Finite Group Databasebeta

← #14313708

Subgroups — #14313708

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#11752544C211yesmaximal, characteristic
2D3×#4005C212yesmaximal, complemented
3#11746727C211yesmaximal, characteristic, complemented
4C3×#64856C211yesmaximal, characteristic, complemented
5#11746561C212yesmaximal, complemented
6#10604356—31nomaximal, Hall
7C2×D3×Dic10C2211yescharacteristic
8C2×#6765C411yescharacteristic
9D3×#704—22no—
10#91758C411yescharacteristic
11C5×#872C411yescharacteristic
12C3×#4021C2211yescharacteristic
13#91457—22no—
14#91422—22no—
15#91389C2211yescharacteristic
16#91364C411yescharacteristic
17#91234C2212yes—
18C3×#4005C2212yes—
19#91175—22no—
20#69164—51nomaximal, Hall
21#65860—31no—
22C2×#4005—32no—
23#64856—31no—
24#64856D311yescharacteristic, complemented
25#64855—32no—
26C2×Dic30C2×C411yescharacteristic
27C2×Dic30C2×C411yescharacteristic
28C2×C4×C5×D3C2×C411yescharacteristic
29C2×C3×D20C2×C411yescharacteristic
30C2×C3×Dic10C2311yescharacteristic
31C2×#1204D412yes—
32C2×#1201—21no—
33C2×D3×Dic5D412yes—
34C2×D5×Dic3—21no—
35D3×Dic10—42no—
36#6765—42no—
37#6762—22no—
38C3×#704—22no—
39#6739—42no—
40D3×#170—42no—
41C3×C42×C5C2×C411yescharacteristic
42C4⋊Dic15—22no—
43C5×(C2×D3)⋊C4—21no—
44C5×Dic3⋊C4—21no—
45C4×C5×Dic3C2×C411yescharacteristic
46C3×#685—22no—
47Dic3⋊Dic5—22no—
48#6665—22no—
49#5675—51no—
50D3×#101—52no—
51C3×#355—51no—
52#4542—51no—
53#4478—52no—
54C2×#709—31no—
55C22×Dic10—31no—
56C2×#704—62no—
57C5×#117—31no—
58#4043—62no—
59#4032—62no—
60#4021—31no—
61#4021C2×D311yescharacteristic
62#4015—31no—
63#4015—31no—
64#4005—32no—
65#4005—62no—
66#4005C2×D312yes—
67#2133—151noSylow
68C22×C5×D3C22⋊C411yescharacteristic
69C22×C3×D5—21no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×Dic15—21no—
73C2×Dic15C22⋊C412yes—
74Dic30—41no—
75Dic30—41no—
76C2×C5×Dic3—21no—
77C2×C5×Dic3C22⋊C411yescharacteristic
78C4×C5×D3—22no—
79C2×C3×Dic5C2×D412yes—
80C3×D20—41no—
81C3×Dic10—41no—
82#1204—42no—
83#1201—42no—
84D3×Dic5—22no—
85D3×Dic5—22no—
86D5×Dic3—42no—
87C3⋊#170—42no—
88C3×#170—42no—
89C2×D3×Q8—51no—
90C2×#237—51no—
91C3×#124—51no—
92#944—51no—
93#936—51no—
94D3×M16—102no—
95#883—102no—
96#878—102no—
97#872AGL(1,𝔽5)11yescharacteristic
98#869—51no—
99C3×#101—52no—
100#836—52no—
101#824—102no—
102C22×C4×C5—31no—
103C2×C22⋊D5—61no—
104C22×Dic5—32no—
105#709—122no—
106C2×D20C4×D311yescharacteristic
107C2×C4×D5—61no—
108C2×Dic10—31no—
109C2×Dic10—32no—
110C2×Dic10—31no—
111C2×Dic10—122no—
112C2×Dic10C22×D311yescharacteristic
113#704—22no—
114#704—62no—
115#704—122no—
116C2×#170—122no—
117C5×C4⋊C4—61no—
118C5×C22⋊C4—61no—
119C42×C5—31no—
120C42×C5C4×D311yescharacteristic
121#685—22no—
122#685—62no—
123C4⋊Dic5—62no—
124C4⋊Dic5—62no—
125#536—151no—
126C2×#101—152no—
127#356—152no—
128#355—51no—
129#355—151no—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C2×C5×D3—41no—
132C2×C5×D3#9912yes—
133C2×C3×D5—42no—
134C2×C3×D5—41no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137Dic15—22no—
138Dic15—41no—
139C3×Dic5—22no—
140C5×Dic3—21no—
141C5×Dic3—41no—
142C2×C3×Q8—51no—
143C2×C3×D4—51no—
144C2×#67—101no—
145C22×Dic3—101no—
146D3×Q8—202no—
147#237—202no—
148C2×C4×D3—52no—
149C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
150C2×Dic6—51no—
151C2×Dic6—52no—
152C2×Dic6—51no—
153C3×M16—102no—
154C3×C22⋊C4—102no—
155C3×C42C2×AGL(1,𝔽5)11yescharacteristic
156#217—102no—
157(C2×D3)⋊C4—21no—
158C4⋊Dic3—102no—
159Dic3⋊C4—21no—
160Dic3⋊C4—102no—
161C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
162#208—102no—
163ΓL(1,𝔽25)—202no—
164D3×C8—202no—
165C23×C5—31no—
166C22×D5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—31no—
169C2×C4×C5—62no—
170C2×C4×C5—61no—
171C2×C4×C5C2×C4×D311yescharacteristic
172C22⋊D5—122no—
173C2×Dic5—32no—
174C2×Dic5—62no—
175C2×Dic5—62no—
176C2×Dic5—61no—
177C2×Dic5D3×D412yes—
178D20—41no—
179C4×D5—122no—
180Dic10—41no—
181Dic10—122no—
182Dic10—121no—
183Dic10—121no—
184#170—42no—
185#170—122no—
186C2×#41—151no—
187C22×Q8—151no—
188C2×M16—302no—
189C4⋊Q8—151no—
190C4⋊Q8—151no—
191#124—51no—
192#124—151no—
193#123—302no—
194C22⋊Q8—302no—
195#117—31no—
196#101—52no—
197#101—152no—
198#101—302no—
199C2×C3×C5—21no—
200C2×C3×C5C2×#9911yescharacteristic
201C3×D5—81no—
202C5×D3—22no—
203C23×C3—101no—
204C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
205C3×Q8—201no—
206C3×D4—201no—
207C2×C3×C4—21no—
208C2×C3×C4—52no—
209C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
210#67—202no—
211C2×Dic3—21no—
212C2×Dic3—52no—
213C2×Dic3—101no—
214C2×Dic3—202no—
215C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
216C4×D3—22no—
217C4×D3—102no—
218C4×D3—102no—
219Dic6—202no—
220Dic6—201no—
221Dic6—201no—
222C3×C8—202no—
223C3⋊C8—202no—
224C22×C5—32no—
225C22×C5—121no—
226C22×C5D3×C22⋊C411yescharacteristic
227C2×D5—42no—
228C2×D5—41no—
229C4×C5—21no—
230C4×C5—41no—
231C4×C5—61no—
232C4×C5—121no—
233Dic5—22no—
234Dic5—62no—
235Dic5—121no—
236#41—602no—
237C2×Q8—51no—
238C2×Q8—152no—
239C2×Q8—151no—
240C2×Q8—151no—
241C2×Q8—602no—
242C2×D4—51no—
243C2×D4—301no—
244C22×C4—31no—
245C22×C4—152no—
246C22×C4—301no—
247M16—102no—
248M16—302no—
249M16—602no—
250C2×C8—602no—
251C4⋊C4—61no—
252C4⋊C4—302no—
253C4⋊C4—302no—
254C22⋊C4—61no—
255C22⋊C4—102no—
256C22⋊C4—302no—
257C42—31no—
258C42D3×AGL(1,𝔽5)11yescharacteristic
259C3×C5#213311yescharacteristic, complemented, Hall
260C22×C3—202no—
261C22×C3—201no—
262C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
263C2×D3—41no—
264C2×D3#399912yes—
265C3×C4—21no—
266C3×C4—41no—
267C3×C4—102no—
268Dic3—21no—
269Dic3—41no—
270Dic3—102no—
271Dic3—201no—
272C2×C5—21no—
273C2×C5—62no—
274C2×C5D3×#9911yescharacteristic
275D5—81no—
276C23—31no—
277C23—101no—
278Q8—201no—
279Q8—601no—
280Q8—601no—
281Q8—602no—
282D4—201no—
283D4—602no—
284C2×C4—21no—
285C2×C4—31no—
286C2×C4—52no—
287C2×C4—62no—
288C2×C4—61no—
289C2×C4—152no—
290C2×C4—302no—
291C2×C4—302no—
292C2×C4—301no—
293C2×C4—602no—
294C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
295C8—202no—
296C8—602no—
297C2×C3—21no—
298C2×C3—401no—
299C2×C3C2×#399911yescharacteristic
300D3—22no—
301C5#6916411yescharacteristic, complemented, Sylow
302C22—32no—
303C22—121no—
304C22—202no—
305C22—201no—
306C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
307C4—21no—
308C4—41no—
309C4—61no—
310C4—102no—
311C4—121no—
312C4—302no—
313C4—601no—
314C3#1060435611yescharacteristic, complemented, Sylow
315C2—21no—
316C2—62no—
317C2—401no—
318C2D3×#399911yescharacteristic
subgroupG/H
centerC2D3×#3999
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC2×C3×C5C2×#99
prime radicalC2×#6765C4
cosocleC2×C3×Dic10C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#2133
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. D3×#4005C2semidirect
3. #11746727C2semidirect
4. C3×#64856C2semidirect
5. #11746561C2semidirect
24. #64856D3semidirect
259. C3×C5#2133semidirect
301. C5#69164semidirect
314. C3#10604356semidirect

Maximal subgroups

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

subgroupindex
#117525442
D3×#40052
#117467272
C3×#648562
#117465612
#106043563
#691645