Finite Group Databasebeta

← C3×#10598791 #14279162

Subgroups — C3×#10598791 #14279162

Order 1920.

324 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 80 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×#65761C211yesmaximal, characteristic
2C3×#65745C211yesmaximal, characteristic
3C3×#65418C211yesmaximal, characteristic
4#10598791C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×#709C2211yescharacteristic
6C3×#4130—21no—
7C3×D5⋊M16—21no—
8C2×C3×C5×M16C411yescharacteristic, complemented
9C22×C3×#168C411yescharacteristic, complemented
10C3×#4013—21no—
11C3×#4011—21no—
12C3×#4005C412yescomplemented
13C3×#3999C412yes—
14C3×#3952—21no—
15C3×#3952—21no—
16C3×#1395—51nomaximal, Hall
17#65761C2×C311yescharacteristic
18#65745C2×C311yescharacteristic
19#65418C2×C311yescharacteristic
20C22×C3×C4×C5C2×C411yescharacteristic
21C2×C3×C22⋊D5D411yescharacteristic
22C2×C3×C22⋊D5Q811yescharacteristic
23C3×#709—41no—
24C3×#709—41no—
25C2×C3×D20C2×C411yescharacteristic
26C2×C3×C4×D5D411yescharacteristic
27C2×C3×C4×D5D411yescharacteristic
28C2×C3×Dic10C2×C411yescharacteristic
29C3×C22⋊AGL(1,𝔽5)—22no—
30C3×#704—22no—
31C3×C4⋊AGL(1,𝔽5)—41no—
32C3×C4×AGL(1,𝔽5)—41no—
33C3×#700—41no—
34C3×D5⋊C8—41no—
35C3×C5×M16—41no—
36C2×C3×C5×C8—21no—
37C2×C3×#168—21no—
38C2×C3×#168—41no—
39C3×#413—51no—
40C3×#410—51no—
41C3×#408—51no—
42C2×#709C22×C311yescharacteristic
43#4130—21no—
44D5⋊M16—21no—
45C2×C5×M16C3×C411yescharacteristic, complemented
46C22×#168C3×C411yescharacteristic, complemented
47#4013—21no—
48#4011—21no—
49#4005C3×C412yescomplemented
50#3999C3×C412yes—
51#3952—21no—
52#3952—21no—
53#1395—51noSylow
54C23×C3×C5C4⋊C411yescharacteristic
55C22×C3×D5C22⋊C411yescharacteristic
56C22×C3×D5C4⋊C411yescharacteristic
57C2×C3×AGL(1,𝔽5)—42no—
58C2×C3×C4×C5—21no—
59C2×C3×C4×C5—21no—
60C2×C3×C4×C5C4211yescharacteristic
61C2×C3×C4×C5C22⋊C411yescharacteristic
62C3×C22⋊D5—41no—
63C3×C22⋊D5—41no—
64C2×C3×Dic5C22⋊C411yescharacteristic
65C2×C3×Dic5C4⋊C411yescharacteristic
66C3×D20—41no—
67C3×C4×D5—21no—
68C3×C4×D5—21no—
69C3×C4×D5—21no—
70C3×C4×D5—21no—
71C3×Dic10—41no—
72C3×#170—42no—
73C3×C5×C8—41no—
74C3×#168—41no—
75C2×C3×#41—51no—
76C2×C3×M16—101no—
77C2×C3×M16AGL(1,𝔽5)11yescharacteristic, complemented
78C22×C3×C8—51no—
79C3×#117—101no—
80C3×#101—52no—
81C3×#100—101no—
82C3×#99—52no—
83C3×#99—101no—
84C3×C22⋊C8—101no—
85C3×C22⋊C8—101no—
86C22×C4×C5C2×C3×C411yescharacteristic
87C2×C22⋊D5C3×D411yescharacteristic
88C2×C22⋊D5C3×Q811yescharacteristic
89#709—41no—
90#709—41no—
91C2×D20C2×C3×C411yescharacteristic
92C2×C4×D5C3×D411yescharacteristic
93C2×C4×D5C3×D411yescharacteristic
94C2×Dic10C2×C3×C411yescharacteristic
95C22⋊AGL(1,𝔽5)—22no—
96#704—22no—
97C4⋊AGL(1,𝔽5)—41no—
98C4×AGL(1,𝔽5)—41no—
99#700—41no—
100D5⋊C8—41no—
101C5×M16—41no—
102C2×C5×C8—21no—
103C2×#168—21no—
104C2×#168—41no—
105#413—51no—
106#410—51no—
107#408—51no—
108C22×C3×C5—21no—
109C22×C3×C5—41no—
110C22×C3×C5#9511yescharacteristic
111C2×C3×D5—21no—
112C2×C3×D5—21no—
113C2×C3×D5—41no—
114C2×C3×D5—41no—
115C3×AGL(1,𝔽5)—82no—
116C3×C4×C5—21no—
117C3×C4×C5#9911yescharacteristic
118C3×C4×C5#9911yescharacteristic
119C3×Dic5—21no—
120C3×Dic5—21no—
121C3×#41—201no—
122C3×#41—201no—
123C2×C3×Q8—51no—
124C2×C3×D4—51no—
125C2×C3×D4—51no—
126C2×C3×D4—51no—
127C22×C3×C4—51no—
128C22×C3×C4—51no—
129C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
130C3×M16—41no—
131C3×M16—102no—
132C3×M16—201no—
133C2×C3×C8—21no—
134C2×C3×C8—101no—
135C2×C3×C8—201no—
136C2×C3×C8—201no—
137C3×C4⋊C4—201no—
138C3×C22⋊C4—102no—
139C3×C42—201no—
140C23×C5C3×C4⋊C411yescharacteristic
141C22×D5C3×C22⋊C411yescharacteristic
142C22×D5C3×C4⋊C411yescharacteristic
143C2×AGL(1,𝔽5)—42no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5C3×C4211yescharacteristic
147C2×C4×C5C3×C22⋊C411yescharacteristic
148C22⋊D5—41no—
149C22⋊D5—41no—
150C2×Dic5C3×C22⋊C411yescharacteristic
151C2×Dic5C3×C4⋊C411yescharacteristic
152D20—41no—
153C4×D5—21no—
154C4×D5—21no—
155C4×D5—21no—
156C4×D5—21no—
157Dic10—41no—
158#170—42no—
159C5×C8—41no—
160#168—41no—
161C2×#41—51no—
162C2×M16—101no—
163C2×M16C3×AGL(1,𝔽5)11yescharacteristic, complemented
164C22×C8—51no—
165#117—101no—
166#101—52no—
167#100—101no—
168#99—52no—
169#99—101no—
170C22⋊C8—101no—
171C22⋊C8—101no—
172C2×C3×C5—21no—
173C2×C3×C5—41no—
174C2×C3×C5#34211yescharacteristic
175C3×D5—41no—
176C3×D5—41no—
177C23×C3—51no—
178C23×C3—51no—
179C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
180C3×Q8—201no—
181C3×D4—201no—
182C3×D4—201no—
183C3×D4—201no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—51no—
187C2×C3×C4—51no—
188C2×C3×C4—101no—
189C2×C3×C4—101no—
190C2×C3×C4—101no—
191C2×C3×C4—101no—
192C2×C3×C4—202no—
193C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
194C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
195C3×C8—41no—
196C3×C8—202no—
197C3×C8—201no—
198C22×C5—21no—
199C22×C5—41no—
200C22×C5C3×#9511yescharacteristic
201C2×D5—21no—
202C2×D5—21no—
203C2×D5—41no—
204C2×D5—41no—
205AGL(1,𝔽5)—82no—
206C4×C5—21no—
207C4×C5C3×#9911yescharacteristic
208C4×C5C3×#9911yescharacteristic
209Dic5—21no—
210Dic5—21no—
211#41—201no—
212#41—201no—
213C2×Q8—51no—
214C2×D4—51no—
215C2×D4—51no—
216C2×D4—51no—
217C22×C4—51no—
218C22×C4—51no—
219C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
220M16—41no—
221M16—102no—
222M16—201no—
223C2×C8—21no—
224C2×C8—101no—
225C2×C8—201no—
226C2×C8—201no—
227C4⋊C4—201no—
228C22⋊C4—102no—
229C42—201no—
230C3×C5#139511yescharacteristic, complemented, Hall
231C22×C3—21no—
232C22×C3—41no—
233C22×C3—101no—
234C22×C3—101no—
235C22×C3—201no—
236C22×C3—201no—
237C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
238C3×C4—21no—
239C3×C4—101no—
240C3×C4—101no—
241C3×C4—402no—
242C3×C4#399911yescharacteristic
243C3×C4#401111yescharacteristic
244C2×C5—21no—
245C2×C5—41no—
246C2×C5C3×#34211yescharacteristic
247D5—41no—
248D5—41no—
249C23—51no—
250C23—51no—
251C23C3×C4⋊AGL(1,𝔽5)11yescharacteristic
252Q8—201no—
253D4—201no—
254D4—201no—
255D4—201no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—51no—
259C2×C4—51no—
260C2×C4—101no—
261C2×C4—101no—
262C2×C4—101no—
263C2×C4—101no—
264C2×C4—202no—
265C2×C4C3×C4×AGL(1,𝔽5)11yescharacteristic
266C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
267C8—41no—
268C8—202no—
269C8—201no—
270C2×C3—21no—
271C2×C3—41no—
272C2×C3—201no—
273C2×C3—201no—
274C2×C3#6491711yescharacteristic
275C5C3×#139511yescharacteristic, complemented, Sylow
276C22—21no—
277C22—41no—
278C22—101no—
279C22—101no—
280C22—201no—
281C22—201no—
282C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
283C4—21no—
284C4—101no—
285C4—101no—
286C4—402no—
287C4C3×#399911yescharacteristic
288C4C3×#401111yescharacteristic
289C3#1059879111yescharacteristic, direct product factor, Sylow
290C2—21no—
291C2—41no—
292C2—201no—
293C2—201no—
294C2C3×#6491711yescharacteristic
subgroupG/H
centerC3×C4#4011
commutatorC2×C4×C5C3×C42
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×M16C4
socleC2×C3×C5#342
prime radicalC2×C3×#709C22
cosocleC2×#709C22×C3
hypercenterC2×C3×M16AGL(1,𝔽5)
hypocenterC5C3×#1395
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×M16

Complements

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

NH ≅ G/Ntype
4. #10598791C3direct (N × H)
8. C2×C3×C5×M16C4semidirect
9. C22×C3×#168C4semidirect
12. C3×#4005C4semidirect
45. C2×C5×M16C3×C4semidirect
46. C22×#168C3×C4semidirect
49. #4005C3×C4semidirect
77. C2×C3×M16AGL(1,𝔽5)semidirect
163. C2×M16C3×AGL(1,𝔽5)semidirect
230. C3×C5#1395semidirect
275. C5C3×#1395semidirect
289. C3#10598791direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#657612
C3×#657452
C3×#654182
#105987913
C3×#13955