Subgroups — C₃×AGL(1,𝔽₅)×AGL(1,ℤ/8) #14416673

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₃×#65793	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65767	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65735	C₂	1	2	yes	maximal, complemented
7	C₃×SD₁₆×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
8	C₃×#65731	C₂	1	2	yes	maximal, complemented
9	C₃×D₈×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
10	C₃×#65727	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×M₁₆×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
12	AGL(1,𝔽₅)×AGL(1,ℤ/8)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×AGL(1,𝔽₅)	—	2	1	no	—
14	C₃×D₅×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
17	C₃×Q₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic, complemented
18	C₃×Q₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic, complemented
19	C₃×D₄×AGL(1,𝔽₅)	—	2	1	no	—
20	C₃×D₄×AGL(1,𝔽₅)	—	2	1	no	—
21	C₃×D₄×AGL(1,𝔽₅)	—	2	1	no	—
22	C₃×D₄×AGL(1,𝔽₅)	—	2	1	no	—
23	C₃×D₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
24	C₃×D₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
25	C₃×D₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic, complemented
26	C₃×D₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic, complemented
27	C₃×#4130	—	2	1	no	—
28	C₃×#4130	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
31	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
32	C₃×D₅⋊M₁₆	C₂²	1	1	yes	characteristic
33	C₃×C₅×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic, complemented
34	C₃×#4095	C₄	1	1	yes	characteristic, complemented
35	C₃×#4078	C₄	1	1	yes	characteristic, complemented
36	C₃×#4060	C₄	1	2	yes	complemented
37	C₃×D₅×SD₁₆	C₂²	1	2	yes	—
38	C₃×#4057	C₄	1	2	yes	complemented
39	C₃×D₅×D₈	C₂²	1	2	yes	—
40	C₃×#4054	C₄	1	1	yes	characteristic, complemented
41	C₃×D₅×M₁₆	C₂²	1	1	yes	characteristic
42	C₃×#4009	C₂²	1	2	yes	complemented
43	C₃×#4007	C₂²	1	2	yes	—
44	C₃×#4007	C₂²	1	2	yes	—
45	C₃×#4007	C₂²	1	2	yes	complemented
46	C₃×#3994	C₂²	1	2	yes	complemented
47	C₃×#3993	C₂²	1	2	yes	complemented
48	C₃×#3992	C₂²	1	2	yes	complemented
49	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
50	C₃×C₄×AGL(1,ℤ/8)	—	5	1	no	maximal, Hall
51	#41×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×D₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
53	D₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
54	#65793	C₂×C₃	1	1	yes	characteristic, complemented
55	#65767	C₂×C₃	1	1	yes	characteristic, complemented
56	#65735	C₂×C₃	1	2	yes	complemented
57	SD₁₆×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
58	#65731	C₂×C₃	1	2	yes	complemented
59	D₈×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
60	#65727	C₂×C₃	1	1	yes	characteristic, complemented
61	M₁₆×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂³×C₃×D₅	—	2	1	no	—
63	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
64	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
65	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
66	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
67	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
68	C₂²×C₃×AGL(1,𝔽₅)	—	4	4	no	—
69	C₂²×C₃×AGL(1,𝔽₅)	D₄	1	1	yes	characteristic
70	C₂²×C₃×AGL(1,𝔽₅)	D₄	1	1	yes	characteristic
71	C₃×C₅×#41	C₂×C₄	1	1	yes	characteristic, complemented
72	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
74	C₃×#713	C₂×C₄	1	1	yes	characteristic, complemented
75	C₃×Q₈×D₅	C₂³	1	1	yes	characteristic
76	C₃×#711	—	2	1	no	—
77	C₃×#711	C₂×C₄	1	1	yes	characteristic, complemented
78	C₃×D₄×D₅	—	2	1	no	—
79	C₃×D₄×D₅	—	2	1	no	—
80	C₃×D₄×D₅	—	2	1	no	—
81	C₃×D₄×D₅	C₂×C₄	1	2	yes	complemented
82	C₃×D₄×D₅	C₂³	1	2	yes	—
83	C₃×D₄×D₅	C₂³	1	1	yes	characteristic
84	C₃×#709	—	2	1	no	—
85	C₃×#709	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×C₃×C₄×D₅	—	2	1	no	—
88	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
89	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
90	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
91	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
92	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
93	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
94	C₃×#704	—	2	1	no	—
95	C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
96	C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
97	C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
98	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
99	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	2	yes	—
100	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
101	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
102	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
103	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
104	C₃×C₄×AGL(1,𝔽₅)	D₄	1	1	yes	characteristic
105	C₃×C₄×AGL(1,𝔽₅)	D₄	1	1	yes	characteristic
106	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
107	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
108	C₃×#700	—	2	1	no	—
109	C₃×D₅⋊C₈	C₂³	1	2	yes	—
110	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
111	C₃×C₅×D₈	C₂×C₄	1	2	yes	complemented
112	C₃×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic, complemented
113	C₃×#688	C₂×C₄	1	2	yes	complemented
114	C₃×#687	C₂×C₄	1	2	yes	complemented
115	C₃×#686	C₂×C₄	1	2	yes	complemented
116	C₃×#686	C₂×C₄	1	2	yes	complemented
117	C₃×#681	C₂×C₄	1	1	yes	characteristic, complemented
118	C₃×D₄₀	C₂×C₄	1	2	yes	complemented
119	C₃×#677	C₂×C₄	1	2	yes	complemented
120	C₃×#676	C₂×C₄	1	2	yes	complemented
121	C₃×C₈×D₅	C₂³	1	2	yes	—
122	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
123	C₃×C₄×#41	—	5	1	no	—
124	C₂×C₃×C₄×D₄	—	5	1	no	—
125	C₃×#442	—	5	2	no	—
126	C₃×#440	—	5	2	no	—
127	C₃×C₄×SD₁₆	—	5	2	no	—
128	C₃×C₄×D₈	—	5	2	no	—
129	C₃×#428	—	5	1	no	—
130	C₃×#418	—	5	1	no	—
131	C₃×#417	—	5	1	no	—
132	C₃×C₄×M₁₆	—	5	1	no	—
133	C₂³×AGL(1,𝔽₅)	—	2	1	no	—
134	D₅×#41	C₂²×C₃	1	1	yes	characteristic
135	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
137	Q₈×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic, complemented
138	Q₈×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic, complemented
139	D₄×AGL(1,𝔽₅)	—	2	1	no	—
140	D₄×AGL(1,𝔽₅)	—	2	1	no	—
141	D₄×AGL(1,𝔽₅)	—	2	1	no	—
142	D₄×AGL(1,𝔽₅)	—	2	1	no	—
143	D₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
144	D₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
145	D₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic, complemented
146	D₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic, complemented
147	#4130	—	2	1	no	—
148	#4130	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₄×AGL(1,𝔽₅)	—	2	1	no	—
151	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
152	D₅⋊M₁₆	C₂²×C₃	1	1	yes	characteristic
153	C₅×AGL(1,ℤ/8)	C₃×C₄	1	1	yes	characteristic, complemented
154	#4095	C₃×C₄	1	1	yes	characteristic, complemented
155	#4078	C₃×C₄	1	1	yes	characteristic, complemented
156	#4060	C₃×C₄	1	2	yes	complemented
157	D₅×SD₁₆	C₂²×C₃	1	2	yes	—
158	#4057	C₃×C₄	1	2	yes	complemented
159	D₅×D₈	C₂²×C₃	1	2	yes	—
160	#4054	C₃×C₄	1	1	yes	characteristic, complemented
161	D₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
162	#4009	C₂²×C₃	1	2	yes	complemented
163	#4007	C₂²×C₃	1	2	yes	—
164	#4007	C₂²×C₃	1	2	yes	—
165	#4007	C₂²×C₃	1	2	yes	complemented
166	#3994	C₂²×C₃	1	2	yes	complemented
167	#3993	C₂²×C₃	1	2	yes	complemented
168	#3992	C₂²×C₃	1	2	yes	complemented
169	C₈×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	complemented
170	C₄×AGL(1,ℤ/8)	—	5	1	no	Sylow
171	C₂³×C₃×C₅	—	2	1	no	—
172	C₂²×C₃×D₅	—	2	1	no	—
173	C₂²×C₃×D₅	—	2	2	no	—
174	C₂²×C₃×D₅	—	2	1	no	—
175	C₂²×C₃×D₅	—	2	2	no	—
176	C₂²×C₃×D₅	—	4	2	no	—
177	C₂²×C₃×D₅	—	4	2	no	—
178	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
179	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
180	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
181	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
182	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
183	C₂×C₃×AGL(1,𝔽₅)	—	4	1	no	—
184	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
185	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
186	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
187	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
188	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
189	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
190	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
191	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
192	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
193	C₃×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic, complemented
194	C₃×C₅×D₄	—	2	1	no	—
195	C₃×C₅×D₄	—	2	1	no	—
196	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
197	C₃×C₅×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₃×C₂²⋊D₅	—	2	1	no	—
201	C₃×C₂²⋊D₅	—	2	1	no	—
202	C₃×C₂²⋊D₅	—	2	2	no	—
203	C₃×C₂²⋊D₅	—	2	1	no	—
204	C₃×C₂²⋊D₅	—	2	2	no	—
205	C₂×C₃×Dic₅	—	2	1	no	—
206	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
207	C₃×D₂₀	—	2	1	no	—
208	C₃×D₂₀	—	2	1	no	—
209	C₃×D₂₀	C₂²×C₄	1	2	yes	—
210	C₃×D₂₀	C₂²×C₄	1	1	yes	characteristic, complemented
211	C₃×C₄×D₅	—	2	1	no	—
212	C₃×C₄×D₅	—	2	1	no	—
213	C₃×C₄×D₅	—	2	1	no	—
214	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
215	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
216	C₃×C₄×D₅	#41	1	1	yes	characteristic
217	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
218	C₃×Dic₁₀	—	2	1	no	—
219	C₃×Dic₁₀	C₂²×C₄	1	1	yes	characteristic, complemented
220	C₃×#170	—	2	2	no	—
221	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
222	C₃×#168	C₂²×C₄	1	2	yes	complemented
223	C₂×C₃×#41	—	5	1	no	—
224	C₂²×C₃×D₄	—	5	1	no	—
225	C₂³×C₃×C₄	—	10	1	no	—
226	C₃×AGL(1,ℤ/8)	—	5	1	no	—
227	C₃×AGL(1,ℤ/8)	—	5	1	no	—
228	C₃×AGL(1,ℤ/8)	—	5	2	no	—
229	C₃×AGL(1,ℤ/8)	—	5	2	no	—
230	C₃×AGL(1,ℤ/8)	—	5	1	no	—
231	C₃×AGL(1,ℤ/8)	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
232	C₂×C₃×SD₁₆	—	5	2	no	—
233	C₂×C₃×D₈	—	5	2	no	—
234	C₂×C₃×M₁₆	—	5	1	no	—
235	C₂×C₃×M₁₆	—	5	1	no	—
236	C₃×C₄×Q₈	—	5	1	no	—
237	C₃×C₄×Q₈	—	5	1	no	—
238	C₃×C₄×D₄	—	5	2	no	—
239	C₃×C₄×D₄	—	5	2	no	—
240	C₃×C₄×D₄	—	5	1	no	—
241	C₃×C₄×D₄	—	5	1	no	—
242	C₃×C₄×D₄	—	10	1	no	—
243	C₃×C₄×D₄	—	10	1	no	—
244	C₃×C₄×D₄	—	10	1	no	—
245	C₃×C₄×D₄	—	10	1	no	—
246	C₃×#117	—	5	1	no	—
247	C₃×#117	—	10	1	no	—
248	C₂×C₃×C₄⋊C₄	—	5	1	no	—
249	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
250	C₂×C₃×C₄²	—	5	1	no	—
251	C₂×C₃×C₄²	—	10	1	no	—
252	C₃×#107	—	5	2	no	—
253	C₃×#106	—	5	2	no	—
254	C₃×#103	—	5	2	no	—
255	C₃×#102	—	5	2	no	—
256	C₃×#102	—	5	2	no	—
257	C₃×#102	—	5	2	no	—
258	C₃×#97	—	5	2	no	—
259	C₃×C₄×C₈	—	5	2	no	—
260	C₂³×D₅	—	2	1	no	—
261	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
262	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
263	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
264	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
265	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
266	C₂²×AGL(1,𝔽₅)	—	4	4	no	—
267	C₂²×AGL(1,𝔽₅)	C₃×D₄	1	1	yes	characteristic
268	C₂²×AGL(1,𝔽₅)	C₃×D₄	1	1	yes	characteristic
269	C₅×#41	C₂×C₃×C₄	1	1	yes	characteristic, complemented
270	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
271	C₂×C₂²⋊D₅	—	2	1	no	—
272	#713	C₂×C₃×C₄	1	1	yes	characteristic, complemented
273	Q₈×D₅	C₂³×C₃	1	1	yes	characteristic
274	#711	—	2	1	no	—
275	#711	C₂×C₃×C₄	1	1	yes	characteristic, complemented
276	D₄×D₅	—	2	1	no	—
277	D₄×D₅	—	2	1	no	—
278	D₄×D₅	—	2	1	no	—
279	D₄×D₅	C₂×C₃×C₄	1	2	yes	complemented
280	D₄×D₅	C₂³×C₃	1	2	yes	—
281	D₄×D₅	C₂³×C₃	1	1	yes	characteristic
282	#709	—	2	1	no	—
283	#709	C₂×C₃×C₄	1	1	yes	characteristic, complemented
284	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic, complemented
285	C₂×C₄×D₅	—	2	1	no	—
286	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
287	C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
288	C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
289	C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
290	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
291	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
292	#704	—	2	1	no	—
293	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
294	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
295	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
296	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
297	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
298	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
299	C₄×AGL(1,𝔽₅)	—	2	1	no	—
300	C₄×AGL(1,𝔽₅)	—	2	1	no	—
301	C₄×AGL(1,𝔽₅)	—	2	1	no	—
302	C₄×AGL(1,𝔽₅)	C₃×D₄	1	1	yes	characteristic
303	C₄×AGL(1,𝔽₅)	C₃×D₄	1	1	yes	characteristic
304	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
305	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
306	#700	—	2	1	no	—
307	D₅⋊C₈	C₂³×C₃	1	2	yes	—
308	C₅×SD₁₆	C₂×C₃×C₄	1	2	yes	complemented
309	C₅×D₈	C₂×C₃×C₄	1	2	yes	complemented
310	C₅×M₁₆	C₂×C₃×C₄	1	1	yes	characteristic, complemented
311	#688	C₂×C₃×C₄	1	2	yes	complemented
312	#687	C₂×C₃×C₄	1	2	yes	complemented
313	#686	C₂×C₃×C₄	1	2	yes	complemented
314	#686	C₂×C₃×C₄	1	2	yes	complemented
315	#681	C₂×C₃×C₄	1	1	yes	characteristic, complemented
316	D₄₀	C₂×C₃×C₄	1	2	yes	complemented
317	#677	C₂×C₃×C₄	1	2	yes	complemented
318	#676	C₂×C₃×C₄	1	2	yes	complemented
319	C₈×D₅	C₂³×C₃	1	2	yes	—
320	C₂×AGL(1,ℤ/8)	—	5	1	no	—
321	C₄×#41	—	5	1	no	—
322	C₂×C₄×D₄	—	5	1	no	—
323	#442	—	5	2	no	—
324	#440	—	5	2	no	—
325	C₄×SD₁₆	—	5	2	no	—
326	C₄×D₈	—	5	2	no	—
327	#428	—	5	1	no	—
328	#418	—	5	1	no	—
329	#417	—	5	1	no	—
330	C₄×M₁₆	—	5	1	no	—
331	C₂²×C₃×C₅	—	2	1	no	—
332	C₂²×C₃×C₅	—	2	2	no	—
333	C₂²×C₃×C₅	—	4	2	no	—
334	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
335	C₂×C₃×D₅	—	2	1	no	—
336	C₂×C₃×D₅	—	2	1	no	—
337	C₂×C₃×D₅	—	2	1	no	—
338	C₂×C₃×D₅	—	2	2	no	—
339	C₂×C₃×D₅	—	4	4	no	—
340	C₂×C₃×D₅	—	4	2	no	—
341	C₂×C₃×D₅	—	4	2	no	—
342	C₂×C₃×D₅	—	4	1	no	—
343	C₂×C₃×D₅	—	4	1	no	—
344	C₂×C₃×D₅	—	4	2	no	—
345	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
346	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
347	C₃×AGL(1,𝔽₅)	—	2	1	no	—
348	C₃×AGL(1,𝔽₅)	—	2	1	no	—
349	C₃×AGL(1,𝔽₅)	—	2	1	no	—
350	C₃×AGL(1,𝔽₅)	—	4	1	no	—
351	C₃×AGL(1,𝔽₅)	—	4	2	no	—
352	C₃×AGL(1,𝔽₅)	—	4	1	no	—
353	C₃×AGL(1,𝔽₅)	AGL(1,ℤ/8)	1	2	yes	direct product factor
354	C₃×C₄×C₅	—	2	1	no	—
355	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
356	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
357	C₃×Dic₅	—	2	1	no	—
358	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
359	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
360	C₂⁴×C₃	—	10	1	no	—
361	C₃×#41	—	5	1	no	—
362	C₃×#41	—	5	1	no	—
363	C₃×#41	—	5	1	no	—
364	C₃×#41	—	10	1	no	—
365	C₃×#41	—	10	1	no	—
366	C₃×#41	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
367	C₂×C₃×Q₈	—	5	1	no	—
368	C₂×C₃×D₄	—	5	2	no	—
369	C₂×C₃×D₄	—	5	2	no	—
370	C₂×C₃×D₄	—	5	1	no	—
371	C₂×C₃×D₄	—	5	1	no	—
372	C₂×C₃×D₄	—	10	1	no	—
373	C₂×C₃×D₄	—	10	1	no	—
374	C₂×C₃×D₄	—	10	1	no	—
375	C₂×C₃×D₄	—	10	1	no	—
376	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
377	C₂²×C₃×C₄	—	5	1	no	—
378	C₂²×C₃×C₄	—	5	1	no	—
379	C₂²×C₃×C₄	—	5	1	no	—
380	C₂²×C₃×C₄	—	10	1	no	—
381	C₂²×C₃×C₄	—	10	1	no	—
382	C₂²×C₃×C₄	—	10	1	no	—
383	C₂²×C₃×C₄	—	10	2	no	—
384	C₂²×C₃×C₄	—	10	2	no	—
385	C₂²×C₃×C₄	—	10	1	no	—
386	C₂²×C₃×C₄	—	20	4	no	—
387	C₃×SD₁₆	—	5	2	no	—
388	C₃×SD₁₆	—	5	2	no	—
389	C₃×SD₁₆	—	5	2	no	—
390	C₃×SD₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
391	C₃×D₈	—	5	2	no	—
392	C₃×D₈	—	5	2	no	—
393	C₃×D₈	—	5	2	no	—
394	C₃×D₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
395	C₃×M₁₆	—	5	1	no	—
396	C₃×M₁₆	—	5	2	no	—
397	C₃×M₁₆	—	10	1	no	—
398	C₃×M₁₆	—	10	1	no	—
399	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
400	C₂×C₃×C₈	—	5	2	no	—
401	C₂×C₃×C₈	—	5	2	no	—
402	C₃×C₄⋊C₄	—	5	1	no	—
403	C₃×C₄⋊C₄	—	5	1	no	—
404	C₃×C₄⋊C₄	—	5	2	no	—
405	C₃×C₄⋊C₄	—	10	1	no	—
406	C₃×C₄⋊C₄	—	10	1	no	—
407	C₃×C₄⋊C₄	—	10	1	no	—
408	C₃×C₂²⋊C₄	—	10	2	no	—
409	C₃×C₂²⋊C₄	—	10	2	no	—
410	C₃×C₂²⋊C₄	—	10	1	no	—
411	C₃×C₂²⋊C₄	—	10	1	no	—
412	C₃×C₂²⋊C₄	—	10	1	no	—
413	C₃×C₄²	—	5	1	no	—
414	C₃×C₄²	—	5	1	no	—
415	C₃×C₄²	—	5	1	no	—
416	C₃×C₄²	—	5	1	no	—
417	C₃×C₄²	—	10	1	no	—
418	C₃×C₄²	—	10	1	no	—
419	C₃×C₄²	—	10	1	no	—
420	C₂³×C₅	—	2	1	no	—
421	C₂²×D₅	—	2	1	no	—
422	C₂²×D₅	—	2	2	no	—
423	C₂²×D₅	—	2	1	no	—
424	C₂²×D₅	—	2	2	no	—
425	C₂²×D₅	—	4	2	no	—
426	C₂²×D₅	—	4	2	no	—
427	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
428	C₂×AGL(1,𝔽₅)	—	2	2	no	—
429	C₂×AGL(1,𝔽₅)	—	2	1	no	—
430	C₂×AGL(1,𝔽₅)	—	2	1	no	—
431	C₂×AGL(1,𝔽₅)	—	2	2	no	—
432	C₂×AGL(1,𝔽₅)	—	4	1	no	—
433	C₂×AGL(1,𝔽₅)	—	4	2	no	—
434	C₂×AGL(1,𝔽₅)	—	4	4	no	—
435	C₂×AGL(1,𝔽₅)	—	4	2	no	—
436	C₂×AGL(1,𝔽₅)	—	4	2	no	—
437	C₂×AGL(1,𝔽₅)	—	4	4	no	—
438	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	1	yes	characteristic
439	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	1	yes	characteristic
440	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	1	yes	characteristic
441	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	1	yes	characteristic
442	C₅×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic, complemented
443	C₅×D₄	—	2	1	no	—
444	C₅×D₄	—	2	1	no	—
445	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
446	C₅×D₄	C₂²×C₃×C₄	1	1	yes	characteristic, complemented
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
449	C₂²⋊D₅	—	2	1	no	—
450	C₂²⋊D₅	—	2	1	no	—
451	C₂²⋊D₅	—	2	2	no	—
452	C₂²⋊D₅	—	2	1	no	—
453	C₂²⋊D₅	—	2	2	no	—
454	C₂×Dic₅	—	2	1	no	—
455	C₂×Dic₅	C₃×#41	1	1	yes	characteristic
456	D₂₀	—	2	1	no	—
457	D₂₀	—	2	1	no	—
458	D₂₀	C₂²×C₃×C₄	1	2	yes	—
459	D₂₀	C₂²×C₃×C₄	1	1	yes	characteristic, complemented
460	C₄×D₅	—	2	1	no	—
461	C₄×D₅	—	2	1	no	—
462	C₄×D₅	—	2	1	no	—
463	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
464	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
465	C₄×D₅	C₃×#41	1	1	yes	characteristic
466	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
467	Dic₁₀	—	2	1	no	—
468	Dic₁₀	C₂²×C₃×C₄	1	1	yes	characteristic, complemented
469	#170	—	2	2	no	—
470	C₅×C₈	C₂²×C₃×C₄	1	2	yes	complemented
471	#168	C₂²×C₃×C₄	1	2	yes	complemented
472	C₂×#41	—	5	1	no	—
473	C₂²×D₄	—	5	1	no	—
474	C₂³×C₄	—	10	1	no	—
475	AGL(1,ℤ/8)	—	5	1	no	—
476	AGL(1,ℤ/8)	—	5	1	no	—
477	AGL(1,ℤ/8)	—	5	2	no	—
478	AGL(1,ℤ/8)	—	5	2	no	—
479	AGL(1,ℤ/8)	—	5	1	no	—
480	AGL(1,ℤ/8)	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
481	C₂×SD₁₆	—	5	2	no	—
482	C₂×D₈	—	5	2	no	—
483	C₂×M₁₆	—	5	1	no	—
484	C₂×M₁₆	—	5	1	no	—
485	C₄×Q₈	—	5	1	no	—
486	C₄×Q₈	—	5	1	no	—
487	C₄×D₄	—	5	2	no	—
488	C₄×D₄	—	5	2	no	—
489	C₄×D₄	—	5	1	no	—
490	C₄×D₄	—	5	1	no	—
491	C₄×D₄	—	10	1	no	—
492	C₄×D₄	—	10	1	no	—
493	C₄×D₄	—	10	1	no	—
494	C₄×D₄	—	10	1	no	—
495	#117	—	5	1	no	—
496	#117	—	10	1	no	—
497	C₂×C₄⋊C₄	—	5	1	no	—
498	C₂×C₂²⋊C₄	—	10	1	no	—
499	C₂×C₄²	—	5	1	no	—
500	C₂×C₄²	—	10	1	no	—
501	#107	—	5	2	no	—
502	#106	—	5	2	no	—
503	#103	—	5	2	no	—
504	#102	—	5	2	no	—
505	#102	—	5	2	no	—
506	#102	—	5	2	no	—
507	#97	—	5	2	no	—
508	C₄×C₈	—	5	2	no	—
509	C₂×C₃×C₅	—	2	1	no	—
510	C₂×C₃×C₅	—	4	2	no	—
511	C₂×C₃×C₅	—	4	1	no	—
512	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
513	C₃×D₅	—	2	1	no	—
514	C₃×D₅	—	4	1	no	—
515	C₃×D₅	—	4	2	no	—
516	C₃×D₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
517	C₃×D₅	#575	1	1	yes	characteristic
518	C₂³×C₃	—	2	1	no	—
519	C₂³×C₃	—	5	1	no	—
520	C₂³×C₃	—	10	1	no	—
521	C₂³×C₃	—	10	2	no	—
522	C₂³×C₃	—	10	2	no	—
523	C₂³×C₃	—	10	1	no	—
524	C₂³×C₃	—	20	2	no	—
525	C₂³×C₃	—	20	2	no	—
526	C₃×Q₈	—	5	1	no	—
527	C₃×Q₈	—	10	1	no	—
528	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
529	C₃×D₄	—	2	1	no	—
530	C₃×D₄	—	2	1	no	—
531	C₃×D₄	—	5	2	no	—
532	C₃×D₄	—	5	1	no	—
533	C₃×D₄	—	10	1	no	—
534	C₃×D₄	—	10	2	no	—
535	C₃×D₄	—	10	2	no	—
536	C₃×D₄	—	10	1	no	—
537	C₃×D₄	—	10	1	no	—
538	C₃×D₄	—	10	1	no	—
539	C₃×D₄	—	10	1	no	—
540	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
541	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
542	C₂×C₃×C₄	—	2	1	no	—
543	C₂×C₃×C₄	—	5	1	no	—
544	C₂×C₃×C₄	—	5	1	no	—
545	C₂×C₃×C₄	—	5	1	no	—
546	C₂×C₃×C₄	—	5	1	no	—
547	C₂×C₃×C₄	—	5	1	no	—
548	C₂×C₃×C₄	—	5	1	no	—
549	C₂×C₃×C₄	—	5	1	no	—
550	C₂×C₃×C₄	—	5	1	no	—
551	C₂×C₃×C₄	—	5	1	no	—
552	C₂×C₃×C₄	—	10	1	no	—
553	C₂×C₃×C₄	—	10	1	no	—
554	C₂×C₃×C₄	—	10	1	no	—
555	C₂×C₃×C₄	—	10	2	no	—
556	C₂×C₃×C₄	—	10	1	no	—
557	C₂×C₃×C₄	—	10	1	no	—
558	C₂×C₃×C₄	—	10	1	no	—
559	C₂×C₃×C₄	—	10	2	no	—
560	C₂×C₃×C₄	—	20	2	no	—
561	C₂×C₃×C₄	—	20	4	no	—
562	C₂×C₃×C₄	—	20	1	no	—
563	C₂×C₃×C₄	—	20	2	no	—
564	C₂×C₃×C₄	—	20	4	no	—
565	C₂×C₃×C₄	—	20	2	no	—
566	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
567	C₃×C₈	—	5	2	no	—
568	C₃×C₈	—	10	2	no	—
569	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
570	C₂²×C₅	—	2	1	no	—
571	C₂²×C₅	—	2	2	no	—
572	C₂²×C₅	—	4	2	no	—
573	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
574	C₂×D₅	—	2	1	no	—
575	C₂×D₅	—	2	1	no	—
576	C₂×D₅	—	2	1	no	—
577	C₂×D₅	—	2	2	no	—
578	C₂×D₅	—	4	4	no	—
579	C₂×D₅	—	4	2	no	—
580	C₂×D₅	—	4	2	no	—
581	C₂×D₅	—	4	1	no	—
582	C₂×D₅	—	4	1	no	—
583	C₂×D₅	—	4	2	no	—
584	C₂×D₅	C₃×C₄×D₄	1	1	yes	characteristic
585	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
586	AGL(1,𝔽₅)	—	2	1	no	—
587	AGL(1,𝔽₅)	—	2	1	no	—
588	AGL(1,𝔽₅)	—	2	1	no	—
589	AGL(1,𝔽₅)	—	4	1	no	—
590	AGL(1,𝔽₅)	—	4	2	no	—
591	AGL(1,𝔽₅)	—	4	1	no	—
592	AGL(1,𝔽₅)	C₃×AGL(1,ℤ/8)	1	2	yes	direct product factor
593	C₄×C₅	—	2	1	no	—
594	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
595	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
596	Dic₅	—	2	1	no	—
597	Dic₅	C₃×C₄×D₄	1	1	yes	characteristic
598	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
599	C₂⁴	—	10	1	no	—
600	#41	—	5	1	no	—
601	#41	—	5	1	no	—
602	#41	—	5	1	no	—
603	#41	—	10	1	no	—
604	#41	—	10	1	no	—
605	#41	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
606	C₂×Q₈	—	5	1	no	—
607	C₂×D₄	—	5	2	no	—
608	C₂×D₄	—	5	2	no	—
609	C₂×D₄	—	5	1	no	—
610	C₂×D₄	—	5	1	no	—
611	C₂×D₄	—	10	1	no	—
612	C₂×D₄	—	10	1	no	—
613	C₂×D₄	—	10	1	no	—
614	C₂×D₄	—	10	1	no	—
615	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
616	C₂²×C₄	—	5	1	no	—
617	C₂²×C₄	—	5	1	no	—
618	C₂²×C₄	—	5	1	no	—
619	C₂²×C₄	—	10	1	no	—
620	C₂²×C₄	—	10	1	no	—
621	C₂²×C₄	—	10	1	no	—
622	C₂²×C₄	—	10	2	no	—
623	C₂²×C₄	—	10	2	no	—
624	C₂²×C₄	—	10	1	no	—
625	C₂²×C₄	—	20	4	no	—
626	SD₁₆	—	5	2	no	—
627	SD₁₆	—	5	2	no	—
628	SD₁₆	—	5	2	no	—
629	SD₁₆	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
630	D₈	—	5	2	no	—
631	D₈	—	5	2	no	—
632	D₈	—	5	2	no	—
633	D₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
634	M₁₆	—	5	1	no	—
635	M₁₆	—	5	2	no	—
636	M₁₆	—	10	1	no	—
637	M₁₆	—	10	1	no	—
638	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
639	C₂×C₈	—	5	2	no	—
640	C₂×C₈	—	5	2	no	—
641	C₄⋊C₄	—	5	1	no	—
642	C₄⋊C₄	—	5	1	no	—
643	C₄⋊C₄	—	5	2	no	—
644	C₄⋊C₄	—	10	1	no	—
645	C₄⋊C₄	—	10	1	no	—
646	C₄⋊C₄	—	10	1	no	—
647	C₂²⋊C₄	—	10	2	no	—
648	C₂²⋊C₄	—	10	2	no	—
649	C₂²⋊C₄	—	10	1	no	—
650	C₂²⋊C₄	—	10	1	no	—
651	C₂²⋊C₄	—	10	1	no	—
652	C₄²	—	5	1	no	—
653	C₄²	—	5	1	no	—
654	C₄²	—	5	1	no	—
655	C₄²	—	5	1	no	—
656	C₄²	—	10	1	no	—
657	C₄²	—	10	1	no	—
658	C₄²	—	10	1	no	—
659	C₃×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
660	C₂²×C₃	—	2	1	no	—
661	C₂²×C₃	—	2	2	no	—
662	C₂²×C₃	—	4	2	no	—
663	C₂²×C₃	—	5	1	no	—
664	C₂²×C₃	—	5	1	no	—
665	C₂²×C₃	—	10	1	no	—
666	C₂²×C₃	—	10	1	no	—
667	C₂²×C₃	—	10	1	no	—
668	C₂²×C₃	—	10	2	no	—
669	C₂²×C₃	—	20	2	no	—
670	C₂²×C₃	—	20	2	no	—
671	C₂²×C₃	—	20	1	no	—
672	C₂²×C₃	—	20	1	no	—
673	C₂²×C₃	—	20	2	no	—
674	C₂²×C₃	—	20	4	no	—
675	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
676	C₃×C₄	—	2	1	no	—
677	C₃×C₄	—	5	2	no	—
678	C₃×C₄	—	5	1	no	—
679	C₃×C₄	—	5	1	no	—
680	C₃×C₄	—	10	1	no	—
681	C₃×C₄	—	10	1	no	—
682	C₃×C₄	—	10	1	no	—
683	C₃×C₄	—	10	1	no	—
684	C₃×C₄	—	20	1	no	—
685	C₃×C₄	—	20	1	no	—
686	C₃×C₄	—	20	2	no	—
687	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
688	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
689	C₂×C₅	—	2	1	no	—
690	C₂×C₅	—	4	2	no	—
691	C₂×C₅	—	4	1	no	—
692	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
693	D₅	—	2	1	no	—
694	D₅	—	4	2	no	—
695	D₅	—	4	1	no	—
696	D₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
697	D₅	C₃×#575	1	1	yes	characteristic
698	C₂³	—	2	1	no	—
699	C₂³	—	5	1	no	—
700	C₂³	—	10	1	no	—
701	C₂³	—	10	2	no	—
702	C₂³	—	10	2	no	—
703	C₂³	—	10	1	no	—
704	C₂³	—	20	2	no	—
705	C₂³	—	20	2	no	—
706	Q₈	—	5	1	no	—
707	Q₈	—	10	1	no	—
708	Q₈	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	5	1	no	—
712	D₄	—	5	2	no	—
713	D₄	—	10	1	no	—
714	D₄	—	10	2	no	—
715	D₄	—	10	2	no	—
716	D₄	—	10	1	no	—
717	D₄	—	10	1	no	—
718	D₄	—	10	1	no	—
719	D₄	—	10	1	no	—
720	D₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
721	D₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	5	1	no	—
724	C₂×C₄	—	5	1	no	—
725	C₂×C₄	—	5	1	no	—
726	C₂×C₄	—	5	1	no	—
727	C₂×C₄	—	5	1	no	—
728	C₂×C₄	—	5	1	no	—
729	C₂×C₄	—	5	1	no	—
730	C₂×C₄	—	5	1	no	—
731	C₂×C₄	—	5	1	no	—
732	C₂×C₄	—	10	1	no	—
733	C₂×C₄	—	10	1	no	—
734	C₂×C₄	—	10	1	no	—
735	C₂×C₄	—	10	2	no	—
736	C₂×C₄	—	10	1	no	—
737	C₂×C₄	—	10	1	no	—
738	C₂×C₄	—	10	1	no	—
739	C₂×C₄	—	10	2	no	—
740	C₂×C₄	—	20	4	no	—
741	C₂×C₄	—	20	2	no	—
742	C₂×C₄	—	20	1	no	—
743	C₂×C₄	—	20	4	no	—
744	C₂×C₄	—	20	2	no	—
745	C₂×C₄	—	20	2	no	—
746	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
747	C₈	—	5	2	no	—
748	C₈	—	10	2	no	—
749	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
750	C₂×C₃	—	2	1	no	—
751	C₂×C₃	—	4	2	no	—
752	C₂×C₃	—	4	1	no	—
753	C₂×C₃	—	5	1	no	—
754	C₂×C₃	—	5	1	no	—
755	C₂×C₃	—	10	1	no	—
756	C₂×C₃	—	20	2	no	—
757	C₂×C₃	—	20	1	no	—
758	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
759	C₅	C₃×C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
760	C₂²	—	2	1	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	5	1	no	—
764	C₂²	—	5	1	no	—
765	C₂²	—	10	1	no	—
766	C₂²	—	10	1	no	—
767	C₂²	—	10	1	no	—
768	C₂²	—	10	2	no	—
769	C₂²	—	20	2	no	—
770	C₂²	—	20	2	no	—
771	C₂²	—	20	1	no	—
772	C₂²	—	20	1	no	—
773	C₂²	—	20	2	no	—
774	C₂²	—	20	4	no	—
775	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
776	C₄	—	2	1	no	—
777	C₄	—	5	2	no	—
778	C₄	—	5	1	no	—
779	C₄	—	5	1	no	—
780	C₄	—	10	1	no	—
781	C₄	—	10	1	no	—
782	C₄	—	10	1	no	—
783	C₄	—	10	1	no	—
784	C₄	—	20	2	no	—
785	C₄	—	20	1	no	—
786	C₄	—	20	1	no	—
787	C₄	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
788	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
789	C₃	AGL(1,𝔽₅)×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
790	C₂	—	2	1	no	—
791	C₂	—	4	2	no	—
792	C₂	—	4	1	no	—
793	C₂	—	5	1	no	—
794	C₂	—	5	1	no	—
795	C₂	—	10	1	no	—
796	C₂	—	20	2	no	—
797	C₂	—	20	1	no	—
798	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×AGL(1,ℤ/8)	C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×D₅×AGL(1,ℤ/8)	C₂
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₃×AGL(1,ℤ/8)	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₃×#41×AGL(1,𝔽₅)	C₂	semidirect
2. C₂×C₃×D₄×AGL(1,𝔽₅)	C₂	semidirect
4. C₃×#65793	C₂	semidirect
5. C₃×#65767	C₂	semidirect
6. C₃×#65735	C₂	semidirect
7. C₃×SD₁₆×AGL(1,𝔽₅)	C₂	semidirect
8. C₃×#65731	C₂	semidirect
9. C₃×D₈×AGL(1,𝔽₅)	C₂	semidirect
10. C₃×#65727	C₂	semidirect
11. C₃×M₁₆×AGL(1,𝔽₅)	C₂	semidirect
12. AGL(1,𝔽₅)×AGL(1,ℤ/8)	C₃	direct (N × H)
17. C₃×Q₈×AGL(1,𝔽₅)	C₂²	semidirect
18. C₃×Q₈×AGL(1,𝔽₅)	C₂²	semidirect
25. C₃×D₄×AGL(1,𝔽₅)	C₂²	semidirect
26. C₃×D₄×AGL(1,𝔽₅)	C₂²	semidirect
33. C₃×C₅×AGL(1,ℤ/8)	C₄	semidirect
34. C₃×#4095	C₄	semidirect
35. C₃×#4078	C₄	semidirect
36. C₃×#4060	C₄	semidirect
38. C₃×#4057	C₄	semidirect
40. C₃×#4054	C₄	semidirect
42. C₃×#4009	C₂²	semidirect
45. C₃×#4007	C₂²	semidirect
46. C₃×#3994	C₂²	semidirect
47. C₃×#3993	C₂²	semidirect
48. C₃×#3992	C₂²	semidirect
49. C₃×C₈×AGL(1,𝔽₅)	C₂²	semidirect
51. #41×AGL(1,𝔽₅)	C₂×C₃	semidirect
52. C₂×D₄×AGL(1,𝔽₅)	C₂×C₃	semidirect
54. #65793	C₂×C₃	semidirect
55. #65767	C₂×C₃	semidirect
56. #65735	C₂×C₃	semidirect
57. SD₁₆×AGL(1,𝔽₅)	C₂×C₃	semidirect
58. #65731	C₂×C₃	semidirect
59. D₈×AGL(1,𝔽₅)	C₂×C₃	semidirect
60. #65727	C₂×C₃	semidirect
61. M₁₆×AGL(1,𝔽₅)	C₂×C₃	semidirect
71. C₃×C₅×#41	C₂×C₄	semidirect
72. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
74. C₃×#713	C₂×C₄	semidirect
77. C₃×#711	C₂×C₄	semidirect
81. C₃×D₄×D₅	C₂×C₄	semidirect
85. C₃×#709	C₂×C₄	semidirect
86. C₂×C₃×D₂₀	C₂×C₄	semidirect
110. C₃×C₅×SD₁₆	C₂×C₄	semidirect
111. C₃×C₅×D₈	C₂×C₄	semidirect
112. C₃×C₅×M₁₆	C₂×C₄	semidirect
113. C₃×#688	C₂×C₄	semidirect
114. C₃×#687	C₂×C₄	semidirect
115. C₃×#686	C₂×C₄	semidirect
116. C₃×#686	C₂×C₄	semidirect
117. C₃×#681	C₂×C₄	semidirect
118. C₃×D₄₀	C₂×C₄	semidirect
119. C₃×#677	C₂×C₄	semidirect
120. C₃×#676	C₂×C₄	semidirect
137. Q₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
138. Q₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
145. D₄×AGL(1,𝔽₅)	C₂²×C₃	semidirect
146. D₄×AGL(1,𝔽₅)	C₂²×C₃	semidirect
153. C₅×AGL(1,ℤ/8)	C₃×C₄	semidirect
154. #4095	C₃×C₄	semidirect
155. #4078	C₃×C₄	semidirect
156. #4060	C₃×C₄	semidirect
158. #4057	C₃×C₄	semidirect
160. #4054	C₃×C₄	semidirect
162. #4009	C₂²×C₃	semidirect
165. #4007	C₂²×C₃	semidirect
166. #3994	C₂²×C₃	semidirect
167. #3993	C₂²×C₃	semidirect
168. #3992	C₂²×C₃	semidirect
169. C₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
193. C₃×C₅×Q₈	C₂²×C₄	semidirect
197. C₃×C₅×D₄	C₂²×C₄	semidirect
210. C₃×D₂₀	C₂²×C₄	semidirect
219. C₃×Dic₁₀	C₂²×C₄	semidirect
221. C₃×C₅×C₈	C₂²×C₄	semidirect
222. C₃×#168	C₂²×C₄	semidirect
231. C₃×AGL(1,ℤ/8)	AGL(1,𝔽₅)	direct (N × H)
269. C₅×#41	C₂×C₃×C₄	semidirect
270. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
272. #713	C₂×C₃×C₄	semidirect
275. #711	C₂×C₃×C₄	semidirect
279. D₄×D₅	C₂×C₃×C₄	semidirect
283. #709	C₂×C₃×C₄	semidirect
284. C₂×D₂₀	C₂×C₃×C₄	semidirect
308. C₅×SD₁₆	C₂×C₃×C₄	semidirect
309. C₅×D₈	C₂×C₃×C₄	semidirect
310. C₅×M₁₆	C₂×C₃×C₄	semidirect
311. #688	C₂×C₃×C₄	semidirect
312. #687	C₂×C₃×C₄	semidirect
313. #686	C₂×C₃×C₄	semidirect
314. #686	C₂×C₃×C₄	semidirect
315. #681	C₂×C₃×C₄	semidirect
316. D₄₀	C₂×C₃×C₄	semidirect
317. #677	C₂×C₃×C₄	semidirect
318. #676	C₂×C₃×C₄	semidirect
353. C₃×AGL(1,𝔽₅)	AGL(1,ℤ/8)	direct (N × H)
366. C₃×#41	C₂×AGL(1,𝔽₅)	semidirect
376. C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	semidirect
390. C₃×SD₁₆	C₂×AGL(1,𝔽₅)	semidirect
394. C₃×D₈	C₂×AGL(1,𝔽₅)	semidirect
399. C₃×M₁₆	C₂×AGL(1,𝔽₅)	semidirect
442. C₅×Q₈	C₂²×C₃×C₄	semidirect
446. C₅×D₄	C₂²×C₃×C₄	semidirect
459. D₂₀	C₂²×C₃×C₄	semidirect
468. Dic₁₀	C₂²×C₃×C₄	semidirect
470. C₅×C₈	C₂²×C₃×C₄	semidirect
471. #168	C₂²×C₃×C₄	semidirect
480. AGL(1,ℤ/8)	C₃×AGL(1,𝔽₅)	direct (N × H)
528. C₃×Q₈	C₂²×AGL(1,𝔽₅)	semidirect
541. C₃×D₄	C₂²×AGL(1,𝔽₅)	semidirect
569. C₃×C₈	C₂²×AGL(1,𝔽₅)	semidirect
592. AGL(1,𝔽₅)	C₃×AGL(1,ℤ/8)	direct (N × H)
605. #41	C₂×C₃×AGL(1,𝔽₅)	semidirect
615. C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
629. SD₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
633. D₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
638. M₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
659. C₃×C₅	C₄×AGL(1,ℤ/8)	semidirect
708. Q₈	C₂²×C₃×AGL(1,𝔽₅)	semidirect
721. D₄	C₂²×C₃×AGL(1,𝔽₅)	semidirect
749. C₈	C₂²×C₃×AGL(1,𝔽₅)	semidirect
759. C₅	C₃×C₄×AGL(1,ℤ/8)	semidirect
789. C₃	AGL(1,𝔽₅)×AGL(1,ℤ/8)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#41×AGL(1,𝔽₅)	2
C₂×C₃×D₄×AGL(1,𝔽₅)	2
C₃×D₅×AGL(1,ℤ/8)	2
C₃×#65793	2
C₃×#65767	2
C₃×#65735	2
C₃×SD₁₆×AGL(1,𝔽₅)	2
C₃×#65731	2
C₃×D₈×AGL(1,𝔽₅)	2
C₃×#65727	2
C₃×M₁₆×AGL(1,𝔽₅)	2
AGL(1,𝔽₅)×AGL(1,ℤ/8)	3
C₃×C₄×AGL(1,ℤ/8)	5

Subgroups — C3×AGL(1,𝔽5)×AGL(1,ℤ/8) #14416673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×AGL(1,𝔽₅)×AGL(1,ℤ/8) #14416673