Finite Group Databasebeta

← C3×#10598137 #14278259

Subgroups — C3×#10598137 #14278259

Order 1920.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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×#393C211yesmaximal, characteristic
2C3×#64746C211yesmaximal, characteristic
3C3×#64745C211yesmaximal, characteristic
4#10598137C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C5×Q8C411yescharacteristic, complemented
6C2×C3×C5×C22⋊C4—21no—
7C2×C3×C5×C22⋊C4C2211yescharacteristic
8C2×C3×C22⋊Dic5—21no—
9C3×C5×#95—21no—
10C3×C5×#95C411yescharacteristic, complemented
11C3×C22⋊#168—21no—
12C3×#1351—51nomaximal, Hall
13C5×#393C2×C311yescharacteristic
14#64746C2×C311yescharacteristic
15#64745C2×C311yescharacteristic
16C24×C3×C5D411yescharacteristic
17C2×C3×C5×Q8—42no—
18C2×C3×C5×Q8—41no—
19C22×C3×C4×C5—21no—
20C22×C3×C4×C5—21no—
21C22×C3×C4×C5C2×C411yescharacteristic
22C22×C3×C4×C5D411yescharacteristic
23C22×C3×Dic5—41no—
24C3×C5×C22⋊C4—41no—
25C3×C5×C22⋊C4—42no—
26C3×C22⋊Dic5—22no—
27C3×C22⋊Dic5—41no—
28C2×C3×#168—41no—
29C3×#393D511yescharacteristic
30C3×#342—51no—
31C3×#323—51no—
32C22×C5×Q8C3×C411yescharacteristic, complemented
33C2×C5×C22⋊C4—21no—
34C2×C5×C22⋊C4C22×C311yescharacteristic
35C2×C22⋊Dic5—21no—
36C5×#95—21no—
37C5×#95C3×C411yescharacteristic, complemented
38C22⋊#168—21no—
39#1351—51noSylow
40C23×C3×C5—21no—
41C23×C3×C5—21no—
42C23×C3×C5—41no—
43C23×C3×C5—41no—
44C23×C3×C5C22⋊C411yescharacteristic
45C23×C3×C5SD1611yescharacteristic
46C23×C3×C5Q1611yescharacteristic
47C3×C5×Q8—42no—
48C3×C5×Q8—42no—
49C2×C3×C4×C5—22no—
50C2×C3×C4×C5—21no—
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5—41no—
53C2×C3×C4×C5—41no—
54C2×C3×C4×C5—41no—
55C2×C3×C4×C5—41no—
56C2×C3×C4×C5—41no—
57C2×C3×C4×C5—41no—
58C2×C3×C4×C5—41no—
59C2×C3×Dic5—42no—
60C2×C3×Dic5—81no—
61C2×C3×Dic5—81no—
62C3×#168—81no—
63C22×C3×Q8Dic511yescharacteristic, complemented
64C2×C3×C22⋊C4—21no—
65C2×C3×C22⋊C4—101no—
66C2×C3×C22⋊C4C2×D511yescharacteristic
67C3×C22⋊C8—101no—
68C3×#95—21no—
69C3×#95Dic511yescharacteristic, complemented
70C24×C5C3×D411yescharacteristic
71C2×C5×Q8—42no—
72C2×C5×Q8—41no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5C2×C3×C411yescharacteristic
76C22×C4×C5C3×D411yescharacteristic
77C22×Dic5—41no—
78C5×C22⋊C4—41no—
79C5×C22⋊C4—42no—
80C22⋊Dic5—22no—
81C22⋊Dic5—41no—
82C2×#168—41no—
83#393C3×D511yescharacteristic
84#342—51no—
85#323—51no—
86C22×C3×C5—21no—
87C22×C3×C5—21no—
88C22×C3×C5—21no—
89C22×C3×C5—21no—
90C22×C3×C5—41no—
91C22×C3×C5—41no—
92C22×C3×C5—41no—
93C22×C3×C5—41no—
94C22×C3×C5—81no—
95C22×C3×C5#9911yescharacteristic
96C22×C3×C5#10311yescharacteristic
97C22×C3×C5#10411yescharacteristic
98C3×C4×C5—42no—
99C3×C4×C5—41no—
100C3×C4×C5—41no—
101C3×C4×C5—81no—
102C3×Dic5—82no—
103C24×C3C22⋊D511yescharacteristic
104C2×C3×Q8—42no—
105C2×C3×Q8—41no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—201no—
109C22×C3×C4C2×Dic511yescharacteristic
110C22×C3×C4C22⋊D511yescharacteristic
111C2×C3×C8—201no—
112C3×C22⋊C4—41no—
113C3×C22⋊C4—42no—
114C3×C22⋊C4—102no—
115C3×C22⋊C4—201no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—41no—
119C23×C5—41no—
120C23×C5C3×C22⋊C411yescharacteristic
121C23×C5C3×SD1611yescharacteristic
122C23×C5C3×Q1611yescharacteristic
123C5×Q8—42no—
124C5×Q8—42no—
125C2×C4×C5—22no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×Dic5—42no—
136C2×Dic5—81no—
137C2×Dic5—81no—
138#168—81no—
139C22×Q8C3×Dic511yescharacteristic, complemented
140C2×C22⋊C4—21no—
141C2×C22⋊C4—101no—
142C2×C22⋊C4C2×C3×D511yescharacteristic
143C22⋊C8—101no—
144#95—21no—
145#95C3×Dic511yescharacteristic, complemented
146C2×C3×C5—21no—
147C2×C3×C5—21no—
148C2×C3×C5—41no—
149C2×C3×C5—41no—
150C2×C3×C5#32811yescharacteristic
151C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
152C2×C3×C5#35411yescharacteristic
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—41no—
156C23×C3—41no—
157C23×C3#68811yescharacteristic
158C23×C3#68911yescharacteristic
159C23×C3C22⋊Dic511yescharacteristic
160C3×Q8—42no—
161C3×Q8—42no—
162C2×C3×C4—22no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—41no—
166C2×C3×C4—41no—
167C2×C3×C4—41no—
168C2×C3×C4—41no—
169C2×C3×C4—41no—
170C2×C3×C4—41no—
171C2×C3×C4—41no—
172C2×C3×C4—202no—
173C2×C3×C4—401no—
174C2×C3×C4—401no—
175C3×C8—401no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5—41no—
181C22×C5—41no—
182C22×C5—41no—
183C22×C5—41no—
184C22×C5—81no—
185C22×C5C3×#9911yescharacteristic
186C22×C5C3×#10311yescharacteristic
187C22×C5C3×#10411yescharacteristic
188C4×C5—42no—
189C4×C5—41no—
190C4×C5—41no—
191C4×C5—81no—
192Dic5—82no—
193C24C3×C22⋊D511yescharacteristic
194C2×Q8—42no—
195C2×Q8—41no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—201no—
199C22×C4C2×C3×Dic511yescharacteristic
200C22×C4C3×C22⋊D511yescharacteristic
201C2×C8—201no—
202C22⋊C4—41no—
203C22⋊C4—42no—
204C22⋊C4—102no—
205C22⋊C4—201no—
206C3×C5#135111yescharacteristic, complemented, Hall
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—41no—
212C22×C3—41no—
213C22×C3—41no—
214C22×C3—41no—
215C22×C3—81no—
216C22×C3#396611yescharacteristic
217C22×C3#396711yescharacteristic
218C22×C3#396911yescharacteristic
219C3×C4—42no—
220C3×C4—41no—
221C3×C4—41no—
222C3×C4—81no—
223C3×C4—402no—
224C2×C5—21no—
225C2×C5—21no—
226C2×C5—41no—
227C2×C5—41no—
228C2×C5C3×#32811yescharacteristic
229C2×C5C3×AΣL(1,𝔽16)11yescharacteristic
230C2×C5C3×#35411yescharacteristic
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C3×#68811yescharacteristic
236C23C3×#68911yescharacteristic
237C23C3×C22⋊Dic511yescharacteristic
238Q8—42no—
239Q8—42no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—202no—
251C2×C4—401no—
252C2×C4—401no—
253C8—401no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—41no—
257C2×C3—41no—
258C2×C3#6475611yescharacteristic
259C2×C3#6475811yescharacteristic
260C2×C3#6476111yescharacteristic
261C5C3×#135111yescharacteristic, complemented, Sylow
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22—81no—
271C22C3×#396611yescharacteristic
272C22C3×#396711yescharacteristic
273C22C3×#396911yescharacteristic
274C4—42no—
275C4—41no—
276C4—41no—
277C4—81no—
278C4—402no—
279C3#1059813711yescharacteristic, direct product factor, Sylow
280C2—21no—
281C2—21no—
282C2—41no—
283C2—41no—
284C2C3×#6475611yescharacteristic
285C2C3×#6475811yescharacteristic
286C2C3×#6476111yescharacteristic
subgroupG/H
centerC22×C3#3966
commutatorC22×C4×C5C2×C3×C4
FrattiniC2×C22⋊C4C2×C3×D5
FittingC3×C5×#393C2
socleC22×C3×C5#99
prime radicalC24×C3×C5D4
cosocleC2×C5×C22⋊C4C22×C3
hypercenterC3×#393D5
hypocenterC5C3×#1351
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C22⋊C4 ◁ C3×#393

Complements

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

NH ≅ G/Ntype
4. #10598137C3direct (N × H)
5. C22×C3×C5×Q8C4semidirect
10. C3×C5×#95C4semidirect
32. C22×C5×Q8C3×C4semidirect
37. C5×#95C3×C4semidirect
63. C22×C3×Q8Dic5semidirect
69. C3×#95Dic5semidirect
139. C22×Q8C3×Dic5semidirect
145. #95C3×Dic5semidirect
206. C3×C5#1351semidirect
261. C5C3×#1351semidirect
279. C3#10598137direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#3932
C3×#647462
C3×#647452
#105981373
C3×#13515