Finite Group Databasebeta

← #14284493

Subgroups — #14284493

Order 1920.

388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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×#66062C211yesmaximal, characteristic
2#11752343C211yesmaximal, characteristic
3#11752343C211yesmaximal, characteristic
4#11746741C214yesmaximal, complemented
5#10604639—31nomaximal, Hall
6C3×C5×C4⋊Q8C411yescharacteristic
7C3×#4092—21no—
8C3×Q8×Dic5—21no—
9C3×#4043—21no—
10C3×#4038C412yes—
11C3×#4036C2212yes—
12C3×#4033—21no—
13C3×C42×D5C2211yescharacteristic
14C3×#4015C411yescharacteristic
15#91233—21no—
16#91233—21no—
17#91232—21no—
18#91232—21no—
19#91231C2212yes—
20#91231C2212yes—
21#71823—51nomaximal, Hall
22#66062D311yescharacteristic
23#65684—31no—
24#65684—31no—
25#64870—34no—
26C2×C3×C5×Q8—21no—
27C2×C3×C4×D5C2×C411yescharacteristic
28C2×C3×C4×D5D411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×Dic10—21no—
31C2×C3⋊#170—22no—
32C2×C3⋊#170—22no—
33C3×C5×C4⋊C4—21no—
34C3×C5×C4⋊C4C2×C412yes—
35C3×C42×C5C2×C411yescharacteristic
36C3×#685—22no—
37C3×C4⋊Dic5—21no—
38C3×C4⋊Dic5—22no—
39C3×C4⋊Dic5C2×C412yes—
40C3×#683—22no—
41C3×C4×Dic5—22no—
42C3×C4×Dic5D411yescharacteristic
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5C2311yescharacteristic
45C3×#533—51no—
46#4926—51no—
47#4926—51no—
48#4543—54no—
49C5×C4⋊Q8Dic311yescharacteristic
50#4092—21no—
51Q8×Dic5—21no—
52#4043—21no—
53#4038Dic312yes—
54#4036C2×D312yes—
55#4033—21no—
56C42×D5C2×D311yescharacteristic
57#4015Dic311yescharacteristic
58#4004—61no—
59#4004—61no—
60#4003—61no—
61#4003—61no—
62#4002—32no—
63#4002—32no—
64#1537—151noSylow
65C22×C3×D5C22⋊C411yescharacteristic
66C3×C5×Q8—42no—
67C2×C3×C4×C5—22no—
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22×C411yescharacteristic
71C2×C3×Dic5—22no—
72C2×C3×Dic5C22⋊C411yescharacteristic
73C2×C3×Dic5C2×D411yescharacteristic
74C2×C3×Dic5C2×D411yescharacteristic
75C3×C4×D5—22no—
76C3×C4×D5—41no—
77C3×C4×D5—41no—
78C3×Dic10—42no—
79C3⋊#170—42no—
80C3⋊#170—42no—
81C3×C4⋊Q8—51no—
82C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
83C3×#125—52no—
84C3×C22⋊Q8—101no—
85C3×C22⋊Q8—101no—
86C3×C4×Q8—101no—
87C3×C4×Q8—101no—
88C3×#117—52no—
89C2×C3×C42—51no—
90#830—101no—
91#830—101no—
92C4⋊(C3⋊C8)—101no—
93C4⋊(C3⋊C8)—101no—
94#803—52no—
95#803—52no—
96C2×C5×Q8—21no—
97C2×C4×D5C2×Dic311yescharacteristic
98C2×C4×D5#6711yescharacteristic
99C2×C4×D5#6711yescharacteristic
100C2×Dic10—21no—
101C2×#170—62no—
102C2×#170—62no—
103C5×C4⋊C4—21no—
104C5×C4⋊C4C2×Dic312yes—
105C42×C5C2×Dic311yescharacteristic
106#685—22no—
107C4⋊Dic5—21no—
108C4⋊Dic5—22no—
109C4⋊Dic5C2×Dic312yes—
110#683—22no—
111C4×Dic5—22no—
112C4×Dic5#6711yescharacteristic
113C4×Dic5#6711yescharacteristic
114C4×Dic5C22×D311yescharacteristic
115#533—51no—
116#432—151no—
117#432—151no—
118#330—154no—
119C22×C3×C5C2×C22⋊C411yescharacteristic
120C2×C3×D5—21no—
121C2×C3×D5—21no—
122C2×C3×D5—21no—
123C3×C4×C5—21no—
124C3×C4×C5—21no—
125C3×C4×C5—21no—
126C3×C4×C5—42no—
127C3×Dic5—21no—
128C3×Dic5—21no—
129C3×Dic5—42no—
130C3×Dic5#10112yes—
131C2×C3×Q8—21no—
132C2×C3×Q8—101no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C22×C3×C4—51no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—52no—
138C3×C4⋊C4—102no—
139C3×C4⋊C4—102no—
140C3×C4⋊C4—101no—
141C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
142C3×C22⋊C4—102no—
143C3×C42—51no—
144C3×C42—51no—
145C3×C42—51no—
146C3×C42—102no—
147C3×C42C2×AGL(1,𝔽5)11yescharacteristic
148C2×C3⋊C8—102no—
149C2×C3⋊C8—102no—
150C22×D5#21711yescharacteristic
151C5×Q8—42no—
152C2×C4×C5—22no—
153C2×C4×C5#21711yescharacteristic
154C2×C4×C5#21711yescharacteristic
155C2×C4×C5C22×Dic311yescharacteristic
156C2×Dic5—22no—
157C2×Dic5#21711yescharacteristic
158C2×Dic5C2×#6711yescharacteristic
159C2×Dic5C2×#6711yescharacteristic
160C4×D5—22no—
161C4×D5—41no—
162C4×D5—41no—
163Dic10—42no—
164#170—122no—
165#170—122no—
166C4⋊Q8—51no—
167C4⋊Q8ΓL(1,𝔽16)11yescharacteristic
168#125—52no—
169C22⋊Q8—101no—
170C22⋊Q8—101no—
171C4×Q8—101no—
172C4×Q8—101no—
173#117—52no—
174C2×C42—51no—
175C4⋊C8—301no—
176C4⋊C8—301no—
177C22⋊C8—301no—
178C22⋊C8—301no—
179#97—152no—
180#97—152no—
181C2×C3×C5C2×#10111yescharacteristic
182C2×C3×C5#42111yescharacteristic
183C2×C3×C5#42111yescharacteristic
184C3×D5—41no—
185C23×C3—51no—
186C3×Q8—42no—
187C3×Q8—202no—
188C2×C3×C4—22no—
189C2×C3×C4—51no—
190C2×C3×C4—51no—
191C2×C3×C4—51no—
192C2×C3×C4—102no—
193C2×C3×C4—102no—
194C2×C3×C4—201no—
195C2×C3×C4—201no—
196C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
197C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
198C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
199C3⋊C8—202no—
200C3⋊C8—202no—
201C22×C5C2×#21711yescharacteristic
202C2×D5—21no—
203C2×D5—21no—
204C2×D5—21no—
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—21no—
208C4×C5—42no—
209Dic5—21no—
210Dic5—21no—
211Dic5—42no—
212Dic5#83612yes—
213C2×Q8—21no—
214C2×Q8—101no—
215C22×C4—51no—
216C22×C4—51no—
217C22×C4—51no—
218C2×C8—302no—
219C2×C8—302no—
220C4⋊C4—21no—
221C4⋊C4—52no—
222C4⋊C4—102no—
223C4⋊C4—102no—
224C4⋊C4—101no—
225C4⋊C4C2×ΓL(1,𝔽16)12yes—
226C22⋊C4—102no—
227C42—51no—
228C42—51no—
229C42—51no—
230C42—102no—
231C42C2×ΓL(1,𝔽16)11yescharacteristic
232C3×C5#153711yescharacteristic, complemented, Hall
233C22×C3—101no—
234C22×C3—101no—
235C22×C3—101no—
236C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—42no—
241C3×C4—52no—
242C3×C4—101no—
243C3×C4—101no—
244C3×C4—202no—
245C2×C5C2×#83611yescharacteristic
246C2×C5#523611yescharacteristic
247C2×C5#523611yescharacteristic
248D5—41no—
249C23—51no—
250Q8—42no—
251Q8—202no—
252C2×C4—22no—
253C2×C4—51no—
254C2×C4—51no—
255C2×C4—51no—
256C2×C4—102no—
257C2×C4—102no—
258C2×C4—201no—
259C2×C4—201no—
260C2×C4#676311yescharacteristic
261C2×C4#676311yescharacteristic
262C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
263C8—602no—
264C8—602no—
265C2×C3—201no—
266C2×C3#6576911yescharacteristic
267C2×C3#6578411yescharacteristic
268C2×C3D5⋊#10111yescharacteristic
269C5#7182311yescharacteristic, complemented, Sylow
270C22—101no—
271C22—101no—
272C22—101no—
273C22C2×#676311yescharacteristic
274C4—21no—
275C4—21no—
276C4—21no—
277C4—42no—
278C4—52no—
279C4—101no—
280C4—101no—
281C4—202no—
282C3#1060463911yescharacteristic, complemented, Sylow
283C2—201no—
284C2#1175242811yescharacteristic
285C2#1175244311yescharacteristic
286C2D5⋊#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#1537
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. #11746741C2semidirect
232. C3×C5#1537semidirect
269. C5#71823semidirect
282. C3#10604639semidirect

Maximal subgroups

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

subgroupindex
C3×#660622
#117523432
#117467412
#106046393
#718235