Finite Group Databasebeta

← #14285279

Subgroups — #14285279

Order 1920.

456 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C2×#91468C211yesmaximal, characteristic
2#11752416C211yesmaximal, characteristic
3C3×#65757C211yesmaximal, characteristic
4#11746509C214yesmaximal, complemented
5#10604279—31nomaximal, Hall
6C22×#1204—21no—
7C2×C4⋊Dic15C411yescharacteristic
8C2×C5×C4⋊Dic3C411yescharacteristic
9C2×C3×C4×Dic5C2211yescharacteristic
10C2×#6668—21no—
11#91468—21no—
12#91468—21no—
13#91468C412yes—
14#91468C2212yes—
15#91241—21no—
16#91233C2212yes—
17#91231—21no—
18C3×C22⋊#170—21no—
19C3×#4004C2212yes—
20C3×#4002—21no—
21#70823—51nomaximal, Hall
22C2×#4034—31no—
23#65757—31no—
24#65757D311yescharacteristic
25#64873—34no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×Dic15—21no—
28C22×C5×Dic3—21no—
29C22×C3×Dic5D411yescharacteristic
30C22×C3×Dic5D411yescharacteristic
31C2×#1204—22no—
32C2×#1204—22no—
33C2×#1204—44no—
34C2×C3⋊#170—22no—
35C2×C3×#170—22no—
36C4⋊Dic15—21no—
37C4⋊Dic15C2×C412yes—
38C5×C4⋊Dic3—21no—
39C5×C4⋊Dic3C2×C412yes—
40C3×C4×Dic5C2×C411yescharacteristic
41C3×C4×Dic5D411yescharacteristic
42C3×C4×Dic5D411yescharacteristic
43C3×C4×Dic5C2311yescharacteristic
44#6668—22no—
45#6668—22no—
46C2×#869—51no—
47C3×#432—51no—
48#4926—51no—
49#4482—54no—
50C22×Dic10—61no—
51C2×C5×C4⋊C4—31no—
52C2×C4⋊Dic5—31no—
53C2×#683—61no—
54C2×C4×Dic5C2×D311yescharacteristic
55#4034—32no—
56#4034—32no—
57#4034—61no—
58#4034—61no—
59C22⋊#170—21no—
60C22⋊#170—61no—
61#4004—32no—
62#4004C2×D312yes—
63#4002—21no—
64#4002—61no—
65#1556—151noSylow
66C23×C3×C5C22⋊C411yescharacteristic
67C2×C3×C4×C5—22no—
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22×C411yescharacteristic
70C2×Dic15—22no—
71C2×Dic15—42no—
72C2×C5×Dic3—22no—
73C2×C5×Dic3—42no—
74C2×C3×Dic5—22no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5C22⋊C411yescharacteristic
77C2×C3×Dic5C22⋊C411yescharacteristic
78C2×C3×Dic5C2×D411yescharacteristic
79C2×C3×Dic5C2×D411yescharacteristic
80#1204—44no—
81#1204—44no—
82C3⋊#170—42no—
83C3×#170—42no—
84C22×Dic6—101no—
85C2×C3×C42—51no—
86C2×C4⋊Dic3—51no—
87C2×C4⋊Dic3—101no—
88C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
89#869—52no—
90#869—52no—
91#869—101no—
92#869—101no—
93C3×C4⋊C8—52no—
94C3×C22⋊C8—101no—
95C3×#97—101no—
96#830—101no—
97C4⋊(C3⋊C8)—52no—
98#803—101no—
99C22×C4×C5—61no—
100C22×C4×C5C4×D311yescharacteristic
101C22×Dic5—61no—
102C22×Dic5D1211yescharacteristic
103C22×Dic5#6711yescharacteristic
104C2×Dic10—62no—
105C2×Dic10—62no—
106C2×Dic10—124no—
107C2×#170—22no—
108C2×#170—62no—
109C5×C4⋊C4—32no—
110C5×C4⋊C4—61no—
111C4⋊Dic5—32no—
112C4⋊Dic5—61no—
113#683—62no—
114#683—62no—
115C4×Dic5C4×D311yescharacteristic
116C4×Dic5D1211yescharacteristic
117C4×Dic5#6711yescharacteristic
118C4×Dic5C22×D311yescharacteristic
119C2×C4⋊Q8—151no—
120#432—51no—
121#432—151no—
122#332—154no—
123C22×C3×C5—21no—
124C22×C3×C5—21no—
125C22×C3×C5#10112yes—
126C22×C3×C5C2×C22⋊C411yescharacteristic
127C3×C4×C5—21no—
128C3×C4×C5—21no—
129Dic15—42no—
130C3×Dic5—21no—
131C3×Dic5—21no—
132C3×Dic5AGL(1,ℤ/8)12yes—
133C3×Dic5#13712yes—
134C5×Dic3—42no—
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
138C22×Dic3—21no—
139C22×Dic3—101no—
140C2×Dic6—102no—
141C2×Dic6—102no—
142C2×Dic6—204no—
143C2×C3×C8—102no—
144C3×C42—51no—
145C3×C42—51no—
146C3×C42—51no—
147C3×C42—51no—
148C4⋊Dic3—21no—
149C4⋊Dic3—52no—
150C4⋊Dic3—102no—
151C4⋊Dic3—102no—
152C4⋊Dic3—101no—
153C4⋊Dic3C2×AGL(1,𝔽5)12yes—
154C2×C3⋊C8—102no—
155C23×C5(C2×D3)⋊C411yescharacteristic
156C2×C4×C5—22no—
157C2×C4×C5—62no—
158C2×C4×C5—122no—
159C2×C4×C5(C2×D3)⋊C411yescharacteristic
160C2×C4×C5C2×C4×D311yescharacteristic
161C2×Dic5—22no—
162C2×Dic5—22no—
163C2×Dic5—62no—
164C2×Dic5—122no—
165C2×Dic5(C2×D3)⋊C411yescharacteristic
166C2×Dic5(C2×D3)⋊C411yescharacteristic
167C2×Dic5C2×D1211yescharacteristic
168C2×Dic5C2×#6711yescharacteristic
169Dic10—124no—
170Dic10—124no—
171#170—42no—
172#170—122no—
173C22×Q8—301no—
174C4⋊Q8—152no—
175C4⋊Q8—152no—
176C4⋊Q8—301no—
177C4⋊Q8—301no—
178C2×C4⋊C4—31no—
179C2×C4⋊C4—151no—
180C2×C4⋊C4—301no—
181C2×C42—51no—
182C4⋊C8—52no—
183C4⋊C8—152no—
184C22⋊C8—101no—
185C22⋊C8—301no—
186#97—101no—
187#97—301no—
188C2×C3×C5—22no—
189C2×C3×C5C2×#10111yescharacteristic
190C2×C3×C5#41811yescharacteristic
191C2×C3×C5#41911yescharacteristic
192C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
193C2×C3×C4—22no—
194C2×C3×C4—51no—
195C2×C3×C4—51no—
196C2×C3×C4—51no—
197C2×C3×C4—51no—
198C2×C3×C4—102no—
199C2×C3×C4—102no—
200C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
201C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
202C2×Dic3—22no—
203C2×Dic3—42no—
204C2×Dic3—102no—
205C2×Dic3—202no—
206Dic6—204no—
207Dic6—204no—
208C3×C8—202no—
209C3⋊C8—202no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5#82412yes—
213C22×C5C2×(C2×D3)⋊C411yescharacteristic
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—122no—
217Dic5—21no—
218Dic5—21no—
219Dic5—122no—
220Dic5#90912yes—
221Dic5#94912yes—
222C2×Q8—302no—
223C2×Q8—302no—
224C2×Q8—604no—
225C22×C4—51no—
226C22×C4—51no—
227C22×C4—61no—
228C22×C4—301no—
229C22×C4D3×AGL(1,𝔽5)11yescharacteristic
230C2×C8—102no—
231C2×C8—302no—
232C4⋊C4—32no—
233C4⋊C4—61no—
234C4⋊C4—152no—
235C4⋊C4—302no—
236C4⋊C4—302no—
237C4⋊C4—301no—
238C42—51no—
239C42—51no—
240C42—51no—
241C42—51no—
242C3×C5#155611yescharacteristic, complemented, Hall
243C22×C3—21no—
244C22×C3—21no—
245C22×C3#400512yes—
246C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—52no—
250C3×C4—52no—
251C3×C4—101no—
252C3×C4—101no—
253Dic3—42no—
254Dic3—202no—
255C2×C5—22no—
256C2×C5#500111yescharacteristic
257C2×C5#512011yescharacteristic
258C2×C5C2×#82411yescharacteristic
259C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
260Q8—604no—
261Q8—604no—
262C2×C4—22no—
263C2×C4—51no—
264C2×C4—51no—
265C2×C4—51no—
266C2×C4—51no—
267C2×C4—62no—
268C2×C4—102no—
269C2×C4—102no—
270C2×C4—122no—
271C2×C4—302no—
272C2×C4—602no—
273C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
274C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
275C8—202no—
276C8—602no—
277C2×C3—22no—
278C2×C3C2×#400511yescharacteristic
279C2×C3#6576711yescharacteristic
280C2×C3#6578211yescharacteristic
281C5#7082311yescharacteristic, complemented, Sylow
282C22—21no—
283C22—21no—
284C22#9117512yes—
285C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
286C4—21no—
287C4—21no—
288C4—52no—
289C4—52no—
290C4—101no—
291C4—101no—
292C4—122no—
293C4—602no—
294C3#1060427911yescharacteristic, complemented, Sylow
295C2—22no—
296C2#1175170611yescharacteristic
297C2#1175171211yescharacteristic
298C2C2×#9117511yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1556
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746509C2semidirect
242. C3×C5#1556semidirect
281. C5#70823semidirect
294. C3#10604279semidirect

Maximal subgroups

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

subgroupindex
C2×#914682
#117524162
C3×#657572
#117465092
#106042793
#708235