Finite Group Databasebeta

← #14292390

Subgroups — #14292390

Order 1920.

364 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 88 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×#65132C211yesmaximal, characteristic
2#11747071C211yesmaximal, characteristic, complemented
3#11747010C211yesmaximal, characteristic, complemented
4#11746889C211yesmaximal, characteristic, complemented
5#11746307C211yesmaximal, characteristic, complemented
6C5×#4479C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599375—31nomaximal, Hall
9#91758C2211yescharacteristic
10C2×C3×D40—21no—
11C3×#4020C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13C2×#6657—21no—
14C2×#6657—21no—
15C2×#6649—21no—
16C3×C5×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊#168)C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×#3953—21no—
21#90990—21no—
22#90965—21no—
23#90955—21no—
24#71008—51nomaximal, Hall
25#65135—31no—
26#65132D311yescharacteristic
27#64982—31no—
28#64977—31no—
29C5×#335—31no—
30#64706—31no—
31#64705—31no—
32C2×Dic30—21no—
33C2×C3×D20—21no—
34C2×C3×D20—21no—
35C2×C3×D20—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C5×C8—21no—
39C3×C42×C5C2311yescharacteristic
40C4⋊Dic15—21no—
41C4⋊Dic15—21no—
42C2×C3⋊#168—21no—
43C2×C5×C3⋊C8—21no—
44C2×C5×C3⋊C8D411yescharacteristic
45C2×C5×C3⋊C8D411yescharacteristic
46C3×#685—21no—
47C3×C4⋊Dic5D411yescharacteristic
48C3×D40—42no—
49#6657—42no—
50#6657—42no—
51#6649—42no—
52C3×#459—51no—
53#5076—51no—
54#5012—51no—
55#5007—51no—
56#4544—51no—
57#4486—51no—
58#4479D511yescharacteristic, complemented
59C2×D40—21no—
60C2×#677—61no—
61C2×#677—61no—
62C2×#676—61no—
63#4020C2×D311yescharacteristic
64C4×D20C2×D311yescharacteristic
65#4015—31no—
66C5×C4⋊C8—31no—
67C5×C4⋊C8C2×D311yescharacteristic
68C4×C5×C8—31no—
69#3953—21no—
70#3953—61no—
71#3952—61no—
72#3950—61no—
73C4⋊#168—31no—
74#1685—151noSylow
75C22×C3×D5—21no—
76C22×C3×D5—41no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4111yescharacteristic
80C2×Dic15—41no—
81Dic30—41no—
82Dic30—41no—
83C2×C3×Dic5—21no—
84C3×D20—21no—
85C3×D20—21no—
86C3×D20—41no—
87C3×D20—41no—
88C3×D20—41no—
89C3×D20—41no—
90C3×D20—81no—
91C3×C4×D5—41no—
92C3×C4×D5—41no—
93C3×C5×C8—41no—
94C3⋊#168—41no—
95C5×C3⋊C8—21no—
96C5×C3⋊C8—41no—
97C5×C3⋊C8D812yescomplemented
98C2×C3×D8—101no—
99C3×#127—51no—
100C3×C4×D4—51no—
101C2×#214—101no—
102C2×#214—101no—
103C2×#208—101no—
104#869—51no—
105C3×C4⋊C8C2×D511yescharacteristic
106C3×#102—101no—
107#832—101no—
108#830—101no—
109#807—101no—
110C4⋊(C3⋊C8)—51no—
111C4⋊(C3⋊C8)C2×D511yescharacteristic
112C4×C3⋊C8C2×D511yescharacteristic
113C2×D20—21no—
114C2×D20—21no—
115C2×D20—21no—
116C2×D20#6711yescharacteristic
117C2×C4×D5—21no—
118C2×Dic10—61no—
119C2×C5×C8—21no—
120C2×C5×C8—31no—
121C2×C5×C8—31no—
122C2×C5×C8—61no—
123C42×C5C22×D311yescharacteristic
124#685—21no—
125C4⋊Dic5—61no—
126C4⋊Dic5—61no—
127C4⋊Dic5#6711yescharacteristic
128C2×#168—61no—
129D40—42no—
130#677—122no—
131#677—122no—
132#676—122no—
133#492—151no—
134#474—151no—
135#459—51no—
136#436—151no—
137#335—31no—
138#332—151no—
139#331—151no—
140C22×C3×C5#12111yescharacteristic
141C2×C3×D5—41no—
142C2×C3×D5—41no—
143C2×C3×D5—41no—
144C2×C3×D5—81no—
145C2×C3×D5—81no—
146C2×C3×D5—81no—
147C3×C4×C5—21no—
148C3×C4×C5C2×D811yescharacteristic
149C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C3×C4×C5#13711yescharacteristic
152Dic15—81no—
153C3×Dic5—41no—
154C2×C3×D4—51no—
155C2×C3×D4—101no—
156C2×C3×D4—101no—
157C2×C3×D4—101no—
158C22×C3×C4—101no—
159C2×Dic6—101no—
160C3×D8—202no—
161C2×C3×C8—21no—
162C3×C4⋊C4—51no—
163C3×C22⋊C4—101no—
164C3×C42C22×D511yescharacteristic
165#214—202no—
166#214—202no—
167C4⋊Dic3—101no—
168C4⋊Dic3—101no—
169#208—202no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—101no—
172C2×C3⋊C8D2011yescharacteristic
173C2×C3⋊C8D2011yescharacteristic
174C22×D5—21no—
175C22×D5—41no—
176C2×C4×C5D3×D411yescharacteristic
177C2×C4×C5#23711yescharacteristic
178C2×C4×C5C2×#6711yescharacteristic
179C2×Dic5—21no—
180C2×Dic5—121no—
181D20—21no—
182D20—21no—
183D20—41no—
184D20—41no—
185D20—41no—
186D20—41no—
187D20—81no—
188C4×D5—41no—
189C4×D5—41no—
190Dic10—121no—
191Dic10—121no—
192C5×C8—32no—
193C5×C8—41no—
194C5×C8—61no—
195C5×C8—121no—
196#168—121no—
197C2×SD16—301no—
198C2×SD16—301no—
199C2×D8—101no—
200C2×M16—301no—
201C4⋊Q8—151no—
202#127—51no—
203C4×D4—51no—
204#107—301no—
205C4⋊C8—31no—
206C4⋊C8—151no—
207C4⋊C8D3×D511yescharacteristic
208#102—101no—
209#102—301no—
210C22⋊C8—301no—
211C4×C8—31no—
212C2×C3×C5#45911yescharacteristic
213C2×C3×C5#46811yescharacteristic
214C2×C3×C5#47111yescharacteristic
215C3×D5—81no—
216C3×D5—161no—
217C23×C3—101no—
218C23×C3—201no—
219C3×D4—101no—
220C3×D4—101no—
221C3×D4—201no—
222C3×D4—201no—
223C3×D4—201no—
224C3×D4—201no—
225C3×D4—401no—
226C2×C3×C4—101no—
227C2×C3×C4—201no—
228C2×C3×C4—201no—
229C2×C3×C4C2×D2011yescharacteristic
230C2×C3×C4D4×D511yescharacteristic
231C2×C3×C4#71311yescharacteristic
232C2×Dic3—201no—
233Dic6—201no—
234Dic6—201no—
235C3×C8—41no—
236C3⋊C8—21no—
237C3⋊C8—41no—
238C3⋊C8—201no—
239C3⋊C8D4012yescomplemented
240C22×C5#93911yescharacteristic
241C2×D5—41no—
242C2×D5—41no—
243C2×D5—41no—
244C2×D5—81no—
245C2×D5—81no—
246C2×D5—81no—
247C4×C5—21no—
248C4×C5D3×D811yescharacteristic
249C4×C5#91111yescharacteristic
250C4×C5#93211yescharacteristic
251C4×C5#95111yescharacteristic
252Dic5—41no—
253Dic5—241no—
254C2×Q8—301no—
255C2×D4—51no—
256C2×D4—101no—
257C2×D4—101no—
258C2×D4—101no—
259C22×C4—101no—
260SD16—602no—
261SD16—602no—
262D8—202no—
263M16—602no—
264C2×C8—21no—
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—61no—
268C2×C8—301no—
269C4⋊C4—51no—
270C4⋊C4—301no—
271C4⋊C4—301no—
272C22⋊C4—101no—
273C42C2×D3×D511yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—201no—
276C22×C3—201no—
277C22×C3—201no—
278C22×C3—401no—
279C22×C3—401no—
280C22×C3—401no—
281C22×C3#404111yescharacteristic
282C3×C4—21no—
283C3×C4—201no—
284C3×C4C2×D4011yescharacteristic
285C3×C4#405411yescharacteristic
286C3×C4#405711yescharacteristic
287C3×C4#406411yescharacteristic
288Dic3—401no—
289C2×C5#504211yescharacteristic
290C2×C5#515011yescharacteristic
291C2×C5#520011yescharacteristic
292D5—81no—
293D5—161no—
294C23—101no—
295C23—201no—
296Q8—601no—
297Q8—601no—
298D4—101no—
299D4—101no—
300D4—201no—
301D4—201no—
302D4—201no—
303D4—201no—
304D4—401no—
305C2×C4—101no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4—601no—
309C2×C4#676611yescharacteristic
310C2×C4D3×D2011yescharacteristic
311C2×C4D5×#6711yescharacteristic
312C8—32no—
313C8—41no—
314C8—61no—
315C8—121no—
316C8—601no—
317C2×C3—401no—
318C2×C3—801no—
319C2×C3#6513211yescharacteristic
320C2×C3#6517511yescharacteristic
321C2×C3#6518711yescharacteristic
322C5#7100811yescharacteristic, complemented, Sylow
323C22—201no—
324C22—201no—
325C22—201no—
326C22—401no—
327C22—401no—
328C22—401no—
329C22#9140911yescharacteristic
330C4—21no—
331C4—201no—
332C4—1201no—
333C4D3×D4011yescharacteristic
334C4#9125411yescharacteristic
335C4#9148911yescharacteristic
336C4#9150811yescharacteristic
337C3#1059937511yescharacteristic, complemented, Sylow
338C2—401no—
339C2—801no—
340C2#1174746311yescharacteristic
341C2#1174775411yescharacteristic
342C2#1174818511yescharacteristic
subgroupG/H
centerC22#91409
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC3×#65132C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1685
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
2. #11747071C2semidirect
3. #11747010C2semidirect
4. #11746889C2semidirect
5. #11746307C2semidirect
6. C5×#4479C2semidirect
7. #11745852C2semidirect
58. #4479D5semidirect
97. C5×C3⋊C8D8semidirect
239. C3⋊C8D40semidirect
274. C3×C5#1685semidirect
322. C5#71008semidirect
337. C3#10599375semidirect

Maximal subgroups

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

subgroupindex
C3×#651322
#117470712
#117470102
#117468892
#117463072
C5×#44792
#117458522
#105993753
#710085