Finite Group Databasebeta

← #14307466

Subgroups — #14307466

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756276C211yesmaximal, characteristic
2#11748611C211yesmaximal, characteristic
3#11748437C211yesmaximal, characteristic
4C5×#4532C211yesmaximal, characteristic
5C3×#64752C211yesmaximal, characteristic
6#11745978C211yesmaximal, characteristic
7#11745976C211yesmaximal, characteristic
8#10599525—31nomaximal, Hall
9C3×C5×#117C2211yescharacteristic
10#91815C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12#91779C412yescomplemented
13#91777C412yescomplemented
14#91767—22no—
15C4×Dic30—22no—
16C2×C4×C5×Dic3C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×C4×Dic5C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#90994—22no—
21#90983—22no—
22#68732—51nomaximal, Hall
23#65851—31no—
24#65407—31no—
25#65221—31no—
26C5×#339—31no—
27#64775—31no—
28#64752D311yescharacteristic
29#64743—31no—
30C22×C3×C4×C5C2311yescharacteristic
31C22×Dic15D412yes—
32C2×Dic30—22no—
33C22×C5×Dic3—21no—
34C22×C3×Dic5—21no—
35C3×C5×C4⋊C4C2×C412yes—
36C3×C5×C22⋊C4—21no—
37C3×C42×C5—21no—
38#6719—21no—
39C4⋊Dic15—22no—
40C4⋊Dic15C2×C412yes—
41#6712—22no—
42#6712—22no—
43C4×Dic15—21no—
44C4×Dic15C2×C411yescharacteristic
45C4×Dic15C2×C411yescharacteristic
46C4×Dic15D412yes—
47C4×C5×Dic3—21no—
48C4×C5×Dic3Q812yescomplemented
49C5×#208—21no—
50C5×#208—21no—
51C2×C5×C3⋊C8—21no—
52C3×C4×Dic5—21no—
53C3×C4×Dic5Q812yescomplemented
54C3×#681—21no—
55C3×#681—21no—
56C2×C3×#168—21no—
57#5517—51no—
58#5118—51no—
59#4932—51no—
60C3×#339—51no—
61#4555—51no—
62#4532D511yescharacteristic
63#4523—51no—
64C2×C5×M16—31no—
65C5×#117C2×D311yescharacteristic
66C2×C42×C5—31no—
67#4072—31no—
68C2×C4×Dic5—31no—
69C2×C4×Dic5C2×D311yescharacteristic
70C2×#681C2×D311yescharacteristic
71#4036—32no—
72#4034—32no—
73#4024—62no—
74C4×Dic10—62no—
75#3963—62no—
76#3946—62no—
77#1995—151noSylow
78C23×C3×C5C2×D411yescharacteristic
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5C22×C411yescharacteristic
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×Q811yescharacteristic
83C2×C3×C4×C5C2×Q811yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×C3×C4×C5#4111yescharacteristic
86C2×Dic15—22no—
87C2×Dic15—42no—
88C2×Dic15C22⋊C412yes—
89C2×Dic15C22⋊C412yes—
90Dic30—44no—
91C2×C5×Dic3—22no—
92C2×C5×Dic3—42no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—42no—
95C3×#168—41no—
96C5×C3⋊C8—41no—
97C2×C3×M16—51no—
98C3×#117C2×D511yescharacteristic
99C2×C3×C42—51no—
100#926—51no—
101C2×C4×Dic3—51no—
102C2×C4×Dic3C2×D511yescharacteristic
103C2×#208C2×D511yescharacteristic
104#890—52no—
105#888—52no—
106#878—102no—
107C4×Dic6—102no—
108C3⋊#95—102no—
109Dic3⋊C8—102no—
110C22×C4×C5—61no—
111C22×C4×C5C22×D311yescharacteristic
112C22×Dic5—21no—
113C22×Dic5—32no—
114C2×Dic10—62no—
115C5×M16—61no—
116C5×M16—61no—
117C2×C5×C8—61no—
118C5×C4⋊C4C4×D312yes—
119C5×C22⋊C4—21no—
120C42×C5—21no—
121C42×C5—32no—
122C42×C5—61no—
123C22⋊Dic5—61no—
124C4⋊Dic5—32no—
125C4⋊Dic5—62no—
126#683—62no—
127#683—62no—
128C4×Dic5—21no—
129C4×Dic5—31no—
130C4×Dic5—31no—
131C4×Dic5—32no—
132C4×Dic5—61no—
133C4×Dic5Dic612yescomplemented
134#681—21no—
135#681—21no—
136C2×#168—21no—
137#533—151no—
138#423—151no—
139#376—151no—
140#339—31no—
141#339—51no—
142#339—151no—
143#339—151no—
144C22×C3×C5—22no—
145C22×C3×C5C2×C22⋊C411yescharacteristic
146C22×C3×C5C22⋊Q811yescharacteristic
147C22×C3×C5C22⋊Q811yescharacteristic
148C3×C4×C5—42no—
149C3×C4×C5C4×Q811yescharacteristic
150C3×C4×C5C4×Q811yescharacteristic
151C3×C4×C5#12411yescharacteristic
152C3×C4×C5C4⋊Q811yescharacteristic
153Dic15—22no—
154Dic15—22no—
155Dic15—42no—
156C3×Dic5—42no—
157C5×Dic3—42no—
158C22×C3×C4—101no—
159C22×C3×C4C22×D511yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—52no—
162C2×Dic6—102no—
163C3×M16—101no—
164C3×M16—101no—
165C2×C3×C8—101no—
166C3×C4⋊C4C4×D512yes—
167C3×C22⋊C4—21no—
168C3×C42—21no—
169C3×C42—52no—
170C3×C42—101no—
171#217—101no—
172C4⋊Dic3—52no—
173C4⋊Dic3—102no—
174Dic3⋊C4—102no—
175Dic3⋊C4—102no—
176C4×Dic3—21no—
177C4×Dic3—51no—
178C4×Dic3—51no—
179C4×Dic3—52no—
180C4×Dic3—101no—
181C4×Dic3Dic1012yescomplemented
182#208—21no—
183#208—21no—
184C2×C3⋊C8—21no—
185C23×C5D3×D411yescharacteristic
186C2×C4×C5—22no—
187C2×C4×C5—62no—
188C2×C4×C5—122no—
189C2×C4×C5C2×Dic611yescharacteristic
190C2×C4×C5C2×C4×D311yescharacteristic
191C2×C4×C5#23511yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5#23711yescharacteristic
194C2×C4×C5D3×Q811yescharacteristic
195C2×Dic5—22no—
196C2×Dic5—32no—
197C2×Dic5—32no—
198C2×Dic5—42no—
199C2×Dic5—62no—
200C2×Dic5—122no—
201Dic10—124no—
202C5×C8—121no—
203#168—41no—
204C2×M16—31no—
205C2×M16—51no—
206C4⋊Q8—152no—
207#125—152no—
208C22⋊Q8—302no—
209C4×Q8—302no—
210#117—151no—
211#117D3×D511yescharacteristic
212C2×C42—31no—
213C2×C42—51no—
214C2×C42—151no—
215C4⋊C8—302no—
216#95—302no—
217C2×C3×C5—21no—
218C2×C3×C5—21no—
219C2×C3×C5#39111yescharacteristic
220C2×C3×C5#42112yes—
221C23×C3D4×D511yescharacteristic
222C2×C3×C4—22no—
223C2×C3×C4—102no—
224C2×C3×C4—202no—
225C2×C3×C4C2×Dic1011yescharacteristic
226C2×C3×C4C2×C4×D511yescharacteristic
227C2×C3×C4#70911yescharacteristic
228C2×C3×C4D4×D511yescharacteristic
229C2×C3×C4#71111yescharacteristic
230C2×C3×C4Q8×D511yescharacteristic
231C2×Dic3—22no—
232C2×Dic3—42no—
233C2×Dic3—52no—
234C2×Dic3—52no—
235C2×Dic3—102no—
236C2×Dic3—202no—
237Dic6—204no—
238C3×C8—201no—
239C3⋊C8—41no—
240C22×C5—22no—
241C22×C5#87811yescharacteristic
242C22×C5D3×C22⋊C411yescharacteristic
243C22×C5#89611yescharacteristic
244C4×C5—42no—
245C4×C5—122no—
246C4×C5C4×Dic611yescharacteristic
247C4×C5#88511yescharacteristic
248C4×C5#88711yescharacteristic
249C4×C5#88811yescharacteristic
250Dic5—42no—
251Dic5—62no—
252Dic5—62no—
253Dic5—122no—
254C2×Q8—302no—
255C22×C4—61no—
256C22×C4—101no—
257C22×C4—152no—
258C22×C4C2×D3×D511yescharacteristic
259M16—61no—
260M16—61no—
261M16—101no—
262M16—101no—
263C2×C8—61no—
264C2×C8—101no—
265C4⋊C4—152no—
266C4⋊C4—302no—
267C4⋊C4—302no—
268C4⋊C4—302no—
269C4⋊C4#120012yes—
270C22⋊C4—21no—
271C22⋊C4—301no—
272C42—21no—
273C42—32no—
274C42—52no—
275C42—61no—
276C42—101no—
277C42—151no—
278C42—151no—
279C42—152no—
280C42—301no—
281C3×C5#199511yescharacteristic, complemented, Hall
282C22×C3—22no—
283C22×C3#402411yescharacteristic
284C22×C3D5×C22⋊C411yescharacteristic
285C22×C3#404211yescharacteristic
286C3×C4—42no—
287C3×C4—202no—
288C3×C4C4×Dic1011yescharacteristic
289C3×C4#403111yescharacteristic
290C3×C4#403311yescharacteristic
291C3×C4#403411yescharacteristic
292Dic3—42no—
293Dic3—102no—
294Dic3—102no—
295Dic3—202no—
296C2×C5—21no—
297C2×C5—21no—
298C2×C5#464611yescharacteristic
299C2×C5#482112yes—
300C23#679011yescharacteristic
301Q8—604no—
302C2×C4—22no—
303C2×C4—62no—
304C2×C4—102no—
305C2×C4—122no—
306C2×C4—152no—
307C2×C4—152no—
308C2×C4—202no—
309C2×C4—302no—
310C2×C4—602no—
311C2×C4D5×Dic611yescharacteristic
312C2×C4#676511yescharacteristic
313C2×C4D3×Dic1011yescharacteristic
314C2×C4#677211yescharacteristic
315C2×C4C2×#120011yescharacteristic
316C2×C4#679011yescharacteristic
317C8—121no—
318C8—201no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3#6493511yescharacteristic
322C2×C3#6511012yes—
323C5#6873211yescharacteristic, complemented, Sylow
324C22—22no—
325C22#9143111yescharacteristic
326C22#9143211yescharacteristic
327C22#9156111yescharacteristic
328C4—42no—
329C4—122no—
330C4—202no—
331C4—302no—
332C4—302no—
333C4—602no—
334C4#9132811yescharacteristic
335C4#9133311yescharacteristic
336C4#9134011yescharacteristic
337C4#9146211yescharacteristic
338C3#1059952511yescharacteristic, complemented, Sylow
339C2—21no—
340C2—21no—
341C2#1174869411yescharacteristic
342C2#1174943112yes—
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1995
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
12. #91779C4semidirect
13. #91777C4semidirect
48. C4×C5×Dic3Q8semidirect
53. C3×C4×Dic5Q8semidirect
133. C4×Dic5Dic6semidirect
181. C4×Dic3Dic10semidirect
281. C3×C5#1995semidirect
323. C5#68732semidirect
338. C3#10599525semidirect

Maximal subgroups

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

subgroupindex
#117562762
#117486112
#117484372
C5×#45322
C3×#647522
#117459782
#117459762
#105995253
#687325