Finite Group Databasebeta

← C2×C3×C5×#485 #14276122

Subgroups — C2×C3×C5×#485 #14276122

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×C3×C5×#117C211yesmaximal, characteristic
3C3×C5×#485C218yesmaximal, direct product factor
4C2×C3×C5×#107C211yesmaximal, characteristic, complemented
5C2×C3×C5×#106C211yesmaximal, characteristic, complemented
6C2×C3×C5×#103C211yesmaximal, characteristic, complemented
7C2×C3×C5×#103C211yesmaximal, characteristic, complemented
8C2×C3×C5×C22⋊C8C211yesmaximal, characteristic
9C2×C5×#485C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C22×C3×C5×C8C2211yescharacteristic
14C3×C5×C22⋊Q8—22no—
15C3×C5×C22⋊Q8C2214yes—
16C3×C5×#117—22no—
17C3×C5×#117C2214yes—
18C2×C3×C5×C4⋊C4—21no—
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4—21no—
23C2×C3×C5×C22⋊C4—21no—
24C2×C3×C42×C5—21no—
25C3×C5×#107C2214yescomplemented
26C3×C5×#106C2214yescomplemented
27C3×C5×#103C2214yescomplemented
28C3×C5×#103C2214yescomplemented
29C3×C5×C22⋊C8C2214yes—
30C2×C3×#485C511yesmaximal, characteristic, direct product factor, Hall
31C2×C5×C22⋊Q8C2×C311yescharacteristic
32C2×C5×#117C2×C311yescharacteristic
33C5×#485C2×C318yesdirect product factor
34C2×C5×#107C2×C311yescharacteristic, complemented
35C2×C5×#106C2×C311yescharacteristic, complemented
36C2×C5×#103C2×C311yescharacteristic, complemented
37C2×C5×#103C2×C311yescharacteristic, complemented
38C2×C5×C22⋊C8C2×C311yescharacteristic
39C24×C3×C5D411yescharacteristic
40C2×C3×C5×Q8—21no—
41C2×C3×C5×Q8—22no—
42C2×C3×C5×Q8—22no—
43C2×C3×C5×Q8C2312yes—
44C22×C3×C4×C5—22no—
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5D412yes—
51C22×C3×C4×C5D411yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C2×C3×C5×C8—22no—
55C2×C3×C5×C8—22no—
56C2×C3×C5×C8C2312yes—
57C2×C3×C5×C8C2312yes—
58C3×C5×C4⋊C4—24no—
59C3×C5×C4⋊C4—21no—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4—21no—
62C3×C5×C4⋊C4C2312yes—
63C3×C5×C4⋊C4C2312yes—
64C3×C5×C4⋊C4C2312yes—
65C3×C5×C22⋊C4—24no—
66C3×C5×C22⋊C4—24no—
67C3×C42×C5—24no—
68C2×C3×C22⋊Q8C2×C511yescharacteristic
69C2×C3×#117C2×C511yescharacteristic
70C3×#485C2×C518yesdirect product factor
71C2×C3×#107C2×C511yescharacteristic, complemented
72C2×C3×#106C2×C511yescharacteristic, complemented
73C2×C3×#103C2×C511yescharacteristic, complemented
74C2×C3×#103C2×C511yescharacteristic, complemented
75C2×C3×C22⋊C8C2×C511yescharacteristic
76C22×C5×Q8C22×C311yescharacteristic
77C23×C4×C5C22×C311yescharacteristic
78C22×C5×C8C22×C311yescharacteristic
79C22×C5×C8C22×C311yescharacteristic
80C5×C22⋊Q8—22no—
81C5×C22⋊Q8C22×C314yes—
82C5×#117—22no—
83C5×#117C22×C314yes—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4C22×C311yescharacteristic
86C2×C5×C4⋊C4C22×C311yescharacteristic
87C2×C5×C4⋊C4C22×C311yescharacteristic
88C2×C5×C22⋊C4—21no—
89C2×C5×C22⋊C4—21no—
90C2×C42×C5—21no—
91C5×#107C22×C314yescomplemented
92C5×#106C22×C314yescomplemented
93C5×#103C22×C314yescomplemented
94C5×#103C22×C314yescomplemented
95C5×C22⋊C8C22×C314yes—
96C2×#485C3×C511yescharacteristic, direct product factor, Sylow
97C23×C3×C5—22no—
98C23×C3×C5—22no—
99C23×C3×C5—22no—
100C23×C3×C5C2×D412yes—
101C23×C3×C5C2×D411yescharacteristic
102C3×C5×Q8—22no—
103C3×C5×Q8—22no—
104C3×C5×Q8—42no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—24no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—42no—
114C2×C3×C4×C5—42no—
115C2×C3×C4×C5—42no—
116C2×C3×C4×C5—42no—
117C2×C3×C4×C5C2×D412yes—
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5#4112yes—
120C2×C3×C4×C5#4112yes—
121C2×C3×C4×C5C2411yescharacteristic
122C3×C5×C8—22no—
123C3×C5×C8—22no—
124C22×C3×Q8C22×C511yescharacteristic
125C23×C3×C4C22×C511yescharacteristic
126C22×C3×C8C22×C511yescharacteristic
127C22×C3×C8C22×C511yescharacteristic
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8C22×C514yes—
130C3×#117—22no—
131C3×#117C22×C514yes—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4C22×C511yescharacteristic
134C2×C3×C4⋊C4C22×C511yescharacteristic
135C2×C3×C4⋊C4C22×C511yescharacteristic
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C42—21no—
139C3×#107C22×C514yescomplemented
140C3×#106C22×C514yescomplemented
141C3×#103C22×C514yescomplemented
142C3×#103C22×C514yescomplemented
143C3×C22⋊C8C22×C514yes—
144C24×C5C3×D411yescharacteristic
145C2×C5×Q8—21no—
146C2×C5×Q8—22no—
147C2×C5×Q8—22no—
148C2×C5×Q8C23×C312yes—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5C3×D411yescharacteristic
156C22×C4×C5C3×D412yes—
157C22×C4×C5C23×C312yes—
158C22×C4×C5C23×C311yescharacteristic
159C2×C5×C8—22no—
160C2×C5×C8—22no—
161C2×C5×C8C23×C312yes—
162C2×C5×C8C23×C312yes—
163C5×C4⋊C4—24no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4C23×C312yes—
168C5×C4⋊C4C23×C312yes—
169C5×C4⋊C4C23×C312yes—
170C5×C22⋊C4—24no—
171C5×C22⋊C4—24no—
172C42×C5—24no—
173C2×C22⋊Q8C2×C3×C511yescharacteristic
174C2×#117C2×C3×C511yescharacteristic
175#485C2×C3×C518yesdirect product factor
176C2×#107C2×C3×C511yescharacteristic, complemented
177C2×#106C2×C3×C511yescharacteristic, complemented
178C2×#103C2×C3×C511yescharacteristic, complemented
179C2×#103C2×C3×C511yescharacteristic, complemented
180C2×C22⋊C8C2×C3×C511yescharacteristic
181C22×C3×C5—22no—
182C22×C3×C5—22no—
183C22×C3×C5—22no—
184C22×C3×C5—44no—
185C22×C3×C5#12312yes—
186C22×C3×C5#13512yes—
187C22×C3×C5#13712yes—
188C22×C3×C5C22×D411yescharacteristic
189C3×C4×C5—22no—
190C3×C4×C5—42no—
191C3×C4×C5—42no—
192C3×C4×C5—42no—
193C3×C4×C5—42no—
194C3×C4×C5#12312yes—
195C3×C4×C5C2×#4111yescharacteristic
196C3×C4×C5C2×#4111yescharacteristic
197C24×C3C5×D411yescharacteristic
198C2×C3×Q8—21no—
199C2×C3×Q8—22no—
200C2×C3×Q8—22no—
201C2×C3×Q8C23×C512yes—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4C5×D411yescharacteristic
209C22×C3×C4C5×D412yes—
210C22×C3×C4C23×C512yes—
211C22×C3×C4C23×C511yescharacteristic
212C2×C3×C8—22no—
213C2×C3×C8—22no—
214C2×C3×C8C23×C512yes—
215C2×C3×C8C23×C512yes—
216C3×C4⋊C4—24no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4C23×C512yes—
221C3×C4⋊C4C23×C512yes—
222C3×C4⋊C4C23×C512yes—
223C3×C22⋊C4—24no—
224C3×C22⋊C4—24no—
225C3×C42—24no—
226C23×C5—22no—
227C23×C5—22no—
228C23×C5—22no—
229C23×C5C2×C3×D412yes—
230C23×C5C2×C3×D411yescharacteristic
231C5×Q8—22no—
232C5×Q8—22no—
233C5×Q8—42no—
234C2×C4×C5—22no—
235C2×C4×C5—24no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5—22no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5C2×C3×D412yes—
247C2×C4×C5C2×C3×D411yescharacteristic
248C2×C4×C5C3×#4112yes—
249C2×C4×C5C3×#4112yes—
250C2×C4×C5C24×C311yescharacteristic
251C5×C8—22no—
252C5×C8—22no—
253C22×Q8C22×C3×C511yescharacteristic
254C23×C4C22×C3×C511yescharacteristic
255C22×C8C22×C3×C511yescharacteristic
256C22×C8C22×C3×C511yescharacteristic
257C22⋊Q8—22no—
258C22⋊Q8C22×C3×C514yes—
259#117—22no—
260#117C22×C3×C514yes—
261C2×C4⋊C4—21no—
262C2×C4⋊C4C22×C3×C511yescharacteristic
263C2×C4⋊C4C22×C3×C511yescharacteristic
264C2×C4⋊C4C22×C3×C511yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C42—21no—
268#107C22×C3×C514yescomplemented
269#106C22×C3×C514yescomplemented
270#103C22×C3×C514yescomplemented
271#103C22×C3×C514yescomplemented
272C22⋊C8C22×C3×C514yes—
273C2×C3×C5—42no—
274C2×C3×C5#48514yesdirect product factor
275C2×C3×C5C2×#12311yescharacteristic
276C2×C3×C5C2×#13511yescharacteristic
277C2×C3×C5C2×#13711yescharacteristic
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3C2×C5×D412yes—
282C23×C3C2×C5×D411yescharacteristic
283C3×Q8—22no—
284C3×Q8—22no—
285C3×Q8—42no—
286C2×C3×C4—22no—
287C2×C3×C4—24no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4C2×C5×D412yes—
299C2×C3×C4C2×C5×D411yescharacteristic
300C2×C3×C4C5×#4112yes—
301C2×C3×C4C5×#4112yes—
302C2×C3×C4C24×C511yescharacteristic
303C3×C8—22no—
304C3×C8—22no—
305C22×C5—22no—
306C22×C5—22no—
307C22×C5—22no—
308C22×C5—44no—
309C22×C5C3×#12312yes—
310C22×C5C3×#13512yes—
311C22×C5C3×#13712yes—
312C22×C5C22×C3×D411yescharacteristic
313C4×C5—22no—
314C4×C5—42no—
315C4×C5—42no—
316C4×C5—42no—
317C4×C5—42no—
318C4×C5C3×#12312yes—
319C4×C5C2×C3×#4111yescharacteristic
320C4×C5C2×C3×#4111yescharacteristic
321C24C3×C5×D411yescharacteristic
322C2×Q8—21no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8C23×C3×C512yes—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4C3×C5×D411yescharacteristic
333C22×C4C3×C5×D412yes—
334C22×C4C23×C3×C512yes—
335C22×C4C23×C3×C511yescharacteristic
336C2×C8—22no—
337C2×C8—22no—
338C2×C8C23×C3×C512yes—
339C2×C8C23×C3×C512yes—
340C4⋊C4—24no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4C23×C3×C512yes—
345C4⋊C4C23×C3×C512yes—
346C4⋊C4C23×C3×C512yes—
347C22⋊C4—24no—
348C22⋊C4—24no—
349C42—24no—
350C3×C5C2×#48511yescharacteristic, direct product factor, Hall
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—44no—
355C22×C3C5×#12312yes—
356C22×C3C5×#13512yes—
357C22×C3C5×#13712yes—
358C22×C3C22×C5×D411yescharacteristic
359C3×C4—22no—
360C3×C4—42no—
361C3×C4—42no—
362C3×C4—42no—
363C3×C4—42no—
364C3×C4C5×#12312yes—
365C3×C4C2×C5×#4111yescharacteristic
366C3×C4C2×C5×#4111yescharacteristic
367C2×C5—42no—
368C2×C5C3×#48514yesdirect product factor
369C2×C5C2×C3×#12311yescharacteristic
370C2×C5C2×C3×#13511yescharacteristic
371C2×C5C2×C3×#13711yescharacteristic
372C23—22no—
373C23—22no—
374C23—22no—
375C23C2×C3×C5×D412yes—
376C23C2×C3×C5×D411yescharacteristic
377Q8—22no—
378Q8—22no—
379Q8—42no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4C2×C3×C5×D412yes—
393C2×C4C2×C3×C5×D411yescharacteristic
394C2×C4C3×C5×#4112yes—
395C2×C4C3×C5×#4112yes—
396C2×C4C24×C3×C511yescharacteristic
397C8—22no—
398C8—22no—
399C2×C3—42no—
400C2×C3C5×#48514yesdirect product factor
401C2×C3C2×C5×#12311yescharacteristic
402C2×C3C2×C5×#13511yescharacteristic
403C2×C3C2×C5×#13711yescharacteristic
404C5C2×C3×#48511yescharacteristic, direct product factor, Sylow
405C22—22no—
406C22—22no—
407C22—22no—
408C22—44no—
409C22C3×C5×#12312yes—
410C22C3×C5×#13512yes—
411C22C3×C5×#13712yes—
412C22C22×C3×C5×D411yescharacteristic
413C4—22no—
414C4—42no—
415C4—42no—
416C4—42no—
417C4—42no—
418C4C3×C5×#12312yes—
419C4C2×C3×C5×#4111yescharacteristic
420C4C2×C3×C5×#4111yescharacteristic
421C3C2×C5×#48511yescharacteristic, direct product factor, Sylow
422C2—42no—
423C2C3×C5×#48514yesdirect product factor
424C2C2×C3×C5×#12311yescharacteristic
425C2C2×C3×C5×#13511yescharacteristic
426C2C2×C3×C5×#13711yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutator, Frattini, cosocleC2×C4C24×C3×C5
prime radicalC24×C3×C5D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C23×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×C5×#485C2direct (N × H)
4. C2×C3×C5×#107C2semidirect
5. C2×C3×C5×#106C2semidirect
6. C2×C3×C5×#103C2semidirect
7. C2×C3×C5×#103C2semidirect
9. C2×C5×#485C3direct (N × H)
25. C3×C5×#107C22semidirect
26. C3×C5×#106C22semidirect
27. C3×C5×#103C22semidirect
28. C3×C5×#103C22semidirect
30. C2×C3×#485C5direct (N × H)
33. C5×#485C2×C3direct (N × H)
34. C2×C5×#107C2×C3semidirect
35. C2×C5×#106C2×C3semidirect
36. C2×C5×#103C2×C3semidirect
37. C2×C5×#103C2×C3semidirect
70. C3×#485C2×C5direct (N × H)
71. C2×C3×#107C2×C5semidirect
72. C2×C3×#106C2×C5semidirect
73. C2×C3×#103C2×C5semidirect
74. C2×C3×#103C2×C5semidirect
91. C5×#107C22×C3semidirect
92. C5×#106C22×C3semidirect
93. C5×#103C22×C3semidirect
94. C5×#103C22×C3semidirect
96. C2×#485C3×C5direct (N × H)
139. C3×#107C22×C5semidirect
140. C3×#106C22×C5semidirect
141. C3×#103C22×C5semidirect
142. C3×#103C22×C5semidirect
175. #485C2×C3×C5direct (N × H)
176. C2×#107C2×C3×C5semidirect
177. C2×#106C2×C3×C5semidirect
178. C2×#103C2×C3×C5semidirect
179. C2×#103C2×C3×C5semidirect
268. #107C22×C3×C5semidirect
269. #106C22×C3×C5semidirect
270. #103C22×C3×C5semidirect
271. #103C22×C3×C5semidirect
274. C2×C3×C5#485direct (N × H)
350. C3×C5C2×#485direct (N × H)
368. C2×C5C3×#485direct (N × H)
400. C2×C3C5×#485direct (N × H)
404. C5C2×C3×#485direct (N × H)
421. C3C2×C5×#485direct (N × H)
423. C2C3×C5×#485direct (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×C22⋊Q82
C2×C3×C5×#1172
C3×C5×#4852
C2×C3×C5×#1072
C2×C3×C5×#1062
C2×C3×C5×#1032
C2×C3×C5×C22⋊C82
C2×C5×#4853
C2×C3×#4855