Finite Group Databasebeta

← #14313522

Subgroups — #14313522

Order 1920.

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

normal subgroups only

This group has 540 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×#65745C211yesmaximal, characteristic, complemented
4#11746554C214yesmaximal, complemented
5#10604918—31nomaximal, Hall
6C22×C5×D12C411yescharacteristic, complemented
7C2×C3×#709C2211yescharacteristic
8#91989—21no—
9C3×#4130—21no—
10#91815C411yescharacteristic, complemented
11#91568—21no—
12#91568—21no—
13#91463C2212yes—
14#91449—21no—
15#91449—21no—
16#91370C412yescomplemented
17#91240—21no—
18#91228C2212yescomplemented
19C3×#4011—21no—
20C3×#3999C2212yescomplemented
21#70061—51nomaximal, Hall
22#66139—31no—
23#65745—31no—
24#65745D311yescharacteristic, complemented
25#64922—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×D20C2311yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×Dic10C2×C411yescharacteristic
40C2×#1201—22no—
41C2×#1201—22no—
42#6763—22no—
43C4⋊ΓL(1,𝔽16)—41no—
44C4×ΓL(1,𝔽16)—41no—
45C3×C22⋊AGL(1,𝔽5)—22no—
46C3×C4⋊AGL(1,𝔽5)—41no—
47C3×C4×AGL(1,𝔽5)—41no—
48#6719—21no—
49C4⋊Dic15—21no—
50C4×Dic15C2×C412yes—
51(C2×D3)⋊Dic5—22no—
52(C2×D3)⋊Dic5—22no—
53#5830—51no—
54C3×#410—51no—
55#5240—51no—
56#4474—54no—
57C22×C5×D4—31no—
58C2×#709C2×D311yescharacteristic
59#4130—21no—
60#4130—61no—
61#4099—61no—
62#4099—61no—
63#4086—32no—
64#4084—61no—
65#4084—61no—
66#4082—32no—
67#4072—31no—
68#4011—21no—
69#4011—61no—
70#3999—32no—
71#3999C2×D312yescomplemented
72#2128—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C22×C5×D3—22no—
75C22×C5×D3—42no—
76C22×C5×D3—82no—
77C22×C3×D5C2×D411yescharacteristic
78C22×C3×D5C2×D411yescharacteristic
79C2×ΓL(1,𝔽16)—42no—
80C2×C3×AGL(1,𝔽5)—42no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×Dic15—22no—
86C5×D12—42no—
87C5×D12—41no—
88C5×D12—41no—
89C3×C22⋊D5—41no—
90C3×C22⋊D5—41no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C3×D20—41no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98C3×Dic10—41no—
99#1201—82no—
100#1201—82no—
101C2×C3×#41—51no—
102C22×D12AGL(1,𝔽5)11yescharacteristic, complemented
103C3×#117—101no—
104#947—52no—
105#940—52no—
106#937—101no—
107#937—101no—
108#930—101no—
109#930—101no—
110#926—51no—
111#926—101no—
112C3×#99—52no—
113C3×#99—101no—
114#834—52no—
115#834—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×D20C22×D311yescharacteristic
129C2×C4×D5D1211yescharacteristic
130C2×C4×D5#6711yescharacteristic
131C2×Dic10C4×D311yescharacteristic
132C22⋊AGL(1,𝔽5)—22no—
133C22⋊AGL(1,𝔽5)—62no—
134C4⋊AGL(1,𝔽5)—41no—
135C4⋊AGL(1,𝔽5)—121no—
136C4×AGL(1,𝔽5)—41no—
137C4×AGL(1,𝔽5)—121no—
138C22⋊Dic5—61no—
139C22⋊Dic5—62no—
140C22⋊Dic5—62no—
141C4⋊Dic5—61no—
142C4×Dic5—32no—
143#535—151no—
144#410—51no—
145#410—151no—
146#353—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×AGL(1,𝔽5)—82no—
160C3×C4×C5—21no—
161C3×C4×C5#9911yescharacteristic
162C3×C4×C5#9911yescharacteristic
163Dic15—42no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C23×D3—21no—
167C3×#41—201no—
168C3×#41—201no—
169C2×C3×Q8—51no—
170C2×C3×D4—51no—
171C2×C3×D4—51no—
172C2×C3×D4—51no—
173C22×C3×C4—51no—
174C22×C3×C4—51no—
175C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
176C2×#67—102no—
177C2×#67—102no—
178C2×D12—21no—
179C2×D12—41no—
180C2×D12—41no—
181C2×D12C2×AGL(1,𝔽5)12yes—
182C3×C4⋊C4—201no—
183C3×C22⋊C4—102no—
184C3×C42—201no—
185#217—101no—
186#217—102no—
187(C2×D3)⋊C4—102no—
188(C2×D3)⋊C4—102no—
189C4⋊Dic3—101no—
190C4⋊Dic3—201no—
191C4×Dic3—52no—
192C4×Dic3—201no—
193C23×C5—62no—
194C23×C5—122no—
195C23×C5—242no—
196C23×C5(C2×D3)⋊C411yescharacteristic
197C22×D5C2×D1211yescharacteristic
198C22×D5C2×#6711yescharacteristic
199C2×AGL(1,𝔽5)—42no—
200C2×AGL(1,𝔽5)—122no—
201C5×D4—122no—
202C5×D4—121no—
203C5×D4—121no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5(C2×D3)⋊C411yescharacteristic
207C2×C4×C5C2×C4×D311yescharacteristic
208C22⋊D5—41no—
209C22⋊D5—41no—
210C22⋊D5—242no—
211C22⋊D5—242no—
212C2×Dic5—62no—
213C2×Dic5(C2×D3)⋊C411yescharacteristic
214C2×Dic5(C2×D3)⋊C411yescharacteristic
215D20—41no—
216C4×D5—21no—
217C4×D5—21no—
218C4×D5—21no—
219C4×D5—21no—
220Dic10—41no—
221C2×#41—51no—
222C22×D4—31no—
223#127—152no—
224#124—152no—
225#121—301no—
226#121—301no—
227#120—301no—
228#120—301no—
229#117—101no—
230#117—151no—
231#117—301no—
232#99—52no—
233#99—101no—
234#99—152no—
235#99—301no—
236C2×C3×C5—21no—
237C2×C3×C5—41no—
238C2×C3×C5C2×#9911yescharacteristic
239C3×D5—41no—
240C3×D5—41no—
241C5×D3—82no—
242C23×C3—51no—
243C23×C3—51no—
244C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
245C22×D3—22no—
246C22×D3—42no—
247C22×D3—82no—
248C3×Q8—201no—
249C3×D4—201no—
250C3×D4—201no—
251C3×D4—201no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—51no—
255C2×C3×C4—51no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4—101no—
260C2×C3×C4—202no—
261C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
262C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
263#67—402no—
264#67—402no—
265C2×Dic3—102no—
266C2×Dic3—202no—
267D12—42no—
268D12—41no—
269D12—41no—
270C22×C5—21no—
271C22×C5—41no—
272C22×C5—122no—
273C22×C5—122no—
274C22×C5—122no—
275C22×C5—244no—
276C22×C5C2×(C2×D3)⋊C411yescharacteristic
277C2×D5—21no—
278C2×D5—21no—
279C2×D5—41no—
280C2×D5—41no—
281AGL(1,𝔽5)—82no—
282AGL(1,𝔽5)—242no—
283C4×C5—21no—
284C4×C5#80611yescharacteristic
285C4×C5#80611yescharacteristic
286Dic5—21no—
287Dic5—21no—
288Dic5—122no—
289C24—61no—
290#41—201no—
291#41—201no—
292C2×Q8—51no—
293C2×D4—32no—
294C2×D4—51no—
295C2×D4—51no—
296C2×D4—51no—
297C2×D4—61no—
298C2×D4—121no—
299C2×D4—121no—
300C2×D4—302no—
301C2×D4—302no—
302C22×C4—51no—
303C22×C4—51no—
304C22×C4D3×AGL(1,𝔽5)11yescharacteristic
305C4⋊C4—201no—
306C4⋊C4—301no—
307C4⋊C4—601no—
308C22⋊C4—102no—
309C22⋊C4—302no—
310C22⋊C4—302no—
311C22⋊C4—301no—
312C22⋊C4—302no—
313C42—152no—
314C42—201no—
315C42—601no—
316C3×C5#212811yescharacteristic, complemented, Hall
317C22×C3—21no—
318C22×C3—41no—
319C22×C3—101no—
320C22×C3—101no—
321C22×C3—201no—
322C22×C3—201no—
323C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
324C2×D3—42no—
325C2×D3—42no—
326C2×D3—42no—
327C2×D3—84no—
328C3×C4—21no—
329C3×C4—101no—
330C3×C4—101no—
331C3×C4—402no—
332C3×C4#401111yescharacteristic
333C3×C4#401111yescharacteristic
334Dic3—202no—
335Dic3—402no—
336C2×C5—21no—
337C2×C5—41no—
338C2×C5—242no—
339C2×C5C2×#80611yescharacteristic
340D5—41no—
341D5—41no—
342C23—51no—
343C23—51no—
344C23—62no—
345C23—122no—
346C23—242no—
347C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
348Q8—201no—
349D4—122no—
350D4—121no—
351D4—121no—
352D4—201no—
353D4—201no—
354D4—201no—
355D4—1202no—
356D4—1202no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—51no—
360C2×C4—51no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—101no—
364C2×C4—101no—
365C2×C4—202no—
366C2×C4—302no—
367C2×C4—602no—
368C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
369C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
370C2×C3—21no—
371C2×C3—41no—
372C2×C3—201no—
373C2×C3—201no—
374C2×C3C2×#401111yescharacteristic
375D3—82no—
376C5#7006111yescharacteristic, complemented, Sylow
377C22—21no—
378C22—41no—
379C22—101no—
380C22—101no—
381C22—122no—
382C22—122no—
383C22—122no—
384C22—201no—
385C22—201no—
386C22—244no—
387C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
388C4—21no—
389C4—101no—
390C4—101no—
391C4—402no—
392C4—602no—
393C4—1202no—
394C4#9117211yescharacteristic
395C4#9117211yescharacteristic
396C3#1060491811yescharacteristic, complemented, Sylow
397C2—21no—
398C2—41no—
399C2—201no—
400C2—201no—
401C2—242no—
402C2C2×#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×D20C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2128
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. #11752404C2semidirect
3. C3×#65745C2semidirect
4. #11746554C2semidirect
6. C22×C5×D12C4semidirect
10. #91815C4semidirect
16. #91370C4semidirect
18. #91228C22semidirect
20. C3×#3999C22semidirect
24. #65745D3semidirect
71. #3999C2×D3semidirect
102. C22×D12AGL(1,𝔽5)semidirect
316. C3×C5#2128semidirect
376. C5#70061semidirect
396. C3#10604918semidirect

Maximal subgroups

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

subgroupindex
#117546042
#117524042
C3×#657452
#117465542
#106049183
#700615