Subgroups — C₈×#3993 #13017318

Order 1280.

446 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#3993	C₂	1	1	yes	maximal, characteristic
2	C₈×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
3	D₅⋊#334	C₂	1	1	yes	maximal, characteristic
4	C₈²×D₅	C₂	1	1	yes	maximal, characteristic
5	#10598530	C₂	1	2	yes	maximal
6	C₂×#3993	C₄	1	2	yes	—
7	C₂×C₈×AGL(1,𝔽₅)	—	2	2	no	—
8	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
9	D₅⋊(C₄⋊C₈)	C₂²	1	2	yes	—
10	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
12	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
13	#64893	C₄	1	2	yes	—
14	(C₂×AGL(1,𝔽₅))⋊C₈	—	2	2	no	—
15	#64883	C₄	1	2	yes	complemented
16	#64881	C₄	1	2	yes	complemented
17	C₅×C₈²	C₄	1	1	yes	characteristic, complemented
18	C₈×#168	C₄	1	1	yes	characteristic, complemented
19	C₈×#168	C₄	1	1	yes	characteristic, complemented
20	C₈×#168	C₄	1	1	yes	characteristic, complemented
21	C₈×#106	—	5	1	no	maximal, Sylow
22	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
23	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
24	C₂×D₅⋊C₈	—	2	2	no	—
25	C₂×C₈×D₅	—	2	1	no	—
26	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×D₅	D₄	1	1	yes	characteristic
29	C₂×C₈×D₅	D₄	1	1	yes	characteristic
30	C₄²×D₅	C₂³	1	1	yes	characteristic
31	(C₂×AGL(1,𝔽₅))⋊C₄	—	2	2	no	—
32	#4004	—	2	2	no	—
33	C₄⋊#170	C₂×C₄	1	4	yes	—
34	#3993	C₈	1	8	yes	direct product factor
35	C₈×AGL(1,𝔽₅)	—	4	4	no	—
36	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
39	C₈×Dic₅	—	2	1	no	—
40	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
41	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
42	C₈×Dic₅	Q₈	1	1	yes	characteristic
43	C₈×Dic₅	Q₈	1	1	yes	characteristic
44	C₄×#168	C₂×C₄	1	1	yes	characteristic
45	C₄×#168	C₂×C₄	1	1	yes	characteristic
46	C₄×#168	C₂×C₄	1	1	yes	characteristic
47	C₄×#106	—	5	1	no	—
48	C₈×C₄⋊C₄	—	5	2	no	—
49	C₂×#334	—	5	1	no	—
50	C₂×C₈²	—	5	1	no	—
51	#1279	—	5	2	no	—
52	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
53	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×D₅	#41	1	1	yes	characteristic
56	C₂×#170	—	2	4	no	—
57	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
58	C₄⋊AGL(1,𝔽₅)	C₂×C₈	1	8	yes	—
59	C₄×AGL(1,𝔽₅)	—	4	2	no	—
60	C₄×AGL(1,𝔽₅)	—	4	2	no	—
61	D₅⋊C₈	—	4	2	no	—
62	D₅⋊C₈	—	4	2	no	—
63	C₂×C₅×C₈	—	2	1	no	—
64	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
65	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
66	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
68	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
69	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
70	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
71	C₄×Dic₅	#41	1	1	yes	characteristic
72	C₂×#168	—	2	1	no	—
73	C₂×#168	C₄²	1	1	yes	characteristic
74	C₂×#168	C₄²	1	1	yes	characteristic
75	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
76	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
77	C₈×D₅	—	2	4	no	—
78	C₈×D₅	—	2	2	no	—
79	C₈×D₅	—	2	2	no	—
80	C₈×D₅	C₂×C₈	1	4	yes	—
81	C₈×D₅	SD₁₆	1	4	yes	—
82	C₂×#106	—	5	2	no	—
83	C₂×C₄⋊C₈	—	5	2	no	—
84	C₂×C₄×C₈	—	5	1	no	—
85	C₂×C₄×C₈	—	5	1	no	—
86	C₂×C₄×C₈	—	5	1	no	—
87	C₂×C₄×C₈	—	10	2	no	—
88	C₄×C₄⋊C₄	—	5	2	no	—
89	#340	—	5	2	no	—
90	#336	—	10	2	no	—
91	#334	—	5	2	no	—
92	#334	—	5	2	no	—
93	C₈²	—	5	1	no	—
94	C₈²	—	5	1	no	—
95	C₈²	—	5	1	no	—
96	C₈²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
97	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
98	C₂×AGL(1,𝔽₅)	—	2	8	no	—
99	C₂×AGL(1,𝔽₅)	—	4	4	no	—
100	C₂×AGL(1,𝔽₅)	—	4	4	no	—
101	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
102	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₅	#117	1	1	yes	characteristic
104	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
105	C₂×Dic₅	C₄×Q₈	1	1	yes	characteristic
106	C₂×Dic₅	C₄×Q₈	1	1	yes	characteristic
107	C₄×D₅	—	2	2	no	—
108	C₄×D₅	C₂²×C₈	1	2	yes	—
109	C₄×D₅	#131	1	2	yes	—
110	C₄×D₅	C₂×SD₁₆	1	2	yes	—
111	C₄×D₅	#135	1	2	yes	—
112	#170	—	4	4	no	—
113	C₅×C₈	—	2	2	no	—
114	C₅×C₈	—	2	1	no	—
115	C₅×C₈	—	2	1	no	—
116	C₅×C₈	C₄×C₈	1	2	yes	complemented
117	C₅×C₈	#106	1	2	yes	complemented
118	#168	—	2	2	no	—
119	#168	—	2	1	no	—
120	#168	—	2	1	no	—
121	#168	C₄×C₈	1	2	yes	complemented
122	#168	#106	1	2	yes	complemented
123	C₂²×C₈	—	5	1	no	—
124	C₂²×C₈	—	5	1	no	—
125	C₂²×C₈	—	5	1	no	—
126	C₂²×C₈	—	5	1	no	—
127	C₂²×C₈	—	10	1	no	—
128	C₂²×C₈	—	10	2	no	—
129	C₂×C₄⋊C₄	—	5	4	no	—
130	C₂×C₄²	—	5	1	no	—
131	C₂×C₄²	—	10	2	no	—
132	#106	—	5	8	no	—
133	C₄⋊C₈	—	5	4	no	—
134	C₄⋊C₈	—	10	2	no	—
135	C₄×C₈	—	5	1	no	—
136	C₄×C₈	—	5	1	no	—
137	C₄×C₈	—	5	1	no	—
138	C₄×C₈	—	5	1	no	—
139	C₄×C₈	—	5	1	no	—
140	C₄×C₈	—	5	1	no	—
141	C₄×C₈	—	5	1	no	—
142	C₄×C₈	—	10	1	no	—
143	C₄×C₈	—	20	4	no	—
144	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
145	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
146	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
147	#95	—	10	2	no	—
148	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
149	C₂×D₅	C₈×D₄	1	2	yes	—
150	C₂×D₅	C₄×SD₁₆	1	2	yes	—
151	C₂×D₅	#443	1	2	yes	—
152	AGL(1,𝔽₅)	—	4	8	no	—
153	C₄×C₅	—	2	1	no	—
154	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
155	C₄×C₅	#405	1	1	yes	characteristic
156	C₄×C₅	C₂×#106	1	1	yes	characteristic
157	C₄×C₅	#427	1	1	yes	characteristic
158	Dic₅	—	2	1	no	—
159	Dic₅	C₄×SD₁₆	1	2	yes	—
160	Dic₅	C₈×Q₈	1	2	yes	—
161	C₂²×C₄	—	5	1	no	—
162	C₂²×C₄	—	5	1	no	—
163	C₂²×C₄	—	5	1	no	—
164	C₂²×C₄	—	10	4	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	5	1	no	—
167	C₂×C₈	—	5	1	no	—
168	C₂×C₈	—	5	4	no	—
169	C₂×C₈	—	5	4	no	—
170	C₂×C₈	—	5	1	no	—
171	C₂×C₈	—	5	1	no	—
172	C₂×C₈	—	10	2	no	—
173	C₂×C₈	—	10	2	no	—
174	C₂×C₈	—	10	4	no	—
175	C₂×C₈	—	10	1	no	—
176	C₂×C₈	—	10	4	no	—
177	C₂×C₈	—	20	2	no	—
178	C₂×C₈	—	20	2	no	—
179	C₂×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
180	C₂×C₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
181	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
182	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
183	C₄⋊C₄	—	5	8	no	—
184	C₄⋊C₄	—	10	4	no	—
185	C₄²	—	5	1	no	—
186	C₄²	—	5	1	no	—
187	C₄²	—	5	1	no	—
188	C₄²	—	20	2	no	—
189	C₄²	—	20	2	no	—
190	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
191	C₂×C₅	C₈×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₅	#1772	1	1	yes	characteristic
193	C₂×C₅	C₄×#106	1	1	yes	characteristic
194	D₅	C₈×SD₁₆	1	4	yes	—
195	C₂³	—	5	1	no	—
196	C₂×C₄	—	5	1	no	—
197	C₂×C₄	—	5	1	no	—
198	C₂×C₄	—	5	2	no	—
199	C₂×C₄	—	5	2	no	—
200	C₂×C₄	—	5	2	no	—
201	C₂×C₄	—	5	2	no	—
202	C₂×C₄	—	5	1	no	—
203	C₂×C₄	—	10	2	no	—
204	C₂×C₄	—	10	8	no	—
205	C₂×C₄	—	20	4	no	—
206	C₂×C₄	—	20	4	no	—
207	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
208	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
209	C₂×C₄	#4130	1	1	yes	characteristic
210	C₈	—	2	2	no	—
211	C₈	—	2	1	no	—
212	C₈	—	2	1	no	—
213	C₈	—	5	2	no	—
214	C₈	—	5	2	no	—
215	C₈	—	10	2	no	—
216	C₈	—	10	1	no	—
217	C₈	—	10	1	no	—
218	C₈	—	20	4	no	—
219	C₈	C₈×AGL(1,𝔽₅)	1	2	yes	complemented
220	C₈	#3993	1	2	yes	direct product factor
221	C₅	C₈×#106	1	1	yes	characteristic, complemented, Sylow
222	C₂²	—	5	2	no	—
223	C₂²	—	5	2	no	—
224	C₂²	—	5	2	no	—
225	C₂²	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	5	2	no	—
228	C₄	—	5	2	no	—
229	C₄	—	10	1	no	—
230	C₄	—	20	8	no	—
231	C₄	C₂×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
232	C₄	#65718	1	1	yes	characteristic
233	C₄	C₂×#3993	1	1	yes	characteristic
234	C₄	#65721	1	1	yes	characteristic
235	C₂	—	5	4	no	—
236	C₂	C₈×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
237	C₂	C₄×#3993	1	1	yes	characteristic
238	C₂	#10603851	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂×C₄×C₈
Frattini	C₄²	C₂²×AGL(1,𝔽₅)
Fitting	C₅×C₈²	C₄
socle	C₂²×C₅	C₄×C₄⋊C₄
prime radical	C₂²×D₅	C₄×D₄
cosocle	C₄²×D₅	C₂³
hypercenter	C₈²	AGL(1,𝔽₅)
hypocenter	C₅	C₈×#106
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
15. #64883	C₄	semidirect
16. #64881	C₄	semidirect
17. C₅×C₈²	C₄	semidirect
18. C₈×#168	C₄	semidirect
19. C₈×#168	C₄	semidirect
20. C₈×#168	C₄	semidirect
34. #3993	C₈	direct (N × H)
96. C₈²	AGL(1,𝔽₅)	semidirect
116. C₅×C₈	C₄×C₈	semidirect
117. C₅×C₈	#106	semidirect
121. #168	C₄×C₈	semidirect
122. #168	#106	semidirect
219. C₈	C₈×AGL(1,𝔽₅)	semidirect
220. C₈	#3993	direct (N × H)
221. C₅	C₈×#106	semidirect

Maximal subgroups

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

subgroup	index
C₄×#3993	2
C₈×C₄⋊AGL(1,𝔽₅)	2
D₅⋊#334	2
C₈²×D₅	2
#10598530	2
C₈×#106	5

Subgroups — C8×#3993 #13017318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#3993 #13017318