Finite Group Databasebeta

← #14288395

Subgroups — #14288395

Order 1920.

508 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 82 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#11754331C211yesmaximal, characteristic
2#11751068C211yesmaximal, characteristic, complemented
3C5×#4967C211yesmaximal, characteristic, complemented
4C3×#65269C211yesmaximal, characteristic, complemented
5#11745958C211yesmaximal, characteristic, complemented
6#11745956C211yesmaximal, characteristic, complemented
7#11745951C211yesmaximal, characteristic, complemented
8#10601960—31nomaximal, Hall
9C2×#6782—21no—
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11#91819C2211yescharacteristic
12C5×#930C2211yescharacteristic
13C2×C3×#683—21no—
14C2×C3×#683C2211yescharacteristic
15#91566—21no—
16#91420—21no—
17#91419—21no—
18#91417—21no—
19#91416—21no—
20#91114C2211yescharacteristic
21#91093—21no—
22#91091—21no—
23C5×#830C2211yescharacteristic
24C5×#809—21no—
25C5×#807—21no—
26C3×#3963—21no—
27C3×#3963C2211yescharacteristic
28#69712—51nomaximal, Hall
29#65931—31no—
30C5×#480—31no—
31#65269D311yescharacteristic, complemented
32#65256—31no—
33#64757—31no—
34#64690—31no—
35#64689—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39C2×D60D411yescharacteristic
40C2×C5×#67—21no—
41C2×C5×D12D411yescharacteristic
42C22×C3×Dic5—21no—
43C22×C3×Dic5D411yescharacteristic
44C22×C3×Dic5D411yescharacteristic
45C2×#1204—21no—
46C2×#1203—21no—
47C2×#1203—21no—
48C2×#1200—21no—
49#6782—42no—
50#6782—42no—
51C2×D3×Dic5—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54#6714—21no—
55C4⋊Dic15D411yescharacteristic
56C2×C3⋊#168—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×C4⋊Dic3D411yescharacteristic
59C2×C5×C3⋊C8—21no—
60C3×#683—21no—
61C3×#683—21no—
62C3×#683—42no—
63#6668—21no—
64#6667—21no—
65(C2×D3)⋊Dic5—21no—
66#5510—51no—
67C3×#398—51no—
68#4967—51no—
69#4967D511yescharacteristic, complemented
70#4528—51no—
71#4451—51no—
72#4451—51no—
73C2×#711—61no—
74C5×#121—31no—
75C2×C5×C4⋊C4C2×D311yescharacteristic
76#4085—61no—
77#4085—61no—
78#4076—31no—
79C2×#683—21no—
80C2×#683C2×D311yescharacteristic
81#4042—61no—
82#4030—61no—
83#4024—61no—
84C5×#107—61no—
85C5×#102—61no—
86C5×C22⋊C8—31no—
87#3963—21no—
88#3963C2×D311yescharacteristic
89C22⋊#168—31no—
90#3941—61no—
91#3939—61no—
92#1610—151noSylow
93C23×C3×C5C2×D411yescharacteristic
94C22×D15—21no—
95C22×C5×D3—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102#1220—41no—
103#1220—41no—
104C2×Dic15—21no—
105D60—41no—
106C5×#67—41no—
107C5×#67—41no—
108C2×C5×Dic3—21no—
109C5×D12—41no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5D812yes—
118#1204—42no—
119#1203—42no—
120#1203—81no—
121#1200—42no—
122D3×Dic5—42no—
123C3⋊#168—41no—
124C5×C3⋊C8—41no—
125C2×#235—101no—
126C2×C3×C4⋊C4—51no—
127C2×C3×C4⋊C4—101no—
128C2×C3×C4⋊C4C2×D511yescharacteristic
129#930—51no—
130#930—101no—
131#930C2×D511yescharacteristic
132#897—101no—
133#897—101no—
134#895—101no—
135#895—101no—
136C3×#95—51no—
137C3×#95—101no—
138#830—51no—
139#830C2×D511yescharacteristic
140#809—21no—
141#809—101no—
142#807—21no—
143#807—101no—
144C2×C5×D4—31no—
145C2×C5×D4—61no—
146C22×C4×C5—21no—
147C22×C4×C5C22×D311yescharacteristic
148C2×C22⋊D5—61no—
149C2×C22⋊D5—61no—
150C2×C22⋊D5—61no—
151C22×Dic5—21no—
152C22×Dic5—61no—
153C22×Dic5#6711yescharacteristic
154C22×Dic5#6711yescharacteristic
155#711—122no—
156#711—122no—
157C2×D20—31no—
158C2×C4×D5—61no—
159C2×Dic10—61no—
160C2×C5×C8—61no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—31no—
164C5×C22⋊C4—61no—
165C22⋊Dic5—61no—
166#685—61no—
167#685—61no—
168C4⋊Dic5—31no—
169#683—21no—
170#683—21no—
171#683—42no—
172#683—61no—
173C2×#168—61no—
174#537—151no—
175#480—31no—
176#480—151no—
177#398—51no—
178#327—151no—
179#327—151no—
180#324—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5#12011yescharacteristic
184C22×C3×C5C2×D811yescharacteristic
185C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
186C2×D15—41no—
187C2×D15—41no—
188C2×D15—41no—
189C2×C5×D3—41no—
190C2×C5×D3—41no—
191C2×C5×D3—41no—
192C3×C4×C5—21no—
193C3×C4×C5—21no—
194C3×C4×C5—81no—
195Dic15—41no—
196C3×Dic5—22no—
197C3×Dic5—42no—
198C3×Dic5—41no—
199C5×Dic3—41no—
200C22×C3×C4—21no—
201C22×C3×C4—51no—
202C22×C3×C4—51no—
203C22×C3×C4—101no—
204C22×C3×C4C22×D511yescharacteristic
205C2×#67—21no—
206C2×#67—101no—
207#235—202no—
208#235—202no—
209C2×D12—51no—
210C2×D12—101no—
211C2×D12—101no—
212C2×D12C22⋊D511yescharacteristic
213C2×C4×D3—101no—
214C2×C4×D3—101no—
215C2×Dic6—101no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—101no—
219C3×C4⋊C4—101no—
220C3×C4⋊C4—202no—
221(C2×D3)⋊C4—21no—
222(C2×D3)⋊C4—101no—
223(C2×D3)⋊C4—101no—
224(C2×D3)⋊C4—101no—
225C4⋊Dic3—51no—
226C4⋊Dic3—101no—
227C4⋊Dic3C22⋊D511yescharacteristic
228C2×C3⋊C8—21no—
229C2×C3⋊C8—101no—
230C23×C5—61no—
231C23×C5C2×#6711yescharacteristic
232C22×D5—61no—
233C5×D4—121no—
234C5×D4—121no—
235C5×D4—121no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—61no—
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5D3×D411yescharacteristic
243C22⋊D5—122no—
244C22⋊D5—121no—
245C22⋊D5—121no—
246C22⋊D5—241no—
247C2×Dic5—21no—
248C2×Dic5—21no—
249C2×Dic5—22no—
250C2×Dic5—21no—
251C2×Dic5—41no—
252C2×Dic5—41no—
253C2×Dic5—41no—
254C2×Dic5—61no—
255C2×Dic5—122no—
256C2×Dic5#21312yes—
257D20—121no—
258C4×D5—122no—
259Dic10—122no—
260C5×C8—121no—
261#168—121no—
262C2×#41—301no—
263C22⋊Q8—301no—
264C22⋊Q8—301no—
265#121—31no—
266#121—151no—
267#121—301no—
268#121—301no—
269#121—301no—
270C2×C4⋊C4—51no—
271C2×C4⋊C4—101no—
272C2×C4⋊C4D3×D511yescharacteristic
273#107—61no—
274#107—301no—
275#102—61no—
276#102—301no—
277C22⋊C8—31no—
278C22⋊C8—151no—
279#95—51no—
280#95—101no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5#44711yescharacteristic
284C2×C3×C5#45611yescharacteristic
285C2×C3×C5#45811yescharacteristic
286D15—81no—
287C5×D3—81no—
288C23×C3D4×D511yescharacteristic
289C22×D3—21no—
290C22×D3—101no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—52no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—102no—
299C2×C3×C4—101no—
300C2×C3×C4—201no—
301C2×C3×C4—201no—
302C2×C3×C4—201no—
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4C2×C22⋊D511yescharacteristic
305#67—41no—
306#67—41no—
307#67—201no—
308#67—201no—
309C2×Dic3—21no—
310C2×Dic3—101no—
311D12—41no—
312D12—201no—
313D12—202no—
314D12—401no—
315C4×D3—202no—
316C4×D3—202no—
317Dic6—202no—
318C3⋊C8—41no—
319C3⋊C8—201no—
320C22×C5—21no—
321C22×C5—21no—
322C22×C5—121no—
323C22×C5—121no—
324C22×C5—121no—
325C22×C5C2×#21311yescharacteristic
326C22×C5#93711yescharacteristic
327C22×C5#94911yescharacteristic
328C2×D5—121no—
329C2×D5—121no—
330C2×D5—121no—
331C4×C5—21no—
332C4×C5—21no—
333C4×C5—81no—
334C4×C5—121no—
335Dic5—22no—
336Dic5—42no—
337Dic5—41no—
338Dic5—121no—
339#41—602no—
340#41—602no—
341C2×Q8—301no—
342C2×D4—31no—
343C2×D4—61no—
344C2×D4—151no—
345C2×D4—301no—
346C2×D4—301no—
347C2×D4—301no—
348C22×C4—21no—
349C22×C4—51no—
350C22×C4—51no—
351C22×C4—101no—
352C22×C4—301no—
353C22×C4—301no—
354C22×C4C2×D3×D511yescharacteristic
355C2×C8—61no—
356C2×C8—301no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—31no—
360C4⋊C4—101no—
361C4⋊C4—101no—
362C4⋊C4—151no—
363C4⋊C4—202no—
364C4⋊C4—301no—
365C22⋊C4—61no—
366C22⋊C4—301no—
367C22⋊C4—301no—
368C22⋊C4—301no—
369C3×C5#161011yescharacteristic, complemented, Hall
370C22×C3—21no—
371C22×C3—21no—
372C22×C3D5×D811yescharacteristic
373C22×C3#405711yescharacteristic
374C22×C3#408311yescharacteristic
375C2×D3—41no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—201no—
379C2×D3—201no—
380C2×D3—201no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—81no—
384C3×C4—102no—
385C3×C4—202no—
386C3×C4—201no—
387Dic3—41no—
388Dic3—201no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—241no—
392C2×C5#503611yescharacteristic
393C2×C5#505311yescharacteristic
394C2×C5#509511yescharacteristic
395D5—241no—
396C23—61no—
397C23—301no—
398C23D5×#6711yescharacteristic
399Q8—602no—
400D4—121no—
401D4—121no—
402D4—121no—
403D4—601no—
404D4—602no—
405D4—601no—
406D4—601no—
407D4—1201no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—52no—
413C2×C4—61no—
414C2×C4—101no—
415C2×C4—101no—
416C2×C4—102no—
417C2×C4—101no—
418C2×C4—201no—
419C2×C4—201no—
420C2×C4—201no—
421C2×C4—301no—
422C2×C4—602no—
423C2×C4—602no—
424C2×C4D3×C22⋊D511yescharacteristic
425C2×C4#679011yescharacteristic
426C8—121no—
427C8—601no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3#6534211yescharacteristic
431C2×C3#6544511yescharacteristic
432C2×C3#6549411yescharacteristic
433D3—81no—
434D3—401no—
435C5#6971211yescharacteristic, complemented, Sylow
436C22—21no—
437C22—21no—
438C22—121no—
439C22—121no—
440C22—121no—
441C22—601no—
442C22—601no—
443C22—601no—
444C22D5×#21311yescharacteristic
445C22#9147811yescharacteristic
446C22#9157711yescharacteristic
447C4—21no—
448C4—21no—
449C4—81no—
450C4—102no—
451C4—121no—
452C4—202no—
453C4—201no—
454C4—601no—
455C3#1060196011yescharacteristic, complemented, Sylow
456C2—21no—
457C2—21no—
458C2—241no—
459C2—1201no—
460C2#1174893911yescharacteristic
461C2#1174915111yescharacteristic
462C2#1174941411yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radical#11754331C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1610
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
2. #11751068C2semidirect
3. C5×#4967C2semidirect
4. C3×#65269C2semidirect
5. #11745958C2semidirect
6. #11745956C2semidirect
7. #11745951C2semidirect
31. #65269D3semidirect
69. #4967D5semidirect
369. C3×C5#1610semidirect
435. C5#69712semidirect
455. C3#10601960semidirect

Maximal subgroups

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

subgroupindex
#117543312
#117510682
C5×#49672
C3×#652692
#117459582
#117459562
#117459512
#106019603
#697125