Finite Group Databasebeta

← #14298390

Subgroups — #14298390

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2#11748341C212yesmaximal
3#11746351C211yesmaximal, characteristic, complemented
4C5×#4530C211yesmaximal, characteristic, complemented
5#11745985C212yesmaximal, complemented
6#10599783—31nomaximal, Hall
7C22×C3×C4×D5C412yes—
8C22×C3×C4×D5C2211yescharacteristic
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×#6710C2212yes—
11C2×C5×#208C2212yes—
12C2×C3×C4⋊Dic5C2211yescharacteristic
13C2×C3×#683C412yes—
14C3×D5×C4⋊C4—22no—
15C3×D5×C4⋊C4—22no—
16#90955—22no—
17#90955—22no—
18#71562—51nomaximal, Hall
19C2×D5×C4⋊C4D311yescharacteristic
20#65415—32no—
21C5×#343—31no—
22#64774—32no—
23#64750—31no—
24C23×C3×D5C2×C411yescharacteristic
25C22×C3×C4×C5C2×C412yes—
26C22×C3×C4×C5C2311yescharacteristic
27C22×C3×Dic5C2×C411yescharacteristic
28C22×C3×Dic5C2×C412yes—
29C2×C3×C4×D5—22no—
30C2×C3×C4×D5—21no—
31C2×C3×C4×D5—21no—
32C2×C3×C4×D5—22no—
33C2×C3×C4×D5—22no—
34C2×C3×C4×D5—44no—
35C2×C3×C4×D5D412yes—
36C2×C3×C4×D5D412yes—
37C3×C5×C4⋊C4—22no—
38#6710—22no—
39#6710—22no—
40C2×C3⋊#168—22no—
41C5×#208—22no—
42C5×#208—22no—
43C2×C5×C3⋊C8—22no—
44C3×C4⋊Dic5—22no—
45C3×#683—24no—
46C22×C3×C4⋊C4—51no—
47#5207—52no—
48#4530—51no—
49#4530—52no—
50#4530D511yescharacteristic, complemented
51C22×C4×D5Dic312yes—
52C22×C4×D5C2×D311yescharacteristic
53C2×C5×M16—32no—
54C2×C5×C4⋊C4C2×D311yescharacteristic
55C2×C4⋊Dic5C2×D311yescharacteristic
56C2×#683Dic312yes—
57C2×#681—32no—
58D5×C4⋊C4—22no—
59D5×C4⋊C4—22no—
60#3952—62no—
61#3952—62no—
62#1821—151noSylow
63C23×C3×C5C22×C411yescharacteristic
64C22×C3×D5—21no—
65C22×C3×D5—21no—
66C22×C3×D5—22no—
67C22×C3×D5—22no—
68C22×C3×D5C22⋊C411yescharacteristic
69C22×C3×D5C22⋊C411yescharacteristic
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—42no—
72C2×C3×C4×C5C2×D412yes—
73C2×C3×C4×C5#4112yes—
74C2×C3×C4×C5#4111yescharacteristic
75C2×C3×C4×C5#4111yescharacteristic
76C2×C3×Dic5—21no—
77C2×C3×Dic5—21no—
78C2×C3×Dic5—22no—
79C2×C3×Dic5—42no—
80C2×C3×Dic5C22⋊C412yes—
81C3×C4×D5—22no—
82C3×C4×D5—22no—
83C3×C4×D5—22no—
84C3×C4×D5—22no—
85C3×C4×D5—44no—
86C3×C4×D5—44no—
87C3⋊#168—42no—
88C5×C3⋊C8—42no—
89C23×C3×C4—51no—
90C23×C3×C4—52no—
91C2×C3×C4⋊C4—52no—
92C2×C3×C4⋊C4—51no—
93C2×C3×C4⋊C4—102no—
94C2×C3×C4⋊C4—102no—
95C2×C3×C4⋊C4C2×D511yescharacteristic
96C2×#208—52no—
97C2×#208C2×D512yes—
98#830—102no—
99#830—102no—
100C23×D5C2×Dic311yescharacteristic
101C22×C4×C5C2×Dic312yes—
102C22×C4×C5C22×D311yescharacteristic
103C22×Dic5C2×Dic311yescharacteristic
104C22×Dic5C2×Dic312yes—
105C2×C4×D5—22no—
106C2×C4×D5—21no—
107C2×C4×D5—21no—
108C2×C4×D5—22no—
109C2×C4×D5—22no—
110C2×C4×D5—44no—
111C2×C4×D5#6712yes—
112C2×C4×D5#6712yes—
113C5×M16—62no—
114C5×M16—62no—
115C2×C5×C8—62no—
116C5×C4⋊C4—22no—
117C4⋊Dic5—22no—
118#683—24no—
119#681—62no—
120#681—62no—
121C2×#168—62no—
122C22×C4⋊C4—51no—
123#407—152no—
124#343—31no—
125#343—152no—
126#343—151no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C22×C3×C5#11711yescharacteristic
131C22×C3×C5#11711yescharacteristic
132C2×C3×D5—24no—
133C2×C3×D5—24no—
134C2×C3×D5—21no—
135C2×C3×D5—21no—
136C2×C3×D5—21no—
137C2×C3×D5—21no—
138C2×C3×D5#10012yes—
139C2×C3×D5#10112yes—
140C3×C4×C5—42no—
141C3×C4×C5#12312yes—
142C3×C4×C5#12312yes—
143C3×Dic5—22no—
144C3×Dic5—42no—
145C24×C3—51no—
146C22×C3×C4—51no—
147C22×C3×C4—52no—
148C22×C3×C4—52no—
149C22×C3×C4—52no—
150C22×C3×C4—102no—
151C22×C3×C4—102no—
152C22×C3×C4—102no—
153C22×C3×C4—101no—
154C22×C3×C4—101no—
155C22×C3×C4—204no—
156C22×C3×C4C4×D512yes—
157C22×C3×C4C22×D511yescharacteristic
158C3×C4⋊C4—22no—
159C3×C4⋊C4—104no—
160C3×C4⋊C4—102no—
161#208—22no—
162#208—22no—
163#208—102no—
164#208—102no—
165C2×C3⋊C8—22no—
166C2×C3⋊C8—102no—
167C23×C5C22×Dic311yescharacteristic
168C22×D5—21no—
169C22×D5—21no—
170C22×D5—22no—
171C22×D5—22no—
172C22×D5#21711yescharacteristic
173C22×D5#21711yescharacteristic
174C2×C4×C5—22no—
175C2×C4×C5—42no—
176C2×C4×C5#23512yes—
177C2×C4×C5#23511yescharacteristic
178C2×C4×C5#23511yescharacteristic
179C2×C4×C5C2×#6712yes—
180C2×Dic5—21no—
181C2×Dic5—21no—
182C2×Dic5—22no—
183C2×Dic5—42no—
184C2×Dic5#21712yes—
185C4×D5—22no—
186C4×D5—22no—
187C4×D5—22no—
188C4×D5—22no—
189C4×D5—44no—
190C4×D5—44no—
191C5×C8—122no—
192#168—122no—
193C23×C4—51no—
194C23×C4—52no—
195C2×M16—32no—
196C2×M16—152no—
197C2×C4⋊C4—52no—
198C2×C4⋊C4—51no—
199C2×C4⋊C4—102no—
200C2×C4⋊C4—102no—
201C2×C4⋊C4D3×D511yescharacteristic
202C22⋊C8—302no—
203C22⋊C8—302no—
204C2×C3×C5—21no—
205C2×C3×C5—21no—
206C2×C3×C5#38111yescharacteristic
207C2×C3×C5C2×#10011yescharacteristic
208C2×C3×C5C2×#10111yescharacteristic
209C3×D5—22no—
210C3×D5—22no—
211C23×C3—51no—
212C23×C3—51no—
213C23×C3—102no—
214C23×C3—102no—
215C23×C3—101no—
216C23×C3—101no—
217C23×C3C2×C4×D511yescharacteristic
218C2×C3×C4—22no—
219C2×C3×C4—42no—
220C2×C3×C4—52no—
221C2×C3×C4—101no—
222C2×C3×C4—101no—
223C2×C3×C4—102no—
224C2×C3×C4—102no—
225C2×C3×C4—102no—
226C2×C3×C4—102no—
227C2×C3×C4—102no—
228C2×C3×C4—204no—
229C2×C3×C4—204no—
230C2×C3×C4—202no—
231C2×C3×C4#70912yes—
232C2×C3×C4D4×D512yes—
233C2×C3×C4#71111yescharacteristic
234C2×C3×C4#71311yescharacteristic
235C3⋊C8—42no—
236C3⋊C8—202no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5#92611yescharacteristic
240C22×C5#92611yescharacteristic
241C22×C5C2×#21711yescharacteristic
242C2×D5—24no—
243C2×D5—24no—
244C2×D5—21no—
245C2×D5—21no—
246C2×D5—21no—
247C2×D5—21no—
248C2×D5#83312yes—
249C2×D5#83612yes—
250C4×C5—42no—
251C4×C5#92912yes—
252C4×C5#92912yes—
253Dic5—22no—
254Dic5—42no—
255C24—51no—
256C22×C4—51no—
257C22×C4—52no—
258C22×C4—52no—
259C22×C4—52no—
260C22×C4—102no—
261C22×C4—102no—
262C22×C4—102no—
263C22×C4—101no—
264C22×C4—101no—
265C22×C4—204no—
266C22×C4D5×Dic312yes—
267C22×C4C2×D3×D511yescharacteristic
268M16—62no—
269M16—62no—
270M16—302no—
271M16—302no—
272C2×C8—62no—
273C2×C8—302no—
274C4⋊C4—22no—
275C4⋊C4—104no—
276C4⋊C4—102no—
277C3×C5#182111yescharacteristic, complemented, Hall
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—52no—
281C22×C3—52no—
282C22×C3—104no—
283C22×C3—104no—
284C22×C3—101no—
285C22×C3—101no—
286C22×C3—101no—
287C22×C3—101no—
288C22×C3#401811yescharacteristic
289C22×C3D5×C22⋊C411yescharacteristic
290C22×C3#403811yescharacteristic
291C3×C4—42no—
292C3×C4—102no—
293C3×C4—202no—
294C3×C4#402912yes—
295C3×C4#404012yes—
296C2×C5—21no—
297C2×C5—21no—
298C2×C5#521111yescharacteristic
299C2×C5C2×#83311yescharacteristic
300C2×C5C2×#83611yescharacteristic
301D5—22no—
302D5—22no—
303C23—51no—
304C23—51no—
305C23—102no—
306C23—102no—
307C23—101no—
308C23—101no—
309C23C2×D5×Dic311yescharacteristic
310C2×C4—22no—
311C2×C4—42no—
312C2×C4—52no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—102no—
316C2×C4—102no—
317C2×C4—102no—
318C2×C4—102no—
319C2×C4—102no—
320C2×C4—204no—
321C2×C4—204no—
322C2×C4—202no—
323C2×C4#677112yes—
324C2×C4#677211yescharacteristic
325C2×C4#677311yescharacteristic
326C2×C4D5×#6712yes—
327C8—122no—
328C8—602no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—102no—
332C2×C3—102no—
333C2×C3#6495311yescharacteristic
334C2×C3D5×#10011yescharacteristic
335C2×C3D5×#10111yescharacteristic
336C5#7156211yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—52no—
340C22—52no—
341C22—104no—
342C22—104no—
343C22—101no—
344C22—101no—
345C22—101no—
346C22—101no—
347C22#9135711yescharacteristic
348C22#9135811yescharacteristic
349C22D5×#21711yescharacteristic
350C4—42no—
351C4—102no—
352C4—202no—
353C4#9134812yes—
354C4#9144712yes—
355C3#1059978311yescharacteristic, complemented, Sylow
356C2—21no—
357C2—21no—
358C2—102no—
359C2—102no—
360C2#1174873711yescharacteristic
361C2D5×#83311yescharacteristic
362C2D5×#83611yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1821
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #11746351C2semidirect
4. C5×#4530C2semidirect
5. #11745985C2semidirect
50. #4530D5semidirect
277. C3×C5#1821semidirect
336. C5#71562semidirect
355. C3#10599783semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
#117483412
#117463512
C5×#45302
#117459852
#105997833
#715625