Finite Group Databasebeta

← C3×#10602751 #14316878

Subgroups — C3×#10602751 #14316878

Order 1920.

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

normal subgroups only

This group has 452 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×#563C211yesmaximal, characteristic, complemented
2C3×#65350C211yesmaximal, characteristic
3C3×#65342C212yesmaximal
4C3×#64761C211yesmaximal, characteristic, complemented
5C3×#64759C212yesmaximal, complemented
6#10602751C311yesmaximal, characteristic, direct product factor, Hall
7C3×#4144C2211yescharacteristic
8C3×C5×C4⋊Q8—21no—
9C3×C5×#126—22no—
10C3×C5×#125—21no—
11C3×C5×#124C2211yescharacteristic
12C3×C5×#123C2212yes—
13C3×C5×C22⋊Q8—22no—
14C3×#4088—21no—
15C3×#4075—22no—
16C3×#3966C2212yes—
17C3×#3965C2211yescharacteristic
18C3×#3938—22no—
19C3×#3937—21no—
20C3×#2201—51nomaximal, Hall
21C5×#563C2×C311yescharacteristic, complemented
22#65350C2×C311yescharacteristic
23#65342C2×C312yes—
24#64761C2×C311yescharacteristic, complemented
25#64759C2×C312yescomplemented
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4C2311yescharacteristic
29C22×C3×C4×C5D412yes—
30C2×C3×C22⋊D5—22no—
31C3×#711—41no—
32C3×D4×D5—41no—
33C3×#709—21no—
34C3×C5×C4⋊C4—21no—
35C3×C5×C4⋊C4—22no—
36C3×C5×C4⋊C4—22no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—22no—
39C3×C5×C22⋊C4—22no—
40C3×C5×C22⋊C4—22no—
41C3×C5×C22⋊C4D412yes—
42C3×C42×C5—21no—
43C3×C42×C5D411yescharacteristic
44C3×C22⋊Dic5—22no—
45C3×#689—41no—
46C3×#688—41no—
47C3×#685—42no—
48C3×#683—42no—
49C3×#681—21no—
50C3×#563D511yescharacteristic, complemented
51C3×#458—52no—
52C3×#455—51no—
53C3×#354—51no—
54C3×#352—52no—
55#4144C22×C311yescharacteristic
56C5×C4⋊Q8—21no—
57C5×#126—22no—
58C5×#125—21no—
59C5×#124C22×C311yescharacteristic
60C5×#123C22×C312yes—
61C5×C22⋊Q8—22no—
62#4088—21no—
63#4075—22no—
64#3966C22×C312yes—
65#3965C22×C311yescharacteristic
66#3938—22no—
67#3937—21no—
68#2201—51noSylow
69C23×C3×C5C2×D412yes—
70C22×C3×D5—22no—
71C3×C5×Q8—41no—
72C3×C5×Q8—81no—
73C3×C5×D4—41no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—42no—
79C2×C3×C4×C5C2×D411yescharacteristic
80C3×C22⋊D5—42no—
81C3×C22⋊D5—41no—
82C2×C3×Dic5—22no—
83C2×C3×Dic5—42no—
84C3×D20—21no—
85C3×C4×D5—41no—
86C3×Dic10—21no—
87C3×#168—41no—
88C3×H(5,𝔽2)—51no—
89C3×#137—101no—
90C3×C4⋊Q8—21no—
91C3×#126—22no—
92C3×#125—21no—
93C3×#124C2×D511yescharacteristic
94C3×#123—102no—
95C3×#123C2×D512yes—
96C3×C22⋊Q8—22no—
97C3×#104—101no—
98C3×#100—51no—
99C3×#99—52no—
100C3×#99—102no—
101C2×C5×Q8—21no—
102C2×C5×Q8C3×D411yescharacteristic
103C2×C5×D4C23×C311yescharacteristic
104C22×C4×C5C3×D412yes—
105C2×C22⋊D5—22no—
106#711—41no—
107D4×D5—41no—
108#709—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—22no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—22no—
114C5×C22⋊C4—22no—
115C5×C22⋊C4—22no—
116C5×C22⋊C4C3×D412yes—
117C42×C5—21no—
118C42×C5C3×D411yescharacteristic
119C22⋊Dic5—22no—
120#689—41no—
121#688—41no—
122#685—42no—
123#683—42no—
124#681—21no—
125#563C3×D511yescharacteristic, complemented
126#458—52no—
127#455—51no—
128#354—51no—
129#352—52no—
130C22×C3×C5—22no—
131C22×C3×C5—42no—
132C22×C3×C5#12011yescharacteristic
133C2×C3×D5—41no—
134C2×C3×D5—82no—
135C3×C4×C5—21no—
136C3×C4×C5—42no—
137C3×C4×C5—41no—
138C3×C4×C5—42no—
139C3×C4×C5—41no—
140C3×Dic5—41no—
141C3×Dic5—82no—
142C3×#41—101no—
143C3×#41—201no—
144C2×C3×Q8—21no—
145C2×C3×Q8C22⋊D511yescharacteristic
146C2×C3×D4—102no—
147C2×C3×D4—201no—
148C2×C3×D4C22×D511yescharacteristic
149C22×C3×C4C22⋊D512yes—
150C3×Q16—201no—
151C3×SD16—201no—
152C3×M16—101no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—202no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—102no—
162C3×C22⋊C4—202no—
163C3×C22⋊C4C22⋊D512yes—
164C3×C42—21no—
165C3×C42C22⋊D511yescharacteristic
166C23×C5C2×C3×D412yes—
167C22×D5—22no—
168C5×Q8—41no—
169C5×Q8—81no—
170C5×D4—41no—
171C2×C4×C5—21no—
172C2×C4×C5—22no—
173C2×C4×C5—21no—
174C2×C4×C5—22no—
175C2×C4×C5—42no—
176C2×C4×C5C2×C3×D411yescharacteristic
177C22⋊D5—42no—
178C22⋊D5—41no—
179C2×Dic5—22no—
180C2×Dic5—42no—
181D20—21no—
182C4×D5—41no—
183Dic10—21no—
184#168—41no—
185H(5,𝔽2)—51no—
186#137—101no—
187C4⋊Q8—21no—
188#126—22no—
189#125—21no—
190#124C2×C3×D511yescharacteristic
191#123—102no—
192#123C2×C3×D512yes—
193C22⋊Q8—22no—
194#104—101no—
195#100—51no—
196#99—52no—
197#99—102no—
198C2×C3×C5—21no—
199C2×C3×C5—42no—
200C2×C3×C5B(4,𝔽2)11yescharacteristic
201C3×D5—81no—
202C23×C3—102no—
203C23×C3C2×C22⋊D512yes—
204C3×Q8—41no—
205C3×Q8—81no—
206C3×Q8—101no—
207C3×D4—41no—
208C3×D4—101no—
209C3×D4—202no—
210C3×D4—201no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—22no—
215C2×C3×C4—42no—
216C2×C3×C4—102no—
217C2×C3×C4—201no—
218C2×C3×C4—202no—
219C2×C3×C4C2×C22⋊D511yescharacteristic
220C3×C8—201no—
221C22×C5—22no—
222C22×C5—42no—
223C22×C5C3×#12011yescharacteristic
224C2×D5—41no—
225C2×D5—82no—
226C4×C5—21no—
227C4×C5—42no—
228C4×C5—41no—
229C4×C5—42no—
230C4×C5—41no—
231Dic5—41no—
232Dic5—82no—
233#41—101no—
234#41—201no—
235C2×Q8—21no—
236C2×Q8C3×C22⋊D511yescharacteristic
237C2×D4—102no—
238C2×D4—201no—
239C2×D4C22×C3×D511yescharacteristic
240C22×C4C3×C22⋊D512yes—
241Q16—201no—
242SD16—201no—
243M16—101no—
244C4⋊C4—21no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—21no—
248C4⋊C4—22no—
249C4⋊C4—202no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—102no—
253C22⋊C4—202no—
254C22⋊C4C3×C22⋊D512yes—
255C42—21no—
256C42C3×C22⋊D511yescharacteristic
257C3×C5#220111yescharacteristic, complemented, Hall
258C22×C3—22no—
259C22×C3—42no—
260C22×C3—201no—
261C22×C3—402no—
262C22×C3#409911yescharacteristic
263C3×C4—21no—
264C3×C4—42no—
265C3×C4—41no—
266C3×C4—42no—
267C3×C4—41no—
268C3×C4—201no—
269C3×C4—402no—
270C2×C5—21no—
271C2×C5—42no—
272C2×C5C3×B(4,𝔽2)11yescharacteristic
273D5—81no—
274C23—102no—
275C23C2×C3×C22⋊D512yes—
276Q8—41no—
277Q8—81no—
278Q8—101no—
279D4—41no—
280D4—101no—
281D4—202no—
282D4—201no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—42no—
288C2×C4—102no—
289C2×C4—201no—
290C2×C4—202no—
291C2×C4C2×C3×C22⋊D511yescharacteristic
292C8—201no—
293C2×C3—21no—
294C2×C3—42no—
295C2×C3—401no—
296C2×C3#6553311yescharacteristic
297C5C3×#220111yescharacteristic, complemented, Sylow
298C22—22no—
299C22—42no—
300C22—201no—
301C22—402no—
302C22C3×#409911yescharacteristic
303C4—21no—
304C4—42no—
305C4—41no—
306C4—42no—
307C4—41no—
308C4—201no—
309C4—402no—
310C3#1060275111yescharacteristic, direct product factor, Sylow
311C2—21no—
312C2—42no—
313C2—401no—
314C2C3×#6553311yescharacteristic
subgroupG/H
centerC2×C3#65533
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#563C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×#4144C22
hypercenterC3×#563D5
hypocenterC5C3×#2201
LCSG ▷ C2×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#563

Complements

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

NH ≅ G/Ntype
1. C3×C5×#563C2semidirect
4. C3×#64761C2semidirect
5. C3×#64759C2semidirect
6. #10602751C3direct (N × H)
21. C5×#563C2×C3semidirect
24. #64761C2×C3semidirect
25. #64759C2×C3semidirect
50. C3×#563D5semidirect
125. #563C3×D5semidirect
257. C3×C5#2201semidirect
297. C5C3×#2201semidirect
310. C3#10602751direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5632
C3×#653502
C3×#653422
C3×#647612
C3×#647592
#106027513
C3×#22015