Finite Group Databasebeta

← #14307398

Subgroups — #14307398

Order 1920.

552 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 134 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
1D5×#869C211yesmaximal, characteristic
2#11752348C211yesmaximal, characteristic
3C3×#65676C211yesmaximal, characteristic
4#11746530C214yesmaximal
5#10604675—31nomaximal, Hall
6C2×D5×Dic6—21no—
7C2×C4⋊ΓL(1,𝔽16)C2212yes—
8C2×C3×D5⋊C8C2212yes—
9#91758C411yescharacteristic, complemented
10C5×#869C411yescharacteristic, complemented
11C3×C42×D5C2211yescharacteristic
12#91468—21no—
13#91468C412yescomplemented
14D5×C4⋊Dic3—21no—
15D5×C4⋊Dic3C2212yes—
16#91376—21no—
17#91235—21no—
18#91235—21no—
19C3×#4002—21no—
20C3×#4002—21no—
21#69828—51nomaximal, Hall
22D5×C4⋊Q8—31no—
23#65689—31no—
24#65676D311yescharacteristic
25#64874—34no—
26C22×ΓL(1,𝔽16)—22no—
27C2×Dic30—21no—
28C2×C5×Dic6—21no—
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×C3×C4×D5C2311yescharacteristic
32C2×#1204—22no—
33C2×D5×Dic3—22no—
34D5×Dic6—44no—
35C4⋊ΓL(1,𝔽16)—24no—
36C2×C3×#170—22no—
37C3×D5⋊C8—22no—
38C3×D5⋊C8Q814yescomplemented
39C3×C42×C5C2×C411yescharacteristic
40C4⋊Dic15—21no—
41C4⋊Dic15C2×C412yes—
42C5×C4⋊Dic3—21no—
43C5×C4⋊Dic3C2×C412yes—
44C3×C4×Dic5C2×C411yescharacteristic
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47#6668—22no—
48#6668—22no—
49C2×#869—51no—
50C2×C3×#97—51no—
51#4936—51no—
52#4551—54no—
53C2×Q8×D5—61no—
54C2×C4⋊AGL(1,𝔽5)—32no—
55C2×D5⋊C8C2×D312yes—
56C5×C4⋊Q8—31no—
57#4090—61no—
58D5×C4⋊C4—32no—
59D5×C4⋊C4—61no—
60#4034—32no—
61#4034—61no—
62C42×D5C2×D311yescharacteristic
63#4015—31no—
64(C2×AGL(1,𝔽5))⋊C4—61no—
65(C2×AGL(1,𝔽5))⋊C4—61no—
66#4002—21no—
67#4002—21no—
68#1993—151noSylow
69C22×C3×D5C2×D411yescharacteristic
70C2×ΓL(1,𝔽16)—42no—
71C2×ΓL(1,𝔽16)—42no—
72C2×ΓL(1,𝔽16)—42no—
73C2×C3×C4×C5C22⋊C411yescharacteristic
74C2×C3×C4×C5C22⋊C411yescharacteristic
75C2×C3×C4×C5C22×C411yescharacteristic
76C2×Dic15—22no—
77Dic30—42no—
78C2×C5×Dic3—22no—
79C5×Dic6—42no—
80C2×C3×Dic5C22⋊C411yescharacteristic
81C2×C3×Dic5C22⋊C411yescharacteristic
82C2×C3×Dic5C2×D411yescharacteristic
83C3×C4×D5—22no—
84C3×C4×D5—22no—
85C3×C4×D5C2×Q812yes—
86C3×C4×D5#4112yes—
87#1204—44no—
88D5×Dic3—44no—
89C3×#170—24no—
90C22×Dic6—101no—
91C22×C3×C8—52no—
92C2×C3×C42—51no—
93C2×C4⋊Dic3—52no—
94C2×C4⋊Dic3—52no—
95C2×C4⋊Dic3—101no—
96#869—51no—
97#869—52no—
98#869—101no—
99#869—101no—
100#869AGL(1,𝔽5)11yescharacteristic, complemented
101C3×#97—101no—
102C3×#97—101no—
103C3⋊#95—101no—
104C3⋊#95—101no—
105C22×AGL(1,𝔽5)—62no—
106C2×C5×Q8—61no—
107Q8×D5—124no—
108C2×C4×D5—62no—
109C2×C4×D5D1211yescharacteristic
110C2×C4×D5D1211yescharacteristic
111C2×C4×D5C22×D311yescharacteristic
112C2×Dic10—61no—
113C2×Dic10—62no—
114C2×#170—22no—
115C4⋊AGL(1,𝔽5)—64no—
116D5⋊C8—22no—
117D5⋊C8Dic614yescomplemented
118C5×C4⋊C4—32no—
119C5×C4⋊C4—61no—
120C42×C5C4×D311yescharacteristic
121C4⋊Dic5—32no—
122C4⋊Dic5—61no—
123#683—62no—
124#683—62no—
125C4×Dic5C4×D311yescharacteristic
126C4×Dic5#6711yescharacteristic
127C4×Dic5#6711yescharacteristic
128C2×C4⋊Q8—151no—
129C2×#97—51no—
130#382—151no—
131#340—154no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C2×C3×D5#12411yescharacteristic
134C2×C3×D5C4⋊Q811yescharacteristic
135C2×C3×D5AGL(1,ℤ/8)12yes—
136C2×C3×D5#13712yes—
137ΓL(1,𝔽16)—82no—
138C3×C4×C5—21no—
139C3×C4×C5—21no—
140C3×C4×C5C4×Q812yes—
141Dic15—42no—
142C3×Dic5—21no—
143C3×Dic5—21no—
144C3×Dic5C22⋊Q812yes—
145C5×Dic3—42no—
146C22×C3×C4—51no—
147C22×C3×C4—51no—
148C22×C3×C4—51no—
149C22×Dic3—102no—
150C22×Dic3—102no—
151C2×Dic6—21no—
152C2×Dic6—102no—
153C2×Dic6—101no—
154C2×Dic6—204no—
155C2×C3×C8—54no—
156C2×C3×C8—102no—
157C2×C3×C8—102no—
158C3×C42—51no—
159C3×C42—51no—
160C3×C42—51no—
161C3×C42C2×AGL(1,𝔽5)11yescharacteristic
162C4⋊Dic3—21no—
163C4⋊Dic3—52no—
164C4⋊Dic3—102no—
165C4⋊Dic3—102no—
166C4⋊Dic3—101no—
167C4⋊Dic3—104no—
168C4⋊Dic3C2×AGL(1,𝔽5)12yes—
169C22×D5C2×D1211yescharacteristic
170C2×AGL(1,𝔽5)—122no—
171C2×AGL(1,𝔽5)—122no—
172C2×AGL(1,𝔽5)—122no—
173C5×Q8—122no—
174C2×C4×C5—62no—
175C2×C4×C5(C2×D3)⋊C411yescharacteristic
176C2×C4×C5(C2×D3)⋊C411yescharacteristic
177C2×C4×C5C2×C4×D311yescharacteristic
178C2×Dic5—62no—
179C2×Dic5(C2×D3)⋊C411yescharacteristic
180C2×Dic5(C2×D3)⋊C411yescharacteristic
181C2×Dic5C2×#6711yescharacteristic
182C4×D5—22no—
183C4×D5—22no—
184C4×D5—124no—
185C4×D5C2×Dic612yes—
186C4×D5#23512yes—
187Dic10—124no—
188Dic10—122no—
189#170—24no—
190C22×Q8—301no—
191C22×C8—52no—
192C4⋊Q8—31no—
193C4⋊Q8—152no—
194C4⋊Q8—151no—
195C4⋊Q8—301no—
196C4⋊Q8—301no—
197C2×C4⋊C4—152no—
198C2×C4⋊C4—152no—
199C2×C4⋊C4—301no—
200C2×C42—51no—
201#97—101no—
202#97—101no—
203#95—301no—
204#95—301no—
205C2×C3×C5#39111yescharacteristic
206C2×C3×C5#41811yescharacteristic
207C2×C3×C5#41911yescharacteristic
208C3×D5#48912yes—
209C3×D5#50112yes—
210C23×C3—51no—
211C2×C3×C4—51no—
212C2×C3×C4—52no—
213C2×C3×C4—52no—
214C2×C3×C4—51no—
215C2×C3×C4—51no—
216C2×C3×C4—102no—
217C2×C3×C4—102no—
218C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
219C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
220C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
221C2×Dic3—22no—
222C2×Dic3—102no—
223C2×Dic3—204no—
224C2×Dic3—202no—
225C2×Dic3—202no—
226C2×Dic3—202no—
227Dic6—42no—
228Dic6—204no—
229Dic6—202no—
230C3×C8—104no—
231C22×C5C2×(C2×D3)⋊C411yescharacteristic
232C2×D5#86911yescharacteristic
233C2×D5#87511yescharacteristic
234C2×D5#90812yes—
235C2×D5#90912yes—
236AGL(1,𝔽5)—242no—
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—122no—
240C4×C5C4×Dic612yes—
241Dic5—21no—
242Dic5—21no—
243Dic5—122no—
244Dic5#92412yes—
245C2×Q8—61no—
246C2×Q8—302no—
247C2×Q8—301no—
248C2×Q8—604no—
249C22×C4—51no—
250C22×C4—51no—
251C22×C4—51no—
252C22×C4—302no—
253C22×C4—302no—
254C2×C8—54no—
255C2×C8—102no—
256C2×C8—102no—
257C4⋊C4—32no—
258C4⋊C4—61no—
259C4⋊C4—152no—
260C4⋊C4—302no—
261C4⋊C4—302no—
262C4⋊C4—304no—
263C4⋊C4—301no—
264C42—51no—
265C42—51no—
266C42—51no—
267C42D3×AGL(1,𝔽5)11yescharacteristic
268C3×C5#199311yescharacteristic, complemented, Hall
269C22×C3—52no—
270C22×C3—52no—
271C22×C3—51no—
272C22×C3—51no—
273C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—52no—
277C3×C4—101no—
278C3×C4—101no—
279C3×C4Q8×AGL(1,𝔽5)12yes—
280Dic3—42no—
281Dic3—202no—
282Dic3—402no—
283C2×C5#492911yescharacteristic
284C2×C5#512011yescharacteristic
285C2×C5#513111yescharacteristic
286D5#470212yes—
287D5#471412yes—
288C23—51no—
289Q8—122no—
290Q8—602no—
291Q8—604no—
292C2×C4—51no—
293C2×C4—52no—
294C2×C4—52no—
295C2×C4—51no—
296C2×C4—51no—
297C2×C4—62no—
298C2×C4—102no—
299C2×C4—102no—
300C2×C4—302no—
301C2×C4—604no—
302C2×C4—602no—
303C2×C4—602no—
304C2×C4—602no—
305C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
306C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
307C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
308C8—104no—
309C2×C3—52no—
310C2×C3—52no—
311C2×C3#6576711yescharacteristic
312C2×C3#6578211yescharacteristic
313C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
314C5#6982811yescharacteristic, complemented, Sylow
315C22—52no—
316C22—52no—
317C22—51no—
318C22—51no—
319C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
320C4—21no—
321C4—21no—
322C4—52no—
323C4—101no—
324C4—101no—
325C4—122no—
326C4—602no—
327C4—1202no—
328C4AGL(1,𝔽5)×Dic612yes—
329C3#1060467511yescharacteristic, complemented, Sylow
330C2—52no—
331C2—52no—
332C2#1175170711yescharacteristic
333C2#1175171211yescharacteristic
334C2#1175174911yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1993
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
9. #91758C4semidirect
10. C5×#869C4semidirect
13. #91468C4semidirect
38. C3×D5⋊C8Q8semidirect
100. #869AGL(1,𝔽5)semidirect
117. D5⋊C8Dic6semidirect
268. C3×C5#1993semidirect
314. C5#69828semidirect
329. C3#10604675semidirect

Maximal subgroups

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

subgroupindex
D5×#8692
#117523482
C3×#656762
#117465302
#106046753
#698285