Finite Group Databasebeta

← #14316876

Subgroups — #14316876

Order 1920.

452 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 67 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#11756431C211yesmaximal, characteristic, complemented
2C3×C5×#455C211yesmaximal, characteristic
3#11751344C212yesmaximal
4#11746362C211yesmaximal, characteristic, complemented
5#11746297C212yesmaximal, complemented
6#10601785—31nomaximal, Hall
7C3×C5×H(5,𝔽2)C2211yescharacteristic
8C3×C5×#137—21no—
9C3×C5×#124C2211yescharacteristic
10#91833—21no—
11#91824—22no—
12#91824C2212yes—
13#91768—22no—
14#91767—22no—
15#91759—21no—
16C3×C5×#104—21no—
17C3×C5×#100C2211yescharacteristic
18#91118—22no—
19#91118C2212yes—
20#70992—51nomaximal, Hall
21#66006—31no—
22C5×#455D311yescharacteristic
23#65532—32no—
24#64761—31no—
25#64696—32no—
26C3×C5×#41—21no—
27C3×C5×#41—41no—
28C2×C3×C5×Q8D411yescharacteristic
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—41no—
31C2×C3×C5×D4C2311yescharacteristic
32C22×Dic15D412yes—
33C2×Dic30—21no—
34C3×C5×Q16—41no—
35C3×C5×SD16—41no—
36C3×C5×M16—21no—
37C3×C5×C22⋊C4—22no—
38C3×C42×C5D411yescharacteristic
39#6719—22no—
40#6719—22no—
41#6719—42no—
42#6719D412yes—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45#6712—22no—
46#6712—22no—
47#6712—22no—
48#6712—42no—
49C4×Dic15—21no—
50#5672—51no—
51C3×#455D511yescharacteristic
52#5243—52no—
53#4541—51no—
54#4476—52no—
55C5×H(5,𝔽2)C2×D311yescharacteristic
56C5×#137—21no—
57C5×#124C2×D311yescharacteristic
58#4090—61no—
59#4081—32no—
60#4081—62no—
61#4025—62no—
62#4024—62no—
63#4016—61no—
64C5×#104—21no—
65C5×#100C2×D311yescharacteristic
66#3966—32no—
67#3966—62no—
68#2201—151noSylow
69C23×C3×C5—22no—
70C23×C3×C5C2×D412yes—
71C3×C5×Q8—21no—
72C3×C5×Q8—41no—
73C3×C5×D4—21no—
74C3×C5×D4—41no—
75C3×C5×D4—42no—
76C3×C5×D4—41no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×Dic15—22no—
83C2×Dic15—22no—
84C2×Dic15—42no—
85C2×Dic15—42no—
86Dic30—81no—
87C3×C5×C8—41no—
88C3×H(5,𝔽2)C2×D511yescharacteristic
89C3×#137—21no—
90C3×#124C2×D511yescharacteristic
91#944—101no—
92#935—52no—
93#935—102no—
94#879—102no—
95#878—102no—
96#870—101no—
97C3×#104—21no—
98C3×#100C2×D511yescharacteristic
99#834—52no—
100#834—102no—
101C5×#41—21no—
102C5×#41—41no—
103C2×C5×Q8#6711yescharacteristic
104C2×C5×D4—22no—
105C2×C5×D4—41no—
106C2×C5×D4C22×D311yescharacteristic
107C22×Dic5—32no—
108C2×Dic10—61no—
109C5×Q16—41no—
110C5×SD16—41no—
111C5×M16—21no—
112C5×C22⋊C4—22no—
113C42×C5#6711yescharacteristic
114C22⋊Dic5—32no—
115C22⋊Dic5—62no—
116C22⋊Dic5—62no—
117C22⋊Dic5—122no—
118C4⋊Dic5—61no—
119C4⋊Dic5—61no—
120#683—62no—
121#683—62no—
122#683—62no—
123#683—122no—
124C4×Dic5—61no—
125#563—151no—
126#458—152no—
127#455D1511yescharacteristic
128#354—151no—
129#352—152no—
130C22×C3×C5—22no—
131C22×C3×C5—42no—
132C22×C3×C5—41no—
133C22×C3×C5—82no—
134C22×C3×C5#12011yescharacteristic
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138C3×C4×C5—41no—
139Dic15—42no—
140Dic15—42no—
141Dic15—82no—
142C3×#41—21no—
143C3×#41—41no—
144C2×C3×Q8C22⋊D511yescharacteristic
145C2×C3×D4—22no—
146C2×C3×D4—41no—
147C2×C3×D4C22×D511yescharacteristic
148C22×Dic3—52no—
149C2×Dic6—101no—
150C3×Q16—41no—
151C3×SD16—41no—
152C3×M16—21no—
153C3×C22⋊C4—22no—
154C3×C42C22⋊D511yescharacteristic
155#217—52no—
156#217—102no—
157#217—102no—
158#217—202no—
159C4⋊Dic3—101no—
160C4⋊Dic3—101no—
161Dic3⋊C4—102no—
162Dic3⋊C4—102no—
163Dic3⋊C4—102no—
164Dic3⋊C4—202no—
165C4×Dic3—101no—
166C23×C5—22no—
167C23×C5D3×D412yes—
168C5×Q8—21no—
169C5×Q8—41no—
170C5×D4—21no—
171C5×D4—41no—
172C5×D4—42no—
173C5×D4—41no—
174C2×C4×C5—22no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—41no—
178C2×C4×C5C2×#6711yescharacteristic
179C2×Dic5—62no—
180C2×Dic5—62no—
181C2×Dic5—122no—
182C2×Dic5—122no—
183Dic10—241no—
184C5×C8—41no—
185H(5,𝔽2)C2×D1511yescharacteristic
186#137—21no—
187C4⋊Q8—301no—
188#126—302no—
189#125—301no—
190#124C2×D1511yescharacteristic
191#123—152no—
192#123—302no—
193C22⋊Q8—302no—
194#104—21no—
195#100C2×D1511yescharacteristic
196#99—152no—
197#99—302no—
198C2×C3×C5—21no—
199C2×C3×C5—42no—
200C2×C3×C5—81no—
201C2×C3×C5B(4,𝔽2)11yescharacteristic
202C23×C3—22no—
203C23×C3D4×D512yes—
204C3×Q8—21no—
205C3×Q8—41no—
206C3×D4—21no—
207C3×D4—41no—
208C3×D4—42no—
209C3×D4—41no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—41no—
214C2×C3×C4C2×C22⋊D511yescharacteristic
215C2×Dic3—102no—
216C2×Dic3—102no—
217C2×Dic3—202no—
218C2×Dic3—202no—
219Dic6—401no—
220C3×C8—41no—
221C22×C5—22no—
222C22×C5—42no—
223C22×C5—41no—
224C22×C5—82no—
225C22×C5#93711yescharacteristic
226C4×C5—21no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—41no—
230Dic5—122no—
231Dic5—122no—
232Dic5—242no—
233#41—21no—
234#41—41no—
235C2×Q8—301no—
236C2×Q8#122011yescharacteristic
237C2×D4—22no—
238C2×D4—41no—
239C2×D4C22×D1511yescharacteristic
240C22×C4—152no—
241Q16—41no—
242SD16—41no—
243M16—21no—
244C4⋊C4—301no—
245C4⋊C4—302no—
246C4⋊C4—302no—
247C4⋊C4—301no—
248C4⋊C4—302no—
249C4⋊C4—602no—
250C22⋊C4—22no—
251C22⋊C4—152no—
252C22⋊C4—302no—
253C22⋊C4—302no—
254C22⋊C4—602no—
255C42—301no—
256C42#122011yescharacteristic
257C3×C5#220111yescharacteristic, complemented, Hall
258C22×C3—22no—
259C22×C3—42no—
260C22×C3—41no—
261C22×C3—82no—
262C22×C3#408311yescharacteristic
263C3×C4—21no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—41no—
267Dic3—202no—
268Dic3—202no—
269Dic3—402no—
270C2×C5—21no—
271C2×C5—42no—
272C2×C5—81no—
273C2×C5#503211yescharacteristic
274C23—22no—
275C23D4×D1512yes—
276Q8—21no—
277Q8—41no—
278Q8—1201no—
279D4—21no—
280D4—41no—
281D4—42no—
282D4—41no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—302no—
288C2×C4—302no—
289C2×C4—602no—
290C2×C4—602no—
291C2×C4C2×#122011yescharacteristic
292C8—41no—
293C2×C3—21no—
294C2×C3—42no—
295C2×C3—81no—
296C2×C3#6532111yescharacteristic
297C5#7099211yescharacteristic, complemented, Sylow
298C22—22no—
299C22—42no—
300C22—41no—
301C22—82no—
302C22#9182611yescharacteristic
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—602no—
308C4—602no—
309C4—1202no—
310C3#1060178511yescharacteristic, complemented, Sylow
311C2—21no—
312C2—42no—
313C2—81no—
314C2#1175113311yescharacteristic
subgroupG/H
centerC2#11751133
commutator, cosocleC2×C3×C5×D4C23
FrattiniC2×D4C22×D15
FittingC3×C5×#455C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×C5×H(5,𝔽2)C22
hypercenter#455D15
hypocenterC3×C5#2201
LCSG ▷ C2×C3×C5×D4 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #11756431C2semidirect
4. #11746362C2semidirect
5. #11746297C2semidirect
257. C3×C5#2201semidirect
297. C5#70992semidirect
310. C3#10601785semidirect

Maximal subgroups

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

subgroupindex
#117564312
C3×C5×#4552
#117513442
#117463622
#117462972
#106017853
#709925