Finite Group Databasebeta

← #14460173

Subgroups — #14460173

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
2C3×#65885C211yesmaximal, characteristic, complemented
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748541C212yesmaximal, complemented
5#11748513C212yesmaximal, complemented
6#11748446C212yesmaximal, complemented
7#11748365C212yesmaximal, complemented
8#11747085C211yesmaximal, characteristic, complemented
9C4×#6653C211yesmaximal, characteristic, complemented
10#11746920C211yesmaximal, characteristic, complemented
11#11746881C211yesmaximal, characteristic, complemented
12#10611174—31nomaximal, Hall
13C2×C3×#709C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91827—21no—
16#91819C2212yes—
17#91815C2212yes—
18#91781—21no—
19#91774—22no—
20C4×D60C2211yescharacteristic
21#91758C2211yescharacteristic
22C22×C5×C3⋊C8C2212yes—
23C3×#4084—21no—
24C3×#4070C2212yes—
25C3×D5×C4⋊C4—21no—
26C3×#4029—22no—
27C3×C4×D20C2211yescharacteristic
28C3×#4015C2211yescharacteristic
29C2×#6658C2212yes—
30C2×#6653C2211yescharacteristic
31C5×#830C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C4×C5×C3⋊C8C2211yescharacteristic
34#90990C2211yescharacteristic
35#90987C2212yes—
36#90971C2212yes—
37#90971C2212yes—
38#90971C2212yes—
39#90968C2211yescharacteristic
40#90965C2211yescharacteristic
41#90965C2212yes—
42#83511—51nomaximal, Hall
43#65897—31no—
44#65885D311yescharacteristic, complemented
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—
57C2×D60C2311yescharacteristic
58C2×C4×D15—21no—
59C2×Dic30—21no—
60C2×C3×C22⋊D5—22no—
61C3×#709—24no—
62C3×#709—42no—
63C2×C3×D20C2311yescharacteristic
64C2×C3×C4×D5—21no—
65C2×C3×C4×D5—22no—
66C2×C3×Dic10C2312yes—
67C3×C5×C4⋊C4D411yescharacteristic
68C3×C5×C22⋊C4D412yes—
69C3×C42×C5C2311yescharacteristic
70#6719—22no—
71#6714—21no—
72#6714—22no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2312yes—
75C4⋊Dic15C2311yescharacteristic
76C4×Dic15—22no—
77C2×C5×C3⋊C8—42no—
78C2×C5×C3⋊C8C2311yescharacteristic
79C2×C5×C3⋊C8C2312yes—
80C2×C5×C3⋊C8C2311yescharacteristic
81C3×C22⋊Dic5—22no—
82C3×#685—21no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×#683—22no—
87#6658—42no—
88#6653—22no—
89C3×#547—51no—
90#5563—51no—
91#5238—52no—
92#5233—52no—
93#5083—51no—
94#5079—51no—
95#5048—52no—
96#5045—52no—
97C4×#213—51no—
98D4×C3⋊C8D511yescharacteristic, complemented
99#5008—51no—
100C2×#709C2×D312yes—
101C22×C5×C8—32no—
102C4×C5×D4C2×D311yescharacteristic
103#4084—21no—
104#4084—61no—
105#4076—32no—
106#4072—32no—
107#4070C2×D312yes—
108C2×D40—31no—
109C2×#677—32no—
110#4038—61no—
111D5×C4⋊C4—21no—
112#4031—62no—
113#4029—22no—
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—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×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—82no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143D60—21no—
144D60—21no—
145C4×D15—42no—
146Dic30—81no—
147C3×C22⋊D5—44no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—22no—
150C3×D20—21no—
151C3×D20#4112yes—
152C3×C4×D5—44no—
153C3×C4×D5—42no—
154C3×Dic10—22no—
155C3×Dic10—22no—
156C5×C3⋊C8—21no—
157C5×C3⋊C8—22no—
158C5×C3⋊C8—21no—
159C2×C3×#41—52no—
160C3×C4⋊Q8—51no—
161C3×#123—102no—
162C3×C22⋊Q8—52no—
163C3×#121—101no—
164C3×C4×D4—51no—
165C3×C4×D4C2×D511yescharacteristic
166C2×C3×C4⋊C4—101no—
167C2×#215—52no—
168#938—101no—
169C2×#213—51no—
170#930—52no—
171#926—52no—
172C22×C3⋊C8C2×D512yes—
173#892—101no—
174#885—102no—
175C4×D12—51no—
176#869—51no—
177#835—52no—
178#835—52no—
179#835—52no—
180#832—51no—
181#832—52no—
182#830C2×D512yes—
183#809—51no—
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—24no—
193#709—42no—
194C2×D20—31no—
195C2×D20C22×D311yescharacteristic
196C2×C4×D5—22no—
197C2×C4×D5—21no—
198C2×C4×D5—61no—
199C2×Dic10—61no—
200C2×Dic10C22×D312yes—
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—61no—
212#685—62no—
213C4⋊Dic5—21no—
214C4⋊Dic5—21no—
215C4⋊Dic5—32no—
216C4⋊Dic5—31no—
217C4⋊Dic5—61no—
218C4⋊Dic5C22×D311yescharacteristic
219#683—22no—
220C4×Dic5—62no—
221D40—62no—
222#677—122no—
223#555—151no—
224#547—51no—
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—41no—
239C2×D15—41no—
240C2×D15—41no—
241C2×C3×D5—22no—
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—41no—
250Dic15—42no—
251C3×Dic5—42no—
252C3×Dic5—41no—
253C3×#41—104no—
254C3×#41—202no—
255C2×C3×Q8—52no—
256C2×C3×D4—51no—
257C2×C3×D4—102no—
258C2×C3×D4D2011yescharacteristic
259C22×C3×C4—101no—
260C22×C3×C4—102no—
261C22×C3×C4C22×D512yes—
262C2×#67—102no—
263C2×D12—51no—
264C2×C4×D3—101no—
265C2×Dic6—101no—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—102no—
268C3×C4⋊C4—101no—
269C3×C4⋊C4—101no—
270C3×C4⋊C4D2011yescharacteristic
271C3×C22⋊C4—102no—
272C3×C22⋊C4—101no—
273C3×C22⋊C4D2012yes—
274C3×C42C22×D511yescharacteristic
275#217—102no—
276#215—202no—
277#213—102no—
278(C2×D3)⋊C4—101no—
279(C2×D3)⋊C4—102no—
280C4⋊Dic3—51no—
281C4⋊Dic3—52no—
282C4⋊Dic3—101no—
283C4×Dic3—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—44no—
299C22⋊D5—242no—
300C2×Dic5—21no—
301C2×Dic5—22no—
302C2×Dic5—61no—
303C2×Dic5—62no—
304D20—21no—
305D20—61no—
306D20—61no—
307D20#23712yes—
308C4×D5—44no—
309C4×D5—42no—
310C4×D5—122no—
311Dic10—22no—
312Dic10—22no—
313Dic10—241no—
314C5×C8—61no—
315C5×C8—62no—
316C5×C8—61no—
317C2×#41—52no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8—32no—
321C4⋊Q8—51no—
322C4⋊Q8—151no—
323#124—302no—
324#123—102no—
325C22⋊Q8—52no—
326#121—101no—
327#121—152no—
328#121—301no—
329C4×D4—51no—
330C4×D4—151no—
331C4×D4D3×D511yescharacteristic
332#117—152no—
333#117—301no—
334C2×C4⋊C4—101no—
335#107—151no—
336#106—152no—
337C4⋊C8—31no—
338#103—152no—
339#103—152no—
340#103—152no—
341#102—151no—
342#102—151no—
343#102—152no—
344C22⋊C8—32no—
345C4×C8—31no—
346C2×C3×C5—42no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—81no—
351C3×D5—42no—
352C23×C3—101no—
353C23×C3C2×D2012yes—
354C22×D3—101no—
355C3×Q8—102no—
356C3×Q8—102no—
357C3×D4—22no—
358C3×D4—52no—
359C3×D4—101no—
360C3×D4—204no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—101no—
364C2×C3×C4—102no—
365C2×C3×C4—204no—
366C2×C3×C4—202no—
367C2×C3×C4C2×D2012yes—
368C2×C3×C4C2×D2011yescharacteristic
369C2×C3×C4C2×D2011yescharacteristic
370C2×C3×C4C23×D511yescharacteristic
371#67—402no—
372C2×Dic3—101no—
373C2×Dic3—102no—
374D12—101no—
375D12—101no—
376C4×D3—202no—
377Dic6—401no—
378C3⋊C8—21no—
379C3⋊C8—22no—
380C3⋊C8—21no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5C22×#6711yescharacteristic
385C2×D5—22no—
386C2×D5—41no—
387C2×D5—41no—
388C2×D5—121no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—22no—
392C4×C5—21no—
393C4×C5#95012yes—
394C4×C5C2×#23711yescharacteristic
395C4×C5#100411yescharacteristic
396Dic5—42no—
397Dic5—41no—
398Dic5—121no—
399Dic5—122no—
400#41—104no—
401#41—202no—
402C2×Q8—52no—
403C2×Q8—301no—
404C2×D4—51no—
405C2×D4—102no—
406C2×D4—151no—
407C2×D4—302no—
408C2×D4#120211yescharacteristic
409C22×C4—101no—
410C22×C4—102no—
411C22×C4—301no—
412C22×C4C2×D3×D512yes—
413SD16—602no—
414D8—302no—
415C2×C8—31no—
416C2×C8—31no—
417C2×C8—32no—
418C2×C8—122no—
419C4⋊C4—51no—
420C4⋊C4—101no—
421C4⋊C4—102no—
422C4⋊C4—101no—
423C4⋊C4—152no—
424C4⋊C4—151no—
425C4⋊C4—301no—
426C4⋊C4#120211yescharacteristic
427C22⋊C4—102no—
428C22⋊C4—101no—
429C22⋊C4—302no—
430C22⋊C4—302no—
431C22⋊C4—301no—
432C22⋊C4#120212yes—
433C42—302no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—102no—
440C22×C3—201no—
441C22×C3—201no—
442C22×C3C22×D2011yescharacteristic
443C2×D3—201no—
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×C5#580611yescharacteristic
457C2×C5C2×#95011yescharacteristic
458C2×C5#583711yescharacteristic
459D5—42no—
460D5—241no—
461C23—101no—
462C23—301no—
463C23C2×#120212yes—
464Q8—102no—
465Q8—102no—
466Q8—1201no—
467D4—22no—
468D4—52no—
469D4—101no—
470D4—204no—
471D4—301no—
472D4—301no—
473D4—1202no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—101no—
477C2×C4—102no—
478C2×C4—204no—
479C2×C4—202no—
480C2×C4—301no—
481C2×C4—302no—
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—202no—
492C2×C3#6588811yescharacteristic
493C2×C3C2×#405011yescharacteristic
494C2×C3#6608511yescharacteristic
495D3—401no—
496C5#8351111yescharacteristic, complemented, Sylow
497C22—22no—
498C22—22no—
499C22—22no—
500C22—102no—
501C22—201no—
502C22—201no—
503C22—601no—
504C22—601no—
505C22—601no—
506C22C22×#120211yescharacteristic
507C4—21no—
508C4—22no—
509C4—201no—
510C4—202no—
511C4—602no—
512C4—601no—
513C4#9131112yes—
514C4D5×#23711yescharacteristic
515C4#9202511yescharacteristic
516C3#1061117411yescharacteristic, complemented, Sylow
517C2—42no—
518C2—202no—
519C2—1201no—
520C2C2×#9131111yescharacteristic
521C2#1175496311yescharacteristic
522C2#1175531011yescharacteristic
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. #11756322C2semidirect
2. C3×#65885C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748541C2semidirect
5. #11748513C2semidirect
6. #11748446C2semidirect
7. #11748365C2semidirect
8. #11747085C2semidirect
9. C4×#6653C2semidirect
10. #11746920C2semidirect
11. #11746881C2semidirect
44. #65885D3semidirect
98. D4×C3⋊C8D5semidirect
435. C3×C5#3303semidirect
496. C5#83511semidirect
516. C3#10611174semidirect

Maximal subgroups

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

subgroupindex
#117563222
C3×#658852
C5×D4×C3⋊C82
#117485412
#117485132
#117484462
#117483652
#117470852
C4×#66532
#117469202
#117468812
#106111743
#835115