Finite Group Databasebeta

← C3×#10599135 #14283974

Subgroups — C3×#10599135 #14283974

Order 1920.

540 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 126 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×#66002C211yesmaximal, characteristic
2C3×#64996C212yesmaximal, complemented
3C3×C5×#329C211yesmaximal, characteristic, complemented
4C3×#64760C211yesmaximal, characteristic, complemented
5C3×#64684C212yesmaximal, complemented
6#10599135C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#713C411yescharacteristic
8C2×C3×#711C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×#4090C411yescharacteristic
11C3×#4086C411yescharacteristic
12C2×C3×#676—22no—
13C3×#4030—22no—
14C3×#4027—22no—
15C3×#4021C2211yescharacteristic
16C3×C42×D5C2211yescharacteristic
17C3×C5×#97C2212yes—
18C3×C8×Dic5—22no—
19C3×#3935C2212yes—
20C3×#1525—51nomaximal, Hall
21#66002C2×C311yescharacteristic
22#64996C2×C312yescomplemented
23C5×#329C2×C311yescharacteristic, complemented
24#64760C2×C311yescharacteristic, complemented
25#64684C2×C312yescomplemented
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×C3×C22⋊D5—21no—
29C2×C3×C22⋊D5—22no—
30C22×C3×Dic5—21no—
31C3×#713—42no—
32C3×#711—42no—
33C2×C3×D20—21no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D412yes—
38C2×C3×Dic10C2×C411yescharacteristic
39C2×C3×C5×C8—22no—
40C3×C5×C22⋊C4—22no—
41C3×C42×C5C2311yescharacteristic
42C3×#685—22no—
43C3×#683—22no—
44C3×C4×Dic5C2×C411yescharacteristic
45C3×C4×Dic5D412yes—
46C2×C3×#168—22no—
47C3×#676—28no—
48C3×#532—51no—
49C3×C4×M16—52no—
50C3×#329—51no—
51C3×#329—52no—
52C3×#329D511yescharacteristic, complemented
53C2×#713C3×C411yescharacteristic
54C2×#711C3×C411yescharacteristic
55C5×#124C22×C311yescharacteristic
56#4090C3×C411yescharacteristic
57#4086C3×C411yescharacteristic
58C2×#676—22no—
59#4030—22no—
60#4027—22no—
61#4021C22×C311yescharacteristic
62C42×D5C22×C311yescharacteristic
63C5×#97C22×C312yes—
64C8×Dic5—22no—
65#3935C22×C312yes—
66#1525—51noSylow
67C23×C3×C5—21no—
68C22×C3×D5—21no—
69C22×C3×D5C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C3×C5×D4—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C3×C22⋊D5—42no—
76C3×C22⋊D5—44no—
77C2×C3×Dic5—21no—
78C2×C3×Dic5—42no—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C2×C3×Dic5C22⋊C412yes—
81C3×D20—41no—
82C3×D20—42no—
83C3×C4×D5—22no—
84C3×C4×D5—24no—
85C3×C4×D5—42no—
86C3×Dic10—41no—
87C3×C5×C8—24no—
88C3×#168—24no—
89C2×C3×#41—51no—
90C2×C3×#41—51no—
91C2×C3×M16—102no—
92C3×C4⋊Q8—51no—
93C3×#127—51no—
94C3×#124—51no—
95C3×#124C2×D511yescharacteristic
96C3×#121—102no—
97C3×C4×D4—102no—
98C2×C3×C42—51no—
99C3×#97—52no—
100C3×#97C2×D512yes—
101C3×C4×C8—102no—
102C2×C5×Q8C2×C3×C411yescharacteristic
103C2×C5×D4C2×C3×C411yescharacteristic
104C2×C22⋊D5—21no—
105C2×C22⋊D5—22no—
106C22×Dic5—21no—
107#713—42no—
108#711—42no—
109C2×D20—21no—
110C2×D20C2×C3×C411yescharacteristic
111C2×C4×D5—21no—
112C2×C4×D5C2×C3×C411yescharacteristic
113C2×C4×D5C3×D412yes—
114C2×Dic10C2×C3×C411yescharacteristic
115C2×C5×C8—22no—
116C5×C22⋊C4—22no—
117C42×C5C23×C311yescharacteristic
118#685—22no—
119#683—22no—
120C4×Dic5C2×C3×C411yescharacteristic
121C4×Dic5C3×D412yes—
122C2×#168—22no—
123#676—28no—
124#532—51no—
125C4×M16—52no—
126#329—51no—
127#329—52no—
128#329C3×D511yescharacteristic, complemented
129C22×C3×C5—41no—
130C22×C3×C5—42no—
131C22×C3×C5C2×C22⋊C411yescharacteristic
132C2×C3×D5—21no—
133C2×C3×D5—22no—
134C2×C3×D5—41no—
135C2×C3×D5—42no—
136C3×C4×C5—21no—
137C3×C4×C5—22no—
138C3×C4×C5—41no—
139C3×Dic5—41no—
140C3×Dic5#10012yes—
141C3×Dic5#10414yes—
142C3×#41—202no—
143C3×#41—202no—
144C2×C3×Q8—51no—
145C2×C3×Q8C4×D511yescharacteristic
146C2×C3×D4—51no—
147C2×C3×D4—101no—
148C2×C3×D4—102no—
149C2×C3×D4—101no—
150C2×C3×D4C4×D511yescharacteristic
151C22×C3×C4—51no—
152C22×C3×C4—52no—
153C22×C3×C4—101no—
154C22×C3×C4—101no—
155C3×M16—108no—
156C2×C3×C8—22no—
157C2×C3×C8—102no—
158C3×C4⋊C4—102no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—102no—
161C3×C42—51no—
162C3×C42—52no—
163C3×C42C22×D511yescharacteristic
164C23×C5—21no—
165C22×D5—21no—
166C22×D5C3×C22⋊C411yescharacteristic
167C5×Q8—41no—
168C5×D4—41no—
169C2×C4×C5—21no—
170C2×C4×C5C22×C3×C411yescharacteristic
171C2×C4×C5C2×C3×D412yes—
172C22⋊D5—42no—
173C22⋊D5—44no—
174C2×Dic5—21no—
175C2×Dic5—42no—
176C2×Dic5C3×C22⋊C411yescharacteristic
177C2×Dic5C3×C22⋊C412yes—
178D20—41no—
179D20—42no—
180C4×D5—22no—
181C4×D5—24no—
182C4×D5—42no—
183Dic10—41no—
184C5×C8—24no—
185#168—24no—
186C2×#41—51no—
187C2×#41—51no—
188C2×M16—102no—
189C4⋊Q8—51no—
190#127—51no—
191#124—51no—
192#124C2×C3×D511yescharacteristic
193#121—102no—
194C4×D4—102no—
195C2×C42—51no—
196#97—52no—
197#97C2×C3×D512yes—
198C4×C8—102no—
199C2×C3×C5—81no—
200C2×C3×C5C2×#10011yescharacteristic
201C2×C3×C5C2×#10412yes—
202C3×D5—41no—
203C3×D5—81no—
204C23×C3—21no—
205C23×C3—51no—
206C23×C3—101no—
207C3×Q8—41no—
208C3×Q8—201no—
209C3×D4—41no—
210C3×D4—201no—
211C3×D4—202no—
212C3×D4—204no—
213C3×D4—202no—
214C2×C3×C4—21no—
215C2×C3×C4—52no—
216C2×C3×C4—51no—
217C2×C3×C4—104no—
218C2×C3×C4—102no—
219C2×C3×C4—101no—
220C2×C3×C4—202no—
221C2×C3×C4—202no—
222C2×C3×C4C2×C4×D511yescharacteristic
223C2×C3×C4D4×D512yes—
224C3×C8—24no—
225C3×C8—104no—
226C22×C5—41no—
227C22×C5—42no—
228C22×C5C2×C3×C22⋊C411yescharacteristic
229C2×D5—21no—
230C2×D5—22no—
231C2×D5—41no—
232C2×D5—42no—
233C4×C5—21no—
234C4×C5—22no—
235C4×C5—41no—
236Dic5—41no—
237Dic5C3×#10012yes—
238Dic5C3×#10414yes—
239#41—202no—
240#41—202no—
241C2×Q8—51no—
242C2×Q8C3×C4×D511yescharacteristic
243C2×D4—51no—
244C2×D4—101no—
245C2×D4—102no—
246C2×D4—101no—
247C2×D4C3×C4×D511yescharacteristic
248C22×C4—51no—
249C22×C4—52no—
250C22×C4—101no—
251C22×C4—101no—
252M16—108no—
253C2×C8—22no—
254C2×C8—102no—
255C4⋊C4—102no—
256C22⋊C4—22no—
257C22⋊C4—102no—
258C42—51no—
259C42—52no—
260C42C22×C3×D511yescharacteristic
261C3×C5#152511yescharacteristic, complemented, Hall
262C22×C3—41no—
263C22×C3—42no—
264C22×C3—101no—
265C22×C3—102no—
266C22×C3—201no—
267C22×C3—202no—
268C22×C3D5×C22⋊C411yescharacteristic
269C3×C4—21no—
270C3×C4—22no—
271C3×C4—41no—
272C3×C4—52no—
273C3×C4—54no—
274C3×C4—201no—
275C2×C5—81no—
276C2×C5C2×C3×#10011yescharacteristic
277C2×C5C2×C3×#10412yes—
278D5—41no—
279D5—81no—
280C23—21no—
281C23—51no—
282C23—101no—
283Q8—41no—
284Q8—201no—
285D4—41no—
286D4—201no—
287D4—202no—
288D4—204no—
289D4—202no—
290C2×C4—21no—
291C2×C4—52no—
292C2×C4—51no—
293C2×C4—104no—
294C2×C4—102no—
295C2×C4—101no—
296C2×C4—202no—
297C2×C4—202no—
298C2×C4C2×C3×C4×D511yescharacteristic
299C2×C4C3×D4×D512yes—
300C8—24no—
301C8—104no—
302C2×C3—81no—
303C2×C3—201no—
304C2×C3—401no—
305C2×C3D5×#10011yescharacteristic
306C2×C3D5×#10412yes—
307C5C3×#152511yescharacteristic, complemented, Sylow
308C22—41no—
309C22—42no—
310C22—101no—
311C22—102no—
312C22—201no—
313C22—202no—
314C22C3×D5×C22⋊C411yescharacteristic
315C4—21no—
316C4—22no—
317C4—41no—
318C4—52no—
319C4—54no—
320C4—201no—
321C3#1059913511yescharacteristic, direct product factor, Sylow
322C2—81no—
323C2—201no—
324C2—401no—
325C2C3×D5×#10011yescharacteristic
326C2C3×D5×#10412yes—
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#329C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66002C2
cosocleC42×C5C23×C3
hypercenterC3×#329D5
hypocenterC5C3×#1525
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#329

Complements

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

NH ≅ G/Ntype
2. C3×#64996C2semidirect
3. C3×C5×#329C2semidirect
4. C3×#64760C2semidirect
5. C3×#64684C2semidirect
6. #10599135C3direct (N × H)
22. #64996C2×C3semidirect
23. C5×#329C2×C3semidirect
24. #64760C2×C3semidirect
25. #64684C2×C3semidirect
52. C3×#329D5semidirect
128. #329C3×D5semidirect
261. C3×C5#1525semidirect
307. C5C3×#1525semidirect
321. C3#10599135direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660022
C3×#649962
C3×C5×#3292
C3×#647602
C3×#646842
#105991353
C3×#15255