Finite Group Databasebeta

← #14313291

Subgroups — #14313291

Order 1920.

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

normal subgroups only

This group has 532 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#11752404C211yesmaximal, characteristic, complemented
3C3×#65761C211yesmaximal, characteristic, complemented
4#11746578C214yesmaximal, complemented
5#10604940—31nomaximal, Hall
6C22×C5×D12C411yescharacteristic, complemented
7C2×C3×#709C2211yescharacteristic
8#91989—21no—
9C3×D5⋊M16—21no—
10#91815C411yescharacteristic, complemented
11#91568C412yescomplemented
12#91568C2212yes—
13#91463—21no—
14#91449—21no—
15#91449—21no—
16#91370—21no—
17#91240C2212yes—
18#91228—21no—
19C3×#4013C2212yes—
20C3×#4005—21no—
21#70146—51nomaximal, Hall
22#66139—31no—
23#65761D311yescharacteristic, complemented
24#65745—31no—
25#64934—34no—
26C23×C5×D3C2×C412yes—
27C22×C3×C4×C5C2×C411yescharacteristic
28C2×C5×D12—21no—
29C2×C5×D12—21no—
30C2×C5×D12—41no—
31C2×C5×D12—41no—
32C2×C3×C22⋊D5C2×C411yescharacteristic
33C2×C3×C22⋊D5C2311yescharacteristic
34C3×#709—41no—
35C3×#709—41no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C2×#1201—22no—
41C2×#1201—22no—
42#6763—22no—
43C4⋊ΓL(1,𝔽16)—41no—
44C4×ΓL(1,𝔽16)—41no—
45C3×#704—22no—
46C3×#700—41no—
47C3×D5⋊C8—41no—
48#6719C2×C412yes—
49C4⋊Dic15—21no—
50C4×Dic15—21no—
51(C2×D3)⋊Dic5—22no—
52(C2×D3)⋊Dic5—22no—
53#5830—51no—
54C3×#413—51no—
55#5240—51no—
56#4475—54no—
57C22×C5×D4—31no—
58C2×#709C2×D311yescharacteristic
59#4130—61no—
60D5⋊M16—21no—
61#4099—32no—
62#4099—32no—
63#4086—61no—
64#4084—61no—
65#4084—61no—
66#4082—61no—
67#4072—31no—
68#4013C2×D312yes—
69#4011—32no—
70#4005—21no—
71#3999—61no—
72#2122—151noSylow
73C23×C3×C5C22×C411yescharacteristic
74C22×C5×D3—22no—
75C22×C5×D3—42no—
76C22×C5×D3—82no—
77C22×C3×D5C22⋊C411yescharacteristic
78C22×C3×D5C2×D411yescharacteristic
79C2×ΓL(1,𝔽16)—42no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×Dic15—22no—
85C5×D12—42no—
86C5×D12—41no—
87C5×D12—41no—
88C3×C22⋊D5—41no—
89C3×C22⋊D5—41no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C2×D411yescharacteristic
92C3×D20—41no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×Dic10—41no—
98#1201—82no—
99#1201—82no—
100C3×#170—42no—
101C2×C3×#41—51no—
102C22×D12AGL(1,𝔽5)11yescharacteristic, complemented
103C2×C3×M16—101no—
104#947—101no—
105#940—101no—
106#937—52no—
107#937—52no—
108#930—101no—
109#930—101no—
110#926—51no—
111#926—101no—
112C3×#101—101no—
113C3×#100—52no—
114#834—52no—
115#834—101no—
116C24×C5—32no—
117C2×C5×D4—61no—
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⋊D5C4×D311yescharacteristic
125C2×C22⋊D5C22×D311yescharacteristic
126#709—41no—
127#709—41no—
128C2×D20D1211yescharacteristic
129C2×C4×D5D1211yescharacteristic
130C2×C4×D5#6711yescharacteristic
131C2×Dic10#6711yescharacteristic
132C22⋊AGL(1,𝔽5)—62no—
133#704—22no—
134C4⋊AGL(1,𝔽5)—121no—
135C4×AGL(1,𝔽5)—121no—
136#700—41no—
137D5⋊C8—41no—
138C22⋊Dic5—32no—
139C22⋊Dic5—62no—
140C22⋊Dic5—62no—
141C4⋊Dic5—61no—
142C4×Dic5—61no—
143#535—151no—
144#413—51no—
145#410—151no—
146AΣL(1,𝔽16)—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—
158ΓL(1,𝔽16)—82no—
159C3×C4×C5—21no—
160C3×C4×C5#9911yescharacteristic
161C3×C4×C5#9911yescharacteristic
162Dic15—42no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C23×D3C2×AGL(1,𝔽5)12yes—
166C3×#41—201no—
167C3×#41—201no—
168C2×C3×Q8—51no—
169C2×C3×D4—51no—
170C2×C3×D4—51no—
171C2×C3×D4—51no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
175C2×#67—102no—
176C2×#67—102no—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—41no—
180C2×D12—41no—
181C3×M16—102no—
182C3×M16—201no—
183C2×C3×C8—201no—
184#217—52no—
185#217—102no—
186(C2×D3)⋊C4—102no—
187(C2×D3)⋊C4—102no—
188C4⋊Dic3—101no—
189C4⋊Dic3—201no—
190C4×Dic3—101no—
191C4×Dic3—201no—
192C23×C5—62no—
193C23×C5—122no—
194C23×C5—242no—
195C23×C5C2×C4×D311yescharacteristic
196C22×D5(C2×D3)⋊C411yescharacteristic
197C22×D5C2×D1211yescharacteristic
198C2×AGL(1,𝔽5)—122no—
199C5×D4—122no—
200C5×D4—121no—
201C5×D4—121no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5(C2×D3)⋊C411yescharacteristic
205C2×C4×C5(C2×D3)⋊C411yescharacteristic
206C22⋊D5—41no—
207C22⋊D5—41no—
208C22⋊D5—242no—
209C22⋊D5—242no—
210C2×Dic5—62no—
211C2×Dic5(C2×D3)⋊C411yescharacteristic
212C2×Dic5C2×#6711yescharacteristic
213D20—41no—
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—21no—
218Dic10—41no—
219#170—42no—
220C2×#41—51no—
221C22×D4—31no—
222C2×M16—101no—
223#127—301no—
224#124—301no—
225#121—301no—
226#121—301no—
227#120—152no—
228#120—152no—
229#117—151no—
230#117—301no—
231#101—101no—
232#100—52no—
233#99—152no—
234#99—301no—
235C2×C3×C5—21no—
236C2×C3×C5—41no—
237C2×C3×C5C2×#9911yescharacteristic
238C3×D5—41no—
239C3×D5—41no—
240C5×D3—82no—
241C23×C3—51no—
242C23×C3—51no—
243C23×C3C22×AGL(1,𝔽5)11yescharacteristic
244C22×D3—22no—
245C22×D3—42no—
246C22×D3—82no—
247C3×Q8—201no—
248C3×D4—201no—
249C3×D4—201no—
250C3×D4—201no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—101no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
260C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
261#67—402no—
262#67—402no—
263C2×Dic3—102no—
264C2×Dic3—202no—
265D12—42no—
266D12—41no—
267D12—41no—
268C3×C8—202no—
269C22×C5—21no—
270C22×C5—41no—
271C22×C5—122no—
272C22×C5—122no—
273C22×C5—122no—
274C22×C5—244no—
275C22×C5C2×(C2×D3)⋊C411yescharacteristic
276C2×D5—21no—
277C2×D5—21no—
278C2×D5—41no—
279C2×D5—41no—
280AGL(1,𝔽5)—242no—
281C4×C5—21no—
282C4×C5#80611yescharacteristic
283C4×C5#80611yescharacteristic
284Dic5—21no—
285Dic5—21no—
286Dic5—122no—
287C24—32no—
288#41—201no—
289#41—201no—
290C2×Q8—51no—
291C2×D4—51no—
292C2×D4—51no—
293C2×D4—51no—
294C2×D4—61no—
295C2×D4—61no—
296C2×D4—121no—
297C2×D4—121no—
298C2×D4—302no—
299C2×D4—302no—
300C22×C4—51no—
301C22×C4—51no—
302C22×C4D3×AGL(1,𝔽5)11yescharacteristic
303M16—102no—
304M16—201no—
305C2×C8—201no—
306C4⋊C4—301no—
307C4⋊C4—601no—
308C22⋊C4—152no—
309C22⋊C4—302no—
310C22⋊C4—302no—
311C22⋊C4—302no—
312C42—301no—
313C42—601no—
314C3×C5#212211yescharacteristic, complemented, Hall
315C22×C3—21no—
316C22×C3—41no—
317C22×C3—101no—
318C22×C3—101no—
319C22×C3—201no—
320C22×C3—201no—
321C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
322C2×D3—42no—
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—84no—
326C3×C4—21no—
327C3×C4—101no—
328C3×C4—101no—
329C3×C4#401111yescharacteristic
330C3×C4#401111yescharacteristic
331Dic3—202no—
332Dic3—402no—
333C2×C5—21no—
334C2×C5—41no—
335C2×C5—242no—
336C2×C5C2×#80611yescharacteristic
337D5—41no—
338D5—41no—
339C23—51no—
340C23—51no—
341C23—62no—
342C23—122no—
343C23—242no—
344C23C2×D3×AGL(1,𝔽5)11yescharacteristic
345Q8—201no—
346D4—122no—
347D4—121no—
348D4—121no—
349D4—201no—
350D4—201no—
351D4—201no—
352D4—1202no—
353D4—1202no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—101no—
359C2×C4—101no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—302no—
363C2×C4—602no—
364C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
365C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
366C8—202no—
367C2×C3—21no—
368C2×C3—41no—
369C2×C3—201no—
370C2×C3—201no—
371C2×C3C2×#401111yescharacteristic
372D3—82no—
373C5#7014611yescharacteristic, complemented, Sylow
374C22—21no—
375C22—41no—
376C22—101no—
377C22—101no—
378C22—122no—
379C22—122no—
380C22—122no—
381C22—201no—
382C22—201no—
383C22—244no—
384C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
385C4—21no—
386C4—101no—
387C4—101no—
388C4—602no—
389C4—1202no—
390C4#9117211yescharacteristic
391C4#9117211yescharacteristic
392C3#1060494011yescharacteristic, complemented, Sylow
393C2—21no—
394C2—41no—
395C2—201no—
396C2—201no—
397C2—242no—
398C2C2×#9117211yescharacteristic
subgroupG/H
centerC2C2×#91172
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5C2×#99
prime radical#11754604C2
cosocleC2×C3×C22⋊D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2122
LCSG ▷ C23×C3×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. #11752404C2semidirect
3. C3×#65761C2semidirect
4. #11746578C2semidirect
6. C22×C5×D12C4semidirect
10. #91815C4semidirect
11. #91568C4semidirect
23. #65761D3semidirect
102. C22×D12AGL(1,𝔽5)semidirect
314. C3×C5#2122semidirect
373. C5#70146semidirect
392. C3#10604940semidirect

Maximal subgroups

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

subgroupindex
#117546042
#117524042
C3×#657612
#117465782
#106049403
#701465