Finite Group Databasebeta

← C3×#10602306 #14317312

Subgroups — C3×#10602306 #14317312

Order 1920.

308 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C3×C5×#509C211yesmaximal, characteristic
2C3×#65485C211yesmaximal, characteristic, complemented
3C3×#65484C211yesmaximal, characteristic, complemented
4C3×#65444C211yesmaximal, characteristic, complemented
5C3×#64783C211yesmaximal, characteristic, complemented
6C3×#64737C211yesmaximal, characteristic, complemented
7C3×#64731C211yesmaximal, characteristic, complemented
8#10602306C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#135C2211yescharacteristic
10C2×C3×C5×D8C2211yescharacteristic
11C3×#4094—21no—
12C3×#4082—21no—
13C2×C3×#687—21no—
14C2×C3×Dic20C2211yescharacteristic
15C3×C5×SD32—21no—
16C3×C5×D16—21no—
17C3×C5×M32C2211yescharacteristic
18C3×#3969—21no—
19C3×#3961—21no—
20C3×#3959—21no—
21C3×#3951C2211yescharacteristic
22C3×C8×Dic5C2211yescharacteristic
23C3×#3944C2211yescharacteristic
24C3×#2212—51nomaximal, Hall
25C5×#509C2×C311yescharacteristic
26#65485C2×C311yescharacteristic, complemented
27#65484C2×C311yescharacteristic, complemented
28#65444C2×C311yescharacteristic, complemented
29#64783C2×C311yescharacteristic, complemented
30#64737C2×C311yescharacteristic, complemented
31#64731C2×C311yescharacteristic, complemented
32C3×C5×#41—21no—
33C2×C3×C5×D4—21no—
34C2×C3×Dic10—21no—
35C3×C5×Q16D411yescharacteristic
36C3×C5×SD16—21no—
37C3×C5×D8—21no—
38C3×C5×D8—21no—
39C3×C5×D8D411yescharacteristic
40C2×C3×C5×C8C2311yescharacteristic
41C3×C22⋊Dic5—42no—
42C3×#687—41no—
43C3×#687—41no—
44C3×C4×Dic5D411yescharacteristic
45C3×#681—21no—
46C3×#681—41no—
47C2×C3×#168—41no—
48C2×C3×#168D411yescharacteristic
49C3×Dic20—21no—
50C3×Dic20—21no—
51C3×C5×C16—21no—
52C3×#672—21no—
53C3×#510—51no—
54C3×#509D511yescharacteristic
55C3×#495—51no—
56C3×#443—51no—
57C3×#364—51no—
58C3×#362—51no—
59C3×#361—51no—
60C5×#135C22×C311yescharacteristic
61C2×C5×D8C22×C311yescharacteristic
62#4094—21no—
63#4082—21no—
64C2×#687—21no—
65C2×Dic20C22×C311yescharacteristic
66C5×SD32—21no—
67C5×D16—21no—
68C5×M32C22×C311yescharacteristic
69#3969—21no—
70#3961—21no—
71#3959—21no—
72#3951C22×C311yescharacteristic
73C8×Dic5C22×C311yescharacteristic
74#3944C22×C311yescharacteristic
75#2212—51noSylow
76C23×C3×C5—41no—
77C3×C5×Q8—21no—
78C3×C5×D4—21no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×Dic5—21no—
85C2×C3×Dic5—41no—
86C3×Dic10—41no—
87C3×Dic10—41no—
88C3×C5×C8C2×D411yescharacteristic
89C3×C5×C8#4111yescharacteristic
90C3×#168—41no—
91C3×#168D811yescharacteristic
92C3×#168D811yescharacteristic
93C3×#135C2×D511yescharacteristic
94C2×C3×Q16—51no—
95C2×C3×SD16—101no—
96C2×C3×D8C2×D511yescharacteristic
97C3×#131—101no—
98C3×#124—101no—
99C3×Q32—101no—
100C3×SD32—21no—
101C3×SD32—101no—
102C3×D16—21no—
103C3×M32—51no—
104C3×M32C2×D511yescharacteristic
105C3×#108—51no—
106C3×#104—101no—
107C3×C4×C8—51no—
108C5×#41—21no—
109C2×C5×D4—21no—
110C2×Dic10—21no—
111C5×Q16C3×D411yescharacteristic
112C5×SD16—21no—
113C5×D8—21no—
114C5×D8—21no—
115C5×D8C3×D411yescharacteristic
116C2×C5×C8C23×C311yescharacteristic
117C22⋊Dic5—42no—
118#687—41no—
119#687—41no—
120C4×Dic5C3×D411yescharacteristic
121#681—21no—
122#681—41no—
123C2×#168—41no—
124C2×#168C3×D411yescharacteristic
125Dic20—21no—
126Dic20—21no—
127C5×C16—21no—
128#672—21no—
129#510—51no—
130#509C3×D511yescharacteristic
131#495—51no—
132#443—51no—
133#364—51no—
134#362—51no—
135#361—51no—
136C22×C3×C5—41no—
137C22×C3×C5—82no—
138C22×C3×C5—81no—
139C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
140C3×C4×C5—41no—
141C3×C4×C5#12111yescharacteristic
142C3×C4×C5C2×D811yescharacteristic
143C3×Dic5—41no—
144C3×Dic5—81no—
145C3×#41—21no—
146C2×C3×Q8—101no—
147C2×C3×D4—21no—
148C3×Q16—101no—
149C3×Q16—101no—
150C3×Q16C22⋊D511yescharacteristic
151C3×SD16—21no—
152C3×SD16—201no—
153C3×SD16—201no—
154C3×D8—21no—
155C3×D8—21no—
156C3×D8C22⋊D511yescharacteristic
157C3×M16—101no—
158C3×M16—201no—
159C2×C3×C8—51no—
160C2×C3×C8—201no—
161C2×C3×C8C22×D511yescharacteristic
162C3×C22⋊C4—202no—
163C3×C42—51no—
164C3×C16—21no—
165C3×C16—101no—
166C23×C5—41no—
167C5×Q8—21no—
168C5×D4—21no—
169C5×D4—41no—
170C5×D4—41no—
171C5×D4—41no—
172C2×C4×C5—41no—
173C2×C4×C5C2×C3×D411yescharacteristic
174C2×Dic5—21no—
175C2×Dic5—41no—
176Dic10—41no—
177Dic10—41no—
178C5×C8C2×C3×D411yescharacteristic
179C5×C8C3×#4111yescharacteristic
180#168—41no—
181#168C3×D811yescharacteristic
182#168C3×D811yescharacteristic
183#135C2×C3×D511yescharacteristic
184C2×Q16—51no—
185C2×SD16—101no—
186C2×D8C2×C3×D511yescharacteristic
187#131—101no—
188#124—101no—
189Q32—101no—
190SD32—21no—
191SD32—101no—
192D16—21no—
193M32—51no—
194M32C2×C3×D511yescharacteristic
195#108—51no—
196#104—101no—
197C4×C8—51no—
198C2×C3×C5—21no—
199C2×C3×C5—81no—
200C2×C3×C5—161no—
201C2×C3×C5#45911yescharacteristic
202C23×C3—41no—
203C3×Q8—21no—
204C3×Q8—201no—
205C3×Q8—201no—
206C3×D4—21no—
207C3×D4—41no—
208C3×D4—41no—
209C3×D4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—101no—
212C2×C3×C4—201no—
213C2×C3×C4D4×D511yescharacteristic
214C3×C8—51no—
215C3×C8—51no—
216C3×C8—201no—
217C3×C8#71111yescharacteristic
218C3×C8C2×C22⋊D511yescharacteristic
219C22×C5—41no—
220C22×C5—82no—
221C22×C5—81no—
222C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
223C4×C5—41no—
224C4×C5C3×#12111yescharacteristic
225C4×C5C2×C3×D811yescharacteristic
226Dic5—41no—
227Dic5—81no—
228#41—21no—
229C2×Q8—101no—
230C2×D4—21no—
231Q16—101no—
232Q16—101no—
233Q16C3×C22⋊D511yescharacteristic
234SD16—21no—
235SD16—201no—
236SD16—201no—
237D8—21no—
238D8—21no—
239D8C3×C22⋊D511yescharacteristic
240M16—101no—
241M16—201no—
242C2×C8—51no—
243C2×C8—201no—
244C2×C8C22×C3×D511yescharacteristic
245C22⋊C4—202no—
246C42—51no—
247C16—21no—
248C16—101no—
249C3×C5#221211yescharacteristic, complemented, Hall
250C22×C3—41no—
251C22×C3—82no—
252C22×C3—81no—
253C22×C3#405711yescharacteristic
254C3×C4—41no—
255C3×C4—201no—
256C3×C4—401no—
257C3×C4D5×D811yescharacteristic
258C3×C4#408511yescharacteristic
259C2×C5—21no—
260C2×C5—81no—
261C2×C5—161no—
262C2×C5C3×#45911yescharacteristic
263C23—41no—
264Q8—21no—
265Q8—201no—
266Q8—201no—
267D4—21no—
268D4—41no—
269D4—41no—
270D4—41no—
271C2×C4—41no—
272C2×C4—101no—
273C2×C4—201no—
274C2×C4C3×D4×D511yescharacteristic
275C8—51no—
276C8—51no—
277C8—201no—
278C8C3×#71111yescharacteristic
279C8C2×C3×C22⋊D511yescharacteristic
280C2×C3—21no—
281C2×C3—81no—
282C2×C3—161no—
283C2×C3#6543911yescharacteristic
284C5C3×#221211yescharacteristic, complemented, Sylow
285C22—41no—
286C22—82no—
287C22—81no—
288C22C3×#405711yescharacteristic
289C4—41no—
290C4—201no—
291C4—401no—
292C4C3×D5×D811yescharacteristic
293C4C3×#408511yescharacteristic
294C3#1060230611yescharacteristic, direct product factor, Sylow
295C2—21no—
296C2—81no—
297C2—161no—
298C2C3×#6543911yescharacteristic
subgroupG/H
centerC2×C3#65439
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
Fitting, prime radicalC3×C5×#509C2
socleC2×C3×C5#459
hypercenterC3×#509D5
hypocenterC5C3×#2212
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#509

Complements

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

NH ≅ G/Ntype
2. C3×#65485C2semidirect
3. C3×#65484C2semidirect
4. C3×#65444C2semidirect
5. C3×#64783C2semidirect
6. C3×#64737C2semidirect
7. C3×#64731C2semidirect
8. #10602306C3direct (N × H)
26. #65485C2×C3semidirect
27. #65484C2×C3semidirect
28. #65444C2×C3semidirect
29. #64783C2×C3semidirect
30. #64737C2×C3semidirect
31. #64731C2×C3semidirect
249. C3×C5#2212semidirect
284. C5C3×#2212semidirect
294. C3#10602306direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5092
C3×#654852
C3×#654842
C3×#654442
C3×#647832
C3×#647372
C3×#647312
#106023063
C3×#22125