Finite Group Databasebeta

← C3×#10599788 #14308912

Subgroups — C3×#10599788 #14308912

Order 1920.

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

normal subgroups only

This group has 564 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, complemented
2C3×#65420C212yesmaximal
3C3×#65277C211yesmaximal, characteristic
4C3×C5×#343C211yesmaximal, characteristic, complemented
5C3×#64775C212yesmaximal, complemented
6#10599788C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×D20C2211yescharacteristic
8C2×C3×C5×M16C2212yes—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×C3×#685—22no—
11C3×#4072C2212yes—
12C3×#4070—22no—
13C2×C3×C4×Dic5C2211yescharacteristic
14C3×#4036—22no—
15C3×#4034—22no—
16C3×#3953—22no—
17C3×#3953—22no—
18C3×#2027—51nomaximal, Hall
19#65834C2×C311yescharacteristic, complemented
20#65420C2×C312yes—
21#65277C2×C311yescharacteristic
22C5×#343C2×C311yescharacteristic, complemented
23#64775C2×C312yescomplemented
24C23×C3×D5—21no—
25C22×C3×C4×C5D412yes—
26C22×C3×C4×C5C2311yescharacteristic
27C22×C3×Dic5—21no—
28C2×C3×D20—22no—
29C2×C3×D20—22no—
30C2×C3×D20—21no—
31C2×C3×D20Q812yescomplemented
32C2×C3×Dic10—22no—
33C3×C5×M16—22no—
34C3×C5×M16—22no—
35C2×C3×C5×C8—22no—
36C3×C5×C4⋊C4—22no—
37C3×C22⋊Dic5—22no—
38C3×#685—44no—
39C3×C4⋊Dic5—22no—
40C3×C4⋊Dic5D412yes—
41C3×C4⋊Dic5D412yes—
42C3×#683—24no—
43C3×C4×Dic5—22no—
44C3×C4×Dic5—22no—
45C3×#544—51no—
46C3×#418—52no—
47C3×#390—51no—
48C3×#343D511yescharacteristic, complemented
49C3×#339—52no—
50C22×D20C22×C311yescharacteristic
51C2×C5×M16C22×C312yes—
52C2×C5×C4⋊C4C22×C311yescharacteristic
53C2×#685—22no—
54#4072C22×C312yes—
55#4070—22no—
56C2×C4×Dic5C22×C311yescharacteristic
57#4036—22no—
58#4034—22no—
59#3953—22no—
60#3953—22no—
61#2027—51noSylow
62C23×C3×C5C2×D411yescharacteristic
63C22×C3×D5—22no—
64C22×C3×D5—42no—
65C22×C3×D5—42no—
66C22×C3×D5—41no—
67C22×C3×D5—41no—
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5—42no—
70C2×C3×C4×C5C2×D412yes—
71C2×C3×C4×C5C2×Q811yescharacteristic
72C2×C3×C4×C5#4112yes—
73C2×C3×C4×C5#4111yescharacteristic
74C2×C3×Dic5—22no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5—41no—
78C2×C3×Dic5—41no—
79C3×D20—24no—
80C3×D20—42no—
81C3×Dic10—82no—
82C3×C5×C8—42no—
83C22×C3×D4—51no—
84C2×C3×M16C2×D512yes—
85C3×C4⋊Q8—102no—
86C3×#125—102no—
87C3×C22⋊Q8—102no—
88C3×#117—52no—
89C2×C3×C4⋊C4C2×D511yescharacteristic
90C2×C3×C22⋊C4—102no—
91C2×C3×C42—51no—
92C3×#102—102no—
93C3×#102—102no—
94C23×D5—21no—
95C22×C4×C5C3×D412yes—
96C22×C4×C5C23×C311yescharacteristic
97C22×Dic5—21no—
98C2×D20—22no—
99C2×D20—22no—
100C2×D20—21no—
101C2×D20C3×Q812yescomplemented
102C2×Dic10—22no—
103C5×M16—22no—
104C5×M16—22no—
105C2×C5×C8—22no—
106C5×C4⋊C4—22no—
107C22⋊Dic5—22no—
108#685—44no—
109C4⋊Dic5—22no—
110C4⋊Dic5C3×D412yes—
111C4⋊Dic5C3×D412yes—
112#683—24no—
113C4×Dic5—22no—
114C4×Dic5—22no—
115#544—51no—
116#418—52no—
117#390—51no—
118#343C3×D511yescharacteristic, complemented
119#339—52no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5#12011yescharacteristic
123C22×C3×C5C22⋊Q811yescharacteristic
124C22×C3×C5#12411yescharacteristic
125C2×C3×D5—44no—
126C2×C3×D5—42no—
127C2×C3×D5—82no—
128C2×C3×D5—81no—
129C2×C3×D5—81no—
130C3×C4×C5—42no—
131C3×C4×C5C22⋊Q812yes—
132C3×C4×C5#12412yes—
133C3×Dic5—42no—
134C3×Dic5—42no—
135C3×Dic5—42no—
136C24×C3—101no—
137C2×C3×Q8—102no—
138C2×C3×D4—52no—
139C2×C3×D4—102no—
140C2×C3×D4—102no—
141C2×C3×D4—101no—
142C22×C3×C4—101no—
143C22×C3×C4D2012yes—
144C22×C3×C4C22×D511yescharacteristic
145C3×M16—22no—
146C3×M16—22no—
147C2×C3×C8—22no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—52no—
150C3×C4⋊C4—52no—
151C3×C4⋊C4—104no—
152C3×C4⋊C4—102no—
153C3×C22⋊C4—102no—
154C3×C22⋊C4—204no—
155C3×C42—102no—
156C3×C42—102no—
157C23×C5C2×C3×D411yescharacteristic
158C22×D5—22no—
159C22×D5—42no—
160C22×D5—42no—
161C22×D5—41no—
162C22×D5—41no—
163C2×C4×C5—22no—
164C2×C4×C5—42no—
165C2×C4×C5C2×C3×D412yes—
166C2×C4×C5C2×C3×Q811yescharacteristic
167C2×C4×C5C3×#4112yes—
168C2×C4×C5C3×#4111yescharacteristic
169C2×Dic5—22no—
170C2×Dic5—22no—
171C2×Dic5—22no—
172C2×Dic5—41no—
173C2×Dic5—41no—
174D20—24no—
175D20—42no—
176Dic10—82no—
177C5×C8—42no—
178C22×D4—51no—
179C2×M16C2×C3×D512yes—
180C4⋊Q8—102no—
181#125—102no—
182C22⋊Q8—102no—
183#117—52no—
184C2×C4⋊C4C2×C3×D511yescharacteristic
185C2×C22⋊C4—102no—
186C2×C42—51no—
187#102—102no—
188#102—102no—
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5#39311yescharacteristic
192C2×C3×C5#45311yescharacteristic
193C2×C3×C5#45411yescharacteristic
194C3×D5—82no—
195C23×C3—102no—
196C23×C3—202no—
197C23×C3—202no—
198C23×C3—201no—
199C23×C3—201no—
200C23×C3C2×D2011yescharacteristic
201C3×Q8—402no—
202C3×D4—104no—
203C3×D4—202no—
204C2×C3×C4—22no—
205C2×C3×C4—42no—
206C2×C3×C4—102no—
207C2×C3×C4—102no—
208C2×C3×C4—102no—
209C2×C3×C4—201no—
210C2×C3×C4—201no—
211C2×C3×C4#70912yes—
212C2×C3×C4D4×D512yes—
213C2×C3×C4#71111yescharacteristic
214C2×C3×C4Q8×D511yescharacteristic
215C3×C8—42no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5C3×#12011yescharacteristic
219C22×C5C3×C22⋊Q811yescharacteristic
220C22×C5C3×#12411yescharacteristic
221C2×D5—44no—
222C2×D5—42no—
223C2×D5—82no—
224C2×D5—81no—
225C2×D5—81no—
226C4×C5—42no—
227C4×C5C3×C22⋊Q812yes—
228C4×C5C3×#12412yes—
229Dic5—42no—
230Dic5—42no—
231Dic5—42no—
232C24—101no—
233C2×Q8—102no—
234C2×D4—52no—
235C2×D4—102no—
236C2×D4—102no—
237C2×D4—101no—
238C22×C4—101no—
239C22×C4C3×D2012yes—
240C22×C4C22×C3×D511yescharacteristic
241M16—22no—
242M16—22no—
243C2×C8—22no—
244C4⋊C4—22no—
245C4⋊C4—52no—
246C4⋊C4—52no—
247C4⋊C4—102no—
248C4⋊C4—104no—
249C22⋊C4—102no—
250C22⋊C4—204no—
251C42—102no—
252C42—102no—
253C3×C5#202711yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—204no—
257C22×C3—202no—
258C22×C3—402no—
259C22×C3—401no—
260C22×C3—401no—
261C22×C3#402111yescharacteristic
262C22×C3#402811yescharacteristic
263C22×C3#404311yescharacteristic
264C3×C4—42no—
265C3×C4—202no—
266C3×C4—202no—
267C3×C4—202no—
268C3×C4#403112yes—
269C3×C4#404212yes—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5C3×#39311yescharacteristic
273C2×C5C3×#45311yescharacteristic
274C2×C5C3×#45411yescharacteristic
275D5—82no—
276C23—102no—
277C23—202no—
278C23—202no—
279C23—201no—
280C23—201no—
281C23C2×C3×D2011yescharacteristic
282Q8—402no—
283D4—104no—
284D4—202no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—102no—
290C2×C4—201no—
291C2×C4—201no—
292C2×C4C3×#70912yes—
293C2×C4C3×D4×D512yes—
294C2×C4C3×#71111yescharacteristic
295C2×C4C3×Q8×D511yescharacteristic
296C8—42no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—402no—
300C2×C3#6496211yescharacteristic
301C2×C3#6503611yescharacteristic
302C2×C3#6504211yescharacteristic
303C5C3×#202711yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—204no—
307C22—202no—
308C22—402no—
309C22—401no—
310C22—401no—
311C22C3×#402111yescharacteristic
312C22C3×#402811yescharacteristic
313C22C3×#404311yescharacteristic
314C4—42no—
315C4—202no—
316C4—202no—
317C4—202no—
318C4C3×#403112yes—
319C4C3×#404212yes—
320C3#1059978811yescharacteristic, direct product factor, Sylow
321C2—21no—
322C2—21no—
323C2—402no—
324C2C3×#6496211yescharacteristic
325C2C3×#6503611yescharacteristic
326C2C3×#6504211yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#343C2
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
hypercenterC3×#343D5
hypocenterC5C3×#2027
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
1. C3×#65834C2semidirect
4. C3×C5×#343C2semidirect
5. C3×#64775C2semidirect
6. #10599788C3direct (N × H)
19. #65834C2×C3semidirect
22. C5×#343C2×C3semidirect
23. #64775C2×C3semidirect
31. C2×C3×D20Q8semidirect
48. C3×#343D5semidirect
101. C2×D20C3×Q8semidirect
118. #343C3×D5semidirect
253. C3×C5#2027semidirect
303. C5C3×#2027semidirect
320. C3#10599788direct (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×#654202
C3×#652772
C3×C5×#3432
C3×#647752
#105997883
C3×#20275