Finite Group Databasebeta

← C3×#10613957 #14321085

Subgroups — C3×#10613957 #14321085

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic
2C2×C3×#4072C211yesmaximal, characteristic
3C22×C3×C4×Dic5C211yesmaximal, characteristic
4C3×#65262C214yesmaximal, complemented
5C3×#65235C214yesmaximal
6C3×C4×#683C214yesmaximal, complemented
7#10613957C311yesmaximal, characteristic, direct product factor, Hall
8C23×C3×C4×C5C2211yescharacteristic
9C23×C3×Dic5C2212yes—
10C3×C5×#117—24no—
11C2×C3×C5×C4⋊C4C2212yes—
12C2×C3×C5×C22⋊C4C2212yes—
13C2×C3×C42×C5C2212yes—
14C2×C3×C22⋊Dic5C2212yes—
15C3×#4072C418yescomplemented
16C2×C3×C4⋊Dic5C2212yes—
17C2×C3×#683C2218yes—
18C2×C3×C4×Dic5—24no—
19C2×C3×C4×Dic5C2212yes—
20C2×C3×C4×Dic5C2212yes—
21C2×C3×C4×Dic5C2212yes—
22C3×#3963C2218yes—
23C3×#2296—51nomaximal, Hall
24C2×C5×#117C2×C311yescharacteristic
25C2×#4072C2×C311yescharacteristic
26C22×C4×Dic5C2×C311yescharacteristic
27#65262C2×C314yescomplemented
28#65235C2×C314yes—
29C4×#683C2×C314yescomplemented
30C24×C3×C5C2311yescharacteristic
31C22×C3×C4×C5C2×C414yes—
32C22×C3×C4×C5D414yes—
33C22×C3×C4×C5Q814yes—
34C22×C3×C4×C5C2314yes—
35C22×C3×C4×C5C2311yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C22×C3×Dic5—24no—
38C22×C3×Dic5—28no—
39C22×C3×Dic5C2314yes—
40C22×C3×Dic5C2314yes—
41C3×C5×C4⋊C4—24no—
42C3×C5×C22⋊C4—24no—
43C3×C42×C5—24no—
44C3×C22⋊Dic5C2×C418yes—
45C3×C4⋊Dic5C2×C418yescomplemented
46C3×#683—216no—
47C3×C4×Dic5—24no—
48C3×C4×Dic5—24no—
49C3×C4×Dic5C2×C418yescomplemented
50C2×C3×#117—51no—
51C2×C3×#117D511yescharacteristic
52C22×C3×C42—51no—
53C3×#389—54no—
54C3×#385—54no—
55C3×C4×C4⋊C4—54no—
56C23×C4×C5C22×C311yescharacteristic
57C23×Dic5C22×C312yes—
58C5×#117—24no—
59C2×C5×C4⋊C4C22×C312yes—
60C2×C5×C22⋊C4C22×C312yes—
61C2×C42×C5C22×C312yes—
62C2×C22⋊Dic5C22×C312yes—
63#4072C3×C418yescomplemented
64C2×C4⋊Dic5C22×C312yes—
65C2×#683C22×C318yes—
66C2×C4×Dic5—24no—
67C2×C4×Dic5C22×C312yes—
68C2×C4×Dic5C22×C312yes—
69C2×C4×Dic5C22×C312yes—
70#3963C22×C318yes—
71#2296—51noSylow
72C23×C3×C5—24no—
73C23×C3×C5C22×C412yes—
74C23×C3×C5C2×D412yes—
75C23×C3×C5C2×Q812yes—
76C23×C3×C5C2411yescharacteristic
77C2×C3×C4×C5—24no—
78C2×C3×C4×C5—28no—
79C2×C3×C4×C5C4⋊C4116yescomplemented
80C2×C3×C4×C5C22×C412yes—
81C2×C3×C4×C5C22×C412yes—
82C2×C3×C4×C5C2×D412yes—
83C2×C3×C4×C5C2×D412yes—
84C2×C3×C4×C5C2×Q812yes—
85C2×C3×C4×C5C2×Q812yes—
86C2×C3×Dic5—216no—
87C2×C3×Dic5—24no—
88C2×C3×Dic5—28no—
89C2×C3×Dic5—24no—
90C2×C3×Dic5C22×C418yes—
91C2×C3×Dic5#4118yes—
92C23×C3×C4—52no—
93C23×C3×C4C2×D511yescharacteristic
94C3×#117—24no—
95C3×#117—58no—
96C2×C3×C4⋊C4—52no—
97C2×C3×C4⋊C4—58no—
98C2×C3×C4⋊C4C2×D512yes—
99C2×C3×C22⋊C4—52no—
100C2×C3×C22⋊C4C2×D512yes—
101C2×C3×C42—52no—
102C2×C3×C42—52no—
103C2×C3×C42—52no—
104C2×C3×C42—104no—
105C2×C3×C42C2×D512yes—
106C3×#95—58no—
107C24×C5C23×C311yescharacteristic
108C22×C4×C5C2×C3×C414yes—
109C22×C4×C5C3×D414yes—
110C22×C4×C5C3×Q814yes—
111C22×C4×C5C23×C314yes—
112C22×C4×C5C23×C311yescharacteristic
113C22×C4×C5C23×C311yescharacteristic
114C22×Dic5—24no—
115C22×Dic5—28no—
116C22×Dic5C23×C314yes—
117C22×Dic5C23×C314yes—
118C5×C4⋊C4—24no—
119C5×C22⋊C4—24no—
120C42×C5—24no—
121C22⋊Dic5C2×C3×C418yes—
122C4⋊Dic5C2×C3×C418yescomplemented
123#683—216no—
124C4×Dic5—24no—
125C4×Dic5—24no—
126C4×Dic5C2×C3×C418yescomplemented
127C2×#117—51no—
128C2×#117C3×D511yescharacteristic
129C22×C42—51no—
130#389—54no—
131#385—54no—
132C4×C4⋊C4—54no—
133C22×C3×C5—24no—
134C22×C3×C5—24no—
135C22×C3×C5—24no—
136C22×C3×C5C2×C4⋊C414yes—
137C22×C3×C5C23×C411yescharacteristic
138C22×C3×C5C22×D411yescharacteristic
139C22×C3×C5C22×Q811yescharacteristic
140C22×C3×C5C2×#4114yes—
141C3×C4×C5—44no—
142C3×C4×C5C2×C4⋊C414yes—
143C3×C4×C5C2×C4⋊C414yes—
144C3×Dic5—28no—
145C3×Dic5—28no—
146C24×C3C22×D511yescharacteristic
147C22×C3×C4—54no—
148C22×C3×C4—54no—
149C22×C3×C4—108no—
150C22×C3×C4—104no—
151C22×C3×C4Dic1014yes—
152C22×C3×C4C4×D514yes—
153C22×C3×C4C22⋊D514yes—
154C22×C3×C4C22×D514yes—
155C22×C3×C4C22×D511yescharacteristic
156C22×C3×C4C22×D511yescharacteristic
157C3×C4⋊C4—24no—
158C3×C4⋊C4—58no—
159C3×C4⋊C4—1016no—
160C3×C22⋊C4—24no—
161C3×C22⋊C4—58no—
162C3×C42—24no—
163C3×C42—58no—
164C3×C42—104no—
165C3×C42—104no—
166C23×C5—24no—
167C23×C5C22×C3×C412yes—
168C23×C5C2×C3×D412yes—
169C23×C5C2×C3×Q812yes—
170C23×C5C24×C311yescharacteristic
171C2×C4×C5—24no—
172C2×C4×C5—28no—
173C2×C4×C5C3×C4⋊C4116yescomplemented
174C2×C4×C5C22×C3×C412yes—
175C2×C4×C5C22×C3×C412yes—
176C2×C4×C5C2×C3×D412yes—
177C2×C4×C5C2×C3×D412yes—
178C2×C4×C5C2×C3×Q812yes—
179C2×C4×C5C2×C3×Q812yes—
180C2×Dic5—216no—
181C2×Dic5—24no—
182C2×Dic5—28no—
183C2×Dic5—24no—
184C2×Dic5C22×C3×C418yes—
185C2×Dic5C3×#4118yes—
186C23×C4—52no—
187C23×C4C2×C3×D511yescharacteristic
188#117—24no—
189#117—58no—
190C2×C4⋊C4—52no—
191C2×C4⋊C4—58no—
192C2×C4⋊C4C2×C3×D512yes—
193C2×C22⋊C4—52no—
194C2×C22⋊C4C2×C3×D512yes—
195C2×C42—52no—
196C2×C42—52no—
197C2×C42—52no—
198C2×C42—104no—
199C2×C42C2×C3×D512yes—
200#95—58no—
201C2×C3×C5—24no—
202C2×C3×C5C22×C4⋊C411yescharacteristic
203C2×C3×C5C4×#4112yes—
204C2×C3×C5#52512yes—
205C2×C3×C5#53312yes—
206C23×C3—24no—
207C23×C3C2×Dic1012yes—
208C23×C3C2×C4×D512yes—
209C23×C3C2×C22⋊D512yes—
210C23×C3C23×D511yescharacteristic
211C2×C3×C4—28no—
212C2×C3×C4—24no—
213C2×C3×C4—58no—
214C2×C3×C4—58no—
215C2×C3×C4—1016no—
216C2×C3×C4—108no—
217C2×C3×C4—104no—
218C2×C3×C4—104no—
219C2×C3×C4#683116yescomplemented
220C2×C3×C4C2×Dic1012yes—
221C2×C3×C4C2×Dic1012yes—
222C2×C3×C4C2×C4×D512yes—
223C2×C3×C4C2×C4×D512yes—
224C2×C3×C4C2×C22⋊D512yes—
225C2×C3×C4C2×C22⋊D512yes—
226C22×C5—24no—
227C22×C5—24no—
228C22×C5—24no—
229C22×C5C2×C3×C4⋊C414yes—
230C22×C5C23×C3×C411yescharacteristic
231C22×C5C22×C3×D411yescharacteristic
232C22×C5C22×C3×Q811yescharacteristic
233C22×C5C2×C3×#4114yes—
234C4×C5—44no—
235C4×C5C2×C3×C4⋊C414yes—
236C4×C5C2×C3×C4⋊C414yes—
237Dic5—28no—
238Dic5—28no—
239C24C22×C3×D511yescharacteristic
240C22×C4—54no—
241C22×C4—54no—
242C22×C4—108no—
243C22×C4—104no—
244C22×C4C3×Dic1014yes—
245C22×C4C3×C4×D514yes—
246C22×C4C3×C22⋊D514yes—
247C22×C4C22×C3×D514yes—
248C22×C4C22×C3×D511yescharacteristic
249C22×C4C22×C3×D511yescharacteristic
250C4⋊C4—24no—
251C4⋊C4—58no—
252C4⋊C4—1016no—
253C22⋊C4—24no—
254C22⋊C4—58no—
255C42—24no—
256C42—58no—
257C42—104no—
258C42—104no—
259C3×C5#229611yescharacteristic, complemented, Hall
260C22×C3—24no—
261C22×C3—24no—
262C22×C3—24no—
263C22×C3C2×#68314yes—
264C22×C3C22×Dic1011yescharacteristic
265C22×C3C22×C4×D511yescharacteristic
266C22×C3D5×#4114yes—
267C22×C3C22×C22⋊D511yescharacteristic
268C3×C4—44no—
269C3×C4—108no—
270C3×C4—108no—
271C3×C4C2×#68314yes—
272C3×C4C2×#68314yes—
273C2×C5—24no—
274C2×C5C22×C3×C4⋊C411yescharacteristic
275C2×C5C3×C4×#4112yes—
276C2×C5C3×#52512yes—
277C2×C5C3×#53312yes—
278C23—24no—
279C23C2×C3×Dic1012yes—
280C23C2×C3×C4×D512yes—
281C23C2×C3×C22⋊D512yes—
282C23C23×C3×D511yescharacteristic
283C2×C4—28no—
284C2×C4—24no—
285C2×C4—58no—
286C2×C4—58no—
287C2×C4—1016no—
288C2×C4—108no—
289C2×C4—104no—
290C2×C4—104no—
291C2×C4C3×#683116yescomplemented
292C2×C4C2×C3×Dic1012yes—
293C2×C4C2×C3×Dic1012yes—
294C2×C4C2×C3×C4×D512yes—
295C2×C4C2×C3×C4×D512yes—
296C2×C4C2×C3×C22⋊D512yes—
297C2×C4C2×C3×C22⋊D512yes—
298C2×C3—24no—
299C2×C3#6585112yes—
300C2×C3#6585612yes—
301C2×C3C22×#68311yescharacteristic
302C2×C3#6616212yes—
303C5C3×#229611yescharacteristic, complemented, Sylow
304C22—24no—
305C22—24no—
306C22—24no—
307C22C2×C3×#68314yes—
308C22C22×C3×Dic1011yescharacteristic
309C22C22×C3×C4×D511yescharacteristic
310C22C3×D5×#4114yes—
311C22C22×C3×C22⋊D511yescharacteristic
312C4—44no—
313C4—108no—
314C4—108no—
315C4C2×C3×#68314yes—
316C4C2×C3×#68314yes—
317C3#1061395711yescharacteristic, direct product factor, Sylow
318C2—24no—
319C2C3×#6585112yes—
320C2C3×#6585612yes—
321C2C22×C3×#68311yescharacteristic
322C2C3×#6616212yes—
subgroupG/H
centerC22×C3×C4C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC2×C3×#117D5
hypocenterC5C3×#2296
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
4. C3×#65262C2semidirect
6. C3×C4×#683C2semidirect
7. #10613957C3direct (N × H)
15. C3×#4072C4semidirect
27. #65262C2×C3semidirect
29. C4×#683C2×C3semidirect
45. C3×C4⋊Dic5C2×C4semidirect
49. C3×C4×Dic5C2×C4semidirect
63. #4072C3×C4semidirect
79. C2×C3×C4×C5C4⋊C4semidirect
122. C4⋊Dic5C2×C3×C4semidirect
126. C4×Dic5C2×C3×C4semidirect
173. C2×C4×C5C3×C4⋊C4semidirect
219. C2×C3×C4#683semidirect
259. C3×C5#2296semidirect
291. C2×C4C3×#683semidirect
303. C5C3×#2296semidirect
317. C3#10613957direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
C2×C3×#40722
C22×C3×C4×Dic52
C3×#652622
C3×#652352
C3×C4×#6832
#106139573
C3×#22965