Finite Group Databasebeta

← #14308910

Subgroups — #14308910

Order 1920.

564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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, complemented
2C3×C5×#390C211yesmaximal, characteristic
3#11751316C212yesmaximal
4#11746351C211yesmaximal, characteristic, complemented
5#11746344C212yesmaximal, complemented
6#10600436—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×C3×C5×C22⋊C4—22no—
10C2×C3×C42×C5C2211yescharacteristic
11#91815C2212yes—
12#91813—22no—
13C2×#6710C2212yes—
14#91779—22no—
15#91777—22no—
16#91116—22no—
17#91116—22no—
18#69643—51nomaximal, Hall
19#65834—31no—
20C5×#390D311yescharacteristic
21#65504—32no—
22#64750—31no—
23#64743—32no—
24C24×C3×C5—21no—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—21no—
28C2×C3×C5×D4Q812yescomplemented
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D412yes—
31C22×C3×C4×C5C2311yescharacteristic
32C2×Dic30—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C22⋊C4—44no—
35C3×C42×C5—22no—
36#6719—22no—
37C4⋊Dic15—22no—
38C4⋊Dic15D412yes—
39C4⋊Dic15D412yes—
40#6712—24no—
41C4×Dic15—22no—
42#6710—22no—
43#6710—22no—
44C2×C3⋊#168—22no—
45#5500—51no—
46C3×#390D511yescharacteristic
47#5215—52no—
48#4530—51no—
49#4523—52no—
50C22×C5×D4C2×D311yescharacteristic
51C2×C5×C4⋊C4C2×D311yescharacteristic
52C2×C5×C22⋊C4—22no—
53C2×C42×C5C2×D311yescharacteristic
54#4072—32no—
55#4070—62no—
56C2×#681—32no—
57#4036—62no—
58#4034—62no—
59#3964—62no—
60#3964—62no—
61#2027—151noSylow
62C23×C3×C5—22no—
63C23×C3×C5—42no—
64C23×C3×C5—42no—
65C23×C3×C5—41no—
66C23×C3×C5—41no—
67C23×C3×C5C2×D411yescharacteristic
68C3×C5×D4—24no—
69C3×C5×D4—42no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—42no—
75C2×C3×C4×C5C2×D412yes—
76C2×C3×C4×C5C2×Q811yescharacteristic
77C2×C3×C4×C5#4112yes—
78C2×C3×C4×C5#4111yescharacteristic
79C2×Dic15—22no—
80C2×Dic15—22no—
81Dic30—82no—
82C3⋊#168—42no—
83C22×C3×D4C2×D511yescharacteristic
84C2×C3×C4⋊C4C2×D511yescharacteristic
85C2×C3×C22⋊C4—22no—
86C2×C3×C42C2×D511yescharacteristic
87#926—52no—
88#924—102no—
89C2×#208—52no—
90#890—102no—
91#888—102no—
92#832—102no—
93#832—102no—
94C24×C5—21no—
95C2×C5×D4—21no—
96C2×C5×D4—22no—
97C2×C5×D4—22no—
98C2×C5×D4Dic612yescomplemented
99C22×C4×C5—21no—
100C22×C4×C5#6712yes—
101C22×C4×C5C22×D311yescharacteristic
102C2×Dic10—62no—
103C5×C4⋊C4—22no—
104C5×C22⋊C4—44no—
105C42×C5—22no—
106C22⋊Dic5—62no—
107C4⋊Dic5—32no—
108C4⋊Dic5—32no—
109C4⋊Dic5—62no—
110#683—64no—
111C4×Dic5—62no—
112#681—62no—
113#681—62no—
114C2×#168—62no—
115#544—151no—
116#418—152no—
117#390D1511yescharacteristic
118#343—151no—
119#339—152no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5—44no—
123C22×C3×C5—42no—
124C22×C3×C5—82no—
125C22×C3×C5—81no—
126C22×C3×C5—81no—
127C22×C3×C5#12011yescharacteristic
128C22×C3×C5C22⋊Q811yescharacteristic
129C22×C3×C5#12411yescharacteristic
130C3×C4×C5—42no—
131C3×C4×C5—42no—
132C3×C4×C5C22⋊Q812yes—
133C3×C4×C5#12412yes—
134Dic15—42no—
135Dic15—42no—
136C24×C3—21no—
137C2×C3×D4—21no—
138C2×C3×D4—22no—
139C2×C3×D4—22no—
140C2×C3×D4Dic1012yescomplemented
141C22×C3×C4—21no—
142C22×C3×C4C22⋊D512yes—
143C22×C3×C4C22×D511yescharacteristic
144C2×Dic6—102no—
145C3×C4⋊C4—22no—
146C3×C22⋊C4—44no—
147C3×C42—22no—
148#217—102no—
149C4⋊Dic3—52no—
150C4⋊Dic3—52no—
151C4⋊Dic3—102no—
152Dic3⋊C4—104no—
153C4×Dic3—102no—
154#208—102no—
155#208—102no—
156C2×C3⋊C8—102no—
157C23×C5—22no—
158C23×C5—42no—
159C23×C5—42no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5C2×#6711yescharacteristic
163C5×D4—24no—
164C5×D4—42no—
165C2×C4×C5—22no—
166C2×C4×C5—22no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—42no—
170C2×C4×C5C2×Dic611yescharacteristic
171C2×C4×C5#23511yescharacteristic
172C2×C4×C5D3×D412yes—
173C2×C4×C5#23712yes—
174C2×Dic5—62no—
175C2×Dic5—62no—
176Dic10—242no—
177#168—122no—
178C22×D4C2×D1511yescharacteristic
179C2×M16—152no—
180C4⋊Q8—302no—
181#125—302no—
182C22⋊Q8—302no—
183#117—152no—
184C2×C4⋊C4C2×D1511yescharacteristic
185C2×C22⋊C4—22no—
186C2×C42C2×D1511yescharacteristic
187#102—302no—
188#102—302no—
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5—82no—
192C2×C3×C5#39311yescharacteristic
193C2×C3×C5#45311yescharacteristic
194C2×C3×C5#45411yescharacteristic
195C23×C3—22no—
196C23×C3—42no—
197C23×C3—42no—
198C23×C3—41no—
199C23×C3—41no—
200C23×C3C2×C22⋊D511yescharacteristic
201C3×D4—24no—
202C3×D4—42no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—42no—
208C2×C3×C4C2×Dic1011yescharacteristic
209C2×C3×C4#70911yescharacteristic
210C2×C3×C4D4×D512yes—
211C2×C3×C4#71112yes—
212C2×Dic3—102no—
213C2×Dic3—102no—
214Dic6—402no—
215C3⋊C8—202no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—44no—
219C22×C5—42no—
220C22×C5—82no—
221C22×C5—81no—
222C22×C5—81no—
223C22×C5#92411yescharacteristic
224C22×C5#93611yescharacteristic
225C22×C5#93711yescharacteristic
226C4×C5—42no—
227C4×C5—42no—
228C4×C5#87812yes—
229C4×C5#88512yes—
230Dic5—122no—
231Dic5—122no—
232C24—21no—
233C2×Q8—302no—
234C2×D4—21no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4Dic3012yescomplemented
238C22×C4—21no—
239C22×C4#122012yes—
240C22×C4C22×D1511yescharacteristic
241M16—302no—
242M16—302no—
243C2×C8—302no—
244C4⋊C4—22no—
245C4⋊C4—152no—
246C4⋊C4—152no—
247C4⋊C4—302no—
248C4⋊C4—304no—
249C22⋊C4—44no—
250C22⋊C4—302no—
251C42—22no—
252C42—302no—
253C3×C5#202711yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—44no—
257C22×C3—42no—
258C22×C3—82no—
259C22×C3—81no—
260C22×C3—81no—
261C22×C3#407011yescharacteristic
262C22×C3#408211yescharacteristic
263C22×C3#408311yescharacteristic
264C3×C4—42no—
265C3×C4—42no—
266C3×C4#402412yes—
267C3×C4#403112yes—
268Dic3—202no—
269Dic3—202no—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5—82no—
273C2×C5#494711yescharacteristic
274C2×C5#506211yescharacteristic
275C2×C5#507711yescharacteristic
276C23—22no—
277C23—42no—
278C23—42no—
279C23—41no—
280C23—41no—
281C23C2×#122011yescharacteristic
282Q8—1202no—
283D4—24no—
284D4—42no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—302no—
291C2×C4—302no—
292C2×C4C2×Dic3011yescharacteristic
293C2×C4#681711yescharacteristic
294C2×C4D4×D1512yes—
295C2×C4#681912yes—
296C8—602no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—82no—
300C2×C3#6523611yescharacteristic
301C2×C3#6535111yescharacteristic
302C2×C3#6536611yescharacteristic
303C5#6964311yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—44no—
307C22—42no—
308C22—82no—
309C22—81no—
310C22—81no—
311C22#9181311yescharacteristic
312C22#9182511yescharacteristic
313C22#9182611yescharacteristic
314C4—42no—
315C4—42no—
316C4—602no—
317C4—602no—
318C4#9176712yes—
319C4#9177412yes—
320C3#1060043611yescharacteristic, complemented, Sylow
321C2—21no—
322C2—21no—
323C2—82no—
324C2#1175104811yescharacteristic
325C2#1175116311yescharacteristic
326C2#1175117811yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#390C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
hypercenter#390D15
hypocenterC3×C5#2027
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #11756259C2semidirect
4. #11746351C2semidirect
5. #11746344C2semidirect
28. C2×C3×C5×D4Q8semidirect
98. C2×C5×D4Dic6semidirect
140. C2×C3×D4Dic10semidirect
237. C2×D4Dic30semidirect
253. C3×C5#2027semidirect
303. C5#69643semidirect
320. C3#10600436semidirect

Maximal subgroups

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

subgroupindex
#117562592
C3×C5×#3902
#117513162
#117463512
#117463442
#106004363
#696435