Finite Group Databasebeta

← #14313326

Subgroups — #14313326

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#11751341C211yesmaximal, characteristic
3C5×#5237C211yesmaximal, characteristic
4#11746001C214yesmaximal, complemented
5#10600940—31nomaximal, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×Dic10C411yescharacteristic, complemented
8#91815—21no—
9C2×C5×#208—21no—
10C3×#4090—21no—
11C3×#4082—21no—
12C3×#4081C412yescomplemented
13C3×#4081C2212yes—
14C3×#4072C411yescharacteristic, complemented
15C3×#4070—21no—
16C3×#4070—21no—
17#91118—21no—
18#91118C2212yes—
19C5×#836—21no—
20C5×#833C2212yes—
21#71870—51nomaximal, Hall
22#66159D311yescharacteristic
23C5×#413—31no—
24#65529—31no—
25#64696—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#6719—22no—
41C4⋊Dic15—41no—
42C4×Dic15—41no—
43C5×#208—22no—
44C5×#208—41no—
45C2×C5×C3⋊C8—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#5240—51no—
55#5237D511yescharacteristic
56#4539—54no—
57C2×C5×#41C2×D311yescharacteristic
58C22×Dic10Dic311yescharacteristic, complemented
59C2×C5×M16—61no—
60#4090—21no—
61#4082—21no—
62#4081Dic312yescomplemented
63#4081C2×D312yes—
64#4072—61no—
65#4072Dic311yescharacteristic, complemented
66#4070—21no—
67#4070—21no—
68C5×#101—61no—
69C5×#100—32no—
70#3966—32no—
71#3966—61no—
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×Dic15—42no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—42no—
94C3×Dic10—42no—
95C3×Dic10—41no—
96C3×Dic10—41no—
97C5×C3⋊C8—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—101no—
108C2×#208—21no—
109#836—21no—
110#834—52no—
111#834—101no—
112#833C2×D512yes—
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×M16—62no—
128C5×M16—121no—
129C2×C5×C8—121no—
130C22⋊Dic5—22no—
131C22⋊Dic5—22no—
132C22⋊Dic5—62no—
133C22⋊Dic5C2×Dic312yes—
134C4⋊Dic5—21no—
135C4⋊Dic5—121no—
136#683—22no—
137#683—22no—
138C4×Dic5—21no—
139C4×Dic5—121no—
140#536—51no—
141#413—31no—
142#410—151no—
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
156Dic15—82no—
157C3×Dic5—42no—
158C3×Dic5—42no—
159C3×#41—41no—
160C3×#41—41no—
161C2×C3×Q8—101no—
162C2×C3×Q8—101no—
163C2×C3×Q8—201no—
164C2×C3×Q8—201no—
165C2×C3×Q8C22⋊D511yescharacteristic
166C2×C3×D4C4×D511yescharacteristic
167C2×C3×D4D2011yescharacteristic
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—102no—
181C4⋊Dic3—201no—
182C4×Dic3—201no—
183#208—22no—
184#208—41no—
185C2×C3⋊C8—41no—
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#21711yescharacteristic
200C2×C4×C5#21711yescharacteristic
201C2×C4×C5#21711yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×Dic5—22no—
204C2×Dic5—22no—
205C2×Dic5—42no—
206C2×Dic5—122no—
207Dic10—42no—
208Dic10—41no—
209Dic10—41no—
210C5×C8—122no—
211C2×#41D3×D511yescharacteristic
212C22×Q8—51no—
213C2×M16—61no—
214C4⋊Q8—101no—
215#124—101no—
216#123—52no—
217#123—52no—
218C22⋊Q8—101no—
219C22⋊Q8—101no—
220#117—51no—
221#117—301no—
222#101—61no—
223#100—32no—
224#99—152no—
225#99—301no—
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×D2011yescharacteristic
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×C22⋊D511yescharacteristic
254C2×Dic3—202no—
255C3⋊C8—42no—
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#83411yescharacteristic
267C4×C5#83411yescharacteristic
268Dic5—42no—
269Dic5—42no—
270Dic5—242no—
271#41—41no—
272#41—41no—
273C2×Q8—101no—
274C2×Q8—101no—
275C2×Q8—201no—
276C2×Q8—201no—
277C2×Q8#120111yescharacteristic
278C2×D4D5×Dic311yescharacteristic
279C2×D4#120211yescharacteristic
280C2×D4C2×D3×D511yescharacteristic
281C22×C4—52no—
282C22×C4D5×Dic311yescharacteristic
283C22×C4#120111yescharacteristic
284C22×C4#120211yescharacteristic
285M16—62no—
286M16—121no—
287C2×C8—121no—
288C4⋊C4—102no—
289C4⋊C4—101no—
290C4⋊C4—102no—
291C4⋊C4—601no—
292C22⋊C4—52no—
293C22⋊C4—102no—
294C22⋊C4—102no—
295C22⋊C4—302no—
296C42—101no—
297C42—601no—
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—402no—
314C2×C5—21no—
315C2×C5—41no—
316C2×C5—41no—
317C2×C5—41no—
318C2×C5C2×#83411yescharacteristic
319C23#666511yescharacteristic
320C23C2×D5×Dic311yescharacteristic
321C23C2×#120211yescharacteristic
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—202no—
338C2×C4—602no—
339C2×C4#666511yescharacteristic
340C2×C4#666511yescharacteristic
341C2×C4#666511yescharacteristic
342C2×C4C2×#120111yescharacteristic
343C8—122no—
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—1202no—
363C4#9099511yescharacteristic
364C4#9099511yescharacteristic
365C3#1060094011yescharacteristic, 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. #11746001C2semidirect
7. C22×C3×Dic10C4semidirect
12. C3×#4081C4semidirect
14. C3×#4072C4semidirect
58. C22×Dic10Dic3semidirect
62. #4081Dic3semidirect
65. #4072Dic3semidirect
298. C3×C5#2123semidirect
349. C5#71870semidirect
365. C3#10600940semidirect

Maximal subgroups

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

subgroupindex
C3×#661592
#117513412
C5×#52372
#117460012
#106009403
#718705