Finite Group Databasebeta

← #14313553

Subgroups — #14313553

Order 1920.

476 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754251C211yesmaximal, characteristic
2#11752404C211yesmaximal, characteristic
3C3×#65745C211yesmaximal, characteristic
4#11746556C214yesmaximal, complemented
5#10604963—31nomaximal, Hall
6C22×C5×Dic6C411yescharacteristic, complemented
7C2×C3×#709C2211yescharacteristic
8#91989—21no—
9C3×#4130—21no—
10#91815C411yescharacteristic, complemented
11#91536—21no—
12#91536—21no—
13#91385C412yescomplemented
14#91368C2212yes—
15#91359—21no—
16#91359—21no—
17#91240—21no—
18#91228C2212yes—
19C3×#4011—21no—
20C3×#3999C2212yes—
21#70059—51nomaximal, Hall
22#66150—31no—
23#65745—31no—
24#65745D311yescharacteristic
25#64928—34no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×C5×Dic3—21no—
28C2×C5×Dic6—21no—
29C2×C5×Dic6—41no—
30C2×C5×Dic6—41no—
31C2×C5×Dic6C2×C412yes—
32C2×C3×C22⋊D5D411yescharacteristic
33C2×C3×C22⋊D5D411yescharacteristic
34C3×#709—41no—
35C3×#709—41no—
36C2×C3×D20C2311yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×Dic10C2×C411yescharacteristic
40#6763—22no—
41C4⋊ΓL(1,𝔽16)—41no—
42C4×ΓL(1,𝔽16)—41no—
43C3×C22⋊AGL(1,𝔽5)—22no—
44C3×C4⋊AGL(1,𝔽5)—41no—
45C3×C4×AGL(1,𝔽5)—41no—
46#6719—21no—
47C4⋊Dic15—21no—
48C4×Dic15C2×C412yes—
49#6669—22no—
50#6669—22no—
51#6665—22no—
52#6665—22no—
53#5825—51no—
54C3×#410—51no—
55#5240—51no—
56#4473—54no—
57C22×C5×Q8—31no—
58C2×#709C2×D311yescharacteristic
59#4130—21no—
60#4130—61no—
61#4093—32no—
62#4092—61no—
63#4092—61no—
64#4090—32no—
65#4075—61no—
66#4075—61no—
67#4072—31no—
68#4011—21no—
69#4011—61no—
70#3999—32no—
71#3999C2×D312yes—
72#2129—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C22×C3×D5C2×D411yescharacteristic
75C22×C3×D5C2×D411yescharacteristic
76C2×ΓL(1,𝔽16)—42no—
77C2×C3×AGL(1,𝔽5)—42no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×Dic15—22no—
83C2×C5×Dic3—22no—
84C2×C5×Dic3—42no—
85C5×Dic6—41no—
86C5×Dic6—41no—
87C5×Dic6—42no—
88C3×C22⋊D5—41no—
89C3×C22⋊D5—41no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C3×D20—41no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×Dic10—41no—
98C2×C3×#41—51no—
99C22×Dic6AGL(1,𝔽5)11yescharacteristic, complemented
100C3×#117—101no—
101#944—52no—
102#936—52no—
103#935—101no—
104#935—101no—
105#926—51no—
106#926—101no—
107#924—101no—
108#924—101no—
109C3×#99—52no—
110C3×#99—101no—
111#834—52no—
112#834—101no—
113C2×C5×Q8—32no—
114C2×C5×Q8—61no—
115C2×C5×Q8—121no—
116C2×C5×Q8—121no—
117C22×C4×C5—61no—
118C22×C4×C5C4×D311yescharacteristic
119C2×C22⋊D5D1211yescharacteristic
120C2×C22⋊D5#6711yescharacteristic
121#709—41no—
122#709—41no—
123C2×D20C22×D311yescharacteristic
124C2×C4×D5D1211yescharacteristic
125C2×C4×D5#6711yescharacteristic
126C2×Dic10C4×D311yescharacteristic
127C22⋊AGL(1,𝔽5)—22no—
128C22⋊AGL(1,𝔽5)—62no—
129C4⋊AGL(1,𝔽5)—41no—
130C4⋊AGL(1,𝔽5)—121no—
131C4×AGL(1,𝔽5)—41no—
132C4×AGL(1,𝔽5)—121no—
133C22⋊Dic5—61no—
134#685—62no—
135#685—62no—
136C4⋊Dic5—61no—
137#683—62no—
138#683—62no—
139C4×Dic5—32no—
140#536—151no—
141#410—51no—
142#410—151no—
143#354—154no—
144C22×C3×C5—21no—
145C22×C3×C5—41no—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C2×C3×D5—21no—
148C2×C3×D5—21no—
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151ΓL(1,𝔽16)—82no—
152C3×AGL(1,𝔽5)—82no—
153C3×C4×C5—21no—
154C3×C4×C5#9911yescharacteristic
155C3×C4×C5#9911yescharacteristic
156Dic15—42no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C5×Dic3—42no—
160C3×#41—201no—
161C3×#41—201no—
162C2×C3×Q8—51no—
163C2×C3×D4—51no—
164C2×C3×D4—51no—
165C2×C3×D4—51no—
166C22×C3×C4—51no—
167C22×C3×C4—51no—
168C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
169C22×Dic3—21no—
170C2×Dic6—21no—
171C2×Dic6—41no—
172C2×Dic6—41no—
173C2×Dic6C2×AGL(1,𝔽5)12yes—
174C3×C4⋊C4—201no—
175C3×C22⋊C4—102no—
176C3×C42—201no—
177#217—102no—
178#217—102no—
179#217—101no—
180#217—102no—
181C4⋊Dic3—101no—
182C4⋊Dic3—201no—
183Dic3⋊C4—102no—
184Dic3⋊C4—102no—
185C4×Dic3—52no—
186C4×Dic3—201no—
187C23×C5(C2×D3)⋊C411yescharacteristic
188C22×D5C2×D1211yescharacteristic
189C22×D5C2×#6711yescharacteristic
190C2×AGL(1,𝔽5)—42no—
191C2×AGL(1,𝔽5)—122no—
192C5×Q8—122no—
193C5×Q8—121no—
194C5×Q8—121no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—62no—
198C2×C4×C5—122no—
199C2×C4×C5(C2×D3)⋊C411yescharacteristic
200C2×C4×C5C2×C4×D311yescharacteristic
201C22⋊D5—41no—
202C22⋊D5—41no—
203C2×Dic5—62no—
204C2×Dic5(C2×D3)⋊C411yescharacteristic
205C2×Dic5(C2×D3)⋊C411yescharacteristic
206D20—41no—
207C4×D5—21no—
208C4×D5—21no—
209C4×D5—21no—
210C4×D5—21no—
211Dic10—41no—
212C2×#41—51no—
213C22×Q8—31no—
214C4⋊Q8—152no—
215#124—152no—
216#123—301no—
217#123—301no—
218C22⋊Q8—301no—
219C22⋊Q8—301no—
220#117—101no—
221#117—151no—
222#117—301no—
223#99—52no—
224#99—101no—
225#99—152no—
226#99—301no—
227C2×C3×C5—21no—
228C2×C3×C5—41no—
229C2×C3×C5C2×#9911yescharacteristic
230C3×D5—41no—
231C3×D5—41no—
232C23×C3—51no—
233C23×C3—51no—
234C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
235C3×Q8—201no—
236C3×D4—201no—
237C3×D4—201no—
238C3×D4—201no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—51no—
242C2×C3×C4—51no—
243C2×C3×C4—101no—
244C2×C3×C4—101no—
245C2×C3×C4—101no—
246C2×C3×C4—101no—
247C2×C3×C4—202no—
248C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
249C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
250C2×Dic3—22no—
251C2×Dic3—42no—
252C2×Dic3—102no—
253C2×Dic3—202no—
254Dic6—41no—
255Dic6—41no—
256Dic6—42no—
257C22×C5—21no—
258C22×C5—41no—
259C22×C5C2×(C2×D3)⋊C411yescharacteristic
260C2×D5—21no—
261C2×D5—21no—
262C2×D5—41no—
263C2×D5—41no—
264AGL(1,𝔽5)—82no—
265AGL(1,𝔽5)—242no—
266C4×C5—21no—
267C4×C5—122no—
268C4×C5#80611yescharacteristic
269C4×C5#80611yescharacteristic
270Dic5—21no—
271Dic5—21no—
272Dic5—122no—
273#41—201no—
274#41—201no—
275C2×Q8—32no—
276C2×Q8—51no—
277C2×Q8—61no—
278C2×Q8—121no—
279C2×Q8—121no—
280C2×D4—51no—
281C2×D4—51no—
282C2×D4—51no—
283C22×C4—51no—
284C22×C4—51no—
285C22×C4—61no—
286C22×C4D3×AGL(1,𝔽5)11yescharacteristic
287C4⋊C4—201no—
288C4⋊C4—302no—
289C4⋊C4—302no—
290C4⋊C4—301no—
291C4⋊C4—601no—
292C22⋊C4—102no—
293C22⋊C4—302no—
294C22⋊C4—302no—
295C22⋊C4—301no—
296C22⋊C4—302no—
297C42—152no—
298C42—201no—
299C42—601no—
300C3×C5#212911yescharacteristic, complemented, Hall
301C22×C3—21no—
302C22×C3—41no—
303C22×C3—101no—
304C22×C3—101no—
305C22×C3—201no—
306C22×C3—201no—
307C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
308C3×C4—21no—
309C3×C4—101no—
310C3×C4—101no—
311C3×C4—402no—
312C3×C4#401111yescharacteristic
313C3×C4#401111yescharacteristic
314Dic3—42no—
315Dic3—202no—
316Dic3—402no—
317C2×C5—21no—
318C2×C5—41no—
319C2×C5C2×#80611yescharacteristic
320D5—41no—
321D5—41no—
322C23—51no—
323C23—51no—
324C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
325Q8—122no—
326Q8—121no—
327Q8—121no—
328Q8—201no—
329D4—201no—
330D4—201no—
331D4—201no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—51no—
335C2×C4—51no—
336C2×C4—62no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—101no—
340C2×C4—101no—
341C2×C4—122no—
342C2×C4—202no—
343C2×C4—302no—
344C2×C4—602no—
345C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
346C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
347C2×C3—21no—
348C2×C3—41no—
349C2×C3—201no—
350C2×C3—201no—
351C2×C3C2×#401111yescharacteristic
352C5#7005911yescharacteristic, complemented, Sylow
353C22—21no—
354C22—41no—
355C22—101no—
356C22—101no—
357C22—201no—
358C22—201no—
359C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
360C4—21no—
361C4—101no—
362C4—101no—
363C4—122no—
364C4—402no—
365C4—602no—
366C4—1202no—
367C4#9117211yescharacteristic
368C4#9117211yescharacteristic
369C3#1060496311yescharacteristic, complemented, Sylow
370C2—21no—
371C2—41no—
372C2—201no—
373C2—201no—
374C2C2×#9117211yescharacteristic
subgroupG/H
centerC2C2×#91172
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5C2×#99
prime radicalC2×C3×#709C22
cosocleC2×C3×D20C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2129
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746556C2semidirect
6. C22×C5×Dic6C4semidirect
10. #91815C4semidirect
13. #91385C4semidirect
99. C22×Dic6AGL(1,𝔽5)semidirect
300. C3×C5#2129semidirect
352. C5#70059semidirect
369. C3#10604963semidirect

Maximal subgroups

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

subgroupindex
#117542512
#117524042
C3×#657452
#117465562
#106049633
#700595