Finite Group Databasebeta

← C3×#10599914 #14316350

Subgroups — C3×#10599914 #14316350

Order 1920.

432 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 98 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×#66082C211yesmaximal, characteristic
2C3×#65426C211yesmaximal, characteristic, complemented
3C3×#65198C212yesmaximal, complemented
4C3×C5×#349C211yesmaximal, characteristic, complemented
5C3×#64738C212yesmaximal, complemented
6#10599914C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#709—21no—
8C2×C3×C5×M16C2211yescharacteristic
9C3×#4070—21no—
10C3×#4055—22no—
11C3×#4054—22no—
12C2×C3×Dic20C2211yescharacteristic, complemented
13C3×#4050—21no—
14C3×#4050C2212yes—
15C3×C5×M32C2212yescomplemented
16C3×#3949C2211yescharacteristic, complemented
17C3×#3948—21no—
18C3×Dic40—22no—
19C3×#3932—22no—
20C3×#2191—51nomaximal, Hall
21#66082C2×C311yescharacteristic
22#65426C2×C311yescharacteristic, complemented
23#65198C2×C312yescomplemented
24C5×#349C2×C311yescharacteristic, complemented
25#64738C2×C312yescomplemented
26C22×C3×C4×C5D411yescharacteristic
27C2×C3×C22⋊D5—41no—
28C3×#709—22no—
29C3×#709—22no—
30C3×#709—41no—
31C3×#709—41no—
32C2×C3×D20—21no—
33C2×C3×C4×D5—41no—
34C2×C3×Dic10—21no—
35C2×C3×Dic10—21no—
36C3×C5×M16—22no—
37C2×C3×C5×C8D411yescharacteristic
38C2×C3×C5×C8C2311yescharacteristic
39C3×C22⋊Dic5—41no—
40C3×C4⋊Dic5—21no—
41C3×#683—41no—
42C3×Dic20—21no—
43C3×Dic20—22no—
44C3×Dic20D412yes—
45C3×D40—21no—
46C3×D40D412yes—
47C3×#677—22no—
48C3×#677—22no—
49C3×C5×C16—22no—
50C3×#575—51no—
51C3×#510—52no—
52C3×#470—51no—
53C3×#360—52no—
54C3×#349D511yescharacteristic, complemented
55C2×#709—21no—
56C2×C5×M16C22×C311yescharacteristic
57#4070—21no—
58#4055—22no—
59#4054—22no—
60C2×Dic20C22×C311yescharacteristic, complemented
61#4050—21no—
62#4050C22×C312yes—
63C5×M32C22×C312yescomplemented
64#3949C22×C311yescharacteristic, complemented
65#3948—21no—
66Dic40—22no—
67#3932—22no—
68#2191—51noSylow
69C23×C3×C5D811yescharacteristic
70C22×C3×D5—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5D811yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C3×C22⋊D5—42no—
76C3×C22⋊D5—42no—
77C2×C3×Dic5—41no—
78C2×C3×Dic5—41no—
79C2×C3×Dic5—41no—
80C3×D20—22no—
81C3×D20—41no—
82C3×C4×D5—42no—
83C3×C4×D5—42no—
84C3×Dic10—22no—
85C3×Dic10—41no—
86C3×Dic10—41no—
87C3×Dic10—41no—
88C3×C5×C8—21no—
89C3×C5×C8C2×D412yes—
90C2×C3×#41—101no—
91C3×#137—102no—
92C3×AGL(1,ℤ/8)—102no—
93C3×#135—52no—
94C3×#135—101no—
95C2×C3×Q16—51no—
96C2×C3×M16C2×D511yescharacteristic
97C3×C22⋊Q8—101no—
98C3×Q32—102no—
99C3×SD32—102no—
100C3×M32C2×D512yescomplemented
101C3×#106—51no—
102C3×#103—101no—
103C22×C4×C5C3×D411yescharacteristic
104C2×C22⋊D5—41no—
105#709—22no—
106#709—22no—
107#709—41no—
108#709—41no—
109C2×D20—21no—
110C2×C4×D5—41no—
111C2×Dic10—21no—
112C2×Dic10—21no—
113C5×M16—22no—
114C2×C5×C8C3×D411yescharacteristic
115C2×C5×C8C23×C311yescharacteristic
116C22⋊Dic5—41no—
117C4⋊Dic5—21no—
118#683—41no—
119Dic20—21no—
120Dic20—22no—
121Dic20C3×D412yes—
122D40—21no—
123D40C3×D412yes—
124#677—22no—
125#677—22no—
126C5×C16—22no—
127#575—51no—
128#510—52no—
129#470—51no—
130#360—52no—
131#349C3×D511yescharacteristic, complemented
132C22×C3×C5—21no—
133C22×C3×C5—41no—
134C22×C3×C5C2×D811yescharacteristic
135C2×C3×D5—42no—
136C2×C3×D5—82no—
137C3×C4×C5—21no—
138C3×C4×C5#12011yescharacteristic
139C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
140C3×Dic5—42no—
141C3×Dic5—81no—
142C3×Dic5—81no—
143C3×#41—102no—
144C3×#41—102no—
145C3×#41—201no—
146C3×#41—201no—
147C2×C3×Q8—101no—
148C2×C3×Q8—101no—
149C2×C3×D4—101no—
150C2×C3×D4—201no—
151C22×C3×C4—201no—
152C22×C3×C4D2011yescharacteristic
153C3×Q16—52no—
154C3×Q16—101no—
155C3×Q16—102no—
156C3×SD16—102no—
157C3×SD16—102no—
158C3×D8—52no—
159C3×D8—101no—
160C3×M16—22no—
161C2×C3×C8D2011yescharacteristic
162C2×C3×C8C22×D511yescharacteristic
163C3×C4⋊C4—101no—
164C3×C4⋊C4—201no—
165C3×C22⋊C4—201no—
166C3×C16—22no—
167C23×C5C3×D811yescharacteristic
168C22×D5—41no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5C3×D811yescharacteristic
172C2×C4×C5C2×C3×D411yescharacteristic
173C22⋊D5—42no—
174C22⋊D5—42no—
175C2×Dic5—41no—
176C2×Dic5—41no—
177C2×Dic5—41no—
178D20—22no—
179D20—41no—
180C4×D5—42no—
181C4×D5—42no—
182Dic10—22no—
183Dic10—41no—
184Dic10—41no—
185Dic10—41no—
186C5×C8—21no—
187C5×C8C2×C3×D412yes—
188C2×#41—101no—
189#137—102no—
190AGL(1,ℤ/8)—102no—
191#135—52no—
192#135—101no—
193C2×Q16—51no—
194C2×M16C2×C3×D511yescharacteristic
195C22⋊Q8—101no—
196Q32—102no—
197SD32—102no—
198M32C2×C3×D512yescomplemented
199#106—51no—
200#103—101no—
201C2×C3×C5—21no—
202C2×C3×C5—41no—
203C2×C3×C5#44711yescharacteristic
204C3×D5—82no—
205C23×C3—201no—
206C23×C3D4011yescharacteristic
207C3×Q8—102no—
208C3×Q8—201no—
209C3×Q8—201no—
210C3×Q8—201no—
211C3×D4—102no—
212C3×D4—201no—
213C3×D4—202no—
214C3×D4—202no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—202no—
218C2×C3×C4—201no—
219C2×C3×C4—202no—
220C2×C3×C4—201no—
221C2×C3×C4—201no—
222C2×C3×C4D4011yescharacteristic
223C2×C3×C4C2×D2011yescharacteristic
224C3×C8—21no—
225C3×C8D4×D512yes—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5C2×C3×D811yescharacteristic
229C2×D5—42no—
230C2×D5—82no—
231C4×C5—21no—
232C4×C5C3×#12011yescharacteristic
233C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
234Dic5—42no—
235Dic5—81no—
236Dic5—81no—
237#41—102no—
238#41—102no—
239#41—201no—
240#41—201no—
241C2×Q8—101no—
242C2×Q8—101no—
243C2×D4—101no—
244C2×D4—201no—
245C22×C4—201no—
246C22×C4C3×D2011yescharacteristic
247Q16—52no—
248Q16—101no—
249Q16—102no—
250SD16—102no—
251SD16—102no—
252D8—52no—
253D8—101no—
254M16—22no—
255C2×C8C3×D2011yescharacteristic
256C2×C8C22×C3×D511yescharacteristic
257C4⋊C4—101no—
258C4⋊C4—201no—
259C22⋊C4—201no—
260C16—22no—
261C3×C5#219111yescharacteristic, complemented, Hall
262C22×C3—21no—
263C22×C3—41no—
264C22×C3—202no—
265C22×C3—402no—
266C22×C3C2×D4011yescharacteristic
267C3×C4—21no—
268C3×C4—202no—
269C3×C4—401no—
270C3×C4—401no—
271C3×C4#402811yescharacteristic
272C3×C4#405411yescharacteristic
273C2×C5—21no—
274C2×C5—41no—
275C2×C5C3×#44711yescharacteristic
276D5—82no—
277C23—201no—
278C23C3×D4011yescharacteristic
279Q8—102no—
280Q8—201no—
281Q8—201no—
282Q8—201no—
283D4—102no—
284D4—201no—
285D4—202no—
286D4—202no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—202no—
290C2×C4—201no—
291C2×C4—202no—
292C2×C4—201no—
293C2×C4—201no—
294C2×C4C3×D4011yescharacteristic
295C2×C4C2×C3×D2011yescharacteristic
296C8—21no—
297C8C3×D4×D512yes—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3—402no—
301C2×C3#6502111yescharacteristic
302C5C3×#219111yescharacteristic, complemented, Sylow
303C22—21no—
304C22—41no—
305C22—202no—
306C22—402no—
307C22C2×C3×D4011yescharacteristic
308C4—21no—
309C4—202no—
310C4—401no—
311C4—401no—
312C4C3×#402811yescharacteristic
313C4C3×#405411yescharacteristic
314C3#1059991411yescharacteristic, direct product factor, Sylow
315C2—21no—
316C2—41no—
317C2—402no—
318C2C3×#6502111yescharacteristic
subgroupG/H
centerC2×C3#65021
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#349C2
socleC2×C3×C5#447
prime radicalC3×#66082C2
hypercenterC3×#349D5
hypocenterC5C3×#2191
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×M16 ◁ C3×#349

Complements

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

NH ≅ G/Ntype
2. C3×#65426C2semidirect
3. C3×#65198C2semidirect
4. C3×C5×#349C2semidirect
5. C3×#64738C2semidirect
6. #10599914C3direct (N × H)
12. C2×C3×Dic20C22semidirect
15. C3×C5×M32C22semidirect
16. C3×#3949C22semidirect
22. #65426C2×C3semidirect
23. #65198C2×C3semidirect
24. C5×#349C2×C3semidirect
25. #64738C2×C3semidirect
54. C3×#349D5semidirect
60. C2×Dic20C22×C3semidirect
63. C5×M32C22×C3semidirect
64. #3949C22×C3semidirect
100. C3×M32C2×D5semidirect
131. #349C3×D5semidirect
198. M32C2×C3×D5semidirect
261. C3×C5#2191semidirect
302. C5C3×#2191semidirect
314. C3#10599914direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660822
C3×#654262
C3×#651982
C3×C5×#3492
C3×#647382
#105999143
C3×#21915