Finite Group Databasebeta

← #14304778

Subgroups — #14304778

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×#416C211yesmaximal, characteristic
2C2×#91121C211yesmaximal, characteristic
3#11751335C211yesmaximal, characteristic
4C2×C8×Dic15C211yesmaximal, characteristic, complemented
5#11751100C211yesmaximal, characteristic, complemented
6#11746373C211yesmaximal, characteristic, complemented
7#11746353C211yesmaximal, characteristic, complemented
8#10601080—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16C3×C5×#103C412yescomplemented
17C3×C5×#102C412yescomplemented
18#91121—22no—
19#91114—22no—
20C8×Dic15—22no—
21C4⋊(C3⋊#168)—22no—
22#70287—51nomaximal, Hall
23C5×#416D311yescharacteristic
24C2×#3969—31no—
25#65523—31no—
26C2×C8×Dic5—31no—
27#65288—31no—
28#64772—31no—
29#64752—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—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8C2×C412yes—
43C3×C5×C4⋊C4C2×C412yes—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5—21no—
46C4×Dic15—21no—
47C4×Dic15D412yes—
48#6710—21no—
49#6710—21no—
50#6710—21no—
51#6710—21no—
52C2×C3⋊#168—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168D412yes—
57C3×#416D511yescharacteristic
58C2×#837—51no—
59#5234—51no—
60C2×C8×Dic3—51no—
61#4999—51no—
62#4552—51no—
63#4532—51no—
64C2×C5×#41C2×D311yescharacteristic
65C22×C5×C8C2×D311yescharacteristic
66C5×#117C2×D311yescharacteristic
67C2×C4×Dic5—31no—
68C2×#681—31no—
69C2×#681—31no—
70C22×#168—31no—
71C5×#103Dic312yescomplemented
72C5×#102Dic312yescomplemented
73#3969—62no—
74C22⋊#168—62no—
75C8×Dic5—62no—
76C4⋊#168—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—22no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×Dic15—24no—
97C2×Dic15—22no—
98C3×C5×C8—22no—
99C3⋊#168—22no—
100C3⋊#168—41no—
101C3⋊#168—41no—
102C2×C3×#41C2×D511yescharacteristic
103C22×C3×C8C2×D511yescharacteristic
104C3×#117C2×D511yescharacteristic
105C2×C4×Dic3—51no—
106C2×#208—51no—
107C2×#208—51no—
108C22×C3⋊C8—51no—
109C3×#103Dic512yescomplemented
110C3×#102Dic512yescomplemented
111#837—102no—
112#830—102no—
113C8×Dic3—102no—
114C4⋊(C3⋊C8)—102no—
115C5×#41—21no—
116C5×#41—21no—
117C5×#41—21no—
118C5×#41—21no—
119C2×C5×Q8C2×Dic311yescharacteristic
120C2×C5×D4—21no—
121C2×C5×D4C2×Dic311yescharacteristic
122C22×C4×C5—21no—
123C22×C4×C5C22×D311yescharacteristic
124C22×Dic5—61no—
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C2×C5×C8C2×Dic312yes—
128C5×C4⋊C4C2×Dic312yes—
129C5×C22⋊C4—21no—
130C42×C5—21no—
131C4×Dic5—32no—
132C4×Dic5—61no—
133#681—61no—
134#681—61no—
135#681—61no—
136#681—61no—
137C2×#168—32no—
138C2×#168—61no—
139C2×#168—61no—
140C2×#168—61no—
141C2×#168—61no—
142#424—151no—
143C2×#104—151no—
144#416D1511yescharacteristic
145#408—151no—
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—42no—
157C3×C4×C5#11711yescharacteristic
158C3×C4×C5C4×D411yescharacteristic
159C3×C4×C5#12111yescharacteristic
160C3×C4×C5#12411yescharacteristic
161Dic15—24no—
162C3×#41—21no—
163C3×#41—21no—
164C3×#41—21no—
165C3×#41—21no—
166C2×C3×Q8C2×Dic511yescharacteristic
167C2×C3×D4—21no—
168C2×C3×D4C2×Dic511yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4C22×D511yescharacteristic
171C22×Dic3—101no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8C2×Dic512yes—
175C3×C4⋊C4C2×Dic512yes—
176C3×C22⋊C4—21no—
177C3×C42—21no—
178C4×Dic3—52no—
179C4×Dic3—101no—
180#208—101no—
181#208—101no—
182#208—101no—
183#208—101no—
184C2×C3⋊C8—52no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C23×C5—21no—
190C23×C5#23711yescharacteristic
191C5×Q8—21no—
192C5×Q8—21no—
193C5×D4—21no—
194C5×D4—21no—
195C5×D4—41no—
196C5×D4—41no—
197C2×C4×C5—22no—
198C2×C4×C5—21no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5#23511yescharacteristic
202C2×C4×C5#23511yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5#23711yescharacteristic
206C2×C4×C5C22×Dic311yescharacteristic
207C2×Dic5—64no—
208C2×Dic5—62no—
209C5×C8—22no—
210#168—62no—
211#168—121no—
212#168—121no—
213C2×#41C2×D1511yescharacteristic
214C2×M16—151no—
215C2×M16—151no—
216C22×C8—151no—
217C22×C8C2×D1511yescharacteristic
218#117C2×D1511yescharacteristic
219C2×C42—151no—
220C4⋊C8—302no—
221#104—302no—
222#103Dic1512yescomplemented
223#102Dic1512yescomplemented
224C22⋊C8—302no—
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#71111yescharacteristic
233C3×Q8—21no—
234C3×Q8—21no—
235C3×D4—21no—
236C3×D4—21no—
237C3×D4—41no—
238C3×D4—41no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4#70911yescharacteristic
244C2×C3×C4#70911yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4#71111yescharacteristic
248C2×C3×C4C22×Dic511yescharacteristic
249C2×Dic3—104no—
250C2×Dic3—102no—
251C3×C8—22no—
252C3⋊C8—102no—
253C3⋊C8—201no—
254C3⋊C8—201no—
255C22×C5—22no—
256C22×C5—42no—
257C22×C5—41no—
258C22×C5#87911yescharacteristic
259C22×C5#88311yescharacteristic
260C22×C5D4×Dic311yescharacteristic
261C4×C5—42no—
262C4×C5—41no—
263C4×C5#88411yescharacteristic
264C4×C5#88511yescharacteristic
265C4×C5#92611yescharacteristic
266C4×C5D4×Dic311yescharacteristic
267Dic5—64no—
268#41—21no—
269#41—21no—
270#41—21no—
271#41—21no—
272C2×Q8C2×Dic1511yescharacteristic
273C2×D4—21no—
274C2×D4C2×Dic1511yescharacteristic
275C22×C4—21no—
276C22×C4—301no—
277C22×C4C22×D1511yescharacteristic
278M16—301no—
279M16—301no—
280M16—301no—
281M16—301no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—152no—
285C2×C8—301no—
286C2×C8—301no—
287C2×C8—301no—
288C2×C8—301no—
289C2×C8C2×Dic1512yes—
290C4⋊C4C2×Dic1512yes—
291C22⋊C4—21no—
292C42—21no—
293C42—152no—
294C42—301no—
295C3×C5#193711yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3—42no—
298C22×C3—41no—
299C22×C3#402511yescharacteristic
300C22×C3#402911yescharacteristic
301C22×C3D4×Dic511yescharacteristic
302C3×C4—42no—
303C3×C4—41no—
304C3×C4#403011yescharacteristic
305C3×C4#403111yescharacteristic
306C3×C4#407211yescharacteristic
307C3×C4D4×Dic511yescharacteristic
308Dic3—104no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5—81no—
312C2×C5#495111yescharacteristic
313C2×C5#519612yes—
314C23—21no—
315C23#681911yescharacteristic
316Q8—21no—
317Q8—21no—
318D4—21no—
319D4—21no—
320D4—41no—
321D4—41no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—304no—
327C2×C4—302no—
328C2×C4#681711yescharacteristic
329C2×C4#681711yescharacteristic
330C2×C4D4×D1511yescharacteristic
331C2×C4D4×D1511yescharacteristic
332C2×C4#681911yescharacteristic
333C2×C4C22×Dic1511yescharacteristic
334C8—22no—
335C8—302no—
336C8—601no—
337C8—601no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—81no—
341C2×C3#6524011yescharacteristic
342C2×C3#6548512yes—
343C5#7028711yescharacteristic, complemented, Sylow
344C22—22no—
345C22—42no—
346C22—41no—
347C22#9176811yescharacteristic
348C22#9177211yescharacteristic
349C22D4×Dic1511yescharacteristic
350C4—42no—
351C4—41no—
352C4—304no—
353C4#9177311yescharacteristic
354C4#9177411yescharacteristic
355C4#9181511yescharacteristic
356C4D4×Dic1511yescharacteristic
357C3#1060108011yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—81no—
361C2#1175105211yescharacteristic
362C2#1175129712yes—
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#416C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4×C5C23
hypercenter#416D15
hypocenterC3×C5#1937
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
4. C2×C8×Dic15C2semidirect
5. #11751100C2semidirect
6. #11746373C2semidirect
7. #11746353C2semidirect
16. C3×C5×#103C4semidirect
17. C3×C5×#102C4semidirect
71. C5×#103Dic3semidirect
72. C5×#102Dic3semidirect
109. C3×#103Dic5semidirect
110. C3×#102Dic5semidirect
222. #103Dic15semidirect
223. #102Dic15semidirect
295. C3×C5#1937semidirect
343. C5#70287semidirect
357. C3#10601080semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4162
C2×#911212
#117513352
C2×C8×Dic152
#117511002
#117463732
#117463532
#106010803
#702875