Finite Group Databasebeta

← #14300391

Subgroups — #14300391

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754130C211yesmaximal, characteristic
2#11751230C211yesmaximal, characteristic
3#11748626C211yesmaximal, characteristic
4#11748441C211yesmaximal, characteristic, complemented
5#11748433C211yesmaximal, characteristic, complemented
6C5×#4559C211yesmaximal, characteristic, complemented
7C3×#64779C211yesmaximal, characteristic, complemented
8#10599827—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C22×C3⋊#168C2211yescharacteristic
12C5×#926C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91292—22no—
17#91291—22no—
18#91290—22no—
19#91104—22no—
20#90997C414yes—
21Dic3⋊#168—22no—
22#90982—22no—
23#69034—51nomaximal, Hall
24#66079—31no—
25#65418—31no—
26#65408—31no—
27#65295—31no—
28#65288—31no—
29C5×#344—31no—
30#64779D311yescharacteristic, complemented
31C22×C3×C4×C5C2311yescharacteristic
32C2×#1220C2×C412yes—
33#6817—21no—
34#6817—21no—
35#6817—21no—
36#6817—21no—
37C2×D60Q811yescharacteristic
38C2×C4×D15D412yes—
39C2×Dic30Q811yescharacteristic
40C3×C5×M16—21no—
41C3×C5×M16—21no—
42C2×C3×C5×C8—21no—
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C5×#217C2×C412yes—
47C5×C4⋊Dic3—21no—
48C4×C5×Dic3—21no—
49C5×#208—21no—
50C5×#208—21no—
51C2×C5×C3⋊C8D412yes—
52C3×C22⋊Dic5C2×C412yes—
53C3×C4⋊Dic5—21no—
54C3×C4×Dic5—21no—
55C3×#681—21no—
56C3×#681—21no—
57C2×C3×#168D412yes—
58#6651—24no—
59#6648—24no—
60#5745—51no—
61#5129—51no—
62#5119—51no—
63#5006—51no—
64#4999—51no—
65C3×#344—51no—
66#4559D511yescharacteristic, complemented
67C2×#709—31no—
68C2×C5×M16—31no—
69C2×C5×M16C2×D311yescharacteristic
70C5×#117—31no—
71#4072C2×D311yescharacteristic
72C2×#681C2×D311yescharacteristic
73C22×#168—31no—
74#4053—62no—
75D5×M16—62no—
76#4047—62no—
77#3952—62no—
78#3946—62no—
79#3938—34no—
80C4⋊#168—62no—
81#1868—151noSylow
82C23×C3×C5C22×C411yescharacteristic
83C22×D15C4⋊C412yes—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×Q811yescharacteristic
88C2×C3×C4×C5#4111yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90#1220—22no—
91#1220—22no—
92C2×Dic15C4⋊C412yes—
93D60—21no—
94D60—21no—
95C4×D15—22no—
96C4×D15—22no—
97Dic30—21no—
98Dic30—21no—
99C2×C5×Dic3—22no—
100C2×C3×Dic5—22no—
101C3×C5×C8—41no—
102C3⋊#168—41no—
103C3×#168—22no—
104C5×C3⋊C8—22no—
105C2×#235—51no—
106C2×C3×M16—51no—
107C2×C3×M16C2×D511yescharacteristic
108C3×#117—51no—
109#926C2×D511yescharacteristic
110C2×#208C2×D511yescharacteristic
111C22×C3⋊C8—51no—
112#907—102no—
113D3×M16—102no—
114#901—102no—
115(C2×D3)⋊C8—102no—
116Dic3⋊C8—102no—
117#806—54no—
118C4⋊(C3⋊C8)—102no—
119C22×C4×C5C22×D311yescharacteristic
120C2×C22⋊D5—32no—
121#709—61no—
122#709—61no—
123#709—61no—
124#709—61no—
125C2×D20—31no—
126C2×C4×D5—32no—
127C2×Dic10—31no—
128C5×M16—21no—
129C5×M16—21no—
130C5×M16—61no—
131C5×M16—61no—
132C2×C5×C8—21no—
133C2×C5×C8—32no—
134C5×C4⋊C4—61no—
135C5×C22⋊C4—32no—
136C42×C5—61no—
137C22⋊Dic5C4×D312yes—
138C4⋊Dic5—21no—
139C4×Dic5—21no—
140#681—21no—
141#681—21no—
142C2×#168—61no—
143C2×#168—61no—
144C2×#168—61no—
145C2×#168D1212yes—
146#676—64no—
147C8×D5—64no—
148#568—151no—
149#424—151no—
150#424—151no—
151#410—151no—
152#408—151no—
153#344—31no—
154#344—51no—
155C22×C3×C5—41no—
156C22×C3×C5C2×C4⋊C411yescharacteristic
157C22×C3×C5C4×D411yescharacteristic
158C22×C3×C5C4×D411yescharacteristic
159C2×D15—22no—
160C2×D15—42no—
161C3×C4×C5#12011yescharacteristic
162C3×C4×C5C22⋊Q811yescharacteristic
163C3×C4×C5C22⋊Q811yescharacteristic
164C3×C4×C5#12311yescharacteristic
165Dic15—22no—
166C3×Dic5—42no—
167C5×Dic3—42no—
168C22×C3×C4C22×D511yescharacteristic
169C2×#67—52no—
170#235—101no—
171#235—101no—
172#235—101no—
173#235—101no—
174C2×D12—51no—
175C2×C4×D3—52no—
176C2×Dic6—51no—
177C3×M16—21no—
178C3×M16—21no—
179C3×M16—101no—
180C3×M16—101no—
181C2×C3×C8—21no—
182C2×C3×C8—52no—
183C3×C4⋊C4—101no—
184C3×C22⋊C4—52no—
185C3×C42—101no—
186#217C4×D512yes—
187C4⋊Dic3—21no—
188C4×Dic3—21no—
189#208—21no—
190#208—21no—
191C2×C3⋊C8—101no—
192C2×C3⋊C8—101no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8D2012yes—
195ΓL(1,𝔽25)—104no—
196D3×C8—104no—
197C23×C5C2×C4×D311yescharacteristic
198C22×D5—32no—
199C2×C4×C5—62no—
200C2×C4×C5C2×D1211yescharacteristic
201C2×C4×C5#23511yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5#23711yescharacteristic
205C2×C4×C5D3×Q811yescharacteristic
206C22⋊D5—62no—
207C22⋊D5—62no—
208C2×Dic5—22no—
209C2×Dic5—32no—
210D20—61no—
211D20—61no—
212C4×D5—62no—
213C4×D5—62no—
214Dic10—61no—
215Dic10—61no—
216C5×C8—41no—
217C5×C8—62no—
218#168—22no—
219#168—121no—
220C2×#41—151no—
221#131—302no—
222#131—302no—
223C2×M16—31no—
224C2×M16—51no—
225C2×M16—302no—
226C2×M16D3×D511yescharacteristic
227C22×C8—151no—
228#117—31no—
229#117—51no—
230C4⋊C8—302no—
231C4⋊C8—302no—
232#99—154no—
233C22⋊C8—302no—
234C2×C3×C5—21no—
235C2×C3×C5—21no—
236C2×C3×C5—21no—
237C2×C3×C5#38511yescharacteristic
238D15—42no—
239C23×C3C2×C4×D511yescharacteristic
240C22×D3—52no—
241C2×C3×C4—102no—
242C2×C3×C4C2×D2011yescharacteristic
243C2×C3×C4#70911yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4#71111yescharacteristic
247C2×C3×C4Q8×D511yescharacteristic
248#67—102no—
249#67—102no—
250C2×Dic3—22no—
251C2×Dic3—52no—
252D12—101no—
253D12—101no—
254C4×D3—102no—
255C4×D3—102no—
256Dic6—101no—
257Dic6—101no—
258C3×C8—41no—
259C3×C8—102no—
260C3⋊C8—22no—
261C3⋊C8—201no—
262C22×C5—41no—
263C22×C5C4×D1211yescharacteristic
264C22×C5#67⋊C411yescharacteristic
265C22×C5D3×C4⋊C411yescharacteristic
266C2×D5—62no—
267C2×D5—122no—
268C4×C5—122no—
269C4×C5#88211yescharacteristic
270C4×C5#88311yescharacteristic
271C4×C5#89611yescharacteristic
272C4×C5#89711yescharacteristic
273Dic5—42no—
274Dic5—62no—
275#41—301no—
276#41—301no—
277#41—301no—
278#41—301no—
279C2×Q8—151no—
280C2×D4—152no—
281C2×D4—151no—
282C22×C4—152no—
283C22×C4C2×D3×D511yescharacteristic
284M16—21no—
285M16—21no—
286M16—61no—
287M16—61no—
288M16—101no—
289M16—101no—
290M16—304no—
291C2×C8—21no—
292C2×C8—32no—
293C2×C8—52no—
294C2×C8—304no—
295C2×C8—301no—
296C2×C8—301no—
297C2×C8—301no—
298C4⋊C4—61no—
299C4⋊C4—101no—
300C22⋊C4—32no—
301C22⋊C4—52no—
302C42—61no—
303C42—101no—
304C3×C5#186811yescharacteristic, complemented, Hall
305C22×C3—41no—
306C22×C3C4×D2011yescharacteristic
307C22×C3#402711yescharacteristic
308C22×C3D5×C4⋊C411yescharacteristic
309C2×D3—102no—
310C2×D3—202no—
311C3×C4—202no—
312C3×C4#402811yescharacteristic
313C3×C4#402911yescharacteristic
314C3×C4#404211yescharacteristic
315C3×C4#404311yescharacteristic
316Dic3—42no—
317Dic3—102no—
318C2×C5—21no—
319C2×C5—21no—
320C2×C5—21no—
321C2×C5#466811yescharacteristic
322D5—122no—
323C23—152no—
324C23C4×D3×D511yescharacteristic
325Q8—301no—
326Q8—301no—
327D4—302no—
328D4—302no—
329D4—301no—
330D4—301no—
331C2×C4—62no—
332C2×C4—102no—
333C2×C4—152no—
334C2×C4—302no—
335C2×C4—302no—
336C2×C4D15⋊Q811yescharacteristic
337C2×C4D5×D1211yescharacteristic
338C2×C4D3×D2011yescharacteristic
339C2×C4#677911yescharacteristic
340C2×C4#678211yescharacteristic
341C2×C4#679011yescharacteristic
342C8—41no—
343C8—62no—
344C8—102no—
345C8—601no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3#6495711yescharacteristic
350D3—202no—
351C5#6903411yescharacteristic, complemented, Sylow
352C22—41no—
353C22—302no—
354C22—602no—
355C22#9139511yescharacteristic
356C22#9140411yescharacteristic
357C22#9140511yescharacteristic
358C4—122no—
359C4—202no—
360C4—302no—
361C4#9141911yescharacteristic
362C4#9142911yescharacteristic
363C4#9147611yescharacteristic
364C4#9156211yescharacteristic
365C3#1059982711yescharacteristic, complemented, Sylow
366C2—21no—
367C2—21no—
368C2—21no—
369C2—602no—
370C2#1174889511yescharacteristic
subgroupG/H
centerC4#91476
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#385
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1868
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #11748441C2semidirect
5. #11748433C2semidirect
6. C5×#4559C2semidirect
7. C3×#64779C2semidirect
30. #64779D3semidirect
66. #4559D5semidirect
304. C3×C5#1868semidirect
351. C5#69034semidirect
365. C3#10599827semidirect

Maximal subgroups

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

subgroupindex
#117541302
#117512302
#117486262
#117484412
#117484332
C5×#45592
C3×#647792
#105998273
#690345