Finite Group Databasebeta

← #14313334

Subgroups — #14313334

Order 1920.

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

normal subgroups only

This group has 468 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×#65761C211yesmaximal, characteristic
4#11746582C214yesmaximal, complemented
5#10604980—31nomaximal, Hall
6C22×C5×Dic6C411yescharacteristic, complemented
7C2×C3×#709C2211yescharacteristic
8#91989—21no—
9C3×D5⋊M16—21no—
10#91815C411yescharacteristic, complemented
11#91536C412yescomplemented
12#91536C2212yes—
13#91385—21no—
14#91368—21no—
15#91359—21no—
16#91359—21no—
17#91240C2212yes—
18#91228—21no—
19C3×#4013C2212yes—
20C3×#4005—21no—
21#70147—51nomaximal, Hall
22#66150—31no—
23#65761D311yescharacteristic
24#65745—31no—
25#64916—34no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×C5×Dic3C2×C412yes—
28C2×C5×Dic6—21no—
29C2×C5×Dic6—21no—
30C2×C5×Dic6—41no—
31C2×C5×Dic6—41no—
32C2×C3×C22⋊D5C2×C411yescharacteristic
33C2×C3×C22⋊D5C2311yescharacteristic
34C3×#709—41no—
35C3×#709—41no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40#6763—22no—
41C4⋊ΓL(1,𝔽16)—41no—
42C4×ΓL(1,𝔽16)—41no—
43C3×#704—22no—
44C3×#700—41no—
45C3×D5⋊C8—41no—
46#6719C2×C412yes—
47C4⋊Dic15—21no—
48C4×Dic15—21no—
49#6669—22no—
50#6669—22no—
51#6665—22no—
52#6665—22no—
53#5825—51no—
54C3×#413—51no—
55#5240—51no—
56#4476—54no—
57C22×C5×Q8—31no—
58C2×#709C2×D311yescharacteristic
59#4130—61no—
60D5⋊M16—21no—
61#4093—61no—
62#4092—61no—
63#4092—61no—
64#4090—61no—
65#4075—32no—
66#4075—32no—
67#4072—31no—
68#4013C2×D312yes—
69#4011—32no—
70#4005—21no—
71#3999—61no—
72#2123—151noSylow
73C23×C3×C5C22×C411yescharacteristic
74C22×C3×D5C22⋊C411yescharacteristic
75C22×C3×D5C2×D411yescharacteristic
76C2×ΓL(1,𝔽16)—42no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C2×Dic15—22no—
82C2×C5×Dic3—22no—
83C2×C5×Dic3—42no—
84C5×Dic6—42no—
85C5×Dic6—41no—
86C5×Dic6—41no—
87C3×C22⋊D5—41no—
88C3×C22⋊D5—41no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C2×D411yescharacteristic
91C3×D20—41no—
92C3×C4×D5—21no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×Dic10—41no—
97C3×#170—42no—
98C2×C3×#41—51no—
99C22×Dic6AGL(1,𝔽5)11yescharacteristic, complemented
100C2×C3×M16—101no—
101#944—101no—
102#936—101no—
103#935—52no—
104#935—52no—
105#926—51no—
106#926—101no—
107#924—101no—
108#924—101no—
109C3×#101—101no—
110C3×#100—52no—
111#834—52no—
112#834—101no—
113C2×C5×Q8—61no—
114C2×C5×Q8—61no—
115C2×C5×Q8—121no—
116C2×C5×Q8—121no—
117C22×C4×C5—32no—
118C22×C4×C5C4×D311yescharacteristic
119C2×C22⋊D5C4×D311yescharacteristic
120C2×C22⋊D5C22×D311yescharacteristic
121#709—41no—
122#709—41no—
123C2×D20D1211yescharacteristic
124C2×C4×D5D1211yescharacteristic
125C2×C4×D5#6711yescharacteristic
126C2×Dic10#6711yescharacteristic
127C22⋊AGL(1,𝔽5)—62no—
128#704—22no—
129C4⋊AGL(1,𝔽5)—121no—
130C4×AGL(1,𝔽5)—121no—
131#700—41no—
132D5⋊C8—41no—
133C22⋊Dic5—32no—
134#685—62no—
135#685—62no—
136C4⋊Dic5—61no—
137#683—62no—
138#683—62no—
139C4×Dic5—61no—
140#536—151no—
141#413—51no—
142#410—151no—
143#352—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×C4×C5—21no—
153C3×C4×C5#9911yescharacteristic
154C3×C4×C5#9911yescharacteristic
155Dic15—42no—
156C3×Dic5—21no—
157C3×Dic5—21no—
158C5×Dic3—42no—
159C3×#41—201no—
160C3×#41—201no—
161C2×C3×Q8—51no—
162C2×C3×D4—51no—
163C2×C3×D4—51no—
164C2×C3×D4—51no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
168C22×Dic3C2×AGL(1,𝔽5)12yes—
169C2×Dic6—21no—
170C2×Dic6—21no—
171C2×Dic6—41no—
172C2×Dic6—41no—
173C3×M16—102no—
174C3×M16—201no—
175C2×C3×C8—201no—
176#217—52no—
177#217—102no—
178#217—102no—
179#217—102no—
180C4⋊Dic3—101no—
181C4⋊Dic3—201no—
182Dic3⋊C4—102no—
183Dic3⋊C4—102no—
184C4×Dic3—101no—
185C4×Dic3—201no—
186C23×C5C2×C4×D311yescharacteristic
187C22×D5(C2×D3)⋊C411yescharacteristic
188C22×D5C2×D1211yescharacteristic
189C2×AGL(1,𝔽5)—122no—
190C5×Q8—122no—
191C5×Q8—121no—
192C5×Q8—121no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—62no—
196C2×C4×C5—122no—
197C2×C4×C5(C2×D3)⋊C411yescharacteristic
198C2×C4×C5(C2×D3)⋊C411yescharacteristic
199C22⋊D5—41no—
200C22⋊D5—41no—
201C2×Dic5—62no—
202C2×Dic5(C2×D3)⋊C411yescharacteristic
203C2×Dic5C2×#6711yescharacteristic
204D20—41no—
205C4×D5—21no—
206C4×D5—21no—
207C4×D5—21no—
208C4×D5—21no—
209Dic10—41no—
210#170—42no—
211C2×#41—51no—
212C22×Q8—31no—
213C2×M16—101no—
214C4⋊Q8—301no—
215#124—301no—
216#123—152no—
217#123—152no—
218C22⋊Q8—301no—
219C22⋊Q8—301no—
220#117—151no—
221#117—301no—
222#101—101no—
223#100—52no—
224#99—152no—
225#99—301no—
226C2×C3×C5—21no—
227C2×C3×C5—41no—
228C2×C3×C5C2×#9911yescharacteristic
229C3×D5—41no—
230C3×D5—41no—
231C23×C3—51no—
232C23×C3—51no—
233C23×C3C22×AGL(1,𝔽5)11yescharacteristic
234C3×Q8—201no—
235C3×D4—201no—
236C3×D4—201no—
237C3×D4—201no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—51no—
241C2×C3×C4—51no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4—101no—
245C2×C3×C4—101no—
246C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
247C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
248C2×Dic3—22no—
249C2×Dic3—42no—
250C2×Dic3—102no—
251C2×Dic3—202no—
252Dic6—42no—
253Dic6—41no—
254Dic6—41no—
255C3×C8—202no—
256C22×C5—21no—
257C22×C5—41no—
258C22×C5C2×(C2×D3)⋊C411yescharacteristic
259C2×D5—21no—
260C2×D5—21no—
261C2×D5—41no—
262C2×D5—41no—
263AGL(1,𝔽5)—242no—
264C4×C5—21no—
265C4×C5—122no—
266C4×C5#80611yescharacteristic
267C4×C5#80611yescharacteristic
268Dic5—21no—
269Dic5—21no—
270Dic5—122no—
271#41—201no—
272#41—201no—
273C2×Q8—51no—
274C2×Q8—61no—
275C2×Q8—61no—
276C2×Q8—121no—
277C2×Q8—121no—
278C2×D4—51no—
279C2×D4—51no—
280C2×D4—51no—
281C22×C4—32no—
282C22×C4—51no—
283C22×C4—51no—
284C22×C4D3×AGL(1,𝔽5)11yescharacteristic
285M16—102no—
286M16—201no—
287C2×C8—201no—
288C4⋊C4—302no—
289C4⋊C4—302no—
290C4⋊C4—301no—
291C4⋊C4—601no—
292C22⋊C4—152no—
293C22⋊C4—302no—
294C22⋊C4—302no—
295C22⋊C4—302no—
296C42—301no—
297C42—601no—
298C3×C5#212311yescharacteristic, complemented, Hall
299C22×C3—21no—
300C22×C3—41no—
301C22×C3—101no—
302C22×C3—101no—
303C22×C3—201no—
304C22×C3—201no—
305C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
306C3×C4—21no—
307C3×C4—101no—
308C3×C4—101no—
309C3×C4#401111yescharacteristic
310C3×C4#401111yescharacteristic
311Dic3—42no—
312Dic3—202no—
313Dic3—402no—
314C2×C5—21no—
315C2×C5—41no—
316C2×C5C2×#80611yescharacteristic
317D5—41no—
318D5—41no—
319C23—51no—
320C23—51no—
321C23C2×D3×AGL(1,𝔽5)11yescharacteristic
322Q8—122no—
323Q8—121no—
324Q8—121no—
325Q8—201no—
326D4—201no—
327D4—201no—
328D4—201no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—51no—
332C2×C4—51no—
333C2×C4—62no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—101no—
337C2×C4—101no—
338C2×C4—122no—
339C2×C4—302no—
340C2×C4—602no—
341C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
342C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
343C8—202no—
344C2×C3—21no—
345C2×C3—41no—
346C2×C3—201no—
347C2×C3—201no—
348C2×C3C2×#401111yescharacteristic
349C5#7014711yescharacteristic, complemented, Sylow
350C22—21no—
351C22—41no—
352C22—101no—
353C22—101no—
354C22—201no—
355C22—201no—
356C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
357C4—21no—
358C4—101no—
359C4—101no—
360C4—122no—
361C4—602no—
362C4—1202no—
363C4#9117211yescharacteristic
364C4#9117211yescharacteristic
365C3#1060498011yescharacteristic, complemented, Sylow
366C2—21no—
367C2—41no—
368C2—201no—
369C2—201no—
370C2C2×#9117211yescharacteristic
subgroupG/H
centerC2C2×#91172
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5C2×#99
prime radicalC2×C3×#709C22
cosocleC2×C3×C22⋊D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2123
LCSG ▷ C23×C3×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. #11746582C2semidirect
6. C22×C5×Dic6C4semidirect
10. #91815C4semidirect
11. #91536C4semidirect
99. C22×Dic6AGL(1,𝔽5)semidirect
298. C3×C5#2123semidirect
349. C5#70147semidirect
365. C3#10604980semidirect

Maximal subgroups

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

subgroupindex
#117542512
#117524042
C3×#657612
#117465822
#106049803
#701475