Finite Group Databasebeta

← C3×#10602022 #14289809

Subgroups — C3×#10602022 #14289809

Order 1920.

388 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66066C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic, complemented
3C3×#65380C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic
7C3×#64676C211yesmaximal, characteristic, complemented
8#10602022C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4093—21no—
12C3×Q8×Dic5—21no—
13C3×#4044—22no—
14C3×#4043—21no—
15C3×#4038—21no—
16C3×C4×D20C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C3×C5×#103—22no—
19C3×C4×C5×C8C2211yescharacteristic
20C3×#3942—21no—
21C3×#3941—21no—
22C3×#3940—21no—
23C3×#3939—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1638—51nomaximal, Hall
27#66066C2×C311yescharacteristic
28C5×#487C2×C311yescharacteristic, complemented
29#65380C2×C311yescharacteristic, complemented
30#65373C2×C311yescharacteristic
31#64767C2×C311yescharacteristic, complemented
32#64679C2×C311yescharacteristic
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D412yes—
44C3×C42×C5C2311yescharacteristic
45C3×#685—22no—
46C3×#685—22no—
47C3×#685—21no—
48C3×C4⋊Dic5—22no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—22no—
53C3×C4×Dic5—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C3×#556—51no—
57C3×#487D511yescharacteristic, complemented
58C3×#477—51no—
59C3×#476—51no—
60C3×#332—51no—
61C3×Q8⋊C8—51no—
62C3×D4⋊C8—51no—
63C5×C4⋊Q8C22×C311yescharacteristic
64C5×C4⋊Q8C22×C311yescharacteristic
65#4093—21no—
66Q8×Dic5—21no—
67#4044—22no—
68#4043—21no—
69#4038—21no—
70C4×D20C22×C311yescharacteristic
71C4×Dic10C22×C311yescharacteristic
72C5×#103—22no—
73C4×C5×C8C22×C311yescharacteristic
74#3942—21no—
75#3941—21no—
76#3940—21no—
77#3939—21no—
78C4⋊#168C22×C311yescharacteristic
79C4⋊#168C22×C311yescharacteristic
80#1638—51noSylow
81C22×C3×D5—21no—
82C3×C5×Q8—42no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C3×D20—21no—
94C3×D20—21no—
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99C3×C5×C8—41no—
100C3×#168—41no—
101C3×#168—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×C4⋊Q8C2×D511yescharacteristic
104C3×#126—102no—
105C3×#124—101no—
106C3×C22⋊Q8—101no—
107C3×C4×Q8—51no—
108C3×C4×Q8—101no—
109C3×C4×D4—51no—
110C3×#117—101no—
111C3×#107—101no—
112C3×#106—101no—
113C3×C4⋊C8—51no—
114C3×C4⋊C8—51no—
115C3×#103—22no—
116C3×#103—101no—
117C3×#102—101no—
118C3×C4×C8C2×D511yescharacteristic
119C2×C5×Q8—21no—
120C2×C5×Q8—21no—
121C2×D20C3×D411yescharacteristic
122C2×C4×D5—21no—
123C2×Dic10C3×D411yescharacteristic
124C2×C5×C8—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4C3×D412yes—
129C42×C5C23×C311yescharacteristic
130#685—22no—
131#685—22no—
132#685—21no—
133C4⋊Dic5—22no—
134C4⋊Dic5C3×D411yescharacteristic
135C4⋊Dic5C3×D411yescharacteristic
136#683—21no—
137C4×Dic5—22no—
138C4×Dic5—21no—
139C2×#168—21no—
140C2×#168—21no—
141#556—51no—
142#487C3×D511yescharacteristic, complemented
143#477—51no—
144#476—51no—
145#332—51no—
146Q8⋊C8—51no—
147D4⋊C8—51no—
148C22×C3×C5#12011yescharacteristic
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151C2×C3×D5—41no—
152C3×C4×C5—21no—
153C3×C4×C5—42no—
154C3×C4×C5—81no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×Dic5—41no—
160C3×Dic5—41no—
161C3×Dic5—41no—
162C2×C3×Q8—21no—
163C2×C3×Q8—21no—
164C2×C3×Q8—51no—
165C2×C3×D4—51no—
166C22×C3×C4—101no—
167C2×C3×C8—21no—
168C2×C3×C8—101no—
169C2×C3×C8—101no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—51no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—102no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4C22⋊D512yes—
178C3×C22⋊C4—102no—
179C3×C22⋊C4—102no—
180C3×C22⋊C4—101no—
181C3×C42—102no—
182C3×C42—101no—
183C3×C42C22×D511yescharacteristic
184C22×D5—21no—
185C5×Q8—42no—
186C5×Q8—41no—
187C5×Q8—41no—
188C2×C4×C5—22no—
189C2×C4×C5—41no—
190C2×C4×C5C2×C3×D411yescharacteristic
191C2×C4×C5C2×C3×D411yescharacteristic
192C2×C4×C5C2×C3×D411yescharacteristic
193C2×Dic5—21no—
194C2×Dic5—21no—
195C2×Dic5—21no—
196D20—21no—
197D20—21no—
198C4×D5—41no—
199C4×D5—41no—
200Dic10—21no—
201Dic10—21no—
202C5×C8—41no—
203#168—41no—
204#168—41no—
205C4⋊Q8C2×C3×D511yescharacteristic
206C4⋊Q8C2×C3×D511yescharacteristic
207#126—102no—
208#124—101no—
209C22⋊Q8—101no—
210C4×Q8—51no—
211C4×Q8—101no—
212C4×D4—51no—
213#117—101no—
214#107—101no—
215#106—101no—
216C4⋊C8—51no—
217C4⋊C8—51no—
218#103—22no—
219#103—101no—
220#102—101no—
221C4×C8C2×C3×D511yescharacteristic
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C3×D5—81no—
226C23×C3—101no—
227C3×Q8—42no—
228C3×Q8—41no—
229C3×Q8—41no—
230C3×Q8—101no—
231C3×Q8—101no—
232C3×D4—101no—
233C3×D4—101no—
234C2×C3×C4—22no—
235C2×C3×C4—41no—
236C2×C3×C4—101no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—201no—
240C2×C3×C4—201no—
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4C2×C22⋊D511yescharacteristic
244C3×C8—41no—
245C3×C8—201no—
246C3×C8—201no—
247C22×C5C3×#12011yescharacteristic
248C2×D5—41no—
249C2×D5—41no—
250C2×D5—41no—
251C4×C5—21no—
252C4×C5—42no—
253C4×C5—81no—
254C4×C5C3×#13511yescharacteristic
255C4×C5C3×#13511yescharacteristic
256C4×C5C3×#13711yescharacteristic
257C4×C5C3×#13711yescharacteristic
258Dic5—41no—
259Dic5—41no—
260Dic5—41no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—51no—
264C2×D4—51no—
265C22×C4—101no—
266C2×C8—21no—
267C2×C8—101no—
268C2×C8—101no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—51no—
273C4⋊C4—51no—
274C4⋊C4—102no—
275C4⋊C4—101no—
276C4⋊C4C3×C22⋊D512yes—
277C22⋊C4—102no—
278C22⋊C4—102no—
279C22⋊C4—101no—
280C42—102no—
281C42—101no—
282C42C22×C3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—201no—
285C22×C3—201no—
286C22×C3—201no—
287C22×C3#408311yescharacteristic
288C3×C4—21no—
289C3×C4—42no—
290C3×C4—81no—
291C3×C4—201no—
292C3×C4—201no—
293C3×C4—201no—
294C3×C4#406111yescharacteristic
295C3×C4#406211yescharacteristic
296C3×C4#406411yescharacteristic
297C3×C4#406511yescharacteristic
298C2×C5C3×#45211yescharacteristic
299C2×C5C3×#45211yescharacteristic
300C2×C5C3×#45411yescharacteristic
301D5—81no—
302C23—101no—
303Q8—42no—
304Q8—41no—
305Q8—41no—
306Q8—101no—
307Q8—101no—
308D4—101no—
309D4—101no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—201no—
316C2×C4—201no—
317C2×C4C3×D4×D511yescharacteristic
318C2×C4C3×D4×D511yescharacteristic
319C2×C4C2×C3×C22⋊D511yescharacteristic
320C8—41no—
321C8—201no—
322C8—201no—
323C2×C3—401no—
324C2×C3#6535111yescharacteristic
325C2×C3#6546211yescharacteristic
326C2×C3#6547611yescharacteristic
327C5C3×#163811yescharacteristic, complemented, Sylow
328C22—201no—
329C22—201no—
330C22—201no—
331C22C3×#408311yescharacteristic
332C4—21no—
333C4—42no—
334C4—81no—
335C4—201no—
336C4—201no—
337C4—201no—
338C4C3×#406111yescharacteristic
339C4C3×#406211yescharacteristic
340C4C3×#406411yescharacteristic
341C4C3×#406511yescharacteristic
342C3#1060202211yescharacteristic, direct product factor, Sylow
343C2—401no—
344C2C3×#6535111yescharacteristic
345C2C3×#6546211yescharacteristic
346C2C3×#6547611yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#487C2
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC3×#487D5
hypocenterC5C3×#1638
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
2. C3×C5×#487C2semidirect
3. C3×#65380C2semidirect
5. C3×#64767C2semidirect
7. C3×#64676C2semidirect
8. #10602022C3direct (N × H)
28. C5×#487C2×C3semidirect
29. #65380C2×C3semidirect
31. #64767C2×C3semidirect
33. #64676C2×C3semidirect
57. C3×#487D5semidirect
142. #487C3×D5semidirect
283. C3×C5#1638semidirect
327. C5C3×#1638semidirect
342. C3#10602022direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660662
C3×C5×#4872
C3×#653802
C3×#653732
C3×#647672
C3×#646792
C3×#646762
#106020223
C3×#16385