Finite Group Databasebeta

← C3×#10599955 #14316942

Subgroups — C3×#10599955 #14316942

Order 1920.

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

normal subgroups only

This group has 432 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×#65351C211yesmaximal, characteristic
3C3×#65041C212yesmaximal, complemented
4C3×C5×#355C211yesmaximal, characteristic, complemented
5C3×#64698C212yesmaximal, complemented
6#10599955C311yesmaximal, characteristic, direct product factor, Hall
7C3×#4147C2211yescharacteristic
8C3×C5×#124C2211yescharacteristic
9C3×#4090C2212yes—
10C3×#4081—21no—
11C3×#4078—21no—
12C3×#4055—22no—
13C3×#4025—22no—
14C3×#4024—22no—
15C3×#4016—21no—
16C3×C5×#101C2212yes—
17C3×#3968C2211yescharacteristic
18C3×#3957—22no—
19C3×#3937—21no—
20C3×#2203—51nomaximal, Hall
21#66006C2×C311yescharacteristic, complemented
22#65351C2×C311yescharacteristic
23#65041C2×C312yescomplemented
24C5×#355C2×C311yescharacteristic, complemented
25#64698C2×C312yescomplemented
26C2×C3×C5×Q8C2311yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C22×C3×Dic5—21no—
29C3×#713—41no—
30C3×Q8×D5—41no—
31C3×#709—21no—
32C3×#709—22no—
33C2×C3×Dic10D412yes—
34C3×C5×M16—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5D411yescharacteristic
37C3×C22⋊Dic5—22no—
38C3×C22⋊Dic5—21no—
39C3×#687—41no—
40C3×#686—41no—
41C3×C4⋊Dic5—21no—
42C3×C4⋊Dic5—21no—
43C3×#683—22no—
44C3×#683—22no—
45C3×#683—22no—
46C3×C4×Dic5D412yes—
47C3×#681—21no—
48C3×Dic20—42no—
49C3×#677—42no—
50C3×#563—51no—
51C3×#456—52no—
52C3×#454—51no—
53C3×#356—52no—
54C3×#355D511yescharacteristic, complemented
55#4147C22×C311yescharacteristic
56C5×#124C22×C311yescharacteristic
57#4090C22×C312yes—
58#4081—21no—
59#4078—21no—
60#4055—22no—
61#4025—22no—
62#4024—22no—
63#4016—21no—
64C5×#101C22×C312yes—
65#3968C22×C311yescharacteristic
66#3957—22no—
67#3937—21no—
68#2203—51noSylow
69C23×C3×C5—21no—
70C3×C5×Q8—41no—
71C3×C5×D4—41no—
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—
78C2×C3×Dic5—81no—
79C3×D20—22no—
80C3×D20—21no—
81C3×C4×D5—41no—
82C3×C4×D5—42no—
83C3×Dic10—22no—
84C3×Dic10—21no—
85C3×Dic10—42no—
86C3×C5×C8—42no—
87C3×#168—41no—
88C3×2−1+4—51no—
89C3×#137—102no—
90C3×AGL(1,ℤ/8)—101no—
91C3×C4⋊Q8—52no—
92C3×#126—102no—
93C3×#125—101no—
94C3×#124C2×D511yescharacteristic
95C3×#123—101no—
96C3×C22⋊Q8—102no—
97C3×#104—102no—
98C3×#104—101no—
99C3×#101—51no—
100C3×#101C2×D512yes—
101C2×C5×Q8C23×C311yescharacteristic
102C2×C5×D4C3×D411yescharacteristic
103C22×Dic5—21no—
104#713—41no—
105Q8×D5—41no—
106#709—21no—
107#709—22no—
108C2×Dic10C3×D412yes—
109C5×M16—22no—
110C5×C22⋊C4—22no—
111C42×C5C3×D411yescharacteristic
112C22⋊Dic5—22no—
113C22⋊Dic5—21no—
114#687—41no—
115#686—41no—
116C4⋊Dic5—21no—
117C4⋊Dic5—21no—
118#683—22no—
119#683—22no—
120#683—22no—
121C4×Dic5C3×D412yes—
122#681—21no—
123Dic20—42no—
124#677—42no—
125#563—51no—
126#456—52no—
127#454—51no—
128#356—52no—
129#355C3×D511yescharacteristic, complemented
130C22×C3×C5—42no—
131C22×C3×C5—41no—
132C22×C3×C5#12011yescharacteristic
133C2×C3×D5—41no—
134C3×C4×C5—21no—
135C3×C4×C5—22no—
136C3×C4×C5—41no—
137C3×Dic5—42no—
138C3×Dic5—41no—
139C3×Dic5—42no—
140C3×#41—101no—
141C3×#41—102no—
142C3×#41—201no—
143C2×C3×Q8—52no—
144C2×C3×Q8—201no—
145C2×C3×Q8C22×D511yescharacteristic
146C2×C3×D4D2011yescharacteristic
147C22×C3×C4—101no—
148C3×Q16—202no—
149C3×SD16—202no—
150C3×SD16—201no—
151C3×D8—201no—
152C3×M16—22no—
153C3×M16—101no—
154C3×C4⋊C4—102no—
155C3×C4⋊C4—101no—
156C3×C4⋊C4—101no—
157C3×C4⋊C4—102no—
158C3×C4⋊C4—102no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—102no—
161C3×C22⋊C4—101no—
162C3×C42—52no—
163C3×C42D2011yescharacteristic
164C23×C5—21no—
165C5×Q8—41no—
166C5×D4—41no—
167C2×C4×C5—21no—
168C2×C4×C5C2×C3×D411yescharacteristic
169C2×C4×C5C2×C3×D412yes—
170C22⋊D5—41no—
171C2×Dic5—22no—
172C2×Dic5—22no—
173C2×Dic5—81no—
174D20—22no—
175D20—21no—
176C4×D5—41no—
177C4×D5—42no—
178Dic10—22no—
179Dic10—21no—
180Dic10—42no—
181C5×C8—42no—
182#168—41no—
1832−1+4—51no—
184#137—102no—
185AGL(1,ℤ/8)—101no—
186C4⋊Q8—52no—
187#126—102no—
188#125—101no—
189#124C2×C3×D511yescharacteristic
190#123—101no—
191C22⋊Q8—102no—
192#104—102no—
193#104—101no—
194#101—51no—
195#101C2×C3×D512yes—
196C2×C3×C5—21no—
197C2×C3×C5—81no—
198C2×C3×C5B(4,𝔽2)11yescharacteristic
199C3×D5—81no—
200C23×C3—21no—
201C3×Q8—41no—
202C3×Q8—101no—
203C3×Q8—102no—
204C3×Q8—202no—
205C3×D4—41no—
206C3×D4—101no—
207C3×D4—102no—
208C3×D4—201no—
209C2×C3×C4—21no—
210C2×C3×C4—102no—
211C2×C3×C4—102no—
212C2×C3×C4—202no—
213C2×C3×C4—201no—
214C2×C3×C4—401no—
215C2×C3×C4C2×D2011yescharacteristic
216C2×C3×C4D4×D512yes—
217C3×C8—42no—
218C3×C8—201no—
219C22×C5—42no—
220C22×C5—41no—
221C22×C5C3×#12011yescharacteristic
222C2×D5—41no—
223C4×C5—21no—
224C4×C5—22no—
225C4×C5—41no—
226Dic5—42no—
227Dic5—41no—
228Dic5—42no—
229#41—101no—
230#41—102no—
231#41—201no—
232C2×Q8—52no—
233C2×Q8—201no—
234C2×Q8C22×C3×D511yescharacteristic
235C2×D4C3×D2011yescharacteristic
236C22×C4—101no—
237Q16—202no—
238SD16—202no—
239SD16—201no—
240D8—201no—
241M16—22no—
242M16—101no—
243C4⋊C4—101no—
244C4⋊C4—102no—
245C4⋊C4—101no—
246C4⋊C4—102no—
247C4⋊C4—102no—
248C22⋊C4—22no—
249C22⋊C4—102no—
250C22⋊C4—101no—
251C42—52no—
252C42C3×D2011yescharacteristic
253C3×C5#220311yescharacteristic, complemented, Hall
254C22×C3—42no—
255C22×C3—41no—
256C22×C3—201no—
257C22×C3#402811yescharacteristic
258C3×C4—22no—
259C3×C4—21no—
260C3×C4—41no—
261C3×C4—202no—
262C3×C4—202no—
263C3×C4—201no—
264C2×C5—21no—
265C2×C5—81no—
266C2×C5C3×B(4,𝔽2)11yescharacteristic
267D5—81no—
268C23—21no—
269Q8—41no—
270Q8—101no—
271Q8—102no—
272Q8—202no—
273D4—41no—
274D4—101no—
275D4—102no—
276D4—201no—
277C2×C4—21no—
278C2×C4—102no—
279C2×C4—102no—
280C2×C4—202no—
281C2×C4—201no—
282C2×C4—401no—
283C2×C4C2×C3×D2011yescharacteristic
284C2×C4C3×D4×D512yes—
285C8—42no—
286C8—201no—
287C2×C3—21no—
288C2×C3—81no—
289C2×C3—401no—
290C2×C3#6503011yescharacteristic
291C5C3×#220311yescharacteristic, complemented, Sylow
292C22—42no—
293C22—41no—
294C22—201no—
295C22C3×#402811yescharacteristic
296C4—22no—
297C4—21no—
298C4—41no—
299C4—202no—
300C4—202no—
301C4—201no—
302C3#1059995511yescharacteristic, direct product factor, Sylow
303C2—21no—
304C2—81no—
305C2—401no—
306C2C3×#6503011yescharacteristic
subgroupG/H
centerC2×C3#65030
commutator, cosocleC2×C5×Q8C23×C3
FrattiniC2×Q8C22×C3×D5
FittingC3×C5×#355C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×#65351C2
hypercenterC3×#355D5
hypocenterC5C3×#2203
LCSG ▷ C2×C5×Q8 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×Q8 ◁ C3×#355

Complements

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

NH ≅ G/Ntype
1. C3×#66006C2semidirect
3. C3×#65041C2semidirect
4. C3×C5×#355C2semidirect
5. C3×#64698C2semidirect
6. #10599955C3direct (N × H)
21. #66006C2×C3semidirect
23. #65041C2×C3semidirect
24. C5×#355C2×C3semidirect
25. #64698C2×C3semidirect
54. C3×#355D5semidirect
129. #355C3×D5semidirect
253. C3×C5#2203semidirect
291. C5C3×#2203semidirect
302. C3#10599955direct (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×#653512
C3×#650412
C3×C5×#3552
C3×#646982
#105999553
C3×#22035