Finite Group Databasebeta

← #14299595

Subgroups — #14299595

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5798C211yesmaximal, characteristic
2#11751322C211yesmaximal, characteristic
3C2×C3×#3965C211yesmaximal, characteristic
4#11748460C212yesmaximal, complemented
5#11745975C212yesmaximal, complemented
6#10602440—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×#6719—22no—
9C2×C4⋊Dic15C2211yescharacteristic
10C2×C4×Dic15C2211yescharacteristic
11C2×C5×#217—22no—
12C5×D4×Dic3—22no—
13C5×D4×Dic3—22no—
14C5×#926C2212yes—
15C2×C3×#681C2212yes—
16C3×#3965C414yescomplemented
17#90988—22no—
18#90985—22no—
19#70068—51nomaximal, Hall
20C5×#518—31no—
21#65510—31no—
22C2×#3965D311yescharacteristic
23#65284—32no—
24#64752—32no—
25C24×C3×C5D412yes—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C412yes—
29C2×C3×C5×D4Q812yes—
30C22×C3×C4×C5C2311yescharacteristic
31C22×Dic15—21no—
32C22×Dic15—21no—
33C22×C5×Dic3—22no—
34C22×C5×Dic3—22no—
35#6719—44no—
36C4⋊Dic15—22no—
37C4×Dic15—22no—
38C5×#217—24no—
39C5×#217—22no—
40C5×C4⋊Dic3D412yes—
41C5×C4⋊Dic3D412yes—
42C4×C5×Dic3—22no—
43C3×#681—22no—
44C3×#681C2×C414yescomplemented
45C2×C3×#168—22no—
46#5798D511yescharacteristic
47C2×C3×#100—51no—
48#5221—51no—
49#5121—52no—
50#4555—52no—
51C22×C5×D4C2×D311yescharacteristic
52C4×C5×D4—62no—
53C4×C5×D4—62no—
54C5×#117—32no—
55C2×C5×C22⋊C4—62no—
56C2×C22⋊Dic5—62no—
57C2×C4⋊Dic5—31no—
58C2×C4×Dic5—31no—
59C2×#681C2×D312yes—
60#3965Dic314yescomplemented
61#3940—62no—
62#3939—62no—
63#1856—151noSylow
64C23×C3×C5—22no—
65C23×C3×C5—22no—
66C23×C3×C5—42no—
67C23×C3×C5—42no—
68C23×C3×C5C4⋊C414yes—
69C23×C3×C5C2×D411yescharacteristic
70C3×C5×D4—24no—
71C3×C5×D4—24no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×C3×C4×C5C2×D412yes—
74C2×C3×C4×C5C2×Q811yescharacteristic
75C2×C3×C4×C5#4112yes—
76C2×Dic15—22no—
77C2×Dic15—41no—
78C2×Dic15—41no—
79C2×Dic15—42no—
80C2×Dic15—41no—
81C2×C5×Dic3—22no—
82C2×C5×Dic3—22no—
83C2×C5×Dic3—82no—
84C2×C5×Dic3—82no—
85C3×#168—24no—
86C22×C3×D4C2×D511yescharacteristic
87C2×C3×M16—52no—
88C2×#217—22no—
89C2×#217—102no—
90D4×Dic3—22no—
91D4×Dic3—22no—
92#926C2×D512yes—
93C2×C4⋊Dic3—51no—
94C2×C4×Dic3—51no—
95C3×#100—54no—
96#818—102no—
97#817—102no—
98C24×C5D1212yes—
99C2×C5×D4—22no—
100C2×C5×D4—22no—
101C2×C5×D4Dic612yes—
102C2×C5×D4C2×Dic312yes—
103C22×C4×C5—62no—
104C22×C4×C5—62no—
105C22×C4×C5C22×D311yescharacteristic
106C22×Dic5—61no—
107C22×Dic5—61no—
108C5×C4⋊C4—32no—
109C5×C4⋊C4—32no—
110C5×C22⋊C4—64no—
111C5×C22⋊C4—62no—
112C42×C5—62no—
113C22⋊Dic5—124no—
114C4⋊Dic5—62no—
115C4×Dic5—62no—
116#681—22no—
117#681C2×Dic314yescomplemented
118C2×#168—22no—
119#518—31no—
120#428—152no—
121C2×#100—51no—
122#390—151no—
123#339—152no—
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5—24no—
127C22×C3×C5—44no—
128C22×C3×C5—42no—
129C22×C3×C5—42no—
130C22×C3×C5—82no—
131C22×C3×C5C2×C4⋊C411yescharacteristic
132C22×C3×C5#12011yescharacteristic
133C22×C3×C5#12311yescharacteristic
134C3×C4×C5C4×D412yes—
135C3×C4×C5C22⋊Q812yes—
136Dic15—42no—
137Dic15—81no—
138C5×Dic3—42no—
139C5×Dic3—42no—
140C24×C3C22⋊D512yes—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4Dic1012yes—
144C2×C3×D4C4×D512yes—
145C22×C3×C4C22×D511yescharacteristic
146C22×Dic3—22no—
147C22×Dic3—22no—
148C22×Dic3—101no—
149C22×Dic3—101no—
150C3×M16—54no—
151C3×M16—102no—
152C2×C3×C8—102no—
153#217—24no—
154#217—22no—
155#217—204no—
156C4⋊Dic3—102no—
157C4⋊Dic3C22⋊D512yes—
158C4⋊Dic3C22⋊D512yes—
159C4×Dic3—22no—
160C4×Dic3—102no—
161C23×C5—22no—
162C23×C5—22no—
163C23×C5—42no—
164C23×C5—42no—
165C23×C5C4⋊Dic314yes—
166C23×C5C2×D1211yescharacteristic
167C5×D4—24no—
168C5×D4—24no—
169C2×C4×C5—62no—
170C2×C4×C5—62no—
171C2×C4×C5—242no—
172C2×C4×C5—242no—
173C2×C4×C5C2×Dic611yescharacteristic
174C2×C4×C5D3×D412yes—
175C2×C4×C5#23712yes—
176C2×C4×C5C22×Dic311yescharacteristic
177C2×Dic5—62no—
178C2×Dic5—121no—
179C2×Dic5—121no—
180C2×Dic5—122no—
181C2×Dic5—121no—
182#168—24no—
183C22×D4D3×D511yescharacteristic
184C2×M16—52no—
185C4×D4—62no—
186C4×D4—62no—
187#117—32no—
188C2×C4⋊C4—151no—
189C2×C22⋊C4—62no—
190C2×C22⋊C4—302no—
191C2×C42—151no—
192#107—302no—
193#106—302no—
194#100—54no—
195C2×C3×C5—21no—
196C2×C3×C5—21no—
197C2×C3×C5—44no—
198C2×C3×C5#38511yescharacteristic
199C2×C3×C5#45311yescharacteristic
200C2×C3×C5#45511yescharacteristic
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—42no—
204C23×C3—42no—
205C23×C3#68314yes—
206C23×C3C2×C22⋊D511yescharacteristic
207C3×D4—24no—
208C3×D4—24no—
209C2×C3×C4C2×Dic1011yescharacteristic
210C2×C3×C4C2×C4×D511yescharacteristic
211C2×C3×C4#70912yes—
212C2×C3×C4C2×C22⋊D512yes—
213C2×Dic3—22no—
214C2×Dic3—22no—
215C2×Dic3—82no—
216C2×Dic3—82no—
217C2×Dic3—102no—
218C2×Dic3—201no—
219C2×Dic3—201no—
220C2×Dic3—202no—
221C2×Dic3—201no—
222C3×C8—104no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—24no—
226C22×C5—44no—
227C22×C5—42no—
228C22×C5—42no—
229C22×C5—82no—
230C22×C5#88211yescharacteristic
231C22×C5#88611yescharacteristic
232C22×C5C2×C4⋊Dic311yescharacteristic
233C4×C5—122no—
234C4×C5—122no—
235C4×C5#87812yes—
236C4×C5D4×Dic312yes—
237Dic5—122no—
238Dic5—241no—
239C24#120312yes—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4D5×Dic312yes—
243C2×D4#120412yes—
244C22×C4—62no—
245C22×C4—62no—
246C22×C4—301no—
247C22×C4—301no—
248C22×C4C2×D3×D511yescharacteristic
249M16—54no—
250M16—102no—
251C2×C8—102no—
252C4⋊C4—32no—
253C4⋊C4—32no—
254C4⋊C4—302no—
255C22⋊C4—64no—
256C22⋊C4—62no—
257C22⋊C4—604no—
258C42—62no—
259C42—302no—
260C3×C5#185611yescharacteristic, complemented, Hall
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—24no—
264C22×C3—44no—
265C22×C3—42no—
266C22×C3—42no—
267C22×C3—82no—
268C22×C3C2×#68311yescharacteristic
269C22×C3#407511yescharacteristic
270C22×C3#409911yescharacteristic
271C3×C4#407012yes—
272C3×C4C4×C22⋊D512yes—
273Dic3—42no—
274Dic3—42no—
275Dic3—202no—
276Dic3—401no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—44no—
280C2×C5#474611yescharacteristic
281C2×C5#474711yescharacteristic
282C2×C5#495011yescharacteristic
283C23—22no—
284C23—22no—
285C23—42no—
286C23—42no—
287C23#666814yes—
288C23C2×#120311yescharacteristic
289D4—24no—
290D4—24no—
291C2×C4—62no—
292C2×C4—62no—
293C2×C4—242no—
294C2×C4—242no—
295C2×C4—302no—
296C2×C4—601no—
297C2×C4—601no—
298C2×C4—602no—
299C2×C4—601no—
300C2×C4C2×D5×Dic311yescharacteristic
301C2×C4#677912yes—
302C2×C4C2×#120411yescharacteristic
303C2×C4D3×C22⋊D512yes—
304C8—104no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—44no—
308C2×C3#6549911yescharacteristic
309C2×C3#6553011yescharacteristic
310C2×C3#6553111yescharacteristic
311C5#7006811yescharacteristic, complemented, Sylow
312C22—21no—
313C22—21no—
314C22—24no—
315C22—44no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22C2×#666811yescharacteristic
320C22#9154211yescharacteristic
321C22#9157011yescharacteristic
322C4—122no—
323C4—122no—
324C4—602no—
325C4—1201no—
326C4Dic3×C22⋊D512yes—
327C4#9157512yes—
328C3#1060244011yescharacteristic, complemented, Sylow
329C2—21no—
330C2—21no—
331C2—44no—
332C2#1174914111yescharacteristic
333C2#1174914811yescharacteristic
334C2#1174951111yescharacteristic
subgroupG/H
centerC22#91570
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5#120
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1856
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11748460C2semidirect
5. #11745975C2semidirect
16. C3×#3965C4semidirect
44. C3×#681C2×C4semidirect
60. #3965Dic3semidirect
117. #681C2×Dic3semidirect
260. C3×C5#1856semidirect
311. C5#70068semidirect
328. C3#10602440semidirect

Maximal subgroups

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

subgroupindex
C5×#57982
#117513222
C2×C3×#39652
#117484602
#117459752
#106024403
#700685