Finite Group Databasebeta

← C3×C5×#2101 #14275135

Subgroups — C3×C5×#2101 #14275135

Order 1920.

396 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#389C211yesmaximal, characteristic
2C3×C5×#382C211yesmaximal, characteristic
3C3×C5×#340C211yesmaximal, characteristic
4C3×C5×#340C211yesmaximal, characteristic
5C3×C5×#340C211yesmaximal, characteristic
6C3×C5×#340C211yesmaximal, characteristic
7C3×C5×#336C211yesmaximal, characteristic
8C5×#2101C311yesmaximal, 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×#95—21no—
18C3×C5×#95—21no—
19C3×C5×#95—21no—
20C3×#2101C511yesmaximal, characteristic, direct product factor, Hall
21C5×#389C2×C311yescharacteristic
22C5×#382C2×C311yescharacteristic
23C5×#340C2×C311yescharacteristic
24C5×#340C2×C311yescharacteristic
25C5×#340C2×C311yescharacteristic
26C5×#340C2×C311yescharacteristic
27C5×#336C2×C311yescharacteristic
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C5×C8—21no—
36C2×C3×C5×C8—21no—
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
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—42no—
49C3×C5×C4⋊C4Q812yes—
50C3×C42×C5—21no—
51C3×C42×C5—21no—
52C3×#389C2×C511yescharacteristic
53C3×#382C2×C511yescharacteristic
54C3×#340C2×C511yescharacteristic
55C3×#340C2×C511yescharacteristic
56C3×#340C2×C511yescharacteristic
57C3×#340C2×C511yescharacteristic
58C3×#336C2×C511yescharacteristic
59C22×C5×C8C22×C311yescharacteristic
60C22×C5×C8C22×C311yescharacteristic
61C2×C5×C4⋊C4—21no—
62C2×C5×C4⋊C4C22×C311yescharacteristic
63C2×C5×C4⋊C4C22×C311yescharacteristic
64C2×C5×C4⋊C4C22×C311yescharacteristic
65C2×C5×C4⋊C4C22×C311yescharacteristic
66C2×C42×C5C22×C311yescharacteristic
67C5×#95—21no—
68C5×#95—21no—
69C5×#95—21no—
70#2101C3×C511yescharacteristic, direct product factor, Sylow
71C23×C3×C5C2×D411yescharacteristic
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—21no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
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×C5C2×Q811yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C2×C3×C4×C5#4111yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C3×C5×C8—41no—
97C3×C5×C8—41no—
98C22×C3×C8C22×C511yescharacteristic
99C22×C3×C8C22×C511yescharacteristic
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C22×C511yescharacteristic
102C2×C3×C4⋊C4C22×C511yescharacteristic
103C2×C3×C4⋊C4C22×C511yescharacteristic
104C2×C3×C4⋊C4C22×C511yescharacteristic
105C2×C3×C42C22×C511yescharacteristic
106C3×#95—21no—
107C3×#95—21no—
108C3×#95—21no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5C3×D411yescharacteristic
114C22×C4×C5C3×D411yescharacteristic
115C22×C4×C5C23×C311yescharacteristic
116C2×C5×C8—21no—
117C2×C5×C8—21no—
118C2×C5×C8—21no—
119C2×C5×C8—21no—
120C2×C5×C8—21no—
121C2×C5×C8—21no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—42no—
130C5×C4⋊C4C3×Q812yes—
131C42×C5—21no—
132C42×C5—21no—
133#389C2×C3×C511yescharacteristic
134#382C2×C3×C511yescharacteristic
135#340C2×C3×C511yescharacteristic
136#340C2×C3×C511yescharacteristic
137#340C2×C3×C511yescharacteristic
138#340C2×C3×C511yescharacteristic
139#336C2×C3×C511yescharacteristic
140C22×C3×C5C22⋊Q811yescharacteristic
141C22×C3×C5#12311yescharacteristic
142C22×C3×C5#12411yescharacteristic
143C22×C3×C5#13511yescharacteristic
144C22×C3×C5#13511yescharacteristic
145C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
146C22×C3×C5#13711yescharacteristic
147C3×C4×C5—42no—
148C3×C4×C5—41no—
149C3×C4×C5—41no—
150C3×C4×C5—81no—
151C3×C4×C5—81no—
152C3×C4×C5—81no—
153C3×C4×C5#12511yescharacteristic
154C3×C4×C5#12511yescharacteristic
155C3×C4×C5#12611yescharacteristic
156C3×C4×C5#12611yescharacteristic
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4C5×D411yescharacteristic
162C22×C3×C4C5×D411yescharacteristic
163C22×C3×C4C23×C511yescharacteristic
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—42no—
178C3×C4⋊C4C5×Q812yes—
179C3×C42—21no—
180C3×C42—21no—
181C23×C5C2×C3×D411yescharacteristic
182C2×C4×C5—22no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5C2×C3×Q811yescharacteristic
201C2×C4×C5C3×#4111yescharacteristic
202C2×C4×C5C3×#4111yescharacteristic
203C2×C4×C5C3×#4111yescharacteristic
204C2×C4×C5C3×#4111yescharacteristic
205C2×C4×C5C3×#4111yescharacteristic
206C5×C8—41no—
207C5×C8—41no—
208C22×C8C22×C3×C511yescharacteristic
209C22×C8C22×C3×C511yescharacteristic
210C2×C4⋊C4—21no—
211C2×C4⋊C4C22×C3×C511yescharacteristic
212C2×C4⋊C4C22×C3×C511yescharacteristic
213C2×C4⋊C4C22×C3×C511yescharacteristic
214C2×C4⋊C4C22×C3×C511yescharacteristic
215C2×C42C22×C3×C511yescharacteristic
216#95—21no—
217#95—21no—
218#95—21no—
219C2×C3×C5#40011yescharacteristic
220C2×C3×C5#47811yescharacteristic
221C2×C3×C5#47911yescharacteristic
222C2×C3×C5#48211yescharacteristic
223C2×C3×C5#48511yescharacteristic
224C2×C3×C5#48811yescharacteristic
225C2×C3×C5#48911yescharacteristic
226C23×C3C2×C5×D411yescharacteristic
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4C2×C5×Q811yescharacteristic
246C2×C3×C4C5×#4111yescharacteristic
247C2×C3×C4C5×#4111yescharacteristic
248C2×C3×C4C5×#4111yescharacteristic
249C2×C3×C4C5×#4111yescharacteristic
250C2×C3×C4C5×#4111yescharacteristic
251C3×C8—41no—
252C3×C8—41no—
253C22×C5C3×C22⋊Q811yescharacteristic
254C22×C5C3×#12311yescharacteristic
255C22×C5C3×#12411yescharacteristic
256C22×C5C3×#13511yescharacteristic
257C22×C5C3×#13511yescharacteristic
258C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
259C22×C5C3×#13711yescharacteristic
260C4×C5—42no—
261C4×C5—41no—
262C4×C5—41no—
263C4×C5—81no—
264C4×C5—81no—
265C4×C5—81no—
266C4×C5C3×#12511yescharacteristic
267C4×C5C3×#12511yescharacteristic
268C4×C5C3×#12611yescharacteristic
269C4×C5C3×#12611yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4C3×C5×D411yescharacteristic
275C22×C4C3×C5×D411yescharacteristic
276C22×C4C23×C3×C511yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—42no—
291C4⋊C4C3×C5×Q812yes—
292C42—21no—
293C42—21no—
294C3×C5#210111yescharacteristic, direct product factor, Hall
295C22×C3C5×C22⋊Q811yescharacteristic
296C22×C3C5×#12311yescharacteristic
297C22×C3C5×#12411yescharacteristic
298C22×C3C5×#13511yescharacteristic
299C22×C3C5×#13511yescharacteristic
300C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
301C22×C3C5×#13711yescharacteristic
302C3×C4—42no—
303C3×C4—41no—
304C3×C4—41no—
305C3×C4—81no—
306C3×C4—81no—
307C3×C4—81no—
308C3×C4C5×#12511yescharacteristic
309C3×C4C5×#12511yescharacteristic
310C3×C4C5×#12611yescharacteristic
311C3×C4C5×#12611yescharacteristic
312C2×C5C3×#40011yescharacteristic
313C2×C5C3×#47811yescharacteristic
314C2×C5C3×#47911yescharacteristic
315C2×C5C3×#48211yescharacteristic
316C2×C5C3×#48511yescharacteristic
317C2×C5C3×#48811yescharacteristic
318C2×C5C3×#48911yescharacteristic
319C23C2×C3×C5×D411yescharacteristic
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4C2×C3×C5×Q811yescharacteristic
339C2×C4C3×C5×#4111yescharacteristic
340C2×C4C3×C5×#4111yescharacteristic
341C2×C4C3×C5×#4111yescharacteristic
342C2×C4C3×C5×#4111yescharacteristic
343C2×C4C3×C5×#4111yescharacteristic
344C8—41no—
345C8—41no—
346C2×C3C5×#40011yescharacteristic
347C2×C3C5×#47811yescharacteristic
348C2×C3C5×#47911yescharacteristic
349C2×C3C5×#48211yescharacteristic
350C2×C3C5×#48511yescharacteristic
351C2×C3C5×#48811yescharacteristic
352C2×C3C5×#48911yescharacteristic
353C5C3×#210111yescharacteristic, direct product factor, Sylow
354C22C3×C5×C22⋊Q811yescharacteristic
355C22C3×C5×#12311yescharacteristic
356C22C3×C5×#12411yescharacteristic
357C22C3×C5×#13511yescharacteristic
358C22C3×C5×#13511yescharacteristic
359C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
360C22C3×C5×#13711yescharacteristic
361C4—42no—
362C4—41no—
363C4—41no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4C3×C5×#12511yescharacteristic
368C4C3×C5×#12511yescharacteristic
369C4C3×C5×#12611yescharacteristic
370C4C3×C5×#12611yescharacteristic
371C3C5×#210111yescharacteristic, direct product factor, Sylow
372C2C3×C5×#40011yescharacteristic
373C2C3×C5×#47811yescharacteristic
374C2C3×C5×#47911yescharacteristic
375C2C3×C5×#48211yescharacteristic
376C2C3×C5×#48511yescharacteristic
377C2C3×C5×#48811yescharacteristic
378C2C3×C5×#48911yescharacteristic
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×#2101C3direct (N × H)
20. C3×#2101C5direct (N × H)
70. #2101C3×C5direct (N × H)
294. C3×C5#2101direct (N × H)
353. C5C3×#2101direct (N × H)
371. C3C5×#2101direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#3892
C3×C5×#3822
C3×C5×#3402
C3×C5×#3362
C5×#21013
C3×#21015