Finite Group Databasebeta

← #14417692

Subgroups — #14417692

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4050C211yesmaximal, characteristic
2#11754499C212yesmaximal, complemented
3#11751202C211yesmaximal, characteristic, complemented
4C2×C5×#818C211yesmaximal, characteristic, complemented
5#11748368C212yesmaximal, complemented
6#11747883C212yesmaximal, complemented
7#11747812C214yesmaximal, complemented
8#11747809C212yesmaximal, complemented
9#10610867—31nomaximal, Hall
10C2×C3×#709C2212yes—
11C22×C3×C5×C8C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×C4⋊Dic3C2212yes—
15C2×C3×Dic20C2211yescharacteristic
16C3×#4050C418yescomplemented
17C2×C3×D40C2211yescharacteristic
18C2×C3×#677C2212yes—
19Dic3×C22⋊D5—24no—
20#91434C2214yes—
21D5×C4⋊Dic3—22no—
22#91358—22no—
23#91331C2214yes—
24#91099C2212yes—
25C8×Dic15C2212yes—
26C5×#818C2212yes—
27C5×#818C2212yes—
28#90970C2214yes—
29#90964C2214yes—
30#83898—51nomaximal, Hall
31C2×#4050D311yescharacteristic
32#65838—32no—
33C2×C5×#107—31no—
34#65390—31no—
35#65255—32no—
36#65178—34no—
37#65162—32no—
38#65161—32no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×C5×Dic3—22no—
41C2×C3×C22⋊D5—22no—
42C3×#709—24no—
43C3×#709C2×C418yescomplemented
44C2×C3×D20C2312yes—
45C2×C3×C4×D5—22no—
46C2×C3×Dic10C2312yes—
47C2×D5×Dic3—24no—
48C2×C3×C5×C8C2×C414yescomplemented
49C2×C3×C5×C8C2311yescharacteristic
50C2×C3×C5×C8C2311yescharacteristic
51#6719D412yes—
52C4⋊Dic15D411yescharacteristic
53C4⋊Dic15D411yescharacteristic
54C4×Dic15C2312yes—
55#6710—22no—
56C2×C3⋊#168C2312yes—
57C5×C4⋊Dic3—22no—
58C5×C4⋊Dic3C2314yes—
59C3×Dic20C2×C414yescomplemented
60C3×D40C2×C414yescomplemented
61C3×#677C2×C418yescomplemented
62#6668—24no—
63#6665—24no—
64Dic3×Dic5—24no—
65C2×C3×#135—51no—
66#5827—52no—
67#5232—52no—
68Dic3×Q16—52no—
69#5164—54no—
70Dic3×D8—52no—
71C2×#818D511yescharacteristic, complemented
72#5101—51no—
73C2×#709C2×D312yes—
74C22×C5×C8C2×D311yescharacteristic
75C2×C5×C4⋊C4—32no—
76C4×C22⋊D5—64no—
77#4072—31no—
78C2×#681—31no—
79C2×Dic20C2×D311yescharacteristic
80#4050Dic318yescomplemented
81C2×D40C2×D311yescharacteristic
82C2×#677C2×D312yes—
83#4039—34no—
84#4038—62no—
85D5×C4⋊C4—62no—
86#4033—34no—
87C5×#107—32no—
88C5×#107—32no—
89#3947—32no—
90C8×Dic5—32no—
91#3942—34no—
92#3941—34no—
93#2951—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—22no—
96C2×C3×C4×C5C22×C412yes—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5#4112yes—
99C2×C3×C4×C5C2411yescharacteristic
100C2×Dic15C2×D412yes—
101C2×Dic15C2×D412yes—
102C2×C5×Dic3—24no—
103C2×C5×Dic3—82no—
104C3×C22⋊D5—28no—
105C2×C3×Dic5—22no—
106C3×D20—22no—
107C3×D20C22×C414yes—
108C3×C4×D5—28no—
109C3×Dic10—22no—
110C3×Dic10C22×C414yes—
111D5×Dic3—84no—
112C3×C5×C8C22×C412yes—
113C3×C5×C8C22×C412yes—
114C3⋊#168—22no—
115C2×C3×#41—52no—
116C3×#135—58no—
117C2×C3×Q16—51no—
118C2×C3×SD16—52no—
119C2×C3×D8—51no—
120C22×C3×C8C2×D511yescharacteristic
121Q8×Dic3—54no—
122D4×Dic3—54no—
123D4×Dic3—104no—
124#926—51no—
125#926—102no—
126C2×C4⋊Dic3—102no—
127C2×C4⋊Dic3C2×D512yes—
128C2×#208—51no—
129#835—54no—
130#832—54no—
131#818C2×D512yes—
132#818C2×D512yes—
133#815—52no—
134C8×Dic3—52no—
135C22×C4×C5—62no—
136C22×C4×C5C22×D311yescharacteristic
137C2×C22⋊D5—22no—
138#709—24no—
139#709C2×Dic318yescomplemented
140C2×D20C22×D312yes—
141C2×C4×D5—22no—
142C2×C4×D5—64no—
143C2×Dic10C22×D312yes—
144C2×C5×C8C2×Dic314yescomplemented
145C2×C5×C8C22×D311yescharacteristic
146C2×C5×C8C22×D311yescharacteristic
147C5×C4⋊C4—34no—
148C5×C4⋊C4—62no—
149C22⋊Dic5—32no—
150#685—64no—
151C4⋊Dic5—31no—
152C4⋊Dic5—31no—
153#683—64no—
154C4×Dic5—32no—
155C4×Dic5—64no—
156#681—62no—
157C2×#168—32no—
158Dic20C2×Dic314yescomplemented
159D40C2×Dic314yescomplemented
160#677C2×Dic318yescomplemented
161C2×#135—51no—
162#520—152no—
163#440—154no—
164C4×Q16—152no—
165C4×D8—152no—
166C2×#107—31no—
167#417—152no—
168#405—151no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5C4×D412yes—
172C22×C3×C5C22×D411yescharacteristic
173C2×C3×D5—24no—
174C2×C3×D5—42no—
175C2×C3×D5—42no—
176C3×C4×C5C4×D412yes—
177C3×C4×C5C23×C411yescharacteristic
178C3×C4×C5C2×#4111yescharacteristic
179Dic15—22no—
180Dic15—22no—
181C3×Dic5—24no—
182C5×Dic3—44no—
183C3×#41—58no—
184C3×#41—104no—
185C2×C3×Q8—52no—
186C2×C3×D4—52no—
187C2×C3×D4—102no—
188C22×C3×C4—102no—
189C22×C3×C4C22×D511yescharacteristic
190C22×Dic3—22no—
191C22×Dic3—104no—
192C3×Q16—54no—
193C3×SD16—58no—
194C3×D8—54no—
195C2×C3×C8C4×D514yescomplemented
196C2×C3×C8C22×D511yescharacteristic
197C2×C3×C8C22×D511yescharacteristic
198#217—52no—
199#217—104no—
200C4⋊Dic3—22no—
201C4⋊Dic3—51no—
202C4⋊Dic3—51no—
203C4⋊Dic3—104no—
204C4⋊Dic3C22×D514yes—
205C4×Dic3—52no—
206C4×Dic3—104no—
207#208—102no—
208C2×C3⋊C8—52no—
209C23×C5D3×D411yescharacteristic
210C22×D5—22no—
211C2×C4×C5—64no—
212C2×C4×C5—242no—
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5#23712yes—
215C2×C4×C5C22×Dic312yes—
216C2×C4×C5C23×D311yescharacteristic
217C22⋊D5—28no—
218C2×Dic5—22no—
219C2×Dic5—32no—
220C2×Dic5—32no—
221D20—22no—
222D20C22×Dic314yes—
223C4×D5—28no—
224C4×D5—244no—
225Dic10—22no—
226Dic10C22×Dic314yes—
227C5×C8C22×Dic312yes—
228C5×C8C22×Dic312yes—
229#168—62no—
230C2×#41—52no—
231#135—58no—
232C2×Q16—51no—
233C2×SD16—52no—
234C2×D8—51no—
235C2×M16—151no—
236C22×C8D3×D511yescharacteristic
237C4×Q8—154no—
238C4×D4—154no—
239C4×D4—304no—
240#117—151no—
241#117—302no—
242C2×C4⋊C4—32no—
243C2×C4⋊C4—302no—
244#107—32no—
245#107—32no—
246#103—154no—
247#102—154no—
248#97—152no—
249C4×C8—152no—
250C2×C3×C5—22no—
251C2×C3×C5C2×C4×D411yescharacteristic
252C2×C3×C5#57611yescharacteristic
253C2×C3×C5#57811yescharacteristic
254C3×D5—44no—
255C23×C3—102no—
256C23×C3D4×D511yescharacteristic
257C3×Q8—54no—
258C3×Q8—102no—
259C3×D4—54no—
260C3×D4—108no—
261C3×D4—102no—
262C2×C3×C4—102no—
263C2×C3×C4—108no—
264C2×C3×C4C2×C4×D512yes—
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4#71312yes—
267C2×C3×C4C23×D511yescharacteristic
268C2×Dic3—24no—
269C2×Dic3—52no—
270C2×Dic3—52no—
271C2×Dic3—82no—
272C2×Dic3—404no—
273C3×C8C2×C4×D512yes—
274C3×C8C2×C4×D512yes—
275C3⋊C8—102no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5D4×Dic312yes—
279C22×C5C2×D3×D411yescharacteristic
280C2×D5—24no—
281C2×D5—42no—
282C2×D5—42no—
283C4×C5—124no—
284C4×C5D4×Dic312yes—
285C4×C5C2×#23711yescharacteristic
286C4×C5C23×Dic311yescharacteristic
287Dic5—24no—
288Dic5—62no—
289Dic5—62no—
290#41—58no—
291#41—104no—
292C2×Q8—52no—
293C2×D4—52no—
294C2×D4—102no—
295C22×C4—62no—
296C22×C4—102no—
297C22×C4—304no—
298C22×C4C2×D3×D511yescharacteristic
299Q16—54no—
300SD16—58no—
301D8—54no—
302M16—302no—
303C2×C8—152no—
304C2×C8D5×Dic314yescomplemented
305C2×C8C2×D3×D511yescharacteristic
306C2×C8C2×D3×D511yescharacteristic
307C4⋊C4—34no—
308C4⋊C4—62no—
309C4⋊C4—151no—
310C4⋊C4—151no—
311C4⋊C4—304no—
312C22⋊C4—152no—
313C22⋊C4—304no—
314C42—152no—
315C42—304no—
316C3×C5#295111yescharacteristic, complemented, Hall
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—104no—
320C22×C3—202no—
321C22×C3—202no—
322C22×C3#403912yes—
323C22×C3C2×D4×D511yescharacteristic
324C3×C4—104no—
325C3×C4#403912yes—
326C3×C4C22×C4×D511yescharacteristic
327C3×C4C2×#71311yescharacteristic
328Dic3—44no—
329Dic3—102no—
330Dic3—102no—
331C2×C5—22no—
332C2×C5#576911yescharacteristic
333C2×C5#577111yescharacteristic
334C2×C5C2×D4×Dic311yescharacteristic
335D5—44no—
336C23—102no—
337C23#677711yescharacteristic
338Q8—54no—
339Q8—102no—
340D4—54no—
341D4—108no—
342D4—102no—
343C2×C4—64no—
344C2×C4—102no—
345C2×C4—108no—
346C2×C4—152no—
347C2×C4—152no—
348C2×C4—242no—
349C2×C4—1204no—
350C2×C4#676612yes—
351C2×C4#677711yescharacteristic
352C2×C4C2×D5×Dic312yes—
353C2×C4C22×D3×D511yescharacteristic
354C8—302no—
355C8C2×D5×Dic312yes—
356C8C2×D5×Dic312yes—
357C2×C3—22no—
358C2×C3—204no—
359C2×C3C2×#403911yescharacteristic
360C2×C3#6609111yescharacteristic
361C2×C3#6610011yescharacteristic
362C5#8389811yescharacteristic, complemented, Sylow
363C22—21no—
364C22—21no—
365C22—104no—
366C22—202no—
367C22—202no—
368C22#9143412yes—
369C22C2×#677711yescharacteristic
370C4—104no—
371C4—124no—
372C4—302no—
373C4—302no—
374C4#9143412yes—
375C4C2×#676611yescharacteristic
376C4C22×D5×Dic311yescharacteristic
377C3#1061086711yescharacteristic, complemented, Sylow
378C2—22no—
379C2—204no—
380C2#1175398311yescharacteristic
381C2#1175400811yescharacteristic
382C2C2×#9143411yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4050C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2951
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #11754499C2semidirect
3. #11751202C2semidirect
4. C2×C5×#818C2semidirect
5. #11748368C2semidirect
6. #11747883C2semidirect
7. #11747812C2semidirect
8. #11747809C2semidirect
16. C3×#4050C4semidirect
43. C3×#709C2×C4semidirect
48. C2×C3×C5×C8C2×C4semidirect
59. C3×Dic20C2×C4semidirect
60. C3×D40C2×C4semidirect
61. C3×#677C2×C4semidirect
71. C2×#818D5semidirect
80. #4050Dic3semidirect
139. #709C2×Dic3semidirect
144. C2×C5×C8C2×Dic3semidirect
158. Dic20C2×Dic3semidirect
159. D40C2×Dic3semidirect
160. #677C2×Dic3semidirect
195. C2×C3×C8C4×D5semidirect
304. C2×C8D5×Dic3semidirect
316. C3×C5#2951semidirect
362. C5#83898semidirect
377. C3#10610867semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40502
#117544992
#117512022
C2×C5×#8182
#117483682
#117478832
#117478122
#117478092
#106108673
#838985