Finite Group Databasebeta

← C3×#10599140 #14284330

Subgroups — C3×#10599140 #14284330

Order 1920.

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

normal subgroups only

This group has 496 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×D5×#124C211yesmaximal, characteristic
2C3×#64994C212yesmaximal, complemented
3C3×C5×#329C211yesmaximal, characteristic, complemented
4C3×#64760C211yesmaximal, characteristic, complemented
5C3×#64684C212yesmaximal, complemented
6#10599140C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×Q8×D5C411yescharacteristic
8C2×C3×D4×D5C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×#4093C411yescharacteristic
11C3×#4082C411yescharacteristic
12C3×#4031—22no—
13C3×D5×C22⋊C4—22no—
14C3×#4021C2211yescharacteristic
15C3×C42×D5C2211yescharacteristic
16C3×C5×#97C2212yescomplemented
17C3×#3952—22no—
18C3×#3946—22no—
19C3×#3935C2212yescomplemented
20C3×#1533—51nomaximal, Hall
21D5×#124C2×C311yescharacteristic
22#64994C2×C312yescomplemented
23C5×#329C2×C311yescharacteristic, complemented
24#64760C2×C311yescharacteristic, complemented
25#64684C2×C312yescomplemented
26C23×C3×D5—21no—
27C2×C3×C5×Q8C2×C411yescharacteristic
28C2×C3×C5×D4C2×C411yescharacteristic
29C2×C3×C22⋊D5—21no—
30C3×Q8×D5—42no—
31C3×D4×D5—42no—
32C2×C3×D20C2×C411yescharacteristic
33C2×C3×C4×D5—21no—
34C2×C3×C4×D5C2×C411yescharacteristic
35C2×C3×C4×D5D412yes—
36C2×C3×Dic10—21no—
37C2×C3×Dic10C2×C411yescharacteristic
38C2×C3×C5×C8—22no—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5C2311yescharacteristic
41C3×C22⋊Dic5—22no—
42C3×#685—22no—
43C3×#685—22no—
44C3×C4×Dic5C2×C411yescharacteristic
45C3×C4×Dic5D412yes—
46C2×C3×#168—22no—
47C2×C3×#124—51no—
48C3×#432—52no—
49C3×#329—51no—
50C3×#329—52no—
51C3×#329D511yescharacteristic, complemented
52C2×Q8×D5C3×C411yescharacteristic
53C2×D4×D5C3×C411yescharacteristic
54C5×#124C22×C311yescharacteristic
55#4093C3×C411yescharacteristic
56#4082C3×C411yescharacteristic
57#4031—22no—
58D5×C22⋊C4—22no—
59#4021C22×C311yescharacteristic
60C42×D5C22×C311yescharacteristic
61C5×#97C22×C312yescomplemented
62#3952—22no—
63#3946—22no—
64#3935C22×C312yescomplemented
65#1533—51noSylow
66C23×C3×C5—21no—
67C22×C3×D5—21no—
68C22×C3×D5—44no—
69C22×C3×D5—42no—
70C22×C3×D5C22⋊C411yescharacteristic
71C3×C5×Q8—41no—
72C3×C5×D4—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5C22×C411yescharacteristic
75C2×C3×C4×C5C2×D412yes—
76C3×C22⋊D5—42no—
77C2×C3×Dic5—21no—
78C2×C3×Dic5C22⋊C412yes—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C3×D20—41no—
81C3×C4×D5—22no—
82C3×C4×D5—42no—
83C3×C4×D5—42no—
84C3×Dic10—42no—
85C3×Dic10—41no—
86C3×C5×C8—42no—
87C3×#168—42no—
88C22×C3×Q8—51no—
89C22×C3×D4—51no—
90C3×#124—51no—
91C3×#124—51no—
92C3×#124—51no—
93C3×#124—102no—
94C3×#124C2×D511yescharacteristic
95C2×C3×C22⋊C4—102no—
96C2×C3×C42—51no—
97C3×C4⋊C8—102no—
98C3×C22⋊C8—102no—
99C3×#97—52no—
100C3×#97C2×D512yescomplemented
101C23×D5—21no—
102C2×C5×Q8C2×C3×C411yescharacteristic
103C2×C5×D4C2×C3×C411yescharacteristic
104C2×C22⋊D5—21no—
105Q8×D5—42no—
106D4×D5—42no—
107C2×D20C2×C3×C411yescharacteristic
108C2×C4×D5—21no—
109C2×C4×D5C2×C3×C411yescharacteristic
110C2×C4×D5C3×D412yes—
111C2×Dic10—21no—
112C2×Dic10C2×C3×C411yescharacteristic
113C2×C5×C8—22no—
114C5×C22⋊C4—22no—
115C42×C5C23×C311yescharacteristic
116C22⋊Dic5—22no—
117#685—22no—
118#685—22no—
119C4×Dic5C2×C3×C411yescharacteristic
120C4×Dic5C3×D412yes—
121C2×#168—22no—
122C2×#124—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—22no—
131C2×C3×D5—41no—
132C2×C3×D5—42no—
133C2×C3×D5—84no—
134C2×C3×D5#10012yes—
135C3×C4×C5—21no—
136C3×C4×C5—22no—
137C3×C4×C5—41no—
138C3×Dic5—21no—
139C3×Dic5—22no—
140C3×Dic5—41no—
141C24×C3—101no—
142C2×C3×Q8—51no—
143C2×C3×Q8—101no—
144C2×C3×Q8—202no—
145C2×C3×Q8C4×D511yescharacteristic
146C2×C3×D4—51no—
147C2×C3×D4—101no—
148C2×C3×D4—202no—
149C2×C3×D4C4×D511yescharacteristic
150C22×C3×C4—51no—
151C22×C3×C4—52no—
152C22×C3×C4—101no—
153C2×C3×C8—22no—
154C2×C3×C8—102no—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—102no—
157C3×C22⋊C4—102no—
158C3×C22⋊C4—102no—
159C3×C42—51no—
160C3×C42—52no—
161C3×C42C22×D511yescharacteristic
162C23×C5—21no—
163C22×D5—21no—
164C22×D5—44no—
165C22×D5—42no—
166C22×D5C3×C22⋊C411yescharacteristic
167C5×Q8—41no—
168C5×D4—41no—
169C2×C4×C5—21no—
170C2×C4×C5C22×C3×C411yescharacteristic
171C2×C4×C5C2×C3×D412yes—
172C22⋊D5—42no—
173C2×Dic5—21no—
174C2×Dic5C3×C22⋊C412yes—
175C2×Dic5C3×C22⋊C411yescharacteristic
176D20—41no—
177C4×D5—22no—
178C4×D5—42no—
179C4×D5—42no—
180Dic10—42no—
181Dic10—41no—
182C5×C8—42no—
183#168—42no—
184C22×Q8—51no—
185C22×D4—51no—
186#124—51no—
187#124—51no—
188#124—51no—
189#124—102no—
190#124C2×C3×D511yescharacteristic
191C2×C22⋊C4—102no—
192C2×C42—51no—
193C4⋊C8—102no—
194C22⋊C8—102no—
195#97—52no—
196#97C2×C3×D512yescomplemented
197C2×C3×C5—81no—
198C2×C3×C5C2×#10011yescharacteristic
199C2×C3×C5#42112yes—
200C3×D5—22no—
201C3×D5—81no—
202C23×C3—21no—
203C23×C3—51no—
204C23×C3—101no—
205C23×C3—202no—
206C23×C3—204no—
207C3×Q8—41no—
208C3×Q8—201no—
209C3×Q8—202no—
210C3×D4—41no—
211C3×D4—201no—
212C3×D4—202no—
213C2×C3×C4—21no—
214C2×C3×C4—52no—
215C2×C3×C4—51no—
216C2×C3×C4—102no—
217C2×C3×C4—101no—
218C2×C3×C4—202no—
219C2×C3×C4—202no—
220C2×C3×C4C2×C4×D511yescharacteristic
221C2×C3×C4D4×D512yes—
222C3×C8—42no—
223C3×C8—202no—
224C22×C5—41no—
225C22×C5—42no—
226C22×C5C2×C3×C22⋊C411yescharacteristic
227C2×D5—22no—
228C2×D5—41no—
229C2×D5—42no—
230C2×D5—84no—
231C2×D5C3×#10012yes—
232C4×C5—21no—
233C4×C5—22no—
234C4×C5—41no—
235Dic5—21no—
236Dic5—22no—
237Dic5—41no—
238C24—101no—
239C2×Q8—51no—
240C2×Q8—101no—
241C2×Q8—202no—
242C2×Q8C3×C4×D511yescharacteristic
243C2×D4—51no—
244C2×D4—101no—
245C2×D4—202no—
246C2×D4C3×C4×D511yescharacteristic
247C22×C4—51no—
248C22×C4—52no—
249C22×C4—101no—
250C2×C8—22no—
251C2×C8—102no—
252C22⋊C4—22no—
253C22⋊C4—102no—
254C22⋊C4—102no—
255C22⋊C4—102no—
256C42—51no—
257C42—52no—
258C42C22×C3×D511yescharacteristic
259C3×C5#153311yescharacteristic, complemented, Hall
260C22×C3—41no—
261C22×C3—42no—
262C22×C3—52no—
263C22×C3—102no—
264C22×C3—201no—
265C22×C3—202no—
266C22×C3—404no—
267C22×C3D5×C22⋊C411yescharacteristic
268C3×C4—21no—
269C3×C4—22no—
270C3×C4—41no—
271C3×C4—101no—
272C3×C4—102no—
273C3×C4—201no—
274C2×C5—81no—
275C2×C5C2×C3×#10011yescharacteristic
276C2×C5C3×#42112yes—
277D5—22no—
278D5—81no—
279C23—21no—
280C23—51no—
281C23—101no—
282C23—202no—
283C23—204no—
284Q8—41no—
285Q8—201no—
286Q8—202no—
287D4—41no—
288D4—201no—
289D4—202no—
290C2×C4—21no—
291C2×C4—52no—
292C2×C4—51no—
293C2×C4—102no—
294C2×C4—101no—
295C2×C4—202no—
296C2×C4—202no—
297C2×C4C2×C3×C4×D511yescharacteristic
298C2×C4C3×D4×D512yes—
299C8—42no—
300C8—202no—
301C2×C3—81no—
302C2×C3—102no—
303C2×C3—401no—
304C2×C3D5×#10011yescharacteristic
305C2×C3#6511012yes—
306C5C3×#153311yescharacteristic, complemented, Sylow
307C22—41no—
308C22—42no—
309C22—52no—
310C22—102no—
311C22—201no—
312C22—202no—
313C22—404no—
314C22C3×D5×C22⋊C411yescharacteristic
315C4—21no—
316C4—22no—
317C4—41no—
318C4—101no—
319C4—102no—
320C4—201no—
321C3#1059914011yescharacteristic, direct product factor, Sylow
322C2—81no—
323C2—102no—
324C2—401no—
325C2C3×D5×#10011yescharacteristic
326C2C3×#6511012yes—
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#329C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D4×D5C4
cosocleC42×C5C23×C3
hypercenterC3×#329D5
hypocenterC5C3×#1533
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. #10599140C3direct (N × H)
16. C3×C5×#97C22semidirect
19. C3×#3935C22semidirect
22. #64994C2×C3semidirect
23. C5×#329C2×C3semidirect
24. #64760C2×C3semidirect
25. #64684C2×C3semidirect
51. C3×#329D5semidirect
61. C5×#97C22×C3semidirect
64. #3935C22×C3semidirect
100. C3×#97C2×D5semidirect
126. #329C3×D5semidirect
196. #97C2×C3×D5semidirect
259. C3×C5#1533semidirect
306. C5C3×#1533semidirect
321. C3#10599140direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#1242
C3×#649942
C3×C5×#3292
C3×#647602
C3×#646842
#105991403
C3×#15335