Finite Group Databasebeta

← C3×#10598998 #14289824

Subgroups — C3×#10598998 #14289824

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×#65876C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic
3C3×#65139C211yesmaximal, characteristic, complemented
4C3×#64970C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10598998C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C3×#4082—21no—
11C3×#4072—21no—
12C3×#4070—21no—
13C3×#4033—21no—
14C3×#4025—22no—
15C3×#4015C2211yescharacteristic
16C3×#4015C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C4×C5×C8C2211yescharacteristic
20C3×#3964—21no—
21C3×#3950—21no—
22C3×#3948—21no—
23C3×#3948—22no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1638—51nomaximal, Hall
27#65876C2×C311yescharacteristic
28#65297C2×C311yescharacteristic
29#65139C2×C311yescharacteristic, complemented
30#64970C2×C311yescharacteristic, complemented
31C5×D4⋊C8C2×C311yescharacteristic
32#64706C2×C311yescharacteristic, complemented
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C3×Dic10—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C3×C22⋊Dic5—22no—
45C3×C22⋊Dic5—22no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5D412yes—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—22no—
52C3×#683—21no—
53C3×C4×Dic5—22no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56C3×#556—51no—
57C3×#487—51no—
58C3×#477—51no—
59C3×#476—51no—
60C3×#332—51no—
61C3×Q8⋊C8—51no—
62C3×D4⋊C8D511yescharacteristic
63C4×C5×D4C22×C311yescharacteristic
64#4082—21no—
65#4072—21no—
66#4070—21no—
67#4033—21no—
68#4025—22no—
69#4015C22×C311yescharacteristic
70#4015C22×C311yescharacteristic
71C4×Dic10C22×C311yescharacteristic
72C5×C4⋊C8C22×C311yescharacteristic
73C4×C5×C8C22×C311yescharacteristic
74#3964—21no—
75#3950—21no—
76#3948—21no—
77#3948—22no—
78#3940—21no—
79C4⋊#168C22×C311yescharacteristic
80#1638—51noSylow
81C23×C3×C5—21no—
82C3×C5×D4—21no—
83C3×C5×D4—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
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—22no—
93C2×C3×Dic5—41no—
94C3×Dic10—21no—
95C3×Dic10—21no—
96C3×Dic10—41no—
97C3×Dic10—41no—
98C3×Dic10—42no—
99C3×C5×C8—41no—
100C3×C5×C8—41no—
101C3×#168—41no—
102C3×C4⋊Q8—51no—
103C3×C4⋊Q8—51no—
104C3×#126—102no—
105C3×#124—101no—
106C3×C22⋊Q8—101no—
107C3×C4×Q8—51no—
108C3×C4×Q8—101no—
109C3×C4×D4C2×D511yescharacteristic
110C3×#117—101no—
111C3×#107—101no—
112C3×#106—101no—
113C3×C4⋊C8—51no—
114C3×C4⋊C8C2×D511yescharacteristic
115C3×#103—102no—
116C3×#103—101no—
117C3×#102—101no—
118C3×C4×C8C2×D511yescharacteristic
119C2×C5×D4C3×D411yescharacteristic
120C22×C4×C5—21no—
121C2×Dic10—21no—
122C2×Dic10—21no—
123C2×Dic10C3×D411yescharacteristic
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C5×C4⋊C4C3×D411yescharacteristic
127C5×C22⋊C4—21no—
128C42×C5C23×C311yescharacteristic
129C22⋊Dic5—22no—
130C22⋊Dic5—22no—
131C4⋊Dic5—21no—
132C4⋊Dic5—21no—
133C4⋊Dic5—21no—
134C4⋊Dic5C3×D412yes—
135C4⋊Dic5C3×D411yescharacteristic
136#683—22no—
137#683—21no—
138C4×Dic5—22no—
139C4×Dic5—21no—
140C2×#168—21no—
141#556—51no—
142#487—51no—
143#477—51no—
144#476—51no—
145#332—51no—
146Q8⋊C8—51no—
147D4⋊C8C3×D511yescharacteristic
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5#12011yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×Dic5—41no—
159C3×Dic5—42no—
160C3×Dic5—41no—
161C3×Dic5—81no—
162C2×C3×Q8—51no—
163C2×C3×Q8—101no—
164C2×C3×Q8—101no—
165C2×C3×D4D2011yescharacteristic
166C22×C3×C4—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—101no—
170C3×C4⋊C4—52no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—102no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4D2011yescharacteristic
178C3×C22⋊C4—21no—
179C3×C22⋊C4—102no—
180C3×C22⋊C4—102no—
181C3×C42—102no—
182C3×C42—101no—
183C3×C42C22×D511yescharacteristic
184C23×C5—21no—
185C5×D4—21no—
186C5×D4—21no—
187C2×C4×C5—21no—
188C2×C4×C5—41no—
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—22no—
196C2×Dic5—41no—
197Dic10—21no—
198Dic10—21no—
199Dic10—41no—
200Dic10—41no—
201Dic10—42no—
202C5×C8—41no—
203C5×C8—41no—
204#168—41no—
205C4⋊Q8—51no—
206C4⋊Q8—51no—
207#126—102no—
208#124—101no—
209C22⋊Q8—101no—
210C4×Q8—51no—
211C4×Q8—101no—
212C4×D4C2×C3×D511yescharacteristic
213#117—101no—
214#107—101no—
215#106—101no—
216C4⋊C8—51no—
217C4⋊C8C2×C3×D511yescharacteristic
218#103—102no—
219#103—101no—
220#102—101no—
221C4×C8C2×C3×D511yescharacteristic
222C2×C3×C5—81no—
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45211yescharacteristic
225C2×C3×C5#45411yescharacteristic
226C23×C3—21no—
227C3×Q8—101no—
228C3×Q8—101no—
229C3×Q8—202no—
230C3×Q8—201no—
231C3×Q8—201no—
232C3×D4—21no—
233C3×D4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—101no—
238C2×C3×C4—102no—
239C2×C3×C4—101no—
240C2×C3×C4—201no—
241C2×C3×C4C2×D2011yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C3×C8—41no—
245C3×C8—41no—
246C3×C8—201no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5C3×#12011yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5C3×#13511yescharacteristic
254C4×C5C3×#13511yescharacteristic
255C4×C5C3×#13711yescharacteristic
256C4×C5C3×#13711yescharacteristic
257Dic5—41no—
258Dic5—42no—
259Dic5—41no—
260Dic5—81no—
261C2×Q8—51no—
262C2×Q8—101no—
263C2×Q8—101no—
264C2×D4C3×D2011yescharacteristic
265C22×C4—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—101no—
269C4⋊C4—52no—
270C4⋊C4—51no—
271C4⋊C4—102no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C4⋊C4—101no—
275C4⋊C4—101no—
276C4⋊C4C3×D2011yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—102no—
279C22⋊C4—102no—
280C42—102no—
281C42—101no—
282C42C22×C3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3#402811yescharacteristic
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—201no—
291C3×C4—201no—
292C3×C4—202no—
293C3×C4—401no—
294C3×C4#405011yescharacteristic
295C3×C4#405511yescharacteristic
296C3×C4#405811yescharacteristic
297C3×C4#406111yescharacteristic
298C2×C5—81no—
299C2×C5C3×#45211yescharacteristic
300C2×C5C3×#45211yescharacteristic
301C2×C5C3×#45411yescharacteristic
302C23—21no—
303Q8—101no—
304Q8—101no—
305Q8—202no—
306Q8—201no—
307Q8—201no—
308D4—21no—
309D4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—101no—
314C2×C4—102no—
315C2×C4—101no—
316C2×C4—201no—
317C2×C4C2×C3×D2011yescharacteristic
318C2×C4C3×D4×D511yescharacteristic
319C2×C4C3×D4×D511yescharacteristic
320C8—41no—
321C8—41no—
322C8—201no—
323C2×C3—81no—
324C2×C3#6502211yescharacteristic
325C2×C3#6507211yescharacteristic
326C2×C3#6511611yescharacteristic
327C5C3×#163811yescharacteristic, complemented, Sylow
328C22—41no—
329C22—41no—
330C22—41no—
331C22C3×#402811yescharacteristic
332C4—21no—
333C4—41no—
334C4—201no—
335C4—201no—
336C4—202no—
337C4—401no—
338C4C3×#405011yescharacteristic
339C4C3×#405511yescharacteristic
340C4C3×#405811yescharacteristic
341C4C3×#406111yescharacteristic
342C3#1059899811yescharacteristic, direct product factor, Sylow
343C2—81no—
344C2C3×#6502211yescharacteristic
345C2C3×#6507211yescharacteristic
346C2C3×#6511611yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1638
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
3. C3×#65139C2semidirect
4. C3×#64970C2semidirect
6. C3×#64706C2semidirect
7. C3×#64676C2semidirect
8. #10598998C3direct (N × H)
29. #65139C2×C3semidirect
30. #64970C2×C3semidirect
32. #64706C2×C3semidirect
33. #64676C2×C3semidirect
283. C3×C5#1638semidirect
327. C5C3×#1638semidirect
342. C3#10598998direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658762
C3×#652972
C3×#651392
C3×#649702
C3×C5×D4⋊C82
C3×#647062
C3×#646762
#105989983
C3×#16385