Finite Group Databasebeta

← C3×#10601937 #14289482

Subgroups — C3×#10601937 #14289482

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×#65877C211yesmaximal, characteristic
2C3×C5×#476C211yesmaximal, characteristic
3C3×#65381C211yesmaximal, characteristic, complemented
4C3×#65380C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic
6C3×#64704C211yesmaximal, characteristic, complemented
7C3×#64701C211yesmaximal, characteristic, complemented
8#10601937C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×D4C2211yescharacteristic
11C2×C3×#689—22no—
12C3×D4×Dic5—21no—
13C2×C3×C4⋊Dic5—21no—
14C3×#4070—21no—
15C3×#4036—21no—
16C3×#4024—22no—
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#102—21no—
22C3×#3942—21no—
23C3×#3939—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1632—51nomaximal, Hall
27#65877C2×C311yescharacteristic
28C5×#476C2×C311yescharacteristic
29#65381C2×C311yescharacteristic, complemented
30#65380C2×C311yescharacteristic, complemented
31D4⋊#168C2×C311yescharacteristic
32#64704C2×C311yescharacteristic, complemented
33#64701C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×Dic5—22no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×Dic10D412yes—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C3×C22⋊Dic5—22no—
47C3×#689—44no—
48C3×C4⋊Dic5—22no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
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×#494—51no—
59C3×#477—51no—
60C3×#476D511yescharacteristic
61C3×#333—51no—
62C3×Q8⋊C8—51no—
63C3×D4⋊C8—51no—
64C5×C4⋊Q8C22×C311yescharacteristic
65C4×C5×D4C22×C311yescharacteristic
66C2×#689—22no—
67D4×Dic5—21no—
68C2×C4⋊Dic5—21no—
69#4070—21no—
70#4036—21no—
71#4024—22no—
72#4015C22×C311yescharacteristic
73C4×Dic10C22×C311yescharacteristic
74C5×#106—21no—
75C5×C4⋊C8C22×C311yescharacteristic
76C5×#102—21no—
77#3942—21no—
78#3939—21no—
79C4⋊#168C22×C311yescharacteristic
80C4×#168C22×C311yescharacteristic
81#1632—51noSylow
82C23×C3×C5—21no—
83C3×C5×Q8—42no—
84C3×C5×D4—21no—
85C3×C5×D4Q1612yescomplemented
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5—82no—
97C3×Dic10—21no—
98C3×Dic10—21no—
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×Q8—51no—
110C3×C4×D4—101no—
111C3×C4×D4C2×D511yescharacteristic
112C2×C3×C4⋊C4—101no—
113C3×#107—101no—
114C3×#106—21no—
115C3×C4⋊C8—51no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×#103—101no—
118C3×#102—21no—
119C3×C4×C8—51no—
120C2×C5×Q8—21no—
121C2×C5×D4C3×D411yescharacteristic
122C22×C4×C5—21no—
123C22×Dic5—22no—
124C2×Dic10C3×D411yescharacteristic
125C2×Dic10C3×D412yes—
126C2×C5×C8—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4C3×D411yescharacteristic
130C5×C22⋊C4—21no—
131C42×C5C23×C311yescharacteristic
132C22⋊Dic5—22no—
133#689—44no—
134C4⋊Dic5—22no—
135C4⋊Dic5—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5C3×D411yescharacteristic
138#683—22no—
139#683—21no—
140C4×Dic5—21no—
141C2×#168—21no—
142C2×#168—21no—
143#554—51no—
144#494—51no—
145#477—51no—
146#476C3×D511yescharacteristic
147#333—51no—
148Q8⋊C8—51no—
149D4⋊C8—51no—
150C22×C3×C5—22no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5#12011yescharacteristic
154C3×C4×C5—21no—
155C3×C4×C5—41no—
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—42no—
163C3×Dic5—41no—
164C2×C3×Q8—21no—
165C2×C3×Q8—51no—
166C2×C3×Q8—52no—
167C2×C3×D4C22⋊D511yescharacteristic
168C22×C3×C4—21no—
169C22×C3×C4—102no—
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—51no—
177C3×C4⋊C4—102no—
178C3×C4⋊C4—102no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4C22⋊D511yescharacteristic
183C3×C22⋊C4—21no—
184C3×C22⋊C4—102no—
185C3×C42—101no—
186C3×C42C22×D511yescharacteristic
187C23×C5—21no—
188C5×Q8—42no—
189C5×D4—21no—
190C5×D4C3×Q1612yescomplemented
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5C2×C3×D411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×C4×C5C2×C3×D411yescharacteristic
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—22no—
201C2×Dic5—82no—
202Dic10—21no—
203Dic10—21no—
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×Q8—51no—
215C4×D4—101no—
216C4×D4C2×C3×D511yescharacteristic
217C2×C4⋊C4—101no—
218#107—101no—
219#106—21no—
220C4⋊C8—51no—
221C4⋊C8C2×C3×D511yescharacteristic
222#103—101no—
223#102—21no—
224C4×C8—51no—
225C2×C3×C5—42no—
226C2×C3×C5#45111yescharacteristic
227C2×C3×C5#45211yescharacteristic
228C2×C3×C5#45311yescharacteristic
229C23×C3—21no—
230C3×Q8—42no—
231C3×Q8—101no—
232C3×Q8—101no—
233C3×Q8—202no—
234C3×D4—21no—
235C3×D4#68912yescomplemented
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—101no—
241C2×C3×C4—101no—
242C2×C3×C4—102no—
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×C5—22no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5C3×#12011yescharacteristic
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—81no—
257C4×C5C2×C3×Q1611yescharacteristic
258C4×C5C3×#13511yescharacteristic
259C4×C5C3×#13711yescharacteristic
260C4×C5C3×#13711yescharacteristic
261Dic5—41no—
262Dic5—42no—
263Dic5—41no—
264C2×Q8—21no—
265C2×Q8—51no—
266C2×Q8—52no—
267C2×D4C3×C22⋊D511yescharacteristic
268C22×C4—21no—
269C22×C4—102no—
270Q16—204no—
271C2×C8—21no—
272C2×C8—101no—
273C2×C8—101no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—51no—
277C4⋊C4—102no—
278C4⋊C4—102no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4C3×C22⋊D511yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—102no—
285C42—101no—
286C42C22×C3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—22no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3#408311yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—81no—
295C3×C4—201no—
296C3×C4—201no—
297C3×C4—202no—
298C3×C4#406111yescharacteristic
299C3×C4#406211yescharacteristic
300C3×C4C2×#68911yescharacteristic
301C3×C4#409711yescharacteristic
302C2×C5—42no—
303C2×C5C3×#45111yescharacteristic
304C2×C5C3×#45211yescharacteristic
305C2×C5C3×#45311yescharacteristic
306C23—21no—
307Q8—42no—
308Q8—101no—
309Q8—101no—
310Q8—202no—
311D4—21no—
312D4C3×#68912yescomplemented
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—101no—
318C2×C4—101no—
319C2×C4—102no—
320C2×C4—402no—
321C2×C4C3×D4×D511yescharacteristic
322C2×C4C3×D4×D511yescharacteristic
323C2×C4C2×C3×C22⋊D511yescharacteristic
324C8—41no—
325C8—102no—
326C8—201no—
327C2×C3—42no—
328C2×C3#6533911yescharacteristic
329C2×C3#6546211yescharacteristic
330C2×C3#6548711yescharacteristic
331C5C3×#163211yescharacteristic, complemented, Sylow
332C22—22no—
333C22—41no—
334C22—41no—
335C22C3×#408311yescharacteristic
336C4—21no—
337C4—41no—
338C4—81no—
339C4—201no—
340C4—201no—
341C4—202no—
342C4C3×#406111yescharacteristic
343C4C3×#406211yescharacteristic
344C4C2×C3×#68911yescharacteristic
345C4C3×#409711yescharacteristic
346C3#1060193711yescharacteristic, direct product factor, Sylow
347C2—42no—
348C2C3×#6533911yescharacteristic
349C2C3×#6546211yescharacteristic
350C2C3×#6548711yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC3×#476D5
hypocenterC5C3×#1632
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
3. C3×#65381C2semidirect
4. C3×#65380C2semidirect
6. C3×#64704C2semidirect
7. C3×#64701C2semidirect
8. #10601937C3direct (N × H)
29. #65381C2×C3semidirect
30. #65380C2×C3semidirect
32. #64704C2×C3semidirect
33. #64701C2×C3semidirect
85. C3×C5×D4Q16semidirect
190. C5×D4C3×Q16semidirect
235. C3×D4#689semidirect
287. C3×C5#1632semidirect
312. D4C3×#689semidirect
331. C5C3×#1632semidirect
346. C3#10601937direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658772
C3×C5×#4762
C3×#653812
C3×#653802
C3×D4⋊#1682
C3×#647042
C3×#647012
#106019373
C3×#16325