Finite Group Databasebeta

← #14416590

Subgroups — #14416590

Order 1920.

984 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
1C2×#91271C211yesmaximal, characteristic
2C4×#6773C212yesmaximal, complemented
3#11750812C211yesmaximal, characteristic, complemented
4C5×#4716C211yesmaximal, characteristic, complemented
5C3×D5×#97C211yesmaximal, characteristic, complemented
6#11747856C211yesmaximal, characteristic, complemented
7#11747772C211yesmaximal, characteristic, complemented
8#11747748C212yesmaximal, complemented
9#11747671C211yesmaximal, characteristic, complemented
10#11747642C212yesmaximal, complemented
11#11747058C212yesmaximal, complemented
12#10611559—31nomaximal, Hall
13C2×#6773C2212yes—
14C2×D120C2211yescharacteristic
15C4×D60C2212yes—
16C2×C5×Dic12C2211yescharacteristic
17C4×C5×Dic6C2212yes—
18C2×C3×C8×D5C2211yescharacteristic
19C2×C3×C8×D5C2211yescharacteristic
20C3×C42×D5C2211yescharacteristic
21#91444—22no—
22C4×#1202—22no—
23#91418C2212yes—
24#91402—22no—
25C4×#1200—22no—
26#91358C2212yes—
27Dic5×Dic6C2212yes—
28C2×#6660C2212yes—
29#91271C418yescomplemented
30C3×C5×#97C2211yescharacteristic
31#91105C2212yes—
32#91101C2211yescharacteristic
33C5×#817C2211yescharacteristic
34C5×#816C2212yes—
35C3×#3947C2211yescharacteristic
36C3×#3947C2211yescharacteristic
37C3×#3935C2211yescharacteristic
38#90988C2212yes—
39#90973C2212yes—
40#90969C2212yes—
41#78494—51nomaximal, Hall
42C2×#4065—31no—
43C4×#713—32no—
44C5×#441—31no—
45#65473—31no—
46#65315—32no—
47#65158—31no—
48#65149—31no—
49#65106—32no—
50#65093—32no—
51#65000—31no—
52D5×#97D311yescharacteristic, complemented
53C2×D60C2312yes—
54C2×C4×D15—22no—
55C2×C5×Dic6C2312yes—
56C2×C3×C4×D5D412yes—
57C2×C3×C4×D5C2311yescharacteristic
58C2×#1202—22no—
59C2×#1200—22no—
60C2×#1200—22no—
61#6773—24no—
62#6773C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C3×C42×C5C2311yescharacteristic
66#6714—22no—
67C4⋊Dic15C2312yes—
68D120C2×C414yescomplemented
69C5×C4⋊Dic3C2312yes—
70C5×Dic3⋊C4—22no—
71C4×C5×Dic3—22no—
72C5×Dic12C2×C414yescomplemented
73C3×C4×Dic5D412yes—
74C3×C4×Dic5C2311yescharacteristic
75C2×C3×#168C2311yescharacteristic
76C2×C3×#168C2311yescharacteristic
77C3×C8×D5—22no—
78C3×C8×D5C2×C414yescomplemented
79Dic3⋊Dic5—22no—
80#6667—22no—
81#6665—22no—
82Dic3×Dic5—22no—
83Dic3×Dic5—22no—
84#6660C2×C418yescomplemented
85C2×#904—51no—
86C4×#235—52no—
87C2×C3×#97—51no—
88#5113—52no—
89#5106—51no—
90#4716—51no—
91#4716D511yescharacteristic, complemented
92#4711—51no—
93#4711—51no—
94#4710—52no—
95#4710—52no—
96C2×#713—32no—
97C2×C5×Q16—31no—
98C4×C5×Q8—32no—
99Q8×Dic5—32no—
100C2×#688—32no—
101#4065—38no—
102C2×D40—31no—
103C2×C8×D5C2×D311yescharacteristic
104C2×C8×D5C2×D311yescharacteristic
105#4039—32no—
106#4039—62no—
107#4038—32no—
108#4038—62no—
109C4×D20—32no—
110C4×D20—62no—
111C42×D5—62no—
112C42×D5C2×D311yescharacteristic
113C5×#106—31no—
114C5×#103—32no—
115C5×#97C2×D311yescharacteristic
116#3967—32no—
117#3953—32no—
118#3949—31no—
119#3947C2×D311yescharacteristic
120#3947C2×D311yescharacteristic
121#3941—32no—
122#3939—32no—
123#3935C2×D311yescharacteristic
124#2943—151noSylow
125C22×D15—22no—
126C22×C3×D5C2×D411yescharacteristic
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2411yescharacteristic
129C2×Dic15—22no—
130D60—22no—
131D60C22×C414yes—
132C4×D15—44no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C5×Dic6—22no—
136C5×Dic6C22×C414yes—
137C2×C3×Dic5C2×D412yes—
138C2×C3×Dic5C2×D411yescharacteristic
139C3×C4×D5—42no—
140C3×C4×D5C22×C412yes—
141C3×C4×D5#4112yes—
142#1202—28no—
143#1200—28no—
144#1200—44no—
145C3×C5×C8—21no—
146C3×C5×C8C22×C412yes—
147C3×#168—21no—
148C3×#168C22×C412yes—
149C2×#235—52no—
150C22×C3×C8—51no—
151C22×C3×C8—51no—
152C2×C3×C42—51no—
153C4×#67—102no—
154C4×#67—102no—
155#926—52no—
156C2×Dic12C2×D511yescharacteristic
157#904—58no—
158C2×D24—51no—
159C2×#204—52no—
160C4×D12—52no—
161C4×D12—52no—
162#872—102no—
163C42×D3—102no—
164C4×Dic6—52no—
165C4×Dic6C2×D512yes—
166C3×#97—51no—
167C3×#97—51no—
168C3×#97—51no—
169C3×#97C2×D511yescharacteristic
170#821—52no—
171#821—52no—
172#818—52no—
173#817—51no—
174#817C2×D511yescharacteristic
175#816—52no—
176#816C2×D512yes—
177C2×C5×Q8—32no—
178#713—38no—
179#713—64no—
180C2×D20—32no—
181C2×D20—62no—
182C2×C4×D5—62no—
183C2×C4×D5—62no—
184C2×C4×D5—62no—
185C2×C4×D5D1212yes—
186C2×C4×D5C22×D311yescharacteristic
187C5×Q16—34no—
188C2×C5×C8C22×D311yescharacteristic
189C2×C5×C8C22×D311yescharacteristic
190C5×C4⋊C4—32no—
191C5×C4⋊C4—62no—
192C42×C5—62no—
193C42×C5C22×D311yescharacteristic
194#688—38no—
195#685—62no—
196#685—62no—
197#685—62no—
198C4⋊Dic5—32no—
199C4⋊Dic5—62no—
200C4×Dic5—62no—
201C4×Dic5—62no—
202C4×Dic5D1212yes—
203C4×Dic5C22×D311yescharacteristic
204C2×#168C22×D311yescharacteristic
205C2×#168C22×D311yescharacteristic
206D40—34no—
207C8×D5—22no—
208C8×D5C4×D314yescomplemented
209C2×#135—151no—
210C4×#41—152no—
211#442—151no—
212#442—151no—
213#441—31no—
214#441—151no—
215#440—152no—
216#440—152no—
217#427—151no—
218#416—152no—
219C2×#97—51no—
220C22×C3×C5C22×D411yescharacteristic
221C2×D15—24no—
222C2×D15—42no—
223C2×D15—42no—
224C2×C3×D5—22no—
225C2×C3×D5C4×D412yes—
226C3×C4×C5—22no—
227C3×C4×C5C23×C411yescharacteristic
228C3×C4×C5C2×#4111yescharacteristic
229Dic15—42no—
230C3×Dic5—22no—
231C3×Dic5C4×D412yes—
232C5×Dic3—24no—
233C5×Dic3—42no—
234C22×C3×C4—51no—
235C22×C3×C4—52no—
236C2×#67—102no—
237#235—58no—
238#235—104no—
239C2×D12—52no—
240C2×C4×D3—102no—
241C2×C4×D3—102no—
242C2×C4×D3—102no—
243C2×Dic6C22×D512yes—
244C2×C3×C8—51no—
245C2×C3×C8—54no—
246C2×C3×C8—51no—
247C2×C3×C8—102no—
248C2×C3×C8C22×D511yescharacteristic
249C2×C3×C8C22×D511yescharacteristic
250C3×C42—52no—
251C3×C42—51no—
252C3×C42C22×D511yescharacteristic
253#217—102no—
254(C2×D3)⋊C4—102no—
255(C2×D3)⋊C4—102no—
256C4⋊Dic3—52no—
257C4⋊Dic3C22×D512yes—
258Dic3⋊C4—22no—
259Dic3⋊C4—102no—
260C4×Dic3—22no—
261C4×Dic3—102no—
262C4×Dic3—102no—
263Dic12C4×D514yescomplemented
264D24—54no—
265#204—58no—
266C22×D5—62no—
267C22×D5C2×D1211yescharacteristic
268C5×Q8—34no—
269C5×Q8—62no—
270C2×C4×C5—62no—
271C2×C4×C5—62no—
272C2×C4×C5C2×D1212yes—
273C2×C4×C5C23×D311yescharacteristic
274C2×Dic5—62no—
275C2×Dic5C2×D1212yes—
276C2×Dic5C2×D1211yescharacteristic
277D20—34no—
278D20—68no—
279D20—62no—
280C4×D5—42no—
281C4×D5—68no—
282C4×D5—124no—
283C4×D5—124no—
284C4×D5C2×C4×D312yes—
285C4×D5#23512yes—
286C5×C8—21no—
287C5×C8C2×C4×D312yes—
288#168—21no—
289#168C2×C4×D312yes—
290C2×#41—152no—
291#135—158no—
292C2×Q16—31no—
293C2×SD16—152no—
294C2×D8—151no—
295C22×C8—51no—
296C22×C8—51no—
297C4×Q8—32no—
298C4×Q8—152no—
299C4×D4—152no—
300C4×D4—152no—
301C4×D4—302no—
302C4×D4—302no—
303#117—152no—
304#117—302no—
305C2×C42—51no—
306C2×C42—302no—
307#107—152no—
308#106—31no—
309#106—151no—
310#103—32no—
311#103—152no—
312#102—152no—
313#102—152no—
314#97—51no—
315#97—51no—
316#97—51no—
317#97D3×D511yescharacteristic
318C2×C3×C5C2×C4×D411yescharacteristic
319C2×C3×C5#57512yes—
320D15—44no—
321C3×D5—22no—
322C23×C3—51no—
323C22×D3—102no—
324C2×C3×C4—51no—
325C2×C3×C4—52no—
326C2×C3×C4—52no—
327C2×C3×C4—52no—
328C2×C3×C4—202no—
329C2×C3×C4D4×D512yes—
330C2×C3×C4C23×D511yescharacteristic
331#67—108no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—102no—
335D12—54no—
336D12—102no—
337C4×D3—108no—
338C4×D3—204no—
339C4×D3—204no—
340Dic6—22no—
341Dic6C2×C4×D514yes—
342C3×C8—21no—
343C3×C8—52no—
344C3×C8—101no—
345C3×C8C2×C4×D512yes—
346C22×C5C22×D1211yescharacteristic
347C2×D5—22no—
348C2×D5—64no—
349C2×D5—122no—
350C2×D5—122no—
351C2×D5C4×D1212yes—
352C4×C5—22no—
353C4×C5—64no—
354C4×C5—122no—
355C4×C5C22×C4×D311yescharacteristic
356C4×C5C2×#23511yescharacteristic
357Dic5—22no—
358Dic5—122no—
359Dic5C4×D1212yes—
360#41—158no—
361#41—304no—
362C2×Q8—32no—
363C2×D4—152no—
364C2×D4—302no—
365C22×C4—51no—
366C22×C4—52no—
367C22×C4—302no—
368C22×C4—302no—
369C22×C4—302no—
370Q16—34no—
371SD16—158no—
372D8—154no—
373C2×C8—51no—
374C2×C8—54no—
375C2×C8—51no—
376C2×C8—102no—
377C2×C8C2×D3×D511yescharacteristic
378C2×C8C2×D3×D511yescharacteristic
379C4⋊C4—32no—
380C4⋊C4—62no—
381C4⋊C4—152no—
382C4⋊C4—302no—
383C22⋊C4—302no—
384C22⋊C4—302no—
385C22⋊C4—302no—
386C42—52no—
387C42—51no—
388C42—62no—
389C42—302no—
390C42—302no—
391C42C2×D3×D511yescharacteristic
392C3×C5#294311yescharacteristic, complemented, Hall
393C22×C3—52no—
394C22×C3—102no—
395C22×C3C2×D4×D511yescharacteristic
396C2×D3—104no—
397C2×D3—202no—
398C2×D3—202no—
399C3×C4—22no—
400C3×C4—52no—
401C3×C4—102no—
402C3×C4C22×C4×D511yescharacteristic
403C3×C4D5×#4111yescharacteristic
404Dic3—24no—
405Dic3—42no—
406Dic3—202no—
407C2×C5C2×C4×D1211yescharacteristic
408C2×C5#574812yes—
409D5—22no—
410D5—124no—
411C23—51no—
412C23—302no—
413Q8—34no—
414Q8—62no—
415D4—154no—
416D4—308no—
417D4—302no—
418C2×C4—51no—
419C2×C4—52no—
420C2×C4—52no—
421C2×C4—52no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—202no—
425C2×C4—308no—
426C2×C4—302no—
427C2×C4—604no—
428C2×C4—604no—
429C2×C4D5×D1212yes—
430C2×C4C22×D3×D511yescharacteristic
431C8—21no—
432C8—52no—
433C8—101no—
434C8C4×D3×D512yes—
435C2×C3—102no—
436C2×C3C4×D4×D511yescharacteristic
437C2×C3#6611112yes—
438D3—204no—
439C5#7849411yescharacteristic, complemented, Sylow
440C22—52no—
441C22—102no—
442C22—304no—
443C22—602no—
444C22—602no—
445C22C2×D5×D1211yescharacteristic
446C4—22no—
447C4—52no—
448C4—64no—
449C4—102no—
450C4—122no—
451C4—602no—
452C4C2×C4×D3×D511yescharacteristic
453C4D5×#23511yescharacteristic
454C3#1061155911yescharacteristic, complemented, Sylow
455C2—102no—
456C2—604no—
457C2C4×D5×D1211yescharacteristic
458C2#1175402112yes—
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C22×D4
prime radicalC2×#91271C2
cosocleC2×C3×C4×C5C24
hypercenter#97D3×D5
hypocenterC3×C5#2943
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C4×#6773C2semidirect
3. #11750812C2semidirect
4. C5×#4716C2semidirect
5. C3×D5×#97C2semidirect
6. #11747856C2semidirect
7. #11747772C2semidirect
8. #11747748C2semidirect
9. #11747671C2semidirect
10. #11747642C2semidirect
11. #11747058C2semidirect
29. #91271C4semidirect
52. D5×#97D3semidirect
62. #6773C2×C4semidirect
68. D120C2×C4semidirect
72. C5×Dic12C2×C4semidirect
78. C3×C8×D5C2×C4semidirect
84. #6660C2×C4semidirect
91. #4716D5semidirect
208. C8×D5C4×D3semidirect
263. Dic12C4×D5semidirect
392. C3×C5#2943semidirect
439. C5#78494semidirect
454. C3#10611559semidirect

Maximal subgroups

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

subgroupindex
C2×#912712
C4×#67732
#117508122
C5×#47162
C3×D5×#972
#117478562
#117477722
#117477482
#117476712
#117476422
#117470582
#106115593
#784945