Finite Group Databasebeta

← #14283185

Subgroups — #14283185

Order 1920.

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

normal subgroups only

This group has 588 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
1D5×#924C211yesmaximal, characteristic
2#11752414C211yesmaximal, characteristic
3C3×C4×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
4#11746503C212yesmaximal, complemented
5#11746502C212yesmaximal, complemented
6#10604500—31nomaximal, Hall
7C22×C3×C4×D5C2211yescharacteristic
8C2×D5×Dic6C411yescharacteristic, complemented
9C2×#6762—21no—
10C2×C3×C22⋊AGL(1,𝔽5)—21no—
11C2×C3×C4×AGL(1,𝔽5)—21no—
12#91813C411yescharacteristic, complemented
13C5×#924C411yescharacteristic, complemented
14#91574—21no—
15D5×#217—21no—
16D5×C4⋊Dic3C411yescharacteristic, complemented
17D5×Dic3⋊C4—21no—
18#91360C2211yescharacteristic
19#91359C2211yescharacteristic
20#91349—21no—
21#91232—21no—
22#91232C2212yes—
23C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
24#69445—51nomaximal, Hall
25D5×C22⋊Q8—31no—
26C4×C22⋊AGL(1,𝔽5)D311yescharacteristic
27#65755—31no—
28#64926—32no—
29#64869—32no—
30C23×C3×D5D411yescharacteristic
31C22×C3×AGL(1,𝔽5)—22no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C2×Dic30C2×C411yescharacteristic
34C2×C5×Dic6C2×C411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C2×C3×C4×D5—42no—
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5C2311yescharacteristic
41C2×#1204—21no—
42C2×D5×Dic3—21no—
43C2×D5×Dic3—21no—
44D5×Dic6—42no—
45#6762—42no—
46C2×C3⋊#170—22no—
47C3×C22⋊AGL(1,𝔽5)—24no—
48C3×C4×AGL(1,𝔽5)—42no—
49#6719—21no—
50C4⋊Dic15C2×C411yescharacteristic
51#6712—21no—
52C5×#217—21no—
53C5×C4⋊Dic3C2×C411yescharacteristic
54C5×Dic3⋊C4—21no—
55Dic3⋊Dic5—21no—
56#6669—21no—
57#6668—21no—
58#6665—21no—
59#6665—21no—
60C2×#924—51no—
61C3×C4×C22⋊C4—51no—
62#5207—51no—
63#4452—52no—
64#4452—52no—
65C2×Q8×D5—31no—
66C22×C4×D5C2×D311yescharacteristic
67C2×C22⋊AGL(1,𝔽5)—21no—
68C2×#704—61no—
69C2×C4×AGL(1,𝔽5)—21no—
70C5×C22⋊Q8—31no—
71#4092—31no—
72#4070—31no—
73#4043—31no—
74#4042—61no—
75D5×C4⋊C4—31no—
76D5×C4⋊C4—61no—
77D5×C22⋊C4—61no—
78#4024—61no—
79(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
80#4003—32no—
81#4003—61no—
82#1508—151noSylow
83C23×C3×C5C22⋊C411yescharacteristic
84C22×C3×D5—22no—
85C22×C3×D5—22no—
86C22×C3×D5—41no—
87C22×C3×D5C22⋊C411yescharacteristic
88C22×C3×D5C2×D411yescharacteristic
89C2×C3×AGL(1,𝔽5)—24no—
90C2×C3×AGL(1,𝔽5)—42no—
91C2×C3×AGL(1,𝔽5)—42no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—21no—
97Dic30—41no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3—21no—
100C5×Dic6—41no—
101C2×C3×Dic5—22no—
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C2×D411yescharacteristic
104C3×C4×D5—22no—
105C3×C4×D5—22no—
106C3×C4×D5—41no—
107C3×C4×D5—41no—
108#1204—42no—
109D5×Dic3—42no—
110D5×Dic3—42no—
111C3⋊#170—42no—
112C23×C3×C4—51no—
113C22×Dic6—51no—
114C2×C3×C22⋊C4—101no—
115C2×C3×C42—101no—
116C2×#217—101no—
117C2×C4⋊Dic3—51no—
118#924—51no—
119#924—51no—
120#924—51no—
121#924—101no—
122#924—101no—
123#924AGL(1,𝔽5)11yescharacteristic, complemented
124C2×Dic3⋊C4—101no—
125C2×#208—101no—
126C3×#95—52no—
127#830—52no—
128#830—101no—
129C23×D5#6711yescharacteristic
130C22×AGL(1,𝔽5)—22no—
131C2×C5×Q8—31no—
132C22×C4×C5C4×D311yescharacteristic
133C22×Dic5D1211yescharacteristic
134Q8×D5—122no—
135C2×C4×D5—42no—
136C2×C4×D5—61no—
137C2×C4×D5—61no—
138C2×C4×D5C4×D311yescharacteristic
139C2×C4×D5D1211yescharacteristic
140C2×C4×D5#6711yescharacteristic
141C2×C4×D5C22×D311yescharacteristic
142C2×Dic10—31no—
143C2×Dic10—61no—
144C22⋊AGL(1,𝔽5)—24no—
145#704—122no—
146C2×#170—62no—
147C4×AGL(1,𝔽5)—42no—
148C5×C4⋊C4—31no—
149C5×C4⋊C4—61no—
150C5×C22⋊C4—61no—
151C22⋊Dic5—61no—
152#685—61no—
153#685—61no—
154C4⋊Dic5—31no—
155C4⋊Dic5—61no—
156#683—61no—
157#683—61no—
158#683—61no—
159C2×C22⋊Q8—151no—
160#407—151no—
161C4×C22⋊C4—51no—
162#328—152no—
163#328—152no—
164C22×C3×C5—21no—
165C22×C3×C5—21no—
166C22×C3×C5—21no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C2×C3×D5—44no—
173C2×C3×D5#10412yes—
174C2×C3×D5#13712yes—
175C3×AGL(1,𝔽5)—44no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178Dic15—41no—
179Dic15—41no—
180C3×Dic5—21no—
181C3×Dic5#9912yes—
182C5×Dic3—41no—
183C5×Dic3—41no—
184C24×C3—51no—
185C22×C3×C4—51no—
186C22×C3×C4—51no—
187C22×C3×C4—51no—
188C22×C3×C4—51no—
189C22×C3×C4—51no—
190C22×C3×C4—102no—
191C22×C3×C4—202no—
192C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
193C22×Dic3—101no—
194C22×Dic3—101no—
195C2×Dic6—51no—
196C2×Dic6—101no—
197C2×Dic6—202no—
198C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
199C3×C22⋊C4—104no—
200C3×C42—202no—
201#217—21no—
202#217—101no—
203#217—101no—
204#217—101no—
205C4⋊Dic3—51no—
206C4⋊Dic3—101no—
207C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
208Dic3⋊C4—21no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212#208—202no—
213C2×C3⋊C8—102no—
214C23×C5(C2×D3)⋊C411yescharacteristic
215C22×D5—22no—
216C22×D5—22no—
217C22×D5—41no—
218C22×D5(C2×D3)⋊C411yescharacteristic
219C22×D5C2×#6711yescharacteristic
220C2×AGL(1,𝔽5)—24no—
221C2×AGL(1,𝔽5)—42no—
222C2×AGL(1,𝔽5)—42no—
223C5×Q8—121no—
224C2×C4×C5—41no—
225C2×C4×C5—61no—
226C2×C4×C5—61no—
227C2×C4×C5(C2×D3)⋊C411yescharacteristic
228C2×C4×C5C2×C4×D311yescharacteristic
229C2×Dic5—22no—
230C2×Dic5—61no—
231C2×Dic5—61no—
232C2×Dic5(C2×D3)⋊C411yescharacteristic
233C2×Dic5C2×D1211yescharacteristic
234C4×D5—22no—
235C4×D5—22no—
236C4×D5—41no—
237C4×D5—41no—
238C4×D5—122no—
239C4×D5—122no—
240Dic10—122no—
241Dic10—121no—
242#170—122no—
243C22×Q8—151no—
244C23×C4—51no—
245C2×M16—301no—
246C22⋊Q8—31no—
247C22⋊Q8—151no—
248C22⋊Q8—151no—
249C22⋊Q8—151no—
250C22⋊Q8—301no—
251C22⋊Q8—301no—
252C2×C4⋊C4—151no—
253C2×C4⋊C4—301no—
254C2×C22⋊C4—101no—
255C2×C22⋊C4—301no—
256C2×C42—101no—
257C22⋊C8—152no—
258C22⋊C8—301no—
259#95—52no—
260C2×C3×C5—41no—
261C2×C3×C5C2×#9911yescharacteristic
262C2×C3×C5#41911yescharacteristic
263C2×C3×C5C2×#10411yescharacteristic
264C3×D5—22no—
265C3×D5—22no—
266C23×C3—51no—
267C23×C3—51no—
268C23×C3—102no—
269C23×C3—102no—
270C23×C3—201no—
271C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
272C2×C3×C4—41no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—102no—
276C2×C3×C4—102no—
277C2×C3×C4—102no—
278C2×C3×C4—104no—
279C2×C3×C4—201no—
280C2×C3×C4—201no—
281C2×C3×C4—202no—
282C2×C3×C4—202no—
283C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
284C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—101no—
288C2×Dic3—101no—
289C2×Dic3—202no—
290C2×Dic3—202no—
291Dic6—41no—
292Dic6—202no—
293Dic6—201no—
294C3⋊C8—202no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5—21no—
298C22×C5C2×(C2×D3)⋊C411yescharacteristic
299C2×D5—21no—
300C2×D5—21no—
301C2×D5—21no—
302C2×D5—21no—
303C2×D5—44no—
304C2×D5#80512yes—
305C2×D5#95112yes—
306AGL(1,𝔽5)—44no—
307C4×C5—21no—
308C4×C5—21no—
309C4×C5—121no—
310C4×C5—121no—
311Dic5—21no—
312Dic5—121no—
313Dic5—121no—
314Dic5#80612yes—
315C24—51no—
316C2×Q8—31no—
317C2×Q8—151no—
318C2×Q8—301no—
319C2×Q8—602no—
320C22×C4—51no—
321C22×C4—51no—
322C22×C4—51no—
323C22×C4—51no—
324C22×C4—51no—
325C22×C4—102no—
326C22×C4—202no—
327C22×C4—301no—
328C22×C4—301no—
329C22×C4D3×AGL(1,𝔽5)11yescharacteristic
330M16—602no—
331C2×C8—302no—
332C4⋊C4—31no—
333C4⋊C4—61no—
334C4⋊C4—151no—
335C4⋊C4—301no—
336C4⋊C4—301no—
337C4⋊C4—301no—
338C4⋊C4—301no—
339C22⋊C4—61no—
340C22⋊C4—104no—
341C22⋊C4—301no—
342C22⋊C4—301no—
343C22⋊C4—301no—
344C42—202no—
345C3×C5#150811yescharacteristic, complemented, Hall
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—52no—
350C22×C3—52no—
351C22×C3—101no—
352C22×C3—101no—
353C22×C3—101no—
354C22×C3—101no—
355C22×C3—204no—
356C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—52no—
360C3×C4—101no—
361C3×C4—204no—
362Dic3—41no—
363Dic3—41no—
364Dic3—201no—
365Dic3—201no—
366C2×C5—41no—
367C2×C5C2×#80511yescharacteristic
368C2×C5C2×#80611yescharacteristic
369C2×C5#500411yescharacteristic
370D5—22no—
371D5—22no—
372C23—51no—
373C23—51no—
374C23—102no—
375C23—102no—
376C23—201no—
377C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
378Q8—121no—
379Q8—601no—
380Q8—602no—
381C2×C4—41no—
382C2×C4—51no—
383C2×C4—51no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—102no—
387C2×C4—102no—
388C2×C4—102no—
389C2×C4—104no—
390C2×C4—201no—
391C2×C4—201no—
392C2×C4—202no—
393C2×C4—202no—
394C2×C4—301no—
395C2×C4—301no—
396C2×C4—602no—
397C2×C4—602no—
398C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
399C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
400C8—602no—
401C2×C3—41no—
402C2×C3—102no—
403C2×C3—102no—
404C2×C3D5⋊#9911yescharacteristic
405C2×C3#6578211yescharacteristic
406C2×C3D5⋊#10411yescharacteristic
407C5#6944511yescharacteristic, complemented, Sylow
408C22—21no—
409C22—21no—
410C22—21no—
411C22—52no—
412C22—52no—
413C22—101no—
414C22—101no—
415C22—101no—
416C22—101no—
417C22—204no—
418C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
419C4—21no—
420C4—21no—
421C4—52no—
422C4—101no—
423C4—121no—
424C4—121no—
425C4—204no—
426C4—601no—
427C4—601no—
428C3#1060450011yescharacteristic, complemented, Sylow
429C2—41no—
430C2—102no—
431C2—102no—
432C2#1175171111yescharacteristic
433C2D5⋊#80511yescharacteristic
434C2D5⋊#80611yescharacteristic
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 radicalC23×C3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1508
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
4. #11746503C2semidirect
5. #11746502C2semidirect
8. C2×D5×Dic6C4semidirect
12. #91813C4semidirect
13. C5×#924C4semidirect
16. D5×C4⋊Dic3C4semidirect
123. #924AGL(1,𝔽5)semidirect
345. C3×C5#1508semidirect
407. C5#69445semidirect
428. C3#10604500semidirect

Maximal subgroups

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

subgroupindex
D5×#9242
#117524142
C3×C4×C22⋊AGL(1,𝔽5)2
#117465032
#117465022
#106045003
#694455