Finite Group Databasebeta

← C3×#10601779 #14316734

Subgroups — C3×#10601779 #14316734

Order 1920.

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

normal subgroups only

This group has 492 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×#66047C211yesmaximal, characteristic, complemented
2C3×C5×#453C211yesmaximal, characteristic
3C3×#65532C212yesmaximal, complemented
4C3×#64765C211yesmaximal, characteristic, complemented
5C3×#64696C212yesmaximal, complemented
6#10601779C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×H(5,𝔽2)C2211yescharacteristic
8C3×C5×AGL(1,ℤ/8)—21no—
9C3×C5×#127C2211yescharacteristic
10C3×#4082—22no—
11C3×#4081—21no—
12C3×#4081—22no—
13C3×#4081C2212yes—
14C3×D4×Dic5—22no—
15C3×C4×Dic10—21no—
16C3×C5×#104—21no—
17C3×C5×#100C2211yescharacteristic
18C3×#3966—22no—
19C3×#3966C2212yes—
20C3×#2198—51nomaximal, Hall
21#66047C2×C311yescharacteristic, complemented
22C5×#453C2×C311yescharacteristic
23#65532C2×C312yescomplemented
24#64765C2×C311yescharacteristic, complemented
25#64696C2×C312yescomplemented
26C3×C5×#41—21no—
27C3×C5×#41—41no—
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—41no—
31C2×C3×C5×D4D411yescharacteristic
32C2×C3×C5×D4C2311yescharacteristic
33C22×C3×Dic5—21no—
34C22×C3×Dic5D412yes—
35C2×C3×Dic10—21no—
36C3×C5×SD16—41no—
37C3×C5×D8—41no—
38C3×C5×M16—21no—
39C3×C42×C5D411yescharacteristic
40C3×C22⋊Dic5—22no—
41C3×C22⋊Dic5—21no—
42C3×C22⋊Dic5—22no—
43C3×C22⋊Dic5—22no—
44C3×C22⋊Dic5—42no—
45C3×C22⋊Dic5D412yes—
46C3×C4⋊Dic5—21no—
47C3×#683—22no—
48C3×#683—42no—
49C3×C4×Dic5—22no—
50C3×#559—51no—
51C3×#458—52no—
52C3×#453D511yescharacteristic
53C3×#353—51no—
54C3×#352—52no—
55C5×H(5,𝔽2)C22×C311yescharacteristic
56C5×AGL(1,ℤ/8)—21no—
57C5×#127C22×C311yescharacteristic
58#4082—22no—
59#4081—21no—
60#4081—22no—
61#4081C22×C312yes—
62D4×Dic5—22no—
63C4×Dic10—21no—
64C5×#104—21no—
65C5×#100C22×C311yescharacteristic
66#3966—22no—
67#3966C22×C312yes—
68#2198—51noSylow
69C23×C3×C5—22no—
70C23×C3×C5—21no—
71C23×C3×C5C2×D412yes—
72C3×C5×Q8—21no—
73C3×C5×D4—21no—
74C3×C5×D4—41no—
75C3×C5×D4—44no—
76C3×C5×D4—41no—
77C3×C5×D4—42no—
78C3×C5×D4—41no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×Dic5—22no—
84C2×C3×Dic5—22no—
85C2×C3×Dic5—42no—
86C2×C3×Dic5—42no—
87C2×C3×Dic5—81no—
88C3×Dic10—42no—
89C3×C5×C8—41no—
90C3×H(5,𝔽2)C2×D511yescharacteristic
91C3×AGL(1,ℤ/8)—21no—
92C3×#127C2×D511yescharacteristic
93C3×#124—102no—
94C3×#123—52no—
95C3×#123—101no—
96C3×#123—102no—
97C3×C4×Q8—101no—
98C3×C4×D4—102no—
99C3×#104—21no—
100C3×#100C2×D511yescharacteristic
101C3×#99—52no—
102C3×#99—102no—
103C5×#41—21no—
104C5×#41—41no—
105C2×C5×D4—22no—
106C2×C5×D4—22no—
107C2×C5×D4—41no—
108C2×C5×D4C3×D411yescharacteristic
109C2×C5×D4C23×C311yescharacteristic
110C22×Dic5—21no—
111C22×Dic5C3×D412yes—
112C2×Dic10—21no—
113C5×SD16—41no—
114C5×D8—41no—
115C5×M16—21no—
116C42×C5C3×D411yescharacteristic
117C22⋊Dic5—22no—
118C22⋊Dic5—21no—
119C22⋊Dic5—22no—
120C22⋊Dic5—22no—
121C22⋊Dic5—42no—
122C22⋊Dic5C3×D412yes—
123C4⋊Dic5—21no—
124#683—22no—
125#683—42no—
126C4×Dic5—22no—
127#559—51no—
128#458—52no—
129#453C3×D511yescharacteristic
130#353—51no—
131#352—52no—
132C22×C3×C5—22no—
133C22×C3×C5—42no—
134C22×C3×C5—42no—
135C22×C3×C5—41no—
136C22×C3×C5—41no—
137C22×C3×C5—82no—
138C22×C3×C5#12011yescharacteristic
139C3×C4×C5—22no—
140C3×C4×C5—21no—
141C3×C4×C5—41no—
142C3×Dic5—42no—
143C3×Dic5—42no—
144C3×Dic5—82no—
145C3×#41—21no—
146C3×#41—41no—
147C2×C3×Q8—101no—
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—41no—
151C2×C3×D4C22⋊D511yescharacteristic
152C2×C3×D4C22×D511yescharacteristic
153C22×C3×C4—52no—
154C22×C3×C4—101no—
155C3×SD16—41no—
156C3×D8—41no—
157C3×M16—21no—
158C3×C4⋊C4—101no—
159C3×C4⋊C4—102no—
160C3×C4⋊C4—202no—
161C3×C22⋊C4—52no—
162C3×C22⋊C4—102no—
163C3×C22⋊C4—101no—
164C3×C22⋊C4—102no—
165C3×C22⋊C4—102no—
166C3×C22⋊C4—202no—
167C3×C42—102no—
168C3×C42C22⋊D511yescharacteristic
169C23×C5—22no—
170C23×C5—21no—
171C23×C5C2×C3×D412yes—
172C5×Q8—21no—
173C5×D4—21no—
174C5×D4—41no—
175C5×D4—41no—
176C5×D4—44no—
177C5×D4—42no—
178C5×D4—41no—
179C2×C4×C5—21no—
180C2×C4×C5—22no—
181C2×C4×C5—41no—
182C2×C4×C5C2×C3×D411yescharacteristic
183C2×Dic5—22no—
184C2×Dic5—22no—
185C2×Dic5—42no—
186C2×Dic5—42no—
187C2×Dic5—81no—
188Dic10—42no—
189C5×C8—41no—
190H(5,𝔽2)C2×C3×D511yescharacteristic
191AGL(1,ℤ/8)—21no—
192#127C2×C3×D511yescharacteristic
193#124—102no—
194#123—52no—
195#123—101no—
196#123—102no—
197C4×Q8—101no—
198C4×D4—102no—
199#104—21no—
200#100C2×C3×D511yescharacteristic
201#99—52no—
202#99—102no—
203C2×C3×C5—21no—
204C2×C3×C5—42no—
205C2×C3×C5—81no—
206C2×C3×C5—81no—
207C2×C3×C5B(4,𝔽2)11yescharacteristic
208C23×C3—22no—
209C23×C3—21no—
210C23×C3D4×D512yes—
211C3×Q8—21no—
212C3×Q8—202no—
213C3×D4—21no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—44no—
217C3×D4—42no—
218C3×D4—41no—
219C2×C3×C4—21no—
220C2×C3×C4—22no—
221C2×C3×C4—41no—
222C2×C3×C4—102no—
223C2×C3×C4—102no—
224C2×C3×C4—202no—
225C2×C3×C4—202no—
226C2×C3×C4—401no—
227C2×C3×C4C2×C22⋊D511yescharacteristic
228C3×C8—41no—
229C22×C5—22no—
230C22×C5—42no—
231C22×C5—42no—
232C22×C5—41no—
233C22×C5—41no—
234C22×C5—82no—
235C22×C5C3×#12011yescharacteristic
236C4×C5—22no—
237C4×C5—21no—
238C4×C5—41no—
239Dic5—42no—
240Dic5—42no—
241Dic5—82no—
242#41—21no—
243#41—41no—
244C2×Q8—101no—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4C3×C22⋊D511yescharacteristic
249C2×D4C22×C3×D511yescharacteristic
250C22×C4—52no—
251C22×C4—101no—
252SD16—41no—
253D8—41no—
254M16—21no—
255C4⋊C4—101no—
256C4⋊C4—102no—
257C4⋊C4—202no—
258C22⋊C4—52no—
259C22⋊C4—102no—
260C22⋊C4—101no—
261C22⋊C4—102no—
262C22⋊C4—102no—
263C22⋊C4—202no—
264C42—102no—
265C42C3×C22⋊D511yescharacteristic
266C3×C5#219811yescharacteristic, complemented, Hall
267C22×C3—22no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—82no—
273C22×C3#408311yescharacteristic
274C3×C4—22no—
275C3×C4—21no—
276C3×C4—41no—
277C3×C4—202no—
278C3×C4—202no—
279C3×C4—402no—
280C2×C5—21no—
281C2×C5—42no—
282C2×C5—81no—
283C2×C5—81no—
284C2×C5C3×B(4,𝔽2)11yescharacteristic
285C23—22no—
286C23—21no—
287C23C3×D4×D512yes—
288Q8—21no—
289Q8—202no—
290D4—21no—
291D4—41no—
292D4—41no—
293D4—44no—
294D4—42no—
295D4—41no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—102no—
300C2×C4—102no—
301C2×C4—202no—
302C2×C4—202no—
303C2×C4—401no—
304C2×C4C2×C3×C22⋊D511yescharacteristic
305C8—41no—
306C2×C3—21no—
307C2×C3—42no—
308C2×C3—81no—
309C2×C3—81no—
310C2×C3#6532111yescharacteristic
311C5C3×#219811yescharacteristic, complemented, Sylow
312C22—22no—
313C22—42no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—82no—
318C22C3×#408311yescharacteristic
319C4—22no—
320C4—21no—
321C4—41no—
322C4—202no—
323C4—202no—
324C4—402no—
325C3#1060177911yescharacteristic, direct product factor, Sylow
326C2—21no—
327C2—42no—
328C2—81no—
329C2—81no—
330C2C3×#6532111yescharacteristic
subgroupG/H
centerC2×C3#65321
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
Fitting, prime radicalC3×C5×#453C2
socleC2×C3×C5B(4,𝔽2)
hypercenterC3×#453D5
hypocenterC5C3×#2198
LCSG ▷ C2×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#453

Complements

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

NH ≅ G/Ntype
1. C3×#66047C2semidirect
3. C3×#65532C2semidirect
4. C3×#64765C2semidirect
5. C3×#64696C2semidirect
6. #10601779C3direct (N × H)
21. #66047C2×C3semidirect
23. #65532C2×C3semidirect
24. #64765C2×C3semidirect
25. #64696C2×C3semidirect
266. C3×C5#2198semidirect
311. C5C3×#2198semidirect
325. C3#10601779direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660472
C3×C5×#4532
C3×#655322
C3×#647652
C3×#646962
#106017793
C3×#21985