Finite Group Databasebeta

← #14313706

Subgroups — #14313706

Order 1920.

460 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 72 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
1#11755162C211yesmaximal, characteristic
2D3×#4005C212yesmaximal, complemented
3#11746800C211yesmaximal, characteristic, complemented
4C3×#64929C211yesmaximal, characteristic, complemented
5#11746558C212yesmaximal, complemented
6#10604999—31nomaximal, Hall
7C2×C5×#239C411yescharacteristic
8C2×D3×Dic10C2211yescharacteristic
9D3×#704—22no—
10#91833C411yescharacteristic
11C3×#4090C2211yescharacteristic
12#91423—22no—
13#91373C411yescharacteristic
14#91371C411yescharacteristic
15#91370C2211yescharacteristic
16#91352—22no—
17#91234C2212yes—
18C3×#4005C2212yes—
19#91175—22no—
20#69171—51nomaximal, Hall
21#66159—31no—
22C2×#4005—32no—
23#64929—31no—
24#64929D311yescharacteristic, complemented
25#64923—32no—
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×Dic30C2×C411yescharacteristic
28C5×#239—42no—
29C2×C5×D12—21no—
30C2×C5×D12C2×C411yescharacteristic
31C2×C4×C5×D3—21no—
32C2×C4×C5×D3C2×C411yescharacteristic
33C2×C3×Dic10C2311yescharacteristic
34C2×#1204D412yes—
35C2×D3×Dic5D412yes—
36D3×Dic10—42no—
37#6762—22no—
38C3×#704—22no—
39#6739—42no—
40D3×#170—42no—
41#6712—22no—
42C4×Dic15C2×C411yescharacteristic
43C3×#683—22no—
44C3×C4×Dic5C2×C411yescharacteristic
45Dic3⋊Dic5—21no—
46(C2×D3)⋊Dic5—21no—
47(C2×D3)⋊Dic5—22no—
48(C2×D3)⋊Dic5—22no—
49#5724—51no—
50D3×#101—52no—
51C3×#356—51no—
52#4548—51no—
53#4477—52no—
54C2×C5×#41—31no—
55C22×Dic10—31no—
56C2×#704—62no—
57#4090—31no—
58#4090C2×D311yescharacteristic
59#4082—31no—
60#4082—31no—
61#4081—62no—
62#4072—31no—
63#4070—62no—
64#4005—32no—
65#4005—62no—
66#4005C2×D312yes—
67#2133—151noSylow
68C22×C5×D3—21no—
69C22×C5×D3C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×Dic15—21no—
74C2×Dic15C22⋊C412yes—
75Dic30—41no—
76C2×C5×Dic3C22⋊C411yescharacteristic
77C5×D12—41no—
78C5×D12—42no—
79C4×C5×D3—22no—
80C4×C5×D3—42no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5C2×D412yes—
83C3×Dic10—41no—
84#1204—42no—
85D3×Dic5—22no—
86D3×Dic5—22no—
87C3⋊#170—42no—
88C3×#170—42no—
89C2×#239AGL(1,𝔽5)11yescharacteristic
90C2×D3×Q8—51no—
91C3×C4⋊Q8—51no—
92#947—51no—
93#944—51no—
94D3×M16—102no—
95#896—102no—
96#894—102no—
97#875—51no—
98#872—51no—
99C3×#101—52no—
100#836—52no—
101#824—102no—
102C5×#41—122no—
103C2×C5×Q8C4×D311yescharacteristic
104C2×C5×D4—31no—
105C2×C5×D4—61no—
106C22×C4×C5—31no—
107C22×C4×C5—61no—
108C22×Dic5—32no—
109C2×Dic10—31no—
110C2×Dic10—32no—
111C2×Dic10—122no—
112C2×Dic10C22×D311yescharacteristic
113#704—22no—
114#704—62no—
115#704—122no—
116C2×#170—122no—
117C22⋊Dic5—62no—
118C22⋊Dic5—61no—
119C22⋊Dic5—62no—
120C4⋊Dic5—61no—
121#683—22no—
122#683—62no—
123C4×Dic5—31no—
124C4×Dic5C4×D311yescharacteristic
125#536—151no—
126C2×#101—152no—
127#356—51no—
128#356—151no—
129#355—152no—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C2×C5×D3—41no—
132C2×C5×D3—42no—
133C2×C5×D3—41no—
134C2×C5×D3#9912yes—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137Dic15—22no—
138Dic15—41no—
139C3×Dic5—22no—
140C3×Dic5—41no—
141C5×Dic3—21no—
142C2×C3×Q8—51no—
143C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
144#239—42no—
145D3×Q8—202no—
146C2×D12—21no—
147C2×D12C2×AGL(1,𝔽5)11yescharacteristic
148C2×C4×D3—21no—
149C2×C4×D3—52no—
150C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
151C2×Dic6—51no—
152C2×Dic6—52no—
153C3×M16—102no—
154C3×C4⋊C4—102no—
155C3×C42—51no—
156(C2×D3)⋊C4—102no—
157(C2×D3)⋊C4—102no—
158(C2×D3)⋊C4—101no—
159Dic3⋊C4—102no—
160Dic3⋊C4—101no—
161C4×Dic3—51no—
162#208—102no—
163ΓL(1,𝔽25)—202no—
164D3×C8—202no—
165C23×C5—31no—
166C23×C5—61no—
167C5×Q8—41no—
168C5×D4—121no—
169C5×D4—122no—
170C2×C4×C5—21no—
171C2×C4×C5—31no—
172C2×C4×C5—62no—
173C2×C4×C5—122no—
174C2×C4×C5C2×C4×D311yescharacteristic
175C2×Dic5—21no—
176C2×Dic5—32no—
177C2×Dic5—62no—
178C2×Dic5—62no—
179C2×Dic5—61no—
180C2×Dic5D3×D412yes—
181Dic10—41no—
182Dic10—122no—
183Dic10—121no—
184#170—42no—
185#170—122no—
186C2×#41—31no—
187C22×Q8—151no—
188C2×M16—302no—
189C4⋊Q8—51no—
190C4⋊Q8—151no—
191#124—151no—
192#124—151no—
193#123—302no—
194C22⋊Q8—302no—
195#117—151no—
196#101—52no—
197#101—152no—
198#101—302no—
199C2×C3×C5—21no—
200C2×C3×C5C2×#9911yescharacteristic
201C5×D3—22no—
202C5×D3—81no—
203C22×D3—21no—
204C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
205C3×Q8—41no—
206C3×Q8—201no—
207C2×C3×C4—21no—
208C2×C3×C4—52no—
209C2×C3×C4—101no—
210C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
211C2×Dic3—52no—
212C2×Dic3—101no—
213C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
214D12—41no—
215D12—42no—
216C4×D3—22no—
217C4×D3—42no—
218C4×D3—102no—
219C4×D3—102no—
220Dic6—202no—
221Dic6—201no—
222C3×C8—202no—
223C3⋊C8—202no—
224C22×C5—32no—
225C22×C5—121no—
226C22×C5—122no—
227C22×C5—121no—
228C22×C5D3×C22⋊C411yescharacteristic
229C4×C5—21no—
230C4×C5—41no—
231C4×C5—61no—
232Dic5—22no—
233Dic5—41no—
234Dic5—62no—
235Dic5—121no—
236#41—122no—
237C2×Q8—51no—
238C2×Q8—152no—
239C2×Q8—151no—
240C2×Q8—602no—
241C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
242C2×D4—31no—
243C2×D4—61no—
244C22×C4—31no—
245C22×C4—61no—
246C22×C4—152no—
247M16—102no—
248M16—302no—
249M16—602no—
250C2×C8—602no—
251C4⋊C4—102no—
252C4⋊C4—302no—
253C4⋊C4—301no—
254C22⋊C4—302no—
255C22⋊C4—302no—
256C22⋊C4—301no—
257C42—51no—
258C42—151no—
259C3×C5#213311yescharacteristic, complemented, Hall
260C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
261C2×D3—41no—
262C2×D3—42no—
263C2×D3—41no—
264C2×D3#401112yes—
265C3×C4—21no—
266C3×C4—41no—
267C3×C4—102no—
268C3×C4—201no—
269Dic3—21no—
270Dic3—102no—
271Dic3—201no—
272C2×C5—21no—
273C2×C5—62no—
274C2×C5—241no—
275C2×C5D3×#9911yescharacteristic
276C23—31no—
277C23—61no—
278Q8—41no—
279Q8—201no—
280Q8—601no—
281Q8—602no—
282D4—121no—
283D4—122no—
284C2×C4—21no—
285C2×C4—31no—
286C2×C4—52no—
287C2×C4—62no—
288C2×C4—101no—
289C2×C4—122no—
290C2×C4—152no—
291C2×C4—302no—
292C2×C4—302no—
293C2×C4—301no—
294C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
295C8—202no—
296C8—602no—
297C2×C3—21no—
298C2×C3C2×#401111yescharacteristic
299D3—22no—
300D3—81no—
301C5#6917111yescharacteristic, complemented, Sylow
302C22—32no—
303C22—121no—
304C22—122no—
305C22—121no—
306C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
307C4—21no—
308C4—41no—
309C4—61no—
310C4—102no—
311C4—201no—
312C4—302no—
313C4—601no—
314C3#1060499911yescharacteristic, complemented, Sylow
315C2—21no—
316C2—62no—
317C2—241no—
318C2D3×#401111yescharacteristic
subgroupG/H
centerC2D3×#4011
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC2×C3×C5C2×#99
prime radicalC2×C5×#239C4
cosocleC2×C3×Dic10C23
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#2133
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. D3×#4005C2semidirect
3. #11746800C2semidirect
4. C3×#64929C2semidirect
5. #11746558C2semidirect
24. #64929D3semidirect
259. C3×C5#2133semidirect
301. C5#69171semidirect
314. C3#10604999semidirect

Maximal subgroups

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

subgroupindex
#117551622
D3×#40052
#117468002
C3×#649292
#117465582
#106049993
#691715