Finite Group Databasebeta

← C3×#10602659 #14303086

Subgroups — C3×#10602659 #14303086

Order 1920.

616 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
1C3×C5×#536C211yesmaximal, characteristic
2C3×#66153C211yesmaximal, characteristic
3C3×#65526C211yesmaximal, characteristic
4C2×C3×#3968C212yesmaximal, complemented
5C3×#64753C212yesmaximal, complemented
6#10602659C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C22×C3×C5×Q8C2211yescharacteristic
9C3×C5×C4⋊Q8—21no—
10C3×C5×#124—21no—
11C3×C5×#123C414yes—
12C3×C5×C22⋊Q8—22no—
13C3×C5×#117C2211yescharacteristic
14C3×#4094—24no—
15C2×C3×#681—22no—
16C2×C3×#681C2212yes—
17C2×C3×#681C2212yes—
18C3×#3968—21no—
19C3×#3968—24no—
20C3×#3965—21no—
21C3×#1915—51nomaximal, Hall
22C5×#536C2×C311yescharacteristic
23#66153C2×C311yescharacteristic
24#65526C2×C311yescharacteristic
25C2×#3968C2×C312yescomplemented
26#64753C2×C312yescomplemented
27C3×C5×#41—22no—
28C3×C5×#41—22no—
29C2×C3×C5×Q8—22no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×Q8—21no—
32C2×C3×C5×Q8—22no—
33C2×C3×C5×Q8D411yescharacteristic
34C2×C3×C5×D4C2×C412yes—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5C2×C412yes—
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C3×C5×C4⋊C4—24no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C22⋊C4—24no—
42C3×C5×C22⋊C4C2×C412yes—
43C3×C42×C5—21no—
44C3×#681—24no—
45C3×#681—22no—
46C3×#681—22no—
47C3×#681—22no—
48C3×#681D414yes—
49C2×C3×#168—24no—
50C2×C3×#168—22no—
51C2×C3×#168—22no—
52C3×#568—51no—
53C3×#536D511yescharacteristic
54C3×#413—51no—
55C2×C3×#101—52no—
56C3×#344—52no—
57C2×C5×#41C22×C311yescharacteristic
58C22×C5×Q8C22×C311yescharacteristic
59C5×C4⋊Q8—21no—
60C5×#124—21no—
61C5×#123C3×C414yes—
62C5×C22⋊Q8—22no—
63C5×#117C22×C311yescharacteristic
64#4094—24no—
65C2×#681—22no—
66C2×#681C22×C312yes—
67C2×#681C22×C312yes—
68#3968—21no—
69#3968—24no—
70#3965—21no—
71#1915—51noSylow
72C23×C3×C5C22⋊C412yes—
73C23×C3×C5C22×C411yescharacteristic
74C3×C5×Q8—22no—
75C3×C5×Q8—41no—
76C3×C5×Q8—42no—
77C3×C5×Q8—41no—
78C3×C5×D4—24no—
79C3×C5×D4—22no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—24no—
85C2×C3×C4×C5C22⋊C412yes—
86C2×C3×C4×C5C2×D412yes—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5#4112yes—
90C3×#168—24no—
91C3×#168—42no—
92C2×C3×#41C2×D511yescharacteristic
93C22×C3×Q8C2×D511yescharacteristic
94C3×#131—104no—
95C2×C3×M16—52no—
96C2×C3×M16—52no—
97C2×C3×M16—102no—
98C3×C4⋊Q8—21no—
99C3×#124—21no—
100C3×#123Dic514yes—
101C3×C22⋊Q8—22no—
102C3×#117C2×D511yescharacteristic
103C3×#101—104no—
104C3×#101—101no—
105C3×#100—101no—
106C5×#41—22no—
107C5×#41—22no—
108C2×C5×Q8—21no—
109C2×C5×Q8—21no—
110C2×C5×Q8—22no—
111C2×C5×Q8—22no—
112C2×C5×Q8C3×D411yescharacteristic
113C2×C5×D4C2×C3×C412yes—
114C2×C5×D4C3×D411yescharacteristic
115C22×C4×C5C2×C3×C412yes—
116C22×C4×C5C3×D412yes—
117C22×C4×C5C23×C311yescharacteristic
118C5×C4⋊C4—24no—
119C5×C4⋊C4—21no—
120C5×C22⋊C4—24no—
121C5×C22⋊C4C2×C3×C412yes—
122C42×C5—21no—
123#681—24no—
124#681—22no—
125#681—22no—
126#681—22no—
127#681C3×D414yes—
128C2×#168—24no—
129C2×#168—22no—
130C2×#168—22no—
131#568—51no—
132#536C3×D511yescharacteristic
133#413—51no—
134C2×#101—52no—
135#344—52no—
136C22×C3×C5—22no—
137C22×C3×C5—41no—
138C22×C3×C5—42no—
139C22×C3×C5C2×C22⋊C411yescharacteristic
140C22×C3×C5C4×D412yes—
141C3×C4×C5—22no—
142C3×C4×C5—42no—
143C3×C4×C5—42no—
144C3×C4×C5#12011yescharacteristic
145C3×C4×C5#12112yes—
146C3×C4×C5#12311yescharacteristic
147C3×#41—22no—
148C3×#41—22no—
149C2×C3×Q8—22no—
150C2×C3×Q8—22no—
151C2×C3×Q8—21no—
152C2×C3×Q8—21no—
153C2×C3×Q8C22⋊D511yescharacteristic
154C2×C3×D4C2×Dic512yes—
155C2×C3×D4C22⋊D511yescharacteristic
156C22×C3×C4C2×Dic512yes—
157C22×C3×C4C22⋊D512yes—
158C22×C3×C4C22×D511yescharacteristic
159C3×M16—54no—
160C3×M16—104no—
161C3×M16—102no—
162C3×M16—102no—
163C3×M16—102no—
164C2×C3×C8—104no—
165C2×C3×C8—102no—
166C2×C3×C8—102no—
167C3×C4⋊C4—24no—
168C3×C4⋊C4—21no—
169C3×C22⋊C4—24no—
170C3×C22⋊C4C2×Dic512yes—
171C3×C42—21no—
172C23×C5C3×C22⋊C412yes—
173C23×C5C22×C3×C411yescharacteristic
174C5×Q8—22no—
175C5×Q8—41no—
176C5×Q8—42no—
177C5×Q8—41no—
178C5×D4—24no—
179C5×D4—22no—
180C2×C4×C5—22no—
181C2×C4×C5—22no—
182C2×C4×C5—22no—
183C2×C4×C5—22no—
184C2×C4×C5—24no—
185C2×C4×C5C3×C22⋊C412yes—
186C2×C4×C5C2×C3×D412yes—
187C2×C4×C5C2×C3×D411yescharacteristic
188C2×C4×C5C2×C3×D411yescharacteristic
189C2×C4×C5C3×#4112yes—
190#168—24no—
191#168—42no—
192C2×#41C2×C3×D511yescharacteristic
193C22×Q8C2×C3×D511yescharacteristic
194#131—104no—
195C2×M16—52no—
196C2×M16—52no—
197C2×M16—102no—
198C4⋊Q8—21no—
199#124—21no—
200#123C3×Dic514yes—
201C22⋊Q8—22no—
202#117C2×C3×D511yescharacteristic
203#101—104no—
204#101—101no—
205#100—101no—
206C2×C3×C5—21no—
207C2×C3×C5—22no—
208C2×C3×C5—42no—
209C2×C3×C5#38611yescharacteristic
210C23×C3C22⋊Dic512yes—
211C23×C3C22×Dic511yescharacteristic
212C3×Q8—22no—
213C3×Q8—41no—
214C3×Q8—41no—
215C3×Q8—42no—
216C3×D4—24no—
217C3×D4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—24no—
223C2×C3×C4C22⋊Dic512yes—
224C2×C3×C4D4×D512yes—
225C2×C3×C4#71112yes—
226C2×C3×C4C2×C22⋊D511yescharacteristic
227C2×C3×C4C2×C22⋊D511yescharacteristic
228C3×C8—104no—
229C3×C8—202no—
230C22×C5—22no—
231C22×C5—41no—
232C22×C5—42no—
233C22×C5C2×C3×C22⋊C411yescharacteristic
234C22×C5C3×C4×D412yes—
235C4×C5—22no—
236C4×C5—42no—
237C4×C5—42no—
238C4×C5C3×#12011yescharacteristic
239C4×C5C3×#12112yes—
240C4×C5C3×#12311yescharacteristic
241#41—22no—
242#41—22no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8C3×C22⋊D511yescharacteristic
248C2×D4C2×C3×Dic512yes—
249C2×D4C3×C22⋊D511yescharacteristic
250C22×C4C2×C3×Dic512yes—
251C22×C4C3×C22⋊D512yes—
252C22×C4C22×C3×D511yescharacteristic
253M16—54no—
254M16—104no—
255M16—102no—
256M16—102no—
257M16—102no—
258C2×C8—104no—
259C2×C8—102no—
260C2×C8—102no—
261C4⋊C4—24no—
262C4⋊C4—21no—
263C22⋊C4—24no—
264C22⋊C4C2×C3×Dic512yes—
265C42—21no—
266C3×C5#191511yescharacteristic, complemented, Hall
267C22×C3—22no—
268C22×C3—41no—
269C22×C3—42no—
270C22×C3D4×Dic512yes—
271C22×C3C2×C22⋊Dic511yescharacteristic
272C3×C4—22no—
273C3×C4—42no—
274C3×C4—42no—
275C3×C4#408111yescharacteristic
276C3×C4#408311yescharacteristic
277C3×C4#408512yes—
278C2×C5—21no—
279C2×C5—22no—
280C2×C5—42no—
281C2×C5C3×#38611yescharacteristic
282C23C3×C22⋊Dic512yes—
283C23C22×C3×Dic511yescharacteristic
284Q8—22no—
285Q8—41no—
286Q8—41no—
287Q8—42no—
288D4—24no—
289D4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4C3×C22⋊Dic512yes—
296C2×C4C3×D4×D512yes—
297C2×C4C3×#71112yes—
298C2×C4C2×C3×C22⋊D511yescharacteristic
299C2×C4C2×C3×C22⋊D511yescharacteristic
300C8—104no—
301C8—202no—
302C2×C3—21no—
303C2×C3—22no—
304C2×C3—42no—
305C2×C3#6550911yescharacteristic
306C5C3×#191511yescharacteristic, complemented, Sylow
307C22—22no—
308C22—41no—
309C22—42no—
310C22C3×D4×Dic512yes—
311C22C2×C3×C22⋊Dic511yescharacteristic
312C4—22no—
313C4—42no—
314C4—42no—
315C4C3×#408111yescharacteristic
316C4C3×#408311yescharacteristic
317C4C3×#408512yes—
318C3#1060265911yescharacteristic, direct product factor, Sylow
319C2—21no—
320C2—22no—
321C2—42no—
322C2C3×#6550911yescharacteristic
subgroupG/H
centerC2×C3#65509
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#536C2
socleC2×C3×C5#386
prime radicalC2×C3×C5×#41C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#536D5
hypocenterC5C3×#1915
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#536

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3968C2semidirect
5. C3×#64753C2semidirect
6. #10602659C3direct (N × H)
25. C2×#3968C2×C3semidirect
26. #64753C2×C3semidirect
266. C3×C5#1915semidirect
306. C5C3×#1915semidirect
318. C3#10602659direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5362
C3×#661532
C3×#655262
C2×C3×#39682
C3×#647532
#106026593
C3×#19155