Finite Group Databasebeta

← C3×#10601785 #14316875

Subgroups — C3×#10601785 #14316875

Order 1920.

452 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 82 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×#66006C211yesmaximal, characteristic, complemented
2C3×C5×#455C211yesmaximal, characteristic
3C3×#65532C212yesmaximal
4C3×#64761C211yesmaximal, characteristic, complemented
5C3×#64696C212yesmaximal, complemented
6#10601785C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×H(5,𝔽2)C2211yescharacteristic
8C3×C5×#137—21no—
9C3×C5×#124C2211yescharacteristic
10C3×#4090—21no—
11C3×#4081—22no—
12C3×#4081C2212yes—
13C3×#4025—22no—
14C3×#4024—22no—
15C3×#4016—21no—
16C3×C5×#104—21no—
17C3×C5×#100C2211yescharacteristic
18C3×#3966—22no—
19C3×#3966C2212yes—
20C3×#2201—51nomaximal, Hall
21#66006C2×C311yescharacteristic, complemented
22C5×#455C2×C311yescharacteristic
23#65532C2×C312yes—
24#64761C2×C311yescharacteristic, complemented
25#64696C2×C312yescomplemented
26C3×C5×#41—21no—
27C3×C5×#41—41no—
28C2×C3×C5×Q8D411yescharacteristic
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—41no—
31C2×C3×C5×D4C2311yescharacteristic
32C22×C3×Dic5D412yes—
33C2×C3×Dic10—21no—
34C3×C5×Q16—41no—
35C3×C5×SD16—41no—
36C3×C5×M16—21no—
37C3×C5×C22⋊C4—22no—
38C3×C42×C5D411yescharacteristic
39C3×C22⋊Dic5—22no—
40C3×C22⋊Dic5—22no—
41C3×C22⋊Dic5—42no—
42C3×C22⋊Dic5D412yes—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×#683—22no—
46C3×#683—22no—
47C3×#683—22no—
48C3×#683—42no—
49C3×C4×Dic5—21no—
50C3×#563—51no—
51C3×#458—52no—
52C3×#455D511yescharacteristic
53C3×#354—51no—
54C3×#352—52no—
55C5×H(5,𝔽2)C22×C311yescharacteristic
56C5×#137—21no—
57C5×#124C22×C311yescharacteristic
58#4090—21no—
59#4081—22no—
60#4081C22×C312yes—
61#4025—22no—
62#4024—22no—
63#4016—21no—
64C5×#104—21no—
65C5×#100C22×C311yescharacteristic
66#3966—22no—
67#3966C22×C312yes—
68#2201—51noSylow
69C23×C3×C5—22no—
70C23×C3×C5C2×D412yes—
71C3×C5×Q8—21no—
72C3×C5×Q8—41no—
73C3×C5×D4—21no—
74C3×C5×D4—41no—
75C3×C5×D4—42no—
76C3×C5×D4—41no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×Dic5—22no—
83C2×C3×Dic5—22no—
84C2×C3×Dic5—42no—
85C2×C3×Dic5—42no—
86C3×Dic10—81no—
87C3×C5×C8—41no—
88C3×H(5,𝔽2)C2×D511yescharacteristic
89C3×#137—21no—
90C3×C4⋊Q8—101no—
91C3×#126—102no—
92C3×#125—101no—
93C3×#124C2×D511yescharacteristic
94C3×#123—52no—
95C3×#123—102no—
96C3×C22⋊Q8—102no—
97C3×#104—21no—
98C3×#100C2×D511yescharacteristic
99C3×#99—52no—
100C3×#99—102no—
101C5×#41—21no—
102C5×#41—41no—
103C2×C5×Q8C3×D411yescharacteristic
104C2×C5×D4—22no—
105C2×C5×D4—41no—
106C2×C5×D4C23×C311yescharacteristic
107C22×Dic5C3×D412yes—
108C2×Dic10—21no—
109C5×Q16—41no—
110C5×SD16—41no—
111C5×M16—21no—
112C5×C22⋊C4—22no—
113C42×C5C3×D411yescharacteristic
114C22⋊Dic5—22no—
115C22⋊Dic5—22no—
116C22⋊Dic5—42no—
117C22⋊Dic5C3×D412yes—
118C4⋊Dic5—21no—
119C4⋊Dic5—21no—
120#683—22no—
121#683—22no—
122#683—22no—
123#683—42no—
124C4×Dic5—21no—
125#563—51no—
126#458—52no—
127#455C3×D511yescharacteristic
128#354—51no—
129#352—52no—
130C22×C3×C5—22no—
131C22×C3×C5—42no—
132C22×C3×C5—41no—
133C22×C3×C5—82no—
134C22×C3×C5#12011yescharacteristic
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138C3×C4×C5—41no—
139C3×Dic5—42no—
140C3×Dic5—42no—
141C3×Dic5—82no—
142C3×#41—21no—
143C3×#41—41no—
144C2×C3×Q8—101no—
145C2×C3×Q8C22⋊D511yescharacteristic
146C2×C3×D4—22no—
147C2×C3×D4—41no—
148C2×C3×D4C22×D511yescharacteristic
149C22×C3×C4—52no—
150C3×Q16—41no—
151C3×SD16—41no—
152C3×M16—21no—
153C3×C4⋊C4—102no—
154C3×C4⋊C4—102no—
155C3×C4⋊C4—101no—
156C3×C4⋊C4—101no—
157C3×C4⋊C4—102no—
158C3×C4⋊C4—202no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—52no—
161C3×C22⋊C4—102no—
162C3×C22⋊C4—102no—
163C3×C22⋊C4—202no—
164C3×C42—101no—
165C3×C42C22⋊D511yescharacteristic
166C23×C5—22no—
167C23×C5C2×C3×D412yes—
168C5×Q8—21no—
169C5×Q8—41no—
170C5×D4—21no—
171C5×D4—41no—
172C5×D4—42no—
173C5×D4—41no—
174C2×C4×C5—22no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—41no—
178C2×C4×C5C2×C3×D411yescharacteristic
179C2×Dic5—22no—
180C2×Dic5—22no—
181C2×Dic5—42no—
182C2×Dic5—42no—
183Dic10—81no—
184C5×C8—41no—
185H(5,𝔽2)C2×C3×D511yescharacteristic
186#137—21no—
187C4⋊Q8—101no—
188#126—102no—
189#125—101no—
190#124C2×C3×D511yescharacteristic
191#123—52no—
192#123—102no—
193C22⋊Q8—102no—
194#104—21no—
195#100C2×C3×D511yescharacteristic
196#99—52no—
197#99—102no—
198C2×C3×C5—21no—
199C2×C3×C5—42no—
200C2×C3×C5—81no—
201C2×C3×C5B(4,𝔽2)11yescharacteristic
202C23×C3—22no—
203C23×C3D4×D512yes—
204C3×Q8—21no—
205C3×Q8—41no—
206C3×Q8—401no—
207C3×D4—21no—
208C3×D4—41no—
209C3×D4—42no—
210C3×D4—41no—
211C2×C3×C4—22no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—41no—
215C2×C3×C4—102no—
216C2×C3×C4—102no—
217C2×C3×C4—202no—
218C2×C3×C4—202no—
219C2×C3×C4C2×C22⋊D511yescharacteristic
220C3×C8—41no—
221C22×C5—22no—
222C22×C5—42no—
223C22×C5—41no—
224C22×C5—82no—
225C22×C5C3×#12011yescharacteristic
226C4×C5—21no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—41no—
230Dic5—42no—
231Dic5—42no—
232Dic5—82no—
233#41—21no—
234#41—41no—
235C2×Q8—101no—
236C2×Q8C3×C22⋊D511yescharacteristic
237C2×D4—22no—
238C2×D4—41no—
239C2×D4C22×C3×D511yescharacteristic
240C22×C4—52no—
241Q16—41no—
242SD16—41no—
243M16—21no—
244C4⋊C4—101no—
245C4⋊C4—102no—
246C4⋊C4—102no—
247C4⋊C4—101no—
248C4⋊C4—102no—
249C4⋊C4—202no—
250C22⋊C4—22no—
251C22⋊C4—52no—
252C22⋊C4—102no—
253C22⋊C4—102no—
254C22⋊C4—202no—
255C42—101no—
256C42C3×C22⋊D511yescharacteristic
257C3×C5#220111yescharacteristic, complemented, Hall
258C22×C3—22no—
259C22×C3—42no—
260C22×C3—41no—
261C22×C3—82no—
262C22×C3#408311yescharacteristic
263C3×C4—21no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4—202no—
268C3×C4—202no—
269C3×C4—402no—
270C2×C5—21no—
271C2×C5—42no—
272C2×C5—81no—
273C2×C5C3×B(4,𝔽2)11yescharacteristic
274C23—22no—
275C23C3×D4×D512yes—
276Q8—21no—
277Q8—41no—
278Q8—401no—
279D4—21no—
280D4—41no—
281D4—42no—
282D4—41no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—202no—
290C2×C4—202no—
291C2×C4C2×C3×C22⋊D511yescharacteristic
292C8—41no—
293C2×C3—21no—
294C2×C3—42no—
295C2×C3—81no—
296C2×C3#6532111yescharacteristic
297C5C3×#220111yescharacteristic, complemented, Sylow
298C22—22no—
299C22—42no—
300C22—41no—
301C22—82no—
302C22C3×#408311yescharacteristic
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—202no—
308C4—202no—
309C4—402no—
310C3#1060178511yescharacteristic, direct product factor, Sylow
311C2—21no—
312C2—42no—
313C2—81no—
314C2C3×#6532111yescharacteristic
subgroupG/H
centerC2×C3#65321
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#455C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×C5×H(5,𝔽2)C22
hypercenterC3×#455D5
hypocenterC5C3×#2201
LCSG ▷ C2×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#455

Complements

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

NH ≅ G/Ntype
1. C3×#66006C2semidirect
4. C3×#64761C2semidirect
5. C3×#64696C2semidirect
6. #10601785C3direct (N × H)
21. #66006C2×C3semidirect
24. #64761C2×C3semidirect
25. #64696C2×C3semidirect
257. C3×C5#2201semidirect
297. C5C3×#2201semidirect
310. C3#10601785direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660062
C3×C5×#4552
C3×#655322
C3×#647612
C3×#646962
#106017853
C3×#22015