Finite Group Databasebeta

← C3×#10599162 #14284482

Subgroups — C3×#10599162 #14284482

Order 1920.

388 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 118 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×#64994C212yesmaximal
3C3×C5×#330C211yesmaximal, characteristic, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5C3×#64685C212yesmaximal, complemented
6#10599162C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×#125C2211yescharacteristic
8C3×#4042—22no—
9C3×#4038C412yes—
10C3×#4034C412yes—
11C3×#4033—22no—
12C3×C42×D5C2211yescharacteristic
13C3×#4016C2211yescharacteristic
14C3×C5×#97C2212yes—
15C3×#3952—22no—
16C3×#3946—22no—
17C3×#3935C2212yes—
18C3×#1537—51nomaximal, Hall
19#66022C2×C311yescharacteristic
20#64994C2×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×#533—51no—
40C3×#432—52no—
41C3×#330—51no—
42C3×#330—52no—
43C3×#330D511yescharacteristic, complemented
44C5×#125C22×C311yescharacteristic
45#4042—22no—
46#4038C3×C412yes—
47#4034C3×C412yes—
48#4033—22no—
49C42×D5C22×C311yescharacteristic
50#4016C22×C311yescharacteristic
51C5×#97C22×C312yes—
52#3952—22no—
53#3946—22no—
54#3935C22×C312yes—
55#1537—51noSylow
56C22×C3×D5C22⋊C411yescharacteristic
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C22×C411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×C3×Dic5—22no—
61C2×C3×Dic5C22⋊C412yes—
62C2×C3×Dic5C22⋊C411yescharacteristic
63C3×C4×D5—22no—
64C3×C4×D5—42no—
65C3×Dic10—44no—
66C3×C5×C8—42no—
67C3×#168—42no—
68C3×C4⋊Q8—52no—
69C3×#125—51no—
70C3×#125C2×D511yescharacteristic
71C3×C22⋊Q8—102no—
72C3×C4×Q8—102no—
73C3×#117—52no—
74C2×C3×C42—51no—
75C3×C4⋊C8—102no—
76C3×C22⋊C8—102no—
77C3×#97—52no—
78C3×#97C2×D512yes—
79C2×C4×D5C2×C3×C411yescharacteristic
80C2×C4×D5C3×D412yes—
81C2×Dic10—22no—
82C2×C5×C8—22no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4C2×C3×C412yes—
85C42×C5C23×C311yescharacteristic
86#685—22no—
87C4⋊Dic5C2×C3×C412yes—
88#683—22no—
89#683—22no—
90C4×Dic5—22no—
91C4×Dic5C2×C3×C411yescharacteristic
92C4×Dic5C3×D412yes—
93C2×#168—22no—
94#533—51no—
95#432—52no—
96#330—51no—
97#330—52no—
98#330C3×D511yescharacteristic, complemented
99C22×C3×C5C2×C22⋊C411yescharacteristic
100C2×C3×D5—21no—
101C2×C3×D5—22no—
102C3×C4×C5—21no—
103C3×C4×C5—22no—
104C3×C4×C5—42no—
105C3×Dic5—22no—
106C3×Dic5—42no—
107C3×Dic5#10112yes—
108C2×C3×Q8—102no—
109C22×C3×C4—51no—
110C22×C3×C4—52no—
111C2×C3×C8—22no—
112C2×C3×C8—102no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—52no—
115C3×C4⋊C4—102no—
116C3×C4⋊C4—102no—
117C3×C4⋊C4C4×D512yes—
118C3×C22⋊C4—102no—
119C3×C42—51no—
120C3×C42—52no—
121C3×C42—102no—
122C3×C42C22×D511yescharacteristic
123C22×D5C3×C22⋊C411yescharacteristic
124C2×C4×C5—22no—
125C2×C4×C5C22×C3×C411yescharacteristic
126C2×C4×C5C2×C3×D412yes—
127C2×Dic5—22no—
128C2×Dic5C3×C22⋊C412yes—
129C2×Dic5C3×C22⋊C411yescharacteristic
130C4×D5—22no—
131C4×D5—42no—
132Dic10—44no—
133C5×C8—42no—
134#168—42no—
135C4⋊Q8—52no—
136#125—51no—
137#125C2×C3×D511yescharacteristic
138C22⋊Q8—102no—
139C4×Q8—102no—
140#117—52no—
141C2×C42—51no—
142C4⋊C8—102no—
143C22⋊C8—102no—
144#97—52no—
145#97C2×C3×D512yes—
146C2×C3×C5C2×#10111yescharacteristic
147C2×C3×C5#42112yes—
148C3×D5—41no—
149C23×C3—51no—
150C3×Q8—204no—
151C2×C3×C4—22no—
152C2×C3×C4—51no—
153C2×C3×C4—52no—
154C2×C3×C4—102no—
155C2×C3×C4—102no—
156C2×C3×C4—202no—
157C2×C3×C4C2×C4×D511yescharacteristic
158C2×C3×C4D4×D512yes—
159C3×C8—42no—
160C3×C8—202no—
161C22×C5C2×C3×C22⋊C411yescharacteristic
162C2×D5—21no—
163C2×D5—22no—
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—42no—
167Dic5—22no—
168Dic5—42no—
169Dic5C3×#10112yes—
170C2×Q8—102no—
171C22×C4—51no—
172C22×C4—52no—
173C2×C8—22no—
174C2×C8—102no—
175C4⋊C4—22no—
176C4⋊C4—52no—
177C4⋊C4—102no—
178C4⋊C4—102no—
179C4⋊C4C3×C4×D512yes—
180C22⋊C4—102no—
181C42—51no—
182C42—52no—
183C42—102no—
184C42C22×C3×D511yescharacteristic
185C3×C5#153711yescharacteristic, complemented, Hall
186C22×C3—101no—
187C22×C3—102no—
188C22×C3D5×C22⋊C411yescharacteristic
189C3×C4—21no—
190C3×C4—22no—
191C3×C4—42no—
192C3×C4—52no—
193C3×C4—102no—
194C3×C4—202no—
195C2×C5C2×C3×#10111yescharacteristic
196C2×C5C3×#42112yes—
197D5—41no—
198C23—51no—
199Q8—204no—
200C2×C4—22no—
201C2×C4—51no—
202C2×C4—52no—
203C2×C4—102no—
204C2×C4—102no—
205C2×C4—202no—
206C2×C4C2×C3×C4×D511yescharacteristic
207C2×C4C3×D4×D512yes—
208C8—42no—
209C8—202no—
210C2×C3—201no—
211C2×C3D5×#10111yescharacteristic
212C2×C3#6511012yes—
213C5C3×#153711yescharacteristic, complemented, Sylow
214C22—101no—
215C22—102no—
216C22C3×D5×C22⋊C411yescharacteristic
217C4—21no—
218C4—22no—
219C4—42no—
220C4—52no—
221C4—102no—
222C4—202no—
223C3#1059916211yescharacteristic, direct product factor, Sylow
224C2—201no—
225C2C3×D5×#10111yescharacteristic
226C2C3×#6511012yes—
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×#1537
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. #10599162C3direct (N × H)
21. C5×#330C2×C3semidirect
22. #64763C2×C3semidirect
23. #64685C2×C3semidirect
43. C3×#330D5semidirect
98. #330C3×D5semidirect
185. C3×C5#1537semidirect
213. C5C3×#1537semidirect
223. C3#10599162direct (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×#649942
C3×C5×#3302
C3×#647632
C3×#646852
#105991623
C3×#15375