Finite Group Databasebeta

← #14302961

Subgroups — #14302961

Order 1920.

628 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 152 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#11756571C211yesmaximal, characteristic, complemented
2C5×#5816C211yesmaximal, characteristic
3C2×C3×#3968C211yesmaximal, characteristic, complemented
4#11748424C212yesmaximal
5#11745971C212yesmaximal, complemented
6#10602657—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C5×#235C2211yescharacteristic
9Q8×Dic15—24no—
10#91815—22no—
11#91815C2212yes—
12C5×#947C412yescomplemented
13C5×#946—22no—
14C5×#944C412yescomplemented
15C5×#929—22no—
16C5×#926C2211yescharacteristic
17C2×C3×#681C2212yes—
18C3×#3968—22no—
19#90978—24no—
20#70105—51nomaximal, Hall
21C5×#536—31no—
22#66146—31no—
23#65525—32no—
24C2×#3968D311yescharacteristic, complemented
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×C5×#67—21no—
33C5×#235—22no—
34C5×#235—22no—
35C2×C5×D12C2×C411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6C2×C411yescharacteristic
38#6719—22no—
39C4⋊Dic15—24no—
40C4⋊Dic15—22no—
41C4×Dic15—24no—
42C4×Dic15D414yes—
43C5×#217—21no—
44C5×(C2×D3)⋊C4—24no—
45C5×C4⋊Dic3—21no—
46C5×Dic3⋊C4—24no—
47C4×C5×Dic3C2×C412yes—
48C3×#681—22no—
49C3×#681—22no—
50C2×C3×#168—22no—
51#5816D511yescharacteristic
52#5812—51no—
53C2×C3×#101—51no—
54#5139—52no—
55#4557—52no—
56C2×C5×#41—31no—
57C22×C5×Q8C2×D311yescharacteristic
58C5×C4⋊Q8—32no—
59C5×#124—32no—
60C5×#123—62no—
61C5×C22⋊Q8—62no—
62C5×#117—31no—
63Q8×Dic5—64no—
64#4072—32no—
65#4072—62no—
66C2×#681C2×D312yes—
67#3969—64no—
68#3968—22no—
69#1912—151noSylow
70C23×C3×C5C2×D411yescharacteristic
71C22×C5×D3—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—
81C2×Dic15—24no—
82C5×#67—41no—
83C5×#67—41no—
84C2×C5×Dic3—22no—
85C2×C5×Dic3—21no—
86C5×D12—22no—
87C4×C5×D3—42no—
88C5×Dic6—22no—
89C3×#168—42no—
90C22×C3×Q8C2×D511yescharacteristic
91C2×#235C2×D511yescharacteristic
92C2×C3×M16—52no—
93#947Dic512yescomplemented
94#946—22no—
95Q8×Dic3—104no—
96#944Dic512yescomplemented
97#929—22no—
98#926—52no—
99#926—102no—
100#926C2×D511yescharacteristic
101C3×#101—102no—
102#825—104no—
103C5×#41—62no—
104C5×#41—62no—
105C2×C5×Q8—22no—
106C2×C5×Q8—22no—
107C2×C5×Q8—31no—
108C2×C5×Q8C4×D312yes—
109C2×C5×Q8#6712yes—
110C2×C5×D4—31no—
111C2×C5×D4—61no—
112C22×C4×C5—61no—
113C22×C4×C5D1212yes—
114C22×C4×C5C22×D311yescharacteristic
115C5×C4⋊C4—64no—
116C5×C4⋊C4—61no—
117C5×C22⋊C4—61no—
118C5×C22⋊C4—64no—
119C42×C5—32no—
120C22⋊Dic5—62no—
121C4⋊Dic5—64no—
122C4⋊Dic5—62no—
123C4×Dic5—34no—
124C4×Dic5—64no—
125#681—22no—
126#681—22no—
127C2×#168—22no—
128#536—31no—
129#519—151no—
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×C5×D3—42no—
138C2×C5×D3—41no—
139C3×C4×C5—24no—
140C3×C4×C5C4×D412yes—
141C3×C4×C5#12112yes—
142Dic15—44no—
143C5×Dic3—42no—
144C5×Dic3—41no—
145C2×C3×Q8—22no—
146C2×C3×Q8—22no—
147C2×C3×Q8C2×Dic512yes—
148C2×C3×Q8C22⋊D512yes—
149C22×C3×C4C22⋊D512yes—
150C22×C3×C4C22×D511yescharacteristic
151C2×#67—21no—
152#235—22no—
153#235—22no—
154C2×D12C2×Dic511yescharacteristic
155C2×C4×D3—21no—
156C2×Dic6C2×Dic511yescharacteristic
157C3×M16—102no—
158C3×M16—102no—
159C2×C3×C8—102no—
160#217—21no—
161#217—102no—
162(C2×D3)⋊C4—24no—
163C4⋊Dic3—21no—
164C4⋊Dic3—104no—
165C4⋊Dic3—102no—
166Dic3⋊C4—24no—
167C4×Dic3—54no—
168C4×Dic3—104no—
169C4×Dic3C2×Dic512yes—
170C23×C5—61no—
171C23×C5C2×D1211yescharacteristic
172C5×Q8—24no—
173C5×Q8—24no—
174C5×Q8—62no—
175C5×D4—62no—
176C5×D4—121no—
177C5×D4—121no—
178C2×C4×C5—22no—
179C2×C4×C5—22no—
180C2×C4×C5—62no—
181C2×C4×C5—61no—
182C2×C4×C5—122no—
183C2×C4×C5(C2×D3)⋊C414yes—
184C2×C4×C5C2×C4×D311yescharacteristic
185C2×C4×C5D3×D412yes—
186C2×C4×C5#23712yes—
187C2×C4×C5C2×#6711yescharacteristic
188C2×Dic5—64no—
189#168—42no—
190C2×#41—31no—
191C22×Q8D3×D511yescharacteristic
192C2×M16—52no—
193C4⋊Q8—32no—
194#124—32no—
195#123—62no—
196C22⋊Q8—62no—
197C4×Q8—304no—
198#117—31no—
199#117—152no—
200#117—302no—
201#104—304no—
202#101—102no—
203C2×C3×C5—21no—
204C2×C3×C5—21no—
205C2×C3×C5—21no—
206C2×C3×C5#38611yescharacteristic
207C5×D3—81no—
208C23×C3C2×C22⋊D511yescharacteristic
209C22×D3—21no—
210C3×Q8—24no—
211C3×Q8—24no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4C22⋊Dic514yes—
215C2×C3×C4D4×D512yes—
216C2×C3×C4#71112yes—
217C2×C3×C4C22×Dic511yescharacteristic
218C2×C3×C4C2×C22⋊D511yescharacteristic
219#67—41no—
220#67—41no—
221C2×Dic3—22no—
222C2×Dic3—21no—
223C2×Dic3—104no—
224D12—22no—
225C4×D3—42no—
226Dic6—22no—
227C3×C8—202no—
228C22×C5—41no—
229C22×C5—122no—
230C22×C5—121no—
231C22×C5#88211yescharacteristic
232C22×C5#88611yescharacteristic
233C22×C5C2×(C2×D3)⋊C411yescharacteristic
234C4×C5—24no—
235C4×C5—122no—
236C4×C5—121no—
237C4×C5#67⋊C412yes—
238C4×C5#93912yes—
239Dic5—124no—
240#41—62no—
241#41—62no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—31no—
245C2×Q8D3×Dic512yes—
246C2×Q8#120112yes—
247C2×D4—31no—
248C2×D4—61no—
249C22×C4—61no—
250C22×C4#120312yes—
251C22×C4C2×D3×D511yescharacteristic
252M16—102no—
253M16—102no—
254C2×C8—102no—
255C4⋊C4—64no—
256C4⋊C4—61no—
257C4⋊C4—304no—
258C4⋊C4—302no—
259C22⋊C4—61no—
260C22⋊C4—64no—
261C22⋊C4—302no—
262C42—32no—
263C42—154no—
264C42—304no—
265C3×C5#191211yescharacteristic, complemented, Hall
266C22×C3—41no—
267C22×C3#408111yescharacteristic
268C22×C3#408311yescharacteristic
269C22×C3C2×C22⋊Dic511yescharacteristic
270C2×D3—42no—
271C2×D3—41no—
272C3×C4—24no—
273C3×C4D4×Dic512yes—
274C3×C4#408512yes—
275Dic3—42no—
276Dic3—41no—
277Dic3—204no—
278C2×C5—21no—
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—241no—
282C2×C5#495811yescharacteristic
283C23—61no—
284C23C2×#120311yescharacteristic
285Q8—24no—
286Q8—24no—
287Q8—62no—
288D4—62no—
289D4—121no—
290D4—121no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—62no—
294C2×C4—61no—
295C2×C4—122no—
296C2×C4—304no—
297C2×C4(C2×D3)⋊Dic514yes—
298C2×C4#678012yes—
299C2×C4C2×D3×Dic511yescharacteristic
300C2×C4C2×#120111yescharacteristic
301C2×C4#679012yes—
302C8—202no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3#6550911yescharacteristic
307D3—81no—
308C5#7010511yescharacteristic, complemented, Sylow
309C22—41no—
310C22—122no—
311C22—121no—
312C22C2×(C2×D3)⋊Dic511yescharacteristic
313C22#9154311yescharacteristic
314C22#9157311yescharacteristic
315C4—24no—
316C4—122no—
317C4—121no—
318C4—604no—
319C4#67⋊Dic512yes—
320C4#9157112yes—
321C3#1060265711yescharacteristic, complemented, Sylow
322C2—21no—
323C2—21no—
324C2—21no—
325C2—241no—
326C2#1174950111yescharacteristic
subgroupG/H
centerC2#11749501
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC2×C3×C5#386
prime radicalC2×C5×#235C22
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
1. #11756571C2semidirect
3. C2×C3×#3968C2semidirect
5. #11745971C2semidirect
12. C5×#947C4semidirect
14. C5×#944C4semidirect
24. C2×#3968D3semidirect
93. #947Dic5semidirect
96. #944Dic5semidirect
265. C3×C5#1912semidirect
308. C5#70105semidirect
321. C3#10602657semidirect

Maximal subgroups

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

subgroupindex
#117565712
C5×#58162
C2×C3×#39682
#117484242
#117459712
#106026573
#701055