Finite Group Databasebeta

← C3×#10602725 #14289818

Subgroups — C3×#10602725 #14289818

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×C5×#556C211yesmaximal, characteristic
2C3×#65382C211yesmaximal, characteristic, complemented
3C3×#65310C211yesmaximal, characteristic, complemented
4C3×#65297C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×Q8⋊#168C211yesmaximal, characteristic, complemented
7C3×D4⋊#168C211yesmaximal, characteristic
8#10602725C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#126—22no—
11C3×C5×#124—21no—
12C3×C5×C22⋊Q8—21no—
13C3×C4×C5×Q8—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C3×C5×#117—21no—
17C3×#4015C2211yescharacteristic
18C3×#3967—21no—
19C3×#3964—21no—
20C3×#3942—22no—
21C3×#3940—21no—
22C3×#3939—21no—
23C3×C4⋊#168C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1638—51nomaximal, Hall
27C5×#556C2×C311yescharacteristic
28#65382C2×C311yescharacteristic, complemented
29#65310C2×C311yescharacteristic, complemented
30#65297C2×C311yescharacteristic
31#64767C2×C311yescharacteristic, complemented
32Q8⋊#168C2×C311yescharacteristic, complemented
33D4⋊#168C2×C311yescharacteristic
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C4⋊C4D412yes—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—22no—
49C3×C42×C5—21no—
50C3×C42×C5C2311yescharacteristic
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C2×C3×#168—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C3×#556D511yescharacteristic
57C3×#487—51no—
58C3×#477—51no—
59C3×#476—51no—
60C3×#332—51no—
61C3×Q8⋊C8—51no—
62C3×D4⋊C8—51no—
63C5×C4⋊Q8C22×C311yescharacteristic
64C5×#126—22no—
65C5×#124—21no—
66C5×C22⋊Q8—21no—
67C4×C5×Q8—21no—
68C4×C5×Q8C22×C311yescharacteristic
69C4×C5×D4C22×C311yescharacteristic
70C5×#117—21no—
71#4015C22×C311yescharacteristic
72#3967—21no—
73#3964—21no—
74#3942—22no—
75#3940—21no—
76#3939—21no—
77C4⋊#168C22×C311yescharacteristic
78C4⋊#168C22×C311yescharacteristic
79C4×#168C22×C311yescharacteristic
80#1638—51noSylow
81C23×C3×C5—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C3×C5×D4—21no—
87C3×C5×D4—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×Dic5—41no—
98C3×Dic10—42no—
99C3×#168—41no—
100C3×#168—41no—
101C3×#168—41no—
102C3×C4⋊Q8—51no—
103C3×C4⋊Q8C2×D511yescharacteristic
104C3×#126—22no—
105C3×#124—21no—
106C3×C22⋊Q8—21no—
107C3×C4×Q8—21no—
108C3×C4×Q8C2×D511yescharacteristic
109C3×C4×D4C2×D511yescharacteristic
110C3×#117—21no—
111C3×#107—101no—
112C3×#106—101no—
113C3×C4⋊C8—51no—
114C3×C4⋊C8—51no—
115C3×#103—101no—
116C3×#103—102no—
117C3×#102—101no—
118C3×C4×C8—51no—
119C2×C5×Q8—21no—
120C2×C5×Q8C3×D411yescharacteristic
121C2×C5×D4C3×D411yescharacteristic
122C22×C4×C5—21no—
123C2×Dic10—21no—
124C5×C4⋊C4—22no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4C3×D411yescharacteristic
128C5×C4⋊C4C3×D411yescharacteristic
129C5×C4⋊C4C3×D412yes—
130C5×C22⋊C4—22no—
131C5×C22⋊C4—22no—
132C5×C22⋊C4—21no—
133C42×C5—22no—
134C42×C5—21no—
135C42×C5C23×C311yescharacteristic
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C2×#168—21no—
139C2×#168—21no—
140C2×#168—21no—
141#556C3×D511yescharacteristic
142#487—51no—
143#477—51no—
144#476—51no—
145#332—51no—
146Q8⋊C8—51no—
147D4⋊C8—51no—
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—41no—
155C3×C4×C5—42no—
156C3×C4×C5—41no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×Dic5—81no—
162C2×C3×Q8—21no—
163C2×C3×Q8—101no—
164C2×C3×Q8C22⋊D511yescharacteristic
165C2×C3×D4C22⋊D511yescharacteristic
166C22×C3×C4—21no—
167C2×C3×C8—101no—
168C2×C3×C8—101no—
169C2×C3×C8—101no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4C22⋊D512yes—
176C3×C4⋊C4C22⋊D511yescharacteristic
177C3×C4⋊C4C22⋊D511yescharacteristic
178C3×C22⋊C4—22no—
179C3×C22⋊C4—22no—
180C3×C22⋊C4—21no—
181C3×C42—22no—
182C3×C42—21no—
183C3×C42C22×D511yescharacteristic
184C23×C5—21no—
185C5×Q8—21no—
186C5×Q8—21no—
187C5×Q8—41no—
188C5×Q8—41no—
189C5×D4—21no—
190C5×D4—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—22no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5C2×C3×D411yescharacteristic
198C2×C4×C5C2×C3×D411yescharacteristic
199C2×C4×C5C2×C3×D411yescharacteristic
200C2×Dic5—41no—
201Dic10—42no—
202#168—41no—
203#168—41no—
204#168—41no—
205C4⋊Q8—51no—
206C4⋊Q8C2×C3×D511yescharacteristic
207#126—22no—
208#124—21no—
209C22⋊Q8—21no—
210C4×Q8—21no—
211C4×Q8C2×C3×D511yescharacteristic
212C4×D4C2×C3×D511yescharacteristic
213#117—21no—
214#107—101no—
215#106—101no—
216C4⋊C8—51no—
217C4⋊C8—51no—
218#103—101no—
219#103—102no—
220#102—101no—
221C4×C8—51no—
222C2×C3×C5—81no—
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45211yescharacteristic
225C2×C3×C5#45411yescharacteristic
226C23×C3—21no—
227C3×Q8—21no—
228C3×Q8—21no—
229C3×Q8—41no—
230C3×Q8—41no—
231C3×Q8—202no—
232C3×D4—21no—
233C3×D4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—22no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—201no—
241C2×C3×C4C2×C22⋊D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×C3×C4C2×C22⋊D511yescharacteristic
244C3×C8—201no—
245C3×C8—201no—
246C3×C8—201no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5C3×#12011yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5—42no—
255C4×C5—41no—
256C4×C5C3×#13511yescharacteristic
257C4×C5C3×#13511yescharacteristic
258C4×C5C3×#13711yescharacteristic
259C4×C5C3×#13711yescharacteristic
260Dic5—81no—
261C2×Q8—21no—
262C2×Q8—101no—
263C2×Q8C3×C22⋊D511yescharacteristic
264C2×D4C3×C22⋊D511yescharacteristic
265C22×C4—21no—
266C2×C8—101no—
267C2×C8—101no—
268C2×C8—101no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C4⋊C4C3×C22⋊D512yes—
275C4⋊C4C3×C22⋊D511yescharacteristic
276C4⋊C4C3×C22⋊D511yescharacteristic
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—21no—
280C42—22no—
281C42—21no—
282C42C22×C3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3#409911yescharacteristic
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—42no—
292C3×C4—41no—
293C3×C4—401no—
294C3×C4#409611yescharacteristic
295C3×C4#409611yescharacteristic
296C3×C4#409711yescharacteristic
297C3×C4#409711yescharacteristic
298C2×C5—81no—
299C2×C5C3×#45211yescharacteristic
300C2×C5C3×#45211yescharacteristic
301C2×C5C3×#45411yescharacteristic
302C23—21no—
303Q8—21no—
304Q8—21no—
305Q8—41no—
306Q8—41no—
307Q8—202no—
308D4—21no—
309D4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—201no—
317C2×C4C2×C3×C22⋊D511yescharacteristic
318C2×C4C2×C3×C22⋊D511yescharacteristic
319C2×C4C2×C3×C22⋊D511yescharacteristic
320C8—201no—
321C8—201no—
322C8—201no—
323C2×C3—81no—
324C2×C3#6552811yescharacteristic
325C2×C3#6552811yescharacteristic
326C2×C3#6553411yescharacteristic
327C5C3×#163811yescharacteristic, complemented, Sylow
328C22—41no—
329C22—41no—
330C22—41no—
331C22C3×#409911yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—42no—
336C4—41no—
337C4—401no—
338C4C3×#409611yescharacteristic
339C4C3×#409611yescharacteristic
340C4C3×#409711yescharacteristic
341C4C3×#409711yescharacteristic
342C3#1060272511yescharacteristic, direct product factor, Sylow
343C2—81no—
344C2C3×#6552811yescharacteristic
345C2C3×#6552811yescharacteristic
346C2C3×#6553411yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#556C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC3×#556D5
hypocenterC5C3×#1638
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#556

Complements

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

NH ≅ G/Ntype
2. C3×#65382C2semidirect
3. C3×#65310C2semidirect
5. C3×#64767C2semidirect
6. C3×Q8⋊#168C2semidirect
8. #10602725C3direct (N × H)
28. #65382C2×C3semidirect
29. #65310C2×C3semidirect
31. #64767C2×C3semidirect
32. Q8⋊#168C2×C3semidirect
283. C3×C5#1638semidirect
327. C5C3×#1638semidirect
342. C3#10602725direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5562
C3×#653822
C3×#653102
C3×#652972
C3×#647672
C3×Q8⋊#1682
C3×D4⋊#1682
#106027253
C3×#16385