Finite Group Databasebeta

← #14478182

Subgroups — #14478182

Order 1920.

720 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
1C2×C3×#4047C211yesmaximal, characteristic
2C2×#91096C211yesmaximal, characteristic, complemented
3C2×C5×#812C211yesmaximal, characteristic, complemented
4#11747525C214yesmaximal, complemented
5#11747524C214yesmaximal, complemented
6D5×#812C214yesmaximal, complemented
7#10613738—31nomaximal, Hall
8C2×C3×#709C411yescharacteristic
9C22×C3×C5×C8C2211yescharacteristic
10C2×C3×#681C411yescharacteristic
11C3×#4047C412yes—
12C3×#4047C412yes—
13C3×#4047C2212yes—
14C3×#4047C2212yes—
15C2×C3×#676C412yes—
16C2×C3×C8×D5C2212yes—
17#91096C2212yes—
18#91096C2212yescomplemented
19C2×C3⋊#672C2212yescomplemented
20C5×#812C2212yes—
21C5×#812C2212yescomplemented
22C2×C5×C3⋊C16C2212yescomplemented
23#90934C2218yescomplemented
24D5×C3⋊C16C2218yescomplemented
25#83780—51nomaximal, Hall
26C2×#4047D311yescharacteristic
27C2×C5×M32—31no—
28C2×#3944—31no—
29#65196—34no—
30D5×M32—34no—
31#65190—34no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C2×C3×C22⋊D5C812yes—
34C3×#709C812yes—
35C3×#709C812yes—
36C3×#709C2×C412yes—
37C3×#709C2×C412yes—
38C2×C3×D20C811yescharacteristic
39C2×C3×C4×D5C2×C412yes—
40C2×C3×Dic10C811yescharacteristic
41C2×C3×C5×C8C2×C411yescharacteristic
42C2×C3×C5×C8C2×C411yescharacteristic
43C2×C3×C5×C8C2×C411yescharacteristic
44C2×C3×C5×C8C2311yescharacteristic
45C2×C3×C5×C8C2311yescharacteristic
46C2×C3×C5×C8C2311yescharacteristic
47C3×#681C2×C412yes—
48C3×#681C2×C412yes—
49C2×C3×#168C2×C412yes—
50C3×#676C2×C414yes—
51C3×#676C2×C414yes—
52C3×C8×D5C2×C414yes—
53C3×C8×D5C2314yes—
54C3⋊#672C2314yes—
55C5×C3⋊C16C2314yes—
56C2×C3×#131—51no—
57#5140—54no—
58#5140—54no—
59C2×#812—51no—
60C2×#812—54no—
61C2×#812D511yescharacteristic, complemented
62C2×#709Dic311yescharacteristic
63C22×C5×C8C2×D311yescharacteristic
64C2×#681Dic311yescharacteristic
65#4047Dic312yes—
66#4047Dic312yes—
67#4047C2×D312yes—
68#4047C2×D312yes—
69C2×#676Dic312yes—
70C2×C8×D5C2×D312yes—
71C5×M32—32no—
72C5×M32—32no—
73C2×C5×C16—32no—
74#3944—32no—
75#3944—32no—
76C2×#672—32no—
77#3930—38no—
78D5×C16—38no—
79#3407—151noSylow
80C23×C3×C5C2×C811yescharacteristic
81C22×C3×D5C2×C812yes—
82C2×C3×C4×C5C2×C811yescharacteristic
83C2×C3×C4×C5C2×C811yescharacteristic
84C2×C3×C4×C5C2×C811yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88C3×C22⋊D5C2×C814yes—
89C3×C22⋊D5C2×C814yes—
90C2×C3×Dic5C2×C812yes—
91C3×D20C2×C812yes—
92C3×D20C2×C812yes—
93C3×C4×D5C2×C814yes—
94C3×C4×D5C22×C414yes—
95C3×Dic10C2×C812yes—
96C3×Dic10C2×C812yes—
97C3×C5×C8C22×C411yescharacteristic
98C3×C5×C8C22×C411yescharacteristic
99C3×C5×C8C22×C411yescharacteristic
100C3×C5×C8C2411yescharacteristic
101C3×#168C22×C414yes—
102C2×C3×#41—51no—
103C3×#131—52no—
104C3×#131—52no—
105C3×#131—52no—
106C3×#131—52no—
107C2×C3×M16—51no—
108C2×C3×M16—52no—
109C22×C3×C8—52no—
110C22×C3×C8C2×D511yescharacteristic
111#812—52no—
112#812—52no—
113#812—58no—
114#812C2×D512yes—
115#812C2×D512yescomplemented
116C2×C3⋊C16—52no—
117C2×C3⋊C16—58no—
118C2×C3⋊C16C2×D512yescomplemented
119C22×C4×C5C2×Dic311yescharacteristic
120C2×C22⋊D5C3⋊C812yes—
121#709C3⋊C812yes—
122#709C3⋊C812yes—
123#709C2×Dic312yes—
124#709C2×Dic312yes—
125C2×D20C3⋊C811yescharacteristic
126C2×C4×D5C2×Dic312yes—
127C2×Dic10C3⋊C811yescharacteristic
128C2×C5×C8C2×Dic311yescharacteristic
129C2×C5×C8C2×Dic311yescharacteristic
130C2×C5×C8C2×Dic311yescharacteristic
131C2×C5×C8C22×D311yescharacteristic
132C2×C5×C8C22×D311yescharacteristic
133C2×C5×C8C22×D311yescharacteristic
134#681C2×Dic312yes—
135#681C2×Dic312yes—
136C2×#168C2×Dic312yes—
137#676C2×Dic314yes—
138#676C2×Dic314yes—
139C8×D5C2×Dic314yes—
140C8×D5C22×D314yes—
141C5×C16—34no—
142#672—34no—
143C2×#131—51no—
144#504—154no—
145#504—154no—
146C2×M32—31no—
147C2×M32—154no—
148C2×M32—151no—
149C22×C3×C5—41no—
150C22×C3×C5C22×C811yescharacteristic
151C22×C3×C5C22×C811yescharacteristic
152C22×C3×C5C22×C811yescharacteristic
153C2×C3×D5—42no—
154C2×C3×D5C22×C814yes—
155C3×C4×C5C22×C811yescharacteristic
156C3×C4×C5C22×C811yescharacteristic
157C3×C4×C5C22×C811yescharacteristic
158C3×C4×C5C23×C411yescharacteristic
159C3×Dic5C22×C814yes—
160C3×#41—52no—
161C3×#41—52no—
162C3×#41—52no—
163C3×#41—52no—
164C2×C3×Q8—51no—
165C2×C3×D4—52no—
166C2×C3×D4—51no—
167C22×C3×C4—52no—
168C22×C3×C4C4×D511yescharacteristic
169C3×M16—52no—
170C3×M16—52no—
171C3×M16—54no—
172C3×M16—54no—
173C2×C3×C8—52no—
174C2×C3×C8—54no—
175C2×C3×C8—54no—
176C2×C3×C8C4×D511yescharacteristic
177C2×C3×C8C4×D511yescharacteristic
178C2×C3×C8C4×D511yescharacteristic
179C2×C3×C8C22×D511yescharacteristic
180C2×C3×C8C22×D511yescharacteristic
181C2×C3×C8C22×D511yescharacteristic
182C3⋊C16—54no—
183C3⋊C16C22×D514yes—
184C23×C5C2×C3⋊C811yescharacteristic
185C22×D5C2×C3⋊C812yes—
186C2×C4×C5C2×C3⋊C811yescharacteristic
187C2×C4×C5C2×C3⋊C811yescharacteristic
188C2×C4×C5C2×C3⋊C811yescharacteristic
189C2×C4×C5C22×Dic311yescharacteristic
190C2×C4×C5C22×Dic311yescharacteristic
191C2×C4×C5C22×Dic311yescharacteristic
192C22⋊D5C2×C3⋊C814yes—
193C22⋊D5C2×C3⋊C814yes—
194C2×Dic5C2×C3⋊C812yes—
195D20C2×C3⋊C812yes—
196D20C2×C3⋊C812yes—
197C4×D5C2×C3⋊C814yes—
198C4×D5C22×Dic314yes—
199Dic10C2×C3⋊C812yes—
200Dic10C2×C3⋊C812yes—
201C5×C8C22×Dic311yescharacteristic
202C5×C8C22×Dic311yescharacteristic
203C5×C8C22×Dic311yescharacteristic
204C5×C8C23×D311yescharacteristic
205#168C22×Dic314yes—
206C2×#41—51no—
207#131—52no—
208#131—52no—
209#131—52no—
210#131—52no—
211C2×M16—51no—
212C2×M16—52no—
213C22×C8—52no—
214C22×C8D3×D511yescharacteristic
215M32—32no—
216M32—32no—
217M32—158no—
218M32—152no—
219M32—152no—
220C2×C16—32no—
221C2×C16—158no—
222C2×C16—152no—
223C2×C3×C5—21no—
224C2×C3×C5—21no—
225C2×C3×C5—21no—
226C2×C3×C5C23×C811yescharacteristic
227C3×D5—24no—
228C23×C3—52no—
229C23×C3C8×D511yescharacteristic
230C3×Q8—52no—
231C3×Q8—52no—
232C3×D4—54no—
233C3×D4—54no—
234C3×D4—52no—
235C3×D4—52no—
236C2×C3×C4—52no—
237C2×C3×C4—54no—
238C2×C3×C4—54no—
239C2×C3×C4C8×D511yescharacteristic
240C2×C3×C4C8×D511yescharacteristic
241C2×C3×C4C8×D511yescharacteristic
242C2×C3×C4C2×C4×D511yescharacteristic
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4C2×C4×D511yescharacteristic
245C3×C8—54no—
246C3×C8C2×C4×D511yescharacteristic
247C3×C8C2×C4×D511yescharacteristic
248C3×C8C2×C4×D511yescharacteristic
249C3×C8C23×D511yescharacteristic
250C22×C5—41no—
251C22×C5C22×C3⋊C811yescharacteristic
252C22×C5C22×C3⋊C811yescharacteristic
253C22×C5C22×C3⋊C811yescharacteristic
254C2×D5—42no—
255C2×D5C22×C3⋊C814yes—
256C4×C5C22×C3⋊C811yescharacteristic
257C4×C5C22×C3⋊C811yescharacteristic
258C4×C5C22×C3⋊C811yescharacteristic
259C4×C5C23×Dic311yescharacteristic
260Dic5C22×C3⋊C814yes—
261#41—52no—
262#41—52no—
263#41—52no—
264#41—52no—
265C2×Q8—51no—
266C2×D4—52no—
267C2×D4—51no—
268C22×C4—52no—
269C22×C4D5×Dic311yescharacteristic
270M16—52no—
271M16—52no—
272M16—54no—
273M16—54no—
274C2×C8—52no—
275C2×C8—54no—
276C2×C8—54no—
277C2×C8D5×Dic311yescharacteristic
278C2×C8D5×Dic311yescharacteristic
279C2×C8D5×Dic311yescharacteristic
280C2×C8C2×D3×D511yescharacteristic
281C2×C8C2×D3×D511yescharacteristic
282C2×C8C2×D3×D511yescharacteristic
283C16—34no—
284C16—154no—
285C3×C5#340711yescharacteristic, complemented, Hall
286C22×C3—41no—
287C22×C3—54no—
288C22×C3—202no—
289C22×C3C2×C8×D511yescharacteristic
290C22×C3C2×C8×D511yescharacteristic
291C22×C3C2×C8×D511yescharacteristic
292C3×C4—54no—
293C3×C4C2×C8×D511yescharacteristic
294C3×C4C2×C8×D511yescharacteristic
295C3×C4C2×C8×D511yescharacteristic
296C3×C4C22×C4×D511yescharacteristic
297C2×C5—21no—
298C2×C5—21no—
299C2×C5—21no—
300C2×C5C23×C3⋊C811yescharacteristic
301D5—24no—
302C23—52no—
303C23D5×C3⋊C811yescharacteristic
304Q8—52no—
305Q8—52no—
306D4—54no—
307D4—54no—
308D4—52no—
309D4—52no—
310C2×C4—52no—
311C2×C4—54no—
312C2×C4—54no—
313C2×C4D5×C3⋊C811yescharacteristic
314C2×C4D5×C3⋊C811yescharacteristic
315C2×C4D5×C3⋊C811yescharacteristic
316C2×C4C2×D5×Dic311yescharacteristic
317C2×C4C2×D5×Dic311yescharacteristic
318C2×C4C2×D5×Dic311yescharacteristic
319C8—54no—
320C8C2×D5×Dic311yescharacteristic
321C8C2×D5×Dic311yescharacteristic
322C8C2×D5×Dic311yescharacteristic
323C8C22×D3×D511yescharacteristic
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—104no—
328C2×C3C22×C8×D511yescharacteristic
329C5#8378011yescharacteristic, complemented, Sylow
330C22—41no—
331C22—54no—
332C22—202no—
333C22C2×D5×C3⋊C811yescharacteristic
334C22C2×D5×C3⋊C811yescharacteristic
335C22C2×D5×C3⋊C811yescharacteristic
336C4—54no—
337C4C2×D5×C3⋊C811yescharacteristic
338C4C2×D5×C3⋊C811yescharacteristic
339C4C2×D5×C3⋊C811yescharacteristic
340C4C22×D5×Dic311yescharacteristic
341C3#1061373811yescharacteristic, complemented, Sylow
342C2—21no—
343C2—21no—
344C2—21no—
345C2—104no—
346C2C22×D5×C3⋊C811yescharacteristic
subgroupG/H
center, FrattiniC8C22×D3×D5
commutator, socleC2×C3×C5C23×C8
FittingC22×C3×C5×C8C22
prime radicalC2×C3×#709C4
cosocleC3×C5×C8C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#3407
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#91096C2semidirect
3. C2×C5×#812C2semidirect
4. #11747525C2semidirect
5. #11747524C2semidirect
6. D5×#812C2semidirect
18. #91096C22semidirect
19. C2×C3⋊#672C22semidirect
21. C5×#812C22semidirect
22. C2×C5×C3⋊C16C22semidirect
23. #90934C22semidirect
24. D5×C3⋊C16C22semidirect
61. C2×#812D5semidirect
115. #812C2×D5semidirect
118. C2×C3⋊C16C2×D5semidirect
285. C3×C5#3407semidirect
329. C5#83780semidirect
341. C3#10613738semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40472
C2×#910962
C2×C5×#8122
#117475252
#117475242
D5×#8122
#106137383
#837805