Finite Group Databasebeta

← #14460221

Subgroups — #14460221

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
1C3×#65897C211yesmaximal, characteristic, complemented
2#11752493C211yesmaximal, characteristic, complemented
3C4×#6715C211yesmaximal, characteristic, complemented
4C5×#5019C211yesmaximal, characteristic, complemented
5#11749160C212yesmaximal, complemented
6#11749120C212yesmaximal, complemented
7#11747501C212yesmaximal, complemented
8#11747344C212yesmaximal, complemented
9#11746996C211yesmaximal, characteristic, complemented
10#11746942C211yesmaximal, characteristic, complemented
11#11746923C211yesmaximal, characteristic, complemented
12#10612182—31nomaximal, Hall
13C2×#6773C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15C2×#6715C2211yescharacteristic
16C4×D60C2211yescharacteristic
17C2×C5×#214C2212yes—
18C5×#869C2211yescharacteristic
19C3×#4084C2212yes—
20C3×#4076—21no—
21C3×#4072—21no—
22C3×#4038C2212yes—
23C3×#4031—22no—
24C3×C4×D20C2211yescharacteristic
25C3×#4015C2211yescharacteristic
26#91465—21no—
27#91437—21no—
28#91359C2212yes—
29#91356—22no—
30C2×D5×C3⋊C8C2212yes—
31#91116C2211yescharacteristic
32#91093C2211yescharacteristic
33#91091C2211yescharacteristic
34C4×C3⋊#168C2211yescharacteristic
35C5×#810C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37#90987C2212yes—
38#90972C2212yes—
39#90972C2212yes—
40#90968C2212yes—
41#90955C2212yes—
42#83652—51nomaximal, Hall
43#66060—31no—
44#65897D311yescharacteristic, complemented
45C5×#461—31no—
46#65461—32no—
47#65460—32no—
48#65370—31no—
49C4×#686—31no—
50#65131—31no—
51#65123—31no—
52#65104—32no—
53#65093—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×C5×Dic6C2312yes—
59C2×C3×C22⋊D5—22no—
60C2×C3×D20D411yescharacteristic
61C2×C3×C4×D5C2312yes—
62C2×C3×Dic10—21no—
63C2×#1202—22no—
64C2×#1200—22no—
65#6773—24no—
66#6773—42no—
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70#6715—22no—
71#6714—21no—
72C4⋊Dic15C2311yescharacteristic
73C2×C3⋊#168C2311yescharacteristic
74C2×C3⋊#168C2311yescharacteristic
75C5×#214—42no—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3—21no—
78C2×C5×C3⋊C8C2312yes—
79C3×C22⋊Dic5—22no—
80C3×#685—22no—
81C3×#685D412yes—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5D411yescharacteristic
84C3×C4⋊Dic5C2312yes—
85C3×C4×Dic5—22no—
86#6669—22no—
87#6665—22no—
88D5×C3⋊C8—42no—
89C3×#555—51no—
90#5551—51no—
91#5093—51no—
92#5084—51no—
93#5041—52no—
94#5037—52no—
95#5019D511yescharacteristic, complemented
96C4×#213—51no—
97D4×C3⋊C8—51no—
98#5002—52no—
99#4996—52no—
100C2×#713—32no—
101C2×C5×SD16—32no—
102C5×C4⋊Q8—31no—
103C4×C5×D4C2×D311yescharacteristic
104#4092—32no—
105#4084C2×D312yes—
106C2×#686—31no—
107#4076—21no—
108#4072—21no—
109C2×C8×D5—32no—
110#4041—61no—
111#4040—62no—
112#4038C2×D312yes—
113D5×C4⋊C4—61no—
114#4031—22no—
115C4×D20—31no—
116C4×D20C2×D311yescharacteristic
117#4015C2×D311yescharacteristic
118C5×C4⋊C8—31no—
119C5×#103—32no—
120#3967—32no—
121#3967—32no—
122#3964—31no—
123#3953—32no—
124#3952—32no—
125#3949—32no—
126#3941—31no—
127#3939—31no—
128C4×#168—31no—
129#3303—151noSylow
130C23×C3×C5—21no—
131C22×D15—21no—
132C22×C3×D5C2×D412yes—
133C3×C5×D4—21no—
134C3×C5×D4—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—42no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—21no—
141D60—21no—
142D60#4112yes—
143C4×D15—42no—
144C2×C5×Dic3—22no—
145C5×Dic6—22no—
146C5×Dic6—22no—
147C3×C22⋊D5—82no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5C2×D412yes—
150C3×D20—22no—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153C3×Dic10—81no—
154#1202—44no—
155#1200—44no—
156C3⋊#168—21no—
157C3⋊#168—21no—
158C5×C3⋊C8—22no—
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×#214C2×D512yes—
170C2×#213—51no—
171#924—52no—
172C22×C3⋊C8—52no—
173D3×C4⋊C4—101no—
174#883—102no—
175C4×D12—51no—
176#869C2×D511yescharacteristic
177#832—51no—
178#830—52no—
179#810—52no—
180#810—52no—
181#810C2×D512yes—
182#809—51no—
183#809—52no—
184#808—52no—
185#807—51no—
186C4⋊(C3⋊C8)C2×D511yescharacteristic
187C4×C3⋊C8—51no—
188C2×C5×Q8—32no—
189C2×C5×D4C22×D311yescharacteristic
190C22×C4×C5—21no—
191C2×C22⋊D5—22no—
192#713—64no—
193#713—122no—
194C2×D20—31no—
195C2×D20—62no—
196C2×D20#6711yescharacteristic
197C2×C4×D5—61no—
198C2×C4×D5—62no—
199C2×C4×D5C22×D312yes—
200C2×Dic10—21no—
201C5×SD16—122no—
202C2×C5×C8—32no—
203C5×C4⋊C4—61no—
204C5×C4⋊C4—61no—
205C5×C4⋊C4C22×D311yescharacteristic
206C5×C22⋊C4—21no—
207C42×C5C22×D311yescharacteristic
208C22⋊Dic5—22no—
209#686—62no—
210#685—22no—
211#685—62no—
212#685—61no—
213#685#6712yes—
214C4⋊Dic5—21no—
215C4⋊Dic5—31no—
216C4⋊Dic5#6711yescharacteristic
217C4⋊Dic5C22×D312yes—
218#683—62no—
219C4×Dic5—22no—
220C2×#168—31no—
221C2×#168—31no—
222C8×D5—122no—
223#555—51no—
224#547—151no—
225#487—151no—
226#485—152no—
227#476—151no—
228#465—152no—
229#461—31no—
230#449—152no—
231C4×D8—151no—
232C8×D4—151no—
233#416—152no—
234C22×C3×C5—41no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—22no—
239C2×D15—41no—
240C2×D15—41no—
241C2×C3×D5—22no—
242C2×C3×D5—22no—
243C2×C3×D5—22no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5#13512yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C5H(5,𝔽2)11yescharacteristic
249Dic15—41no—
250C3×Dic5—22no—
251C3×Dic5—42no—
252C5×Dic3—42no—
253C2×C3×Q8—101no—
254C2×C3×D4—51no—
255C2×C3×D4—102no—
256C2×C3×D4C22×D511yescharacteristic
257C22×C3×C4—21no—
258C22×C3×C4—52no—
259C2×#67—102no—
260#235—104no—
261#235—202no—
262C2×D12—51no—
263C2×C4×D3—102no—
264C2×C4×D3—101no—
265C2×Dic6C22×D512yes—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—52no—
268C3×C4⋊C4—101no—
269C3×C4⋊C4C22×D511yescharacteristic
270C3×C22⋊C4—21no—
271C3×C22⋊C4—52no—
272C3×C22⋊C4—102no—
273C3×C22⋊C4—102no—
274C3×C42—102no—
275C3×C42C22×D511yescharacteristic
276#217—102no—
277#214—42no—
278#213—102no—
279(C2×D3)⋊C4—101no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—51no—
283Dic3⋊C4—102no—
284C2×C3⋊C8—51no—
285C2×C3⋊C8—51no—
286C2×C3⋊C8—202no—
287C2×C3⋊C8C22×D512yes—
288C23×C5—21no—
289C22×D5—61no—
290C22×D5C2×#6712yes—
291C5×Q8—62no—
292C5×Q8—62no—
293C5×D4—21no—
294C5×D4—21no—
295C2×C4×C5—21no—
296C2×C4×C5—42no—
297C2×C4×C5—62no—
298C2×C4×C5C2×#6711yescharacteristic
299C2×C4×C5C2×#6711yescharacteristic
300C2×C4×C5C23×D311yescharacteristic
301C22⋊D5—82no—
302C2×Dic5—22no—
303C2×Dic5—61no—
304C2×Dic5C2×#6712yes—
305D20—22no—
306D20—32no—
307D20—61no—
308D20—124no—
309C4×D5—22no—
310C4×D5—22no—
311C4×D5—124no—
312C4×D5—122no—
313Dic10—81no—
314C5×C8—62no—
315#168—61no—
316#168—61no—
317C2×#41—152no—
318C2×SD16—32no—
319C2×D8—151no—
320C22×C8—152no—
321C4⋊Q8—31no—
322C4⋊Q8—51no—
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—32no—
339#103—152no—
340#103—152no—
341#102—152no—
342#102—151no—
343#102—151no—
344C22⋊C8—152no—
345C4×C8—151no—
346C2×C3×C5—81no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—42no—
351C3×D5—42no—
352C23×C3—21no—
353C23×C3—52no—
354C22×D3—101no—
355C3×Q8—401no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—102no—
359C3×D4—402no—
360C2×C3×C4—21no—
361C2×C3×C4—42no—
362C2×C3×C4—52no—
363C2×C3×C4—102no—
364C2×C3×C4—102no—
365C2×C3×C4—102no—
366C2×C3×C4D4×D511yescharacteristic
367C2×C3×C4D4×D511yescharacteristic
368C2×C3×C4C23×D511yescharacteristic
369#67—204no—
370C2×Dic3—22no—
371C2×Dic3—101no—
372D12—52no—
373D12—101no—
374C4×D3—204no—
375C4×D3—202no—
376Dic6—22no—
377Dic6—22no—
378C3⋊C8—22no—
379C3⋊C8—101no—
380C3⋊C8—101no—
381C22×C5—41no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5C22×#6711yescharacteristic
385C2×D5—22no—
386C2×D5—22no—
387C2×D5—22no—
388C2×D5—62no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—21no—
392C4×C5—41no—
393C4×C5—122no—
394C4×C5#95012yes—
395C4×C5D3×#4111yescharacteristic
396C4×C5#100911yescharacteristic
397Dic5—22no—
398Dic5—42no—
399Dic5—121no—
400#41—304no—
401#41—602no—
402C2×Q8—32no—
403C2×Q8—101no—
404C2×D4—51no—
405C2×D4—102no—
406C2×D4—151no—
407C2×D4—302no—
408C2×D4C2×D3×D511yescharacteristic
409C22×C4—21no—
410C22×C4—52no—
411C22×C4—302no—
412C22×C4—301no—
413SD16—122no—
414D8—302no—
415C2×C8—32no—
416C2×C8—151no—
417C2×C8—151no—
418C2×C8—602no—
419C4⋊C4—51no—
420C4⋊C4—52no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C4⋊C4—101no—
424C4⋊C4—151no—
425C4⋊C4—302no—
426C4⋊C4C2×D3×D511yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—52no—
429C22⋊C4—102no—
430C22⋊C4—102no—
431C22⋊C4—302no—
432C22⋊C4—301no—
433C42—102no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—102no—
440C22×C3—102no—
441C22×C3—102no—
442C22×C3C2×D4×D511yescharacteristic
443C2×D3—102no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—102no—
449C3×C4—202no—
450C3×C4#406212yes—
451C3×C4#414411yescharacteristic
452C3×C4D5×#4111yescharacteristic
453Dic3—42no—
454Dic3—201no—
455C2×C5—81no—
456C2×C5C2×#95011yescharacteristic
457C2×C5#582911yescharacteristic
458C2×C5#583611yescharacteristic
459D5—42no—
460D5—122no—
461C23—21no—
462C23—52no—
463C23—301no—
464Q8—62no—
465Q8—62no—
466Q8—401no—
467D4—21no—
468D4—21no—
469D4—102no—
470D4—152no—
471D4—301no—
472D4—402no—
473D4—604no—
474C2×C4—21no—
475C2×C4—42no—
476C2×C4—52no—
477C2×C4—62no—
478C2×C4—102no—
479C2×C4—102no—
480C2×C4—102no—
481C2×C4—301no—
482C2×C4—604no—
483C2×C4—602no—
484C2×C4D5×#6711yescharacteristic
485C2×C4D5×#6711yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—62no—
488C8—301no—
489C8—301no—
490C2×C3—81no—
491C2×C3—202no—
492C2×C3#6594611yescharacteristic
493C2×C3C2×#406211yescharacteristic
494C2×C3#6611211yescharacteristic
495D3—202no—
496C5#8365211yescharacteristic, complemented, Sylow
497C22—41no—
498C22—41no—
499C22—41no—
500C22—102no—
501C22—102no—
502C22—102no—
503C22—302no—
504C22—601no—
505C22—601no—
506C22C2×D5×#6711yescharacteristic
507C4—21no—
508C4—41no—
509C4—102no—
510C4—122no—
511C4—202no—
512C4—601no—
513C4#9149212yes—
514C4#9201611yescharacteristic
515C4#9201811yescharacteristic
516C3#1061218211yescharacteristic, complemented, Sylow
517C2—81no—
518C2—202no—
519C2—602no—
520C2#1175464111yescharacteristic
521C2C2×#9149211yescharacteristic
522C2#1175533511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#65897C2semidirect
2. #11752493C2semidirect
3. C4×#6715C2semidirect
4. C5×#5019C2semidirect
5. #11749160C2semidirect
6. #11749120C2semidirect
7. #11747501C2semidirect
8. #11747344C2semidirect
9. #11746996C2semidirect
10. #11746942C2semidirect
11. #11746923C2semidirect
44. #65897D3semidirect
95. #5019D5semidirect
435. C3×C5#3303semidirect
496. C5#83652semidirect
516. C3#10612182semidirect

Maximal subgroups

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

subgroupindex
C3×#658972
#117524932
C4×#67152
C5×#50192
#117491602
#117491202
#117475012
#117473442
#117469962
#117469422
#117469232
#106121823
#836525