Finite Group Databasebeta

← C3×#10597947 #14278124

Subgroups — C3×#10597947 #14278124

Order 1920.

336 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 70 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×#65280C211yesmaximal, characteristic
2C3×C5×#324C211yesmaximal, characteristic, complemented
3C3×#64750C211yesmaximal, characteristic, complemented
4#10597947C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×D20C411yescharacteristic
6C2×C3×C5×C4⋊C4C2211yescharacteristic
7C2×C3×#685—21no—
8C2×C3×#685—21no—
9C2×C3×#681—21no—
10C3×C5×C22⋊C8—21no—
11C3×#3963C411yescharacteristic
12C3×#1345—51nomaximal, Hall
13#65280C2×C311yescharacteristic
14C5×#324C2×C311yescharacteristic, complemented
15#64750C2×C311yescharacteristic, complemented
16C23×C3×D5—21no—
17C22×C3×C4×C5C2×C411yescharacteristic
18C22×C3×C4×C5D411yescharacteristic
19C22×C3×C4×C5D411yescharacteristic
20C22×C3×Dic5—21no—
21C2×C3×D20—41no—
22C2×C3×D20—42no—
23C2×C3×C5×C8—41no—
24C3×C5×C4⋊C4—41no—
25C3×#685—42no—
26C3×#685—41no—
27C3×#685—41no—
28C3×#681—22no—
29C3×#681—41no—
30C2×C3×#168—41no—
31C3×#394—51no—
32C3×#343—51no—
33C3×#324D511yescharacteristic, complemented
34C22×D20C3×C411yescharacteristic
35C2×C5×C4⋊C4C22×C311yescharacteristic
36C2×#685—21no—
37C2×#685—21no—
38C2×#681—21no—
39C5×C22⋊C8—21no—
40#3963C3×C411yescharacteristic
41#1345—51noSylow
42C23×C3×C5C22⋊C411yescharacteristic
43C22×C3×D5—22no—
44C22×C3×D5—41no—
45C22×C3×D5—41no—
46C22×C3×D5—41no—
47C22×C3×D5—41no—
48C22×C3×D5—41no—
49C22×C3×D5—41no—
50C2×C3×C4×C5—21no—
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5—21no—
53C2×C3×C4×C5—21no—
54C2×C3×C4×C5—41no—
55C2×C3×C4×C5—41no—
56C2×C3×C4×C5D811yescharacteristic
57C2×C3×C4×C5SD1611yescharacteristic
58C2×C3×Dic5—41no—
59C2×C3×Dic5—41no—
60C2×C3×Dic5—41no—
61C3×D20—42no—
62C3×D20—42no—
63C3×C5×C8—81no—
64C3×#168—42no—
65C22×C3×D4—51no—
66C2×C3×M16—101no—
67C2×C3×C4⋊C4C2×D511yescharacteristic
68C2×C3×C22⋊C4—101no—
69C2×C3×C22⋊C4—101no—
70C3×C22⋊C8—21no—
71C3×#95—51no—
72C23×D5—21no—
73C22×C4×C5C2×C3×C411yescharacteristic
74C22×C4×C5C3×D411yescharacteristic
75C22×C4×C5C3×D411yescharacteristic
76C22×Dic5—21no—
77C2×D20—41no—
78C2×D20—42no—
79C2×C5×C8—41no—
80C5×C4⋊C4—41no—
81#685—42no—
82#685—41no—
83#685—41no—
84#681—22no—
85#681—41no—
86C2×#168—41no—
87#394—51no—
88#343—51no—
89#324C3×D511yescharacteristic, complemented
90C22×C3×C5—21no—
91C22×C3×C5—21no—
92C22×C3×C5#9911yescharacteristic
93C22×C3×C5#10211yescharacteristic
94C22×C3×C5#10411yescharacteristic
95C2×C3×D5—42no—
96C2×C3×D5—42no—
97C2×C3×D5—42no—
98C2×C3×D5—81no—
99C2×C3×D5—81no—
100C2×C3×D5—81no—
101C2×C3×D5—81no—
102C3×C4×C5—21no—
103C3×C4×C5—21no—
104C3×C4×C5—41no—
105C3×C4×C5—41no—
106C3×Dic5—81no—
107C24×C3—101no—
108C2×C3×D4—201no—
109C2×C3×D4—202no—
110C22×C3×C4—101no—
111C22×C3×C4C4×D511yescharacteristic
112C22×C3×C4D2011yescharacteristic
113C22×C3×C4C22⋊D511yescharacteristic
114C3×M16—102no—
115C3×M16—201no—
116C2×C3×C8—41no—
117C2×C3×C8—201no—
118C3×C4⋊C4—41no—
119C3×C22⋊C4—202no—
120C3×C22⋊C4—201no—
121C3×C22⋊C4—201no—
122C23×C5C3×C22⋊C411yescharacteristic
123C22×D5—22no—
124C22×D5—41no—
125C22×D5—41no—
126C22×D5—41no—
127C22×D5—41no—
128C22×D5—41no—
129C22×D5—41no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5C3×D811yescharacteristic
137C2×C4×C5C3×SD1611yescharacteristic
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141D20—42no—
142D20—42no—
143C5×C8—81no—
144#168—42no—
145C22×D4—51no—
146C2×M16—101no—
147C2×C4⋊C4C2×C3×D511yescharacteristic
148C2×C22⋊C4—101no—
149C2×C22⋊C4—101no—
150C22⋊C8—21no—
151#95—51no—
152C2×C3×C5—21no—
153C2×C3×C5—21no—
154C2×C3×C5#32711yescharacteristic
155C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
156C2×C3×C5#35511yescharacteristic
157C3×D5—82no—
158C23×C3—102no—
159C23×C3—201no—
160C23×C3—201no—
161C23×C3—201no—
162C23×C3—201no—
163C23×C3—201no—
164C23×C3—201no—
165C23×C3#68511yescharacteristic
166C3×D4—202no—
167C3×D4—202no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—41no—
173C2×C3×C4—41no—
174C2×C3×C4—201no—
175C2×C3×C4—201no—
176C2×C3×C4—201no—
177C2×C3×C4#67711yescharacteristic
178C2×C3×C4D4011yescharacteristic
179C3×C8—81no—
180C3×C8—202no—
181C22×C5—21no—
182C22×C5—21no—
183C22×C5C3×#9911yescharacteristic
184C22×C5C3×#10211yescharacteristic
185C22×C5C3×#10411yescharacteristic
186C2×D5—42no—
187C2×D5—42no—
188C2×D5—42no—
189C2×D5—81no—
190C2×D5—81no—
191C2×D5—81no—
192C2×D5—81no—
193C4×C5—21no—
194C4×C5—21no—
195C4×C5—41no—
196C4×C5—41no—
197Dic5—81no—
198C24—101no—
199C2×D4—201no—
200C2×D4—202no—
201C22×C4—101no—
202C22×C4C3×C4×D511yescharacteristic
203C22×C4C3×D2011yescharacteristic
204C22×C4C3×C22⋊D511yescharacteristic
205M16—102no—
206M16—201no—
207C2×C8—41no—
208C2×C8—201no—
209C4⋊C4—41no—
210C22⋊C4—202no—
211C22⋊C4—201no—
212C22⋊C4—201no—
213C3×C5#134511yescharacteristic, complemented, Hall
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—202no—
217C22×C3—202no—
218C22×C3—202no—
219C22×C3—401no—
220C22×C3—401no—
221C22×C3—401no—
222C22×C3—401no—
223C22×C3#393811yescharacteristic
224C22×C3#395311yescharacteristic
225C22×C3#395711yescharacteristic
226C3×C4—21no—
227C3×C4—21no—
228C3×C4—41no—
229C3×C4—41no—
230C3×C4—401no—
231C2×C5—21no—
232C2×C5—21no—
233C2×C5C3×#32711yescharacteristic
234C2×C5C3×AΣL(1,𝔽16)11yescharacteristic
235C2×C5C3×#35511yescharacteristic
236D5—82no—
237C23—102no—
238C23—201no—
239C23—201no—
240C23—201no—
241C23—201no—
242C23—201no—
243C23—201no—
244C23C3×#68511yescharacteristic
245D4—202no—
246D4—202no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—201no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4C3×#67711yescharacteristic
257C2×C4C3×D4011yescharacteristic
258C8—81no—
259C8—202no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—402no—
263C2×C3#6469011yescharacteristic
264C2×C3#6469111yescharacteristic
265C2×C3#6469711yescharacteristic
266C5C3×#134511yescharacteristic, complemented, Sylow
267C22—21no—
268C22—21no—
269C22—202no—
270C22—202no—
271C22—202no—
272C22—401no—
273C22—401no—
274C22—401no—
275C22—401no—
276C22C3×#393811yescharacteristic
277C22C3×#395311yescharacteristic
278C22C3×#395711yescharacteristic
279C4—21no—
280C4—21no—
281C4—41no—
282C4—41no—
283C4—401no—
284C3#1059794711yescharacteristic, direct product factor, Sylow
285C2—21no—
286C2—21no—
287C2—402no—
288C2C3×#6469011yescharacteristic
289C2C3×#6469111yescharacteristic
290C2C3×#6469711yescharacteristic
subgroupG/H
centerC22×C3#3938
commutatorC22×C4×C5C2×C3×C4
FrattiniC2×C4⋊C4C2×C3×D5
FittingC3×C5×#324C2
socleC22×C3×C5#99
prime radicalC22×C3×D20C4
cosocleC2×C5×C4⋊C4C22×C3
hypercenterC3×#324D5
hypocenterC5C3×#1345
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
2. C3×C5×#324C2semidirect
3. C3×#64750C2semidirect
4. #10597947C3direct (N × H)
14. C5×#324C2×C3semidirect
15. #64750C2×C3semidirect
33. C3×#324D5semidirect
89. #324C3×D5semidirect
213. C3×C5#1345semidirect
266. C5C3×#1345semidirect
284. C3#10597947direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#652802
C3×C5×#3242
C3×#647502
#105979473
C3×#13455