Finite Group Databasebeta

← #14292176

Subgroups — #14292176

Order 1920.

332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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#11751191C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic
3#11750949C211yesmaximal, characteristic
4#11750931C211yesmaximal, characteristic, complemented
5C3×C5×#332C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic
7#11746300C211yesmaximal, characteristic, complemented
8#10599263—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6718—21no—
11C2×#6706—21no—
12#91763C2211yescharacteristic
13C4×Dic30C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16#91119—21no—
17#91105—21no—
18#91098—21no—
19C8×Dic15—21no—
20#91093—21no—
21#91093—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68470—51nomaximal, Hall
25#65379—31no—
26#65377—31no—
27#65137—31no—
28#65119—31no—
29C5×#332D311yescharacteristic, complemented
30#64705—31no—
31#64699—31no—
32C2×C3×C5×Q8—21no—
33C2×D60—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×Dic30D411yescharacteristic
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42#6718—42no—
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C2×C3⋊#168D411yescharacteristic
48C2×C3⋊#168D411yescharacteristic
49#6706—42no—
50#5090—51no—
51#5088—51no—
52#4848—51no—
53#4830—51no—
54C3×#332D511yescharacteristic, complemented
55#4485—51no—
56#4479—51no—
57C5×C4⋊Q8C2×D311yescharacteristic
58C2×#689—61no—
59C2×#677—61no—
60#4020—31no—
61C4×Dic10—31no—
62C5×C4⋊C8C2×D311yescharacteristic
63C5×C4⋊C8C2×D311yescharacteristic
64#3967—61no—
65#3953—61no—
66#3946—61no—
67C8×Dic5—61no—
68#3941—61no—
69#3941—61no—
70C4⋊#168—31no—
71C4×#168—31no—
72#1682—151noSylow
73C22×D15—41no—
74C3×C5×Q8—41no—
75C3×C5×Q8—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4111yescharacteristic
80C2×Dic15—21no—
81C2×Dic15—21no—
82D60—41no—
83D60—41no—
84D60—41no—
85D60—41no—
86D60—81no—
87Dic30—21no—
88Dic30D812yes—
89C3×C5×C8—41no—
90C3×C5×C8—41no—
91C3⋊#168—21no—
92C3⋊#168—21no—
93C3⋊#168—41no—
94C3×C4⋊Q8C2×D511yescharacteristic
95C2×#216—101no—
96C2×#204—101no—
97#874—51no—
98C4×Dic6—51no—
99C3×C4⋊C8C2×D511yescharacteristic
100C3×C4⋊C8C2×D511yescharacteristic
101#835—101no—
102#821—101no—
103Dic3⋊C8—101no—
104C8×Dic3—101no—
105#809—101no—
106#809—101no—
107C4⋊(C3⋊C8)—51no—
108C4×C3⋊C8—51no—
109C2×C5×Q8—21no—
110C2×D20—61no—
111C2×D20—61no—
112C2×D20—61no—
113C2×Dic10—31no—
114C2×C5×C8—21no—
115C2×C5×C8—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C42×C5C22×D311yescharacteristic
119#689—122no—
120C4⋊Dic5—31no—
121#683—61no—
122C4×Dic5—61no—
123C2×#168—31no—
124C2×#168—31no—
125C2×#168—61no—
126#677—122no—
127#486—151no—
128#462—151no—
129#460—151no—
130C8×Q8—151no—
131#335—151no—
132#332D1511yescharacteristic, complemented
133#331—151no—
134C22×C3×C5#12111yescharacteristic
135C2×D15—81no—
136C2×D15—81no—
137C2×D15—81no—
138C3×C4×C5—21no—
139C3×C4×C5—81no—
140C3×C4×C5C2×D811yescharacteristic
141C3×C4×C5#13511yescharacteristic
142C3×C4×C5#13511yescharacteristic
143C3×C4×C5#13711yescharacteristic
144Dic15—22no—
145Dic15—41no—
146C2×C3×Q8—21no—
147C2×D12—101no—
148C2×D12—101no—
149C2×D12—101no—
150C2×Dic6—51no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C42C22×D511yescharacteristic
156#216—202no—
157C4⋊Dic3—51no—
158Dic3⋊C4—101no—
159C4×Dic3—101no—
160C2×C3⋊C8—51no—
161C2×C3⋊C8—51no—
162C2×C3⋊C8—101no—
163#204—202no—
164C22×D5—121no—
165C5×Q8—41no—
166C5×Q8—41no—
167C2×C4×C5—41no—
168C2×C4×C5#23511yescharacteristic
169C2×C4×C5D3×D411yescharacteristic
170C2×C4×C5D3×D411yescharacteristic
171C2×Dic5—61no—
172C2×Dic5—61no—
173D20—121no—
174D20—121no—
175D20—121no—
176D20—121no—
177D20—241no—
178Dic10—32no—
179Dic10—61no—
180C5×C8—41no—
181C5×C8—41no—
182#168—61no—
183#168—61no—
184#168—121no—
185C2×Q16—301no—
186C2×SD16—301no—
187C4⋊Q8C2×D1511yescharacteristic
188#127—151no—
189C4×Q8—151no—
190C4⋊C8—151no—
191C4⋊C8—301no—
192C4⋊C8C2×D1511yescharacteristic
193C4⋊C8C2×D1511yescharacteristic
194#103—301no—
195#102—301no—
196#102—301no—
197#102—301no—
198C4×C8—151no—
199C4×C8—301no—
200C2×C3×C5#46411yescharacteristic
201C2×C3×C5#46611yescharacteristic
202C2×C3×C5#47111yescharacteristic
203D15—161no—
204C22×D3—201no—
205C3×Q8—41no—
206C3×Q8—41no—
207C2×C3×C4—41no—
208C2×C3×C4#70911yescharacteristic
209C2×C3×C4D4×D511yescharacteristic
210C2×C3×C4D4×D511yescharacteristic
211C2×Dic3—101no—
212C2×Dic3—101no—
213D12—201no—
214D12—201no—
215D12—201no—
216D12—201no—
217D12—401no—
218Dic6—52no—
219Dic6—101no—
220C3×C8—41no—
221C3×C8—41no—
222C3⋊C8—101no—
223C3⋊C8—101no—
224C3⋊C8—201no—
225C22×C5#88411yescharacteristic
226C2×D5—241no—
227C2×D5—241no—
228C2×D5—241no—
229C4×C5—21no—
230C4×C5—81no—
231C4×C5D3×D811yescharacteristic
232C4×C5#91611yescharacteristic
233C4×C5#91611yescharacteristic
234C4×C5#91811yescharacteristic
235Dic5—62no—
236Dic5—121no—
237C2×Q8—21no—
238C2×Q8—151no—
239C2×D4—301no—
240C2×D4—301no—
241C2×D4—301no—
242Q16—602no—
243SD16—602no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—151no—
247C2×C8—151no—
248C2×C8—301no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—151no—
252C4⋊C4—301no—
253C42—301no—
254C42C22×D1511yescharacteristic
255C3×C5#168211yescharacteristic, complemented, Hall
256C22×C3#403011yescharacteristic
257C2×D3—401no—
258C2×D3—401no—
259C2×D3—401no—
260C3×C4—21no—
261C3×C4—81no—
262C3×C4D5×D811yescharacteristic
263C3×C4#406211yescharacteristic
264C3×C4#406211yescharacteristic
265C3×C4#406411yescharacteristic
266Dic3—102no—
267Dic3—201no—
268C2×C5#475411yescharacteristic
269C2×C5#477511yescharacteristic
270C2×C5#479811yescharacteristic
271D5—481no—
272C23—601no—
273Q8—41no—
274Q8—41no—
275Q8—152no—
276Q8—301no—
277D4—601no—
278D4—601no—
279D4—601no—
280D4—601no—
281D4—1201no—
282C2×C4—41no—
283C2×C4—301no—
284C2×C4—301no—
285C2×C4#681711yescharacteristic
286C2×C4D4×D1511yescharacteristic
287C2×C4D4×D1511yescharacteristic
288C8—41no—
289C8—41no—
290C8—301no—
291C8—301no—
292C8—601no—
293C2×C3#6504311yescharacteristic
294C2×C3#6506411yescharacteristic
295C2×C3#6508711yescharacteristic
296D3—801no—
297C5#6847011yescharacteristic, complemented, Sylow
298C22—1201no—
299C22—1201no—
300C22—1201no—
301C22#9177311yescharacteristic
302C4—21no—
303C4—81no—
304C4—302no—
305C4—601no—
306C4D8×D1511yescharacteristic
307C4#9180511yescharacteristic
308C4#9180511yescharacteristic
309C4#9180711yescharacteristic
310C3#1059926311yescharacteristic, complemented, Sylow
311C2—2401no—
312C2#1175085511yescharacteristic
313C2#1175087611yescharacteristic
314C2#1175089911yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5#121
prime radical#91763C22
hypercenter#332D15
hypocenterC3×C5#1682
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #11751191C2semidirect
4. #11750931C2semidirect
5. C3×C5×#332C2semidirect
7. #11746300C2semidirect
29. C5×#332D3semidirect
54. C3×#332D5semidirect
132. #332D15semidirect
255. C3×C5#1682semidirect
297. C5#68470semidirect
310. C3#10599263semidirect

Maximal subgroups

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

subgroupindex
#117511912
#117511892
#117509492
#117509312
C3×C5×#3322
#117463062
#117463002
#105992633
#684705