Finite Group Databasebeta

← #14316901

Subgroups — #14316901

Order 1920.

452 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×#66006C211yesmaximal, characteristic, complemented
2C5×#5061C211yesmaximal, characteristic
3#11749183C212yesmaximal
4#11746362C211yesmaximal, characteristic, complemented
5#11746001C212yesmaximal, complemented
6#10601785—31nomaximal, Hall
7C5×#1004C2211yescharacteristic
8C3×C5×#124C2211yescharacteristic
9C5×#942—21no—
10C3×#4090—21no—
11C3×#4081C2212yes—
12C3×#4025—22no—
13C3×#4024—22no—
14C3×#4016—21no—
15#91539—22no—
16#91118C2212yes—
17C5×#833C2211yescharacteristic
18C5×#805—21no—
19#90996—22no—
20#71958—51nomaximal, Hall
21#66006D311yescharacteristic, complemented
22C5×#455—31no—
23#65532—32no—
24#64761—31no—
25#64696—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4C2311yescharacteristic
28C2×C5×#67—22no—
29C5×#237—41no—
30C5×D3×D4—41no—
31C5×#235—21no—
32C22×C3×Dic5D412yes—
33C2×C3×Dic10—21no—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5D411yescharacteristic
36#6719—22no—
37C5×#216—41no—
38C5×#215—41no—
39C5×#208—21no—
40C3×C22⋊Dic5—22no—
41C3×C22⋊Dic5D412yes—
42C3×C4⋊Dic5—21no—
43C3×C4⋊Dic5—21no—
44C3×#683—22no—
45C3×#683—22no—
46C3×#683—22no—
47C3×C4×Dic5—21no—
48#6669—42no—
49(C2×D3)⋊Dic5—42no—
50C3×#563—51no—
51#5061D511yescharacteristic
52#5053—52no—
53#4541—51no—
54#4539—52no—
55C5×H(5,𝔽2)—31no—
56C5×#137—61no—
57C5×#124C2×D311yescharacteristic
58#4090—21no—
59#4081—62no—
60#4081C2×D312yes—
61#4025—22no—
62#4024—22no—
63#4016—21no—
64C5×#104—61no—
65C5×#100—31no—
66#3966—32no—
67#3966—62no—
68#2201—151noSylow
69C23×C3×C5C2×D412yes—
70C22×C5×D3—22no—
71C3×C5×Q8—41no—
72C3×C5×D4—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×Dic15—42no—
77C5×#67—42no—
78C5×#67—41no—
79C2×C5×Dic3—22no—
80C5×D12—21no—
81C4×C5×D3—41no—
82C5×Dic6—21no—
83C2×C3×Dic5—22no—
84C2×C3×Dic5—22no—
85C2×C3×Dic5—42no—
86C3×Dic10—81no—
87C5×C3⋊C8—41no—
88#1004C2×D511yescharacteristic
89C3×C4⋊Q8—101no—
90C3×#126—102no—
91C3×#125—101no—
92C3×#124C2×D511yescharacteristic
93C3×#123—52no—
94C3×C22⋊Q8—102no—
95#942—21no—
96#929—102no—
97#834—52no—
98#833C2×D511yescharacteristic
99#806—102no—
100#805—21no—
101C5×#41—61no—
102C5×#41—121no—
103C2×C5×Q8#6711yescharacteristic
104C2×C5×D4—62no—
105C2×C5×D4—121no—
106C2×C5×D4C22×D311yescharacteristic
107C22×Dic5#6712yes—
108C2×Dic10—21no—
109C5×Q16—121no—
110C5×SD16—121no—
111C5×M16—61no—
112C5×C22⋊C4—22no—
113C42×C5#6711yescharacteristic
114C22⋊Dic5—22no—
115C22⋊Dic5—62no—
116C22⋊Dic5—122no—
117C22⋊Dic5#6712yes—
118C4⋊Dic5—21no—
119C4⋊Dic5—21no—
120#683—22no—
121#683—22no—
122#683—22no—
123#683—122no—
124C4×Dic5—21no—
125#563—51no—
126#458—152no—
127#455—31no—
128#354—151no—
129#352—152no—
130C22×C3×C5—22no—
131C22×C3×C5—42no—
132C22×C3×C5#12011yescharacteristic
133C2×C5×D3—41no—
134C2×C5×D3—82no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138Dic15—82no—
139C3×Dic5—42no—
140C3×Dic5—42no—
141C5×Dic3—41no—
142C2×C3×Q8—101no—
143C2×C3×Q8C22⋊D511yescharacteristic
144C2×C3×D4C22×D511yescharacteristic
145C22×C3×C4—52no—
146C2×#67—22no—
147#237—41no—
148D3×D4—41no—
149#235—21no—
150C3×C4⋊C4—102no—
151C3×C4⋊C4—102no—
152C3×C4⋊C4—101no—
153C3×C4⋊C4—101no—
154C3×C4⋊C4—102no—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—52no—
157C3×C22⋊C4—102no—
158C3×C42—101no—
159C3×C42C22⋊D511yescharacteristic
160#217—102no—
161#216—41no—
162#215—41no—
163(C2×D3)⋊C4—202no—
164Dic3⋊C4—202no—
165#208—21no—
166C23×C5—62no—
167C23×C5C2×#6712yes—
168C5×Q8—41no—
169C5×Q8—61no—
170C5×D4—41no—
171C5×D4—61no—
172C5×D4—122no—
173C5×D4—121no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—62no—
177C2×C4×C5—121no—
178C2×C4×C5C2×#6711yescharacteristic
179C2×Dic5—22no—
180C2×Dic5—22no—
181C2×Dic5—42no—
182C2×Dic5—122no—
183Dic10—81no—
184C5×C8—121no—
185H(5,𝔽2)—31no—
186#137—61no—
187C4⋊Q8—101no—
188#126—102no—
189#125—101no—
190#124D3×D511yescharacteristic
191#123—52no—
192#123—302no—
193C22⋊Q8—102no—
194#104—61no—
195#100—31no—
196#99—152no—
197#99—302no—
198C2×C3×C5—21no—
199C2×C3×C5—42no—
200C2×C3×C5B(4,𝔽2)11yescharacteristic
201C5×D3—81no—
202C23×C3D4×D512yes—
203C22×D3—22no—
204C3×Q8—41no—
205C3×Q8—401no—
206C3×D4—41no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—102no—
210C2×C3×C4—102no—
211C2×C3×C4—202no—
212C2×C3×C4C2×C22⋊D511yescharacteristic
213#67—42no—
214#67—41no—
215C2×Dic3—22no—
216C2×Dic3—202no—
217D12—21no—
218C4×D3—41no—
219Dic6—21no—
220C3⋊C8—41no—
221C22×C5—22no—
222C22×C5—42no—
223C22×C5—121no—
224C22×C5—242no—
225C22×C5#95311yescharacteristic
226C4×C5—21no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—121no—
230Dic5—42no—
231Dic5—42no—
232Dic5—242no—
233#41—61no—
234#41—121no—
235C2×Q8—101no—
236C2×Q8#120111yescharacteristic
237C2×D4—62no—
238C2×D4—121no—
239C2×D4C2×D3×D511yescharacteristic
240C22×C4—52no—
241Q16—121no—
242SD16—121no—
243M16—61no—
244C4⋊C4—101no—
245C4⋊C4—102no—
246C4⋊C4—102no—
247C4⋊C4—101no—
248C4⋊C4—102no—
249C4⋊C4—602no—
250C22⋊C4—22no—
251C22⋊C4—52no—
252C22⋊C4—102no—
253C22⋊C4—302no—
254C22⋊C4—602no—
255C42—101no—
256C42#120111yescharacteristic
257C3×C5#220111yescharacteristic, complemented, Hall
258C22×C3—22no—
259C22×C3—42no—
260C22×C3#408311yescharacteristic
261C2×D3—41no—
262C2×D3—82no—
263C3×C4—21no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—202no—
267C3×C4—202no—
268Dic3—41no—
269Dic3—402no—
270C2×C5—21no—
271C2×C5—42no—
272C2×C5—241no—
273C2×C5#524411yescharacteristic
274C23—62no—
275C23D5×#6712yes—
276Q8—41no—
277Q8—61no—
278Q8—401no—
279D4—41no—
280D4—61no—
281D4—122no—
282D4—121no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—62no—
286C2×C4—102no—
287C2×C4—102no—
288C2×C4—121no—
289C2×C4—202no—
290C2×C4—602no—
291C2×C4C2×#120111yescharacteristic
292C8—121no—
293C2×C3—21no—
294C2×C3—42no—
295C2×C3#6532111yescharacteristic
296D3—81no—
297C5#7195811yescharacteristic, complemented, Sylow
298C22—22no—
299C22—42no—
300C22—121no—
301C22—242no—
302C22#9156311yescharacteristic
303C4—21no—
304C4—41no—
305C4—41no—
306C4—121no—
307C4—202no—
308C4—202no—
309C4—1202no—
310C3#1060178511yescharacteristic, complemented, Sylow
311C2—21no—
312C2—42no—
313C2—241no—
314C2#1174917511yescharacteristic
subgroupG/H
centerC2#11749175
commutator, cosocleC2×C3×C5×D4C23
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#124C22
socleC2×C3×C5B(4,𝔽2)
prime radicalC5×#1004C22
hypercenter#124D3×D5
hypocenterC3×C5#2201
LCSG ▷ C2×C3×C5×D4 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#66006C2semidirect
4. #11746362C2semidirect
5. #11746001C2semidirect
21. #66006D3semidirect
257. C3×C5#2201semidirect
297. C5#71958semidirect
310. C3#10601785semidirect

Maximal subgroups

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

subgroupindex
C3×#660062
C5×#50612
#117491832
#117463622
#117460012
#106017853
#719585