Finite Group Databasebeta

← #11754739

Subgroups — #11754739

Order 960.

424 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 130 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
1D4×Dic15C211yesmaximal, characteristic
2C5×#936C211yesmaximal, characteristic
3C3×#4082C211yesmaximal, characteristic
4#91576C212yesmaximal, complemented
5#91532C212yesmaximal, complemented
6#91531C212yesmaximal, complemented
7#91530C212yesmaximal, complemented
8C4×#1204C211yesmaximal, characteristic, complemented
9#91385C211yesmaximal, characteristic, complemented
10Dic5×Dic6C211yesmaximal, characteristic, complemented
11Dic3×Dic10C211yesmaximal, characteristic, complemented
12#66005—31nomaximal, Hall
13C2×C3×C5×D4C2211yescharacteristic
14C22×Dic15C2212yes—
15C2×C5×Dic6C2211yescharacteristic
16C2×C3×Dic10C2211yescharacteristic
17C2×#1204C2211yescharacteristic
18#6719C2212yes—
19C4⋊Dic15C2211yescharacteristic
20C4×Dic15C2211yescharacteristic
21C5×#217C2212yes—
22C5×#217C2212yes—
23C4×C5×Dic3C2211yescharacteristic
24C3×C22⋊Dic5C2212yes—
25C3×C22⋊Dic5C2212yes—
26C3×C4×Dic5C2211yescharacteristic
27Dic3⋊Dic5C2211yescharacteristic
28Dic3⋊Dic5C2212yes—
29#6669C2211yescharacteristic
30#6669C2212yes—
31#6669C2212yes—
32#6668C2211yescharacteristic
33#6668C2212yes—
34Dic3×Dic5C2212yes—
35Dic3×Dic5C2212yes—
36#5671—51nomaximal, Hall
37C5×#124—31no—
38Q8×Dic5—31no—
39#4090—31no—
40#4082D311yescharacteristic
41D4×Dic5—31no—
42#4025—32no—
43#4025—32no—
44#4024—32no—
45#4023—32no—
46C4×Dic10—31no—
47C4×Dic10—31no—
48C23×C3×C5C2312yes—
49C3×C5×D4—22no—
50C2×C3×C4×C5C2311yescharacteristic
51C2×Dic15—24no—
52C2×Dic15C2312yes—
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55C2×C5×Dic3C2311yescharacteristic
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C5×Dic6—22no—
59C2×C3×Dic5C2311yescharacteristic
60C2×C3×Dic5C2312yes—
61C2×C3×Dic5C2311yescharacteristic
62C3×Dic10—22no—
63#1204—22no—
64C3×#124—51no—
65Q8×Dic3—51no—
66#944—51no—
67#936D511yescharacteristic
68D4×Dic3—51no—
69#879—52no—
70#879—52no—
71#878—52no—
72#877—52no—
73C4×Dic6—51no—
74C4×Dic6—51no—
75C2×C5×Q8—31no—
76C2×C5×D4C2×D311yescharacteristic
77C22×Dic5—32no—
78C2×Dic10—31no—
79C2×Dic10C2×D311yescharacteristic
80C5×C22⋊C4—32no—
81C5×C22⋊C4—32no—
82C42×C5—31no—
83C22⋊Dic5—32no—
84C22⋊Dic5C2×D312yes—
85C22⋊Dic5C2×D312yes—
86C4⋊Dic5—31no—
87C4⋊Dic5—31no—
88C4⋊Dic5—32no—
89#683—32no—
90#683—31no—
91#683—31no—
92#683—32no—
93#683—32no—
94C4×Dic5—31no—
95C4×Dic5—32no—
96C4×Dic5—32no—
97C4×Dic5C2×D311yescharacteristic
98#556—151noSylow
99C22×C3×C5—22no—
100C22×C3×C5—22no—
101C22×C3×C5—22no—
102C22×C3×C5C2411yescharacteristic
103C3×C4×C5#4112yes—
104Dic15—22no—
105Dic15—21no—
106Dic15#4112yes—
107C3×Dic5—21no—
108C3×Dic5—22no—
109C3×Dic5—21no—
110C5×Dic3—21no—
111C5×Dic3—22no—
112C5×Dic3—21no—
113C2×C3×Q8—51no—
114C2×C3×D4C2×D511yescharacteristic
115C22×Dic3—52no—
116C2×Dic6—51no—
117C2×Dic6C2×D511yescharacteristic
118C3×C22⋊C4—52no—
119C3×C22⋊C4—52no—
120C3×C42—51no—
121#217—52no—
122#217C2×D512yes—
123#217C2×D512yes—
124C4⋊Dic3—51no—
125C4⋊Dic3—51no—
126C4⋊Dic3—52no—
127Dic3⋊C4—51no—
128Dic3⋊C4—52no—
129Dic3⋊C4—52no—
130Dic3⋊C4—52no—
131Dic3⋊C4—51no—
132C4×Dic3—51no—
133C4×Dic3—52no—
134C4×Dic3—52no—
135C4×Dic3C2×D511yescharacteristic
136C23×C5C22×D312yes—
137C5×Q8—62no—
138C5×D4—22no—
139C2×C4×C5—31no—
140C2×C4×C5—32no—
141C2×C4×C5—31no—
142C2×C4×C5C22×D311yescharacteristic
143C2×Dic5—31no—
144C2×Dic5—32no—
145C2×Dic5—31no—
146C2×Dic5—64no—
147C2×Dic5C22×D311yescharacteristic
148C2×Dic5C22×D312yes—
149C2×Dic5C22×D311yescharacteristic
150Dic10—22no—
151Dic10—62no—
152C4⋊Q8—151no—
153#126—152no—
154#126—152no—
155#124—31no—
156#124—51no—
157C22⋊Q8—152no—
158C4×Q8—151no—
159C4×Q8—151no—
160C4×Q8—151no—
161C4×D4—151no—
162#117—152no—
163C2×C3×C5—42no—
164C2×C3×C5C2×#4111yescharacteristic
165C2×C3×C5C2×#4111yescharacteristic
166C2×C3×C52−1+411yescharacteristic
167C23×C3C22×D512yes—
168C3×Q8—102no—
169C3×D4—22no—
170C2×C3×C4—51no—
171C2×C3×C4—52no—
172C2×C3×C4—51no—
173C2×C3×C4C22×D511yescharacteristic
174C2×Dic3—51no—
175C2×Dic3—52no—
176C2×Dic3—51no—
177C2×Dic3—104no—
178C2×Dic3C22×D511yescharacteristic
179C2×Dic3C22×D512yes—
180C2×Dic3C22×D511yescharacteristic
181Dic6—22no—
182Dic6—102no—
183C22×C5—22no—
184C22×C5—22no—
185C22×C5—22no—
186C22×C5C23×D311yescharacteristic
187C4×C5—62no—
188C4×C5—61no—
189C4×C5—61no—
190C4×C5#23712yes—
191Dic5—22no—
192Dic5—21no—
193Dic5—21no—
194Dic5—32no—
195Dic5—62no—
196Dic5—61no—
197C2×Q8—31no—
198C2×Q8—51no—
199C2×Q8—151no—
200C2×D4D3×D511yescharacteristic
201C22×C4—152no—
202C4⋊C4—151no—
203C4⋊C4—152no—
204C4⋊C4—152no—
205C4⋊C4—152no—
206C4⋊C4—151no—
207C4⋊C4—151no—
208C4⋊C4—152no—
209C4⋊C4—151no—
210C22⋊C4—32no—
211C22⋊C4—32no—
212C22⋊C4—52no—
213C22⋊C4—52no—
214C22⋊C4—152no—
215C42—31no—
216C42—51no—
217C42—152no—
218C42—152no—
219C42—151no—
220C3×C5#55611yescharacteristic, complemented, Hall
221C22×C3—22no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3C23×D511yescharacteristic
225C3×C4—102no—
226C3×C4—101no—
227C3×C4—101no—
228C3×C4#71112yes—
229Dic3—22no—
230Dic3—21no—
231Dic3—21no—
232Dic3—52no—
233Dic3—102no—
234Dic3—101no—
235C2×C5—42no—
236C2×C5C2×#23711yescharacteristic
237C2×C5D3×#4111yescharacteristic
238C2×C5#101011yescharacteristic
239C23C2×D3×D512yes—
240Q8—62no—
241Q8—102no—
242Q8—302no—
243D4—22no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—32no—
247C2×C4—51no—
248C2×C4—51no—
249C2×C4—52no—
250C2×C4—151no—
251C2×C4—152no—
252C2×C4—151no—
253C2×C4—304no—
254C2×C4C2×D3×D511yescharacteristic
255C2×C3—42no—
256C2×C3C2×#71111yescharacteristic
257C2×C3D5×#4111yescharacteristic
258C2×C3#415011yescharacteristic
259C5#567111yescharacteristic, complemented, Sylow
260C22—22no—
261C22—22no—
262C22—22no—
263C22C22×D3×D511yescharacteristic
264C4—61no—
265C4—61no—
266C4—62no—
267C4—101no—
268C4—101no—
269C4—102no—
270C4—152no—
271C4—301no—
272C4—302no—
273C4#678012yes—
274C3#6600511yescharacteristic, complemented, Sylow
275C2—42no—
276C2#9202011yescharacteristic
277C2#9202411yescharacteristic
278C2C2×#678011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
Fitting, prime radicalC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
4. #91576C2semidirect
5. #91532C2semidirect
6. #91531C2semidirect
7. #91530C2semidirect
8. C4×#1204C2semidirect
9. #91385C2semidirect
10. Dic5×Dic6C2semidirect
11. Dic3×Dic10C2semidirect
220. C3×C5#556semidirect
259. C5#5671semidirect
274. C3#66005semidirect

Maximal subgroups

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

subgroupindex
D4×Dic152
C5×#9362
C3×#40822
#915762
#915322
#915312
#915302
C4×#12042
#913852
Dic5×Dic62
Dic3×Dic102
#660053
#56715