Finite Group Databasebeta

← #14288397

Subgroups — #14288397

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#11754357C211yesmaximal, characteristic
2#11751068C211yesmaximal, characteristic, complemented
3C5×#4983C211yesmaximal, characteristic, complemented
4C3×#65256C211yesmaximal, characteristic, complemented
5#11745959C211yesmaximal, characteristic, complemented
6#11745954C211yesmaximal, characteristic, complemented
7#11745952C211yesmaximal, characteristic, complemented
8#10600505—31nomaximal, Hall
9C2×#6779—21no—
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11#91819C2211yescharacteristic
12C2×C5×Dic3⋊C4—21no—
13C2×C5×Dic3⋊C4C2211yescharacteristic
14C3×#4076C2211yescharacteristic
15#91569—21no—
16#91459—21no—
17#91429—21no—
18#91422—21no—
19#91409—21no—
20#91114C2211yescharacteristic
21#91093—21no—
22#91091—21no—
23C5×C3⋊#95—21no—
24C5×C3⋊#95C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3941—21no—
27C3×#3939—21no—
28#71167—51nomaximal, Hall
29#65844—31no—
30C5×#398—31no—
31#65256—31no—
32#65256D311yescharacteristic, complemented
33#64748—31no—
34#64671—31no—
35#64671—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39C2×D60D411yescharacteristic
40C22×C5×Dic3—21no—
41C22×C5×Dic3D411yescharacteristic
42C22×C5×Dic3D411yescharacteristic
43C2×C3×C22⋊D5—21no—
44C2×C3×D20D411yescharacteristic
45C2×#1204—21no—
46C2×#1202—21no—
47C2×#1202—21no—
48C2×#1200—21no—
49#6779—42no—
50#6779—42no—
51C2×D5×Dic3—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54#6714—21no—
55C4⋊Dic15D411yescharacteristic
56C2×C3⋊#168—21no—
57C5×Dic3⋊C4—21no—
58C5×Dic3⋊C4—21no—
59C5×Dic3⋊C4—42no—
60C3×#685—21no—
61C3×C4⋊Dic5D411yescharacteristic
62C2×C3×#168—21no—
63Dic3⋊Dic5—21no—
64#6667—21no—
65#6665—21no—
66#5597—51no—
67C3×#480—51no—
68#4983D511yescharacteristic, complemented
69#4967—51no—
70#4537—51no—
71#4470—51no—
72#4469—51no—
73C2×#709—61no—
74C2×C5×C4⋊C4—31no—
75C2×C5×C4⋊C4—61no—
76C2×C5×C4⋊C4C2×D311yescharacteristic
77#4076—31no—
78#4076—61no—
79#4076C2×D311yescharacteristic
80#4043—61no—
81#4043—61no—
82#4041—61no—
83#4041—61no—
84C5×#95—31no—
85C5×#95—61no—
86C22⋊#168—31no—
87C22⋊#168C2×D311yescharacteristic
88#3941—21no—
89#3941—61no—
90#3939—21no—
91#3939—61no—
92#1610—151noSylow
93C23×C3×C5C2×D411yescharacteristic
94C22×D15—21no—
95C22×C3×D5—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—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—22no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3—41no—
113C2×C5×Dic3D812yes—
114C3×C22⋊D5—41no—
115C3×C22⋊D5—41no—
116C2×C3×Dic5—21no—
117C3×D20—41no—
118#1204—42no—
119#1202—42no—
120#1202—81no—
121#1200—42no—
122D5×Dic3—42no—
123C3⋊#168—41no—
124C3×#168—41no—
125C2×#237—101no—
126C3×#121—51no—
127C2×C3×C4⋊C4C2×D511yescharacteristic
128#939—101no—
129#939—101no—
130#930—51no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4C2×D511yescharacteristic
133#896—101no—
134#884—101no—
135#878—101no—
136C3×#107—101no—
137C3×#102—101no—
138C3×C22⋊C8—51no—
139C3⋊#95—21no—
140C3⋊#95C2×D511yescharacteristic
141#830—51no—
142#809—101no—
143#807—101no—
144C22×C4×C5—21no—
145C22×C4×C5—31no—
146C22×C4×C5—31no—
147C22×C4×C5—61no—
148C22×C4×C5C22×D311yescharacteristic
149C2×C22⋊D5—21no—
150C2×C22⋊D5—61no—
151#709—122no—
152#709—122no—
153C2×D20—31no—
154C2×D20—61no—
155C2×D20—61no—
156C2×D20#6711yescharacteristic
157C2×C4×D5—61no—
158C2×C4×D5—61no—
159C2×Dic10—61no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—61no—
163C5×C4⋊C4—61no—
164C5×C4⋊C4—122no—
165#685—21no—
166#685—61no—
167#685—61no—
168#685—61no—
169C4⋊Dic5—31no—
170C4⋊Dic5—61no—
171C4⋊Dic5#6711yescharacteristic
172C2×#168—21no—
173C2×#168—61no—
174#537—151no—
175#480—51no—
176#480—151no—
177#398—31no—
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×C3×D5—41no—
190C2×C3×D5—41no—
191C2×C3×D5—41no—
192C3×C4×C5—21no—
193C3×C4×C5—21no—
194C3×C4×C5—81no—
195Dic15—41no—
196C3×Dic5—41no—
197C5×Dic3—22no—
198C5×Dic3—42no—
199C5×Dic3—41no—
200C2×C3×D4—51no—
201C2×C3×D4—101no—
202C22×C3×C4—21no—
203C22×C3×C4C22×D511yescharacteristic
204C2×#67—101no—
205C2×#67—101no—
206C2×#67—101no—
207C22×Dic3—21no—
208C22×Dic3—101no—
209C22×Dic3C22⋊D511yescharacteristic
210C22×Dic3C22⋊D511yescharacteristic
211#237—202no—
212#237—202no—
213C2×D12—51no—
214C2×C4×D3—101no—
215C2×Dic6—101no—
216C2×C3×C8—101no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—51no—
220C3×C22⋊C4—101no—
221#217—101no—
222(C2×D3)⋊C4—101no—
223(C2×D3)⋊C4—101no—
224C4⋊Dic3—51no—
225Dic3⋊C4—21no—
226Dic3⋊C4—21no—
227Dic3⋊C4—42no—
228Dic3⋊C4—101no—
229C2×C3⋊C8—101no—
230C23×C5D3×D411yescharacteristic
231C22×D5—21no—
232C22×D5—61no—
233C2×C4×C5—32no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—61no—
239C2×C4×C5—61no—
240C2×C4×C5—62no—
241C2×C4×C5—61no—
242C2×C4×C5—121no—
243C2×C4×C5—121no—
244C2×C4×C5—121no—
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C22⋊D5—41no—
248C22⋊D5—41no—
249C22⋊D5—121no—
250C22⋊D5—121no—
251C2×Dic5—21no—
252C2×Dic5—61no—
253D20—41no—
254D20—121no—
255D20—122no—
256D20—241no—
257C4×D5—122no—
258C4×D5—122no—
259Dic10—122no—
260#168—41no—
261#168—121no—
262C2×#41—301no—
263C22⋊Q8—301no—
264C22⋊Q8—301no—
265#121—51no—
266#121—151no—
267#121—301no—
268#121—301no—
269#121—301no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—61no—
272C2×C4⋊C4D3×D511yescharacteristic
273#107—101no—
274#107—301no—
275#102—101no—
276#102—301no—
277C22⋊C8—51no—
278C22⋊C8—151no—
279#95—31no—
280#95—61no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5#44711yescharacteristic
284C2×C3×C5#45611yescharacteristic
285C2×C3×C5#45811yescharacteristic
286D15—81no—
287C3×D5—81no—
288C23×C3—101no—
289C23×C3C2×C22⋊D511yescharacteristic
290C22×D3—101no—
291C3×D4—201no—
292C3×D4—201no—
293C3×D4—201no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—101no—
299C2×C3×C4D4×D511yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301#67—202no—
302#67—201no—
303#67—201no—
304#67—401no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—22no—
308C2×Dic3—21no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—101no—
313C2×Dic3—202no—
314C2×Dic3#68612yes—
315D12—201no—
316C4×D3—202no—
317Dic6—202no—
318C3×C8—201no—
319C3⋊C8—201no—
320C22×C5—21no—
321C22×C5—21no—
322C22×C5D3×D811yescharacteristic
323C22×C5#91111yescharacteristic
324C22×C5#93711yescharacteristic
325C2×D5—41no—
326C2×D5—41no—
327C2×D5—41no—
328C2×D5—121no—
329C2×D5—121no—
330C2×D5—121no—
331C4×C5—21no—
332C4×C5—21no—
333C4×C5—62no—
334C4×C5—81no—
335C4×C5—122no—
336C4×C5—121no—
337Dic5—41no—
338Dic5—121no—
339#41—602no—
340#41—602no—
341C2×Q8—301no—
342C2×D4—51no—
343C2×D4—101no—
344C2×D4—151no—
345C2×D4—301no—
346C2×D4—301no—
347C2×D4—301no—
348C22×C4—21no—
349C22×C4—31no—
350C22×C4—31no—
351C22×C4—61no—
352C22×C4—301no—
353C22×C4—301no—
354C22×C4C2×D3×D511yescharacteristic
355C2×C8—101no—
356C2×C8—301no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—51no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—122no—
363C4⋊C4—151no—
364C4⋊C4—301no—
365C22⋊C4—101no—
366C22⋊C4—301no—
367C22⋊C4—301no—
368C22⋊C4—301no—
369C3×C5#161011yescharacteristic, complemented, Hall
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—201no—
373C22×C3—201no—
374C22×C3—201no—
375C22×C3C2×#68611yescharacteristic
376C22×C3#408311yescharacteristic
377C22×C3#409511yescharacteristic
378C2×D3—201no—
379C2×D3—201no—
380C2×D3—201no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—81no—
384C3×C4—201no—
385Dic3—22no—
386Dic3—42no—
387Dic3—41no—
388Dic3—201no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5#505311yescharacteristic
392C2×C5#515611yescharacteristic
393C2×C5#520511yescharacteristic
394D5—81no—
395D5—241no—
396C23—101no—
397C23—301no—
398C23D3×C22⋊D511yescharacteristic
399Q8—602no—
400D4—201no—
401D4—201no—
402D4—201no—
403D4—601no—
404D4—602no—
405D4—601no—
406D4—601no—
407D4—1201no—
408C2×C4—32no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—62no—
416C2×C4—61no—
417C2×C4—101no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—301no—
422C2×C4—602no—
423C2×C4—602no—
424C2×C4D5×#6711yescharacteristic
425C2×C4#679011yescharacteristic
426C8—201no—
427C8—601no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—401no—
431C2×C3#6532511yescharacteristic
432C2×C3#6534211yescharacteristic
433C2×C3#6538411yescharacteristic
434D3—401no—
435C5#7116711yescharacteristic, complemented, Sylow
436C22—21no—
437C22—21no—
438C22—201no—
439C22—201no—
440C22—201no—
441C22—601no—
442C22—601no—
443C22—601no—
444C22D3×#68611yescharacteristic
445C22#9148011yescharacteristic
446C22#9157711yescharacteristic
447C4—21no—
448C4—21no—
449C4—62no—
450C4—81no—
451C4—122no—
452C4—121no—
453C4—201no—
454C4—601no—
455C3#1060050511yescharacteristic, complemented, Sylow
456C2—21no—
457C2—21no—
458C2—401no—
459C2—1201no—
460C2#1174893911yescharacteristic
461C2#1174915211yescharacteristic
462C2#1174941311yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radical#11754357C2
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×#4983C2semidirect
4. C3×#65256C2semidirect
5. #11745959C2semidirect
6. #11745954C2semidirect
7. #11745952C2semidirect
32. #65256D3semidirect
68. #4983D5semidirect
369. C3×C5#1610semidirect
435. C5#71167semidirect
455. C3#10600505semidirect

Maximal subgroups

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

subgroupindex
#117543572
#117510682
C5×#49832
C3×#652562
#117459592
#117459542
#117459522
#106005053
#711675