Finite Group Databasebeta

← C3×#10599142 #14284451

Subgroups — C3×#10599142 #14284451

Order 1920.

476 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 118 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×#66002C211yesmaximal, characteristic
2C3×#64994C212yesmaximal, complemented
3C3×C5×#329C211yesmaximal, characteristic, complemented
4C3×#64760C211yesmaximal, characteristic, complemented
5C3×#64684C212yesmaximal, complemented
6#10599142C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#713C411yescharacteristic
8C2×C3×#711C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×#4090C411yescharacteristic
11C3×#4086C411yescharacteristic
12C3×#4030—22no—
13C3×#4027—22no—
14C3×#4021C2211yescharacteristic
15C3×C42×D5C2211yescharacteristic
16C3×C5×#97C2212yes—
17C3×#3952—22no—
18C3×#3946—22no—
19C3×#3935C2212yes—
20C3×#1536—51nomaximal, Hall
21#66002C2×C311yescharacteristic
22#64994C2×C312yescomplemented
23C5×#329C2×C311yescharacteristic, complemented
24#64760C2×C311yescharacteristic, complemented
25#64684C2×C312yescomplemented
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×C3×C22⋊D5—21no—
29C2×C3×C22⋊D5—22no—
30C22×C3×Dic5—21no—
31C3×#713—42no—
32C3×#711—42no—
33C2×C3×D20—21no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D412yes—
38C2×C3×Dic10C2×C411yescharacteristic
39C2×C3×C5×C8—22no—
40C3×C5×C22⋊C4—22no—
41C3×C42×C5C2311yescharacteristic
42C3×#685—22no—
43C3×#683—22no—
44C3×C4×Dic5C2×C411yescharacteristic
45C3×C4×Dic5D412yes—
46C2×C3×#168—22no—
47C3×#532—51no—
48C3×#432—52no—
49C3×#329—51no—
50C3×#329—52no—
51C3×#329D511yescharacteristic, complemented
52C2×#713C3×C411yescharacteristic
53C2×#711C3×C411yescharacteristic
54C5×#124C22×C311yescharacteristic
55#4090C3×C411yescharacteristic
56#4086C3×C411yescharacteristic
57#4030—22no—
58#4027—22no—
59#4021C22×C311yescharacteristic
60C42×D5C22×C311yescharacteristic
61C5×#97C22×C312yes—
62#3952—22no—
63#3946—22no—
64#3935C22×C312yes—
65#1536—51noSylow
66C23×C3×C5—21no—
67C22×C3×D5—21no—
68C22×C3×D5C22⋊C411yescharacteristic
69C3×C5×Q8—41no—
70C3×C5×D4—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×C3×C4×C5C2×D412yes—
74C3×C22⋊D5—44no—
75C3×C22⋊D5—42no—
76C2×C3×Dic5—21no—
77C2×C3×Dic5—42no—
78C2×C3×Dic5C22⋊C412yes—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C3×D20—41no—
81C3×D20—42no—
82C3×C4×D5—22no—
83C3×C4×D5—42no—
84C3×C4×D5—42no—
85C3×Dic10—41no—
86C3×C5×C8—42no—
87C3×#168—42no—
88C2×C3×#41—51no—
89C2×C3×#41—51no—
90C3×C4⋊Q8—51no—
91C3×#127—51no—
92C3×#124—51no—
93C3×#124C2×D511yescharacteristic
94C3×#121—102no—
95C3×C4×D4—102no—
96C2×C3×C42—51no—
97C3×C4⋊C8—102no—
98C3×C22⋊C8—102no—
99C3×#97—52no—
100C3×#97C2×D512yes—
101C2×C5×Q8C2×C3×C411yescharacteristic
102C2×C5×D4C2×C3×C411yescharacteristic
103C2×C22⋊D5—21no—
104C2×C22⋊D5—22no—
105C22×Dic5—21no—
106#713—42no—
107#711—42no—
108C2×D20—21no—
109C2×D20C2×C3×C411yescharacteristic
110C2×C4×D5—21no—
111C2×C4×D5C2×C3×C411yescharacteristic
112C2×C4×D5C3×D412yes—
113C2×Dic10C2×C3×C411yescharacteristic
114C2×C5×C8—22no—
115C5×C22⋊C4—22no—
116C42×C5C23×C311yescharacteristic
117#685—22no—
118#683—22no—
119C4×Dic5C2×C3×C411yescharacteristic
120C4×Dic5C3×D412yes—
121C2×#168—22no—
122#532—51no—
123#432—52no—
124#329—51no—
125#329—52no—
126#329C3×D511yescharacteristic, complemented
127C22×C3×C5—41no—
128C22×C3×C5—42no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C2×C3×D5—21no—
131C2×C3×D5—22no—
132C2×C3×D5—41no—
133C2×C3×D5—42no—
134C3×C4×C5—21no—
135C3×C4×C5—22no—
136C3×C4×C5—41no—
137C3×Dic5—22no—
138C3×Dic5—41no—
139C3×Dic5#10012yes—
140C3×#41—202no—
141C3×#41—202no—
142C2×C3×Q8—51no—
143C2×C3×Q8C4×D511yescharacteristic
144C2×C3×D4—51no—
145C2×C3×D4—101no—
146C2×C3×D4—102no—
147C2×C3×D4—101no—
148C2×C3×D4C4×D511yescharacteristic
149C22×C3×C4—51no—
150C22×C3×C4—52no—
151C22×C3×C4—101no—
152C22×C3×C4—101no—
153C2×C3×C8—22no—
154C2×C3×C8—102no—
155C3×C4⋊C4—102no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—102no—
158C3×C42—51no—
159C3×C42—52no—
160C3×C42C22×D511yescharacteristic
161C23×C5—21no—
162C22×D5—21no—
163C22×D5C3×C22⋊C411yescharacteristic
164C5×Q8—41no—
165C5×D4—41no—
166C2×C4×C5—21no—
167C2×C4×C5C22×C3×C411yescharacteristic
168C2×C4×C5C2×C3×D412yes—
169C22⋊D5—44no—
170C22⋊D5—42no—
171C2×Dic5—21no—
172C2×Dic5—42no—
173C2×Dic5C3×C22⋊C412yes—
174C2×Dic5C3×C22⋊C411yescharacteristic
175D20—41no—
176D20—42no—
177C4×D5—22no—
178C4×D5—42no—
179C4×D5—42no—
180Dic10—41no—
181C5×C8—42no—
182#168—42no—
183C2×#41—51no—
184C2×#41—51no—
185C4⋊Q8—51no—
186#127—51no—
187#124—51no—
188#124C2×C3×D511yescharacteristic
189#121—102no—
190C4×D4—102no—
191C2×C42—51no—
192C4⋊C8—102no—
193C22⋊C8—102no—
194#97—52no—
195#97C2×C3×D512yes—
196C2×C3×C5—81no—
197C2×C3×C5C2×#10011yescharacteristic
198C2×C3×C5#42112yes—
199C3×D5—41no—
200C3×D5—81no—
201C23×C3—21no—
202C23×C3—51no—
203C23×C3—101no—
204C3×Q8—41no—
205C3×Q8—201no—
206C3×D4—41no—
207C3×D4—201no—
208C3×D4—202no—
209C3×D4—204no—
210C3×D4—202no—
211C2×C3×C4—21no—
212C2×C3×C4—51no—
213C2×C3×C4—52no—
214C2×C3×C4—102no—
215C2×C3×C4—101no—
216C2×C3×C4—202no—
217C2×C3×C4—202no—
218C2×C3×C4—202no—
219C2×C3×C4C2×C4×D511yescharacteristic
220C2×C3×C4D4×D512yes—
221C3×C8—42no—
222C3×C8—202no—
223C22×C5—41no—
224C22×C5—42no—
225C22×C5C2×C3×C22⋊C411yescharacteristic
226C2×D5—21no—
227C2×D5—22no—
228C2×D5—41no—
229C2×D5—42no—
230C4×C5—21no—
231C4×C5—22no—
232C4×C5—41no—
233Dic5—22no—
234Dic5—41no—
235Dic5C3×#10012yes—
236#41—202no—
237#41—202no—
238C2×Q8—51no—
239C2×Q8C3×C4×D511yescharacteristic
240C2×D4—51no—
241C2×D4—101no—
242C2×D4—102no—
243C2×D4—101no—
244C2×D4C3×C4×D511yescharacteristic
245C22×C4—51no—
246C22×C4—52no—
247C22×C4—101no—
248C22×C4—101no—
249C2×C8—22no—
250C2×C8—102no—
251C4⋊C4—102no—
252C22⋊C4—22no—
253C22⋊C4—102no—
254C42—51no—
255C42—52no—
256C42C22×C3×D511yescharacteristic
257C3×C5#153611yescharacteristic, complemented, Hall
258C22×C3—41no—
259C22×C3—42no—
260C22×C3—101no—
261C22×C3—102no—
262C22×C3—201no—
263C22×C3—202no—
264C22×C3D5×C22⋊C411yescharacteristic
265C3×C4—21no—
266C3×C4—22no—
267C3×C4—41no—
268C3×C4—52no—
269C3×C4—102no—
270C3×C4—201no—
271C2×C5—81no—
272C2×C5C2×C3×#10011yescharacteristic
273C2×C5C3×#42112yes—
274D5—41no—
275D5—81no—
276C23—21no—
277C23—51no—
278C23—101no—
279Q8—41no—
280Q8—201no—
281D4—41no—
282D4—201no—
283D4—202no—
284D4—204no—
285D4—202no—
286C2×C4—21no—
287C2×C4—51no—
288C2×C4—52no—
289C2×C4—102no—
290C2×C4—101no—
291C2×C4—202no—
292C2×C4—202no—
293C2×C4—202no—
294C2×C4C2×C3×C4×D511yescharacteristic
295C2×C4C3×D4×D512yes—
296C8—42no—
297C8—202no—
298C2×C3—81no—
299C2×C3—201no—
300C2×C3—401no—
301C2×C3D5×#10011yescharacteristic
302C2×C3#6511012yes—
303C5C3×#153611yescharacteristic, complemented, Sylow
304C22—41no—
305C22—42no—
306C22—101no—
307C22—102no—
308C22—201no—
309C22—202no—
310C22C3×D5×C22⋊C411yescharacteristic
311C4—21no—
312C4—22no—
313C4—41no—
314C4—52no—
315C4—102no—
316C4—201no—
317C3#1059914211yescharacteristic, direct product factor, Sylow
318C2—81no—
319C2—201no—
320C2—401no—
321C2C3×D5×#10011yescharacteristic
322C2C3×#6511012yes—
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#329C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66002C2
cosocleC42×C5C23×C3
hypercenterC3×#329D5
hypocenterC5C3×#1536
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#329

Complements

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

NH ≅ G/Ntype
2. C3×#64994C2semidirect
3. C3×C5×#329C2semidirect
4. C3×#64760C2semidirect
5. C3×#64684C2semidirect
6. #10599142C3direct (N × H)
22. #64994C2×C3semidirect
23. C5×#329C2×C3semidirect
24. #64760C2×C3semidirect
25. #64684C2×C3semidirect
51. C3×#329D5semidirect
126. #329C3×D5semidirect
257. C3×C5#1536semidirect
303. C5C3×#1536semidirect
317. C3#10599142direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660022
C3×#649942
C3×C5×#3292
C3×#647602
C3×#646842
#105991423
C3×#15365