Finite Group Databasebeta

← #14316937

Subgroups — #14316937

Order 1920.

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

normal subgroups only

This group has 432 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×#563C211yesmaximal, characteristic, complemented
2#11751196C212yesmaximal, complemented
3#11751163C211yesmaximal, characteristic
4#11746369C212yesmaximal, complemented
5#11746363C211yesmaximal, characteristic, complemented
6#10602752—31nomaximal, Hall
7#92098C2211yescharacteristic
8C3×C5×C4⋊Q8C2212yes—
9C3×C5×#126—22no—
10C3×C5×#125—21no—
11C3×C5×#124C2211yescharacteristic
12C3×C5×#123—21no—
13C3×C5×C22⋊Q8—22no—
14#91831—22no—
15#91821—21no—
16#91120C2212yes—
17#91120C2211yescharacteristic
18#91089—22no—
19#91089—21no—
20#71959—51nomaximal, Hall
21C5×#563D311yescharacteristic, complemented
22#65384—32no—
23#65351—31no—
24#64768—32no—
25#64762—31no—
26C2×C3×C5×Q8D412yes—
27C2×C3×C5×Q8C2311yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C22×C3×C4×C5—21no—
30#6821—41no—
31Q8×D15—41no—
32#6817—21no—
33#6817—22no—
34C3×C5×C4⋊C4—21no—
35C3×C5×C4⋊C4—22no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—22no—
38C3×C5×C4⋊C4—22no—
39C3×C5×C22⋊C4—22no—
40C3×C5×C22⋊C4—21no—
41C3×C5×C22⋊C4—22no—
42C3×C42×C5D411yescharacteristic
43C3×C42×C5D412yes—
44#6718—42no—
45#6717—42no—
46#6716—41no—
47#6715—41no—
48#6710—21no—
49#6710—22no—
50C3×#563D511yescharacteristic, complemented
51#5095—52no—
52#5062—51no—
53#4548—52no—
54#4542—51no—
55#4147—31no—
56C5×C4⋊Q8C2×D312yes—
57C5×#126—22no—
58C5×#125—21no—
59C5×#124C2×D311yescharacteristic
60C5×#123—21no—
61C5×C22⋊Q8—22no—
62#4088—62no—
63#4078—61no—
64#3968—31no—
65#3968—32no—
66#3937—61no—
67#3937—62no—
68#2203—151noSylow
69C23×C3×C5—21no—
70C3×C5×Q8—41no—
71C3×C5×Q8—42no—
72C3×C5×D4—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—81no—
77C2×C3×C4×C5C2×D412yes—
78C2×C3×C4×C5C2×D411yescharacteristic
79#1220—41no—
80D60—21no—
81D60—22no—
82C4×D15—41no—
83C4×D15—42no—
84Dic30—21no—
85Dic30—22no—
86C3⋊#168—41no—
87C3⋊#168—42no—
88#1007—51no—
89C3×C4⋊Q8C2×D512yes—
90C3×#126—22no—
91C3×#125—21no—
92C3×#124C2×D511yescharacteristic
93C3×#123—21no—
94C3×C22⋊Q8—22no—
95#942—102no—
96#932—101no—
97#836—52no—
98#836—51no—
99#805—101no—
100#805—102no—
101C2×C5×Q8#6712yes—
102C2×C5×Q8C22×D311yescharacteristic
103C2×C5×D4#6711yescharacteristic
104C22×C4×C5—21no—
105#713—121no—
106Q8×D5—121no—
107#709—61no—
108#709—62no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—22no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—22no—
114C5×C22⋊C4—22no—
115C5×C22⋊C4—21no—
116C5×C22⋊C4—22no—
117C42×C5#6711yescharacteristic
118C42×C5#6712yes—
119#689—122no—
120#688—122no—
121#687—121no—
122#686—121no—
123#681—61no—
124#681—62no—
125#563D1511yescharacteristic, complemented
126#456—152no—
127#454—151no—
128#356—152no—
129#355—151no—
130C22×C3×C5—42no—
131C22×C3×C5—41no—
132C22×C3×C5#12011yescharacteristic
133C2×D15—41no—
134C3×C4×C5—21no—
135C3×C4×C5—22no—
136C3×C4×C5—41no—
137C3×C4×C5—42no—
138C3×C4×C5—42no—
139Dic15—41no—
140C2×C3×Q8C22⋊D512yes—
141C2×C3×Q8C22×D511yescharacteristic
142C2×C3×D4C22⋊D511yescharacteristic
143C22×C3×C4—21no—
144#239—201no—
145D3×Q8—201no—
146#235—101no—
147#235—102no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—22no—
152C3×C4⋊C4—22no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—21no—
155C3×C22⋊C4—22no—
156C3×C42C22⋊D511yescharacteristic
157C3×C42C22⋊D512yes—
158#216—202no—
159#215—202no—
160#214—201no—
161#213—201no—
162#208—101no—
163#208—102no—
164C23×C5—21no—
165C5×Q8—41no—
166C5×Q8—42no—
167C5×D4—41no—
168C2×C4×C5—21no—
169C2×C4×C5—22no—
170C2×C4×C5—22no—
171C2×C4×C5—81no—
172C2×C4×C5C2×#6712yes—
173C2×C4×C5C2×#6711yescharacteristic
174C22⋊D5—121no—
175D20—61no—
176D20—62no—
177C4×D5—121no—
178C4×D5—122no—
179Dic10—61no—
180Dic10—62no—
181#168—121no—
182#168—122no—
1832−1+4—151no—
184#137—302no—
185AGL(1,ℤ/8)—301no—
186C4⋊Q8C2×D1512yes—
187#126—22no—
188#125—21no—
189#124C2×D1511yescharacteristic
190#123—21no—
191C22⋊Q8—22no—
192#104—301no—
193#104—302no—
194#101—152no—
195#101—151no—
196C2×C3×C5—21no—
197C2×C3×C5—81no—
198C2×C3×C5B(4,𝔽2)11yescharacteristic
199D15—81no—
200C23×C3—21no—
201C3×Q8—41no—
202C3×Q8—42no—
203C3×D4—41no—
204C2×C3×C4—21no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—81no—
208C2×C3×C4C2×C22⋊D512yes—
209C2×C3×C4C2×C22⋊D511yescharacteristic
210#67—201no—
211D12—101no—
212D12—102no—
213C4×D3—201no—
214C4×D3—202no—
215Dic6—101no—
216Dic6—102no—
217C3⋊C8—201no—
218C3⋊C8—202no—
219C22×C5—42no—
220C22×C5—41no—
221C22×C5#95311yescharacteristic
222C2×D5—121no—
223C4×C5—21no—
224C4×C5—22no—
225C4×C5—41no—
226C4×C5—42no—
227C4×C5—42no—
228Dic5—121no—
229#41—301no—
230#41—302no—
231#41—601no—
232C2×Q8—601no—
233C2×Q8#122012yes—
234C2×Q8C22×D1511yescharacteristic
235C2×D4#122011yescharacteristic
236C22×C4—21no—
237Q16—602no—
238SD16—601no—
239SD16—602no—
240D8—601no—
241M16—301no—
242M16—302no—
243C4⋊C4—21no—
244C4⋊C4—22no—
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—21no—
250C22⋊C4—22no—
251C42#122011yescharacteristic
252C42#122012yes—
253C3×C5#220311yescharacteristic, complemented, Hall
254C22×C3—42no—
255C22×C3—41no—
256C22×C3#409911yescharacteristic
257C2×D3—201no—
258C3×C4—21no—
259C3×C4—22no—
260C3×C4—41no—
261C3×C4—42no—
262C3×C4—42no—
263Dic3—201no—
264C2×C5—21no—
265C2×C5—81no—
266C2×C5#524411yescharacteristic
267D5—241no—
268C23—21no—
269Q8—41no—
270Q8—42no—
271Q8—301no—
272Q8—302no—
273D4—41no—
274D4—301no—
275D4—302no—
276D4—601no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—81no—
281C2×C4—601no—
282C2×C4—602no—
283C2×C4C2×#122012yes—
284C2×C4C2×#122011yescharacteristic
285C8—601no—
286C8—602no—
287C2×C3—21no—
288C2×C3—81no—
289C2×C3#6553311yescharacteristic
290D3—401no—
291C5#7195911yescharacteristic, complemented, Sylow
292C22—42no—
293C22—41no—
294C22—601no—
295C22#9184211yescharacteristic
296C4—21no—
297C4—22no—
298C4—41no—
299C4—42no—
300C4—42no—
301C4—601no—
302C3#1060275211yescharacteristic, complemented, Sylow
303C2—21no—
304C2—81no—
305C2—1201no—
306C2#1175134511yescharacteristic
subgroupG/H
centerC2#11751345
commutator, cosocleC2×C3×C5×Q8C23
FrattiniC2×Q8C22×D15
FittingC3×C5×#563C2
socleC2×C3×C5B(4,𝔽2)
prime radical#11751163C2
hypercenter#563D15
hypocenterC3×C5#2203
LCSG ▷ C2×C3×C5×Q8 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #563

Complements

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

NH ≅ G/Ntype
1. C3×C5×#563C2semidirect
2. #11751196C2semidirect
4. #11746369C2semidirect
5. #11746363C2semidirect
21. C5×#563D3semidirect
50. C3×#563D5semidirect
125. #563D15semidirect
253. C3×C5#2203semidirect
291. C5#71959semidirect
302. C3#10602752semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5632
#117511962
#117511632
#117463692
#117463632
#106027523
#719595