Finite Group Databasebeta

← #14298593

Subgroups — #14298593

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65856C211yesmaximal, characteristic
2#11752420C211yesmaximal, characteristic
3#11752404C211yesmaximal, characteristic
4#11746734C212yesmaximal, complemented
5#11746733C212yesmaximal, complemented
6#10604377—31nomaximal, Hall
7C2×C3×#709C2211yescharacteristic
8#91989C2212yes—
9D5⋊#208C2212yes—
10C3×C5×#117C411yescharacteristic, complemented
11C2×C3×C4×Dic5C411yescharacteristic, complemented
12C3×#4039—21no—
13C3×#4033—21no—
14C3×#4027—21no—
15C3×#4027—21no—
16C3×#4018C411yescharacteristic, complemented
17C3×#4018C2211yescharacteristic
18C3×C42×D5C411yescharacteristic, complemented
19C3×C42×D5C2211yescharacteristic
20#91242—21no—
21#91240—21no—
22#91234—21no—
23#91228—21no—
24#71644—51nomaximal, Hall
25#65856D311yescharacteristic
26#65761—31no—
27#65745—31no—
28#64863—32no—
29#64862—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×C3×C22⋊D5D411yescharacteristic
32C2×C3×C22⋊D5D411yescharacteristic
33C22×C3×Dic5—21no—
34C3×#709—22no—
35C3×#709—22no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5C2311yescharacteristic
41C2×C3×Dic10D411yescharacteristic
42#6763—22no—
43#6762—22no—
44C4⋊ΓL(1,𝔽16)—22no—
45C4×ΓL(1,𝔽16)—22no—
46#6758—22no—
47D5⋊(C3⋊C8)—22no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C22⋊C4—21no—
50C3×C42×C5C2×C411yescharacteristic
51C3×C42×C5C2×C411yescharacteristic
52C3×#685—21no—
53C3×#685—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5C2×C411yescharacteristic
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×#41—51no—
62#5240—51no—
63#5237—51no—
64#4531—52no—
65#4523—52no—
66C2×#709C2×D311yescharacteristic
67#4130—32no—
68D5⋊M16—32no—
69C5×#117Dic311yescharacteristic, complemented
70C2×C4×Dic5Dic311yescharacteristic, complemented
71#4039—21no—
72#4033—21no—
73#4027—21no—
74#4027—21no—
75#4018Dic311yescharacteristic, complemented
76#4018C2×D311yescharacteristic
77C42×D5Dic311yescharacteristic, complemented
78C42×D5C2×D311yescharacteristic
79#4013—61no—
80#4011—61no—
81#4005—61no—
82#3999—61no—
83#1827—151noSylow
84C23×C3×C5C22⋊C411yescharacteristic
85C22×C3×D5C22⋊C411yescharacteristic
86C22×C3×D5C2×D411yescharacteristic
87C2×ΓL(1,𝔽16)—42no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C3×C22⋊D5—22no—
95C3×C22⋊D5—22no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—42no—
99C2×C3×Dic5C22⋊C411yescharacteristic
100C2×C3×Dic5C2×D411yescharacteristic
101C3×D20—22no—
102C3×C4×D5—21no—
103C3×C4×D5—21no—
104C3×C4×D5—42no—
105C3×C4×D5—42no—
106C3×C4×D5#4112yes—
107C3×C4×D5#4112yes—
108C3×Dic10—22no—
109C3⋊#170—42no—
110C2×C3×#41—51no—
111C3×C4×Q8—101no—
112C3×C4×D4—101no—
113C3×C4×D4—101no—
114C3×C4×D4—101no—
115C3×#117—51no—
116C3×#117—51no—
117C3×#117AGL(1,𝔽5)11yescharacteristic, complemented
118C2×C3×C42—51no—
119C2×C3×C42—51no—
120C2×C3×C42—51no—
121#926—52no—
122C2×#208—52no—
123#836—101no—
124#834—101no—
125#834—101no—
126#833—101no—
127C22×C4×C5C2×Dic311yescharacteristic
128C2×C22⋊D5#6711yescharacteristic
129C2×C22⋊D5#6711yescharacteristic
130C22×Dic5—21no—
131#709—22no—
132#709—22no—
133C2×D20#6711yescharacteristic
134C2×C4×D5—21no—
135C2×C4×D5—21no—
136C2×C4×D5C2×Dic311yescharacteristic
137C2×C4×D5C22×D311yescharacteristic
138C2×Dic10#6711yescharacteristic
139C22⋊AGL(1,𝔽5)—62no—
140#704—62no—
141C4⋊AGL(1,𝔽5)—62no—
142C4×AGL(1,𝔽5)—62no—
143#700—62no—
144D5⋊C8—62no—
145C5×C4⋊C4—21no—
146C5×C22⋊C4—21no—
147C42×C5C2×Dic311yescharacteristic
148C42×C5C2×Dic311yescharacteristic
149#685—21no—
150#685—21no—
151#683—21no—
152#683—21no—
153C4×Dic5—21no—
154C4×Dic5—21no—
155C4×Dic5—21no—
156C4×Dic5C2×Dic311yescharacteristic
157C4×Dic5C2×Dic311yescharacteristic
158C4×#41—51no—
159#413—151no—
160#410—151no—
161#339—152no—
162H(3,ℤ/4)—152no—
163C22×C3×C5—21no—
164C22×C3×C5—41no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×C3×D5—21no—
167C2×C3×D5—41no—
168C2×C3×D5—41no—
169C2×C3×D5#12312yes—
170ΓL(1,𝔽16)—82no—
171C3×C4×C5—21no—
172C3×C4×C5—41no—
173C3×C4×C5—41no—
174C3×C4×C5#11711yescharacteristic
175C3×C4×C5#11711yescharacteristic
176C3×Dic5—22no—
177C3×Dic5—21no—
178C3×Dic5—41no—
179C3×Dic5#12312yes—
180C3×#41—102no—
181C3×#41—102no—
182C2×C3×Q8—51no—
183C2×C3×D4—51no—
184C2×C3×D4—51no—
185C2×C3×D4—51no—
186C22×C3×C4—51no—
187C22×C3×C4—51no—
188C22×C3×C4—101no—
189C22×C3×C4—101no—
190C22×C3×C4—101no—
191C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
192C3×C4⋊C4—21no—
193C3×C4⋊C4—101no—
194C3×C4⋊C4—101no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—101no—
197C3×C22⋊C4—101no—
198C3×C42—51no—
199C3×C42—51no—
200C3×C42—101no—
201C3×C42—101no—
202C3×C42—101no—
203C3×C42C2×AGL(1,𝔽5)11yescharacteristic
204C3×C42C2×AGL(1,𝔽5)11yescharacteristic
205#217—102no—
206C4⋊Dic3—102no—
207C4×Dic3—102no—
208#208—102no—
209#208—102no—
210C2×C3⋊C8—102no—
211C23×C5#21711yescharacteristic
212C22×D5#21711yescharacteristic
213C22×D5C2×#6711yescharacteristic
214C2×AGL(1,𝔽5)—122no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5#21711yescharacteristic
220C2×C4×C5C22×Dic311yescharacteristic
221C22⋊D5—22no—
222C22⋊D5—22no—
223C2×Dic5—21no—
224C2×Dic5—21no—
225C2×Dic5—42no—
226C2×Dic5#21711yescharacteristic
227C2×Dic5C2×#6711yescharacteristic
228D20—22no—
229C4×D5—21no—
230C4×D5—21no—
231C4×D5—42no—
232C4×D5—42no—
233C4×D5#23512yes—
234C4×D5#23512yes—
235Dic10—22no—
236#170—122no—
237C2×#41—51no—
238C2×M16—152no—
239C4×Q8—101no—
240C4×D4—101no—
241C4×D4—101no—
242C4×D4—101no—
243#117—51no—
244#117—51no—
245#117—152no—
246#117ΓL(1,𝔽16)11yescharacteristic, complemented
247C2×C42—51no—
248C2×C42—51no—
249C2×C42—51no—
250#101—301no—
251#100—301no—
252#99—301no—
253#99—301no—
254C2×C3×C5—21no—
255C2×C3×C5—41no—
256C2×C3×C5#38111yescharacteristic
257C3×D5—22no—
258C3×D5—41no—
259C23×C3—51no—
260C23×C3—51no—
261C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
262C3×Q8—102no—
263C3×D4—102no—
264C3×D4—102no—
265C3×D4—102no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—51no—
271C2×C3×C4—52no—
272C2×C3×C4—52no—
273C2×C3×C4—51no—
274C2×C3×C4—101no—
275C2×C3×C4—101no—
276C2×C3×C4—101no—
277C2×C3×C4—101no—
278C2×C3×C4—202no—
279C2×C3×C4—202no—
280C2×C3×C4—202no—
281C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
282C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
283C2×Dic3—202no—
284C3⋊C8—202no—
285C22×C5—21no—
286C22×C5—41no—
287C22×C5C2×#21711yescharacteristic
288C2×D5—21no—
289C2×D5—41no—
290C2×D5—41no—
291C2×D5#92912yes—
292AGL(1,𝔽5)—242no—
293C4×C5—21no—
294C4×C5—41no—
295C4×C5—41no—
296C4×C5#92611yescharacteristic
297C4×C5#92611yescharacteristic
298Dic5—22no—
299Dic5—21no—
300Dic5—41no—
301Dic5#92912yes—
302#41—102no—
303#41—102no—
304C2×Q8—51no—
305C2×D4—51no—
306C2×D4—51no—
307C2×D4—51no—
308C22×C4—51no—
309C22×C4—51no—
310C22×C4—101no—
311C22×C4—101no—
312C22×C4—101no—
313C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
314M16—302no—
315M16—302no—
316C2×C8—302no—
317C4⋊C4—21no—
318C4⋊C4—101no—
319C4⋊C4—101no—
320C4⋊C4—302no—
321C22⋊C4—21no—
322C22⋊C4—101no—
323C22⋊C4—101no—
324C22⋊C4—302no—
325C42—51no—
326C42—51no—
327C42—101no—
328C42—101no—
329C42—101no—
330C42—302no—
331C42C2×ΓL(1,𝔽16)11yescharacteristic
332C42C2×ΓL(1,𝔽16)11yescharacteristic
333C3×C5#182711yescharacteristic, complemented, Hall
334C22×C3—21no—
335C22×C3—41no—
336C22×C3—52no—
337C22×C3—101no—
338C22×C3—201no—
339C22×C3—201no—
340C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—52no—
345C3×C4—102no—
346C3×C4—101no—
347C3×C4—201no—
348C3×C4#413011yescharacteristic
349C3×C4#413011yescharacteristic
350Dic3—402no—
351C2×C5—21no—
352C2×C5—41no—
353C2×C5#521111yescharacteristic
354D5—22no—
355D5—41no—
356C23—51no—
357C23—51no—
358C23#676311yescharacteristic
359Q8—102no—
360D4—102no—
361D4—102no—
362D4—102no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—51no—
368C2×C4—52no—
369C2×C4—52no—
370C2×C4—51no—
371C2×C4—101no—
372C2×C4—101no—
373C2×C4—101no—
374C2×C4—101no—
375C2×C4—202no—
376C2×C4—202no—
377C2×C4—202no—
378C2×C4—602no—
379C2×C4#676311yescharacteristic
380C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
381C8—602no—
382C2×C3—21no—
383C2×C3—41no—
384C2×C3—102no—
385C2×C3—201no—
386C2×C3#6576411yescharacteristic
387C5#7164411yescharacteristic, complemented, Sylow
388C22—21no—
389C22—41no—
390C22—52no—
391C22—101no—
392C22—201no—
393C22—201no—
394C22C2×#676311yescharacteristic
395C4—21no—
396C4—41no—
397C4—41no—
398C4—52no—
399C4—102no—
400C4—101no—
401C4—201no—
402C4—1202no—
403C4#9198911yescharacteristic
404C4#9198911yescharacteristic
405C3#1060437711yescharacteristic, complemented, Sylow
406C2—21no—
407C2—41no—
408C2—102no—
409C2—201no—
410C2#1175242311yescharacteristic
subgroupG/H
centerC4#91989
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#117C4
socleC2×C3×C5#381
prime radicalC2×C3×#709C22
cosocleC2×C3×C4×D5C23
hypercenter#117ΓL(1,𝔽16)
hypocenterC3×C5#1827
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C42 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #11746734C2semidirect
5. #11746733C2semidirect
10. C3×C5×#117C4semidirect
11. C2×C3×C4×Dic5C4semidirect
16. C3×#4018C4semidirect
18. C3×C42×D5C4semidirect
69. C5×#117Dic3semidirect
70. C2×C4×Dic5Dic3semidirect
75. #4018Dic3semidirect
77. C42×D5Dic3semidirect
117. C3×#117AGL(1,𝔽5)semidirect
246. #117ΓL(1,𝔽16)semidirect
333. C3×C5#1827semidirect
387. C5#71644semidirect
405. C3#10604377semidirect

Maximal subgroups

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

subgroupindex
C3×#658562
#117524202
#117524042
#117467342
#117467332
#106043773
#716445