Finite Group Databasebeta

← C3×#10599962 #14317014

Subgroups — C3×#10599962 #14317014

Order 1920.

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

normal subgroups only

This group has 448 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×#66056C211yesmaximal, characteristic, complemented
2C3×#65384C211yesmaximal, characteristic
3C3×#65041C212yesmaximal
4C3×C5×#356C211yesmaximal, characteristic, complemented
5C3×#64698C212yesmaximal, complemented
6#10599962C311yesmaximal, characteristic, direct product factor, Hall
7C3×#4147C2211yescharacteristic
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×#4090—21no—
10C3×#4090C2212yes—
11C3×#4088—21no—
12C3×#4055—22no—
13C3×#4034—22no—
14C3×#4033—22no—
15C3×C4×Dic10—21no—
16C3×C5×#101C2212yes—
17C3×#3968C2211yescharacteristic
18C3×#3957—22no—
19C3×#3937—21no—
20C3×#2205—51nomaximal, Hall
21#66056C2×C311yescharacteristic, complemented
22#65384C2×C311yescharacteristic
23#65041C2×C312yes—
24C5×#356C2×C311yescharacteristic, complemented
25#64698C2×C312yescomplemented
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×Q8C2311yescharacteristic
28C3×#713—41no—
29C3×Q8×D5—41no—
30C3×#709—21no—
31C3×#709—22no—
32C2×C3×Dic10—21no—
33C2×C3×Dic10—21no—
34C2×C3×Dic10D412yes—
35C3×C5×M16—22no—
36C3×C5×C4⋊C4—22no—
37C3×C42×C5D411yescharacteristic
38C3×#689—41no—
39C3×#688—41no—
40C3×C4⋊Dic5—21no—
41C3×#683—22no—
42C3×#683—22no—
43C3×#683—22no—
44C3×C4×Dic5—21no—
45C3×C4×Dic5—22no—
46C3×C4×Dic5D412yes—
47C3×#681—21no—
48C3×Dic20—42no—
49C3×#677—42no—
50C3×Q82—51no—
51C3×#456—51no—
52C3×#456—52no—
53C3×#356—52no—
54C3×#356D511yescharacteristic, complemented
55#4147C22×C311yescharacteristic
56C5×C4⋊Q8C22×C311yescharacteristic
57#4090—21no—
58#4090C22×C312yes—
59#4088—21no—
60#4055—22no—
61#4034—22no—
62#4033—22no—
63C4×Dic10—21no—
64C5×#101C22×C312yes—
65#3968C22×C311yescharacteristic
66#3957—22no—
67#3937—21no—
68#2205—51noSylow
69C3×C5×Q8—41no—
70C3×C5×Q8—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C3×C22⋊D5—41no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5—22no—
78C3×D20—22no—
79C3×D20—21no—
80C3×C4×D5—41no—
81C3×C4×D5—42no—
82C3×Dic10—24no—
83C3×Dic10—22no—
84C3×Dic10—21no—
85C3×Dic10—42no—
86C3×Dic10—81no—
87C3×C5×C8—42no—
88C3×#168—41no—
89C3×2−1+4—51no—
90C3×#137—102no—
91C3×#137—101no—
92C3×C4⋊Q8—52no—
93C3×C4⋊Q8—102no—
94C3×C4⋊Q8—101no—
95C3×C4⋊Q8C2×D511yescharacteristic
96C3×C4×Q8—102no—
97C3×C4×Q8—101no—
98C3×#104—102no—
99C3×#104—101no—
100C3×#101—51no—
101C3×#101C2×D512yes—
102C2×C5×Q8C3×D411yescharacteristic
103C2×C5×Q8C23×C311yescharacteristic
104#713—41no—
105Q8×D5—41no—
106#709—21no—
107#709—22no—
108C2×Dic10—21no—
109C2×Dic10—21no—
110C2×Dic10C3×D412yes—
111C5×M16—22no—
112C5×C4⋊C4—22no—
113C42×C5C3×D411yescharacteristic
114#689—41no—
115#688—41no—
116C4⋊Dic5—21no—
117#683—22no—
118#683—22no—
119#683—22no—
120C4×Dic5—22no—
121C4×Dic5—21no—
122C4×Dic5C3×D412yes—
123#681—21no—
124Dic20—42no—
125#677—42no—
126Q82—51no—
127#456—51no—
128#456—52no—
129#356—52no—
130#356C3×D511yescharacteristic, complemented
131C22×C3×C5#12011yescharacteristic
132C2×C3×D5—41no—
133C3×C4×C5—22no—
134C3×C4×C5—21no—
135C3×C4×C5—22no—
136C3×C4×C5—41no—
137C3×Dic5—24no—
138C3×Dic5—41no—
139C3×Dic5—42no—
140C3×#41—101no—
141C3×#41—102no—
142C3×#41—201no—
143C2×C3×Q8—52no—
144C2×C3×Q8—101no—
145C2×C3×Q8—101no—
146C2×C3×Q8—201no—
147C2×C3×Q8D2011yescharacteristic
148C2×C3×Q8C22×D511yescharacteristic
149C3×Q16—202no—
150C3×Q16—201no—
151C3×SD16—202no—
152C3×SD16—201no—
153C3×M16—22no—
154C3×M16—101no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—102no—
157C3×C4⋊C4—101no—
158C3×C4⋊C4—102no—
159C3×C4⋊C4—102no—
160C3×C42—52no—
161C3×C42—102no—
162C3×C42—101no—
163C3×C42D2011yescharacteristic
164C5×Q8—41no—
165C5×Q8—41no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5C2×C3×D411yescharacteristic
169C2×C4×C5C2×C3×D412yes—
170C22⋊D5—41no—
171C2×Dic5—22no—
172C2×Dic5—22no—
173D20—22no—
174D20—21no—
175C4×D5—41no—
176C4×D5—42no—
177Dic10—24no—
178Dic10—22no—
179Dic10—21no—
180Dic10—42no—
181Dic10—81no—
182C5×C8—42no—
183#168—41no—
1842−1+4—51no—
185#137—102no—
186#137—101no—
187C4⋊Q8—52no—
188C4⋊Q8—102no—
189C4⋊Q8—101no—
190C4⋊Q8C2×C3×D511yescharacteristic
191C4×Q8—102no—
192C4×Q8—101no—
193#104—102no—
194#104—101no—
195#101—51no—
196#101C2×C3×D512yes—
197C2×C3×C5—21no—
198C2×C3×C5B(4,𝔽2)11yescharacteristic
199C3×D5—81no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—104no—
203C3×Q8—102no—
204C3×Q8—101no—
205C3×Q8—202no—
206C3×Q8—401no—
207C3×D4—102no—
208C3×D4—101no—
209C3×D4—201no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—102no—
213C2×C3×C4—102no—
214C2×C3×C4—202no—
215C2×C3×C4—201no—
216C2×C3×C4C2×D2011yescharacteristic
217C2×C3×C4D4×D512yes—
218C3×C8—42no—
219C3×C8—201no—
220C22×C5C3×#12011yescharacteristic
221C2×D5—41no—
222C4×C5—22no—
223C4×C5—21no—
224C4×C5—22no—
225C4×C5—41no—
226Dic5—24no—
227Dic5—41no—
228Dic5—42no—
229#41—101no—
230#41—102no—
231#41—201no—
232C2×Q8—52no—
233C2×Q8—101no—
234C2×Q8—101no—
235C2×Q8—201no—
236C2×Q8C3×D2011yescharacteristic
237C2×Q8C22×C3×D511yescharacteristic
238Q16—202no—
239Q16—201no—
240SD16—202no—
241SD16—201no—
242M16—22no—
243M16—101no—
244C4⋊C4—22no—
245C4⋊C4—102no—
246C4⋊C4—101no—
247C4⋊C4—102no—
248C4⋊C4—102no—
249C42—52no—
250C42—102no—
251C42—101no—
252C42C3×D2011yescharacteristic
253C3×C5#220511yescharacteristic, complemented, Hall
254C22×C3—201no—
255C22×C3#402811yescharacteristic
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—21no—
259C3×C4—41no—
260C3×C4—104no—
261C3×C4—202no—
262C3×C4—201no—
263C2×C5—21no—
264C2×C5C3×B(4,𝔽2)11yescharacteristic
265D5—81no—
266Q8—41no—
267Q8—41no—
268Q8—104no—
269Q8—102no—
270Q8—101no—
271Q8—202no—
272Q8—401no—
273D4—102no—
274D4—101no—
275D4—201no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—102no—
279C2×C4—102no—
280C2×C4—202no—
281C2×C4—201no—
282C2×C4C2×C3×D2011yescharacteristic
283C2×C4C3×D4×D512yes—
284C8—42no—
285C8—201no—
286C2×C3—21no—
287C2×C3—401no—
288C2×C3#6503011yescharacteristic
289C5C3×#220511yescharacteristic, complemented, Sylow
290C22—201no—
291C22C3×#402811yescharacteristic
292C4—22no—
293C4—22no—
294C4—21no—
295C4—41no—
296C4—104no—
297C4—202no—
298C4—201no—
299C3#1059996211yescharacteristic, direct product factor, Sylow
300C2—21no—
301C2—401no—
302C2C3×#6503011yescharacteristic
subgroupG/H
centerC2×C3#65030
commutator, cosocleC2×C5×Q8C23×C3
FrattiniC2×Q8C22×C3×D5
FittingC3×C5×#356C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×#4147C22
hypercenterC3×#356D5
hypocenterC5C3×#2205
LCSG ▷ C2×C5×Q8 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×Q8 ◁ C3×#356

Complements

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

NH ≅ G/Ntype
1. C3×#66056C2semidirect
4. C3×C5×#356C2semidirect
5. C3×#64698C2semidirect
6. #10599962C3direct (N × H)
21. #66056C2×C3semidirect
24. C5×#356C2×C3semidirect
25. #64698C2×C3semidirect
54. C3×#356D5semidirect
130. #356C3×D5semidirect
253. C3×C5#2205semidirect
289. C5C3×#2205semidirect
299. C3#10599962direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660562
C3×#653842
C3×#650412
C3×C5×#3562
C3×#646982
#105999623
C3×#22055