Finite Group Databasebeta

← C3×#10602748 #14290944

Subgroups — C3×#10602748 #14290944

Order 1920.

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

normal subgroups only

This group has 412 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, complemented
2C3×#65356C212yesmaximal, complemented
3C3×#65347C211yesmaximal, characteristic
4C3×#64763C212yesmaximal, complemented
5C3×#64760C211yesmaximal, characteristic, complemented
6#10602748C311yesmaximal, 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×#688—21no—
14C2×C3×#686—21no—
15C3×#4020C2211yescharacteristic
16C3×#3941—22no—
17C3×#3941—22no—
18C3×#3935C2211yescharacteristic
19C3×#3935C2212yes—
20C3×#1657—51nomaximal, Hall
21C5×#563C2×C311yescharacteristic, complemented
22#65356C2×C312yescomplemented
23#65347C2×C311yescharacteristic
24#64763C2×C312yescomplemented
25#64760C2×C311yescharacteristic, complemented
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C22×C3×C4×C5—21no—
30C2×C3×D20—21no—
31C2×C3×D20—22no—
32C3×C5×C4⋊C4—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4—22no—
35C3×C5×C4⋊C4D412yes—
36C3×C5×C4⋊C4D412yes—
37C3×C5×C22⋊C4—22no—
38C3×C5×C22⋊C4—21no—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5—21no—
41C3×C42×C5C2311yescharacteristic
42C3×#688—42no—
43C3×#686—42no—
44C2×C3×#168—21no—
45C2×C3×#168—22no—
46C3×#563D511yescharacteristic, complemented
47C3×#496—51no—
48C3×#490—52no—
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×#688—21no—
58C2×#686—21no—
59#4020C22×C311yescharacteristic
60#3941—22no—
61#3941—22no—
62#3935C22×C311yescharacteristic
63#3935C22×C312yes—
64#1657—51noSylow
65C23×C3×C5—21no—
66C22×C3×D5—41no—
67C3×C5×Q8—41no—
68C3×C5×Q8—81no—
69C3×C5×D4—41no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—81no—
74C2×C3×C4×C5C2×D412yes—
75C2×C3×C4×C5C2×D411yescharacteristic
76C3×D20—41no—
77C3×D20—41no—
78C3×D20—44no—
79C3×#168—22no—
80C3×#168—42no—
81C2×C3×SD16—101no—
82C2×C3×D8—101no—
83C3×C4⋊Q8—21no—
84C3×#127—51no—
85C3×#126—22no—
86C3×#125C2×D512yes—
87C3×#124C2×D511yescharacteristic
88C3×#123—21no—
89C3×C22⋊Q8—22no—
90C3×#102—102no—
91C3×#102—102no—
92C3×#97—52no—
93C3×#97—51no—
94C2×C5×Q8—21no—
95C2×C5×Q8C3×D411yescharacteristic
96C2×C5×D4C3×D411yescharacteristic
97C22×C4×C5—21no—
98C2×D20—22no—
99C2×D20—21no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4—22no—
102C5×C4⋊C4—22no—
103C5×C4⋊C4C3×D412yes—
104C5×C4⋊C4C3×D412yes—
105C5×C22⋊C4—22no—
106C5×C22⋊C4—21no—
107C5×C22⋊C4—22no—
108C42×C5—21no—
109C42×C5C23×C311yescharacteristic
110#688—42no—
111#686—42no—
112C2×#168—21no—
113C2×#168—22no—
114#563C3×D511yescharacteristic, complemented
115#496—51no—
116#490—52no—
117#330—52no—
118#329—51no—
119C22×C3×C5—41no—
120C22×C3×C5—42no—
121C22×C3×C5#12011yescharacteristic
122C2×C3×D5—81no—
123C2×C3×D5—82no—
124C3×C4×C5—21no—
125C3×C4×C5—22no—
126C3×C4×C5—42no—
127C3×C4×C5—41no—
128C3×C4×C5—42no—
129C2×C3×Q8—21no—
130C2×C3×Q8C22⋊D511yescharacteristic
131C2×C3×D4—102no—
132C2×C3×D4—101no—
133C2×C3×D4C22⋊D511yescharacteristic
134C22×C3×C4—21no—
135C3×SD16—202no—
136C3×D8—202no—
137C2×C3×C8—101no—
138C2×C3×C8—102no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—22no—
142C3×C4⋊C4C22⋊D512yes—
143C3×C4⋊C4C22⋊D512yes—
144C3×C22⋊C4—22no—
145C3×C22⋊C4—21no—
146C3×C22⋊C4—22no—
147C3×C42—21no—
148C3×C42C22×D511yescharacteristic
149C23×C5—21no—
150C22×D5—41no—
151C5×Q8—41no—
152C5×Q8—81no—
153C5×D4—41no—
154C2×C4×C5—22no—
155C2×C4×C5—21no—
156C2×C4×C5—22no—
157C2×C4×C5—81no—
158C2×C4×C5C2×C3×D412yes—
159C2×C4×C5C2×C3×D411yescharacteristic
160D20—41no—
161D20—41no—
162D20—44no—
163#168—22no—
164#168—42no—
165C2×SD16—101no—
166C2×D8—101no—
167C4⋊Q8—21no—
168#127—51no—
169#126—22no—
170#125C2×C3×D512yes—
171#124C2×C3×D511yescharacteristic
172#123—21no—
173C22⋊Q8—22no—
174#102—102no—
175#102—102no—
176#97—52no—
177#97—51no—
178C2×C3×C5—81no—
179C2×C3×C5#45311yescharacteristic
180C2×C3×C5#45412yes—
181C3×D5—161no—
182C23×C3—21no—
183C23×C3—201no—
184C3×Q8—41no—
185C3×Q8—81no—
186C3×D4—41no—
187C3×D4—201no—
188C3×D4—201no—
189C3×D4—204no—
190C2×C3×C4—22no—
191C2×C3×C4—21no—
192C2×C3×C4—22no—
193C2×C3×C4—81no—
194C2×C3×C4C2×C22⋊D512yes—
195C2×C3×C4C2×C22⋊D511yescharacteristic
196C3×C8—102no—
197C3×C8—202no—
198C22×C5—41no—
199C22×C5—42no—
200C22×C5C3×#12011yescharacteristic
201C2×D5—81no—
202C2×D5—82no—
203C4×C5—21no—
204C4×C5—22no—
205C4×C5—42no—
206C4×C5—41no—
207C4×C5—42no—
208C2×Q8—21no—
209C2×Q8C3×C22⋊D511yescharacteristic
210C2×D4—102no—
211C2×D4—101no—
212C2×D4C3×C22⋊D511yescharacteristic
213C22×C4—21no—
214SD16—202no—
215D8—202no—
216C2×C8—101no—
217C2×C8—102no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4C3×C22⋊D512yes—
222C4⋊C4C3×C22⋊D512yes—
223C22⋊C4—22no—
224C22⋊C4—21no—
225C22⋊C4—22no—
226C42—21no—
227C42C22×C3×D511yescharacteristic
228C3×C5#165711yescharacteristic, complemented, Hall
229C22×C3—41no—
230C22×C3—42no—
231C22×C3—401no—
232C22×C3—402no—
233C22×C3#409911yescharacteristic
234C3×C4—21no—
235C3×C4—22no—
236C3×C4—42no—
237C3×C4—41no—
238C3×C4—42no—
239C2×C5—81no—
240C2×C5C3×#45311yescharacteristic
241C2×C5C3×#45412yes—
242D5—161no—
243C23—21no—
244C23—201no—
245Q8—41no—
246Q8—81no—
247D4—41no—
248D4—201no—
249D4—201no—
250D4—204no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—81no—
255C2×C4C2×C3×C22⋊D512yes—
256C2×C4C2×C3×C22⋊D511yescharacteristic
257C8—102no—
258C8—202no—
259C2×C3—81no—
260C2×C3—801no—
261C2×C3#6553011yescharacteristic
262C2×C3#6553412yes—
263C5C3×#165711yescharacteristic, complemented, Sylow
264C22—41no—
265C22—42no—
266C22—401no—
267C22—402no—
268C22C3×#409911yescharacteristic
269C4—21no—
270C4—22no—
271C4—42no—
272C4—41no—
273C4—42no—
274C3#1060274811yescharacteristic, direct product factor, Sylow
275C2—81no—
276C2—801no—
277C2C3×#6553011yescharacteristic
278C2C3×#6553412yes—
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#563C2
socleC22×C3×C5#120
prime radicalC3×#65347C2
hypercenterC3×#563D5
hypocenterC5C3×#1657
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
1. C3×C5×#563C2semidirect
2. C3×#65356C2semidirect
4. C3×#64763C2semidirect
5. C3×#64760C2semidirect
6. #10602748C3direct (N × H)
21. C5×#563C2×C3semidirect
22. #65356C2×C3semidirect
24. #64763C2×C3semidirect
25. #64760C2×C3semidirect
46. C3×#563D5semidirect
114. #563C3×D5semidirect
228. C3×C5#1657semidirect
263. C5C3×#1657semidirect
274. C3#10602748direct (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×#653562
C3×#653472
C3×#647632
C3×#647602
#106027483
C3×#16575