Finite Group Databasebeta

← #11756434

Subgroups — #11756434

Order 960.

540 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×Q8×D15C211yesmaximal, characteristic, complemented
2C2×#6819C211yesmaximal, characteristic
3C3×C5×#124C211yesmaximal, characteristic, complemented
4#91833C211yesmaximal, characteristic, complemented
5#91825C211yesmaximal, characteristic, complemented
6#91772C214yesmaximal, complemented
7#91767C214yesmaximal, complemented
8#91761C211yesmaximal, characteristic, complemented
9#91758C211yesmaximal, characteristic, complemented
10#66009—31nomaximal, Hall
11C2×C3×C5×Q8C2211yescharacteristic
12C2×C3×C5×D4C2211yescharacteristic
13C2×#1220C2212yes—
14C22×Dic15C2212yes—
15Q8×D15—24no—
16#6819—24no—
17C2×C4×D15C2212yes—
18C2×C4×D15C2211yescharacteristic
19C2×Dic30C2211yescharacteristic
20C2×Dic30C2211yescharacteristic
21C2×Dic30C2212yes—
22C3×C5×C22⋊C4C2214yes—
23C3×C42×C5C2211yescharacteristic
24#6719C2214yes—
25#6714C2212yes—
26C4⋊Dic15C2214yes—
27#6712C2212yes—
28#6712C2214yes—
29C4×Dic15C2211yescharacteristic
30#5675—51nomaximal, Hall
31C2×Q8×D5—31no—
32C2×#711—31no—
33C5×#124D311yescharacteristic, complemented
34#4090—31no—
35#4082—31no—
36#4029—34no—
37#4024—34no—
38#4018—31no—
39#4015—31no—
40C23×C3×C5C2312yes—
41C22×D15C2311yescharacteristic
42C3×C5×Q8—22no—
43C3×C5×D4—22no—
44C2×C3×C4×C5C2312yes—
45C2×C3×C4×C5C2312yes—
46C2×C3×C4×C5C2311yescharacteristic
47#1220—24no—
48C2×Dic15—24no—
49C2×Dic15C2312yes—
50C2×Dic15C2312yes—
51C2×Dic15C2312yes—
52C2×Dic15C2311yescharacteristic
53C4×D15—24no—
54C4×D15D414yes—
55Dic30—22no—
56Dic30—22no—
57Dic30—24no—
58C2×D3×Q8—51no—
59C2×#237—51no—
60C3×#124D511yescharacteristic, complemented
61#944—51no—
62#936—51no—
63#883—54no—
64#878—54no—
65#872—51no—
66#869—51no—
67C2×C5×Q8C2×D311yescharacteristic
68C2×C5×D4C2×D311yescharacteristic
69C2×C22⋊D5—32no—
70C22×Dic5—32no—
71Q8×D5—64no—
72#711—64no—
73C2×C4×D5—31no—
74C2×C4×D5—32no—
75C2×Dic10—31no—
76C2×Dic10—31no—
77C2×Dic10—32no—
78C5×C22⋊C4C2×D314yes—
79C42×C5C2×D311yescharacteristic
80C22⋊Dic5—34no—
81#685—32no—
82C4⋊Dic5—34no—
83#683—32no—
84#683—34no—
85C4×Dic5—31no—
86#536—151noSylow
87C22×C3×C5—22no—
88C22×C3×C5—24no—
89C22×C3×C5C2411yescharacteristic
90C2×D15—22no—
91C2×D15C2×D412yes—
92C3×C4×C5—22no—
93C3×C4×C5—22no—
94C3×C4×C5C2×D412yes—
95Dic15—22no—
96Dic15—22no—
97Dic15—22no—
98Dic15C2×D412yes—
99C2×C3×Q8C2×D511yescharacteristic
100C2×C3×D4C2×D511yescharacteristic
101C2×#67—52no—
102C22×Dic3—52no—
103D3×Q8—104no—
104#237—104no—
105C2×C4×D3—51no—
106C2×C4×D3—52no—
107C2×Dic6—51no—
108C2×Dic6—51no—
109C2×Dic6—52no—
110C3×C22⋊C4C2×D514yes—
111C3×C42C2×D511yescharacteristic
112#217—54no—
113(C2×D3)⋊C4—52no—
114C4⋊Dic3—54no—
115Dic3⋊C4—52no—
116Dic3⋊C4—54no—
117C4×Dic3—51no—
118C23×C5C22×D312yes—
119C22×D5—31no—
120C5×Q8—22no—
121C5×D4—22no—
122C2×C4×C5C22×D312yes—
123C2×C4×C5C22×D312yes—
124C2×C4×C5C22×D311yescharacteristic
125C22⋊D5—64no—
126C2×Dic5—31no—
127C2×Dic5—32no—
128C2×Dic5—32no—
129C2×Dic5—32no—
130C2×Dic5—64no—
131C4×D5—34no—
132C4×D5—64no—
133Dic10—64no—
134Dic10—62no—
135Dic10—62no—
136C2×#41—151no—
137C22×Q8—151no—
138C4⋊Q8—151no—
139C4⋊Q8—151no—
140#124—151no—
141#124D1511yescharacteristic, complemented
142#123—154no—
143C22⋊Q8—154no—
144#117—151no—
145C2×C3×C5—42no—
146C2×C3×C5C22×D411yescharacteristic
147C2×C3×C52−1+412yes—
148D15—22no—
149C23×C3C22×D512yes—
150C22×D3—51no—
151C3×Q8—22no—
152C3×D4—22no—
153C2×C3×C4C22×D512yes—
154C2×C3×C4C22×D512yes—
155C2×C3×C4C22×D511yescharacteristic
156#67—104no—
157C2×Dic3—51no—
158C2×Dic3—52no—
159C2×Dic3—52no—
160C2×Dic3—52no—
161C2×Dic3—104no—
162C4×D3—54no—
163C4×D3—104no—
164Dic6—104no—
165Dic6—102no—
166Dic6—102no—
167C22×C5—22no—
168C22×C5—24no—
169C22×C5C23×D311yescharacteristic
170C2×D5—32no—
171C2×D5—62no—
172C4×C5—22no—
173C4×C5—22no—
174C4×C5D3×D412yes—
175Dic5—32no—
176Dic5—62no—
177Dic5—62no—
178Dic5—62no—
179#41—304no—
180C2×Q8—152no—
181C2×Q8—151no—
182C2×Q8—151no—
183C2×Q8—304no—
184C2×Q8C2×D1511yescharacteristic
185C2×D4—152no—
186C2×D4C2×D1511yescharacteristic
187C22×C4—151no—
188C22×C4—152no—
189C22×C4—152no—
190C4⋊C4—152no—
191C4⋊C4—154no—
192C4⋊C4—154no—
193C22⋊C4—154no—
194C22⋊C4—152no—
195C22⋊C4C2×D1514yes—
196C42—151no—
197C42C2×D1511yescharacteristic
198C3×C5#53611yescharacteristic, complemented, Hall
199C22×C3—22no—
200C22×C3—24no—
201C22×C3C23×D511yescharacteristic
202C2×D3—52no—
203C2×D3—102no—
204C3×C4—22no—
205C3×C4—22no—
206C3×C4D4×D512yes—
207Dic3—52no—
208Dic3—102no—
209Dic3—102no—
210Dic3—102no—
211C2×C5—42no—
212C2×C5C2×D3×D411yescharacteristic
213C2×C5#101012yes—
214D5—62no—
215C23—151no—
216C23C22×D1512yes—
217Q8—22no—
218Q8—304no—
219Q8—302no—
220Q8—302no—
221D4—22no—
222D4—304no—
223C2×C4—151no—
224C2×C4—154no—
225C2×C4—152no—
226C2×C4—152no—
227C2×C4—152no—
228C2×C4—304no—
229C2×C4—304no—
230C2×C4C22×D1512yes—
231C2×C4C22×D1512yes—
232C2×C4C22×D1511yescharacteristic
233C2×C3—42no—
234C2×C3C2×D4×D511yescharacteristic
235C2×C3#415012yes—
236D3—102no—
237C5#567511yescharacteristic, complemented, Sylow
238C22—22no—
239C22—24no—
240C22—152no—
241C22—302no—
242C22C23×D1511yescharacteristic
243C4—22no—
244C4—22no—
245C4—152no—
246C4—302no—
247C4—302no—
248C4—302no—
249C4D4×D1512yes—
250C3#6600911yescharacteristic, complemented, Sylow
251C2—42no—
252C2—302no—
253C2C2×D4×D1511yescharacteristic
254C2#9210112yes—
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#124C2
prime radicalC2×#6819C2
hypercenter#124D15
hypocenterC3×C5#536
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D15C2semidirect
3. C3×C5×#124C2semidirect
4. #91833C2semidirect
5. #91825C2semidirect
6. #91772C2semidirect
7. #91767C2semidirect
8. #91761C2semidirect
9. #91758C2semidirect
33. C5×#124D3semidirect
60. C3×#124D5semidirect
141. #124D15semidirect
198. C3×C5#536semidirect
237. C5#5675semidirect
250. C3#66009semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D152
C2×#68192
C3×C5×#1242
#918332
#918252
#917722
#917672
#917612
#917582
#660093
#56755