Finite Group Databasebeta

← #14291630

Subgroups — #14291630

Order 1920.

300 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 87 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
2#11751181C211yesmaximal, characteristic
3#11750951C211yesmaximal, characteristic
4#11750931C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic
6#11746302C211yesmaximal, characteristic
7#11746301C211yesmaximal, characteristic
8#10599259—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6718—21no—
11#91758C2211yescharacteristic
12C4×Dic30C2211yescharacteristic
13C3×C5×C4⋊C8C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15#91119—21no—
16#91102—21no—
17#91100—21no—
18#91098—21no—
19C8×Dic15—21no—
20#91092—21no—
21#91092—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68466—51nomaximal, Hall
25#65379—31no—
26#65368—31no—
27#65139—31no—
28#65119—31no—
29C5×#332D311yescharacteristic
30#64701—31no—
31#64700—31no—
32C2×C3×C5×Q8—21no—
33C2×Dic30—21no—
34C2×Dic30D411yescharacteristic
35C2×C3×C5×C8—21no—
36C2×C3×C5×C8—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C42×C5C2311yescharacteristic
40#6718—42no—
41C4⋊Dic15—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C2×C3⋊#168D411yescharacteristic
48C2×C3⋊#168D411yescharacteristic
49#5090—51no—
50#5080—51no—
51#4850—51no—
52#4830—51no—
53C3×#332D511yescharacteristic
54#4481—51no—
55#4480—51no—
56C5×C4⋊Q8C2×D311yescharacteristic
57C2×#689—61no—
58#4015—31no—
59C4×Dic10—31no—
60C5×C4⋊C8C2×D311yescharacteristic
61C5×C4⋊C8C2×D311yescharacteristic
62#3967—61no—
63#3950—61no—
64#3948—61no—
65#3946—61no—
66C8×Dic5—61no—
67#3940—61no—
68#3940—61no—
69C4⋊#168—31no—
70C4×#168—31no—
71#1672—151noSylow
72C3×C5×Q8—41no—
73C3×C5×Q8—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5#4111yescharacteristic
78C2×Dic15—21no—
79C2×Dic15—21no—
80C2×Dic15—41no—
81Dic30—21no—
82Dic30—81no—
83Dic30SD1612yes—
84C3×C5×C8—41no—
85C3×C5×C8—41no—
86C3⋊#168—21no—
87C3⋊#168—41no—
88C3⋊#168Q1612yescomplemented
89C3×C4⋊Q8C2×D511yescharacteristic
90C2×#216—101no—
91#869—51no—
92C4×Dic6—51no—
93C3×C4⋊C8C2×D511yescharacteristic
94C3×C4⋊C8C2×D511yescharacteristic
95#835—101no—
96#818—101no—
97#816—101no—
98Dic3⋊C8—101no—
99C8×Dic3—101no—
100#808—101no—
101#808—101no—
102C4⋊(C3⋊C8)—51no—
103C4×C3⋊C8—51no—
104C2×C5×Q8—21no—
105C2×Dic10—31no—
106C2×Dic10—61no—
107C2×C5×C8—21no—
108C2×C5×C8—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C42×C5C22×D311yescharacteristic
112#689—122no—
113C4⋊Dic5—31no—
114C4⋊Dic5—61no—
115C4⋊Dic5—61no—
116#683—61no—
117C4×Dic5—61no—
118C2×#168—31no—
119C2×#168—31no—
120C2×#168—61no—
121#498—151no—
122#477—151no—
123#462—151no—
124C8×Q8—151no—
125#334—151no—
126#333—151no—
127#332D1511yescharacteristic
128C22×C3×C5#12111yescharacteristic
129C3×C4×C5—21no—
130C3×C4×C5—81no—
131C3×C4×C5C2×SD1611yescharacteristic
132C3×C4×C5C2×Q1611yescharacteristic
133C3×C4×C5#13511yescharacteristic
134C3×C4×C5#13711yescharacteristic
135Dic15—22no—
136Dic15—41no—
137Dic15—81no—
138C2×C3×Q8—21no—
139C2×Dic6—51no—
140C2×Dic6—101no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C42C22×D511yescharacteristic
146#216—202no—
147C4⋊Dic3—51no—
148C4⋊Dic3—101no—
149C4⋊Dic3—101no—
150Dic3⋊C4—101no—
151C4×Dic3—101no—
152C2×C3⋊C8—51no—
153C2×C3⋊C8—51no—
154C2×C3⋊C8—101no—
155C5×Q8—41no—
156C5×Q8—41no—
157C2×C4×C5—41no—
158C2×C4×C5#23511yescharacteristic
159C2×C4×C5D3×D411yescharacteristic
160C2×C4×C5D3×D411yescharacteristic
161C2×Dic5—61no—
162C2×Dic5—61no—
163C2×Dic5—121no—
164Dic10—32no—
165Dic10—61no—
166Dic10—241no—
167C5×C8—41no—
168C5×C8—41no—
169#168—32no—
170#168—61no—
171#168—121no—
172C2×Q16—301no—
173C4⋊Q8—151no—
174C4⋊Q8C2×D1511yescharacteristic
175C4×Q8—151no—
176#107—301no—
177#106—301no—
178#106—301no—
179C4⋊C8—151no—
180C4⋊C8—301no—
181C4⋊C8C2×D1511yescharacteristic
182C4⋊C8C2×D1511yescharacteristic
183#103—301no—
184#103—301no—
185C4×C8—151no—
186C4×C8—301no—
187C2×C3×C5#46211yescharacteristic
188C2×C3×C5#46511yescharacteristic
189C2×C3×C5#47111yescharacteristic
190C3×Q8—41no—
191C3×Q8—41no—
192C2×C3×C4—41no—
193C2×C3×C4#70911yescharacteristic
194C2×C3×C4D4×D511yescharacteristic
195C2×C3×C4D4×D511yescharacteristic
196C2×Dic3—101no—
197C2×Dic3—101no—
198C2×Dic3—201no—
199Dic6—52no—
200Dic6—101no—
201Dic6—401no—
202C3×C8—41no—
203C3×C8—41no—
204C3⋊C8—52no—
205C3⋊C8—101no—
206C3⋊C8—201no—
207C22×C5#88411yescharacteristic
208C4×C5—21no—
209C4×C5—81no—
210C4×C5#91211yescharacteristic
211C4×C5D3×SD1611yescharacteristic
212C4×C5#91511yescharacteristic
213C4×C5D3×Q1611yescharacteristic
214Dic5—62no—
215Dic5—121no—
216Dic5—241no—
217C2×Q8—21no—
218C2×Q8—151no—
219C2×Q8—301no—
220Q16—602no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—151no—
224C2×C8—151no—
225C2×C8—301no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—151no—
229C4⋊C4—301no—
230C4⋊C4—301no—
231C4⋊C4—301no—
232C42—301no—
233C42C22×D1511yescharacteristic
234C3×C5#167211yescharacteristic, complemented, Hall
235C22×C3#403011yescharacteristic
236C3×C4—21no—
237C3×C4—81no—
238C3×C4#405811yescharacteristic
239C3×C4D5×SD1611yescharacteristic
240C3×C4#406111yescharacteristic
241C3×C4D5×Q1611yescharacteristic
242Dic3—102no—
243Dic3—201no—
244Dic3—401no—
245C2×C5#475411yescharacteristic
246C2×C5#477811yescharacteristic
247C2×C5#479511yescharacteristic
248Q8—41no—
249Q8—41no—
250Q8—152no—
251Q8—301no—
252Q8—1201no—
253C2×C4—41no—
254C2×C4—301no—
255C2×C4—301no—
256C2×C4—601no—
257C2×C4#681711yescharacteristic
258C2×C4D4×D1511yescharacteristic
259C2×C4D4×D1511yescharacteristic
260C8—41no—
261C8—41no—
262C8—152no—
263C8—301no—
264C8—601no—
265C2×C3#6504311yescharacteristic
266C2×C3#6506711yescharacteristic
267C2×C3#6508211yescharacteristic
268C5#6846611yescharacteristic, complemented, Sylow
269C22#9177311yescharacteristic
270C4—21no—
271C4—81no—
272C4—302no—
273C4—601no—
274C4—1201no—
275C4#9180111yescharacteristic
276C4SD16×D1511yescharacteristic
277C4#9180411yescharacteristic
278C4Q16×D1511yescharacteristic
279C3#1059925911yescharacteristic, complemented, Sylow
280C2#1175085511yescharacteristic
281C2#1175087911yescharacteristic
282C2#1175089611yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socle, prime radicalC22×C3×C5#121
hypercenter#332D15
hypocenterC3×C5#1672
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
88. C3⋊#168Q16semidirect
234. C3×C5#1672semidirect
268. C5#68466semidirect
279. C3#10599259semidirect

Maximal subgroups

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

subgroupindex
#117511912
#117511812
#117509512
#117509312
C3×C5×#3322
#117463022
#117463012
#105992593
#684665