Finite Group Databasebeta

← #14316976

Subgroups — #14316976

Order 1920.

472 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 79 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×#555C211yesmaximal, characteristic, complemented
2#11751196C211yesmaximal, characteristic, complemented
3#11751163C212yesmaximal, complemented
4#11746369C211yesmaximal, characteristic, complemented
5#11746363C212yesmaximal, complemented
6#10602723—31nomaximal, Hall
7#92098C2211yescharacteristic
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×#124—21no—
10C3×C5×#124C2212yes—
11C3×C5×#121—22no—
12C3×C4×C5×D4—21no—
13C3×C5×#117—22no—
14#91831—21no—
15#91821—22no—
16#91120C2211yescharacteristic
17#91120C2212yes—
18#91089—21no—
19#91089—22no—
20#71930—51nomaximal, Hall
21C5×#555D311yescharacteristic, complemented
22#65384—31no—
23#65351—32no—
24#64768—31no—
25#64762—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×Q8C2311yescharacteristic
28C2×C3×C5×D4—21no—
29C2×C3×C5×D4—21no—
30C2×C3×C5×D4D412yes—
31C22×C3×C4×C5—22no—
32#6821—41no—
33Q8×D15—41no—
34#6817—22no—
35#6817—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—22no—
38C3×C5×C22⋊C4—22no—
39C3×C5×C22⋊C4—22no—
40C3×C5×C22⋊C4—22no—
41C3×C42×C5—21no—
42C3×C42×C5D412yes—
43C3×C42×C5D411yescharacteristic
44#6718—41no—
45#6717—41no—
46#6716—42no—
47#6715—42no—
48#6710—22no—
49#6710—21no—
50C3×#555D511yescharacteristic, complemented
51#5095—51no—
52#5062—52no—
53#4548—51no—
54#4542—52no—
55#4147—31no—
56C5×C4⋊Q8C2×D311yescharacteristic
57C5×#124—21no—
58C5×#124C2×D312yes—
59C5×#121—22no—
60C4×C5×D4—21no—
61C5×#117—22no—
62#4088—61no—
63#4078—62no—
64#3968—32no—
65#3968—31no—
66#3937—62no—
67#3937—61no—
68#2204—151noSylow
69C23×C3×C5—22no—
70C3×C5×Q8—41no—
71C3×C5×Q8—41no—
72C3×C5×D4—42no—
73C3×C5×D4—42no—
74C3×C5×D4—81no—
75C2×C3×C4×C5—21no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—44no—
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5C2×D412yes—
81#1220—41no—
82D60—22no—
83D60—21no—
84C4×D15—42no—
85C4×D15—41no—
86Dic30—22no—
87Dic30—21no—
88C3⋊#168—42no—
89C3⋊#168—41no—
90#1007—51no—
91C3×C4⋊Q8C2×D511yescharacteristic
92C3×#124—21no—
93C3×#124C2×D512yes—
94C3×#121—22no—
95C3×C4×D4—21no—
96C3×#117—22no—
97#942—101no—
98#932—102no—
99#836—51no—
100#836—52no—
101#805—102no—
102#805—101no—
103C2×C5×Q8#6711yescharacteristic
104C2×C5×Q8C22×D311yescharacteristic
105C2×C5×D4—21no—
106C2×C5×D4—21no—
107C2×C5×D4#6712yes—
108C22×C4×C5—22no—
109#713—121no—
110Q8×D5—121no—
111#709—62no—
112#709—61no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—22no—
115C5×C22⋊C4—22no—
116C5×C22⋊C4—22no—
117C5×C22⋊C4—22no—
118C42×C5—21no—
119C42×C5#6712yes—
120C42×C5#6711yescharacteristic
121#689—121no—
122#688—121no—
123#687—122no—
124#686—122no—
125#681—62no—
126#681—61no—
127#555D1511yescharacteristic, complemented
128#456—151no—
129#454—152no—
130#356—151no—
131#355—152no—
132C22×C3×C5—42no—
133C22×C3×C5—42no—
134C22×C3×C5—42no—
135C22×C3×C5#12011yescharacteristic
136C2×D15—41no—
137C3×C4×C5—22no—
138C3×C4×C5—22no—
139C3×C4×C5—21no—
140C3×C4×C5—42no—
141C3×C4×C5—41no—
142Dic15—41no—
143C2×C3×Q8C22⋊D511yescharacteristic
144C2×C3×Q8C22×D511yescharacteristic
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4C22⋊D512yes—
148C22×C3×C4—22no—
149#239—201no—
150D3×Q8—201no—
151#235—102no—
152#235—101no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—22no—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—22no—
158C3×C42—21no—
159C3×C42C22⋊D512yes—
160C3×C42C22⋊D511yescharacteristic
161#216—201no—
162#215—201no—
163#214—202no—
164#213—202no—
165#208—102no—
166#208—101no—
167C23×C5—22no—
168C5×Q8—41no—
169C5×Q8—41no—
170C5×D4—42no—
171C5×D4—42no—
172C5×D4—81no—
173C2×C4×C5—21no—
174C2×C4×C5—22no—
175C2×C4×C5—21no—
176C2×C4×C5—44no—
177C2×C4×C5C2×#6711yescharacteristic
178C2×C4×C5C2×#6712yes—
179C22⋊D5—121no—
180D20—62no—
181D20—61no—
182C4×D5—122no—
183C4×D5—121no—
184Dic10—62no—
185Dic10—61no—
186#168—122no—
187#168—121no—
1882−1+4—151no—
189#137—301no—
190AGL(1,ℤ/8)—302no—
191C4⋊Q8C2×D1511yescharacteristic
192#124—21no—
193#124C2×D1512yes—
194#121—22no—
195C4×D4—21no—
196#117—22no—
197#104—302no—
198#104—301no—
199#101—151no—
200#101—152no—
201C2×C3×C5—21no—
202C2×C3×C5—82no—
203C2×C3×C5B(4,𝔽2)11yescharacteristic
204D15—81no—
205C23×C3—22no—
206C3×Q8—41no—
207C3×Q8—41no—
208C3×D4—42no—
209C3×D4—42no—
210C3×D4—81no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—44no—
215C2×C3×C4C2×C22⋊D511yescharacteristic
216C2×C3×C4C2×C22⋊D512yes—
217#67—201no—
218D12—102no—
219D12—101no—
220C4×D3—202no—
221C4×D3—201no—
222Dic6—102no—
223Dic6—101no—
224C3⋊C8—202no—
225C3⋊C8—201no—
226C22×C5—42no—
227C22×C5—42no—
228C22×C5—42no—
229C22×C5#95311yescharacteristic
230C2×D5—121no—
231C4×C5—22no—
232C4×C5—22no—
233C4×C5—21no—
234C4×C5—42no—
235C4×C5—41no—
236Dic5—121no—
237#41—302no—
238#41—301no—
239#41—601no—
240C2×Q8—601no—
241C2×Q8#122011yescharacteristic
242C2×Q8C22×D1511yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4#122012yes—
246C22×C4—22no—
247Q16—601no—
248SD16—602no—
249SD16—601no—
250D8—602no—
251M16—302no—
252M16—301no—
253C4⋊C4—21no—
254C4⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C42—21no—
259C42#122012yes—
260C42#122011yescharacteristic
261C3×C5#220411yescharacteristic, complemented, Hall
262C22×C3—42no—
263C22×C3—42no—
264C22×C3—42no—
265C22×C3#409911yescharacteristic
266C2×D3—201no—
267C3×C4—22no—
268C3×C4—22no—
269C3×C4—21no—
270C3×C4—42no—
271C3×C4—41no—
272Dic3—201no—
273C2×C5—21no—
274C2×C5—82no—
275C2×C5#524411yescharacteristic
276D5—241no—
277C23—22no—
278Q8—41no—
279Q8—41no—
280Q8—302no—
281Q8—301no—
282D4—42no—
283D4—42no—
284D4—81no—
285D4—302no—
286D4—301no—
287D4—601no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—44no—
292C2×C4—602no—
293C2×C4—601no—
294C2×C4C2×#122011yescharacteristic
295C2×C4C2×#122012yes—
296C8—602no—
297C8—601no—
298C2×C3—21no—
299C2×C3—82no—
300C2×C3#6553311yescharacteristic
301D3—401no—
302C5#7193011yescharacteristic, complemented, Sylow
303C22—42no—
304C22—42no—
305C22—42no—
306C22—601no—
307C22#9184211yescharacteristic
308C4—22no—
309C4—22no—
310C4—21no—
311C4—42no—
312C4—41no—
313C4—601no—
314C3#1060272311yescharacteristic, complemented, Sylow
315C2—21no—
316C2—82no—
317C2—1201no—
318C2#1175134511yescharacteristic
subgroupG/H
centerC2#11751345
commutator, cosocleC2×C3×C5×Q8C23
FrattiniC2×Q8C22×D15
FittingC3×C5×#555C2
socleC2×C3×C5B(4,𝔽2)
hypercenter#555D15
hypocenterC3×C5#2204
LCSG ▷ C2×C3×C5×Q8 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #555

Complements

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

NH ≅ G/Ntype
1. C3×C5×#555C2semidirect
2. #11751196C2semidirect
3. #11751163C2semidirect
4. #11746369C2semidirect
5. #11746363C2semidirect
21. C5×#555D3semidirect
50. C3×#555D5semidirect
127. #555D15semidirect
261. C3×C5#2204semidirect
302. C5#71930semidirect
314. C3#10602723semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5552
#117511962
#117511632
#117463692
#117463632
#106027233
#719305