Finite Group Databasebeta

← #14316973

Subgroups — #14316973

Order 1920.

472 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 67 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#11756493C211yesmaximal, characteristic, complemented
2C3×C5×#456C211yesmaximal, characteristic, complemented
3#11751346C212yesmaximal, complemented
4#11746369C211yesmaximal, characteristic, complemented
5#11746298C212yesmaximal, complemented
6#10601787—31nomaximal, Hall
7C3×C5×2−1+4C2211yescharacteristic
8C3×C5×#137—21no—
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91838—22no—
11#91836—21no—
12#91836C2212yes—
13#91784—22no—
14#91781—22no—
15C4×D60—21no—
16C3×C5×#104—21no—
17C3×C5×#101C2211yescharacteristic
18#91121—22no—
19#91120C2212yes—
20#70994—51nomaximal, Hall
21#66068—31no—
22C5×#456D311yescharacteristic, complemented
23#65534—32no—
24#64768—31no—
25#64697—32no—
26C3×C5×#41—22no—
27C3×C5×#41—21no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8—41no—
30C2×C3×C5×Q8D411yescharacteristic
31C2×C3×C5×Q8C2311yescharacteristic
32C2×D60—21no—
33C2×D60—21no—
34C2×D60D412yes—
35C2×C4×D15—22no—
36C3×C5×Q16—41no—
37C3×C5×SD16—41no—
38C3×C5×M16—21no—
39C3×C5×C4⋊C4—22no—
40C3×C42×C5D411yescharacteristic
41#6717—42no—
42#6715—42no—
43#6714—22no—
44#6714—22no—
45#6714—22no—
46C4⋊Dic15—21no—
47C4×Dic15—21no—
48C4×Dic15D412yes—
49#6710—22no—
50#5734—51no—
51C3×#456D511yescharacteristic, complemented
52#5245—52no—
53#4548—51no—
54#4477—52no—
55C5×2−1+4C2×D311yescharacteristic
56C5×#137—21no—
57C5×C4⋊Q8C2×D311yescharacteristic
58#4095—62no—
59#4093—32no—
60#4093—61no—
61#4041—62no—
62#4038—62no—
63C4×D20—61no—
64C5×#104—21no—
65C5×#101C2×D311yescharacteristic
66#3969—62no—
67#3968—32no—
68#2204—151noSylow
69C22×D15—22no—
70C3×C5×Q8—22no—
71C3×C5×Q8—21no—
72C3×C5×Q8—41no—
73C3×C5×Q8—41no—
74C3×C5×D4—22no—
75C3×C5×D4—21no—
76C3×C5×D4—41no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—42no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C2×D412yes—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×Dic15—22no—
84D60—42no—
85D60—42no—
86D60—81no—
87C4×D15—44no—
88C3×C5×C8—41no—
89C3⋊#168—42no—
90C3×2−1+4C2×D511yescharacteristic
91C3×#137—21no—
92C3×C4⋊Q8C2×D511yescharacteristic
93#949—102no—
94#947—52no—
95#947—101no—
96#895—102no—
97#892—102no—
98C4×D12—101no—
99C3×#104—21no—
100C3×#101C2×D511yescharacteristic
101#837—102no—
102#836—52no—
103C5×#41—22no—
104C5×#41—21no—
105C5×#41—41no—
106C2×C5×Q8—41no—
107C2×C5×Q8#6711yescharacteristic
108C2×C5×Q8C22×D311yescharacteristic
109C2×D20—32no—
110C2×D20—61no—
111C2×D20—61no—
112C2×C4×D5—62no—
113C5×Q16—41no—
114C5×SD16—41no—
115C5×M16—21no—
116C5×C4⋊C4—22no—
117C42×C5#6711yescharacteristic
118#688—122no—
119#686—122no—
120#685—62no—
121#685—62no—
122#685—62no—
123C4⋊Dic5—61no—
124C4×Dic5—32no—
125C4×Dic5—61no—
126#681—62no—
127#555—151no—
128#456D1511yescharacteristic, complemented
129#454—152no—
130#356—151no—
131#355—152no—
132C22×C3×C5—41no—
133C22×C3×C5#12011yescharacteristic
134C2×D15—42no—
135C2×D15—42no—
136C2×D15—42no—
137C3×C4×C5—22no—
138C3×C4×C5—22no—
139C3×C4×C5—21no—
140C3×C4×C5—41no—
141C3×C4×C5—41no—
142Dic15—42no—
143C3×#41—22no—
144C3×#41—21no—
145C3×#41—41no—
146C2×C3×Q8—41no—
147C2×C3×Q8C22⋊D511yescharacteristic
148C2×C3×Q8C22×D511yescharacteristic
149C2×D12—52no—
150C2×D12—101no—
151C2×D12—101no—
152C2×C4×D3—102no—
153C3×Q16—41no—
154C3×SD16—41no—
155C3×M16—21no—
156C3×C4⋊C4—22no—
157C3×C42C22⋊D511yescharacteristic
158#215—202no—
159#213—202no—
160(C2×D3)⋊C4—102no—
161(C2×D3)⋊C4—102no—
162(C2×D3)⋊C4—102no—
163C4⋊Dic3—101no—
164C4×Dic3—52no—
165C4×Dic3—101no—
166#208—102no—
167C22×D5—62no—
168C5×Q8—22no—
169C5×Q8—21no—
170C5×Q8—41no—
171C5×Q8—41no—
172C5×D4—22no—
173C5×D4—21no—
174C5×D4—41no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—42no—
178C2×C4×C5—41no—
179C2×C4×C5D3×D412yes—
180C2×C4×C5C2×#6711yescharacteristic
181C2×Dic5—62no—
182D20—122no—
183D20—122no—
184D20—241no—
185C4×D5—124no—
186C5×C8—41no—
187#168—122no—
1882−1+4C2×D1511yescharacteristic
189#137—21no—
190AGL(1,ℤ/8)—302no—
191C4⋊Q8C2×D1511yescharacteristic
192#124—152no—
193#124—301no—
194#121—302no—
195C4×D4—301no—
196#117—302no—
197#104—21no—
198#104—302no—
199#101—152no—
200#101C2×D1511yescharacteristic
201C2×C3×C5—21no—
202C2×C3×C5—81no—
203C2×C3×C5B(4,𝔽2)11yescharacteristic
204D15—82no—
205C22×D3—102no—
206C3×Q8—22no—
207C3×Q8—21no—
208C3×Q8—41no—
209C3×Q8—41no—
210C3×D4—22no—
211C3×D4—21no—
212C3×D4—41no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—42no—
216C2×C3×C4—41no—
217C2×C3×C4D4×D512yes—
218C2×C3×C4C2×C22⋊D511yescharacteristic
219C2×Dic3—102no—
220D12—202no—
221D12—202no—
222D12—401no—
223C4×D3—204no—
224C3×C8—41no—
225C3⋊C8—202no—
226C22×C5—41no—
227C22×C5#93711yescharacteristic
228C2×D5—122no—
229C2×D5—122no—
230C2×D5—122no—
231C4×C5—22no—
232C4×C5—22no—
233C4×C5—21no—
234C4×C5—41no—
235C4×C5—41no—
236Dic5—122no—
237#41—22no—
238#41—21no—
239#41—41no—
240C2×Q8—41no—
241C2×Q8#122011yescharacteristic
242C2×Q8C22×D1511yescharacteristic
243C2×D4—152no—
244C2×D4—301no—
245C2×D4—301no—
246C22×C4—302no—
247Q16—41no—
248SD16—41no—
249SD16—602no—
250D8—602no—
251M16—21no—
252M16—302no—
253C4⋊C4—22no—
254C4⋊C4—301no—
255C22⋊C4—302no—
256C22⋊C4—302no—
257C22⋊C4—302no—
258C42—152no—
259C42—301no—
260C42#122011yescharacteristic
261C3×C5#220411yescharacteristic, complemented, Hall
262C22×C3—41no—
263C22×C3#408311yescharacteristic
264C2×D3—202no—
265C2×D3—202no—
266C2×D3—202no—
267C3×C4—22no—
268C3×C4—22no—
269C3×C4—21no—
270C3×C4—41no—
271C3×C4—41no—
272Dic3—202no—
273C2×C5—21no—
274C2×C5—81no—
275C2×C5#503211yescharacteristic
276D5—242no—
277C23—302no—
278Q8—22no—
279Q8—21no—
280Q8—41no—
281Q8—41no—
282D4—22no—
283D4—21no—
284D4—41no—
285D4—602no—
286D4—602no—
287D4—1201no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—302no—
293C2×C4—604no—
294C2×C4D4×D1512yes—
295C2×C4C2×#122011yescharacteristic
296C8—41no—
297C8—602no—
298C2×C3—21no—
299C2×C3—81no—
300C2×C3#6532111yescharacteristic
301D3—402no—
302C5#7099411yescharacteristic, complemented, Sylow
303C22—41no—
304C22—602no—
305C22—602no—
306C22—602no—
307C22#9182611yescharacteristic
308C4—22no—
309C4—21no—
310C4—22no—
311C4—41no—
312C4—41no—
313C4—602no—
314C3#1060178711yescharacteristic, complemented, Sylow
315C2—21no—
316C2—81no—
317C2—1202no—
318C2#1175113311yescharacteristic
subgroupG/H
centerC2#11751133
commutator, cosocleC2×C3×C5×Q8C23
FrattiniC2×Q8C22×D15
FittingC3×C5×#456C2
socleC2×C3×C5B(4,𝔽2)
hypercenter#456D15
hypocenterC3×C5#2204
LCSG ▷ C2×C3×C5×Q8 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #11756493C2semidirect
2. C3×C5×#456C2semidirect
3. #11751346C2semidirect
4. #11746369C2semidirect
5. #11746298C2semidirect
22. C5×#456D3semidirect
51. C3×#456D5semidirect
128. #456D15semidirect
261. C3×C5#2204semidirect
302. C5#70994semidirect
314. C3#10601787semidirect

Maximal subgroups

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

subgroupindex
#117564932
C3×C5×#4562
#117513462
#117463692
#117462982
#106017873
#709945