Finite Group Databasebeta

← #14460172

Subgroups — #14460172

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#11756310C211yesmaximal, characteristic, complemented
2C3×#65897C211yesmaximal, characteristic, complemented
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748550C212yesmaximal, complemented
5#11748539C212yesmaximal, complemented
6#11748412C212yesmaximal, complemented
7#11748411C212yesmaximal, complemented
8#11747062C211yesmaximal, characteristic, complemented
9C4×#6653C211yesmaximal, characteristic, complemented
10#11746942C211yesmaximal, characteristic, complemented
11#11746921C211yesmaximal, characteristic, complemented
12#10611174—31nomaximal, Hall
13C2×#6817C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91827—21no—
16#91813C2212yes—
17C4⋊C4×D15—21no—
18#91772—22no—
19C4×D60C2211yescharacteristic
20#91758C2211yescharacteristic
21C22×C5×C3⋊C8C2212yes—
22C3×#4084—21no—
23C3×#4076C2212yes—
24C3×#4072C2212yes—
25C3×#4038—21no—
26C3×#4031—22no—
27C3×C4×D20C2211yescharacteristic
28C3×#4015C2211yescharacteristic
29C2×#6657C2212yes—
30C2×#6653C2211yescharacteristic
31C5×#830C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C4×C5×C3⋊C8C2211yescharacteristic
34#90990C2211yescharacteristic
35#90987C2212yes—
36#90974C2212yes—
37#90974C2212yes—
38#90974C2212yes—
39#90968C2211yescharacteristic
40#90968C2212yes—
41#90965C2211yescharacteristic
42#83652—51nomaximal, Hall
43#65897D311yescharacteristic, complemented
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×D40—31no—
53#64970—31no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×#1220—22no—
57#6817—24no—
58#6817—42no—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×C4×D15—22no—
62C2×Dic30C2312yes—
63C2×C3×C22⋊D5—22no—
64C2×C3×D20C2311yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×Dic10—21no—
67C3×C5×C4⋊C4D411yescharacteristic
68C3×C5×C22⋊C4D412yes—
69C3×C42×C5C2311yescharacteristic
70#6719—22no—
71#6714—21no—
72C4⋊Dic15—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2311yescharacteristic
75#6712—22no—
76C2×C5×C3⋊C8—42no—
77C2×C5×C3⋊C8C2311yescharacteristic
78C2×C5×C3⋊C8C2312yes—
79C2×C5×C3⋊C8C2311yescharacteristic
80C3×C22⋊Dic5—22no—
81C3×#685—21no—
82C3×#685—22no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5C2312yes—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4×Dic5—22no—
87#6657—42no—
88#6653—22no—
89C3×#555—51no—
90#5551—51no—
91#5093—51no—
92#5084—51no—
93#5041—52no—
94#5037—52no—
95#5019—51no—
96C4×#213—51no—
97D4×C3⋊C8D511yescharacteristic, complemented
98#5002—52no—
99#4996—52no—
100C2×#709—32no—
101C22×C5×C8—32no—
102C4×C5×D4C2×D311yescharacteristic
103#4084—21no—
104#4084—61no—
105#4076C2×D312yes—
106#4072C2×D312yes—
107#4070—32no—
108C2×D40—31no—
109C2×#677—32no—
110#4038—21no—
111D5×C4⋊C4—61no—
112#4031—22no—
113#4029—62no—
114C4×D20—31no—
115C4×D20C2×D311yescharacteristic
116#4015—31no—
117#4015C2×D311yescharacteristic
118C5×C4⋊C8—31no—
119C5×C22⋊C8—32no—
120C4×C5×C8—31no—
121#3953—31no—
122#3953—32no—
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×C3×D5—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—
141C2×Dic15—21no—
142C2×Dic15—22no—
143D60—21no—
144D60#4112yes—
145C4×D15—44no—
146C4×D15—42no—
147Dic30—22no—
148Dic30—22no—
149C3×C22⋊D5—82no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—22no—
152C3×D20—21no—
153C3×D20—21no—
154C3×C4×D5—42no—
155C3×Dic10—81no—
156C5×C3⋊C8—21no—
157C5×C3⋊C8—22no—
158C5×C3⋊C8—21no—
159C2×#235—52no—
160C3×C4⋊Q8—51no—
161C3×#124—102no—
162C3×#121—52no—
163C3×#121—101no—
164C3×C4×D4—51no—
165C3×C4×D4C2×D511yescharacteristic
166C3×#117—52no—
167C3×#117—101no—
168#938—101no—
169C2×#214—52no—
170C2×#213—51no—
171#924—52no—
172C22×C3⋊C8C2×D512yes—
173D3×C4⋊C4—101no—
174#883—102no—
175C4×D12—51no—
176#869—51no—
177#832—51no—
178#830C2×D512yes—
179#810—52no—
180#810—52no—
181#810—52no—
182#809—51no—
183#809—52no—
184#808—52no—
185#807—51no—
186C4⋊(C3⋊C8)C2×D511yescharacteristic
187C4×C3⋊C8C2×D511yescharacteristic
188C2×C5×D4#6711yescharacteristic
189C22×C4×C5C22×D312yes—
190C2×C22⋊D5—22no—
191C2×C22⋊D5—62no—
192#709—64no—
193#709—122no—
194C2×D20—31no—
195C2×D20C22×D311yescharacteristic
196C2×C4×D5—21no—
197C2×C4×D5—62no—
198C2×C4×D5—61no—
199C2×Dic10—21no—
200C2×Dic10—32no—
201C2×C5×C8—31no—
202C2×C5×C8—32no—
203C2×C5×C8—31no—
204C2×C5×C8—122no—
205C5×C4⋊C4#6711yescharacteristic
206C5×C22⋊C4#6712yes—
207C42×C5C22×D311yescharacteristic
208C22⋊Dic5—22no—
209C22⋊Dic5—62no—
210#685—21no—
211#685—22no—
212#685—61no—
213C4⋊Dic5—21no—
214C4⋊Dic5—31no—
215C4⋊Dic5—61no—
216C4⋊Dic5—61no—
217C4⋊Dic5C22×D312yes—
218C4⋊Dic5C22×D311yescharacteristic
219#683—62no—
220C4×Dic5—22no—
221D40—62no—
222#677—122no—
223#555—51no—
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×D4—31no—
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×C3×D5—41no—
242C2×C3×D5—41no—
243C2×C3×D5—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—
251C3×Dic5—41no—
252C3×Dic5—42no—
253C2×C3×Q8—101no—
254C2×C3×D4—51no—
255C2×C3×D4—102no—
256C2×C3×D4D2011yescharacteristic
257C22×C3×C4—101no—
258C22×C3×C4C22×D512yes—
259C2×#67—102no—
260#235—104no—
261#235—202no—
262C2×D12—51no—
263C2×C4×D3—101no—
264C2×C4×D3—102no—
265C2×Dic6—52no—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—52no—
268C3×C4⋊C4—101no—
269C3×C4⋊C4D2011yescharacteristic
270C3×C22⋊C4—102no—
271C3×C22⋊C4—102no—
272C3×C22⋊C4—101no—
273C3×C22⋊C4D2012yes—
274C3×C42—102no—
275C3×C42C22×D511yescharacteristic
276#217—102no—
277#214—202no—
278#213—102no—
279(C2×D3)⋊C4—101no—
280C4⋊Dic3—51no—
281C4⋊Dic3—101no—
282C4⋊Dic3—101no—
283Dic3⋊C4—102no—
284C2×C3⋊C8—42no—
285C2×C3⋊C8C22×D511yescharacteristic
286C2×C3⋊C8C22×D511yescharacteristic
287C2×C3⋊C8C22×D512yes—
288C23×C5C2×#6712yes—
289C22×D5—21no—
290C22×D5—61no—
291C5×D4—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5C2×#6712yes—
295C2×C4×C5C2×#6711yescharacteristic
296C2×C4×C5C2×#6711yescharacteristic
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5—82no—
299C22⋊D5—124no—
300C2×Dic5—21no—
301C2×Dic5—22no—
302C2×Dic5—61no—
303C2×Dic5—62no—
304D20—21no—
305D20—21no—
306D20—32no—
307D20—61no—
308C4×D5—42no—
309C4×D5—124no—
310C4×D5—122no—
311Dic10—62no—
312Dic10—62no—
313Dic10—81no—
314C5×C8—61no—
315C5×C8—62no—
316C5×C8—61no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8—32no—
321C4⋊Q8—51no—
322C4⋊Q8—151no—
323#124—102no—
324#123—302no—
325C22⋊Q8—152no—
326#121—52no—
327#121—101no—
328#121—301no—
329C4×D4—51no—
330C4×D4—151no—
331C4×D4D3×D511yescharacteristic
332#117—52no—
333#117—101no—
334C2×C4⋊C4—301no—
335#107—151no—
336#106—152no—
337C4⋊C8—31no—
338#103—152no—
339#103—152no—
340#103—152no—
341#102—151no—
342#102—152no—
343#102—151no—
344C22⋊C8—32no—
345C4×C8—31no—
346C2×C3×C5—42no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—42no—
351C3×D5—81no—
352C23×C3—101no—
353C23×C3C2×D2012yes—
354C22×D3—101no—
355C3×Q8—401no—
356C3×D4—22no—
357C3×D4—101no—
358C3×D4—101no—
359C3×D4—402no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—101no—
363C2×C3×C4—102no—
364C2×C3×C4—202no—
365C2×C3×C4C2×D2012yes—
366C2×C3×C4C2×D2011yescharacteristic
367C2×C3×C4C2×D2011yescharacteristic
368C2×C3×C4C23×D511yescharacteristic
369#67—204no—
370C2×Dic3—101no—
371C2×Dic3—102no—
372D12—52no—
373D12—101no—
374C4×D3—204no—
375C4×D3—202no—
376Dic6—102no—
377Dic6—102no—
378C3⋊C8—21no—
379C3⋊C8—22no—
380C3⋊C8—21no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5C22×#6711yescharacteristic
385C2×D5—41no—
386C2×D5—41no—
387C2×D5—41no—
388C2×D5—62no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—22no—
392C4×C5—21no—
393C4×C5#95012yes—
394C4×C5D3×#4111yescharacteristic
395C4×C5#100911yescharacteristic
396Dic5—41no—
397Dic5—42no—
398Dic5—121no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—101no—
403C2×Q8—152no—
404C2×D4—51no—
405C2×D4—102no—
406C2×D4—151no—
407C2×D4—302no—
408C2×D4#120211yescharacteristic
409C22×C4—101no—
410C22×C4—301no—
411C22×C4—302no—
412C22×C4C2×D3×D512yes—
413SD16—602no—
414D8—302no—
415C2×C8—31no—
416C2×C8—31no—
417C2×C8—32no—
418C2×C8—122no—
419C4⋊C4—52no—
420C4⋊C4—51no—
421C4⋊C4—101no—
422C4⋊C4—151no—
423C4⋊C4—301no—
424C4⋊C4—302no—
425C4⋊C4—301no—
426C4⋊C4#120211yescharacteristic
427C22⋊C4—102no—
428C22⋊C4—102no—
429C22⋊C4—101no—
430C22⋊C4—302no—
431C22⋊C4—301no—
432C22⋊C4#120212yes—
433C42—102no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—201no—
440C22×C3—201no—
441C22×C3—201no—
442C22×C3C22×D2011yescharacteristic
443C2×D3—102no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—201no—
449C3×C4—202no—
450C3×C4#405012yes—
451C3×C4#414411yescharacteristic
452C3×C4D5×#4111yescharacteristic
453Dic3—201no—
454Dic3—202no—
455C2×C5—42no—
456C2×C5C2×#95011yescharacteristic
457C2×C5#582911yescharacteristic
458C2×C5#583611yescharacteristic
459D5—81no—
460D5—122no—
461C23—101no—
462C23—301no—
463C23C2×#120212yes—
464Q8—302no—
465Q8—302no—
466Q8—401no—
467D4—22no—
468D4—101no—
469D4—101no—
470D4—152no—
471D4—301no—
472D4—402no—
473D4—604no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—101no—
477C2×C4—102no—
478C2×C4—202no—
479C2×C4—301no—
480C2×C4—302no—
481C2×C4—604no—
482C2×C4—602no—
483C2×C4C2×#120212yes—
484C2×C4C2×#120211yescharacteristic
485C2×C4C2×#120211yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—61no—
488C8—61no—
489C8—62no—
490C2×C3—42no—
491C2×C3—401no—
492C2×C3#6588811yescharacteristic
493C2×C3C2×#405011yescharacteristic
494C2×C3#6608511yescharacteristic
495D3—202no—
496C5#8365211yescharacteristic, complemented, Sylow
497C22—22no—
498C22—22no—
499C22—22no—
500C22—201no—
501C22—201no—
502C22—201no—
503C22—302no—
504C22—601no—
505C22—601no—
506C22C22×#120211yescharacteristic
507C4—21no—
508C4—22no—
509C4—202no—
510C4—201no—
511C4—601no—
512C4—602no—
513C4#9131112yes—
514C4#9202411yescharacteristic
515C4#9202711yescharacteristic
516C3#1061117411yescharacteristic, complemented, Sylow
517C2—42no—
518C2—401no—
519C2—602no—
520C2C2×#9131111yescharacteristic
521C2#1175498011yescharacteristic
522C2#1175530911yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3303
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756310C2semidirect
2. C3×#65897C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748550C2semidirect
5. #11748539C2semidirect
6. #11748412C2semidirect
7. #11748411C2semidirect
8. #11747062C2semidirect
9. C4×#6653C2semidirect
10. #11746942C2semidirect
11. #11746921C2semidirect
43. #65897D3semidirect
97. D4×C3⋊C8D5semidirect
435. C3×C5#3303semidirect
496. C5#83652semidirect
516. C3#10611174semidirect

Maximal subgroups

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

subgroupindex
#117563102
C3×#658972
C5×D4×C3⋊C82
#117485502
#117485392
#117484122
#117484112
#117470622
C4×#66532
#117469422
#117469212
#106111743
#836525