Finite Group Databasebeta

← #14318555

Subgroups — #14318555

Order 1920.

248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 79 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×C5×#470C211yesmaximal, characteristic
2#11751226C211yesmaximal, characteristic
3#11746386C212yesmaximal, complemented
4#11746374C211yesmaximal, characteristic
5#11746308C212yesmaximal, complemented
6#10601883—31nomaximal, Hall
7C2×C3×C5×Q16C2211yescharacteristic
8C2×C3×C5×M16C2211yescharacteristic
9C3×C5×C22⋊Q8—21no—
10C2×#6710—21no—
11C3×C5×#106C2211yescharacteristic
12C3×C5×#103—21no—
13#91103—21no—
14#91103C2212yes—
15#91096C2212yes—
16#71090—51nomaximal, Hall
17C5×#470D311yescharacteristic
18#65414—31no—
19#64785—32no—
20#64773—31no—
21#64707—32no—
22C2×C3×C5×Q8—21no—
23C22×C3×C4×C5D411yescharacteristic
24C3×C5×Q16—22no—
25C3×C5×M16—22no—
26C2×C3×C5×C8D411yescharacteristic
27C2×C3×C5×C8C2311yescharacteristic
28C3×C5×C4⋊C4—21no—
29C3×C5×C4⋊C4—41no—
30C3×C5×C22⋊C4—41no—
31#6710—22no—
32#6710—41no—
33C2×C3⋊#168—41no—
34C3⋊#672—22no—
35C3×#470D511yescharacteristic
36#5125—51no—
37#4565—52no—
38#4553—51no—
39#4487—52no—
40C2×C5×Q16C2×D311yescharacteristic
41C2×C5×M16C2×D311yescharacteristic
42C5×C22⋊Q8—21no—
43C2×#681—61no—
44C5×#106C2×D311yescharacteristic
45C5×#103—21no—
46#3951—32no—
47#3951—61no—
48#3944—32no—
49#2239—151noSylow
50C23×C3×C5SD1611yescharacteristic
51C3×C5×Q8—41no—
52C3×C5×Q8—41no—
53C2×C3×C4×C5—21no—
54C2×C3×C4×C5—21no—
55C2×C3×C4×C5—41no—
56C2×C3×C4×C5—41no—
57C2×C3×C4×C5SD1611yescharacteristic
58C2×C3×C4×C5C2×D411yescharacteristic
59C3×C5×C8—21no—
60C3×C5×C8#4112yes—
61C3⋊#168—42no—
62C2×C3×Q16C2×D511yescharacteristic
63C2×C3×M16C2×D511yescharacteristic
64C3×C22⋊Q8—21no—
65C2×#208—101no—
66C3×#106C2×D511yescharacteristic
67C3×#103—21no—
68#819—52no—
69#819—101no—
70#812—52no—
71C2×C5×Q8—21no—
72C22×C4×C5#6711yescharacteristic
73C5×Q16—22no—
74C5×M16—22no—
75C2×C5×C8#6711yescharacteristic
76C2×C5×C8C22×D311yescharacteristic
77C5×C4⋊C4—21no—
78C5×C4⋊C4—41no—
79C5×C22⋊C4—41no—
80#681—62no—
81#681—121no—
82C2×#168—121no—
83#672—62no—
84#470D1511yescharacteristic
85#430—151no—
86#365—152no—
87#362—152no—
88#349—151no—
89C22×C3×C5—21no—
90C22×C3×C5—41no—
91C22×C3×C5C2×SD1611yescharacteristic
92C3×C4×C5—21no—
93C3×C4×C5—81no—
94C3×C4×C5—81no—
95C3×C4×C5#12311yescharacteristic
96C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
97C2×C3×Q8—21no—
98C22×C3×C4C22⋊D511yescharacteristic
99C3×Q16—22no—
100C3×M16—22no—
101C2×C3×C8C22⋊D511yescharacteristic
102C2×C3×C8C22×D511yescharacteristic
103C3×C4⋊C4—21no—
104C3×C4⋊C4—41no—
105C3×C22⋊C4—41no—
106#208—102no—
107#208—201no—
108C2×C3⋊C8—201no—
109C3⋊C16—102no—
110C23×C5#21411yescharacteristic
111C5×Q8—41no—
112C5×Q8—41no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5#21411yescharacteristic
118C2×C4×C5C2×#6711yescharacteristic
119C5×C8—21no—
120C5×C8#23712yes—
121#168—122no—
122C2×Q16C2×D1511yescharacteristic
123C2×M16—301no—
124C2×M16C2×D1511yescharacteristic
125C22⋊Q8—21no—
126M32—152no—
127#108—152no—
128#108—301no—
129#106C2×D1511yescharacteristic
130#103—21no—
131C2×C3×C5—21no—
132C2×C3×C5—41no—
133C2×C3×C5#48111yescharacteristic
134C23×C3#68711yescharacteristic
135C3×Q8—41no—
136C3×Q8—41no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—41no—
140C2×C3×C4—41no—
141C2×C3×C4#68711yescharacteristic
142C2×C3×C4C2×C22⋊D511yescharacteristic
143C3×C8—21no—
144C3×C8#71112yes—
145C3⋊C8—202no—
146C22×C5—21no—
147C22×C5—41no—
148C22×C5C2×#21411yescharacteristic
149C4×C5—21no—
150C4×C5—81no—
151C4×C5—81no—
152C4×C5#93511yescharacteristic
153C4×C5#94911yescharacteristic
154C2×Q8—21no—
155C22×C4#122011yescharacteristic
156Q16—22no—
157M16—22no—
158M16—302no—
159M16—601no—
160C2×C8—601no—
161C2×C8#122011yescharacteristic
162C2×C8C22×D1511yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—41no—
165C22⋊C4—41no—
166C16—302no—
167C3×C5#223911yescharacteristic, complemented, Hall
168C22×C3—21no—
169C22×C3—41no—
170C22×C3C2×#68711yescharacteristic
171C3×C4—21no—
172C3×C4—81no—
173C3×C4—81no—
174C3×C4#408111yescharacteristic
175C3×C4#409511yescharacteristic
176C2×C5—21no—
177C2×C5—41no—
178C2×C5#503411yescharacteristic
179C23#671611yescharacteristic
180Q8—41no—
181Q8—41no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4#671611yescharacteristic
187C2×C4C2×#122011yescharacteristic
188C8—21no—
189C8—602no—
190C8#681912yes—
191C2×C3—21no—
192C2×C3—41no—
193C2×C3#6532311yescharacteristic
194C5#7109011yescharacteristic, complemented, Sylow
195C22—21no—
196C22—41no—
197C22C2×#671611yescharacteristic
198C4—21no—
199C4—81no—
200C4—81no—
201C4#9182411yescharacteristic
202C4#9183811yescharacteristic
203C3#1060188311yescharacteristic, complemented, Sylow
204C2—21no—
205C2—41no—
206C2#1175113511yescharacteristic
subgroupG/H
centerC2#11751135
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#470C2
socleC2×C3×C5#481
prime radicalC23×C3×C5SD16
hypercenter#470D15
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
3. #11746386C2semidirect
5. #11746308C2semidirect
167. C3×C5#2239semidirect
194. C5#71090semidirect
203. C3#10601883semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4702
#117512262
#117463862
#117463742
#117463082
#106018833
#710905