Finite Group Databasebeta

← #14285260

Subgroups — #14285260

Order 1920.

456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C3×D5×C4⋊Q8C211yesmaximal, characteristic
2#11752343C211yesmaximal, characteristic
3#11752343C211yesmaximal, characteristic
4#11746744C214yesmaximal, complemented
5#10604661—31nomaximal, Hall
6C2×C3×Q8×D5—21no—
7C3×C5×C4⋊Q8C411yescharacteristic
8C3×#4090—21no—
9C3×D5×C4⋊C4—21no—
10C3×D5×C4⋊C4C412yes—
11C3×#4034—21no—
12C3×#4034C2212yes—
13C3×C42×D5C2211yescharacteristic
14C3×#4015C411yescharacteristic
15#91233C2212yes—
16#91233C2212yes—
17#91232—21no—
18#91232—21no—
19#91231—21no—
20#91231—21no—
21#71776—51nomaximal, Hall
22D5×C4⋊Q8D311yescharacteristic
23#65684—31no—
24#65684—31no—
25#64873—34no—
26C2×C3×C5×Q8—21no—
27C3×Q8×D5—44no—
28C2×C3×C4×D5—22no—
29C2×C3×C4×D5C2×C411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×Dic10—21no—
33C2×C3×Dic10—22no—
34C2×C3⋊#170—22no—
35C2×C3⋊#170—22no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4C2×C412yes—
38C3×C42×C5C2×C411yescharacteristic
39C3×C4⋊Dic5—21no—
40C3×C4⋊Dic5C2×C412yes—
41C3×#683—22no—
42C3×#683—22no—
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5C2311yescharacteristic
46C2×C3×C4⋊Q8—51no—
47#4926—51no—
48#4926—51no—
49#4547—54no—
50C2×Q8×D5—21no—
51C5×C4⋊Q8Dic311yescharacteristic
52#4090—21no—
53D5×C4⋊C4—21no—
54D5×C4⋊C4Dic312yes—
55#4034—21no—
56#4034C2×D312yes—
57C42×D5C2×D311yescharacteristic
58#4015Dic311yescharacteristic
59#4004—32no—
60#4004—32no—
61#4003—61no—
62#4003—61no—
63#4002—61no—
64#4002—61no—
65#1556—151noSylow
66C22×C3×D5C22⋊C411yescharacteristic
67C3×C5×Q8—42no—
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×C3×Dic5—22no—
73C2×C3×Dic5C22⋊C411yescharacteristic
74C2×C3×Dic5C2×D411yescharacteristic
75C2×C3×Dic5C2×D411yescharacteristic
76C3×C4×D5—22no—
77C3×C4×D5—22no—
78C3×C4×D5—22no—
79C3×C4×D5—44no—
80C3×Dic10—42no—
81C3×Dic10—44no—
82C3⋊#170—42no—
83C3⋊#170—42no—
84C22×C3×Q8—101no—
85C3×C4⋊Q8—52no—
86C3×C4⋊Q8—51no—
87C3×C4⋊Q8—101no—
88C3×C4⋊Q8—101no—
89C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
90C2×C3×C4⋊C4—52no—
91C2×C3×C4⋊C4—101no—
92C2×C3×C42—51no—
93#830—101no—
94#830—101no—
95C4⋊(C3⋊C8)—52no—
96C4⋊(C3⋊C8)—52no—
97#803—101no—
98#803—101no—
99C2×C5×Q8—21no—
100Q8×D5—44no—
101C2×C4×D5—22no—
102C2×C4×D5C2×Dic311yescharacteristic
103C2×C4×D5#6711yescharacteristic
104C2×C4×D5#6711yescharacteristic
105C2×Dic10—21no—
106C2×Dic10—22no—
107C2×#170—62no—
108C2×#170—62no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4C2×Dic312yes—
111C42×C5C2×Dic311yescharacteristic
112C4⋊Dic5—21no—
113C4⋊Dic5C2×Dic312yes—
114#683—22no—
115#683—22no—
116C4×Dic5#6711yescharacteristic
117C4×Dic5#6711yescharacteristic
118C4×Dic5C22×D311yescharacteristic
119C2×C4⋊Q8—51no—
120#432—151no—
121#432—151no—
122#332—154no—
123C22×C3×C5C2×C22⋊C411yescharacteristic
124C2×C3×D5—21no—
125C2×C3×D5—21no—
126C2×C3×D5#10112yes—
127C3×C4×C5—21no—
128C3×C4×C5—21no—
129C3×C4×C5—21no—
130C3×C4×C5—42no—
131C3×Dic5—21no—
132C3×Dic5—42no—
133C3×Dic5AGL(1,ℤ/8)12yes—
134C3×Dic5#13712yes—
135C2×C3×Q8—21no—
136C2×C3×Q8—102no—
137C2×C3×Q8—101no—
138C2×C3×Q8—204no—
139C22×C3×C4—51no—
140C22×C3×C4—51no—
141C22×C3×C4—51no—
142C22×C3×C4—102no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—52no—
145C3×C4⋊C4—102no—
146C3×C4⋊C4—102no—
147C3×C4⋊C4—101no—
148C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
149C3×C42—51no—
150C3×C42—51no—
151C3×C42—51no—
152C3×C42C2×AGL(1,𝔽5)11yescharacteristic
153C2×C3⋊C8—102no—
154C2×C3⋊C8—102no—
155C22×D5#21711yescharacteristic
156C5×Q8—42no—
157C2×C4×C5—22no—
158C2×C4×C5#21711yescharacteristic
159C2×C4×C5#21711yescharacteristic
160C2×C4×C5C22×Dic311yescharacteristic
161C2×Dic5—22no—
162C2×Dic5#21711yescharacteristic
163C2×Dic5C2×#6711yescharacteristic
164C2×Dic5C2×#6711yescharacteristic
165C4×D5—22no—
166C4×D5—22no—
167C4×D5—22no—
168C4×D5—44no—
169Dic10—42no—
170Dic10—44no—
171#170—122no—
172#170—122no—
173C22×Q8—101no—
174C4⋊Q8—52no—
175C4⋊Q8—51no—
176C4⋊Q8—101no—
177C4⋊Q8—101no—
178C4⋊Q8ΓL(1,𝔽16)11yescharacteristic
179C2×C4⋊C4—52no—
180C2×C4⋊C4—101no—
181C2×C42—51no—
182C4⋊C8—152no—
183C4⋊C8—152no—
184C22⋊C8—301no—
185C22⋊C8—301no—
186#97—301no—
187#97—301no—
188C2×C3×C5C2×#10111yescharacteristic
189C2×C3×C5#41811yescharacteristic
190C2×C3×C5#41911yescharacteristic
191C3×D5—22no—
192C23×C3—51no—
193C3×Q8—42no—
194C3×Q8—202no—
195C3×Q8—204no—
196C2×C3×C4—22no—
197C2×C3×C4—51no—
198C2×C3×C4—51no—
199C2×C3×C4—51no—
200C2×C3×C4—102no—
201C2×C3×C4—102no—
202C2×C3×C4—102no—
203C2×C3×C4—102no—
204C2×C3×C4—204no—
205C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
206C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
207C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
208C3⋊C8—202no—
209C3⋊C8—202no—
210C22×C5C2×#21711yescharacteristic
211C2×D5—21no—
212C2×D5—21no—
213C2×D5#83612yes—
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—21no—
217C4×C5—42no—
218Dic5—21no—
219Dic5—42no—
220Dic5#93212yes—
221Dic5#94212yes—
222C2×Q8—21no—
223C2×Q8—102no—
224C2×Q8—101no—
225C2×Q8—204no—
226C22×C4—51no—
227C22×C4—51no—
228C22×C4—51no—
229C22×C4—102no—
230C2×C8—302no—
231C2×C8—302no—
232C4⋊C4—21no—
233C4⋊C4—52no—
234C4⋊C4—102no—
235C4⋊C4—102no—
236C4⋊C4—101no—
237C4⋊C4C2×ΓL(1,𝔽16)12yes—
238C42—51no—
239C42—51no—
240C42—51no—
241C42C2×ΓL(1,𝔽16)11yescharacteristic
242C3×C5#155611yescharacteristic, complemented, Hall
243C22×C3—52no—
244C22×C3—101no—
245C22×C3—101no—
246C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—42no—
251C3×C4—52no—
252C3×C4—52no—
253C3×C4—101no—
254C3×C4—202no—
255C2×C5#521511yescharacteristic
256C2×C5#522511yescharacteristic
257C2×C5C2×#83611yescharacteristic
258D5—22no—
259C23—51no—
260Q8—42no—
261Q8—202no—
262Q8—204no—
263C2×C4—22no—
264C2×C4—51no—
265C2×C4—51no—
266C2×C4—51no—
267C2×C4—102no—
268C2×C4—102no—
269C2×C4—102no—
270C2×C4—102no—
271C2×C4—204no—
272C2×C4#676311yescharacteristic
273C2×C4#676311yescharacteristic
274C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
275C8—602no—
276C8—602no—
277C2×C3—102no—
278C2×C3#6576711yescharacteristic
279C2×C3#6578211yescharacteristic
280C2×C3D5⋊#10111yescharacteristic
281C5#7177611yescharacteristic, complemented, Sylow
282C22—52no—
283C22—101no—
284C22—101no—
285C22C2×#676311yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—42no—
290C4—52no—
291C4—52no—
292C4—101no—
293C4—202no—
294C3#1060466111yescharacteristic, complemented, Sylow
295C2—102no—
296C2#1175242611yescharacteristic
297C2#1175244111yescharacteristic
298C2D5⋊#83611yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×C4⋊Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊Q8ΓL(1,𝔽16)
hypocenterC3×C5#1556
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11746744C2semidirect
242. C3×C5#1556semidirect
281. C5#71776semidirect
294. C3#10604661semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
#117523432
#117467442
#106046613
#717765