Finite Group Databasebeta

← #14316735

Subgroups — #14316735

Order 1920.

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

normal subgroups only

This group has 492 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#11756472C211yesmaximal, characteristic, complemented
2C3×C5×#453C211yesmaximal, characteristic
3#11751344C212yesmaximal, complemented
4#11746366C211yesmaximal, characteristic, complemented
5#11746297C212yesmaximal, complemented
6#10601779—31nomaximal, Hall
7C3×C5×H(5,𝔽2)C2211yescharacteristic
8C3×C5×AGL(1,ℤ/8)—21no—
9C3×C5×#127C2211yescharacteristic
10#91825—22no—
11#91824—21no—
12#91824—22no—
13#91824C2212yes—
14D4×Dic15—22no—
15C4×Dic30—21no—
16C3×C5×#104—21no—
17C3×C5×#100C2211yescharacteristic
18#91118—22no—
19#91118C2212yes—
20#70986—51nomaximal, Hall
21#66047—31no—
22C5×#453D311yescharacteristic
23#65532—32no—
24#64765—31no—
25#64696—32no—
26C3×C5×#41—21no—
27C3×C5×#41—41no—
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—41no—
31C2×C3×C5×D4D411yescharacteristic
32C2×C3×C5×D4C2311yescharacteristic
33C22×Dic15—21no—
34C22×Dic15D412yes—
35C2×Dic30—21no—
36C3×C5×SD16—41no—
37C3×C5×D8—41no—
38C3×C5×M16—21no—
39C3×C42×C5D411yescharacteristic
40#6719—22no—
41#6719—21no—
42#6719—22no—
43#6719—22no—
44#6719—42no—
45#6719D412yes—
46C4⋊Dic15—21no—
47#6712—22no—
48#6712—42no—
49C4×Dic15—22no—
50#5713—51no—
51C3×#453D511yescharacteristic
52#5243—52no—
53#4545—51no—
54#4476—52no—
55C5×H(5,𝔽2)C2×D311yescharacteristic
56C5×AGL(1,ℤ/8)—21no—
57C5×#127C2×D311yescharacteristic
58#4082—62no—
59#4081—32no—
60#4081—61no—
61#4081—62no—
62D4×Dic5—62no—
63C4×Dic10—61no—
64C5×#104—21no—
65C5×#100C2×D311yescharacteristic
66#3966—32no—
67#3966—62no—
68#2198—151noSylow
69C23×C3×C5—22no—
70C23×C3×C5—21no—
71C23×C3×C5C2×D412yes—
72C3×C5×Q8—21no—
73C3×C5×D4—21no—
74C3×C5×D4—41no—
75C3×C5×D4—44no—
76C3×C5×D4—41no—
77C3×C5×D4—42no—
78C3×C5×D4—41no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×Dic15—22no—
84C2×Dic15—22no—
85C2×Dic15—42no—
86C2×Dic15—42no—
87C2×Dic15—81no—
88Dic30—42no—
89C3×C5×C8—41no—
90C3×H(5,𝔽2)C2×D511yescharacteristic
91C3×AGL(1,ℤ/8)—21no—
92C3×#127C2×D511yescharacteristic
93#936—102no—
94#935—52no—
95#935—101no—
96#935—102no—
97D4×Dic3—102no—
98C4×Dic6—101no—
99C3×#104—21no—
100C3×#100C2×D511yescharacteristic
101#834—52no—
102#834—102no—
103C5×#41—21no—
104C5×#41—41no—
105C2×C5×D4—22no—
106C2×C5×D4—22no—
107C2×C5×D4—41no—
108C2×C5×D4#6711yescharacteristic
109C2×C5×D4C22×D311yescharacteristic
110C22×Dic5—32no—
111C22×Dic5—61no—
112C2×Dic10—61no—
113C5×SD16—41no—
114C5×D8—41no—
115C5×M16—21no—
116C42×C5#6711yescharacteristic
117C22⋊Dic5—32no—
118C22⋊Dic5—62no—
119C22⋊Dic5—61no—
120C22⋊Dic5—62no—
121C22⋊Dic5—62no—
122C22⋊Dic5—122no—
123C4⋊Dic5—61no—
124#683—62no—
125#683—122no—
126C4×Dic5—62no—
127#559—151no—
128#458—152no—
129#453D1511yescharacteristic
130#353—151no—
131#352—152no—
132C22×C3×C5—22no—
133C22×C3×C5—42no—
134C22×C3×C5—42no—
135C22×C3×C5—41no—
136C22×C3×C5—41no—
137C22×C3×C5—82no—
138C22×C3×C5#12011yescharacteristic
139C3×C4×C5—22no—
140C3×C4×C5—21no—
141C3×C4×C5—41no—
142Dic15—42no—
143Dic15—42no—
144Dic15—82no—
145C3×#41—21no—
146C3×#41—41no—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—41no—
150C2×C3×D4C22⋊D511yescharacteristic
151C2×C3×D4C22×D511yescharacteristic
152C22×Dic3—52no—
153C22×Dic3—101no—
154C2×Dic6—101no—
155C3×SD16—41no—
156C3×D8—41no—
157C3×M16—21no—
158C3×C42C22⋊D511yescharacteristic
159#217—52no—
160#217—102no—
161#217—101no—
162#217—102no—
163#217—102no—
164#217—202no—
165C4⋊Dic3—101no—
166Dic3⋊C4—102no—
167Dic3⋊C4—202no—
168C4×Dic3—102no—
169C23×C5—22no—
170C23×C5—21no—
171C23×C5D3×D412yes—
172C5×Q8—21no—
173C5×D4—21no—
174C5×D4—41no—
175C5×D4—41no—
176C5×D4—44no—
177C5×D4—42no—
178C5×D4—41no—
179C2×C4×C5—21no—
180C2×C4×C5—22no—
181C2×C4×C5—41no—
182C2×C4×C5C2×#6711yescharacteristic
183C2×Dic5—62no—
184C2×Dic5—62no—
185C2×Dic5—122no—
186C2×Dic5—122no—
187C2×Dic5—241no—
188Dic10—122no—
189C5×C8—41no—
190H(5,𝔽2)C2×D1511yescharacteristic
191AGL(1,ℤ/8)—21no—
192#127C2×D1511yescharacteristic
193#124—302no—
194#123—152no—
195#123—301no—
196#123—302no—
197C4×Q8—301no—
198C4×D4—302no—
199#104—21no—
200#100C2×D1511yescharacteristic
201#99—152no—
202#99—302no—
203C2×C3×C5—21no—
204C2×C3×C5—42no—
205C2×C3×C5—81no—
206C2×C3×C5—81no—
207C2×C3×C5B(4,𝔽2)11yescharacteristic
208C23×C3—22no—
209C23×C3—21no—
210C23×C3D4×D512yes—
211C3×Q8—21no—
212C3×D4—21no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—44no—
216C3×D4—42no—
217C3×D4—41no—
218C2×C3×C4—21no—
219C2×C3×C4—22no—
220C2×C3×C4—41no—
221C2×C3×C4C2×C22⋊D511yescharacteristic
222C2×Dic3—102no—
223C2×Dic3—102no—
224C2×Dic3—202no—
225C2×Dic3—202no—
226C2×Dic3—401no—
227Dic6—202no—
228C3×C8—41no—
229C22×C5—22no—
230C22×C5—42no—
231C22×C5—42no—
232C22×C5—41no—
233C22×C5—41no—
234C22×C5—82no—
235C22×C5#93711yescharacteristic
236C4×C5—22no—
237C4×C5—21no—
238C4×C5—41no—
239Dic5—122no—
240Dic5—122no—
241Dic5—242no—
242#41—21no—
243#41—41no—
244C2×Q8—301no—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4#122011yescharacteristic
249C2×D4C22×D1511yescharacteristic
250C22×C4—152no—
251C22×C4—301no—
252SD16—41no—
253D8—41no—
254M16—21no—
255C4⋊C4—301no—
256C4⋊C4—302no—
257C4⋊C4—602no—
258C22⋊C4—152no—
259C22⋊C4—302no—
260C22⋊C4—301no—
261C22⋊C4—302no—
262C22⋊C4—302no—
263C22⋊C4—602no—
264C42—302no—
265C42#122011yescharacteristic
266C3×C5#219811yescharacteristic, complemented, Hall
267C22×C3—22no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—82no—
273C22×C3#408311yescharacteristic
274C3×C4—22no—
275C3×C4—21no—
276C3×C4—41no—
277Dic3—202no—
278Dic3—202no—
279Dic3—402no—
280C2×C5—21no—
281C2×C5—42no—
282C2×C5—81no—
283C2×C5—81no—
284C2×C5#503211yescharacteristic
285C23—22no—
286C23—21no—
287C23D4×D1512yes—
288Q8—21no—
289Q8—602no—
290D4—21no—
291D4—41no—
292D4—41no—
293D4—44no—
294D4—42no—
295D4—41no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—302no—
300C2×C4—302no—
301C2×C4—602no—
302C2×C4—602no—
303C2×C4—1201no—
304C2×C4C2×#122011yescharacteristic
305C8—41no—
306C2×C3—21no—
307C2×C3—42no—
308C2×C3—81no—
309C2×C3—81no—
310C2×C3#6532111yescharacteristic
311C5#7098611yescharacteristic, complemented, Sylow
312C22—22no—
313C22—42no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—82no—
318C22#9182611yescharacteristic
319C4—22no—
320C4—21no—
321C4—41no—
322C4—602no—
323C4—602no—
324C4—1202no—
325C3#1060177911yescharacteristic, complemented, Sylow
326C2—21no—
327C2—42no—
328C2—81no—
329C2—81no—
330C2#1175113311yescharacteristic
subgroupG/H
centerC2#11751133
commutator, cosocleC2×C3×C5×D4C23
FrattiniC2×D4C22×D15
Fitting, prime radicalC3×C5×#453C2
socleC2×C3×C5B(4,𝔽2)
hypercenter#453D15
hypocenterC3×C5#2198
LCSG ▷ C2×C3×C5×D4 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #11756472C2semidirect
3. #11751344C2semidirect
4. #11746366C2semidirect
5. #11746297C2semidirect
266. C3×C5#2198semidirect
311. C5#70986semidirect
325. C3#10601779semidirect

Maximal subgroups

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

subgroupindex
#117564722
C3×C5×#4532
#117513442
#117463662
#117462972
#106017793
#709865