Finite Group Databasebeta

← #14438705

Subgroups — #14438705

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5668C211yesmaximal, characteristic
2D3×#4016C211yesmaximal, characteristic, complemented
3#11751157C211yesmaximal, characteristic, complemented
4C3×#65345C211yesmaximal, characteristic, complemented
5#11749201C212yesmaximal, complemented
6#11749192C212yesmaximal, complemented
7#11748955C212yesmaximal, complemented
8#11748946C212yesmaximal, complemented
9C4×#6650C211yesmaximal, characteristic, complemented
10#11746907C211yesmaximal, characteristic, complemented
11#11746903C211yesmaximal, characteristic, complemented
12#10615015—31nomaximal, Hall
13C2×C5×#239C2211yescharacteristic
14C2×C5×#237C2211yescharacteristic
15C3×C5×#124C2211yescharacteristic
16#91759C2211yescharacteristic
17C5×#944C2211yescharacteristic
18C5×#940C2211yescharacteristic
19C5×#884—22no—
20C5×#67⋊C4—22no—
21C5×#875C2211yescharacteristic
22C42×C5×D3C2211yescharacteristic
23C3×#4016C2211yescharacteristic
24D3×C4⋊Dic5C2212yes—
25D3×#683—22no—
26#91381C2212yes—
27#91379—22no—
28C2×#6650C2212yes—
29#91119C2212yes—
30#91116C2212yes—
31C4×C3⋊#168C2211yescharacteristic
32C3×#3967C2212yes—
33C3×#3964C2212yes—
34C3×C4×#168C2211yescharacteristic
35#90973C2212yes—
36#90972C2212yes—
37#90967C2212yes—
38#90966C2212yes—
39#90953C2212yes—
40#81641—51nomaximal, Hall
41C5×#532—31no—
42C2×#4016—31no—
43#65521—32no—
44#65521—32no—
45#65371—32no—
46#65360—32no—
47#65345—31no—
48#65345—31no—
49#65345—31no—
50#65345D311yescharacteristic, complemented
51C4×#681—31no—
52C2×C3×C5×Q8C2311yescharacteristic
53C2×C3×C5×D4C2311yescharacteristic
54C2×C5×#67—21no—
55C2×C5×#67—22no—
56C22×C5×Dic3—21no—
57C5×#239—24no—
58C5×#237—24no—
59C2×C5×D12—21no—
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C4×C5×D3D412yes—
63C2×C4×C5×D3C2311yescharacteristic
64C2×C5×Dic6C2311yescharacteristic
65C2×D3×Dic5—22no—
66C3×C5×C22⋊C4—22no—
67C3×C42×C5C2311yescharacteristic
68C4⋊Dic15C2312yes—
69#6712—22no—
70C2×C3⋊#168C2312yes—
71C5×(C2×D3)⋊C4—22no—
72C5×Dic3⋊C4—22no—
73C4×C5×Dic3D412yes—
74C4×C5×Dic3C2311yescharacteristic
75C3×C4⋊Dic5C2312yes—
76C3×#683—22no—
77C2×C3×#168C2312yes—
78Dic3⋊Dic5—22no—
79#6669—22no—
80#6668—22no—
81#6650—24no—
82D3×#125—51no—
83#5668D511yescharacteristic
84C3×#488—51no—
85#5068—51no—
86#5056—51no—
87#4803—52no—
88#4797—52no—
89#4771—52no—
90#4764—52no—
91#4697—51no—
92C4×ΓL(1,𝔽25)—51no—
93C2×C5×#41—31no—
94C2×C5×#41—31no—
95C5×C4⋊Q8—31no—
96C5×#127—31no—
97C5×#124—31no—
98C5×#124C2×D311yescharacteristic
99C5×#121—62no—
100C4×C5×D4—62no—
101C2×C42×C5—31no—
102C2×C4⋊Dic5—32no—
103C2×#683—62no—
104C2×#681—32no—
105#4016—31no—
106#4016—32no—
107#4016—62no—
108#4016C2×D311yescharacteristic
109#3967—32no—
110#3967—32no—
111#3967—32no—
112#3967C2×D312yes—
113#3964—32no—
114#3964—32no—
115#3964—32no—
116#3964C2×D312yes—
117#3935—32no—
118C4×#168—31no—
119C4×#168C2×D311yescharacteristic
120#3142—151noSylow
121C23×C3×C5—21no—
122C22×C5×D3—21no—
123C22×C5×D3C2×D411yescharacteristic
124C3×C5×Q8—22no—
125C3×C5×D4—22no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2411yescharacteristic
129C2×Dic15—22no—
130C5×#67—44no—
131C5×#67—42no—
132C2×C5×Dic3—21no—
133C2×C5×Dic3—42no—
134C2×C5×Dic3C2×D412yes—
135C2×C5×Dic3C2×D411yescharacteristic
136C5×D12—22no—
137C5×D12—42no—
138C4×C5×D3—42no—
139C4×C5×D3—42no—
140C4×C5×D3#4114yes—
141C5×Dic6—22no—
142C2×C3×Dic5—22no—
143D3×Dic5—44no—
144C3⋊#168—22no—
145C3×#168—22no—
146C2×#239C2×D511yescharacteristic
147C2×#237C2×D511yescharacteristic
148C3×#125—51no—
149C3×#124C2×D511yescharacteristic
150#944C2×D511yescharacteristic
151#940C2×D511yescharacteristic
152C2×ΓL(1,𝔽25)—52no—
153D3×C4⋊C4—52no—
154D3×C4⋊C4—102no—
155#890—52no—
156#889—102no—
157#884—22no—
158#67⋊C4—22no—
159#875C2×D511yescharacteristic
160C42×D3C2×D511yescharacteristic
161#870—51no—
162C3×#103—52no—
163C3×#102—52no—
164C3×C4×C8—51no—
165#835—52no—
166#832—52no—
167#821—52no—
168#816—52no—
169#815—52no—
170#810—52no—
171#809—52no—
172C4×C3⋊C8—51no—
173C5×#41—64no—
174C5×#41—64no—
175C2×C5×Q8—31no—
176C2×C5×Q8C22×D311yescharacteristic
177C2×C5×D4—31no—
178C2×C5×D4—61no—
179C2×C5×D4—62no—
180C2×C5×D4—61no—
181C2×C5×D4C22×D311yescharacteristic
182C22×C4×C5—31no—
183C22×C4×C5—32no—
184C22×C4×C5—61no—
185C22×C4×C5—61no—
186C22×Dic5—62no—
187C5×C4⋊C4—62no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—62no—
190C42×C5—32no—
191C42×C5—31no—
192C42×C5C22×D311yescharacteristic
193C4⋊Dic5—32no—
194C4⋊Dic5—62no—
195C4⋊Dic5C22×D312yes—
196#683—22no—
197#683—62no—
198#683—62no—
199#683—62no—
200#681—64no—
201C2×#168—32no—
202C2×#168C22×D312yes—
203#532—31no—
204C2×#125—151no—
205#491—152no—
206#490—152no—
207#488—51no—
208#488—151no—
209#488—151no—
210#488—151no—
211#417—152no—
212#417—152no—
213C4×M16—151no—
214C22×C3×C5—41no—
215C22×C3×C5—42no—
216C22×C3×C5C22×D411yescharacteristic
217C2×C5×D3—22no—
218C2×C5×D3—41no—
219C2×C5×D3—42no—
220C2×C5×D3#12412yes—
221C3×C4×C5—22no—
222C3×C4×C5—41no—
223C3×C4×C5C2×#4112yes—
224Dic15—42no—
225C3×Dic5—42no—
226C5×Dic3—22no—
227C5×Dic3—41no—
228C5×Dic3#12412yes—
229C2×C3×Q8C22×D511yescharacteristic
230C2×C3×D4C22×D511yescharacteristic
231C2×#67—21no—
232C2×#67—22no—
233C22×Dic3—21no—
234#239—24no—
235#237—24no—
236C2×D12—21no—
237C2×D12C22×D511yescharacteristic
238C2×C4×D3—21no—
239C2×C4×D3—102no—
240C2×C4×D3C22⋊D512yes—
241C2×C4×D3C22×D511yescharacteristic
242C2×Dic6C22×D511yescharacteristic
243C2×C3×C8—52no—
244C3×C4⋊C4—52no—
245C3×C4⋊C4—102no—
246C3×C22⋊C4—22no—
247C3×C42C22×D511yescharacteristic
248(C2×D3)⋊C4—22no—
249C4⋊Dic3—52no—
250C4⋊Dic3—102no—
251Dic3⋊C4—22no—
252Dic3⋊C4—102no—
253Dic3⋊C4—102no—
254Dic3⋊C4—102no—
255C4×Dic3C22⋊D512yes—
256C4×Dic3C22×D511yescharacteristic
257C2×C3⋊C8—52no—
258ΓL(1,𝔽25)—104no—
259C23×C5—21no—
260C23×C5—31no—
261C23×C5—61no—
262C5×Q8—22no—
263C5×Q8—62no—
264C5×D4—22no—
265C5×D4—62no—
266C5×D4—122no—
267C5×D4—124no—
268C5×D4—122no—
269C2×C4×C5—21no—
270C2×C4×C5—31no—
271C2×C4×C5—34no—
272C2×C4×C5—32no—
273C2×C4×C5—61no—
274C2×C4×C5—122no—
275C2×C4×C5—122no—
276C2×C4×C5—122no—
277C2×C4×C5D3×D412yes—
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—22no—
280C2×Dic5—62no—
281C2×Dic5—124no—
282#168—22no—
283#168—62no—
284C2×#41—31no—
285C2×#41—31no—
286C2×M16—152no—
287C4⋊Q8—31no—
288#127—31no—
289#125—51no—
290#125—152no—
291#125—151no—
292#125—302no—
293#124—31no—
294#124D3×D511yescharacteristic
295#121—62no—
296C4×D4—62no—
297C2×C4⋊C4—152no—
298C2×C4⋊C4—302no—
299C2×C42—31no—
300#103—52no—
301#103—152no—
302#103—152no—
303#103—152no—
304#102—52no—
305#102—152no—
306#102—152no—
307#102—152no—
308#97—152no—
309C4×C8—51no—
310C4×C8—151no—
311C2×C3×C5—81no—
312C2×C3×C5C2×#12411yescharacteristic
313C2×C3×C5#57512yes—
314C5×D3—22no—
315C5×D3—81no—
316C23×C3—21no—
317C22×D3—21no—
318C22×D3C2×C22⋊D511yescharacteristic
319C3×Q8—22no—
320C3×D4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—102no—
323C2×C3×C4C2×C22⋊D512yes—
324C2×C3×C4C23×D511yescharacteristic
325#67—44no—
326#67—42no—
327C2×Dic3—21no—
328C2×Dic3—42no—
329C2×Dic3—102no—
330C2×Dic3C2×C22⋊D512yes—
331C2×Dic3C2×C22⋊D511yescharacteristic
332D12—22no—
333D12—42no—
334C4×D3—42no—
335C4×D3—42no—
336C4×D3—204no—
337C4×D3#71114yes—
338Dic6—22no—
339C3×C8—102no—
340C3⋊C8—102no—
341C22×C5—32no—
342C22×C5—41no—
343C22×C5—42no—
344C22×C5—62no—
345C22×C5—121no—
346C22×C5—122no—
347C22×C5C2×D3×D411yescharacteristic
348C4×C5—22no—
349C4×C5—32no—
350C4×C5—41no—
351C4×C5—62no—
352C4×C5—121no—
353C4×C5D3×#4112yes—
354Dic5—42no—
355Dic5—122no—
356#41—64no—
357#41—64no—
358C2×Q8—31no—
359C2×Q8C2×D3×D511yescharacteristic
360C2×D4—31no—
361C2×D4—61no—
362C2×D4—62no—
363C2×D4—61no—
364C2×D4C2×D3×D511yescharacteristic
365C22×C4—31no—
366C22×C4—32no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—302no—
370M16—304no—
371C2×C8—52no—
372C2×C8—152no—
373C4⋊C4—52no—
374C4⋊C4—62no—
375C4⋊C4—102no—
376C4⋊C4—152no—
377C4⋊C4—302no—
378C4⋊C4—302no—
379C4⋊C4—302no—
380C4⋊C4—302no—
381C22⋊C4—22no—
382C22⋊C4—62no—
383C42—32no—
384C42—31no—
385C42C2×D3×D511yescharacteristic
386C3×C5#314211yescharacteristic, complemented, Hall
387C22×C3—41no—
388C22×C3—42no—
389C22×C3C22×C22⋊D511yescharacteristic
390C2×D3—22no—
391C2×D3—41no—
392C2×D3—42no—
393C2×D3#408212yes—
394C3×C4—22no—
395C3×C4—41no—
396C3×C4—202no—
397C3×C4C2×#71112yes—
398Dic3—22no—
399Dic3—41no—
400Dic3—202no—
401Dic3#408212yes—
402C2×C5—62no—
403C2×C5—81no—
404C2×C5—241no—
405C2×C5D3×#12411yescharacteristic
406C2×C5#576812yes—
407C23—21no—
408C23—31no—
409C23—61no—
410Q8—22no—
411Q8—62no—
412D4—22no—
413D4—62no—
414D4—122no—
415D4—124no—
416D4—122no—
417C2×C4—21no—
418C2×C4—31no—
419C2×C4—34no—
420C2×C4—32no—
421C2×C4—61no—
422C2×C4—102no—
423C2×C4—122no—
424C2×C4—122no—
425C2×C4—122no—
426C2×C4—302no—
427C2×C4—604no—
428C2×C4D3×C22⋊D512yes—
429C2×C4C22×D3×D511yescharacteristic
430C8—102no—
431C8—302no—
432C2×C3—81no—
433C2×C3C2×#408211yescharacteristic
434C2×C3#6615612yes—
435D3—22no—
436D3—81no—
437C5#8164111yescharacteristic, complemented, Sylow
438C22—32no—
439C22—42no—
440C22—41no—
441C22—62no—
442C22—122no—
443C22—121no—
444C22C2×D3×C22⋊D511yescharacteristic
445C4—22no—
446C4—32no—
447C4—41no—
448C4—62no—
449C4—121no—
450C4—202no—
451C4—602no—
452C4D3×#71112yes—
453C3#1061501511yescharacteristic, complemented, Sylow
454C2—62no—
455C2—81no—
456C2—241no—
457C2D3×#408211yescharacteristic
458C2#1175532212yes—
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC5×#5668C2
hypercenter#124D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. D3×#4016C2semidirect
3. #11751157C2semidirect
4. C3×#65345C2semidirect
5. #11749201C2semidirect
6. #11749192C2semidirect
7. #11748955C2semidirect
8. #11748946C2semidirect
9. C4×#6650C2semidirect
10. #11746907C2semidirect
11. #11746903C2semidirect
50. #65345D3semidirect
386. C3×C5#3142semidirect
437. C5#81641semidirect
453. C3#10615015semidirect

Maximal subgroups

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

subgroupindex
C5×#56682
D3×#40162
#117511572
C3×#653452
#117492012
#117491922
#117489552
#117489462
C4×#66502
#117469072
#117469032
#106150153
#816415