Finite Group Databasebeta

← C3×C5×#2085 #14275119

Subgroups — C3×C5×#2085 #14275119

Order 1920.

428 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#107C211yesmaximal, characteristic
2C2×C3×C5×#106C211yesmaximal, characteristic
3C3×C5×#389C211yesmaximal, characteristic
4C3×C5×#382C211yesmaximal, characteristic
5C3×C5×#340C211yesmaximal, characteristic
6C3×C5×#340C211yesmaximal, characteristic
7C3×C5×#336C211yesmaximal, characteristic
8C5×#2085C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×C8C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C3×C5×C4⋊C4—21no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C3×C5×#107—22no—
18C3×C5×#106—22no—
19C3×C5×#95—21no—
20C3×C5×#95—21no—
21C3×C5×#95—21no—
22C3×#2085C511yesmaximal, characteristic, direct product factor, Hall
23C2×C5×#107C2×C311yescharacteristic
24C2×C5×#106C2×C311yescharacteristic
25C5×#389C2×C311yescharacteristic
26C5×#382C2×C311yescharacteristic
27C5×#340C2×C311yescharacteristic
28C5×#340C2×C311yescharacteristic
29C5×#336C2×C311yescharacteristic
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8Q812yes—
42C2×C3×C5×C8Q812yes—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—42no—
51C3×C5×C4⋊C4D412yes—
52C3×C42×C5—21no—
53C3×C42×C5—21no—
54C2×C3×#107C2×C511yescharacteristic
55C2×C3×#106C2×C511yescharacteristic
56C3×#389C2×C511yescharacteristic
57C3×#382C2×C511yescharacteristic
58C3×#340C2×C511yescharacteristic
59C3×#340C2×C511yescharacteristic
60C3×#336C2×C511yescharacteristic
61C22×C5×C8C22×C311yescharacteristic
62C22×C5×C8C22×C311yescharacteristic
63C2×C5×C4⋊C4—21no—
64C2×C5×C4⋊C4C22×C311yescharacteristic
65C2×C5×C4⋊C4C22×C311yescharacteristic
66C2×C5×C4⋊C4C22×C311yescharacteristic
67C2×C5×C4⋊C4C22×C311yescharacteristic
68C2×C42×C5C22×C311yescharacteristic
69C5×#107—22no—
70C5×#106—22no—
71C5×#95—21no—
72C5×#95—21no—
73C5×#95—21no—
74#2085C3×C511yescharacteristic, direct product factor, Sylow
75C23×C3×C5C2×D411yescharacteristic
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×Q811yescharacteristic
96C2×C3×C4×C5C2×Q811yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C3×C5×C8—22no—
101C3×C5×C8—22no—
102C22×C3×C8C22×C511yescharacteristic
103C22×C3×C8C22×C511yescharacteristic
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C22×C511yescharacteristic
106C2×C3×C4⋊C4C22×C511yescharacteristic
107C2×C3×C4⋊C4C22×C511yescharacteristic
108C2×C3×C4⋊C4C22×C511yescharacteristic
109C2×C3×C42C22×C511yescharacteristic
110C3×#107—22no—
111C3×#106—22no—
112C3×#95—21no—
113C3×#95—21no—
114C3×#95—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—21no—
119C22×C4×C5C3×D411yescharacteristic
120C22×C4×C5C3×D411yescharacteristic
121C22×C4×C5C23×C311yescharacteristic
122C2×C5×C8—21no—
123C2×C5×C8—21no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C2×C5×C8C3×Q812yes—
127C2×C5×C8C3×Q812yes—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—42no—
136C5×C4⋊C4C3×D412yes—
137C42×C5—21no—
138C42×C5—21no—
139C2×#107C2×C3×C511yescharacteristic
140C2×#106C2×C3×C511yescharacteristic
141#389C2×C3×C511yescharacteristic
142#382C2×C3×C511yescharacteristic
143#340C2×C3×C511yescharacteristic
144#340C2×C3×C511yescharacteristic
145#336C2×C3×C511yescharacteristic
146C22×C3×C5#12111yescharacteristic
147C22×C3×C5#12311yescharacteristic
148C22×C3×C5C4⋊Q811yescharacteristic
149C22×C3×C5#13511yescharacteristic
150C22×C3×C5#13511yescharacteristic
151C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
152C22×C3×C5#13711yescharacteristic
153C3×C4×C5—42no—
154C3×C4×C5—41no—
155C3×C4×C5—41no—
156C3×C4×C5—81no—
157C3×C4×C5—81no—
158C3×C4×C5—81no—
159C3×C4×C5C22⋊Q811yescharacteristic
160C3×C4×C5C22⋊Q811yescharacteristic
161C3×C4×C5#12511yescharacteristic
162C3×C4×C5#12511yescharacteristic
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4C5×D411yescharacteristic
168C22×C3×C4C5×D411yescharacteristic
169C22×C3×C4C23×C511yescharacteristic
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8C5×Q812yes—
175C2×C3×C8C5×Q812yes—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—42no—
184C3×C4⋊C4C5×D412yes—
185C3×C42—21no—
186C3×C42—21no—
187C23×C5C2×C3×D411yescharacteristic
188C2×C4×C5—22no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5C2×C3×D411yescharacteristic
207C2×C4×C5C2×C3×Q811yescharacteristic
208C2×C4×C5C2×C3×Q811yescharacteristic
209C2×C4×C5C3×#4111yescharacteristic
210C2×C4×C5C3×#4111yescharacteristic
211C2×C4×C5C3×#4111yescharacteristic
212C5×C8—22no—
213C5×C8—22no—
214C22×C8C22×C3×C511yescharacteristic
215C22×C8C22×C3×C511yescharacteristic
216C2×C4⋊C4—21no—
217C2×C4⋊C4C22×C3×C511yescharacteristic
218C2×C4⋊C4C22×C3×C511yescharacteristic
219C2×C4⋊C4C22×C3×C511yescharacteristic
220C2×C4⋊C4C22×C3×C511yescharacteristic
221C2×C42C22×C3×C511yescharacteristic
222#107—22no—
223#106—22no—
224#95—21no—
225#95—21no—
226#95—21no—
227C2×C3×C5#39811yescharacteristic
228C2×C3×C5#46311yescharacteristic
229C2×C3×C5#46411yescharacteristic
230C2×C3×C5#48211yescharacteristic
231C2×C3×C5#48511yescharacteristic
232C2×C3×C5#49911yescharacteristic
233C2×C3×C5#50111yescharacteristic
234C23×C3C2×C5×D411yescharacteristic
235C2×C3×C4—22no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4C2×C5×D411yescharacteristic
254C2×C3×C4C2×C5×Q811yescharacteristic
255C2×C3×C4C2×C5×Q811yescharacteristic
256C2×C3×C4C5×#4111yescharacteristic
257C2×C3×C4C5×#4111yescharacteristic
258C2×C3×C4C5×#4111yescharacteristic
259C3×C8—22no—
260C3×C8—22no—
261C22×C5C3×#12111yescharacteristic
262C22×C5C3×#12311yescharacteristic
263C22×C5C3×C4⋊Q811yescharacteristic
264C22×C5C3×#13511yescharacteristic
265C22×C5C3×#13511yescharacteristic
266C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
267C22×C5C3×#13711yescharacteristic
268C4×C5—42no—
269C4×C5—41no—
270C4×C5—41no—
271C4×C5—81no—
272C4×C5—81no—
273C4×C5—81no—
274C4×C5C3×C22⋊Q811yescharacteristic
275C4×C5C3×C22⋊Q811yescharacteristic
276C4×C5C3×#12511yescharacteristic
277C4×C5C3×#12511yescharacteristic
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4C3×C5×D411yescharacteristic
283C22×C4C3×C5×D411yescharacteristic
284C22×C4C23×C3×C511yescharacteristic
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8C3×C5×Q812yes—
290C2×C8C3×C5×Q812yes—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—42no—
299C4⋊C4C3×C5×D412yes—
300C42—21no—
301C42—21no—
302C3×C5#208511yescharacteristic, direct product factor, Hall
303C22×C3C5×#12111yescharacteristic
304C22×C3C5×#12311yescharacteristic
305C22×C3C5×C4⋊Q811yescharacteristic
306C22×C3C5×#13511yescharacteristic
307C22×C3C5×#13511yescharacteristic
308C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
309C22×C3C5×#13711yescharacteristic
310C3×C4—42no—
311C3×C4—41no—
312C3×C4—41no—
313C3×C4—81no—
314C3×C4—81no—
315C3×C4—81no—
316C3×C4C5×C22⋊Q811yescharacteristic
317C3×C4C5×C22⋊Q811yescharacteristic
318C3×C4C5×#12511yescharacteristic
319C3×C4C5×#12511yescharacteristic
320C2×C5C3×#39811yescharacteristic
321C2×C5C3×#46311yescharacteristic
322C2×C5C3×#46411yescharacteristic
323C2×C5C3×#48211yescharacteristic
324C2×C5C3×#48511yescharacteristic
325C2×C5C3×#49911yescharacteristic
326C2×C5C3×#50111yescharacteristic
327C23C2×C3×C5×D411yescharacteristic
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4C2×C3×C5×D411yescharacteristic
347C2×C4C2×C3×C5×Q811yescharacteristic
348C2×C4C2×C3×C5×Q811yescharacteristic
349C2×C4C3×C5×#4111yescharacteristic
350C2×C4C3×C5×#4111yescharacteristic
351C2×C4C3×C5×#4111yescharacteristic
352C8—22no—
353C8—22no—
354C2×C3C5×#39811yescharacteristic
355C2×C3C5×#46311yescharacteristic
356C2×C3C5×#46411yescharacteristic
357C2×C3C5×#48211yescharacteristic
358C2×C3C5×#48511yescharacteristic
359C2×C3C5×#49911yescharacteristic
360C2×C3C5×#50111yescharacteristic
361C5C3×#208511yescharacteristic, direct product factor, Sylow
362C22C3×C5×#12111yescharacteristic
363C22C3×C5×#12311yescharacteristic
364C22C3×C5×C4⋊Q811yescharacteristic
365C22C3×C5×#13511yescharacteristic
366C22C3×C5×#13511yescharacteristic
367C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
368C22C3×C5×#13711yescharacteristic
369C4—42no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4C3×C5×C22⋊Q811yescharacteristic
376C4C3×C5×C22⋊Q811yescharacteristic
377C4C3×C5×#12511yescharacteristic
378C4C3×C5×#12511yescharacteristic
379C3C5×#208511yescharacteristic, direct product factor, Sylow
380C2C3×C5×#39811yescharacteristic
381C2C3×C5×#46311yescharacteristic
382C2C3×C5×#46411yescharacteristic
383C2C3×C5×#48211yescharacteristic
384C2C3×C5×#48511yescharacteristic
385C2C3×C5×#49911yescharacteristic
386C2C3×C5×#50111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C3×C5C2×D4
commutator, Frattini, cosocleC22×C4C23×C3×C5
LCSG ▷ C22×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
8. C5×#2085C3direct (N × H)
22. C3×#2085C5direct (N × H)
74. #2085C3×C5direct (N × H)
302. C3×C5#2085direct (N × H)
361. C5C3×#2085direct (N × H)
379. C3C5×#2085direct (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×#1072
C2×C3×C5×#1062
C3×C5×#3892
C3×C5×#3822
C3×C5×#3402
C3×C5×#3362
C5×#20853
C3×#20855