Finite Group Databasebeta

← C3×#10601817 #14292412

Subgroups — C3×#10601817 #14292412

Order 1920.

336 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×C5×#460C211yesmaximal, characteristic
2C3×#65365C211yesmaximal, characteristic
3C3×#65313C211yesmaximal, characteristic, complemented
4C3×#65309C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64699C211yesmaximal, characteristic, complemented
8#10601817C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12C2×C3×#687—21no—
13C2×C3×#687—21no—
14C3×#4015C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×#102—21no—
17C3×#3967—21no—
18C3×#3940—21no—
19C3×C4⋊#168—21no—
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×#3935—21no—
23C3×C4×#168C2211yescharacteristic
24C3×#1686—51nomaximal, Hall
25C5×#460C2×C311yescharacteristic
26#65365C2×C311yescharacteristic
27#65313C2×C311yescharacteristic, complemented
28#65309C2×C311yescharacteristic, complemented
29#64764C2×C311yescharacteristic
30#64706C2×C311yescharacteristic, complemented
31#64699C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8D411yescharacteristic
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×Dic10—21no—
37C3×C5×SD16—42no—
38C2×C3×C5×C8—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5—21no—
42C3×C42×C5C2311yescharacteristic
43C3×#687—42no—
44C3×#687—42no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C2×C3×#168—21no—
48C2×C3×#168—21no—
49C2×C3×#168D411yescharacteristic
50C2×C3×#168D411yescharacteristic
51C3×#492—51no—
52C3×#475—51no—
53C3×#460D511yescharacteristic
54C3×#446—51no—
55C3×#335—51no—
56C3×#332—51no—
57C3×#331—51no—
58C2×C5×SD16—21no—
59C5×#127C22×C311yescharacteristic
60C4×C5×Q8C22×C311yescharacteristic
61C2×#687—21no—
62C2×#687—21no—
63#4015C22×C311yescharacteristic
64C5×C4⋊C8C22×C311yescharacteristic
65C5×#102—21no—
66#3967—21no—
67#3940—21no—
68C4⋊#168—21no—
69C4⋊#168C22×C311yescharacteristic
70C4⋊#168C22×C311yescharacteristic
71#3935—21no—
72C4×#168C22×C311yescharacteristic
73#1686—51noSylow
74C23×C3×C5—41no—
75C3×C5×Q8—21no—
76C3×C5×Q8—21no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—81no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5#4111yescharacteristic
87C2×C3×Dic5—41no—
88C3×Dic10—41no—
89C3×Dic10—41no—
90C3×C5×C8—41no—
91C3×#168—21no—
92C3×#168—41no—
93C3×#168—41no—
94C3×#168SD1612yescomplemented
95C2×C3×SD16—21no—
96C2×C3×SD16—101no—
97C2×C3×SD16—101no—
98C3×C4⋊Q8—51no—
99C3×#127C2×D511yescharacteristic
100C3×C4×Q8C2×D511yescharacteristic
101C3×#106—101no—
102C3×C4⋊C8—51no—
103C3×C4⋊C8—51no—
104C3×C4⋊C8—101no—
105C3×C4⋊C8C2×D511yescharacteristic
106C3×#103—101no—
107C3×#102—21no—
108C3×#97—101no—
109C3×C4×C8—51no—
110C2×C5×Q8C3×D411yescharacteristic
111C2×C5×D4—21no—
112C2×C5×D4—21no—
113C2×C5×D4—21no—
114C2×Dic10—21no—
115C5×SD16—42no—
116C2×C5×C8—21no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4C3×D411yescharacteristic
119C42×C5—21no—
120C42×C5C23×C311yescharacteristic
121#687—42no—
122#687—42no—
123C4⋊Dic5—21no—
124C4⋊Dic5—21no—
125C2×#168—21no—
126C2×#168—21no—
127C2×#168C3×D411yescharacteristic
128C2×#168C3×D411yescharacteristic
129#492—51no—
130#475—51no—
131#460C3×D511yescharacteristic
132#446—51no—
133#335—51no—
134#332—51no—
135#331—51no—
136C22×C3×C5—81no—
137C22×C3×C5—81no—
138C22×C3×C5—81no—
139C22×C3×C5#12111yescharacteristic
140C3×C4×C5—21no—
141C3×C4×C5—41no—
142C3×C4×C5—41no—
143C3×C4×C5C2×SD1611yescharacteristic
144C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
145C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
146C3×C4×C5#13711yescharacteristic
147C3×Dic5—81no—
148C2×C3×Q8—101no—
149C2×C3×Q8C22⋊D511yescharacteristic
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C3×SD16—42no—
154C3×SD16—202no—
155C3×SD16—202no—
156C2×C3×C8—21no—
157C2×C3×C8—51no—
158C2×C3×C8—51no—
159C2×C3×C8—101no—
160C2×C3×C8—101no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—101no—
163C3×C4⋊C4—101no—
164C3×C4⋊C4C22⋊D511yescharacteristic
165C3×C42—21no—
166C3×C42C22×D511yescharacteristic
167C23×C5—41no—
168C5×Q8—21no—
169C5×Q8—21no—
170C5×D4—41no—
171C5×D4—41no—
172C5×D4—41no—
173C5×D4—41no—
174C5×D4—81no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5C2×C3×D411yescharacteristic
178C2×C4×C5C2×C3×D411yescharacteristic
179C2×C4×C5C3×#4111yescharacteristic
180C2×Dic5—41no—
181Dic10—41no—
182Dic10—41no—
183C5×C8—41no—
184#168—21no—
185#168—41no—
186#168—41no—
187#168C3×SD1612yescomplemented
188C2×SD16—21no—
189C2×SD16—101no—
190C2×SD16—101no—
191C4⋊Q8—51no—
192#127C2×C3×D511yescharacteristic
193C4×Q8C2×C3×D511yescharacteristic
194#106—101no—
195C4⋊C8—51no—
196C4⋊C8—51no—
197C4⋊C8—101no—
198C4⋊C8C2×C3×D511yescharacteristic
199#103—101no—
200#102—21no—
201#97—101no—
202C4×C8—51no—
203C2×C3×C5—161no—
204C2×C3×C5#46011yescharacteristic
205C2×C3×C5#46811yescharacteristic
206C2×C3×C5#47111yescharacteristic
207C23×C3—41no—
208C3×Q8—21no—
209C3×Q8—21no—
210C3×Q8—201no—
211C3×Q8—201no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—81no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—201no—
220C2×C3×C4D4×D511yescharacteristic
221C2×C3×C4#71111yescharacteristic
222C2×C3×C4C2×C22⋊D511yescharacteristic
223C3×C8—41no—
224C3×C8—52no—
225C3×C8—101no—
226C3×C8—201no—
227C3×C8—201no—
228C22×C5—81no—
229C22×C5—81no—
230C22×C5—81no—
231C22×C5C3×#12111yescharacteristic
232C4×C5—21no—
233C4×C5—41no—
234C4×C5—41no—
235C4×C5C2×C3×SD1611yescharacteristic
236C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
237C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
238C4×C5C3×#13711yescharacteristic
239Dic5—81no—
240C2×Q8—101no—
241C2×Q8C3×C22⋊D511yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245SD16—42no—
246SD16—202no—
247SD16—202no—
248C2×C8—21no—
249C2×C8—51no—
250C2×C8—51no—
251C2×C8—101no—
252C2×C8—101no—
253C4⋊C4—21no—
254C4⋊C4—101no—
255C4⋊C4—101no—
256C4⋊C4C3×C22⋊D511yescharacteristic
257C42—21no—
258C42C22×C3×D511yescharacteristic
259C3×C5#168611yescharacteristic, complemented, Hall
260C22×C3—81no—
261C22×C3—81no—
262C22×C3—81no—
263C22×C3#408511yescharacteristic
264C3×C4—21no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4—401no—
268C3×C4D5×SD1611yescharacteristic
269C3×C4#406011yescharacteristic
270C3×C4#407811yescharacteristic
271C3×C4#409711yescharacteristic
272C2×C5—161no—
273C2×C5C3×#46011yescharacteristic
274C2×C5C3×#46811yescharacteristic
275C2×C5C3×#47111yescharacteristic
276C23—41no—
277Q8—21no—
278Q8—21no—
279Q8—201no—
280Q8—201no—
281D4—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—201no—
289C2×C4C3×D4×D511yescharacteristic
290C2×C4C3×#71111yescharacteristic
291C2×C4C2×C3×C22⋊D511yescharacteristic
292C8—41no—
293C8—52no—
294C8—101no—
295C8—201no—
296C8—201no—
297C2×C3—161no—
298C2×C3#6533111yescharacteristic
299C2×C3#6545211yescharacteristic
300C2×C3#6548911yescharacteristic
301C5C3×#168611yescharacteristic, complemented, Sylow
302C22—81no—
303C22—81no—
304C22—81no—
305C22C3×#408511yescharacteristic
306C4—21no—
307C4—41no—
308C4—41no—
309C4—401no—
310C4C3×D5×SD1611yescharacteristic
311C4C3×#406011yescharacteristic
312C4C3×#407811yescharacteristic
313C4C3×#409711yescharacteristic
314C3#1060181711yescharacteristic, direct product factor, Sylow
315C2—161no—
316C2C3×#6533111yescharacteristic
317C2C3×#6545211yescharacteristic
318C2C3×#6548911yescharacteristic
subgroupG/H
centerC22×C3#4085
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#460C2
socleC22×C3×C5#121
prime radicalC3×C5×#127C22
hypercenterC3×#460D5
hypocenterC5C3×#1686
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
3. C3×#65313C2semidirect
4. C3×#65309C2semidirect
6. C3×#64706C2semidirect
7. C3×#64699C2semidirect
8. #10601817C3direct (N × H)
27. #65313C2×C3semidirect
28. #65309C2×C3semidirect
30. #64706C2×C3semidirect
31. #64699C2×C3semidirect
94. C3×#168SD16semidirect
187. #168C3×SD16semidirect
259. C3×C5#1686semidirect
301. C5C3×#1686semidirect
314. C3#10601817direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4602
C3×#653652
C3×#653132
C3×#653092
C3×#647642
C3×#647062
C3×#646992
#106018173
C3×#16865