Finite Group Databasebeta

← #11755266

Subgroups — #11755266

Order 960.

424 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 148 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#91833C211yesmaximal, characteristic
2C5×#944C211yesmaximal, characteristic
3C3×#4090C211yesmaximal, characteristic
4#91329C212yesmaximal
5#91328C212yesmaximal
6#91327C212yesmaximal
7#91325C212yesmaximal
8#91324C212yesmaximal
9#91323C212yesmaximal
10#66056—31nomaximal, Hall
11C2×C3×C5×Q8C2211yescharacteristic
12C2×Dic30C2211yescharacteristic
13C2×C5×Dic6C2211yescharacteristic
14C2×C3×Dic10C2211yescharacteristic
15C2×#1204C2212yes—
16C2×#1204C2212yes—
17#6712C2212yes—
18#6712C2212yes—
19C4×Dic15C2211yescharacteristic
20C5×Dic3⋊C4C2212yes—
21C5×Dic3⋊C4C2212yes—
22C4×C5×Dic3C2211yescharacteristic
23C3×#683C2212yes—
24C3×#683C2212yes—
25C3×C4×Dic5C2211yescharacteristic
26Dic3⋊Dic5C2212yes—
27#6669C2212yes—
28#6668C2212yes—
29Dic3×Dic5C2212yes—
30Dic3×Dic5C2212yes—
31Dic3×Dic5C2212yes—
32#5722—51nomaximal, Hall
33C5×C4⋊Q8—31no—
34#4090—31no—
35#4090—32no—
36#4090D311yescharacteristic
37#4034—32no—
38#4034—32no—
39#4033—32no—
40#4033—32no—
41C4×Dic10—32no—
42C3×C5×Q8—41no—
43C2×C3×C4×C5C2311yescharacteristic
44C2×C3×C4×C5C2311yescharacteristic
45C2×C3×C4×C5C2311yescharacteristic
46C2×Dic15C2312yes—
47C2×Dic15C2312yes—
48Dic30—41no—
49C2×C5×Dic3C2312yes—
50C2×C5×Dic3C2312yes—
51C5×Dic6—41no—
52C2×C3×Dic5C2312yes—
53C2×C3×Dic5C2312yes—
54C3×Dic10—41no—
55#1204—42no—
56#1204Q818yescomplemented
57C3×C4⋊Q8—51no—
58#944—51no—
59#944—52no—
60#944D511yescharacteristic
61#888—52no—
62#888—52no—
63#887—52no—
64#887—52no—
65C4×Dic6—52no—
66C2×C5×Q8—31no—
67C2×C5×Q8C2×D311yescharacteristic
68C2×Dic10—32no—
69C2×Dic10—31no—
70C2×Dic10—32no—
71C2×Dic10C2×D311yescharacteristic
72C5×C4⋊C4—32no—
73C5×C4⋊C4—32no—
74C42×C5—31no—
75C4⋊Dic5—32no—
76#683—32no—
77#683—32no—
78#683—32no—
79#683—32no—
80#683C2×D312yes—
81#683C2×D312yes—
82C4×Dic5—31no—
83C4×Dic5—32no—
84C4×Dic5—32no—
85C4×Dic5—32no—
86C4×Dic5C2×D311yescharacteristic
87Q82—151noSylow
88C22×C3×C5C2411yescharacteristic
89C3×C4×C5—21no—
90C3×C4×C5—21no—
91C3×C4×C5—21no—
92Dic15—22no—
93Dic15C2×Q814yes—
94C3×Dic5—22no—
95C3×Dic5C2×Q814yes—
96C5×Dic3—22no—
97C5×Dic3C2×Q814yes—
98C2×C3×Q8—51no—
99C2×C3×Q8C2×D511yescharacteristic
100C2×Dic6—52no—
101C2×Dic6—51no—
102C2×Dic6—52no—
103C2×Dic6C2×D511yescharacteristic
104C3×C4⋊C4—52no—
105C3×C4⋊C4—52no—
106C3×C42—51no—
107C4⋊Dic3—52no—
108Dic3⋊C4—52no—
109Dic3⋊C4—52no—
110Dic3⋊C4—52no—
111Dic3⋊C4—52no—
112Dic3⋊C4C2×D512yes—
113Dic3⋊C4C2×D512yes—
114C4×Dic3—51no—
115C4×Dic3—52no—
116C4×Dic3—52no—
117C4×Dic3—52no—
118C4×Dic3C2×D511yescharacteristic
119C5×Q8—41no—
120C5×Q8—121no—
121C2×C4×C5—32no—
122C2×C4×C5—32no—
123C2×C4×C5C22×D311yescharacteristic
124C2×C4×C5C22×D311yescharacteristic
125C2×C4×C5C22×D311yescharacteristic
126C2×Dic5—32no—
127C2×Dic5—32no—
128C2×Dic5C22×D312yes—
129C2×Dic5C22×D312yes—
130Dic10—38no—
131Dic10—41no—
132Dic10—122no—
133Dic10—121no—
134C4⋊Q8—31no—
135C4⋊Q8—51no—
136C4⋊Q8—152no—
137C4⋊Q8—152no—
138C4⋊Q8—152no—
139C4⋊Q8—151no—
140C4×Q8—152no—
141C4×Q8—152no—
142C4×Q8—152no—
143C2×C3×C5C22×Q812yes—
144C2×C3×C5H(5,𝔽2)11yescharacteristic
145C3×Q8—41no—
146C3×Q8—201no—
147C2×C3×C4—52no—
148C2×C3×C4—52no—
149C2×C3×C4C22×D511yescharacteristic
150C2×C3×C4C22×D511yescharacteristic
151C2×C3×C4C22×D511yescharacteristic
152C2×Dic3—52no—
153C2×Dic3—52no—
154C2×Dic3C22×D512yes—
155C2×Dic3C22×D512yes—
156Dic6—41no—
157Dic6—58no—
158Dic6—202no—
159Dic6—201no—
160C22×C5C23×D311yescharacteristic
161C4×C5—21no—
162C4×C5—21no—
163C4×C5—21no—
164C4×C5—34no—
165C4×C5—62no—
166Dic5—22no—
167Dic5—34no—
168Dic5—62no—
169Dic5D3×Q814yes—
170C2×Q8—31no—
171C2×Q8—51no—
172C2×Q8—152no—
173C2×Q8—152no—
174C2×Q8—151no—
175C2×Q8D3×D511yescharacteristic
176C4⋊C4—32no—
177C4⋊C4—32no—
178C4⋊C4—52no—
179C4⋊C4—52no—
180C4⋊C4—152no—
181C4⋊C4—152no—
182C4⋊C4—152no—
183C4⋊C4—152no—
184C4⋊C4—152no—
185C42—31no—
186C42—51no—
187C42—152no—
188C42—152no—
189C42—152no—
190C42—151no—
191C3×C5Q8211yescharacteristic, complemented, Hall
192C22×C3C23×D511yescharacteristic
193C3×C4—21no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—54no—
197C3×C4—102no—
198Dic3—22no—
199Dic3—54no—
200Dic3—102no—
201Dic3Q8×D514yes—
202C2×C5#100411yescharacteristic
203C2×C5C2×D3×Q812yes—
204Q8—41no—
205Q8—121no—
206Q8—158no—
207Q8—201no—
208Q8—601no—
209Q8—602no—
210C2×C4—32no—
211C2×C4—32no—
212C2×C4—52no—
213C2×C4—52no—
214C2×C4—152no—
215C2×C4—152no—
216C2×C4C2×D3×D511yescharacteristic
217C2×C4C2×D3×D511yescharacteristic
218C2×C4C2×D3×D511yescharacteristic
219C2×C3#414411yescharacteristic
220C2×C3C2×Q8×D512yes—
221C5#572211yescharacteristic, complemented, Sylow
222C22C22×D3×D511yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—34no—
227C4—54no—
228C4—62no—
229C4—102no—
230C4—154no—
231C4—302no—
232C3#6605611yescharacteristic, complemented, Sylow
233C2D3×Q8×D512yes—
234C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, prime radical, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5Q82
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
56. #1204Q8semidirect
191. C3×C5Q82semidirect
221. C5#5722semidirect
232. C3#66056semidirect

Maximal subgroups

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

subgroupindex
#918332
C5×#9442
C3×#40902
#913292
#913282
#913272
#913252
#913242
#913232
#660563
#57225