Finite Group Databasebeta

← C3×#10598826 #14278126

Subgroups — C3×#10598826 #14278126

Order 1920.

336 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 60 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×#65511C211yesmaximal, characteristic
2C3×#64919C211yesmaximal, characteristic, complemented
3C3×#64914C211yesmaximal, characteristic, complemented
4#10598826C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C5×D4C411yescharacteristic
6C2×C3×#704—21no—
7C2×C3×C22⋊Dic5—21no—
8C2×C3×C22⋊Dic5—21no—
9C2×C3×#683C2211yescharacteristic
10C3×C22⋊#170—21no—
11C3×#3963C411yescharacteristic
12C3×#1345—51nomaximal, Hall
13#65511C2×C311yescharacteristic
14#64919C2×C311yescharacteristic, complemented
15#64914C2×C311yescharacteristic, complemented
16C24×C3×C5—21no—
17C2×C3×C5×D4—41no—
18C2×C3×C5×D4—42no—
19C22×C3×C4×C5C2×C411yescharacteristic
20C22×C3×Dic5—21no—
21C22×C3×Dic5D411yescharacteristic
22C22×C3×Dic5D411yescharacteristic
23C3×#704—22no—
24C3×#704—41no—
25C2×C3×#170—41no—
26C2×C3×#170—41no—
27C3×C22⋊Dic5—42no—
28C3×C22⋊Dic5—41no—
29C3×C22⋊Dic5—41no—
30C3×#683—41no—
31C3×#394—51no—
32C3×#343—51no—
33C3×#324—51no—
34C22×C5×D4C3×C411yescharacteristic
35C2×#704—21no—
36C2×C22⋊Dic5—21no—
37C2×C22⋊Dic5—21no—
38C2×#683C22×C311yescharacteristic
39C22⋊#170—21no—
40#3963C3×C411yescharacteristic
41#1345—51noSylow
42C23×C3×C5—22no—
43C23×C3×C5—41no—
44C23×C3×C5—41no—
45C23×C3×C5—41no—
46C23×C3×C5—41no—
47C23×C3×C5—41no—
48C23×C3×C5—41no—
49C23×C3×C5C22⋊C411yescharacteristic
50C3×C5×D4—42no—
51C3×C5×D4—42no—
52C2×C3×C4×C5—21no—
53C2×C3×C4×C5—41no—
54C2×C3×Dic5—21no—
55C2×C3×Dic5—21no—
56C2×C3×Dic5—21no—
57C2×C3×Dic5—41no—
58C2×C3×Dic5—41no—
59C2×C3×Dic5—41no—
60C2×C3×Dic5—41no—
61C2×C3×Dic5D811yescharacteristic
62C2×C3×Dic5SD1611yescharacteristic
63C3×#170—42no—
64C3×#170—81no—
65C22×C3×D4AGL(1,𝔽5)11yescharacteristic
66C2×C3×M16—101no—
67C2×C3×C4⋊C4—51no—
68C2×C3×C22⋊C4—101no—
69C2×C3×C22⋊C4—101no—
70C3×C22⋊C8—101no—
71C3×#95—51no—
72C24×C5—21no—
73C2×C5×D4—41no—
74C2×C5×D4—42no—
75C22×C4×C5C2×C3×C411yescharacteristic
76C22×Dic5—21no—
77C22×Dic5C3×D411yescharacteristic
78C22×Dic5C3×D411yescharacteristic
79#704—22no—
80#704—41no—
81C2×#170—41no—
82C2×#170—41no—
83C22⋊Dic5—42no—
84C22⋊Dic5—41no—
85C22⋊Dic5—41no—
86#683—41no—
87#394—51no—
88#343—51no—
89#324—51no—
90C22×C3×C5—21no—
91C22×C3×C5—21no—
92C22×C3×C5—42no—
93C22×C3×C5—42no—
94C22×C3×C5—42no—
95C22×C3×C5—81no—
96C22×C3×C5—81no—
97C22×C3×C5—81no—
98C22×C3×C5—81no—
99C22×C3×C5#9911yescharacteristic
100C22×C3×C5#10211yescharacteristic
101C22×C3×C5#10411yescharacteristic
102C3×C4×C5—41no—
103C3×Dic5—21no—
104C3×Dic5—21no—
105C3×Dic5—41no—
106C3×Dic5—81no—
107C24×C3—21no—
108C2×C3×D4—41no—
109C2×C3×D4—42no—
110C22×C3×C4—51no—
111C22×C3×C4—51no—
112C22×C3×C4—101no—
113C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
114C3×M16—102no—
115C3×M16—201no—
116C2×C3×C8—201no—
117C2×C3×C8—201no—
118C3×C4⋊C4—201no—
119C3×C22⋊C4—201no—
120C3×C22⋊C4—201no—
121C3×C22⋊C4—202no—
122C23×C5—22no—
123C23×C5—41no—
124C23×C5—41no—
125C23×C5—41no—
126C23×C5—41no—
127C23×C5—41no—
128C23×C5—41no—
129C23×C5C3×C22⋊C411yescharacteristic
130C5×D4—42no—
131C5×D4—42no—
132C2×C4×C5—21no—
133C2×C4×C5—41no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—41no—
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5C3×D811yescharacteristic
142C2×Dic5C3×SD1611yescharacteristic
143#170—42no—
144#170—81no—
145C22×D4C3×AGL(1,𝔽5)11yescharacteristic
146C2×M16—101no—
147C2×C4⋊C4—51no—
148C2×C22⋊C4—101no—
149C2×C22⋊C4—101no—
150C22⋊C8—101no—
151#95—51no—
152C2×C3×C5—21no—
153C2×C3×C5—21no—
154C2×C3×C5—82no—
155C2×C3×C5#32711yescharacteristic
156C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
157C2×C3×C5#35511yescharacteristic
158C23×C3—22no—
159C23×C3—41no—
160C23×C3—41no—
161C23×C3—41no—
162C23×C3—41no—
163C23×C3—41no—
164C23×C3—41no—
165C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
166C3×D4—42no—
167C3×D4—42no—
168C2×C3×C4—21no—
169C2×C3×C4—41no—
170C2×C3×C4—51no—
171C2×C3×C4—51no—
172C2×C3×C4—101no—
173C2×C3×C4—101no—
174C2×C3×C4—101no—
175C2×C3×C4—201no—
176C2×C3×C4—201no—
177C2×C3×C4—201no—
178C2×C3×C4—201no—
179C3×C8—202no—
180C3×C8—401no—
181C22×C5—21no—
182C22×C5—21no—
183C22×C5—42no—
184C22×C5—42no—
185C22×C5—42no—
186C22×C5—81no—
187C22×C5—81no—
188C22×C5—81no—
189C22×C5—81no—
190C22×C5C3×#9911yescharacteristic
191C22×C5C3×#10211yescharacteristic
192C22×C5C3×#10411yescharacteristic
193C4×C5—41no—
194Dic5—21no—
195Dic5—21no—
196Dic5—41no—
197Dic5—81no—
198C24—21no—
199C2×D4—41no—
200C2×D4—42no—
201C22×C4—51no—
202C22×C4—51no—
203C22×C4—101no—
204C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
205M16—102no—
206M16—201no—
207C2×C8—201no—
208C2×C8—201no—
209C4⋊C4—201no—
210C22⋊C4—201no—
211C22⋊C4—201no—
212C22⋊C4—202no—
213C3×C5#134511yescharacteristic, complemented, Hall
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—42no—
217C22×C3—42no—
218C22×C3—42no—
219C22×C3—81no—
220C22×C3—81no—
221C22×C3—81no—
222C22×C3—81no—
223C22×C3#400711yescharacteristic
224C22×C3#400811yescharacteristic
225C22×C3#401111yescharacteristic
226C3×C4—41no—
227C3×C4—101no—
228C3×C4—101no—
229C3×C4—201no—
230C3×C4—401no—
231C2×C5—21no—
232C2×C5—21no—
233C2×C5—82no—
234C2×C5C3×#32711yescharacteristic
235C2×C5C3×AΣL(1,𝔽16)11yescharacteristic
236C2×C5C3×#35511yescharacteristic
237C23—22no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
245D4—42no—
246D4—42no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—51no—
250C2×C4—51no—
251C2×C4—101no—
252C2×C4—101no—
253C2×C4—101no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4—201no—
257C2×C4—201no—
258C8—202no—
259C8—401no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—82no—
263C2×C3#6492011yescharacteristic
264C2×C3#6492311yescharacteristic
265C2×C3#6493411yescharacteristic
266C5C3×#134511yescharacteristic, complemented, Sylow
267C22—21no—
268C22—21no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—81no—
273C22—81no—
274C22—81no—
275C22—81no—
276C22C3×#400711yescharacteristic
277C22C3×#400811yescharacteristic
278C22C3×#401111yescharacteristic
279C4—41no—
280C4—101no—
281C4—101no—
282C4—201no—
283C4—401no—
284C3#1059882611yescharacteristic, direct product factor, Sylow
285C2—21no—
286C2—21no—
287C2—82no—
288C2C3×#6492011yescharacteristic
289C2C3×#6492311yescharacteristic
290C2C3×#6493411yescharacteristic
subgroupG/H
centerC22×C3#4011
commutatorC22×C4×C5C2×C3×C4
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
Fitting, prime radicalC22×C3×C5×D4C4
socleC22×C3×C5#99
cosocleC2×#683C22×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C3×#1345
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×#64919C2semidirect
3. C3×#64914C2semidirect
4. #10598826C3direct (N × H)
14. #64919C2×C3semidirect
15. #64914C2×C3semidirect
213. C3×C5#1345semidirect
266. C5C3×#1345semidirect
284. C3#10598826direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#655112
C3×#649192
C3×#649142
#105988263
C3×#13455