Finite Group Databasebeta

← #14289191

Subgroups — #14289191

Order 1920.

420 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752482C211yesmaximal, characteristic, complemented
2C3×#64983C211yesmaximal, characteristic
3#11747083C211yesmaximal, characteristic
4#11747068C211yesmaximal, characteristic
5#11746277C211yesmaximal, characteristic, complemented
6C5×#4456C211yesmaximal, characteristic, complemented
7#11745856C211yesmaximal, characteristic, complemented
8#10599045—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C3×#4020C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91389—21no—
14#91384—21no—
15#91346—22no—
16#91344—21no—
17Dic3×Dic10—21no—
18C2×#6657—21no—
19C2×#6655—21no—
20C3×C4×C5×C8C2211yescharacteristic
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3953—22no—
24#90965—21no—
25#90964—21no—
26#71204—51nomaximal, Hall
27#65904—31no—
28#65316—31no—
29#65137—31no—
30#64983D311yescharacteristic
31C5×Q8⋊C8—31no—
32#64702—31no—
33#64676—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×Dic6D411yescharacteristic
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×Dic10—21no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15D411yescharacteristic
43#6712—21no—
44C4×Dic15—21no—
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D412yes—
52Dic3⋊Dic5—22no—
53Dic3⋊Dic5—22no—
54#6668—22no—
55Dic3×Dic5—22no—
56#6657—42no—
57#6655—42no—
58#5721—51no—
59C3×#486—51no—
60#5075—51no—
61#5075—51no—
62#4547—51no—
63#4456—51no—
64#4456D511yescharacteristic, complemented
65C4×C5×Q8—31no—
66Q8×Dic5—61no—
67C2×#688—61no—
68C2×#677—61no—
69#4036—61no—
70#4036—62no—
71#4020C2×D311yescharacteristic
72#4015—61no—
73#4015C2×D311yescharacteristic
74C4×Dic10—31no—
75C4×Dic10—61no—
76C5×C4⋊C8—31no—
77C4×C5×C8C2×D311yescharacteristic
78#3953—22no—
79#3953—61no—
80#3941—61no—
81C4⋊#168—31no—
82#1626—151noSylow
83C22×C3×D5—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—21no—
89Dic30—21no—
90Dic30—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C5×Dic6—21no—
94C5×Dic6SD1612yescomplemented
95C2×C3×Dic5—22no—
96C3×D20—42no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8—51no—
107C3×#127—51no—
108Q8×Dic3—101no—
109#944—101no—
110C2×#214—101no—
111C2×#214—101no—
112#890—101no—
113#889—102no—
114#887—101no—
115C4×Dic6—51no—
116C4×Dic6C2×D511yescharacteristic
117C3×#102—102no—
118C3×C4×C8C2×D511yescharacteristic
119#832—101no—
120#832—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—31no—
124C2×D20—21no—
125C2×D20—21no—
126C2×D20—21no—
127C2×Dic10—21no—
128C2×Dic10—31no—
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C42×C5—61no—
134C42×C5C22×D311yescharacteristic
135#688—122no—
136C4⋊Dic5—21no—
137C4⋊Dic5—31no—
138C4⋊Dic5—62no—
139C4⋊Dic5—62no—
140C4⋊Dic5#6712yes—
141#683—62no—
142#683—61no—
143C4×Dic5—62no—
144C4×Dic5—61no—
145C2×#168—61no—
146#677—122no—
147#557—151no—
148#486—51no—
149#460—151no—
150#460—151no—
151#332—151no—
152Q8⋊C8—31no—
153Q8⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—81no—
156C2×C3×D5—81no—
157C2×C3×D5—81no—
158C3×C4×C5—21no—
159C3×C4×C5C2×SD1611yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—41no—
164Dic15—41no—
165C3×Dic5—42no—
166C5×Dic3—22no—
167C5×Dic3—41no—
168C2×C3×Q8—101no—
169C2×C3×D4—101no—
170C2×C3×D4—101no—
171C2×C3×D4—101no—
172C2×Dic6—51no—
173C2×Dic6D2011yescharacteristic
174C2×C3×C8—21no—
175C3×C4⋊C4—52no—
176C3×C4⋊C4—101no—
177C3×C42C22×D511yescharacteristic
178#214—202no—
179#214—202no—
180C4⋊Dic3—51no—
181C4⋊Dic3—102no—
182C4⋊Dic3D2011yescharacteristic
183Dic3⋊C4—21no—
184Dic3⋊C4—102no—
185Dic3⋊C4—102no—
186Dic3⋊C4—101no—
187C4×Dic3—21no—
188C4×Dic3—102no—
189C4×Dic3—101no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C22×D5—41no—
193C5×Q8—32no—
194C5×Q8—61no—
195C2×C4×C5—61no—
196C2×C4×C5—61no—
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—22no—
201C2×Dic5—61no—
202C2×Dic5—61no—
203D20—42no—
204D20—41no—
205D20—41no—
206D20—41no—
207D20—41no—
208Dic10—41no—
209Dic10—41no—
210Dic10—61no—
211Dic10—61no—
212C5×C8—41no—
213C5×C8—121no—
214#168—121no—
215C2×SD16—301no—
216C2×SD16—301no—
217C4⋊Q8—51no—
218C4⋊Q8—301no—
219#127—51no—
220#125—301no—
221#125—302no—
222C4×Q8—31no—
223C4×Q8—151no—
224C4×Q8—301no—
225C4×Q8—301no—
226C4⋊C8—31no—
227C4⋊C8—151no—
228#102—102no—
229#102—301no—
230#102—301no—
231C4×C8D3×D511yescharacteristic
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—161no—
236C23×C3—201no—
237C3×Q8—201no—
238C3×Q8—201no—
239C3×D4—202no—
240C3×D4—201no—
241C3×D4—201no—
242C3×D4—201no—
243C3×D4—201no—
244C2×C3×C4—102no—
245C2×C3×C4C2×D2011yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—101no—
251C2×Dic3—101no—
252Dic6—21no—
253Dic6—101no—
254Dic6—101no—
255Dic6#67712yescomplemented
256C3×C8—41no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5#93711yescharacteristic
260C2×D5—81no—
261C2×D5—81no—
262C2×D5—81no—
263C4×C5—21no—
264C4×C5—62no—
265C4×C5—121no—
266C4×C5#91111yescharacteristic
267C4×C5#91211yescharacteristic
268C4×C5D3×SD1611yescharacteristic
269C4×C5#91511yescharacteristic
270Dic5—42no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—31no—
274C2×Q8—101no—
275C2×Q8—151no—
276C2×D4—101no—
277C2×D4—101no—
278C2×D4—101no—
279SD16—602no—
280SD16—602no—
281C2×C8—21no—
282C2×C8—61no—
283C2×C8—301no—
284C4⋊C4—31no—
285C4⋊C4—52no—
286C4⋊C4—61no—
287C4⋊C4—101no—
288C4⋊C4—151no—
289C4⋊C4—302no—
290C4⋊C4—302no—
291C4⋊C4—302no—
292C4⋊C4—301no—
293C42—61no—
294C42—302no—
295C42—301no—
296C42C2×D3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3—401no—
299C22×C3—401no—
300C22×C3—401no—
301C22×C3#402811yescharacteristic
302C3×C4—21no—
303C3×C4—202no—
304C3×C4C2×#67711yescharacteristic
305C3×C4#405511yescharacteristic
306C3×C4#406011yescharacteristic
307C3×C4#406511yescharacteristic
308Dic3—22no—
309Dic3—41no—
310Dic3—201no—
311Dic3—201no—
312C2×C5#506211yescharacteristic
313C2×C5#515811yescharacteristic
314C2×C5#517011yescharacteristic
315D5—161no—
316C23—201no—
317Q8—32no—
318Q8—61no—
319Q8—201no—
320Q8—201no—
321Q8—301no—
322Q8—301no—
323D4—202no—
324D4—201no—
325D4—201no—
326D4—201no—
327D4—201no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—102no—
331C2×C4—301no—
332C2×C4—301no—
333C2×C4D3×D2011yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C8—41no—
337C8—121no—
338C8—601no—
339C2×C3—801no—
340C2×C3#6502711yescharacteristic
341C2×C3#6510011yescharacteristic
342C2×C3#6511611yescharacteristic
343C5#7120411yescharacteristic, complemented, Sylow
344C22—401no—
345C22—401no—
346C22—401no—
347C22#9147411yescharacteristic
348C4—21no—
349C4—62no—
350C4—121no—
351C4—202no—
352C4—601no—
353C4—601no—
354C4D3×#67711yescharacteristic
355C4#9125811yescharacteristic
356C4#9127411yescharacteristic
357C4#9127711yescharacteristic
358C3#1059904511yescharacteristic, complemented, Sylow
359C2—801no—
360C2#1174712111yescharacteristic
361C2#1174812411yescharacteristic
362C2#1174815011yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#1626
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752482C2semidirect
5. #11746277C2semidirect
6. C5×#4456C2semidirect
7. #11745856C2semidirect
64. #4456D5semidirect
94. C5×Dic6SD16semidirect
255. Dic6#677semidirect
297. C3×C5#1626semidirect
343. C5#71204semidirect
358. C3#10599045semidirect

Maximal subgroups

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

subgroupindex
#117524822
C3×#649832
#117470832
#117470682
#117462772
C5×#44562
#117458562
#105990453
#712045