Finite Group Databasebeta

← #14308913

Subgroups — #14308913

Order 1920.

564 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#11756259C211yesmaximal, characteristic, complemented
2#11751232C212yesmaximal
3#11751089C211yesmaximal, characteristic
4C3×C5×#343C211yesmaximal, characteristic, complemented
5#11746376C212yesmaximal, complemented
6#10599788—31nomaximal, Hall
7C22×D60C2211yescharacteristic
8C2×C3×C5×M16C2212yes—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×#6714—22no—
11#91815C2212yes—
12#91813—22no—
13C2×C4×Dic15C2211yescharacteristic
14#91779—22no—
15#91777—22no—
16#91105—22no—
17#91105—22no—
18#68995—51nomaximal, Hall
19#65834—31no—
20#65420—32no—
21#65277—31no—
22C5×#343D311yescharacteristic, complemented
23#64775—32no—
24C23×D15—21no—
25C22×C3×C4×C5D412yes—
26C22×C3×C4×C5C2311yescharacteristic
27C22×Dic15—21no—
28C2×D60—22no—
29C2×D60—22no—
30C2×D60—21no—
31C2×D60Q812yescomplemented
32C2×Dic30—22no—
33C3×C5×M16—22no—
34C3×C5×M16—22no—
35C2×C3×C5×C8—22no—
36C3×C5×C4⋊C4—22no—
37#6719—22no—
38#6714—44no—
39C4⋊Dic15—22no—
40C4⋊Dic15D412yes—
41C4⋊Dic15D412yes—
42#6712—24no—
43C4×Dic15—22no—
44C4×Dic15—22no—
45#5500—51no—
46#5131—52no—
47#4988—51no—
48C3×#343D511yescharacteristic, complemented
49#4555—52no—
50C22×D20—31no—
51C2×C5×M16C2×D312yes—
52C2×C5×C4⋊C4C2×D311yescharacteristic
53C2×#685—62no—
54#4072—32no—
55#4070—62no—
56C2×C4×Dic5—31no—
57#4036—62no—
58#4034—62no—
59#3953—62no—
60#3953—62no—
61#2027—151noSylow
62C23×C3×C5C2×D411yescharacteristic
63C22×D15—22no—
64C22×D15—42no—
65C22×D15—42no—
66C22×D15—41no—
67C22×D15—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×Dic15—22no—
75C2×Dic15—22no—
76C2×Dic15—22no—
77C2×Dic15—41no—
78C2×Dic15—41no—
79D60—24no—
80D60—42no—
81Dic30—82no—
82C3×C5×C8—42no—
83C22×D12—51no—
84C2×C3×M16C2×D512yes—
85C2×C3×C4⋊C4C2×D511yescharacteristic
86C2×(C2×D3)⋊C4—102no—
87#926—52no—
88#924—102no—
89C2×C4×Dic3—51no—
90#890—102no—
91#888—102no—
92#821—102no—
93#821—102no—
94C23×D5—61no—
95C22×C4×C5D1212yes—
96C22×C4×C5C22×D311yescharacteristic
97C22×Dic5—61no—
98C2×D20—32no—
99C2×D20—62no—
100C2×D20—62no—
101C2×D20—61no—
102C2×Dic10—62no—
103C5×M16—22no—
104C5×M16—22no—
105C2×C5×C8—22no—
106C5×C4⋊C4—22no—
107C22⋊Dic5—62no—
108#685—124no—
109C4⋊Dic5—32no—
110C4⋊Dic5—32no—
111C4⋊Dic5—62no—
112#683—64no—
113C4×Dic5—62no—
114C4×Dic5—62no—
115#544—151no—
116#418—152no—
117#390—151no—
118#343D1511yescharacteristic, complemented
119#339—152no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5#12011yescharacteristic
123C22×C3×C5C22⋊Q811yescharacteristic
124C22×C3×C5#12411yescharacteristic
125C2×D15—44no—
126C2×D15—42no—
127C2×D15—82no—
128C2×D15—81no—
129C2×D15—81no—
130C3×C4×C5—42no—
131C3×C4×C5C22⋊Q812yes—
132C3×C4×C5#12412yes—
133Dic15—42no—
134Dic15—42no—
135Dic15—42no—
136C23×D3—101no—
137C22×C3×C4D2012yes—
138C22×C3×C4C22×D511yescharacteristic
139C22×Dic3—101no—
140C2×D12—52no—
141C2×D12—102no—
142C2×D12—102no—
143C2×D12—101no—
144C2×Dic6—102no—
145C3×M16—22no—
146C3×M16—22no—
147C2×C3×C8—22no—
148C3×C4⋊C4—22no—
149#217—102no—
150(C2×D3)⋊C4—204no—
151C4⋊Dic3—52no—
152C4⋊Dic3—52no—
153C4⋊Dic3—102no—
154Dic3⋊C4—104no—
155C4×Dic3—102no—
156C4×Dic3—102no—
157C23×C5C2×D1211yescharacteristic
158C22×D5—62no—
159C22×D5—122no—
160C22×D5—122no—
161C22×D5—121no—
162C22×D5—121no—
163C2×C4×C5—22no—
164C2×C4×C5—42no—
165C2×C4×C5#23512yes—
166C2×C4×C5D3×D412yes—
167C2×C4×C5#23711yescharacteristic
168C2×C4×C5D3×Q811yescharacteristic
169C2×Dic5—62no—
170C2×Dic5—62no—
171C2×Dic5—62no—
172C2×Dic5—121no—
173C2×Dic5—121no—
174D20—64no—
175D20—122no—
176Dic10—242no—
177C5×C8—42no—
178C22×D4—151no—
179C2×M16C2×D1512yes—
180C4⋊Q8—302no—
181#125—302no—
182C22⋊Q8—302no—
183#117—152no—
184C2×C4⋊C4C2×D1511yescharacteristic
185C2×C22⋊C4—302no—
186C2×C42—151no—
187#102—302no—
188#102—302no—
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5#39311yescharacteristic
192C2×C3×C5#45311yescharacteristic
193C2×C3×C5#45411yescharacteristic
194D15—82no—
195C23×C3C2×D2011yescharacteristic
196C22×D3—102no—
197C22×D3—202no—
198C22×D3—202no—
199C22×D3—201no—
200C22×D3—201no—
201C2×C3×C4—22no—
202C2×C3×C4—42no—
203C2×C3×C4#70912yes—
204C2×C3×C4D4×D512yes—
205C2×C3×C4#71111yescharacteristic
206C2×C3×C4Q8×D511yescharacteristic
207C2×Dic3—102no—
208C2×Dic3—102no—
209C2×Dic3—102no—
210C2×Dic3—201no—
211C2×Dic3—201no—
212D12—104no—
213D12—202no—
214Dic6—402no—
215C3×C8—42no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5#87511yescharacteristic
219C22×C5#88211yescharacteristic
220C22×C5#89711yescharacteristic
221C2×D5—124no—
222C2×D5—122no—
223C2×D5—242no—
224C2×D5—241no—
225C2×D5—241no—
226C4×C5—42no—
227C4×C5#88512yes—
228C4×C5#89612yes—
229Dic5—122no—
230Dic5—122no—
231Dic5—122no—
232C24—301no—
233C2×Q8—302no—
234C2×D4—152no—
235C2×D4—302no—
236C2×D4—302no—
237C2×D4—301no—
238C22×C4—301no—
239C22×C4D6012yes—
240C22×C4C22×D1511yescharacteristic
241M16—22no—
242M16—22no—
243C2×C8—22no—
244C4⋊C4—22no—
245C4⋊C4—152no—
246C4⋊C4—152no—
247C4⋊C4—302no—
248C4⋊C4—304no—
249C22⋊C4—302no—
250C22⋊C4—604no—
251C42—302no—
252C42—302no—
253C3×C5#202711yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3#402111yescharacteristic
257C22×C3#402811yescharacteristic
258C22×C3#404311yescharacteristic
259C2×D3—204no—
260C2×D3—202no—
261C2×D3—402no—
262C2×D3—401no—
263C2×D3—401no—
264C3×C4—42no—
265C3×C4#403112yes—
266C3×C4#404212yes—
267Dic3—202no—
268Dic3—202no—
269Dic3—202no—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5#467311yescharacteristic
273C2×C5#474711yescharacteristic
274C2×C5#475311yescharacteristic
275D5—242no—
276C23—302no—
277C23—602no—
278C23—602no—
279C23—601no—
280C23—601no—
281C23C2×D6011yescharacteristic
282Q8—1202no—
283D4—304no—
284D4—602no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—302no—
288C2×C4—302no—
289C2×C4—302no—
290C2×C4—601no—
291C2×C4—601no—
292C2×C4#681712yes—
293C2×C4D4×D1512yes—
294C2×C4#681911yescharacteristic
295C2×C4Q8×D1511yescharacteristic
296C8—42no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#6496211yescharacteristic
300C2×C3#6503611yescharacteristic
301C2×C3#6504211yescharacteristic
302D3—402no—
303C5#6899511yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—604no—
307C22—602no—
308C22—1202no—
309C22—1201no—
310C22—1201no—
311C22#9176411yescharacteristic
312C22#9177111yescharacteristic
313C22#9178611yescharacteristic
314C4—42no—
315C4—602no—
316C4—602no—
317C4—602no—
318C4#9177412yes—
319C4#9178512yes—
320C3#1059978811yescharacteristic, complemented, Sylow
321C2—21no—
322C2—21no—
323C2—1202no—
324C2#1175077411yescharacteristic
325C2#1175084811yescharacteristic
326C2#1175085411yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#343C2
socleC22×C3×C5#120
prime radicalC22×D60C22
hypercenter#343D15
hypocenterC3×C5#2027
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. #11756259C2semidirect
4. C3×C5×#343C2semidirect
5. #11746376C2semidirect
22. C5×#343D3semidirect
31. C2×D60Q8semidirect
48. C3×#343D5semidirect
118. #343D15semidirect
253. C3×C5#2027semidirect
303. C5#68995semidirect
320. C3#10599788semidirect

Maximal subgroups

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

subgroupindex
#117562592
#117512322
#117510892
C3×C5×#3432
#117463762
#105997883
#689955