Finite Group Databasebeta

← #14417655

Subgroups — #14417655

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91270C211yesmaximal, characteristic
2#11752669C212yesmaximal, complemented
3C4×Dic60C211yesmaximal, characteristic, complemented
4C4×C5×D24C211yesmaximal, characteristic, complemented
5C3×#64978C211yesmaximal, characteristic, complemented
6#11747851C211yesmaximal, characteristic, complemented
7Dic5×D24C211yesmaximal, characteristic, complemented
8#11747747C212yesmaximal, complemented
9D5×#818C211yesmaximal, characteristic, complemented
10#11747605C212yesmaximal, complemented
11#11747056C212yesmaximal, complemented
12#10611320—31nomaximal, Hall
13C2×#6772C2212yes—
14C2×Dic60C2211yescharacteristic
15C4×Dic30C2212yes—
16C2×C5×D24C2211yescharacteristic
17C4×C5×D12C2212yes—
18C2×C3×#676C2211yescharacteristic
19C2×C3×C8×D5C2211yescharacteristic
20C3×#4018C2211yescharacteristic
21#91442—22no—
22#91441—22no—
23Dic5×D12C2212yes—
24D5×C4⋊Dic3C2212yes—
25#91400—22no—
26D3×#683—22no—
27#91333C2212yes—
28C2×#6659C2212yes—
29#91270C418yescomplemented
30C3×C4×C5×C8C2211yescharacteristic
31#91102C2211yescharacteristic
32#91100C2212yes—
33C5×#821C2212yes—
34C5×#818C2211yescharacteristic
35C3×#3947C2211yescharacteristic
36C3×C8×Dic5C2211yescharacteristic
37C3×#3935C2211yescharacteristic
38#90988C2212yes—
39#90975C2212yes—
40#90967C2212yes—
41#78562—51nomaximal, Hall
42C2×#4058—31no—
43#65880—32no—
44C4×C5×D8—31no—
45D8×Dic5—31no—
46#65307—32no—
47D5×#107—31no—
48#65162—31no—
49#65060—32no—
50#65046—32no—
51C4×Dic20—31no—
52#64978D311yescharacteristic, complemented
53C2×Dic30C2312yes—
54C2×C5×D12C2312yes—
55C2×C4×C5×D3—22no—
56C2×C3×C4×D5C2311yescharacteristic
57C2×#1201—22no—
58C2×D3×Dic5—22no—
59C2×D3×Dic5—22no—
60C2×D5×Dic3—22no—
61#6772—24no—
62#6772C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C3×C42×C5C2311yescharacteristic
66C4⋊Dic15C2312yes—
67#6712—22no—
68C4×Dic15—22no—
69Dic60C2×C414yescomplemented
70C5×(C2×D3)⋊C4—22no—
71C5×C4⋊Dic3C2312yes—
72C5×D24C2×C414yescomplemented
73C3×#685D411yescharacteristic
74C3×#685D411yescharacteristic
75C3×#683D411yescharacteristic
76C3×#683D411yescharacteristic
77C3×C4×Dic5C2311yescharacteristic
78C2×C3×#168C2311yescharacteristic
79C2×C3×#168C2311yescharacteristic
80C3×#676—22no—
81C3×C8×D5C2×C414yescomplemented
82#6669—22no—
83#6668—22no—
84(C2×D3)⋊Dic5—22no—
85Dic3×Dic5—22no—
86#6659C2×C418yescomplemented
87C2×#904—51no—
88#5523—52no—
89C3×#405—51no—
90#5133—52no—
91C2×#818—51no—
92#4710—52no—
93#4710—52no—
94C4×Dic12—51no—
95C4×Dic12—51no—
96C4×D24—51no—
97C4×D24D511yescharacteristic, complemented
98C2×#711—32no—
99C2×C5×D8—31no—
100C4×C5×D4—32no—
101D4×Dic5—32no—
102C2×#687—32no—
103C4×C22⋊D5—62no—
104C2×#683—62no—
105#4058—38no—
106C2×Dic20—31no—
107C2×#676C2×D311yescharacteristic
108C2×C8×D5C2×D311yescharacteristic
109D5×C4⋊C4—32no—
110#4033—32no—
111#4027—62no—
112#4023—62no—
113#4018C2×D311yescharacteristic
114C4×Dic10—32no—
115C5×#107—31no—
116C5×#102—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3964—32no—
119#3950—31no—
120#3948—32no—
121#3947C2×D311yescharacteristic
122C8×Dic5C2×D311yescharacteristic
123#3942—32no—
124#3939—32no—
125#3935C2×D311yescharacteristic
126#2951—151noSylow
127C22×C5×D3—22no—
128C22×C3×D5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133C2×Dic15—22no—
134Dic30—22no—
135Dic30C22×C414yes—
136C2×C5×Dic3—22no—
137C5×D12—22no—
138C5×D12C22×C414yes—
139C4×C5×D3—82no—
140C2×C3×Dic5C2×D411yescharacteristic
141C2×C3×Dic5C2×D411yescharacteristic
142C2×C3×Dic5C2×D411yescharacteristic
143C3×C4×D5C22×C412yes—
144C3×C4×D5#4112yes—
145#1201—28no—
146D3×Dic5—28no—
147D3×Dic5—82no—
148D5×Dic3—82no—
149C3×C5×C8—21no—
150C3×C5×C8C22×C412yes—
151C3×#168—21no—
152C3×#168C22×C412yes—
153C2×#235—52no—
154C2×C3×M16—51no—
155C22×C3×C8—51no—
156C3×#117—51no—
157C2×C4⋊Dic3—52no—
158C2×Dic12—51no—
159#904—58no—
160C2×D24C2×D511yescharacteristic
161C2×#204—52no—
162#892—102no—
163D3×C4⋊C4—102no—
164#67⋊C4—102no—
165#67⋊C4—102no—
166C4×D12—52no—
167C4×D12C2×D512yes—
168C4×Dic6—52no—
169C4×Dic6—52no—
170C3×#97—51no—
171C3×#97—51no—
172C3×C4×C8—51no—
173C3×C4×C8C2×D511yescharacteristic
174#821—52no—
175#821C2×D512yes—
176#818—51no—
177#818—52no—
178#818C2×D511yescharacteristic
179#816—52no—
180#816—52no—
181C2×C5×D4—32no—
182C22×C4×C5—62no—
183C2×C22⋊D5—62no—
184C22×Dic5—62no—
185C22×Dic5—62no—
186#711—38no—
187#711—64no—
188C2×C4×D5—62no—
189C2×C4×D5C22×D311yescharacteristic
190C2×Dic10—32no—
191C5×D8—34no—
192C2×C5×C8C22×D311yescharacteristic
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4—32no—
195C5×C22⋊C4—62no—
196C42×C5C22×D311yescharacteristic
197C22⋊Dic5—62no—
198#687—38no—
199#685D1211yescharacteristic
200#685D1211yescharacteristic
201C4⋊Dic5—32no—
202#683—62no—
203#683—62no—
204#683—62no—
205#683D1211yescharacteristic
206#683D1211yescharacteristic
207C4×Dic5—62no—
208C4×Dic5—62no—
209C4×Dic5C22×D311yescharacteristic
210C2×#168C22×D311yescharacteristic
211C2×#168C22×D311yescharacteristic
212Dic20—34no—
213#676—22no—
214C8×D5C4×D314yescomplemented
215C2×#135—151no—
216#520—152no—
217#440—152no—
218#440—152no—
219C4×Q16—151no—
220C4×Q16—151no—
221C4×D8—31no—
222C4×D8—151no—
223C2×#107—151no—
224#417—152no—
225#405—51no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—24no—
228C2×C5×D3—42no—
229C2×C5×D3—42no—
230C2×C3×D5—21no—
231C2×C3×D5—21no—
232C2×C3×D5C4×D412yes—
233C3×C4×C5—21no—
234C3×C4×C5—21no—
235C3×C4×C5C23×C411yescharacteristic
236C3×C4×C5C2×#4111yescharacteristic
237Dic15—24no—
238Dic15—42no—
239C3×Dic5—21no—
240C3×Dic5—21no—
241C3×Dic5C4×D412yes—
242C5×Dic3—42no—
243C22×C3×C4—51no—
244C2×#67—102no—
245C22×Dic3—102no—
246#235—58no—
247#235—104no—
248C2×D12C22×D512yes—
249C2×C4×D3—22no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×Dic6—52no—
253C3×M16—102no—
254C2×C3×C8—51no—
255C2×C3×C8—54no—
256C2×C3×C8—51no—
257C2×C3×C8C22×D511yescharacteristic
258C2×C3×C8C22×D511yescharacteristic
259C3×C4⋊C4—51no—
260C3×C4⋊C4—51no—
261C3×C22⋊C4—51no—
262C3×C22⋊C4—51no—
263C3×C42—51no—
264C3×C42C22×D511yescharacteristic
265(C2×D3)⋊C4—22no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—52no—
268C4⋊Dic3—102no—
269C4⋊Dic3C22×D512yes—
270Dic3⋊C4—102no—
271Dic3⋊C4—102no—
272C4×Dic3—102no—
273C4×Dic3—102no—
274Dic12—54no—
275D24C4×D514yescomplemented
276#204—58no—
277C23×C5—62no—
278C22×D5C2×D1211yescharacteristic
279C5×D4—34no—
280C5×D4—62no—
281C2×C4×C5—62no—
282C2×C4×C5—242no—
283C2×C4×C5C2×D1211yescharacteristic
284C2×C4×C5C2×D1211yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C22⋊D5—68no—
287C2×Dic5—62no—
288C2×Dic5—68no—
289C2×Dic5—62no—
290C2×Dic5—242no—
291C2×Dic5C2×D1211yescharacteristic
292C2×Dic5C2×D1211yescharacteristic
293C2×Dic5C2×D1211yescharacteristic
294C4×D5—242no—
295C4×D5C2×C4×D312yes—
296C4×D5#23512yes—
297Dic10—34no—
298Dic10—62no—
299C5×C8—21no—
300C5×C8C2×C4×D312yes—
301#168—21no—
302#168C2×C4×D312yes—
303C2×#41—152no—
304#135—158no—
305C2×Q16—151no—
306C2×SD16—152no—
307C2×D8—31no—
308C2×M16—51no—
309C22×C8—51no—
310C4×Q8—152no—
311C4×Q8—152no—
312C4×D4—32no—
313C4×D4—152no—
314C4×D4—302no—
315C4×D4—302no—
316#117—51no—
317#117—302no—
318C2×C4⋊C4—152no—
319C2×C4⋊C4—302no—
320#107—31no—
321#107—152no—
322#107—151no—
323#103—152no—
324#103—152no—
325#102—32no—
326#102—152no—
327#97—51no—
328#97—51no—
329C4×C8—51no—
330C4×C8D3×D511yescharacteristic
331C2×C3×C5C2×C4×D411yescharacteristic
332C2×C3×C5#57611yescharacteristic
333C2×C3×C5#57811yescharacteristic
334C3×D5—22no—
335C5×D3—44no—
336C23×C3—51no—
337C22×D3—22no—
338C2×C3×C4—51no—
339C2×C3×C4—52no—
340C2×C3×C4—52no—
341C2×C3×C4—51no—
342C2×C3×C4—51no—
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4C23×D511yescharacteristic
346#67—108no—
347C2×Dic3—22no—
348C2×Dic3—102no—
349C2×Dic3—102no—
350C2×Dic3—402no—
351D12—22no—
352D12C2×C4×D514yes—
353C4×D3—82no—
354C4×D3—108no—
355C4×D3—402no—
356Dic6—54no—
357Dic6—102no—
358C3×C8—21no—
359C3×C8—52no—
360C3×C8—101no—
361C3×C8C2×C4×D512yes—
362C22×C5—64no—
363C22×C5—122no—
364C22×C5—122no—
365C22×C5C22×D1211yescharacteristic
366C2×D5—21no—
367C2×D5—21no—
368C2×D5C4×D1212yes—
369C4×C5—21no—
370C4×C5—21no—
371C4×C5—122no—
372C4×C5C22×C4×D311yescharacteristic
373C4×C5C2×#23511yescharacteristic
374Dic5—21no—
375Dic5—21no—
376Dic5—64no—
377Dic5—122no—
378Dic5C4×D1212yes—
379#41—158no—
380#41—304no—
381C2×Q8—152no—
382C2×D4—32no—
383C2×D4—302no—
384C22×C4—51no—
385C22×C4—62no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389Q16—154no—
390SD16—158no—
391D8—34no—
392M16—102no—
393C2×C8—51no—
394C2×C8—54no—
395C2×C8—51no—
396C2×C8C2×D3×D511yescharacteristic
397C2×C8C2×D3×D511yescharacteristic
398C4⋊C4—32no—
399C4⋊C4—51no—
400C4⋊C4—51no—
401C4⋊C4—152no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C4⋊C4—302no—
405C22⋊C4—51no—
406C22⋊C4—51no—
407C22⋊C4—62no—
408C22⋊C4—302no—
409C42—51no—
410C42—302no—
411C42—302no—
412C42C2×D3×D511yescharacteristic
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3—52no—
415C22×C3—101no—
416C22×C3—101no—
417C22×C3C2×D4×D511yescharacteristic
418C2×D3—24no—
419C2×D3—42no—
420C2×D3—42no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—52no—
424C3×C4—101no—
425C3×C4—101no—
426C3×C4C22×C4×D511yescharacteristic
427C3×C4D5×#4111yescharacteristic
428Dic3—42no—
429Dic3—104no—
430Dic3—202no—
431C2×C5—124no—
432C2×C5C2×C4×D1211yescharacteristic
433C2×C5#575211yescharacteristic
434C2×C5#575311yescharacteristic
435D5—22no—
436C23—51no—
437C23—62no—
438Q8—154no—
439Q8—302no—
440D4—34no—
441D4—62no—
442D4—308no—
443C2×C4—51no—
444C2×C4—52no—
445C2×C4—52no—
446C2×C4—51no—
447C2×C4—51no—
448C2×C4—62no—
449C2×C4—242no—
450C2×C4—308no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—1202no—
454C2×C4—1202no—
455C2×C4D5×D1211yescharacteristic
456C2×C4D5×D1211yescharacteristic
457C2×C4C22×D3×D511yescharacteristic
458C8—21no—
459C8—52no—
460C8—101no—
461C8C4×D3×D512yes—
462C2×C3—102no—
463C2×C3C4×D4×D511yescharacteristic
464C2×C3#6609111yescharacteristic
465C2×C3#6610511yescharacteristic
466D3—44no—
467C5#7856211yescharacteristic, complemented, Sylow
468C22—52no—
469C22—64no—
470C22—101no—
471C22—101no—
472C22—122no—
473C22—122no—
474C22C2×D5×D1211yescharacteristic
475C4—21no—
476C4—21no—
477C4—52no—
478C4—101no—
479C4—101no—
480C4—122no—
481C4—304no—
482C4—602no—
483C4C2×C4×D3×D511yescharacteristic
484C4D5×#23511yescharacteristic
485C3#1061132011yescharacteristic, complemented, Sylow
486C2—102no—
487C2—124no—
488C2C4×D5×D1211yescharacteristic
489C2#1175396111yescharacteristic
490C2#1175398811yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91270C2
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5#2951
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11752669C2semidirect
3. C4×Dic60C2semidirect
4. C4×C5×D24C2semidirect
5. C3×#64978C2semidirect
6. #11747851C2semidirect
7. Dic5×D24C2semidirect
8. #11747747C2semidirect
9. D5×#818C2semidirect
10. #11747605C2semidirect
11. #11747056C2semidirect
29. #91270C4semidirect
52. #64978D3semidirect
62. #6772C2×C4semidirect
69. Dic60C2×C4semidirect
72. C5×D24C2×C4semidirect
81. C3×C8×D5C2×C4semidirect
86. #6659C2×C4semidirect
97. C4×D24D5semidirect
214. C8×D5C4×D3semidirect
275. D24C4×D5semidirect
413. C3×C5#2951semidirect
467. C5#78562semidirect
485. C3#10611320semidirect

Maximal subgroups

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

subgroupindex
C2×#912702
#117526692
C4×Dic602
C4×C5×D242
C3×#649782
#117478512
Dic5×D242
#117477472
D5×#8182
#117476052
#117470562
#106113203
#785625