Finite Group Databasebeta

← #14313153

Subgroups — #14313153

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#11754801C211yesmaximal, characteristic
2C5×#4740C211yesmaximal, characteristic, complemented
3#11749126C211yesmaximal, characteristic, complemented
4#11746293C211yesmaximal, characteristic, complemented
5C3×#64691C211yesmaximal, characteristic, complemented
6#11746005C211yesmaximal, characteristic, complemented
7#11745994C211yesmaximal, characteristic, complemented
8#10600849—31nomaximal, Hall
9C2×C5×#237C2211yescharacteristic
10C22×D5×Dic3C411yescharacteristic, complemented
11#91824C2211yescharacteristic
12C5×#877—21no—
13C3×#4083C2211yescharacteristic
14#91563C411yescharacteristic, complemented
15Dic3×C22⋊D5—21no—
16#91549—21no—
17#91543C411yescharacteristic, complemented
18#91529C411yescharacteristic, complemented
19#91441—21no—
20#91421—21no—
21D3×#681—21no—
22C3×C5×#99C2211yescharacteristic
23#91117C2211yescharacteristic
24C5×#834C2211yescharacteristic
25C5×#806—21no—
26C3×#3965C2211yescharacteristic
27#90962—21no—
28#69136—51nomaximal, Hall
29#66162—31no—
30C5×#410—31no—
31#65526—31no—
32#64692—31no—
33#64692—31no—
34#64691—31no—
35#64691D311yescharacteristic, complemented
36C23×C3×D5C2×C411yescharacteristic
37C2×C3×C5×D4C2311yescharacteristic
38C22×Dic15C2×C411yescharacteristic
39C2×C5×#67C2×C411yescharacteristic
40C2×C5×#67D411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C5×Dic3D411yescharacteristic
43C5×#237—41no—
44C5×#237—41no—
45C2×C4×C5×D3D411yescharacteristic
46C2×C5×Dic6D411yescharacteristic
47C2×C3×C22⋊D5—21no—
48C2×#1201—21no—
49C2×D5×Dic3—21no—
50C2×D5×Dic3—21no—
51C2×D5×Dic3—41no—
52C2×D5×Dic3—41no—
53C3×C5×C22⋊C4—21no—
54#6719—21no—
55#6719C2×C411yescharacteristic
56#6712—21no—
57#6710—21no—
58C5×#217—21no—
59C5×Dic3⋊C4—41no—
60C4×C5×Dic3—41no—
61C3×C22⋊Dic5C2×C411yescharacteristic
62C3×#685—21no—
63C3×#681—21no—
64Dic3⋊Dic5—21no—
65#6668—21no—
66(C2×D3)⋊Dic5—21no—
67#6665—21no—
68Dic3×Dic5—21no—
69#6650—41no—
70D3×#168—41no—
71#5586—51no—
72#4745—51no—
73#4740D511yescharacteristic, complemented
74C3×AΣL(1,𝔽16)—51no—
75#4536—51no—
76#4476—51no—
77#4472—51no—
78C2×C5×#41—31no—
79C22×C4×D5—31no—
80C5×#117—61no—
81#4092—61no—
82#4084—61no—
83#4083—31no—
84#4083C2×D311yescharacteristic
85#4081—31no—
86#4081—31no—
87C4×C22⋊D5—61no—
88C4×C22⋊D5—61no—
89#4072—31no—
90C2×#681—61no—
91C5×#99—31no—
92C5×#99—61no—
93C5×#99C2×D311yescharacteristic
94#3968—61no—
95#3965—31no—
96#3965C2×D311yescharacteristic
97#2120—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C5×D3C22⋊C411yescharacteristic
101C22×C3×D5—21no—
102C22×C3×D5—42no—
103C22×C3×D5—41no—
104C3×C5×D4—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—41no—
110C5×#67—41no—
111C5×#67—41no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3C22⋊C411yescharacteristic
118C2×C5×Dic3C22⋊C411yescharacteristic
119C2×C5×Dic3C22⋊C411yescharacteristic
120C4×C5×D3—21no—
121C4×C5×D3—21no—
122C5×Dic6—41no—
123C3×C22⋊D5—42no—
124C2×C3×Dic5—21no—
125#1201—42no—
126D5×Dic3—42no—
127D5×Dic3—41no—
128D5×Dic3—41no—
129C3⋊#168—41no—
130C3×#168—41no—
131C23×Dic3—51no—
132C2×#237C2×D511yescharacteristic
133C3×#120—51no—
134#953—51no—
135#939—101no—
136#935—51no—
137D4×Dic3—101no—
138D3×M16—101no—
139#886—51no—
140#67⋊C4—101no—
141#878—101no—
142#877—21no—
143#877—51no—
144C3×#100—51no—
145C3×#99C2×D511yescharacteristic
146#834C2×D511yescharacteristic
147#833—51no—
148#824—101no—
149#806—21no—
150C23×D5C4×D311yescharacteristic
151C5×#41—121no—
152C5×#41—121no—
153C2×C5×Q8—31no—
154C2×C5×D4—31no—
155C2×C5×D4—31no—
156C2×C5×D4C22×D311yescharacteristic
157C22×C4×C5—31no—
158C22×C4×C5—31no—
159C22×C4×C5—31no—
160C2×C22⋊D5—21no—
161C2×C22⋊D5—61no—
162C22×Dic5—31no—
163C2×C4×D5—61no—
164C2×C4×D5—61no—
165C2×C4×D5—121no—
166C2×C4×D5—121no—
167C5×C4⋊C4—121no—
168C5×C22⋊C4—21no—
169C5×C22⋊C4—61no—
170C42×C5—121no—
171C22⋊Dic5—31no—
172C22⋊Dic5—61no—
173C22⋊Dic5—61no—
174C22⋊Dic5C4×D311yescharacteristic
175#685—21no—
176#685—61no—
177C4⋊Dic5—61no—
178#683—61no—
179#683—61no—
180C4×Dic5—61no—
181#681—21no—
182#681—61no—
183#681—121no—
184C2×#168—121no—
185#525—151no—
186#413—151no—
187#410—31no—
188#352—151no—
189#352—151no—
190AΣL(1,𝔽16)—51no—
191AΣL(1,𝔽16)—151no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—41no—
195C22×C3×C5—41no—
196C22×C3×C5C2×C22⋊C411yescharacteristic
197C2×C5×D3—21no—
198C2×C5×D3—41no—
199C2×C3×D5—22no—
200C2×C3×D5—41no—
201C2×C3×D5—42no—
202C2×C3×D5—41no—
203C2×C3×D5—42no—
204C3×C4×C5—21no—
205C3×C4×C5—81no—
206Dic15—41no—
207Dic15—41no—
208C3×Dic5—41no—
209C5×Dic3—21no—
210C5×Dic3—21no—
211C5×Dic3—81no—
212C5×Dic3#9911yescharacteristic
213C5×Dic3#9911yescharacteristic
214C24×C3—51no—
215C2×C3×D4—101no—
216C2×C3×D4C22×D511yescharacteristic
217C2×#67—101no—
218C2×#67C4×D511yescharacteristic
219C2×#67C22⋊D511yescharacteristic
220C22×Dic3—51no—
221C22×Dic3—101no—
222C22×Dic3—101no—
223C22×Dic3—201no—
224C22×Dic3—201no—
225C22×Dic3C4×D511yescharacteristic
226C22×Dic3C22⋊D511yescharacteristic
227#237—41no—
228#237—41no—
229C2×C4×D3D2011yescharacteristic
230C2×Dic6D2011yescharacteristic
231C3×M16—101no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—51no—
234C3×C22⋊C4—101no—
235#217—21no—
236#217—51no—
237#217—101no—
238#217—101no—
239(C2×D3)⋊C4—101no—
240C4⋊Dic3—101no—
241Dic3⋊C4—41no—
242Dic3⋊C4—101no—
243Dic3⋊C4—101no—
244C4×Dic3—41no—
245C4×Dic3—101no—
246#208—101no—
247ΓL(1,𝔽25)—201no—
248D3×C8—201no—
249C23×C5—31no—
250C23×C5C2×C4×D311yescharacteristic
251C23×C5D3×D411yescharacteristic
252C22×D5—21no—
253C22×D5—42no—
254C22×D5—41no—
255C5×Q8—121no—
256C5×D4—41no—
257C5×D4—121no—
258C5×D4—121no—
259C2×C4×C5—31no—
260C2×C4×C5—31no—
261C2×C4×C5—31no—
262C2×C4×C5—41no—
263C2×C4×C5—61no—
264C2×C4×C5—61no—
265C2×C4×C5—61no—
266C2×C4×C5—61no—
267C2×C4×C5—61no—
268C2×C4×C5—61no—
269C2×C4×C5—121no—
270C2×C4×C5D3×D411yescharacteristic
271C22⋊D5—42no—
272C22⋊D5—122no—
273C2×Dic5—21no—
274C2×Dic5—61no—
275C2×Dic5—61no—
276C2×Dic5—121no—
277C4×D5—121no—
278C4×D5—121no—
279C4×D5—122no—
280#168—41no—
281#168—121no—
282C2×#41—31no—
283C23×C4—151no—
284C2×M16—301no—
285#123—151no—
286#123—151no—
287C22⋊Q8—301no—
288#121—301no—
289#120—51no—
290#120—151no—
291C4×D4—301no—
292C4×D4—301no—
293#117—61no—
294#117—151no—
295#101—301no—
296#100—51no—
297#100—151no—
298#99—31no—
299#99—61no—
300#99D3×D511yescharacteristic
301C2×C3×C5—21no—
302C2×C3×C5—41no—
303C2×C3×C5—41no—
304C2×C3×C5C2×#9911yescharacteristic
305C3×D5—42no—
306C5×D3—41no—
307C23×C3—101no—
308C23×C3—201no—
309C23×C3—202no—
310C23×C3C2×C4×D511yescharacteristic
311C23×C3C2×C22⋊D511yescharacteristic
312C22×D3#68511yescharacteristic
313C3×D4—41no—
314C3×D4—202no—
315C2×C3×C4—41no—
316C2×C3×C4—101no—
317C2×C3×C4C2×D2011yescharacteristic
318#67—41no—
319#67—41no—
320#67—202no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—41no—
326C2×Dic3—101no—
327C2×Dic3—101no—
328C2×Dic3—202no—
329C2×Dic3—201no—
330C2×Dic3—201no—
331C2×Dic3—201no—
332C2×Dic3#68511yescharacteristic
333C2×Dic3#68511yescharacteristic
334C2×Dic3#68511yescharacteristic
335C4×D3—21no—
336C4×D3—21no—
337Dic6—41no—
338C3×C8—201no—
339C3⋊C8—201no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5—41no—
343C22×C5—41no—
344C22×C5—61no—
345C22×C5—121no—
346C22×C5D3×C22⋊C411yescharacteristic
347C2×D5—22no—
348C2×D5—41no—
349C2×D5—42no—
350C2×D5—41no—
351C2×D5—42no—
352C4×C5—21no—
353C4×C5—31no—
354C4×C5—31no—
355C4×C5—61no—
356C4×C5—61no—
357C4×C5—81no—
358C4×C5—241no—
359Dic5—41no—
360Dic5—121no—
361Dic5—121no—
362C24—51no—
363#41—121no—
364#41—121no—
365C2×Q8—31no—
366C2×D4—31no—
367C2×D4—31no—
368C2×D4—101no—
369C2×D4—301no—
370C2×D4C2×D3×D511yescharacteristic
371C22×C4—31no—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—151no—
375C22×C4—301no—
376C22×C4—301no—
377C22×C4—601no—
378C22×C4—601no—
379M16—101no—
380M16—301no—
381M16—601no—
382C2×C8—601no—
383C4⋊C4—121no—
384C4⋊C4—301no—
385C4⋊C4—301no—
386C4⋊C4—301no—
387C22⋊C4—21no—
388C22⋊C4—51no—
389C22⋊C4—61no—
390C22⋊C4—101no—
391C22⋊C4—151no—
392C22⋊C4—301no—
393C22⋊C4—301no—
394C22⋊C4—301no—
395C42—121no—
396C42—301no—
397C3×C5#212011yescharacteristic, complemented, Hall
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—102no—
403C22×C3—201no—
404C22×C3—202no—
405C22×C3—202no—
406C22×C3—201no—
407C22×C3C2×#68511yescharacteristic
408C2×D3—21no—
409C2×D3—41no—
410C3×C4—21no—
411C3×C4—81no—
412C3×C4—201no—
413Dic3—21no—
414Dic3—21no—
415Dic3—81no—
416Dic3—201no—
417Dic3—201no—
418Dic3#393811yescharacteristic
419Dic3#393811yescharacteristic
420C2×C5—21no—
421C2×C5—41no—
422C2×C5—41no—
423C2×C5—121no—
424C2×C5D3×#9911yescharacteristic
425D5—42no—
426C23—31no—
427C23—101no—
428C23—201no—
429C23—202no—
430C23C4×D3×D511yescharacteristic
431C23D3×C22⋊D511yescharacteristic
432Q8—121no—
433D4—41no—
434D4—121no—
435D4—121no—
436D4—202no—
437D4—602no—
438C2×C4—31no—
439C2×C4—31no—
440C2×C4—31no—
441C2×C4—41no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—101no—
449C2×C4—121no—
450C2×C4—301no—
451C2×C4—301no—
452C2×C4—601no—
453C2×C4—601no—
454C2×C4—602no—
455C2×C4—601no—
456C2×C4D3×D2011yescharacteristic
457C8—201no—
458C8—601no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—41no—
462C2×C3—202no—
463C2×C3C2×#393811yescharacteristic
464D3—41no—
465C5#6913611yescharacteristic, complemented, Sylow
466C22—21no—
467C22—21no—
468C22—41no—
469C22—41no—
470C22—61no—
471C22—102no—
472C22—121no—
473C22—201no—
474C22—202no—
475C22—202no—
476C22—201no—
477C22D3×#68511yescharacteristic
478C4—21no—
479C4—31no—
480C4—31no—
481C4—61no—
482C4—61no—
483C4—81no—
484C4—201no—
485C4—241no—
486C4—601no—
487C4—601no—
488C3#1060084911yescharacteristic, complemented, Sylow
489C2—21no—
490C2—41no—
491C2—41no—
492C2—121no—
493C2—202no—
494C2D3×#393811yescharacteristic
subgroupG/H
centerC2D3×#3938
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#99C22
socleC2×C3×C5C2×#99
prime radical#11754801C2
cosocleC2×C3×C5×D4C23
hypercenter#99D3×D5
hypocenterC3×C5#2120
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
2. C5×#4740C2semidirect
3. #11749126C2semidirect
4. #11746293C2semidirect
5. C3×#64691C2semidirect
6. #11746005C2semidirect
7. #11745994C2semidirect
10. C22×D5×Dic3C4semidirect
14. #91563C4semidirect
17. #91543C4semidirect
18. #91529C4semidirect
35. #64691D3semidirect
73. #4740D5semidirect
397. C3×C5#2120semidirect
465. C5#69136semidirect
488. C3#10600849semidirect

Maximal subgroups

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

subgroupindex
#117548012
C5×#47402
#117491262
#117462932
C3×#646912
#117460052
#117459942
#106008493
#691365