Finite Group Databasebeta

← #11750879

Subgroups — #11750879

Order 960.

248 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 65 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#91827C211yesmaximal, characteristic
2C2×#6716C211yesmaximal, characteristic, complemented
3C2×C8×D15C211yesmaximal, characteristic, complemented
4#91786C211yesmaximal, characteristic, complemented
5C3×C5×#102C211yesmaximal, characteristic, complemented
6#91100C211yesmaximal, characteristic, complemented
7#91092C211yesmaximal, characteristic, complemented
8#65067—31nomaximal, Hall
9C2×C3×C5×D4C2211yescharacteristic
10C2×#1220—21no—
11C2×C4×D15C2211yescharacteristic
12C2×Dic30C2211yescharacteristic
13C2×C3×C5×C8C2211yescharacteristic
14C3×C5×C4⋊C4C2211yescharacteristic
15#6719—21no—
16#6716—22no—
17#6714—21no—
18C4⋊Dic15—21no—
19C4⋊Dic15C2211yescharacteristic
20C2×C3⋊#168C2211yescharacteristic
21C8×D15—22no—
22#4778—51nomaximal, Hall
23#4084—31no—
24C2×#687—31no—
25C2×C8×D5—31no—
26#4043—31no—
27C5×#102D311yescharacteristic, complemented
28#3948—31no—
29#3940—31no—
30C23×C3×C5—21no—
31C22×D15D411yescharacteristic
32C3×C5×D4—21no—
33C3×C5×D4—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5C2311yescharacteristic
36#1220—42no—
37C2×Dic15—21no—
38C2×Dic15—21no—
39C2×Dic15D411yescharacteristic
40C4×D15—21no—
41C4×D15—21no—
42Dic30—21no—
43Dic30—21no—
44C3×C5×C8—21no—
45C3⋊#168D412yescomplemented
46#938—51no—
47C2×#214—51no—
48C2×D3×C8—51no—
49#897—51no—
50C3×#102D511yescharacteristic, complemented
51#816—51no—
52#808—51no—
53C2×C5×D4C2×D311yescharacteristic
54C2×C22⋊D5—61no—
55C2×C4×D5—31no—
56C2×Dic10—31no—
57C2×C5×C8C2×D311yescharacteristic
58C5×C4⋊C4C2×D311yescharacteristic
59C22⋊Dic5—61no—
60#687—62no—
61#685—61no—
62C4⋊Dic5—31no—
63C4⋊Dic5—61no—
64C2×#168—31no—
65C8×D5—62no—
66#465—151noSylow
67C22×C3×C5—41no—
68C22×C3×C5—41no—
69C22×C3×C5—41no—
70C22×C3×C5C2×D411yescharacteristic
71C2×D15—21no—
72C2×D15—21no—
73C2×D15SD1612yescomplemented
74C3×C4×C5—41no—
75C3×C4×C5C2×D411yescharacteristic
76C3×C4×C5#4111yescharacteristic
77Dic15—21no—
78Dic15—41no—
79Dic15—41no—
80C2×C3×D4C2×D511yescharacteristic
81C2×#67—101no—
82C2×C4×D3—51no—
83C2×Dic6—51no—
84C2×C3×C8C2×D511yescharacteristic
85C3×C4⋊C4C2×D511yescharacteristic
86#217—101no—
87#214—102no—
88(C2×D3)⋊C4—101no—
89C4⋊Dic3—51no—
90C4⋊Dic3—101no—
91C2×C3⋊C8—51no—
92D3×C8—102no—
93C23×C5—21no—
94C22×D5—31no—
95C5×D4—21no—
96C5×D4—21no—
97C2×C4×C5—21no—
98C2×C4×C5C22×D311yescharacteristic
99C22⋊D5—122no—
100C2×Dic5—31no—
101C2×Dic5—61no—
102C2×Dic5—61no—
103C4×D5—61no—
104C4×D5—61no—
105Dic10—61no—
106Dic10—61no—
107C5×C8—21no—
108#168—32no—
109C2×SD16—151no—
110C22×C8—151no—
111C22⋊Q8—151no—
112#121—151no—
113#106—151no—
114#103—151no—
115#102D1511yescharacteristic, complemented
116C2×C3×C5—81no—
117C2×C3×C5#12111yescharacteristic
118C2×C3×C5C2×SD1611yescharacteristic
119C2×C3×C5#13511yescharacteristic
120D15—22no—
121C23×C3—21no—
122C22×D3—51no—
123C3×D4—21no—
124C3×D4—21no—
125C2×C3×C4—21no—
126C2×C3×C4C22×D511yescharacteristic
127#67—202no—
128C2×Dic3—51no—
129C2×Dic3—101no—
130C2×Dic3—101no—
131C4×D3—101no—
132C4×D3—101no—
133Dic6—101no—
134Dic6—101no—
135C3×C8—21no—
136C3⋊C8—52no—
137C22×C5—41no—
138C22×C5—41no—
139C22×C5—41no—
140C22×C5D3×D411yescharacteristic
141C2×D5—32no—
142C2×D5—61no—
143C2×D5—61no—
144C4×C5—41no—
145C4×C5#23511yescharacteristic
146C4×C5D3×D411yescharacteristic
147Dic5—61no—
148Dic5—121no—
149Dic5—121no—
150C2×Q8—151no—
151C2×D4—301no—
152C2×D4C2×D1511yescharacteristic
153C22×C4—151no—
154SD16—302no—
155C2×C8—151no—
156C2×C8—302no—
157C2×C8C2×D1511yescharacteristic
158C4⋊C4—151no—
159C4⋊C4—301no—
160C4⋊C4C2×D1511yescharacteristic
161C22⋊C4—301no—
162C22⋊C4—301no—
163C3×C5#46511yescharacteristic, complemented, Hall
164C22×C3—41no—
165C22×C3—41no—
166C22×C3—41no—
167C22×C3D4×D511yescharacteristic
168C2×D3—52no—
169C2×D3—101no—
170C2×D3—101no—
171C3×C4—41no—
172C3×C4#70911yescharacteristic
173C3×C4D4×D511yescharacteristic
174Dic3—101no—
175Dic3—201no—
176Dic3—201no—
177C2×C5—81no—
178C2×C5#88411yescharacteristic
179C2×C5#91211yescharacteristic
180C2×C5D3×SD1611yescharacteristic
181D5—62no—
182C23—21no—
183C23—151no—
184Q8—301no—
185Q8—301no—
186D4—21no—
187D4—21no—
188D4—602no—
189C2×C4—21no—
190C2×C4—151no—
191C2×C4—301no—
192C2×C4—301no—
193C2×C4—301no—
194C2×C4—301no—
195C2×C4C22×D1511yescharacteristic
196C8—21no—
197C8—152no—
198C2×C3—81no—
199C2×C3#403011yescharacteristic
200C2×C3#405811yescharacteristic
201C2×C3D5×SD1611yescharacteristic
202D3—102no—
203C5#477811yescharacteristic, complemented, Sylow
204C22—41no—
205C22—41no—
206C22—41no—
207C22—152no—
208C22—301no—
209C22—301no—
210C22D4×D1511yescharacteristic
211C4—41no—
212C4—301no—
213C4—601no—
214C4—601no—
215C4#681711yescharacteristic
216C4D4×D1511yescharacteristic
217C3#6506711yescharacteristic, complemented, Sylow
218C2—81no—
219C2—302no—
220C2#9177311yescharacteristic
221C2#9180111yescharacteristic
222C2SD16×D1511yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#102C2
socleC22×C3×C5C2×D4
prime radical#91827C2
hypercenter#102D15
hypocenterC3×C5#465
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#6716C2semidirect
3. C2×C8×D15C2semidirect
4. #91786C2semidirect
5. C3×C5×#102C2semidirect
6. #91100C2semidirect
7. #91092C2semidirect
27. C5×#102D3semidirect
45. C3⋊#168D4semidirect
50. C3×#102D5semidirect
73. C2×D15SD16semidirect
115. #102D15semidirect
163. C3×C5#465semidirect
203. C5#4778semidirect
217. C3#65067semidirect

Maximal subgroups

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

subgroupindex
#918272
C2×#67162
C2×C8×D152
#917862
C3×C5×#1022
#911002
#910922
#650673
#47785