Finite Group Databasebeta

← #14313321

Subgroups — #14313321

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66159C211yesmaximal, characteristic
2#11751338C211yesmaximal, characteristic
3C5×#5240C211yesmaximal, characteristic
4#11746000C214yesmaximal, complemented
5#10600851—31nomaximal, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×Dic10C411yescharacteristic, complemented
8C2×#6710—21no—
9C5×#926—21no—
10C3×#4090—21no—
11C3×#4082—21no—
12C3×#4081C412yescomplemented
13C3×#4081C2212yes—
14C3×#4072C411yescharacteristic, complemented
15C3×#4070—21no—
16C3×#4070—21no—
17#91120—21no—
18#91117C2212yes—
19C5×#834—21no—
20C5×#834C2212yes—
21#71870—51nomaximal, Hall
22#66159D311yescharacteristic
23C5×#410—31no—
24#65526—31no—
25#64692—34no—
26C3×C5×#41—41no—
27C3×C5×#41—41no—
28C2×C3×C5×Q8D411yescharacteristic
29C2×C3×C5×D4C2×C411yescharacteristic
30C2×C3×C5×D4D411yescharacteristic
31C2×C3×C5×D4C2311yescharacteristic
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×Dic5C2×C412yes—
36C2×C3×Dic10—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10—41no—
39C2×C3×Dic10—41no—
40#6710—22no—
41#6710—41no—
42C2×C3⋊#168—41no—
43C5×#217—22no—
44C5×C4⋊Dic3—41no—
45C4×C5×Dic3—41no—
46C3×C22⋊Dic5—22no—
47C3×C22⋊Dic5—22no—
48C3×C22⋊Dic5C2×C412yes—
49C3×C4⋊Dic5—21no—
50C3×#683—22no—
51C3×#683—22no—
52C3×C4×Dic5—21no—
53C3×#536—51no—
54#5240D511yescharacteristic
55#5237—51no—
56#4539—54no—
57C2×C5×#41C2×D311yescharacteristic
58C22×Dic10Dic311yescharacteristic, complemented
59C5×#117—61no—
60#4090—21no—
61#4082—21no—
62#4081Dic312yescomplemented
63#4081C2×D312yes—
64#4072Dic311yescharacteristic, complemented
65#4070—21no—
66#4070—21no—
67C2×#681—61no—
68C5×#99—32no—
69C5×#99—61no—
70#3968—61no—
71#3965—32no—
72#2123—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22×C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C3×C5×Q8—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C5×Dic3—42no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—42no—
94C3×Dic10—42no—
95C3×Dic10—41no—
96C3×Dic10—41no—
97C3⋊#168—42no—
98C2×C3×#41C2×D511yescharacteristic
99C22×C3×Q8—51no—
100C3×C4⋊Q8—101no—
101C3×#124—101no—
102C3×#123—52no—
103C3×#123—52no—
104C3×C22⋊Q8—101no—
105C3×C22⋊Q8—101no—
106C3×#117—51no—
107#926—21no—
108C2×#208—101no—
109#836—101no—
110#834—21no—
111#834C2×D512yes—
112#833—52no—
113C5×#41—41no—
114C5×#41—41no—
115C2×C5×Q8#6711yescharacteristic
116C2×C5×D4C2×Dic311yescharacteristic
117C2×C5×D4#6711yescharacteristic
118C2×C5×D4C22×D311yescharacteristic
119C22×C4×C5C2×Dic311yescharacteristic
120C22×C4×C5#6711yescharacteristic
121C22×C4×C5#6711yescharacteristic
122C22×Dic5C2×Dic312yes—
123C2×Dic10—21no—
124C2×Dic10—21no—
125C2×Dic10—41no—
126C2×Dic10—41no—
127C5×C4⋊C4—121no—
128C5×C22⋊C4—62no—
129C42×C5—121no—
130C22⋊Dic5—22no—
131C22⋊Dic5—22no—
132C22⋊Dic5C2×Dic312yes—
133C4⋊Dic5—21no—
134#683—22no—
135#683—22no—
136C4×Dic5—21no—
137#681—62no—
138#681—121no—
139C2×#168—121no—
140#536—51no—
141#413—151no—
142#410—31no—
143#352—154no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—41no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5#9911yescharacteristic
155C3×C4×C5#9911yescharacteristic
156C3×Dic5—42no—
157C3×Dic5—42no—
158C5×Dic3—82no—
159C3×#41—41no—
160C3×#41—41no—
161C2×C3×Q8—101no—
162C2×C3×Q8—101no—
163C2×C3×Q8—201no—
164C2×C3×Q8—201no—
165C2×C3×Q8D2011yescharacteristic
166C2×C3×D4C4×D511yescharacteristic
167C2×C3×D4C22⋊D511yescharacteristic
168C2×C3×D4C22×D511yescharacteristic
169C22×C3×C4—52no—
170C22×C3×C4C4×D511yescharacteristic
171C22×C3×C4D2011yescharacteristic
172C22×C3×C4C22⋊D511yescharacteristic
173C3×C4⋊C4—102no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—102no—
176C3×C22⋊C4—52no—
177C3×C22⋊C4—102no—
178C3×C22⋊C4—102no—
179C3×C42—101no—
180#217—22no—
181C4⋊Dic3—41no—
182C4×Dic3—41no—
183#208—102no—
184#208—201no—
185C2×C3⋊C8—201no—
186C23×C5#21711yescharacteristic
187C23×C5C22×Dic311yescharacteristic
188C23×C5C2×#6711yescharacteristic
189C5×Q8—41no—
190C5×D4—41no—
191C5×D4—41no—
192C5×D4—41no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—122no—
200C2×C4×C5#21711yescharacteristic
201C2×C4×C5#21711yescharacteristic
202C2×C4×C5#21711yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×Dic5—22no—
205C2×Dic5—22no—
206C2×Dic5—42no—
207Dic10—42no—
208Dic10—41no—
209Dic10—41no—
210#168—122no—
211C2×#41D3×D511yescharacteristic
212C22×Q8—51no—
213C2×M16—301no—
214C4⋊Q8—101no—
215#124—101no—
216#123—52no—
217#123—52no—
218C22⋊Q8—101no—
219C22⋊Q8—101no—
220#117—51no—
221#117—61no—
222#101—301no—
223#100—152no—
224#99—32no—
225#99—61no—
226C2×C3×C5—21no—
227C2×C3×C5—41no—
228C2×C3×C5—41no—
229C2×C3×C5—41no—
230C2×C3×C5C2×#9911yescharacteristic
231C23×C3#68511yescharacteristic
232C23×C3C2×C4×D511yescharacteristic
233C23×C3C2×C22⋊D511yescharacteristic
234C3×Q8—41no—
235C3×Q8—202no—
236C3×Q8—201no—
237C3×Q8—201no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—102no—
248C2×C3×C4—102no—
249C2×C3×C4—202no—
250C2×C3×C4#68511yescharacteristic
251C2×C3×C4#68511yescharacteristic
252C2×C3×C4#68511yescharacteristic
253C2×C3×C4C2×D2011yescharacteristic
254C2×Dic3—42no—
255C3⋊C8—202no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5C2×#21711yescharacteristic
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—242no—
267C4×C5#83411yescharacteristic
268C4×C5#83411yescharacteristic
269Dic5—42no—
270Dic5—42no—
271#41—41no—
272#41—41no—
273C2×Q8—101no—
274C2×Q8—101no—
275C2×Q8—201no—
276C2×Q8—201no—
277C2×Q8#120211yescharacteristic
278C2×D4D5×Dic311yescharacteristic
279C2×D4#120111yescharacteristic
280C2×D4C2×D3×D511yescharacteristic
281C22×C4—52no—
282C22×C4D5×Dic311yescharacteristic
283C22×C4#120111yescharacteristic
284C22×C4#120211yescharacteristic
285M16—302no—
286M16—601no—
287C2×C8—601no—
288C4⋊C4—102no—
289C4⋊C4—101no—
290C4⋊C4—102no—
291C4⋊C4—121no—
292C22⋊C4—52no—
293C22⋊C4—62no—
294C22⋊C4—102no—
295C22⋊C4—102no—
296C42—101no—
297C42—121no—
298C3×C5#212311yescharacteristic, complemented, Hall
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3C2×#68511yescharacteristic
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—202no—
310C3×C4—202no—
311C3×C4#393811yescharacteristic
312C3×C4#393811yescharacteristic
313Dic3—82no—
314C2×C5—21no—
315C2×C5—41no—
316C2×C5—41no—
317C2×C5—41no—
318C2×C5C2×#83411yescharacteristic
319C23#666511yescharacteristic
320C23C2×D5×Dic311yescharacteristic
321C23C2×#120111yescharacteristic
322Q8—41no—
323Q8—202no—
324Q8—201no—
325Q8—201no—
326D4—41no—
327D4—41no—
328D4—41no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—102no—
336C2×C4—102no—
337C2×C4—122no—
338C2×C4—202no—
339C2×C4#666511yescharacteristic
340C2×C4#666511yescharacteristic
341C2×C4#666511yescharacteristic
342C2×C4C2×#120211yescharacteristic
343C8—602no—
344C2×C3—21no—
345C2×C3—41no—
346C2×C3—41no—
347C2×C3—41no—
348C2×C3C2×#393811yescharacteristic
349C5#7187011yescharacteristic, complemented, Sylow
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22C2×#666511yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—202no—
361C4—202no—
362C4—242no—
363C4#9099511yescharacteristic
364C4#9099511yescharacteristic
365C3#1060085111yescharacteristic, complemented, Sylow
366C2—21no—
367C2—41no—
368C2—41no—
369C2—41no—
370C2C2×#9099511yescharacteristic
subgroupG/H
centerC2C2×#90995
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
cosocleC2×C3×C5×D4C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2123
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #11746000C2semidirect
7. C22×C3×Dic10C4semidirect
12. C3×#4081C4semidirect
14. C3×#4072C4semidirect
58. C22×Dic10Dic3semidirect
62. #4081Dic3semidirect
64. #4072Dic3semidirect
298. C3×C5#2123semidirect
349. C5#71870semidirect
365. C3#10600851semidirect

Maximal subgroups

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

subgroupindex
C3×#661592
#117513382
C5×#52402
#117460002
#106008513
#718705