Finite Group Databasebeta

← #14298853

Subgroups — #14298853

Order 1920.

432 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 116 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
1#11751751C212yesmaximal
2C8×D5×Dic3C211yesmaximal, characteristic
3#11746764C211yesmaximal, characteristic
4C3×#64893C211yesmaximal, characteristic
5#11746529C212yesmaximal
6#10603846—31nomaximal, Hall
7C2×C4⋊ΓL(1,𝔽16)C2212yes—
8C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
9C2×C3×C8×D5C2211yescharacteristic
10C4×D5×Dic3C2211yescharacteristic
11C2×D5×C3⋊C8C2211yescharacteristic
12(C2×AGL(1,𝔽5))⋊Dic3—22no—
13(C2×AGL(1,𝔽5))⋊Dic3—22no—
14C8×Dic15C411yescharacteristic, complemented
15C5×C8×Dic3C411yescharacteristic, complemented
16#90951C411yescharacteristic, complemented
17Dic3×#168C411yescharacteristic, complemented
18#68848—51nomaximal, Hall
19#65689—32no—
20C4×C8×D5—31no—
21#64893—31no—
22#64893—32no—
23#64893D311yescharacteristic
24C22×ΓL(1,𝔽16)—22no—
25C22×C3×AGL(1,𝔽5)—22no—
26C2×C3×C4×D5C2311yescharacteristic
27C2×D5×Dic3D411yescharacteristic
28C2×D5×Dic3D411yescharacteristic
29C4⋊ΓL(1,𝔽16)—22no—
30C4⋊ΓL(1,𝔽16)—22no—
31C3×C4⋊AGL(1,𝔽5)—22no—
32C3×C4⋊AGL(1,𝔽5)—22no—
33C2×C3×C5×C8C2×C411yescharacteristic
34C4×Dic15C2×C411yescharacteristic
35C2×C3⋊#168C2×C411yescharacteristic
36C4×C5×Dic3C2×C411yescharacteristic
37C2×C5×C3⋊C8C2×C411yescharacteristic
38C2×C3×#168C2×C411yescharacteristic
39C3×C8×D5—22no—
40Dic3×Dic5Q811yescharacteristic
41Dic3×Dic5Q811yescharacteristic
42D5×C3⋊C8—22no—
43C2×C8×Dic3—51no—
44#4977—52no—
45C3×#340—51no—
46#4551—51no—
47#4529—52no—
48C2×C4⋊AGL(1,𝔽5)—32no—
49C2×C4⋊AGL(1,𝔽5)C2×D312yes—
50C2×C8×D5—31no—
51C2×C8×D5C2×D311yescharacteristic
52C42×D5—31no—
53(C2×AGL(1,𝔽5))⋊C4—62no—
54(C2×AGL(1,𝔽5))⋊C4—62no—
55C4×C5×C8—31no—
56C8×Dic5—31no—
57C8×Dic5—31no—
58C4×#168—31no—
59#1835—151noSylow
60C22×C3×D5C2×D411yescharacteristic
61C2×ΓL(1,𝔽16)—42no—
62C2×ΓL(1,𝔽16)—42no—
63C2×ΓL(1,𝔽16)—42no—
64C2×C3×AGL(1,𝔽5)—42no—
65C2×C3×AGL(1,𝔽5)—42no—
66C2×C3×AGL(1,𝔽5)—42no—
67C2×C3×C4×C5C22×C411yescharacteristic
68C2×Dic15C4⋊C411yescharacteristic
69C2×Dic15C4⋊C411yescharacteristic
70C2×C5×Dic3C4⋊C411yescharacteristic
71C2×C5×Dic3C4⋊C411yescharacteristic
72C2×C3×Dic5C2×Q811yescharacteristic
73C3×C4×D5#4112yes—
74C3×C4×D5#4112yes—
75D5×Dic3—21no—
76D5×Dic3—22no—
77D5×Dic3—21no—
78C3×C5×C8—21no—
79C3⋊#168—21no—
80C3×#168—21no—
81C5×C3⋊C8—21no—
82C22×C3×C8—51no—
83C2×C3×C4⋊C4—52no—
84C2×C4⋊Dic3—52no—
85C2×C4×Dic3—51no—
86C22×C3⋊C8—51no—
87C3⋊#95—102no—
88C3⋊#95—102no—
89C8×Dic3—51no—
90C8×Dic3—51no—
91C8×Dic3—51no—
92C8×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
93C22×AGL(1,𝔽5)—22no—
94C22×AGL(1,𝔽5)—62no—
95C2×C4×D5—31no—
96C2×C4×D5—31no—
97C2×C4×D5C22×D311yescharacteristic
98C4⋊AGL(1,𝔽5)—22no—
99C4⋊AGL(1,𝔽5)—22no—
100C4⋊AGL(1,𝔽5)—62no—
101C4⋊AGL(1,𝔽5)—62no—
102C2×C5×C8—31no—
103C2×C5×C8C4×D311yescharacteristic
104C42×C5—31no—
105C4×Dic5—31no—
106C4×Dic5—31no—
107C4×Dic5—31no—
108C2×#168—31no—
109C2×#168C4×D311yescharacteristic
110C8×D5—22no—
111C8×D5—62no—
112C2×C4×C8—151no—
113#382—152no—
114#340—51no—
115#340—152no—
116#340—151no—
117C22×C3×C5C2×C4⋊C411yescharacteristic
118C2×C3×D5#12412yes—
119C2×C3×D5#13511yescharacteristic
120C2×C3×D5#13512yes—
121C2×C3×D5#13511yescharacteristic
122ΓL(1,𝔽16)—82no—
123C3×AGL(1,𝔽5)—82no—
124C3×C4×C5#11711yescharacteristic
125C3×C4×C5#11711yescharacteristic
126Dic15—21no—
127Dic15—21no—
128C3×Dic5#12512yes—
129C5×Dic3—21no—
130C5×Dic3—21no—
131C22×C3×C4—51no—
132C22×C3×C4—102no—
133C22×Dic3—51no—
134C22×Dic3—51no—
135C22×Dic3—102no—
136C2×C3×C8—51no—
137C2×C3×C8—102no—
138C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
139C3×C4⋊C4—102no—
140C3×C4⋊C4—102no—
141C4⋊Dic3—102no—
142C4⋊Dic3—102no—
143C4×Dic3—51no—
144C4×Dic3—51no—
145C4×Dic3—51no—
146C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
147C2×C3⋊C8—51no—
148C2×C3⋊C8—102no—
149C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
150C22×D5D3×D411yescharacteristic
151C2×AGL(1,𝔽5)—42no—
152C2×AGL(1,𝔽5)—42no—
153C2×AGL(1,𝔽5)—42no—
154C2×AGL(1,𝔽5)—122no—
155C2×AGL(1,𝔽5)—122no—
156C2×AGL(1,𝔽5)—122no—
157C2×C4×C5—31no—
158C2×C4×C5—31no—
159C2×C4×C5C2×C4×D311yescharacteristic
160C2×Dic5—31no—
161C2×Dic5—31no—
162C2×Dic5D3×Q811yescharacteristic
163C4×D5—61no—
164C4×D5—62no—
165C4×D5—61no—
166C4×D5#23512yes—
167C4×D5#23712yes—
168C5×C8—21no—
169C5×C8—61no—
170#168—21no—
171#168—61no—
172C22×C8—51no—
173C22×C8—151no—
174C2×C4⋊C4—52no—
175C2×C4⋊C4—152no—
176C2×C42—151no—
177C4×C8—31no—
178C4×C8—151no—
179C4×C8—151no—
180C4×C8—151no—
181#95—302no—
182#95—302no—
183C2×C3×C5#38211yescharacteristic
184C2×C3×C5#42711yescharacteristic
185C2×C3×C5#42711yescharacteristic
186C3×D5#48812yes—
187C3×D5#48812yes—
188C23×C3—51no—
189C2×C3×C4—51no—
190C2×C3×C4—52no—
191C2×C3×C4—52no—
192C2×C3×C4—202no—
193C2×C3×C4—202no—
194C2×C3×C4—202no—
195C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
196C2×Dic3—51no—
197C2×Dic3—51no—
198C2×Dic3—101no—
199C2×Dic3—102no—
200C2×Dic3—101no—
201C2×Dic3—202no—
202C2×Dic3—202no—
203C2×Dic3—202no—
204C2×Dic3C4⋊AGL(1,𝔽5)11yescharacteristic
205C2×Dic3C4⋊AGL(1,𝔽5)11yescharacteristic
206C3×C8—21no—
207C3×C8—101no—
208C3⋊C8—21no—
209C3⋊C8—101no—
210C22×C5D3×C4⋊C411yescharacteristic
211C2×D5#88512yes—
212C2×D5#91211yescharacteristic
213C2×D5#91612yes—
214C2×D5#91911yescharacteristic
215AGL(1,𝔽5)—82no—
216AGL(1,𝔽5)—242no—
217C4×C5—61no—
218C4×C5—61no—
219C4×C5#87211yescharacteristic
220C4×C5#87711yescharacteristic
221Dic5—61no—
222Dic5—61no—
223Dic5#88912yes—
224C22×C4—51no—
225C22×C4—102no—
226C22×C4—151no—
227C22×C4—151no—
228C22×C4—302no—
229C2×C8—31no—
230C2×C8—51no—
231C2×C8—102no—
232C2×C8—151no—
233C2×C8—302no—
234C2×C8D3×AGL(1,𝔽5)11yescharacteristic
235C4⋊C4—102no—
236C4⋊C4—102no—
237C4⋊C4—302no—
238C4⋊C4—302no—
239C42—31no—
240C42—151no—
241C42—151no—
242C42—151no—
243C3×C5#183511yescharacteristic, complemented, Hall
244C22×C3—52no—
245C22×C3—51no—
246C22×C3—52no—
247C22×C3—51no—
248C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
249C3×C4—52no—
250C3×C4—402no—
251C3×C4#413011yescharacteristic
252C3×C4#413011yescharacteristic
253Dic3—21no—
254Dic3—21no—
255Dic3—101no—
256Dic3—101no—
257Dic3—402no—
258C2×C5#465011yescharacteristic
259C2×C5#486011yescharacteristic
260C2×C5#488011yescharacteristic
261D5#476812yes—
262D5#480012yes—
263C23—51no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—51no—
267C2×C4—52no—
268C2×C4—52no—
269C2×C4—151no—
270C2×C4—151no—
271C2×C4—202no—
272C2×C4—202no—
273C2×C4—202no—
274C2×C4—302no—
275C2×C4—301no—
276C2×C4—301no—
277C2×C4—602no—
278C2×C4—602no—
279C2×C4—602no—
280C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
281C8—21no—
282C8—61no—
283C8—101no—
284C8—301no—
285C2×C3—52no—
286C2×C3—52no—
287C2×C3#6568911yescharacteristic
288C2×C3#6572111yescharacteristic
289C2×C3#6572111yescharacteristic
290C5#6884811yescharacteristic, complemented, Sylow
291C22—52no—
292C22—52no—
293C22—51no—
294C22—51no—
295C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
296C4—52no—
297C4—61no—
298C4—61no—
299C4—301no—
300C4—301no—
301C4—402no—
302C4—1202no—
303C4#9190911yescharacteristic
304C4#9192311yescharacteristic
305C3#1060384611yescharacteristic, complemented, Sylow
306C2—52no—
307C2—52no—
308C2#1175165711yescharacteristic
309C2#1175165811yescharacteristic
310C2#1175174611yescharacteristic
subgroupG/H
centerC22D3×C4⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5#1835
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
14. C8×Dic15C4semidirect
15. C5×C8×Dic3C4semidirect
16. #90951C4semidirect
17. Dic3×#168C4semidirect
92. C8×Dic3AGL(1,𝔽5)semidirect
243. C3×C5#1835semidirect
290. C5#68848semidirect
305. C3#10603846semidirect

Maximal subgroups

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

subgroupindex
#117517512
C8×D5×Dic32
#117467642
C3×#648932
#117465292
#106038463
#688485