Finite Group Databasebeta

← #14313546

Subgroups — #14313546

Order 1920.

476 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 78 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#11756434C211yesmaximal, characteristic
2#11749174C212yesmaximal
3C5×#4541C211yesmaximal, characteristic, complemented
4C3×#64761C211yesmaximal, characteristic, complemented
5#11746011C212yesmaximal, complemented
6#10599952—31nomaximal, Hall
7C2×Q8×D15C411yescharacteristic, complemented
8C2×#6819C2211yescharacteristic
9C3×C5×#124C2211yescharacteristic
10#91833C411yescharacteristic, complemented
11#91825C2211yescharacteristic
12#91772—22no—
13#91767—22no—
14#91761C411yescharacteristic, complemented
15#91758C411yescharacteristic, complemented
16#91532—22no—
17C5×#834C2212yes—
18C3×#3966C2212yes—
19#90997—22no—
20#69159—51nomaximal, Hall
21#66009—31no—
22#65029—32no—
23C5×#354—31no—
24#64761D311yescharacteristic, complemented
25#64693—32no—
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×C3×C5×D4C2311yescharacteristic
28C2×#1220D412yes—
29C22×Dic15D412yes—
30Q8×D15—42no—
31#6819—42no—
32C2×C4×D15—21no—
33C2×C4×D15C2×C411yescharacteristic
34C2×Dic30—21no—
35C2×Dic30C2×C411yescharacteristic
36C2×Dic30C2×C411yescharacteristic
37C3×C5×C22⋊C4—22no—
38C3×C42×C5C2×C411yescharacteristic
39#6719—22no—
40#6714—21no—
41C4⋊Dic15—22no—
42#6712—21no—
43#6712—22no—
44C4×Dic15C2×C411yescharacteristic
45C5×#217—22no—
46C3×C22⋊Dic5—22no—
47#6669—42no—
48Dic3×Dic5—42no—
49#5675—51no—
50#4740—52no—
51C3×#354—51no—
52#4541D511yescharacteristic, complemented
53#4473—52no—
54C2×Q8×D5—31no—
55C2×#711—31no—
56C5×#124C2×D311yescharacteristic
57#4090—31no—
58#4082—31no—
59#4029—62no—
60#4024—62no—
61#4023—62no—
62#4018—31no—
63#4015—31no—
64C5×#99—32no—
65#3966C2×D312yes—
66#3938—62no—
67#2129—151noSylow
68C23×C3×C5C2×D412yes—
69C22×D15C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C3×C5×D4—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5C22×C411yescharacteristic
75#1220—42no—
76C2×Dic15—22no—
77C2×Dic15—22no—
78C2×Dic15—21no—
79C2×Dic15—21no—
80C2×Dic15C22⋊C412yes—
81C2×Dic15C22⋊C411yescharacteristic
82C4×D15—22no—
83C4×D15—42no—
84Dic30—41no—
85Dic30—42no—
86Dic30—41no—
87C2×C5×Dic3—42no—
88C2×C3×Dic5—42no—
89C2×D3×Q8—51no—
90C2×#237—51no—
91C3×#124C2×D511yescharacteristic
92#944—51no—
93#936—51no—
94#883—102no—
95#878—102no—
96#877—102no—
97#872—51no—
98#869—51no—
99C3×#99—52no—
100#834C2×D512yes—
101#806—102no—
102C2×C5×Q8C4×D311yescharacteristic
103C2×C5×D4C22×D311yescharacteristic
104C2×C22⋊D5—32no—
105C22×Dic5—32no—
106Q8×D5—122no—
107#711—122no—
108C2×C4×D5—31no—
109C2×C4×D5—61no—
110C2×Dic10—31no—
111C2×Dic10—31no—
112C2×Dic10—61no—
113C5×C22⋊C4—22no—
114C5×C22⋊C4—62no—
115C42×C5C4×D311yescharacteristic
116C22⋊Dic5—22no—
117C22⋊Dic5—62no—
118#685—61no—
119C4⋊Dic5—62no—
120#683—61no—
121#683—62no—
122#683—122no—
123C4×Dic5—31no—
124C4×Dic5—122no—
125#536—151no—
126#410—152no—
127#354—31no—
128#354—51no—
129#354—152no—
130C22×C3×C5—22no—
131C22×C3×C5—42no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C2×D15—21no—
134C2×D15—41no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138Dic15—22no—
139Dic15—41no—
140Dic15—41no—
141Dic15#9912yes—
142C3×Dic5—82no—
143C5×Dic3—82no—
144C2×C3×Q8C4×D511yescharacteristic
145C2×C3×D4C22×D511yescharacteristic
146C2×#67—52no—
147C22×Dic3—52no—
148D3×Q8—202no—
149#237—202no—
150C2×C4×D3—51no—
151C2×C4×D3—101no—
152C2×Dic6—51no—
153C2×Dic6—51no—
154C2×Dic6—101no—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—102no—
157C3×C42C4×D511yescharacteristic
158#217—22no—
159#217—102no—
160(C2×D3)⋊C4—101no—
161C4⋊Dic3—102no—
162Dic3⋊C4—101no—
163Dic3⋊C4—102no—
164Dic3⋊C4—202no—
165C4×Dic3—51no—
166C4×Dic3—202no—
167C23×C5D3×D412yes—
168C22×D5—31no—
169C5×Q8—41no—
170C5×D4—41no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—122no—
174C2×C4×C5C2×C4×D311yescharacteristic
175C22⋊D5—122no—
176C2×Dic5—31no—
177C2×Dic5—32no—
178C2×Dic5—42no—
179C2×Dic5—62no—
180C2×Dic5—62no—
181C2×Dic5—61no—
182C2×Dic5—61no—
183C4×D5—62no—
184C4×D5—122no—
185Dic10—122no—
186Dic10—121no—
187Dic10—121no—
188C2×#41—151no—
189C22×Q8—151no—
190C4⋊Q8—151no—
191C4⋊Q8—151no—
192#124—151no—
193#124D3×D511yescharacteristic
194#123—302no—
195C22⋊Q8—302no—
196#117—151no—
197#117—302no—
198#99—32no—
199#99—52no—
200#99—302no—
201C2×C3×C5—21no—
202C2×C3×C5—42no—
203C2×C3×C5C2×#9911yescharacteristic
204D15—41no—
205C23×C3D4×D512yes—
206C22×D3—51no—
207C3×Q8—41no—
208C3×D4—41no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—202no—
212C2×C3×C4C2×C4×D511yescharacteristic
213#67—202no—
214C2×Dic3—42no—
215C2×Dic3—51no—
216C2×Dic3—52no—
217C2×Dic3—102no—
218C2×Dic3—102no—
219C2×Dic3—101no—
220C2×Dic3—101no—
221C4×D3—102no—
222C4×D3—202no—
223Dic6—202no—
224Dic6—201no—
225Dic6—201no—
226C22×C5—22no—
227C22×C5—42no—
228C22×C5D3×C22⋊C411yescharacteristic
229C2×D5—61no—
230C2×D5—121no—
231C4×C5—21no—
232C4×C5—41no—
233C4×C5—41no—
234C4×C5—242no—
235Dic5—32no—
236Dic5—62no—
237Dic5—82no—
238Dic5—121no—
239Dic5—121no—
240#41—602no—
241C2×Q8—151no—
242C2×Q8—151no—
243C2×Q8—301no—
244C2×Q8—602no—
245C2×Q8#120011yescharacteristic
246C2×D4—152no—
247C2×D4C2×D3×D511yescharacteristic
248C22×C4—152no—
249C22×C4—151no—
250C22×C4—301no—
251C4⋊C4—301no—
252C4⋊C4—302no—
253C4⋊C4—302no—
254C4⋊C4—602no—
255C22⋊C4—22no—
256C22⋊C4—62no—
257C22⋊C4—102no—
258C22⋊C4—301no—
259C22⋊C4—302no—
260C42—151no—
261C42—602no—
262C42#120011yescharacteristic
263C3×C5#212911yescharacteristic, complemented, Hall
264C22×C3—22no—
265C22×C3—42no—
266C22×C3D5×C22⋊C411yescharacteristic
267C2×D3—101no—
268C2×D3—201no—
269C3×C4—21no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—402no—
273Dic3—52no—
274Dic3—82no—
275Dic3—102no—
276Dic3—201no—
277Dic3—201no—
278C2×C5—21no—
279C2×C5—42no—
280C2×C5D3×#9911yescharacteristic
281D5—121no—
282C23—151no—
283C23#679012yes—
284Q8—41no—
285Q8—601no—
286Q8—601no—
287Q8—602no—
288D4—41no—
289D4—602no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—122no—
293C2×C4—151no—
294C2×C4—152no—
295C2×C4—202no—
296C2×C4—302no—
297C2×C4—302no—
298C2×C4—302no—
299C2×C4—301no—
300C2×C4—301no—
301C2×C4—602no—
302C2×C4C2×#120011yescharacteristic
303C2×C3—21no—
304C2×C3—42no—
305C2×C3D5×#9911yescharacteristic
306D3—201no—
307C5#6915911yescharacteristic, complemented, Sylow
308C22—22no—
309C22—42no—
310C22—301no—
311C22—601no—
312C22#9156111yescharacteristic
313C4—21no—
314C4—41no—
315C4—41no—
316C4—152no—
317C4—242no—
318C4—302no—
319C4—402no—
320C4—601no—
321C4—601no—
322C3#1059995211yescharacteristic, complemented, Sylow
323C2—21no—
324C2—42no—
325C2—601no—
326C2#1174917111yescharacteristic
subgroupG/H
centerC2#11749171
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#124C22
socleC2×C3×C5C2×#99
prime radicalC2×#6819C22
cosocleC2×C3×C5×D4C23
hypercenter#124D3×D5
hypocenterC3×C5#2129
LCSG ▷ C2×C3×C4×C5 ▷ 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
3. C5×#4541C2semidirect
4. C3×#64761C2semidirect
5. #11746011C2semidirect
7. C2×Q8×D15C4semidirect
10. #91833C4semidirect
14. #91761C4semidirect
15. #91758C4semidirect
24. #64761D3semidirect
52. #4541D5semidirect
263. C3×C5#2129semidirect
307. C5#69159semidirect
322. C3#10599952semidirect

Maximal subgroups

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

subgroupindex
#117564342
#117491742
C5×#45412
C3×#647612
#117460112
#105999523
#691595