Finite Group Databasebeta

← C3×#10599948 #14316884

Subgroups — C3×#10599948 #14316884

Order 1920.

452 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 82 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×#66006C211yesmaximal, characteristic, complemented
2C3×#65350C211yesmaximal, characteristic
3C3×#65031C212yesmaximal
4C3×C5×#354C211yesmaximal, characteristic, complemented
5C3×#64692C212yesmaximal, complemented
6#10599948C311yesmaximal, characteristic, direct product factor, Hall
7C3×#4144C2211yescharacteristic
8C3×C5×#124C2211yescharacteristic
9C3×#4090—21no—
10C3×#4088—21no—
11C3×#4081C2212yes—
12C3×#4032—22no—
13C3×#4025—22no—
14C3×#4024—22no—
15C3×#4016—21no—
16C3×C5×#99C2212yes—
17C3×#3965C2211yescharacteristic
18C3×#3938—22no—
19C3×#3937—21no—
20C3×#2201—51nomaximal, Hall
21#66006C2×C311yescharacteristic, complemented
22#65350C2×C311yescharacteristic
23#65031C2×C312yes—
24C5×#354C2×C311yescharacteristic, complemented
25#64692C2×C312yescomplemented
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4C2311yescharacteristic
28C2×C3×C22⋊D5—22no—
29C22×C3×Dic5D412yes—
30C3×#711—41no—
31C3×D4×D5—41no—
32C3×#709—21no—
33C2×C3×Dic10—21no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5D411yescharacteristic
37C3×C22⋊Dic5—22no—
38C3×C22⋊Dic5D412yes—
39C3×#689—41no—
40C3×#688—41no—
41C3×#685—42no—
42C3×C4⋊Dic5—21no—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—42no—
45C3×#683—22no—
46C3×#683—22no—
47C3×#683—22no—
48C3×C4×Dic5—21no—
49C3×#681—21no—
50C3×#563—51no—
51C3×#458—52no—
52C3×#455—51no—
53C3×#354D511yescharacteristic, complemented
54C3×#352—52no—
55#4144C22×C311yescharacteristic
56C5×#124C22×C311yescharacteristic
57#4090—21no—
58#4088—21no—
59#4081C22×C312yes—
60#4032—22no—
61#4025—22no—
62#4024—22no—
63#4016—21no—
64C5×#99C22×C312yes—
65#3965C22×C311yescharacteristic
66#3938—22no—
67#3937—21no—
68#2201—51noSylow
69C23×C3×C5C2×D412yes—
70C22×C3×D5—22no—
71C3×C5×Q8—41no—
72C3×C5×D4—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—42no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C3×C22⋊D5—42no—
78C3×C22⋊D5—41no—
79C2×C3×Dic5—22no—
80C2×C3×Dic5—22no—
81C2×C3×Dic5—22no—
82C2×C3×Dic5—42no—
83C3×D20—21no—
84C3×C4×D5—41no—
85C3×Dic10—21no—
86C3×Dic10—81no—
87C3×#168—41no—
88C3×H(5,𝔽2)—51no—
89C3×#137—101no—
90C3×C4⋊Q8—101no—
91C3×#126—102no—
92C3×#125—101no—
93C3×#124C2×D511yescharacteristic
94C3×#123—52no—
95C3×#123—102no—
96C3×C22⋊Q8—102no—
97C3×#104—101no—
98C3×#100—51no—
99C3×#99—102no—
100C3×#99C2×D512yes—
101C2×C5×Q8C3×D411yescharacteristic
102C2×C5×D4C23×C311yescharacteristic
103C2×C22⋊D5—22no—
104C22×Dic5C3×D412yes—
105#711—41no—
106D4×D5—41no—
107#709—21no—
108C2×Dic10—21no—
109C5×C22⋊C4—22no—
110C5×C22⋊C4—22no—
111C42×C5C3×D411yescharacteristic
112C22⋊Dic5—22no—
113C22⋊Dic5C3×D412yes—
114#689—41no—
115#688—41no—
116#685—42no—
117C4⋊Dic5—21no—
118C4⋊Dic5—21no—
119C4⋊Dic5—42no—
120#683—22no—
121#683—22no—
122#683—22no—
123C4×Dic5—21no—
124#681—21no—
125#563—51no—
126#458—52no—
127#455—51no—
128#354C3×D511yescharacteristic, complemented
129#352—52no—
130C22×C3×C5—22no—
131C22×C3×C5—42no—
132C22×C3×C5#12011yescharacteristic
133C2×C3×D5—41no—
134C2×C3×D5—82no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138C3×C4×C5—82no—
139C3×Dic5—42no—
140C3×Dic5—41no—
141C3×Dic5—42no—
142C3×#41—101no—
143C3×#41—201no—
144C2×C3×Q8—101no—
145C2×C3×Q8D2011yescharacteristic
146C2×C3×D4—102no—
147C2×C3×D4—201no—
148C2×C3×D4C22×D511yescharacteristic
149C22×C3×C4—52no—
150C3×Q16—201no—
151C3×SD16—201no—
152C3×M16—101no—
153C3×C4⋊C4—102no—
154C3×C4⋊C4—102no—
155C3×C4⋊C4—101no—
156C3×C4⋊C4—101no—
157C3×C4⋊C4—102no—
158C3×C4⋊C4—202no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—52no—
162C3×C22⋊C4—102no—
163C3×C22⋊C4—202no—
164C3×C42—101no—
165C3×C42D2011yescharacteristic
166C23×C5C2×C3×D412yes—
167C22×D5—22no—
168C5×Q8—41no—
169C5×D4—41no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—42no—
173C2×C4×C5C2×C3×D411yescharacteristic
174C22⋊D5—42no—
175C22⋊D5—41no—
176C2×Dic5—22no—
177C2×Dic5—22no—
178C2×Dic5—22no—
179C2×Dic5—42no—
180D20—21no—
181C4×D5—41no—
182Dic10—21no—
183Dic10—81no—
184#168—41no—
185H(5,𝔽2)—51no—
186#137—101no—
187C4⋊Q8—101no—
188#126—102no—
189#125—101no—
190#124C2×C3×D511yescharacteristic
191#123—52no—
192#123—102no—
193C22⋊Q8—102no—
194#104—101no—
195#100—51no—
196#99—102no—
197#99C2×C3×D512yes—
198C2×C3×C5—21no—
199C2×C3×C5—42no—
200C2×C3×C5B(4,𝔽2)11yescharacteristic
201C3×D5—81no—
202C23×C3—102no—
203C23×C3D4×D512yes—
204C3×Q8—41no—
205C3×Q8—101no—
206C3×Q8—401no—
207C3×D4—41no—
208C3×D4—101no—
209C3×D4—202no—
210C3×D4—201no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—42no—
214C2×C3×C4—102no—
215C2×C3×C4—102no—
216C2×C3×C4—102no—
217C2×C3×C4—201no—
218C2×C3×C4—202no—
219C2×C3×C4C2×D2011yescharacteristic
220C3×C8—201no—
221C22×C5—22no—
222C22×C5—42no—
223C22×C5C3×#12011yescharacteristic
224C2×D5—41no—
225C2×D5—82no—
226C4×C5—21no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—82no—
230Dic5—42no—
231Dic5—41no—
232Dic5—42no—
233#41—101no—
234#41—201no—
235C2×Q8—101no—
236C2×Q8C3×D2011yescharacteristic
237C2×D4—102no—
238C2×D4—201no—
239C2×D4C22×C3×D511yescharacteristic
240C22×C4—52no—
241Q16—201no—
242SD16—201no—
243M16—101no—
244C4⋊C4—101no—
245C4⋊C4—102no—
246C4⋊C4—102no—
247C4⋊C4—101no—
248C4⋊C4—102no—
249C4⋊C4—202no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—52no—
253C22⋊C4—102no—
254C22⋊C4—202no—
255C42—101no—
256C42C3×D2011yescharacteristic
257C3×C5#220111yescharacteristic, complemented, Hall
258C22×C3—22no—
259C22×C3—42no—
260C22×C3—201no—
261C22×C3—402no—
262C22×C3#402811yescharacteristic
263C3×C4—21no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—82no—
267C3×C4—202no—
268C3×C4—201no—
269C3×C4—202no—
270C2×C5—21no—
271C2×C5—42no—
272C2×C5C3×B(4,𝔽2)11yescharacteristic
273D5—81no—
274C23—102no—
275C23C3×D4×D512yes—
276Q8—41no—
277Q8—101no—
278Q8—401no—
279D4—41no—
280D4—101no—
281D4—202no—
282D4—201no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—102no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—201no—
290C2×C4—202no—
291C2×C4C2×C3×D2011yescharacteristic
292C8—201no—
293C2×C3—21no—
294C2×C3—42no—
295C2×C3—401no—
296C2×C3#6503011yescharacteristic
297C5C3×#220111yescharacteristic, complemented, Sylow
298C22—22no—
299C22—42no—
300C22—201no—
301C22—402no—
302C22C3×#402811yescharacteristic
303C4—21no—
304C4—41no—
305C4—41no—
306C4—82no—
307C4—202no—
308C4—201no—
309C4—202no—
310C3#1059994811yescharacteristic, direct product factor, Sylow
311C2—21no—
312C2—42no—
313C2—401no—
314C2C3×#6503011yescharacteristic
subgroupG/H
centerC2×C3#65030
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#354C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×#4144C22
hypercenterC3×#354D5
hypocenterC5C3×#2201
LCSG ▷ C2×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#354

Complements

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

NH ≅ G/Ntype
1. C3×#66006C2semidirect
4. C3×C5×#354C2semidirect
5. C3×#64692C2semidirect
6. #10599948C3direct (N × H)
21. #66006C2×C3semidirect
24. C5×#354C2×C3semidirect
25. #64692C2×C3semidirect
53. C3×#354D5semidirect
128. #354C3×D5semidirect
257. C3×C5#2201semidirect
297. C5C3×#2201semidirect
310. C3#10599948direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660062
C3×#653502
C3×#650312
C3×C5×#3542
C3×#646922
#105999483
C3×#22015