Finite Group Databasebeta

← #14279449

Subgroups — #14279449

Order 1920.

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

normal subgroups only

This group has 220 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#11751177C211yesmaximal, characteristic
2C3×C5×#353C211yesmaximal, characteristic
3#11746366C211yesmaximal, characteristic
4#10598031—31nomaximal, Hall
5C3×C5×#127C2211yescharacteristic
6C2×#6716—21no—
7C2×#6716—21no—
8#91758C411yescharacteristic, complemented
9C3×C5×#99—21no—
10#91118—21no—
11C4×C3⋊#168C411yescharacteristic, complemented
12#67540—51nomaximal, Hall
13#65365—31no—
14C5×#353D311yescharacteristic
15#64765—31no—
16C2×C3×C5×D4—41no—
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C2×Dic30—21no—
20C3×C5×C22⋊C4—41no—
21C3×C42×C5C2×C411yescharacteristic
22#6719—41no—
23#6716—42no—
24#6716—42no—
25C4⋊Dic15—41no—
26C2×C3⋊#168—21no—
27#5076—51no—
28C3×#353D511yescharacteristic
29#4545—51no—
30C5×#127C2×D311yescharacteristic
31C2×#687—61no—
32C2×#687—61no—
33#4015—31no—
34C5×#99—21no—
35#3966—61no—
36C4×#168—31no—
37#1409—151noSylow
38C23×C3×C5—21no—
39C23×C3×C5—21no—
40C3×C5×D4—41no—
41C3×C5×D4—41no—
42C3×C5×D4—82no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—81no—
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C2×Dic15—41no—
47C2×Dic15—81no—
48Dic30—41no—
49Dic30—41no—
50C3⋊#168—22no—
51C3×#127C2×D511yescharacteristic
52C2×#214—101no—
53C2×#214—101no—
54#869—51no—
55C3×#99—21no—
56#834—101no—
57C4×C3⋊C8—51no—
58C2×C5×D4—41no—
59C2×C5×D4D1211yescharacteristic
60C2×C5×D4#6711yescharacteristic
61C2×Dic10—61no—
62C5×C22⋊C4—41no—
63C42×C5C4×D311yescharacteristic
64C22⋊Dic5—121no—
65#687—122no—
66#687—122no—
67C4⋊Dic5—121no—
68C2×#168—61no—
69#492—151no—
70#353—151no—
71#353D1511yescharacteristic
72C22×C3×C5—41no—
73C22×C3×C5—41no—
74C22×C3×C5—81no—
75C22×C3×C5—81no—
76C22×C3×C5#9911yescharacteristic
77C3×C4×C5—22no—
78C3×C4×C5—21no—
79C3×C4×C5—161no—
80Dic15—81no—
81Dic15—161no—
82C2×C3×D4—41no—
83C2×C3×D4D2011yescharacteristic
84C2×C3×D4C22⋊D511yescharacteristic
85C2×Dic6—101no—
86C3×C22⋊C4—41no—
87C3×C42C4×D511yescharacteristic
88#217—201no—
89#214—202no—
90#214—202no—
91C4⋊Dic3—201no—
92C2×C3⋊C8—101no—
93C23×C5—21no—
94C23×C5—21no—
95C5×D4—41no—
96C5×D4—41no—
97C5×D4—82no—
98C2×C4×C5—21no—
99C2×C4×C5—81no—
100C2×C4×C5(C2×D3)⋊C411yescharacteristic
101C2×Dic5—121no—
102C2×Dic5—241no—
103Dic10—121no—
104Dic10—121no—
105#168—62no—
106C2×SD16—301no—
107C2×SD16—301no—
108C4⋊Q8—151no—
109#127C2×D1511yescharacteristic
110#99—21no—
111#99—301no—
112C4×C8—151no—
113C2×C3×C5—21no—
114C2×C3×C5—81no—
115C2×C3×C5—81no—
116C2×C3×C5#35311yescharacteristic
117C23×C3—21no—
118C23×C3—21no—
119C3×D4—41no—
120C3×D4—41no—
121C3×D4—82no—
122C2×C3×C4—21no—
123C2×C3×C4—81no—
124C2×C3×C4#68511yescharacteristic
125C2×Dic3—201no—
126C2×Dic3—401no—
127Dic6—201no—
128Dic6—201no—
129C3⋊C8—102no—
130C22×C5—41no—
131C22×C5—41no—
132C22×C5—81no—
133C22×C5—81no—
134C22×C5#80611yescharacteristic
135C4×C5—22no—
136C4×C5—21no—
137C4×C5—161no—
138Dic5—241no—
139Dic5—481no—
140C2×Q8—301no—
141C2×D4—41no—
142C2×D4D6011yescharacteristic
143C2×D4#122011yescharacteristic
144SD16—602no—
145SD16—602no—
146C2×C8—301no—
147C4⋊C4—601no—
148C22⋊C4—41no—
149C22⋊C4—601no—
150C42C4×D1511yescharacteristic
151C3×C5#140911yescharacteristic, complemented, Hall
152C22×C3—41no—
153C22×C3—41no—
154C22×C3—81no—
155C22×C3—81no—
156C22×C3#393811yescharacteristic
157C3×C4—22no—
158C3×C4—21no—
159C3×C4—161no—
160Dic3—401no—
161Dic3—801no—
162C2×C5—21no—
163C2×C5—81no—
164C2×C5—81no—
165C2×C5#447411yescharacteristic
166C23—21no—
167C23—21no—
168Q8—601no—
169Q8—601no—
170D4—41no—
171D4—41no—
172D4—82no—
173C2×C4—21no—
174C2×C4—81no—
175C2×C4—601no—
176C2×C4—1201no—
177C2×C4#671411yescharacteristic
178C8—302no—
179C2×C3—21no—
180C2×C3—81no—
181C2×C3—81no—
182C2×C3#6469411yescharacteristic
183C5#6754011yescharacteristic, complemented, Sylow
184C22—41no—
185C22—41no—
186C22—81no—
187C22—81no—
188C22#9109011yescharacteristic
189C4—22no—
190C4—21no—
191C4—161no—
192C4—1201no—
193C4—2401no—
194C3#1059803111yescharacteristic, complemented, Sylow
195C2—21no—
196C2—81no—
197C2—81no—
198C2#1174629511yescharacteristic
subgroupG/H
centerC2#11746295
commutatorC3×C42×C5C2×C4
Frattini#127C2×D15
FittingC3×C5×#353C2
socleC2×C3×C5#353
prime radical, cosocleC3×C5×#127C22
hypercenter#353D15
hypocenterC3×C5#1409
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
8. #91758C4semidirect
11. C4×C3⋊#168C4semidirect
151. C3×C5#1409semidirect
183. C5#67540semidirect
194. C3#10598031semidirect

Maximal subgroups

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

subgroupindex
#117511772
C3×C5×#3532
#117463662
#105980313
#675405