Finite Group Databasebeta

← #14460224

Subgroups — #14460224

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#11752718C211yesmaximal, characteristic, complemented
2#11752532C211yesmaximal, characteristic, complemented
3#11750782C211yesmaximal, characteristic, complemented
4C5×C8×D12C211yesmaximal, characteristic, complemented
5C3×C4×D40C211yesmaximal, characteristic, complemented
6#11748149C212yesmaximal, complemented
7#11748137C212yesmaximal, complemented
8#11747908C212yesmaximal, complemented
9#11747683C212yesmaximal, complemented
10#11747062C211yesmaximal, characteristic, complemented
11#11746881C211yesmaximal, characteristic, complemented
12#10611174—31nomaximal, Hall
13C2×#6765C2212yes—
14#91758C2211yescharacteristic
15#91758C2211yescharacteristic
16C2×C5×D3×C8C2212yes—
17C4×C5×D12C2211yescharacteristic
18C2×C3×D40C2211yescharacteristic
19C3×C4×D20C2211yescharacteristic
20C3×C4×D20C2211yescharacteristic
21#91462—22no—
22#91456C2212yes—
23#91449—21no—
24#91449—21no—
25#91414—22no—
26D5×C4⋊Dic3—21no—
27#91365C2212yes—
28#91358—21no—
29#91338C2212yes—
30C2×#6657C2212yes—
31C3×C4×C5×C8C2211yescharacteristic
32#91100C2212yes—
33#91100C2212yes—
34C5×(C2×D3)⋊C8C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×#3953C2211yescharacteristic
37C3×#3953C2211yescharacteristic
38C3×#3950C2211yescharacteristic
39#90987C2212yes—
40#90974C2212yes—
41#90965C2212yes—
42#79610—51nomaximal, Hall
43#65897—31no—
44#65885—31no—
45C5×C8×D4—31no—
46#65403—32no—
47#65402—32no—
48#65131—31no—
49#65130—31no—
50#65023—32no—
51#65012—32no—
52C4×D40D311yescharacteristic, complemented
53#64970—31no—
54C2×Dic30—21no—
55C2×Dic30C2312yes—
56C2×C5×D12D411yescharacteristic
57C2×C4×C5×D3C2312yes—
58C2×C3×D20C2311yescharacteristic
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×C4×D5—21no—
62C2×#1201—22no—
63C2×#1201—22no—
64C2×D5×Dic3—22no—
65#6765—24no—
66#6765—42no—
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C42×C5C2311yescharacteristic
70C4⋊Dic15—21no—
71C4⋊Dic15—21no—
72C4⋊Dic15—21no—
73C4⋊Dic15C2312yes—
74C5×(C2×D3)⋊C4D412yes—
75C5×C4⋊Dic3D411yescharacteristic
76C2×C5×C3⋊C8C2312yes—
77C5×D3×C8—42no—
78C3×#685—21no—
79C3×#685—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4⋊Dic5C2311yescharacteristic
82C3×D40—22no—
83#6668—22no—
84(C2×D3)⋊Dic5—22no—
85(C2×D3)⋊Dic5—22no—
86#6665—22no—
87Dic3×Dic5—22no—
88#6657—42no—
89#5563—51no—
90#5555—51no—
91C3×C4×D8—51no—
92#5158—52no—
93#5019—51no—
94#5008—51no—
95#4888—52no—
96#4778—52no—
97#4772—52no—
98C8×D12D511yescharacteristic, complemented
99#4681—51no—
100C2×#709—32no—
101C22×C5×C8—32no—
102C4×C5×D4—31no—
103#4084—61no—
104#4084—61no—
105#4076—32no—
106#4072—32no—
107#4070—32no—
108C2×D40C2×D311yescharacteristic
109C2×#677—32no—
110#4038—61no—
111D5×C4⋊C4—61no—
112#4031—62no—
113#4029—62no—
114C4×D20C2×D311yescharacteristic
115C4×D20C2×D311yescharacteristic
116#4015—31no—
117#4015—31no—
118C5×C4⋊C8—31no—
119C5×C22⋊C8—32no—
120C4×C5×C8C2×D311yescharacteristic
121#3953—32no—
122#3953C2×D311yescharacteristic
123#3953C2×D311yescharacteristic
124#3950C2×D311yescharacteristic
125#3949—32no—
126#3948—32no—
127#3948—32no—
128#3948—32no—
129#3303—151noSylow
130C22×C5×D3C2×D412yes—
131C22×C3×D5—21no—
132C22×C3×D5—21no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137C2×Dic15—22no—
138Dic30—22no—
139Dic30—22no—
140Dic30—81no—
141C2×C5×Dic3C2×D412yes—
142C5×D12—22no—
143C4×C5×D3—22no—
144C4×C5×D3—22no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C3×D20—21no—
148C3×D20—21no—
149C3×D20—21no—
150C3×D20#4112yes—
151C3×C4×D5—42no—
152C3×C4×D5—42no—
153#1201—44no—
154#1201—82no—
155D5×Dic3—44no—
156C3×C5×C8—21no—
157C3×C5×C8—21no—
158C5×C3⋊C8—22no—
159C2×#237—52no—
160C2×C3×D8—51no—
161C3×C4×D4—51no—
162C3×C4×D4—51no—
163#938—52no—
164C2×#214—52no—
165#930—101no—
166#930—101no—
167#926—101no—
168C2×C4⋊Dic3—101no—
169C2×D3×C8C2×D512yes—
170#897—52no—
171#892—52no—
172#886—102no—
173#885—102no—
174C4×D12C2×D511yescharacteristic
175#869—51no—
176#869—51no—
177C3×#107—51no—
178C3×#102—51no—
179C3×#102—51no—
180C3×C4×C8C2×D511yescharacteristic
181#832—52no—
182(C2×D3)⋊C8C2×D512yes—
183#816—52no—
184#816—52no—
185#810—52no—
186#808—52no—
187C4⋊(C3⋊C8)C2×D511yescharacteristic
188C2×C5×D4—31no—
189C22×C4×C5—32no—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192#709—64no—
193#709—122no—
194C2×D20C22×D311yescharacteristic
195C2×D20C22×D311yescharacteristic
196C2×C4×D5—21no—
197C2×C4×D5—21no—
198C2×C4×D5—62no—
199C2×Dic10—32no—
200C2×Dic10—61no—
201C2×C5×C8—32no—
202C2×C5×C8—122no—
203C2×C5×C8C22×D311yescharacteristic
204C2×C5×C8C22×D311yescharacteristic
205C5×C4⋊C4—31no—
206C5×C22⋊C4—32no—
207C42×C5C22×D311yescharacteristic
208C22⋊Dic5—62no—
209C22⋊Dic5—62no—
210#685—21no—
211#685—21no—
212#685—62no—
213C4⋊Dic5—32no—
214C4⋊Dic5—61no—
215C4⋊Dic5—61no—
216C4⋊Dic5—61no—
217C4⋊Dic5C22×D311yescharacteristic
218C4⋊Dic5C22×D311yescharacteristic
219#683—62no—
220C4×Dic5—62no—
221D40—22no—
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—51no—
232C8×D4—31no—
233#416—152no—
234C22×C3×C5C22×D411yescharacteristic
235C2×C5×D3—22no—
236C2×C5×D3—22no—
237C2×C5×D3—22no—
238C2×C3×D5—22no—
239C2×C3×D5—41no—
240C2×C3×D5—41no—
241C2×C3×D5—41no—
242C2×C3×D5—41no—
243C2×C3×D5—41no—
244C3×C4×C5—21no—
245C3×C4×C5#13512yes—
246C3×C4×C5C2×#4111yescharacteristic
247C3×C4×C5H(5,𝔽2)11yescharacteristic
248Dic15—42no—
249Dic15—42no—
250C3×Dic5—41no—
251C3×Dic5—41no—
252C5×Dic3—22no—
253C2×C3×D4—51no—
254C2×C3×D4—51no—
255C22×C3×C4—101no—
256C22×C3×C4—101no—
257C2×#67—102no—
258C2×#67—102no—
259C22×Dic3—102no—
260#237—104no—
261#237—202no—
262C2×D12D2011yescharacteristic
263C2×C4×D3C22×D512yes—
264C2×Dic6—52no—
265C2×Dic6—101no—
266C3×D8—102no—
267C2×C3×C8C22×D511yescharacteristic
268C2×C3×C8C22×D511yescharacteristic
269C3×C4⋊C4—51no—
270C3×C4⋊C4—51no—
271C3×C22⋊C4—101no—
272C3×C22⋊C4—101no—
273C3×C42C22×D511yescharacteristic
274#217—102no—
275#214—202no—
276(C2×D3)⋊C4—102no—
277(C2×D3)⋊C4—102no—
278(C2×D3)⋊C4D2012yes—
279C4⋊Dic3—52no—
280C4⋊Dic3—101no—
281C4⋊Dic3—101no—
282C4⋊Dic3—101no—
283C4⋊Dic3—102no—
284C4⋊Dic3D2011yescharacteristic
285C4×Dic3—102no—
286C2×C3⋊C8C22×D512yes—
287D3×C8—42no—
288C23×C5—32no—
289C22×D5—21no—
290C22×D5—21no—
291C5×D4—62no—
292C2×C4×C5—32no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5—124no—
299C22⋊D5—242no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304D20—21no—
305D20—21no—
306D20—21no—
307D20#23512yes—
308C4×D5—42no—
309C4×D5—42no—
310C4×D5—124no—
311Dic10—62no—
312Dic10—62no—
313Dic10—241no—
314C5×C8—21no—
315C5×C8—21no—
316C5×C8—62no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—51no—
320C22×C8—32no—
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—31no—
330C4×D4—51no—
331C4×D4—51no—
332#117—152no—
333#117—301no—
334C2×C4⋊C4—301no—
335#107—51no—
336#106—152no—
337C4⋊C8—31no—
338#103—152no—
339#103—152no—
340#103—152no—
341#102—51no—
342#102—51no—
343#102—152no—
344C22⋊C8—32no—
345C4×C8D3×D511yescharacteristic
346C2×C3×C5#54611yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5#57711yescharacteristic
349C3×D5—42no—
350C3×D5—81no—
351C5×D3—42no—
352C23×C3—101no—
353C23×C3—101no—
354C22×D3C2×D2012yes—
355C3×D4—52no—
356C3×D4—101no—
357C3×D4—101no—
358C3×D4—101no—
359C2×C3×C4—101no—
360C2×C3×C4—101no—
361C2×C3×C4—202no—
362C2×C3×C4—202no—
363C2×C3×C4C2×D2011yescharacteristic
364C2×C3×C4C2×D2011yescharacteristic
365C2×C3×C4C23×D511yescharacteristic
366#67—204no—
367#67—402no—
368C2×Dic3—102no—
369C2×Dic3—102no—
370C2×Dic3—204no—
371C2×Dic3C2×D2012yes—
372D12—22no—
373C4×D3—22no—
374C4×D3—22no—
375Dic6—102no—
376Dic6—102no—
377Dic6—401no—
378C3×C8—21no—
379C3×C8—21no—
380C3⋊C8—22no—
381C22×C5—62no—
382C22×C5—62no—
383C22×C5—62no—
384C22×C5C2×D3×D411yescharacteristic
385C2×D5—22no—
386C2×D5—41no—
387C2×D5—41no—
388C2×D5—41no—
389C2×D5—41no—
390C2×D5—41no—
391C4×C5—21no—
392C4×C5—62no—
393C4×C5#91212yes—
394C4×C5C2×#23511yescharacteristic
395C4×C5#100911yescharacteristic
396Dic5—41no—
397Dic5—41no—
398Dic5—122no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—152no—
403C2×Q8—301no—
404C2×D4—31no—
405C2×D4—51no—
406C2×D4—51no—
407C2×D4—302no—
408C2×D4—302no—
409C22×C4—32no—
410C22×C4—101no—
411C22×C4—101no—
412C22×C4—302no—
413SD16—602no—
414D8—102no—
415C2×C8—32no—
416C2×C8—122no—
417C2×C8C2×D3×D511yescharacteristic
418C2×C8C2×D3×D511yescharacteristic
419C4⋊C4—31no—
420C4⋊C4—51no—
421C4⋊C4—51no—
422C4⋊C4—152no—
423C4⋊C4—302no—
424C4⋊C4—301no—
425C4⋊C4—301no—
426C4⋊C4—301no—
427C22⋊C4—32no—
428C22⋊C4—101no—
429C22⋊C4—101no—
430C22⋊C4—302no—
431C22⋊C4—302no—
432C22⋊C4—302no—
433C42—302no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—102no—
437C22×C3—201no—
438C22×C3—201no—
439C22×C3—201no—
440C22×C3—201no—
441C22×C3—201no—
442C22×C3C22×D2011yescharacteristic
443C2×D3—22no—
444C2×D3—22no—
445C2×D3—22no—
446C3×C4—21no—
447C3×C4—201no—
448C3×C4—201no—
449C3×C4#405012yes—
450C3×C4#414411yescharacteristic
451C3×C4D5×#4111yescharacteristic
452Dic3—22no—
453Dic3—202no—
454Dic3—202no—
455C2×C5—122no—
456C2×C5#555011yescharacteristic
457C2×C5C2×#91211yescharacteristic
458C2×C5#577011yescharacteristic
459D5—42no—
460D5—81no—
461C23—32no—
462C23—101no—
463C23—101no—
464Q8—302no—
465Q8—302no—
466Q8—1201no—
467D4—52no—
468D4—62no—
469D4—101no—
470D4—101no—
471D4—101no—
472D4—604no—
473D4—1202no—
474C2×C4—32no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—101no—
478C2×C4—101no—
479C2×C4—202no—
480C2×C4—202no—
481C2×C4—302no—
482C2×C4—302no—
483C2×C4—604no—
484C2×C4D3×D2011yescharacteristic
485C2×C4D3×D2011yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—21no—
488C8—21no—
489C8—62no—
490C2×C3—202no—
491C2×C3—401no—
492C2×C3#6588811yescharacteristic
493C2×C3C2×#405011yescharacteristic
494C2×C3#6608511yescharacteristic
495D3—42no—
496C5#7961011yescharacteristic, complemented, Sylow
497C22—62no—
498C22—62no—
499C22—62no—
500C22—102no—
501C22—201no—
502C22—201no—
503C22—201no—
504C22—201no—
505C22—201no—
506C22C2×D3×D2011yescharacteristic
507C4—21no—
508C4—62no—
509C4—201no—
510C4—201no—
511C4—602no—
512C4—602no—
513C4#9127312yes—
514C4D5×#23511yescharacteristic
515C4#9201811yescharacteristic
516C3#1061117411yescharacteristic, complemented, Sylow
517C2—122no—
518C2—202no—
519C2—401no—
520C2#1175274011yescharacteristic
521C2#1175397211yescharacteristic
522C2C2×#9127311yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×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. #11752718C2semidirect
2. #11752532C2semidirect
3. #11750782C2semidirect
4. C5×C8×D12C2semidirect
5. C3×C4×D40C2semidirect
6. #11748149C2semidirect
7. #11748137C2semidirect
8. #11747908C2semidirect
9. #11747683C2semidirect
10. #11747062C2semidirect
11. #11746881C2semidirect
52. C4×D40D3semidirect
98. C8×D12D5semidirect
435. C3×C5#3303semidirect
496. C5#79610semidirect
516. C3#10611174semidirect

Maximal subgroups

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

subgroupindex
#117527182
#117525322
#117507822
C5×C8×D122
C3×C4×D402
#117481492
#117481372
#117479082
#117476832
#117470622
#117468812
#106111743
#796105