Finite Group Databasebeta

← #11747412

Subgroups — #11747412

Order 960.

216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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×#4033C211yesmaximal, characteristic
2#91376C211yesmaximal, characteristic
3C2×#6662C211yesmaximal, characteristic
4C2×#6661C211yesmaximal, characteristic
5#91094C211yesmaximal, characteristic
6C5×#810C211yesmaximal, characteristic
7#90982C211yesmaximal, characteristic
8#65082—31nomaximal, Hall
9C2×Dic30C2211yescharacteristic
10C2×C5×Dic6C2211yescharacteristic
11C2×C3×Dic10C2211yescharacteristic
12C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3⋊#168C2211yescharacteristic
14C2×C5×C3⋊C8C2211yescharacteristic
15C3×#683—21no—
16C3×C4×Dic5—21no—
17C3×C4×Dic5C2211yescharacteristic
18#6668—21no—
19#6668—21no—
20#6662—22no—
21#6661—22no—
22#5031—51nomaximal, Hall
23#4090—31no—
24C2×#689—31no—
25C2×Dic20—31no—
26#4033D311yescharacteristic
27C5×#103—31no—
28#3946—31no—
29#3942—31no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33Dic30—21no—
34Dic30—21no—
35C2×C5×Dic3—21no—
36C5×Dic6—21no—
37C5×Dic6—21no—
38C2×C3×Dic5—21no—
39C2×C3×Dic5D411yescharacteristic
40C2×C3×Dic5D411yescharacteristic
41C3×Dic10—21no—
42C3×Dic10D412yes—
43C3⋊#168—21no—
44C5×C3⋊C8—21no—
45C3×C4×Q8—51no—
46C2×#216—51no—
47C2×#216—51no—
48#869—51no—
49#810—51no—
50#810D511yescharacteristic
51C4⋊(C3⋊C8)—51no—
52C2×C5×Q8—31no—
53C2×Dic10—31no—
54C2×Dic10C2×D311yescharacteristic
55C2×C5×C8—31no—
56C5×C4⋊C4C2×D311yescharacteristic
57#689—62no—
58#683—21no—
59#683—61no—
60#683—61no—
61C4×Dic5—21no—
62C4×Dic5C2×D311yescharacteristic
63C2×#168—31no—
64Dic20—62no—
65#462—151noSylow
66C22×C3×C5C2×D411yescharacteristic
67C3×C4×C5—41no—
68C3×C4×C5C2×D411yescharacteristic
69C3×C4×C5#4111yescharacteristic
70Dic15—41no—
71C3×Dic5—22no—
72C3×Dic5—21no—
73C3×Dic5Q1612yescomplemented
74C5×Dic3—41no—
75C2×C3×Q8—51no—
76C2×Dic6—51no—
77C2×Dic6C2×D511yescharacteristic
78C3×C4⋊C4—101no—
79C3×C4⋊C4C2×D511yescharacteristic
80C3×C42—51no—
81C3×C42—101no—
82#216—102no—
83#216—102no—
84C4⋊Dic3—101no—
85C4⋊Dic3—101no—
86C2×C3⋊C8—51no—
87C2×C3⋊C8C2×D511yescharacteristic
88C5×Q8—61no—
89C5×Q8—61no—
90C2×C4×C5—21no—
91C2×C4×C5—61no—
92C2×C4×C5C22×D311yescharacteristic
93C2×Dic5—21no—
94C2×Dic5—61no—
95C2×Dic5#6711yescharacteristic
96C2×Dic5#6711yescharacteristic
97Dic10—21no—
98Dic10—61no—
99Dic10—61no—
100Dic10D1212yes—
101C5×C8—61no—
102#168—61no—
103C2×Q16—151no—
104C2×Q16—151no—
105C4⋊Q8—151no—
106C4×Q8—51no—
107C4⋊C8—151no—
108#103—31no—
109#103—151no—
110C2×C3×C5#12111yescharacteristic
111C2×C3×C5C2×Q1611yescharacteristic
112C2×C3×C5#13711yescharacteristic
113C3×Q8—52no—
114C3×Q8—101no—
115C2×C3×C4—21no—
116C2×C3×C4—51no—
117C2×C3×C4—51no—
118C2×C3×C4—101no—
119C2×C3×C4C22×D511yescharacteristic
120C2×Dic3—21no—
121C2×Dic3—101no—
122Dic6—21no—
123Dic6—21no—
124Dic6—101no—
125Dic6—101no—
126C3⋊C8—21no—
127C3⋊C8—101no—
128C22×C5C2×#6711yescharacteristic
129C4×C5—41no—
130C4×C5—121no—
131C4×C5C2×D1211yescharacteristic
132C4×C5#23511yescharacteristic
133Dic5—22no—
134Dic5—21no—
135Dic5—121no—
136Dic5#21612yescomplemented
137C2×Q8—31no—
138C2×Q8—51no—
139C2×Q8—151no—
140Q16—302no—
141Q16—302no—
142C2×C8—31no—
143C2×C8—151no—
144C4⋊C4—101no—
145C4⋊C4—301no—
146C4⋊C4—301no—
147C4⋊C4D3×D511yescharacteristic
148C42—51no—
149C42—101no—
150C3×C5#46211yescharacteristic, complemented, Hall
151C22×C3D4×D511yescharacteristic
152C3×C4—41no—
153C3×C4—52no—
154C3×C4—102no—
155C3×C4—101no—
156C3×C4#70911yescharacteristic
157C3×C4D4×D511yescharacteristic
158Dic3—41no—
159Dic3—201no—
160C2×C5#93011yescharacteristic
161C2×C5C2×#21611yescharacteristic
162C2×C5#95111yescharacteristic
163Q8—52no—
164Q8—61no—
165Q8—61no—
166Q8—101no—
167Q8—301no—
168Q8—301no—
169C2×C4—21no—
170C2×C4—51no—
171C2×C4—51no—
172C2×C4—61no—
173C2×C4—101no—
174C2×C4—301no—
175C2×C4C2×D3×D511yescharacteristic
176C8—61no—
177C8—301no—
178C2×C3#403011yescharacteristic
179C2×C3#406111yescharacteristic
180C2×C3D5×Q1611yescharacteristic
181C5#503111yescharacteristic, complemented, Sylow
182C22D5×#6711yescharacteristic
183C4—41no—
184C4—52no—
185C4—102no—
186C4—101no—
187C4—121no—
188C4—601no—
189C4#677111yescharacteristic
190C4D5×D1211yescharacteristic
191C3#6508211yescharacteristic, complemented, Sylow
192C2#9144811yescharacteristic
193C2#9148411yescharacteristic
194C2D5×#21611yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socle, prime radicalC22×C3×C5C2×D4
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#462
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
73. C3×Dic5Q16semidirect
136. Dic5#216semidirect
150. C3×C5#462semidirect
181. C5#5031semidirect
191. C3#65082semidirect

Maximal subgroups

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

subgroupindex
C3×#40332
#913762
C2×#66622
C2×#66612
#910942
C5×#8102
#909822
#650823
#50315