Finite Group Databasebeta

← C3×#10599952 #14313528

Subgroups — C3×#10599952 #14313528

Order 1920.

476 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 110 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×#66009C211yesmaximal, characteristic
2C3×#65029C212yesmaximal
3C3×C5×#354C211yesmaximal, characteristic, complemented
4C3×#64761C211yesmaximal, characteristic, complemented
5C3×#64693C212yesmaximal, complemented
6#10599952C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×Q8×D5C411yescharacteristic, complemented
8C2×C3×#711C2211yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×#4090C411yescharacteristic, complemented
11C3×#4082C2211yescharacteristic
12C3×#4029—22no—
13C3×#4024—22no—
14C3×#4023—22no—
15C3×#4018C411yescharacteristic, complemented
16C3×#4015C411yescharacteristic, complemented
17C3×C5×#99C2212yes—
18C3×#3966C2212yes—
19C3×#3938—22no—
20C3×#2129—51nomaximal, Hall
21#66009C2×C311yescharacteristic
22#65029C2×C312yes—
23C5×#354C2×C311yescharacteristic, complemented
24#64761C2×C311yescharacteristic, complemented
25#64693C2×C312yescomplemented
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×C3×C5×D4C2311yescharacteristic
28C2×C3×C22⋊D5D412yes—
29C22×C3×Dic5D412yes—
30C3×Q8×D5—42no—
31C3×#711—42no—
32C2×C3×C4×D5—21no—
33C2×C3×C4×D5C2×C411yescharacteristic
34C2×C3×Dic10—21no—
35C2×C3×Dic10C2×C411yescharacteristic
36C2×C3×Dic10C2×C411yescharacteristic
37C3×C5×C22⋊C4—22no—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5C2×C411yescharacteristic
40C3×C22⋊Dic5—22no—
41C3×C22⋊Dic5—22no—
42C3×#685—21no—
43C3×C4⋊Dic5—22no—
44C3×#683—22no—
45C3×#683—21no—
46C3×#683—42no—
47C3×C4×Dic5—42no—
48C3×C4×Dic5C2×C411yescharacteristic
49C3×#536—51no—
50C3×#410—52no—
51C3×#354—51no—
52C3×#354—52no—
53C3×#354D511yescharacteristic, complemented
54C2×Q8×D5C3×C411yescharacteristic, complemented
55C2×#711C22×C311yescharacteristic
56C5×#124C22×C311yescharacteristic
57#4090C3×C411yescharacteristic, complemented
58#4082C22×C311yescharacteristic
59#4029—22no—
60#4024—22no—
61#4023—22no—
62#4018C3×C411yescharacteristic, complemented
63#4015C3×C411yescharacteristic, complemented
64C5×#99C22×C312yes—
65#3966C22×C312yes—
66#3938—22no—
67#2129—51noSylow
68C23×C3×C5C2×D412yes—
69C22×C3×D5C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C3×C5×D4—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—42no—
75C2×C3×C4×C5C22×C411yescharacteristic
76C3×C22⋊D5—42no—
77C2×C3×Dic5—22no—
78C2×C3×Dic5—22no—
79C2×C3×Dic5—21no—
80C2×C3×Dic5—21no—
81C2×C3×Dic5—42no—
82C2×C3×Dic5C22⋊C412yes—
83C2×C3×Dic5C22⋊C411yescharacteristic
84C3×C4×D5—22no—
85C3×C4×D5—42no—
86C3×Dic10—41no—
87C3×Dic10—42no—
88C3×Dic10—41no—
89C2×C3×#41—51no—
90C22×C3×Q8—51no—
91C3×C4⋊Q8—51no—
92C3×C4⋊Q8—51no—
93C3×#124—51no—
94C3×#124C2×D511yescharacteristic
95C3×#123—102no—
96C3×C22⋊Q8—102no—
97C3×#117—51no—
98C3×#117—102no—
99C3×#99—52no—
100C3×#99—102no—
101C3×#99C2×D512yes—
102C2×C5×Q8C2×C3×C411yescharacteristic
103C2×C5×D4C23×C311yescharacteristic
104C2×C22⋊D5C3×D412yes—
105C22×Dic5C3×D412yes—
106Q8×D5—42no—
107#711—42no—
108C2×C4×D5—21no—
109C2×C4×D5C2×C3×C411yescharacteristic
110C2×Dic10—21no—
111C2×Dic10C2×C3×C411yescharacteristic
112C2×Dic10C2×C3×C411yescharacteristic
113C5×C22⋊C4—22no—
114C5×C22⋊C4—22no—
115C42×C5C2×C3×C411yescharacteristic
116C22⋊Dic5—22no—
117C22⋊Dic5—22no—
118#685—21no—
119C4⋊Dic5—22no—
120#683—21no—
121#683—22no—
122#683—42no—
123C4×Dic5—42no—
124C4×Dic5C2×C3×C411yescharacteristic
125#536—51no—
126#410—52no—
127#354—51no—
128#354—52no—
129#354C3×D511yescharacteristic, complemented
130C22×C3×C5—22no—
131C22×C3×C5—42no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C2×C3×D5—21no—
134C2×C3×D5—41no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138C3×C4×C5—82no—
139C3×Dic5—22no—
140C3×Dic5—41no—
141C3×Dic5—41no—
142C3×Dic5—82no—
143C3×Dic5#9912yes—
144C3×#41—202no—
145C2×C3×Q8—51no—
146C2×C3×Q8—51no—
147C2×C3×Q8—101no—
148C2×C3×Q8—202no—
149C2×C3×Q8C4×D511yescharacteristic
150C2×C3×D4—52no—
151C2×C3×D4C22×D511yescharacteristic
152C22×C3×C4—52no—
153C22×C3×C4—51no—
154C22×C3×C4—101no—
155C3×C4⋊C4—101no—
156C3×C4⋊C4—102no—
157C3×C4⋊C4—102no—
158C3×C4⋊C4—202no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—101no—
162C3×C22⋊C4—102no—
163C3×C22⋊C4—102no—
164C3×C42—51no—
165C3×C42—202no—
166C3×C42C4×D511yescharacteristic
167C23×C5C2×C3×D412yes—
168C22×D5C3×C22⋊C411yescharacteristic
169C5×Q8—41no—
170C5×D4—41no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—42no—
174C2×C4×C5C22×C3×C411yescharacteristic
175C22⋊D5—42no—
176C2×Dic5—22no—
177C2×Dic5—22no—
178C2×Dic5—21no—
179C2×Dic5—21no—
180C2×Dic5—42no—
181C2×Dic5C3×C22⋊C412yes—
182C2×Dic5C3×C22⋊C411yescharacteristic
183C4×D5—22no—
184C4×D5—42no—
185Dic10—41no—
186Dic10—42no—
187Dic10—41no—
188C2×#41—51no—
189C22×Q8—51no—
190C4⋊Q8—51no—
191C4⋊Q8—51no—
192#124—51no—
193#124C2×C3×D511yescharacteristic
194#123—102no—
195C22⋊Q8—102no—
196#117—51no—
197#117—102no—
198#99—52no—
199#99—102no—
200#99C2×C3×D512yes—
201C2×C3×C5—21no—
202C2×C3×C5—42no—
203C2×C3×C5C2×#9911yescharacteristic
204C3×D5—41no—
205C23×C3—51no—
206C23×C3D4×D512yes—
207C3×Q8—41no—
208C3×Q8—201no—
209C3×Q8—201no—
210C3×Q8—202no—
211C3×D4—41no—
212C3×D4—202no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—42no—
216C2×C3×C4—51no—
217C2×C3×C4—52no—
218C2×C3×C4—102no—
219C2×C3×C4—102no—
220C2×C3×C4—102no—
221C2×C3×C4—101no—
222C2×C3×C4—101no—
223C2×C3×C4—202no—
224C2×C3×C4—202no—
225C2×C3×C4C2×C4×D511yescharacteristic
226C22×C5—22no—
227C22×C5—42no—
228C22×C5C2×C3×C22⋊C411yescharacteristic
229C2×D5—21no—
230C2×D5—41no—
231C4×C5—21no—
232C4×C5—41no—
233C4×C5—41no—
234C4×C5—82no—
235Dic5—22no—
236Dic5—41no—
237Dic5—41no—
238Dic5—82no—
239Dic5C3×#9912yes—
240#41—202no—
241C2×Q8—51no—
242C2×Q8—51no—
243C2×Q8—101no—
244C2×Q8—202no—
245C2×Q8C3×C4×D511yescharacteristic
246C2×D4—52no—
247C2×D4C22×C3×D511yescharacteristic
248C22×C4—52no—
249C22×C4—51no—
250C22×C4—101no—
251C4⋊C4—101no—
252C4⋊C4—102no—
253C4⋊C4—102no—
254C4⋊C4—202no—
255C22⋊C4—22no—
256C22⋊C4—22no—
257C22⋊C4—101no—
258C22⋊C4—102no—
259C22⋊C4—102no—
260C42—51no—
261C42—202no—
262C42C3×C4×D511yescharacteristic
263C3×C5#212911yescharacteristic, complemented, Hall
264C22×C3—22no—
265C22×C3—42no—
266C22×C3—101no—
267C22×C3—201no—
268C22×C3D5×C22⋊C411yescharacteristic
269C3×C4—21no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—52no—
273C3×C4—82no—
274C3×C4—102no—
275C3×C4—201no—
276C3×C4—201no—
277C3×C4—402no—
278C2×C5—21no—
279C2×C5—42no—
280C2×C5C2×C3×#9911yescharacteristic
281D5—41no—
282C23—51no—
283C23C3×D4×D512yes—
284Q8—41no—
285Q8—201no—
286Q8—201no—
287Q8—202no—
288D4—41no—
289D4—202no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—51no—
294C2×C4—52no—
295C2×C4—102no—
296C2×C4—102no—
297C2×C4—102no—
298C2×C4—101no—
299C2×C4—101no—
300C2×C4—202no—
301C2×C4—202no—
302C2×C4C2×C3×C4×D511yescharacteristic
303C2×C3—21no—
304C2×C3—42no—
305C2×C3—201no—
306C2×C3D5×#9911yescharacteristic
307C5C3×#212911yescharacteristic, complemented, Sylow
308C22—22no—
309C22—42no—
310C22—101no—
311C22—201no—
312C22C3×D5×C22⋊C411yescharacteristic
313C4—21no—
314C4—41no—
315C4—41no—
316C4—52no—
317C4—82no—
318C4—102no—
319C4—201no—
320C4—201no—
321C4—402no—
322C3#1059995211yescharacteristic, direct product factor, Sylow
323C2—21no—
324C2—42no—
325C2—201no—
326C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#354C2
socleC2×C3×C5C2×#99
prime radicalC2×C3×#711C22
cosocleC2×C5×D4C23×C3
hypercenterC3×#354D5
hypocenterC5C3×#2129
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#354

Complements

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

NH ≅ G/Ntype
3. C3×C5×#354C2semidirect
4. C3×#64761C2semidirect
5. C3×#64693C2semidirect
6. #10599952C3direct (N × H)
7. C2×C3×Q8×D5C4semidirect
10. C3×#4090C4semidirect
15. C3×#4018C4semidirect
16. C3×#4015C4semidirect
23. C5×#354C2×C3semidirect
24. #64761C2×C3semidirect
25. #64693C2×C3semidirect
53. C3×#354D5semidirect
54. C2×Q8×D5C3×C4semidirect
57. #4090C3×C4semidirect
62. #4018C3×C4semidirect
63. #4015C3×C4semidirect
129. #354C3×D5semidirect
263. C3×C5#2129semidirect
307. C5C3×#2129semidirect
322. C3#10599952direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660092
C3×#650292
C3×C5×#3542
C3×#647612
C3×#646932
#105999523
C3×#21295