Finite Group Databasebeta

← #14283454

Subgroups — #14283454

Order 1920.

572 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 98 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#11754563C211yesmaximal, characteristic
2#11752415C211yesmaximal, characteristic, complemented
3C3×#65765C211yesmaximal, characteristic, complemented
4#11746502C212yesmaximal, complemented
5#11746496C212yesmaximal, complemented
6#10604991—31nomaximal, Hall
7C2×C5×#235C411yescharacteristic, complemented
8C22×C3×C4×D5C2211yescharacteristic
9C2×#6758—21no—
10C2×C3×C22⋊AGL(1,𝔽5)—21no—
11C2×C3×C4⋊AGL(1,𝔽5)—21no—
12#91815C411yescharacteristic, complemented
13#91563—21no—
14#91539—21no—
15#91449C411yescharacteristic, complemented
16#91449C2211yescharacteristic
17C4×#1201—21no—
18C4×#1201—21no—
19#91359C411yescharacteristic, complemented
20#91359C2211yescharacteristic
21#91241—21no—
22#91232C2212yes—
23C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
24#69508—51nomaximal, Hall
25#66162—31no—
26#65765D311yescharacteristic, complemented
27#65756—31no—
28#64926—32no—
29#64920—32no—
30C23×C3×D5D411yescharacteristic
31C22×C3×AGL(1,𝔽5)—22no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C2×C5×#67—21no—
34C5×#235—42no—
35C2×C5×D12C2×C411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6C2×C411yescharacteristic
38C22×C3×Dic5D411yescharacteristic
39C2×C3×C4×D5—42no—
40C2×C3×C4×D5C2×C411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5C2311yescharacteristic
44C2×#1201—21no—
45C2×#1201—21no—
46C2×C3⋊#170—22no—
47#6758—42no—
48C3×C22⋊AGL(1,𝔽5)—42no—
49C3×C4⋊AGL(1,𝔽5)—42no—
50#6719—21no—
51C4⋊Dic15C2×C411yescharacteristic
52C4⋊Dic15C2×C411yescharacteristic
53C4×Dic15—21no—
54#6669—21no—
55#6669—21no—
56(C2×D3)⋊Dic5—21no—
57(C2×D3)⋊Dic5—21no—
58#6665—21no—
59#6665—21no—
60#5791—51no—
61C3×#380—51no—
62#5207—51no—
63#4452—52no—
64#4451—52no—
65C2×C5×#41—31no—
66C22×C4×D5C2×D311yescharacteristic
67C2×C22⋊AGL(1,𝔽5)—21no—
68C2×C4⋊AGL(1,𝔽5)—21no—
69C2×#700—61no—
70#4092—31no—
71#4092—31no—
72#4084—31no—
73#4084—31no—
74#4083—61no—
75#4081—61no—
76C4×C22⋊D5—61no—
77C4×C22⋊D5—61no—
78#4072—31no—
79C22⋊#170—61no—
80(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
81#4003—32no—
82#1513—151noSylow
83C23×C3×C5C22⋊C411yescharacteristic
84C22×C5×D3—21no—
85C22×C3×D5—21no—
86C22×C3×D5—21no—
87C22×C3×D5—41no—
88C22×C3×D5—41no—
89C22×C3×D5C22⋊C411yescharacteristic
90C22×C3×D5C2×D411yescharacteristic
91C2×C3×AGL(1,𝔽5)—42no—
92C2×C3×AGL(1,𝔽5)—42no—
93C2×C3×AGL(1,𝔽5)—42no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5C22⋊C411yescharacteristic
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15—21no—
99C5×#67—42no—
100C2×C5×Dic3—21no—
101C5×D12—41no—
102C4×C5×D3—42no—
103C5×Dic6—41no—
104C2×C3×Dic5—41no—
105C2×C3×Dic5C22⋊C411yescharacteristic
106C2×C3×Dic5C2×D411yescharacteristic
107C3×C4×D5—22no—
108C3×C4×D5—22no—
109C3×C4×D5—41no—
110C3×C4×D5—41no—
111#1201—42no—
112#1201—41no—
113#1201—41no—
114C3⋊#170—42no—
115C23×C3×C4—51no—
116C2×#235AGL(1,𝔽5)11yescharacteristic, complemented
117C2×C3×C4⋊C4—101no—
118C2×C3×C22⋊C4—101no—
119#953—101no—
120#930—51no—
121#930—51no—
122#929—101no—
123C4×#67—101no—
124C4×#67—101no—
125#926—51no—
126#924—51no—
127#924—51no—
128C2×#208—101no—
129C3×#95—52no—
130#830—52no—
131#830—101no—
132C23×D5#6711yescharacteristic
133C22×AGL(1,𝔽5)—22no—
134C5×#41—122no—
135C2×C5×Q8—31no—
136C2×C5×D4—31no—
137C2×C5×D4—61no—
138C22×C4×C5—61no—
139C22×C4×C5C4×D311yescharacteristic
140C2×C22⋊D5—61no—
141C2×C22⋊D5—61no—
142C22×Dic5D1211yescharacteristic
143C2×C4×D5—42no—
144C2×C4×D5C4×D311yescharacteristic
145C2×C4×D5D1211yescharacteristic
146C2×C4×D5#6711yescharacteristic
147C2×C4×D5C22×D311yescharacteristic
148C22⋊AGL(1,𝔽5)—42no—
149C2×#170—62no—
150C4⋊AGL(1,𝔽5)—42no—
151#700—122no—
152C22⋊Dic5—61no—
153C22⋊Dic5—61no—
154C22⋊Dic5—61no—
155#685—61no—
156#685—61no—
157C4⋊Dic5—31no—
158C4⋊Dic5—31no—
159#683—61no—
160#683—61no—
161C4×Dic5—61no—
162#525—151no—
163#407—151no—
164#380—51no—
165#328—152no—
166#327—152no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×C5×D3—41no—
172C2×C5×D3—41no—
173C2×C5×D3—41no—
174C2×C3×D5—21no—
175C2×C3×D5—21no—
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5—21no—
179C2×C3×D5—42no—
180C2×C3×D5—42no—
181C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
182C2×C3×D5#13711yescharacteristic
183C3×AGL(1,𝔽5)—82no—
184C3×C4×C5—21no—
185C3×C4×C5#9912yes—
186Dic15—41no—
187Dic15—41no—
188C3×Dic5—21no—
189C3×Dic5—21no—
190C5×Dic3—41no—
191C24×C3—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4—51no—
197C22×C3×C4—102no—
198C22×C3×C4—202no—
199C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
200C2×#67—21no—
201C2×#67—101no—
202C2×#67—101no—
203#235—42no—
204C2×D12C2×AGL(1,𝔽5)11yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
207C3×C4⋊C4—202no—
208C3×C22⋊C4—202no—
209#217—101no—
210#217—101no—
211#217—101no—
212(C2×D3)⋊C4—101no—
213(C2×D3)⋊C4—101no—
214C4⋊Dic3—51no—
215C4⋊Dic3—51no—
216Dic3⋊C4—101no—
217Dic3⋊C4—101no—
218C4×Dic3—101no—
219#208—202no—
220C2×C3⋊C8—102no—
221C23×C5—61no—
222C23×C5(C2×D3)⋊C411yescharacteristic
223C22×D5—21no—
224C22×D5—21no—
225C22×D5—41no—
226C22×D5—41no—
227C22×D5(C2×D3)⋊C411yescharacteristic
228C22×D5C2×#6711yescharacteristic
229C2×AGL(1,𝔽5)—42no—
230C2×AGL(1,𝔽5)—42no—
231C2×AGL(1,𝔽5)—42no—
232C5×Q8—121no—
233C5×D4—121no—
234C5×D4—122no—
235C2×C4×C5—22no—
236C2×C4×C5—61no—
237C2×C4×C5—122no—
238C2×C4×C5(C2×D3)⋊C411yescharacteristic
239C2×C4×C5C2×C4×D311yescharacteristic
240C22⋊D5—122no—
241C22⋊D5—121no—
242C22⋊D5—121no—
243C2×Dic5—41no—
244C2×Dic5—61no—
245C2×Dic5—61no—
246C2×Dic5(C2×D3)⋊C411yescharacteristic
247C2×Dic5C2×D1211yescharacteristic
248C4×D5—22no—
249C4×D5—22no—
250C4×D5—41no—
251C4×D5—41no—
252#170—122no—
253C2×#41—31no—
254C23×C4—51no—
255C2×M16—301no—
256#123—301no—
257C22⋊Q8—151no—
258C22⋊Q8—151no—
259#121—151no—
260#121—151no—
261#120—301no—
262C4×D4—301no—
263C4×D4—301no—
264#117—151no—
265C2×C4⋊C4—101no—
266C2×C22⋊C4—101no—
267C22⋊C8—152no—
268C22⋊C8—301no—
269#95—52no—
270C2×C3×C5—41no—
271C2×C3×C5C2×#9911yescharacteristic
272C2×C3×C5#41711yescharacteristic
273C2×C3×C5#42111yescharacteristic
274C3×D5—21no—
275C3×D5—21no—
276C3×D5—41no—
277C5×D3—81no—
278C23×C3—51no—
279C23×C3—51no—
280C23×C3—101no—
281C23×C3—101no—
282C23×C3—201no—
283C23×C3—201no—
284C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
285C22×D3—21no—
286C2×C3×C4—22no—
287C2×C3×C4—51no—
288C2×C3×C4—51no—
289C2×C3×C4—102no—
290C2×C3×C4—102no—
291C2×C3×C4—201no—
292C2×C3×C4—201no—
293C2×C3×C4—201no—
294C2×C3×C4—202no—
295C2×C3×C4—202no—
296C2×C3×C4—202no—
297C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
298C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
299#67—42no—
300#67—201no—
301#67—201no—
302#67—202no—
303C2×Dic3—21no—
304C2×Dic3—101no—
305C2×Dic3—101no—
306D12—41no—
307C4×D3—42no—
308Dic6—41no—
309C3⋊C8—202no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—121no—
314C22×C5—121no—
315C22×C5—121no—
316C22×C5C2×(C2×D3)⋊C411yescharacteristic
317C2×D5—21no—
318C2×D5—21no—
319C2×D5—21no—
320C2×D5—21no—
321C2×D5—21no—
322C2×D5—42no—
323C2×D5—42no—
324C2×D5#93211yescharacteristic
325C2×D5#94211yescharacteristic
326AGL(1,𝔽5)—82no—
327C4×C5—21no—
328C4×C5—121no—
329C4×C5#80612yes—
330Dic5—21no—
331Dic5—21no—
332Dic5—121no—
333Dic5—121no—
334C24—51no—
335#41—122no—
336C2×Q8—31no—
337C2×D4—31no—
338C2×D4—61no—
339C2×D4—301no—
340C2×D4—301no—
341C22×C4—51no—
342C22×C4—51no—
343C22×C4—51no—
344C22×C4—51no—
345C22×C4—51no—
346C22×C4—61no—
347C22×C4—102no—
348C22×C4—202no—
349C22×C4D3×AGL(1,𝔽5)11yescharacteristic
350M16—602no—
351C2×C8—302no—
352C4⋊C4—151no—
353C4⋊C4—151no—
354C4⋊C4—202no—
355C4⋊C4—301no—
356C4⋊C4—301no—
357C22⋊C4—202no—
358C22⋊C4—301no—
359C22⋊C4—301no—
360C22⋊C4—301no—
361C22⋊C4—301no—
362C22⋊C4—301no—
363C42—301no—
364C3×C5#151311yescharacteristic, complemented, Hall
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—51no—
369C22×C3—51no—
370C22×C3—101no—
371C22×C3—101no—
372C22×C3—101no—
373C22×C3—101no—
374C22×C3—101no—
375C22×C3—202no—
376C22×C3—202no—
377C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—41no—
381C3×C4—21no—
382C3×C4—101no—
383C3×C4—101no—
384C3×C4—402no—
385C3×C4#401112yes—
386Dic3—41no—
387Dic3—201no—
388Dic3—201no—
389C2×C5—41no—
390C2×C5—241no—
391C2×C5C2×#80611yescharacteristic
392C2×C5#496611yescharacteristic
393C2×C5#500511yescharacteristic
394D5—21no—
395D5—21no—
396D5—41no—
397C23—51no—
398C23—51no—
399C23—61no—
400C23—101no—
401C23—101no—
402C23—201no—
403C23—201no—
404C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
405Q8—121no—
406D4—121no—
407D4—122no—
408D4—601no—
409D4—601no—
410D4—602no—
411C2×C4—22no—
412C2×C4—51no—
413C2×C4—51no—
414C2×C4—61no—
415C2×C4—102no—
416C2×C4—102no—
417C2×C4—122no—
418C2×C4—201no—
419C2×C4—201no—
420C2×C4—201no—
421C2×C4—202no—
422C2×C4—202no—
423C2×C4—202no—
424C2×C4—301no—
425C2×C4—301no—
426C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
427C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
428C8—602no—
429C2×C3—41no—
430C2×C3—101no—
431C2×C3—101no—
432C2×C3—201no—
433C2×C3#6579311yescharacteristic
434C2×C3#6579511yescharacteristic
435C2×C3C2×#401111yescharacteristic
436D3—81no—
437C5#6950811yescharacteristic, complemented, Sylow
438C22—21no—
439C22—21no—
440C22—21no—
441C22—51no—
442C22—51no—
443C22—101no—
444C22—101no—
445C22—101no—
446C22—101no—
447C22—101no—
448C22—121no—
449C22—121no—
450C22—121no—
451C22—202no—
452C22—202no—
453C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
454C4—21no—
455C4—101no—
456C4—101no—
457C4—121no—
458C4—402no—
459C4—601no—
460C4—601no—
461C4#9117212yes—
462C3#1060499111yescharacteristic, complemented, Sylow
463C2—41no—
464C2—101no—
465C2—101no—
466C2—201no—
467C2—241no—
468C2#1175170511yescharacteristic
469C2#1175172011yescharacteristic
470C2C2×#9117211yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#11754563C2
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1513
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752415C2semidirect
3. C3×#65765C2semidirect
4. #11746502C2semidirect
5. #11746496C2semidirect
7. C2×C5×#235C4semidirect
12. #91815C4semidirect
15. #91449C4semidirect
19. #91359C4semidirect
26. #65765D3semidirect
116. C2×#235AGL(1,𝔽5)semidirect
364. C3×C5#1513semidirect
437. C5#69508semidirect
462. C3#10604991semidirect

Maximal subgroups

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

subgroupindex
#117545632
#117524152
C3×#657652
#117465022
#117464962
#106049913
#695085