Finite Group Databasebeta

← #14279464

Subgroups — #14279464

Order 1920.

208 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 41 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#11751186C211yesmaximal, characteristic
2C3×C5×#356C211yesmaximal, characteristic, complemented
3#11746369C211yesmaximal, characteristic, complemented
4#10598043—31nomaximal, Hall
5C3×C5×C4⋊Q8C2211yescharacteristic
6C2×#6717—21no—
7C2×#6717—21no—
8#91763C411yescharacteristic
9C3×C5×#101—21no—
10#91120—21no—
11C4×C3⋊#168C411yescharacteristic
12#67552—51nomaximal, Hall
13#65374—31no—
14C5×#356D311yescharacteristic, complemented
15#64768—31no—
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×Q8D411yescharacteristic
18C2×D60—21no—
19C2×D60—41no—
20C3×C5×M16—41no—
21C3×C5×C4⋊C4—41no—
22C3×C42×C5C2×C411yescharacteristic
23#6717—42no—
24#6717—42no—
25#6710—41no—
26C2×C3⋊#168—21no—
27#5085—51no—
28C3×#356D511yescharacteristic, complemented
29#4548—51no—
30C5×C4⋊Q8C2×D311yescharacteristic
31C2×#688—61no—
32C2×#688—61no—
33#4020—31no—
34C5×#101—21no—
35#3968—61no—
36C4×#168—31no—
37#1410—151noSylow
38C22×D15—41no—
39C3×C5×Q8—41no—
40C3×C5×Q8—41no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45D60—41no—
46D60—41no—
47D60—82no—
48C3×C5×C8—81no—
49C3⋊#168—22no—
50C3⋊#168—81no—
51C3×C4⋊Q8C2×D511yescharacteristic
52C2×#215—101no—
53C2×#215—101no—
54#874—51no—
55C3×#101—21no—
56#836—101no—
57C4×C3⋊C8—51no—
58C2×C5×Q8D1211yescharacteristic
59C2×C5×Q8#6711yescharacteristic
60C2×D20—61no—
61C2×D20—121no—
62C5×M16—41no—
63C5×C4⋊C4—41no—
64C42×C5C4×D311yescharacteristic
65#688—122no—
66#688—122no—
67#681—121no—
68C2×#168—61no—
69#492—151no—
70#356—151no—
71#356D1511yescharacteristic, complemented
72C22×C3×C5#9911yescharacteristic
73C2×D15—82no—
74C2×D15—81no—
75C3×C4×C5—22no—
76C3×C4×C5—21no—
77C3×C4×C5—41no—
78C3×C4×C5—41no—
79C2×C3×Q8D2011yescharacteristic
80C2×C3×Q8C22⋊D511yescharacteristic
81C2×D12—101no—
82C2×D12—201no—
83C3×M16—41no—
84C3×C4⋊C4—41no—
85C3×C42C4×D511yescharacteristic
86#215—202no—
87#215—202no—
88#208—201no—
89C2×C3⋊C8—101no—
90C22×D5—121no—
91C5×Q8—41no—
92C5×Q8—41no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5(C2×D3)⋊C411yescharacteristic
97D20—121no—
98D20—121no—
99D20—242no—
100C5×C8—81no—
101#168—62no—
102#168—241no—
103C2×SD16—301no—
104C2×SD16—301no—
105C4⋊Q8C2×D1511yescharacteristic
106#127—151no—
107#101—21no—
108#101—301no—
109C4×C8—151no—
110C2×C3×C5—21no—
111C2×C3×C5#35311yescharacteristic
112D15—161no—
113C22×D3—201no—
114C3×Q8—41no—
115C3×Q8—41no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4#68511yescharacteristic
120D12—201no—
121D12—201no—
122D12—402no—
123C3×C8—81no—
124C3⋊C8—102no—
125C3⋊C8—401no—
126C22×C5#80611yescharacteristic
127C2×D5—242no—
128C2×D5—241no—
129C4×C5—22no—
130C4×C5—21no—
131C4×C5—41no—
132C4×C5—41no—
133C2×Q8D6011yescharacteristic
134C2×Q8#122011yescharacteristic
135C2×D4—301no—
136C2×D4—601no—
137SD16—602no—
138SD16—602no—
139M16—41no—
140M16—601no—
141C2×C8—301no—
142C4⋊C4—41no—
143C42C4×D1511yescharacteristic
144C3×C5#141011yescharacteristic, complemented, Hall
145C22×C3#393811yescharacteristic
146C2×D3—402no—
147C2×D3—401no—
148C3×C4—22no—
149C3×C4—21no—
150C3×C4—41no—
151C3×C4—41no—
152C2×C5—21no—
153C2×C5#447411yescharacteristic
154D5—481no—
155C23—601no—
156Q8—41no—
157Q8—41no—
158D4—601no—
159D4—601no—
160D4—1202no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4#671411yescharacteristic
165C8—81no—
166C8—302no—
167C8—1201no—
168C2×C3—21no—
169C2×C3#6469411yescharacteristic
170D3—801no—
171C5#6755211yescharacteristic, complemented, Sylow
172C22—1202no—
173C22—1201no—
174C22#9109011yescharacteristic
175C4—22no—
176C4—21no—
177C4—41no—
178C4—41no—
179C3#1059804311yescharacteristic, complemented, Sylow
180C2—21no—
181C2—2401no—
182C2#1174629511yescharacteristic
subgroupG/H
centerC2#11746295
commutatorC3×C42×C5C2×C4
FrattiniC4⋊Q8C2×D15
FittingC3×C5×#356C2
socleC2×C3×C5#353
prime radical#91763C4
cosocleC3×C5×C4⋊Q8C22
hypercenter#356D15
hypocenterC3×C5#1410
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. C3×C5×#356C2semidirect
3. #11746369C2semidirect
14. C5×#356D3semidirect
28. C3×#356D5semidirect
71. #356D15semidirect
144. C3×C5#1410semidirect
171. C5#67552semidirect
179. C3#10598043semidirect

Maximal subgroups

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

subgroupindex
#117511862
C3×C5×#3562
#117463692
#105980433
#675525