Finite Group Databasebeta

← #14287786

Subgroups — #14287786

Order 1920.

544 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 84 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×#65849C211yesmaximal, characteristic, complemented
2C5×#4991C211yesmaximal, characteristic, complemented
3#11748537C211yesmaximal, characteristic, complemented
4#11748516C211yesmaximal, characteristic
5#11746349C211yesmaximal, characteristic, complemented
6#11745961C211yesmaximal, characteristic, complemented
7#11745954C211yesmaximal, characteristic, complemented
8#10600495—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C5×(C2×D3)⋊C4—21no—
12C2×C5×(C2×D3)⋊C4—21no—
13C3×#4076C2211yescharacteristic
14C3×#4075—21no—
15C3×C4×C22⋊D5—21no—
16C3×#4070C2211yescharacteristic
17C3×#4044—21no—
18C3×#4042—21no—
19C3×#4040—21no—
20C3×#4035—21no—
21C2×#6656—21no—
22C2×#6652—21no—
23#91114C2211yescharacteristic
24#91114C2211yescharacteristic
25C5×C3⋊#95C2211yescharacteristic
26#90966—21no—
27#90966—21no—
28#71888—51nomaximal, Hall
29#65849D311yescharacteristic, complemented
30C5×#394—31no—
31#65507—31no—
32#65506—31no—
33#64748—31no—
34#64672—31no—
35#64671—31no—
36C23×C5×D3—21no—
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×C5×Dic3—21no—
41C2×C5×D12—21no—
42C2×C5×D12—21no—
43C2×C5×D12—42no—
44C2×C3×C22⋊D5—21no—
45C2×C3×D20D411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×Dic10D411yescharacteristic
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C5×(C2×D3)⋊C4—42no—
53C5×(C2×D3)⋊C4—42no—
54C3×C22⋊Dic5—21no—
55C3×#685—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×C4⋊Dic5D411yescharacteristic
60C3×C4⋊Dic5D411yescharacteristic
61C3×#683—21no—
62C3×#683—21no—
63C3×#683—21no—
64C3×#683—21no—
65C3×C4×Dic5—21no—
66#6656—42no—
67#6652—42no—
68C3×#539—51no—
69#5046—51no—
70#5036—51no—
71#4991D511yescharacteristic, complemented
72#4538—51no—
73#4537—51no—
74#4528—51no—
75C22×C5×D4—31no—
76C2×C5×C4⋊C4C2×D311yescharacteristic
77C2×C5×C22⋊C4—61no—
78C2×C5×C22⋊C4—61no—
79C2×#687—61no—
80C2×#686—61no—
81#4076C2×D311yescharacteristic
82#4075—21no—
83C4×C22⋊D5—21no—
84#4070C2×D311yescharacteristic
85#4044—21no—
86#4042—21no—
87#4040—21no—
88#4035—21no—
89C5×#95—31no—
90#3964—61no—
91#3964—61no—
92C22⋊#168—31no—
93C22⋊#168—31no—
94#1597—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—22no—
97C22×C5×D3—41no—
98C22×C5×D3—41no—
99C22×C5×D3—41no—
100C22×C5×D3—41no—
101C22×C5×D3—41no—
102C22×C5×D3—41no—
103C22×C3×D5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C5×Dic3—41no—
113C2×C5×Dic3—41no—
114C2×C5×Dic3—41no—
115C5×D12—22no—
116C5×D12—22no—
117C5×D12—41no—
118C5×D12—41no—
119C3×C22⋊D5—41no—
120C3×C22⋊D5—41no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—21no—
124C3×D20—41no—
125C3×C4×D5—81no—
126C3×Dic10—41no—
127C3⋊#168—41no—
128C3⋊#168—41no—
129C22×D12C2×D511yescharacteristic
130C3×#126—101no—
131C3×#125—101no—
132C3×#123—101no—
133C3×#123—101no—
134C3×C22⋊Q8—51no—
135C3×C22⋊Q8—101no—
136C3×#121—51no—
137C3×C4×D4—101no—
138C2×C3×C4⋊C4C2×D511yescharacteristic
139C2×#215—101no—
140C2×#213—101no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C3⋊#95C2×D511yescharacteristic
144#830—51no—
145#830—51no—
146#809—101no—
147#809—101no—
148C24×C5—61no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C2×C5×D4—122no—
152C22×C4×C5—61no—
153C22×C4×C5#6711yescharacteristic
154C22×C4×C5#6711yescharacteristic
155C22×C4×C5C22×D311yescharacteristic
156C2×C22⋊D5—21no—
157C2×D20#6711yescharacteristic
158C2×C4×D5—21no—
159C2×Dic10#6711yescharacteristic
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C22⋊C4—122no—
163C5×C22⋊C4—122no—
164C22⋊Dic5—21no—
165#687—122no—
166#686—122no—
167#685—21no—
168#685—21no—
169#685—21no—
170#685—21no—
171C4⋊Dic5#6711yescharacteristic
172C4⋊Dic5#6711yescharacteristic
173#683—21no—
174#683—21no—
175#683—21no—
176#683—21no—
177C4×Dic5—21no—
178C2×#168—61no—
179C2×#168—61no—
180#539—51no—
181#450—151no—
182#447—151no—
183#394—31no—
184#328—151no—
185#327—151no—
186#324—151no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5#12011yescharacteristic
190C22×C3×C5#13511yescharacteristic
191C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
192C2×C5×D3—42no—
193C2×C5×D3—42no—
194C2×C5×D3—42no—
195C2×C5×D3—81no—
196C2×C5×D3—81no—
197C2×C5×D3—81no—
198C2×C5×D3—81no—
199C2×C3×D5—41no—
200C2×C3×D5—41no—
201C2×C3×D5—41no—
202C3×C4×C5—21no—
203C3×C4×C5—21no—
204C3×C4×C5—41no—
205C3×C4×C5—41no—
206C3×Dic5—41no—
207C3×Dic5—41no—
208C3×Dic5—41no—
209C5×Dic3—81no—
210C23×D3—21no—
211C2×C3×Q8—51no—
212C2×C3×D4—51no—
213C2×C3×D4—101no—
214C22×C3×C4—101no—
215C22×C3×C4C22⋊D511yescharacteristic
216C22×C3×C4C22⋊D511yescharacteristic
217C22×C3×C4C22×D511yescharacteristic
218C22×Dic3—21no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—42no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—51no—
225C3×C4⋊C4—51no—
226C3×C4⋊C4—101no—
227C3×C4⋊C4—101no—
228C3×C4⋊C4—101no—
229C3×C4⋊C4—101no—
230C3×C22⋊C4—101no—
231C3×C22⋊C4—101no—
232C3×C22⋊C4—101no—
233C3×C22⋊C4—101no—
234C3×C22⋊C4—101no—
235C3×C42—101no—
236#215—202no—
237#213—202no—
238(C2×D3)⋊C4—42no—
239(C2×D3)⋊C4—42no—
240C2×C3⋊C8—101no—
241C2×C3⋊C8—101no—
242C23×C5—62no—
243C23×C5—121no—
244C23×C5—121no—
245C23×C5—121no—
246C23×C5—121no—
247C23×C5—121no—
248C23×C5—121no—
249C23×C5C2×#6711yescharacteristic
250C22×D5—21no—
251C5×D4—62no—
252C5×D4—62no—
253C5×D4—121no—
254C5×D4—121no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—121no—
262C2×C4×C5—121no—
263C2×C4×C5—121no—
264C2×C4×C5C2×#6711yescharacteristic
265C2×C4×C5C2×#6711yescharacteristic
266C22⋊D5—41no—
267C22⋊D5—41no—
268C2×Dic5—21no—
269C2×Dic5—21no—
270C2×Dic5—21no—
271D20—41no—
272C4×D5—81no—
273Dic10—41no—
274#168—121no—
275#168—121no—
276C22×D4—31no—
277C2×SD16—301no—
278C2×D8—301no—
279#126—101no—
280#125—101no—
281#123—101no—
282#123—101no—
283C22⋊Q8—51no—
284C22⋊Q8—101no—
285#121—51no—
286C4×D4—101no—
287C2×C4⋊C4D3×D511yescharacteristic
288C2×C22⋊C4—61no—
289C2×C22⋊C4—61no—
290#102—301no—
291#102—301no—
292C22⋊C8—151no—
293C22⋊C8—151no—
294#95—31no—
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5#44911yescharacteristic
298C2×C3×C5#45411yescharacteristic
299C2×C3×C5B(4,𝔽2)11yescharacteristic
300C3×D5—81no—
301C5×D3—82no—
302C23×C3—101no—
303C23×C3C2×C22⋊D511yescharacteristic
304C22×D3—22no—
305C22×D3—41no—
306C22×D3—41no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—41no—
310C22×D3—41no—
311C3×Q8—201no—
312C3×D4—201no—
313C3×D4—201no—
314C3×D4—201no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—101no—
324C2×C3×C4—401no—
325C2×C3×C4D4×D511yescharacteristic
326C2×C3×C4D4×D511yescharacteristic
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330D12—22no—
331D12—22no—
332D12—41no—
333D12—41no—
334C3⋊C8—201no—
335C3⋊C8—201no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—122no—
339C22×C5—122no—
340C22×C5—122no—
341C22×C5—241no—
342C22×C5—241no—
343C22×C5—241no—
344C22×C5—241no—
345C22×C5#94911yescharacteristic
346C22×C5#95011yescharacteristic
347C22×C5#95311yescharacteristic
348C2×D5—41no—
349C2×D5—41no—
350C2×D5—41no—
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—41no—
355C4×C5—241no—
356Dic5—41no—
357Dic5—41no—
358Dic5—41no—
359C24—61no—
360C2×Q8—51no—
361C2×D4—51no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—101no—
365C2×D4—122no—
366C22×C4—61no—
367C22×C4—101no—
368C22×C4#120111yescharacteristic
369C22×C4#120111yescharacteristic
370C22×C4C2×D3×D511yescharacteristic
371SD16—602no—
372D8—602no—
373C2×C8—301no—
374C2×C8—301no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—51no—
378C4⋊C4—51no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C4⋊C4—101no—
382C4⋊C4—101no—
383C22⋊C4—101no—
384C22⋊C4—101no—
385C22⋊C4—101no—
386C22⋊C4—101no—
387C22⋊C4—101no—
388C22⋊C4—122no—
389C22⋊C4—122no—
390C42—101no—
391C3×C5#159711yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—201no—
395C22×C3—201no—
396C22×C3—201no—
397C22×C3#407811yescharacteristic
398C22×C3#408311yescharacteristic
399C22×C3#409611yescharacteristic
400C2×D3—42no—
401C2×D3—42no—
402C2×D3—42no—
403C2×D3—81no—
404C2×D3—81no—
405C2×D3—81no—
406C2×D3—81no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4—201no—
412C3×C4—201no—
413C3×C4—201no—
414Dic3—81no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—242no—
418C2×C5#523811yescharacteristic
419C2×C5#524411yescharacteristic
420C2×C5#524511yescharacteristic
421D5—81no—
422C23—62no—
423C23—101no—
424C23—121no—
425C23—121no—
426C23—121no—
427C23—121no—
428C23—121no—
429C23—121no—
430C23C2×#120111yescharacteristic
431Q8—201no—
432D4—62no—
433D4—62no—
434D4—121no—
435D4—121no—
436D4—201no—
437D4—201no—
438D4—201no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—101no—
446C2×C4—101no—
447C2×C4—101no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4—121no—
451C2×C4—401no—
452C2×C4D5×#6711yescharacteristic
453C2×C4D5×#6711yescharacteristic
454C8—601no—
455C8—601no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—401no—
459C2×C3#6532111yescharacteristic
460C2×C3#6532611yescharacteristic
461C2×C3#6535111yescharacteristic
462D3—82no—
463C5#7188811yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—122no—
467C22—122no—
468C22—122no—
469C22—201no—
470C22—201no—
471C22—201no—
472C22—241no—
473C22—241no—
474C22—241no—
475C22—241no—
476C22#9129711yescharacteristic
477C22#9129911yescharacteristic
478C22#9156311yescharacteristic
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—201no—
484C4—201no—
485C4—201no—
486C4—241no—
487C3#1060049511yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—242no—
491C2—401no—
492C2#1174851111yescharacteristic
493C2#1174917511yescharacteristic
494C2#1174938311yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radical#11748516C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1597
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65849C2semidirect
2. C5×#4991C2semidirect
3. #11748537C2semidirect
5. #11746349C2semidirect
6. #11745961C2semidirect
7. #11745954C2semidirect
29. #65849D3semidirect
71. #4991D5semidirect
391. C3×C5#1597semidirect
463. C5#71888semidirect
487. C3#10600495semidirect

Maximal subgroups

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

subgroupindex
C3×#658492
C5×#49912
#117485372
#117485162
#117463492
#117459612
#117459542
#106004953
#718885