Finite Group Databasebeta

← #14285425

Subgroups — #14285425

Order 1920.

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

normal subgroups only

This group has 508 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×#66002C211yesmaximal, characteristic
2#11752341C212yesmaximal, complemented
3#11746802C212yesmaximal, complemented
4#11746796C212yesmaximal, complemented
5#10604558—31nomaximal, Hall
6C2×C3×#713C411yescharacteristic
7C2×C3×#711C411yescharacteristic
8C2×#6758—22no—
9C3×C5×#124C411yescharacteristic
10C3×#4090C2211yescharacteristic
11C3×#4086C2211yescharacteristic
12C3×#4030—22no—
13C3×#4027—22no—
14C3×#4021C411yescharacteristic
15C3×C42×D5C2211yescharacteristic
16#91233—22no—
17#91233C2214yes—
18#71810—51nomaximal, Hall
19#66002D311yescharacteristic
20#65682—32no—
21#64931—32no—
22#64925—32no—
23C2×C3×C5×Q8C2×C411yescharacteristic
24C2×C3×C5×D4C2×C411yescharacteristic
25C2×C3×C22⋊D5—21no—
26C2×C3×C22⋊D5—22no—
27C22×C3×Dic5—21no—
28C3×#713—42no—
29C3×#711—42no—
30C2×C3×D20—21no—
31C2×C3×D20C2×C411yescharacteristic
32C2×C3×C4×D5—21no—
33C2×C3×C4×D5C2×C411yescharacteristic
34C2×C3×C4×D5D412yes—
35C2×C3×Dic10C2×C411yescharacteristic
36C2×C3⋊#170—24no—
37#6758—44no—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5C2×C411yescharacteristic
40C3×#685—22no—
41C3×#683—22no—
42C3×C4×Dic5D412yes—
43C3×C4×Dic5C2311yescharacteristic
44C3×#532—51no—
45#4924—52no—
46#4546—52no—
47#4544—52no—
48C2×#713Dic311yescharacteristic
49C2×#711Dic311yescharacteristic
50C2×#700—62no—
51C5×#124Dic311yescharacteristic
52#4090C2×D311yescharacteristic
53#4086C2×D311yescharacteristic
54#4030—22no—
55#4027—22no—
56#4021Dic311yescharacteristic
57C42×D5C2×D311yescharacteristic
58#4004—34no—
59#4004—62no—
60#1560—151noSylow
61C23×C3×C5—21no—
62C22×C3×D5—21no—
63C22×C3×D5C22⋊C411yescharacteristic
64C3×C5×Q8—41no—
65C3×C5×D4—41no—
66C2×C3×C4×C5—21no—
67C2×C3×C4×C5C22⋊C412yes—
68C2×C3×C4×C5C22×C411yescharacteristic
69C3×C22⋊D5—42no—
70C3×C22⋊D5—42no—
71C3×C22⋊D5—42no—
72C2×C3×Dic5—21no—
73C2×C3×Dic5—42no—
74C2×C3×Dic5C22⋊C411yescharacteristic
75C2×C3×Dic5C2×D412yes—
76C3×D20—41no—
77C3×D20—42no—
78C3×C4×D5—22no—
79C3×C4×D5—22no—
80C3×C4×D5—22no—
81C3×C4×D5—42no—
82C3×Dic10—41no—
83C3⋊#170—44no—
84C2×C3×#41—51no—
85C2×C3×#41—51no—
86C3×C4⋊Q8—51no—
87C3×#127—51no—
88C3×#124—51no—
89C3×#124AGL(1,𝔽5)11yescharacteristic
90C3×#121—102no—
91C3×C4×D4—102no—
92C2×C3×C42—51no—
93C2×#208—102no—
94C4⋊(C3⋊C8)—54no—
95C4⋊(C3⋊C8)—102no—
96C2×C5×Q8C2×Dic311yescharacteristic
97C2×C5×D4C2×Dic311yescharacteristic
98C2×C22⋊D5—21no—
99C2×C22⋊D5—22no—
100C22×Dic5—21no—
101#713—42no—
102#711—42no—
103C2×D20—21no—
104C2×D20C2×Dic311yescharacteristic
105C2×C4×D5—21no—
106C2×C4×D5C2×Dic311yescharacteristic
107C2×C4×D5#6712yes—
108C2×Dic10C2×Dic311yescharacteristic
109C2×#170—64no—
110#700—124no—
111C5×C22⋊C4—22no—
112C42×C5C2×Dic311yescharacteristic
113#685—22no—
114#683—22no—
115C4×Dic5#6712yes—
116C4×Dic5C22×D311yescharacteristic
117#532—51no—
118#423—152no—
119#333—152no—
120#331—152no—
121C22×C3×C5—41no—
122C22×C3×C5—42no—
123C22×C3×C5C2×C22⋊C411yescharacteristic
124C2×C3×D5—21no—
125C2×C3×D5—22no—
126C2×C3×D5—41no—
127C2×C3×D5—42no—
128C3×C4×C5—21no—
129C3×C4×C5—22no—
130C3×C4×C5—41no—
131C3×Dic5—41no—
132C3×Dic5#10012yes—
133C3×Dic5AGL(1,ℤ/8)12yes—
134C3×Dic5#13712yes—
135C3×#41—202no—
136C3×#41—202no—
137C2×C3×Q8—51no—
138C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
139C2×C3×D4—51no—
140C2×C3×D4—101no—
141C2×C3×D4—102no—
142C2×C3×D4—101no—
143C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
144C22×C3×C4—52no—
145C22×C3×C4—51no—
146C22×C3×C4—101no—
147C22×C3×C4—101no—
148C3×C4⋊C4—102no—
149C3×C22⋊C4—22no—
150C3×C22⋊C4—102no—
151C3×C42—52no—
152C3×C42—51no—
153C3×C42C2×AGL(1,𝔽5)11yescharacteristic
154#208—204no—
155C2×C3⋊C8—104no—
156C23×C5—21no—
157C22×D5—21no—
158C22×D5#21711yescharacteristic
159C5×Q8—41no—
160C5×D4—41no—
161C2×C4×C5—21no—
162C2×C4×C5#21712yes—
163C2×C4×C5C22×Dic311yescharacteristic
164C22⋊D5—42no—
165C22⋊D5—42no—
166C22⋊D5—42no—
167C2×Dic5—21no—
168C2×Dic5—42no—
169C2×Dic5#21711yescharacteristic
170C2×Dic5C2×#6712yes—
171D20—41no—
172D20—42no—
173C4×D5—22no—
174C4×D5—22no—
175C4×D5—22no—
176C4×D5—42no—
177Dic10—41no—
178#170—124no—
179C2×#41—51no—
180C2×#41—51no—
181C2×M16—302no—
182C4⋊Q8—51no—
183#127—51no—
184#124—51no—
185#124ΓL(1,𝔽16)11yescharacteristic
186#121—102no—
187C4×D4—102no—
188C2×C42—51no—
189C4⋊C8—154no—
190C4⋊C8—302no—
191C2×C3×C5—81no—
192C2×C3×C5C2×#10011yescharacteristic
193C2×C3×C5#41712yes—
194C3×D5—41no—
195C3×D5—81no—
196C23×C3—21no—
197C23×C3—51no—
198C23×C3—101no—
199C3×Q8—41no—
200C3×Q8—201no—
201C3×D4—41no—
202C3×D4—201no—
203C3×D4—202no—
204C3×D4—202no—
205C3×D4—202no—
206C3×D4—202no—
207C2×C3×C4—21no—
208C2×C3×C4—51no—
209C2×C3×C4—52no—
210C2×C3×C4—102no—
211C2×C3×C4—102no—
212C2×C3×C4—102no—
213C2×C3×C4—101no—
214C2×C3×C4—202no—
215C2×C3×C4—202no—
216C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
217C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
218C3⋊C8—204no—
219C22×C5—41no—
220C22×C5—42no—
221C22×C5C2×#21711yescharacteristic
222C2×D5—21no—
223C2×D5—22no—
224C2×D5—41no—
225C2×D5—42no—
226C4×C5—21no—
227C4×C5—22no—
228C4×C5—41no—
229Dic5—41no—
230Dic5#83312yes—
231Dic5#94912yes—
232Dic5#95112yes—
233#41—202no—
234#41—202no—
235C2×Q8—51no—
236C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
237C2×D4—51no—
238C2×D4—101no—
239C2×D4—102no—
240C2×D4—101no—
241C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
242C22×C4—52no—
243C22×C4—51no—
244C22×C4—101no—
245C22×C4—101no—
246M16—604no—
247C2×C8—304no—
248C4⋊C4—102no—
249C22⋊C4—22no—
250C22⋊C4—102no—
251C42—52no—
252C42—51no—
253C42C2×ΓL(1,𝔽16)11yescharacteristic
254C3×C5#156011yescharacteristic, complemented, Hall
255C22×C3—42no—
256C22×C3—41no—
257C22×C3—102no—
258C22×C3—101no—
259C22×C3—202no—
260C22×C3—201no—
261C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
262C3×C4—22no—
263C3×C4—21no—
264C3×C4—41no—
265C3×C4—52no—
266C3×C4—52no—
267C3×C4—52no—
268C3×C4—201no—
269C2×C5—81no—
270C2×C5C2×#83311yescharacteristic
271C2×C5#523212yes—
272D5—41no—
273D5—81no—
274C23—21no—
275C23—51no—
276C23—101no—
277Q8—41no—
278Q8—201no—
279D4—41no—
280D4—201no—
281D4—202no—
282D4—202no—
283D4—202no—
284D4—202no—
285C2×C4—21no—
286C2×C4—52no—
287C2×C4—51no—
288C2×C4—102no—
289C2×C4—102no—
290C2×C4—102no—
291C2×C4—101no—
292C2×C4—202no—
293C2×C4—202no—
294C2×C4#676312yes—
295C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
296C8—604no—
297C2×C3—81no—
298C2×C3—201no—
299C2×C3—401no—
300C2×C3D5⋊#10011yescharacteristic
301C2×C3#6579312yes—
302C5#7181011yescharacteristic, complemented, Sylow
303C22—42no—
304C22—41no—
305C22—102no—
306C22—101no—
307C22—202no—
308C22—201no—
309C22C2×#676311yescharacteristic
310C4—22no—
311C4—21no—
312C4—41no—
313C4—52no—
314C4—52no—
315C4—52no—
316C4—201no—
317C3#1060455811yescharacteristic, complemented, Sylow
318C2—81no—
319C2—201no—
320C2—401no—
321C2D5⋊#83311yescharacteristic
322C2#1175245212yes—
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#124C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66002C2
cosocleC3×C4×Dic5C23
hypercenter#124ΓL(1,𝔽16)
hypocenterC3×C5#1560
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11752341C2semidirect
3. #11746802C2semidirect
4. #11746796C2semidirect
254. C3×C5#1560semidirect
302. C5#71810semidirect
317. C3#10604558semidirect

Maximal subgroups

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

subgroupindex
C3×#660022
#117523412
#117468022
#117467962
#106045583
#718105