Finite Group Databasebeta

← C3×C5×#2189 #14275223

Subgroups — C3×C5×#2189 #14275223

Order 1920.

440 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#135C211yesmaximal, characteristic
2C2×C3×C5×Q32C211yesmaximal, characteristic, complemented
3C2×C3×C5×SD32C211yesmaximal, characteristic, complemented
4C3×C5×#467C211yesmaximal, characteristic, complemented
5C3×C5×#358C211yesmaximal, characteristic, complemented
6C3×C5×#357C211yesmaximal, characteristic, complemented
7C3×C5×C22⋊C16C211yesmaximal, characteristic, complemented
8C5×#2189C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41—21no—
10C3×C5×#135—22no—
11C3×C5×#135—22no—
12C2×C3×C5×Q16C2211yescharacteristic
13C2×C3×C5×Q16C2211yescharacteristic
14C2×C3×C5×SD16—21no—
15C2×C3×C5×D8C2211yescharacteristic
16C22×C3×C5×C8C2211yescharacteristic
17C3×C5×C22⋊Q8—21no—
18C3×C5×Q32—22no—
19C3×C5×SD32—22no—
20C2×C3×C5×C16C2211yescharacteristic
21C2×C3×C5×C16C2211yescharacteristic
22C3×C5×#107C2211yescharacteristic
23C3×C5×#103—21no—
24C3×#2189C511yesmaximal, characteristic, direct product factor, Hall
25C2×C5×#135C2×C311yescharacteristic
26C2×C5×Q32C2×C311yescharacteristic, complemented
27C2×C5×SD32C2×C311yescharacteristic, complemented
28C5×#467C2×C311yescharacteristic, complemented
29C5×#358C2×C311yescharacteristic, complemented
30C5×#357C2×C311yescharacteristic, complemented
31C5×C22⋊C16C2×C311yescharacteristic, complemented
32C3×C5×#41—24no—
33C3×C5×#41—42no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—41no—
38C22×C3×C4×C5—41no—
39C22×C3×C4×C5D411yescharacteristic
40C3×C5×Q16—21no—
41C3×C5×Q16—21no—
42C3×C5×Q16—21no—
43C3×C5×Q16D412yes—
44C3×C5×SD16—24no—
45C3×C5×D8—21no—
46C3×C5×D8D412yes—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8D411yescharacteristic
50C2×C3×C5×C8C2311yescharacteristic
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—41no—
53C3×C5×C22⋊C4—41no—
54C3×C5×C16—21no—
55C3×C5×C16—21no—
56C2×C3×#135C2×C511yescharacteristic
57C2×C3×Q32C2×C511yescharacteristic, complemented
58C2×C3×SD32C2×C511yescharacteristic, complemented
59C3×#467C2×C511yescharacteristic, complemented
60C3×#358C2×C511yescharacteristic, complemented
61C3×#357C2×C511yescharacteristic, complemented
62C3×C22⋊C16C2×C511yescharacteristic, complemented
63C2×C5×#41—21no—
64C5×#135—22no—
65C5×#135—22no—
66C2×C5×Q16C22×C311yescharacteristic
67C2×C5×Q16C22×C311yescharacteristic
68C2×C5×SD16—21no—
69C2×C5×D8C22×C311yescharacteristic
70C22×C5×C8C22×C311yescharacteristic
71C5×C22⋊Q8—21no—
72C5×Q32—22no—
73C5×SD32—22no—
74C2×C5×C16C22×C311yescharacteristic
75C2×C5×C16C22×C311yescharacteristic
76C5×#107C22×C311yescharacteristic
77C5×#103—21no—
78#2189C3×C511yescharacteristic, direct product factor, Sylow
79C23×C3×C5—41no—
80C23×C3×C5D811yescharacteristic
81C3×C5×Q8—22no—
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C3×C5×D4—22no—
86C3×C5×D4—44no—
87C3×C5×D4—41no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—44no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5D811yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C3×C5×C8—21no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C2×C3×#41—21no—
100C3×#135—22no—
101C3×#135—22no—
102C2×C3×Q16C22×C511yescharacteristic
103C2×C3×Q16C22×C511yescharacteristic
104C2×C3×SD16—21no—
105C2×C3×D8C22×C511yescharacteristic
106C22×C3×C8C22×C511yescharacteristic
107C3×C22⋊Q8—21no—
108C3×Q32—22no—
109C3×SD32—22no—
110C2×C3×C16C22×C511yescharacteristic
111C2×C3×C16C22×C511yescharacteristic
112C3×#107C22×C511yescharacteristic
113C3×#103—21no—
114C5×#41—24no—
115C5×#41—42no—
116C2×C5×Q8—21no—
117C2×C5×Q8—21no—
118C2×C5×D4—21no—
119C2×C5×D4—41no—
120C22×C4×C5—41no—
121C22×C4×C5C3×D411yescharacteristic
122C5×Q16—21no—
123C5×Q16—21no—
124C5×Q16—21no—
125C5×Q16C3×D412yes—
126C5×SD16—24no—
127C5×D8—21no—
128C5×D8C3×D412yes—
129C2×C5×C8—21no—
130C2×C5×C8—21no—
131C2×C5×C8C3×D411yescharacteristic
132C2×C5×C8C23×C311yescharacteristic
133C5×C4⋊C4—21no—
134C5×C4⋊C4—41no—
135C5×C22⋊C4—41no—
136C5×C16—21no—
137C5×C16—21no—
138C2×#135C2×C3×C511yescharacteristic
139C2×Q32C2×C3×C511yescharacteristic, complemented
140C2×SD32C2×C3×C511yescharacteristic, complemented
141#467C2×C3×C511yescharacteristic, complemented
142#358C2×C3×C511yescharacteristic, complemented
143#357C2×C3×C511yescharacteristic, complemented
144C22⋊C16C2×C3×C511yescharacteristic, complemented
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—42no—
149C22×C3×C5—81no—
150C22×C3×C5—81no—
151C22×C3×C5C2×D811yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—42no—
154C3×C4×C5—81no—
155C3×C4×C5—81no—
156C3×C4×C5#12011yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C3×#41—24no—
159C3×#41—42no—
160C2×C3×Q8—21no—
161C2×C3×Q8—21no—
162C2×C3×D4—21no—
163C2×C3×D4—41no—
164C22×C3×C4—41no—
165C22×C3×C4C5×D411yescharacteristic
166C3×Q16—21no—
167C3×Q16—21no—
168C3×Q16—21no—
169C3×Q16C5×D412yes—
170C3×SD16—24no—
171C3×D8—21no—
172C3×D8C5×D412yes—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8C5×D411yescharacteristic
176C2×C3×C8C23×C511yescharacteristic
177C3×C4⋊C4—21no—
178C3×C4⋊C4—41no—
179C3×C22⋊C4—41no—
180C3×C16—21no—
181C3×C16—21no—
182C23×C5—41no—
183C23×C5C3×D811yescharacteristic
184C5×Q8—22no—
185C5×Q8—41no—
186C5×Q8—41no—
187C5×Q8—41no—
188C5×D4—22no—
189C5×D4—44no—
190C5×D4—41no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—44no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5C3×D811yescharacteristic
198C2×C4×C5C2×C3×D411yescharacteristic
199C5×C8—21no—
200C5×C8C2×C3×D411yescharacteristic
201C5×C8C2×C3×D411yescharacteristic
202C2×#41—21no—
203#135—22no—
204#135—22no—
205C2×Q16C22×C3×C511yescharacteristic
206C2×Q16C22×C3×C511yescharacteristic
207C2×SD16—21no—
208C2×D8C22×C3×C511yescharacteristic
209C22×C8C22×C3×C511yescharacteristic
210C22⋊Q8—21no—
211Q32—22no—
212SD32—22no—
213C2×C16C22×C3×C511yescharacteristic
214C2×C16C22×C3×C511yescharacteristic
215#107C22×C3×C511yescharacteristic
216#103—21no—
217C2×C3×C5—41no—
218C2×C3×C5—82no—
219C2×C3×C5#44711yescharacteristic
220C2×C3×C5#50811yescharacteristic
221C2×C3×C5#51011yescharacteristic
222C23×C3—41no—
223C23×C3C5×D811yescharacteristic
224C3×Q8—22no—
225C3×Q8—41no—
226C3×Q8—41no—
227C3×Q8—41no—
228C3×D4—22no—
229C3×D4—44no—
230C3×D4—41no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—44no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4C5×D811yescharacteristic
238C2×C3×C4C2×C5×D411yescharacteristic
239C3×C8—21no—
240C3×C8C2×C5×D411yescharacteristic
241C3×C8C2×C5×D411yescharacteristic
242C22×C5—21no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5—42no—
246C22×C5—81no—
247C22×C5—81no—
248C22×C5C2×C3×D811yescharacteristic
249C4×C5—21no—
250C4×C5—42no—
251C4×C5—81no—
252C4×C5—81no—
253C4×C5C3×#12011yescharacteristic
254C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
255#41—24no—
256#41—42no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—41no—
262C22×C4C3×C5×D411yescharacteristic
263Q16—21no—
264Q16—21no—
265Q16—21no—
266Q16C3×C5×D412yes—
267SD16—24no—
268D8—21no—
269D8C3×C5×D412yes—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8C3×C5×D411yescharacteristic
273C2×C8C23×C3×C511yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—41no—
276C22⋊C4—41no—
277C16—21no—
278C16—21no—
279C3×C5#218911yescharacteristic, direct product factor, Hall
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—42no—
284C22×C3—81no—
285C22×C3—81no—
286C22×C3C2×C5×D811yescharacteristic
287C3×C4—21no—
288C3×C4—42no—
289C3×C4—81no—
290C3×C4—81no—
291C3×C4C5×#12011yescharacteristic
292C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
293C2×C5—41no—
294C2×C5—82no—
295C2×C5C3×#44711yescharacteristic
296C2×C5C3×#50811yescharacteristic
297C2×C5C3×#51011yescharacteristic
298C23—41no—
299C23C3×C5×D811yescharacteristic
300Q8—22no—
301Q8—41no—
302Q8—41no—
303Q8—41no—
304D4—22no—
305D4—44no—
306D4—41no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4C3×C5×D811yescharacteristic
314C2×C4C2×C3×C5×D411yescharacteristic
315C8—21no—
316C8C2×C3×C5×D411yescharacteristic
317C8C2×C3×C5×D411yescharacteristic
318C2×C3—41no—
319C2×C3—82no—
320C2×C3C5×#44711yescharacteristic
321C2×C3C5×#50811yescharacteristic
322C2×C3C5×#51011yescharacteristic
323C5C3×#218911yescharacteristic, direct product factor, Sylow
324C22—21no—
325C22—21no—
326C22—21no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22C2×C3×C5×D811yescharacteristic
331C4—21no—
332C4—42no—
333C4—81no—
334C4—81no—
335C4C3×C5×#12011yescharacteristic
336C4C3×C5×AGL(1,ℤ/8)11yescharacteristic
337C3C5×#218911yescharacteristic, direct product factor, Sylow
338C2—41no—
339C2—82no—
340C2C3×C5×#44711yescharacteristic
341C2C3×C5×#50811yescharacteristic
342C2C3×C5×#51011yescharacteristic
subgroupG/H
center, socleC22×C3×C5C2×D8
commutator, Frattini, cosocleC2×C8C23×C3×C5
prime radicalC2×C3×C5×#135C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×Q32C2semidirect
3. C2×C3×C5×SD32C2semidirect
4. C3×C5×#467C2semidirect
5. C3×C5×#358C2semidirect
6. C3×C5×#357C2semidirect
7. C3×C5×C22⋊C16C2semidirect
8. C5×#2189C3direct (N × H)
24. C3×#2189C5direct (N × H)
26. C2×C5×Q32C2×C3semidirect
27. C2×C5×SD32C2×C3semidirect
28. C5×#467C2×C3semidirect
29. C5×#358C2×C3semidirect
30. C5×#357C2×C3semidirect
31. C5×C22⋊C16C2×C3semidirect
57. C2×C3×Q32C2×C5semidirect
58. C2×C3×SD32C2×C5semidirect
59. C3×#467C2×C5semidirect
60. C3×#358C2×C5semidirect
61. C3×#357C2×C5semidirect
62. C3×C22⋊C16C2×C5semidirect
78. #2189C3×C5direct (N × H)
139. C2×Q32C2×C3×C5semidirect
140. C2×SD32C2×C3×C5semidirect
141. #467C2×C3×C5semidirect
142. #358C2×C3×C5semidirect
143. #357C2×C3×C5semidirect
144. C22⋊C16C2×C3×C5semidirect
279. C3×C5#2189direct (N × H)
323. C5C3×#2189direct (N × H)
337. C3C5×#2189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1352
C2×C3×C5×Q322
C2×C3×C5×SD322
C3×C5×#4672
C3×C5×#3582
C3×C5×#3572
C3×C5×C22⋊C162
C5×#21893
C3×#21895