Finite Group Databasebeta

← #14289684

Subgroups — #14289684

Order 1920.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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#11756480C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic
3#11751192C211yesmaximal, characteristic
4#11751192C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic
6#11746277C211yesmaximal, characteristic
7#11746277C211yesmaximal, characteristic
8#10602029—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11Q8×Dic15—21no—
12#91833—21no—
13#91779—21no—
14#91778—22no—
15#91776—21no—
16C4×Dic30C2211yescharacteristic
17C4×Dic30C2211yescharacteristic
18C3×C5×#103—22no—
19C3×C4×C5×C8C2211yescharacteristic
20#91094—21no—
21#91094—21no—
22#91091—21no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71236—51nomaximal, Hall
27#66055—31no—
28C5×#487D311yescharacteristic
29#65380—31no—
30#65380—31no—
31#64767—31no—
32#64676—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×Dic30D411yescharacteristic
37C2×Dic30D411yescharacteristic
38C2×C3×C5×C8—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D412yes—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15—22no—
45C4⋊Dic15D411yescharacteristic
46C4⋊Dic15D411yescharacteristic
47#6712—22no—
48#6712—22no—
49#6712—21no—
50#6712—21no—
51C4×Dic15—22no—
52C4×Dic15—21no—
53C4×Dic15—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56#5721—51no—
57C3×#487D511yescharacteristic
58#5091—51no—
59#5091—51no—
60#4547—51no—
61#4456—51no—
62#4456—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C5×C4⋊Q8C2×D311yescharacteristic
65Q8×Dic5—61no—
66#4090—61no—
67#4036—61no—
68#4035—62no—
69#4033—61no—
70C4×Dic10—31no—
71C4×Dic10—31no—
72C5×#103—22no—
73C4×C5×C8C2×D311yescharacteristic
74#3942—61no—
75#3942—61no—
76#3939—61no—
77#3939—61no—
78C4⋊#168—31no—
79C4⋊#168—31no—
80#1636—151noSylow
81C3×C5×Q8—42no—
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—21no—
93Dic30—21no—
94Dic30—21no—
95Dic30—21no—
96Dic30Q1612yes—
97C3×C5×C8—41no—
98C3⋊#168—41no—
99C3⋊#168—41no—
100C3×C4⋊Q8C2×D511yescharacteristic
101C3×C4⋊Q8C2×D511yescharacteristic
102Q8×Dic3—101no—
103#944—101no—
104#890—101no—
105#889—102no—
106#887—101no—
107C4×Dic6—51no—
108C4×Dic6—51no—
109C3×#103—22no—
110C3×C4×C8C2×D511yescharacteristic
111#810—101no—
112#810—101no—
113#807—101no—
114#807—101no—
115C4⋊(C3⋊C8)—51no—
116C4⋊(C3⋊C8)—51no—
117C2×C5×Q8—21no—
118C2×C5×Q8—21no—
119C2×Dic10—31no—
120C2×Dic10—31no—
121C2×C5×C8—21no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4#6712yes—
126C42×C5C22×D311yescharacteristic
127C4⋊Dic5—31no—
128C4⋊Dic5—31no—
129C4⋊Dic5—62no—
130#683—62no—
131#683—62no—
132#683—61no—
133#683—61no—
134C4×Dic5—62no—
135C4×Dic5—61no—
136C4×Dic5—61no—
137C2×#168—61no—
138C2×#168—61no—
139#557—151no—
140#487D1511yescharacteristic
141#477—151no—
142#477—151no—
143#332—151no—
144Q8⋊C8—151no—
145Q8⋊C8—151no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—42no—
149C3×C4×C5—81no—
150C3×C4×C5C2×Q1611yescharacteristic
151C3×C4×C5#13511yescharacteristic
152C3×C4×C5#13711yescharacteristic
153C3×C4×C5#13711yescharacteristic
154Dic15—22no—
155Dic15—41no—
156Dic15—41no—
157Dic15—41no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×Dic6—51no—
161C2×Dic6—51no—
162C2×C3×C8—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4C22⋊D512yes—
167C3×C42C22×D511yescharacteristic
168C4⋊Dic3—51no—
169C4⋊Dic3—51no—
170C4⋊Dic3—102no—
171Dic3⋊C4—102no—
172Dic3⋊C4—102no—
173Dic3⋊C4—101no—
174Dic3⋊C4—101no—
175C4×Dic3—102no—
176C4×Dic3—101no—
177C4×Dic3—101no—
178C2×C3⋊C8—101no—
179C2×C3⋊C8—101no—
180C5×Q8—42no—
181C5×Q8—41no—
182C5×Q8—41no—
183C2×C4×C5—22no—
184C2×C4×C5—41no—
185C2×C4×C5D3×D411yescharacteristic
186C2×C4×C5D3×D411yescharacteristic
187C2×C4×C5C2×#6711yescharacteristic
188C2×Dic5—61no—
189C2×Dic5—61no—
190C2×Dic5—61no—
191C2×Dic5—61no—
192Dic10—32no—
193Dic10—61no—
194Dic10—61no—
195Dic10—61no—
196C5×C8—41no—
197#168—121no—
198#168—121no—
199C4⋊Q8—301no—
200C4⋊Q8C2×D1511yescharacteristic
201C4⋊Q8C2×D1511yescharacteristic
202#125—301no—
203#125—302no—
204C4×Q8—151no—
205C4×Q8—151no—
206C4×Q8—301no—
207C4×Q8—301no—
208#107—301no—
209#107—301no—
210C4⋊C8—151no—
211C4⋊C8—151no—
212#103—22no—
213#103—301no—
214#103—301no—
215C4×C8C2×D1511yescharacteristic
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—42no—
220C3×Q8—41no—
221C3×Q8—41no—
222C2×C3×C4—22no—
223C2×C3×C4—41no—
224C2×C3×C4D4×D511yescharacteristic
225C2×C3×C4D4×D511yescharacteristic
226C2×C3×C4C2×C22⋊D511yescharacteristic
227C2×Dic3—101no—
228C2×Dic3—101no—
229C2×Dic3—101no—
230C2×Dic3—101no—
231Dic6—52no—
232Dic6—101no—
233Dic6—101no—
234Dic6—101no—
235C3×C8—41no—
236C3⋊C8—201no—
237C3⋊C8—201no—
238C22×C5#93711yescharacteristic
239C4×C5—21no—
240C4×C5—42no—
241C4×C5—81no—
242C4×C5#91511yescharacteristic
243C4×C5#91611yescharacteristic
244C4×C5D3×Q1611yescharacteristic
245C4×C5#91811yescharacteristic
246Dic5—62no—
247Dic5—121no—
248Dic5—121no—
249Dic5—121no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—151no—
253C2×Q8—151no—
254C2×C8—21no—
255C2×C8—301no—
256C2×C8—301no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—151no—
261C4⋊C4—151no—
262C4⋊C4—302no—
263C4⋊C4—302no—
264C4⋊C4—302no—
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4#122012yes—
268C42—302no—
269C42—301no—
270C42—301no—
271C42C22×D1511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#408311yescharacteristic
274C3×C4—21no—
275C3×C4—42no—
276C3×C4—81no—
277C3×C4#406111yescharacteristic
278C3×C4#406211yescharacteristic
279C3×C4D5×Q1611yescharacteristic
280C3×C4#406411yescharacteristic
281Dic3—102no—
282Dic3—201no—
283Dic3—201no—
284Dic3—201no—
285C2×C5#506211yescharacteristic
286C2×C5#517311yescharacteristic
287C2×C5#518611yescharacteristic
288Q8—42no—
289Q8—41no—
290Q8—41no—
291Q8—152no—
292Q8—301no—
293Q8—301no—
294Q8—301no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—301no—
298C2×C4—301no—
299C2×C4—301no—
300C2×C4—301no—
301C2×C4D4×D1511yescharacteristic
302C2×C4D4×D1511yescharacteristic
303C2×C4C2×#122011yescharacteristic
304C8—41no—
305C8—601no—
306C8—601no—
307C2×C3#6535111yescharacteristic
308C2×C3#6546211yescharacteristic
309C2×C3#6547511yescharacteristic
310C5#7123611yescharacteristic, complemented, Sylow
311C22#9182611yescharacteristic
312C4—21no—
313C4—42no—
314C4—81no—
315C4—302no—
316C4—601no—
317C4—601no—
318C4—601no—
319C4#9180411yescharacteristic
320C4#9180511yescharacteristic
321C4Q16×D1511yescharacteristic
322C4#9180711yescharacteristic
323C3#1060202911yescharacteristic, complemented, Sylow
324C2#1175116311yescharacteristic
325C2#1175127411yescharacteristic
326C2#1175128711yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#487C2
socle, prime radicalC22×C3×C5#120
hypercenter#487D15
hypocenterC3×C5#1636
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
272. C3×C5#1636semidirect
310. C5#71236semidirect
323. C3#10602029semidirect

Maximal subgroups

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

subgroupindex
#117564802
C3×C5×#4872
#117511922
#117463682
#117462772
#106020293
#712365