Finite Group Databasebeta

← #14289181

Subgroups — #14289181

Order 1920.

420 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#65901C211yesmaximal, characteristic, complemented
2C5×#5027C211yesmaximal, characteristic
3#11747060C211yesmaximal, characteristic
4#11746901C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10601827—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C2×C5×#215—21no—
11C5×#874C2211yescharacteristic
12C3×#4090—21no—
13C3×#4035—22no—
14C3×#4033—21no—
15C3×#4016—21no—
16C3×#4015C2211yescharacteristic
17C3×C4×Dic10—21no—
18C3×C4×Dic10C2211yescharacteristic
19C2×#6656—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C5×#809—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90966—22no—
25#90966—21no—
26#71935—51nomaximal, Hall
27#65901D311yescharacteristic, complemented
28C5×#460—31no—
29#65364—31no—
30#65359—31no—
31Q8⋊#168—31no—
32#64704—31no—
33#64702—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C3×Dic10—21no—
39C2×C3×Dic10D411yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C5×#215—42no—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×C4⋊Dic5D412yes—
51C3×#683—22no—
52C3×#683—22no—
53C3×#683—22no—
54C3×#683—21no—
55C3×C4×Dic5—22no—
56C3×C4×Dic5—21no—
57#6656—42no—
58C3×#557—51no—
59#5088—51no—
60#5027—51no—
61#5027D511yescharacteristic
62#4547—51no—
63#4535—51no—
64#4535—51no—
65C2×C5×SD16—61no—
66C5×#127—31no—
67C4×C5×Q8C2×D311yescharacteristic
68#4090—21no—
69C2×#687—61no—
70#4035—22no—
71#4033—21no—
72#4016—21no—
73#4015C2×D311yescharacteristic
74C4×Dic10—21no—
75C4×Dic10C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C5×#102—61no—
78#3964—62no—
79#3964—61no—
80C4⋊#168—31no—
81C4×#168—31no—
82#1626—151noSylow
83C22×C5×D3—41no—
84C3×C5×Q8—21no—
85C3×C5×Q8—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C5×D12—42no—
92C5×D12—41no—
93C5×D12—41no—
94C5×D12—41no—
95C5×D12—41no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—22no—
99C3×Dic10—21no—
100C3×Dic10—41no—
101C3×Dic10—41no—
102C3×Dic10SD1612yescomplemented
103C3⋊#168—41no—
104C3⋊#168—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8—51no—
107C3×C4⋊Q8—101no—
108C3×#125—101no—
109C3×#125—102no—
110C3×C4×Q8—51no—
111C3×C4×Q8—101no—
112C3×C4×Q8—101no—
113C3×C4×Q8C2×D511yescharacteristic
114C2×#215—21no—
115C2×#215—101no—
116#874C2×D511yescharacteristic
117#809—21no—
118#809—101no—
119#809—102no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8—51no—
123C2×C5×Q8#6711yescharacteristic
124C2×C5×D4—61no—
125C2×C5×D4—61no—
126C2×C5×D4—61no—
127C2×Dic10—21no—
128C2×Dic10#6711yescharacteristic
129C5×SD16—122no—
130C2×C5×C8—61no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4#6711yescharacteristic
133C42×C5—21no—
134C42×C5C22×D311yescharacteristic
135#687—122no—
136C4⋊Dic5—21no—
137C4⋊Dic5#6711yescharacteristic
138C4⋊Dic5#6712yes—
139#683—22no—
140#683—22no—
141#683—22no—
142#683—21no—
143C4×Dic5—22no—
144C4×Dic5—21no—
145C2×#168—61no—
146C2×#168—61no—
147#557—51no—
148#486—151no—
149#460—31no—
150#460—151no—
151#332—151no—
152Q8⋊C8—151no—
153Q8⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×C5×D3—81no—
156C2×C5×D3—81no—
157C2×C5×D3—81no—
158C3×C4×C5—21no—
159C3×C4×C5—41no—
160C3×C4×C5—41no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C3×Dic5—22no—
166C3×Dic5—42no—
167C3×Dic5—41no—
168C2×C3×Q8—51no—
169C2×C3×Q8—101no—
170C2×C3×Q8C22⋊D511yescharacteristic
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—52no—
177C3×C4⋊C4—102no—
178C3×C4⋊C4—102no—
179C3×C4⋊C4—102no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4C22⋊D511yescharacteristic
183C3×C42—21no—
184C3×C42—102no—
185C3×C42—101no—
186C3×C42C22×D511yescharacteristic
187#215—42no—
188#215—202no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—101no—
191C2×C3⋊C8—101no—
192C23×C5—121no—
193C5×Q8—21no—
194C5×Q8—21no—
195C5×D4—122no—
196C5×D4—121no—
197C5×D4—121no—
198C5×D4—121no—
199C5×D4—121no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5C2×#6711yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C2×Dic5—21no—
206C2×Dic5—21no—
207C2×Dic5—22no—
208Dic10—21no—
209Dic10—41no—
210Dic10—41no—
211Dic10#21512yescomplemented
212C5×C8—121no—
213#168—121no—
214#168—121no—
215C2×SD16—61no—
216C2×SD16—301no—
217C4⋊Q8—51no—
218C4⋊Q8—101no—
219#127—31no—
220#125—101no—
221#125—102no—
222C4×Q8—51no—
223C4×Q8—101no—
224C4×Q8—101no—
225C4×Q8D3×D511yescharacteristic
226C4⋊C8—31no—
227C4⋊C8—151no—
228#102—61no—
229#102—301no—
230#102—302no—
231C4×C8—151no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C5×D3—161no—
236C22×D3—41no—
237C3×Q8—21no—
238C3×Q8—21no—
239C3×Q8—52no—
240C3×Q8—101no—
241C3×Q8—201no—
242C3×Q8—201no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—101no—
246C2×C3×C4—101no—
247C2×C3×C4—102no—
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251D12—42no—
252D12—41no—
253D12—41no—
254D12—41no—
255D12—41no—
256C3⋊C8—41no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5—241no—
260C22×C5—241no—
261C22×C5—241no—
262C22×C5#95311yescharacteristic
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5C2×#21511yescharacteristic
267C4×C5#94211yescharacteristic
268C4×C5#94911yescharacteristic
269C4×C5#95011yescharacteristic
270Dic5—22no—
271Dic5—42no—
272Dic5—41no—
273C2×Q8—51no—
274C2×Q8—101no—
275C2×Q8#120111yescharacteristic
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—61no—
279SD16—122no—
280SD16—602no—
281C2×C8—61no—
282C2×C8—301no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—51no—
286C4⋊C4—52no—
287C4⋊C4—102no—
288C4⋊C4—102no—
289C4⋊C4—102no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4#120111yescharacteristic
293C42—21no—
294C42—102no—
295C42—101no—
296C42C2×D3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3#408311yescharacteristic
299C2×D3—81no—
300C2×D3—81no—
301C2×D3—81no—
302C3×C4—21no—
303C3×C4—41no—
304C3×C4—41no—
305C3×C4—102no—
306C3×C4—202no—
307C3×C4—201no—
308C3×C4D5×SD1611yescharacteristic
309C3×C4#406111yescharacteristic
310C3×C4#407811yescharacteristic
311C3×C4#409611yescharacteristic
312C2×C5—481no—
313C2×C5#522711yescharacteristic
314C2×C5#523811yescharacteristic
315C2×C5#524511yescharacteristic
316C23—121no—
317Q8—21no—
318Q8—21no—
319Q8—52no—
320Q8—101no—
321Q8—201no—
322Q8—201no—
323D4—122no—
324D4—121no—
325D4—121no—
326D4—121no—
327D4—121no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—102no—
333C2×C4C2×#120111yescharacteristic
334C2×C4D5×#6711yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C8—121no—
337C8—601no—
338C8—601no—
339C2×C3#6532611yescharacteristic
340C2×C3#6545911yescharacteristic
341C2×C3#6549011yescharacteristic
342D3—161no—
343C5#7193511yescharacteristic, complemented, Sylow
344C22—241no—
345C22—241no—
346C22—241no—
347C22#9156311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—102no—
352C4—201no—
353C4—202no—
354C4#9129711yescharacteristic
355C4#9129911yescharacteristic
356C4D5×#21511yescharacteristic
357C4#9151311yescharacteristic
358C3#1060182711yescharacteristic, complemented, Sylow
359C2—481no—
360C2#1174851111yescharacteristic
361C2#1174926711yescharacteristic
362C2#1174945611yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1626
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#65901C2semidirect
5. #11746356C2semidirect
6. #11745856C2semidirect
7. #11745840C2semidirect
27. #65901D3semidirect
102. C3×Dic10SD16semidirect
211. Dic10#215semidirect
297. C3×C5#1626semidirect
343. C5#71935semidirect
358. C3#10601827semidirect

Maximal subgroups

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

subgroupindex
C3×#659012
C5×#50272
#117470602
#117469012
#117463562
#117458562
#117458402
#106018273
#719355