Finite Group Databasebeta

← C3×#10603931 #14299626

Subgroups — C3×#10603931 #14299626

Order 1920.

544 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 136 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×#66262C211yesmaximal, characteristic
2C3×(C2×AGL(1,𝔽5))⋊Q8C211yesmaximal, characteristic
3C3×#65727C212yesmaximal
4C3×D5×#101C211yesmaximal, characteristic
5C3×#64900C212yesmaximal
6#10603931C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×Q8×D5C2211yescharacteristic
8C3×Q8×AGL(1,𝔽5)—22no—
9C3×Q8×AGL(1,𝔽5)—22no—
10C3×#4130—22no—
11C3×#4130C2212yes—
12C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
13C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
14C3×D5×M16C2212yes—
15C3×(C2×AGL(1,𝔽5))⋊C4—22no—
16C3×#3994—22no—
17C3×#3993—22no—
18C3×C5×#101C411yescharacteristic, complemented
19C3×#3968C411yescharacteristic, complemented
20C3×#3956C412yescomplemented
21C3×#1857—51nomaximal, Hall
22#66262C2×C311yescharacteristic
23(C2×AGL(1,𝔽5))⋊Q8C2×C311yescharacteristic
24#65727C2×C312yes—
25D5×#101C2×C311yescharacteristic
26#64900C2×C312yes—
27C22×C3×AGL(1,𝔽5)—21no—
28C22×C3×AGL(1,𝔽5)—21no—
29C2×C3×C5×Q8C2×C411yescharacteristic
30C3×Q8×D5—22no—
31C3×Q8×D5—22no—
32C2×C3×C4×D5D412yes—
33C2×C3×C4×D5C2311yescharacteristic
34C2×C3×Dic10C2×C411yescharacteristic
35C2×C3×Dic10Q812yes—
36C3×C22⋊AGL(1,𝔽5)—22no—
37C3×C4⋊AGL(1,𝔽5)—22no—
38C3×C4⋊AGL(1,𝔽5)—22no—
39C3×C4⋊AGL(1,𝔽5)—22no—
40C3×C4⋊AGL(1,𝔽5)D412yes—
41C3×C4⋊AGL(1,𝔽5)D412yes—
42C3×C4×AGL(1,𝔽5)—24no—
43C3×C4×AGL(1,𝔽5)—22no—
44C3×C4×AGL(1,𝔽5)—22no—
45C3×C5×M16C2×C412yes—
46C3×#681C2×C412yes—
47C3×#676—22no—
48C3×C8×D5—22no—
49C3×#519—51no—
50C3×#428—52no—
51C2×C3×#101—51no—
52C3×#391—51no—
53C3×#339—52no—
54C2×Q8×D5C22×C311yescharacteristic
55Q8×AGL(1,𝔽5)—22no—
56Q8×AGL(1,𝔽5)—22no—
57#4130—22no—
58#4130C22×C312yes—
59C2×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
60C2×C4×AGL(1,𝔽5)C22×C311yescharacteristic
61D5×M16C22×C312yes—
62(C2×AGL(1,𝔽5))⋊C4—22no—
63#3994—22no—
64#3993—22no—
65C5×#101C3×C411yescharacteristic, complemented
66#3968C3×C411yescharacteristic, complemented
67#3956C3×C412yescomplemented
68#1857—51noSylow
69C22×C3×D5C2×D411yescharacteristic
70C2×C3×AGL(1,𝔽5)—22no—
71C2×C3×AGL(1,𝔽5)—22no—
72C2×C3×AGL(1,𝔽5)—22no—
73C2×C3×AGL(1,𝔽5)—41no—
74C2×C3×AGL(1,𝔽5)—41no—
75C2×C3×AGL(1,𝔽5)—42no—
76C2×C3×AGL(1,𝔽5)—41no—
77C3×C5×Q8—22no—
78C2×C3×C4×C5C4⋊C412yes—
79C2×C3×C4×C5C22×C411yescharacteristic
80C2×C3×Dic5C4⋊C412yes—
81C2×C3×Dic5C2×Q811yescharacteristic
82C3×C4×D5—22no—
83C3×C4×D5—22no—
84C3×C4×D5C2×D412yes—
85C3×C4×D5#4112yes—
86C3×Dic10—22no—
87C3×Dic10—24no—
88C3×C5×C8—22no—
89C3×#168—22no—
90C22×C3×Q8—51no—
91C2×C3×M16—52no—
92C3×C4×Q8—102no—
93C3×C4×Q8—102no—
94C3×#117—52no—
95C3×#117—102no—
96C2×C3×C4⋊C4—51no—
97C2×C3×C42—51no—
98C3×#107—102no—
99C3×#106—102no—
100C3×#101—51no—
101C3×#101—52no—
102C3×#101AGL(1,𝔽5)11yescharacteristic, complemented
103C3×#95—102no—
104C22×AGL(1,𝔽5)—21no—
105C22×AGL(1,𝔽5)—21no—
106C2×C5×Q8C2×C3×C411yescharacteristic
107Q8×D5—22no—
108Q8×D5—22no—
109C2×C4×D5C3×D412yes—
110C2×C4×D5C23×C311yescharacteristic
111C2×Dic10C2×C3×C411yescharacteristic
112C2×Dic10C3×Q812yes—
113C22⋊AGL(1,𝔽5)—22no—
114C4⋊AGL(1,𝔽5)—22no—
115C4⋊AGL(1,𝔽5)—22no—
116C4⋊AGL(1,𝔽5)—22no—
117C4⋊AGL(1,𝔽5)C3×D412yes—
118C4⋊AGL(1,𝔽5)C3×D412yes—
119C4×AGL(1,𝔽5)—24no—
120C4×AGL(1,𝔽5)—22no—
121C4×AGL(1,𝔽5)—22no—
122C5×M16C2×C3×C412yes—
123#681C2×C3×C412yes—
124#676—22no—
125C8×D5—22no—
126#519—51no—
127#428—52no—
128C2×#101—51no—
129#391—51no—
130#339—52no—
131C22×C3×C5C2×C4⋊C411yescharacteristic
132C2×C3×D5—21no—
133C2×C3×D5—21no—
134C2×C3×D5#12011yescharacteristic
135C2×C3×D5#12311yescharacteristic
136C3×AGL(1,𝔽5)—42no—
137C3×AGL(1,𝔽5)—42no—
138C3×AGL(1,𝔽5)—42no—
139C3×AGL(1,𝔽5)—81no—
140C3×C4×C5—22no—
141C3×C4×C5C4×D412yes—
142C3×Dic5—22no—
143C3×Dic5C22⋊Q812yes—
144C2×C3×Q8—52no—
145C2×C3×Q8—51no—
146C2×C3×Q8—102no—
147C2×C3×Q8—102no—
148C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
149C22×C3×C4—51no—
150C22×C3×C4—52no—
151C22×C3×C4—101no—
152C22×C3×C4—101no—
153C3×M16—52no—
154C3×M16—102no—
155C3×M16C2×AGL(1,𝔽5)12yes—
156C2×C3×C8—102no—
157C3×C4⋊C4—52no—
158C3×C4⋊C4—52no—
159C3×C4⋊C4—102no—
160C3×C4⋊C4—102no—
161C3×C4⋊C4—102no—
162C3×C22⋊C4—102no—
163C3×C42—102no—
164C3×C42—102no—
165C3×C42—104no—
166C22×D5C2×C3×D411yescharacteristic
167C2×AGL(1,𝔽5)—22no—
168C2×AGL(1,𝔽5)—22no—
169C2×AGL(1,𝔽5)—22no—
170C2×AGL(1,𝔽5)—41no—
171C2×AGL(1,𝔽5)—41no—
172C2×AGL(1,𝔽5)—42no—
173C2×AGL(1,𝔽5)—41no—
174C5×Q8—22no—
175C2×C4×C5C3×C4⋊C412yes—
176C2×C4×C5C22×C3×C411yescharacteristic
177C2×Dic5C3×C4⋊C412yes—
178C2×Dic5C2×C3×Q811yescharacteristic
179C4×D5—22no—
180C4×D5—22no—
181C4×D5C2×C3×D412yes—
182C4×D5C3×#4112yes—
183Dic10—22no—
184Dic10—24no—
185C5×C8—22no—
186#168—22no—
187C22×Q8—51no—
188C2×M16—52no—
189C4×Q8—102no—
190C4×Q8—102no—
191#117—52no—
192#117—102no—
193C2×C4⋊C4—51no—
194C2×C42—51no—
195#107—102no—
196#106—102no—
197#101—51no—
198#101—52no—
199#101C3×AGL(1,𝔽5)11yescharacteristic, complemented
200#95—102no—
201C2×C3×C5—21no—
202C2×C3×C5#38511yescharacteristic
203C3×D5—21no—
204C3×D5#45411yescharacteristic
205C3×D5#45611yescharacteristic
206C23×C3—51no—
207C3×Q8—22no—
208C3×Q8—104no—
209C3×Q8—102no—
210C2×C3×C4—51no—
211C2×C3×C4—52no—
212C2×C3×C4—52no—
213C2×C3×C4—52no—
214C2×C3×C4—102no—
215C2×C3×C4—102no—
216C2×C3×C4—102no—
217C2×C3×C4—102no—
218C2×C3×C4—102no—
219C2×C3×C4—201no—
220C2×C3×C4—201no—
221C2×C3×C4—201no—
222C2×C3×C4—202no—
223C2×C3×C4C4⋊AGL(1,𝔽5)12yes—
224C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
225C3×C8—22no—
226C3×C8—102no—
227C22×C5C2×C3×C4⋊C411yescharacteristic
228C2×D5—21no—
229C2×D5—21no—
230C2×D5C3×#12011yescharacteristic
231C2×D5C3×#12311yescharacteristic
232AGL(1,𝔽5)—42no—
233AGL(1,𝔽5)—42no—
234AGL(1,𝔽5)—42no—
235AGL(1,𝔽5)—81no—
236C4×C5—22no—
237C4×C5C3×C4×D412yes—
238Dic5—22no—
239Dic5C3×C22⋊Q812yes—
240C2×Q8—52no—
241C2×Q8—51no—
242C2×Q8—102no—
243C2×Q8—102no—
244C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
245C22×C4—51no—
246C22×C4—52no—
247C22×C4—101no—
248C22×C4—101no—
249M16—52no—
250M16—102no—
251M16C2×C3×AGL(1,𝔽5)12yes—
252C2×C8—102no—
253C4⋊C4—52no—
254C4⋊C4—52no—
255C4⋊C4—102no—
256C4⋊C4—102no—
257C4⋊C4—102no—
258C22⋊C4—102no—
259C42—102no—
260C42—102no—
261C42—104no—
262C3×C5#185711yescharacteristic, complemented, Hall
263C22×C3—51no—
264C22×C3—51no—
265C22×C3—101no—
266C22×C3—101no—
267C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
268C3×C4—22no—
269C3×C4—52no—
270C3×C4—102no—
271C3×C4—202no—
272C3×C4—202no—
273C3×C4—202no—
274C3×C4—401no—
275C3×C4D4×AGL(1,𝔽5)12yes—
276C2×C5—21no—
277C2×C5C3×#38511yescharacteristic
278D5—21no—
279D5C3×#45411yescharacteristic
280D5C3×#45611yescharacteristic
281C23—51no—
282Q8—22no—
283Q8—104no—
284Q8—102no—
285C2×C4—51no—
286C2×C4—52no—
287C2×C4—52no—
288C2×C4—52no—
289C2×C4—102no—
290C2×C4—102no—
291C2×C4—102no—
292C2×C4—102no—
293C2×C4—102no—
294C2×C4—201no—
295C2×C4—201no—
296C2×C4—201no—
297C2×C4—202no—
298C2×C4C3×C4⋊AGL(1,𝔽5)12yes—
299C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
300C8—22no—
301C8—102no—
302C2×C3—21no—
303C2×C3—51no—
304C2×C3—51no—
305C2×C3—101no—
306C2×C3#6569911yescharacteristic
307C5C3×#185711yescharacteristic, complemented, Sylow
308C22—51no—
309C22—51no—
310C22—101no—
311C22—101no—
312C22C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
313C4—22no—
314C4—52no—
315C4—102no—
316C4—202no—
317C4—202no—
318C4—202no—
319C4—401no—
320C4C3×D4×AGL(1,𝔽5)12yes—
321C3#1060393111yescharacteristic, direct product factor, Sylow
322C2—21no—
323C2—51no—
324C2—51no—
325C2—101no—
326C2C3×#6569911yescharacteristic
subgroupG/H
centerC2×C3#65699
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#101C4
socleC2×C3×C5#385
prime radicalC22×C3×D5C2×D4
cosocleC2×C4×D5C23×C3
hypercenterC3×#101AGL(1,𝔽5)
hypocenterC5C3×#1857
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#101

Complements

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

NH ≅ G/Ntype
6. #10603931C3direct (N × H)
18. C3×C5×#101C4semidirect
19. C3×#3968C4semidirect
20. C3×#3956C4semidirect
65. C5×#101C3×C4semidirect
66. #3968C3×C4semidirect
67. #3956C3×C4semidirect
102. C3×#101AGL(1,𝔽5)semidirect
199. #101C3×AGL(1,𝔽5)semidirect
262. C3×C5#1857semidirect
307. C5C3×#1857semidirect
321. C3#10603931direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#662622
C3×(C2×AGL(1,𝔽5))⋊Q82
C3×#657272
C3×D5×#1012
C3×#649002
#106039313
C3×#18575