Finite Group Databasebeta

← #14282334

Subgroups — #14282334

Order 1920.

504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×C3×#4033C211yesmaximal, characteristic
2#11752418C211yesmaximal, characteristic
3C4×#6762C211yesmaximal, characteristic
4#11746743C214yesmaximal, complemented
5#10604275—31nomaximal, Hall
6C22×C3×Dic10C411yescharacteristic
7C2×#6762—21no—
8C2×C3×C5×C4⋊C4C411yescharacteristic
9C2×C3×#683—21no—
10C2×C3×C4×Dic5—21no—
11C2×C3×C4×Dic5C2211yescharacteristic
12C3×#4033—21no—
13C3×#4033—21no—
14C3×#4033C412yes—
15C3×#4033C2212yes—
16#91241—21no—
17#91231—21no—
18#91231—21no—
19C4⋊(C3⋊#170)C2212yes—
20C4×C3⋊#170C2212yes—
21#71623—51nomaximal, Hall
22C2×#4033D311yescharacteristic
23#65759—31no—
24C4×#704—31no—
25#64872—34no—
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×Dic5—21no—
29C22×C3×Dic5D411yescharacteristic
30C22×C3×Dic5D411yescharacteristic
31C2×C3×Dic10—21no—
32C2×C3×Dic10—24no—
33C2×C3×Dic10C2×C412yes—
34#6762—24no—
35C2×C3⋊#170—22no—
36C2×C3⋊#170—22no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4C2×C412yes—
39C3×#683—22no—
40C3×#683—22no—
41C3×C4×Dic5—22no—
42C3×C4×Dic5—22no—
43C3×C4×Dic5C2×C411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5C2311yescharacteristic
47C2×C3×C4×Q8—51no—
48#4926—51no—
49C4×#208—51no—
50#4535—54no—
51C22×Dic10Dic311yescharacteristic
52C2×#704—61no—
53C2×C5×C4⋊C4Dic311yescharacteristic
54C2×#683—21no—
55C2×C4×Dic5—21no—
56C2×C4×Dic5C2×D311yescharacteristic
57#4033—21no—
58#4033—21no—
59#4033Dic312yes—
60#4033C2×D312yes—
61C22⋊#170—61no—
62#4002—61no—
63#4002—61no—
64C4⋊#170—32no—
65C4×#170—32no—
66#1491—151noSylow
67C23×C3×C5C22⋊C411yescharacteristic
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5—42no—
71C2×C3×C4×C5C22⋊C411yescharacteristic
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×C3×Dic5—24no—
74C2×C3×Dic5—22no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5C22⋊C411yescharacteristic
78C2×C3×Dic5C22⋊C411yescharacteristic
79C2×C3×Dic5C2×D411yescharacteristic
80C2×C3×Dic5C2×D411yescharacteristic
81C3×Dic10—24no—
82C3×Dic10—22no—
83C3×Dic10M1614yescomplemented
84C3⋊#170—24no—
85C3⋊#170—42no—
86C22×C3×Q8—51no—
87C3×C4×Q8—52no—
88C3×C4×Q8—52no—
89C3×C4×Q8—101no—
90C3×C4×Q8—101no—
91C2×C3×C4⋊C4—101no—
92C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
93C2×C3×C42—51no—
94C2×C3×C42—101no—
95C2×#208—101no—
96#830—101no—
97C4⋊(C3⋊C8)—52no—
98#803—101no—
99#803—101no—
100C4×C3⋊C8—52no—
101C22×C4×C5—21no—
102C22×C4×C5C2×Dic311yescharacteristic
103C22×Dic5—21no—
104C22×Dic5#6711yescharacteristic
105C22×Dic5#6711yescharacteristic
106C2×Dic10—21no—
107C2×Dic10—24no—
108C2×Dic10C2×Dic312yes—
109#704—64no—
110C2×#170—62no—
111C2×#170—62no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4C2×Dic312yes—
114#683—22no—
115#683—22no—
116C4×Dic5—22no—
117C4×Dic5—22no—
118C4×Dic5C2×Dic311yescharacteristic
119C4×Dic5#6711yescharacteristic
120C4×Dic5#6711yescharacteristic
121C4×Dic5C22×D311yescharacteristic
122C2×C4×Q8—51no—
123#432—151no—
124C4×M16—151no—
125Q8⋊C8—154no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5#10412yes—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C3×C4×C5—21no—
131C3×C4×C5—42no—
132C3×C4×C5C2×M1612yes—
133C3×Dic5—24no—
134C3×Dic5—21no—
135C3×Dic5—21no—
136C3×Dic5—21no—
137C3×Dic5#13712yes—
138C2×C3×Q8—52no—
139C2×C3×Q8—104no—
140C2×C3×Q8—101no—
141C22×C3×C4—21no—
142C22×C3×C4—51no—
143C22×C3×C4—51no—
144C22×C3×C4—101no—
145C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
146C3×C4⋊C4—21no—
147C3×C4⋊C4—102no—
148C3×C4⋊C4—102no—
149C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
150C3×C42—51no—
151C3×C42—51no—
152C3×C42—51no—
153C3×C42—51no—
154C3×C42—102no—
155C3×C42—102no—
156#208—104no—
157C2×C3⋊C8—102no—
158C2×C3⋊C8—102no—
159C23×C5#21711yescharacteristic
160C2×C4×C5—22no—
161C2×C4×C5—22no—
162C2×C4×C5—42no—
163C2×C4×C5#21711yescharacteristic
164C2×C4×C5C22×Dic311yescharacteristic
165C2×Dic5—24no—
166C2×Dic5—22no—
167C2×Dic5—22no—
168C2×Dic5—22no—
169C2×Dic5#21711yescharacteristic
170C2×Dic5#21711yescharacteristic
171C2×Dic5C2×#6711yescharacteristic
172C2×Dic5C2×#6711yescharacteristic
173Dic10—24no—
174Dic10—22no—
175Dic10#20814yescomplemented
176#170—64no—
177#170—122no—
178C22×Q8—51no—
179C2×M16—301no—
180C4×Q8—52no—
181C4×Q8—52no—
182C4×Q8—101no—
183C4×Q8—101no—
184C2×C4⋊C4—101no—
185C2×C4⋊C4ΓL(1,𝔽16)11yescharacteristic
186C2×C42—51no—
187C2×C42—101no—
188C4⋊C8—152no—
189C22⋊C8—301no—
190#97—301no—
191#97—301no—
192C4×C8—152no—
193C2×C3×C5—22no—
194C2×C3×C5#40711yescharacteristic
195C2×C3×C5#41911yescharacteristic
196C2×C3×C5C2×#10411yescharacteristic
197C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
198C3×Q8—54no—
199C3×Q8—104no—
200C3×Q8—102no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—42no—
204C2×C3×C4—51no—
205C2×C3×C4—51no—
206C2×C3×C4—51no—
207C2×C3×C4—51no—
208C2×C3×C4—102no—
209C2×C3×C4—104no—
210C2×C3×C4—102no—
211C2×C3×C4—102no—
212C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
213C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
214C3⋊C8—104no—
215C3⋊C8—202no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5#83712yes—
219C22×C5C2×#21711yescharacteristic
220C4×C5—21no—
221C4×C5—42no—
222C4×C5C2×#20812yes—
223Dic5—24no—
224Dic5—21no—
225Dic5—21no—
226Dic5—21no—
227Dic5#94212yes—
228C2×Q8—52no—
229C2×Q8—104no—
230C2×Q8—101no—
231C22×C4—21no—
232C22×C4—51no—
233C22×C4—51no—
234C22×C4—101no—
235C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
236M16—304no—
237C2×C8—302no—
238C2×C8—302no—
239C4⋊C4—21no—
240C4⋊C4—102no—
241C4⋊C4—102no—
242C4⋊C4C2×ΓL(1,𝔽16)12yes—
243C42—51no—
244C42—51no—
245C42—51no—
246C42—51no—
247C42—102no—
248C42—102no—
249C3×C5#149111yescharacteristic, complemented, Hall
250C22×C3—21no—
251C22×C3—21no—
252C22×C3#400812yes—
253C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
254C3×C4—21no—
255C3×C4—42no—
256C3×C4—52no—
257C3×C4—104no—
258C3×C4—101no—
259C3×C4—101no—
260C3×C4—101no—
261C3×C4D5⋊M1612yes—
262C2×C5—22no—
263C2×C5#520711yescharacteristic
264C2×C5#522511yescharacteristic
265C2×C5C2×#83711yescharacteristic
266C23#676311yescharacteristic
267Q8—54no—
268Q8—104no—
269Q8—102no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—42no—
273C2×C4—51no—
274C2×C4—51no—
275C2×C4—51no—
276C2×C4—51no—
277C2×C4—102no—
278C2×C4—104no—
279C2×C4—102no—
280C2×C4—102no—
281C2×C4#676311yescharacteristic
282C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
283C8—304no—
284C8—602no—
285C2×C3—22no—
286C2×C3#6575511yescharacteristic
287C2×C3C2×#400811yescharacteristic
288C2×C3#6578211yescharacteristic
289C5#7162311yescharacteristic, complemented, Sylow
290C22—21no—
291C22—21no—
292C22#9123712yes—
293C22C2×#676311yescharacteristic
294C4—21no—
295C4—42no—
296C4—52no—
297C4—104no—
298C4—101no—
299C4—101no—
300C4—101no—
301C4D5⋊#20812yes—
302C3#1060427511yescharacteristic, complemented, Sylow
303C2—22no—
304C2#1175241411yescharacteristic
305C2C2×#9123711yescharacteristic
306C2#1175244111yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1491
LCSG ▷ C2×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
4. #11746743C2semidirect
83. C3×Dic10M16semidirect
175. Dic10#208semidirect
249. C3×C5#1491semidirect
289. C5#71623semidirect
302. C3#10604275semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40332
#117524182
C4×#67622
#117467432
#106042753
#716235