Finite Group Databasebeta

← #14289022

Subgroups — #14289022

Order 1920.

456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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#11752473C211yesmaximal, characteristic, complemented
2#11751176C211yesmaximal, characteristic
3C5×#5076C211yesmaximal, characteristic
4C3×#65364C211yesmaximal, characteristic
5#11745862C211yesmaximal, characteristic, complemented
6#11745844C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10602062—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6716—21no—
11C4×Dic30C2211yescharacteristic
12C2×C5×#214—22no—
13C5×#869C2211yescharacteristic
14C2×C3×#687—21no—
15C3×C4×Dic10C2211yescharacteristic
16#91470—21no—
17#91468—21no—
18#91333—21no—
19#91331—21no—
20#91329—22no—
21#91116—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24C3×#3964—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71033—51nomaximal, Hall
27#66056—31no—
28C5×#492—31no—
29#65364—31no—
30#65364D311yescharacteristic
31#64766—31no—
32#64676—31no—
33#64676—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×Dic30D411yescharacteristic
38C2×C5×Dic6D412yes—
39C2×C3×Dic10D411yescharacteristic
40C2×#1204—22no—
41C3×C42×C5C2311yescharacteristic
42#6716—42no—
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C5×#214—44no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C2×C5×C3⋊C8—21no—
51C3×#687—42no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56#6669—22no—
57#6668—22no—
58Dic3×Dic5—22no—
59Q8×Dic6—51no—
60C3×#460—51no—
61#5076D511yescharacteristic
62#5075—51no—
63#4535—51no—
64#4484—51no—
65#4481—51no—
66C2×C5×SD16—62no—
67C5×C4⋊Q8—31no—
68C5×#127C2×D311yescharacteristic
69#4090—62no—
70C2×#687—21no—
71C2×#687—61no—
72#4034—61no—
73#4034—61no—
74#4033—61no—
75#4033—61no—
76C4×Dic10—31no—
77C4×Dic10C2×D311yescharacteristic
78C4×C5×C8—31no—
79#3964—21no—
80#3964—61no—
81C4⋊#168—31no—
82C4⋊#168C2×D311yescharacteristic
83#1623—151noSylow
84C23×C3×C5—41no—
85C3×C5×D4—42no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×Dic15—21no—
94C2×Dic15—21no—
95Dic30—21no—
96Dic30SD1612yescomplemented
97C2×C5×Dic3—22no—
98C5×Dic6—42no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×Dic10—21no—
102C3×Dic10SD1612yescomplemented
103#1204—82no—
104C3⋊#168—41no—
105C3×#168—41no—
106C5×C3⋊C8—22no—
107C2×C3×SD16—101no—
108C3×#127C2×D511yescharacteristic
109C3×C4×Q8—51no—
110Q8×Dic3—101no—
111C2×#214—22no—
112C2×#214—101no—
113#888—101no—
114#888—102no—
115#869—101no—
116#869C2×D511yescharacteristic
117C4×Dic6—51no—
118C4×Dic6—101no—
119C3×C4⋊C8—51no—
120C3×#102—101no—
121#832—101no—
122C4⋊(C3⋊C8)—51no—
123C4×C3⋊C8C2×D511yescharacteristic
124C2×C5×Q8—32no—
125C2×C5×D4—21no—
126C2×C5×D4—21no—
127C2×C5×D4—21no—
128C2×Dic10—31no—
129C2×Dic10—62no—
130C2×Dic10#6711yescharacteristic
131C5×SD16—124no—
132C2×C5×C8—61no—
133C5×C4⋊C4—61no—
134C5×C4⋊C4—61no—
135C42×C5C22×D311yescharacteristic
136#687—42no—
137#687—122no—
138C4⋊Dic5—31no—
139C4⋊Dic5#6711yescharacteristic
140#683—21no—
141#683—62no—
142#683—62no—
143#683—61no—
144C4×Dic5—21no—
145C4×Dic5—62no—
146C4×Dic5—61no—
147C2×#168—21no—
148C2×#168—61no—
149Q82—151no—
150#492—31no—
151#460—51no—
152#460—151no—
153#333—151no—
154Q8⋊C8—151no—
155Q8⋊C8—151no—
156C22×C3×C5—81no—
157C22×C3×C5—81no—
158C22×C3×C5—81no—
159C22×C3×C5#12011yescharacteristic
160C3×C4×C5—21no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5C2×SD1611yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—22no—
166Dic15—41no—
167C3×Dic5—22no—
168C3×Dic5—41no—
169C5×Dic3—42no—
170C2×C3×Q8—51no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×Dic6—51no—
175C2×Dic6—102no—
176C2×Dic6C22⋊D512yes—
177C3×SD16—202no—
178C2×C3×C8—101no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—101no—
181C3×C42—101no—
182C3×C42C22×D511yescharacteristic
183#214—44no—
184#214—202no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—51no—
188C4⋊Dic3—102no—
189Dic3⋊C4—102no—
190Dic3⋊C4—101no—
191C4×Dic3—102no—
192C4×Dic3—101no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—101no—
195C23×C5—41no—
196C5×Q8—122no—
197C5×D4—42no—
198C5×D4—41no—
199C5×D4—41no—
200C5×D4—41no—
201C5×D4—41no—
202C2×C4×C5—62no—
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×Dic5—21no—
207C2×Dic5—21no—
208C2×Dic5—61no—
209C2×Dic5—61no—
210Dic10—21no—
211Dic10—32no—
212Dic10—61no—
213Dic10—242no—
214Dic10#21412yescomplemented
215C5×C8—62no—
216#168—41no—
217#168—121no—
218C2×SD16—62no—
219C2×SD16—101no—
220C2×SD16—301no—
221C4⋊Q8—31no—
222C4⋊Q8—301no—
223C4⋊Q8—301no—
224C4⋊Q8—302no—
225#127D3×D511yescharacteristic
226C4×Q8—51no—
227C4×Q8—151no—
228C4×Q8—301no—
229C4×Q8—301no—
230C4⋊C8—51no—
231C4⋊C8—151no—
232#102—101no—
233#102—301no—
234C4×C8—31no—
235C2×C3×C5—161no—
236C2×C3×C5#44811yescharacteristic
237C2×C3×C5#44811yescharacteristic
238C2×C3×C5#45311yescharacteristic
239C23×C3—41no—
240C3×Q8—52no—
241C3×Q8—101no—
242C3×D4—42no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4C2×C22⋊D511yescharacteristic
252C2×Dic3—22no—
253C2×Dic3—101no—
254C2×Dic3—101no—
255Dic6—42no—
256Dic6—52no—
257Dic6—101no—
258Dic6—402no—
259C3×C8—201no—
260C3⋊C8—22no—
261C3⋊C8—201no—
262C22×C5—81no—
263C22×C5—81no—
264C22×C5—81no—
265C22×C5#93711yescharacteristic
266C4×C5—21no—
267C4×C5—122no—
268C4×C5D3×SD1611yescharacteristic
269C4×C5#91511yescharacteristic
270C4×C5C2×#21411yescharacteristic
271C4×C5#95111yescharacteristic
272Dic5—22no—
273Dic5—41no—
274Dic5—62no—
275Dic5—121no—
276C2×Q8—32no—
277C2×Q8—51no—
278C2×Q8—151no—
279C2×Q8—302no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283SD16—124no—
284SD16—202no—
285SD16—602no—
286C2×C8—61no—
287C2×C8—101no—
288C2×C8—301no—
289C4⋊C4—51no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—101no—
293C4⋊C4—151no—
294C4⋊C4—302no—
295C4⋊C4—302no—
296C4⋊C4—301no—
297C42—101no—
298C42—302no—
299C42—301no—
300C42C2×D3×D511yescharacteristic
301C3×C5#162311yescharacteristic, complemented, Hall
302C22×C3—81no—
303C22×C3—81no—
304C22×C3—81no—
305C22×C3#408311yescharacteristic
306C3×C4—21no—
307C3×C4—102no—
308C3×C4—201no—
309C3×C4D5×SD1611yescharacteristic
310C3×C4D5×SD1611yescharacteristic
311C3×C4#406111yescharacteristic
312C3×C4#406111yescharacteristic
313Dic3—42no—
314Dic3—102no—
315Dic3—201no—
316C2×C5—161no—
317C2×C5#504011yescharacteristic
318C2×C5#517011yescharacteristic
319C2×C5#519811yescharacteristic
320C23—41no—
321Q8—52no—
322Q8—101no—
323Q8—122no—
324Q8—152no—
325Q8—301no—
326Q8—1202no—
327D4—42no—
328D4—41no—
329D4—41no—
330D4—41no—
331D4—41no—
332C2×C4—62no—
333C2×C4—101no—
334C2×C4—101no—
335C2×C4—301no—
336C2×C4—301no—
337C2×C4D5×#6711yescharacteristic
338C2×C4D3×C22⋊D511yescharacteristic
339C2×C4#679011yescharacteristic
340C8—62no—
341C8—201no—
342C8—601no—
343C2×C3—161no—
344C2×C3#6536611yescharacteristic
345C2×C3#6545911yescharacteristic
346C2×C3#6545911yescharacteristic
347C5#7103311yescharacteristic, complemented, Sylow
348C22—81no—
349C22—81no—
350C22—81no—
351C22#9157711yescharacteristic
352C4—21no—
353C4—102no—
354C4—122no—
355C4—201no—
356C4—302no—
357C4—601no—
358C4D5×#21411yescharacteristic
359C4#9148411yescharacteristic
360C4#9148711yescharacteristic
361C4#9148811yescharacteristic
362C3#1060206211yescharacteristic, complemented, Sylow
363C2—161no—
364C2#1174915411yescharacteristic
365C2#1174915611yescharacteristic
366C2#1174916511yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
Fitting, prime radicalC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1623
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11752473C2semidirect
5. #11745862C2semidirect
6. #11745844C2semidirect
7. #11745841C2semidirect
96. Dic30SD16semidirect
102. C3×Dic10SD16semidirect
214. Dic10#214semidirect
301. C3×C5#1623semidirect
347. C5#71033semidirect
362. C3#10602062semidirect

Maximal subgroups

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

subgroupindex
#117524732
#117511762
C5×#50762
C3×#653642
#117458622
#117458442
#117458412
#106020623
#710335