Finite Group Databasebeta

← #14295521

Subgroups — #14295521

Order 1920.

568 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 137 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×#91992C211yesmaximal, characteristic
2#11752444C211yesmaximal, characteristic
3#11752387C212yesmaximal, complemented
4C3×#65040C211yesmaximal, characteristic
5#11746773C212yesmaximal, complemented
6#10603932—31nomaximal, Hall
7C2×C3×#713C2211yescharacteristic
8#91992—22no—
9#91992—22no—
10#91989C2212yes—
11C2×#6758C412yescomplemented
12C2×#6758C2211yescharacteristic
13C2×D5⋊(C3⋊C8)C412yescomplemented
14C2×D5⋊(C3⋊C8)C2211yescharacteristic
15C3×D5×M16C2212yes—
16#91228C414yes—
17#91221—22no—
18C8×ΓL(1,𝔽16)—22no—
19C3×C5×#101C411yescharacteristic, complemented
20C3×#3968C411yescharacteristic, complemented
21C3×#3955C412yescomplemented
22#70133—51nomaximal, Hall
23C2×#4133—31no—
24#65785—31no—
25#65728—32no—
26#65040D311yescharacteristic
27#64902—32no—
28C2×C3×C5×Q8C2×C411yescharacteristic
29C3×#713—22no—
30C3×#713—22no—
31C2×C3×D20C2×C412yes—
32C2×C3×D20C2×C411yescharacteristic
33C2×C3×C4×D5C2×C412yes—
34C2×C3×C4×D5C2311yescharacteristic
35#6763C2×C414yes—
36C2×C3⋊#170C2×C412yes—
37C2×C3⋊#170C2×C411yescharacteristic
38C2×C3⋊#170C2×C411yescharacteristic
39C4⋊ΓL(1,𝔽16)—22no—
40C4×ΓL(1,𝔽16)—22no—
41#6758—22no—
42#6758—24no—
43D5⋊(C3⋊C8)—22no—
44D5⋊(C3⋊C8)—22no—
45D5⋊(C3⋊C8)D412yes—
46D5⋊(C3⋊C8)D412yes—
47C3×C5×M16C2×C412yes—
48C3×#681C2×C412yes—
49C3×#676—22no—
50C3×C8×D5—22no—
51C2×#948—51no—
52C3×#413—51no—
53#5240—51no—
54#5122—52no—
55#4559—52no—
56C2×#713C2×D311yescharacteristic
57#4133—62no—
58#4133—62no—
59#4130—32no—
60C2×#700—32no—
61C2×#700—31no—
62C2×D5⋊C8—31no—
63C2×D5⋊C8—32no—
64D5×M16C2×D312yes—
65#3999—34no—
66#3992—62no—
67C8×AGL(1,𝔽5)—62no—
68C5×#101Dic311yescharacteristic, complemented
69#3968Dic311yescharacteristic, complemented
70#3955Dic312yescomplemented
71#1757—151noSylow
72C22×C3×D5C4212yes—
73C22×C3×D5C22×C411yescharacteristic
74C2×ΓL(1,𝔽16)—24no—
75C3×C5×Q8—22no—
76C2×C3×C4×C5C4212yes—
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×C3×Dic5C22×C411yescharacteristic
79C3×D20—24no—
80C3×D20—22no—
81C3×C4×D5—22no—
82C3×C4×D5—22no—
83C3×C4×D5C2×D412yes—
84C3×C4×D5#4112yes—
85C3⋊#170—22no—
86C3⋊#170C22⋊C411yescharacteristic
87C3⋊#170C22⋊C411yescharacteristic
88C3⋊#170C22⋊C412yes—
89C3×C5×C8—22no—
90C3×#168—22no—
91C2×C3×#41—51no—
92C2×C3×M16—52no—
93#948—102no—
94#948—102no—
95#926—52no—
96C2×#208—52no—
97C2×#208—51no—
98C22×C3⋊C8—51no—
99C22×C3⋊C8—52no—
100C3×#101—51no—
101C3×#101AGL(1,𝔽5)11yescharacteristic, complemented
102C3×#100—52no—
103#834—54no—
104#815—102no—
105C8×Dic3—102no—
106C2×C5×Q8C2×Dic311yescharacteristic
107#713—22no—
108#713—22no—
109C2×D20C4×D312yes—
110C2×D20C2×Dic311yescharacteristic
111C2×C4×D5C4×D312yes—
112C2×C4×D5C22×D311yescharacteristic
113C22⋊AGL(1,𝔽5)—34no—
114C2×#170—31no—
115C2×#170—31no—
116C2×#170—32no—
117C4⋊AGL(1,𝔽5)—62no—
118C4×AGL(1,𝔽5)—62no—
119#700—64no—
120#700—62no—
121D5⋊C8—32no—
122D5⋊C8—32no—
123D5⋊C8—62no—
124D5⋊C8—62no—
125C5×M16C2×Dic312yes—
126#681C2×Dic312yes—
127#676—22no—
128C8×D5—22no—
129C2×#131—151no—
130#413—51no—
131#410—151no—
132#405—152no—
133#344—152no—
134C22×C3×C5C2×C4211yescharacteristic
135C2×C3×D5—22no—
136C2×C3×D5—41no—
137C2×C3×D5—42no—
138C2×C3×D5C4×D412yes—
139ΓL(1,𝔽16)—44no—
140C3×C4×C5—22no—
141C3×C4×C5C4×D412yes—
142C3×Dic5C2×C22⋊C411yescharacteristic
143C3×Dic5#11711yescharacteristic
144C3×#41—102no—
145C3×#41—102no—
146C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
147C2×C3×D4—52no—
148C2×C3×D4—51no—
149C22×C3×C4—51no—
150C22×C3×C4—52no—
151C3×M16—52no—
152C3×M16—102no—
153C3×M16C2×AGL(1,𝔽5)12yes—
154C2×C3×C8—102no—
155#217—54no—
156C4⋊Dic3—102no—
157C4×Dic3—102no—
158#208—104no—
159#208—102no—
160C2×C3⋊C8—52no—
161C2×C3⋊C8—52no—
162C2×C3⋊C8—51no—
163C2×C3⋊C8—51no—
164C2×C3⋊C8—52no—
165C2×C3⋊C8—102no—
166C2×C3⋊C8—102no—
167C22×D5C4×Dic312yes—
168C22×D5C2×C4×D311yescharacteristic
169C2×AGL(1,𝔽5)—64no—
170C5×Q8—22no—
171C2×C4×C5C4×Dic312yes—
172C2×C4×C5C22×Dic311yescharacteristic
173C2×Dic5C2×C4×D311yescharacteristic
174D20—24no—
175D20—22no—
176C4×D5—22no—
177C4×D5—22no—
178C4×D5D3×D412yes—
179C4×D5#23712yes—
180#170—31no—
181#170—31no—
182#170—32no—
183#170—62no—
184C5×C8—22no—
185#168—22no—
186C2×#41—51no—
187#131—302no—
188#131—302no—
189C2×M16—52no—
190C2×M16—151no—
191C2×M16—152no—
192C22×C8—151no—
193C22×C8—152no—
194#117—152no—
195#101—51no—
196#101ΓL(1,𝔽16)11yescharacteristic, complemented
197#100—52no—
198#99—154no—
199#97—302no—
200C4×C8—302no—
201C2×C3×C5—21no—
202C2×C3×C5C4×C22⋊C411yescharacteristic
203C3×D5—22no—
204C3×D5—42no—
205C23×C3—51no—
206C23×C3—52no—
207C3×Q8—22no—
208C3×D4—104no—
209C3×D4—102no—
210C2×C3×C4—51no—
211C2×C3×C4—52no—
212C2×C3×C4—52no—
213C2×C3×C4—102no—
214C2×C3×C4—102no—
215C2×C3×C4C4×AGL(1,𝔽5)12yes—
216C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
217C2×Dic3—104no—
218C3×C8—22no—
219C3×C8—102no—
220C3⋊C8—51no—
221C3⋊C8—51no—
222C3⋊C8—52no—
223C3⋊C8—102no—
224C22×C5C2×C4×Dic311yescharacteristic
225C2×D5—22no—
226C2×D5—41no—
227C2×D5—42no—
228C2×D5#67⋊C412yes—
229AGL(1,𝔽5)—124no—
230C4×C5—22no—
231C4×C5D4×Dic312yes—
232Dic5#87711yescharacteristic
233Dic5D3×C22⋊C411yescharacteristic
234#41—102no—
235#41—102no—
236C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
237C2×D4—52no—
238C2×D4—51no—
239C22×C4—51no—
240C22×C4—52no—
241M16—52no—
242M16—102no—
243M16—304no—
244M16—302no—
245M16C2×ΓL(1,𝔽16)12yes—
246C2×C8—102no—
247C2×C8—152no—
248C2×C8—152no—
249C2×C8—151no—
250C2×C8—151no—
251C2×C8—152no—
252C2×C8—302no—
253C2×C8—302no—
254C4⋊C4—302no—
255C22⋊C4—154no—
256C42—302no—
257C3×C5#175711yescharacteristic, complemented, Hall
258C22×C3—52no—
259C22×C3—102no—
260C22×C3—201no—
261C22×C3—202no—
262C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
263C3×C4—22no—
264C3×C4—51no—
265C3×C4—51no—
266C3×C4D4×AGL(1,𝔽5)12yes—
267Dic3—204no—
268C2×C5—21no—
269C2×C5Dic3×C22⋊C411yescharacteristic
270D5—22no—
271D5—42no—
272C23—51no—
273C23—52no—
274Q8—22no—
275D4—104no—
276D4—102no—
277C2×C4—51no—
278C2×C4—52no—
279C2×C4—52no—
280C2×C4—102no—
281C2×C4—102no—
282C2×C4—304no—
283C2×C4C4×ΓL(1,𝔽16)12yes—
284C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
285C8—22no—
286C8—102no—
287C8—151no—
288C8—151no—
289C8—152no—
290C8—302no—
291C2×C3—21no—
292C2×C3—102no—
293C2×C3—202no—
294C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
295C5#7013311yescharacteristic, complemented, Sylow
296C22—52no—
297C22—102no—
298C22—201no—
299C22—202no—
300C22C2×C4×ΓL(1,𝔽16)11yescharacteristic
301C4—22no—
302C4—51no—
303C4—51no—
304C4—604no—
305C4D4×ΓL(1,𝔽16)12yes—
306C3#1060393211yescharacteristic, complemented, Sylow
307C2—21no—
308C2—102no—
309C2—202no—
310C2C22⋊C4×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
centerC2C22⋊C4×ΓL(1,𝔽16)
commutatorC22×C3×C5C2×C42
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#101C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC2×C3×#713C22
cosocleC2×C3×C4×D5C23
hypercenter#101ΓL(1,𝔽16)
hypocenterC3×C5#1757
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
3. #11752387C2semidirect
5. #11746773C2semidirect
11. C2×#6758C4semidirect
13. C2×D5⋊(C3⋊C8)C4semidirect
19. C3×C5×#101C4semidirect
20. C3×#3968C4semidirect
21. C3×#3955C4semidirect
68. C5×#101Dic3semidirect
69. #3968Dic3semidirect
70. #3955Dic3semidirect
101. C3×#101AGL(1,𝔽5)semidirect
196. #101ΓL(1,𝔽16)semidirect
257. C3×C5#1757semidirect
295. C5#70133semidirect
306. C3#10603932semidirect

Maximal subgroups

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

subgroupindex
C2×#919922
#117524442
#117523872
C3×#650402
#117467732
#106039323
#701335