Finite Group Databasebeta

← #14304781

Subgroups — #14304781

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#408C211yesmaximal, characteristic
2C2×#91121C211yesmaximal, characteristic
3#11751334C211yesmaximal, characteristic
4#11751203C211yesmaximal, characteristic, complemented
5C2×C8×Dic15C211yesmaximal, characteristic, complemented
6#11746379C211yesmaximal, characteristic, complemented
7#11746376C211yesmaximal, characteristic, complemented
8#10600790—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16C3×C5×C22⋊C8—22no—
17#91121—22no—
18#91119C412yescomplemented
19#91116C412yescomplemented
20#91098—22no—
21C8×Dic15—22no—
22#69997—51nomaximal, Hall
23C5×#408D311yescharacteristic
24C2×#3969—31no—
25#65522—31no—
26#65391—31no—
27C2×C8×Dic5—31no—
28#64778—31no—
29#64775—31no—
30C3×C5×#41—21no—
31C3×C5×#41—21no—
32C3×C5×#41—21no—
33C3×C5×#41—21no—
34C2×C3×C5×Q8C2×C411yescharacteristic
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C3×C5×M16—21no—
41C3×C5×M16—21no—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8D412yes—
46#6719—21no—
47C4⋊Dic15C2×C412yes—
48C4×Dic15—21no—
49C4×Dic15—21no—
50C4×Dic15D412yes—
51#6710—21no—
52#6710—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168C2×C412yes—
57C3×#408D511yescharacteristic
58C2×#837—51no—
59#5233—51no—
60#5102—51no—
61C2×C8×Dic3—51no—
62#4558—51no—
63#4555—51no—
64C2×C5×#41C2×D311yescharacteristic
65C2×C5×M16C2×D311yescharacteristic
66C22×C5×C8C2×D311yescharacteristic
67#4072—31no—
68C2×C4×Dic5—31no—
69C2×#681—31no—
70C22×#168—31no—
71C5×C22⋊C8—22no—
72#3969—62no—
73#3967—32no—
74#3964—32no—
75#3946—62no—
76C8×Dic5—62no—
77#1937—151noSylow
78C23×C3×C5—21no—
79C23×C3×C5#4111yescharacteristic
80C3×C5×Q8—21no—
81C3×C5×Q8—21no—
82C3×C5×D4—21no—
83C3×C5×D4—21no—
84C3×C5×D4—41no—
85C3×C5×D4—41no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5#4111yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×Dic15—24no—
96C2×Dic15—22no—
97C2×Dic15—22no—
98C3×C5×C8—22no—
99C3×C5×C8—41no—
100C3⋊#168—22no—
101C3⋊#168—41no—
102C2×C3×#41C2×D511yescharacteristic
103C2×C3×M16C2×D511yescharacteristic
104C22×C3×C8C2×D511yescharacteristic
105#926—51no—
106C2×C4×Dic3—51no—
107C2×#208—51no—
108C22×C3⋊C8—51no—
109C3×C22⋊C8—22no—
110#837—102no—
111#835—52no—
112#832—52no—
113Dic3⋊C8—102no—
114C8×Dic3—102no—
115C5×#41—21no—
116C5×#41—21no—
117C5×#41—21no—
118C5×#41—21no—
119C2×C5×Q8C4×D311yescharacteristic
120C2×C5×D4—21no—
121C2×C5×D4C4×D311yescharacteristic
122C22×C4×C5—21no—
123C22×C4×C5C22×D311yescharacteristic
124C22×Dic5—61no—
125C5×M16—21no—
126C5×M16—21no—
127C2×C5×C8—21no—
128C2×C5×C8—21no—
129C2×C5×C8—21no—
130C2×C5×C8#6712yes—
131C22⋊Dic5—61no—
132C4⋊Dic5—32no—
133C4×Dic5—32no—
134C4×Dic5—61no—
135C4×Dic5—61no—
136#681—61no—
137#681—61no—
138C2×#168—32no—
139C2×#168—61no—
140C2×#168—61no—
141C2×#168—61no—
142#424—151no—
143C2×#104—151no—
144#416—151no—
145#408D1511yescharacteristic
146C2×C4×C8—151no—
147#341—151no—
148#339—151no—
149C22×C3×C5—22no—
150C22×C3×C5—41no—
151C22×C3×C5—42no—
152C22×C3×C5C4×D411yescharacteristic
153C22×C3×C5#12311yescharacteristic
154C22×C3×C5#12611yescharacteristic
155C3×C4×C5—41no—
156C3×C4×C5#11711yescharacteristic
157C3×C4×C5C4×D411yescharacteristic
158C3×C4×C5#12111yescharacteristic
159C3×C4×C5#12411yescharacteristic
160Dic15—24no—
161Dic15—42no—
162C3×#41—21no—
163C3×#41—21no—
164C3×#41—21no—
165C3×#41—21no—
166C2×C3×Q8C4×D511yescharacteristic
167C2×C3×D4—21no—
168C2×C3×D4C4×D511yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4C22×D511yescharacteristic
171C22×Dic3—101no—
172C3×M16—21no—
173C3×M16—21no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8C22⋊D512yes—
178#217—101no—
179C4⋊Dic3—52no—
180C4×Dic3—52no—
181C4×Dic3—101no—
182C4×Dic3—101no—
183#208—101no—
184#208—101no—
185C2×C3⋊C8—52no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C23×C5—21no—
190C23×C5#23511yescharacteristic
191C5×Q8—21no—
192C5×Q8—21no—
193C5×D4—21no—
194C5×D4—21no—
195C5×D4—41no—
196C5×D4—41no—
197C2×C4×C5—21no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5#23711yescharacteristic
203C2×C4×C5#23711yescharacteristic
204C2×C4×C5#23711yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×Dic5—64no—
207C2×Dic5—62no—
208C2×Dic5—62no—
209C5×C8—22no—
210C5×C8—41no—
211#168—62no—
212#168—121no—
213C2×#41C2×D1511yescharacteristic
214C2×M16—151no—
215C2×M16C2×D1511yescharacteristic
216C22×C8—151no—
217C22×C8C2×D1511yescharacteristic
218#117—151no—
219C2×C42—151no—
220C4⋊C8—302no—
221#104—302no—
222#103—152no—
223#102—152no—
224C22⋊C8—22no—
225C4×C8—302no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5—81no—
229C2×C3×C5#38811yescharacteristic
230C2×C3×C5#44312yes—
231C23×C3—21no—
232C23×C3#70911yescharacteristic
233C3×Q8—21no—
234C3×Q8—21no—
235C3×D4—21no—
236C3×D4—21no—
237C3×D4—41no—
238C3×D4—41no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4C2×C4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4#71111yescharacteristic
245C2×C3×C4#71111yescharacteristic
246C2×C3×C4#71111yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248C2×Dic3—104no—
249C2×Dic3—102no—
250C2×Dic3—102no—
251C3×C8—22no—
252C3×C8—41no—
253C3⋊C8—102no—
254C3⋊C8—201no—
255C22×C5—22no—
256C22×C5—42no—
257C22×C5—41no—
258C22×C5#87911yescharacteristic
259C22×C5#88311yescharacteristic
260C22×C5C4×#6711yescharacteristic
261C4×C5—41no—
262C4×C5#87711yescharacteristic
263C4×C5#67⋊C411yescharacteristic
264C4×C5#93611yescharacteristic
265C4×C5#93911yescharacteristic
266Dic5—64no—
267Dic5—122no—
268#41—21no—
269#41—21no—
270#41—21no—
271#41—21no—
272C2×Q8C4×D1511yescharacteristic
273C2×D4—21no—
274C2×D4C4×D1511yescharacteristic
275C22×C4—21no—
276C22×C4—301no—
277C22×C4C22×D1511yescharacteristic
278M16—21no—
279M16—21no—
280M16—301no—
281M16—301no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—152no—
286C2×C8—301no—
287C2×C8—301no—
288C2×C8—301no—
289C2×C8#122012yes—
290C4⋊C4—152no—
291C22⋊C4—301no—
292C42—152no—
293C42—301no—
294C42—301no—
295C3×C5#193711yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3—42no—
298C22×C3—41no—
299C22×C3#402511yescharacteristic
300C22×C3#402911yescharacteristic
301C22×C3C4×C22⋊D511yescharacteristic
302C3×C4—41no—
303C3×C4#402311yescharacteristic
304C3×C4#402711yescharacteristic
305C3×C4#408211yescharacteristic
306C3×C4#408511yescharacteristic
307Dic3—104no—
308Dic3—202no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5—81no—
312C2×C5#494511yescharacteristic
313C2×C5#514412yes—
314C23—21no—
315C23#681711yescharacteristic
316Q8—21no—
317Q8—21no—
318D4—21no—
319D4—21no—
320D4—41no—
321D4—41no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—304no—
326C2×C4—302no—
327C2×C4—302no—
328C2×C4C2×C4×D1511yescharacteristic
329C2×C4D4×D1511yescharacteristic
330C2×C4#681911yescharacteristic
331C2×C4#681911yescharacteristic
332C2×C4#681911yescharacteristic
333C2×C4C2×#122011yescharacteristic
334C8—22no—
335C8—41no—
336C8—302no—
337C8—601no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—81no—
341C2×C3#6523411yescharacteristic
342C2×C3#6543312yes—
343C5#6999711yescharacteristic, complemented, Sylow
344C22—22no—
345C22—42no—
346C22—41no—
347C22#9176811yescharacteristic
348C22#9177211yescharacteristic
349C22C4×#122011yescharacteristic
350C4—41no—
351C4—304no—
352C4—602no—
353C4#9176611yescharacteristic
354C4#9177011yescharacteristic
355C4#9182511yescharacteristic
356C4#9182811yescharacteristic
357C3#1060079011yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—81no—
361C2#1175104611yescharacteristic
362C2#1175124512yes—
subgroupG/H
centerC2×C4C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#408C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4×C5C23
hypercenter#408D15
hypocenterC3×C5#1937
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
4. #11751203C2semidirect
5. C2×C8×Dic15C2semidirect
6. #11746379C2semidirect
7. #11746376C2semidirect
18. #91119C4semidirect
19. #91116C4semidirect
295. C3×C5#1937semidirect
343. C5#69997semidirect
357. C3#10600790semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4082
C2×#911212
#117513342
#117512032
C2×C8×Dic152
#117463792
#117463762
#106007903
#699975