Finite Group Databasebeta

← #14289031

Subgroups — #14289031

Order 1920.

456 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 104 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×Q8×Dic10C211yesmaximal, characteristic, complemented
2C5×#5027C211yesmaximal, characteristic
3#11747081C211yesmaximal, characteristic
4#11747060C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745861C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10601826—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C2×C5×#215—21no—
11C5×#874C2211yescharacteristic
12C3×Q8×Dic5—21no—
13C3×#4034—22no—
14C3×#4034—21no—
15C3×#4015—21no—
16C3×#4015C2211yescharacteristic
17C3×C4×Dic10—21no—
18C3×C4×Dic10C2211yescharacteristic
19C2×#6656—22no—
20C2×#6656—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×#809—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25#90966—21no—
26#71939—51nomaximal, Hall
27Q8×Dic10D311yescharacteristic, complemented
28C5×#460—31no—
29#65365—31no—
30#65364—31no—
31Q8⋊#168—31no—
32#64704—31no—
33#64701—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C3×Dic10—22no—
39C2×C3×Dic10D411yescharacteristic
40C2×C3×Dic10D412yes—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C5×#215—42no—
48C2×C5×C3⋊C8—21no—
49C3×C4⋊Dic5—22no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—22no—
54C3×#683—21no—
55C3×C4×Dic5—22no—
56C3×C4×Dic5—21no—
57#6656—44no—
58#6656—42no—
59C3×Q82—51no—
60#5085—51no—
61#5027—51no—
62#5027D511yescharacteristic
63#4546—51no—
64#4535—51no—
65#4535—51no—
66C2×C5×SD16—61no—
67C5×#127—31no—
68C4×C5×Q8C2×D311yescharacteristic
69Q8×Dic5—21no—
70C2×#687—61no—
71C2×#687—62no—
72#4034—22no—
73#4034—21no—
74#4015—21no—
75#4015C2×D311yescharacteristic
76C4×Dic10—21no—
77C4×Dic10C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C5×#102—61no—
80#3964—61no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1623—151noSylow
84C22×C5×D3—41no—
85C3×C5×Q8—21no—
86C3×C5×Q8SD1612yescomplemented
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C5×D12—42no—
93C5×D12—41no—
94C5×D12—41no—
95C5×D12—41no—
96C5×D12—41no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—22no—
99C2×C3×Dic5—21no—
100C3×Dic10—21no—
101C3×Dic10—42no—
102C3×Dic10—82no—
103C3×Dic10SD1612yescomplemented
104C3⋊#168—22no—
105C3⋊#168—41no—
106C5×C3⋊C8—41no—
107C3×C4⋊Q8—51no—
108C3×C4⋊Q8—101no—
109C3×C4⋊Q8—102no—
110C3×C4⋊Q8—101no—
111C3×C4×Q8—51no—
112C3×C4×Q8—101no—
113C3×C4×Q8—101no—
114C3×C4×Q8C2×D511yescharacteristic
115C2×#215—21no—
116C2×#215—101no—
117C2×#215—102no—
118#874C2×D511yescharacteristic
119#809—21no—
120#809—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C4×C3⋊C8—51no—
124C2×C5×Q8#6711yescharacteristic
125C2×C5×D4—61no—
126C2×C5×D4—61no—
127C2×C5×D4—61no—
128C2×Dic10—22no—
129C2×Dic10#6711yescharacteristic
130C2×Dic10#6712yes—
131C5×SD16—122no—
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4#6711yescharacteristic
135C42×C5—21no—
136C42×C5C22×D311yescharacteristic
137#687—124no—
138#687—122no—
139C4⋊Dic5—22no—
140C4⋊Dic5—21no—
141C4⋊Dic5—21no—
142C4⋊Dic5#6711yescharacteristic
143#683—22no—
144#683—21no—
145C4×Dic5—22no—
146C4×Dic5—21no—
147C2×#168—61no—
148C2×#168—61no—
149Q82—51no—
150#492—151no—
151#460—31no—
152#460—151no—
153#333—151no—
154Q8⋊C8—151no—
155Q8⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—81no—
158C2×C5×D3—81no—
159C2×C5×D3—81no—
160C3×C4×C5—22no—
161C3×C4×C5—21no—
162C3×C4×C5—41no—
163C3×C4×C5C2×SD1611yescharacteristic
164C3×C4×C5C2×SD1611yescharacteristic
165C3×C4×C5#13711yescharacteristic
166C3×C4×C5#13711yescharacteristic
167C3×Dic5—22no—
168C3×Dic5—42no—
169C3×Dic5—41no—
170C2×C3×Q8—51no—
171C2×C3×Q8—52no—
172C2×C3×Q8—102no—
173C2×C3×Q8C22⋊D511yescharacteristic
174C2×D12—21no—
175C2×D12—21no—
176C2×D12—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—51no—
179C3×C4⋊C4—102no—
180C3×C4⋊C4—102no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4—101no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4C22⋊D511yescharacteristic
185C3×C42—21no—
186C3×C42—102no—
187C3×C42—101no—
188C3×C42C22×D511yescharacteristic
189#215—42no—
190#215—204no—
191#215—202no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C23×C5—121no—
196C5×Q8—21no—
197C5×Q8#21512yescomplemented
198C5×D4—122no—
199C5×D4—121no—
200C5×D4—121no—
201C5×D4—121no—
202C5×D4—121no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5C2×#6711yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C2×Dic5—21no—
209C2×Dic5—22no—
210C2×Dic5—21no—
211Dic10—21no—
212Dic10—42no—
213Dic10—82no—
214Dic10#21512yescomplemented
215C5×C8—121no—
216#168—62no—
217#168—121no—
218C2×SD16—61no—
219C2×SD16—301no—
220C2×SD16—302no—
221C4⋊Q8—51no—
222C4⋊Q8—101no—
223C4⋊Q8—102no—
224C4⋊Q8—101no—
225#127—31no—
226C4×Q8—51no—
227C4×Q8—101no—
228C4×Q8—101no—
229C4×Q8D3×D511yescharacteristic
230C4⋊C8—31no—
231C4⋊C8—151no—
232#102—61no—
233#102—301no—
234C4×C8—151no—
235C2×C3×C5#44811yescharacteristic
236C2×C3×C5#44811yescharacteristic
237C2×C3×C5#45311yescharacteristic
238C5×D3—161no—
239C22×D3—41no—
240C3×Q8—21no—
241C3×Q8—52no—
242C3×Q8—101no—
243C3×Q8—202no—
244C3×Q8—402no—
245C3×Q8#68712yescomplemented
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—101no—
249C2×C3×C4—101no—
250C2×C3×C4—102no—
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253C2×C3×C4C2×C22⋊D511yescharacteristic
254D12—42no—
255D12—41no—
256D12—41no—
257D12—41no—
258D12—41no—
259C3⋊C8—41no—
260C3⋊C8—102no—
261C3⋊C8—201no—
262C22×C5—241no—
263C22×C5—241no—
264C22×C5—241no—
265C22×C5#95311yescharacteristic
266C4×C5—22no—
267C4×C5—21no—
268C4×C5—41no—
269C4×C5C2×#21511yescharacteristic
270C4×C5C2×#21511yescharacteristic
271C4×C5#94211yescharacteristic
272C4×C5#94211yescharacteristic
273Dic5—22no—
274Dic5—42no—
275Dic5—41no—
276C2×Q8—51no—
277C2×Q8—52no—
278C2×Q8—102no—
279C2×Q8#120111yescharacteristic
280C2×D4—61no—
281C2×D4—61no—
282C2×D4—61no—
283SD16—122no—
284SD16—604no—
285SD16—602no—
286C2×C8—61no—
287C2×C8—301no—
288C2×C8—301no—
289C4⋊C4—21no—
290C4⋊C4—51no—
291C4⋊C4—102no—
292C4⋊C4—102no—
293C4⋊C4—101no—
294C4⋊C4—101no—
295C4⋊C4—101no—
296C4⋊C4#120111yescharacteristic
297C42—21no—
298C42—102no—
299C42—101no—
300C42C2×D3×D511yescharacteristic
301C3×C5#162311yescharacteristic, complemented, Hall
302C22×C3#408311yescharacteristic
303C2×D3—81no—
304C2×D3—81no—
305C2×D3—81no—
306C3×C4—22no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—102no—
310C3×C4—202no—
311C3×C4—201no—
312C3×C4D5×SD1611yescharacteristic
313C3×C4#406111yescharacteristic
314C3×C4C2×#68711yescharacteristic
315C3×C4#409711yescharacteristic
316C2×C5—481no—
317C2×C5#522711yescharacteristic
318C2×C5#522711yescharacteristic
319C2×C5#524111yescharacteristic
320C23—121no—
321Q8—21no—
322Q8—52no—
323Q8—101no—
324Q8—202no—
325Q8—402no—
326Q8#665612yescomplemented
327D4—122no—
328D4—121no—
329D4—121no—
330D4—121no—
331D4—121no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—102no—
337C2×C4C2×#120111yescharacteristic
338C2×C4D5×#6711yescharacteristic
339C2×C4D5×#6711yescharacteristic
340C8—121no—
341C8—302no—
342C8—601no—
343C2×C3#6532911yescharacteristic
344C2×C3#6545911yescharacteristic
345C2×C3#6548711yescharacteristic
346D3—161no—
347C5#7193911yescharacteristic, complemented, Sylow
348C22—241no—
349C22—241no—
350C22—241no—
351C22#9156311yescharacteristic
352C4—21no—
353C4—22no—
354C4—41no—
355C4—102no—
356C4—202no—
357C4—201no—
358C4C2×#665611yescharacteristic
359C4#9130911yescharacteristic
360C4D5×#21511yescharacteristic
361C4#9151311yescharacteristic
362C3#1060182611yescharacteristic, complemented, Sylow
363C2—481no—
364C2#1174852911yescharacteristic
365C2#1174926711yescharacteristic
366C2#1174941711yescharacteristic
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#1623
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×Q8×Dic10C2semidirect
5. #11746356C2semidirect
6. #11745861C2semidirect
7. #11745840C2semidirect
27. Q8×Dic10D3semidirect
86. C3×C5×Q8SD16semidirect
103. C3×Dic10SD16semidirect
197. C5×Q8#215semidirect
214. Dic10#215semidirect
245. C3×Q8#687semidirect
301. C3×C5#1623semidirect
326. Q8#6656semidirect
347. C5#71939semidirect
362. C3#10601826semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic102
C5×#50272
#117470812
#117470602
#117463562
#117458612
#117458402
#106018263
#719395