Finite Group Databasebeta

← C3×#10604279 #14285257

Subgroups — C3×#10604279 #14285257

Order 1920.

456 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C2×C3×#4034C211yesmaximal, characteristic
2C3×#65757C211yesmaximal, characteristic
3C3×#65757C211yesmaximal, characteristic
4C3×#64873C214yesmaximal, complemented
5#10604279C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×Dic10—21no—
7C2×C3×C5×C4⋊C4C411yescharacteristic
8C2×C3×C4⋊Dic5C411yescharacteristic
9C2×C3×#683—21no—
10C2×C3×C4×Dic5C2211yescharacteristic
11C3×#4034—21no—
12C3×#4034—21no—
13C3×#4034C412yes—
14C3×#4034C2212yes—
15C3×C22⋊#170—21no—
16C3×C22⋊#170—21no—
17C3×#4004C2212yes—
18C3×#4004C2212yes—
19C3×#4002—21no—
20C3×#4002—21no—
21C3×#1556—51nomaximal, Hall
22C2×#4034C2×C311yescharacteristic
23#65757C2×C311yescharacteristic
24#65757C2×C311yescharacteristic
25#64873C2×C314yescomplemented
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×Dic5—21no—
29C22×C3×Dic5D411yescharacteristic
30C22×C3×Dic5D411yescharacteristic
31C2×C3×Dic10—22no—
32C2×C3×Dic10—22no—
33C2×C3×Dic10—44no—
34C2×C3×#170—22no—
35C2×C3×#170—22no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4C2×C412yes—
38C3×C4⋊Dic5—21no—
39C3×C4⋊Dic5C2×C412yes—
40C3×#683—22no—
41C3×#683—22no—
42C3×C4×Dic5C2×C411yescharacteristic
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5C2311yescharacteristic
46C2×C3×C4⋊Q8—51no—
47C3×#432—51no—
48C3×#432—51no—
49C3×#332—54no—
50C22×Dic10—21no—
51C2×C5×C4⋊C4C3×C411yescharacteristic
52C2×C4⋊Dic5C3×C411yescharacteristic
53C2×#683—21no—
54C2×C4×Dic5C22×C311yescharacteristic
55#4034—21no—
56#4034—21no—
57#4034C3×C412yes—
58#4034C22×C312yes—
59C22⋊#170—21no—
60C22⋊#170—21no—
61#4004C22×C312yes—
62#4004C22×C312yes—
63#4002—21no—
64#4002—21no—
65#1556—51noSylow
66C23×C3×C5C22⋊C411yescharacteristic
67C2×C3×C4×C5—22no—
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5—42no—
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×C3×Dic5—22no—
73C2×C3×Dic5—22no—
74C2×C3×Dic5—22no—
75C2×C3×Dic5—42no—
76C2×C3×Dic5C22⋊C411yescharacteristic
77C2×C3×Dic5C22⋊C411yescharacteristic
78C2×C3×Dic5C2×D411yescharacteristic
79C2×C3×Dic5C2×D411yescharacteristic
80C3×Dic10—44no—
81C3×Dic10—44no—
82C3×#170—42no—
83C3×#170—42no—
84C22×C3×Q8—101no—
85C3×C4⋊Q8—52no—
86C3×C4⋊Q8—52no—
87C3×C4⋊Q8—101no—
88C3×C4⋊Q8—101no—
89C2×C3×C4⋊C4—51no—
90C2×C3×C4⋊C4—101no—
91C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
92C2×C3×C42—51no—
93C3×C4⋊C8—52no—
94C3×C4⋊C8—52no—
95C3×C22⋊C8—101no—
96C3×C22⋊C8—101no—
97C3×#97—101no—
98C3×#97—101no—
99C22×C4×C5—21no—
100C22×C4×C5C2×C3×C411yescharacteristic
101C22×Dic5—21no—
102C22×Dic5C3×D411yescharacteristic
103C22×Dic5C3×D411yescharacteristic
104C2×Dic10—22no—
105C2×Dic10—22no—
106C2×Dic10—44no—
107C2×#170—22no—
108C2×#170—22no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4C2×C3×C412yes—
111C4⋊Dic5—21no—
112C4⋊Dic5C2×C3×C412yes—
113#683—22no—
114#683—22no—
115C4×Dic5C2×C3×C411yescharacteristic
116C4×Dic5C3×D411yescharacteristic
117C4×Dic5C3×D411yescharacteristic
118C4×Dic5C23×C311yescharacteristic
119C2×C4⋊Q8—51no—
120#432—51no—
121#432—51no—
122#332—54no—
123C22×C3×C5—21no—
124C22×C3×C5—21no—
125C22×C3×C5#10112yes—
126C22×C3×C5C2×C22⋊C411yescharacteristic
127C3×C4×C5—21no—
128C3×C4×C5—21no—
129C3×C4×C5—42no—
130C3×Dic5—21no—
131C3×Dic5—21no—
132C3×Dic5—42no—
133C3×Dic5AGL(1,ℤ/8)12yes—
134C3×Dic5#13712yes—
135C2×C3×Q8—102no—
136C2×C3×Q8—102no—
137C2×C3×Q8—204no—
138C22×C3×C4—21no—
139C22×C3×C4—51no—
140C22×C3×C4—51no—
141C22×C3×C4—101no—
142C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
143C2×C3×C8—102no—
144C2×C3×C8—102no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—52no—
147C3×C4⋊C4—102no—
148C3×C4⋊C4—102no—
149C3×C4⋊C4—101no—
150C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
151C3×C42—51no—
152C3×C42—51no—
153C3×C42—51no—
154C3×C42—51no—
155C23×C5C3×C22⋊C411yescharacteristic
156C2×C4×C5—22no—
157C2×C4×C5—22no—
158C2×C4×C5—42no—
159C2×C4×C5C3×C22⋊C411yescharacteristic
160C2×C4×C5C22×C3×C411yescharacteristic
161C2×Dic5—22no—
162C2×Dic5—22no—
163C2×Dic5—22no—
164C2×Dic5—42no—
165C2×Dic5C3×C22⋊C411yescharacteristic
166C2×Dic5C3×C22⋊C411yescharacteristic
167C2×Dic5C2×C3×D411yescharacteristic
168C2×Dic5C2×C3×D411yescharacteristic
169Dic10—44no—
170Dic10—44no—
171#170—42no—
172#170—42no—
173C22×Q8—101no—
174C4⋊Q8—52no—
175C4⋊Q8—52no—
176C4⋊Q8—101no—
177C4⋊Q8—101no—
178C2×C4⋊C4—51no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic
181C2×C42—51no—
182C4⋊C8—52no—
183C4⋊C8—52no—
184C22⋊C8—101no—
185C22⋊C8—101no—
186#97—101no—
187#97—101no—
188C2×C3×C5—22no—
189C2×C3×C5C2×#10111yescharacteristic
190C2×C3×C5#41811yescharacteristic
191C2×C3×C5#41911yescharacteristic
192C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
193C3×Q8—204no—
194C3×Q8—204no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—42no—
198C2×C3×C4—51no—
199C2×C3×C4—51no—
200C2×C3×C4—51no—
201C2×C3×C4—51no—
202C2×C3×C4—102no—
203C2×C3×C4—102no—
204C2×C3×C4—102no—
205C2×C3×C4—202no—
206C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
207C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
208C3×C8—202no—
209C3×C8—202no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5C3×#10112yes—
213C22×C5C2×C3×C22⋊C411yescharacteristic
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—42no—
217Dic5—21no—
218Dic5—21no—
219Dic5—42no—
220Dic5C3×AGL(1,ℤ/8)12yes—
221Dic5C3×#13712yes—
222C2×Q8—102no—
223C2×Q8—102no—
224C2×Q8—204no—
225C22×C4—21no—
226C22×C4—51no—
227C22×C4—51no—
228C22×C4—101no—
229C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
230C2×C8—102no—
231C2×C8—102no—
232C4⋊C4—21no—
233C4⋊C4—52no—
234C4⋊C4—102no—
235C4⋊C4—102no—
236C4⋊C4—101no—
237C4⋊C4C2×C3×AGL(1,𝔽5)12yes—
238C42—51no—
239C42—51no—
240C42—51no—
241C42—51no—
242C3×C5#155611yescharacteristic, complemented, Hall
243C22×C3—21no—
244C22×C3—21no—
245C22×C3#400512yes—
246C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—42no—
250C3×C4—52no—
251C3×C4—52no—
252C3×C4—101no—
253C3×C4—101no—
254C3×C4—202no—
255C2×C5—22no—
256C2×C5C2×C3×#10111yescharacteristic
257C2×C5C3×#41811yescharacteristic
258C2×C5C3×#41911yescharacteristic
259C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
260Q8—204no—
261Q8—204no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—51no—
266C2×C4—51no—
267C2×C4—51no—
268C2×C4—51no—
269C2×C4—102no—
270C2×C4—102no—
271C2×C4—102no—
272C2×C4—202no—
273C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
274C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
275C8—202no—
276C8—202no—
277C2×C3—22no—
278C2×C3C2×#400511yescharacteristic
279C2×C3#6576711yescharacteristic
280C2×C3#6578211yescharacteristic
281C5C3×#155611yescharacteristic, complemented, Sylow
282C22—21no—
283C22—21no—
284C22C3×#400512yes—
285C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
286C4—21no—
287C4—21no—
288C4—42no—
289C4—52no—
290C4—52no—
291C4—101no—
292C4—101no—
293C4—202no—
294C3#1060427911yescharacteristic, direct product factor, Sylow
295C2—22no—
296C2C2×C3×#400511yescharacteristic
297C2C3×#6576711yescharacteristic
298C2C3×#6578211yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC4×Dic5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1556
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#64873C2semidirect
5. #10604279C3direct (N × H)
25. #64873C2×C3semidirect
242. C3×C5#1556semidirect
281. C5C3×#1556semidirect
294. C3#10604279direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40342
C3×#657572
C3×#648732
#106042793
C3×#15565