Finite Group Databasebeta

← #14316904

Subgroups — #14316904

Order 1920.

452 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 68 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×#5672C211yesmaximal, characteristic, complemented
2#11751162C211yesmaximal, characteristic
3#11749186C212yesmaximal
4C3×#64761C211yesmaximal, characteristic, complemented
5#11746002C212yesmaximal, complemented
6#10602751—31nomaximal, Hall
7#92095C2211yescharacteristic
8C3×C5×#124C2211yescharacteristic
9#91831—21no—
10C5×#944—21no—
11C5×#935C2212yes—
12C5×#879—22no—
13C5×#878—22no—
14C5×#870—21no—
15#91542—22no—
16#91117C2211yescharacteristic
17#91089—21no—
18C3×#3966C2212yes—
19#90997—22no—
20#69155—51nomaximal, Hall
21C5×#563—31no—
22#65350—31no—
23#65342—32no—
24#64761D311yescharacteristic, complemented
25#64759—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4C2311yescharacteristic
28C2×#1220—22no—
29#6819—41no—
30D4×D15—41no—
31#6817—21no—
32C22×C5×Dic3D412yes—
33C2×C5×Dic6—21no—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5D411yescharacteristic
36#6718—41no—
37#6717—41no—
38#6710—21no—
39C5×#217—22no—
40C5×#217D412yes—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3—21no—
43C5×Dic3⋊C4—22no—
44C5×Dic3⋊C4—22no—
45C5×Dic3⋊C4—22no—
46C4×C5×Dic3—21no—
47C3×C22⋊Dic5—22no—
48#6668—42no—
49#6667—42no—
50#5672D511yescharacteristic, complemented
51#5061—51no—
52#4742—52no—
53C3×#354—51no—
54#4472—52no—
55#4144—31no—
56C5×C4⋊Q8—61no—
57C5×#126—62no—
58C5×#125—61no—
59C5×#124C2×D311yescharacteristic
60C5×#123—32no—
61C5×C22⋊Q8—62no—
62#4088—61no—
63#4075—62no—
64#3966C2×D312yes—
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×D4—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5C2×D411yescharacteristic
76#1220—42no—
77#1220—41no—
78C2×Dic15—22no—
79D60—21no—
80C4×D15—41no—
81Dic30—21no—
82C2×C5×Dic3—22no—
83C2×C5×Dic3—22no—
84C2×C5×Dic3—42no—
85C5×Dic6—81no—
86C2×C3×Dic5—42no—
87C3⋊#168—41no—
88#1004—51no—
89C3×#124C2×D511yescharacteristic
90#944—21no—
91#942—101no—
92#935C2×D512yes—
93#886—102no—
94#879—22no—
95#878—22no—
96#870—21no—
97C3×#99—52no—
98#833—51no—
99#806—102no—
100#805—101no—
101C2×C5×Q8—61no—
102C2×C5×Q8D1211yescharacteristic
103C2×C5×D4C22×D311yescharacteristic
104C22×C4×C5—32no—
105C2×C22⋊D5—62no—
106#711—121no—
107D4×D5—121no—
108#709—61no—
109C5×C4⋊C4—61no—
110C5×C4⋊C4—62no—
111C5×C4⋊C4—62no—
112C5×C4⋊C4—61no—
113C5×C4⋊C4—62no—
114C5×C22⋊C4—22no—
115C5×C22⋊C4—32no—
116C5×C22⋊C4—62no—
117C42×C5—61no—
118C42×C5D1211yescharacteristic
119C22⋊Dic5—22no—
120#689—121no—
121#688—121no—
122#685—122no—
123#683—122no—
124#681—61no—
125#563—31no—
126#458—152no—
127#455—151no—
128#354—51no—
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—41no—
137C3×C4×C5—41no—
138Dic15—41no—
139C3×Dic5—82no—
140C5×Dic3—42no—
141C5×Dic3—42no—
142C2×C3×Q8C22⋊D511yescharacteristic
143C2×C3×D4C22×D511yescharacteristic
144C2×#67—102no—
145C22×Dic3C22⋊D512yes—
146#237—201no—
147D3×D4—201no—
148#235—101no—
149C2×Dic6—21no—
150C3×C22⋊C4—22no—
151C3×C22⋊C4—102no—
152C3×C42C22⋊D511yescharacteristic
153#217—22no—
154#217C22⋊D512yes—
155#216—201no—
156#215—201no—
157(C2×D3)⋊C4—202no—
158C4⋊Dic3—21no—
159C4⋊Dic3—21no—
160C4⋊Dic3—202no—
161Dic3⋊C4—22no—
162Dic3⋊C4—22no—
163Dic3⋊C4—22no—
164C4×Dic3—21no—
165#208—101no—
166C23×C5D3×D412yes—
167C22×D5—62no—
168C5×Q8—41no—
169C5×Q8—241no—
170C5×D4—41no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—62no—
174C2×C4×C5—62no—
175C2×C4×C5—122no—
176C2×C4×C5C2×D1211yescharacteristic
177C22⋊D5—122no—
178C22⋊D5—121no—
179C2×Dic5—42no—
180C2×Dic5—62no—
181D20—61no—
182C4×D5—121no—
183Dic10—61no—
184#168—121no—
185H(5,𝔽2)—151no—
186#137—301no—
187C4⋊Q8—61no—
188#126—62no—
189#125—61no—
190#124D3×D511yescharacteristic
191#123—32no—
192#123—302no—
193C22⋊Q8—62no—
194#104—301no—
195#100—151no—
196#99—52no—
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×D4—41no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—202no—
209C2×C3×C4C2×C22⋊D511yescharacteristic
210#67—202no—
211#67—201no—
212C2×Dic3—22no—
213C2×Dic3—22no—
214C2×Dic3—42no—
215C2×Dic3—102no—
216D12—101no—
217C4×D3—201no—
218Dic6—81no—
219Dic6—101no—
220C3⋊C8—201no—
221C22×C5—22no—
222C22×C5—42no—
223C22×C5#88211yescharacteristic
224C2×D5—121no—
225C2×D5—242no—
226C4×C5—21no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—122no—
230C4×C5—122no—
231Dic5—82no—
232Dic5—121no—
233#41—301no—
234#41—601no—
235C2×Q8—61no—
236C2×Q8#120311yescharacteristic
237C2×D4—302no—
238C2×D4—601no—
239C2×D4C2×D3×D511yescharacteristic
240C22×C4—32no—
241Q16—601no—
242SD16—601no—
243M16—301no—
244C4⋊C4—61no—
245C4⋊C4—62no—
246C4⋊C4—62no—
247C4⋊C4—61no—
248C4⋊C4—62no—
249C4⋊C4—602no—
250C22⋊C4—22no—
251C22⋊C4—32no—
252C22⋊C4—62no—
253C22⋊C4—102no—
254C22⋊C4—602no—
255C42—61no—
256C42#120311yescharacteristic
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—41no—
265C3×C4—41no—
266C3×C4—402no—
267Dic3—42no—
268Dic3—42no—
269Dic3—201no—
270C2×C5—21no—
271C2×C5—42no—
272C2×C5#474111yescharacteristic
273D5—241no—
274C23—302no—
275C23D3×C22⋊D512yes—
276Q8—41no—
277Q8—241no—
278Q8—301no—
279D4—41no—
280D4—301no—
281D4—602no—
282D4—601no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—62no—
286C2×C4—62no—
287C2×C4—122no—
288C2×C4—202no—
289C2×C4—302no—
290C2×C4—601no—
291C2×C4C2×#120311yescharacteristic
292C8—601no—
293C2×C3—21no—
294C2×C3—42no—
295C2×C3#6553311yescharacteristic
296D3—401no—
297C5#6915511yescharacteristic, complemented, Sylow
298C22—22no—
299C22—42no—
300C22—601no—
301C22—1202no—
302C22#9157011yescharacteristic
303C4—21no—
304C4—41no—
305C4—41no—
306C4—122no—
307C4—122no—
308C4—402no—
309C4—601no—
310C3#1060275111yescharacteristic, complemented, Sylow
311C2—21no—
312C2—42no—
313C2—1201no—
314C2#1174917811yescharacteristic
subgroupG/H
centerC2#11749178
commutator, cosocleC2×C3×C5×D4C23
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#124C22
socleC2×C3×C5B(4,𝔽2)
prime radical#92095C22
hypercenter#124D3×D5
hypocenterC3×C5#2201
LCSG ▷ C2×C3×C5×D4 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C5×#5672C2semidirect
4. C3×#64761C2semidirect
5. #11746002C2semidirect
24. #64761D3semidirect
50. #5672D5semidirect
257. C3×C5#2201semidirect
297. C5#69155semidirect
310. C3#10602751semidirect

Maximal subgroups

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

subgroupindex
C5×#56722
#117511622
#117491862
C3×#647612
#117460022
#106027513
#691555