Finite Group Databasebeta

← C3×C5×#1662 #14274696

Subgroups — C3×C5×#1662 #14274696

Order 1920.

392 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 120 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×#562C211yesmaximal, characteristic
2C3×C5×#491C211yesmaximal, characteristic, complemented
3C3×C5×#489C212yesmaximal, complemented
4C3×C5×#330C211yesmaximal, characteristic, complemented
5C3×C5×#329C212yesmaximal, complemented
6C5×#1662C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×#125C2211yescharacteristic
9C3×C5×#124C2212yes—
10C3×C5×#123—22no—
11C3×C5×C22⋊Q8—22no—
12C3×C5×#121—22no—
13C3×C5×#103—22no—
14C3×C5×#103—22no—
15C3×C5×#102—22no—
16C3×C5×#97C2212yes—
17C3×C5×#97C2211yescharacteristic
18C3×#1662C511yesmaximal, characteristic, direct product factor, Hall
19C5×#562C2×C311yescharacteristic
20C5×#491C2×C311yescharacteristic, complemented
21C5×#489C2×C312yescomplemented
22C5×#330C2×C311yescharacteristic, complemented
23C5×#329C2×C312yescomplemented
24C2×C3×C5×Q8—21no—
25C2×C3×C5×Q8D412yes—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4D412yes—
28C22×C3×C4×C5—22no—
29C2×C3×C5×C8—22no—
30C2×C3×C5×C8—21no—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4D412yes—
35C3×C5×C22⋊C4—22no—
36C3×C5×C22⋊C4—22no—
37C3×C5×C22⋊C4—22no—
38C3×C42×C5C2311yescharacteristic
39C3×#562C2×C511yescharacteristic
40C3×#491C2×C511yescharacteristic, complemented
41C3×#489C2×C512yescomplemented
42C3×#330C2×C511yescharacteristic, complemented
43C3×#329C2×C512yescomplemented
44C5×C4⋊Q8C22×C311yescharacteristic
45C5×#125C22×C311yescharacteristic
46C5×#124C22×C312yes—
47C5×#123—22no—
48C5×C22⋊Q8—22no—
49C5×#121—22no—
50C5×#103—22no—
51C5×#103—22no—
52C5×#102—22no—
53C5×#97C22×C311yescharacteristic
54C5×#97C22×C312yes—
55#1662C3×C511yescharacteristic, direct product factor, Sylow
56C23×C3×C5—22no—
57C3×C5×Q8—42no—
58C3×C5×Q8—42no—
59C3×C5×D4—42no—
60C3×C5×D4—82no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5—82no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C3×C5×C8—41no—
68C3×C5×C8—42no—
69C3×C4⋊Q8C22×C511yescharacteristic
70C3×#125C22×C511yescharacteristic
71C3×#124C22×C512yes—
72C3×#123—22no—
73C3×C22⋊Q8—22no—
74C3×#121—22no—
75C3×#103—22no—
76C3×#103—22no—
77C3×#102—22no—
78C3×#97C22×C511yescharacteristic
79C3×#97C22×C512yes—
80C2×C5×Q8—21no—
81C2×C5×Q8C3×D412yes—
82C2×C5×D4—22no—
83C2×C5×D4C3×D412yes—
84C22×C4×C5—22no—
85C2×C5×C8—22no—
86C2×C5×C8—21no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—22no—
89C5×C4⋊C4—22no—
90C5×C4⋊C4C3×D412yes—
91C5×C22⋊C4—22no—
92C5×C22⋊C4—22no—
93C5×C22⋊C4—22no—
94C42×C5C23×C311yescharacteristic
95#562C2×C3×C511yescharacteristic
96#491C2×C3×C511yescharacteristic, complemented
97#489C2×C3×C512yescomplemented
98#330C2×C3×C511yescharacteristic, complemented
99#329C2×C3×C512yescomplemented
100C22×C3×C5—42no—
101C22×C3×C5—42no—
102C22×C3×C5—42no—
103C22×C3×C5#12011yescharacteristic
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107C3×C4×C5—42no—
108C3×C4×C5—81no—
109C2×C3×Q8—21no—
110C2×C3×Q8C5×D412yes—
111C2×C3×D4—22no—
112C2×C3×D4C5×D412yes—
113C22×C3×C4—22no—
114C2×C3×C8—22no—
115C2×C3×C8—21no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—22no—
119C3×C4⋊C4C5×D412yes—
120C3×C22⋊C4—22no—
121C3×C22⋊C4—22no—
122C3×C22⋊C4—22no—
123C3×C42C23×C511yescharacteristic
124C23×C5—22no—
125C5×Q8—42no—
126C5×Q8—42no—
127C5×D4—42no—
128C5×D4—82no—
129C2×C4×C5—22no—
130C2×C4×C5—22no—
131C2×C4×C5—41no—
132C2×C4×C5—82no—
133C2×C4×C5C2×C3×D411yescharacteristic
134C2×C4×C5C2×C3×D412yes—
135C5×C8—41no—
136C5×C8—42no—
137C4⋊Q8C22×C3×C511yescharacteristic
138#125C22×C3×C511yescharacteristic
139#124C22×C3×C512yes—
140#123—22no—
141C22⋊Q8—22no—
142#121—22no—
143#103—22no—
144#103—22no—
145#102—22no—
146#97C22×C3×C511yescharacteristic
147#97C22×C3×C512yes—
148C2×C3×C5—82no—
149C2×C3×C5#45411yescharacteristic
150C2×C3×C5#45512yes—
151C23×C3—22no—
152C3×Q8—42no—
153C3×Q8—42no—
154C3×D4—42no—
155C3×D4—82no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—41no—
159C2×C3×C4—82no—
160C2×C3×C4C2×C5×D411yescharacteristic
161C2×C3×C4C2×C5×D412yes—
162C3×C8—41no—
163C3×C8—42no—
164C22×C5—42no—
165C22×C5—42no—
166C22×C5—42no—
167C22×C5C3×#12011yescharacteristic
168C4×C5—21no—
169C4×C5—22no—
170C4×C5—42no—
171C4×C5—42no—
172C4×C5—81no—
173C2×Q8—21no—
174C2×Q8C3×C5×D412yes—
175C2×D4—22no—
176C2×D4C3×C5×D412yes—
177C22×C4—22no—
178C2×C8—22no—
179C2×C8—21no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4C3×C5×D412yes—
184C22⋊C4—22no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C42C23×C3×C511yescharacteristic
188C3×C5#166211yescharacteristic, direct product factor, Hall
189C22×C3—42no—
190C22×C3—42no—
191C22×C3—42no—
192C22×C3C5×#12011yescharacteristic
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196C3×C4—42no—
197C3×C4—81no—
198C2×C5—82no—
199C2×C5C3×#45411yescharacteristic
200C2×C5C3×#45512yes—
201C23—22no—
202Q8—42no—
203Q8—42no—
204D4—42no—
205D4—82no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—82no—
210C2×C4C2×C3×C5×D411yescharacteristic
211C2×C4C2×C3×C5×D412yes—
212C8—41no—
213C8—42no—
214C2×C3—82no—
215C2×C3C5×#45411yescharacteristic
216C2×C3C5×#45512yes—
217C5C3×#166211yescharacteristic, direct product factor, Sylow
218C22—42no—
219C22—42no—
220C22—42no—
221C22C3×C5×#12011yescharacteristic
222C4—21no—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—81no—
227C3C5×#166211yescharacteristic, direct product factor, Sylow
228C2—82no—
229C2C3×C5×#45411yescharacteristic
230C2C3×C5×#45512yes—
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC3×C5×#562C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C5×#491C2semidirect
3. C3×C5×#489C2semidirect
4. C3×C5×#330C2semidirect
5. C3×C5×#329C2semidirect
6. C5×#1662C3direct (N × H)
18. C3×#1662C5direct (N × H)
20. C5×#491C2×C3semidirect
21. C5×#489C2×C3semidirect
22. C5×#330C2×C3semidirect
23. C5×#329C2×C3semidirect
40. C3×#491C2×C5semidirect
41. C3×#489C2×C5semidirect
42. C3×#330C2×C5semidirect
43. C3×#329C2×C5semidirect
55. #1662C3×C5direct (N × H)
96. #491C2×C3×C5semidirect
97. #489C2×C3×C5semidirect
98. #330C2×C3×C5semidirect
99. #329C2×C3×C5semidirect
188. C3×C5#1662direct (N × H)
217. C5C3×#1662direct (N × H)
227. C3C5×#1662direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5622
C3×C5×#4912
C3×C5×#4892
C3×C5×#3302
C3×C5×#3292
C5×#16623
C3×#16625