Finite Group Databasebeta

← C3×#10598767 #14277118

Subgroups — C3×#10598767 #14277118

Order 1920.

368 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 96 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×#65756C212yesmaximal
2C2×C3×#3952C211yesmaximal, characteristic
3#10598767C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×C4×D5C2211yescharacteristic
5C2×C3×#700—22no—
6C22×C3×C5×C8C411yescharacteristic
7C22×C3×#168C411yescharacteristic
8C3×C22⋊#170—22no—
9C3×#4003C414yes—
10C3×#3952—22no—
11C3×#1293—51nomaximal, Hall
12#65756C2×C312yes—
13C2×#3952C2×C311yescharacteristic
14C23×C3×D5Q811yescharacteristic
15C22×C3×C4×C5C2×C411yescharacteristic
16C22×C3×Dic5D411yescharacteristic
17C2×C3×C4×D5—41no—
18C2×C3×C4×D5—41no—
19C2×C3×C4×D5C2×C412yes—
20C2×C3×C4×D5D412yes—
21C2×C3×#170—24no—
22C3×#700—42no—
23C3×#700—42no—
24C2×C3×C5×C8—21no—
25C2×C3×C5×C8—41no—
26C2×C3×#168—21no—
27C2×C3×#168—41no—
28C3×#407—52no—
29C2×C3×C22⋊C8—51no—
30C22×C4×D5C22×C311yescharacteristic
31C2×#700—22no—
32C22×C5×C8C3×C411yescharacteristic
33C22×#168C3×C411yescharacteristic
34C22⋊#170—22no—
35#4003C3×C414yes—
36#3952—22no—
37#1293—51noSylow
38C23×C3×C5C4⋊C411yescharacteristic
39C22×C3×D5—21no—
40C22×C3×D5—21no—
41C22×C3×D5—41no—
42C22×C3×D5—41no—
43C22×C3×D5C4⋊C412yes—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5—21no—
46C2×C3×C4×C5C4211yescharacteristic
47C2×C3×C4×C5C22⋊C411yescharacteristic
48C2×C3×Dic5—41no—
49C2×C3×Dic5C22⋊C412yes—
50C3×C4×D5—22no—
51C3×C4×D5—22no—
52C3×C4×D5—42no—
53C3×#170—44no—
54C3×C5×C8—41no—
55C3×#168—41no—
56C23×C3×C4—51no—
57C2×C3×M16—102no—
58C22×C3×C8—51no—
59C22×C3×C8AGL(1,𝔽5)11yescharacteristic
60C3×C22⋊C8—54no—
61C3×C22⋊C8—102no—
62C3×C22⋊C8—102no—
63C23×D5C3×Q811yescharacteristic
64C22×C4×C5C2×C3×C411yescharacteristic
65C22×Dic5C3×D411yescharacteristic
66C2×C4×D5—41no—
67C2×C4×D5—41no—
68C2×C4×D5C2×C3×C412yes—
69C2×C4×D5C3×D412yes—
70C2×#170—24no—
71#700—42no—
72#700—42no—
73C2×C5×C8—21no—
74C2×C5×C8—41no—
75C2×#168—21no—
76C2×#168—41no—
77#407—52no—
78C2×C22⋊C8—51no—
79C22×C3×C5—21no—
80C22×C3×C5—21no—
81C22×C3×C5#9511yescharacteristic
82C22×C3×C5#10811yescharacteristic
83C22×C3×C5#10811yescharacteristic
84C2×C3×D5—22no—
85C2×C3×D5—22no—
86C2×C3×D5—22no—
87C2×C3×D5—42no—
88C2×C3×D5—42no—
89C3×C4×C5—21no—
90C3×C4×C5#9911yescharacteristic
91C3×C4×C5#9911yescharacteristic
92C3×Dic5—22no—
93C24×C3—51no—
94C22×C3×C4—51no—
95C22×C3×C4—52no—
96C22×C3×C4—52no—
97C22×C3×C4—201no—
98C22×C3×C4—201no—
99C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
100C3×M16—202no—
101C3×M16—202no—
102C2×C3×C8—21no—
103C2×C3×C8—41no—
104C2×C3×C8—104no—
105C2×C3×C8—101no—
106C2×C3×C8—201no—
107C23×C5C3×C4⋊C411yescharacteristic
108C22×D5—21no—
109C22×D5—21no—
110C22×D5—41no—
111C22×D5—41no—
112C22×D5C3×C4⋊C412yes—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5C3×C4211yescharacteristic
116C2×C4×C5C3×C22⋊C411yescharacteristic
117C2×Dic5—41no—
118C2×Dic5C3×C22⋊C412yes—
119C4×D5—22no—
120C4×D5—22no—
121C4×D5—42no—
122#170—44no—
123C5×C8—41no—
124#168—41no—
125C23×C4—51no—
126C2×M16—102no—
127C22×C8—51no—
128C22×C8C3×AGL(1,𝔽5)11yescharacteristic
129C22⋊C8—54no—
130C22⋊C8—102no—
131C22⋊C8—102no—
132C2×C3×C5—21no—
133C2×C3×C5—21no—
134C2×C3×C5#33811yescharacteristic
135C2×C3×C5#34111yescharacteristic
136C2×C3×C5#34211yescharacteristic
137C3×D5—42no—
138C23×C3—52no—
139C23×C3—101no—
140C23×C3—101no—
141C23×C3—201no—
142C23×C3—201no—
143C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—52no—
147C2×C3×C4—102no—
148C2×C3×C4—102no—
149C2×C3×C4—202no—
150C2×C3×C4—201no—
151C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
152C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
153C3×C8—41no—
154C3×C8—204no—
155C3×C8—201no—
156C22×C5—21no—
157C22×C5—21no—
158C22×C5C3×#9511yescharacteristic
159C22×C5C3×#10811yescharacteristic
160C22×C5C3×#10811yescharacteristic
161C2×D5—22no—
162C2×D5—22no—
163C2×D5—22no—
164C2×D5—42no—
165C2×D5—42no—
166C4×C5—21no—
167C4×C5C3×#9911yescharacteristic
168C4×C5C3×#9911yescharacteristic
169Dic5—22no—
170C24—51no—
171C22×C4—51no—
172C22×C4—52no—
173C22×C4—52no—
174C22×C4—201no—
175C22×C4—201no—
176C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
177M16—202no—
178M16—202no—
179C2×C8—21no—
180C2×C8—41no—
181C2×C8—104no—
182C2×C8—101no—
183C2×C8—201no—
184C3×C5#129311yescharacteristic, complemented, Hall
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—102no—
188C22×C3—102no—
189C22×C3—102no—
190C22×C3—202no—
191C22×C3—202no—
192C22×C3#399511yescharacteristic
193C22×C3#399611yescharacteristic
194C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
195C3×C4—21no—
196C3×C4—102no—
197C3×C4#399911yescharacteristic
198C3×C4#401111yescharacteristic
199C2×C5—21no—
200C2×C5—21no—
201C2×C5C3×#33811yescharacteristic
202C2×C5C3×#34111yescharacteristic
203C2×C5C3×#34211yescharacteristic
204D5—42no—
205C23—52no—
206C23—101no—
207C23—101no—
208C23—201no—
209C23—201no—
210C23C3×C4⋊AGL(1,𝔽5)11yescharacteristic
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—52no—
214C2×C4—102no—
215C2×C4—102no—
216C2×C4—202no—
217C2×C4—201no—
218C2×C4C3×C4×AGL(1,𝔽5)11yescharacteristic
219C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
220C8—41no—
221C8—204no—
222C8—201no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—202no—
226C2×C3#6489611yescharacteristic
227C2×C3#6489711yescharacteristic
228C2×C3#6491711yescharacteristic
229C5C3×#129311yescharacteristic, complemented, Sylow
230C22—21no—
231C22—21no—
232C22—102no—
233C22—102no—
234C22—102no—
235C22—202no—
236C22—202no—
237C22C3×#399511yescharacteristic
238C22C3×#399611yescharacteristic
239C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
240C4—21no—
241C4—102no—
242C4C3×#399911yescharacteristic
243C4C3×#401111yescharacteristic
244C3#1059876711yescharacteristic, direct product factor, Sylow
245C2—21no—
246C2—21no—
247C2—202no—
248C2C3×#6489611yescharacteristic
249C2C3×#6489711yescharacteristic
250C2C3×#6491711yescharacteristic
subgroupG/H
centerC22×C3(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C3×C42
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC22×C3×C5#95
prime radicalC23×C3×D5Q8
cosocleC22×C4×D5C22×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C3×#1293
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8

Complements

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

NH ≅ G/Ntype
3. #10598767C3direct (N × H)
184. C3×C5#1293semidirect
229. C5C3×#1293semidirect
244. C3#10598767direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#657562
C2×C3×#39522
#105987673
C3×#12935