Finite Group Databasebeta

← #14313763

Subgroups — #14313763

Order 1920.

460 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 96 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×#66058C211yesmaximal, characteristic
2#11749369C212yesmaximal
3#11746369C211yesmaximal, characteristic, complemented
4C5×#4548C211yesmaximal, characteristic, complemented
5#11746015C212yesmaximal, complemented
6#10599966—31nomaximal, Hall
7C2×C3×#713C2211yescharacteristic
8C2×C3×Q8×D5C411yescharacteristic
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×#4093C411yescharacteristic
11C3×#4090C2211yescharacteristic
12C3×#4042—22no—
13C3×#4040—22no—
14C3×#4021C411yescharacteristic
15C3×#4018C411yescharacteristic
16D5×#208—22no—
17#91120C2212yes—
18C5×#836C2212yes—
19#90958—22no—
20#71873—51nomaximal, Hall
21#66058D311yescharacteristic
22#65040—32no—
23C5×#356—31no—
24#64768—31no—
25#64698—32no—
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×C3×C5×Q8C2311yescharacteristic
28C3×#713—42no—
29C3×Q8×D5—42no—
30C2×C3×D20C2×C411yescharacteristic
31C2×C3×D20D412yes—
32C2×C3×C4×D5—21no—
33C2×C3×C4×D5C2×C411yescharacteristic
34C2×C3×C4×D5D412yes—
35C2×C3×Dic10—21no—
36C2×C3×Dic10C2×C411yescharacteristic
37C3×C5×C4⋊C4—22no—
38C3×C42×C5C2×C411yescharacteristic
39#6710—22no—
40C5×#208—22no—
41C3×#685—22no—
42C3×#685—21no—
43C3×#685—22no—
44C3×#683—22no—
45C3×#683—21no—
46C3×C4×Dic5C2×C411yescharacteristic
47#6649—42no—
48D5×C3⋊C8—42no—
49C3×#536—51no—
50#5237—52no—
51#4548—51no—
52#4548—52no—
53#4548D511yescharacteristic, complemented
54C2×#713C2×D311yescharacteristic
55C2×Q8×D5Dic311yescharacteristic
56C5×C4⋊Q8C2×D311yescharacteristic
57#4093Dic311yescharacteristic
58#4090C2×D311yescharacteristic
59D5×M16—62no—
60#4042—22no—
61#4040—22no—
62#4021Dic311yescharacteristic
63#4018Dic311yescharacteristic
64C5×#101—32no—
65#3968—32no—
66#3955—62no—
67#2135—151noSylow
68C22×C3×D5C22⋊C412yes—
69C22×C3×D5C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C3×C5×Q8—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5C22×C411yescharacteristic
75C2×C3×C4×C5C2×D412yes—
76C2×C3×Dic5—21no—
77C2×C3×Dic5—21no—
78C2×C3×Dic5C22⋊C411yescharacteristic
79C3×D20—41no—
80C3×D20—42no—
81C3×C4×D5—22no—
82C3×C4×D5—22no—
83C3×C4×D5—22no—
84C3×C4×D5—42no—
85C3×Dic10—42no—
86C3×Dic10—41no—
87C3⋊#168—42no—
88C5×C3⋊C8—42no—
89C2×C3×#41—51no—
90C22×C3×Q8—51no—
91C3×C4⋊Q8—51no—
92C3×C4⋊Q8C2×D511yescharacteristic
93C3×#124—51no—
94C3×#124—51no—
95C3×#123—102no—
96C3×C22⋊Q8—102no—
97C3×#117—51no—
98C2×#208—102no—
99#836—52no—
100#836C2×D512yes—
101#833—102no—
102C2×C5×Q8C2×Dic311yescharacteristic
103C2×C5×Q8C22×D311yescharacteristic
104#713—42no—
105Q8×D5—42no—
106C2×D20C2×Dic311yescharacteristic
107C2×D20#6712yes—
108C2×C4×D5—21no—
109C2×C4×D5C2×Dic311yescharacteristic
110C2×C4×D5#6712yes—
111C2×Dic10—21no—
112C2×Dic10C2×Dic311yescharacteristic
113C5×M16—62no—
114C5×C4⋊C4—22no—
115C42×C5C2×Dic311yescharacteristic
116#685—21no—
117#685—22no—
118#685—22no—
119#683—22no—
120#683—21no—
121C4×Dic5C2×Dic311yescharacteristic
122#681—62no—
123#676—122no—
124C8×D5—122no—
125#536—51no—
126#413—152no—
127#356—31no—
128#356—152no—
129#356—151no—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C2×C3×D5—21no—
132C2×C3×D5—22no—
133C2×C3×D5—42no—
134C2×C3×D5—41no—
135C3×C4×C5—22no—
136C3×C4×C5—21no—
137C3×C4×C5—41no—
138C3×C4×C5—41no—
139C3×Dic5—41no—
140C3×Dic5—41no—
141C3×Dic5#9912yes—
142C3×#41—202no—
143C2×C3×Q8—51no—
144C2×C3×Q8—101no—
145C2×C3×Q8—202no—
146C2×C3×Q8C4×D511yescharacteristic
147C2×C3×Q8C22×D511yescharacteristic
148C2×C3×D4—51no—
149C2×C3×D4—52no—
150C22×C3×C4—51no—
151C22×C3×C4—52no—
152C22×C3×C4—101no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—101no—
155C3×C4⋊C4—102no—
156C3×C22⋊C4—101no—
157C3×C22⋊C4—102no—
158C3×C22⋊C4—102no—
159C3×C42—51no—
160C3×C42C4×D511yescharacteristic
161#208—22no—
162#208—102no—
163#208—202no—
164C2×C3⋊C8—202no—
165C22×D5#21712yes—
166C22×D5#21711yescharacteristic
167C5×Q8—41no—
168C5×Q8—41no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5C22×Dic311yescharacteristic
172C2×C4×C5C2×#6712yes—
173C2×Dic5—21no—
174C2×Dic5—21no—
175C2×Dic5#21711yescharacteristic
176D20—41no—
177D20—42no—
178C4×D5—22no—
179C4×D5—22no—
180C4×D5—22no—
181C4×D5—42no—
182Dic10—42no—
183Dic10—41no—
184C5×C8—122no—
185#168—122no—
186C2×#41—51no—
187C22×Q8—51no—
188C2×M16—302no—
189C4⋊Q8—51no—
190C4⋊Q8D3×D511yescharacteristic
191#124—51no—
192#124—51no—
193#123—102no—
194C22⋊Q8—102no—
195#117—51no—
196#101—32no—
197#101—152no—
198#100—302no—
199C2×C3×C5—21no—
200C2×C3×C5C2×#9911yescharacteristic
201C3×D5—41no—
202C3×D5—42no—
203C23×C3—52no—
204C23×C3—51no—
205C3×Q8—41no—
206C3×Q8—41no—
207C3×Q8—201no—
208C3×Q8—202no—
209C3×D4—202no—
210C3×D4—201no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—51no—
214C2×C3×C4—102no—
215C2×C3×C4—102no—
216C2×C3×C4—102no—
217C2×C3×C4—101no—
218C2×C3×C4—101no—
219C2×C3×C4—202no—
220C2×C3×C4C2×C4×D511yescharacteristic
221C2×C3×C4D4×D512yes—
222C3⋊C8—42no—
223C3⋊C8—202no—
224C22×C5C2×#21711yescharacteristic
225C2×D5—21no—
226C2×D5—22no—
227C2×D5—42no—
228C2×D5—41no—
229C4×C5—22no—
230C4×C5—21no—
231C4×C5—41no—
232C4×C5—41no—
233Dic5—41no—
234Dic5—41no—
235Dic5#83412yes—
236#41—202no—
237C2×Q8—51no—
238C2×Q8—101no—
239C2×Q8—202no—
240C2×Q8D5×Dic311yescharacteristic
241C2×Q8C2×D3×D511yescharacteristic
242C2×D4—51no—
243C2×D4—52no—
244C22×C4—51no—
245C22×C4—52no—
246C22×C4—101no—
247M16—62no—
248M16—302no—
249M16—602no—
250C2×C8—602no—
251C4⋊C4—22no—
252C4⋊C4—101no—
253C4⋊C4—102no—
254C22⋊C4—101no—
255C22⋊C4—102no—
256C22⋊C4—102no—
257C42—51no—
258C42D5×Dic311yescharacteristic
259C3×C5#213511yescharacteristic, complemented, Hall
260C22×C3—101no—
261C22×C3—102no—
262C22×C3—202no—
263C22×C3—201no—
264C22×C3D5×C22⋊C411yescharacteristic
265C3×C4—22no—
266C3×C4—21no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4—52no—
270C3×C4—201no—
271C3×C4—201no—
272C2×C5—21no—
273C2×C5C2×#83411yescharacteristic
274D5—41no—
275D5—42no—
276C23—52no—
277C23—51no—
278Q8—41no—
279Q8—41no—
280Q8—201no—
281Q8—202no—
282D4—202no—
283D4—201no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—51no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—102no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—202no—
293C2×C4C2×D5×Dic311yescharacteristic
294C2×C4D5×#6712yes—
295C8—122no—
296C8—602no—
297C2×C3—21no—
298C2×C3—201no—
299C2×C3—202no—
300C2×C3D5×#9911yescharacteristic
301C5#7187311yescharacteristic, complemented, Sylow
302C22—101no—
303C22—102no—
304C22—202no—
305C22—201no—
306C22D5×#21711yescharacteristic
307C4—22no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—52no—
312C4—201no—
313C4—201no—
314C3#1059996611yescharacteristic, complemented, Sylow
315C2—21no—
316C2—201no—
317C2—202no—
318C2D5×#83411yescharacteristic
subgroupG/H
centerC2D5×#834
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC2×C3×C5C2×#99
prime radicalC2×C3×#713C22
cosocleC2×C3×C5×Q8C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#2135
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11746369C2semidirect
4. C5×#4548C2semidirect
5. #11746015C2semidirect
53. #4548D5semidirect
259. C3×C5#2135semidirect
301. C5#71873semidirect
314. C3#10599966semidirect

Maximal subgroups

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

subgroupindex
C3×#660582
#117493692
#117463692
C5×#45482
#117460152
#105999663
#718735