Finite Group Databasebeta

← C3×C5×#1634 #14274668

Subgroups — C3×C5×#1634 #14274668

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×#555C211yesmaximal, characteristic
2C3×C5×#494C211yesmaximal, characteristic, complemented
3C3×C5×#476C212yesmaximal, complemented
4C3×C5×#333C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C212yesmaximal, complemented
6C5×#1634C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×Q16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#124—22no—
11C3×C5×#121—22no—
12C3×C4×C5×D4C2212yes—
13C3×C5×#117—22no—
14C3×C5×#106—22no—
15C3×C5×C4⋊C8C2212yes—
16C3×C5×#102—22no—
17C3×C4×C5×C8C2211yescharacteristic
18C3×#1634C511yesmaximal, characteristic, direct product factor, Hall
19C5×#555C2×C311yescharacteristic
20C5×#494C2×C311yescharacteristic, complemented
21C5×#476C2×C312yescomplemented
22C5×#333C2×C311yescharacteristic, complemented
23C5×D4⋊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×Q16—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×#555C2×C511yescharacteristic
40C3×#494C2×C511yescharacteristic, complemented
41C3×#476C2×C512yescomplemented
42C3×#333C2×C511yescharacteristic, complemented
43C3×D4⋊C8C2×C512yescomplemented
44C2×C5×Q16—22no—
45C5×C4⋊Q8C22×C311yescharacteristic
46C5×C4⋊Q8C22×C311yescharacteristic
47C5×#124—22no—
48C5×#121—22no—
49C4×C5×D4C22×C312yes—
50C5×#117—22no—
51C5×#106—22no—
52C5×C4⋊C8C22×C312yes—
53C5×#102—22no—
54C4×C5×C8C22×C311yescharacteristic
55#1634C3×C511yescharacteristic, direct product factor, Sylow
56C23×C3×C5—22no—
57C3×C5×Q8—42no—
58C3×C5×Q8—42no—
59C3×C5×D4—22no—
60C3×C5×D4—22no—
61C3×C5×D4—82no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—42no—
65C2×C3×C4×C5—42no—
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×C3×C4×C5C2×D412yes—
69C3×C5×C8—22no—
70C3×C5×C8—42no—
71C2×C3×Q16—22no—
72C3×C4⋊Q8C22×C511yescharacteristic
73C3×C4⋊Q8C22×C511yescharacteristic
74C3×#124—22no—
75C3×#121—22no—
76C3×C4×D4C22×C512yes—
77C3×#117—22no—
78C3×#106—22no—
79C3×C4⋊C8C22×C512yes—
80C3×#102—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×Q16—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#555C2×C3×C511yescharacteristic
98#494C2×C3×C511yescharacteristic, complemented
99#476C2×C3×C512yescomplemented
100#333C2×C3×C511yescharacteristic, complemented
101D4⋊C8C2×C3×C512yescomplemented
102C22×C3×C5—42no—
103C22×C3×C5—42no—
104C22×C3×C5—42no—
105C22×C3×C5#12011yescharacteristic
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5—42no—
109C3×C4×C5—81no—
110C3×C4×C5#13512yes—
111C3×C4×C5#13712yes—
112C2×C3×Q8—21no—
113C2×C3×Q8C5×D412yes—
114C2×C3×D4—22no—
115C2×C3×D4C5×D412yes—
116C22×C3×C4—22no—
117C3×Q16—44no—
118C2×C3×C8—21no—
119C2×C3×C8—22no—
120C3×C4⋊C4—22no—
121C3×C4⋊C4—22no—
122C3×C4⋊C4C5×D412yes—
123C3×C22⋊C4—24no—
124C3×C22⋊C4—22no—
125C3×C42—22no—
126C3×C42C23×C511yescharacteristic
127C23×C5—22no—
128C5×Q8—42no—
129C5×Q8—42no—
130C5×D4—22no—
131C5×D4—22no—
132C5×D4—82no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—42no—
136C2×C4×C5—42no—
137C2×C4×C5—41no—
138C2×C4×C5C2×C3×D411yescharacteristic
139C2×C4×C5C2×C3×D412yes—
140C5×C8—22no—
141C5×C8—42no—
142C2×Q16—22no—
143C4⋊Q8C22×C3×C511yescharacteristic
144C4⋊Q8C22×C3×C511yescharacteristic
145#124—22no—
146#121—22no—
147C4×D4C22×C3×C512yes—
148#117—22no—
149#106—22no—
150C4⋊C8C22×C3×C512yes—
151#102—22no—
152C4×C8C22×C3×C511yescharacteristic
153C2×C3×C5—82no—
154C2×C3×C5#45212yes—
155C2×C3×C5#45311yescharacteristic
156C23×C3—22no—
157C3×Q8—42no—
158C3×Q8—42no—
159C3×D4—22no—
160C3×D4—22no—
161C3×D4—82no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—42no—
165C2×C3×C4—42no—
166C2×C3×C4—41no—
167C2×C3×C4C2×C5×D411yescharacteristic
168C2×C3×C4C2×C5×D412yes—
169C3×C8—22no—
170C3×C8—42no—
171C22×C5—42no—
172C22×C5—42no—
173C22×C5—42no—
174C22×C5C3×#12011yescharacteristic
175C4×C5—21no—
176C4×C5—42no—
177C4×C5—42no—
178C4×C5—81no—
179C4×C5C3×#13512yes—
180C4×C5C3×#13712yes—
181C2×Q8—21no—
182C2×Q8C3×C5×D412yes—
183C2×D4—22no—
184C2×D4C3×C5×D412yes—
185C22×C4—22no—
186Q16—44no—
187C2×C8—21no—
188C2×C8—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4C3×C5×D412yes—
192C22⋊C4—24no—
193C22⋊C4—22no—
194C42—22no—
195C42C23×C3×C511yescharacteristic
196C3×C5#163411yescharacteristic, direct product factor, Hall
197C22×C3—42no—
198C22×C3—42no—
199C22×C3—42no—
200C22×C3C5×#12011yescharacteristic
201C3×C4—21no—
202C3×C4—42no—
203C3×C4—42no—
204C3×C4—81no—
205C3×C4C5×#13512yes—
206C3×C4C5×#13712yes—
207C2×C5—82no—
208C2×C5C3×#45212yes—
209C2×C5C3×#45311yescharacteristic
210C23—22no—
211Q8—42no—
212Q8—42no—
213D4—22no—
214D4—22no—
215D4—82no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4C2×C3×C5×D411yescharacteristic
222C2×C4C2×C3×C5×D412yes—
223C8—22no—
224C8—42no—
225C2×C3—82no—
226C2×C3C5×#45212yes—
227C2×C3C5×#45311yescharacteristic
228C5C3×#163411yescharacteristic, direct product factor, Sylow
229C22—42no—
230C22—42no—
231C22—42no—
232C22C3×C5×#12011yescharacteristic
233C4—21no—
234C4—42no—
235C4—42no—
236C4—81no—
237C4C3×C5×#13512yes—
238C4C3×C5×#13712yes—
239C3C5×#163411yescharacteristic, direct product factor, Sylow
240C2—82no—
241C2C3×C5×#45212yes—
242C2C3×C5×#45311yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC3×C5×#555C2
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×#494C2semidirect
3. C3×C5×#476C2semidirect
4. C3×C5×#333C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C5×#1634C3direct (N × H)
18. C3×#1634C5direct (N × H)
20. C5×#494C2×C3semidirect
21. C5×#476C2×C3semidirect
22. C5×#333C2×C3semidirect
23. C5×D4⋊C8C2×C3semidirect
40. C3×#494C2×C5semidirect
41. C3×#476C2×C5semidirect
42. C3×#333C2×C5semidirect
43. C3×D4⋊C8C2×C5semidirect
55. #1634C3×C5direct (N × H)
98. #494C2×C3×C5semidirect
99. #476C2×C3×C5semidirect
100. #333C2×C3×C5semidirect
101. D4⋊C8C2×C3×C5semidirect
196. C3×C5#1634direct (N × H)
228. C5C3×#1634direct (N × H)
239. C3C5×#1634direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5552
C3×C5×#4942
C3×C5×#4762
C3×C5×#3332
C3×C5×D4⋊C82
C5×#16343
C3×#16345