#168—21no—
304#168—61no—
305C2×#41—152no—
306#135—158no—
307C2×Q16—51no—
308C2×SD16—152no—
309C2×D8—151no—
310C22×C8—31no—
311C22×C8—151no—
312C4×Q8—52no—
313C4×Q8—152no—
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—302no—
317C4×D4—302no—
318#117—32no—
319#117—302no—
320C2×C42—151no—
321C2×C42—302no—
322#107—31no—
323#107D3×D511yescharacteristic
324#106—32no—
325#103—52no—
326#103—152no—
327#102—152no—
328#102—152no—
329C4×C8—51no—
330C4×C8—151no—
331C4×C8—151no—
332C4×C8—151no—
333C2×C3×C5C2×C4×D411yescharacteristic
334C2×C3×C5C2×#13511yescharacteristic
335C2×C3×C5C2×#13511yescharacteristic
336D15—44no—
337C5×D3—22no—
338C22×D3—102no—
339C22×D3D4×D511yescharacteristic
340C3×Q8—54no—
341C3×Q8—102no—
342C2×C3×C4—22no—
343C2×C3×C4—51no—
344C2×C3×C4—51no—
345C2×C3×C4—102no—
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—22no—
348C2×Dic3—51no—
349C2×Dic3—51no—
350C2×Dic3D4×D511yescharacteristic
351D12—54no—
352D12—108no—
353D12—102no—
354C4×D3—102no—
355C4×D3—102no—
356C4×D3—108no—
357C4×D3—204no—
358C4×D3—204no—
359C4×D3C2×C4×D512yes—
360C4×D3#71312yes—
361C3×C8—101no—
362C3×C8C2×C4×D512yes—
363C3⋊C8—101no—
364C3⋊C8C2×C4×D512yes—
365C22×C5—32no—
366C22×C5—61no—
367C22×C5—61no—
368C22×C5C2×D3×D411yescharacteristic
369C2×D5—64no—
370C2×D5—122no—
371C2×D5—122no—
372C4×C5—32no—
373C4×C5—42no—
374C4×C5—122no—
375C4×C5C22×C4×D311yescharacteristic
376C4×C5D3×#4111yescharacteristic
377Dic5—21no—
378Dic5—24no—
379Dic5—32no—
380Dic5—61no—
381Dic5#91912yescomplemented
382#41—158no—
383#41—304no—
384C2×Q8—52no—
385C2×D4—152no—
386C2×D4—302no—
387C22×C4—31no—
388C22×C4—151no—
389C22×C4—151no—
390C22×C4—302no—
391C22×C4—302no—
392C22×C4—302no—
393Q16—54no—
394SD16—158no—
395D8—154no—
396C2×C8—31no—
397C2×C8—34no—
398C2×C8—51no—
399C2×C8—151no—
400C2×C8—302no—
401C2×C8C2×D3×D511yescharacteristic
402C4⋊C4—32no—
403C4⋊C4—102no—
404C4⋊C4—302no—
405C4⋊C4C2×D3×D512yes—
406C22⋊C4—62no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—51no—
410C42—62no—
411C42—102no—
412C42—151no—
413C42—151no—
414C42—151no—
415C42—302no—
416C3×C5C4×#13511yescharacteristic, complemented, Hall
417C22×C3C2×D4×D511yescharacteristic
418C2×D3—21no—
419C2×D3—21no—
420C2×D3—104no—
421C2×D3—202no—
422C2×D3—202no—
423C2×D3#403912yes—
424C3×C4—42no—
425C3×C4—52no—
426C3×C4—104no—
427C3×C4—101no—
428C3×C4C22×C4×D511yescharacteristic
429C3×C4C2×#71311yescharacteristic
430Dic3—42no—
431Dic3—52no—
432Dic3—101no—
433Dic3#403912yes—
434C2×C5—62no—
435C2×C5C4×D3×D411yescharacteristic
436C2×C5C2×#91911yescharacteristic
437C2×C5D3×#13511yescharacteristic
438D5—124no—
439C23—31no—
440C23—302no—
441Q8—54no—
442Q8—102no—
443D4—154no—
444D4—308no—
445D4—302no—
446C2×C4—22no—
447C2×C4—31no—
448C2×C4—32no—
449C2×C4—32no—
450C2×C4—51no—
451C2×C4—51no—
452C2×C4—62no—
453C2×C4—102no—
454C2×C4—151no—
455C2×C4—151no—
456C2×C4—308no—
457C2×C4—302no—
458C2×C4—302no—
459C2×C4—604no—
460C2×C4—604no—
461C2×C4C22×D3×D511yescharacteristic
462C8—32no—
463C8—101no—
464C8—301no—
465C8C4×D3×D512yes—
466C2×C3C2×#403911yescharacteristic
467C2×C3D5×#13511yescharacteristic
468C2×C3D5×#13511yescharacteristic
469D3—22no—
470D3—204no—
471C5C4×#91911yescharacteristic, complemented, Sylow
472C22—32no—
473C22—61no—
474C22—61no—
475C22—304no—
476C22—602no—
477C22—602no—
478C22D3×D4×D511yescharacteristic
479C4—32no—
480C4—42no—
481C4—52no—
482C4—101no—
483C4—104no—
484C4—122no—
485C4—152no—
486C4—301no—
487C4C2×C4×D3×D511yescharacteristic
488C4D3×#71311yescharacteristic
489C3#1061089611yescharacteristic, complemented, Sylow
490C2—62no—
491C2—604no—
492C2D3×#403911yescharacteristic
493C2#1175405311yescharacteristic
494C2D5×#91911yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC2×#91275C2
cosocleC2×C3×C4×C5C24
hypercenter#107D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #11753408C2semidirect
3. #11750973C2semidirect
4. C5×#4880C2semidirect
5. C3×#65162C2semidirect
6. #11747883C2semidirect
7. #11747766C2semidirect
8. D3×C8×Dic5C2semidirect
9. #11747504C2semidirect
10. #11747272C2semidirect
11. #11747225C2semidirect
29. #91275C4semidirect
48. #65162D3semidirect
63. #6769C2×C4semidirect
69. D120C2×C4semidirect
74. C5×D3×C8C2×C4semidirect
79. C3×Dic20C2×C4semidirect
85. #6658C2×C4semidirect
92. #4880D5semidirect
213. Dic20C4×D3semidirect
238. Dic15#135semidirect
241. C3×Dic5#135semidirect
277. D3×C8C4×D5semidirect
381. Dic5#919semidirect
416. C3×C5C4×#135semidirect
471. C5C4×#919semidirect
489. C3#10610896semidirect

Maximal subgroups

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

subgroupindex
C2×#912752
#117534082
#117509732
C5×#48802
C3×#651622
#117478832
#117477662
D3×C8×Dic52
#117475042
#117472722
#117472252
#106108963
C4×#9195