Finite Group Databasebeta

← #14288406

Subgroups — #14288406

Order 1920.

508 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5510C211yesmaximal, characteristic
2C3×#65272C211yesmaximal, characteristic, complemented
3#11748381C212yesmaximal, complemented
4#11746349C211yesmaximal, characteristic, complemented
5#11745956C212yesmaximal, complemented
6#10602667—31nomaximal, Hall
7C2×C5×#235—21no—
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C5×#930—21no—
10C5×#930C2212yes—
11C5×#897—22no—
12C5×#895—22no—
13C2×C3×C4⋊Dic5C2211yescharacteristic
14C2×C3×#683—21no—
15#91114C2212yes—
16C3×#3963—21no—
17C3×#3963C2211yescharacteristic
18#90989—22no—
19#90966—22no—
20#69712—51nomaximal, Hall
21C5×#537—31no—
22#65322—32no—
23#65272D311yescharacteristic, complemented
24#64757—32no—
25#64748—31no—
26C22×C3×C4×C5D411yescharacteristic
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5C2311yescharacteristic
29C2×C5×#67—22no—
30C5×#235—42no—
31C5×#235—42no—
32C2×C5×D12—21no—
33C2×C5×D12—21no—
34C2×C5×D12D412yes—
35C2×C4×C5×D3—22no—
36C2×C5×Dic6—21no—
37C22×C3×Dic5—21no—
38C22×C3×Dic5—21no—
39C3×C5×C4⋊C4—22no—
40C2×C3⋊#168—22no—
41C5×(C2×D3)⋊C4—22no—
42C5×(C2×D3)⋊C4—22no—
43C5×C4⋊Dic3—21no—
44C5×C4⋊Dic3D412yes—
45C3×C4⋊Dic5—22no—
46C3×#683—42no—
47#5510D511yescharacteristic
48C3×#398—51no—
49#4967—52no—
50#4528—51no—
51#4451—52no—
52C2×C5×#41—61no—
53C5×C22⋊Q8—62no—
54C5×#121—32no—
55C5×#121—62no—
56C5×#121—61no—
57C2×C5×C4⋊C4C2×D311yescharacteristic
58C2×C4⋊Dic5C2×D311yescharacteristic
59C2×#683—21no—
60#3964—62no—
61#3963—21no—
62#3963C2×D311yescharacteristic
63C22⋊#168—32no—
64#3939—62no—
65#1610—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C22×C5×D3—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—
75C5×#67—42no—
76C5×#67—42no—
77C2×C5×Dic3—22no—
78C5×D12—42no—
79C5×D12—42no—
80C5×D12—81no—
81C4×C5×D3—44no—
82C5×Dic6—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—
89C3⋊#168—42no—
90C2×#235—21no—
91C2×C3×C4⋊C4—51no—
92C2×C3×C4⋊C4—101no—
93C2×C3×C4⋊C4C2×D511yescharacteristic
94#930—21no—
95#930C2×D512yes—
96#897—22no—
97#895—22no—
98C3×#95—51no—
99C3×#95—101no—
100#830—52no—
101#809—102no—
102#807—102no—
103C5×#41—122no—
104C5×#41—122no—
105C2×C5×Q8—61no—
106C2×C5×D4—32no—
107C2×C5×D4—61no—
108C2×C5×D4—61no—
109C2×C5×D4—62no—
110C22×C4×C5—62no—
111C22×C4×C5#6711yescharacteristic
112C22×C4×C5#6711yescharacteristic
113C22×C4×C5C22×D311yescharacteristic
114C22×Dic5—21no—
115C22×Dic5—21no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—32no—
118C5×C4⋊C4—61no—
119C5×C22⋊C4—62no—
120C5×C22⋊C4—62no—
121C4⋊Dic5—22no—
122#683—42no—
123C2×#168—62no—
124#537—31no—
125#480—152no—
126#398—51no—
127#327—152no—
128#324—151no—
129C22×C3×C5—21no—
130C22×C3×C5—21no—
131C22×C3×C5#12011yescharacteristic
132C22×C3×C5C2×D811yescharacteristic
133C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
134C2×C5×D3—42no—
135C2×C5×D3—42no—
136C2×C5×D3—42no—
137C3×C4×C5—22no—
138C3×C4×C5—22no—
139C3×C4×C5—41no—
140C3×Dic5—42no—
141C3×Dic5—81no—
142C5×Dic3—42no—
143C22×C3×C4—101no—
144C22×C3×C4—101no—
145C22×C3×C4C22⋊D511yescharacteristic
146C22×C3×C4C22⋊D511yescharacteristic
147C22×C3×C4C22×D511yescharacteristic
148C2×#67—22no—
149#235—42no—
150#235—42no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12C22⋊D512yes—
154C2×C4×D3—22no—
155C2×Dic6—21no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—102no—
158C3×C4⋊C4—202no—
159(C2×D3)⋊C4—22no—
160(C2×D3)⋊C4—22no—
161C4⋊Dic3—21no—
162C4⋊Dic3C22⋊D512yes—
163C2×C3⋊C8—102no—
164C23×C5—62no—
165C23×C5C2×#6711yescharacteristic
166C5×Q8—122no—
167C5×D4—122no—
168C5×D4—122no—
169C5×D4—122no—
170C5×D4—122no—
171C5×D4—241no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—62no—
178C2×C4×C5—124no—
179C2×C4×C5#21312yes—
180C2×C4×C5D3×D412yes—
181C2×Dic5—22no—
182C2×Dic5—41no—
183C2×Dic5—41no—
184C2×Dic5—41no—
185C2×Dic5—41no—
186C2×Dic5—41no—
187#168—122no—
188C2×#41—61no—
189C22⋊Q8—62no—
190#121—32no—
191#121—62no—
192#121—61no—
193C2×C4⋊C4—51no—
194C2×C4⋊C4—101no—
195C2×C4⋊C4D3×D511yescharacteristic
196#107—302no—
197#102—302no—
198C22⋊C8—152no—
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
206C5×D3—82no—
207C23×C3C2×C22⋊D511yescharacteristic
208C22×D3—22no—
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×C4#68612yes—
221C2×C3×C4C2×C22⋊D512yes—
222#67—42no—
223#67—42no—
224C2×Dic3—22no—
225D12—42no—
226D12—42no—
227D12—81no—
228C4×D3—44no—
229Dic6—42no—
230C3⋊C8—202no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5—122no—
234C22×C5—122no—
235C22×C5—122no—
236C22×C5C2×#21311yescharacteristic
237C22×C5#93711yescharacteristic
238C22×C5#94911yescharacteristic
239C4×C5—22no—
240C4×C5—22no—
241C4×C5—41no—
242C4×C5—122no—
243Dic5—42no—
244Dic5—81no—
245#41—122no—
246#41—122no—
247C2×Q8—61no—
248C2×D4—32no—
249C2×D4—61no—
250C2×D4—61no—
251C2×D4—62no—
252C22×C4—62no—
253C22×C4—101no—
254C22×C4—101no—
255C22×C4#120111yescharacteristic
256C22×C4#120111yescharacteristic
257C22×C4C2×D3×D511yescharacteristic
258C2×C8—302no—
259C4⋊C4—22no—
260C4⋊C4—32no—
261C4⋊C4—61no—
262C4⋊C4—102no—
263C4⋊C4—202no—
264C22⋊C4—62no—
265C22⋊C4—62no—
266C3×C5#161011yescharacteristic, complemented, Hall
267C22×C3—21no—
268C22×C3—21no—
269C22×C3C2×#68611yescharacteristic
270C22×C3#407811yescharacteristic
271C22×C3#409911yescharacteristic
272C2×D3—42no—
273C2×D3—42no—
274C2×D3—42no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—41no—
278C3×C4—202no—
279C3×C4—401no—
280Dic3—42no—
281C2×C5—21no—
282C2×C5—21no—
283C2×C5—242no—
284C2×C5#503611yescharacteristic
285C2×C5#505311yescharacteristic
286C2×C5#509511yescharacteristic
287C23—62no—
288C23C2×#120111yescharacteristic
289Q8—122no—
290D4—122no—
291D4—122no—
292D4—122no—
293D4—122no—
294D4—241no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—62no—
301C2×C4—102no—
302C2×C4—124no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4—201no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4#665212yes—
309C2×C4D3×C22⋊D512yes—
310C8—602no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3#6550611yescharacteristic
314C2×C3#6553211yescharacteristic
315C2×C3#6553511yescharacteristic
316D3—82no—
317C5#6971211yescharacteristic, complemented, Sylow
318C22—21no—
319C22—21no—
320C22—122no—
321C22—122no—
322C22—122no—
323C22C2×#665211yescharacteristic
324C22#9129911yescharacteristic
325C22#9156811yescharacteristic
326C4—22no—
327C4—22no—
328C4—41no—
329C4—122no—
330C4—202no—
331C4—401no—
332C3#1060266711yescharacteristic, complemented, Sylow
333C2—21no—
334C2—21no—
335C2—242no—
336C2#1174851611yescharacteristic
337C2#1174918311yescharacteristic
338C2#1174939311yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC5×#5510C2
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. #11748381C2semidirect
4. #11746349C2semidirect
5. #11745956C2semidirect
23. #65272D3semidirect
266. C3×C5#1610semidirect
317. C5#69712semidirect
332. C3#10602667semidirect

Maximal subgroups

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

subgroupindex
C5×#55102
C3×#652722
#117483812
#117463492
#117459562
#106026673
#697125