Finite Group Databasebeta

← #14301745

Subgroups — #14301745

Order 1920.

684 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 110 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×#66256C211yesmaximal, characteristic, complemented
2#11754795C211yesmaximal, characteristic
3#11752436C211yesmaximal, characteristic, complemented
4#11752000C212yesmaximal, complemented
5#11746575C212yesmaximal, complemented
6#10604463—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C22×D3×Dic5C2211yescharacteristic
9C2×#6762C2212yes—
10C2×C3×#704—21no—
11C2×C3×#704C2212yes—
12C3×#4131—24no—
13C3×D5⋊M16—21no—
14#91824C411yescharacteristic
15C5×#937C411yescharacteristic
16#91568C411yescharacteristic
17#91565—21no—
18Dic5×#67—21no—
19#91537C411yescharacteristic
20#91528C2211yescharacteristic
21#91440—21no—
22#91410—21no—
23#91242—21no—
24#91234—21no—
25(C2×D3)⋊#170—24no—
26#72029—51nomaximal, Hall
27#66256D311yescharacteristic, complemented
28#65920—31no—
29#65798—32no—
30#65777—31no—
31#64867—32no—
32C23×C5×D3C2×C411yescharacteristic
33C2×C3×C5×D4C2×C411yescharacteristic
34C22×Dic15C2×C411yescharacteristic
35C2×C5×#67—21no—
36C2×C3×C22⋊D5C2×C411yescharacteristic
37C2×C3×C22⋊D5D411yescharacteristic
38C22×C3×Dic5D411yescharacteristic
39C22×C3×Dic5C2311yescharacteristic
40C3×#711—22no—
41C3×#711—22no—
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×Dic10D411yescharacteristic
44C2×#1201—21no—
45C2×D3×Dic5—21no—
46C2×D3×Dic5—22no—
47C2×D3×Dic5—21no—
48C2×D3×Dic5—22no—
49#6762—22no—
50#6762—22no—
51C2×C3⋊#170—22no—
52C3×#704—22no—
53C3×#704—22no—
54C3×#704—22no—
55C2×C3×#170—22no—
56C2×C3×#170D414yescomplemented
57C3×#700—22no—
58C3×D5⋊C8—22no—
59#6719—21no—
60#6719C2×C411yescharacteristic
61#6712—21no—
62C5×#217C2×C411yescharacteristic
63C5×(C2×D3)⋊C4—21no—
64Dic3⋊Dic5—21no—
65#6668—21no—
66(C2×D3)⋊Dic5—21no—
67#6665—21no—
68Dic3×Dic5—21no—
69C3×#568—51no—
70#5828—51no—
71#5237—51no—
72#5126—52no—
73#4556—52no—
74C23×Dic5—31no—
75C2×#711C2×D311yescharacteristic
76C2×#704—21no—
77C2×#704—32no—
78C2×#704C2×D312yes—
79#4131—24no—
80D5⋊M16—21no—
81C5×#120—31no—
82#4099—31no—
83#4085—61no—
84#4081—31no—
85D4×Dic5—61no—
86#4032—31no—
87#4027—61no—
88#4024—61no—
89#4023—31no—
90#4013—61no—
91C22⋊#170—64no—
92#4005—61no—
93#1891—151noSylow
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C22×C411yescharacteristic
96C22×C5×D3—21no—
97C22×C5×D3—22no—
98C22×C5×D3—42no—
99C22×C3×D5C22⋊C411yescharacteristic
100C3×C5×D4—22no—
101C2×C3×C4×C5C22⋊C411yescharacteristic
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—22no—
105C5×#67—42no—
106C2×C5×Dic3—21no—
107C3×C22⋊D5—22no—
108C3×C22⋊D5—22no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5C22⋊C411yescharacteristic
112C2×C3×Dic5C2×D412yes—
113C2×C3×Dic5C2×D411yescharacteristic
114C2×C3×Dic5C2×D411yescharacteristic
115C2×C3×Dic5#4112yes—
116C3×C4×D5—21no—
117C3×C4×D5—21no—
118C3×Dic10—22no—
119#1201—42no—
120D3×Dic5—41no—
121D3×Dic5—42no—
122D3×Dic5—41no—
123C3⋊#170—42no—
124C3×#170—24no—
125C2×C3×#41—51no—
126C22×C4×D3—51no—
127C3×#131—104no—
128C2×C3×M16—52no—
129C2×C3×M16—101no—
130C2×C3×M16—101no—
131#946—101no—
132#938—101no—
133#937—51no—
134#937AGL(1,𝔽5)11yescharacteristic
135#935—51no—
136#935—51no—
137C4×#67—101no—
138C4×#67—101no—
139#926—51no—
140C2×#208—52no—
141#836—101no—
142#833—101no—
143(C2×D3)⋊C8—104no—
144C24×C5—31no—
145C2×C5×D4—61no—
146C2×C5×D4C4×D311yescharacteristic
147C2×C22⋊D5—61no—
148C2×C22⋊D5C4×D311yescharacteristic
149C2×C22⋊D5D1211yescharacteristic
150C22×Dic5—31no—
151C22×Dic5—61no—
152C22×Dic5—62no—
153C22×Dic5—62no—
154C22×Dic5—61no—
155C22×Dic5#6711yescharacteristic
156C22×Dic5C22×D311yescharacteristic
157#711—22no—
158#711—22no—
159C2×C4×D5#6711yescharacteristic
160C2×Dic10D1211yescharacteristic
161#704—22no—
162#704—22no—
163#704—22no—
164#704—62no—
165#704—62no—
166C2×#170—22no—
167C2×#170—62no—
168C2×#170#6714yescomplemented
169#700—22no—
170D5⋊C8—22no—
171C5×C22⋊C4—31no—
172C5×C22⋊C4—61no—
173C22⋊Dic5—31no—
174C22⋊Dic5—61no—
175C22⋊Dic5—61no—
176#685—61no—
177C4⋊Dic5—61no—
178#683—61no—
179#683—61no—
180C4×Dic5—61no—
181#568—51no—
182#525—151no—
183#413—151no—
184#407—152no—
185#344—152no—
186C22×C3×C5—21no—
187C22×C3×C5—41no—
188C22×C3×C5—41no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5C4×D412yes—
191C2×C5×D3—22no—
192C2×C5×D3—24no—
193C2×C5×D3—41no—
194C2×C5×D3—42no—
195C2×C5×D3—41no—
196C2×C3×D5—21no—
197C2×C3×D5—41no—
198C3×C4×C5—21no—
199Dic15—41no—
200Dic15—41no—
201C3×Dic5—21no—
202C3×Dic5#12011yescharacteristic
203C3×Dic5#12112yes—
204C3×Dic5#12311yescharacteristic
205C5×Dic3—41no—
206C23×D3C2×AGL(1,𝔽5)11yescharacteristic
207C3×#41—102no—
208C3×#41—102no—
209C2×C3×Q8—51no—
210C2×C3×D4—51no—
211C2×C3×D4—51no—
212C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
213C22×C3×C4—51no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C2×#67—21no—
217C2×#67—101no—
218C22×Dic3—51no—
219C2×C4×D3—102no—
220C2×C4×D3—101no—
221C2×C4×D3—101no—
222C2×C4×D3—102no—
223C3×M16—102no—
224C3×M16—102no—
225C3×M16—102no—
226C3×M16—102no—
227C2×C3×C8—54no—
228C2×C3×C8—102no—
229C2×C3×C8—102no—
230#217—51no—
231#217—101no—
232#217—101no—
233#217C2×AGL(1,𝔽5)11yescharacteristic
234(C2×D3)⋊C4—21no—
235(C2×D3)⋊C4—101no—
236C4⋊Dic3—101no—
237Dic3⋊C4—101no—
238Dic3⋊C4—101no—
239C4×Dic3—101no—
240#208—102no—
241#208—102no—
242C2×C3⋊C8—102no—
243C23×C5—61no—
244C23×C5—62no—
245C23×C5—122no—
246C23×C5(C2×D3)⋊C411yescharacteristic
247C23×C5C2×C4×D311yescharacteristic
248C22×D5(C2×D3)⋊C411yescharacteristic
249C5×D4—22no—
250C5×D4—122no—
251C2×C4×C5—61no—
252C2×C4×C5(C2×D3)⋊C411yescharacteristic
253C22⋊D5—22no—
254C22⋊D5—22no—
255C22⋊D5—122no—
256C2×Dic5—21no—
257C2×Dic5—21no—
258C2×Dic5—61no—
259C2×Dic5—61no—
260C2×Dic5—62no—
261C2×Dic5—121no—
262C2×Dic5—122no—
263C2×Dic5—121no—
264C2×Dic5(C2×D3)⋊C411yescharacteristic
265C2×Dic5C2×D1211yescharacteristic
266C2×Dic5#23512yes—
267C2×Dic5C2×#6711yescharacteristic
268C2×Dic5C2×#6712yes—
269C4×D5—21no—
270C4×D5—21no—
271Dic10—22no—
272#170—24no—
273#170—122no—
274C2×#41—51no—
275C23×C4—151no—
276#131—104no—
277C2×M16—52no—
278C2×M16—101no—
279C2×M16—101no—
280C2×M16—152no—
281#123—151no—
282#123—151no—
283C22⋊Q8—301no—
284#121—301no—
285#120—31no—
286#120—151no—
287C4×D4—301no—
288C4×D4—301no—
289#117—151no—
290#101—301no—
291#100—301no—
292C22⋊C8—304no—
293C2×C3×C5—21no—
294C2×C3×C5—22no—
295C2×C3×C5—41no—
296C2×C3×C5#38611yescharacteristic
297C3×D5—41no—
298C5×D3—42no—
299C23×C3—51no—
300C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
301C23×C3C22×AGL(1,𝔽5)11yescharacteristic
302C22×D3—22no—
303C22×D3—21no—
304C22×D3—42no—
305C3×Q8—102no—
306C3×D4—22no—
307C3×D4—102no—
308C3×D4—102no—
309C2×C3×C4—52no—
310C2×C3×C4—52no—
311C2×C3×C4—51no—
312C2×C3×C4—51no—
313C2×C3×C4—51no—
314C2×C3×C4—101no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
319#67—42no—
320#67—202no—
321C2×Dic3—21no—
322C2×Dic3—102no—
323C2×Dic3—101no—
324C2×Dic3—101no—
325C4×D3—201no—
326C4×D3—202no—
327C4×D3—201no—
328C3×C8—104no—
329C3⋊C8—202no—
330C22×C5—21no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5—62no—
334C22×C5—64no—
335C22×C5—121no—
336C22×C5—122no—
337C22×C5—121no—
338C22×C5C2×(C2×D3)⋊C411yescharacteristic
339C22×C5C4×#6712yes—
340C2×D5—21no—
341C2×D5—41no—
342C4×C5—21no—
343C4×C5—121no—
344Dic5—21no—
345Dic5—121no—
346Dic5—121no—
347Dic5#92911yescharacteristic
348Dic5#93012yes—
349Dic5#95311yescharacteristic
350C24—31no—
351#41—102no—
352#41—102no—
353C2×Q8—51no—
354C2×D4—51no—
355C2×D4—51no—
356C2×D4—61no—
357C2×D4—301no—
358C2×D4D3×AGL(1,𝔽5)11yescharacteristic
359C22×C4—51no—
360C22×C4—51no—
361C22×C4—51no—
362C22×C4—151no—
363C22×C4—302no—
364C22×C4—301no—
365C22×C4—301no—
366C22×C4—302no—
367M16—102no—
368M16—102no—
369M16—102no—
370M16—102no—
371M16—302no—
372M16—302no—
373C2×C8—54no—
374C2×C8—102no—
375C2×C8—102no—
376C2×C8—302no—
377C4⋊C4—301no—
378C4⋊C4—301no—
379C4⋊C4—301no—
380C22⋊C4—31no—
381C22⋊C4—61no—
382C22⋊C4—151no—
383C22⋊C4—301no—
384C22⋊C4—301no—
385C22⋊C4—301no—
386C42—301no—
387C3×C5#189111yescharacteristic, complemented, Hall
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—101no—
392C22×C3—201no—
393C22×C3D4×AGL(1,𝔽5)12yes—
394C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
395C2×D3—22no—
396C2×D3—24no—
397C2×D3—41no—
398C2×D3—42no—
399C2×D3—41no—
400C3×C4—21no—
401C3×C4—51no—
402C3×C4—52no—
403C3×C4—51no—
404C3×C4—101no—
405Dic3—41no—
406Dic3—201no—
407Dic3—201no—
408C2×C5—21no—
409C2×C5—22no—
410C2×C5—41no—
411C2×C5—122no—
412C2×C5#521311yescharacteristic
413D5—41no—
414C23—51no—
415C23—61no—
416C23—62no—
417C23—122no—
418C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
419C23C2×D3×AGL(1,𝔽5)11yescharacteristic
420Q8—102no—
421D4—22no—
422D4—102no—
423D4—102no—
424D4—122no—
425D4—602no—
426C2×C4—51no—
427C2×C4—51no—
428C2×C4—52no—
429C2×C4—52no—
430C2×C4—51no—
431C2×C4—61no—
432C2×C4—101no—
433C2×C4—101no—
434C2×C4—101no—
435C2×C4—101no—
436C2×C4—301no—
437C2×C4—301no—
438C2×C4—302no—
439C2×C4—601no—
440C2×C4—602no—
441C2×C4—601no—
442C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
443C8—104no—
444C8—602no—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—41no—
448C2×C3—201no—
449C2×C3#6577911yescharacteristic
450D3—42no—
451C5#7202911yescharacteristic, complemented, Sylow
452C22—21no—
453C22—41no—
454C22—41no—
455C22—62no—
456C22—64no—
457C22—101no—
458C22—121no—
459C22—122no—
460C22—121no—
461C22—201no—
462C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
463C22AGL(1,𝔽5)×#6712yes—
464C4—21no—
465C4—51no—
466C4—52no—
467C4—51no—
468C4—101no—
469C4—121no—
470C4—601no—
471C4—601no—
472C3#1060446311yescharacteristic, complemented, Sylow
473C2—21no—
474C2—22no—
475C2—41no—
476C2—122no—
477C2—201no—
478C2#1175202211yescharacteristic
subgroupG/H
centerC2#11752022
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC2×C3×C5#386
prime radical#11754795C2
cosocleC22×C3×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1891
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C3×#66256C2semidirect
3. #11752436C2semidirect
4. #11752000C2semidirect
5. #11746575C2semidirect
27. #66256D3semidirect
56. C2×C3×#170D4semidirect
168. C2×#170#67semidirect
387. C3×C5#1891semidirect
451. C5#72029semidirect
472. C3#10604463semidirect

Maximal subgroups

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

subgroupindex
C3×#662562
#117547952
#117524362
#117520002
#117465752
#106044633
#720295