Finite Group Databasebeta

← #14284352

Subgroups — #14284352

Order 1920.

496 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
1C2×C5×#875C211yesmaximal, characteristic
2#11751027C211yesmaximal, characteristic, complemented
3C3×#65215C211yesmaximal, characteristic, complemented
4#11745847C214yesmaximal, complemented
5#10602512—31nomaximal, Hall
6C22×C5×D12C411yescharacteristic
7C22×C5×Dic6C411yescharacteristic
8C2×C3×C42×C5C2211yescharacteristic
9C2×C5×(C2×D3)⋊C4—21no—
10C2×C5×(C2×D3)⋊C4—21no—
11C5×#875—21no—
12C5×#875—21no—
13C5×#875C412yes—
14C5×#875C2212yes—
15#91114—21no—
16C4⋊(C3⋊#168)—21no—
17#91087C2212yescomplemented
18C3×C22⋊#168—21no—
19C3×C4⋊#168—21no—
20C3×#3935C2212yescomplemented
21#70808—51nomaximal, Hall
22C2×C5×#124—31no—
23#65215—31no—
24#65215D311yescharacteristic, complemented
25#64760—34no—
26C23×C5×D3—21no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5D411yescharacteristic
29C22×C3×C4×C5D411yescharacteristic
30C22×C5×Dic3—21no—
31C2×C5×D12—21no—
32C2×C5×D12—42no—
33C2×C5×D12C2×C412yes—
34C2×C5×Dic6—21no—
35C2×C5×Dic6—42no—
36C2×C5×Dic6C2×C412yes—
37C3×C42×C5C2×C411yescharacteristic
38C3×C42×C5D411yescharacteristic
39C3×C42×C5D411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41C2×C3⋊#168—22no—
42C5×(C2×D3)⋊C4—22no—
43C5×(C2×D3)⋊C4—22no—
44C5×(C2×D3)⋊C4—22no—
45C5×(C2×D3)⋊C4—22no—
46C2×C3×#168—22no—
47C2×#875D511yescharacteristic
48C3×#432—51no—
49#4926—51no—
50#4464—54no—
51C22×C5×Q8—31no—
52C22×C5×D4—31no—
53C5×#124—32no—
54C5×#124—32no—
55C5×#124—61no—
56C5×#124—61no—
57C2×C5×C22⋊C4—61no—
58C2×C5×C22⋊C4—61no—
59C2×C42×C5C2×D311yescharacteristic
60C22⋊#168—21no—
61C22⋊#168—61no—
62C4⋊#168—21no—
63C4⋊#168—61no—
64#3935—32no—
65#3935C2×D312yescomplemented
66#1533—151noSylow
67C23×C3×C5C22⋊C411yescharacteristic
68C22×C5×D3—22no—
69C22×C5×D3—42no—
70C22×C5×D3—42no—
71C22×C5×D3—42no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C22⋊C411yescharacteristic
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×C4×C5C22⋊C411yescharacteristic
78C2×C3×C4×C5C22×C411yescharacteristic
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C5×Dic3—22no—
82C2×C5×Dic3—42no—
83C5×D12—42no—
84C5×D12—42no—
85C5×Dic6—42no—
86C5×Dic6—42no—
87C3⋊#168—42no—
88C3×#168—42no—
89C22×D12Dic511yescharacteristic
90C22×Dic6Dic511yescharacteristic
91C2×C3×C42C2×D511yescharacteristic
92C2×(C2×D3)⋊C4—21no—
93C2×(C2×D3)⋊C4—21no—
94#875—21no—
95#875—21no—
96#875Dic512yes—
97#875C2×D512yes—
98C3×C4⋊C8—101no—
99C3×C22⋊C8—101no—
100C3×#97—52no—
101#830—101no—
102C4⋊(C3⋊C8)—101no—
103#803—52no—
104C24×C5—61no—
105C2×C5×Q8—32no—
106C2×C5×Q8—61no—
107C2×C5×Q8—122no—
108C2×C5×D4—32no—
109C2×C5×D4—61no—
110C2×C5×D4—122no—
111C22×C4×C5—61no—
112C22×C4×C5C4×D311yescharacteristic
113C22×C4×C5D1211yescharacteristic
114C22×C4×C5#6711yescharacteristic
115C5×C22⋊C4—62no—
116C5×C22⋊C4—62no—
117C5×C22⋊C4—62no—
118C5×C22⋊C4—62no—
119C42×C5C4×D311yescharacteristic
120C42×C5D1211yescharacteristic
121C42×C5#6711yescharacteristic
122C42×C5C22×D311yescharacteristic
123C2×#168—22no—
124C2×#168—62no—
125C2×#124—31no—
126#432—51no—
127#432—151no—
128#329—154no—
129C22×C3×C5—21no—
130C22×C3×C5—21no—
131C22×C3×C5#10012yes—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C2×C5×D3—42no—
134C2×C5×D3—42no—
135C2×C5×D3—42no—
136C2×C5×D3—84no—
137C3×C4×C5—21no—
138C3×C4×C5—21no—
139C3×C4×C5—21no—
140C3×C4×C5—21no—
141C3×C4×C5—21no—
142C3×C4×C5—21no—
143C5×Dic3—42no—
144C23×D3—21no—
145C22×C3×C4C2×Dic511yescharacteristic
146C22×C3×C4C22⋊D511yescharacteristic
147C22×C3×C4C22⋊D511yescharacteristic
148C22×Dic3—21no—
149C2×D12—21no—
150C2×D12—42no—
151C2×D12C2×Dic512yes—
152C2×Dic6—21no—
153C2×Dic6—42no—
154C2×Dic6C2×Dic512yes—
155C2×C3×C8—102no—
156C3×C42C2×Dic511yescharacteristic
157C3×C42C22⋊D511yescharacteristic
158C3×C42C22⋊D511yescharacteristic
159C3×C42C22×D511yescharacteristic
160(C2×D3)⋊C4—22no—
161(C2×D3)⋊C4—22no—
162(C2×D3)⋊C4—22no—
163(C2×D3)⋊C4—22no—
164C2×C3⋊C8—102no—
165C23×C5—62no—
166C23×C5—122no—
167C23×C5—122no—
168C23×C5—122no—
169C23×C5(C2×D3)⋊C411yescharacteristic
170C5×Q8—122no—
171C5×Q8—122no—
172C5×D4—122no—
173C5×D4—122no—
174C2×C4×C5—22no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—62no—
178C2×C4×C5—122no—
179C2×C4×C5(C2×D3)⋊C411yescharacteristic
180C2×C4×C5(C2×D3)⋊C411yescharacteristic
181C2×C4×C5(C2×D3)⋊C411yescharacteristic
182C2×C4×C5C2×C4×D311yescharacteristic
183C2×C4×C5C2×D1211yescharacteristic
184C2×C4×C5C2×#6711yescharacteristic
185#168—42no—
186#168—122no—
187C22×Q8—31no—
188C22×D4—31no—
189#124—32no—
190#124—32no—
191#124—61no—
192#124—61no—
193C2×C22⋊C4—61no—
194C2×C22⋊C4—61no—
195C2×C42D3×D511yescharacteristic
196C4⋊C8—101no—
197C4⋊C8—301no—
198C22⋊C8—101no—
199C22⋊C8—301no—
200#97—52no—
201#97—152no—
202C2×C3×C5—22no—
203C2×C3×C5C2×#10011yescharacteristic
204C2×C3×C5#42111yescharacteristic
205C2×C3×C5#42111yescharacteristic
206C5×D3—82no—
207C23×C3C22⋊Dic511yescharacteristic
208C22×D3—22no—
209C22×D3—42no—
210C22×D3—42no—
211C22×D3—42no—
212C2×C3×C4—22no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4C22⋊Dic511yescharacteristic
216C2×C3×C4C22⋊Dic511yescharacteristic
217C2×C3×C4C22⋊Dic511yescharacteristic
218C2×C3×C4C22×Dic511yescharacteristic
219C2×C3×C4C2×C22⋊D511yescharacteristic
220C2×C3×C4C2×C22⋊D511yescharacteristic
221C2×Dic3—22no—
222C2×Dic3—42no—
223D12—42no—
224D12—42no—
225Dic6—42no—
226Dic6—42no—
227C3×C8—202no—
228C3⋊C8—202no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—122no—
232C22×C5—122no—
233C22×C5—122no—
234C22×C5—244no—
235C22×C5#82312yes—
236C22×C5C2×(C2×D3)⋊C411yescharacteristic
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—21no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—122no—
244C24—61no—
245C2×Q8—32no—
246C2×Q8—61no—
247C2×Q8—122no—
248C2×D4—32no—
249C2×D4—61no—
250C2×D4—122no—
251C22×C4—61no—
252C22×C4D3×Dic511yescharacteristic
253C22×C4#120111yescharacteristic
254C22×C4#120311yescharacteristic
255C2×C8—102no—
256C2×C8—302no—
257C22⋊C4—62no—
258C22⋊C4—62no—
259C22⋊C4—62no—
260C22⋊C4—62no—
261C42D3×Dic511yescharacteristic
262C42#120111yescharacteristic
263C42#120311yescharacteristic
264C42C2×D3×D511yescharacteristic
265C3×C5#153311yescharacteristic, complemented, Hall
266C22×C3—21no—
267C22×C3—21no—
268C22×C3#396512yes—
269C22×C3C2×C22⋊Dic511yescharacteristic
270C2×D3—42no—
271C2×D3—42no—
272C2×D3—42no—
273C2×D3—84no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280Dic3—42no—
281C2×C5—22no—
282C2×C5—242no—
283C2×C5#500511yescharacteristic
284C2×C5C2×#82311yescharacteristic
285C2×C5#513911yescharacteristic
286C23—62no—
287C23—122no—
288C23—122no—
289C23—122no—
290C23(C2×D3)⋊Dic511yescharacteristic
291Q8—122no—
292Q8—122no—
293D4—122no—
294D4—122no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—62no—
299C2×C4—122no—
300C2×C4(C2×D3)⋊Dic511yescharacteristic
301C2×C4(C2×D3)⋊Dic511yescharacteristic
302C2×C4(C2×D3)⋊Dic511yescharacteristic
303C2×C4C2×D3×Dic511yescharacteristic
304C2×C4C2×#120111yescharacteristic
305C2×C4C2×#120311yescharacteristic
306C8—202no—
307C8—602no—
308C2×C3—22no—
309C2×C3C2×#396511yescharacteristic
310C2×C3#6552511yescharacteristic
311C2×C3#6552511yescharacteristic
312D3—82no—
313C5#7080811yescharacteristic, complemented, Sylow
314C22—21no—
315C22—21no—
316C22—122no—
317C22—122no—
318C22—122no—
319C22—244no—
320C22#9095912yes—
321C22C2×(C2×D3)⋊Dic511yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—122no—
329C3#1060251211yescharacteristic, complemented, Sylow
330C2—22no—
331C2—242no—
332C2C2×#9095911yescharacteristic
333C2#1174842411yescharacteristic
334C2#1174842511yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D12C4
cosocleC3×C42×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1533
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751027C2semidirect
3. C3×#65215C2semidirect
4. #11745847C2semidirect
17. #91087C22semidirect
20. C3×#3935C22semidirect
24. #65215D3semidirect
65. #3935C2×D3semidirect
265. C3×C5#1533semidirect
313. C5#70808semidirect
329. C3#10602512semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8752
#117510272
C3×#652152
#117458472
#106025123
#708085