Finite Group Databasebeta

← #14293716

Subgroups — #14293716

Order 1920.

440 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C3×C5×#492C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic, complemented
3#11751181C211yesmaximal, characteristic, complemented
4#11751177C211yesmaximal, characteristic, complemented
5#11751174C211yesmaximal, characteristic
6#11750795C211yesmaximal, characteristic, complemented
7#11746275C211yesmaximal, characteristic, complemented
8#10602052—31nomaximal, Hall
9C2×C3×C5×SD16—22no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#127C2211yescharacteristic
12C2×#6716—22no—
13C2×#6715—22no—
14#91763C2211yescharacteristic
15#91758C2211yescharacteristic
16C3×C4×C5×C8C2211yescharacteristic
17#91105—22no—
18#91093—22no—
19#91092—22no—
20C4×C3⋊#168C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22#71259—51nomaximal, Hall
23C5×#492D311yescharacteristic, complemented
24#65377—31no—
25#65368—31no—
26#65365—31no—
27#65362—31no—
28#64983—31no—
29#64674—31no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×Dic30—21no—
38C3×C5×SD16—44no—
39C2×C3×C5×C8D412yes—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43#6716—44no—
44#6715—44no—
45C4⋊Dic15—21no—
46C4⋊Dic15—21no—
47C2×C3⋊#168D412yes—
48C2×C3⋊#168D412yes—
49C3×#492D511yescharacteristic, complemented
50#5088—51no—
51#5080—51no—
52#5076—51no—
53#5073—51no—
54#4694—51no—
55#4454—51no—
56C2×C5×SD16—22no—
57C5×C4⋊Q8C2×D311yescharacteristic
58C5×#127C2×D311yescharacteristic
59C2×#687—62no—
60C2×#686—62no—
61#4020—31no—
62#4015—31no—
63C4×C5×C8C2×D311yescharacteristic
64#3953—62no—
65#3941—62no—
66#3940—62no—
67C4×#168—31no—
68C4×#168—31no—
69#1715—151noSylow
70C23×C3×C5—41no—
71C22×D15—41no—
72C3×C5×Q8—42no—
73C3×C5×D4—42no—
74C3×C5×D4—42no—
75C3×C5×D4—42no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×Dic15—41no—
81D60—42no—
82D60—42no—
83D60—42no—
84Dic30—42no—
85C3×C5×C8—22no—
86C3⋊#168—22no—
87C3⋊#168SD1614yescomplemented
88C2×C3×SD16—22no—
89C3×C4⋊Q8C2×D511yescharacteristic
90C3×#127C2×D511yescharacteristic
91C2×#214—102no—
92C2×#213—102no—
93#874—51no—
94#869—51no—
95C3×C4×C8C2×D511yescharacteristic
96#821—102no—
97#809—102no—
98#808—102no—
99C4×C3⋊C8—51no—
100C4×C3⋊C8—51no—
101C2×C5×Q8—21no—
102C2×C5×D4—21no—
103C2×C5×D4—21no—
104C2×C5×D4—21no—
105C2×D20—61no—
106C2×D20—61no—
107C2×D20—61no—
108C2×Dic10—61no—
109C5×SD16—44no—
110C2×C5×C8#6712yes—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C42×C5C22×D311yescharacteristic
114#687—124no—
115#686—124no—
116C4⋊Dic5—61no—
117C4⋊Dic5—61no—
118C2×#168—32no—
119C2×#168—32no—
120#498—151no—
121#493—151no—
122#492—151no—
123#492D1511yescharacteristic, complemented
124#486—151no—
125#486—151no—
126#322—151no—
127C22×C3×C5—81no—
128C22×C3×C5—81no—
129C22×C3×C5—81no—
130C22×C3×C5#12711yescharacteristic
131C2×D15—81no—
132C2×D15—81no—
133C2×D15—81no—
134C3×C4×C5—81no—
135C3×C4×C5C2×SD1612yes—
136C3×C4×C5AGL(1,ℤ/8)12yes—
137C3×C4×C5AGL(1,ℤ/8)12yes—
138Dic15—81no—
139C2×C3×Q8—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×D12—101no—
144C2×D12—101no—
145C2×D12—101no—
146C2×Dic6—101no—
147C3×SD16—44no—
148C2×C3×C8C22⋊D512yes—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C42C22×D511yescharacteristic
152#214—204no—
153#213—204no—
154C4⋊Dic3—101no—
155C4⋊Dic3—101no—
156C2×C3⋊C8—52no—
157C2×C3⋊C8—52no—
158C23×C5—41no—
159C22×D5—121no—
160C5×Q8—42no—
161C5×D4—42no—
162C5×D4—42no—
163C5×D4—42no—
164C2×C4×C5—41no—
165C2×C4×C5D3×D411yescharacteristic
166C2×C4×C5D3×D411yescharacteristic
167C2×C4×C5C2×#6711yescharacteristic
168C2×Dic5—121no—
169D20—122no—
170D20—122no—
171D20—122no—
172Dic10—122no—
173C5×C8—22no—
174#168—34no—
175#168—62no—
176C2×SD16—22no—
177C2×SD16—302no—
178C2×D8—302no—
179C4⋊Q8—151no—
180C4⋊Q8C2×D1511yescharacteristic
181#127—151no—
182#127C2×D1511yescharacteristic
183#106—302no—
184#102—302no—
185#102—302no—
186C4×C8—151no—
187C4×C8—151no—
188C4×C8C2×D1511yescharacteristic
189C2×C3×C5—161no—
190C2×C3×C5#49211yescharacteristic
191C2×C3×C5#49611yescharacteristic
192C2×C3×C5#49611yescharacteristic
193D15—161no—
194C23×C3—41no—
195C22×D3—201no—
196C3×Q8—42no—
197C3×D4—42no—
198C3×D4—42no—
199C3×D4—42no—
200C2×C3×C4—41no—
201C2×C3×C4D4×D511yescharacteristic
202C2×C3×C4D4×D511yescharacteristic
203C2×C3×C4C2×C22⋊D511yescharacteristic
204C2×Dic3—201no—
205D12—202no—
206D12—202no—
207D12—202no—
208Dic6—202no—
209C3×C8—22no—
210C3⋊C8—54no—
211C3⋊C8—102no—
212C22×C5—81no—
213C22×C5—81no—
214C22×C5—81no—
215C22×C5#94011yescharacteristic
216C2×D5—241no—
217C2×D5—241no—
218C2×D5—241no—
219C4×C5—81no—
220C4×C5D3×SD1612yes—
221C4×C5#91412yes—
222C4×C5#93212yes—
223Dic5—241no—
224C2×Q8—21no—
225C2×Q8—301no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—301no—
230C2×D4—301no—
231C2×D4—301no—
232SD16—44no—
233SD16—604no—
234D8—604no—
235C2×C8—152no—
236C2×C8—152no—
237C2×C8#122012yes—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—301no—
241C4⋊C4—301no—
242C42C22×D1511yescharacteristic
243C3×C5#171511yescharacteristic, complemented, Hall
244C22×C3—81no—
245C22×C3—81no—
246C22×C3—81no—
247C22×C3#408611yescharacteristic
248C2×D3—401no—
249C2×D3—401no—
250C2×D3—401no—
251C3×C4—81no—
252C3×C4D5×SD1612yes—
253C3×C4#406012yes—
254C3×C4#407812yes—
255Dic3—401no—
256C2×C5—161no—
257C2×C5#507411yescharacteristic
258C2×C5#517511yescharacteristic
259C2×C5#517611yescharacteristic
260D5—481no—
261C23—41no—
262C23—601no—
263Q8—42no—
264Q8—602no—
265D4—42no—
266D4—42no—
267D4—42no—
268D4—602no—
269D4—602no—
270D4—602no—
271C2×C4—41no—
272C2×C4—601no—
273C2×C4D4×D1511yescharacteristic
274C2×C4D4×D1511yescharacteristic
275C2×C4C2×#122011yescharacteristic
276C8—22no—
277C8—154no—
278C8—302no—
279C2×C3—161no—
280C2×C3#6536311yescharacteristic
281C2×C3#6546411yescharacteristic
282C2×C3#6546511yescharacteristic
283D3—801no—
284C5#7125911yescharacteristic, complemented, Sylow
285C22—81no—
286C22—81no—
287C22—81no—
288C22—1201no—
289C22—1201no—
290C22—1201no—
291C22#9182911yescharacteristic
292C4—81no—
293C4—1201no—
294C4SD16×D1512yes—
295C4#9180312yes—
296C4#9182112yes—
297C3#1060205211yescharacteristic, complemented, Sylow
298C2—161no—
299C2—2401no—
300C2#1175117511yescharacteristic
301C2#1175127611yescharacteristic
302C2#1175127711yescharacteristic
subgroupG/H
centerC22#91829
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#492C2
socleC22×C3×C5#127
prime radical#11751174C2
hypercenter#492D15
hypocenterC3×C5#1715
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C3×C5×#492C2semidirect
2. #11751189C2semidirect
3. #11751181C2semidirect
4. #11751177C2semidirect
6. #11750795C2semidirect
7. #11746275C2semidirect
23. C5×#492D3semidirect
49. C3×#492D5semidirect
87. C3⋊#168SD16semidirect
123. #492D15semidirect
243. C3×C5#1715semidirect
284. C5#71259semidirect
297. C3#10602052semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4922
#117511892
#117511812
#117511772
#117511742
#117507952
#117462752
#106020523
#712595