Finite Group Databasebeta

← #14313901

Subgroups — #14313901

Order 1920.

464 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#135C211yesmaximal, characteristic
2C2×#91223C211yesmaximal, characteristic, complemented
3D5⋊#812C211yesmaximal, characteristic, complemented
4#11746779C212yesmaximal, complemented
5#11746775C212yesmaximal, complemented
6#10604856—31nomaximal, Hall
7C3×D5×#41—21no—
8C2×C4⋊ΓL(1,𝔽16)—21no—
9C3×C5×#135C411yescharacteristic, complemented
10C3×#4096—21no—
11C3×#4065C411yescharacteristic, complemented
12C3×D5×Q16C2211yescharacteristic
13C3×#4062—21no—
14C3×D5×SD16—21no—
15C3×#4058C411yescharacteristic, complemented
16C3×D5×D8C2211yescharacteristic
17C3×#4050C411yescharacteristic, complemented
18C2×C3×C8×D5C2211yescharacteristic
19#91227—21no—
20#91223—21no—
21#91223C2212yes—
22#91219—21no—
23D5⋊(C3⋊C16)C2212yes—
24#72078—51nomaximal, Hall
25D5×#135D311yescharacteristic
26C2×#3994—31no—
27D5⋊M32—31no—
28#64908—32no—
29#64904—32no—
30C22×ΓL(1,𝔽16)—41no—
31C3×C5×#41—21no—
32C3×#713—21no—
33C3×Q8×D5—21no—
34C3×#711—21no—
35C3×#711—41no—
36C3×D4×D5—21no—
37C3×D4×D5—41no—
38C3×#709—21no—
39C3×#709—41no—
40C2×C3×C4×D5—41no—
41C2×C3×C4×D5D411yescharacteristic
42C4⋊ΓL(1,𝔽16)—22no—
43C4⋊ΓL(1,𝔽16)—41no—
44C3×C5×Q16C2×C411yescharacteristic, complemented
45C3×C5×SD16—21no—
46C3×C5×D8C2×C411yescharacteristic, complemented
47C2×C3×C5×C8C2×C411yescharacteristic
48C3×#689—21no—
49C3×#688—21no—
50C3×#687—21no—
51C3×#686—21no—
52C2×C3×#168D411yescharacteristic
53C3×Dic20C2×C411yescharacteristic, complemented
54C3×D40C2×C411yescharacteristic, complemented
55C3×#677—21no—
56C3×C8×D5C2×C411yescharacteristic
57C3×C8×D5D411yescharacteristic
58C3×C8×D5D411yescharacteristic
59C3×C8×D5C2311yescharacteristic
60C3⋊#674—22no—
61C2×C3×#135—51no—
62C2×#818—51no—
63C2×#812—51no—
64#4564—52no—
65#4562—52no—
66D5×#41—21no—
67C2×C4⋊AGL(1,𝔽5)—61no—
68C5×#135Dic311yescharacteristic, complemented
69#4096—21no—
70#4065Dic311yescharacteristic, complemented
71D5×Q16C2×D311yescharacteristic
72#4062—21no—
73D5×SD16—21no—
74#4058Dic311yescharacteristic, complemented
75D5×D8C2×D311yescharacteristic
76#4050Dic311yescharacteristic, complemented
77C2×C8×D5C2×D311yescharacteristic
78#3998—61no—
79#3994—32no—
80#3994—61no—
81#3990—61no—
82D5⋊C16—32no—
83#2139—151noSylow
84C22×C3×D5—41no—
85C22×C3×D5D811yescharacteristic
86C2×ΓL(1,𝔽16)—42no—
87C2×ΓL(1,𝔽16)—82no—
88C3×C5×Q8—21no—
89C3×C5×D4—21no—
90C3×C5×D4—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C3×C22⋊D5—41no—
94C3×C22⋊D5—41no—
95C3×C22⋊D5—41no—
96C2×C3×Dic5—41no—
97C2×C3×Dic5SD1611yescharacteristic
98C3×D20—21no—
99C3×D20—41no—
100C3×C4×D5—41no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×C4×D5C22⋊C411yescharacteristic
104C3×C4×D5D811yescharacteristic
105C3×C4×D5SD1611yescharacteristic
106C3×C4×D5C2×D411yescharacteristic
107C3×Dic10—21no—
108C3×Dic10—41no—
109C3×C5×C8C22⋊C411yescharacteristic
110C3×C5×C8C22×C411yescharacteristic
111C3×#168C22⋊C411yescharacteristic
112C3×#168C2×D411yescharacteristic
113C2×C3×#41—101no—
114C3×#135—51no—
115C3×#135—51no—
116C3×#135—51no—
117C3×#135—101no—
118C3×#135—101no—
119C3×#135AGL(1,𝔽5)11yescharacteristic, complemented
120C2×C3×Q16—51no—
121C2×C3×SD16—101no—
122C2×C3×D8—51no—
123C22×C3×C8—51no—
124C2×C4⋊Dic3—101no—
125#818—52no—
126#818—101no—
127#812—101no—
128#812—101no—
129C2×C3⋊C16—52no—
130C22×AGL(1,𝔽5)—121no—
131C5×#41—21no—
132#713—21no—
133Q8×D5—21no—
134#711—21no—
135#711—41no—
136D4×D5—21no—
137D4×D5—41no—
138#709—21no—
139#709—41no—
140C2×C4×D5—41no—
141C2×C4×D5#6711yescharacteristic
142C4⋊AGL(1,𝔽5)—62no—
143C4⋊AGL(1,𝔽5)—121no—
144C5×Q16C2×Dic311yescharacteristic, complemented
145C5×SD16—21no—
146C5×D8C2×Dic311yescharacteristic, complemented
147C2×C5×C8C2×Dic311yescharacteristic
148#689—21no—
149#688—21no—
150#687—21no—
151#686—21no—
152C2×#168#6711yescharacteristic
153Dic20C2×Dic311yescharacteristic, complemented
154D40C2×Dic311yescharacteristic, complemented
155#677—21no—
156C8×D5C2×Dic311yescharacteristic
157C8×D5#6711yescharacteristic
158C8×D5#6711yescharacteristic
159C8×D5C22×D311yescharacteristic
160#674—62no—
161C2×#135—51no—
162C2×M32—151no—
163C2×#107—151no—
164#358—152no—
165#357—152no—
166C22×C3×C5—41no—
167C22×C3×C5#10211yescharacteristic
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—41no—
171C2×C3×D5—81no—
172C2×C3×D5—81no—
173C2×C3×D5#10211yescharacteristic
174C2×C3×D5C2×D811yescharacteristic
175ΓL(1,𝔽16)—82no—
176C3×C4×C5—41no—
177C3×C4×C5#10211yescharacteristic
178C3×C4×C5C2×C22⋊C411yescharacteristic
179C3×Dic5—41no—
180C3×Dic5#10211yescharacteristic
181C3×Dic5C2×SD1611yescharacteristic
182C3×#41—21no—
183C3×#41—101no—
184C3×#41—101no—
185C3×#41—101no—
186C3×#41—201no—
187C3×#41—201no—
188C2×C3×Q8—101no—
189C2×C3×D4—101no—
190C2×C3×D4—201no—
191C22×C3×C4—51no—
192C22×C3×C4—201no—
193C22×Dic3—201no—
194C3×Q16—51no—
195C3×Q16—101no—
196C3×Q16C2×AGL(1,𝔽5)11yescharacteristic, complemented
197C3×SD16—21no—
198C3×SD16—101no—
199C3×SD16—101no—
200C3×SD16—101no—
201C3×D8—51no—
202C3×D8—101no—
203C3×D8C2×AGL(1,𝔽5)11yescharacteristic, complemented
204C2×C3×C8—51no—
205C2×C3×C8—51no—
206C2×C3×C8—51no—
207C2×C3×C8—51no—
208C2×C3×C8—51no—
209C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
210C4⋊Dic3—102no—
211C4⋊Dic3—201no—
212C3⋊C16—102no—
213C22×D5—41no—
214C22×D5#21311yescharacteristic
215C2×AGL(1,𝔽5)—122no—
216C2×AGL(1,𝔽5)—242no—
217C5×Q8—21no—
218C5×D4—21no—
219C5×D4—41no—
220C2×C4×C5—41no—
221C2×C4×C5#21711yescharacteristic
222C22⋊D5—41no—
223C22⋊D5—41no—
224C22⋊D5—41no—
225C2×Dic5—41no—
226C2×Dic5#21411yescharacteristic
227D20—21no—
228D20—41no—
229C4×D5—41no—
230C4×D5—41no—
231C4×D5—41no—
232C4×D5#21311yescharacteristic
233C4×D5#21411yescharacteristic
234C4×D5#21711yescharacteristic
235C4×D5C2×#6711yescharacteristic
236Dic10—21no—
237Dic10—41no—
238C5×C8#21711yescharacteristic
239C5×C8C22×Dic311yescharacteristic
240#168#21711yescharacteristic
241#168C2×#6711yescharacteristic
242C2×#41—101no—
243#135—51no—
244#135—51no—
245#135—51no—
246#135—101no—
247#135—101no—
248#135ΓL(1,𝔽16)11yescharacteristic, complemented
249C2×Q16—51no—
250C2×SD16—101no—
251C2×D8—51no—
252C22×C8—51no—
253C2×C4⋊C4—301no—
254M32—301no—
255M32—301no—
256C2×C16—152no—
257#107—152no—
258#107—301no—
259C2×C3×C5—21no—
260C2×C3×C5—81no—
261C2×C3×C5C2×#10211yescharacteristic
262C3×D5—21no—
263C3×D5—81no—
264C3×D5#50911yescharacteristic
265C3×D5#51011yescharacteristic
266C23×C3—51no—
267C23×C3—201no—
268C3×Q8—21no—
269C3×Q8—101no—
270C3×Q8—201no—
271C3×D4—21no—
272C3×D4—41no—
273C3×D4—101no—
274C3×D4—201no—
275C3×D4—201no—
276C3×D4—201no—
277C3×D4—201no—
278C2×C3×C4—41no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—51no—
282C2×C3×C4—51no—
283C2×C3×C4—51no—
284C2×C3×C4—201no—
285C2×C3×C4—201no—
286C2×C3×C4—201no—
287C2×C3×C4—201no—
288C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
289C2×Dic3—202no—
290C2×Dic3—402no—
291C3×C8—51no—
292C3×C8—51no—
293C3×C8C22⋊AGL(1,𝔽5)11yescharacteristic
294C3×C8C22×AGL(1,𝔽5)11yescharacteristic
295C22×C5—41no—
296C22×C5#83211yescharacteristic
297C2×D5—21no—
298C2×D5—21no—
299C2×D5—41no—
300C2×D5—81no—
301C2×D5—81no—
302C2×D5#83211yescharacteristic
303C2×D5C2×#21311yescharacteristic
304AGL(1,𝔽5)—242no—
305C4×C5—41no—
306C4×C5#83211yescharacteristic
307C4×C5C2×#21711yescharacteristic
308Dic5—41no—
309Dic5#83211yescharacteristic
310Dic5C2×#21411yescharacteristic
311#41—21no—
312#41—101no—
313#41—101no—
314#41—101no—
315#41—201no—
316#41—201no—
317C2×Q8—101no—
318C2×D4—101no—
319C2×D4—201no—
320C22×C4—51no—
321C22×C4—201no—
322C22×C4—601no—
323Q16—51no—
324Q16—101no—
325Q16C2×ΓL(1,𝔽16)11yescharacteristic, complemented
326SD16—21no—
327SD16—101no—
328SD16—101no—
329SD16—101no—
330D8—51no—
331D8—101no—
332D8C2×ΓL(1,𝔽16)11yescharacteristic, complemented
333C2×C8—51no—
334C2×C8—51no—
335C2×C8—51no—
336C2×C8—51no—
337C2×C8—51no—
338C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
339C4⋊C4—302no—
340C4⋊C4—601no—
341C16—302no—
342C3×C5#213911yescharacteristic, complemented, Hall
343C22×C3—41no—
344C22×C3—51no—
345C22×C3—51no—
346C22×C3—101no—
347C22×C3—101no—
348C22×C3—201no—
349C22×C3—401no—
350C22×C3—401no—
351C22×C3#400711yescharacteristic
352C3×C4—41no—
353C3×C4—51no—
354C3×C4—51no—
355C3×C4—201no—
356C3×C4#400711yescharacteristic
357C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
358Dic3—402no—
359C2×C5—21no—
360C2×C5—81no—
361C2×C5C2×#83211yescharacteristic
362D5—21no—
363D5—81no—
364D5#519311yescharacteristic
365D5#519511yescharacteristic
366C23—51no—
367C23—201no—
368Q8—21no—
369Q8—101no—
370Q8—201no—
371D4—21no—
372D4—41no—
373D4—101no—
374D4—201no—
375D4—201no—
376D4—201no—
377D4—201no—
378C2×C4—41no—
379C2×C4—51no—
380C2×C4—51no—
381C2×C4—51no—
382C2×C4—51no—
383C2×C4—51no—
384C2×C4—201no—
385C2×C4—201no—
386C2×C4—201no—
387C2×C4—201no—
388C2×C4—602no—
389C2×C4—1202no—
390C2×C4#676311yescharacteristic
391C8—51no—
392C8—51no—
393C8#676311yescharacteristic
394C8C22×ΓL(1,𝔽16)11yescharacteristic
395C2×C3—21no—
396C2×C3—51no—
397C2×C3—51no—
398C2×C3—81no—
399C2×C3—101no—
400C2×C3—401no—
401C2×C3C2×#400711yescharacteristic
402C5#7207811yescharacteristic, complemented, Sylow
403C22—41no—
404C22—51no—
405C22—51no—
406C22—101no—
407C22—101no—
408C22—201no—
409C22—401no—
410C22—401no—
411C22#9123611yescharacteristic
412C4—41no—
413C4—51no—
414C4—51no—
415C4—201no—
416C4—1202no—
417C4#9123611yescharacteristic
418C4C2×#676311yescharacteristic
419C3#1060485611yescharacteristic, complemented, Sylow
420C2—21no—
421C2—51no—
422C2—51no—
423C2—81no—
424C2—101no—
425C2—401no—
426C2C2×#9123611yescharacteristic
subgroupG/H
centerC2C2×#91236
commutatorC3×C5×C8C22×C4
FrattiniC8C22×ΓL(1,𝔽16)
FittingC3×C5×#135C4
socleC2×C3×C5C2×#102
prime radicalC3×D5×#135C2
cosocleC3×C8×D5C23
hypercenter#135ΓL(1,𝔽16)
hypocenterC3×C5#2139
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. C2×#91223C2semidirect
3. D5⋊#812C2semidirect
4. #11746779C2semidirect
5. #11746775C2semidirect
9. C3×C5×#135C4semidirect
11. C3×#4065C4semidirect
15. C3×#4058C4semidirect
17. C3×#4050C4semidirect
44. C3×C5×Q16C2×C4semidirect
46. C3×C5×D8C2×C4semidirect
53. C3×Dic20C2×C4semidirect
54. C3×D40C2×C4semidirect
68. C5×#135Dic3semidirect
70. #4065Dic3semidirect
74. #4058Dic3semidirect
76. #4050Dic3semidirect
119. C3×#135AGL(1,𝔽5)semidirect
144. C5×Q16C2×Dic3semidirect
146. C5×D8C2×Dic3semidirect
153. Dic20C2×Dic3semidirect
154. D40C2×Dic3semidirect
196. C3×Q16C2×AGL(1,𝔽5)semidirect
203. C3×D8C2×AGL(1,𝔽5)semidirect
248. #135ΓL(1,𝔽16)semidirect
325. Q16C2×ΓL(1,𝔽16)semidirect
332. D8C2×ΓL(1,𝔽16)semidirect
342. C3×C5#2139semidirect
402. C5#72078semidirect
419. C3#10604856semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1352
C2×#912232
D5⋊#8122
#117467792
#117467752
#106048563
#720785