Finite Group Databasebeta

← #14303614

Subgroups — #14303614

Order 1920.

372 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752367C211yesmaximal, characteristic
2#11752360C211yesmaximal, characteristic
3C3×#65149C211yesmaximal, characteristic
4#11746767C211yesmaximal, characteristic
5#11746763C211yesmaximal, characteristic
6#11746746C211yesmaximal, characteristic
7#11746746C211yesmaximal, characteristic
8#10604055—31nomaximal, Hall
9C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
10C2×#6758C2211yescharacteristic
11C2×#6758C2211yescharacteristic
12C2×D5⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C8×D5C2211yescharacteristic
14C3×#4038C2211yescharacteristic
15C3×#4038C2211yescharacteristic
16#91233—21no—
17#91231—21no—
18C4⋊(C3⋊#170)—21no—
19C4×C3⋊#170—21no—
20C3×C5×#106C411yescharacteristic, complemented
21C3×#3949C411yescharacteristic, complemented
22C3×#3939C411yescharacteristic, complemented
23C3×#3939C411yescharacteristic, complemented
24#70661—51nomaximal, Hall
25#65708—31no—
26#65701—31no—
27#65149D311yescharacteristic
28#64896—31no—
29(C2×AGL(1,𝔽5))⋊C8—31no—
30#64875—31no—
31#64875—31no—
32C22×ΓL(1,𝔽16)—21no—
33C2×C3×C4×D5C2311yescharacteristic
34C2×C3⋊#170—21no—
35C2×C3⋊#170—21no—
36C2×C3⋊#170D411yescharacteristic
37C2×C3⋊#170D411yescharacteristic
38C4×ΓL(1,𝔽16)—21no—
39C4×ΓL(1,𝔽16)—21no—
40#6758—21no—
41#6758—21no—
42#6758—21no—
43#6758Q812yes—
44D5⋊(C3⋊C8)—21no—
45D5⋊(C3⋊C8)—21no—
46C2×C3×C5×C8C2×C411yescharacteristic
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×#685—21no—
50C3×#685—21no—
51C3×C4⋊Dic5C2×C411yescharacteristic
52C3×C4⋊Dic5C2×C411yescharacteristic
53C3×C4×Dic5—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168C2×C411yescharacteristic
56C3×C8×D5—21no—
57C3×C8×D5—21no—
58C3×#427—51no—
59#4999—51no—
60#4997—51no—
61#4552—51no—
62#4550—51no—
63#4532—51no—
64#4532—51no—
65C2×C4×AGL(1,𝔽5)—31no—
66C2×#700—31no—
67C2×#700—31no—
68C2×D5⋊C8—31no—
69C2×C8×D5C2×D311yescharacteristic
70#4038C2×D311yescharacteristic
71#4038C2×D311yescharacteristic
72#4004—61no—
73#4002—61no—
74C4⋊#170—61no—
75C4×#170—61no—
76C5×#106Dic311yescharacteristic, complemented
77#3949Dic311yescharacteristic, complemented
78#3939Dic311yescharacteristic, complemented
79#3939Dic311yescharacteristic, complemented
80#1922—151noSylow
81C22×C3×D5#4111yescharacteristic
82C2×ΓL(1,𝔽16)—22no—
83C2×ΓL(1,𝔽16)—41no—
84C2×ΓL(1,𝔽16)—41no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×Dic5—21no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5C2×D411yescharacteristic
91C3×C4×D5C2×Q811yescharacteristic
92C3×C4×D5#4111yescharacteristic
93C3×C4×D5#4111yescharacteristic
94C3×C4×D5#4111yescharacteristic
95C3⋊#170—22no—
96C3⋊#170—21no—
97C3⋊#170—21no—
98C3⋊#170—41no—
99C3×C5×C8—21no—
100C3×#168—21no—
101C22×C3×C8—51no—
102C3×#117—51no—
103C3×#117—51no—
104C2×C4×Dic3—51no—
105C2×#208—51no—
106C2×#208—51no—
107C22×C3⋊C8—51no—
108C3×#107—51no—
109C3×#107—51no—
110C3×#106—51no—
111C3×#106AGL(1,𝔽5)11yescharacteristic, complemented
112C4⋊(C3⋊C8)—101no—
113C4⋊(C3⋊C8)—101no—
114#803—101no—
115C4×C3⋊C8—101no—
116C22×AGL(1,𝔽5)—61no—
117C2×C4×D5C22×D311yescharacteristic
118C2×#170—31no—
119C2×#170—31no—
120C2×#170—61no—
121C2×#170—61no—
122C4×AGL(1,𝔽5)—61no—
123C4×AGL(1,𝔽5)—61no—
124#700—32no—
125#700—61no—
126#700—61no—
127#700—61no—
128D5⋊C8—61no—
129D5⋊C8—61no—
130C2×C5×C8C2×Dic311yescharacteristic
131C5×C4⋊C4C2×Dic311yescharacteristic
132C5×C4⋊C4C2×Dic311yescharacteristic
133#685—21no—
134#685—21no—
135C4⋊Dic5C2×Dic311yescharacteristic
136C4⋊Dic5C2×Dic311yescharacteristic
137C4×Dic5—21no—
138C4×Dic5—21no—
139C2×#168C2×Dic311yescharacteristic
140C8×D5—21no—
141C8×D5—21no—
142#427—51no—
143#424—151no—
144#405—151no—
145#341—151no—
146#339—151no—
147#339—151no—
148#336—151no—
149C22×C3×C5C4×D411yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5#12511yescharacteristic
153C2×C3×D5#12611yescharacteristic
154ΓL(1,𝔽16)—42no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5#11711yescharacteristic
158C3×C4×C5C4×Q811yescharacteristic
159C3×Dic5—41no—
160C3×Dic5—41no—
161C3×Dic5C22⋊Q811yescharacteristic
162C3×Dic5#12311yescharacteristic
163C22×C3×C4—51no—
164C22×Dic3—101no—
165C2×C3×C8—51no—
166C2×C3×C8—101no—
167C2×C3×C8—101no—
168C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
169C3×C4⋊C4—51no—
170C3×C4⋊C4—51no—
171C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
172C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
173C3×C22⋊C4—101no—
174C3×C22⋊C4—101no—
175C3×C42—101no—
176C3×C42—101no—
177C4×Dic3—101no—
178C4×Dic3—101no—
179#208—52no—
180#208—101no—
181#208—101no—
182#208—101no—
183C2×C3⋊C8—51no—
184C2×C3⋊C8—51no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C22×D5#23711yescharacteristic
190C2×AGL(1,𝔽5)—62no—
191C2×AGL(1,𝔽5)—121no—
192C2×AGL(1,𝔽5)—121no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5C22×Dic311yescharacteristic
196C2×Dic5—21no—
197C2×Dic5—21no—
198C2×Dic5D3×D411yescharacteristic
199C4×D5#23511yescharacteristic
200C4×D5#23511yescharacteristic
201C4×D5D3×Q811yescharacteristic
202C4×D5#23911yescharacteristic
203#170—61no—
204#170—61no—
205#170—62no—
206#170—121no—
207C5×C8—21no—
208#168—21no—
209C2×M16—151no—
210C2×M16—151no—
211C22×C8—51no—
212C22×C8—151no—
213#117—51no—
214#117—51no—
215C2×C42—151no—
216#107—51no—
217#107—51no—
218#106—51no—
219#106ΓL(1,𝔽16)11yescharacteristic, complemented
220C4⋊C8—301no—
221C4⋊C8—301no—
222#97—301no—
223C4×C8—301no—
224C2×C3×C5#38711yescharacteristic
225C2×C3×C5#44311yescharacteristic
226C2×C3×C5#44411yescharacteristic
227C3×D5—21no—
228C3×D5—21no—
229C23×C3—51no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—51no—
233C2×C3×C4—51no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—51no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
240C2×Dic3—102no—
241C2×Dic3—201no—
242C2×Dic3—201no—
243C3×C8—21no—
244C3×C8—101no—
245C3⋊C8—101no—
246C3⋊C8—101no—
247C3⋊C8—102no—
248C3⋊C8—201no—
249C22×C5D4×Dic311yescharacteristic
250C2×D5—21no—
251C2×D5—21no—
252C2×D5#88911yescharacteristic
253C2×D5#89811yescharacteristic
254AGL(1,𝔽5)—122no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5#92611yescharacteristic
258C4×C5Q8×Dic311yescharacteristic
259Dic5—41no—
260Dic5—41no—
261Dic5#89411yescharacteristic
262Dic5#89611yescharacteristic
263C22×C4—51no—
264C22×C4—301no—
265M16—152no—
266M16—301no—
267M16—301no—
268M16—301no—
269C2×C8—51no—
270C2×C8—101no—
271C2×C8—101no—
272C2×C8—151no—
273C2×C8—151no—
274C2×C8—301no—
275C2×C8—301no—
276C2×C8—301no—
277C2×C8—301no—
278C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
279C4⋊C4—51no—
280C4⋊C4—51no—
281C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
282C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
283C22⋊C4—101no—
284C22⋊C4—101no—
285C42—101no—
286C42—101no—
287C42—301no—
288C42—301no—
289C3×C5#192211yescharacteristic, complemented, Hall
290C22×C3—51no—
291C22×C3—51no—
292C22×C3—101no—
293C22×C3—101no—
294C22×C3D4×AGL(1,𝔽5)11yescharacteristic
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—51no—
298C3×C4—51no—
299C3×C4—201no—
300C3×C4—201no—
301C3×C4#413011yescharacteristic
302C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
303Dic3—202no—
304C2×C5#498011yescharacteristic
305C2×C5#519611yescharacteristic
306C2×C5#519711yescharacteristic
307D5—21no—
308D5—21no—
309C23—51no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—51no—
313C2×C4—51no—
314C2×C4—51no—
315C2×C4—51no—
316C2×C4—51no—
317C2×C4—101no—
318C2×C4—101no—
319C2×C4—302no—
320C2×C4—601no—
321C2×C4—601no—
322C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
323C8—21no—
324C8—101no—
325C8—301no—
326C8—301no—
327C8—302no—
328C8—601no—
329C2×C3—101no—
330C2×C3—101no—
331C2×C3#6571111yescharacteristic
332C2×C3#6573611yescharacteristic
333C2×C3#6573711yescharacteristic
334C5#7066111yescharacteristic, complemented, Sylow
335C22—51no—
336C22—51no—
337C22—101no—
338C22—101no—
339C22D4×ΓL(1,𝔽16)11yescharacteristic
340C4—41no—
341C4—41no—
342C4—51no—
343C4—51no—
344C4—201no—
345C4—201no—
346C4—602no—
347C4#9198911yescharacteristic
348C4Q8×ΓL(1,𝔽16)11yescharacteristic
349C3#1060405511yescharacteristic, complemented, Sylow
350C2—101no—
351C2—101no—
352C2#1175237011yescharacteristic
353C2#1175239511yescharacteristic
354C2#1175239611yescharacteristic
subgroupG/H
centerC22D4×ΓL(1,𝔽16)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#106C4
socleC22×C3×C5C4×D4
prime radicalC22×C3×D5#41
cosocleC2×C3×C4×D5C23
hypercenter#106ΓL(1,𝔽16)
hypocenterC3×C5#1922
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
20. C3×C5×#106C4semidirect
21. C3×#3949C4semidirect
22. C3×#3939C4semidirect
23. C3×#3939C4semidirect
76. C5×#106Dic3semidirect
77. #3949Dic3semidirect
78. #3939Dic3semidirect
79. #3939Dic3semidirect
111. C3×#106AGL(1,𝔽5)semidirect
219. #106ΓL(1,𝔽16)semidirect
289. C3×C5#1922semidirect
334. C5#70661semidirect
349. C3#10604055semidirect

Maximal subgroups

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

subgroupindex
#117523672
#117523602
C3×#651492
#117467672
#117467632
#117467462
#106040553
#706615