Finite Group Databasebeta

← #11755013

Subgroups — #11755013

Order 960.

424 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 132 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
1#91825C211yesmaximal, characteristic
2C5×D4×Dic3C211yesmaximal, characteristic
3C3×#4082C211yesmaximal, characteristic
4#91575C212yesmaximal, complemented
5#91531C212yesmaximal, complemented
6#91530C212yesmaximal, complemented
7#91529C212yesmaximal, complemented
8C4×#1204C211yesmaximal, characteristic, complemented
9#91389C211yesmaximal, characteristic, complemented
10#91333C211yesmaximal, characteristic, complemented
11#91331C211yesmaximal, characteristic, complemented
12#65876—31nomaximal, Hall
13C2×C3×C5×D4C2211yescharacteristic
14C2×Dic30C2211yescharacteristic
15C22×C5×Dic3C2212yes—
16C2×C3×Dic10C2211yescharacteristic
17C2×#1204C2211yescharacteristic
18#6719C2212yes—
19#6719C2212yes—
20C4×Dic15C2211yescharacteristic
21C5×#217C2212yes—
22C5×C4⋊Dic3C2211yescharacteristic
23C4×C5×Dic3C2211yescharacteristic
24C3×C22⋊Dic5C2212yes—
25C3×C22⋊Dic5C2212yes—
26C3×C4×Dic5C2211yescharacteristic
27Dic3⋊Dic5C2211yescharacteristic
28Dic3⋊Dic5C2212yes—
29Dic3⋊Dic5C2212yes—
30#6669C2211yescharacteristic
31#6669C2212yes—
32#6668C2211yescharacteristic
33#6668C2212yes—
34Dic3×Dic5C2212yes—
35Dic3×Dic5C2212yes—
36#5671—51nomaximal, Hall
37C4×C5×D4—31no—
38#4082—31no—
39#4082D311yescharacteristic
40#4072—32no—
41#4070—32no—
42#4033—31no—
43#4033—31no—
44#4025—32no—
45#4025—32no—
46#4015—31no—
47C4×Dic10—31no—
48C23×C3×C5C2312yes—
49C3×C5×D4—22no—
50C2×C3×C4×C5C2311yescharacteristic
51C2×Dic15C2311yescharacteristic
52C2×Dic15C2312yes—
53C2×Dic15C2311yescharacteristic
54Dic30—22no—
55C2×C5×Dic3—24no—
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C2×C5×Dic3C2311yescharacteristic
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#936—51no—
68D4×Dic3D511yescharacteristic
69#879—52no—
70#879—52no—
71#878—52no—
72#877—52no—
73C4×Dic6—51no—
74C4×Dic6—51no—
75C2×C5×D4C2×D311yescharacteristic
76C22×C4×C5—32no—
77C2×Dic10—31no—
78C2×Dic10—31no—
79C2×Dic10C2×D311yescharacteristic
80C5×C4⋊C4—31no—
81C5×C22⋊C4—32no—
82C42×C5—31no—
83C22⋊Dic5—32no—
84C22⋊Dic5—32no—
85C22⋊Dic5C2×D312yes—
86C22⋊Dic5C2×D312yes—
87C4⋊Dic5—31no—
88C4⋊Dic5—32no—
89C4⋊Dic5—32no—
90#683—31no—
91#683—32no—
92#683—31no—
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—21no—
105Dic15—22no—
106Dic15—21no—
107C3×Dic5—21no—
108C3×Dic5—22no—
109C3×Dic5—21no—
110C5×Dic3—22no—
111C5×Dic3—21no—
112C5×Dic3#4112yes—
113C2×C3×Q8—51no—
114C2×C3×D4C2×D511yescharacteristic
115C22×Dic3C2×D512yes—
116C2×Dic6—51no—
117C2×Dic6—51no—
118C3×C22⋊C4—52no—
119C3×C22⋊C4—52no—
120C3×C42—51no—
121#217—52no—
122#217—52no—
123#217C2×D512yes—
124C4⋊Dic3—51no—
125C4⋊Dic3—52no—
126C4⋊Dic3C2×D511yescharacteristic
127Dic3⋊C4—52no—
128Dic3⋊C4—51no—
129Dic3⋊C4—51no—
130Dic3⋊C4—52no—
131Dic3⋊C4—52no—
132C4×Dic3—51no—
133C4×Dic3—52no—
134C4×Dic3—52no—
135C4×Dic3C2×D511yescharacteristic
136C23×C5C22×D312yes—
137C5×D4—22no—
138C2×C4×C5—31no—
139C2×C4×C5—32no—
140C2×C4×C5—31no—
141C2×C4×C5—64no—
142C2×C4×C5C22×D311yescharacteristic
143C2×Dic5—31no—
144C2×Dic5—31no—
145C2×Dic5—32no—
146C2×Dic5C22×D311yescharacteristic
147C2×Dic5C22×D312yes—
148C2×Dic5C22×D311yescharacteristic
149Dic10—22no—
150Dic10—62no—
151Dic10—62no—
152C4⋊Q8—151no—
153#126—152no—
154#126—152no—
155#124—51no—
156#124—151no—
157C22⋊Q8—152no—
158C4×Q8—151no—
159C4×Q8—151no—
160C4×Q8—151no—
161C4×D4—31no—
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—24no—
175C2×Dic3—51no—
176C2×Dic3—52no—
177C2×Dic3—51no—
178C2×Dic3C22×D512yes—
179C2×Dic3C22×D511yescharacteristic
180C2×Dic3C22×D511yescharacteristic
181Dic6—102no—
182Dic6—102no—
183C22×C5—22no—
184C22×C5—22no—
185C22×C5—22no—
186C22×C5C23×D311yescharacteristic
187C4×C5—32no—
188C4×C5—62no—
189C4×C5—61no—
190C4×C5#23712yes—
191Dic5—22no—
192Dic5—21no—
193Dic5—21no—
194Dic5—62no—
195Dic5—61no—
196Dic5—61no—
197C2×Q8—51no—
198C2×Q8—151no—
199C2×Q8—151no—
200C2×D4D3×D511yescharacteristic
201C22×C4—32no—
202C4⋊C4—31no—
203C4⋊C4—151no—
204C4⋊C4—152no—
205C4⋊C4—152no—
206C4⋊C4—152no—
207C4⋊C4—151no—
208C4⋊C4—151no—
209C4⋊C4—152no—
210C22⋊C4—32no—
211C22⋊C4—52no—
212C22⋊C4—52no—
213C22⋊C4—152no—
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#70912yes—
229Dic3—22no—
230Dic3—21no—
231Dic3—102no—
232Dic3—101no—
233Dic3—101no—
234Dic3#71112yes—
235C2×C5—42no—
236C2×C5C2×#23711yescharacteristic
237C2×C5D3×#4111yescharacteristic
238C2×C5#101011yescharacteristic
239C23C2×D3×D512yes—
240Q8—102no—
241Q8—302no—
242Q8—302no—
243D4—22no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—32no—
247C2×C4—51no—
248C2×C4—51no—
249C2×C4—52no—
250C2×C4—64no—
251C2×C4—151no—
252C2×C4—151no—
253C2×C4—152no—
254C2×C4C2×D3×D511yescharacteristic
255C2×C3—42no—
256C2×C3C2×#70911yescharacteristic
257C2×C3C2×#71111yescharacteristic
258C2×C3#415011yescharacteristic
259C5#567111yescharacteristic, complemented, Sylow
260C22—22no—
261C22—22no—
262C22—22no—
263C22C22×D3×D511yescharacteristic
264C4—32no—
265C4—61no—
266C4—62no—
267C4—101no—
268C4—101no—
269C4—102no—
270C4—301no—
271C4—301no—
272C4—302no—
273C4#677912yes—
274C3#6587611yescharacteristic, complemented, Sylow
275C2—42no—
276C2#9202011yescharacteristic
277C2D3×#71111yescharacteristic
278C2C2×#677911yescharacteristic
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. #91575C2semidirect
5. #91531C2semidirect
6. #91530C2semidirect
7. #91529C2semidirect
8. C4×#1204C2semidirect
9. #91389C2semidirect
10. #91333C2semidirect
11. #91331C2semidirect
220. C3×C5#556semidirect
259. C5#5671semidirect
274. C3#65876semidirect

Maximal subgroups

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

subgroupindex
#918252
C5×D4×Dic32
C3×#40822
#915752
#915312
#915302
#915292
C4×#12042
#913892
#913332
#913312
#658763
#56715