Finite Group Databasebeta

← C3×#10602749 #14291041

Subgroups — C3×#10602749 #14291041

Order 1920.

392 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 98 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×C5×#563C211yesmaximal, characteristic
2C3×#65354C212yesmaximal, complemented
3C3×#65349C211yesmaximal, characteristic
4C3×#64763C212yesmaximal, complemented
5C3×#64760C211yesmaximal, characteristic
6#10602749C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8—21no—
8C3×C5×#126—22no—
9C3×C5×#125C2212yes—
10C3×C5×#124C2211yescharacteristic
11C3×C5×#123—21no—
12C3×C5×C22⋊Q8—22no—
13C2×C3×#689—21no—
14C2×C3×#687—21no—
15C3×#4015C2211yescharacteristic
16C3×#3940—22no—
17C3×#3939—22no—
18C3×#3935C2212yes—
19C3×#3935C2211yescharacteristic
20C3×#1660—51nomaximal, Hall
21C5×#563C2×C311yescharacteristic
22#65354C2×C312yescomplemented
23#65349C2×C311yescharacteristic
24#64763C2×C312yescomplemented
25#64760C2×C311yescharacteristic
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C22×C3×C4×C5—21no—
30C2×C3×Dic10—21no—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4D412yes—
35C3×C5×C4⋊C4D412yes—
36C3×C5×C22⋊C4—22no—
37C3×C5×C22⋊C4—21no—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5—21no—
40C3×C42×C5C2311yescharacteristic
41C3×#689—42no—
42C3×#687—42no—
43C3×C4⋊Dic5—22no—
44C2×C3×#168—21no—
45C2×C3×#168—22no—
46C3×#563D511yescharacteristic
47C3×#501—52no—
48C3×#497—51no—
49C3×#330—52no—
50C3×#329—51no—
51C5×C4⋊Q8—21no—
52C5×#126—22no—
53C5×#125C22×C312yes—
54C5×#124C22×C311yescharacteristic
55C5×#123—21no—
56C5×C22⋊Q8—22no—
57C2×#689—21no—
58C2×#687—21no—
59#4015C22×C311yescharacteristic
60#3940—22no—
61#3939—22no—
62#3935C22×C311yescharacteristic
63#3935C22×C312yes—
64#1660—51noSylow
65C23×C3×C5—21no—
66C3×C5×Q8—41no—
67C3×C5×Q8—81no—
68C3×C5×D4—41no—
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—81no—
73C2×C3×C4×C5C2×D412yes—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×Dic5—41no—
76C3×Dic10—41no—
77C3×Dic10—41no—
78C3×#168—24no—
79C3×#168—22no—
80C2×C3×Q16—101no—
81C2×C3×SD16—101no—
82C3×C4⋊Q8—21no—
83C3×C4⋊Q8—51no—
84C3×#126—22no—
85C3×#125C2×D512yes—
86C3×#124C2×D511yescharacteristic
87C3×#123—21no—
88C3×C22⋊Q8—22no—
89C3×#107—102no—
90C3×#106—102no—
91C3×#97—52no—
92C3×#97—51no—
93C2×C5×Q8—21no—
94C2×C5×Q8C3×D411yescharacteristic
95C2×C5×D4C3×D411yescharacteristic
96C22×C4×C5—21no—
97C2×Dic10—21no—
98C5×C4⋊C4—22no—
99C5×C4⋊C4—22no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4C3×D412yes—
102C5×C4⋊C4C3×D412yes—
103C5×C22⋊C4—22no—
104C5×C22⋊C4—21no—
105C5×C22⋊C4—22no—
106C42×C5—21no—
107C42×C5C23×C311yescharacteristic
108#689—42no—
109#687—42no—
110C4⋊Dic5—22no—
111C2×#168—22no—
112C2×#168—21no—
113#563C3×D511yescharacteristic
114#501—52no—
115#497—51no—
116#330—52no—
117#329—51no—
118C22×C3×C5—41no—
119C22×C3×C5—42no—
120C22×C3×C5#12011yescharacteristic
121C3×C4×C5—21no—
122C3×C4×C5—22no—
123C3×C4×C5—42no—
124C3×C4×C5—41no—
125C3×C4×C5—42no—
126C3×Dic5—81no—
127C2×C3×Q8—21no—
128C2×C3×Q8—101no—
129C2×C3×Q8C22⋊D511yescharacteristic
130C2×C3×D4C22⋊D511yescharacteristic
131C22×C3×C4—21no—
132C3×Q16—202no—
133C3×SD16—202no—
134C2×C3×C8—102no—
135C2×C3×C8—101no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—22no—
139C3×C4⋊C4—102no—
140C3×C4⋊C4C22⋊D512yes—
141C3×C4⋊C4C22⋊D512yes—
142C3×C22⋊C4—22no—
143C3×C22⋊C4—21no—
144C3×C22⋊C4—22no—
145C3×C42—21no—
146C3×C42C22×D511yescharacteristic
147C23×C5—21no—
148C5×Q8—41no—
149C5×Q8—81no—
150C5×D4—41no—
151C2×C4×C5—22no—
152C2×C4×C5—21no—
153C2×C4×C5—22no—
154C2×C4×C5—81no—
155C2×C4×C5C2×C3×D412yes—
156C2×C4×C5C2×C3×D411yescharacteristic
157C2×Dic5—41no—
158Dic10—41no—
159Dic10—41no—
160#168—24no—
161#168—22no—
162C2×Q16—101no—
163C2×SD16—101no—
164C4⋊Q8—21no—
165C4⋊Q8—51no—
166#126—22no—
167#125C2×C3×D512yes—
168#124C2×C3×D511yescharacteristic
169#123—21no—
170C22⋊Q8—22no—
171#107—102no—
172#106—102no—
173#97—52no—
174#97—51no—
175C2×C3×C5—81no—
176C2×C3×C5#45311yescharacteristic
177C2×C3×C5#45612yes—
178C23×C3—21no—
179C3×Q8—41no—
180C3×Q8—81no—
181C3×Q8—201no—
182C3×Q8—201no—
183C3×D4—41no—
184C2×C3×C4—22no—
185C2×C3×C4—21no—
186C2×C3×C4—22no—
187C2×C3×C4—81no—
188C2×C3×C4—201no—
189C2×C3×C4C2×C22⋊D512yes—
190C2×C3×C4C2×C22⋊D511yescharacteristic
191C3×C8—104no—
192C3×C8—102no—
193C22×C5—41no—
194C22×C5—42no—
195C22×C5C3×#12011yescharacteristic
196C4×C5—21no—
197C4×C5—22no—
198C4×C5—42no—
199C4×C5—41no—
200C4×C5—42no—
201Dic5—81no—
202C2×Q8—21no—
203C2×Q8—101no—
204C2×Q8C3×C22⋊D511yescharacteristic
205C2×D4C3×C22⋊D511yescharacteristic
206C22×C4—21no—
207Q16—202no—
208SD16—202no—
209C2×C8—102no—
210C2×C8—101no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—102no—
215C4⋊C4C3×C22⋊D512yes—
216C4⋊C4C3×C22⋊D512yes—
217C22⋊C4—22no—
218C22⋊C4—21no—
219C22⋊C4—22no—
220C42—21no—
221C42C22×C3×D511yescharacteristic
222C3×C5#166011yescharacteristic, complemented, Hall
223C22×C3—41no—
224C22×C3—42no—
225C22×C3#409911yescharacteristic
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—42no—
229C3×C4—41no—
230C3×C4—42no—
231C3×C4—401no—
232C2×C5—81no—
233C2×C5C3×#45311yescharacteristic
234C2×C5C3×#45612yes—
235C23—21no—
236Q8—41no—
237Q8—81no—
238Q8—201no—
239Q8—201no—
240D4—41no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—81no—
245C2×C4—201no—
246C2×C4C2×C3×C22⋊D512yes—
247C2×C4C2×C3×C22⋊D511yescharacteristic
248C8—102no—
249C8—104no—
250C2×C3—81no—
251C2×C3#6553011yescharacteristic
252C2×C3#6553512yes—
253C5C3×#166011yescharacteristic, complemented, Sylow
254C22—41no—
255C22—42no—
256C22C3×#409911yescharacteristic
257C4—21no—
258C4—22no—
259C4—42no—
260C4—41no—
261C4—42no—
262C4—401no—
263C3#1060274911yescharacteristic, direct product factor, Sylow
264C2—81no—
265C2C3×#6553011yescharacteristic
266C2C3×#6553512yes—
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#563C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC3×#563D5
hypocenterC5C3×#1660
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#563

Complements

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

NH ≅ G/Ntype
2. C3×#65354C2semidirect
4. C3×#64763C2semidirect
6. #10602749C3direct (N × H)
22. #65354C2×C3semidirect
24. #64763C2×C3semidirect
222. C3×C5#1660semidirect
253. C5C3×#1660semidirect
263. C3#10602749direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5632
C3×#653542
C3×#653492
C3×#647632
C3×#647602
#106027493
C3×#16605