Finite Group Databasebeta

← #14288408

Subgroups — #14288408

Order 1920.

508 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756269C211yesmaximal, characteristic
2C3×#65272C211yesmaximal, characteristic, complemented
3#11748474C212yesmaximal, complemented
4C5×#4528C211yesmaximal, characteristic, complemented
5#11745958C212yesmaximal, complemented
6#10598928—31nomaximal, Hall
7C2×#6817—21no—
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9#91819—21no—
10#91819C2212yes—
11#91786—22no—
12#91784—22no—
13C2×C3×C4⋊Dic5C2211yescharacteristic
14C2×C3×#683—21no—
15C5×#830C2212yes—
16C3×#3963—21no—
17C3×#3963C2211yescharacteristic
18#90990—22no—
19#90968—22no—
20#69712—51nomaximal, Hall
21#65844—31no—
22#65272D311yescharacteristic, complemented
23#65025—32no—
24C5×#324—31no—
25#64690—32no—
26C22×C3×C4×C5D411yescharacteristic
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5C2311yescharacteristic
29C2×#1220—22no—
30#6817—42no—
31#6817—42no—
32C2×D60—21no—
33C2×D60—21no—
34C2×D60D412yes—
35C2×C4×D15—22no—
36C2×Dic30—21no—
37C22×C3×Dic5—21no—
38C22×C3×Dic5—21no—
39C3×C5×C4⋊C4—22no—
40#6714—22no—
41#6714—22no—
42C4⋊Dic15—21no—
43C4⋊Dic15D412yes—
44C2×C5×C3⋊C8—22no—
45C3×C4⋊Dic5—22no—
46C3×#683—42no—
47#5510—51no—
48C3×#398—51no—
49#4967—52no—
50#4528D511yescharacteristic, complemented
51#4451—52no—
52C2×#709—61no—
53C2×C5×C4⋊C4C2×D311yescharacteristic
54#4076—32no—
55#4076—61no—
56C2×C4⋊Dic5C2×D311yescharacteristic
57C2×#683—21no—
58#4043—62no—
59#4041—62no—
60C5×C22⋊C8—32no—
61#3963—21no—
62#3963C2×D311yescharacteristic
63#3953—62no—
64#3950—62no—
65#1610—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C22×D15—22no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5D812yes—
74C2×C3×C4×C5C2×D412yes—
75#1220—42no—
76#1220—42no—
77C2×Dic15—22no—
78D60—42no—
79D60—42no—
80D60—81no—
81C4×D15—44no—
82Dic30—42no—
83C2×C3×Dic5—22no—
84C2×C3×Dic5—41no—
85C2×C3×Dic5—41no—
86C2×C3×Dic5—41no—
87C2×C3×Dic5—41no—
88C2×C3×Dic5—41no—
89C5×C3⋊C8—42no—
90C2×#235—101no—
91C2×C3×C4⋊C4—51no—
92C2×C3×C4⋊C4—101no—
93C2×C3×C4⋊C4C2×D511yescharacteristic
94#930—52no—
95#930—101no—
96#897—102no—
97#895—102no—
98C3×#95—51no—
99C3×#95—101no—
100#830C2×D512yes—
101#809—102no—
102#807—102no—
103C22×C4×C5#6711yescharacteristic
104C22×C4×C5#6711yescharacteristic
105C22×C4×C5C22×D311yescharacteristic
106C2×C22⋊D5—62no—
107C22×Dic5—21no—
108C22×Dic5—21no—
109#709—122no—
110#709—122no—
111C2×D20—32no—
112C2×D20—61no—
113C2×D20—61no—
114C2×C4×D5—62no—
115C2×Dic10—61no—
116C2×C5×C8—62no—
117C5×C4⋊C4—22no—
118#685—62no—
119#685—62no—
120C4⋊Dic5—22no—
121C4⋊Dic5—32no—
122C4⋊Dic5—61no—
123#683—42no—
124#537—151no—
125#480—152no—
126#398—51no—
127#327—152no—
128#324—31no—
129C22×C3×C5—21no—
130C22×C3×C5—21no—
131C22×C3×C5#12011yescharacteristic
132C22×C3×C5C2×D811yescharacteristic
133C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
134C2×D15—42no—
135C2×D15—42no—
136C2×D15—42no—
137C3×C4×C5—22no—
138C3×C4×C5—22no—
139C3×C4×C5—41no—
140Dic15—42no—
141C3×Dic5—42no—
142C3×Dic5—81no—
143C22×C3×C4—101no—
144C22×C3×C4—101no—
145C22×C3×C4D2011yescharacteristic
146C22×C3×C4D2011yescharacteristic
147C22×C3×C4C22×D511yescharacteristic
148C2×#67—102no—
149#235—202no—
150#235—202no—
151C2×D12—52no—
152C2×D12—101no—
153C2×D12—101no—
154C2×C4×D3—102no—
155C2×Dic6—101no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—102no—
158C3×C4⋊C4—202no—
159(C2×D3)⋊C4—102no—
160(C2×D3)⋊C4—102no—
161C4⋊Dic3—52no—
162C4⋊Dic3—101no—
163C2×C3⋊C8—22no—
164C23×C5C2×#6711yescharacteristic
165C22×D5—62no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5#21312yes—
172C2×C4×C5D3×D412yes—
173C22⋊D5—122no—
174C22⋊D5—122no—
175C2×Dic5—22no—
176C2×Dic5—41no—
177C2×Dic5—41no—
178C2×Dic5—41no—
179C2×Dic5—41no—
180C2×Dic5—41no—
181C2×Dic5—62no—
182D20—122no—
183D20—122no—
184D20—241no—
185C4×D5—124no—
186Dic10—122no—
187C5×C8—122no—
188C2×#41—301no—
189C22⋊Q8—302no—
190#121—152no—
191#121—302no—
192#121—301no—
193C2×C4⋊C4—51no—
194C2×C4⋊C4—101no—
195C2×C4⋊C4D3×D511yescharacteristic
196#107—302no—
197#102—302no—
198C22⋊C8—32no—
199#95—51no—
200#95—101no—
201C2×C3×C5—21no—
202C2×C3×C5—21no—
203C2×C3×C5#44711yescharacteristic
204C2×C3×C5#45611yescharacteristic
205C2×C3×C5#45811yescharacteristic
206D15—82no—
207C23×C3C2×D2011yescharacteristic
208C22×D3—102no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—102no—
215C2×C3×C4—201no—
216C2×C3×C4—201no—
217C2×C3×C4—201no—
218C2×C3×C4—201no—
219C2×C3×C4—201no—
220C2×C3×C4D4012yes—
221C2×C3×C4D4×D512yes—
222#67—202no—
223#67—202no—
224C2×Dic3—102no—
225D12—202no—
226D12—202no—
227D12—401no—
228C4×D3—204no—
229Dic6—202no—
230C3⋊C8—42no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5C2×#21311yescharacteristic
234C22×C5#93711yescharacteristic
235C22×C5#94911yescharacteristic
236C2×D5—122no—
237C2×D5—122no—
238C2×D5—122no—
239C4×C5—22no—
240C4×C5—22no—
241C4×C5—41no—
242Dic5—42no—
243Dic5—81no—
244Dic5—122no—
245#41—602no—
246#41—602no—
247C2×Q8—301no—
248C2×D4—152no—
249C2×D4—301no—
250C2×D4—301no—
251C2×D4—302no—
252C22×C4—101no—
253C22×C4—101no—
254C22×C4—302no—
255C22×C4#120211yescharacteristic
256C22×C4#120211yescharacteristic
257C22×C4C2×D3×D511yescharacteristic
258C2×C8—62no—
259C4⋊C4—22no—
260C4⋊C4—102no—
261C4⋊C4—152no—
262C4⋊C4—202no—
263C4⋊C4—301no—
264C22⋊C4—302no—
265C22⋊C4—302no—
266C3×C5#161011yescharacteristic, complemented, Hall
267C22×C3—21no—
268C22×C3—21no—
269C22×C3#402811yescharacteristic
270C22×C3C2×D4011yescharacteristic
271C22×C3#405411yescharacteristic
272C2×D3—202no—
273C2×D3—202no—
274C2×D3—202no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—41no—
278C3×C4—202no—
279C3×C4—401no—
280Dic3—202no—
281C2×C5—21no—
282C2×C5—21no—
283C2×C5#503611yescharacteristic
284C2×C5#505311yescharacteristic
285C2×C5#509511yescharacteristic
286D5—242no—
287C23—302no—
288C23C2×#120211yescharacteristic
289Q8—602no—
290D4—602no—
291D4—602no—
292D4—602no—
293D4—602no—
294D4—1201no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—102no—
301C2×C4—201no—
302C2×C4—201no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4—201no—
306C2×C4—302no—
307C2×C4—604no—
308C2×C4#665312yes—
309C2×C4#679012yes—
310C8—122no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3#6502111yescharacteristic
314C2×C3#6503111yescharacteristic
315C2×C3#6504111yescharacteristic
316D3—402no—
317C5#6971211yescharacteristic, complemented, Sylow
318C22—21no—
319C22—21no—
320C22—602no—
321C22—602no—
322C22—602no—
323C22C2×#665311yescharacteristic
324C22#9130111yescharacteristic
325C22#9157211yescharacteristic
326C4—22no—
327C4—22no—
328C4—41no—
329C4—202no—
330C4—401no—
331C4—602no—
332C3#1059892811yescharacteristic, complemented, Sylow
333C2—21no—
334C2—21no—
335C2—1202no—
336C2#1174852411yescharacteristic
337C2#1174918511yescharacteristic
338C2#1174939511yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radical#11756269C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1610
LCSG ▷ C22×C3×C4×C5 ▷ C22×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
2. C3×#65272C2semidirect
3. #11748474C2semidirect
4. C5×#4528C2semidirect
5. #11745958C2semidirect
22. #65272D3semidirect
50. #4528D5semidirect
266. C3×C5#1610semidirect
317. C5#69712semidirect
332. C3#10598928semidirect

Maximal subgroups

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

subgroupindex
#117562692
C3×#652722
#117484742
C5×#45282
#117459582
#105989283
#697125