Finite Group Databasebeta

← #14302959

Subgroups — #14302959

Order 1920.

628 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 148 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#11756575C211yesmaximal, characteristic
2C5×#5812C211yesmaximal, characteristic, complemented
3C2×C3×#3968C211yesmaximal, characteristic, complemented
4#11748428C212yesmaximal
5#11745971C212yesmaximal, complemented
6#10602456—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×#6817C2211yescharacteristic
9#91836C412yescomplemented
10#91835—22no—
11#91833C412yescomplemented
12#91818—22no—
13#91815C2211yescharacteristic
14C5×Q8×Dic3—24no—
15C5×#926—22no—
16C5×#926C2212yes—
17C2×C3×#681C2212yes—
18C3×#3968—22no—
19#90980—24no—
20#70105—51nomaximal, Hall
21C5×#519—31no—
22#66150—31no—
23C2×#3968D311yescharacteristic, complemented
24#65294—32no—
25#64751—32no—
26C2×C3×C5×Q8—22no—
27C2×C3×C5×Q8—22no—
28C2×C3×C5×Q8C2×C412yes—
29C2×C3×C5×Q8D412yes—
30C22×C3×C4×C5D412yes—
31C22×C3×C4×C5C2311yescharacteristic
32C2×#1220—21no—
33#6817—22no—
34#6817—22no—
35C2×D60C2×C411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30C2×C411yescharacteristic
38#6719—21no—
39#6714—24no—
40C4⋊Dic15—21no—
41#6712—24no—
42C4×Dic15C2×C412yes—
43C5×#217—22no—
44C5×C4⋊Dic3—24no—
45C5×C4⋊Dic3—22no—
46C4×C5×Dic3—24no—
47C4×C5×Dic3D414yes—
48C3×#681—22no—
49C3×#681—22no—
50C2×C3×#168—22no—
51#5816—51no—
52#5812D511yescharacteristic, complemented
53C2×C3×#101—51no—
54#5139—52no—
55#4557—52no—
56C22×C5×Q8C2×D311yescharacteristic
57C2×#709—31no—
58C4×C5×Q8—64no—
59C5×#117—32no—
60C5×#117—62no—
61#4093—32no—
62#4092—62no—
63#4090—32no—
64#4075—62no—
65#4072—31no—
66C2×#681C2×D312yes—
67#3968—22no—
68#3937—64no—
69#1912—151noSylow
70C23×C3×C5C2×D411yescharacteristic
71C22×D15—21no—
72C3×C5×Q8—24no—
73C3×C5×Q8—24no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5C22⋊C414yes—
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×C3×C4×C5C2×D412yes—
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5#4112yes—
81#1220—41no—
82#1220—41no—
83C2×Dic15—22no—
84C2×Dic15—21no—
85D60—22no—
86C4×D15—42no—
87Dic30—22no—
88C2×C5×Dic3—24no—
89C3×#168—42no—
90C22×C3×Q8C2×D511yescharacteristic
91C2×#235—51no—
92C2×C3×M16—52no—
93#947—52no—
94#946—102no—
95Q8×Dic3—24no—
96#944—52no—
97#929—102no—
98#926—22no—
99#926—51no—
100#926C2×D512yes—
101C3×#101—102no—
102#825—104no—
103C2×C5×Q8—22no—
104C2×C5×Q8—22no—
105C2×C5×Q8C4×D312yes—
106C2×C5×Q8#6712yes—
107C22×C4×C5D1212yes—
108C22×C4×C5C22×D311yescharacteristic
109C2×C22⋊D5—61no—
110#709—62no—
111#709—62no—
112C2×D20—31no—
113C2×C4×D5—61no—
114C2×Dic10—31no—
115C5×C4⋊C4—64no—
116C5×C4⋊C4—62no—
117C5×C22⋊C4—62no—
118C42×C5—34no—
119C42×C5—64no—
120C22⋊Dic5—61no—
121#685—64no—
122C4⋊Dic5—61no—
123#683—64no—
124C4×Dic5—32no—
125#681—22no—
126#681—22no—
127C2×#168—22no—
128#536—151no—
129#519—31no—
130#421—152no—
131C2×#101—51no—
132H(3,ℤ/4)—152no—
133C22×C3×C5—41no—
134C22×C3×C5C2×C22⋊C411yescharacteristic
135C22×C3×C5#12011yescharacteristic
136C22×C3×C5#12311yescharacteristic
137C2×D15—42no—
138C2×D15—41no—
139C3×C4×C5—24no—
140C3×C4×C5C4×D412yes—
141C3×C4×C5#12112yes—
142Dic15—42no—
143Dic15—41no—
144C5×Dic3—44no—
145C2×C3×Q8—22no—
146C2×C3×Q8—22no—
147C2×C3×Q8C4×D512yes—
148C2×C3×Q8D2012yes—
149C22×C3×C4C22⋊D512yes—
150C22×C3×C4C22×D511yescharacteristic
151C2×#67—101no—
152#235—102no—
153#235—102no—
154C2×D12—51no—
155C2×C4×D3—101no—
156C2×Dic6—51no—
157C3×M16—102no—
158C3×M16—102no—
159C2×C3×C8—102no—
160#217—22no—
161#217—101no—
162(C2×D3)⋊C4—104no—
163C4⋊Dic3—24no—
164C4⋊Dic3—22no—
165C4⋊Dic3—101no—
166Dic3⋊C4—104no—
167C4×Dic3—24no—
168C4×Dic3—52no—
169C4×Dic3C22⋊D514yes—
170C23×C5C2×D1211yescharacteristic
171C22×D5—61no—
172C5×Q8—24no—
173C5×Q8—24no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—64no—
177C2×C4×C5(C2×D3)⋊C414yes—
178C2×C4×C5C2×C4×D311yescharacteristic
179C2×C4×C5D3×D412yes—
180C2×C4×C5#23712yes—
181C2×C4×C5C2×#6711yescharacteristic
182C22⋊D5—121no—
183C22⋊D5—121no—
184C2×Dic5—62no—
185C2×Dic5—61no—
186D20—62no—
187C4×D5—122no—
188Dic10—62no—
189#168—42no—
190C2×#41—151no—
191C22×Q8D3×D511yescharacteristic
192C2×M16—52no—
193C4⋊Q8—152no—
194#124—152no—
195#123—302no—
196C22⋊Q8—302no—
197C4×Q8—64no—
198#117—32no—
199#117—62no—
200#117—151no—
201#104—304no—
202#101—102no—
203C2×C3×C5—21no—
204C2×C3×C5—21no—
205C2×C3×C5—21no—
206C2×C3×C5#38611yescharacteristic
207D15—81no—
208C23×C3C2×C22⋊D511yescharacteristic
209C22×D3—101no—
210C3×Q8—24no—
211C3×Q8—24no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4#68514yes—
215C2×C3×C4C2×C4×D511yescharacteristic
216C2×C3×C4C2×D2011yescharacteristic
217C2×C3×C4#70912yes—
218C2×C3×C4C2×C22⋊D512yes—
219#67—201no—
220#67—201no—
221C2×Dic3—24no—
222C2×Dic3—102no—
223C2×Dic3—101no—
224D12—102no—
225C4×D3—202no—
226Dic6—102no—
227C3×C8—202no—
228C22×C5—41no—
229C22×C5#88211yescharacteristic
230C22×C5#88611yescharacteristic
231C22×C5C2×(C2×D3)⋊C411yescharacteristic
232C2×D5—122no—
233C2×D5—121no—
234C4×C5—24no—
235C4×C5—124no—
236C4×C5#67⋊C412yes—
237C4×C5#93912yes—
238Dic5—122no—
239Dic5—121no—
240#41—302no—
241#41—302no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—151no—
245C2×Q8#120012yes—
246C2×Q8#120212yes—
247C2×D4—151no—
248C2×D4—301no—
249C22×C4—301no—
250C22×C4#120312yes—
251C22×C4C2×D3×D511yescharacteristic
252M16—102no—
253M16—102no—
254C2×C8—102no—
255C4⋊C4—64no—
256C4⋊C4—62no—
257C4⋊C4—304no—
258C4⋊C4—301no—
259C22⋊C4—62no—
260C22⋊C4—301no—
261C22⋊C4—304no—
262C42—34no—
263C42—64no—
264C42—152no—
265C3×C5#191211yescharacteristic, complemented, Hall
266C22×C3—41no—
267C22×C3C2×#68511yescharacteristic
268C22×C3#407511yescharacteristic
269C22×C3#409911yescharacteristic
270C2×D3—202no—
271C2×D3—201no—
272C3×C4—24no—
273C3×C4C4×C22⋊D512yes—
274C3×C4#407612yes—
275Dic3—44no—
276Dic3—202no—
277Dic3—201no—
278C2×C5—21no—
279C2×C5—21no—
280C2×C5—21no—
281C2×C5#495811yescharacteristic
282D5—241no—
283C23—301no—
284C23C2×#120311yescharacteristic
285Q8—24no—
286Q8—24no—
287Q8—302no—
288D4—302no—
289D4—601no—
290D4—601no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—64no—
294C2×C4—302no—
295C2×C4—301no—
296C2×C4—602no—
297C2×C4#666714yes—
298C2×C4#677912yes—
299C2×C4C2×#120011yescharacteristic
300C2×C4C2×#120211yescharacteristic
301C2×C4D3×C22⋊D512yes—
302C8—202no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3#6550211yescharacteristic
307D3—401no—
308C5#7010511yescharacteristic, complemented, Sylow
309C22—41no—
310C22—602no—
311C22—601no—
312C22C2×#666711yescharacteristic
313C22#9154211yescharacteristic
314C22#9157011yescharacteristic
315C4—24no—
316C4—124no—
317C4—602no—
318C4—601no—
319C4#9155612yes—
320C4#9156912yes—
321C3#1060245611yescharacteristic, complemented, Sylow
322C2—21no—
323C2—21no—
324C2—21no—
325C2—1201no—
326C2#1174949811yescharacteristic
subgroupG/H
centerC2#11749498
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC2×C3×C5#386
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1912
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5812C2semidirect
3. C2×C3×#3968C2semidirect
5. #11745971C2semidirect
9. #91836C4semidirect
11. #91833C4semidirect
23. C2×#3968D3semidirect
52. #5812D5semidirect
265. C3×C5#1912semidirect
308. C5#70105semidirect
321. C3#10602456semidirect

Maximal subgroups

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

subgroupindex
#117565752
C5×#58122
C2×C3×#39682
#117484282
#117459712
#106024563
#701055