Finite Group Databasebeta

← #14300374

Subgroups — #14300374

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
1C5×#5745C211yesmaximal, characteristic
2C3×#65408C211yesmaximal, characteristic, complemented
3#11748625C211yesmaximal, characteristic
4#11748435C211yesmaximal, characteristic, complemented
5#11748345C211yesmaximal, characteristic
6#11746377C211yesmaximal, characteristic, complemented
7#11745992C211yesmaximal, characteristic, complemented
8#10602819—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C5×#907—22no—
15C5×D3×M16—22no—
16C5×#901—22no—
17C3×#4072C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C3×#3946—22no—
20#90996C414yes—
21#90983—22no—
22(C2×D3)⋊#168—22no—
23#70546—51nomaximal, Hall
24C5×#568—31no—
25#65529—31no—
26#65523—31no—
27#65408—31no—
28#65408D311yescharacteristic, complemented
29#64776—31no—
30#64776—31no—
31C22×C3×C4×C5C2311yescharacteristic
32C2×C5×#67C2×C412yes—
33C5×#235—21no—
34C5×#235—21no—
35C5×#235—21no—
36C5×#235—21no—
37C2×C5×D12Q811yescharacteristic
38C2×C4×C5×D3D412yes—
39C2×C5×Dic6Q811yescharacteristic
40C3×C5×M16—21no—
41C3×C5×M16—21no—
42C2×C3×C5×C8D412yes—
43#6719C2×C412yes—
44C4⋊Dic15—21no—
45C4×Dic15—21no—
46#6710—21no—
47#6710—21no—
48C2×C3⋊#168—21no—
49C5×#208—21no—
50C5×#208—21no—
51C2×C5×C3⋊C8D412yes—
52C5×ΓL(1,𝔽25)—24no—
53C5×D3×C8—24no—
54C3×C22⋊Dic5C2×C412yes—
55C3×C4⋊Dic5—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60#5745D511yescharacteristic
61C3×#424—51no—
62#5110—51no—
63#5102—51no—
64#5006—51no—
65#4556—51no—
66#4533—51no—
67C2×C5×#41—31no—
68C5×#131—62no—
69C5×#131—62no—
70C2×C5×M16—31no—
71C2×C5×M16—62no—
72C2×C5×M16C2×D311yescharacteristic
73#4072—31no—
74#4072C2×D311yescharacteristic
75C2×#681—31no—
76C22×#168C2×D311yescharacteristic
77#3966—34no—
78C22⋊#168—62no—
79#3946—22no—
80#3946—62no—
81#1868—151noSylow
82C23×C3×C5C22×C411yescharacteristic
83C22×C5×D3C4⋊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
90C2×Dic15—22no—
91C5×#67—22no—
92C5×#67—22no—
93C2×C5×Dic3C4⋊C412yes—
94C5×D12—21no—
95C5×D12—21no—
96C4×C5×D3—22no—
97C4×C5×D3—22no—
98C5×Dic6—21no—
99C5×Dic6—21no—
100C2×C3×Dic5—22no—
101C3×C5×C8—22no—
102C3⋊#168—41no—
103C3×#168—41no—
104C5×C3⋊C8—22no—
105C2×#235C2×D511yescharacteristic
106C2×C3×M16C2×D511yescharacteristic
107C22×C3×C8—51no—
108C3×#117—51no—
109#926—51no—
110C2×#208—51no—
111C2×#208C2×D511yescharacteristic
112#907—22no—
113D3×M16—22no—
114#901—22no—
115C3×C4⋊C8—102no—
116(C2×D3)⋊C8—102no—
117Dic3⋊C8—102no—
118#806—54no—
119C5×#41—61no—
120C5×#41—61no—
121C5×#41—61no—
122C5×#41—61no—
123C2×C5×Q8—31no—
124C2×C5×D4—32no—
125C2×C5×D4—31no—
126C22×C4×C5—32no—
127C22×C4×C5C22×D311yescharacteristic
128C5×M16—21no—
129C5×M16—21no—
130C5×M16—64no—
131C5×M16—61no—
132C5×M16—61no—
133C2×C5×C8—32no—
134C2×C5×C8—64no—
135C2×C5×C8#6712yes—
136C22⋊Dic5—32no—
137C22⋊Dic5C4×D312yes—
138C4⋊Dic5—21no—
139C4⋊Dic5—61no—
140C4×Dic5—21no—
141C4×Dic5—61no—
142#681—61no—
143#681—61no—
144C2×#168—21no—
145C2×#168—21no—
146C2×#168—21no—
147C2×#168—61no—
148#568—31no—
149#424—51no—
150#424—151no—
151#410—151no—
152#408—151no—
153#344—151no—
154#344—151no—
155C22×C3×C5—41no—
156C22×C3×C5C2×C4⋊C411yescharacteristic
157C22×C3×C5C4×D411yescharacteristic
158C22×C3×C5C4×D411yescharacteristic
159C2×C5×D3—22no—
160C2×C5×D3—42no—
161C3×C4×C5#12011yescharacteristic
162C3×C4×C5C22⋊Q811yescharacteristic
163C3×C4×C5C22⋊Q811yescharacteristic
164C3×C4×C5#12311yescharacteristic
165Dic15—42no—
166C3×Dic5—42no—
167C5×Dic3—22no—
168C22×C3×C4C22×D511yescharacteristic
169C2×#67C4×D512yes—
170#235—21no—
171#235—21no—
172#235—21no—
173#235—21no—
174C2×D12Dic1011yescharacteristic
175C2×C4×D3C22⋊D512yes—
176C2×Dic6Dic1011yescharacteristic
177C3×M16—21no—
178C3×M16—21no—
179C2×C3×C8—101no—
180C2×C3×C8—101no—
181C2×C3×C8—101no—
182C2×C3×C8C22⋊D512yes—
183C3×C4⋊C4—101no—
184C3×C22⋊C4—52no—
185C3×C42—101no—
186#217—52no—
187C4⋊Dic3—101no—
188C4×Dic3—101no—
189#208—21no—
190#208—21no—
191#208—101no—
192#208—101no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8C22⋊D512yes—
195ΓL(1,𝔽25)—24no—
196D3×C8—24no—
197C23×C5—32no—
198C23×C5C2×C4×D311yescharacteristic
199C5×Q8—61no—
200C5×Q8—61no—
201C5×D4—62no—
202C5×D4—62no—
203C5×D4—61no—
204C5×D4—61no—
205C2×C4×C5—32no—
206C2×C4×C5—62no—
207C2×C4×C5—62no—
208C2×C4×C5#23511yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×Q811yescharacteristic
212C2×C4×C5#23911yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C2×Dic5—22no—
215C2×Dic5—62no—
216C5×C8—22no—
217C5×C8—62no—
218#168—41no—
219#168—121no—
220C2×#41—31no—
221#131—62no—
222#131—62no—
223C2×M16—31no—
224C2×M16—62no—
225C2×M16—151no—
226C2×M16D3×D511yescharacteristic
227C22×C8—51no—
228#117—51no—
229#117—151no—
230C4⋊C8—102no—
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
238C5×D3—42no—
239C23×C3C2×C4×D511yescharacteristic
240C22×D3#68312yes—
241C2×C3×C4—102no—
242C2×C3×C4C2×Dic1011yescharacteristic
243C2×C3×C4#70911yescharacteristic
244C2×C3×C4#70911yescharacteristic
245C2×C3×C4C2×C22⋊D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248#67—22no—
249#67—22no—
250C2×Dic3—102no—
251C2×Dic3#68312yes—
252D12—21no—
253D12—21no—
254C4×D3—22no—
255C4×D3—22no—
256Dic6—21no—
257Dic6—21no—
258C3×C8—22no—
259C3×C8—201no—
260C3⋊C8—22no—
261C3⋊C8—201no—
262C22×C5—41no—
263C22×C5—62no—
264C22×C5—122no—
265C22×C5D3×C4⋊C411yescharacteristic
266C22×C5#89311yescharacteristic
267C22×C5C4×#6711yescharacteristic
268C4×C5—62no—
269C4×C5#89411yescharacteristic
270C4×C5#89611yescharacteristic
271C4×C5#93711yescharacteristic
272C4×C5#94611yescharacteristic
273Dic5—42no—
274Dic5—122no—
275#41—61no—
276#41—61no—
277#41—61no—
278#41—61no—
279C2×Q8—31no—
280C2×D4—32no—
281C2×D4—31no—
282C22×C4—32no—
283C22×C4C2×D3×D511yescharacteristic
284M16—21no—
285M16—21no—
286M16—64no—
287M16—61no—
288M16—61no—
289M16—301no—
290M16—301no—
291C2×C8—32no—
292C2×C8—64no—
293C2×C8—101no—
294C2×C8—101no—
295C2×C8—101no—
296C2×C8—301no—
297C2×C8#120112yes—
298C4⋊C4—101no—
299C4⋊C4—301no—
300C22⋊C4—52no—
301C22⋊C4—152no—
302C42—101no—
303C42—301no—
304C3×C5#186811yescharacteristic, complemented, Hall
305C22×C3—41no—
306C22×C3C2×#68311yescharacteristic
307C22×C3C4×C22⋊D511yescharacteristic
308C22×C3C4×C22⋊D511yescharacteristic
309C2×D3—22no—
310C2×D3—42no—
311C3×C4—202no—
312C3×C4#407011yescharacteristic
313C3×C4#407011yescharacteristic
314C3×C4#407511yescharacteristic
315C3×C4#409911yescharacteristic
316Dic3—22no—
317Dic3—202no—
318C2×C5—21no—
319C2×C5—21no—
320C2×C5—21no—
321C2×C5—122no—
322C2×C5#498911yescharacteristic
323C23—32no—
324C23C4×D3×D511yescharacteristic
325Q8—61no—
326Q8—61no—
327D4—62no—
328D4—62no—
329D4—61no—
330D4—61no—
331C2×C4—32no—
332C2×C4—62no—
333C2×C4—62no—
334C2×C4—102no—
335C2×C4—302no—
336C2×C4D3×Dic1011yescharacteristic
337C2×C4#676911yescharacteristic
338C2×C4#677111yescharacteristic
339C2×C4C2×#120111yescharacteristic
340C2×C4D3×C22⋊D511yescharacteristic
341C2×C4D3×C22⋊D511yescharacteristic
342C8—22no—
343C8—62no—
344C8—201no—
345C8—601no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3#6549911yescharacteristic
350D3—42no—
351C5#7054611yescharacteristic, complemented, Sylow
352C22—41no—
353C22—62no—
354C22—122no—
355C22D3×#68311yescharacteristic
356C22C4×#120111yescharacteristic
357C22#9144611yescharacteristic
358C4—62no—
359C4—202no—
360C4—602no—
361C4#9135111yescharacteristic
362C4#9135211yescharacteristic
363C4#9136911yescharacteristic
364C4#9156811yescharacteristic
365C3#1060281911yescharacteristic, complemented, Sylow
366C2—21no—
367C2—21no—
368C2—21no—
369C2—122no—
370C2#1174871611yescharacteristic
subgroupG/H
centerC4#91568
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#385
prime radicalC2×C5×#235C22
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
2. C3×#65408C2semidirect
4. #11748435C2semidirect
6. #11746377C2semidirect
7. #11745992C2semidirect
28. #65408D3semidirect
304. C3×C5#1868semidirect
351. C5#70546semidirect
365. C3#10602819semidirect

Maximal subgroups

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

subgroupindex
C5×#57452
C3×#654082
#117486252
#117484352
#117483452
#117463772
#117459922
#106028193
#705465