Finite Group Databasebeta

← #14316342

Subgroups — #14316342

Order 1920.

432 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 83 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#11756507C211yesmaximal, characteristic
2C3×C5×#470C211yesmaximal, characteristic, complemented
3#11751280C212yesmaximal, complemented
4#11746374C211yesmaximal, characteristic, complemented
5#11746309C212yesmaximal, complemented
6#10601884—31nomaximal, Hall
7C2×#6817—21no—
8C2×C3×C5×Q16C2211yescharacteristic, complemented
9C2×C3×C5×M16C2211yescharacteristic
10C3×C5×C22⋊Q8—21no—
11#91798—22no—
12#91797—22no—
13#91793—21no—
14#91793C2212yes—
15C3×C5×#106C2211yescharacteristic, complemented
16C3×C5×#103—21no—
17#91113—22no—
18#91112—22no—
19#91096C2212yescomplemented
20#71091—51nomaximal, Hall
21#66082—31no—
22C5×#470D311yescharacteristic, complemented
23#65468—32no—
24#64773—31no—
25#64708—32no—
26C2×C3×C5×Q8—21no—
27C22×C3×C4×C5D411yescharacteristic
28C2×#1220—41no—
29#6817—22no—
30#6817—22no—
31#6817—41no—
32#6817—41no—
33C2×D60—21no—
34C2×C4×D15—41no—
35C2×Dic30—21no—
36C3×C5×Q16—22no—
37C3×C5×M16—22no—
38C2×C3×C5×C8D411yescharacteristic
39C2×C3×C5×C8C2311yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—41no—
42C3×C5×C22⋊C4—41no—
43Dic60—21no—
44Dic60D412yes—
45D120—21no—
46D120D412yes—
47#6706—22no—
48#6706—22no—
49C3⋊#672—22no—
50#5748—51no—
51C3×#470D511yescharacteristic, complemented
52#5179—52no—
53#4553—51no—
54#4488—52no—
55C2×#709—61no—
56C2×C5×Q16C2×D311yescharacteristic, complemented
57C2×C5×M16C2×D311yescharacteristic
58C5×C22⋊Q8—21no—
59#4055—62no—
60#4054—62no—
61#4050—32no—
62#4050—61no—
63C5×#106C2×D311yescharacteristic, complemented
64C5×#103—21no—
65#3961—62no—
66#3960—62no—
67#3944—32no—
68#2191—151noSylow
69C23×C3×C5D811yescharacteristic
70C22×D15—41no—
71C3×C5×Q8—41no—
72C3×C5×Q8—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5D811yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79#1220—42no—
80#1220—42no—
81C2×Dic15—41no—
82D60—22no—
83D60—41no—
84C4×D15—42no—
85C4×D15—42no—
86Dic30—22no—
87Dic30—41no—
88C3×C5×C8—21no—
89C3×C5×C8C2×D412yes—
90C2×#235—101no—
91C2×C3×Q16C2×D511yescharacteristic, complemented
92C2×C3×M16C2×D511yescharacteristic
93C3×C22⋊Q8—21no—
94#909—102no—
95#908—102no—
96#904—52no—
97#904—101no—
98C3×#106C2×D511yescharacteristic, complemented
99C3×#103—21no—
100#829—102no—
101#828—102no—
102#812—52no—
103C2×C5×Q8—21no—
104C22×C4×C5#6711yescharacteristic
105C2×C22⋊D5—121no—
106#709—62no—
107#709—62no—
108#709—121no—
109#709—121no—
110C2×D20—61no—
111C2×C4×D5—121no—
112C2×Dic10—61no—
113C5×Q16—22no—
114C5×M16—22no—
115C2×C5×C8#6711yescharacteristic
116C2×C5×C8C22×D311yescharacteristic
117C5×C4⋊C4—21no—
118C5×C4⋊C4—41no—
119C5×C22⋊C4—41no—
120Dic20—32no—
121Dic20—61no—
122D40—32no—
123D40—61no—
124#677—62no—
125#677—62no—
126#672—62no—
127#575—151no—
128#510—152no—
129#470D1511yescharacteristic, complemented
130#360—152no—
131#349—151no—
132C22×C3×C5—21no—
133C22×C3×C5—41no—
134C22×C3×C5C2×D811yescharacteristic
135C2×D15—42no—
136C2×D15—82no—
137C3×C4×C5—21no—
138C3×C4×C5—81no—
139C3×C4×C5—81no—
140C3×C4×C5#12011yescharacteristic
141C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
142Dic15—42no—
143C2×C3×Q8—21no—
144C22×C3×C4C22⋊D511yescharacteristic
145C2×#67—201no—
146#235—102no—
147#235—102no—
148#235—201no—
149#235—201no—
150C2×D12—101no—
151C2×C4×D3—201no—
152C2×Dic6—101no—
153C3×Q16—22no—
154C3×M16—22no—
155C2×C3×C8C22⋊D511yescharacteristic
156C2×C3×C8C22×D511yescharacteristic
157C3×C4⋊C4—21no—
158C3×C4⋊C4—41no—
159C3×C22⋊C4—41no—
160Dic12—52no—
161Dic12—101no—
162D24—52no—
163D24—101no—
164#204—102no—
165#204—102no—
166C3⋊C16—102no—
167C23×C5#21311yescharacteristic
168C22×D5—121no—
169C5×Q8—41no—
170C5×Q8—41no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5#21311yescharacteristic
176C2×C4×C5C2×#6711yescharacteristic
177C22⋊D5—122no—
178C22⋊D5—122no—
179C2×Dic5—121no—
180D20—62no—
181D20—121no—
182C4×D5—122no—
183C4×D5—122no—
184Dic10—62no—
185Dic10—121no—
186C5×C8—21no—
187C5×C8D3×D412yes—
188C2×#41—301no—
189#137—302no—
190AGL(1,ℤ/8)—302no—
191#135—152no—
192#135—301no—
193C2×Q16C2×D1511yescharacteristic, complemented
194C2×M16C2×D1511yescharacteristic
195C22⋊Q8—21no—
196Q32—302no—
197SD32—302no—
198M32—152no—
199#106C2×D1511yescharacteristic, complemented
200#103—21no—
201C2×C3×C5—21no—
202C2×C3×C5—41no—
203C2×C3×C5#44711yescharacteristic
204D15—82no—
205C23×C3#68611yescharacteristic
206C22×D3—201no—
207C3×Q8—41no—
208C3×Q8—41no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4#68611yescharacteristic
214C2×C3×C4C2×C22⋊D511yescharacteristic
215#67—202no—
216#67—202no—
217C2×Dic3—201no—
218D12—102no—
219D12—201no—
220C4×D3—202no—
221C4×D3—202no—
222Dic6—102no—
223Dic6—201no—
224C3×C8—21no—
225C3×C8D4×D512yes—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5C2×#21311yescharacteristic
229C2×D5—122no—
230C2×D5—242no—
231C4×C5—21no—
232C4×C5—81no—
233C4×C5—81no—
234C4×C5#93711yescharacteristic
235C4×C5#94911yescharacteristic
236Dic5—122no—
237#41—302no—
238#41—302no—
239#41—601no—
240#41—601no—
241C2×Q8—21no—
242C2×Q8—301no—
243C2×D4—301no—
244C2×D4—601no—
245C22×C4—601no—
246C22×C4#122011yescharacteristic
247Q16—22no—
248Q16—152no—
249Q16—301no—
250SD16—302no—
251SD16—302no—
252D8—152no—
253D8—301no—
254M16—22no—
255C2×C8#122011yescharacteristic
256C2×C8C22×D1511yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—41no—
259C22⋊C4—41no—
260C16—302no—
261C3×C5#219111yescharacteristic, complemented, Hall
262C22×C3—21no—
263C22×C3—41no—
264C22×C3C2×#68611yescharacteristic
265C2×D3—202no—
266C2×D3—402no—
267C3×C4—21no—
268C3×C4—81no—
269C3×C4—81no—
270C3×C4#408311yescharacteristic
271C3×C4#409511yescharacteristic
272Dic3—202no—
273C2×C5—21no—
274C2×C5—41no—
275C2×C5#503611yescharacteristic
276D5—242no—
277C23—601no—
278C23#671511yescharacteristic
279Q8—41no—
280Q8—41no—
281Q8—302no—
282Q8—601no—
283D4—302no—
284D4—601no—
285D4—602no—
286D4—602no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—602no—
292C2×C4—601no—
293C2×C4—602no—
294C2×C4#671511yescharacteristic
295C2×C4C2×#122011yescharacteristic
296C8—21no—
297C8D4×D1512yes—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3#6532511yescharacteristic
301D3—402no—
302C5#7109111yescharacteristic, complemented, Sylow
303C22—21no—
304C22—41no—
305C22—602no—
306C22—1202no—
307C22C2×#671511yescharacteristic
308C4—21no—
309C4—81no—
310C4—81no—
311C4—602no—
312C4#9182611yescharacteristic
313C4#9183811yescharacteristic
314C3#1060188411yescharacteristic, complemented, Sylow
315C2—21no—
316C2—41no—
317C2—1202no—
318C2#1175113711yescharacteristic
subgroupG/H
centerC2#11751137
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#470C2
socleC2×C3×C5#447
prime radical#11756507C2
hypercenter#470D15
hypocenterC3×C5#2191
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
2. C3×C5×#470C2semidirect
3. #11751280C2semidirect
4. #11746374C2semidirect
5. #11746309C2semidirect
8. C2×C3×C5×Q16C22semidirect
15. C3×C5×#106C22semidirect
19. #91096C22semidirect
22. C5×#470D3semidirect
51. C3×#470D5semidirect
56. C2×C5×Q16C2×D3semidirect
63. C5×#106C2×D3semidirect
91. C2×C3×Q16C2×D5semidirect
98. C3×#106C2×D5semidirect
129. #470D15semidirect
193. C2×Q16C2×D15semidirect
199. #106C2×D15semidirect
261. C3×C5#2191semidirect
302. C5#71091semidirect
314. C3#10601884semidirect

Maximal subgroups

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

subgroupindex
#117565072
C3×C5×#4702
#117512802
#117463742
#117463092
#106018843
#710915