Finite Group Databasebeta

← #14460210

Subgroups — #14460210

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#11752715C211yesmaximal, characteristic, complemented
2#11752676C211yesmaximal, characteristic, complemented
3#11750942C211yesmaximal, characteristic, complemented
4C5×#4842C211yesmaximal, characteristic, complemented
5C3×#65123C211yesmaximal, characteristic, complemented
6#11748163C212yesmaximal, complemented
7#11748135C212yesmaximal, complemented
8#11747897C212yesmaximal, complemented
9#11747676C212yesmaximal, complemented
10C4×#6654C211yesmaximal, characteristic, complemented
11#11746930C211yesmaximal, characteristic, complemented
12#10612807—31nomaximal, Hall
13C2×#6772C2212yes—
14C2×#6706C2212yes—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18C5×#869C2211yescharacteristic
19C2×C3×C8×D5C2212yes—
20C3×C4×D20C2211yescharacteristic
21#91465—21no—
22#91457—22no—
23#91456—21no—
24#91455—22no—
25#91450C2212yes—
26D3×C4⋊Dic5—21no—
27#91360C2212yes—
28#91358C2212yes—
29#91347—21no—
30C2×#6654C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic
32#91100C2212yes—
33C5×#821C2212yes—
34C5×#817C2212yes—
35C3×#3952C2212yes—
36C3×C4×#168C2211yescharacteristic
37#90988C2211yescharacteristic
38#90975C2212yes—
39#90975C2212yes—
40#90969C2211yescharacteristic
41#90967C2211yescharacteristic
42#79443—51nomaximal, Hall
43#66068—31no—
44#65889—31no—
45C5×#476—31no—
46#65382—31no—
47C4×#686—31no—
48#65156—32no—
49#65153—32no—
50#65130—31no—
51#65123D311yescharacteristic, complemented
52#65070—32no—
53#65061—32no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2312yes—
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C2×C5×Dic6—21no—
60C2×C3×D20D411yescharacteristic
61C2×C3×C4×D5C2312yes—
62C2×#1202—22no—
63C2×#1201—22no—
64C2×D3×Dic5—22no—
65#6772—24no—
66#6772—42no—
67C2×C3×C5×C8C2312yes—
68C3×C42×C5C2311yescharacteristic
69#6714—21no—
70C4⋊Dic15—21no—
71C4⋊Dic15—21no—
72C4⋊Dic15C2311yescharacteristic
73#6706—42no—
74C5×(C2×D3)⋊C4—21no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2312yes—
77C5×C4⋊Dic3C2311yescharacteristic
78C3×#685D412yes—
79C3×C4⋊Dic5D411yescharacteristic
80C2×C3×#168C2311yescharacteristic
81C2×C3×#168C2311yescharacteristic
82C3×C8×D5—42no—
83Dic3⋊Dic5—22no—
84#6667—22no—
85#6665—22no—
86#6665—22no—
87Dic3×Dic5—22no—
88#6654—22no—
89#5563—51no—
90#5551—51no—
91C3×C8×D4—51no—
92#5114—52no—
93#5113—52no—
94#4842D511yescharacteristic, complemented
95#4841—51no—
96#4734—52no—
97#4723—52no—
98C4×D24—51no—
99#4681—51no—
100C2×#711—32no—
101C5×C4⋊Q8—31no—
102C4×C5×D4—31no—
103#4093—62no—
104C2×#686—31no—
105#4076—61no—
106C2×C4⋊Dic5—61no—
107C2×#677—32no—
108C2×C8×D5C2×D312yes—
109#4043—32no—
110#4041—32no—
111#4041—61no—
112#4038—32no—
113#4038—61no—
114#4032—62no—
115C4×D20—31no—
116C4×D20C2×D311yescharacteristic
117#4015—31no—
118C5×#106—32no—
119C5×C4⋊C8C2×D311yescharacteristic
120C5×#102—32no—
121#3964—31no—
122#3952C2×D312yes—
123#3948—32no—
124#3942—32no—
125#3942—32no—
126#3941—31no—
127#3939—31no—
128C4×#168C2×D311yescharacteristic
129#3303—151noSylow
130C22×D15—21no—
131C22×C5×D3—21no—
132C22×C3×D5C2×D412yes—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—21no—
137C2×Dic15—22no—
138D60—21no—
139D60—21no—
140C4×D15—42no—
141Dic30—22no—
142Dic30—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—21no—
145C5×D12—21no—
146C5×D12#4112yes—
147C4×C5×D3—42no—
148C5×Dic6—81no—
149C2×C3×Dic5C2×D412yes—
150C3×D20—22no—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153#1202—82no—
154#1201—44no—
155D3×Dic5—44no—
156C3×C5×C8—22no—
157C3×#168—21no—
158C3×#168—21no—
159C2×#235—52no—
160C22×C3×C8—52no—
161C3×C4×D4—51no—
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×D12C2×D511yescharacteristic
175#869—51no—
176#869C2×D511yescharacteristic
177C3×C4⋊C8C2×D511yescharacteristic
178C3×C22⋊C8—52no—
179C3×C4×C8—51no—
180#821—51no—
181#821—51no—
182#821C2×D512yes—
183#818—51no—
184#817C2×D512yes—
185#816—52no—
186#816—52no—
187#816—52no—
188C2×C5×Q8—61no—
189C2×C5×D4—31no—
190C22×C4×C5—61no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—64no—
194#711—122no—
195C2×D20—31no—
196C2×D20—62no—
197C2×D20D1211yescharacteristic
198C2×C4×D5—61no—
199C2×C4×D5C22×D312yes—
200C2×Dic10—32no—
201C2×C5×C8C22×D312yes—
202C5×C4⋊C4—31no—
203C5×C4⋊C4—32no—
204C5×C4⋊C4—61no—
205C5×C22⋊C4—61no—
206C42×C5C22×D311yescharacteristic
207#686—62no—
208#685—62no—
209#685—62no—
210#685—61no—
211#685—62no—
212#685D1212yes—
213C4⋊Dic5—31no—
214C4⋊Dic5—61no—
215C4⋊Dic5—61no—
216C4⋊Dic5—62no—
217C4⋊Dic5D1211yescharacteristic
218C4×Dic5—62no—
219C2×#168C22×D311yescharacteristic
220C2×#168C22×D311yescharacteristic
221#677—122no—
222C8×D5—42no—
223#555—151no—
224#547—151no—
225#487—151no—
226#485—152no—
227#476—31no—
228#465—152no—
229#461—151no—
230#449—152no—
231C4×D8—151no—
232C8×D4—51no—
233#416—152no—
234C22×C3×C5C22×D411yescharacteristic
235C2×D15—41no—
236C2×D15—41no—
237C2×D15—41no—
238C2×C5×D3—22no—
239C2×C5×D3—41no—
240C2×C5×D3—41no—
241C2×C3×D5—22no—
242C2×C3×D5—22no—
243C2×C3×D5—22no—
244C3×C4×C5—21no—
245C3×C4×C5#13512yes—
246C3×C4×C5C2×#4111yescharacteristic
247C3×C4×C5H(5,𝔽2)11yescharacteristic
248Dic15—42no—
249Dic15—41no—
250C3×Dic5—22no—
251C5×Dic3—41no—
252C5×Dic3—42no—
253C2×C3×D4—51no—
254C22×C3×C4—52no—
255C2×#67—102no—
256C2×#67—102no—
257#235—104no—
258#235—202no—
259C2×D12—51no—
260C2×D12C22×D511yescharacteristic
261C2×C4×D3—21no—
262C2×C4×D3—102no—
263C2×C4×D3—101no—
264C2×Dic6—21no—
265C2×Dic6—52no—
266C2×C3×C8—51no—
267C2×C3×C8—51no—
268C2×C3×C8—202no—
269C2×C3×C8C22×D512yes—
270C3×C4⋊C4—51no—
271C3×C22⋊C4—52no—
272C3×C42C22×D511yescharacteristic
273#217—102no—
274#217—102no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—102no—
277(C2×D3)⋊C4—101no—
278C4⋊Dic3—21no—
279C4⋊Dic3—51no—
280C4⋊Dic3—101no—
281C4⋊Dic3—101no—
282C4⋊Dic3C22×D512yes—
283C4⋊Dic3C22×D511yescharacteristic
284Dic3⋊C4—102no—
285C4×Dic3—102no—
286D24—102no—
287#204—202no—
288C23×C5—61no—
289C22×D5—61no—
290C22×D5C2×D1212yes—
291C5×Q8—241no—
292C5×D4—32no—
293C5×D4—61no—
294C2×C4×C5—62no—
295C2×C4×C5—61no—
296C2×C4×C5—122no—
297C2×C4×C5C2×D1211yescharacteristic
298C2×C4×C5C2×D1211yescharacteristic
299C2×C4×C5C23×D311yescharacteristic
300C22⋊D5—124no—
301C2×Dic5—61no—
302C2×Dic5—62no—
303C2×Dic5—124no—
304C2×Dic5C2×D1212yes—
305D20—22no—
306D20—61no—
307D20—61no—
308D20—242no—
309C4×D5—22no—
310C4×D5—22no—
311C4×D5—122no—
312Dic10—62no—
313Dic10—62no—
314C5×C8—22no—
315#168—21no—
316#168—21no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8—52no—
321C4⋊Q8—31no—
322C4⋊Q8—151no—
323#124—302no—
324#123—302no—
325C22⋊Q8—152no—
326#121—152no—
327#121—301no—
328#121—301no—
329C4×D4—31no—
330C4×D4—51no—
331C4×D4—151no—
332#117—152no—
333#117—301no—
334C2×C4⋊C4—301no—
335#107—151no—
336#106—32no—
337C4⋊C8D3×D511yescharacteristic
338#103—152no—
339#103—152no—
340#103—152no—
341#102—32no—
342#102—151no—
343#102—151no—
344C22⋊C8—52no—
345C4×C8—51no—
346C2×C3×C5#54611yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5#57711yescharacteristic
349D15—81no—
350C3×D5—42no—
351C5×D3—42no—
352C23×C3—52no—
353C22×D3—21no—
354C22×D3—101no—
355C3×D4—102no—
356C2×C3×C4—52no—
357C2×C3×C4—102no—
358C2×C3×C4—102no—
359C2×C3×C4D4×D511yescharacteristic
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362#67—204no—
363#67—402no—
364C2×Dic3—22no—
365C2×Dic3—21no—
366C2×Dic3—101no—
367C2×Dic3—102no—
368D12—21no—
369D12—101no—
370D12—101no—
371D12#71312yes—
372C4×D3—42no—
373C4×D3—204no—
374C4×D3—202no—
375Dic6—81no—
376Dic6—102no—
377Dic6—102no—
378C3×C8—22no—
379C3×C8—101no—
380C3×C8—101no—
381C22×C5—62no—
382C22×C5—121no—
383C22×C5—121no—
384C22×C5C22×D1211yescharacteristic
385C2×D5—22no—
386C2×D5—22no—
387C2×D5—22no—
388C2×D5—121no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—21no—
392C4×C5—121no—
393C4×C5—122no—
394C4×C5#90412yes—
395C4×C5#100411yescharacteristic
396C4×C5D3×#4111yescharacteristic
397Dic5—22no—
398Dic5—121no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—61no—
403C2×Q8—152no—
404C2×D4—31no—
405C2×D4—51no—
406C2×D4—151no—
407C2×D4—302no—
408C2×D4—302no—
409C22×C4—52no—
410C22×C4—61no—
411C22×C4—302no—
412C22×C4—301no—
413SD16—602no—
414D8—302no—
415C2×C8—51no—
416C2×C8—51no—
417C2×C8—202no—
418C2×C8C2×D3×D512yes—
419C4⋊C4—32no—
420C4⋊C4—31no—
421C4⋊C4—51no—
422C4⋊C4—61no—
423C4⋊C4—151no—
424C4⋊C4—302no—
425C4⋊C4—301no—
426C4⋊C4—301no—
427C22⋊C4—52no—
428C22⋊C4—61no—
429C22⋊C4—302no—
430C22⋊C4—302no—
431C22⋊C4—302no—
432C22⋊C4—301no—
433C42—302no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—102no—
437C22×C3—102no—
438C22×C3—102no—
439C22×C3C2×D4×D511yescharacteristic
440C2×D3—22no—
441C2×D3—41no—
442C2×D3—41no—
443C2×D3—201no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—21no—
447C3×C4—102no—
448C3×C4#406212yes—
449C3×C4C2×#71311yescharacteristic
450C3×C4#414911yescharacteristic
451Dic3—41no—
452Dic3—42no—
453Dic3—201no—
454Dic3—202no—
455C2×C5—122no—
456C2×C5#555411yescharacteristic
457C2×C5C2×#90411yescharacteristic
458C2×C5#575111yescharacteristic
459D5—42no—
460D5—241no—
461C23—52no—
462C23—61no—
463C23—301no—
464Q8—241no—
465Q8—302no—
466Q8—302no—
467D4—32no—
468D4—61no—
469D4—102no—
470D4—301no—
471D4—301no—
472D4—604no—
473D4—1202no—
474C2×C4—52no—
475C2×C4—62no—
476C2×C4—61no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—122no—
480C2×C4—301no—
481C2×C4—302no—
482C2×C4—604no—
483C2×C4—602no—
484C2×C4D5×D1211yescharacteristic
485C2×C4D5×D1211yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—22no—
488C8—101no—
489C8—101no—
490C2×C3—202no—
491C2×C3#6596411yescharacteristic
492C2×C3C2×#406211yescharacteristic
493C2×C3#6610911yescharacteristic
494D3—42no—
495D3—401no—
496C5#7944311yescharacteristic, complemented, Sylow
497C22—62no—
498C22—102no—
499C22—102no—
500C22—102no—
501C22—121no—
502C22—121no—
503C22—601no—
504C22—601no—
505C22—601no—
506C22C2×D5×D1211yescharacteristic
507C4—21no—
508C4—102no—
509C4—121no—
510C4—122no—
511C4—601no—
512C4—602no—
513C4#9126912yes—
514C4#9202611yescharacteristic
515C4D3×#71311yescharacteristic
516C3#1061280711yescharacteristic, complemented, Sylow
517C2—122no—
518C2—202no—
519C2—1201no—
520C2#1175387611yescharacteristic
521C2C2×#9126911yescharacteristic
522C2#1175402311yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3303
LCSG ▷ C2×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
1. #11752715C2semidirect
2. #11752676C2semidirect
3. #11750942C2semidirect
4. C5×#4842C2semidirect
5. C3×#65123C2semidirect
6. #11748163C2semidirect
7. #11748135C2semidirect
8. #11747897C2semidirect
9. #11747676C2semidirect
10. C4×#6654C2semidirect
11. #11746930C2semidirect
51. #65123D3semidirect
94. #4842D5semidirect
435. C3×C5#3303semidirect
496. C5#79443semidirect
516. C3#10612807semidirect

Maximal subgroups

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

subgroupindex
#117527152
#117526762
#117509422
C5×#48422
C3×#651232
#117481632
#117481352
#117478972
#117476762
C4×#66542
#117469302
#106128073
#794435