Finite Group Databasebeta

← #14316738

Subgroups — #14316738

Order 1920.

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

normal subgroups only

This group has 492 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×#559C211yesmaximal, characteristic, complemented
2#11751178C211yesmaximal, characteristic
3#11751154C212yesmaximal, complemented
4#11746366C211yesmaximal, characteristic, complemented
5#11746360C212yesmaximal, complemented
6#10602739—31nomaximal, Hall
7#92095C2211yescharacteristic
8C3×C5×#127C2211yescharacteristic
9C3×C5×#124—22no—
10C3×C5×#123—21no—
11C3×C5×#123C2212yes—
12C3×C4×C5×Q8—21no—
13C3×C4×C5×D4—22no—
14#91821—21no—
15#91818—22no—
16#91118C2212yes—
17#91117C2211yescharacteristic
18#91090—22no—
19#91089—21no—
20#71946—51nomaximal, Hall
21C5×#559D311yescharacteristic, complemented
22#65366—31no—
23#65342—32no—
24#64765—31no—
25#64759—32no—
26C2×C3×C5×Q8—21no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4D411yescharacteristic
29C2×C3×C5×D4C2311yescharacteristic
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5D412yes—
32C2×#1220—22no—
33#6819—41no—
34D4×D15—41no—
35#6817—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—22no—
38C3×C5×C22⋊C4—22no—
39C3×C5×C22⋊C4—21no—
40C3×C5×C22⋊C4—22no—
41C3×C5×C22⋊C4D412yes—
42C3×C42×C5—22no—
43C3×C42×C5D411yescharacteristic
44#6719—22no—
45#6716—41no—
46#6715—41no—
47#6714—42no—
48#6712—42no—
49#6710—21no—
50C3×#559D511yescharacteristic, complemented
51#5077—51no—
52#5053—52no—
53#4545—51no—
54#4539—52no—
55#4144—31no—
56C5×#127C2×D311yescharacteristic
57C5×#124—22no—
58C5×#123—21no—
59C5×#123C2×D312yes—
60C4×C5×Q8—21no—
61C4×C5×D4—22no—
62#4078—61no—
63#4075—62no—
64#3966—32no—
65#3965—31no—
66#3938—62no—
67#3937—61no—
68#2198—151noSylow
69C23×C3×C5—21no—
70C23×C3×C5C2×D412yes—
71C22×D15—22no—
72C3×C5×Q8—42no—
73C3×C5×D4—41no—
74C3×C5×D4—44no—
75C3×C5×D4—41no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5—42no—
80C2×C3×C4×C5—81no—
81C2×C3×C4×C5C2×D411yescharacteristic
82#1220—42no—
83#1220—41no—
84C2×Dic15—22no—
85C2×Dic15—42no—
86D60—21no—
87C4×D15—41no—
88Dic30—21no—
89C3⋊#168—41no—
90#1004—51no—
91C3×#127C2×D511yescharacteristic
92C3×#124—22no—
93C3×#123—21no—
94C3×#123C2×D512yes—
95C3×C4×Q8—21no—
96C3×C4×D4—22no—
97#932—101no—
98#929—102no—
99#834—52no—
100#833—51no—
101#806—102no—
102#805—101no—
103C2×C5×Q8—21no—
104C2×C5×D4—22no—
105C2×C5×D4#6711yescharacteristic
106C2×C5×D4C22×D311yescharacteristic
107C22×C4×C5—21no—
108C22×C4×C5#6712yes—
109C2×C22⋊D5—62no—
110#711—121no—
111D4×D5—121no—
112#709—61no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—22no—
115C5×C22⋊C4—22no—
116C5×C22⋊C4—21no—
117C5×C22⋊C4—22no—
118C5×C22⋊C4#6712yes—
119C42×C5—22no—
120C42×C5#6711yescharacteristic
121C22⋊Dic5—62no—
122#687—121no—
123#686—121no—
124#685—122no—
125#683—122no—
126#681—61no—
127#559D1511yescharacteristic, complemented
128#458—152no—
129#453—151no—
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#12011yescharacteristic
137C2×D15—41no—
138C2×D15—82no—
139C3×C4×C5—22no—
140C3×C4×C5—21no—
141C3×C4×C5—42no—
142C3×C4×C5—42no—
143Dic15—41no—
144Dic15—82no—
145C2×C3×Q8—21no—
146C2×C3×D4—22no—
147C2×C3×D4C22⋊D511yescharacteristic
148C2×C3×D4C22×D511yescharacteristic
149C22×C3×C4—21no—
150C22×C3×C4C22⋊D512yes—
151C2×#67—102no—
152#237—201no—
153D3×D4—201no—
154#235—101no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—22no—
157C3×C22⋊C4—22no—
158C3×C22⋊C4—21no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4C22⋊D512yes—
161C3×C42—22no—
162C3×C42C22⋊D511yescharacteristic
163#217—102no—
164#214—201no—
165#213—201no—
166(C2×D3)⋊C4—202no—
167Dic3⋊C4—202no—
168#208—101no—
169C23×C5—21no—
170C23×C5C2×#6712yes—
171C22×D5—62no—
172C5×Q8—42no—
173C5×D4—41no—
174C5×D4—41no—
175C5×D4—44no—
176C2×C4×C5—21no—
177C2×C4×C5—22no—
178C2×C4×C5—22no—
179C2×C4×C5—42no—
180C2×C4×C5—81no—
181C2×C4×C5C2×#6711yescharacteristic
182C22⋊D5—122no—
183C22⋊D5—121no—
184C2×Dic5—62no—
185C2×Dic5—122no—
186D20—61no—
187C4×D5—121no—
188Dic10—61no—
189#168—121no—
190H(5,𝔽2)—151no—
191AGL(1,ℤ/8)—301no—
192#127C2×D1511yescharacteristic
193#124—22no—
194#123—21no—
195#123—302no—
196#123C2×D1512yes—
197C4×Q8—21no—
198C4×D4—22no—
199#104—301no—
200#100—151no—
201#99—152no—
202#99—302no—
203C2×C3×C5—21no—
204C2×C3×C5—42no—
205C2×C3×C5—81no—
206C2×C3×C5B(4,𝔽2)11yescharacteristic
207D15—81no—
208C23×C3—21no—
209C23×C3C2×C22⋊D512yes—
210C22×D3—102no—
211C3×Q8—42no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—44no—
215C2×C3×C4—21no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—42no—
219C2×C3×C4—81no—
220C2×C3×C4C2×C22⋊D511yescharacteristic
221#67—202no—
222#67—201no—
223C2×Dic3—102no—
224C2×Dic3—202no—
225D12—101no—
226C4×D3—201no—
227Dic6—101no—
228C3⋊C8—201no—
229C22×C5—22no—
230C22×C5—42no—
231C22×C5—42no—
232C22×C5—41no—
233C22×C5#95311yescharacteristic
234C2×D5—121no—
235C2×D5—242no—
236C4×C5—22no—
237C4×C5—21no—
238C4×C5—42no—
239C4×C5—42no—
240Dic5—121no—
241Dic5—242no—
242#41—301no—
243#41—601no—
244C2×Q8—21no—
245C2×D4—22no—
246C2×D4—302no—
247C2×D4—601no—
248C2×D4#122011yescharacteristic
249C2×D4C22×D1511yescharacteristic
250C22×C4—21no—
251C22×C4#122012yes—
252SD16—601no—
253D8—601no—
254M16—301no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—602no—
258C22⋊C4—22no—
259C22⋊C4—21no—
260C22⋊C4—22no—
261C22⋊C4—302no—
262C22⋊C4—602no—
263C22⋊C4#122012yes—
264C42—22no—
265C42#122011yescharacteristic
266C3×C5#219811yescharacteristic, complemented, Hall
267C22×C3—22no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—41no—
271C22×C3#409911yescharacteristic
272C2×D3—201no—
273C2×D3—402no—
274C3×C4—22no—
275C3×C4—21no—
276C3×C4—42no—
277C3×C4—42no—
278Dic3—201no—
279Dic3—402no—
280C2×C5—21no—
281C2×C5—42no—
282C2×C5—81no—
283C2×C5#524411yescharacteristic
284D5—241no—
285C23—21no—
286C23—302no—
287C23C2×#122012yes—
288Q8—42no—
289Q8—301no—
290D4—41no—
291D4—41no—
292D4—44no—
293D4—301no—
294D4—602no—
295D4—601no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—81no—
301C2×C4—302no—
302C2×C4—601no—
303C2×C4—602no—
304C2×C4C2×#122011yescharacteristic
305C8—601no—
306C2×C3—21no—
307C2×C3—42no—
308C2×C3—81no—
309C2×C3#6553311yescharacteristic
310D3—401no—
311C5#7194611yescharacteristic, complemented, Sylow
312C22—22no—
313C22—42no—
314C22—42no—
315C22—41no—
316C22—601no—
317C22—1202no—
318C22#9184211yescharacteristic
319C4—22no—
320C4—21no—
321C4—42no—
322C4—42no—
323C4—601no—
324C4—1202no—
325C3#1060273911yescharacteristic, complemented, Sylow
326C2—21no—
327C2—42no—
328C2—81no—
329C2—1201no—
330C2#1175134511yescharacteristic
subgroupG/H
centerC2#11751345
commutator, cosocleC2×C3×C5×D4C23
FrattiniC2×D4C22×D15
FittingC3×C5×#559C2
socleC2×C3×C5B(4,𝔽2)
prime radical#11751178C2
hypercenter#559D15
hypocenterC3×C5#2198
LCSG ▷ C2×C3×C5×D4 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #559

Complements

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

NH ≅ G/Ntype
1. C3×C5×#559C2semidirect
3. #11751154C2semidirect
4. #11746366C2semidirect
5. #11746360C2semidirect
21. C5×#559D3semidirect
50. C3×#559D5semidirect
127. #559D15semidirect
266. C3×C5#2198semidirect
311. C5#71946semidirect
325. C3#10602739semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5592
#117511782
#117511542
#117463662
#117463602
#106027393
#719465