Finite Group Databasebeta

← C3×#10602043 #14290977

Subgroups — C3×#10602043 #14290977

Order 1920.

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

normal subgroups only

This group has 364 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, complemented
2C3×C5×#490C211yesmaximal, characteristic
3C3×#65360C212yesmaximal
4C3×#64763C211yesmaximal, characteristic, complemented
5C3×#64685C212yesmaximal, complemented
6#10602043C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×#127C2211yescharacteristic
8C3×C5×#125C2211yescharacteristic
9C3×#4036—22no—
10C3×#4035—22no—
11C3×#4035—22no—
12C3×#4016C2212yes—
13C3×C5×#102—22no—
14C3×C5×#97C2211yescharacteristic
15C3×#3964—22no—
16C3×#3964—22no—
17C3×#3935C2212yes—
18C3×#1658—51nomaximal, Hall
19C5⋊#564C2×C311yescharacteristic, complemented
20C5×#490C2×C311yescharacteristic
21#65360C2×C312yes—
22#64763C2×C311yescharacteristic, complemented
23#64685C2×C312yescomplemented
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4—21no—
26C2×C3×C5×C8—21no—
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×#490—52no—
41C3×#490D511yescharacteristic
42C3×#330—51no—
43C3×#330—52no—
44C5×#127C22×C311yescharacteristic
45C5×#125C22×C311yescharacteristic
46#4036—22no—
47#4035—22no—
48#4035—22no—
49#4016C22×C312yes—
50C5×#102—22no—
51C5×#97C22×C311yescharacteristic
52#3964—22no—
53#3964—22no—
54#3935C22×C312yes—
55#1658—51noSylow
56C23×C3×C5—41no—
57C3×C5×D4—44no—
58C3×C5×D4—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C2×D412yes—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×Dic5—22no—
63C2×C3×Dic5—22no—
64C3×C5×C8—41no—
65C3×#168—42no—
66C3×#127C2×D511yescharacteristic
67C3×#125—52no—
68C3×#125—102no—
69C3×#125—102no—
70C3×#125—102no—
71C3×#125C2×D511yescharacteristic
72C3×#102—22no—
73C3×#102—102no—
74C3×#102—102no—
75C3×#97—52no—
76C3×#97C2×D511yescharacteristic
77C2×C5×D4—22no—
78C2×C5×D4—21no—
79C2×C5×C8—21no—
80C5×C4⋊C4—22no—
81C5×C4⋊C4C3×D412yes—
82C42×C5C23×C311yescharacteristic
83C4⋊Dic5—22no—
84C4⋊Dic5C3×D412yes—
85C4⋊Dic5C3×D412yes—
86#683—22no—
87#683—22no—
88#683—22no—
89#683—22no—
90C4×Dic5—22no—
91C2×#168—22no—
92#564—51no—
93#490—52no—
94#490C3×D511yescharacteristic
95#330—51no—
96#330—52no—
97C22×C3×C5—81no—
98C22×C3×C5—82no—
99C22×C3×C5#12011yescharacteristic
100C3×C4×C5—22no—
101C3×C4×C5—21no—
102C3×C4×C5—42no—
103C3×Dic5—42no—
104C3×Dic5—42no—
105C2×C3×D4—22no—
106C2×C3×D4—21no—
107C2×C3×C8—21no—
108C2×C3×C8—102no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—52no—
111C3×C4⋊C4—52no—
112C3×C4⋊C4—102no—
113C3×C4⋊C4—102no—
114C3×C4⋊C4—102no—
115C3×C4⋊C4—102no—
116C3×C4⋊C4—102no—
117C3×C4⋊C4C22⋊D512yes—
118C3×C42—102no—
119C3×C42C22×D511yescharacteristic
120C23×C5—41no—
121C5×D4—44no—
122C5×D4—42no—
123C2×C4×C5—22no—
124C2×C4×C5C2×C3×D412yes—
125C2×C4×C5C2×C3×D411yescharacteristic
126C2×Dic5—22no—
127C2×Dic5—22no—
128C5×C8—41no—
129#168—42no—
130#127C2×C3×D511yescharacteristic
131#125—52no—
132#125—102no—
133#125—102no—
134#125—102no—
135#125C2×C3×D511yescharacteristic
136#102—22no—
137#102—102no—
138#102—102no—
139#97—52no—
140#97C2×C3×D511yescharacteristic
141C2×C3×C5—161no—
142C2×C3×C5#45411yescharacteristic
143C2×C3×C5#45412yes—
144C23×C3—41no—
145C3×D4—42no—
146C3×D4—44no—
147C2×C3×C4—22no—
148C2×C3×C4—102no—
149C2×C3×C4—102no—
150C2×C3×C4D4×D512yes—
151C2×C3×C4C2×C22⋊D511yescharacteristic
152C3×C8—41no—
153C3×C8—202no—
154C22×C5—81no—
155C22×C5—82no—
156C22×C5C3×#12011yescharacteristic
157C4×C5—22no—
158C4×C5—21no—
159C4×C5—42no—
160Dic5—42no—
161Dic5—42no—
162C2×D4—22no—
163C2×D4—21no—
164C2×C8—21no—
165C2×C8—102no—
166C4⋊C4—22no—
167C4⋊C4—52no—
168C4⋊C4—52no—
169C4⋊C4—102no—
170C4⋊C4—102no—
171C4⋊C4—102no—
172C4⋊C4—102no—
173C4⋊C4—102no—
174C4⋊C4C3×C22⋊D512yes—
175C42—102no—
176C42C22×C3×D511yescharacteristic
177C3×C5#165811yescharacteristic, complemented, Hall
178C22×C3—81no—
179C22×C3—82no—
180C22×C3#408311yescharacteristic
181C3×C4—21no—
182C3×C4—22no—
183C3×C4—42no—
184C3×C4—202no—
185C3×C4—202no—
186C2×C5—161no—
187C2×C5C3×#45411yescharacteristic
188C2×C5C3×#45412yes—
189C23—41no—
190D4—42no—
191D4—44no—
192C2×C4—22no—
193C2×C4—102no—
194C2×C4—102no—
195C2×C4C3×D4×D512yes—
196C2×C4C2×C3×C22⋊D511yescharacteristic
197C8—41no—
198C8—202no—
199C2×C3—161no—
200C2×C3#6535111yescharacteristic
201C2×C3#6549012yes—
202C5C3×#165811yescharacteristic, complemented, Sylow
203C22—81no—
204C22—82no—
205C22C3×#408311yescharacteristic
206C4—21no—
207C4—22no—
208C4—42no—
209C4—202no—
210C4—202no—
211C3#1060204311yescharacteristic, direct product factor, Sylow
212C2—161no—
213C2C3×#6535111yescharacteristic
214C2C3×#6549012yes—
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#490C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenterC3×#490D5
hypocenterC5C3×#1658
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#490

Complements

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

NH ≅ G/Ntype
1. C3×C5⋊#564C2semidirect
4. C3×#64763C2semidirect
5. C3×#64685C2semidirect
6. #10602043C3direct (N × H)
19. C5⋊#564C2×C3semidirect
22. #64763C2×C3semidirect
23. #64685C2×C3semidirect
177. C3×C5#1658semidirect
202. C5C3×#1658semidirect
211. C3#10602043direct (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×#4902
C3×#653602
C3×#647632
C3×#646852
#106020433
C3×#16585