Finite Group Databasebeta

← #14308921

Subgroups — #14308921

Order 1920.

564 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C5×#5500C211yesmaximal, characteristic, complemented
2#11751089C211yesmaximal, characteristic
3#11748396C212yesmaximal
4C3×#64750C211yesmaximal, characteristic, complemented
5#11745975C212yesmaximal, complemented
6#10602696—31nomaximal, Hall
7C22×D60C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×#6714—22no—
10C2×C4×Dic15C2211yescharacteristic
11C5×#926C2212yes—
12C5×#924—22no—
13C5×#890—22no—
14C5×#888—22no—
15C2×C3×#681C2212yes—
16#90969—22no—
17#90969—22no—
18#68995—51nomaximal, Hall
19C5×#544—31no—
20#65290—32no—
21#65277—31no—
22#64752—32no—
23#64750D311yescharacteristic, complemented
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×C5×Dic6—22no—
33C3×C5×C4⋊C4—22no—
34#6714—44no—
35C4×Dic15—22no—
36C5×#217—22no—
37C5×C4⋊Dic3—22no—
38C5×C4⋊Dic3D412yes—
39C5×C4⋊Dic3D412yes—
40C5×Dic3⋊C4—24no—
41C4×C5×Dic3—22no—
42C3×#681—22no—
43C3×#681—22no—
44C2×C3×#168—22no—
45#5500D511yescharacteristic, complemented
46#5131—52no—
47#4988—51no—
48C3×#343—51no—
49#4555—52no—
50C22×D20—31no—
51C5×C4⋊Q8—62no—
52C5×#125—62no—
53C5×C22⋊Q8—62no—
54C5×#117—32no—
55C2×C5×C4⋊C4C2×D311yescharacteristic
56C2×#685—62no—
57C2×C4×Dic5—31no—
58C2×#681C2×D312yes—
59#3941—62no—
60#3941—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—41no—
76C2×Dic15—41no—
77D60—24no—
78D60—42no—
79C2×C5×Dic3—22no—
80C2×C5×Dic3—22no—
81C5×Dic6—82no—
82C3×#168—42no—
83C22×D12—51no—
84C2×C3×M16—52no—
85C2×C3×C4⋊C4C2×D511yescharacteristic
86C2×(C2×D3)⋊C4—102no—
87#926C2×D512yes—
88#924—22no—
89C2×C4×Dic3—51no—
90#890—22no—
91#888—22no—
92#821—102no—
93#821—102no—
94C23×D5—61no—
95C2×C5×Q8—62no—
96C22×C4×C5D1212yes—
97C22×C4×C5C22×D311yescharacteristic
98C22×Dic5—61no—
99C2×D20—32no—
100C2×D20—62no—
101C2×D20—62no—
102C2×D20—61no—
103C5×C4⋊C4—22no—
104C5×C4⋊C4—32no—
105C5×C4⋊C4—32no—
106C5×C4⋊C4—62no—
107C5×C4⋊C4—64no—
108C5×C22⋊C4—62no—
109C42×C5—62no—
110#685—124no—
111C4×Dic5—62no—
112#681—22no—
113#681—22no—
114C2×#168—22no—
115#544—31no—
116#418—152no—
117#390—151no—
118#343—51no—
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—
134C5×Dic3—42no—
135C5×Dic3—42no—
136C23×D3—101no—
137C22×C3×C4C22⋊D512yes—
138C22×C3×C4C22×D511yescharacteristic
139C22×Dic3—101no—
140C2×D12—52no—
141C2×D12—102no—
142C2×D12—102no—
143C2×D12—101no—
144C2×Dic6—22no—
145C3×M16—102no—
146C3×M16—102no—
147C2×C3×C8—102no—
148C3×C4⋊C4—22no—
149#217—22no—
150(C2×D3)⋊C4—204no—
151C4⋊Dic3—22no—
152C4⋊Dic3C22⋊D512yes—
153C4⋊Dic3C22⋊D512yes—
154Dic3⋊C4—24no—
155C4×Dic3—22no—
156C4×Dic3—102no—
157C23×C5C2×D1211yescharacteristic
158C22×D5—62no—
159C22×D5—122no—
160C22×D5—122no—
161C22×D5—121no—
162C22×D5—121no—
163C5×Q8—242no—
164C2×C4×C5—22no—
165C2×C4×C5—42no—
166C2×C4×C5—62no—
167C2×C4×C5—62no—
168C2×C4×C5#23512yes—
169C2×C4×C5D3×D412yes—
170C2×C4×C5#23711yescharacteristic
171C2×C4×C5D3×Q811yescharacteristic
172C2×Dic5—62no—
173C2×Dic5—121no—
174C2×Dic5—121no—
175D20—64no—
176D20—122no—
177#168—42no—
178C22×D4—151no—
179C2×M16—52no—
180C4⋊Q8—62no—
181#125—62no—
182C22⋊Q8—62no—
183#117—32no—
184C2×C4⋊C4D3×D511yescharacteristic
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×C22⋊D511yescharacteristic
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×C4Q8×D511yescharacteristic
204C2×C3×C4#71311yescharacteristic
205C2×C3×C4#71312yes—
206C2×C3×C4C2×C22⋊D512yes—
207C2×Dic3—22no—
208C2×Dic3—22no—
209C2×Dic3—102no—
210C2×Dic3—201no—
211C2×Dic3—201no—
212D12—104no—
213D12—202no—
214Dic6—82no—
215C3×C8—202no—
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—122no—
228C4×C5—122no—
229C4×C5#88512yes—
230C4×C5#89612yes—
231Dic5—122no—
232C24—301no—
233C2×Q8—62no—
234C2×D4—152no—
235C2×D4—301no—
236C2×D4—302no—
237C2×D4—302no—
238C22×C4—301no—
239C22×C4#120312yes—
240C22×C4C2×D3×D511yescharacteristic
241M16—102no—
242M16—102no—
243C2×C8—102no—
244C4⋊C4—22no—
245C4⋊C4—32no—
246C4⋊C4—32no—
247C4⋊C4—62no—
248C4⋊C4—64no—
249C22⋊C4—62no—
250C22⋊C4—604no—
251C42—62no—
252C42—302no—
253C3×C5#202711yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3#409211yescharacteristic
257C22×C3#409311yescharacteristic
258C22×C3#409911yescharacteristic
259C2×D3—204no—
260C2×D3—202no—
261C2×D3—402no—
262C2×D3—401no—
263C2×D3—401no—
264C3×C4—42no—
265C3×C4#409212yes—
266C3×C4#409312yes—
267Dic3—42no—
268Dic3—42no—
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×#120311yescharacteristic
282Q8—242no—
283D4—304no—
284D4—602no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—62no—
288C2×C4—62no—
289C2×C4—302no—
290C2×C4—601no—
291C2×C4—601no—
292C2×C4#676611yescharacteristic
293C2×C4D15⋊Q811yescharacteristic
294C2×C4#677312yes—
295C2×C4D3×C22⋊D512yes—
296C8—202no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#6552011yescharacteristic
300C2×C3#6553011yescharacteristic
301C2×C3#6553411yescharacteristic
302D3—402no—
303C5#6899511yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—604no—
307C22—602no—
308C22—1202no—
309C22—1201no—
310C22—1201no—
311C22#9137511yescharacteristic
312C22#9138311yescharacteristic
313C22#9157011yescharacteristic
314C4—42no—
315C4—122no—
316C4—122no—
317C4—602no—
318C4#9142412yes—
319C4#9145512yes—
320C3#1060269611yescharacteristic, complemented, Sylow
321C2—21no—
322C2—21no—
323C2—1202no—
324C2#1174878411yescharacteristic
325C2#1174914111yescharacteristic
326C2#1174938711yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC22×D60C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2027
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×#5500C2semidirect
4. C3×#64750C2semidirect
5. #11745975C2semidirect
23. #64750D3semidirect
31. C2×D60Q8semidirect
45. #5500D5semidirect
253. C3×C5#2027semidirect
303. C5#68995semidirect
320. C3#10602696semidirect

Maximal subgroups

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

subgroupindex
C5×#55002
#117510892
#117483962
C3×#647502
#117459752
#106026963
#689955