Finite Group Databasebeta

← #14297800

Subgroups — #14297800

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D5×Dic6C211yesmaximal, characteristic
2D5⋊(C4⋊(C3⋊C8))C211yesmaximal, characteristic
3C3×#65689C211yesmaximal, characteristic
4C2×#91153C212yesmaximal
5#11746528C212yesmaximal
6#10604452—31nomaximal, Hall
7C2×D5×Dic6C2211yescharacteristic
8C2×D5⋊(C3⋊C8)C2212yes—
9C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
10C4×Dic30C411yescharacteristic, complemented
11C4×C5×Dic6C411yescharacteristic, complemented
12C3×C42×D5C2211yescharacteristic
13C4×#1204—21no—
14D5×C4⋊Dic3C2211yescharacteristic
15D5×Dic3⋊C4—21no—
16C4×D5×Dic3—21no—
17#91333C411yescharacteristic, complemented
18Dic5×Dic6C411yescharacteristic, complemented
19#91323—21no—
20#91233—21no—
21C4⋊(C3⋊#170)—21no—
22C3×(C2×AGL(1,𝔽5))⋊C4—21no—
23C3×(C2×AGL(1,𝔽5))⋊C4—21no—
24#91153—24no—
25#69559—51nomaximal, Hall
26C4×Q8×D5—31no—
27C2×#4009—32no—
28#65689D311yescharacteristic
29D5⋊(C4⋊C8)—31no—
30#64874—32no—
31C22×C3×AGL(1,𝔽5)—22no—
32C2×Dic30C2×C411yescharacteristic
33C2×C5×Dic6C2×C411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×C3×C4×D5C2311yescharacteristic
37C2×#1204—21no—
38C2×D5×Dic3—21no—
39C2×D5×Dic3—21no—
40D5×Dic6—21no—
41D5×Dic6—21no—
42D5×Dic6D412yes—
43D5×Dic6Q812yes—
44C2×C3⋊#170—22no—
45D5⋊(C3⋊C8)—22no—
46D5⋊(C3⋊C8)—22no—
47C3×C4⋊AGL(1,𝔽5)—22no—
48C3×C4⋊AGL(1,𝔽5)—22no—
49C3×C42×C5C2×C411yescharacteristic
50C4⋊Dic15C2×C411yescharacteristic
51#6712—21no—
52C4×Dic15—21no—
53C5×C4⋊Dic3C2×C411yescharacteristic
54C5×Dic3⋊C4—21no—
55C4×C5×Dic3—21no—
56C3×C4×Dic5C2×C411yescharacteristic
57C3×C4×Dic5D411yescharacteristic
58C3×C4×Dic5D411yescharacteristic
59Dic3⋊Dic5—21no—
60#6669—21no—
61#6668—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5—21no—
64C2×C4×Dic6—51no—
65C3×#382—51no—
66C2×#810—52no—
67C2×C4⋊(C3⋊C8)—51no—
68#4529—52no—
69C2×Q8×D5—31no—
70C2×C4⋊AGL(1,𝔽5)C2×D312yes—
71C2×D5⋊C8—32no—
72C4×C5×Q8—31no—
73Q8×Dic5—31no—
74D5×C4⋊C4—31no—
75D5×C4⋊C4—61no—
76#4033—31no—
77#4033—61no—
78C42×D5—61no—
79C42×D5C2×D311yescharacteristic
80C4×Dic10—31no—
81C4×Dic10—61no—
82#4009—64no—
83(C2×AGL(1,𝔽5))⋊C4—21no—
84(C2×AGL(1,𝔽5))⋊C4—21no—
85#4004—61no—
86C4⋊#170—61no—
87#1805—151noSylow
88C22×C3×D5C2×D411yescharacteristic
89C2×C3×AGL(1,𝔽5)—42no—
90C2×C3×AGL(1,𝔽5)—42no—
91C2×C3×AGL(1,𝔽5)—42no—
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—21no—
97Dic30—21no—
98Dic30C4⋊C412yes—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—21no—
101C5×Dic6—21no—
102C5×Dic6C4⋊C412yes—
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C2×D411yescharacteristic
106C3×C4×D5—22no—
107C3×C4×D5—22no—
108C3×C4×D5C2×D411yescharacteristic
109C3×C4×D5C2×Q811yescharacteristic
110C3×C4×D5#4111yescharacteristic
111C3×C4×D5#4111yescharacteristic
112#1204—22no—
113#1204—22no—
114D5×Dic3—22no—
115D5×Dic3—22no—
116D5×Dic3—42no—
117C3⋊#170—42no—
118C22×Dic6—51no—
119C2×C3×C4⋊C4—52no—
120C2×C3×C42—51no—
121C2×C4⋊Dic3—51no—
122C2×Dic3⋊C4—101no—
123C2×C4×Dic3—101no—
124C22×C3⋊C8—52no—
125C4×Dic6—51no—
126C4×Dic6—51no—
127C4×Dic6—51no—
128C4×Dic6—101no—
129C4×Dic6—101no—
130C4×Dic6AGL(1,𝔽5)11yescharacteristic, complemented
131C3×#95—101no—
132C3×#95—101no—
133#810—104no—
134C4⋊(C3⋊C8)—101no—
135C4⋊(C3⋊C8)—101no—
136C22×AGL(1,𝔽5)—22no—
137C2×C5×Q8—31no—
138Q8×D5—32no—
139Q8×D5—32no—
140Q8×D5—61no—
141Q8×D5—61no—
142C2×C4×D5—61no—
143C2×C4×D5—61no—
144C2×C4×D5#6711yescharacteristic
145C2×C4×D5#6711yescharacteristic
146C2×C4×D5C22×D311yescharacteristic
147C2×Dic10—31no—
148C2×Dic10—61no—
149C2×#170—62no—
150C4⋊AGL(1,𝔽5)—22no—
151C4⋊AGL(1,𝔽5)—22no—
152D5⋊C8—62no—
153D5⋊C8—62no—
154C5×C4⋊C4—31no—
155C5×C4⋊C4—61no—
156C42×C5—61no—
157C42×C5C4×D311yescharacteristic
158C4⋊Dic5—31no—
159C4⋊Dic5—61no—
160#683—61no—
161#683—61no—
162#683—61no—
163C4×Dic5—61no—
164C4×Dic5—61no—
165C4×Dic5—61no—
166C4×Dic5C4×D311yescharacteristic
167C4×Dic5D1211yescharacteristic
168C4×Dic5D1211yescharacteristic
169C2×C4×Q8—151no—
170C2×C4⋊C8—151no—
171C2×#103—152no—
172#382—51no—
173#340—152no—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C2×C3×D5#12111yescharacteristic
176C2×C3×D5C22⋊Q811yescharacteristic
177C2×C3×D5#13512yes—
178C2×C3×D5#13712yes—
179C3×AGL(1,𝔽5)—82no—
180C3×C4×C5—21no—
181C3×C4×C5—21no—
182C3×C4×C5C2×C4⋊C411yescharacteristic
183C3×C4×C5#11711yescharacteristic
184Dic15—22no—
185Dic15—41no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5#12111yescharacteristic
189C3×Dic5C22⋊Q811yescharacteristic
190C5×Dic3—22no—
191C5×Dic3—41no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4—102no—
196C22×Dic3—101no—
197C22×Dic3—101no—
198C2×Dic6—51no—
199C2×Dic6—52no—
200C2×Dic6—52no—
201C2×Dic6—101no—
202C2×Dic6—101no—
203C2×Dic6—101no—
204C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
205C3×C4⋊C4—102no—
206C3×C4⋊C4—102no—
207C3×C42—51no—
208C3×C42—51no—
209C3×C42—51no—
210C3×C42C2×AGL(1,𝔽5)11yescharacteristic
211C4⋊Dic3—51no—
212C4⋊Dic3—101no—
213C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
214Dic3⋊C4—21no—
215Dic3⋊C4—101no—
216Dic3⋊C4—101no—
217Dic3⋊C4—101no—
218C4×Dic3—21no—
219C4×Dic3—101no—
220C4×Dic3—101no—
221C4×Dic3—101no—
222C2×C3⋊C8—102no—
223C2×C3⋊C8—102no—
224C2×C3⋊C8—102no—
225C22×D5C2×#6711yescharacteristic
226C2×AGL(1,𝔽5)—42no—
227C2×AGL(1,𝔽5)—42no—
228C2×AGL(1,𝔽5)—42no—
229C5×Q8—32no—
230C5×Q8—61no—
231C2×C4×C5—61no—
232C2×C4×C5—61no—
233C2×C4×C5(C2×D3)⋊C411yescharacteristic
234C2×C4×C5(C2×D3)⋊C411yescharacteristic
235C2×C4×C5C2×C4×D311yescharacteristic
236C2×Dic5—61no—
237C2×Dic5—61no—
238C2×Dic5(C2×D3)⋊C411yescharacteristic
239C2×Dic5(C2×D3)⋊C411yescharacteristic
240C2×Dic5C2×D1211yescharacteristic
241C4×D5—22no—
242C4×D5—22no—
243C4×D5—62no—
244C4×D5—62no—
245C4×D5—122no—
246C4×D5D3×D411yescharacteristic
247C4×D5#23711yescharacteristic
248C4×D5D3×Q811yescharacteristic
249C4×D5#23911yescharacteristic
250Dic10—32no—
251Dic10—61no—
252Dic10—62no—
253Dic10—62no—
254#170—122no—
255C22×Q8—151no—
256C22×C8—152no—
257C4×Q8—31no—
258C4×Q8—151no—
259C4×Q8—151no—
260C4×Q8—151no—
261C4×Q8—301no—
262C4×Q8—301no—
263C2×C4⋊C4—52no—
264C2×C4⋊C4—151no—
265C2×C4⋊C4—301no—
266C2×C42—51no—
267C2×C42—301no—
268C4⋊C8—301no—
269C4⋊C8—301no—
270#103—304no—
271#95—101no—
272#95—101no—
273C2×C3×C5#38011yescharacteristic
274C2×C3×C5#41611yescharacteristic
275C2×C3×C5#41911yescharacteristic
276C3×D5#46412yes—
277C3×D5#47912yes—
278C23×C3—51no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—51no—
282C2×C3×C4—51no—
283C2×C3×C4—51no—
284C2×C3×C4—51no—
285C2×C3×C4—51no—
286C2×C3×C4—102no—
287C2×C3×C4—102no—
288C2×C3×C4—202no—
289C2×C3×C4—202no—
290C2×C3×C4—202no—
291C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
292C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
293C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—102no—
297C2×Dic3—102no—
298C2×Dic3—101no—
299C2×Dic3—101no—
300C2×Dic3—202no—
301Dic6—21no—
302Dic6—52no—
303Dic6—102no—
304Dic6—102no—
305Dic6—101no—
306Dic6C4⋊AGL(1,𝔽5)12yes—
307C3⋊C8—202no—
308C22×C5C2×(C2×D3)⋊C411yescharacteristic
309C2×D5#93811yescharacteristic
310C2×D5#94611yescharacteristic
311C2×D5#95012yes—
312C2×D5#95112yes—
313AGL(1,𝔽5)—82no—
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—62no—
317C4×C5—121no—
318C4×C5D3×C4⋊C411yescharacteristic
319C4×C5#89211yescharacteristic
320Dic5—21no—
321Dic5—21no—
322Dic5—62no—
323Dic5—121no—
324Dic5#89511yescharacteristic
325Dic5#89711yescharacteristic
326C2×Q8—31no—
327C2×Q8—152no—
328C2×Q8—152no—
329C2×Q8—151no—
330C2×Q8—301no—
331C2×Q8—301no—
332C2×Q8—301no—
333C22×C4—51no—
334C22×C4—51no—
335C22×C4—51no—
336C22×C4—102no—
337C22×C4—301no—
338C22×C4—301no—
339C2×C8—302no—
340C2×C8—302no—
341C2×C8—302no—
342C4⋊C4—31no—
343C4⋊C4—61no—
344C4⋊C4—102no—
345C4⋊C4—102no—
346C4⋊C4—151no—
347C4⋊C4—301no—
348C4⋊C4—301no—
349C4⋊C4—301no—
350C4⋊C4—301no—
351C42—51no—
352C42—51no—
353C42—51no—
354C42—61no—
355C42—301no—
356C42—301no—
357C42—301no—
358C42D3×AGL(1,𝔽5)11yescharacteristic
359C3×C5#180511yescharacteristic, complemented, Hall
360C22×C3—52no—
361C22×C3—51no—
362C22×C3—51no—
363C22×C3—52no—
364C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—51no—
368C3×C4—51no—
369C3×C4—101no—
370C3×C4—101no—
371C3×C4—402no—
372C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
373C3×C4#413011yescharacteristic
374Dic3—22no—
375Dic3—41no—
376Dic3—102no—
377Dic3—201no—
378C2×C5#498711yescharacteristic
379C2×C5#500211yescharacteristic
380C2×C5#500411yescharacteristic
381D5#505412yes—
382D5#506312yes—
383C23—51no—
384Q8—32no—
385Q8—61no—
386Q8—152no—
387Q8—302no—
388Q8—302no—
389Q8—301no—
390C2×C4—51no—
391C2×C4—51no—
392C2×C4—51no—
393C2×C4—51no—
394C2×C4—51no—
395C2×C4—51no—
396C2×C4—51no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—102no—
400C2×C4—102no—
401C2×C4—202no—
402C2×C4—202no—
403C2×C4—202no—
404C2×C4—302no—
405C2×C4—302no—
406C2×C4—301no—
407C2×C4—301no—
408C2×C4—602no—
409C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
410C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
411C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
412C8—602no—
413C2×C3—52no—
414C2×C3—52no—
415C2×C3#6576511yescharacteristic
416C2×C3#6578211yescharacteristic
417C2×C3#6579411yescharacteristic
418C5#6955911yescharacteristic, complemented, Sylow
419C22—52no—
420C22—52no—
421C22—51no—
422C22—51no—
423C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
424C4—21no—
425C4—21no—
426C4—51no—
427C4—51no—
428C4—62no—
429C4—101no—
430C4—101no—
431C4—121no—
432C4—302no—
433C4—402no—
434C4—601no—
435C4#9190711yescharacteristic
436C4D3×C4⋊AGL(1,𝔽5)11yescharacteristic
437C3#1060445211yescharacteristic, complemented, Sylow
438C2—52no—
439C2—52no—
440C2#1175170311yescharacteristic
441C2#1175171111yescharacteristic
442C2#1175185511yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1805
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
10. C4×Dic30C4semidirect
11. C4×C5×Dic6C4semidirect
17. #91333C4semidirect
18. Dic5×Dic6C4semidirect
130. C4×Dic6AGL(1,𝔽5)semidirect
359. C3×C5#1805semidirect
418. C5#69559semidirect
437. C3#10604452semidirect

Maximal subgroups

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

subgroupindex
C4×D5×Dic62
D5⋊(C4⋊(C3⋊C8))2
C3×#656892
C2×#911532
#117465282
#106044523
#695595