Finite Group Databasebeta

← C3×#10599155 #14284005

Subgroups — C3×#10599155 #14284005

Order 1920.

452 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 126 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×#66022C211yesmaximal, characteristic
2C3×#64996C212yesmaximal
3C3×C5×#330C211yesmaximal, characteristic, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5C3×#64685C212yesmaximal, complemented
6#10599155C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×#125C2211yescharacteristic
8C2×C3×#676—22no—
9C3×#4042—22no—
10C3×#4038C412yes—
11C3×#4034C412yes—
12C3×#4033—22no—
13C3×C42×D5C2211yescharacteristic
14C3×#4016C2211yescharacteristic
15C3×C5×#97C2212yes—
16C3×C8×Dic5—22no—
17C3×#3935C2212yes—
18C3×#1526—51nomaximal, Hall
19#66022C2×C311yescharacteristic
20#64996C2×C312yes—
21C5×#330C2×C311yescharacteristic, complemented
22#64763C2×C311yescharacteristic, complemented
23#64685C2×C312yescomplemented
24C2×C3×C4×D5C2×C411yescharacteristic
25C2×C3×C4×D5D412yes—
26C2×C3×Dic10—22no—
27C2×C3×C5×C8—22no—
28C3×C5×C4⋊C4—22no—
29C3×C5×C4⋊C4C2×C412yes—
30C3×C42×C5C2311yescharacteristic
31C3×#685—22no—
32C3×C4⋊Dic5C2×C412yes—
33C3×#683—22no—
34C3×#683—22no—
35C3×C4×Dic5—22no—
36C3×C4×Dic5C2×C411yescharacteristic
37C3×C4×Dic5D412yes—
38C2×C3×#168—22no—
39C3×#676—28no—
40C3×#533—51no—
41C3×C4×M16—52no—
42C3×#330—51no—
43C3×#330—52no—
44C3×#330D511yescharacteristic, complemented
45C5×#125C22×C311yescharacteristic
46C2×#676—22no—
47#4042—22no—
48#4038C3×C412yes—
49#4034C3×C412yes—
50#4033—22no—
51C42×D5C22×C311yescharacteristic
52#4016C22×C311yescharacteristic
53C5×#97C22×C312yes—
54C8×Dic5—22no—
55#3935C22×C312yes—
56#1526—51noSylow
57C22×C3×D5C22⋊C411yescharacteristic
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C22×C411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×C3×Dic5—22no—
62C2×C3×Dic5C22⋊C411yescharacteristic
63C2×C3×Dic5C22⋊C412yes—
64C3×C4×D5—22no—
65C3×C4×D5—24no—
66C3×Dic10—44no—
67C3×C5×C8—24no—
68C3×#168—24no—
69C2×C3×M16—102no—
70C3×C4⋊Q8—52no—
71C3×#125—51no—
72C3×#125C2×D511yescharacteristic
73C3×C22⋊Q8—102no—
74C3×C4×Q8—102no—
75C3×#117—52no—
76C2×C3×C42—51no—
77C3×#97—52no—
78C3×#97C2×D512yes—
79C3×C4×C8—102no—
80C2×C4×D5C2×C3×C411yescharacteristic
81C2×C4×D5C3×D412yes—
82C2×Dic10—22no—
83C2×C5×C8—22no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4C2×C3×C412yes—
86C42×C5C23×C311yescharacteristic
87#685—22no—
88C4⋊Dic5C2×C3×C412yes—
89#683—22no—
90#683—22no—
91C4×Dic5—22no—
92C4×Dic5C2×C3×C411yescharacteristic
93C4×Dic5C3×D412yes—
94C2×#168—22no—
95#676—28no—
96#533—51no—
97C4×M16—52no—
98#330—51no—
99#330—52no—
100#330C3×D511yescharacteristic, complemented
101C22×C3×C5C2×C22⋊C411yescharacteristic
102C2×C3×D5—21no—
103C2×C3×D5—22no—
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107C3×Dic5—42no—
108C3×Dic5#10112yes—
109C3×Dic5#10414yes—
110C2×C3×Q8—102no—
111C22×C3×C4—51no—
112C22×C3×C4—52no—
113C3×M16—108no—
114C2×C3×C8—22no—
115C2×C3×C8—102no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—52no—
118C3×C4⋊C4—102no—
119C3×C4⋊C4—102no—
120C3×C4⋊C4C4×D512yes—
121C3×C22⋊C4—102no—
122C3×C42—51no—
123C3×C42—52no—
124C3×C42—102no—
125C3×C42C22×D511yescharacteristic
126C22×D5C3×C22⋊C411yescharacteristic
127C2×C4×C5—22no—
128C2×C4×C5C22×C3×C411yescharacteristic
129C2×C4×C5C2×C3×D412yes—
130C2×Dic5—22no—
131C2×Dic5C3×C22⋊C411yescharacteristic
132C2×Dic5C3×C22⋊C412yes—
133C4×D5—22no—
134C4×D5—24no—
135Dic10—44no—
136C5×C8—24no—
137#168—24no—
138C2×M16—102no—
139C4⋊Q8—52no—
140#125—51no—
141#125C2×C3×D511yescharacteristic
142C22⋊Q8—102no—
143C4×Q8—102no—
144#117—52no—
145C2×C42—51no—
146#97—52no—
147#97C2×C3×D512yes—
148C4×C8—102no—
149C2×C3×C5C2×#10111yescharacteristic
150C2×C3×C5C2×#10412yes—
151C3×D5—41no—
152C23×C3—51no—
153C3×Q8—204no—
154C2×C3×C4—22no—
155C2×C3×C4—51no—
156C2×C3×C4—52no—
157C2×C3×C4—104no—
158C2×C3×C4—102no—
159C2×C3×C4—102no—
160C2×C3×C4C2×C4×D511yescharacteristic
161C2×C3×C4D4×D512yes—
162C3×C8—24no—
163C3×C8—104no—
164C22×C5C2×C3×C22⋊C411yescharacteristic
165C2×D5—21no—
166C2×D5—22no—
167C4×C5—21no—
168C4×C5—22no—
169C4×C5—42no—
170Dic5—42no—
171Dic5C3×#10112yes—
172Dic5C3×#10414yes—
173C2×Q8—102no—
174C22×C4—51no—
175C22×C4—52no—
176M16—108no—
177C2×C8—22no—
178C2×C8—102no—
179C4⋊C4—22no—
180C4⋊C4—52no—
181C4⋊C4—102no—
182C4⋊C4—102no—
183C4⋊C4C3×C4×D512yes—
184C22⋊C4—102no—
185C42—51no—
186C42—52no—
187C42—102no—
188C42C22×C3×D511yescharacteristic
189C3×C5#152611yescharacteristic, complemented, Hall
190C22×C3—101no—
191C22×C3—102no—
192C22×C3D5×C22⋊C411yescharacteristic
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196C3×C4—52no—
197C3×C4—54no—
198C3×C4—202no—
199C2×C5C2×C3×#10111yescharacteristic
200C2×C5C2×C3×#10412yes—
201D5—41no—
202C23—51no—
203Q8—204no—
204C2×C4—22no—
205C2×C4—51no—
206C2×C4—52no—
207C2×C4—104no—
208C2×C4—102no—
209C2×C4—102no—
210C2×C4C2×C3×C4×D511yescharacteristic
211C2×C4C3×D4×D512yes—
212C8—24no—
213C8—104no—
214C2×C3—201no—
215C2×C3D5×#10111yescharacteristic
216C2×C3D5×#10412yes—
217C5C3×#152611yescharacteristic, complemented, Sylow
218C22—101no—
219C22—102no—
220C22C3×D5×C22⋊C411yescharacteristic
221C4—21no—
222C4—22no—
223C4—42no—
224C4—52no—
225C4—54no—
226C4—202no—
227C3#1059915511yescharacteristic, direct product factor, Sylow
228C2—201no—
229C2C3×D5×#10111yescharacteristic
230C2C3×D5×#10412yes—
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC42×C5C23×C3
hypercenterC3×#330D5
hypocenterC5C3×#1526
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#330

Complements

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

NH ≅ G/Ntype
3. C3×C5×#330C2semidirect
4. C3×#64763C2semidirect
5. C3×#64685C2semidirect
6. #10599155C3direct (N × H)
21. C5×#330C2×C3semidirect
22. #64763C2×C3semidirect
23. #64685C2×C3semidirect
44. C3×#330D5semidirect
100. #330C3×D5semidirect
189. C3×C5#1526semidirect
217. C5C3×#1526semidirect
227. C3#10599155direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660222
C3×#649962
C3×C5×#3302
C3×#647632
C3×#646852
#105991553
C3×#15265