Finite Group Databasebeta

← C3×#10602096 #14289479

Subgroups — C3×#10602096 #14289479

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×#66064C211yesmaximal, characteristic
2C3×C5×#494C211yesmaximal, characteristic, complemented
3C3×#65380C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic
5C3×#64766C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic
7C3×#64676C211yesmaximal, characteristic, complemented
8#10602096C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×Q16—22no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×#4092—22no—
13C3×#4043—21no—
14C3×#4039—21no—
15C3×D5×C4⋊C4—21no—
16C3×#4036—21no—
17C3×C4×D20C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C4×C5×C8C2211yescharacteristic
20C3×#3942—21no—
21C3×#3941—21no—
22C3×#3940—21no—
23C3×#3939—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1632—51nomaximal, Hall
27#66064C2×C311yescharacteristic
28C5×#494C2×C311yescharacteristic, complemented
29#65380C2×C311yescharacteristic, complemented
30#65373C2×C311yescharacteristic
31#64766C2×C311yescharacteristic, complemented
32#64679C2×C311yescharacteristic
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D412yes—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—22no—
39C2×C3×Dic10D411yescharacteristic
40C3×C5×Q16—44no—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47C3×#685—22no—
48C3×#685—21no—
49C3×C4⋊Dic5—22no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×C4⋊Dic5D411yescharacteristic
52C3×#683—22no—
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57C3×#554—51no—
58C3×#494D511yescharacteristic, complemented
59C3×#477—51no—
60C3×#476—51no—
61C3×#333—51no—
62C3×Q8⋊C8—51no—
63C3×D4⋊C8—51no—
64C2×C5×Q16—22no—
65C5×C4⋊Q8C22×C311yescharacteristic
66C5×C4⋊Q8C22×C311yescharacteristic
67#4092—22no—
68#4043—21no—
69#4039—21no—
70D5×C4⋊C4—21no—
71#4036—21no—
72C4×D20C22×C311yescharacteristic
73C4×Dic10C22×C311yescharacteristic
74C4×C5×C8C22×C311yescharacteristic
75#3942—21no—
76#3941—21no—
77#3940—21no—
78#3939—21no—
79C4⋊#168C22×C311yescharacteristic
80C4⋊#168C22×C311yescharacteristic
81#1632—51noSylow
82C22×C3×D5—21no—
83C3×C5×Q8—42no—
84C3×C5×Q8—42no—
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×D20Q1612yescomplemented
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97C3×C4×D5—82no—
98C3×Dic10—21no—
99C3×Dic10—21no—
100C3×C5×C8—22no—
101C3×#168—41no—
102C3×#168—41no—
103C2×C3×Q16—22no—
104C3×C4⋊Q8C2×D511yescharacteristic
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×#125—101no—
107C3×C22⋊Q8—101no—
108C3×C22⋊Q8—102no—
109C3×C4×Q8—51no—
110C3×C4×D4—51no—
111C3×C4×D4—101no—
112C2×C3×C4⋊C4—101no—
113C3×#107—101no—
114C3×#106—101no—
115C3×C4⋊C8—51no—
116C3×C4⋊C8—51no—
117C3×#103—101no—
118C3×#102—101no—
119C3×C4×C8C2×D511yescharacteristic
120C2×C5×Q8—21no—
121C2×C5×Q8C3×D412yes—
122C2×D20C3×D411yescharacteristic
123C2×C4×D5—21no—
124C2×C4×D5—22no—
125C2×Dic10C3×D411yescharacteristic
126C5×Q16—44no—
127C2×C5×C8—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C42×C5C23×C311yescharacteristic
133#685—22no—
134#685—21no—
135C4⋊Dic5—22no—
136C4⋊Dic5C3×D411yescharacteristic
137C4⋊Dic5C3×D411yescharacteristic
138#683—22no—
139#683—21no—
140C4×Dic5—21no—
141C2×#168—21no—
142C2×#168—21no—
143#554—51no—
144#494C3×D511yescharacteristic, complemented
145#477—51no—
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—42no—
156C3×C4×C5—81no—
157C3×C4×C5C2×Q1611yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×Dic5—41no—
162C3×Dic5—41no—
163C3×Dic5—41no—
164C2×C3×Q8—21no—
165C2×C3×Q8—51no—
166C2×C3×Q8C22⋊D512yes—
167C2×C3×D4—51no—
168C22×C3×C4—102no—
169C22×C3×C4—101no—
170C3×Q16—44no—
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—21no—
178C3×C4⋊C4—51no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—102no—
181C3×C4⋊C4—102no—
182C3×C4⋊C4—101no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—101no—
185C3×C42—101no—
186C3×C42C22×D511yescharacteristic
187C22×D5—21no—
188C5×Q8—42no—
189C5×Q8—42no—
190C2×C4×C5—22no—
191C2×C4×C5—41no—
192C2×C4×C5C2×C3×D411yescharacteristic
193C2×C4×C5C2×C3×D411yescharacteristic
194C2×C4×C5C2×C3×D411yescharacteristic
195C2×Dic5—21no—
196C2×Dic5—21no—
197C2×Dic5—21no—
198D20—21no—
199D20C3×Q1612yescomplemented
200C4×D5—41no—
201C4×D5—41no—
202C4×D5—82no—
203Dic10—21no—
204Dic10—21no—
205C5×C8—22no—
206#168—41no—
207#168—41no—
208C2×Q16—22no—
209C4⋊Q8C2×C3×D511yescharacteristic
210C4⋊Q8C2×C3×D511yescharacteristic
211#125—101no—
212C22⋊Q8—101no—
213C22⋊Q8—102no—
214C4×Q8—51no—
215C4×D4—51no—
216C4×D4—101no—
217C2×C4⋊C4—101no—
218#107—101no—
219#106—101no—
220C4⋊C8—51no—
221C4⋊C8—51no—
222#103—101no—
223#102—101no—
224C4×C8C2×C3×D511yescharacteristic
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C3×D5—42no—
229C23×C3—101no—
230C3×Q8—42no—
231C3×Q8—42no—
232C3×Q8—101no—
233C3×Q8—101no—
234C3×D4—52no—
235C3×D4—101no—
236C2×C3×C4—22no—
237C2×C3×C4—41no—
238C2×C3×C4—101no—
239C2×C3×C4—101no—
240C2×C3×C4—101no—
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—22no—
248C3×C8—201no—
249C3×C8—201no—
250C22×C5C3×#12011yescharacteristic
251C2×D5—22no—
252C2×D5—41no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—42no—
256C4×C5—81no—
257C4×C5C2×C3×Q1611yescharacteristic
258C4×C5C3×#13511yescharacteristic
259C4×C5C3×#13711yescharacteristic
260C4×C5C3×#13711yescharacteristic
261Dic5—41no—
262Dic5—41no—
263Dic5—41no—
264C2×Q8—21no—
265C2×Q8—51no—
266C2×Q8C3×C22⋊D512yes—
267C2×D4—51no—
268C22×C4—102no—
269C22×C4—101no—
270Q16—44no—
271C2×C8—21no—
272C2×C8—101no—
273C2×C8—101no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—51no—
279C4⋊C4—51no—
280C4⋊C4—102no—
281C4⋊C4—102no—
282C4⋊C4—101no—
283C22⋊C4—102no—
284C22⋊C4—101no—
285C42—101no—
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—42no—
294C3×C4—81no—
295C3×C4—201no—
296C3×C4—201no—
297C3×C4—201no—
298C3×C4D5×Q1611yescharacteristic
299C3×C4#406411yescharacteristic
300C3×C4#406411yescharacteristic
301C3×C4#406511yescharacteristic
302C2×C5C3×#45111yescharacteristic
303C2×C5C3×#45211yescharacteristic
304C2×C5C3×#45311yescharacteristic
305D5—42no—
306C23—101no—
307Q8—42no—
308Q8—42no—
309Q8—101no—
310Q8—101no—
311D4—52no—
312D4—101no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—201no—
319C2×C4—201no—
320C2×C4—402no—
321C2×C4C3×D4×D511yescharacteristic
322C2×C4C3×D4×D511yescharacteristic
323C2×C4C2×C3×C22⋊D511yescharacteristic
324C8—22no—
325C8—201no—
326C8—201no—
327C2×C3—202no—
328C2×C3#6536611yescharacteristic
329C2×C3#6547511yescharacteristic
330C2×C3#6547611yescharacteristic
331C5C3×#163211yescharacteristic, complemented, Sylow
332C22—102no—
333C22—201no—
334C22—201no—
335C22C3×#408311yescharacteristic
336C4—21no—
337C4—42no—
338C4—81no—
339C4—201no—
340C4—201no—
341C4—201no—
342C4C3×D5×Q1611yescharacteristic
343C4C3×#406411yescharacteristic
344C4C3×#406411yescharacteristic
345C4C3×#406511yescharacteristic
346C3#1060209611yescharacteristic, direct product factor, Sylow
347C2—202no—
348C2C3×#6536611yescharacteristic
349C2C3×#6547511yescharacteristic
350C2C3×#6547611yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#494C2
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC3×#494D5
hypocenterC5C3×#1632
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#494

Complements

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

NH ≅ G/Ntype
2. C3×C5×#494C2semidirect
3. C3×#65380C2semidirect
5. C3×#64766C2semidirect
7. C3×#64676C2semidirect
8. #10602096C3direct (N × H)
28. C5×#494C2×C3semidirect
29. #65380C2×C3semidirect
31. #64766C2×C3semidirect
33. #64676C2×C3semidirect
58. C3×#494D5semidirect
94. C3×D20Q16semidirect
144. #494C3×D5semidirect
199. D20C3×Q16semidirect
287. C3×C5#1632semidirect
331. C5C3×#1632semidirect
346. C3#10602096direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660642
C3×C5×#4942
C3×#653802
C3×#653732
C3×#647662
C3×#646792
C3×#646762
#106020963
C3×#16325