Finite Group Databasebeta

← #14307988

Subgroups — #14307988

Order 1920.

812 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#537C211yesmaximal, characteristic, complemented
2C2×#91838C212yesmaximal, complemented
3C2×#91121C212yesmaximal, complemented
4#11751089C211yesmaximal, characteristic, complemented
5#11746351C211yesmaximal, characteristic, complemented
6#10602672—31nomaximal, Hall
7C2×C3×C5×#41C2212yes—
8C22×D60C2211yescharacteristic
9C3×C5×C22⋊Q8—22no—
10C3×C5×#121—22no—
11C3×C5×#121—22no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13#91838—24no—
14#91838—24no—
15C2×#6717—22no—
16C2×#6715—22no—
17C2×#6714—22no—
18C2×C4×Dic15C2211yescharacteristic
19C2×#6710C2212yes—
20#91121—24no—
21#71879—51nomaximal, Hall
22C5×#537D311yescharacteristic, complemented
23C2×#4095—32no—
24C2×#3969—32no—
25#65277—31no—
26#64750—31no—
27C23×D15—21no—
28C3×C5×#41—22no—
29C3×C5×#41—22no—
30C3×C5×#41—22no—
31C3×C5×#41—22no—
32C2×C3×C5×Q8D412yes—
33C2×C3×C5×D4—22no—
34C2×C3×C5×D4—22no—
35C2×C3×C5×D4D412yes—
36C22×C3×C4×C5—22no—
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×D60—22no—
41C2×D60—22no—
42C2×D60—21no—
43C2×D60D412yescomplemented
44C3×C5×C4⋊C4—22no—
45C3×C5×C4⋊C4—22no—
46C3×C5×C22⋊C4—24no—
47#6717—28no—
48#6715—28no—
49#6714—44no—
50C4×Dic15—22no—
51#6710—22no—
52#6710D414yescomplemented
53C2×C3⋊#168—22no—
54C3×#537D511yescharacteristic, complemented
55C2×#949—52no—
56C2×#837—52no—
57#4988—51no—
58#4530—51no—
59C2×C5×#41C2×D312yes—
60C22×D20—31no—
61C5×C22⋊Q8—22no—
62C5×#121—22no—
63C5×#121—22no—
64C2×C5×C4⋊C4C2×D311yescharacteristic
65#4095—64no—
66#4095—64no—
67C2×#688—62no—
68C2×#686—62no—
69C2×#685—62no—
70C2×C4×Dic5—31no—
71C2×#681—32no—
72#3969—64no—
73#2006—151noSylow
74C23×C3×C5—22no—
75C23×C3×C5C2×D411yescharacteristic
76C22×D15—22no—
77C22×D15—42no—
78C22×D15—42no—
79C22×D15—41no—
80C22×D15—41no—
81C3×C5×Q8—22no—
82C3×C5×Q8—22no—
83C3×C5×D4—22no—
84C3×C5×D4—22no—
85C3×C5×D4—42no—
86C3×C5×D4—42no—
87C3×C5×D4—82no—
88C2×C3×C4×C5—22no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5—42no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D412yes—
95C2×C3×C4×C5C2×D412yes—
96C2×C3×C4×C5#4111yescharacteristic
97C2×Dic15—22no—
98C2×Dic15—41no—
99C2×Dic15—41no—
100D60—24no—
101D60—42no—
102C3⋊#168—24no—
103C2×C3×#41C2×D512yes—
104C22×D12—51no—
105C3×C22⋊Q8—22no—
106C3×#121—22no—
107C3×#121—22no—
108C2×C3×C4⋊C4C2×D511yescharacteristic
109#949—104no—
110#949—104no—
111C2×#215—102no—
112C2×#213—102no—
113C2×(C2×D3)⋊C4—102no—
114C2×C4×Dic3—51no—
115C2×#208—52no—
116#837—104no—
117C23×D5—61no—
118C5×#41—22no—
119C5×#41—22no—
120C5×#41—22no—
121C5×#41—22no—
122C2×C5×Q8#6712yes—
123C2×C5×D4—22no—
124C2×C5×D4—22no—
125C2×C5×D4#6712yes—
126C22×C4×C5—22no—
127C22×C4×C5#6712yes—
128C22×C4×C5C22×D311yescharacteristic
129C22×Dic5—61no—
130C2×D20—32no—
131C2×D20—62no—
132C2×D20—62no—
133C2×D20—61no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—22no—
136C5×C22⋊C4—24no—
137#688—68no—
138#686—68no—
139#685—124no—
140C4×Dic5—62no—
141#681—34no—
142#681—62no—
143C2×#168—62no—
144C2×AGL(1,ℤ/8)—152no—
145#537D1511yescharacteristic, complemented
146C2×#104—152no—
147#390—151no—
148#343—151no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—42no—
152C22×C3×C5—42no—
153C22×C3×C5—42no—
154C22×C3×C5#12011yescharacteristic
155C22×C3×C5#12111yescharacteristic
156C22×C3×C5#12711yescharacteristic
157C2×D15—44no—
158C2×D15—42no—
159C2×D15—82no—
160C2×D15—81no—
161C2×D15—81no—
162C3×C4×C5—42no—
163C3×C4×C5—42no—
164C3×C4×C5#12012yes—
165C3×C4×C5#12112yes—
166Dic15—42no—
167C23×D3—101no—
168C3×#41—22no—
169C3×#41—22no—
170C3×#41—22no—
171C3×#41—22no—
172C2×C3×Q8C22⋊D512yes—
173C2×C3×D4—22no—
174C2×C3×D4—22no—
175C2×C3×D4C22⋊D512yes—
176C22×C3×C4—22no—
177C22×C3×C4C22⋊D512yes—
178C22×C3×C4C22×D511yescharacteristic
179C22×Dic3—101no—
180C2×D12—52no—
181C2×D12—102no—
182C2×D12—102no—
183C2×D12—101no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—22no—
186C3×C22⋊C4—24no—
187#215—108no—
188#213—108no—
189(C2×D3)⋊C4—204no—
190C4×Dic3—102no—
191#208—54no—
192#208—102no—
193C2×C3⋊C8—102no—
194C23×C5—22no—
195C23×C5C2×#6711yescharacteristic
196C22×D5—62no—
197C22×D5—122no—
198C22×D5—122no—
199C22×D5—121no—
200C22×D5—121no—
201C5×Q8—22no—
202C5×Q8—22no—
203C5×D4—22no—
204C5×D4—22no—
205C5×D4—42no—
206C5×D4—42no—
207C5×D4—82no—
208C2×C4×C5—22no—
209C2×C4×C5—22no—
210C2×C4×C5—42no—
211C2×C4×C5—42no—
212C2×C4×C5—42no—
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5D3×D412yes—
215C2×C4×C5#23711yescharacteristic
216C2×C4×C5C2×#6712yes—
217C2×Dic5—62no—
218C2×Dic5—121no—
219C2×Dic5—121no—
220D20—64no—
221D20—122no—
222#168—64no—
223C2×#41C2×D1512yes—
224C22×D4—151no—
225AGL(1,ℤ/8)—304no—
226AGL(1,ℤ/8)—304no—
227C2×SD16—302no—
228C2×D8—302no—
229C2×M16—152no—
230C22⋊Q8—22no—
231#121—22no—
232#121—22no—
233C2×C4⋊C4C2×D1511yescharacteristic
234C2×C22⋊C4—302no—
235C2×C42—151no—
236#104—304no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5—82no—
240C2×C3×C5#39211yescharacteristic
241C2×C3×C5#45311yescharacteristic
242C2×C3×C5#45411yescharacteristic
243D15—82no—
244C23×C3—22no—
245C23×C3C2×C22⋊D511yescharacteristic
246C22×D3—102no—
247C22×D3—202no—
248C22×D3—202no—
249C22×D3—201no—
250C22×D3—201no—
251C3×Q8—22no—
252C3×Q8—22no—
253C3×D4—22no—
254C3×D4—22no—
255C3×D4—42no—
256C3×D4—42no—
257C3×D4—82no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4D4×D512yes—
265C2×C3×C4#71111yescharacteristic
266C2×C3×C4C2×C22⋊D512yes—
267C2×Dic3—102no—
268C2×Dic3—201no—
269C2×Dic3—201no—
270D12—104no—
271D12—202no—
272C3⋊C8—104no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—42no—
276C22×C5—42no—
277C22×C5—42no—
278C22×C5#93811yescharacteristic
279C22×C5#94011yescharacteristic
280C22×C5#95311yescharacteristic
281C2×D5—124no—
282C2×D5—122no—
283C2×D5—242no—
284C2×D5—241no—
285C2×D5—241no—
286C4×C5—42no—
287C4×C5—42no—
288C4×C5#93712yes—
289C4×C5#93912yes—
290Dic5—122no—
291C24—301no—
292#41—22no—
293#41—22no—
294#41—22no—
295#41—22no—
296C2×Q8#122012yes—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—152no—
300C2×D4—302no—
301C2×D4—301no—
302C2×D4—302no—
303C2×D4#122012yes—
304C22×C4—22no—
305C22×C4—301no—
306C22×C4#122012yes—
307C22×C4C22×D1511yescharacteristic
308SD16—308no—
309D8—308no—
310M16—154no—
311M16—302no—
312C2×C8—302no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C22⋊C4—24no—
316C22⋊C4—604no—
317C42—302no—
318C3×C5#200611yescharacteristic, complemented, Hall
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3#408411yescharacteristic
325C22×C3#408611yescharacteristic
326C22×C3#409911yescharacteristic
327C2×D3—204no—
328C2×D3—202no—
329C2×D3—402no—
330C2×D3—401no—
331C2×D3—401no—
332C3×C4—42no—
333C3×C4—42no—
334C3×C4#408312yes—
335C3×C4#408512yes—
336Dic3—202no—
337C2×C5—21no—
338C2×C5—21no—
339C2×C5—82no—
340C2×C5#522311yescharacteristic
341C2×C5#524111yescharacteristic
342C2×C5#524511yescharacteristic
343D5—242no—
344C23—22no—
345C23—302no—
346C23—602no—
347C23—602no—
348C23—601no—
349C23—601no—
350C23C2×#122011yescharacteristic
351Q8—22no—
352Q8—22no—
353D4—22no—
354D4—22no—
355D4—42no—
356D4—42no—
357D4—82no—
358D4—304no—
359D4—602no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—302no—
366C2×C4—601no—
367C2×C4—601no—
368C2×C4D4×D1511yescharacteristic
369C2×C4D4×D1512yes—
370C2×C4#681911yescharacteristic
371C2×C4C2×#122012yes—
372C8—304no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—82no—
376C2×C3#6551211yescharacteristic
377C2×C3#6553011yescharacteristic
378C2×C3#6553411yescharacteristic
379D3—402no—
380C5#7187911yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—604no—
387C22—602no—
388C22—1202no—
389C22—1201no—
390C22—1201no—
391C22#9182711yescharacteristic
392C22#9182911yescharacteristic
393C22#9184211yescharacteristic
394C4—42no—
395C4—42no—
396C4—602no—
397C4#9182612yes—
398C4#9182812yes—
399C3#1060267211yescharacteristic, complemented, Sylow
400C2—21no—
401C2—21no—
402C2—82no—
403C2—1202no—
404C2#1175132411yescharacteristic
405C2#1175134211yescharacteristic
406C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#537C2
socleC22×C3×C5#120
hypercenter#537D15
hypocenterC3×C5#2006
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C3×C5×#537C2semidirect
2. C2×#91838C2semidirect
3. C2×#91121C2semidirect
4. #11751089C2semidirect
5. #11746351C2semidirect
22. C5×#537D3semidirect
43. C2×D60D4semidirect
52. #6710D4semidirect
54. C3×#537D5semidirect
145. #537D15semidirect
318. C3×C5#2006semidirect
380. C5#71879semidirect
399. C3#10602672semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5372
C2×#918382
C2×#911212
#117510892
#117463512
#106026723
#718795