Finite Group Databasebeta

← C2×C3×C5×#479 #14276109

Subgroups — C2×C3×C5×#479 #14276109

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic
2C2×C3×C4×C5×Q8C211yesmaximal, characteristic
3C3×C5×#479C218yesmaximal, direct product factor
4C2×C3×C5×#107C211yesmaximal, characteristic
5C2×C3×C5×#106C211yesmaximal, characteristic
6C2×C3×C5×C4⋊C8C211yesmaximal, characteristic
7C2×C3×C5×#103C211yesmaximal, characteristic
8C2×C3×C5×#103C211yesmaximal, characteristic
9C2×C5×#479C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C3×C5×#125—22no—
14C3×C5×#125C2214yes—
15C3×C4×C5×Q8—22no—
16C3×C4×C5×Q8C2214yes—
17C2×C3×C5×C4⋊C4—21no—
18C2×C3×C5×C4⋊C4—21no—
19C2×C3×C5×C4⋊C4—21no—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C42×C5—21no—
24C2×C3×C42×C5C2211yescharacteristic
25C3×C5×#107C2214yes—
26C3×C5×#106C2214yes—
27C3×C5×C4⋊C8C2214yes—
28C3×C5×#103C2214yes—
29C3×C5×#103C2214yes—
30C2×C3×#479C511yesmaximal, characteristic, direct product factor, Hall
31C2×C5×#125C2×C311yescharacteristic
32C2×C4×C5×Q8C2×C311yescharacteristic
33C5×#479C2×C318yesdirect product factor
34C2×C5×#107C2×C311yescharacteristic
35C2×C5×#106C2×C311yescharacteristic
36C2×C5×C4⋊C8C2×C311yescharacteristic
37C2×C5×#103C2×C311yescharacteristic
38C2×C5×#103C2×C311yescharacteristic
39C2×C3×C5×Q8—21no—
40C2×C3×C5×Q8—22no—
41C2×C3×C5×Q8Q814yes—
42C2×C3×C5×Q8C2312yes—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5D411yescharacteristic
48C22×C3×C4×C5D411yescharacteristic
49C22×C3×C4×C5C2311yescharacteristic
50C2×C3×C5×C8—22no—
51C2×C3×C5×C8—22no—
52C2×C3×C5×C8C2312yes—
53C2×C3×C5×C8C2312yes—
54C3×C5×C4⋊C4—24no—
55C3×C5×C4⋊C4—24no—
56C3×C5×C4⋊C4—24no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C4⋊C4—21no—
60C3×C5×C4⋊C4C2312yes—
61C3×C5×C4⋊C4C2312yes—
62C3×C5×C4⋊C4C2312yes—
63C3×C42×C5—24no—
64C3×C42×C5D412yes—
65C3×C42×C5C2312yes—
66C2×C3×#125C2×C511yescharacteristic
67C2×C3×C4×Q8C2×C511yescharacteristic
68C3×#479C2×C518yesdirect product factor
69C2×C3×#107C2×C511yescharacteristic
70C2×C3×#106C2×C511yescharacteristic
71C2×C3×C4⋊C8C2×C511yescharacteristic
72C2×C3×#103C2×C511yescharacteristic
73C2×C3×#103C2×C511yescharacteristic
74C22×C5×Q8C22×C311yescharacteristic
75C22×C5×C8C22×C311yescharacteristic
76C22×C5×C8C22×C311yescharacteristic
77C5×#125—22no—
78C5×#125C22×C314yes—
79C4×C5×Q8—22no—
80C4×C5×Q8C22×C314yes—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4C22×C311yescharacteristic
85C2×C5×C4⋊C4C22×C311yescharacteristic
86C2×C5×C4⋊C4C22×C311yescharacteristic
87C2×C42×C5—21no—
88C2×C42×C5C22×C311yescharacteristic
89C5×#107C22×C314yes—
90C5×#106C22×C314yes—
91C5×C4⋊C8C22×C314yes—
92C5×#103C22×C314yes—
93C5×#103C22×C314yes—
94C2×#479C3×C511yescharacteristic, direct product factor, Sylow
95C23×C3×C5C2×D411yescharacteristic
96C3×C5×Q8—24no—
97C3×C5×Q8—22no—
98C3×C5×Q8C2×Q814yes—
99C2×C3×C4×C5—24no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5—42no—
109C2×C3×C4×C5C2×D412yes—
110C2×C3×C4×C5C2×D412yes—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×Q812yes—
113C2×C3×C4×C5#4112yes—
114C2×C3×C4×C5C2411yescharacteristic
115C3×C5×C8—22no—
116C3×C5×C8—22no—
117C22×C3×Q8C22×C511yescharacteristic
118C22×C3×C8C22×C511yescharacteristic
119C22×C3×C8C22×C511yescharacteristic
120C3×#125—22no—
121C3×#125C22×C514yes—
122C3×C4×Q8—22no—
123C3×C4×Q8C22×C514yes—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4C22×C511yescharacteristic
128C2×C3×C4⋊C4C22×C511yescharacteristic
129C2×C3×C4⋊C4C22×C511yescharacteristic
130C2×C3×C42—21no—
131C2×C3×C42C22×C511yescharacteristic
132C3×#107C22×C514yes—
133C3×#106C22×C514yes—
134C3×C4⋊C8C22×C514yes—
135C3×#103C22×C514yes—
136C3×#103C22×C514yes—
137C2×C5×Q8—21no—
138C2×C5×Q8—22no—
139C2×C5×Q8C3×Q814yes—
140C2×C5×Q8C23×C312yes—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5C3×D411yescharacteristic
146C22×C4×C5C3×D411yescharacteristic
147C22×C4×C5C23×C311yescharacteristic
148C2×C5×C8—22no—
149C2×C5×C8—22no—
150C2×C5×C8C23×C312yes—
151C2×C5×C8C23×C312yes—
152C5×C4⋊C4—24no—
153C5×C4⋊C4—24no—
154C5×C4⋊C4—24no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4C23×C312yes—
159C5×C4⋊C4C23×C312yes—
160C5×C4⋊C4C23×C312yes—
161C42×C5—24no—
162C42×C5C3×D412yes—
163C42×C5C23×C312yes—
164C2×#125C2×C3×C511yescharacteristic
165C2×C4×Q8C2×C3×C511yescharacteristic
166#479C2×C3×C518yesdirect product factor
167C2×#107C2×C3×C511yescharacteristic
168C2×#106C2×C3×C511yescharacteristic
169C2×C4⋊C8C2×C3×C511yescharacteristic
170C2×#103C2×C3×C511yescharacteristic
171C2×#103C2×C3×C511yescharacteristic
172C22×C3×C5C22⋊Q812yes—
173C22×C3×C5#13512yes—
174C22×C3×C5#13712yes—
175C22×C3×C5C22×D411yescharacteristic
176C3×C4×C5—24no—
177C3×C4×C5—22no—
178C3×C4×C5—22no—
179C3×C4×C5—42no—
180C3×C4×C5—42no—
181C3×C4×C5—42no—
182C3×C4×C5C22⋊Q812yes—
183C3×C4×C5C22×Q811yescharacteristic
184C3×C4×C5C2×#4111yescharacteristic
185C2×C3×Q8—21no—
186C2×C3×Q8—22no—
187C2×C3×Q8C5×Q814yes—
188C2×C3×Q8C23×C512yes—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4C5×D411yescharacteristic
194C22×C3×C4C5×D411yescharacteristic
195C22×C3×C4C23×C511yescharacteristic
196C2×C3×C8—22no—
197C2×C3×C8—22no—
198C2×C3×C8C23×C512yes—
199C2×C3×C8C23×C512yes—
200C3×C4⋊C4—24no—
201C3×C4⋊C4—24no—
202C3×C4⋊C4—24no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4C23×C512yes—
207C3×C4⋊C4C23×C512yes—
208C3×C4⋊C4C23×C512yes—
209C3×C42—24no—
210C3×C42C5×D412yes—
211C3×C42C23×C512yes—
212C23×C5C2×C3×D411yescharacteristic
213C5×Q8—24no—
214C5×Q8—22no—
215C5×Q8C2×C3×Q814yes—
216C2×C4×C5—24no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5—22no—
222C2×C4×C5—22no—
223C2×C4×C5—42no—
224C2×C4×C5—42no—
225C2×C4×C5—42no—
226C2×C4×C5C2×C3×D412yes—
227C2×C4×C5C2×C3×D412yes—
228C2×C4×C5C2×C3×D411yescharacteristic
229C2×C4×C5C2×C3×Q812yes—
230C2×C4×C5C3×#4112yes—
231C2×C4×C5C24×C311yescharacteristic
232C5×C8—22no—
233C5×C8—22no—
234C22×Q8C22×C3×C511yescharacteristic
235C22×C8C22×C3×C511yescharacteristic
236C22×C8C22×C3×C511yescharacteristic
237#125—22no—
238#125C22×C3×C514yes—
239C4×Q8—22no—
240C4×Q8C22×C3×C514yes—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4C22×C3×C511yescharacteristic
245C2×C4⋊C4C22×C3×C511yescharacteristic
246C2×C4⋊C4C22×C3×C511yescharacteristic
247C2×C42—21no—
248C2×C42C22×C3×C511yescharacteristic
249#107C22×C3×C514yes—
250#106C22×C3×C514yes—
251C4⋊C8C22×C3×C514yes—
252#103C22×C3×C514yes—
253#103C22×C3×C514yes—
254C2×C3×C5#47914yesdirect product factor
255C2×C3×C5C2×C22⋊Q811yescharacteristic
256C2×C3×C5C2×#13511yescharacteristic
257C2×C3×C5C2×#13711yescharacteristic
258C23×C3C2×C5×D411yescharacteristic
259C3×Q8—24no—
260C3×Q8—22no—
261C3×Q8C2×C5×Q814yes—
262C2×C3×C4—24no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4C2×C5×D412yes—
273C2×C3×C4C2×C5×D412yes—
274C2×C3×C4C2×C5×D411yescharacteristic
275C2×C3×C4C2×C5×Q812yes—
276C2×C3×C4C5×#4112yes—
277C2×C3×C4C24×C511yescharacteristic
278C3×C8—22no—
279C3×C8—22no—
280C22×C5C3×C22⋊Q812yes—
281C22×C5C3×#13512yes—
282C22×C5C3×#13712yes—
283C22×C5C22×C3×D411yescharacteristic
284C4×C5—22no—
285C4×C5—22no—
286C4×C5—24no—
287C4×C5—42no—
288C4×C5—42no—
289C4×C5—42no—
290C4×C5C3×C22⋊Q812yes—
291C4×C5C22×C3×Q811yescharacteristic
292C4×C5C2×C3×#4111yescharacteristic
293C2×Q8—21no—
294C2×Q8—22no—
295C2×Q8C3×C5×Q814yes—
296C2×Q8C23×C3×C512yes—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4C3×C5×D411yescharacteristic
302C22×C4C3×C5×D411yescharacteristic
303C22×C4C23×C3×C511yescharacteristic
304C2×C8—22no—
305C2×C8—22no—
306C2×C8C23×C3×C512yes—
307C2×C8C23×C3×C512yes—
308C4⋊C4—24no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4C23×C3×C512yes—
315C4⋊C4C23×C3×C512yes—
316C4⋊C4C23×C3×C512yes—
317C42—24no—
318C42C3×C5×D412yes—
319C42C23×C3×C512yes—
320C3×C5C2×#47911yescharacteristic, direct product factor, Hall
321C22×C3C5×C22⋊Q812yes—
322C22×C3C5×#13512yes—
323C22×C3C5×#13712yes—
324C22×C3C22×C5×D411yescharacteristic
325C3×C4—24no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—42no—
329C3×C4—42no—
330C3×C4—42no—
331C3×C4C5×C22⋊Q812yes—
332C3×C4C22×C5×Q811yescharacteristic
333C3×C4C2×C5×#4111yescharacteristic
334C2×C5C3×#47914yesdirect product factor
335C2×C5C2×C3×C22⋊Q811yescharacteristic
336C2×C5C2×C3×#13511yescharacteristic
337C2×C5C2×C3×#13711yescharacteristic
338C23C2×C3×C5×D411yescharacteristic
339Q8—24no—
340Q8—22no—
341Q8C2×C3×C5×Q814yes—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4C2×C3×C5×D412yes—
353C2×C4C2×C3×C5×D412yes—
354C2×C4C2×C3×C5×D411yescharacteristic
355C2×C4C2×C3×C5×Q812yes—
356C2×C4C3×C5×#4112yes—
357C2×C4C24×C3×C511yescharacteristic
358C8—22no—
359C8—22no—
360C2×C3C5×#47914yesdirect product factor
361C2×C3C2×C5×C22⋊Q811yescharacteristic
362C2×C3C2×C5×#13511yescharacteristic
363C2×C3C2×C5×#13711yescharacteristic
364C5C2×C3×#47911yescharacteristic, direct product factor, Sylow
365C22C3×C5×C22⋊Q812yes—
366C22C3×C5×#13512yes—
367C22C3×C5×#13712yes—
368C22C22×C3×C5×D411yescharacteristic
369C4—24no—
370C4—22no—
371C4—22no—
372C4—42no—
373C4—42no—
374C4—42no—
375C4C3×C5×C22⋊Q812yes—
376C4C22×C3×C5×Q811yescharacteristic
377C4C2×C3×C5×#4111yescharacteristic
378C3C2×C5×#47911yescharacteristic, direct product factor, Sylow
379C2C3×C5×#47914yesdirect product factor
380C2C2×C3×C5×C22⋊Q811yescharacteristic
381C2C2×C3×C5×#13511yescharacteristic
382C2C2×C3×C5×#13711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C3×C5C2×D4
commutator, Frattini, cosocleC2×C4C24×C3×C5
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×C5×#479C2direct (N × H)
9. C2×C5×#479C3direct (N × H)
30. C2×C3×#479C5direct (N × H)
33. C5×#479C2×C3direct (N × H)
68. C3×#479C2×C5direct (N × H)
94. C2×#479C3×C5direct (N × H)
166. #479C2×C3×C5direct (N × H)
254. C2×C3×C5#479direct (N × H)
320. C3×C5C2×#479direct (N × H)
334. C2×C5C3×#479direct (N × H)
360. C2×C3C5×#479direct (N × H)
364. C5C2×C3×#479direct (N × H)
378. C3C2×C5×#479direct (N × H)
379. C2C3×C5×#479direct (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×#1252
C2×C3×C4×C5×Q82
C3×C5×#4792
C2×C3×C5×#1072
C2×C3×C5×#1062
C2×C3×C5×C4⋊C82
C2×C3×C5×#1032
C2×C5×#4793
C2×C3×#4795