Finite Group Databasebeta

← #14316879

Subgroups — #14316879

Order 1920.

452 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C3×C5×#563C211yesmaximal, characteristic, complemented
2#11751162C211yesmaximal, characteristic
3#11751154C212yesmaximal
4#11746362C211yesmaximal, characteristic, complemented
5#11746360C212yesmaximal, complemented
6#10602751—31nomaximal, Hall
7#92095C2211yescharacteristic
8C3×C5×C4⋊Q8—21no—
9C3×C5×#126—22no—
10C3×C5×#125—21no—
11C3×C5×#124C2211yescharacteristic
12C3×C5×#123C2212yes—
13C3×C5×C22⋊Q8—22no—
14#91831—21no—
15#91818—22no—
16#91118C2212yes—
17#91117C2211yescharacteristic
18#91090—22no—
19#91089—21no—
20#71958—51nomaximal, Hall
21C5×#563D311yescharacteristic, complemented
22#65350—31no—
23#65342—32no—
24#64761—31no—
25#64759—32no—
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4C2311yescharacteristic
29C22×C3×C4×C5D412yes—
30C2×#1220—22no—
31#6819—41no—
32D4×D15—41no—
33#6817—21no—
34C3×C5×C4⋊C4—21no—
35C3×C5×C4⋊C4—22no—
36C3×C5×C4⋊C4—22no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—22no—
39C3×C5×C22⋊C4—22no—
40C3×C5×C22⋊C4—22no—
41C3×C5×C22⋊C4D412yes—
42C3×C42×C5—21no—
43C3×C42×C5D411yescharacteristic
44#6719—22no—
45#6718—41no—
46#6717—41no—
47#6714—42no—
48#6712—42no—
49#6710—21no—
50C3×#563D511yescharacteristic, complemented
51#5061—51no—
52#5053—52no—
53#4541—51no—
54#4539—52no—
55#4144—31no—
56C5×C4⋊Q8—21no—
57C5×#126—22no—
58C5×#125—21no—
59C5×#124C2×D311yescharacteristic
60C5×#123C2×D312yes—
61C5×C22⋊Q8—22no—
62#4088—61no—
63#4075—62no—
64#3966—32no—
65#3965—31no—
66#3938—62no—
67#3937—61no—
68#2201—151noSylow
69C23×C3×C5C2×D412yes—
70C22×D15—22no—
71C3×C5×Q8—41no—
72C3×C5×Q8—81no—
73C3×C5×D4—41no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—42no—
79C2×C3×C4×C5C2×D411yescharacteristic
80#1220—42no—
81#1220—41no—
82C2×Dic15—22no—
83C2×Dic15—42no—
84D60—21no—
85C4×D15—41no—
86Dic30—21no—
87C3⋊#168—41no—
88#1004—51no—
89C3×C4⋊Q8—21no—
90C3×#126—22no—
91C3×#125—21no—
92C3×#124C2×D511yescharacteristic
93C3×#123C2×D512yes—
94C3×C22⋊Q8—22no—
95#942—101no—
96#929—102no—
97#834—52no—
98#833—51no—
99#806—102no—
100#805—101no—
101C2×C5×Q8—21no—
102C2×C5×Q8#6711yescharacteristic
103C2×C5×D4C22×D311yescharacteristic
104C22×C4×C5#6712yes—
105C2×C22⋊D5—62no—
106#711—121no—
107D4×D5—121no—
108#709—61no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—22no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—22no—
114C5×C22⋊C4—22no—
115C5×C22⋊C4—22no—
116C5×C22⋊C4#6712yes—
117C42×C5—21no—
118C42×C5#6711yescharacteristic
119C22⋊Dic5—62no—
120#689—121no—
121#688—121no—
122#685—122no—
123#683—122no—
124#681—61no—
125#563D1511yescharacteristic, complemented
126#458—152no—
127#455—151no—
128#354—151no—
129#352—152no—
130C22×C3×C5—22no—
131C22×C3×C5—42no—
132C22×C3×C5#12011yescharacteristic
133C2×D15—41no—
134C2×D15—82no—
135C3×C4×C5—21no—
136C3×C4×C5—42no—
137C3×C4×C5—41no—
138C3×C4×C5—42no—
139C3×C4×C5—41no—
140Dic15—41no—
141Dic15—82no—
142C2×C3×Q8—21no—
143C2×C3×Q8C22⋊D511yescharacteristic
144C2×C3×D4C22×D511yescharacteristic
145C22×C3×C4C22⋊D512yes—
146C2×#67—102no—
147#237—201no—
148D3×D4—201no—
149#235—101no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—22no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—22no—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4C22⋊D512yes—
158C3×C42—21no—
159C3×C42C22⋊D511yescharacteristic
160#217—102no—
161#216—201no—
162#215—201no—
163(C2×D3)⋊C4—202no—
164Dic3⋊C4—202no—
165#208—101no—
166C23×C5C2×#6712yes—
167C22×D5—62no—
168C5×Q8—41no—
169C5×Q8—81no—
170C5×D4—41no—
171C2×C4×C5—21no—
172C2×C4×C5—22no—
173C2×C4×C5—21no—
174C2×C4×C5—22no—
175C2×C4×C5—42no—
176C2×C4×C5C2×#6711yescharacteristic
177C22⋊D5—122no—
178C22⋊D5—121no—
179C2×Dic5—62no—
180C2×Dic5—122no—
181D20—61no—
182C4×D5—121no—
183Dic10—61no—
184#168—121no—
185H(5,𝔽2)—151no—
186#137—301no—
187C4⋊Q8—21no—
188#126—22no—
189#125—21no—
190#124C2×D1511yescharacteristic
191#123—302no—
192#123C2×D1512yes—
193C22⋊Q8—22no—
194#104—301no—
195#100—151no—
196#99—152no—
197#99—302no—
198C2×C3×C5—21no—
199C2×C3×C5—42no—
200C2×C3×C5B(4,𝔽2)11yescharacteristic
201D15—81no—
202C23×C3C2×C22⋊D512yes—
203C22×D3—102no—
204C3×Q8—41no—
205C3×Q8—81no—
206C3×D4—41no—
207C2×C3×C4—21no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—22no—
211C2×C3×C4—42no—
212C2×C3×C4C2×C22⋊D511yescharacteristic
213#67—202no—
214#67—201no—
215C2×Dic3—102no—
216C2×Dic3—202no—
217D12—101no—
218C4×D3—201no—
219Dic6—101no—
220C3⋊C8—201no—
221C22×C5—22no—
222C22×C5—42no—
223C22×C5#95311yescharacteristic
224C2×D5—121no—
225C2×D5—242no—
226C4×C5—21no—
227C4×C5—42no—
228C4×C5—41no—
229C4×C5—42no—
230C4×C5—41no—
231Dic5—121no—
232Dic5—242no—
233#41—301no—
234#41—601no—
235C2×Q8—21no—
236C2×Q8#122011yescharacteristic
237C2×D4—302no—
238C2×D4—601no—
239C2×D4C22×D1511yescharacteristic
240C22×C4#122012yes—
241Q16—601no—
242SD16—601no—
243M16—301no—
244C4⋊C4—21no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—21no—
248C4⋊C4—22no—
249C4⋊C4—602no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—302no—
253C22⋊C4—602no—
254C22⋊C4#122012yes—
255C42—21no—
256C42#122011yescharacteristic
257C3×C5#220111yescharacteristic, complemented, Hall
258C22×C3—22no—
259C22×C3—42no—
260C22×C3#409911yescharacteristic
261C2×D3—201no—
262C2×D3—402no—
263C3×C4—21no—
264C3×C4—42no—
265C3×C4—41no—
266C3×C4—42no—
267C3×C4—41no—
268Dic3—201no—
269Dic3—402no—
270C2×C5—21no—
271C2×C5—42no—
272C2×C5#524411yescharacteristic
273D5—241no—
274C23—302no—
275C23C2×#122012yes—
276Q8—41no—
277Q8—81no—
278Q8—301no—
279D4—41no—
280D4—301no—
281D4—602no—
282D4—601no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—42no—
288C2×C4—302no—
289C2×C4—601no—
290C2×C4—602no—
291C2×C4C2×#122011yescharacteristic
292C8—601no—
293C2×C3—21no—
294C2×C3—42no—
295C2×C3#6553311yescharacteristic
296D3—401no—
297C5#7195811yescharacteristic, complemented, Sylow
298C22—22no—
299C22—42no—
300C22—601no—
301C22—1202no—
302C22#9184211yescharacteristic
303C4—21no—
304C4—42no—
305C4—41no—
306C4—42no—
307C4—41no—
308C4—601no—
309C4—1202no—
310C3#1060275111yescharacteristic, complemented, Sylow
311C2—21no—
312C2—42no—
313C2—1201no—
314C2#1175134511yescharacteristic
subgroupG/H
centerC2#11751345
commutator, cosocleC2×C3×C5×D4C23
FrattiniC2×D4C22×D15
FittingC3×C5×#563C2
socleC2×C3×C5B(4,𝔽2)
prime radical#92095C22
hypercenter#563D15
hypocenterC3×C5#2201
LCSG ▷ C2×C3×C5×D4 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #563

Complements

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

NH ≅ G/Ntype
1. C3×C5×#563C2semidirect
4. #11746362C2semidirect
5. #11746360C2semidirect
21. C5×#563D3semidirect
50. C3×#563D5semidirect
125. #563D15semidirect
257. C3×C5#2201semidirect
297. C5#71958semidirect
310. C3#10602751semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5632
#117511622
#117511542
#117463622
#117463602
#106027513
#719585