Finite Group Databasebeta

← #14316760

Subgroups — #14316760

Order 1920.

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

normal subgroups only

This group has 492 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×#66047C211yesmaximal, characteristic, complemented
2C5×#5077C211yesmaximal, characteristic
3#11749183C212yesmaximal, complemented
4#11746366C211yesmaximal, characteristic, complemented
5#11746001C212yesmaximal, complemented
6#10601779—31nomaximal, Hall
7C5×#1004C2211yescharacteristic
8C3×C5×#127C2211yescharacteristic
9C5×#932—21no—
10C3×#4082—22no—
11C3×#4081—21no—
12C3×#4081C2212yes—
13C3×D4×Dic5—22no—
14C3×C4×Dic10—21no—
15#91539—22no—
16#91118C2212yes—
17C5×#833C2211yescharacteristic
18C5×#805—21no—
19#90996—22no—
20#71946—51nomaximal, Hall
21#66047D311yescharacteristic, complemented
22C5×#453—31no—
23#65532—32no—
24#64765—31no—
25#64696—32no—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4D411yescharacteristic
28C2×C3×C5×D4C2311yescharacteristic
29C2×C5×#67—22no—
30C5×#237—41no—
31C5×D3×D4—41no—
32C5×#235—21no—
33C22×C3×Dic5—21no—
34C22×C3×Dic5D412yes—
35C2×C3×Dic10—21no—
36C3×C42×C5D411yescharacteristic
37#6719—22no—
38C5×#214—41no—
39C5×#213—41no—
40C5×#208—21no—
41C3×C22⋊Dic5—22no—
42C3×C22⋊Dic5—21no—
43C3×C22⋊Dic5—22no—
44C3×C22⋊Dic5D412yes—
45C3×C4⋊Dic5—21no—
46C3×#683—22no—
47C3×C4×Dic5—22no—
48#6669—42no—
49(C2×D3)⋊Dic5—42no—
50C3×#559—51no—
51#5077D511yescharacteristic
52#5053—52no—
53#4545—51no—
54#4539—52no—
55C5×H(5,𝔽2)—31no—
56C5×AGL(1,ℤ/8)—61no—
57C5×#127C2×D311yescharacteristic
58#4082—22no—
59#4081—21no—
60#4081—62no—
61#4081C2×D312yes—
62D4×Dic5—22no—
63C4×Dic10—21no—
64C5×#104—61no—
65C5×#100—31no—
66#3966—32no—
67#3966—62no—
68#2198—151noSylow
69C23×C3×C5—21no—
70C23×C3×C5C2×D412yes—
71C22×C5×D3—22no—
72C3×C5×D4—41no—
73C3×C5×D4—44no—
74C3×C5×D4—41no—
75C2×C3×C4×C5—21no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×Dic15—42no—
78C5×#67—42no—
79C5×#67—41no—
80C2×C5×Dic3—22no—
81C5×D12—21no—
82C4×C5×D3—41no—
83C5×Dic6—21no—
84C2×C3×Dic5—22no—
85C2×C3×Dic5—22no—
86C2×C3×Dic5—42no—
87C2×C3×Dic5—81no—
88C3×Dic10—42no—
89C5×C3⋊C8—41no—
90#1004C2×D511yescharacteristic
91C3×#127C2×D511yescharacteristic
92C3×#124—102no—
93C3×#123—52no—
94C3×#123—101no—
95C3×C4×Q8—101no—
96C3×C4×D4—102no—
97#932—21no—
98#929—102no—
99#834—52no—
100#833C2×D511yescharacteristic
101#806—102no—
102#805—21no—
103C5×#41—61no—
104C5×#41—121no—
105C2×C5×D4—22no—
106C2×C5×D4—62no—
107C2×C5×D4—121no—
108C2×C5×D4#6711yescharacteristic
109C2×C5×D4C22×D311yescharacteristic
110C22×Dic5—21no—
111C22×Dic5#6712yes—
112C2×Dic10—21no—
113C5×SD16—121no—
114C5×D8—121no—
115C5×M16—61no—
116C42×C5#6711yescharacteristic
117C22⋊Dic5—22no—
118C22⋊Dic5—21no—
119C22⋊Dic5—22no—
120C22⋊Dic5—62no—
121C22⋊Dic5—122no—
122C22⋊Dic5#6712yes—
123C4⋊Dic5—21no—
124#683—22no—
125#683—122no—
126C4×Dic5—22no—
127#559—51no—
128#458—152no—
129#453—31no—
130#353—151no—
131#352—152no—
132C22×C3×C5—22no—
133C22×C3×C5—42no—
134C22×C3×C5—42no—
135C22×C3×C5—41no—
136C22×C3×C5#12011yescharacteristic
137C2×C5×D3—41no—
138C2×C5×D3—82no—
139C3×C4×C5—22no—
140C3×C4×C5—21no—
141Dic15—82no—
142C3×Dic5—42no—
143C3×Dic5—42no—
144C5×Dic3—41no—
145C2×C3×Q8—101no—
146C2×C3×D4—22no—
147C2×C3×D4C22⋊D511yescharacteristic
148C2×C3×D4C22×D511yescharacteristic
149C22×C3×C4—52no—
150C22×C3×C4—101no—
151C2×#67—22no—
152#237—41no—
153D3×D4—41no—
154#235—21no—
155C3×C4⋊C4—101no—
156C3×C4⋊C4—102no—
157C3×C22⋊C4—52no—
158C3×C22⋊C4—102no—
159C3×C22⋊C4—101no—
160C3×C22⋊C4—102no—
161C3×C42—102no—
162C3×C42C22⋊D511yescharacteristic
163#217—102no—
164#214—41no—
165#213—41no—
166(C2×D3)⋊C4—202no—
167Dic3⋊C4—202no—
168#208—21no—
169C23×C5—21no—
170C23×C5—62no—
171C23×C5C2×#6712yes—
172C5×Q8—61no—
173C5×D4—41no—
174C5×D4—41no—
175C5×D4—44no—
176C5×D4—61no—
177C5×D4—122no—
178C5×D4—121no—
179C2×C4×C5—21no—
180C2×C4×C5—62no—
181C2×C4×C5—121no—
182C2×C4×C5C2×#6711yescharacteristic
183C2×Dic5—22no—
184C2×Dic5—22no—
185C2×Dic5—42no—
186C2×Dic5—81no—
187C2×Dic5—122no—
188Dic10—42no—
189C5×C8—121no—
190H(5,𝔽2)—31no—
191AGL(1,ℤ/8)—61no—
192#127D3×D511yescharacteristic
193#124—102no—
194#123—52no—
195#123—101no—
196#123—302no—
197C4×Q8—101no—
198C4×D4—102no—
199#104—61no—
200#100—31no—
201#99—152no—
202#99—302no—
203C2×C3×C5—21no—
204C2×C3×C5—42no—
205C2×C3×C5—81no—
206C2×C3×C5B(4,𝔽2)11yescharacteristic
207C5×D3—81no—
208C23×C3—21no—
209C23×C3D4×D512yes—
210C22×D3—22no—
211C3×Q8—202no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—44no—
215C2×C3×C4—21no—
216C2×C3×C4—102no—
217C2×C3×C4—102no—
218C2×C3×C4—202no—
219C2×C3×C4—401no—
220C2×C3×C4C2×C22⋊D511yescharacteristic
221#67—42no—
222#67—41no—
223C2×Dic3—22no—
224C2×Dic3—202no—
225D12—21no—
226C4×D3—41no—
227Dic6—21no—
228C3⋊C8—41no—
229C22×C5—22no—
230C22×C5—42no—
231C22×C5—42no—
232C22×C5—41no—
233C22×C5—121no—
234C22×C5—242no—
235C22×C5#95311yescharacteristic
236C4×C5—22no—
237C4×C5—21no—
238C4×C5—121no—
239Dic5—42no—
240Dic5—42no—
241Dic5—242no—
242#41—61no—
243#41—121no—
244C2×Q8—101no—
245C2×D4—22no—
246C2×D4—62no—
247C2×D4—121no—
248C2×D4#120111yescharacteristic
249C2×D4C2×D3×D511yescharacteristic
250C22×C4—52no—
251C22×C4—101no—
252SD16—121no—
253D8—121no—
254M16—61no—
255C4⋊C4—101no—
256C4⋊C4—102no—
257C4⋊C4—602no—
258C22⋊C4—52no—
259C22⋊C4—102no—
260C22⋊C4—101no—
261C22⋊C4—102no—
262C22⋊C4—302no—
263C22⋊C4—602no—
264C42—102no—
265C42#120111yescharacteristic
266C3×C5#219811yescharacteristic, complemented, Hall
267C22×C3—22no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—41no—
271C22×C3#408311yescharacteristic
272C2×D3—41no—
273C2×D3—82no—
274C3×C4—22no—
275C3×C4—21no—
276C3×C4—202no—
277C3×C4—202no—
278Dic3—41no—
279Dic3—402no—
280C2×C5—21no—
281C2×C5—42no—
282C2×C5—81no—
283C2×C5—241no—
284C2×C5#524411yescharacteristic
285C23—21no—
286C23—62no—
287C23D5×#6712yes—
288Q8—61no—
289Q8—202no—
290D4—41no—
291D4—41no—
292D4—44no—
293D4—61no—
294D4—122no—
295D4—121no—
296C2×C4—21no—
297C2×C4—62no—
298C2×C4—102no—
299C2×C4—102no—
300C2×C4—121no—
301C2×C4—202no—
302C2×C4—401no—
303C2×C4—602no—
304C2×C4C2×#120111yescharacteristic
305C8—121no—
306C2×C3—21no—
307C2×C3—42no—
308C2×C3—81no—
309C2×C3#6532111yescharacteristic
310D3—81no—
311C5#7194611yescharacteristic, complemented, Sylow
312C22—22no—
313C22—42no—
314C22—42no—
315C22—41no—
316C22—121no—
317C22—242no—
318C22#9156311yescharacteristic
319C4—22no—
320C4—21no—
321C4—121no—
322C4—202no—
323C4—202no—
324C4—1202no—
325C3#1060177911yescharacteristic, complemented, Sylow
326C2—21no—
327C2—42no—
328C2—81no—
329C2—241no—
330C2#1174917511yescharacteristic
subgroupG/H
centerC2#11749175
commutator, cosocleC2×C3×C5×D4C23
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#127C22
socleC2×C3×C5B(4,𝔽2)
prime radicalC5×#5077C2
hypercenter#127D3×D5
hypocenterC3×C5#2198
LCSG ▷ C2×C3×C5×D4 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#66047C2semidirect
3. #11749183C2semidirect
4. #11746366C2semidirect
5. #11746001C2semidirect
21. #66047D3semidirect
266. C3×C5#2198semidirect
311. C5#71946semidirect
325. C3#10601779semidirect

Maximal subgroups

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

subgroupindex
C3×#660472
C5×#50772
#117491832
#117463662
#117460012
#106017793
#719465