Finite Group Databasebeta

← C3×#10602045 #14291176

Subgroups — C3×#10602045 #14291176

Order 1920.

344 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 90 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⋊#564C211yesmaximal, characteristic
2C3×C5×#491C211yesmaximal, characteristic
3C3×#65369C212yesmaximal
4C3×#64763C211yesmaximal, characteristic
5C3×#64685C212yesmaximal
6#10602045C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×#125C2211yescharacteristic
9C3×#4036—22no—
10C3×#4035—22no—
11C3×#4035—22no—
12C3×#4016C2212yes—
13C3×C5×#103—22no—
14C3×C5×#97C2211yescharacteristic
15C3×#3940—22no—
16C3×#3939—22no—
17C3×#3935C2212yes—
18C3×#1663—51nomaximal, Hall
19C5⋊#564C2×C311yescharacteristic
20C5×#491C2×C311yescharacteristic
21#65369C2×C312yes—
22#64763C2×C311yescharacteristic
23#64685C2×C312yes—
24C2×C3×C5×Q8—21no—
25C2×C3×C5×C8—21no—
26C3×C5×C4⋊C4—22no—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4D412yes—
29C3×C42×C5C2311yescharacteristic
30C3×C4⋊Dic5—22no—
31C3×C4⋊Dic5D412yes—
32C3×C4⋊Dic5D412yes—
33C3×#683—22no—
34C3×#683—22no—
35C3×#683—22no—
36C3×#683—22no—
37C3×C4×Dic5—22no—
38C2×C3×#168—22no—
39C3×#564—51no—
40C3×#501—52no—
41C3×#491D511yescharacteristic
42C3×#330—51no—
43C3×#330—52no—
44C5×C4⋊Q8C22×C311yescharacteristic
45C5×#125C22×C311yescharacteristic
46#4036—22no—
47#4035—22no—
48#4035—22no—
49#4016C22×C312yes—
50C5×#103—22no—
51C5×#97C22×C311yescharacteristic
52#3940—22no—
53#3939—22no—
54#3935C22×C312yes—
55#1663—51noSylow
56C3×C5×Q8—42no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5—41no—
59C2×C3×C4×C5C2×D412yes—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×Dic5—22no—
62C2×C3×Dic5—22no—
63C3×C5×C8—41no—
64C3×#168—24no—
65C3×C4⋊Q8C2×D511yescharacteristic
66C3×#125—52no—
67C3×#125—102no—
68C3×#125—102no—
69C3×#125—102no—
70C3×#125C2×D511yescharacteristic
71C3×#107—102no—
72C3×#106—102no—
73C3×#103—22no—
74C3×#97—52no—
75C3×#97C2×D511yescharacteristic
76C2×C5×Q8—21no—
77C2×C5×C8—21no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4—22no—
80C5×C4⋊C4C3×D412yes—
81C42×C5C23×C311yescharacteristic
82C4⋊Dic5—22no—
83C4⋊Dic5C3×D412yes—
84C4⋊Dic5C3×D412yes—
85#683—22no—
86#683—22no—
87#683—22no—
88#683—22no—
89C4×Dic5—22no—
90C2×#168—22no—
91#564—51no—
92#501—52no—
93#491C3×D511yescharacteristic
94#330—51no—
95#330—52no—
96C22×C3×C5#12011yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5—22no—
99C3×C4×C5—42no—
100C3×C4×C5—81no—
101C3×Dic5—42no—
102C3×Dic5—42no—
103C2×C3×Q8—21no—
104C2×C3×C8—21no—
105C2×C3×C8—102no—
106C3×C4⋊C4—22no—
107C3×C4⋊C4—22no—
108C3×C4⋊C4—52no—
109C3×C4⋊C4—52no—
110C3×C4⋊C4—102no—
111C3×C4⋊C4—102no—
112C3×C4⋊C4—102no—
113C3×C4⋊C4—102no—
114C3×C4⋊C4—102no—
115C3×C4⋊C4C22⋊D512yes—
116C3×C42—102no—
117C3×C42C22×D511yescharacteristic
118C5×Q8—42no—
119C2×C4×C5—22no—
120C2×C4×C5—41no—
121C2×C4×C5C2×C3×D412yes—
122C2×C4×C5C2×C3×D411yescharacteristic
123C2×Dic5—22no—
124C2×Dic5—22no—
125C5×C8—41no—
126#168—24no—
127C4⋊Q8C2×C3×D511yescharacteristic
128#125—52no—
129#125—102no—
130#125—102no—
131#125—102no—
132#125C2×C3×D511yescharacteristic
133#107—102no—
134#106—102no—
135#103—22no—
136#97—52no—
137#97C2×C3×D511yescharacteristic
138C2×C3×C5#45411yescharacteristic
139C2×C3×C5#45612yes—
140C3×Q8—42no—
141C2×C3×C4—22no—
142C2×C3×C4—41no—
143C2×C3×C4—102no—
144C2×C3×C4—102no—
145C2×C3×C4D4×D512yes—
146C2×C3×C4C2×C22⋊D511yescharacteristic
147C3×C8—41no—
148C3×C8—104no—
149C22×C5C3×#12011yescharacteristic
150C4×C5—21no—
151C4×C5—22no—
152C4×C5—42no—
153C4×C5—81no—
154Dic5—42no—
155Dic5—42no—
156C2×Q8—21no—
157C2×C8—21no—
158C2×C8—102no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—52no—
162C4⋊C4—52no—
163C4⋊C4—102no—
164C4⋊C4—102no—
165C4⋊C4—102no—
166C4⋊C4—102no—
167C4⋊C4—102no—
168C4⋊C4C3×C22⋊D512yes—
169C42—102no—
170C42C22×C3×D511yescharacteristic
171C3×C5#166311yescharacteristic, complemented, Hall
172C22×C3#408311yescharacteristic
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—42no—
176C3×C4—81no—
177C3×C4—202no—
178C3×C4—202no—
179C2×C5C3×#45411yescharacteristic
180C2×C5C3×#45612yes—
181Q8—42no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—102no—
185C2×C4—102no—
186C2×C4C3×D4×D512yes—
187C2×C4C2×C3×C22⋊D511yescharacteristic
188C8—41no—
189C8—104no—
190C2×C3#6535111yescharacteristic
191C2×C3#6549412yes—
192C5C3×#166311yescharacteristic, complemented, Sylow
193C22C3×#408311yescharacteristic
194C4—21no—
195C4—22no—
196C4—42no—
197C4—81no—
198C4—202no—
199C4—202no—
200C3#1060204511yescharacteristic, direct product factor, Sylow
201C2C3×#6535111yescharacteristic
202C2C3×#6549412yes—
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#491C2
socle, prime radicalC22×C3×C5#120
hypercenterC3×#491D5
hypocenterC5C3×#1663
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#491

Complements

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

NH ≅ G/Ntype
6. #10602045C3direct (N × H)
171. C3×C5#1663semidirect
192. C5C3×#1663semidirect
200. C3#10602045direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5⋊#5642
C3×C5×#4912
C3×#653692
C3×#647632
C3×#646852
#106020453
C3×#16635