Finite Group Databasebeta

← #14292596

Subgroups — #14292596

Order 1920.

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

normal subgroups only

This group has 304 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#11751195C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic
3#11750952C211yesmaximal, characteristic
4#11750932C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic
6#11746303C211yesmaximal, characteristic
7#11746301C211yesmaximal, characteristic
8#10599266—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6718—21no—
11C2×#6718—21no—
12#91758C2211yescharacteristic
13C4×Dic30C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16#91101—21no—
17#91100—21no—
18#91099—21no—
19#91098—21no—
20#91094—21no—
21#91092—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68473—51nomaximal, Hall
25#65383—31no—
26#65381—31no—
27#65140—31no—
28#65120—31no—
29C5×#332D311yescharacteristic
30#64702—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—
41#6718—42no—
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15D411yescharacteristic
45#6712—21no—
46C4×Dic15—21no—
47C2×C3⋊#168—21no—
48C2×C3⋊#168D411yescharacteristic
49C2×C3⋊#168D411yescharacteristic
50#5094—51no—
51#5092—51no—
52#4851—51no—
53#4831—51no—
54C3×#332D511yescharacteristic
55#4482—51no—
56#4480—51no—
57C5×C4⋊Q8C2×D311yescharacteristic
58C2×#689—61no—
59C2×#689—61no—
60#4015—31no—
61C4×Dic10—31no—
62C5×C4⋊C8C2×D311yescharacteristic
63C5×C4⋊C8C2×D311yescharacteristic
64#3949—61no—
65#3948—61no—
66#3947—61no—
67#3946—61no—
68#3942—61no—
69#3940—61no—
70C4⋊#168—31no—
71C4×#168—31no—
72#1690—151noSylow
73C3×C5×Q8—41no—
74C3×C5×Q8—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5#4111yescharacteristic
79C2×Dic15—21no—
80C2×Dic15—21no—
81C2×Dic15—41no—
82Dic30—21no—
83Dic30—21no—
84Dic30—41no—
85Dic30—41no—
86C3×C5×C8—41no—
87C3×C5×C8—41no—
88C3⋊#168—21no—
89C3⋊#168—41no—
90C3⋊#168SD1612yes—
91C3×C4⋊Q8C2×D511yescharacteristic
92C2×#216—101no—
93C2×#216—101no—
94#869—51no—
95C4×Dic6—51no—
96C3×C4⋊C8C2×D511yescharacteristic
97C3×C4⋊C8C2×D511yescharacteristic
98#817—101no—
99#816—101no—
100#815—101no—
101Dic3⋊C8—101no—
102#810—101no—
103#808—101no—
104C4⋊(C3⋊C8)—51no—
105C4×C3⋊C8—51no—
106C2×C5×Q8—21no—
107C2×Dic10—31no—
108C2×Dic10—61no—
109C2×C5×C8—21no—
110C2×C5×C8—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C42×C5C22×D311yescharacteristic
114#689—122no—
115#689—122no—
116C4⋊Dic5—31no—
117C4⋊Dic5—61no—
118C4⋊Dic5—61no—
119#683—61no—
120C4×Dic5—61no—
121C2×#168—31no—
122C2×#168—31no—
123C2×#168—61no—
124#494—151no—
125#475—151no—
126#475—151no—
127#446—151no—
128#334—151no—
129#332—151no—
130#332D1511yescharacteristic
131C22×C3×C5#12111yescharacteristic
132C3×C4×C5—21no—
133C3×C4×C5—81no—
134C3×C4×C5C2×SD1611yescharacteristic
135C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
136C3×C4×C5#13711yescharacteristic
137C3×C4×C5#13711yescharacteristic
138Dic15—41no—
139Dic15—41no—
140Dic15—81no—
141C2×C3×Q8—21no—
142C2×Dic6—51no—
143C2×Dic6—101no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C42C22×D511yescharacteristic
149#216—202no—
150#216—202no—
151C4⋊Dic3—51no—
152C4⋊Dic3—101no—
153C4⋊Dic3—101no—
154Dic3⋊C4—101no—
155C4×Dic3—101no—
156C2×C3⋊C8—51no—
157C2×C3⋊C8—51no—
158C2×C3⋊C8—101no—
159C5×Q8—41no—
160C5×Q8—41no—
161C2×C4×C5—41no—
162C2×C4×C5#23511yescharacteristic
163C2×C4×C5D3×D411yescharacteristic
164C2×C4×C5D3×D411yescharacteristic
165C2×Dic5—61no—
166C2×Dic5—61no—
167C2×Dic5—121no—
168Dic10—61no—
169Dic10—61no—
170Dic10—121no—
171Dic10—121no—
172C5×C8—41no—
173C5×C8—41no—
174#168—32no—
175#168—61no—
176#168—121no—
177C2×Q16—301no—
178C2×Q16—301no—
179C4⋊Q8—151no—
180C4⋊Q8C2×D1511yescharacteristic
181C4×Q8—151no—
182#106—301no—
183#106—301no—
184C4⋊C8—151no—
185C4⋊C8—301no—
186C4⋊C8C2×D1511yescharacteristic
187C4⋊C8C2×D1511yescharacteristic
188#103—301no—
189#103—301no—
190#97—301no—
191C4×C8—151no—
192C2×C3×C5#46011yescharacteristic
193C2×C3×C5#47011yescharacteristic
194C2×C3×C5#47311yescharacteristic
195C3×Q8—41no—
196C3×Q8—41no—
197C2×C3×C4—41no—
198C2×C3×C4#70911yescharacteristic
199C2×C3×C4D4×D511yescharacteristic
200C2×C3×C4D4×D511yescharacteristic
201C2×Dic3—101no—
202C2×Dic3—101no—
203C2×Dic3—201no—
204Dic6—101no—
205Dic6—101no—
206Dic6—201no—
207Dic6—201no—
208C3×C8—41no—
209C3×C8—41no—
210C3⋊C8—52no—
211C3⋊C8—101no—
212C3⋊C8—201no—
213C22×C5#88411yescharacteristic
214C4×C5—21no—
215C4×C5—81no—
216C4×C5#91111yescharacteristic
217C4×C5D3×SD1611yescharacteristic
218C4×C5#91511yescharacteristic
219C4×C5#91811yescharacteristic
220Dic5—121no—
221Dic5—121no—
222Dic5—241no—
223C2×Q8—21no—
224C2×Q8—151no—
225C2×Q8—301no—
226Q16—602no—
227Q16—602no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—151no—
231C2×C8—151no—
232C2×C8—301no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—151no—
236C4⋊C4—301no—
237C4⋊C4—301no—
238C4⋊C4—301no—
239C42—301no—
240C42C22×D1511yescharacteristic
241C3×C5#169011yescharacteristic, complemented, Hall
242C22×C3#403011yescharacteristic
243C3×C4—21no—
244C3×C4—81no—
245C3×C4#405711yescharacteristic
246C3×C4D5×SD1611yescharacteristic
247C3×C4#406111yescharacteristic
248C3×C4#406411yescharacteristic
249Dic3—201no—
250Dic3—201no—
251Dic3—401no—
252C2×C5#475511yescharacteristic
253C2×C5#476211yescharacteristic
254C2×C5#481611yescharacteristic
255Q8—41no—
256Q8—41no—
257Q8—301no—
258Q8—301no—
259Q8—601no—
260Q8—601no—
261C2×C4—41no—
262C2×C4—301no—
263C2×C4—301no—
264C2×C4—601no—
265C2×C4#681711yescharacteristic
266C2×C4D4×D1511yescharacteristic
267C2×C4D4×D1511yescharacteristic
268C8—41no—
269C8—41no—
270C8—152no—
271C8—301no—
272C8—601no—
273C2×C3#6504411yescharacteristic
274C2×C3#6505111yescharacteristic
275C2×C3#6510511yescharacteristic
276C5#6847311yescharacteristic, complemented, Sylow
277C22#9177311yescharacteristic
278C4—21no—
279C4—81no—
280C4—601no—
281C4—601no—
282C4—1201no—
283C4#9180011yescharacteristic
284C4SD16×D1511yescharacteristic
285C4#9180411yescharacteristic
286C4#9180711yescharacteristic
287C3#1059926611yescharacteristic, complemented, Sylow
288C2#1175085611yescharacteristic
289C2#1175086311yescharacteristic
290C2#1175091711yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socle, prime radicalC22×C3×C5#121
hypercenter#332D15
hypocenterC3×C5#1690
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
241. C3×C5#1690semidirect
276. C5#68473semidirect
287. C3#10599266semidirect

Maximal subgroups

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

subgroupindex
#117511952
#117511932
#117509522
#117509322
C3×C5×#3322
#117463032
#117463012
#105992663
#684735