Finite Group Databasebeta

← C3×#10600329 #14309000

Subgroups — C3×#10600329 #14309000

Order 1920.

580 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 138 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×#65817C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic
3C3×#65500C212yesmaximal
4C3×#64747C212yesmaximal
5C3×#64746C211yesmaximal, characteristic
6#10600329C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×C3×C5×C22⋊C4C2211yescharacteristic
10C2×C3×C22⋊Dic5C2212yes—
11C2×C3×C22⋊Dic5C2212yes—
12C3×#4070—22no—
13C3×#4024—24no—
14C3×C5×#95—22no—
15C3×#3963—24no—
16C3×#2030—51nomaximal, Hall
17#65817C2×C311yescharacteristic
18C5×#381C2×C311yescharacteristic
19#65500C2×C312yes—
20#64747C2×C312yes—
21#64746C2×C311yescharacteristic
22C24×C3×C5C2311yescharacteristic
23C22×C3×C4×C5—22no—
24C22×C3×C4×C5—21no—
25C22×C3×C4×C5—21no—
26C22×C3×C4×C5—22no—
27C22×C3×C4×C5—21no—
28C22×C3×C4×C5D412yes—
29C22×C3×C4×C5Q812yescomplemented
30C22×C3×Dic5—22no—
31C22×C3×Dic5D414yes—
32C2×C3×Dic10—22no—
33C3×C5×C22⋊C4—22no—
34C3×C5×C22⋊C4—22no—
35C3×C22⋊Dic5—22no—
36C3×C22⋊Dic5—22no—
37C3×C22⋊Dic5—22no—
38C3×C22⋊Dic5—22no—
39C3×C4⋊Dic5—22no—
40C3×#683—24no—
41C3×#543—51no—
42C3×#381—52no—
43C3×#381D511yescharacteristic
44C3×#342—51no—
45C3×#342—52no—
46C23×C4×C5C22×C311yescharacteristic
47C2×C5×C22⋊C4C22×C311yescharacteristic
48C2×C5×C22⋊C4C22×C311yescharacteristic
49C2×C22⋊Dic5C22×C312yes—
50C2×C22⋊Dic5C22×C312yes—
51#4070—22no—
52#4024—24no—
53C5×#95—22no—
54#3963—24no—
55#2030—51noSylow
56C23×C3×C5—42no—
57C23×C3×C5C2×D412yes—
58C23×C3×C5C2×D411yescharacteristic
59C23×C3×C5C2×Q811yescharacteristic
60C23×C3×C5#4111yescharacteristic
61C23×C3×C5#4112yes—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—24no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5—42no—
67C2×C3×C4×C5—41no—
68C2×C3×C4×C5—42no—
69C2×C3×C4×C5—42no—
70C2×C3×C4×C5—41no—
71C2×C3×Dic5—24no—
72C2×C3×Dic5—44no—
73C2×C3×Dic5—44no—
74C2×C3×Dic5—42no—
75C3×Dic10—82no—
76C23×C3×C4C2×D511yescharacteristic
77C3×C22⋊Q8—104no—
78C3×C22⋊Q8—102no—
79C2×C3×C22⋊C4—52no—
80C2×C3×C22⋊C4—52no—
81C2×C3×C22⋊C4C2×D511yescharacteristic
82C2×C3×C22⋊C4C2×D511yescharacteristic
83C3×#95—22no—
84C3×#95—104no—
85C24×C5C23×C311yescharacteristic
86C22×C4×C5—22no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—22no—
90C22×C4×C5—21no—
91C22×C4×C5C3×D412yes—
92C22×C4×C5C3×Q812yescomplemented
93C22×Dic5—22no—
94C22×Dic5C3×D414yes—
95C2×Dic10—22no—
96C5×C22⋊C4—22no—
97C5×C22⋊C4—22no—
98C22⋊Dic5—22no—
99C22⋊Dic5—22no—
100C22⋊Dic5—22no—
101C22⋊Dic5—22no—
102C4⋊Dic5—22no—
103#683—24no—
104#543—51no—
105#381—52no—
106#381C3×D511yescharacteristic
107#342—51no—
108#342—52no—
109C22×C3×C5—24no—
110C22×C3×C5—22no—
111C22×C3×C5—41no—
112C22×C3×C5—41no—
113C22×C3×C5—42no—
114C22×C3×C5#12011yescharacteristic
115C22×C3×C5C22⋊Q812yes—
116C22×C3×C5C22⋊Q811yescharacteristic
117C22×C3×C5#12412yes—
118C22×C3×C5#12411yescharacteristic
119C3×C4×C5—42no—
120C3×C4×C5—42no—
121C3×C4×C5—81no—
122C3×Dic5—44no—
123C3×Dic5—82no—
124C24×C3C22×D511yescharacteristic
125C2×C3×Q8—102no—
126C22×C3×C4—21no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—54no—
132C22×C3×C4—102no—
133C22×C3×C4Dic1012yescomplemented
134C22×C3×C4C22⋊D512yes—
135C3×C4⋊C4—104no—
136C3×C4⋊C4—102no—
137C3×C22⋊C4—22no—
138C3×C22⋊C4—22no—
139C3×C22⋊C4—102no—
140C3×C22⋊C4—102no—
141C3×C22⋊C4—102no—
142C3×C22⋊C4—102no—
143C23×C5—42no—
144C23×C5C2×C3×D412yes—
145C23×C5C2×C3×D411yescharacteristic
146C23×C5C2×C3×Q811yescharacteristic
147C23×C5C3×#4111yescharacteristic
148C23×C5C3×#4112yes—
149C2×C4×C5—22no—
150C2×C4×C5—24no—
151C2×C4×C5—22no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—42no—
155C2×C4×C5—42no—
156C2×C4×C5—42no—
157C2×C4×C5—41no—
158C2×Dic5—24no—
159C2×Dic5—44no—
160C2×Dic5—44no—
161C2×Dic5—42no—
162Dic10—82no—
163C23×C4C2×C3×D511yescharacteristic
164C22⋊Q8—104no—
165C22⋊Q8—102no—
166C2×C22⋊C4—52no—
167C2×C22⋊C4—52no—
168C2×C22⋊C4C2×C3×D511yescharacteristic
169C2×C22⋊C4C2×C3×D511yescharacteristic
170#95—22no—
171#95—104no—
172C2×C3×C5—22no—
173C2×C3×C5—21no—
174C2×C3×C5—22no—
175C2×C3×C5—21no—
176C2×C3×C5#39311yescharacteristic
177C2×C3×C5#45812yes—
178C23×C3—42no—
179C23×C3C2×Dic1011yescharacteristic
180C23×C3#70911yescharacteristic
181C23×C3D4×D512yes—
182C23×C3#71112yes—
183C23×C3C2×C22⋊D511yescharacteristic
184C3×Q8—402no—
185C2×C3×C4—24no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—42no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4—41no—
194C2×C3×C4—104no—
195C2×C3×C4—204no—
196C2×C3×C4—204no—
197C2×C3×C4—202no—
198C22×C5—24no—
199C22×C5—22no—
200C22×C5—41no—
201C22×C5—41no—
202C22×C5—42no—
203C22×C5C3×#12011yescharacteristic
204C22×C5C3×C22⋊Q812yes—
205C22×C5C3×C22⋊Q811yescharacteristic
206C22×C5C3×#12411yescharacteristic
207C22×C5C3×#12412yes—
208C4×C5—42no—
209C4×C5—42no—
210C4×C5—81no—
211Dic5—44no—
212Dic5—82no—
213C24C22×C3×D511yescharacteristic
214C2×Q8—102no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—54no—
221C22×C4—102no—
222C22×C4C3×Dic1012yescomplemented
223C22×C4C3×C22⋊D512yes—
224C4⋊C4—104no—
225C4⋊C4—102no—
226C22⋊C4—22no—
227C22⋊C4—22no—
228C22⋊C4—102no—
229C22⋊C4—102no—
230C22⋊C4—102no—
231C22⋊C4—102no—
232C3×C5#203011yescharacteristic, complemented, Hall
233C22×C3—22no—
234C22×C3—24no—
235C22×C3—41no—
236C22×C3—41no—
237C22×C3—42no—
238C22×C3#402412yes—
239C22×C3#403112yes—
240C22×C3#407011yescharacteristic
241C22×C3#408211yescharacteristic
242C22×C3#408311yescharacteristic
243C3×C4—42no—
244C3×C4—42no—
245C3×C4—81no—
246C3×C4—204no—
247C3×C4—402no—
248C2×C5—22no—
249C2×C5—21no—
250C2×C5—22no—
251C2×C5—21no—
252C2×C5C3×#39311yescharacteristic
253C2×C5C3×#45812yes—
254C23—42no—
255C23C2×C3×Dic1011yescharacteristic
256C23C3×#70911yescharacteristic
257C23C3×D4×D512yes—
258C23C3×#71112yes—
259C23C2×C3×C22⋊D511yescharacteristic
260Q8—402no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—104no—
271C2×C4—204no—
272C2×C4—204no—
273C2×C4—202no—
274C2×C3—21no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—21no—
278C2×C3#6523611yescharacteristic
279C2×C3#6534212yes—
280C5C3×#203011yescharacteristic, complemented, Sylow
281C22—22no—
282C22—24no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22C3×#402412yes—
287C22C3×#403112yes—
288C22C3×#407011yescharacteristic
289C22C3×#408211yescharacteristic
290C22C3×#408311yescharacteristic
291C4—42no—
292C4—42no—
293C4—81no—
294C4—204no—
295C4—402no—
296C3#1060032911yescharacteristic, direct product factor, Sylow
297C2—21no—
298C2—22no—
299C2—22no—
300C2—21no—
301C2C3×#6523611yescharacteristic
302C2C3×#6534212yes—
subgroupG/H
centerC22×C3#4083
commutator, cosocleC24×C5C23×C3
FrattiniC24C22×C3×D5
FittingC3×C5×#381C2
socleC22×C3×C5#120
prime radicalC24×C3×C5C23
hypercenterC3×#381D5
hypocenterC5C3×#2030
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
6. #10600329C3direct (N × H)
29. C22×C3×C4×C5Q8semidirect
92. C22×C4×C5C3×Q8semidirect
133. C22×C3×C4Dic10semidirect
222. C22×C4C3×Dic10semidirect
232. C3×C5#2030semidirect
280. C5C3×#2030semidirect
296. C3#10600329direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658172
C3×C5×#3812
C3×#655002
C3×#647472
C3×#647462
#106003293
C3×#20305