Finite Group Databasebeta

← #14313179

Subgroups — #14313179

Order 1920.

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

normal subgroups only

This group has 528 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#11754577C211yesmaximal, characteristic
2#11752404C211yesmaximal, characteristic, complemented
3C3×#65761C211yesmaximal, characteristic, complemented
4#11746582C212yesmaximal, complemented
5#11746578C212yesmaximal, complemented
6#10604887—31nomaximal, Hall
7C22×C4×C5×D3C411yescharacteristic, complemented
8C2×C3×#709C2211yescharacteristic
9#91989—21no—
10C3×D5⋊M16—21no—
11#91815C411yescharacteristic, complemented
12#91568C411yescharacteristic, complemented
13#91568C2211yescharacteristic
14#91536C411yescharacteristic, complemented
15#91536C2211yescharacteristic
16#91456—21no—
17C4×#1201—21no—
18C4×#1201—21no—
19#91369—21no—
20#91240C2212yes—
21#91228—21no—
22C3×#4013C2212yes—
23C3×#4005—21no—
24#70145—51nomaximal, Hall
25#66125—31no—
26#65761D311yescharacteristic, complemented
27#65745—31no—
28#64934—32no—
29#64916—32no—
30C23×C5×D3C2×C411yescharacteristic
31C22×C3×C4×C5C2×C411yescharacteristic
32C22×C5×Dic3C2×C411yescharacteristic
33C2×C4×C5×D3—21no—
34C2×C4×C5×D3—21no—
35C2×C4×C5×D3—41no—
36C2×C4×C5×D3—41no—
37C2×C3×C22⋊D5C2×C411yescharacteristic
38C2×C3×C22⋊D5C2311yescharacteristic
39C3×#709—41no—
40C3×#709—41no—
41C2×C3×D20D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×Dic10D411yescharacteristic
45C2×#1201—21no—
46C2×#1201—21no—
47#6763—22no—
48C4⋊ΓL(1,𝔽16)—41no—
49C4×ΓL(1,𝔽16)—41no—
50C3×#704—22no—
51C3×#700—41no—
52C3×D5⋊C8—41no—
53#6719C2×C411yescharacteristic
54#6719C2×C411yescharacteristic
55C4⋊Dic15—21no—
56C4×Dic15—21no—
57#6669—21no—
58#6669—21no—
59(C2×D3)⋊Dic5—21no—
60(C2×D3)⋊Dic5—21no—
61#6665—21no—
62#6665—21no—
63#5828—51no—
64C3×#413—51no—
65#5240—51no—
66#4476—52no—
67#4475—52no—
68C23×C4×C5—31no—
69C2×#709C2×D311yescharacteristic
70#4130—61no—
71D5⋊M16—21no—
72#4099—31no—
73#4099—31no—
74#4076—61no—
75#4075—31no—
76#4075—31no—
77C4×C22⋊D5—61no—
78C4×C22⋊D5—61no—
79#4072—31no—
80#4070—61no—
81#4013C2×D312yes—
82#4011—32no—
83#4005—21no—
84#3999—61no—
85#2120—151noSylow
86C23×C3×C5C22×C411yescharacteristic
87C22×C5×D3—21no—
88C22×C5×D3—42no—
89C22×C5×D3—41no—
90C22×C3×D5C22⋊C411yescharacteristic
91C22×C3×D5C2×D411yescharacteristic
92C2×ΓL(1,𝔽16)—42no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C22⋊C411yescharacteristic
96C2×C3×C4×C5C22⋊C411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—41no—
101C4×C5×D3—42no—
102C4×C5×D3—41no—
103C4×C5×D3—41no—
104C3×C22⋊D5—41no—
105C3×C22⋊D5—41no—
106C2×C3×Dic5C22⋊C411yescharacteristic
107C2×C3×Dic5C2×D411yescharacteristic
108C3×D20—41no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113C3×Dic10—41no—
114#1201—42no—
115#1201—42no—
116C3×#170—42no—
117C2×C3×#41—51no—
118C22×C4×D3AGL(1,𝔽5)11yescharacteristic, complemented
119C2×C3×M16—101no—
120#946—101no—
121#938—101no—
122#937—51no—
123#937—51no—
124#935—51no—
125#935—51no—
126C4×#67—101no—
127C4×#67—101no—
128#926—51no—
129#926—101no—
130C3×#101—101no—
131C3×#100—52no—
132#834—52no—
133#834—101no—
134C24×C5—31no—
135C22×C4×C5—31no—
136C22×C4×C5—61no—
137C22×C4×C5—61no—
138C22×C4×C5—121no—
139C22×C4×C5—121no—
140C22×C4×C5C4×D311yescharacteristic
141C2×C22⋊D5—61no—
142C2×C22⋊D5—61no—
143C2×C22⋊D5C4×D311yescharacteristic
144C2×C22⋊D5C22×D311yescharacteristic
145#709—41no—
146#709—41no—
147C2×D20D1211yescharacteristic
148C2×C4×D5D1211yescharacteristic
149C2×C4×D5#6711yescharacteristic
150C2×Dic10#6711yescharacteristic
151C22⋊AGL(1,𝔽5)—62no—
152#704—22no—
153C4⋊AGL(1,𝔽5)—121no—
154C4×AGL(1,𝔽5)—121no—
155#700—41no—
156D5⋊C8—41no—
157C22⋊Dic5—31no—
158C22⋊Dic5—31no—
159C22⋊Dic5—61no—
160C22⋊Dic5—61no—
161#685—61no—
162#685—61no—
163C4⋊Dic5—61no—
164#683—61no—
165#683—61no—
166C4×Dic5—61no—
167#525—151no—
168#413—51no—
169#410—151no—
170#352—152no—
171AΣL(1,𝔽16)—152no—
172C22×C3×C5—21no—
173C22×C3×C5—41no—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C2×C5×D3—22no—
176C2×C5×D3—41no—
177C2×C5×D3—42no—
178C2×C5×D3—41no—
179C2×C5×D3—42no—
180C2×C3×D5—21no—
181C2×C3×D5—21no—
182C2×C3×D5—41no—
183C2×C3×D5—41no—
184ΓL(1,𝔽16)—82no—
185C3×C4×C5—21no—
186C3×C4×C5#9911yescharacteristic
187C3×C4×C5#9911yescharacteristic
188Dic15—41no—
189Dic15—41no—
190C3×Dic5—21no—
191C3×Dic5—21no—
192C5×Dic3—41no—
193C23×D3C2×AGL(1,𝔽5)11yescharacteristic
194C3×#41—201no—
195C3×#41—201no—
196C2×C3×Q8—51no—
197C2×C3×D4—51no—
198C2×C3×D4—51no—
199C2×C3×D4—51no—
200C22×C3×C4—51no—
201C22×C3×C4—51no—
202C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
203C2×#67—101no—
204C2×#67—101no—
205C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
206C2×C4×D3—21no—
207C2×C4×D3—21no—
208C2×C4×D3—41no—
209C2×C4×D3—41no—
210C3×M16—102no—
211C3×M16—201no—
212C2×C3×C8—201no—
213#217—51no—
214#217—51no—
215#217—101no—
216#217—101no—
217#217—102no—
218(C2×D3)⋊C4—101no—
219(C2×D3)⋊C4—101no—
220C4⋊Dic3—101no—
221C4⋊Dic3—201no—
222Dic3⋊C4—101no—
223Dic3⋊C4—101no—
224C4×Dic3—101no—
225C4×Dic3—201no—
226C23×C5—61no—
227C23×C5—121no—
228C23×C5—122no—
229C23×C5C2×C4×D311yescharacteristic
230C22×D5(C2×D3)⋊C411yescharacteristic
231C22×D5C2×D1211yescharacteristic
232C2×AGL(1,𝔽5)—122no—
233C2×C4×C5—21no—
234C2×C4×C5—21no—
235C2×C4×C5—61no—
236C2×C4×C5—122no—
237C2×C4×C5—121no—
238C2×C4×C5—121no—
239C2×C4×C5—121no—
240C2×C4×C5(C2×D3)⋊C411yescharacteristic
241C2×C4×C5(C2×D3)⋊C411yescharacteristic
242C22⋊D5—41no—
243C22⋊D5—41no—
244C22⋊D5—122no—
245C22⋊D5—122no—
246C2×Dic5—61no—
247C2×Dic5—61no—
248C2×Dic5(C2×D3)⋊C411yescharacteristic
249C2×Dic5C2×#6711yescharacteristic
250D20—41no—
251C4×D5—21no—
252C4×D5—21no—
253C4×D5—21no—
254C4×D5—21no—
255Dic10—41no—
256#170—42no—
257C2×#41—51no—
258C23×C4—31no—
259C2×M16—101no—
260#123—151no—
261#123—151no—
262C22⋊Q8—301no—
263#121—301no—
264#120—151no—
265#120—151no—
266C4×D4—301no—
267C4×D4—301no—
268#117—151no—
269#117—301no—
270#101—101no—
271#100—52no—
272#99—152no—
273#99—301no—
274C2×C3×C5—21no—
275C2×C3×C5—41no—
276C2×C3×C5C2×#9911yescharacteristic
277C3×D5—41no—
278C3×D5—41no—
279C5×D3—42no—
280C23×C3—51no—
281C23×C3—51no—
282C23×C3C22×AGL(1,𝔽5)11yescharacteristic
283C22×D3—21no—
284C22×D3—42no—
285C22×D3—41no—
286C3×Q8—201no—
287C3×D4—201no—
288C3×D4—201no—
289C3×D4—201no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—51no—
293C2×C3×C4—51no—
294C2×C3×C4—101no—
295C2×C3×C4—101no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
299C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
300#67—202no—
301#67—202no—
302C2×Dic3—21no—
303C2×Dic3—41no—
304C2×Dic3—101no—
305C2×Dic3—101no—
306C2×Dic3—202no—
307C4×D3—42no—
308C4×D3—41no—
309C4×D3—41no—
310C3×C8—202no—
311C22×C5—21no—
312C22×C5—41no—
313C22×C5—62no—
314C22×C5—121no—
315C22×C5—122no—
316C22×C5—122no—
317C22×C5—121no—
318C22×C5C2×(C2×D3)⋊C411yescharacteristic
319C2×D5—21no—
320C2×D5—21no—
321C2×D5—41no—
322C2×D5—41no—
323AGL(1,𝔽5)—242no—
324C4×C5—21no—
325C4×C5—121no—
326C4×C5#80611yescharacteristic
327C4×C5#80611yescharacteristic
328Dic5—21no—
329Dic5—21no—
330Dic5—121no—
331Dic5—121no—
332C24—31no—
333#41—201no—
334#41—201no—
335C2×Q8—51no—
336C2×D4—51no—
337C2×D4—51no—
338C2×D4—51no—
339C2×D4—301no—
340C2×D4—301no—
341C22×C4—31no—
342C22×C4—51no—
343C22×C4—51no—
344C22×C4—61no—
345C22×C4—61no—
346C22×C4—121no—
347C22×C4—121no—
348C22×C4D3×AGL(1,𝔽5)11yescharacteristic
349M16—102no—
350M16—201no—
351C2×C8—201no—
352C4⋊C4—301no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C4⋊C4—601no—
356C22⋊C4—151no—
357C22⋊C4—151no—
358C22⋊C4—301no—
359C22⋊C4—301no—
360C22⋊C4—301no—
361C22⋊C4—301no—
362C22⋊C4—302no—
363C42—301no—
364C42—601no—
365C3×C5#212011yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—41no—
368C22×C3—101no—
369C22×C3—101no—
370C22×C3—201no—
371C22×C3—201no—
372C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
373C2×D3—22no—
374C2×D3—41no—
375C2×D3—42no—
376C2×D3—41no—
377C2×D3—42no—
378C3×C4—21no—
379C3×C4—101no—
380C3×C4—101no—
381C3×C4#401111yescharacteristic
382C3×C4#401111yescharacteristic
383Dic3—41no—
384Dic3—201no—
385Dic3—201no—
386Dic3—402no—
387C2×C5—21no—
388C2×C5—41no—
389C2×C5—122no—
390C2×C5C2×#80611yescharacteristic
391D5—41no—
392D5—41no—
393C23—51no—
394C23—51no—
395C23—61no—
396C23—121no—
397C23—122no—
398C23C2×D3×AGL(1,𝔽5)11yescharacteristic
399Q8—201no—
400D4—201no—
401D4—201no—
402D4—201no—
403D4—602no—
404D4—602no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—51no—
408C2×C4—51no—
409C2×C4—61no—
410C2×C4—101no—
411C2×C4—101no—
412C2×C4—101no—
413C2×C4—101no—
414C2×C4—122no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—301no—
419C2×C4—301no—
420C2×C4—602no—
421C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
422C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
423C8—202no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—201no—
427C2×C3—201no—
428C2×C3C2×#401111yescharacteristic
429D3—42no—
430C5#7014511yescharacteristic, complemented, Sylow
431C22—21no—
432C22—41no—
433C22—62no—
434C22—101no—
435C22—101no—
436C22—121no—
437C22—122no—
438C22—122no—
439C22—121no—
440C22—201no—
441C22—201no—
442C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
443C4—21no—
444C4—101no—
445C4—101no—
446C4—121no—
447C4—601no—
448C4—601no—
449C4—1202no—
450C4#9117211yescharacteristic
451C4#9117211yescharacteristic
452C3#1060488711yescharacteristic, complemented, Sylow
453C2—21no—
454C2—41no—
455C2—122no—
456C2—201no—
457C2—201no—
458C2C2×#9117211yescharacteristic
subgroupG/H
centerC4#91172
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5C2×#99
prime radical#11754577C2
cosocleC2×C3×C22⋊D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2120
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752404C2semidirect
3. C3×#65761C2semidirect
4. #11746582C2semidirect
5. #11746578C2semidirect
7. C22×C4×C5×D3C4semidirect
11. #91815C4semidirect
12. #91568C4semidirect
14. #91536C4semidirect
26. #65761D3semidirect
118. C22×C4×D3AGL(1,𝔽5)semidirect
365. C3×C5#2120semidirect
430. C5#70145semidirect
452. C3#10604887semidirect

Maximal subgroups

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

subgroupindex
#117545772
#117524042
C3×#657612
#117465822
#117465782
#106048873
#701455