Finite Group Databasebeta

← C3×#10602001 #14291905

Subgroups — C3×#10602001 #14291905

Order 1920.

320 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#486C211yesmaximal, characteristic
2C3×#65380C211yesmaximal, characteristic, complemented
3C3×#65364C211yesmaximal, characteristic
4C3×C8×Dic10C211yesmaximal, characteristic, complemented
5C3×#64766C211yesmaximal, characteristic, complemented
6C3×#64764C211yesmaximal, characteristic
7C3×#64677C211yesmaximal, characteristic, complemented
8#10602001C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C2×C3×#687—21no—
12C3×C4×Dic10C2211yescharacteristic
13C3×C5×#102—21no—
14C3×C5×#102—21no—
15C3×C4×C5×C8C2211yescharacteristic
16C3×#3964—21no—
17C3×#3946—21no—
18C3×C8×Dic5—21no—
19C3×#3942—21no—
20C3×#3939—21no—
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24C3×#1678—51nomaximal, Hall
25C5×#486C2×C311yescharacteristic
26#65380C2×C311yescharacteristic, complemented
27#65364C2×C311yescharacteristic
28C8×Dic10C2×C311yescharacteristic, complemented
29#64766C2×C311yescharacteristic, complemented
30#64764C2×C311yescharacteristic
31#64677C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×Dic10D411yescharacteristic
37C2×C3×C5×C8D411yescharacteristic
38C2×C3×C5×C8D411yescharacteristic
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C3×#687—42no—
43C3×C4⋊Dic5D411yescharacteristic
44C3×#683—21no—
45C3×C4×Dic5—21no—
46C2×C3×#168—21no—
47C2×C3×#168—21no—
48C2×C3×#168—21no—
49C3×#486D511yescharacteristic
50C3×#477—51no—
51C3×#460—51no—
52C3×C8×Q8—51no—
53C3×#334—51no—
54C3×#333—51no—
55C3×#331—51no—
56C5×C4⋊Q8C22×C311yescharacteristic
57C5×#127C22×C311yescharacteristic
58C2×#687—21no—
59C4×Dic10C22×C311yescharacteristic
60C5×#102—21no—
61C5×#102—21no—
62C4×C5×C8C22×C311yescharacteristic
63#3964—21no—
64#3946—21no—
65C8×Dic5—21no—
66#3942—21no—
67#3939—21no—
68C4⋊#168C22×C311yescharacteristic
69C4⋊#168C22×C311yescharacteristic
70C4⋊#168C22×C311yescharacteristic
71#1678—51noSylow
72C23×C3×C5—41no—
73C3×C5×Q8—81no—
74C3×C5×D4—41no—
75C3×C5×D4—41no—
76C3×C5×D4—41no—
77C3×C5×D4—41no—
78C3×C5×D4—81no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5#4111yescharacteristic
83C2×C3×Dic5—21no—
84C2×C3×Dic5—21no—
85C3×Dic10—21no—
86C3×Dic10SD1612yes—
87C3×C5×C8—21no—
88C3×C5×C8—21no—
89C3×#168—41no—
90C3×#168—41no—
91C3×#168—41no—
92C2×C3×SD16—101no—
93C3×C4⋊Q8C2×D511yescharacteristic
94C3×#127C2×D511yescharacteristic
95C3×C4×Q8—51no—
96C3×#107—101no—
97C3×C4⋊C8—51no—
98C3×C4⋊C8—51no—
99C3×C4⋊C8—51no—
100C3×C4⋊C8—101no—
101C3×#103—101no—
102C3×#102—21no—
103C3×#102—21no—
104C3×#102—101no—
105C3×C4×C8—101no—
106C3×C4×C8C2×D511yescharacteristic
107C2×C5×Q8—21no—
108C2×C5×D4—21no—
109C2×C5×D4—21no—
110C2×C5×D4—21no—
111C2×Dic10C3×D411yescharacteristic
112C2×C5×C8C3×D411yescharacteristic
113C2×C5×C8C3×D411yescharacteristic
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C42×C5C23×C311yescharacteristic
117#687—42no—
118C4⋊Dic5C3×D411yescharacteristic
119#683—21no—
120C4×Dic5—21no—
121C2×#168—21no—
122C2×#168—21no—
123C2×#168—21no—
124#486C3×D511yescharacteristic
125#477—51no—
126#460—51no—
127C8×Q8—51no—
128#334—51no—
129#333—51no—
130#331—51no—
131C22×C3×C5—81no—
132C22×C3×C5—81no—
133C22×C3×C5—81no—
134C22×C3×C5#12111yescharacteristic
135C3×C4×C5—21no—
136C3×C4×C5—81no—
137C3×C4×C5C2×SD1611yescharacteristic
138C3×C4×C5#13511yescharacteristic
139C3×C4×C5#13511yescharacteristic
140C3×C4×C5#13711yescharacteristic
141C3×Dic5—22no—
142C3×Dic5—41no—
143C2×C3×Q8—21no—
144C2×C3×Q8—51no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C3×SD16—202no—
149C2×C3×C8—101no—
150C2×C3×C8—101no—
151C2×C3×C8—101no—
152C2×C3×C8C22⋊D511yescharacteristic
153C2×C3×C8C22⋊D511yescharacteristic
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—51no—
157C3×C4⋊C4—101no—
158C3×C42—101no—
159C3×C42C22×D511yescharacteristic
160C23×C5—41no—
161C5×Q8—81no—
162C5×D4—41no—
163C5×D4—41no—
164C5×D4—41no—
165C5×D4—41no—
166C5×D4—81no—
167C2×C4×C5—41no—
168C2×C4×C5C2×C3×D411yescharacteristic
169C2×C4×C5C2×C3×D411yescharacteristic
170C2×C4×C5C3×#4111yescharacteristic
171C2×Dic5—21no—
172C2×Dic5—21no—
173Dic10—21no—
174Dic10C3×SD1612yes—
175C5×C8—21no—
176C5×C8—21no—
177#168—41no—
178#168—41no—
179#168—41no—
180C2×SD16—101no—
181C4⋊Q8C2×C3×D511yescharacteristic
182#127C2×C3×D511yescharacteristic
183C4×Q8—51no—
184#107—101no—
185C4⋊C8—51no—
186C4⋊C8—51no—
187C4⋊C8—51no—
188C4⋊C8—101no—
189#103—101no—
190#102—21no—
191#102—21no—
192#102—101no—
193C4×C8—101no—
194C4×C8C2×C3×D511yescharacteristic
195C2×C3×C5—161no—
196C2×C3×C5#46411yescharacteristic
197C2×C3×C5#46511yescharacteristic
198C2×C3×C5#47211yescharacteristic
199C23×C3—41no—
200C3×Q8—52no—
201C3×Q8—81no—
202C3×Q8—101no—
203C3×D4—41no—
204C3×D4—41no—
205C3×D4—41no—
206C3×D4—41no—
207C3×D4—81no—
208C2×C3×C4—41no—
209C2×C3×C4—101no—
210C2×C3×C4—101no—
211C2×C3×C4D4×D511yescharacteristic
212C2×C3×C4#71111yescharacteristic
213C2×C3×C4C2×C22⋊D511yescharacteristic
214C3×C8—21no—
215C3×C8—21no—
216C3×C8—201no—
217C3×C8—201no—
218C3×C8—201no—
219C22×C5—81no—
220C22×C5—81no—
221C22×C5—81no—
222C22×C5C3×#12111yescharacteristic
223C4×C5—21no—
224C4×C5—81no—
225C4×C5C2×C3×SD1611yescharacteristic
226C4×C5C3×#13511yescharacteristic
227C4×C5C3×#13511yescharacteristic
228C4×C5C3×#13711yescharacteristic
229Dic5—22no—
230Dic5—41no—
231C2×Q8—21no—
232C2×Q8—51no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—21no—
236SD16—202no—
237C2×C8—101no—
238C2×C8—101no—
239C2×C8—101no—
240C2×C8C3×C22⋊D511yescharacteristic
241C2×C8C3×C22⋊D511yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—51no—
245C4⋊C4—101no—
246C42—101no—
247C42C22×C3×D511yescharacteristic
248C3×C5#167811yescharacteristic, complemented, Hall
249C22×C3—81no—
250C22×C3—81no—
251C22×C3—81no—
252C22×C3#408411yescharacteristic
253C3×C4—21no—
254C3×C4—81no—
255C3×C4—102no—
256C3×C4—201no—
257C3×C4D5×SD1611yescharacteristic
258C3×C4#406211yescharacteristic
259C3×C4#409611yescharacteristic
260C3×C4#409711yescharacteristic
261C2×C5—161no—
262C2×C5C3×#46411yescharacteristic
263C2×C5C3×#46511yescharacteristic
264C2×C5C3×#47211yescharacteristic
265C23—41no—
266Q8—52no—
267Q8—81no—
268Q8—101no—
269D4—41no—
270D4—41no—
271D4—41no—
272D4—41no—
273D4—81no—
274C2×C4—41no—
275C2×C4—101no—
276C2×C4—101no—
277C2×C4C3×D4×D511yescharacteristic
278C2×C4C3×#71111yescharacteristic
279C2×C4C2×C3×C22⋊D511yescharacteristic
280C8—21no—
281C8—21no—
282C8—201no—
283C8—201no—
284C8—201no—
285C2×C3—161no—
286C2×C3#6534311yescharacteristic
287C2×C3#6544911yescharacteristic
288C2×C3#6546011yescharacteristic
289C5C3×#167811yescharacteristic, complemented, Sylow
290C22—81no—
291C22—81no—
292C22—81no—
293C22C3×#408411yescharacteristic
294C4—21no—
295C4—81no—
296C4—102no—
297C4—201no—
298C4C3×D5×SD1611yescharacteristic
299C4C3×#406211yescharacteristic
300C4C3×#409611yescharacteristic
301C4C3×#409711yescharacteristic
302C3#1060200111yescharacteristic, direct product factor, Sylow
303C2—161no—
304C2C3×#6534311yescharacteristic
305C2C3×#6544911yescharacteristic
306C2C3×#6546011yescharacteristic
subgroupG/H
centerC22×C3#4084
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#486C2
socleC22×C3×C5#121
prime radicalC3×C5×#127C22
hypercenterC3×#486D5
hypocenterC5C3×#1678
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#486

Complements

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

NH ≅ G/Ntype
2. C3×#65380C2semidirect
4. C3×C8×Dic10C2semidirect
5. C3×#64766C2semidirect
7. C3×#64677C2semidirect
8. #10602001C3direct (N × H)
26. #65380C2×C3semidirect
28. C8×Dic10C2×C3semidirect
29. #64766C2×C3semidirect
31. #64677C2×C3semidirect
248. C3×C5#1678semidirect
289. C5C3×#1678semidirect
302. C3#10602001direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4862
C3×#653802
C3×#653642
C3×C8×Dic102
C3×#647662
C3×#647642
C3×#646772
#106020013
C3×#16785