Finite Group Databasebeta

← C3×#10602621 #14284658

Subgroups — C3×#10602621 #14284658

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#533C211yesmaximal, characteristic
2C3×#65214C211yesmaximal, characteristic
3C2×C3×C4⋊#168C211yesmaximal, characteristic
4C3×#64767C212yesmaximal, complemented
5C3×#64766C212yesmaximal, complemented
6#10602621C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×#125—21no—
10C3×C5×C22⋊Q8—21no—
11C3×C5×C22⋊Q8C412yes—
12C3×C4×C5×Q8—21no—
13C3×C4×C5×Q8C412yes—
14C3×C5×#117—21no—
15C2×C3×C42×C5C2211yescharacteristic
16C22×C3×#168—21no—
17C3×C22⋊#168—21no—
18C3×C4⋊#168—21no—
19C3×C4⋊#168C2212yes—
20C3×C4⋊#168C2212yes—
21C3×C4×#168—21no—
22C3×#1542—51nomaximal, Hall
23C5×#533C2×C311yescharacteristic
24#65214C2×C311yescharacteristic
25C2×C4⋊#168C2×C311yescharacteristic
26#64767C2×C312yescomplemented
27#64766C2×C312yescomplemented
28C2×C3×C5×Q8—21no—
29C2×C3×C5×Q8C2×C412yes—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4—22no—
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4C2×C412yes—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5—22no—
41C3×C42×C5C2×C411yescharacteristic
42C3×C42×C5D411yescharacteristic
43C3×C42×C5D411yescharacteristic
44C3×C42×C5C2311yescharacteristic
45C2×C3×#168—22no—
46C2×C3×#168—22no—
47C2×C3×#168—42no—
48C3×#533D511yescharacteristic
49C3×#431—51no—
50C2×C3×C4⋊C8—51no—
51C3×#333—52no—
52C3×#332—52no—
53C5×C4⋊Q8C22×C311yescharacteristic
54C5×C4⋊Q8C22×C311yescharacteristic
55C5×#125—21no—
56C5×C22⋊Q8—21no—
57C5×C22⋊Q8C3×C412yes—
58C4×C5×Q8—21no—
59C4×C5×Q8C3×C412yes—
60C5×#117—21no—
61C2×C42×C5C22×C311yescharacteristic
62C22×#168—21no—
63C22⋊#168—21no—
64C4⋊#168—21no—
65C4⋊#168C22×C312yes—
66C4⋊#168C22×C312yes—
67C4×#168—21no—
68#1542—51noSylow
69C23×C3×C5C22⋊C411yescharacteristic
70C3×C5×Q8—42no—
71C3×C5×Q8—42no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×C4×C5C22⋊C411yescharacteristic
78C2×C3×C4×C5C22⋊C411yescharacteristic
79C2×C3×C4×C5SD1612yes—
80C2×C3×C4×C5Q1612yes—
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C3×#168—42no—
85C3×#168—42no—
86C22×C3×C8—101no—
87C3×C4⋊Q8C2×D511yescharacteristic
88C3×C4⋊Q8C2×D511yescharacteristic
89C3×#125—21no—
90C3×C22⋊Q8—21no—
91C3×C22⋊Q8Dic512yes—
92C3×C4×Q8—21no—
93C3×C4×Q8Dic512yes—
94C3×#117—21no—
95C2×C3×C42C2×D511yescharacteristic
96C3×C4⋊C8—52no—
97C3×C4⋊C8—52no—
98C3×C4⋊C8—101no—
99C3×C22⋊C8—101no—
100C3×C4×C8—101no—
101C2×C5×Q8—21no—
102C2×C5×Q8C2×C3×C412yes—
103C22×C4×C5C2×C3×C411yescharacteristic
104C22×C4×C5C3×D411yescharacteristic
105C22×C4×C5C3×D411yescharacteristic
106C5×C4⋊C4—22no—
107C5×C4⋊C4—22no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4C2×C3×C412yes—
112C5×C22⋊C4—22no—
113C42×C5—22no—
114C42×C5C2×C3×C411yescharacteristic
115C42×C5C3×D411yescharacteristic
116C42×C5C3×D411yescharacteristic
117C42×C5C23×C311yescharacteristic
118C2×#168—22no—
119C2×#168—22no—
120C2×#168—42no—
121#533C3×D511yescharacteristic
122#431—51no—
123C2×C4⋊C8—51no—
124#333—52no—
125#332—52no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5#10312yes—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C3×C4×C5—21no—
131C3×C4×C5—21no—
132C3×C4×C5—21no—
133C3×C4×C5—42no—
134C3×C4×C5—42no—
135C3×C4×C5#10312yes—
136C3×C4×C5C2×SD1611yescharacteristic
137C3×C4×C5C2×Q1611yescharacteristic
138C3×C4×C5#13512yes—
139C2×C3×Q8—21no—
140C2×C3×Q8C2×Dic512yes—
141C22×C3×C4C2×Dic511yescharacteristic
142C22×C3×C4C22⋊D511yescharacteristic
143C22×C3×C4C22⋊D511yescharacteristic
144C2×C3×C8—102no—
145C2×C3×C8—102no—
146C2×C3×C8—202no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4C2×Dic512yes—
153C3×C22⋊C4—22no—
154C3×C42—22no—
155C3×C42C2×Dic511yescharacteristic
156C3×C42C22⋊D511yescharacteristic
157C3×C42C22⋊D511yescharacteristic
158C3×C42C22×D511yescharacteristic
159C23×C5C3×C22⋊C411yescharacteristic
160C5×Q8—42no—
161C5×Q8—42no—
162C2×C4×C5—22no—
163C2×C4×C5—22no—
164C2×C4×C5—22no—
165C2×C4×C5—41no—
166C2×C4×C5C3×C22⋊C411yescharacteristic
167C2×C4×C5C3×C22⋊C411yescharacteristic
168C2×C4×C5C3×C22⋊C411yescharacteristic
169C2×C4×C5C3×SD1612yes—
170C2×C4×C5C3×Q1612yes—
171C2×C4×C5C22×C3×C411yescharacteristic
172C2×C4×C5C2×C3×D411yescharacteristic
173C2×C4×C5C2×C3×D411yescharacteristic
174#168—42no—
175#168—42no—
176C22×C8—101no—
177C4⋊Q8C2×C3×D511yescharacteristic
178C4⋊Q8C2×C3×D511yescharacteristic
179#125—21no—
180C22⋊Q8—21no—
181C22⋊Q8C3×Dic512yes—
182C4×Q8—21no—
183C4×Q8C3×Dic512yes—
184#117—21no—
185C2×C42C2×C3×D511yescharacteristic
186C4⋊C8—52no—
187C4⋊C8—52no—
188C4⋊C8—101no—
189C22⋊C8—101no—
190C4×C8—101no—
191C2×C3×C5—22no—
192C2×C3×C5#41311yescharacteristic
193C2×C3×C5C2×#10311yescharacteristic
194C2×C3×C5#41611yescharacteristic
195C23×C3C22⋊Dic511yescharacteristic
196C3×Q8—42no—
197C3×Q8—42no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—41no—
202C2×C3×C4#68812yes—
203C2×C3×C4#68912yes—
204C2×C3×C4C22⋊Dic511yescharacteristic
205C2×C3×C4C22⋊Dic511yescharacteristic
206C2×C3×C4C22⋊Dic511yescharacteristic
207C2×C3×C4C22×Dic511yescharacteristic
208C2×C3×C4C2×C22⋊D511yescharacteristic
209C2×C3×C4C2×C22⋊D511yescharacteristic
210C3×C8—202no—
211C3×C8—202no—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5C3×#10312yes—
215C22×C5C2×C3×C22⋊C411yescharacteristic
216C4×C5—21no—
217C4×C5—21no—
218C4×C5—21no—
219C4×C5—42no—
220C4×C5—42no—
221C4×C5C3×#10312yes—
222C4×C5C2×C3×SD1611yescharacteristic
223C4×C5C2×C3×Q1611yescharacteristic
224C4×C5C3×#13512yes—
225C2×Q8—21no—
226C2×Q8C2×C3×Dic512yes—
227C22×C4C2×C3×Dic511yescharacteristic
228C22×C4C3×C22⋊D511yescharacteristic
229C22×C4C3×C22⋊D511yescharacteristic
230C2×C8—102no—
231C2×C8—102no—
232C2×C8—202no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4C2×C3×Dic512yes—
239C22⋊C4—22no—
240C42—22no—
241C42C2×C3×Dic511yescharacteristic
242C42C3×C22⋊D511yescharacteristic
243C42C3×C22⋊D511yescharacteristic
244C42C22×C3×D511yescharacteristic
245C3×C5#154211yescharacteristic, complemented, Hall
246C22×C3—21no—
247C22×C3—21no—
248C22×C3#396712yes—
249C22×C3C2×C22⋊Dic511yescharacteristic
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—42no—
254C3×C4—42no—
255C3×C4#396712yes—
256C3×C4C2×#68811yescharacteristic
257C3×C4C2×#68911yescharacteristic
258C3×C4#409612yes—
259C2×C5—22no—
260C2×C5C3×#41311yescharacteristic
261C2×C5C2×C3×#10311yescharacteristic
262C2×C5C3×#41611yescharacteristic
263C23C3×C22⋊Dic511yescharacteristic
264Q8—42no—
265Q8—42no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4C3×#68812yes—
271C2×C4C3×#68912yes—
272C2×C4C3×C22⋊Dic511yescharacteristic
273C2×C4C3×C22⋊Dic511yescharacteristic
274C2×C4C3×C22⋊Dic511yescharacteristic
275C2×C4C22×C3×Dic511yescharacteristic
276C2×C4C2×C3×C22⋊D511yescharacteristic
277C2×C4C2×C3×C22⋊D511yescharacteristic
278C8—202no—
279C8—202no—
280C2×C3—22no—
281C2×C3C2×#396711yescharacteristic
282C2×C3#6552211yescharacteristic
283C2×C3#6552611yescharacteristic
284C5C3×#154211yescharacteristic, complemented, Sylow
285C22—21no—
286C22—21no—
287C22C3×#396712yes—
288C22C2×C3×C22⋊Dic511yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—42no—
293C4—42no—
294C4C3×#396712yes—
295C4C2×C3×#68811yescharacteristic
296C4C2×C3×#68911yescharacteristic
297C4C3×#409612yes—
298C3#1060262111yescharacteristic, direct product factor, Sylow
299C2—22no—
300C2C2×C3×#396711yescharacteristic
301C2C3×#6552211yescharacteristic
302C2C3×#6552611yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊Dic5
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#533C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC42×C5C23×C3
hypercenterC3×#533D5
hypocenterC5C3×#1542
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#533

Complements

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

NH ≅ G/Ntype
4. C3×#64767C2semidirect
5. C3×#64766C2semidirect
6. #10602621C3direct (N × H)
26. #64767C2×C3semidirect
27. #64766C2×C3semidirect
245. C3×C5#1542semidirect
284. C5C3×#1542semidirect
298. C3#10602621direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5332
C3×#652142
C2×C3×C4⋊#1682
C3×#647672
C3×#647662
#106026213
C3×#15425