Finite Group Databasebeta

← C3×#10602440 #14299573

Subgroups — C3×#10602440 #14299573

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#518C211yesmaximal, characteristic
2C3×#65510C211yesmaximal, characteristic
3C2×C3×#3965C211yesmaximal, characteristic
4C3×#65284C212yesmaximal, complemented
5C3×#64752C212yesmaximal, complemented
6#10602440C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C3×C4×C5×D4—22no—
9C3×C4×C5×D4—22no—
10C3×C5×#117C2212yes—
11C2×C3×C5×C22⋊C4—22no—
12C2×C3×C22⋊Dic5—22no—
13C2×C3×C4⋊Dic5C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×#681C2212yes—
16C3×#3965C414yescomplemented
17C3×#3940—22no—
18C3×#3939—22no—
19C3×#1856—51nomaximal, Hall
20C5×#518C2×C311yescharacteristic
21#65510C2×C311yescharacteristic
22C2×#3965C2×C311yescharacteristic
23#65284C2×C312yescomplemented
24#64752C2×C312yescomplemented
25C24×C3×C5D412yes—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C412yes—
29C2×C3×C5×D4Q812yes—
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5—22no—
32C22×C3×C4×C5C2311yescharacteristic
33C22×C3×Dic5—21no—
34C22×C3×Dic5—21no—
35C3×C5×C4⋊C4D412yes—
36C3×C5×C4⋊C4D412yes—
37C3×C5×C22⋊C4—24no—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5—22no—
40C3×C22⋊Dic5—44no—
41C3×C4⋊Dic5—22no—
42C3×C4×Dic5—22no—
43C3×#681—22no—
44C3×#681C2×C414yescomplemented
45C2×C3×#168—22no—
46C3×#518D511yescharacteristic
47C3×#428—52no—
48C2×C3×#100—51no—
49C3×#390—51no—
50C3×#339—52no—
51C22×C5×D4C22×C311yescharacteristic
52C4×C5×D4—22no—
53C4×C5×D4—22no—
54C5×#117C22×C312yes—
55C2×C5×C22⋊C4—22no—
56C2×C22⋊Dic5—22no—
57C2×C4⋊Dic5C22×C311yescharacteristic
58C2×C4×Dic5C22×C311yescharacteristic
59C2×#681C22×C312yes—
60#3965C3×C414yescomplemented
61#3940—22no—
62#3939—22no—
63#1856—51noSylow
64C23×C3×C5—22no—
65C23×C3×C5—22no—
66C23×C3×C5—42no—
67C23×C3×C5—42no—
68C23×C3×C5C4⋊C414yes—
69C23×C3×C5C2×D411yescharacteristic
70C3×C5×D4—24no—
71C3×C5×D4—24no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—82no—
75C2×C3×C4×C5—82no—
76C2×C3×C4×C5C22×C411yescharacteristic
77C2×C3×C4×C5C2×D412yes—
78C2×C3×C4×C5C2×Q811yescharacteristic
79C2×C3×C4×C5#4112yes—
80C2×C3×Dic5—22no—
81C2×C3×Dic5—41no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5—42no—
84C2×C3×Dic5—41no—
85C3×#168—24no—
86C22×C3×D4C2×D511yescharacteristic
87C2×C3×M16—52no—
88C3×C4×D4—22no—
89C3×C4×D4—22no—
90C3×#117C2×D512yes—
91C2×C3×C4⋊C4—51no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—102no—
94C2×C3×C42—51no—
95C3×#107—102no—
96C3×#106—102no—
97C3×#100—54no—
98C24×C5C3×D412yes—
99C2×C5×D4—22no—
100C2×C5×D4—22no—
101C2×C5×D4C2×C3×C412yes—
102C2×C5×D4C3×Q812yes—
103C22×C4×C5—22no—
104C22×C4×C5—22no—
105C22×C4×C5C23×C311yescharacteristic
106C22×Dic5—21no—
107C22×Dic5—21no—
108C5×C4⋊C4C3×D412yes—
109C5×C4⋊C4C3×D412yes—
110C5×C22⋊C4—24no—
111C5×C22⋊C4—22no—
112C42×C5—22no—
113C22⋊Dic5—44no—
114C4⋊Dic5—22no—
115C4×Dic5—22no—
116#681—22no—
117#681C2×C3×C414yescomplemented
118C2×#168—22no—
119#518C3×D511yescharacteristic
120#428—52no—
121C2×#100—51no—
122#390—51no—
123#339—52no—
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5—24no—
127C22×C3×C5—44no—
128C22×C3×C5—42no—
129C22×C3×C5—42no—
130C22×C3×C5—82no—
131C22×C3×C5C2×C4⋊C411yescharacteristic
132C22×C3×C5#12011yescharacteristic
133C22×C3×C5#12311yescharacteristic
134C3×C4×C5—42no—
135C3×C4×C5—42no—
136C3×C4×C5C4×D412yes—
137C3×C4×C5C22⋊Q812yes—
138C3×Dic5—42no—
139C3×Dic5—81no—
140C24×C3C22⋊D512yes—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4Dic1012yes—
144C2×C3×D4C4×D512yes—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—101no—
148C22×C3×C4—101no—
149C22×C3×C4C22×D511yescharacteristic
150C3×M16—54no—
151C3×M16—102no—
152C2×C3×C8—102no—
153C3×C4⋊C4—102no—
154C3×C4⋊C4C22⋊D512yes—
155C3×C4⋊C4C22⋊D512yes—
156C3×C22⋊C4—24no—
157C3×C22⋊C4—22no—
158C3×C22⋊C4—204no—
159C3×C42—22no—
160C3×C42—102no—
161C23×C5—22no—
162C23×C5—22no—
163C23×C5—42no—
164C23×C5—42no—
165C23×C5C3×C4⋊C414yes—
166C23×C5C2×C3×D411yescharacteristic
167C5×D4—24no—
168C5×D4—24no—
169C2×C4×C5—22no—
170C2×C4×C5—22no—
171C2×C4×C5—82no—
172C2×C4×C5—82no—
173C2×C4×C5C22×C3×C411yescharacteristic
174C2×C4×C5C2×C3×D412yes—
175C2×C4×C5C2×C3×Q811yescharacteristic
176C2×C4×C5C3×#4112yes—
177C2×Dic5—22no—
178C2×Dic5—41no—
179C2×Dic5—41no—
180C2×Dic5—42no—
181C2×Dic5—41no—
182#168—24no—
183C22×D4C2×C3×D511yescharacteristic
184C2×M16—52no—
185C4×D4—22no—
186C4×D4—22no—
187#117C2×C3×D512yes—
188C2×C4⋊C4—51no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—102no—
191C2×C42—51no—
192#107—102no—
193#106—102no—
194#100—54no—
195C2×C3×C5—21no—
196C2×C3×C5—21no—
197C2×C3×C5—44no—
198C2×C3×C5#38511yescharacteristic
199C2×C3×C5#45311yescharacteristic
200C2×C3×C5#45511yescharacteristic
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—42no—
204C23×C3—42no—
205C23×C3#68314yes—
206C23×C3C2×C22⋊D511yescharacteristic
207C3×D4—24no—
208C3×D4—24no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—82no—
212C2×C3×C4—82no—
213C2×C3×C4—102no—
214C2×C3×C4—201no—
215C2×C3×C4—201no—
216C2×C3×C4—202no—
217C2×C3×C4—201no—
218C2×C3×C4C2×Dic1011yescharacteristic
219C2×C3×C4C2×C4×D511yescharacteristic
220C2×C3×C4#70912yes—
221C2×C3×C4C2×C22⋊D512yes—
222C3×C8—104no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—24no—
226C22×C5—44no—
227C22×C5—42no—
228C22×C5—42no—
229C22×C5—82no—
230C22×C5C2×C3×C4⋊C411yescharacteristic
231C22×C5C3×#12011yescharacteristic
232C22×C5C3×#12311yescharacteristic
233C4×C5—42no—
234C4×C5—42no—
235C4×C5C3×C4×D412yes—
236C4×C5C3×C22⋊Q812yes—
237Dic5—42no—
238Dic5—81no—
239C24C3×C22⋊D512yes—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4C3×Dic1012yes—
243C2×D4C3×C4×D512yes—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—101no—
247C22×C4—101no—
248C22×C4C22×C3×D511yescharacteristic
249M16—54no—
250M16—102no—
251C2×C8—102no—
252C4⋊C4—102no—
253C4⋊C4C3×C22⋊D512yes—
254C4⋊C4C3×C22⋊D512yes—
255C22⋊C4—24no—
256C22⋊C4—22no—
257C22⋊C4—204no—
258C42—22no—
259C42—102no—
260C3×C5#185611yescharacteristic, complemented, Hall
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—24no—
264C22×C3—44no—
265C22×C3—42no—
266C22×C3—42no—
267C22×C3—82no—
268C22×C3C2×#68311yescharacteristic
269C22×C3#407511yescharacteristic
270C22×C3#409911yescharacteristic
271C3×C4—42no—
272C3×C4—42no—
273C3×C4—202no—
274C3×C4—401no—
275C3×C4#407012yes—
276C3×C4C4×C22⋊D512yes—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—44no—
280C2×C5C3×#38511yescharacteristic
281C2×C5C3×#45311yescharacteristic
282C2×C5C3×#45511yescharacteristic
283C23—22no—
284C23—22no—
285C23—42no—
286C23—42no—
287C23C3×#68314yes—
288C23C2×C3×C22⋊D511yescharacteristic
289D4—24no—
290D4—24no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—102no—
296C2×C4—201no—
297C2×C4—201no—
298C2×C4—202no—
299C2×C4—201no—
300C2×C4C2×C3×Dic1011yescharacteristic
301C2×C4C2×C3×C4×D511yescharacteristic
302C2×C4C3×#70912yes—
303C2×C4C2×C3×C22⋊D512yes—
304C8—104no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—44no—
308C2×C3#6549911yescharacteristic
309C2×C3#6553011yescharacteristic
310C2×C3#6553111yescharacteristic
311C5C3×#185611yescharacteristic, complemented, Sylow
312C22—21no—
313C22—21no—
314C22—24no—
315C22—44no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22C2×C3×#68311yescharacteristic
320C22C3×#407511yescharacteristic
321C22C3×#409911yescharacteristic
322C4—42no—
323C4—42no—
324C4—202no—
325C4—401no—
326C4C3×#407012yes—
327C4C3×C4×C22⋊D512yes—
328C3#1060244011yescharacteristic, direct product factor, Sylow
329C2—21no—
330C2—21no—
331C2—44no—
332C2C3×#6549911yescharacteristic
333C2C3×#6553011yescharacteristic
334C2C3×#6553111yescharacteristic
subgroupG/H
centerC22×C3#4099
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#518C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#518D5
hypocenterC5C3×#1856
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#518

Complements

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

NH ≅ G/Ntype
4. C3×#65284C2semidirect
5. C3×#64752C2semidirect
6. #10602440C3direct (N × H)
16. C3×#3965C4semidirect
23. #65284C2×C3semidirect
24. #64752C2×C3semidirect
44. C3×#681C2×C4semidirect
60. #3965C3×C4semidirect
117. #681C2×C3×C4semidirect
260. C3×C5#1856semidirect
311. C5C3×#1856semidirect
328. C3#10602440direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5182
C3×#655102
C2×C3×#39652
C3×#652842
C3×#647522
#106024403
C3×#18565