Finite Group Databasebeta

← #14460113

Subgroups — #14460113

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756322C211yesmaximal, characteristic, complemented
2#11756310C211yesmaximal, characteristic, complemented
3C3×C5×C8×D4C211yesmaximal, characteristic, complemented
4#11751215C212yesmaximal, complemented
5#11751214C212yesmaximal, complemented
6#11750943C211yesmaximal, characteristic, complemented
7#11750942C211yesmaximal, characteristic, complemented
8#11750835C212yesmaximal, complemented
9#11750824C212yesmaximal, complemented
10C4×D120C211yesmaximal, characteristic, complemented
11#11750782C211yesmaximal, characteristic, complemented
12#10611174—31nomaximal, Hall
13C2×#6817C2212yes—
14C22×C3×C5×C8C2212yes—
15C3×C4×C5×D4C2211yescharacteristic
16#91827—21no—
17#91827—21no—
18#91819C2212yes—
19#91815C2212yes—
20#91813C2212yes—
21C2×D120C2211yescharacteristic
22C2×#6706C2212yes—
23#91781—21no—
24C4⋊C4×D15—21no—
25#91774—22no—
26#91772—22no—
27C4×D60C2211yescharacteristic
28C4×D60C2211yescharacteristic
29#91758C2211yescharacteristic
30#91758C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic
32C3×C5×C22⋊C8C2212yes—
33C3×C4×C5×C8C2211yescharacteristic
34#91105C2212yes—
35#91105C2211yescharacteristic
36#91105C2211yescharacteristic
37#91102C2211yescharacteristic
38#91101C2212yes—
39#91100C2212yes—
40#91100C2212yes—
41#91100C2212yes—
42#79443—51nomaximal, Hall
43#65897—31no—
44#65885—31no—
45C5×C8×D4D311yescharacteristic, complemented
46#65403—32no—
47#65402—32no—
48#65131—31no—
49#65130—31no—
50#65023—32no—
51#65012—32no—
52C4×D40—31no—
53#64970—31no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×#1220—22no—
57C2×#1220—22no—
58#6817—24no—
59#6817—42no—
60C2×D60C2311yescharacteristic
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×C4×D15—21no—
64C2×C4×D15—22no—
65C2×Dic30—21no—
66C2×Dic30C2312yes—
67C2×C3×C5×C8—42no—
68C2×C3×C5×C8C2312yes—
69C2×C3×C5×C8C2311yescharacteristic
70C2×C3×C5×C8C2311yescharacteristic
71C3×C5×C4⋊C4D411yescharacteristic
72C3×C5×C22⋊C4D412yes—
73C3×C42×C5C2311yescharacteristic
74#6719—22no—
75#6719—22no—
76#6714—21no—
77#6714—21no—
78#6714—22no—
79C4⋊Dic15—21no—
80C4⋊Dic15—21no—
81C4⋊Dic15—21no—
82C4⋊Dic15C2312yes—
83C4⋊Dic15C2311yescharacteristic
84C4⋊Dic15C2311yescharacteristic
85#6712—22no—
86C4×Dic15—22no—
87D120—22no—
88#6706—42no—
89#5563—51no—
90#5551—51no—
91C3×C8×D4D511yescharacteristic, complemented
92#5114—52no—
93#5113—52no—
94#4842—51no—
95#4841—51no—
96#4734—52no—
97#4723—52no—
98C4×D24—51no—
99#4681—51no—
100C2×#709—32no—
101C22×C5×C8C2×D312yes—
102C4×C5×D4C2×D311yescharacteristic
103#4084—61no—
104#4084—61no—
105#4076—32no—
106#4072—32no—
107#4070—32no—
108C2×D40—31no—
109C2×#677—32no—
110#4038—61no—
111D5×C4⋊C4—61no—
112#4031—62no—
113#4029—62no—
114C4×D20—31no—
115C4×D20—31no—
116#4015—31no—
117#4015—31no—
118C5×C4⋊C8C2×D311yescharacteristic
119C5×C22⋊C8C2×D312yes—
120C4×C5×C8C2×D311yescharacteristic
121#3953—32no—
122#3953—31no—
123#3953—31no—
124#3950—31no—
125#3949—32no—
126#3948—32no—
127#3948—32no—
128#3948—32no—
129#3303—151noSylow
130C23×C3×C5C2×D412yes—
131C22×D15—21no—
132C22×D15—21no—
133C3×C5×D4—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140#1220—44no—
141#1220—82no—
142C2×Dic15—21no—
143C2×Dic15—22no—
144C2×Dic15—21no—
145C2×Dic15—22no—
146D60—21no—
147D60—21no—
148D60—21no—
149D60#4112yes—
150C4×D15—44no—
151C4×D15—42no—
152C4×D15—42no—
153Dic30—22no—
154Dic30—22no—
155Dic30—81no—
156C3×C5×C8—21no—
157C3×C5×C8—22no—
158C3×C5×C8—21no—
159C2×#235—52no—
160C22×C3×C8C2×D512yes—
161C3×C4×D4C2×D511yescharacteristic
162#938—101no—
163#938—101no—
164#930—52no—
165#926—52no—
166#924—52no—
167C2×D24—51no—
168C2×#204—52no—
169#892—101no—
170D3×C4⋊C4—101no—
171#885—102no—
172#883—102no—
173C4×D12—51no—
174C4×D12—51no—
175#869—51no—
176#869—51no—
177C3×C4⋊C8C2×D511yescharacteristic
178C3×C22⋊C8C2×D512yes—
179C3×C4×C8C2×D511yescharacteristic
180#821—51no—
181#821—51no—
182#821—52no—
183#818—51no—
184#817—52no—
185#816—52no—
186#816—52no—
187#816—52no—
188C2×C5×D4D1211yescharacteristic
189C22×C4×C5C22×D312yes—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192#709—64no—
193#709—122no—
194C2×D20—31no—
195C2×D20—31no—
196C2×C4×D5—62no—
197C2×C4×D5—61no—
198C2×C4×D5—61no—
199C2×Dic10—32no—
200C2×Dic10—61no—
201C2×C5×C8—42no—
202C2×C5×C8C22×D311yescharacteristic
203C2×C5×C8C22×D312yes—
204C2×C5×C8C22×D311yescharacteristic
205C5×C4⋊C4D1211yescharacteristic
206C5×C22⋊C4D1212yes—
207C42×C5C22×D311yescharacteristic
208C22⋊Dic5—62no—
209C22⋊Dic5—62no—
210#685—61no—
211#685—61no—
212#685—62no—
213C4⋊Dic5—32no—
214C4⋊Dic5—31no—
215C4⋊Dic5—31no—
216C4⋊Dic5—61no—
217C4⋊Dic5—61no—
218C4⋊Dic5—61no—
219#683—62no—
220C4×Dic5—62no—
221D40—62no—
222#677—122no—
223#555—151no—
224#547—151no—
225#487—151no—
226#485—152no—
227#476—151no—
228#465—152no—
229#461—151no—
230#449—152no—
231C4×D8—151no—
232C8×D4D1511yescharacteristic, complemented
233#416—152no—
234C22×C3×C5—22no—
235C22×C3×C5—22no—
236C22×C3×C5—22no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—22no—
239C2×D15—41no—
240C2×D15—41no—
241C2×D15—41no—
242C2×D15—41no—
243C2×D15—41no—
244C3×C4×C5—22no—
245C3×C4×C5—21no—
246C3×C4×C5#13512yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C5H(5,𝔽2)11yescharacteristic
249Dic15—42no—
250Dic15—41no—
251Dic15—41no—
252Dic15—42no—
253C2×C3×D4D2011yescharacteristic
254C22×C3×C4C22×D512yes—
255C2×#67—102no—
256C2×#67—102no—
257#235—104no—
258#235—202no—
259C2×D12—51no—
260C2×D12—51no—
261C2×C4×D3—101no—
262C2×C4×D3—101no—
263C2×C4×D3—102no—
264C2×Dic6—52no—
265C2×Dic6—101no—
266C2×C3×C8—42no—
267C2×C3×C8C22×D511yescharacteristic
268C2×C3×C8C22×D511yescharacteristic
269C2×C3×C8C22×D512yes—
270C3×C4⋊C4D2011yescharacteristic
271C3×C22⋊C4D2012yes—
272C3×C42C22×D511yescharacteristic
273#217—102no—
274#217—102no—
275(C2×D3)⋊C4—101no—
276(C2×D3)⋊C4—101no—
277(C2×D3)⋊C4—102no—
278C4⋊Dic3—52no—
279C4⋊Dic3—51no—
280C4⋊Dic3—51no—
281C4⋊Dic3—101no—
282C4⋊Dic3—101no—
283C4⋊Dic3—101no—
284Dic3⋊C4—102no—
285C4×Dic3—102no—
286D24—102no—
287#204—202no—
288C23×C5C2×D1212yes—
289C22×D5—61no—
290C22×D5—61no—
291C5×D4—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5C2×D1212yes—
295C2×C4×C5C2×D1211yescharacteristic
296C2×C4×C5C2×D1211yescharacteristic
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5—124no—
299C22⋊D5—242no—
300C2×Dic5—61no—
301C2×Dic5—62no—
302C2×Dic5—61no—
303C2×Dic5—62no—
304D20—32no—
305D20—61no—
306D20—61no—
307D20—61no—
308C4×D5—124no—
309C4×D5—122no—
310C4×D5—122no—
311Dic10—62no—
312Dic10—62no—
313Dic10—241no—
314C5×C8—22no—
315C5×C8—21no—
316C5×C8—21no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8C2×D1512yes—
321C4⋊Q8—151no—
322C4⋊Q8—151no—
323#124—302no—
324#123—302no—
325C22⋊Q8—152no—
326#121—152no—
327#121—301no—
328#121—301no—
329C4×D4—151no—
330C4×D4—151no—
331C4×D4C2×D1511yescharacteristic
332#117—152no—
333#117—301no—
334C2×C4⋊C4—301no—
335#107—151no—
336#106—152no—
337C4⋊C8C2×D1511yescharacteristic
338#103—152no—
339#103—152no—
340#103—152no—
341#102—151no—
342#102—152no—
343#102—151no—
344C22⋊C8C2×D1512yes—
345C4×C8C2×D1511yescharacteristic
346C2×C3×C5—42no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—42no—
351D15—81no—
352C23×C3C2×D2012yes—
353C22×D3—101no—
354C22×D3—101no—
355C3×D4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4C2×D2012yes—
359C2×C3×C4C2×D2011yescharacteristic
360C2×C3×C4C2×D2011yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362#67—204no—
363#67—402no—
364C2×Dic3—101no—
365C2×Dic3—102no—
366C2×Dic3—101no—
367C2×Dic3—102no—
368D12—52no—
369D12—101no—
370D12—101no—
371D12—101no—
372C4×D3—204no—
373C4×D3—202no—
374C4×D3—202no—
375Dic6—102no—
376Dic6—102no—
377Dic6—401no—
378C3×C8—22no—
379C3×C8—21no—
380C3×C8—21no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5C22×D1211yescharacteristic
385C2×D5—62no—
386C2×D5—121no—
387C2×D5—121no—
388C2×D5—121no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—21no—
392C4×C5—22no—
393C4×C5#90412yes—
394C4×C5#100411yescharacteristic
395C4×C5D3×#4111yescharacteristic
396Dic5—121no—
397Dic5—121no—
398Dic5—122no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—152no—
403C2×Q8—301no—
404C2×D4—151no—
405C2×D4—151no—
406C2×D4—302no—
407C2×D4—302no—
408C2×D4D6011yescharacteristic
409C22×C4—301no—
410C22×C4—302no—
411C22×C4—301no—
412C22×C4C22×D1512yes—
413SD16—602no—
414D8—302no—
415C2×C8—42no—
416C2×C8C22×D1511yescharacteristic
417C2×C8C22×D1511yescharacteristic
418C2×C8C22×D1512yes—
419C4⋊C4—152no—
420C4⋊C4—151no—
421C4⋊C4—151no—
422C4⋊C4—301no—
423C4⋊C4—302no—
424C4⋊C4—301no—
425C4⋊C4—301no—
426C4⋊C4D6011yescharacteristic
427C22⋊C4—302no—
428C22⋊C4—302no—
429C22⋊C4—302no—
430C22⋊C4—301no—
431C22⋊C4—301no—
432C22⋊C4D6012yes—
433C42—302no—
434C42C22×D1511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3C22×D2011yescharacteristic
440C2×D3—102no—
441C2×D3—201no—
442C2×D3—201no—
443C2×D3—201no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4#405012yes—
449C3×C4#414411yescharacteristic
450C3×C4D5×#4111yescharacteristic
451Dic3—201no—
452Dic3—201no—
453Dic3—202no—
454Dic3—202no—
455C2×C5—42no—
456C2×C5#555411yescharacteristic
457C2×C5C2×#90411yescharacteristic
458C2×C5#575111yescharacteristic
459D5—122no—
460D5—241no—
461C23—301no—
462C23—301no—
463C23C2×D6012yes—
464Q8—302no—
465Q8—302no—
466Q8—1201no—
467D4—22no—
468D4—152no—
469D4—301no—
470D4—301no—
471D4—301no—
472D4—604no—
473D4—1202no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—301no—
477C2×C4—302no—
478C2×C4—301no—
479C2×C4—302no—
480C2×C4—604no—
481C2×C4—602no—
482C2×C4—602no—
483C2×C4C2×D6012yes—
484C2×C4C2×D6011yescharacteristic
485C2×C4C2×D6011yescharacteristic
486C2×C4C23×D1511yescharacteristic
487C8—21no—
488C8—22no—
489C8—21no—
490C2×C3—42no—
491C2×C3#6588811yescharacteristic
492C2×C3C2×#405011yescharacteristic
493C2×C3#6608511yescharacteristic
494D3—202no—
495D3—401no—
496C5#7944311yescharacteristic, complemented, Sylow
497C22—22no—
498C22—22no—
499C22—22no—
500C22—302no—
501C22—601no—
502C22—601no—
503C22—601no—
504C22—601no—
505C22—601no—
506C22C22×D6011yescharacteristic
507C4—22no—
508C4—21no—
509C4—602no—
510C4—601no—
511C4—601no—
512C4—602no—
513C4#9179312yes—
514C4#9209511yescharacteristic
515C4#41×D1511yescharacteristic
516C3#1061117411yescharacteristic, complemented, Sylow
517C2—42no—
518C2—602no—
519C2—1201no—
520C2#1175631311yescharacteristic
521C2C2×#9179311yescharacteristic
522C2#1175651011yescharacteristic
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×C8×D4C2
socleC22×C3×C5C22×D4
hypercenterC8×D4D15
hypocenterC3×C5#3303
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #11756322C2semidirect
2. #11756310C2semidirect
3. C3×C5×C8×D4C2semidirect
4. #11751215C2semidirect
5. #11751214C2semidirect
6. #11750943C2semidirect
7. #11750942C2semidirect
8. #11750835C2semidirect
9. #11750824C2semidirect
10. C4×D120C2semidirect
11. #11750782C2semidirect
45. C5×C8×D4D3semidirect
91. C3×C8×D4D5semidirect
232. C8×D4D15semidirect
435. C3×C5#3303semidirect
496. C5#79443semidirect
516. C3#10611174semidirect

Maximal subgroups

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

subgroupindex
#117563222
#117563102
C3×C5×C8×D42
#117512152
#117512142
#117509432
#117509422
#117508352
#117508242
C4×D1202
#117507822
#106111743
#794435