Finite Group Databasebeta

← #14292407

Subgroups — #14292407

Order 1920.

364 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 84 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×#65135C211yesmaximal, characteristic, complemented
2#11747081C211yesmaximal, characteristic, complemented
3#11747026C211yesmaximal, characteristic
4#11747013C211yesmaximal, characteristic, complemented
5#11746300C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7#11745856C211yesmaximal, characteristic, complemented
8#10599191—31nomaximal, Hall
9C5×#874C2211yescharacteristic
10C3×C4×D20C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C2×#6656—21no—
13C2×#6656—21no—
14C2×#6652—21no—
15C2×#6649—21no—
16C3×C5×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊#168)C2211yescharacteristic
18C4×C3⋊#168C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×#3953—21no—
21C3×#3950—21no—
22#90966—21no—
23#90955—21no—
24#71104—51nomaximal, Hall
25#65365—31no—
26#65361—31no—
27#65135D311yescharacteristic, complemented
28#65127—31no—
29C5×#331—31no—
30#64702—31no—
31#64699—31no—
32C2×C5×D12—21no—
33C2×C5×D12—21no—
34C2×C5×D12—21no—
35C2×C3×D20D411yescharacteristic
36C2×C3×C4×D5—21no—
37C2×C3×Dic10—21no—
38C2×C3×C5×C8—21no—
39C3×C42×C5C2311yescharacteristic
40C2×C3⋊#168—21no—
41C2×C3⋊#168D411yescharacteristic
42C2×C3⋊#168D411yescharacteristic
43C2×C5×C3⋊C8—21no—
44C3×#685—21no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5D411yescharacteristic
48#6656—42no—
49#6656—42no—
50#6652—42no—
51#6649—42no—
52C3×#474—51no—
53#5085—51no—
54#5015—51no—
55#5012—51no—
56#4547—51no—
57#4485D511yescharacteristic, complemented
58#4479—51no—
59C5×#127—31no—
60C2×#687—61no—
61C2×#687—61no—
62C2×#686—61no—
63C2×#676—61no—
64C4×D20C2×D311yescharacteristic
65#4015C2×D311yescharacteristic
66C5×C4⋊C8—31no—
67C5×C4⋊C8C2×D311yescharacteristic
68#3964—61no—
69#3953—21no—
70#3952—61no—
71#3950—21no—
72C4⋊#168—31no—
73C4×#168—31no—
74#1685—151noSylow
75C22×C5×D3—41no—
76C22×C3×D5—21no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4111yescharacteristic
80C5×D12—41no—
81C5×D12—41no—
82C5×D12—41no—
83C5×D12—41no—
84C5×D12—81no—
85C2×C3×Dic5—21no—
86C2×C3×Dic5—41no—
87C3×D20—21no—
88C3×D20—21no—
89C3×C4×D5—41no—
90C3×C4×D5—41no—
91C3×Dic10—41no—
92C3×Dic10—41no—
93C3×C5×C8—41no—
94C3⋊#168—21no—
95C3⋊#168—41no—
96C3⋊#168D812yescomplemented
97C5×C3⋊C8—41no—
98C3×C4⋊Q8—51no—
99C3×C4×D4—51no—
100C2×#215—101no—
101C2×#215—101no—
102C2×#213—101no—
103C2×#208—101no—
104#874C2×D511yescharacteristic
105C3×#107—101no—
106C3×C4⋊C8C2×D511yescharacteristic
107C3×#102—101no—
108#830—101no—
109#809—101no—
110C4⋊(C3⋊C8)—51no—
111C4⋊(C3⋊C8)C2×D511yescharacteristic
112C4×C3⋊C8—51no—
113C2×C5×D4—61no—
114C2×C5×D4—61no—
115C2×C5×D4—61no—
116C2×D20#6711yescharacteristic
117C2×C4×D5—21no—
118C2×Dic10—21no—
119C2×C5×C8—21no—
120C2×C5×C8—61no—
121C42×C5C22×D311yescharacteristic
122#687—122no—
123#687—122no—
124#686—122no—
125#685—21no—
126C4⋊Dic5—21no—
127C4⋊Dic5—21no—
128C4⋊Dic5#6711yescharacteristic
129C2×#168—31no—
130C2×#168—31no—
131C2×#168—61no—
132#676—122no—
133#492—151no—
134#474—51no—
135#459—151no—
136#436—151no—
137#335—151no—
138#332—151no—
139#331—31no—
140C22×C3×C5#12111yescharacteristic
141C2×C5×D3—81no—
142C2×C5×D3—81no—
143C2×C5×D3—81no—
144C2×C3×D5—41no—
145C2×C3×D5—41no—
146C2×C3×D5—41no—
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
152C3×Dic5—41no—
153C3×Dic5—81no—
154C2×C3×Q8—101no—
155C2×C3×D4—51no—
156C22×C3×C4—101no—
157C2×D12—21no—
158C2×D12—21no—
159C2×D12—21no—
160C2×C3×C8—21no—
161C3×C4⋊C4—51no—
162C3×C4⋊C4—101no—
163C3×C4⋊C4—101no—
164C3×C22⋊C4—101no—
165C3×C42C22×D511yescharacteristic
166#215—202no—
167#215—202no—
168#213—202no—
169#208—202no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—51no—
172C2×C3⋊C8—51no—
173C2×C3⋊C8—101no—
174C23×C5—121no—
175C22×D5—21no—
176C5×D4—121no—
177C5×D4—121no—
178C5×D4—121no—
179C5×D4—121no—
180C5×D4—241no—
181C2×C4×C5D3×D411yescharacteristic
182C2×C4×C5#23711yescharacteristic
183C2×C4×C5C2×#6711yescharacteristic
184C2×Dic5—21no—
185C2×Dic5—41no—
186D20—21no—
187D20—21no—
188C4×D5—41no—
189C4×D5—41no—
190Dic10—41no—
191Dic10—41no—
192C5×C8—41no—
193C5×C8—121no—
194#168—32no—
195#168—61no—
196#168—121no—
197C2×SD16—301no—
198C2×SD16—301no—
199C2×D8—301no—
200C2×M16—301no—
201C4⋊Q8—51no—
202#127—31no—
203C4×D4—51no—
204#107—101no—
205C4⋊C8—31no—
206C4⋊C8—151no—
207C4⋊C8D3×D511yescharacteristic
208#102—101no—
209#102—301no—
210C22⋊C8—301no—
211C4×C8—151no—
212C2×C3×C5#45911yescharacteristic
213C2×C3×C5#46811yescharacteristic
214C2×C3×C5#47111yescharacteristic
215C3×D5—81no—
216C5×D3—161no—
217C23×C3—101no—
218C22×D3—41no—
219C3×Q8—201no—
220C3×Q8—201no—
221C3×D4—101no—
222C3×D4—101no—
223C2×C3×C4—101no—
224C2×C3×C4—201no—
225C2×C3×C4—201no—
226C2×C3×C4—201no—
227C2×C3×C4#70911yescharacteristic
228C2×C3×C4D4×D511yescharacteristic
229C2×C3×C4D4×D511yescharacteristic
230D12—41no—
231D12—41no—
232D12—41no—
233D12—41no—
234D12—81no—
235C3×C8—41no—
236C3⋊C8—41no—
237C3⋊C8—52no—
238C3⋊C8—101no—
239C3⋊C8—201no—
240C22×C5—241no—
241C22×C5—241no—
242C22×C5—241no—
243C22×C5#93911yescharacteristic
244C2×D5—41no—
245C2×D5—41no—
246C2×D5—41no—
247C4×C5—21no—
248C4×C5D3×D811yescharacteristic
249C4×C5#91111yescharacteristic
250C4×C5#94211yescharacteristic
251C4×C5#94911yescharacteristic
252Dic5—41no—
253Dic5—81no—
254C2×Q8—101no—
255C2×D4—51no—
256C2×D4—61no—
257C2×D4—61no—
258C2×D4—61no—
259C22×C4—101no—
260SD16—602no—
261SD16—602no—
262D8—602no—
263M16—602no—
264C2×C8—21no—
265C2×C8—61no—
266C2×C8—151no—
267C2×C8—151no—
268C2×C8—301no—
269C4⋊C4—51no—
270C4⋊C4—101no—
271C4⋊C4—101no—
272C22⋊C4—101no—
273C42C2×D3×D511yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—201no—
276C22×C3—201no—
277C22×C3—201no—
278C22×C3#403011yescharacteristic
279C2×D3—81no—
280C2×D3—81no—
281C2×D3—81no—
282C3×C4—21no—
283C3×C4—201no—
284C3×C4—401no—
285C3×C4D5×D811yescharacteristic
286C3×C4#405711yescharacteristic
287C3×C4#406011yescharacteristic
288C3×C4#406111yescharacteristic
289C2×C5—481no—
290C2×C5#504911yescharacteristic
291C2×C5#515011yescharacteristic
292C2×C5#520311yescharacteristic
293D5—81no—
294C23—101no—
295C23—121no—
296Q8—201no—
297Q8—201no—
298D4—101no—
299D4—101no—
300D4—121no—
301D4—121no—
302D4—121no—
303D4—121no—
304D4—241no—
305C2×C4—101no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4#676511yescharacteristic
310C2×C4#677711yescharacteristic
311C2×C4D5×#6711yescharacteristic
312C8—41no—
313C8—121no—
314C8—152no—
315C8—301no—
316C8—601no—
317C2×C3—401no—
318C2×C3#6503711yescharacteristic
319C2×C3#6506911yescharacteristic
320C2×C3#6507511yescharacteristic
321D3—161no—
322C5#7110411yescharacteristic, complemented, Sylow
323C22—201no—
324C22—201no—
325C22—201no—
326C22—241no—
327C22—241no—
328C22—241no—
329C22#9140811yescharacteristic
330C4—21no—
331C4—201no—
332C4—401no—
333C4#9125611yescharacteristic
334C4#9125811yescharacteristic
335C4#9147811yescharacteristic
336C4#9151311yescharacteristic
337C3#1059919111yescharacteristic, complemented, Sylow
338C2—401no—
339C2—481no—
340C2#1174731111yescharacteristic
341C2#1174775011yescharacteristic
342C2#1174817811yescharacteristic
subgroupG/H
centerC22#91408
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radical#11747026C2
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
1. C3×#65135C2semidirect
2. #11747081C2semidirect
4. #11747013C2semidirect
5. #11746300C2semidirect
6. C5×#4485C2semidirect
7. #11745856C2semidirect
27. #65135D3semidirect
57. #4485D5semidirect
96. C3⋊#168D8semidirect
274. C3×C5#1685semidirect
322. C5#71104semidirect
337. C3#10599191semidirect

Maximal subgroups

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

subgroupindex
C3×#651352
#117470812
#117470262
#117470132
#117463002
C5×#44852
#117458562
#105991913
#711045