Finite Group Databasebeta

← C3×#10600436 #14308909

Subgroups — C3×#10600436 #14308909

Order 1920.

564 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65834C211yesmaximal, characteristic, complemented
2C3×C5×#390C211yesmaximal, characteristic
3C3×#65504C212yesmaximal
4C3×#64750C211yesmaximal, characteristic, complemented
5C3×#64743C212yesmaximal, complemented
6#10600436C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×C3×C5×C22⋊C4—22no—
10C2×C3×C42×C5C2211yescharacteristic
11C3×#4072C2212yes—
12C3×#4070—22no—
13C2×C3×#681C2212yes—
14C3×#4036—22no—
15C3×#4034—22no—
16C3×#3964—22no—
17C3×#3964—22no—
18C3×#2027—51nomaximal, Hall
19#65834C2×C311yescharacteristic, complemented
20C5×#390C2×C311yescharacteristic
21#65504C2×C312yes—
22#64750C2×C311yescharacteristic, complemented
23#64743C2×C312yescomplemented
24C24×C3×C5—21no—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—21no—
28C2×C3×C5×D4Q812yescomplemented
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D412yes—
31C22×C3×C4×C5C2311yescharacteristic
32C2×C3×Dic10—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C22⋊C4—44no—
35C3×C42×C5—22no—
36C3×C22⋊Dic5—22no—
37C3×C4⋊Dic5—22no—
38C3×C4⋊Dic5D412yes—
39C3×C4⋊Dic5D412yes—
40C3×#683—24no—
41C3×C4×Dic5—22no—
42C3×#681—22no—
43C3×#681—22no—
44C2×C3×#168—22no—
45C3×#544—51no—
46C3×#418—52no—
47C3×#390D511yescharacteristic
48C3×#343—51no—
49C3×#339—52no—
50C22×C5×D4C22×C311yescharacteristic
51C2×C5×C4⋊C4C22×C311yescharacteristic
52C2×C5×C22⋊C4—22no—
53C2×C42×C5C22×C311yescharacteristic
54#4072C22×C312yes—
55#4070—22no—
56C2×#681C22×C312yes—
57#4036—22no—
58#4034—22no—
59#3964—22no—
60#3964—22no—
61#2027—51noSylow
62C23×C3×C5—22no—
63C23×C3×C5—42no—
64C23×C3×C5—42no—
65C23×C3×C5—41no—
66C23×C3×C5—41no—
67C23×C3×C5C2×D411yescharacteristic
68C3×C5×D4—24no—
69C3×C5×D4—42no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—42no—
75C2×C3×C4×C5C2×D412yes—
76C2×C3×C4×C5C2×Q811yescharacteristic
77C2×C3×C4×C5#4112yes—
78C2×C3×C4×C5#4111yescharacteristic
79C2×C3×Dic5—22no—
80C2×C3×Dic5—22no—
81C3×Dic10—82no—
82C3×#168—42no—
83C22×C3×D4C2×D511yescharacteristic
84C2×C3×M16—52no—
85C3×C4⋊Q8—102no—
86C3×#125—102no—
87C3×C22⋊Q8—102no—
88C3×#117—52no—
89C2×C3×C4⋊C4C2×D511yescharacteristic
90C2×C3×C22⋊C4—22no—
91C2×C3×C42C2×D511yescharacteristic
92C3×#102—102no—
93C3×#102—102no—
94C24×C5—21no—
95C2×C5×D4—22no—
96C2×C5×D4—22no—
97C2×C5×D4—21no—
98C2×C5×D4C3×Q812yescomplemented
99C22×C4×C5—21no—
100C22×C4×C5C3×D412yes—
101C22×C4×C5C23×C311yescharacteristic
102C2×Dic10—22no—
103C5×C4⋊C4—22no—
104C5×C22⋊C4—44no—
105C42×C5—22no—
106C22⋊Dic5—22no—
107C4⋊Dic5—22no—
108C4⋊Dic5C3×D412yes—
109C4⋊Dic5C3×D412yes—
110#683—24no—
111C4×Dic5—22no—
112#681—22no—
113#681—22no—
114C2×#168—22no—
115#544—51no—
116#418—52no—
117#390C3×D511yescharacteristic
118#343—51no—
119#339—52no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5—44no—
123C22×C3×C5—42no—
124C22×C3×C5—82no—
125C22×C3×C5—81no—
126C22×C3×C5—81no—
127C22×C3×C5#12011yescharacteristic
128C22×C3×C5C22⋊Q811yescharacteristic
129C22×C3×C5#12411yescharacteristic
130C3×C4×C5—42no—
131C3×C4×C5—42no—
132C3×C4×C5C22⋊Q812yes—
133C3×C4×C5#12412yes—
134C3×Dic5—42no—
135C3×Dic5—42no—
136C24×C3—21no—
137C2×C3×Q8—102no—
138C2×C3×D4—21no—
139C2×C3×D4—22no—
140C2×C3×D4—22no—
141C2×C3×D4Dic1012yescomplemented
142C22×C3×C4—21no—
143C22×C3×C4C22⋊D512yes—
144C22×C3×C4C22×D511yescharacteristic
145C3×M16—102no—
146C3×M16—102no—
147C2×C3×C8—102no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—52no—
150C3×C4⋊C4—52no—
151C3×C4⋊C4—104no—
152C3×C4⋊C4—102no—
153C3×C22⋊C4—44no—
154C3×C22⋊C4—102no—
155C3×C42—22no—
156C3×C42—102no—
157C23×C5—22no—
158C23×C5—42no—
159C23×C5—42no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5C2×C3×D411yescharacteristic
163C5×D4—24no—
164C5×D4—42no—
165C2×C4×C5—22no—
166C2×C4×C5—22no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—42no—
170C2×C4×C5C2×C3×D412yes—
171C2×C4×C5C2×C3×Q811yescharacteristic
172C2×C4×C5C3×#4111yescharacteristic
173C2×C4×C5C3×#4112yes—
174C2×Dic5—22no—
175C2×Dic5—22no—
176Dic10—82no—
177#168—42no—
178C22×D4C2×C3×D511yescharacteristic
179C2×M16—52no—
180C4⋊Q8—102no—
181#125—102no—
182C22⋊Q8—102no—
183#117—52no—
184C2×C4⋊C4C2×C3×D511yescharacteristic
185C2×C22⋊C4—22no—
186C2×C42C2×C3×D511yescharacteristic
187#102—102no—
188#102—102no—
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5—82no—
192C2×C3×C5#39311yescharacteristic
193C2×C3×C5#45311yescharacteristic
194C2×C3×C5#45411yescharacteristic
195C23×C3—22no—
196C23×C3—42no—
197C23×C3—42no—
198C23×C3—41no—
199C23×C3—41no—
200C23×C3C2×C22⋊D511yescharacteristic
201C3×Q8—402no—
202C3×D4—24no—
203C3×D4—42no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—42no—
209C2×C3×C4—102no—
210C2×C3×C4—102no—
211C2×C3×C4C2×Dic1011yescharacteristic
212C2×C3×C4#70911yescharacteristic
213C2×C3×C4D4×D512yes—
214C2×C3×C4#71112yes—
215C3×C8—202no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—44no—
219C22×C5—42no—
220C22×C5—82no—
221C22×C5—81no—
222C22×C5—81no—
223C22×C5C3×#12011yescharacteristic
224C22×C5C3×C22⋊Q811yescharacteristic
225C22×C5C3×#12411yescharacteristic
226C4×C5—42no—
227C4×C5—42no—
228C4×C5C3×C22⋊Q812yes—
229C4×C5C3×#12412yes—
230Dic5—42no—
231Dic5—42no—
232C24—21no—
233C2×Q8—102no—
234C2×D4—21no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4C3×Dic1012yescomplemented
238C22×C4—21no—
239C22×C4C3×C22⋊D512yes—
240C22×C4C22×C3×D511yescharacteristic
241M16—102no—
242M16—102no—
243C2×C8—102no—
244C4⋊C4—22no—
245C4⋊C4—52no—
246C4⋊C4—52no—
247C4⋊C4—102no—
248C4⋊C4—104no—
249C22⋊C4—44no—
250C22⋊C4—102no—
251C42—22no—
252C42—102no—
253C3×C5#202711yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—44no—
257C22×C3—42no—
258C22×C3—82no—
259C22×C3—81no—
260C22×C3—81no—
261C22×C3#407011yescharacteristic
262C22×C3#408211yescharacteristic
263C22×C3#408311yescharacteristic
264C3×C4—42no—
265C3×C4—42no—
266C3×C4—202no—
267C3×C4—202no—
268C3×C4#402412yes—
269C3×C4#403112yes—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5—82no—
273C2×C5C3×#39311yescharacteristic
274C2×C5C3×#45311yescharacteristic
275C2×C5C3×#45411yescharacteristic
276C23—22no—
277C23—42no—
278C23—42no—
279C23—41no—
280C23—41no—
281C23C2×C3×C22⋊D511yescharacteristic
282Q8—402no—
283D4—24no—
284D4—42no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—102no—
291C2×C4—102no—
292C2×C4C2×C3×Dic1011yescharacteristic
293C2×C4C3×#70911yescharacteristic
294C2×C4C3×D4×D512yes—
295C2×C4C3×#71112yes—
296C8—202no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—82no—
300C2×C3#6523611yescharacteristic
301C2×C3#6535111yescharacteristic
302C2×C3#6536611yescharacteristic
303C5C3×#202711yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—44no—
307C22—42no—
308C22—82no—
309C22—81no—
310C22—81no—
311C22C3×#407011yescharacteristic
312C22C3×#408211yescharacteristic
313C22C3×#408311yescharacteristic
314C4—42no—
315C4—42no—
316C4—202no—
317C4—202no—
318C4C3×#402412yes—
319C4C3×#403112yes—
320C3#1060043611yescharacteristic, direct product factor, Sylow
321C2—21no—
322C2—21no—
323C2—82no—
324C2C3×#6523611yescharacteristic
325C2C3×#6535111yescharacteristic
326C2C3×#6536611yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#390C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
hypercenterC3×#390D5
hypocenterC5C3×#2027
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
1. C3×#65834C2semidirect
4. C3×#64750C2semidirect
5. C3×#64743C2semidirect
6. #10600436C3direct (N × H)
19. #65834C2×C3semidirect
22. #64750C2×C3semidirect
23. #64743C2×C3semidirect
28. C2×C3×C5×D4Q8semidirect
98. C2×C5×D4C3×Q8semidirect
141. C2×C3×D4Dic10semidirect
237. C2×D4C3×Dic10semidirect
253. C3×C5#2027semidirect
303. C5C3×#2027semidirect
320. C3#10600436direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658342
C3×C5×#3902
C3×#655042
C3×#647502
C3×#647432
#106004363
C3×#20275