Finite Group Databasebeta

← C3×#10598041 #14279364

Subgroups — C3×#10598041 #14279364

Order 1920.

212 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 46 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×#65384C211yesmaximal, characteristic
2C3×C5×#356C211yesmaximal, characteristic, complemented
3C3×#64766C211yesmaximal, characteristic, complemented
4#10598041C311yesmaximal, characteristic, direct product factor, Hall
5C3×#4147C411yescharacteristic
6C3×C5×C4⋊Q8C2211yescharacteristic
7C3×#4088—21no—
8C3×C5×#101—21no—
9C3×#3968C411yescharacteristic
10C3×#3937—21no—
11C3×C4⋊#168—21no—
12C3×#1405—51nomaximal, Hall
13#65384C2×C311yescharacteristic
14C5×#356C2×C311yescharacteristic, complemented
15#64766C2×C311yescharacteristic, complemented
16C2×C3×C5×Q8C2×C411yescharacteristic
17C2×C3×C5×Q8D411yescharacteristic
18C3×#713—41no—
19C3×Q8×D5—41no—
20C3×#709—21no—
21C3×#709—41no—
22C3×C5×M16—41no—
23C3×C5×C4⋊C4—41no—
24C3×C42×C5D411yescharacteristic
25C3×#689—41no—
26C3×#688—41no—
27C3×#681—21no—
28C2×C3×#168—41no—
29C3×#456—51no—
30C3×#356D511yescharacteristic, complemented
31C3×#333—51no—
32#4147C3×C411yescharacteristic
33C5×C4⋊Q8C22×C311yescharacteristic
34#4088—21no—
35C5×#101—21no—
36#3968C3×C411yescharacteristic
37#3937—21no—
38C4⋊#168—21no—
39#1405—51noSylow
40C3×C5×Q8—41no—
41C3×C5×Q8—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C3×C22⋊D5—41no—
47C3×D20—21no—
48C3×D20—41no—
49C3×C4×D5—41no—
50C3×C4×D5—42no—
51C3×Dic10—21no—
52C3×Dic10—41no—
53C3×C5×C8—81no—
54C3×#168—41no—
55C3×#168—81no—
56C3×2−1+4—51no—
57C3×#137—101no—
58C3×C4⋊Q8C2×D511yescharacteristic
59C3×C4⋊C8—101no—
60C3×#104—101no—
61C3×#101—21no—
62C3×#101—51no—
63C2×C5×Q8C2×C3×C411yescharacteristic
64C2×C5×Q8C3×D411yescharacteristic
65#713—41no—
66Q8×D5—41no—
67#709—21no—
68#709—41no—
69C5×M16—41no—
70C5×C4⋊C4—41no—
71C42×C5C3×D411yescharacteristic
72#689—41no—
73#688—41no—
74#681—21no—
75C2×#168—41no—
76#456—51no—
77#356C3×D511yescharacteristic, complemented
78#333—51no—
79C22×C3×C5#9911yescharacteristic
80C2×C3×D5—41no—
81C3×C4×C5—21no—
82C3×C4×C5—21no—
83C3×C4×C5—21no—
84C3×C4×C5—41no—
85C3×C4×C5—41no—
86C3×Dic5—41no—
87C3×#41—101no—
88C3×#41—201no—
89C3×#41—201no—
90C2×C3×Q8—201no—
91C2×C3×Q8C4×D511yescharacteristic
92C2×C3×Q8C22⋊D511yescharacteristic
93C3×Q16—201no—
94C3×SD16—201no—
95C3×M16—41no—
96C3×M16—101no—
97C2×C3×C8—201no—
98C3×C4⋊C4—41no—
99C3×C42D2011yescharacteristic
100C5×Q8—41no—
101C5×Q8—41no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5C3×C22⋊C411yescharacteristic
106C22⋊D5—41no—
107D20—21no—
108D20—41no—
109C4×D5—41no—
110C4×D5—42no—
111Dic10—21no—
112Dic10—41no—
113C5×C8—81no—
114#168—41no—
115#168—81no—
1162−1+4—51no—
117#137—101no—
118C4⋊Q8C2×C3×D511yescharacteristic
119C4⋊C8—101no—
120#104—101no—
121#101—21no—
122#101—51no—
123C2×C3×C5—21no—
124C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
125C3×D5—81no—
126C3×Q8—41no—
127C3×Q8—41no—
128C3×Q8—101no—
129C3×Q8—201no—
130C3×D4—101no—
131C3×D4—201no—
132C3×D4—201no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—201no—
137C2×C3×C4—202no—
138C2×C3×C4#68511yescharacteristic
139C3×C8—81no—
140C3×C8—201no—
141C3×C8—401no—
142C22×C5C3×#9911yescharacteristic
143C2×D5—41no—
144C4×C5—21no—
145C4×C5—21no—
146C4×C5—21no—
147C4×C5—41no—
148C4×C5—41no—
149Dic5—41no—
150#41—101no—
151#41—201no—
152#41—201no—
153C2×Q8—201no—
154C2×Q8C3×C4×D511yescharacteristic
155C2×Q8C3×C22⋊D511yescharacteristic
156Q16—201no—
157SD16—201no—
158M16—41no—
159M16—101no—
160C2×C8—201no—
161C4⋊C4—41no—
162C42C3×D2011yescharacteristic
163C3×C5#140511yescharacteristic, complemented, Hall
164C22×C3—201no—
165C22×C3#393811yescharacteristic
166C3×C4—21no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—41no—
170C3×C4—41no—
171C3×C4—201no—
172C2×C5—21no—
173C2×C5C3×AΣL(1,𝔽16)11yescharacteristic
174D5—81no—
175Q8—41no—
176Q8—41no—
177Q8—101no—
178Q8—201no—
179D4—101no—
180D4—201no—
181D4—201no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—201no—
186C2×C4—202no—
187C2×C4C3×#68511yescharacteristic
188C8—81no—
189C8—201no—
190C8—401no—
191C2×C3—21no—
192C2×C3—401no—
193C2×C3#6469111yescharacteristic
194C5C3×#140511yescharacteristic, complemented, Sylow
195C22—201no—
196C22C3×#393811yescharacteristic
197C4—21no—
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—201no—
203C3#1059804111yescharacteristic, direct product factor, Sylow
204C2—21no—
205C2—401no—
206C2C3×#6469111yescharacteristic
subgroupG/H
centerC2×C3#64691
commutatorC2×C5×Q8C2×C3×C4
FrattiniC4⋊Q8C2×C3×D5
FittingC3×C5×#356C2
socleC2×C3×C5AΣL(1,𝔽16)
prime radicalC3×#4147C4
cosocleC5×C4⋊Q8C22×C3
hypercenterC3×#356D5
hypocenterC5C3×#1405
LCSG ▷ C2×C5×Q8 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊Q8 ◁ C3×#356

Complements

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

NH ≅ G/Ntype
2. C3×C5×#356C2semidirect
3. C3×#64766C2semidirect
4. #10598041C3direct (N × H)
14. C5×#356C2×C3semidirect
15. #64766C2×C3semidirect
30. C3×#356D5semidirect
77. #356C3×D5semidirect
163. C3×C5#1405semidirect
194. C5C3×#1405semidirect
203. C3#10598041direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653842
C3×C5×#3562
C3×#647662
#105980413
C3×#14055