Finite Group Databasebeta

← C3×#10601949 #14289485

Subgroups — C3×#10601949 #14289485

Order 1920.

428 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65913C211yesmaximal, characteristic
2C3×C5×#477C211yesmaximal, characteristic, complemented
3C3×#65381C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic
7C3×#64701C211yesmaximal, characteristic, complemented
8#10601949C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×Q8C2211yescharacteristic
11C3×#4092—21no—
12C2×C3×#689—22no—
13C3×#4042—22no—
14C3×D5×C4⋊C4—21no—
15C3×C4×D20—21no—
16C3×C4×D20C2211yescharacteristic
17C3×#4016—21no—
18C3×#4015C2211yescharacteristic
19C3×C5×#107—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#103—21no—
22C3×#3941—21no—
23C3×#3940—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1632—51nomaximal, Hall
27#65913C2×C311yescharacteristic
28C5×#477C2×C311yescharacteristic, complemented
29#65381C2×C311yescharacteristic, complemented
30#65373C2×C311yescharacteristic
31Q8⋊#168C2×C311yescharacteristic, complemented
32#64703C2×C311yescharacteristic
33#64701C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—22no—
39C2×C3×Dic10D412yes—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47C3×#689—44no—
48C3×#685—22no—
49C3×#685—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—22no—
54C3×#683—22no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57C3×#554—51no—
58C3×#494—51no—
59C3×#477D511yescharacteristic, complemented
60C3×#476—51no—
61C3×#333—51no—
62C3×Q8⋊C8—51no—
63C3×D4⋊C8—51no—
64C5×C4⋊Q8C22×C311yescharacteristic
65C4×C5×Q8C22×C311yescharacteristic
66#4092—21no—
67C2×#689—22no—
68#4042—22no—
69D5×C4⋊C4—21no—
70C4×D20—21no—
71C4×D20C22×C311yescharacteristic
72#4016—21no—
73#4015C22×C311yescharacteristic
74C5×#107—21no—
75C5×C4⋊C8C22×C311yescharacteristic
76C5×#103—21no—
77#3941—21no—
78#3940—21no—
79C4⋊#168C22×C311yescharacteristic
80C4×#168C22×C311yescharacteristic
81#1632—51noSylow
82C22×C3×D5—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—42no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×Dic5—21no—
93C2×C3×Dic5—22no—
94C3×D20—21no—
95C3×D20Q1612yescomplemented
96C3×C4×D5—41no—
97C3×C4×D5—41no—
98C3×C4×D5—82no—
99C3×Dic10—42no—
100C3×C5×C8—41no—
101C3×#168—22no—
102C3×#168—41no—
103C2×C3×Q16—102no—
104C3×C4⋊Q8—51no—
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×#125—101no—
107C3×C22⋊Q8—102no—
108C3×C22⋊Q8—101no—
109C3×C4×Q8C2×D511yescharacteristic
110C3×C4×D4—51no—
111C3×C4×D4—101no—
112C2×C3×C4⋊C4—101no—
113C3×#107—21no—
114C3×#106—101no—
115C3×C4⋊C8—51no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×#103—21no—
118C3×#102—101no—
119C3×C4×C8—51no—
120C2×C5×Q8—21no—
121C2×C5×Q8C3×D411yescharacteristic
122C2×D20C3×D411yescharacteristic
123C2×C4×D5—21no—
124C2×C4×D5—22no—
125C2×Dic10C3×D412yes—
126C2×C5×C8—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4C3×D411yescharacteristic
131C42×C5—21no—
132C42×C5C23×C311yescharacteristic
133#689—44no—
134#685—22no—
135#685—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5C3×D411yescharacteristic
139#683—22no—
140#683—22no—
141C2×#168—21no—
142C2×#168—21no—
143#554—51no—
144#494—51no—
145#477C3×D511yescharacteristic, complemented
146#476—51no—
147#333—51no—
148Q8⋊C8—51no—
149D4⋊C8—51no—
150C22×C3×C5#12011yescharacteristic
151C2×C3×D5—22no—
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5—81no—
158C3×C4×C5C2×Q1611yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×Dic5—41no—
163C3×Dic5—42no—
164C2×C3×Q8—21no—
165C2×C3×Q8—52no—
166C2×C3×Q8C22⋊D511yescharacteristic
167C2×C3×D4—51no—
168C22×C3×C4—102no—
169C22×C3×C4—101no—
170C3×Q16—204no—
171C2×C3×C8—21no—
172C2×C3×C8—101no—
173C2×C3×C8—101no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—51no—
178C3×C4⋊C4—102no—
179C3×C4⋊C4—102no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4C22⋊D511yescharacteristic
183C3×C22⋊C4—102no—
184C3×C22⋊C4—101no—
185C3×C42—21no—
186C3×C42C22×D511yescharacteristic
187C22×D5—21no—
188C5×Q8—21no—
189C5×Q8—21no—
190C5×Q8—42no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—41no—
194C2×C4×C5C2×C3×D411yescharacteristic
195C2×C4×C5C2×C3×D411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×Dic5—21no—
198C2×Dic5—22no—
199D20—21no—
200D20C3×Q1612yescomplemented
201C4×D5—41no—
202C4×D5—41no—
203C4×D5—82no—
204Dic10—42no—
205C5×C8—41no—
206#168—22no—
207#168—41no—
208C2×Q16—102no—
209C4⋊Q8—51no—
210C4⋊Q8C2×C3×D511yescharacteristic
211#125—101no—
212C22⋊Q8—102no—
213C22⋊Q8—101no—
214C4×Q8C2×C3×D511yescharacteristic
215C4×D4—51no—
216C4×D4—101no—
217C2×C4⋊C4—101no—
218#107—21no—
219#106—101no—
220C4⋊C8—51no—
221C4⋊C8C2×C3×D511yescharacteristic
222#103—21no—
223#102—101no—
224C4×C8—51no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C3×D5—42no—
229C23×C3—101no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—42no—
233C3×Q8—202no—
234C3×D4—52no—
235C3×D4—101no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—41no—
239C2×C3×C4—101no—
240C2×C3×C4—102no—
241C2×C3×C4—201no—
242C2×C3×C4—201no—
243C2×C3×C4—402no—
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C3×C8—41no—
248C3×C8—102no—
249C3×C8—201no—
250C22×C5C3×#12011yescharacteristic
251C2×D5—22no—
252C2×D5—41no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—81no—
258C4×C5C2×C3×Q1611yescharacteristic
259C4×C5C3×#13511yescharacteristic
260C4×C5C3×#13711yescharacteristic
261C4×C5C3×#13711yescharacteristic
262Dic5—41no—
263Dic5—42no—
264C2×Q8—21no—
265C2×Q8—52no—
266C2×Q8C3×C22⋊D511yescharacteristic
267C2×D4—51no—
268C22×C4—102no—
269C22×C4—101no—
270Q16—204no—
271C2×C8—21no—
272C2×C8—101no—
273C2×C8—101no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—51no—
278C4⋊C4—102no—
279C4⋊C4—102no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4C3×C22⋊D511yescharacteristic
283C22⋊C4—102no—
284C22⋊C4—101no—
285C42—21no—
286C42C22×C3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—102no—
289C22×C3—201no—
290C22×C3—201no—
291C22×C3#408311yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—81no—
296C3×C4—201no—
297C3×C4—202no—
298C3×C4D5×Q1611yescharacteristic
299C3×C4#406411yescharacteristic
300C3×C4#408811yescharacteristic
301C3×C4#409611yescharacteristic
302C2×C5C3×#45111yescharacteristic
303C2×C5C3×#45211yescharacteristic
304C2×C5C3×#45311yescharacteristic
305D5—42no—
306C23—101no—
307Q8—21no—
308Q8—21no—
309Q8—42no—
310Q8—202no—
311D4—52no—
312D4—101no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—101no—
317C2×C4—102no—
318C2×C4—201no—
319C2×C4—201no—
320C2×C4—402no—
321C2×C4C3×D4×D511yescharacteristic
322C2×C4C3×D4×D511yescharacteristic
323C2×C4C2×C3×C22⋊D511yescharacteristic
324C8—41no—
325C8—102no—
326C8—201no—
327C2×C3—202no—
328C2×C3#6533611yescharacteristic
329C2×C3#6547511yescharacteristic
330C2×C3#6548711yescharacteristic
331C5C3×#163211yescharacteristic, complemented, Sylow
332C22—102no—
333C22—201no—
334C22—201no—
335C22C3×#408311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—201no—
341C4—202no—
342C4C3×D5×Q1611yescharacteristic
343C4C3×#406411yescharacteristic
344C4C3×#408811yescharacteristic
345C4C3×#409611yescharacteristic
346C3#1060194911yescharacteristic, direct product factor, Sylow
347C2—202no—
348C2C3×#6533611yescharacteristic
349C2C3×#6547511yescharacteristic
350C2C3×#6548711yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#477C2
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC3×#477D5
hypocenterC5C3×#1632
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
2. C3×C5×#477C2semidirect
3. C3×#65381C2semidirect
5. C3×Q8⋊#168C2semidirect
7. C3×#64701C2semidirect
8. #10601949C3direct (N × H)
28. C5×#477C2×C3semidirect
29. #65381C2×C3semidirect
31. Q8⋊#168C2×C3semidirect
33. #64701C2×C3semidirect
59. C3×#477D5semidirect
95. C3×D20Q16semidirect
145. #477C3×D5semidirect
200. D20C3×Q16semidirect
287. C3×C5#1632semidirect
331. C5C3×#1632semidirect
346. C3#10601949direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659132
C3×C5×#4772
C3×#653812
C3×#653732
C3×Q8⋊#1682
C3×#647032
C3×#647012
#106019493
C3×#16325