Finite Group Databasebeta

← C3×#10604658 #14284816

Subgroups — C3×#10604658 #14284816

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C4⋊Q8C211yesmaximal, characteristic
2C3×#65682C211yesmaximal, characteristic
3C3×#65678C211yesmaximal, characteristic
4C3×#64873C214yesmaximal, complemented
5#10604658C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×Q8×D5—21no—
7C2×C3×#700—21no—
8C3×C5×C4⋊Q8C411yescharacteristic
9C3×#4090—21no—
10C3×D5×C4⋊C4—21no—
11C3×D5×C4⋊C4C412yes—
12C3×#4034—21no—
13C3×#4034C2212yes—
14C3×C42×D5C2211yescharacteristic
15C3×#4015C411yescharacteristic
16C3×#4004—21no—
17C3×#4004C2212yes—
18C3×#4004C2212yes—
19C3×#4003—21no—
20C3×C4×#170—21no—
21C3×#1546—51nomaximal, Hall
22D5×C4⋊Q8C2×C311yescharacteristic
23#65682C2×C311yescharacteristic
24#65678C2×C311yescharacteristic
25#64873C2×C314yescomplemented
26C2×C3×C5×Q8—21no—
27C3×Q8×D5—42no—
28C3×Q8×D5—42no—
29C2×C3×C4×D5—22no—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×C4×D5D411yescharacteristic
33C2×C3×Dic10—21no—
34C2×C3×Dic10—22no—
35C2×C3×#170—22no—
36C2×C3×#170—22no—
37C3×#700—42no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4C2×C412yes—
40C3×C42×C5C2×C411yescharacteristic
41C3×C4⋊Dic5—21no—
42C3×C4⋊Dic5C2×C412yes—
43C3×#683—22no—
44C3×#683—22no—
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5C2311yescharacteristic
48C2×C3×C4⋊Q8—51no—
49C3×#431—51no—
50C3×#423—51no—
51C3×#332—54no—
52C2×Q8×D5—21no—
53C2×#700—21no—
54C5×C4⋊Q8C3×C411yescharacteristic
55#4090—21no—
56D5×C4⋊C4—21no—
57D5×C4⋊C4C3×C412yes—
58#4034—21no—
59#4034C22×C312yes—
60C42×D5C22×C311yescharacteristic
61#4015C3×C411yescharacteristic
62#4004—21no—
63#4004C22×C312yes—
64#4004C22×C312yes—
65#4003—21no—
66C4×#170—21no—
67#1546—51noSylow
68C22×C3×D5C22⋊C411yescharacteristic
69C3×C5×Q8—42no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5C22⋊C411yescharacteristic
72C2×C3×C4×C5C22⋊C411yescharacteristic
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×Dic5—22no—
75C2×C3×Dic5C22⋊C411yescharacteristic
76C2×C3×Dic5C2×D411yescharacteristic
77C2×C3×Dic5C2×D411yescharacteristic
78C3×C4×D5—22no—
79C3×C4×D5—22no—
80C3×C4×D5—44no—
81C3×C4×D5D812yes—
82C3×C4×D5SD1612yes—
83C3×Dic10—42no—
84C3×Dic10—42no—
85C3×Dic10—42no—
86C3×#170—42no—
87C3×#170—42no—
88C22×C3×Q8—101no—
89C2×C3×M16—101no—
90C3×C4⋊Q8—52no—
91C3×C4⋊Q8—51no—
92C3×C4⋊Q8—101no—
93C3×C4⋊Q8—101no—
94C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
95C2×C3×C4⋊C4—52no—
96C2×C3×C4⋊C4—101no—
97C2×C3×C42—51no—
98C3×C4⋊C8—52no—
99C3×C4⋊C8—52no—
100C3×C4⋊C8—101no—
101C3×C22⋊C8—101no—
102C3×C4×C8—101no—
103C2×C5×Q8—21no—
104Q8×D5—42no—
105Q8×D5—42no—
106C2×C4×D5—22no—
107C2×C4×D5C2×C3×C411yescharacteristic
108C2×C4×D5C3×D411yescharacteristic
109C2×C4×D5C3×D411yescharacteristic
110C2×Dic10—21no—
111C2×Dic10—22no—
112C2×#170—22no—
113C2×#170—22no—
114#700—42no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4C2×C3×C412yes—
117C42×C5C2×C3×C411yescharacteristic
118C4⋊Dic5—21no—
119C4⋊Dic5C2×C3×C412yes—
120#683—22no—
121#683—22no—
122C4×Dic5C3×D411yescharacteristic
123C4×Dic5C3×D411yescharacteristic
124C4×Dic5C23×C311yescharacteristic
125C2×C4⋊Q8—51no—
126#431—51no—
127#423—51no—
128#332—54no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C2×C3×D5—21no—
131C2×C3×D5—21no—
132C2×C3×D5#10212yes—
133C3×C4×C5—21no—
134C3×C4×C5—21no—
135C3×C4×C5—42no—
136C3×C4×C5#10212yes—
137C3×Dic5—42no—
138C3×Dic5#10112yes—
139C3×Dic5C2×D811yescharacteristic
140C3×Dic5C2×SD1611yescharacteristic
141C3×Dic5#13712yes—
142C2×C3×Q8—21no—
143C2×C3×Q8—102no—
144C2×C3×Q8—101no—
145C2×C3×Q8—202no—
146C2×C3×Q8—202no—
147C22×C3×C4—51no—
148C22×C3×C4—51no—
149C22×C3×C4—51no—
150C22×C3×C4—102no—
151C3×M16—202no—
152C2×C3×C8—102no—
153C2×C3×C8—102no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—52no—
156C3×C4⋊C4—102no—
157C3×C4⋊C4—102no—
158C3×C4⋊C4—101no—
159C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
160C3×C42—51no—
161C3×C42—51no—
162C3×C42—51no—
163C3×C42C2×AGL(1,𝔽5)11yescharacteristic
164C22×D5C3×C22⋊C411yescharacteristic
165C5×Q8—42no—
166C2×C4×C5—22no—
167C2×C4×C5C3×C22⋊C411yescharacteristic
168C2×C4×C5C3×C22⋊C411yescharacteristic
169C2×C4×C5C22×C3×C411yescharacteristic
170C2×Dic5—22no—
171C2×Dic5C3×C22⋊C411yescharacteristic
172C2×Dic5C2×C3×D411yescharacteristic
173C2×Dic5C2×C3×D411yescharacteristic
174C4×D5—22no—
175C4×D5—22no—
176C4×D5—44no—
177C4×D5C3×D812yes—
178C4×D5C3×SD1612yes—
179Dic10—42no—
180Dic10—42no—
181Dic10—42no—
182#170—42no—
183#170—42no—
184C22×Q8—101no—
185C2×M16—101no—
186C4⋊Q8—52no—
187C4⋊Q8—51no—
188C4⋊Q8—101no—
189C4⋊Q8—101no—
190C4⋊Q8C3×AGL(1,𝔽5)11yescharacteristic
191C2×C4⋊C4—52no—
192C2×C4⋊C4—101no—
193C2×C42—51no—
194C4⋊C8—52no—
195C4⋊C8—52no—
196C4⋊C8—101no—
197C22⋊C8—101no—
198C4×C8—101no—
199C2×C3×C5C2×#10111yescharacteristic
200C2×C3×C5C2×#10211yescharacteristic
201C2×C3×C5#41911yescharacteristic
202C3×D5—22no—
203C23×C3—51no—
204C3×Q8—42no—
205C3×Q8—202no—
206C3×Q8—202no—
207C3×Q8—202no—
208C2×C3×C4—22no—
209C2×C3×C4—51no—
210C2×C3×C4—51no—
211C2×C3×C4—51no—
212C2×C3×C4—52no—
213C2×C3×C4—52no—
214C2×C3×C4—102no—
215C2×C3×C4—102no—
216C2×C3×C4—102no—
217C2×C3×C4—204no—
218C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
219C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
220C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
221C3×C8—202no—
222C3×C8—202no—
223C22×C5C2×C3×C22⋊C411yescharacteristic
224C2×D5—21no—
225C2×D5—21no—
226C2×D5C3×#10212yes—
227C4×C5—21no—
228C4×C5—21no—
229C4×C5—42no—
230C4×C5C3×#10212yes—
231Dic5—42no—
232Dic5C3×#10112yes—
233Dic5C2×C3×D811yescharacteristic
234Dic5C2×C3×SD1611yescharacteristic
235Dic5C3×#13712yes—
236C2×Q8—21no—
237C2×Q8—102no—
238C2×Q8—101no—
239C2×Q8—202no—
240C2×Q8—202no—
241C22×C4—51no—
242C22×C4—51no—
243C22×C4—51no—
244C22×C4—102no—
245M16—202no—
246C2×C8—102no—
247C2×C8—102no—
248C4⋊C4—21no—
249C4⋊C4—52no—
250C4⋊C4—102no—
251C4⋊C4—102no—
252C4⋊C4—101no—
253C4⋊C4C2×C3×AGL(1,𝔽5)12yes—
254C42—51no—
255C42—51no—
256C42—51no—
257C42C2×C3×AGL(1,𝔽5)11yescharacteristic
258C3×C5#154611yescharacteristic, complemented, Hall
259C22×C3—52no—
260C22×C3—101no—
261C22×C3—101no—
262C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—42no—
266C3×C4—51no—
267C3×C4—51no—
268C3×C4—52no—
269C3×C4—52no—
270C3×C4—202no—
271C3×C4#400712yes—
272C2×C5C2×C3×#10111yescharacteristic
273C2×C5C2×C3×#10211yescharacteristic
274C2×C5C3×#41911yescharacteristic
275D5—22no—
276C23—51no—
277Q8—42no—
278Q8—202no—
279Q8—202no—
280Q8—202no—
281C2×C4—22no—
282C2×C4—51no—
283C2×C4—51no—
284C2×C4—51no—
285C2×C4—52no—
286C2×C4—52no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—102no—
290C2×C4—204no—
291C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
292C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
293C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
294C8—202no—
295C8—202no—
296C2×C3—102no—
297C2×C3C2×#400711yescharacteristic
298C2×C3#6578211yescharacteristic
299C2×C3D5⋊#10111yescharacteristic
300C5C3×#154611yescharacteristic, complemented, Sylow
301C22—52no—
302C22—101no—
303C22—101no—
304C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
305C4—21no—
306C4—21no—
307C4—42no—
308C4—51no—
309C4—51no—
310C4—52no—
311C4—52no—
312C4—202no—
313C4C3×#400712yes—
314C3#1060465811yescharacteristic, direct product factor, Sylow
315C2—102no—
316C2C2×C3×#400711yescharacteristic
317C2C3×#6578211yescharacteristic
318C2C3×D5⋊#10111yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×C4⋊Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC4×Dic5C23×C3
hypercenterC3×C4⋊Q8AGL(1,𝔽5)
hypocenterC5C3×#1546
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C3×#64873C2semidirect
5. #10604658C3direct (N × H)
25. #64873C2×C3semidirect
258. C3×C5#1546semidirect
300. C5C3×#1546semidirect
314. C3#10604658direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
C3×#656822
C3×#656782
C3×#648732
#106046583
C3×#15465