Finite Group Databasebeta

← C3×C5×#2068 #14275102

Subgroups — C3×C5×#2068 #14275102

Order 1920.

496 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×#107C211yesmaximal, characteristic
2C2×C3×C5×C4⋊C8C211yesmaximal, characteristic
3C2×C3×C5×#103C211yesmaximal, characteristic
4C2×C3×C5×#103C211yesmaximal, characteristic
5C3×C5×#391C211yesmaximal, characteristic
6C3×C5×#389C211yesmaximal, characteristic
7C3×C5×#340C211yesmaximal, characteristic
8C5×#2068C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4—21no—
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×C4⋊C8—22no—
19C3×C5×#103—22no—
20C3×C5×#103—22no—
21C3×C5×#95—21no—
22C3×C5×#95—21no—
23C3×C5×#95—21no—
24C3×#2068C511yesmaximal, characteristic, direct product factor, Hall
25C2×C5×#107C2×C311yescharacteristic
26C2×C5×C4⋊C8C2×C311yescharacteristic
27C2×C5×#103C2×C311yescharacteristic
28C2×C5×#103C2×C311yescharacteristic
29C5×#391C2×C311yescharacteristic
30C5×#389C2×C311yescharacteristic
31C5×#340C2×C311yescharacteristic
32C2×C3×C5×Q8—21no—
33C2×C3×C5×Q8—21no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8Q812yes—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8D412yes—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C4⋊C4—42no—
57C3×C5×C4⋊C4D412yes—
58C3×C42×C5—21no—
59C3×C42×C5—21no—
60C2×C3×#107C2×C511yescharacteristic
61C2×C3×C4⋊C8C2×C511yescharacteristic
62C2×C3×#103C2×C511yescharacteristic
63C2×C3×#103C2×C511yescharacteristic
64C3×#391C2×C511yescharacteristic
65C3×#389C2×C511yescharacteristic
66C3×#340C2×C511yescharacteristic
67C22×C5×Q8C22×C311yescharacteristic
68C22×C5×C8C22×C311yescharacteristic
69C22×C5×C8C22×C311yescharacteristic
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4C22×C311yescharacteristic
72C2×C5×C4⋊C4C22×C311yescharacteristic
73C2×C5×C4⋊C4C22×C311yescharacteristic
74C2×C42×C5C22×C311yescharacteristic
75C5×#107—22no—
76C5×C4⋊C8—22no—
77C5×#103—22no—
78C5×#103—22no—
79C5×#95—21no—
80C5×#95—21no—
81C5×#95—21no—
82#2068C3×C511yescharacteristic, direct product factor, Sylow
83C23×C3×C5C2×D411yescharacteristic
84C3×C5×Q8—22no—
85C3×C5×Q8—22no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5Q1612yes—
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×Q811yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C3×C5×C8—22no—
113C3×C5×C8—41no—
114C22×C3×Q8C22×C511yescharacteristic
115C22×C3×C8C22×C511yescharacteristic
116C22×C3×C8C22×C511yescharacteristic
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4C22×C511yescharacteristic
119C2×C3×C4⋊C4C22×C511yescharacteristic
120C2×C3×C4⋊C4C22×C511yescharacteristic
121C2×C3×C42C22×C511yescharacteristic
122C3×#107—22no—
123C3×C4⋊C8—22no—
124C3×#103—22no—
125C3×#103—22no—
126C3×#95—21no—
127C3×#95—21no—
128C3×#95—21no—
129C2×C5×Q8—21no—
130C2×C5×Q8—21no—
131C2×C5×Q8—21no—
132C2×C5×Q8—21no—
133C2×C5×Q8—21no—
134C2×C5×Q8C3×Q812yes—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5C3×D411yescharacteristic
140C22×C4×C5C3×D411yescharacteristic
141C22×C4×C5C23×C311yescharacteristic
142C2×C5×C8—21no—
143C2×C5×C8—21no—
144C2×C5×C8—21no—
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C2×C5×C8C3×D412yes—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—42no—
154C5×C4⋊C4C3×D412yes—
155C42×C5—21no—
156C42×C5—21no—
157C2×#107C2×C3×C511yescharacteristic
158C2×C4⋊C8C2×C3×C511yescharacteristic
159C2×#103C2×C3×C511yescharacteristic
160C2×#103C2×C3×C511yescharacteristic
161#391C2×C3×C511yescharacteristic
162#389C2×C3×C511yescharacteristic
163#340C2×C3×C511yescharacteristic
164C22×C3×C5#12111yescharacteristic
165C22×C3×C5#12111yescharacteristic
166C22×C3×C5C22⋊Q811yescharacteristic
167C22×C3×C5C2×Q1611yescharacteristic
168C22×C3×C5#13511yescharacteristic
169C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
170C22×C3×C5#13711yescharacteristic
171C3×C4×C5—22no—
172C3×C4×C5—42no—
173C3×C4×C5—42no—
174C3×C4×C5—41no—
175C3×C4×C5—81no—
176C3×C4×C5—81no—
177C3×C4×C5#12111yescharacteristic
178C3×C4×C5C22⋊Q811yescharacteristic
179C3×C4×C5C22⋊Q811yescharacteristic
180C3×C4×C5#12611yescharacteristic
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8C5×Q812yes—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4C5×D411yescharacteristic
192C22×C3×C4C5×D411yescharacteristic
193C22×C3×C4C23×C511yescharacteristic
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8C5×D412yes—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—42no—
206C3×C4⋊C4C5×D412yes—
207C3×C42—21no—
208C3×C42—21no—
209C23×C5C2×C3×D411yescharacteristic
210C5×Q8—22no—
211C5×Q8—22no—
212C5×Q8—41no—
213C5×Q8—41no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5C3×Q1612yes—
232C2×C4×C5C2×C3×D411yescharacteristic
233C2×C4×C5C2×C3×D411yescharacteristic
234C2×C4×C5C2×C3×Q811yescharacteristic
235C2×C4×C5C3×#4111yescharacteristic
236C2×C4×C5C3×#4111yescharacteristic
237C2×C4×C5C3×#4111yescharacteristic
238C5×C8—22no—
239C5×C8—41no—
240C22×Q8C22×C3×C511yescharacteristic
241C22×C8C22×C3×C511yescharacteristic
242C22×C8C22×C3×C511yescharacteristic
243C2×C4⋊C4—21no—
244C2×C4⋊C4C22×C3×C511yescharacteristic
245C2×C4⋊C4C22×C3×C511yescharacteristic
246C2×C4⋊C4C22×C3×C511yescharacteristic
247C2×C42C22×C3×C511yescharacteristic
248#107—22no—
249C4⋊C8—22no—
250#103—22no—
251#103—22no—
252#95—21no—
253#95—21no—
254#95—21no—
255C2×C3×C5#39611yescharacteristic
256C2×C3×C5#46211yescharacteristic
257C2×C3×C5#46311yescharacteristic
258C2×C3×C5#46711yescharacteristic
259C2×C3×C5#46811yescharacteristic
260C2×C3×C5#47711yescharacteristic
261C2×C3×C5#47911yescharacteristic
262C23×C3C2×C5×D411yescharacteristic
263C3×Q8—22no—
264C3×Q8—22no—
265C3×Q8—41no—
266C3×Q8—41no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4C5×Q1612yes—
285C2×C3×C4C2×C5×D411yescharacteristic
286C2×C3×C4C2×C5×D411yescharacteristic
287C2×C3×C4C2×C5×Q811yescharacteristic
288C2×C3×C4C5×#4111yescharacteristic
289C2×C3×C4C5×#4111yescharacteristic
290C2×C3×C4C5×#4111yescharacteristic
291C3×C8—22no—
292C3×C8—41no—
293C22×C5C3×#12111yescharacteristic
294C22×C5C3×#12111yescharacteristic
295C22×C5C3×C22⋊Q811yescharacteristic
296C22×C5C2×C3×Q1611yescharacteristic
297C22×C5C3×#13511yescharacteristic
298C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
299C22×C5C3×#13711yescharacteristic
300C4×C5—22no—
301C4×C5—42no—
302C4×C5—42no—
303C4×C5—41no—
304C4×C5—81no—
305C4×C5—81no—
306C4×C5C3×#12111yescharacteristic
307C4×C5C3×C22⋊Q811yescharacteristic
308C4×C5C3×C22⋊Q811yescharacteristic
309C4×C5C3×#12611yescharacteristic
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8C3×C5×Q812yes—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4C3×C5×D411yescharacteristic
321C22×C4C3×C5×D411yescharacteristic
322C22×C4C23×C3×C511yescharacteristic
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8C3×C5×D412yes—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—42no—
335C4⋊C4C3×C5×D412yes—
336C42—21no—
337C42—21no—
338C3×C5#206811yescharacteristic, direct product factor, Hall
339C22×C3C5×#12111yescharacteristic
340C22×C3C5×#12111yescharacteristic
341C22×C3C5×C22⋊Q811yescharacteristic
342C22×C3C2×C5×Q1611yescharacteristic
343C22×C3C5×#13511yescharacteristic
344C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
345C22×C3C5×#13711yescharacteristic
346C3×C4—22no—
347C3×C4—42no—
348C3×C4—42no—
349C3×C4—41no—
350C3×C4—81no—
351C3×C4—81no—
352C3×C4C5×#12111yescharacteristic
353C3×C4C5×C22⋊Q811yescharacteristic
354C3×C4C5×C22⋊Q811yescharacteristic
355C3×C4C5×#12611yescharacteristic
356C2×C5C3×#39611yescharacteristic
357C2×C5C3×#46211yescharacteristic
358C2×C5C3×#46311yescharacteristic
359C2×C5C3×#46711yescharacteristic
360C2×C5C3×#46811yescharacteristic
361C2×C5C3×#47711yescharacteristic
362C2×C5C3×#47911yescharacteristic
363C23C2×C3×C5×D411yescharacteristic
364Q8—22no—
365Q8—22no—
366Q8—41no—
367Q8—41no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4C3×C5×Q1612yes—
386C2×C4C2×C3×C5×D411yescharacteristic
387C2×C4C2×C3×C5×D411yescharacteristic
388C2×C4C2×C3×C5×Q811yescharacteristic
389C2×C4C3×C5×#4111yescharacteristic
390C2×C4C3×C5×#4111yescharacteristic
391C2×C4C3×C5×#4111yescharacteristic
392C8—22no—
393C8—41no—
394C2×C3C5×#39611yescharacteristic
395C2×C3C5×#46211yescharacteristic
396C2×C3C5×#46311yescharacteristic
397C2×C3C5×#46711yescharacteristic
398C2×C3C5×#46811yescharacteristic
399C2×C3C5×#47711yescharacteristic
400C2×C3C5×#47911yescharacteristic
401C5C3×#206811yescharacteristic, direct product factor, Sylow
402C22C3×C5×#12111yescharacteristic
403C22C3×C5×#12111yescharacteristic
404C22C3×C5×C22⋊Q811yescharacteristic
405C22C2×C3×C5×Q1611yescharacteristic
406C22C3×C5×#13511yescharacteristic
407C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
408C22C3×C5×#13711yescharacteristic
409C4—22no—
410C4—42no—
411C4—41no—
412C4—42no—
413C4—81no—
414C4—81no—
415C4C3×C5×#12111yescharacteristic
416C4C3×C5×C22⋊Q811yescharacteristic
417C4C3×C5×C22⋊Q811yescharacteristic
418C4C3×C5×#12611yescharacteristic
419C3C5×#206811yescharacteristic, direct product factor, Sylow
420C2C3×C5×#39611yescharacteristic
421C2C3×C5×#46211yescharacteristic
422C2C3×C5×#46311yescharacteristic
423C2C3×C5×#46711yescharacteristic
424C2C3×C5×#46811yescharacteristic
425C2C3×C5×#47711yescharacteristic
426C2C3×C5×#47911yescharacteristic
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×#2068C3direct (N × H)
24. C3×#2068C5direct (N × H)
82. #2068C3×C5direct (N × H)
338. C3×C5#2068direct (N × H)
401. C5C3×#2068direct (N × H)
419. C3C5×#2068direct (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×C4⋊C82
C2×C3×C5×#1032
C3×C5×#3912
C3×C5×#3892
C3×C5×#3402
C5×#20683
C3×#20685