Finite Group Databasebeta

← C3×#10599957 #14313668

Subgroups — C3×#10599957 #14313668

Order 1920.

460 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 110 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×#66009C211yesmaximal, characteristic
2C3×D5×#101C212yesmaximal, complemented
3C3×C5×#355C211yesmaximal, characteristic, complemented
4C3×#64762C211yesmaximal, characteristic, complemented
5C3×#64698C212yesmaximal, complemented
6#10599957C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×Q8×D5C2211yescharacteristic
8C2×C3×#711C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×#4090C2211yescharacteristic
11C3×#4082C411yescharacteristic
12C3×D5×M16—22no—
13C3×#4029—22no—
14C3×#4024—22no—
15C3×#4018C411yescharacteristic
16C3×#4015C411yescharacteristic
17C3×C5×#101C2212yes—
18C3×#3968C2212yes—
19C3×#3956—22no—
20C3×#2133—51nomaximal, Hall
21#66009C2×C311yescharacteristic
22D5×#101C2×C312yescomplemented
23C5×#355C2×C311yescharacteristic, complemented
24#64762C2×C311yescharacteristic, complemented
25#64698C2×C312yescomplemented
26C2×C3×C5×Q8C2311yescharacteristic
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×C3×C22⋊D5—21no—
29C22×C3×Dic5—21no—
30C3×Q8×D5—42no—
31C3×#711—42no—
32C2×C3×C4×D5C2×C411yescharacteristic
33C2×C3×C4×D5D412yes—
34C2×C3×Dic10C2×C411yescharacteristic
35C2×C3×Dic10C2×C411yescharacteristic
36C2×C3×Dic10D412yes—
37C3×C5×M16—22no—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5C2×C411yescharacteristic
40C3×C22⋊Dic5—22no—
41C3×#685—21no—
42C3×C4⋊Dic5—22no—
43C3×#683—22no—
44C3×#683—21no—
45C3×C4×Dic5C2×C411yescharacteristic
46C3×#681—22no—
47C3×#676—42no—
48C3×C8×D5—42no—
49C3×#536—51no—
50C2×C3×#101—52no—
51C3×#356—52no—
52C3×#355—51no—
53C3×#355D511yescharacteristic, complemented
54C2×Q8×D5C22×C311yescharacteristic
55C2×#711C3×C411yescharacteristic
56C5×#124C22×C311yescharacteristic
57#4090C22×C311yescharacteristic
58#4082C3×C411yescharacteristic
59D5×M16—22no—
60#4029—22no—
61#4024—22no—
62#4018C3×C411yescharacteristic
63#4015C3×C411yescharacteristic
64C5×#101C22×C312yes—
65#3968C22×C312yes—
66#3956—22no—
67#2133—51noSylow
68C23×C3×C5—21no—
69C22×C3×D5C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C3×C5×D4—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C3×C22⋊D5—42no—
76C2×C3×Dic5—21no—
77C2×C3×Dic5—21no—
78C2×C3×Dic5—42no—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C2×C3×Dic5C22⋊C412yes—
81C3×C4×D5—22no—
82C3×C4×D5—22no—
83C3×C4×D5—22no—
84C3×Dic10—41no—
85C3×Dic10—42no—
86C3×Dic10—41no—
87C3×C5×C8—42no—
88C3×#168—42no—
89C2×C3×#41—51no—
90C22×C3×Q8—51no—
91C2×C3×M16—102no—
92C3×C4⋊Q8—51no—
93C3×C4⋊Q8—51no—
94C3×#124—51no—
95C3×#124C2×D511yescharacteristic
96C3×#123—102no—
97C3×C22⋊Q8—102no—
98C3×#117—51no—
99C3×#101—52no—
100C3×#101—102no—
101C3×#101C2×D512yes—
102C2×C5×Q8C23×C311yescharacteristic
103C2×C5×D4C2×C3×C411yescharacteristic
104C2×C22⋊D5—21no—
105C22×Dic5—21no—
106Q8×D5—42no—
107#711—42no—
108C2×C4×D5C2×C3×C411yescharacteristic
109C2×C4×D5C3×D412yes—
110C2×Dic10C2×C3×C411yescharacteristic
111C2×Dic10C2×C3×C411yescharacteristic
112C2×Dic10C3×D412yes—
113C5×M16—22no—
114C5×C22⋊C4—22no—
115C42×C5C2×C3×C411yescharacteristic
116C22⋊Dic5—22no—
117#685—21no—
118C4⋊Dic5—22no—
119#683—22no—
120#683—21no—
121C4×Dic5C2×C3×C411yescharacteristic
122#681—22no—
123#676—42no—
124C8×D5—42no—
125#536—51no—
126C2×#101—52no—
127#356—52no—
128#355—51no—
129#355C3×D511yescharacteristic, complemented
130C22×C3×C5—42no—
131C22×C3×C5—41no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C2×C3×D5—41no—
134C2×C3×D5#9912yes—
135C3×C4×C5—22no—
136C3×C4×C5—21no—
137C3×C4×C5—41no—
138C3×Dic5—21no—
139C3×Dic5—22no—
140C3×Dic5—41no—
141C3×Dic5—41no—
142C3×#41—202no—
143C2×C3×Q8—51no—
144C2×C3×Q8—52no—
145C2×C3×Q8—51no—
146C2×C3×Q8—202no—
147C2×C3×Q8C22×D511yescharacteristic
148C2×C3×D4—101no—
149C2×C3×D4C4×D511yescharacteristic
150C22×C3×C4—51no—
151C22×C3×C4—52no—
152C22×C3×C4—101no—
153C3×M16—22no—
154C3×M16—102no—
155C3×M16—202no—
156C2×C3×C8—202no—
157C3×C4⋊C4—101no—
158C3×C4⋊C4—102no—
159C3×C4⋊C4—102no—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—101no—
162C3×C22⋊C4—102no—
163C3×C42—51no—
164C3×C42C4×D511yescharacteristic
165C23×C5—21no—
166C22×D5C3×C22⋊C411yescharacteristic
167C5×Q8—41no—
168C5×D4—41no—
169C2×C4×C5—21no—
170C2×C4×C5C22×C3×C411yescharacteristic
171C2×C4×C5C2×C3×D412yes—
172C22⋊D5—42no—
173C2×Dic5—21no—
174C2×Dic5—21no—
175C2×Dic5—42no—
176C2×Dic5C3×C22⋊C411yescharacteristic
177C2×Dic5C3×C22⋊C412yes—
178C4×D5—22no—
179C4×D5—22no—
180C4×D5—22no—
181Dic10—41no—
182Dic10—42no—
183Dic10—41no—
184C5×C8—42no—
185#168—42no—
186C2×#41—51no—
187C22×Q8—51no—
188C2×M16—102no—
189C4⋊Q8—51no—
190C4⋊Q8—51no—
191#124—51no—
192#124C2×C3×D511yescharacteristic
193#123—102no—
194C22⋊Q8—102no—
195#117—51no—
196#101—52no—
197#101—102no—
198#101C2×C3×D512yes—
199C2×C3×C5—21no—
200C2×C3×C5—81no—
201C2×C3×C5C2×#9911yescharacteristic
202C3×D5—22no—
203C23×C3—21no—
204C23×C3—51no—
205C3×Q8—41no—
206C3×Q8—202no—
207C3×Q8—201no—
208C3×Q8—201no—
209C3×D4—41no—
210C3×D4—202no—
211C2×C3×C4—21no—
212C2×C3×C4—52no—
213C2×C3×C4—51no—
214C2×C3×C4—102no—
215C2×C3×C4—102no—
216C2×C3×C4—102no—
217C2×C3×C4—101no—
218C2×C3×C4—101no—
219C2×C3×C4—202no—
220C2×C3×C4C2×C4×D511yescharacteristic
221C2×C3×C4D4×D512yes—
222C3×C8—42no—
223C3×C8—202no—
224C22×C5—42no—
225C22×C5—41no—
226C22×C5C2×C3×C22⋊C411yescharacteristic
227C2×D5—41no—
228C2×D5C3×#9912yes—
229C4×C5—22no—
230C4×C5—21no—
231C4×C5—41no—
232Dic5—21no—
233Dic5—22no—
234Dic5—41no—
235Dic5—41no—
236#41—202no—
237C2×Q8—51no—
238C2×Q8—52no—
239C2×Q8—51no—
240C2×Q8—202no—
241C2×Q8C22×C3×D511yescharacteristic
242C2×D4—101no—
243C2×D4C3×C4×D511yescharacteristic
244C22×C4—51no—
245C22×C4—52no—
246C22×C4—101no—
247M16—22no—
248M16—102no—
249M16—202no—
250C2×C8—202no—
251C4⋊C4—101no—
252C4⋊C4—102no—
253C4⋊C4—102no—
254C22⋊C4—22no—
255C22⋊C4—101no—
256C22⋊C4—102no—
257C42—51no—
258C42C3×C4×D511yescharacteristic
259C3×C5#213311yescharacteristic, complemented, Hall
260C22×C3—42no—
261C22×C3—41no—
262C22×C3—52no—
263C22×C3—201no—
264C22×C3D5×C22⋊C411yescharacteristic
265C3×C4—22no—
266C3×C4—21no—
267C3×C4—41no—
268C3×C4—101no—
269C3×C4—102no—
270C3×C4—201no—
271C3×C4—201no—
272C2×C5—21no—
273C2×C5—81no—
274C2×C5C2×C3×#9911yescharacteristic
275D5—22no—
276C23—21no—
277C23—51no—
278Q8—41no—
279Q8—202no—
280Q8—201no—
281Q8—201no—
282D4—41no—
283D4—202no—
284C2×C4—21no—
285C2×C4—52no—
286C2×C4—51no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—102no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—202no—
293C2×C4C2×C3×C4×D511yescharacteristic
294C2×C4C3×D4×D512yes—
295C8—42no—
296C8—202no—
297C2×C3—21no—
298C2×C3—81no—
299C2×C3—102no—
300C2×C3D5×#9911yescharacteristic
301C5C3×#213311yescharacteristic, complemented, Sylow
302C22—42no—
303C22—41no—
304C22—52no—
305C22—201no—
306C22C3×D5×C22⋊C411yescharacteristic
307C4—22no—
308C4—21no—
309C4—41no—
310C4—101no—
311C4—102no—
312C4—201no—
313C4—201no—
314C3#1059995711yescharacteristic, direct product factor, Sylow
315C2—21no—
316C2—81no—
317C2—102no—
318C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×Q8C22×C3×D5
FittingC3×C5×#355C2
socleC2×C3×C5C2×#99
prime radicalC2×C3×#711C4
cosocleC2×C5×Q8C23×C3
hypercenterC3×#355D5
hypocenterC5C3×#2133
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×Q8 ◁ C3×#355

Complements

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

NH ≅ G/Ntype
2. C3×D5×#101C2semidirect
3. C3×C5×#355C2semidirect
4. C3×#64762C2semidirect
5. C3×#64698C2semidirect
6. #10599957C3direct (N × H)
22. D5×#101C2×C3semidirect
23. C5×#355C2×C3semidirect
24. #64762C2×C3semidirect
25. #64698C2×C3semidirect
53. C3×#355D5semidirect
129. #355C3×D5semidirect
259. C3×C5#2133semidirect
301. C5C3×#2133semidirect
314. C3#10599957direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660092
C3×D5×#1012
C3×C5×#3552
C3×#647622
C3×#646982
#105999573
C3×#21335