Finite Group Databasebeta

← #14288103

Subgroups — #14288103

Order 1920.

564 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 91 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×C5×#395C211yesmaximal, characteristic, complemented
3#11751328C212yesmaximal, complemented
4#11746349C211yesmaximal, characteristic, complemented
5#11746272C212yesmaximal, complemented
6#10600499—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×#6817—21no—
9C2×C3×C5×C4⋊C4—21no—
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×#6717—22no—
12#91819—21no—
13#91819C2212yes—
14#91786—22no—
15#91784—22no—
16C3×C5×#95—21no—
17C3×C5×#95C2211yescharacteristic
18#91119—22no—
19#91114C2212yes—
20#69706—51nomaximal, Hall
21#65844—31no—
22C5×#395D311yescharacteristic, complemented
23#65516—32no—
24#64748—31no—
25#64671—32no—
26C2×C3×C5×Q8—22no—
27C2×C3×C5×Q8—42no—
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C2×#1220—22no—
34#6817—42no—
35#6817—42no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60D412yes—
39C2×C4×D15—22no—
40C2×Dic30—21no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—42no—
43#6717—44no—
44#6714—22no—
45#6714—22no—
46C4⋊Dic15—21no—
47C4⋊Dic15D412yes—
48C2×C3⋊#168—22no—
49#5510—51no—
50C3×#395D511yescharacteristic, complemented
51#5227—52no—
52#4528—51no—
53#4451—52no—
54C22×C5×Q8C2×D311yescharacteristic
55C2×#709—61no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4C2×D311yescharacteristic
58C2×#688—62no—
59#4076—32no—
60#4076—61no—
61#4043—62no—
62#4041—62no—
63C5×#95—21no—
64C5×#95C2×D311yescharacteristic
65#3967—62no—
66C22⋊#168—32no—
67#1604—151noSylow
68C23×C3×C5C2×D411yescharacteristic
69C22×D15—22no—
70C3×C5×Q8—24no—
71C3×C5×Q8—42no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5SD1612yescomplemented
84C2×C3×C4×C5C2×D412yes—
85#1220—42no—
86#1220—42no—
87C2×Dic15—22no—
88D60—42no—
89D60—42no—
90D60—81no—
91C4×D15—44no—
92Dic30—42no—
93C3⋊#168—42no—
94C22×C3×Q8C2×D511yescharacteristic
95C2×#235—101no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2×D511yescharacteristic
98C2×#215—102no—
99#930—52no—
100#930—101no—
101#897—102no—
102#895—102no—
103C3×#95—21no—
104C3×#95C2×D511yescharacteristic
105#835—102no—
106#830—52no—
107C2×C5×Q8—22no—
108C2×C5×Q8—42no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5#6711yescharacteristic
112C22×C4×C5#6711yescharacteristic
113C22×C4×C5C22×D311yescharacteristic
114C2×C22⋊D5—62no—
115#709—122no—
116#709—122no—
117C2×D20—32no—
118C2×D20—61no—
119C2×D20—61no—
120C2×C4×D5—62no—
121C2×Dic10—61no—
122C5×C4⋊C4—22no—
123C5×C4⋊C4—42no—
124#688—124no—
125#685—62no—
126#685—62no—
127C4⋊Dic5—32no—
128C4⋊Dic5—61no—
129C2×#168—62no—
130#537—151no—
131#448—152no—
132#395D1511yescharacteristic, complemented
133#327—152no—
134#324—151no—
135C22×C3×C5—21no—
136C22×C3×C5—21no—
137C22×C3×C5#12011yescharacteristic
138C22×C3×C5C2×SD1611yescharacteristic
139C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
140C2×D15—42no—
141C2×D15—42no—
142C2×D15—42no—
143C3×C4×C5—22no—
144C3×C4×C5—22no—
145C3×C4×C5—42no—
146C3×C4×C5—41no—
147C3×C4×C5—42no—
148Dic15—42no—
149C2×C3×Q8—22no—
150C2×C3×Q8—42no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4C22⋊D511yescharacteristic
154C22×C3×C4C22⋊D511yescharacteristic
155C22×C3×C4C22×D511yescharacteristic
156C2×#67—102no—
157#235—202no—
158#235—202no—
159C2×D12—52no—
160C2×D12—101no—
161C2×D12—101no—
162C2×C4×D3—102no—
163C2×Dic6—101no—
164C3×C4⋊C4—22no—
165C3×C4⋊C4—42no—
166#215—204no—
167(C2×D3)⋊C4—102no—
168(C2×D3)⋊C4—102no—
169C4⋊Dic3—52no—
170C4⋊Dic3—101no—
171C2×C3⋊C8—102no—
172C23×C5C2×#6711yescharacteristic
173C22×D5—62no—
174C5×Q8—24no—
175C5×Q8—42no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—22no—
179C2×C4×C5—22no—
180C2×C4×C5—21no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5#21512yescomplemented
188C2×C4×C5D3×D412yes—
189C22⋊D5—122no—
190C22⋊D5—122no—
191C2×Dic5—62no—
192D20—122no—
193D20—122no—
194D20—241no—
195C4×D5—124no—
196Dic10—122no—
197#168—122no—
198C2×#41—301no—
199C22×Q8C2×D1511yescharacteristic
200C2×SD16—302no—
201C22⋊Q8—302no—
202#121—152no—
203#121—302no—
204#121—301no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C2×D1511yescharacteristic
207#103—302no—
208C22⋊C8—152no—
209#95—21no—
210#95C2×D1511yescharacteristic
211C2×C3×C5—21no—
212C2×C3×C5—21no—
213C2×C3×C5#45011yescharacteristic
214C2×C3×C5#45611yescharacteristic
215C2×C3×C5B(4,𝔽2)11yescharacteristic
216D15—82no—
217C23×C3C2×C22⋊D511yescharacteristic
218C22×D3—102no—
219C3×Q8—24no—
220C3×Q8—42no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—21no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4#68812yescomplemented
233C2×C3×C4D4×D512yes—
234#67—202no—
235#67—202no—
236C2×Dic3—102no—
237D12—202no—
238D12—202no—
239D12—401no—
240C4×D3—204no—
241Dic6—202no—
242C3⋊C8—202no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5#93711yescharacteristic
246C22×C5C2×#21511yescharacteristic
247C22×C5#94911yescharacteristic
248C2×D5—122no—
249C2×D5—122no—
250C2×D5—122no—
251C4×C5—22no—
252C4×C5—22no—
253C4×C5—42no—
254C4×C5—41no—
255C4×C5—42no—
256Dic5—122no—
257#41—602no—
258#41—602no—
259C2×Q8—22no—
260C2×Q8—42no—
261C2×Q8—301no—
262C2×D4—152no—
263C2×D4—301no—
264C2×D4—301no—
265C2×D4—302no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—302no—
269C22×C4#122011yescharacteristic
270C22×C4#122011yescharacteristic
271C22×C4C22×D1511yescharacteristic
272SD16—604no—
273C2×C8—302no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—152no—
277C4⋊C4—301no—
278C22⋊C4—302no—
279C22⋊C4—302no—
280C3×C5#160411yescharacteristic, complemented, Hall
281C22×C3—21no—
282C22×C3—21no—
283C22×C3#408311yescharacteristic
284C22×C3C2×#68811yescharacteristic
285C22×C3#409511yescharacteristic
286C2×D3—202no—
287C2×D3—202no—
288C2×D3—202no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—42no—
292C3×C4—41no—
293C3×C4—42no—
294Dic3—202no—
295C2×C5—21no—
296C2×C5—21no—
297C2×C5#503211yescharacteristic
298C2×C5#504611yescharacteristic
299C2×C5#509511yescharacteristic
300D5—242no—
301C23—302no—
302C23C2×#122011yescharacteristic
303Q8—24no—
304Q8—42no—
305Q8—602no—
306D4—602no—
307D4—602no—
308D4—602no—
309D4—602no—
310D4—1201no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—302no—
323C2×C4—604no—
324C2×C4#671712yescomplemented
325C2×C4D4×D1512yes—
326C8—602no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3#6532111yescharacteristic
330C2×C3#6533511yescharacteristic
331C2×C3#6538411yescharacteristic
332D3—402no—
333C5#6970611yescharacteristic, complemented, Sylow
334C22—21no—
335C22—21no—
336C22—602no—
337C22—602no—
338C22—602no—
339C22#9182611yescharacteristic
340C22C2×#671711yescharacteristic
341C22#9183811yescharacteristic
342C4—22no—
343C4—22no—
344C4—42no—
345C4—42no—
346C4—41no—
347C4—602no—
348C3#1060049911yescharacteristic, complemented, Sylow
349C2—21no—
350C2—21no—
351C2—1202no—
352C2#1175113311yescharacteristic
353C2#1175114711yescharacteristic
354C2#1175119611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#395C2
socleC22×C3×C5#120
prime radical#11756269C2
hypercenter#395D15
hypocenterC3×C5#1604
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C3×C5×#395C2semidirect
3. #11751328C2semidirect
4. #11746349C2semidirect
5. #11746272C2semidirect
22. C5×#395D3semidirect
50. C3×#395D5semidirect
83. C2×C3×C4×C5SD16semidirect
132. #395D15semidirect
187. C2×C4×C5#215semidirect
232. C2×C3×C4#688semidirect
280. C3×C5#1604semidirect
324. C2×C4#6717semidirect
333. C5#69706semidirect
348. C3#10600499semidirect

Maximal subgroups

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

subgroupindex
#117562692
C3×C5×#3952
#117513282
#117463492
#117462722
#106004993
#697065