Finite Group Databasebeta

← #14308964

Subgroups — #14308964

Order 1920.

492 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 116 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#11756259C211yesmaximal, characteristic
2C3×#65263C211yesmaximal, characteristic
3#11748400C212yesmaximal
4C5×#4530C211yesmaximal, characteristic
5#11745978C212yesmaximal
6#10599791—31nomaximal, Hall
7C22×C3×Dic10C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9#91815C2212yes—
10#91813—22no—
11#91779—22no—
12#91777—22no—
13C2×C5×#208C2212yes—
14C2×C3×C4×Dic5C2211yescharacteristic
15C3×#3963—22no—
16#90971—22no—
17#90971—22no—
18#69673—51nomaximal, Hall
19#65834—31no—
20#65409—32no—
21#65263D311yescharacteristic
22C5×#343—31no—
23#64775—32no—
24C22×C3×C4×C5D412yes—
25C22×C3×C4×C5C2311yescharacteristic
26C2×Dic30—22no—
27C22×C3×Dic5—21no—
28C22×C3×Dic5—21no—
29C2×C3×Dic10—22no—
30C2×C3×Dic10—22no—
31C2×C3×Dic10—21no—
32C2×C3×Dic10Q812yescomplemented
33C3×C5×C4⋊C4—22no—
34#6719—22no—
35C4⋊Dic15—22no—
36C4⋊Dic15D412yes—
37C4⋊Dic15D412yes—
38#6712—24no—
39C4×Dic15—22no—
40C5×#208—22no—
41C5×#208—22no—
42C2×C5×C3⋊C8—22no—
43C3×C4×Dic5—22no—
44#5500—51no—
45C3×#391—51no—
46#5225—52no—
47#4530D511yescharacteristic
48#4523—52no—
49C22×Dic10C2×D311yescharacteristic
50C2×C5×M16—32no—
51C2×C5×C4⋊C4C2×D311yescharacteristic
52#4072—32no—
53#4070—62no—
54C2×C4×Dic5C2×D311yescharacteristic
55#4036—62no—
56#4034—62no—
57#3963—22no—
58#3948—62no—
59#3948—62no—
60#2028—151noSylow
61C23×C3×C5C2×D411yescharacteristic
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5C2×D412yes—
65C2×C3×C4×C5C2×Q811yescharacteristic
66C2×C3×C4×C5#4112yes—
67C2×C3×C4×C5#4111yescharacteristic
68C2×Dic15—22no—
69C2×Dic15—22no—
70Dic30—82no—
71C2×C3×Dic5—22no—
72C2×C3×Dic5—22no—
73C2×C3×Dic5—41no—
74C2×C3×Dic5—41no—
75C2×C3×Dic5—41no—
76C2×C3×Dic5—41no—
77C3×Dic10—24no—
78C3×Dic10—42no—
79C5×C3⋊C8—42no—
80C22×C3×Q8—51no—
81C2×C3×C4⋊C4C2×D511yescharacteristic
82C2×C3×C42—51no—
83#926—52no—
84#924—102no—
85C2×#208C2×D512yes—
86#890—102no—
87#888—102no—
88C3×#95—102no—
89#835—102no—
90#835—102no—
91C22×C4×C5#6712yes—
92C22×C4×C5C22×D311yescharacteristic
93C22×Dic5—21no—
94C22×Dic5—21no—
95C2×Dic10—22no—
96C2×Dic10—22no—
97C2×Dic10—21no—
98C2×Dic10—62no—
99C2×Dic10Dic612yescomplemented
100C5×M16—62no—
101C5×M16—62no—
102C2×C5×C8—62no—
103C5×C4⋊C4—22no—
104C22⋊Dic5—62no—
105C4⋊Dic5—32no—
106C4⋊Dic5—32no—
107C4⋊Dic5—62no—
108#683—64no—
109C4×Dic5—22no—
110C4×Dic5—62no—
111#544—151no—
112#419—152no—
113#391—51no—
114#343—31no—
115#339—152no—
116C22×C3×C5—21no—
117C22×C3×C5—21no—
118C22×C3×C5#12011yescharacteristic
119C22×C3×C5C22⋊Q811yescharacteristic
120C22×C3×C5#12411yescharacteristic
121C3×C4×C5—42no—
122C3×C4×C5C22⋊Q812yes—
123C3×C4×C5#12412yes—
124Dic15—42no—
125Dic15—42no—
126C3×Dic5—42no—
127C3×Dic5—42no—
128C2×C3×Q8—52no—
129C2×C3×Q8—101no—
130C2×C3×Q8—102no—
131C2×C3×Q8—102no—
132C22×C3×C4—101no—
133C22×C3×C4—101no—
134C22×C3×C4D2012yes—
135C22×C3×C4C22×D511yescharacteristic
136C2×Dic6—102no—
137C3×C4⋊C4—22no—
138C3×C42—102no—
139#217—102no—
140C4⋊Dic3—52no—
141C4⋊Dic3—52no—
142C4⋊Dic3—102no—
143Dic3⋊C4—104no—
144C4×Dic3—102no—
145#208—22no—
146#208—22no—
147C2×C3⋊C8—22no—
148C23×C5C2×#6711yescharacteristic
149C2×C4×C5—22no—
150C2×C4×C5—42no—
151C2×C4×C5C2×Dic611yescharacteristic
152C2×C4×C5#23511yescharacteristic
153C2×C4×C5D3×D412yes—
154C2×C4×C5#23712yes—
155C2×Dic5—22no—
156C2×Dic5—22no—
157C2×Dic5—41no—
158C2×Dic5—41no—
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—62no—
162C2×Dic5—62no—
163Dic10—24no—
164Dic10—42no—
165Dic10—242no—
166C5×C8—122no—
167C22×Q8—51no—
168C2×M16—32no—
169C4⋊Q8—302no—
170#125—302no—
171C22⋊Q8—302no—
172#117—152no—
173C2×C4⋊C4D3×D511yescharacteristic
174C2×C42—51no—
175#103—302no—
176#103—302no—
177#95—102no—
178C2×C3×C5—21no—
179C2×C3×C5—21no—
180C2×C3×C5#39311yescharacteristic
181C2×C3×C5#45511yescharacteristic
182C2×C3×C5#45611yescharacteristic
183C23×C3C2×D2011yescharacteristic
184C3×Q8—104no—
185C3×Q8—202no—
186C2×C3×C4—22no—
187C2×C3×C4—42no—
188C2×C3×C4—102no—
189C2×C3×C4—102no—
190C2×C3×C4—201no—
191C2×C3×C4—201no—
192C2×C3×C4—201no—
193C2×C3×C4—201no—
194C2×C3×C4#70912yes—
195C2×C3×C4D4×D512yes—
196C2×C3×C4#71111yescharacteristic
197C2×C3×C4Q8×D511yescharacteristic
198C2×Dic3—102no—
199C2×Dic3—102no—
200Dic6—402no—
201C3⋊C8—42no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5#92411yescharacteristic
205C22×C5#93611yescharacteristic
206C22×C5#93711yescharacteristic
207C4×C5—42no—
208C4×C5#87812yes—
209C4×C5#88512yes—
210Dic5—42no—
211Dic5—42no—
212Dic5—122no—
213Dic5—122no—
214C2×Q8—52no—
215C2×Q8—101no—
216C2×Q8—102no—
217C2×Q8—102no—
218C2×Q8—302no—
219C22×C4—101no—
220C22×C4—101no—
221C22×C4#120212yes—
222C22×C4C2×D3×D511yescharacteristic
223M16—62no—
224M16—62no—
225C2×C8—62no—
226C4⋊C4—22no—
227C4⋊C4—152no—
228C4⋊C4—152no—
229C4⋊C4—302no—
230C4⋊C4—304no—
231C22⋊C4—302no—
232C42—102no—
233C42—302no—
234C3×C5#202811yescharacteristic, complemented, Hall
235C22×C3—21no—
236C22×C3—21no—
237C22×C3#402111yescharacteristic
238C22×C3#402811yescharacteristic
239C22×C3#404311yescharacteristic
240C3×C4—42no—
241C3×C4—202no—
242C3×C4—202no—
243C3×C4#403112yes—
244C3×C4#404212yes—
245Dic3—202no—
246Dic3—202no—
247C2×C5—21no—
248C2×C5—21no—
249C2×C5#494711yescharacteristic
250C2×C5#506111yescharacteristic
251C2×C5#509511yescharacteristic
252C23C2×#120211yescharacteristic
253Q8—104no—
254Q8—202no—
255Q8—1202no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—102no—
259C2×C4—102no—
260C2×C4—201no—
261C2×C4—201no—
262C2×C4—201no—
263C2×C4—201no—
264C2×C4—302no—
265C2×C4—302no—
266C2×C4D5×Dic611yescharacteristic
267C2×C4#676512yes—
268C2×C4#677211yescharacteristic
269C2×C4#679012yes—
270C8—122no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#6496211yescharacteristic
274C2×C3#6503511yescharacteristic
275C2×C3#6504111yescharacteristic
276C5#6967311yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22#9136011yescharacteristic
280C22#9136411yescharacteristic
281C22#9157211yescharacteristic
282C4—42no—
283C4—202no—
284C4—202no—
285C4—602no—
286C4—602no—
287C4#9143112yes—
288C4#9146212yes—
289C3#1059979111yescharacteristic, complemented, Sylow
290C2—21no—
291C2—21no—
292C2#1174879311yescharacteristic
293C2#1174914911yescharacteristic
294C2#1174939511yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2028
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
32. C2×C3×Dic10Q8semidirect
99. C2×Dic10Dic6semidirect
234. C3×C5#2028semidirect
276. C5#69673semidirect
289. C3#10599791semidirect

Maximal subgroups

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

subgroupindex
#117562592
C3×#652632
#117484002
C5×#45302
#117459782
#105997913
#696735