Finite Group Databasebeta

← C3×#10599791 #14308951

Subgroups — C3×#10599791 #14308951

Order 1920.

492 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 134 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×#65834C211yesmaximal, characteristic
2C3×#65409C212yesmaximal
3C3×#65263C211yesmaximal, characteristic
4C3×C5×#343C211yesmaximal, characteristic
5C3×#64775C212yesmaximal
6#10599791C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×Dic10C2211yescharacteristic
8C2×C3×C5×M16C2212yes—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C3×#4072C2212yes—
11C3×#4070—22no—
12C2×C3×C4×Dic5C2211yescharacteristic
13C3×#4036—22no—
14C3×#4034—22no—
15C3×#3963—22no—
16C3×#3948—22no—
17C3×#3948—22no—
18C3×#2028—51nomaximal, Hall
19#65834C2×C311yescharacteristic
20#65409C2×C312yes—
21#65263C2×C311yescharacteristic
22C5×#343C2×C311yescharacteristic
23#64775C2×C312yes—
24C22×C3×C4×C5D412yes—
25C22×C3×C4×C5C2311yescharacteristic
26C22×C3×Dic5—21no—
27C22×C3×Dic5—21no—
28C2×C3×Dic10—22no—
29C2×C3×Dic10—22no—
30C2×C3×Dic10—21no—
31C2×C3×Dic10—22no—
32C2×C3×Dic10Q812yescomplemented
33C3×C5×M16—22no—
34C3×C5×M16—22no—
35C2×C3×C5×C8—22no—
36C3×C5×C4⋊C4—22no—
37C3×C22⋊Dic5—22no—
38C3×C4⋊Dic5—22no—
39C3×C4⋊Dic5D412yes—
40C3×C4⋊Dic5D412yes—
41C3×#683—24no—
42C3×C4×Dic5—22no—
43C3×C4×Dic5—22no—
44C3×#544—51no—
45C3×#419—52no—
46C3×#391—51no—
47C3×#343D511yescharacteristic
48C3×#339—52no—
49C22×Dic10C22×C311yescharacteristic
50C2×C5×M16C22×C312yes—
51C2×C5×C4⋊C4C22×C311yescharacteristic
52#4072C22×C312yes—
53#4070—22no—
54C2×C4×Dic5C22×C311yescharacteristic
55#4036—22no—
56#4034—22no—
57#3963—22no—
58#3948—22no—
59#3948—22no—
60#2028—51noSylow
61C23×C3×C5C2×D411yescharacteristic
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5C2×D412yes—
65C2×C3×C4×C5C2×Q811yescharacteristic
66C2×C3×C4×C5#4112yes—
67C2×C3×C4×C5#4111yescharacteristic
68C2×C3×Dic5—22no—
69C2×C3×Dic5—22no—
70C2×C3×Dic5—22no—
71C2×C3×Dic5—22no—
72C2×C3×Dic5—41no—
73C2×C3×Dic5—41no—
74C2×C3×Dic5—41no—
75C2×C3×Dic5—41no—
76C3×Dic10—24no—
77C3×Dic10—42no—
78C3×Dic10—82no—
79C3×C5×C8—42no—
80C22×C3×Q8—51no—
81C2×C3×M16C2×D512yes—
82C3×C4⋊Q8—102no—
83C3×#125—102no—
84C3×C22⋊Q8—102no—
85C3×#117—52no—
86C2×C3×C4⋊C4C2×D511yescharacteristic
87C2×C3×C42—51no—
88C3×#103—102no—
89C3×#103—102no—
90C3×#95—102no—
91C22×C4×C5C3×D412yes—
92C22×C4×C5C23×C311yescharacteristic
93C22×Dic5—21no—
94C22×Dic5—21no—
95C2×Dic10—22no—
96C2×Dic10—22no—
97C2×Dic10—21no—
98C2×Dic10—22no—
99C2×Dic10C3×Q812yescomplemented
100C5×M16—22no—
101C5×M16—22no—
102C2×C5×C8—22no—
103C5×C4⋊C4—22no—
104C22⋊Dic5—22no—
105C4⋊Dic5—22no—
106C4⋊Dic5C3×D412yes—
107C4⋊Dic5C3×D412yes—
108#683—24no—
109C4×Dic5—22no—
110C4×Dic5—22no—
111#544—51no—
112#419—52no—
113#391—51no—
114#343C3×D511yescharacteristic
115#339—52no—
116C22×C3×C5—21no—
117C22×C3×C5—21no—
118C22×C3×C5#12011yescharacteristic
119C22×C3×C5C22⋊Q811yescharacteristic
120C22×C3×C5#12411yescharacteristic
121C3×C4×C5—42no—
122C3×C4×C5C22⋊Q812yes—
123C3×C4×C5#12412yes—
124C3×Dic5—42no—
125C3×Dic5—42no—
126C3×Dic5—42no—
127C3×Dic5—42no—
128C2×C3×Q8—52no—
129C2×C3×Q8—102no—
130C2×C3×Q8—101no—
131C2×C3×Q8—102no—
132C2×C3×Q8—102no—
133C22×C3×C4—101no—
134C22×C3×C4—101no—
135C22×C3×C4D2012yes—
136C22×C3×C4C22×D511yescharacteristic
137C3×M16—22no—
138C3×M16—22no—
139C2×C3×C8—22no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—52no—
142C3×C4⋊C4—52no—
143C3×C4⋊C4—104no—
144C3×C4⋊C4—102no—
145C3×C22⋊C4—102no—
146C3×C42—102no—
147C3×C42—102no—
148C23×C5C2×C3×D411yescharacteristic
149C2×C4×C5—22no—
150C2×C4×C5—42no—
151C2×C4×C5C2×C3×D412yes—
152C2×C4×C5C2×C3×Q811yescharacteristic
153C2×C4×C5C3×#4112yes—
154C2×C4×C5C3×#4111yescharacteristic
155C2×Dic5—22no—
156C2×Dic5—22no—
157C2×Dic5—22no—
158C2×Dic5—22no—
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163Dic10—24no—
164Dic10—42no—
165Dic10—82no—
166C5×C8—42no—
167C22×Q8—51no—
168C2×M16C2×C3×D512yes—
169C4⋊Q8—102no—
170#125—102no—
171C22⋊Q8—102no—
172#117—52no—
173C2×C4⋊C4C2×C3×D511yescharacteristic
174C2×C42—51no—
175#103—102no—
176#103—102no—
177#95—102no—
178C2×C3×C5—21no—
179C2×C3×C5—21no—
180C2×C3×C5#39311yescharacteristic
181C2×C3×C5#45511yescharacteristic
182C2×C3×C5#45611yescharacteristic
183C23×C3C2×D2011yescharacteristic
184C3×Q8—104no—
185C3×Q8—202no—
186C3×Q8—402no—
187C2×C3×C4—22no—
188C2×C3×C4—42no—
189C2×C3×C4—102no—
190C2×C3×C4—102no—
191C2×C3×C4—102no—
192C2×C3×C4—102no—
193C2×C3×C4—201no—
194C2×C3×C4—201no—
195C2×C3×C4—201no—
196C2×C3×C4—201no—
197C2×C3×C4#70912yes—
198C2×C3×C4D4×D512yes—
199C2×C3×C4#71111yescharacteristic
200C2×C3×C4Q8×D511yescharacteristic
201C3×C8—42no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5C3×#12011yescharacteristic
205C22×C5C3×C22⋊Q811yescharacteristic
206C22×C5C3×#12411yescharacteristic
207C4×C5—42no—
208C4×C5C3×C22⋊Q812yes—
209C4×C5C3×#12412yes—
210Dic5—42no—
211Dic5—42no—
212Dic5—42no—
213Dic5—42no—
214C2×Q8—52no—
215C2×Q8—102no—
216C2×Q8—101no—
217C2×Q8—102no—
218C2×Q8—102no—
219C22×C4—101no—
220C22×C4—101no—
221C22×C4C3×D2012yes—
222C22×C4C22×C3×D511yescharacteristic
223M16—22no—
224M16—22no—
225C2×C8—22no—
226C4⋊C4—22no—
227C4⋊C4—52no—
228C4⋊C4—52no—
229C4⋊C4—102no—
230C4⋊C4—104no—
231C22⋊C4—102no—
232C42—102no—
233C42—102no—
234C3×C5#202811yescharacteristic, complemented, Hall
235C22×C3—21no—
236C22×C3—21no—
237C22×C3#402111yescharacteristic
238C22×C3#402811yescharacteristic
239C22×C3#404311yescharacteristic
240C3×C4—42no—
241C3×C4—202no—
242C3×C4—202no—
243C3×C4—202no—
244C3×C4—202no—
245C3×C4#403112yes—
246C3×C4#404212yes—
247C2×C5—21no—
248C2×C5—21no—
249C2×C5C3×#39311yescharacteristic
250C2×C5C3×#45511yescharacteristic
251C2×C5C3×#45611yescharacteristic
252C23C2×C3×D2011yescharacteristic
253Q8—104no—
254Q8—202no—
255Q8—402no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—102no—
259C2×C4—102no—
260C2×C4—102no—
261C2×C4—102no—
262C2×C4—201no—
263C2×C4—201no—
264C2×C4—201no—
265C2×C4—201no—
266C2×C4C3×#70912yes—
267C2×C4C3×D4×D512yes—
268C2×C4C3×#71111yescharacteristic
269C2×C4C3×Q8×D511yescharacteristic
270C8—42no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#6496211yescharacteristic
274C2×C3#6503511yescharacteristic
275C2×C3#6504111yescharacteristic
276C5C3×#202811yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22C3×#402111yescharacteristic
280C22C3×#402811yescharacteristic
281C22C3×#404311yescharacteristic
282C4—42no—
283C4—202no—
284C4—202no—
285C4—202no—
286C4—202no—
287C4C3×#403112yes—
288C4C3×#404212yes—
289C3#1059979111yescharacteristic, direct product factor, Sylow
290C2—21no—
291C2—21no—
292C2C3×#6496211yescharacteristic
293C2C3×#6503511yescharacteristic
294C2C3×#6504111yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#343C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenterC3×#343D5
hypocenterC5C3×#2028
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
6. #10599791C3direct (N × H)
32. C2×C3×Dic10Q8semidirect
99. C2×Dic10C3×Q8semidirect
234. C3×C5#2028semidirect
276. C5C3×#2028semidirect
289. C3#10599791direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658342
C3×#654092
C3×#652632
C3×C5×#3432
C3×#647752
#105997913
C3×#20285