Finite Group Databasebeta

← C3×#10602680 #14288609

Subgroups — C3×#10602680 #14288609

Order 1920.

416 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#539C211yesmaximal, characteristic
2C3×#65333C211yesmaximal, characteristic, complemented
3C3×#65323C211yesmaximal, characteristic
4C3×#65275C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6C3×#64757C211yesmaximal, characteristic
7C3×#64748C211yesmaximal, characteristic, complemented
8#10602680C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#126—21no—
10C3×C5×#125—21no—
11C3×C5×#123—21no—
12C3×C5×#123—21no—
13C3×C5×C22⋊Q8—21no—
14C3×C5×C22⋊Q8C2211yescharacteristic
15C3×C5×#121C2211yescharacteristic
16C3×C4×C5×D4—21no—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C3×#3967—21no—
20C3×#3964—21no—
21C3×#3963—21no—
22C3×#3963—21no—
23C3×#3963C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3940—21no—
27C3×#3939—21no—
28C3×#1615—51nomaximal, Hall
29C5×#539C2×C311yescharacteristic
30#65333C2×C311yescharacteristic, complemented
31#65323C2×C311yescharacteristic
32#65275C2×C311yescharacteristic, complemented
33#64758C2×C311yescharacteristic, complemented
34#64757C2×C311yescharacteristic
35#64748C2×C311yescharacteristic, complemented
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5D411yescharacteristic
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5C2311yescharacteristic
43C22×C3×Dic5—21no—
44C22×C3×Dic5—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—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C42×C5—21no—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C3×#539D511yescharacteristic
64C3×#484—51no—
65C3×#481—51no—
66C3×#400—51no—
67C3×#328—51no—
68C3×#327—51no—
69C3×#324—51no—
70C5×#126—21no—
71C5×#125—21no—
72C5×#123—21no—
73C5×#123—21no—
74C5×C22⋊Q8—21no—
75C5×C22⋊Q8C22×C311yescharacteristic
76C5×#121C22×C311yescharacteristic
77C4×C5×D4—21no—
78C2×C5×C4⋊C4C22×C311yescharacteristic
79C2×C4⋊Dic5C22×C311yescharacteristic
80#3967—21no—
81#3964—21no—
82#3963—21no—
83#3963—21no—
84#3963C22×C311yescharacteristic
85C22⋊#168C22×C311yescharacteristic
86C22⋊#168C22×C311yescharacteristic
87#3940—21no—
88#3939—21no—
89#1615—51noSylow
90C23×C3×C5—21no—
91C23×C3×C5C2×D411yescharacteristic
92C3×C5×Q8—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—81no—
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×Dic5—41no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5—42no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—41no—
113C3×#168—41no—
114C3×#168—41no—
115C3×#126—21no—
116C3×#125—21no—
117C3×#123—21no—
118C3×#123—21no—
119C3×C22⋊Q8—21no—
120C3×C22⋊Q8C2×D511yescharacteristic
121C3×#121C2×D511yescharacteristic
122C3×C4×D4—21no—
123C2×C3×C4⋊C4—51no—
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C3×#107—101no—
126C3×#106—101no—
127C3×#103—101no—
128C3×#102—101no—
129C3×C22⋊C8—51no—
130C3×C22⋊C8—51no—
131C3×#95—51no—
132C3×#95—101no—
133C3×#95—101no—
134C2×C5×Q8C3×D411yescharacteristic
135C2×C5×D4—21no—
136C2×C5×D4C3×D411yescharacteristic
137C22×C4×C5—21no—
138C22×C4×C5C3×D411yescharacteristic
139C22×C4×C5C3×D411yescharacteristic
140C22×C4×C5C23×C311yescharacteristic
141C22×Dic5—21no—
142C22×Dic5—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4C3×D411yescharacteristic
150C5×C4⋊C4C3×D411yescharacteristic
151C5×C22⋊C4—21no—
152C5×C22⋊C4—21no—
153C5×C22⋊C4—21no—
154C5×C22⋊C4—21no—
155C5×C22⋊C4—21no—
156C42×C5—21no—
157C4⋊Dic5—21no—
158C4⋊Dic5—21no—
159C2×#168—21no—
160C2×#168—21no—
161#539C3×D511yescharacteristic
162#484—51no—
163#481—51no—
164#400—51no—
165#328—51no—
166#327—51no—
167#324—51no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5#12011yescharacteristic
174C22×C3×C5#13511yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×C4×C5—41no—
183C3×Dic5—81no—
184C3×Dic5—81no—
185C2×C3×Q8C22⋊D511yescharacteristic
186C2×C3×D4—21no—
187C2×C3×D4C22⋊D511yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4—101no—
190C22×C3×C4—101no—
191C22×C3×C4C22⋊D511yescharacteristic
192C22×C3×C4C22⋊D511yescharacteristic
193C22×C3×C4C22×D511yescharacteristic
194C2×C3×C8—101no—
195C2×C3×C8—101no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4—101no—
204C3×C4⋊C4C22⋊D511yescharacteristic
205C3×C4⋊C4C22⋊D511yescharacteristic
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—21no—
211C3×C42—21no—
212C23×C5—21no—
213C23×C5C2×C3×D411yescharacteristic
214C5×Q8—41no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—81no—
228C2×C4×C5C2×C3×D411yescharacteristic
229C2×C4×C5C2×C3×D411yescharacteristic
230C2×Dic5—41no—
231C2×Dic5—41no—
232C2×Dic5—42no—
233C2×Dic5—41no—
234C2×Dic5—41no—
235#168—41no—
236#168—41no—
237#126—21no—
238#125—21no—
239#123—21no—
240#123—21no—
241C22⋊Q8—21no—
242C22⋊Q8C2×C3×D511yescharacteristic
243#121C2×C3×D511yescharacteristic
244C4×D4—21no—
245C2×C4⋊C4—51no—
246C2×C4⋊C4C2×C3×D511yescharacteristic
247#107—101no—
248#106—101no—
249#103—101no—
250#102—101no—
251C22⋊C8—51no—
252C22⋊C8—51no—
253#95—51no—
254#95—101no—
255#95—101no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—81no—
259C2×C3×C5#45211yescharacteristic
260C2×C3×C5#45411yescharacteristic
261C2×C3×C5#45811yescharacteristic
262C23×C3—21no—
263C23×C3C2×C22⋊D511yescharacteristic
264C3×Q8—41no—
265C3×D4—41no—
266C3×D4—41no—
267C3×D4—41no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—81no—
278C2×C3×C4—201no—
279C2×C3×C4—201no—
280C2×C3×C4—202no—
281C2×C3×C4—201no—
282C2×C3×C4—201no—
283C2×C3×C4C2×C22⋊D511yescharacteristic
284C2×C3×C4C2×C22⋊D511yescharacteristic
285C3×C8—201no—
286C3×C8—201no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—41no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5C3×#12011yescharacteristic
293C22×C5C3×#13511yescharacteristic
294C22×C5C3×#13711yescharacteristic
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—41no—
299C4×C5—41no—
300C4×C5—41no—
301C4×C5—41no—
302Dic5—81no—
303Dic5—81no—
304C2×Q8C3×C22⋊D511yescharacteristic
305C2×D4—21no—
306C2×D4C3×C22⋊D511yescharacteristic
307C22×C4—21no—
308C22×C4—101no—
309C22×C4—101no—
310C22×C4C3×C22⋊D511yescharacteristic
311C22×C4C3×C22⋊D511yescharacteristic
312C22×C4C22×C3×D511yescharacteristic
313C2×C8—101no—
314C2×C8—101no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—101no—
322C4⋊C4—101no—
323C4⋊C4C3×C22⋊D511yescharacteristic
324C4⋊C4C3×C22⋊D511yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C42—21no—
331C3×C5#161511yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3#409611yescharacteristic
338C22×C3#409711yescharacteristic
339C22×C3#409911yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—401no—
348C3×C4—401no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5—81no—
352C2×C5C3×#45211yescharacteristic
353C2×C5C3×#45411yescharacteristic
354C2×C5C3×#45811yescharacteristic
355C23—21no—
356C23C2×C3×C22⋊D511yescharacteristic
357Q8—41no—
358D4—41no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—201no—
372C2×C4—201no—
373C2×C4—202no—
374C2×C4—201no—
375C2×C4—201no—
376C2×C4C2×C3×C22⋊D511yescharacteristic
377C2×C4C2×C3×C22⋊D511yescharacteristic
378C8—201no—
379C8—201no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—81no—
383C2×C3#6552811yescharacteristic
384C2×C3#6553211yescharacteristic
385C2×C3#6553411yescharacteristic
386C5C3×#161511yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22C3×#409611yescharacteristic
393C22C3×#409711yescharacteristic
394C22C3×#409911yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—401no—
403C4—401no—
404C3#1060268011yescharacteristic, direct product factor, Sylow
405C2—21no—
406C2—21no—
407C2—81no—
408C2C3×#6552811yescharacteristic
409C2C3×#6553211yescharacteristic
410C2C3×#6553411yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#539C2
socleC22×C3×C5#120
prime radicalC3×C5×#121C22
hypercenterC3×#539D5
hypocenterC5C3×#1615
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#539

Complements

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

NH ≅ G/Ntype
2. C3×#65333C2semidirect
4. C3×#65275C2semidirect
5. C3×#64758C2semidirect
7. C3×#64748C2semidirect
8. #10602680C3direct (N × H)
30. #65333C2×C3semidirect
32. #65275C2×C3semidirect
33. #64758C2×C3semidirect
35. #64748C2×C3semidirect
331. C3×C5#1615semidirect
386. C5C3×#1615semidirect
404. C3#10602680direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5392
C3×#653332
C3×#653232
C3×#652752
C3×#647582
C3×#647572
C3×#647482
#106026803
C3×#16155