Finite Group Databasebeta

← #14313740

Subgroups — #14313740

Order 1920.

524 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 86 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#11754604C211yesmaximal, characteristic
2#11752420C211yesmaximal, characteristic, complemented
3C3×#65761C211yesmaximal, characteristic, complemented
4#11746558C214yesmaximal, complemented
5#10604920—31nomaximal, Hall
6C22×C5×D12C411yescharacteristic
7C2×C3×#709C2211yescharacteristic
8D5⋊#208—21no—
9C3×D5⋊M16—21no—
10#91815C411yescharacteristic
11#91568—21no—
12#91568—21no—
13#91463C412yes—
14#91449—21no—
15#91449—21no—
16#91370C2212yes—
17#91242—21no—
18#91234C2212yescomplemented
19C3×#4013—21no—
20C3×#4005C2212yescomplemented
21#70149—51nomaximal, Hall
22#66139—31no—
23#65761—31no—
24#65761D311yescharacteristic, complemented
25#64923—34no—
26C23×C5×D3—21no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C2×C5×D12—21no—
29C2×C5×D12—41no—
30C2×C5×D12—41no—
31C2×C5×D12C2×C412yes—
32C2×C3×C22⋊D5D411yescharacteristic
33C2×C3×C22⋊D5D411yescharacteristic
34C3×#709—41no—
35C3×#709—41no—
36C2×C3×D20C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×Dic10C2311yescharacteristic
40C2×#1201—22no—
41C2×#1201—22no—
42#6762—22no—
43#6758—41no—
44D5⋊(C3⋊C8)—41no—
45C3×#704—22no—
46C3×#700—41no—
47C3×D5⋊C8—41no—
48#6719—21no—
49C4⋊Dic15—21no—
50C4×Dic15C2×C412yes—
51(C2×D3)⋊Dic5—22no—
52(C2×D3)⋊Dic5—22no—
53#5830—51no—
54C3×#413—51no—
55#5237—51no—
56#4477—54no—
57C22×C5×D4—31no—
58C2×#709C2×D311yescharacteristic
59D5⋊M16—21no—
60D5⋊M16—61no—
61#4099—61no—
62#4099—61no—
63#4086—32no—
64#4084—61no—
65#4084—61no—
66#4082—32no—
67#4072—31no—
68#4013—21no—
69#4013—61no—
70#4005—32no—
71#4005C2×D312yescomplemented
72#2134—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C22×C5×D3—22no—
75C22×C5×D3—42no—
76C22×C5×D3—82no—
77C22×C3×D5C22⋊C411yescharacteristic
78C22×C3×D5C22⋊C411yescharacteristic
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—22no—
84C5×D12—42no—
85C5×D12—41no—
86C5×D12—41no—
87C3×C22⋊D5—41no—
88C3×C22⋊D5—41no—
89C2×C3×Dic5C2×D411yescharacteristic
90C2×C3×Dic5C2×D411yescharacteristic
91C3×D20—41no—
92C3×C4×D5—21no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×Dic10—41no—
97#1201—82no—
98#1201—82no—
99C3⋊#170—42no—
100C3×#170—42no—
101C2×C3×#41—51no—
102C22×D12AGL(1,𝔽5)11yescharacteristic
103C2×C3×M16—101no—
104#947—52no—
105#940—52no—
106#937—101no—
107#937—101no—
108#930—101no—
109#930—101no—
110#926—51no—
111C2×#208—101no—
112C3×#101—52no—
113C3×#100—101no—
114#836—52no—
115#833—101no—
116C24×C5—61no—
117C2×C5×D4—32no—
118C2×C5×D4—61no—
119C2×C5×D4—121no—
120C2×C5×D4—121no—
121C22×C4×C5C4×D311yescharacteristic
122C2×C22⋊D5—62no—
123C2×C22⋊D5—62no—
124C2×C22⋊D5D1211yescharacteristic
125C2×C22⋊D5#6711yescharacteristic
126#709—41no—
127#709—41no—
128C2×D20C4×D311yescharacteristic
129C2×C4×D5D1211yescharacteristic
130C2×C4×D5#6711yescharacteristic
131C2×Dic10C22×D311yescharacteristic
132#704—22no—
133#704—62no—
134#700—41no—
135#700—121no—
136D5⋊C8—41no—
137D5⋊C8—121no—
138C22⋊Dic5—61no—
139C22⋊Dic5—62no—
140C22⋊Dic5—62no—
141C4⋊Dic5—61no—
142C4×Dic5—32no—
143#535—151no—
144#413—51no—
145#413—151no—
146#355—154no—
147C22×C3×C5—21no—
148C22×C3×C5—41no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×C5×D3—42no—
151C2×C5×D3—42no—
152C2×C5×D3—42no—
153C2×C5×D3—84no—
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C3×C4×C5—21no—
159C3×C4×C5#9911yescharacteristic
160C3×C4×C5#9911yescharacteristic
161Dic15—42no—
162C3×Dic5—21no—
163C3×Dic5—21no—
164C23×D3—21no—
165C3×#41—201no—
166C3×#41—201no—
167C2×C3×Q8—51no—
168C2×C3×D4—51no—
169C2×C3×D4—51no—
170C2×C3×D4—51no—
171C22×C3×C4—51no—
172C22×C3×C4—51no—
173C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
174C2×#67—102no—
175C2×#67—102no—
176C2×D12—21no—
177C2×D12—41no—
178C2×D12—41no—
179C2×D12C2×AGL(1,𝔽5)12yes—
180C3×M16—102no—
181C3×M16—201no—
182C2×C3×C8—201no—
183#217—101no—
184(C2×D3)⋊C4—102no—
185(C2×D3)⋊C4—102no—
186C4⋊Dic3—101no—
187C4×Dic3—52no—
188#208—102no—
189#208—201no—
190C2×C3⋊C8—201no—
191C23×C5—62no—
192C23×C5—122no—
193C23×C5—242no—
194C23×C5(C2×D3)⋊C411yescharacteristic
195C22×D5(C2×D3)⋊C411yescharacteristic
196C22×D5(C2×D3)⋊C411yescharacteristic
197C5×D4—122no—
198C5×D4—121no—
199C5×D4—121no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5(C2×D3)⋊C411yescharacteristic
203C2×C4×C5C2×C4×D311yescharacteristic
204C22⋊D5—41no—
205C22⋊D5—41no—
206C22⋊D5—242no—
207C22⋊D5—242no—
208C2×Dic5—62no—
209C2×Dic5C2×D1211yescharacteristic
210C2×Dic5C2×#6711yescharacteristic
211D20—41no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—21no—
216Dic10—41no—
217#170—42no—
218#170—122no—
219C2×#41—51no—
220C22×D4—31no—
221C2×M16—101no—
222C2×M16—301no—
223#127—152no—
224#124—152no—
225#121—301no—
226#121—301no—
227#120—301no—
228#120—301no—
229#117—151no—
230#101—52no—
231#101—152no—
232#100—101no—
233#100—301no—
234C2×C3×C5—21no—
235C2×C3×C5—41no—
236C2×C3×C5C2×#9911yescharacteristic
237C3×D5—41no—
238C3×D5—41no—
239C5×D3—82no—
240C23×C3—51no—
241C23×C3—51no—
242C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
243C22×D3—22no—
244C22×D3—42no—
245C22×D3—82no—
246C3×Q8—201no—
247C3×D4—201no—
248C3×D4—201no—
249C3×D4—201no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—51no—
253C2×C3×C4—51no—
254C2×C3×C4—101no—
255C2×C3×C4—101no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
259C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
260#67—402no—
261#67—402no—
262C2×Dic3—102no—
263D12—42no—
264D12—41no—
265D12—41no—
266C3×C8—202no—
267C3⋊C8—202no—
268C22×C5—21no—
269C22×C5—41no—
270C22×C5—122no—
271C22×C5—122no—
272C22×C5—122no—
273C22×C5—244no—
274C22×C5C2×(C2×D3)⋊C411yescharacteristic
275C2×D5—21no—
276C2×D5—21no—
277C2×D5—41no—
278C2×D5—41no—
279C4×C5—21no—
280C4×C5#80611yescharacteristic
281C4×C5#80611yescharacteristic
282Dic5—21no—
283Dic5—21no—
284Dic5—122no—
285C24—61no—
286#41—201no—
287#41—201no—
288C2×Q8—51no—
289C2×D4—32no—
290C2×D4—51no—
291C2×D4—51no—
292C2×D4—51no—
293C2×D4—61no—
294C2×D4—121no—
295C2×D4—121no—
296C2×D4—302no—
297C2×D4—302no—
298C22×C4—51no—
299C22×C4—51no—
300C22×C4D3×AGL(1,𝔽5)11yescharacteristic
301M16—102no—
302M16—201no—
303M16—302no—
304M16—601no—
305C2×C8—201no—
306C2×C8—601no—
307C4⋊C4—301no—
308C22⋊C4—302no—
309C22⋊C4—302no—
310C22⋊C4—301no—
311C42—152no—
312C3×C5#213411yescharacteristic, complemented, Hall
313C22×C3—21no—
314C22×C3—41no—
315C22×C3—101no—
316C22×C3—101no—
317C22×C3—201no—
318C22×C3—201no—
319C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
320C2×D3—42no—
321C2×D3—42no—
322C2×D3—42no—
323C2×D3—84no—
324C3×C4—21no—
325C3×C4—101no—
326C3×C4—101no—
327C3×C4#401111yescharacteristic
328C3×C4#401111yescharacteristic
329Dic3—202no—
330C2×C5—21no—
331C2×C5—41no—
332C2×C5—242no—
333C2×C5C2×#80611yescharacteristic
334D5—41no—
335D5—41no—
336C23—51no—
337C23—51no—
338C23—62no—
339C23—122no—
340C23—242no—
341C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
342Q8—201no—
343D4—122no—
344D4—121no—
345D4—121no—
346D4—201no—
347D4—201no—
348D4—201no—
349D4—1202no—
350D4—1202no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—51no—
354C2×C4—51no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—101no—
358C2×C4—101no—
359C2×C4—302no—
360C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
361C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
362C8—202no—
363C8—602no—
364C2×C3—21no—
365C2×C3—41no—
366C2×C3—201no—
367C2×C3—201no—
368C2×C3C2×#401111yescharacteristic
369D3—82no—
370C5#7014911yescharacteristic, complemented, Sylow
371C22—21no—
372C22—41no—
373C22—101no—
374C22—101no—
375C22—122no—
376C22—122no—
377C22—122no—
378C22—201no—
379C22—201no—
380C22—244no—
381C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
382C4—21no—
383C4—101no—
384C4—101no—
385C4—602no—
386C4#9117211yescharacteristic
387C4#9117211yescharacteristic
388C3#1060492011yescharacteristic, complemented, Sylow
389C2—21no—
390C2—41no—
391C2—201no—
392C2—201no—
393C2—242no—
394C2C2×#9117211yescharacteristic
subgroupG/H
centerC2C2×#91172
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5C2×#99
prime radical#11754604C2
cosocleC2×C3×Dic10C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2134
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752420C2semidirect
3. C3×#65761C2semidirect
4. #11746558C2semidirect
18. #91234C22semidirect
20. C3×#4005C22semidirect
24. #65761D3semidirect
71. #4005C2×D3semidirect
312. C3×C5#2134semidirect
370. C5#70149semidirect
388. C3#10604920semidirect

Maximal subgroups

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

subgroupindex
#117546042
#117524202
C3×#657612
#117465582
#106049203
#701495