Finite Group Databasebeta

← #14460228

Subgroups — #14460228

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×#66060C211yesmaximal, characteristic, complemented
2#11752715C211yesmaximal, characteristic, complemented
3#11751184C211yesmaximal, characteristic, complemented
4C5×#5079C211yesmaximal, characteristic, complemented
5#11749272C212yesmaximal, complemented
6#11749269C212yesmaximal, complemented
7#11749209C212yesmaximal, complemented
8#11749207C212yesmaximal, complemented
9C4×#6653C211yesmaximal, characteristic, complemented
10C3⋊C8×D20C211yesmaximal, characteristic, complemented
11#11746880C211yesmaximal, characteristic, complemented
12#10613346—31nomaximal, Hall
13C2×C3×#713C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C2×#6717C2212yes—
16C4×D60C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×#4092C2212yes—
19C3×#4041—21no—
20C3×#4040—22no—
21C3×D5×C4⋊C4—21no—
22C3×C4×D20C2211yescharacteristic
23C3×C4×D20C2211yescharacteristic
24#91465—21no—
25#91455—22no—
26#91450C2212yes—
27#91358C2212yes—
28#91347—21no—
29C2×#6653C2211yescharacteristic
30C2×D5×C3⋊C8C2212yes—
31#91119C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C5×#835C2212yes—
34C5×#835C2212yes—
35C4×C5×C3⋊C8C2211yescharacteristic
36#90990C2211yescharacteristic
37#90986C2212yes—
38#90968C2211yescharacteristic
39#90965C2211yescharacteristic
40#90964C2212yes—
41#90955C2212yes—
42#83511—51nomaximal, Hall
43#66068—31no—
44#66060D311yescharacteristic, complemented
45C5×#487—31no—
46#65373—31no—
47#65372—31no—
48#65103—32no—
49#65100—32no—
50#65096—32no—
51#65093—32no—
52C4×D40—31no—
53C8×D20—31no—
54C2×C3×C5×Q8C2312yes—
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C5×Dic6—21no—
58C3×#713—24no—
59C3×#713—42no—
60C2×C3×D20—22no—
61C2×C3×D20D411yescharacteristic
62C2×C3×D20C2311yescharacteristic
63C2×C3×C4×D5—21no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5C2312yes—
66C2×#1202—22no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70#6717—42no—
71#6714—21no—
72C4⋊Dic15C2311yescharacteristic
73C2×C3⋊#168C2312yes—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C2×C5×C3⋊C8C2311yescharacteristic
77C2×C5×C3⋊C8C2311yescharacteristic
78C3×#685—22no—
79C3×#685—21no—
80C3×#685D412yes—
81C3×C4⋊Dic5D411yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×#683—22no—
84#6667—22no—
85#6665—22no—
86Dic3×Dic5—22no—
87#6653—22no—
88D5×C3⋊C8—42no—
89C3×#547—51no—
90#5563—51no—
91#5238—52no—
92#5233—52no—
93#5083—51no—
94#5079D511yescharacteristic, complemented
95#5048—52no—
96#5045—52no—
97C4×#213—51no—
98D4×C3⋊C8—51no—
99#5008—51no—
100C2×#713C2×D312yes—
101C5×C4⋊Q8—31no—
102C5×C4⋊Q8C2×D311yescharacteristic
103#4093—62no—
104#4092C2×D312yes—
105C2×#688—32no—
106C2×D40—31no—
107C2×C8×D5—32no—
108#4041—21no—
109#4041—32no—
110#4041—61no—
111#4040—22no—
112#4038—32no—
113#4038—61no—
114D5×C4⋊C4—21no—
115C4×D20—31no—
116C4×D20C2×D311yescharacteristic
117C4×D20C2×D311yescharacteristic
118C5×#103—32no—
119C5×#103—32no—
120C4×C5×C8—31no—
121#3967—32no—
122#3953—31no—
123#3953—31no—
124#3952—32no—
125#3950—31no—
126#3941—32no—
127#3940—32no—
128C4⋊#168—31no—
129#3303—151noSylow
130C22×D15—21no—
131C22×C3×D5—21no—
132C22×C3×D5C2×D412yes—
133C3×C5×Q8—22no—
134C3×C5×Q8—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—21no—
140D60—21no—
141D60—21no—
142C4×D15—42no—
143C2×C5×Dic3—22no—
144C5×Dic6—81no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5C2×D412yes—
147C3×D20—22no—
148C3×D20—21no—
149C3×D20—44no—
150C3×D20#4112yes—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153C3×C4×D5—44no—
154C3×C4×D5—42no—
155#1202—82no—
156C3⋊#168—22no—
157C5×C3⋊C8—21no—
158C5×C3⋊C8—21no—
159C2×C3×#41—52no—
160C3×C4⋊Q8C2×D511yescharacteristic
161C3×#123—102no—
162C3×C22⋊Q8—52no—
163C3×#121—101no—
164C3×C4×D4—51no—
165C3×C4×D4—51no—
166C2×C3×C4⋊C4—101no—
167C2×#215—52no—
168#938—101no—
169C2×#213—51no—
170#930—52no—
171#926—52no—
172C22×C3⋊C8—52no—
173#892—101no—
174#885—102no—
175C4×D12—51no—
176#869C2×D511yescharacteristic
177#835—52no—
178#835C2×D512yes—
179#835C2×D512yes—
180#832—52no—
181#832—51no—
182#830—52no—
183#809—51no—
184#808—52no—
185#807—51no—
186C4⋊(C3⋊C8)—51no—
187C4×C3⋊C8C2×D511yescharacteristic
188C2×C5×Q8—61no—
189C2×C5×Q8C22×D312yes—
190#713—24no—
191#713—42no—
192C2×D20—22no—
193C2×D20—31no—
194C2×D20—62no—
195C2×D20#6711yescharacteristic
196C2×D20C22×D311yescharacteristic
197C2×C4×D5—21no—
198C2×C4×D5—22no—
199C2×C4×D5—61no—
200C2×C4×D5C22×D312yes—
201C2×C5×C8—31no—
202C2×C5×C8—31no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—32no—
206C5×C4⋊C4—61no—
207C42×C5C22×D311yescharacteristic
208#688—122no—
209#685—22no—
210#685—21no—
211#685—62no—
212#685—61no—
213#685—62no—
214#685#6712yes—
215C4⋊Dic5—31no—
216C4⋊Dic5#6711yescharacteristic
217C4⋊Dic5C22×D311yescharacteristic
218#683—22no—
219C4×Dic5—62no—
220C2×#168—32no—
221D40—62no—
222C8×D5—122no—
223#555—151no—
224#547—51no—
225#487—31no—
226#485—152no—
227#476—151no—
228#465—152no—
229#461—151no—
230#449—152no—
231C4×D8—151no—
232C8×D4—151no—
233#416—152no—
234C22×C3×C5C22×D411yescharacteristic
235C2×D15—41no—
236C2×D15—41no—
237C2×D15—41no—
238C2×C3×D5—22no—
239C2×C3×D5—22no—
240C2×C3×D5—22no—
241C2×C3×D5—22no—
242C2×C3×D5—41no—
243C2×C3×D5—41no—
244C3×C4×C5—21no—
245C3×C4×C5—42no—
246C3×C4×C5#13512yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C5H(5,𝔽2)11yescharacteristic
249Dic15—41no—
250C3×Dic5—22no—
251C3×Dic5—41no—
252C5×Dic3—42no—
253C3×#41—104no—
254C3×#41—202no—
255C2×C3×Q8C22×D512yes—
256C2×C3×D4—51no—
257C2×C3×D4—51no—
258C2×C3×D4—102no—
259C22×C3×C4—52no—
260C22×C3×C4—102no—
261C22×C3×C4—101no—
262C2×#67—102no—
263C2×D12—51no—
264C2×C4×D3—101no—
265C2×Dic6—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—51no—
269C3×C4⋊C4—51no—
270C3×C4⋊C4—102no—
271C3×C22⋊C4—52no—
272C3×C22⋊C4—102no—
273C3×C22⋊C4—101no—
274C3×C42C22×D511yescharacteristic
275#217—102no—
276#215—202no—
277#213—102no—
278(C2×D3)⋊C4—102no—
279(C2×D3)⋊C4—101no—
280C4⋊Dic3—21no—
281C4⋊Dic3—51no—
282C4⋊Dic3C22×D512yes—
283C4×Dic3—102no—
284C2×C3⋊C8—52no—
285C2×C3⋊C8—202no—
286C2×C3⋊C8C22×D511yescharacteristic
287C2×C3⋊C8C22×D511yescharacteristic
288C22×D5—21no—
289C22×D5—61no—
290C22×D5C2×#6712yes—
291C5×Q8—22no—
292C5×Q8—22no—
293C5×Q8—241no—
294C2×C4×C5—22no—
295C2×C4×C5—62no—
296C2×C4×C5C2×#6711yescharacteristic
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C2×Dic5—21no—
300C2×Dic5—61no—
301C2×Dic5C2×#6712yes—
302D20—22no—
303D20—21no—
304D20—44no—
305D20—61no—
306D20—61no—
307D20—242no—
308D20#23712yes—
309C4×D5—22no—
310C4×D5—22no—
311C4×D5—44no—
312C4×D5—42no—
313C4×D5—122no—
314C5×C8—61no—
315C5×C8—61no—
316#168—62no—
317C2×#41—52no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8—152no—
321C4⋊Q8—31no—
322C4⋊Q8D3×D511yescharacteristic
323#124—302no—
324#123—102no—
325C22⋊Q8—52no—
326#121—101no—
327#121—152no—
328#121—301no—
329C4×D4—51no—
330C4×D4—51no—
331C4×D4—151no—
332#117—152no—
333#117—301no—
334C2×C4⋊C4—101no—
335#107—151no—
336#106—152no—
337C4⋊C8—151no—
338#103—32no—
339#103—32no—
340#103—152no—
341#102—152no—
342#102—151no—
343#102—151no—
344C22⋊C8—152no—
345C4×C8—31no—
346C2×C3×C5#54611yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5#57711yescharacteristic
349D15—81no—
350C3×D5—42no—
351C3×D5—42no—
352C23×C3—52no—
353C23×C3—101no—
354C22×D3—101no—
355C3×Q8—22no—
356C3×Q8—22no—
357C3×D4—52no—
358C3×D4—101no—
359C3×D4—102no—
360C3×D4—204no—
361C2×C3×C4—22no—
362C2×C3×C4—52no—
363C2×C3×C4—102no—
364C2×C3×C4—102no—
365C2×C3×C4—101no—
366C2×C3×C4—204no—
367C2×C3×C4—202no—
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4C23×D511yescharacteristic
371#67—402no—
372C2×Dic3—22no—
373C2×Dic3—101no—
374D12—101no—
375D12—101no—
376C4×D3—202no—
377Dic6—81no—
378C3⋊C8—21no—
379C3⋊C8—21no—
380C3⋊C8—102no—
381C22×C5C22×#6711yescharacteristic
382C2×D5—22no—
383C2×D5—22no—
384C2×D5—22no—
385C2×D5—22no—
386C2×D5—41no—
387C2×D5—41no—
388C2×D5—121no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—21no—
392C4×C5—42no—
393C4×C5—122no—
394C4×C5#95012yes—
395C4×C5C2×#23711yescharacteristic
396C4×C5#100411yescharacteristic
397Dic5—22no—
398Dic5—41no—
399Dic5—121no—
400#41—104no—
401#41—202no—
402C2×Q8—61no—
403C2×Q8C2×D3×D512yes—
404C2×D4—51no—
405C2×D4—51no—
406C2×D4—102no—
407C2×D4—151no—
408C2×D4—302no—
409C22×C4—52no—
410C22×C4—102no—
411C22×C4—101no—
412C22×C4—301no—
413SD16—602no—
414D8—302no—
415C2×C8—31no—
416C2×C8—31no—
417C2×C8—152no—
418C2×C8—602no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—32no—
422C4⋊C4—51no—
423C4⋊C4—51no—
424C4⋊C4—61no—
425C4⋊C4—102no—
426C4⋊C4—151no—
427C22⋊C4—52no—
428C22⋊C4—102no—
429C22⋊C4—101no—
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×C3—102no—
440C22×C3—201no—
441C22×C3—201no—
442C22×C3C2×D4×D511yescharacteristic
443C2×D3—201no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—21no—
447C3×C4—42no—
448C3×C4—102no—
449C3×C4—201no—
450C3×C4#406512yes—
451C3×C4D5×#4111yescharacteristic
452C3×C4#414911yescharacteristic
453Dic3—42no—
454Dic3—201no—
455C2×C5#580611yescharacteristic
456C2×C5C2×#95011yescharacteristic
457C2×C5#583711yescharacteristic
458D5—42no—
459D5—42no—
460D5—241no—
461C23—52no—
462C23—101no—
463C23—301no—
464Q8—22no—
465Q8—22no—
466Q8—241no—
467D4—52no—
468D4—101no—
469D4—102no—
470D4—204no—
471D4—301no—
472D4—301no—
473D4—1202no—
474C2×C4—22no—
475C2×C4—52no—
476C2×C4—62no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—101no—
480C2×C4—204no—
481C2×C4—202no—
482C2×C4—301no—
483C2×C4—602no—
484C2×C4D5×#6711yescharacteristic
485C2×C4D5×#6711yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—61no—
488C8—61no—
489C8—302no—
490C2×C3—202no—
491C2×C3—202no—
492C2×C3#6601011yescharacteristic
493C2×C3#6609611yescharacteristic
494C2×C3C2×#406511yescharacteristic
495D3—401no—
496C5#8351111yescharacteristic, complemented, Sylow
497C22—102no—
498C22—102no—
499C22—102no—
500C22—102no—
501C22—201no—
502C22—201no—
503C22—601no—
504C22—601no—
505C22—601no—
506C22C2×D5×#6711yescharacteristic
507C4—21no—
508C4—42no—
509C4—102no—
510C4—122no—
511C4—201no—
512C4—601no—
513C4#9151612yes—
514C4D5×#23711yescharacteristic
515C4#9202611yescharacteristic
516C3#1061334611yescharacteristic, complemented, Sylow
517C2—202no—
518C2—202no—
519C2—1201no—
520C2#1175493111yescharacteristic
521C2#1175508511yescharacteristic
522C2C2×#9151611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3303
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66060C2semidirect
2. #11752715C2semidirect
3. #11751184C2semidirect
4. C5×#5079C2semidirect
5. #11749272C2semidirect
6. #11749269C2semidirect
7. #11749209C2semidirect
8. #11749207C2semidirect
9. C4×#6653C2semidirect
10. C3⋊C8×D20C2semidirect
11. #11746880C2semidirect
44. #66060D3semidirect
94. #5079D5semidirect
435. C3×C5#3303semidirect
496. C5#83511semidirect
516. C3#10613346semidirect

Maximal subgroups

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

subgroupindex
C3×#660602
#117527152
#117511842
C5×#50792
#117492722
#117492692
#117492092
#117492072
C4×#66532
C3⋊C8×D202
#117468802
#106133463
#835115