Finite Group Databasebeta

← C3×C5×#1630 #14274664

Subgroups — C3×C5×#1630 #14274664

Order 1920.

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

normal subgroups only

This group has 436 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×C5×#559C211yesmaximal, characteristic
2C3×C5×#492C211yesmaximal, characteristic
3C3×C5×#477C212yesmaximal, complemented
4C3×C5×#331C211yesmaximal, characteristic
5C3×C5×Q8⋊C8C212yesmaximal, complemented
6C5×#1630C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×SD16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×#127C2211yescharacteristic
10C3×C5×#124—22no—
11C3×C5×#123—22no—
12C3×C4×C5×Q8C2212yes—
13C3×C4×C5×D4—22no—
14C3×C5×#107—22no—
15C3×C5×C4⋊C8C2212yes—
16C3×C5×#103—22no—
17C3×C4×C5×C8C2211yescharacteristic
18C3×#1630C511yesmaximal, characteristic, direct product factor, Hall
19C5×#559C2×C311yescharacteristic
20C5×#492C2×C311yescharacteristic
21C5×#477C2×C312yescomplemented
22C5×#331C2×C311yescharacteristic
23C5×Q8⋊C8C2×C312yescomplemented
24C2×C3×C5×Q8—21no—
25C2×C3×C5×Q8D412yes—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4D412yes—
28C22×C3×C4×C5—22no—
29C3×C5×SD16—44no—
30C2×C3×C5×C8—21no—
31C2×C3×C5×C8—22no—
32C3×C5×C4⋊C4—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4D412yes—
35C3×C5×C22⋊C4—24no—
36C3×C5×C22⋊C4—22no—
37C3×C42×C5—22no—
38C3×C42×C5C2311yescharacteristic
39C3×#559C2×C511yescharacteristic
40C3×#492C2×C511yescharacteristic
41C3×#477C2×C512yescomplemented
42C3×#331C2×C511yescharacteristic
43C3×Q8⋊C8C2×C512yescomplemented
44C2×C5×SD16—22no—
45C5×C4⋊Q8C22×C311yescharacteristic
46C5×#127C22×C311yescharacteristic
47C5×#124—22no—
48C5×#123—22no—
49C4×C5×Q8C22×C312yes—
50C4×C5×D4—22no—
51C5×#107—22no—
52C5×C4⋊C8C22×C312yes—
53C5×#103—22no—
54C4×C5×C8C22×C311yescharacteristic
55#1630C3×C511yescharacteristic, direct product factor, Sylow
56C23×C3×C5—22no—
57C3×C5×Q8—22no—
58C3×C5×Q8—22no—
59C3×C5×Q8—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C3×C5×D4—42no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5—82no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×C3×C4×C5C2×D412yes—
69C3×C5×C8—22no—
70C3×C5×C8—42no—
71C2×C3×SD16—22no—
72C3×C4⋊Q8C22×C511yescharacteristic
73C3×#127C22×C511yescharacteristic
74C3×#124—22no—
75C3×#123—22no—
76C3×C4×Q8C22×C512yes—
77C3×C4×D4—22no—
78C3×#107—22no—
79C3×C4⋊C8C22×C512yes—
80C3×#103—22no—
81C3×C4×C8C22×C511yescharacteristic
82C2×C5×Q8—21no—
83C2×C5×Q8C3×D412yes—
84C2×C5×D4—22no—
85C2×C5×D4C3×D412yes—
86C22×C4×C5—22no—
87C5×SD16—44no—
88C2×C5×C8—21no—
89C2×C5×C8—22no—
90C5×C4⋊C4—22no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4C3×D412yes—
93C5×C22⋊C4—24no—
94C5×C22⋊C4—22no—
95C42×C5—22no—
96C42×C5C23×C311yescharacteristic
97#559C2×C3×C511yescharacteristic
98#492C2×C3×C511yescharacteristic
99#477C2×C3×C512yescomplemented
100#331C2×C3×C511yescharacteristic
101Q8⋊C8C2×C3×C512yescomplemented
102C22×C3×C5—44no—
103C22×C3×C5—42no—
104C22×C3×C5#12011yescharacteristic
105C3×C4×C5—21no—
106C3×C4×C5—42no—
107C3×C4×C5—42no—
108C3×C4×C5—81no—
109C3×C4×C5#13512yes—
110C3×C4×C5#13712yes—
111C2×C3×Q8—21no—
112C2×C3×Q8C5×D412yes—
113C2×C3×D4—22no—
114C2×C3×D4C5×D412yes—
115C22×C3×C4—22no—
116C3×SD16—44no—
117C2×C3×C8—21no—
118C2×C3×C8—22no—
119C3×C4⋊C4—22no—
120C3×C4⋊C4—22no—
121C3×C4⋊C4C5×D412yes—
122C3×C22⋊C4—24no—
123C3×C22⋊C4—22no—
124C3×C42—22no—
125C3×C42C23×C511yescharacteristic
126C23×C5—22no—
127C5×Q8—22no—
128C5×Q8—22no—
129C5×Q8—42no—
130C5×D4—42no—
131C5×D4—42no—
132C5×D4—42no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—41no—
136C2×C4×C5—82no—
137C2×C4×C5C2×C3×D411yescharacteristic
138C2×C4×C5C2×C3×D412yes—
139C5×C8—22no—
140C5×C8—42no—
141C2×SD16—22no—
142C4⋊Q8C22×C3×C511yescharacteristic
143#127C22×C3×C511yescharacteristic
144#124—22no—
145#123—22no—
146C4×Q8C22×C3×C512yes—
147C4×D4—22no—
148#107—22no—
149C4⋊C8C22×C3×C512yes—
150#103—22no—
151C4×C8C22×C3×C511yescharacteristic
152C2×C3×C5—82no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155C23×C3—22no—
156C3×Q8—22no—
157C3×Q8—22no—
158C3×Q8—42no—
159C3×D4—42no—
160C3×D4—42no—
161C3×D4—42no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—41no—
165C2×C3×C4—82no—
166C2×C3×C4C2×C5×D411yescharacteristic
167C2×C3×C4C2×C5×D412yes—
168C3×C8—22no—
169C3×C8—42no—
170C22×C5—44no—
171C22×C5—42no—
172C22×C5C3×#12011yescharacteristic
173C4×C5—21no—
174C4×C5—42no—
175C4×C5—42no—
176C4×C5—81no—
177C4×C5C3×#13512yes—
178C4×C5C3×#13712yes—
179C2×Q8—21no—
180C2×Q8C3×C5×D412yes—
181C2×D4—22no—
182C2×D4C3×C5×D412yes—
183C22×C4—22no—
184SD16—44no—
185C2×C8—21no—
186C2×C8—22no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4C3×C5×D412yes—
190C22⋊C4—24no—
191C22⋊C4—22no—
192C42—22no—
193C42C23×C3×C511yescharacteristic
194C3×C5#163011yescharacteristic, direct product factor, Hall
195C22×C3—44no—
196C22×C3—42no—
197C22×C3C5×#12011yescharacteristic
198C3×C4—21no—
199C3×C4—42no—
200C3×C4—42no—
201C3×C4—81no—
202C3×C4C5×#13512yes—
203C3×C4C5×#13712yes—
204C2×C5—82no—
205C2×C5C3×#45212yes—
206C2×C5C3×#45311yescharacteristic
207C23—22no—
208Q8—22no—
209Q8—22no—
210Q8—42no—
211D4—42no—
212D4—42no—
213D4—42no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—82no—
218C2×C4C2×C3×C5×D411yescharacteristic
219C2×C4C2×C3×C5×D412yes—
220C8—22no—
221C8—42no—
222C2×C3—82no—
223C2×C3C5×#45212yes—
224C2×C3C5×#45311yescharacteristic
225C5C3×#163011yescharacteristic, direct product factor, Sylow
226C22—44no—
227C22—42no—
228C22C3×C5×#12011yescharacteristic
229C4—21no—
230C4—42no—
231C4—42no—
232C4—81no—
233C4C3×C5×#13512yes—
234C4C3×C5×#13712yes—
235C3C5×#163011yescharacteristic, direct product factor, Sylow
236C2—82no—
237C2C3×C5×#45212yes—
238C2C3×C5×#45311yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC3×C5×#127C22
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
3. C3×C5×#477C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. C5×#1630C3direct (N × H)
18. C3×#1630C5direct (N × H)
21. C5×#477C2×C3semidirect
23. C5×Q8⋊C8C2×C3semidirect
41. C3×#477C2×C5semidirect
43. C3×Q8⋊C8C2×C5semidirect
55. #1630C3×C5direct (N × H)
99. #477C2×C3×C5semidirect
101. Q8⋊C8C2×C3×C5semidirect
194. C3×C5#1630direct (N × H)
225. C5C3×#1630direct (N × H)
235. C3C5×#1630direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5592
C3×C5×#4922
C3×C5×#4772
C3×C5×#3312
C3×C5×Q8⋊C82
C5×#16303
C3×#16305