Finite Group Databasebeta

← C3×#10602100 #14289542

Subgroups — C3×#10602100 #14289542

Order 1920.

412 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 114 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×#66056C211yesmaximal, characteristic
2C3×C5×#494C211yesmaximal, characteristic
3C3×#65380C212yesmaximal
4C3×#64766C211yesmaximal, characteristic
5C3×#64676C212yesmaximal
6#10602100C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×Q16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×#4090—22no—
11C3×#4034—22no—
12C3×#4033—22no—
13C3×C4×Dic10C2212yes—
14C3×C4×C5×C8C2211yescharacteristic
15C3×#3942—22no—
16C3×#3939—22no—
17C3×C4⋊#168C2212yes—
18C3×#1633—51nomaximal, Hall
19#66056C2×C311yescharacteristic
20C5×#494C2×C311yescharacteristic
21#65380C2×C312yes—
22#64766C2×C311yescharacteristic
23#64676C2×C312yes—
24C2×C3×C5×Q8—21no—
25C2×C3×C5×Q8D412yes—
26C2×C3×Dic10—22no—
27C2×C3×Dic10D412yes—
28C3×C5×Q16—44no—
29C2×C3×C5×C8—21no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C3×C4⋊Dic5D412yes—
34C3×#683—24no—
35C3×#683—22no—
36C3×C4×Dic5—22no—
37C3×C4×Dic5—22no—
38C2×C3×#168—22no—
39C3×Q82—51no—
40C3×#494D511yescharacteristic
41C3×#477—52no—
42C3×#333—51no—
43C3×Q8⋊C8—52no—
44C2×C5×Q16—22no—
45C5×C4⋊Q8C22×C311yescharacteristic
46C5×C4⋊Q8C22×C311yescharacteristic
47#4090—22no—
48#4034—22no—
49#4033—22no—
50C4×Dic10C22×C312yes—
51C4×C5×C8C22×C311yescharacteristic
52#3942—22no—
53#3939—22no—
54C4⋊#168C22×C312yes—
55#1633—51noSylow
56C3×C5×Q8—42no—
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5—41no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×C3×Dic5—22no—
63C2×C3×Dic5—22no—
64C3×Dic10—22no—
65C3×Dic10—82no—
66C3×Dic10Q1614yescomplemented
67C3×C5×C8—22no—
68C3×#168—42no—
69C2×C3×Q16—22no—
70C3×C4⋊Q8—102no—
71C3×C4⋊Q8—102no—
72C3×C4⋊Q8C2×D511yescharacteristic
73C3×C4⋊Q8C2×D511yescharacteristic
74C3×C4×Q8—52no—
75C3×C4×Q8—102no—
76C3×#107—102no—
77C3×C4⋊C8—52no—
78C3×#103—102no—
79C3×C4×C8C2×D511yescharacteristic
80C2×C5×Q8—21no—
81C2×C5×Q8C3×D412yes—
82C2×Dic10—22no—
83C2×Dic10C3×D412yes—
84C5×Q16—44no—
85C2×C5×C8—21no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—22no—
88C42×C5C23×C311yescharacteristic
89C4⋊Dic5C3×D412yes—
90#683—24no—
91#683—22no—
92C4×Dic5—22no—
93C4×Dic5—22no—
94C2×#168—22no—
95Q82—51no—
96#494C3×D511yescharacteristic
97#477—52no—
98#333—51no—
99Q8⋊C8—52no—
100C22×C3×C5#12011yescharacteristic
101C3×C4×C5—21no—
102C3×C4×C5—42no—
103C3×C4×C5—81no—
104C3×C4×C5C2×Q1612yes—
105C3×C4×C5#13712yes—
106C3×Dic5—24no—
107C3×Dic5—42no—
108C2×C3×Q8—21no—
109C2×C3×Q8—52no—
110C2×C3×Q8—102no—
111C2×C3×Q8C22⋊D512yes—
112C3×Q16—44no—
113C2×C3×C8—21no—
114C2×C3×C8—102no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—52no—
118C3×C4⋊C4—104no—
119C3×C4⋊C4—102no—
120C3×C42—102no—
121C3×C42—102no—
122C3×C42C22×D511yescharacteristic
123C5×Q8—42no—
124C5×Q8—42no—
125C2×C4×C5—22no—
126C2×C4×C5—41no—
127C2×C4×C5C2×C3×D412yes—
128C2×C4×C5C2×C3×D411yescharacteristic
129C2×Dic5—22no—
130C2×Dic5—22no—
131Dic10—22no—
132Dic10—82no—
133Dic10C3×Q1614yescomplemented
134C5×C8—22no—
135#168—42no—
136C2×Q16—22no—
137C4⋊Q8—102no—
138C4⋊Q8—102no—
139C4⋊Q8C2×C3×D511yescharacteristic
140C4⋊Q8C2×C3×D511yescharacteristic
141C4×Q8—52no—
142C4×Q8—102no—
143#107—102no—
144C4⋊C8—52no—
145#103—102no—
146C4×C8C2×C3×D511yescharacteristic
147C2×C3×C5#45112yes—
148C2×C3×C5#45311yescharacteristic
149C3×Q8—42no—
150C3×Q8—42no—
151C3×Q8—54no—
152C3×Q8—102no—
153C3×Q8—402no—
154C2×C3×C4—22no—
155C2×C3×C4—41no—
156C2×C3×C4—102no—
157C2×C3×C4—102no—
158C2×C3×C4D4×D512yes—
159C2×C3×C4C2×C22⋊D511yescharacteristic
160C3×C8—22no—
161C3×C8—202no—
162C22×C5C3×#12011yescharacteristic
163C4×C5—21no—
164C4×C5—42no—
165C4×C5—81no—
166C4×C5C2×C3×Q1612yes—
167C4×C5C3×#13712yes—
168Dic5—24no—
169Dic5—42no—
170C2×Q8—21no—
171C2×Q8—52no—
172C2×Q8—102no—
173C2×Q8C3×C22⋊D512yes—
174Q16—44no—
175C2×C8—21no—
176C2×C8—102no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—52no—
180C4⋊C4—104no—
181C4⋊C4—102no—
182C42—102no—
183C42—102no—
184C42C22×C3×D511yescharacteristic
185C3×C5#163311yescharacteristic, complemented, Hall
186C22×C3#408311yescharacteristic
187C3×C4—21no—
188C3×C4—42no—
189C3×C4—81no—
190C3×C4—104no—
191C3×C4—202no—
192C3×C4D5×Q1612yes—
193C3×C4#406412yes—
194C2×C5C3×#45112yes—
195C2×C5C3×#45311yescharacteristic
196Q8—42no—
197Q8—42no—
198Q8—54no—
199Q8—102no—
200Q8—402no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—102no—
204C2×C4—102no—
205C2×C4C3×D4×D512yes—
206C2×C4C2×C3×C22⋊D511yescharacteristic
207C8—22no—
208C8—202no—
209C2×C3#6536611yescharacteristic
210C2×C3#6547512yes—
211C5C3×#163311yescharacteristic, complemented, Sylow
212C22C3×#408311yescharacteristic
213C4—21no—
214C4—42no—
215C4—81no—
216C4—104no—
217C4—202no—
218C4C3×D5×Q1612yes—
219C4C3×#406412yes—
220C3#1060210011yescharacteristic, direct product factor, Sylow
221C2C3×#6536611yescharacteristic
222C2C3×#6547512yes—
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#494C2
socle, prime radicalC22×C3×C5#120
hypercenterC3×#494D5
hypocenterC5C3×#1633
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#494

Complements

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

NH ≅ G/Ntype
6. #10602100C3direct (N × H)
66. C3×Dic10Q16semidirect
133. Dic10C3×Q16semidirect
185. C3×C5#1633semidirect
211. C5C3×#1633semidirect
220. C3#10602100direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660562
C3×C5×#4942
C3×#653802
C3×#647662
C3×#646762
#106021003
C3×#16335