Subgroups — C₂×C₃×#66108 #14509961

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4149	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4144	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4096	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#686	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66108	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4062	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4060	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4057	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×D₅×D₈	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#4054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#66108	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₂²⋊D₅	—	2	2	no	—
17	C₃×#4149	—	2	4	no	—
18	C₃×#4149	C₂²	1	8	yes	complemented
19	C₂×C₃×#713	C₂²	1	2	yes	complemented
20	C₃×#4144	—	2	4	no	—
21	C₃×#4144	C₂²	1	8	yes	complemented
22	C₂×C₃×#711	—	2	1	no	—
23	C₂×C₃×#711	C₂²	1	2	yes	complemented
24	C₂×C₃×D₄×D₅	—	2	2	no	—
25	C₂×C₃×D₄×D₅	—	2	1	no	—
26	C₂×C₃×D₄×D₅	C₂²	1	2	yes	complemented
27	C₂×C₃×D₄×D₅	C₂²	1	2	yes	complemented
28	C₂×C₃×#709	—	2	1	no	—
29	C₂×C₃×#709	C₂²	1	1	yes	characteristic
30	C₂×C₃×#709	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×D₂₀	—	2	1	no	—
32	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
35	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
36	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₃×#4096	C₂²	1	8	yes	complemented
38	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×#688	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×#686	C₂²	1	2	yes	complemented
42	C₂×C₃×#686	C₂²	1	2	yes	complemented
43	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×#686	C₂²	1	8	yes	complemented
45	C₂²×C₃×#168	C₂²	1	1	yes	characteristic, complemented
46	C₃×#4062	C₂²	1	16	yes	complemented
47	C₃×#4060	C₂²	1	16	yes	complemented
48	C₃×#4057	C₂²	1	16	yes	complemented
49	C₃×D₅×D₈	C₂²	1	16	yes	complemented
50	C₃×#4054	C₂²	1	8	yes	complemented
51	C₃×#4053	C₂²	1	8	yes	complemented
52	C₂×C₃×D₄₀	C₂²	1	2	yes	complemented
53	C₂×C₃×#677	C₂²	1	2	yes	complemented
54	C₂×C₃×#676	C₂²	1	2	yes	complemented
55	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
56	C₂×C₃×#576	—	5	1	no	maximal, Hall
57	C₂×#4149	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×#4144	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×#4096	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂²×#686	C₂×C₃	1	1	yes	characteristic, complemented
62	#66108	C₂×C₃	1	16	yes	direct product factor
63	C₂×#4062	C₂×C₃	1	2	yes	complemented
64	C₂×#4060	C₂×C₃	1	2	yes	complemented
65	C₂×#4057	C₂×C₃	1	2	yes	complemented
66	C₂×D₅×D₈	C₂×C₃	1	2	yes	complemented
67	C₂×#4054	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂⁴×C₃×C₅	—	2	1	no	—
70	C₂³×C₃×D₅	—	2	1	no	—
71	C₂³×C₃×D₅	—	2	2	no	—
72	C₂³×C₃×D₅	—	2	2	no	—
73	C₃×C₅×#41	—	2	2	no	—
74	C₃×C₅×#41	C₂³	1	4	yes	complemented
75	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₅×D₄	—	2	1	no	—
77	C₂×C₃×C₅×D₄	—	2	1	no	—
78	C₂×C₃×C₅×D₄	—	2	2	no	—
79	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
80	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
82	C₂²×C₃×C₄×C₅	—	2	1	no	—
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
85	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
86	C₂×C₃×C₂²⋊D₅	—	2	16	no	—
87	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
88	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
89	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
90	C₂²×C₃×Dic₅	—	2	2	no	—
91	C₃×#713	—	2	4	no	—
92	C₃×#713	C₂³	1	8	yes	complemented
93	C₃×#711	—	2	4	no	—
94	C₃×#711	—	2	8	no	—
95	C₃×#711	C₂³	1	8	yes	complemented
96	C₃×D₄×D₅	—	2	16	no	—
97	C₃×D₄×D₅	—	2	8	no	—
98	C₃×D₄×D₅	—	2	4	no	—
99	C₃×D₄×D₅	—	2	4	no	—
100	C₃×D₄×D₅	C₂³	1	8	yes	complemented
101	C₃×D₄×D₅	C₂³	1	8	yes	complemented
102	C₃×#709	—	2	2	no	—
103	C₃×#709	—	2	8	no	—
104	C₃×#709	D₄	1	4	yes	—
105	C₃×#709	C₂³	1	4	yes	—
106	C₃×#709	C₂³	1	4	yes	complemented
107	C₂×C₃×D₂₀	—	2	2	no	—
108	C₂×C₃×D₂₀	—	2	1	no	—
109	C₂×C₃×D₂₀	—	2	2	no	—
110	C₂×C₃×D₂₀	—	2	8	no	—
111	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
112	C₂×C₃×D₂₀	C₂³	1	2	yes	—
113	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
114	C₂×C₃×D₂₀	C₂³	1	4	yes	complemented
115	C₂×C₃×C₄×D₅	—	2	1	no	—
116	C₂×C₃×C₄×D₅	—	2	2	no	—
117	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
118	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
119	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
120	C₃×C₅×SD₁₆	C₂³	1	8	yes	complemented
121	C₃×C₅×D₈	C₂³	1	8	yes	complemented
122	C₃×C₅×M₁₆	C₂³	1	4	yes	complemented
123	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
124	C₃×#689	C₂³	1	4	yes	complemented
125	C₃×#688	C₂³	1	4	yes	complemented
126	C₃×#687	C₂³	1	4	yes	complemented
127	C₃×#686	C₂³	1	8	yes	complemented
128	C₃×#686	C₂³	1	8	yes	complemented
129	C₃×#686	C₂³	1	4	yes	complemented
130	C₂×C₃×#168	C₂³	1	1	yes	characteristic
131	C₂×C₃×#168	C₂³	1	1	yes	characteristic
132	C₂×C₃×#168	C₂³	1	4	yes	complemented
133	C₃×D₄₀	C₂³	1	8	yes	complemented
134	C₃×#677	C₂³	1	8	yes	complemented
135	C₃×#676	C₂³	1	8	yes	complemented
136	C₃×C₈×D₅	C₂³	1	8	yes	complemented
137	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
138	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
139	C₃×#576	—	5	16	no	—
140	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
141	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
142	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
143	C₂×C₃×AGL(1,ℤ/8)	D₅	1	1	yes	characteristic, complemented
144	C₂×C₃×#135	—	5	1	no	—
145	C₂×C₃×#135	—	5	2	no	—
146	C₂²×C₃×D₈	—	5	1	no	—
147	C₂²×C₃×D₈	—	5	2	no	—
148	C₂×C₃×#131	—	5	1	no	—
149	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₂²×C₂²⋊D₅	—	2	2	no	—
152	#4149	—	2	4	no	—
153	#4149	C₂²×C₃	1	8	yes	complemented
154	C₂×#713	C₂²×C₃	1	2	yes	complemented
155	#4144	—	2	4	no	—
156	#4144	C₂²×C₃	1	8	yes	complemented
157	C₂×#711	—	2	1	no	—
158	C₂×#711	C₂²×C₃	1	2	yes	complemented
159	C₂×D₄×D₅	—	2	2	no	—
160	C₂×D₄×D₅	—	2	1	no	—
161	C₂×D₄×D₅	C₂²×C₃	1	2	yes	complemented
162	C₂×D₄×D₅	C₂²×C₃	1	2	yes	complemented
163	C₂×#709	—	2	1	no	—
164	C₂×#709	C₂²×C₃	1	1	yes	characteristic
165	C₂×#709	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂²×D₂₀	—	2	1	no	—
167	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	8	yes	complemented
169	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
170	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
171	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
172	#4096	C₂²×C₃	1	8	yes	complemented
173	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₂×#688	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₂×#686	C₂²×C₃	1	2	yes	complemented
178	C₂×#686	C₂²×C₃	1	2	yes	complemented
179	C₂×#686	C₂²×C₃	1	8	yes	complemented
180	C₂²×#168	C₂²×C₃	1	1	yes	characteristic, complemented
181	#4062	C₂²×C₃	1	16	yes	complemented
182	#4060	C₂²×C₃	1	16	yes	complemented
183	#4057	C₂²×C₃	1	16	yes	complemented
184	D₅×D₈	C₂²×C₃	1	16	yes	complemented
185	#4054	C₂²×C₃	1	8	yes	complemented
186	#4053	C₂²×C₃	1	8	yes	complemented
187	C₂×D₄₀	C₂²×C₃	1	2	yes	complemented
188	C₂×#677	C₂²×C₃	1	2	yes	complemented
189	C₂×#676	C₂²×C₃	1	2	yes	complemented
190	C₂×C₈×D₅	C₂²×C₃	1	2	yes	complemented
191	C₂×#576	—	5	1	no	Sylow
192	C₂³×C₃×C₅	—	2	2	no	—
193	C₂³×C₃×C₅	—	2	1	no	—
194	C₂³×C₃×C₅	—	2	4	no	—
195	C₂³×C₃×C₅	—	8	2	no	—
196	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₃×D₅	—	2	2	no	—
198	C₂²×C₃×D₅	—	2	1	no	—
199	C₂²×C₃×D₅	—	2	4	no	—
200	C₂²×C₃×D₅	—	2	8	no	—
201	C₂²×C₃×D₅	—	2	8	no	—
202	C₂²×C₃×D₅	—	8	4	no	—
203	C₂²×C₃×D₅	—	8	4	no	—
204	C₂²×C₃×D₅	—	8	2	no	—
205	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	C₂⁴	1	2	yes	—
208	C₃×C₅×D₄	—	2	4	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₃×C₅×D₄	—	2	2	no	—
211	C₃×C₅×D₄	—	2	4	no	—
212	C₃×C₅×D₄	C₂⁴	1	4	yes	—
213	C₃×C₅×D₄	C₂⁴	1	2	yes	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	4	no	—
216	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
218	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
219	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
220	C₃×C₂²⋊D₅	—	2	4	no	—
221	C₃×C₂²⋊D₅	—	2	8	no	—
222	C₃×C₂²⋊D₅	—	2	8	no	—
223	C₃×C₂²⋊D₅	—	2	8	no	—
224	C₃×C₂²⋊D₅	C₂×D₄	1	8	yes	—
225	C₂×C₃×Dic₅	—	2	1	no	—
226	C₂×C₃×Dic₅	—	2	8	no	—
227	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
228	C₃×D₂₀	—	2	8	no	—
229	C₃×D₂₀	—	2	4	no	—
230	C₃×D₂₀	—	2	2	no	—
231	C₃×D₂₀	—	2	1	no	—
232	C₃×D₂₀	C₂×D₄	1	4	yes	—
233	C₃×D₂₀	C₂⁴	1	4	yes	—
234	C₃×D₂₀	C₂⁴	1	2	yes	—
235	C₃×C₄×D₅	—	2	4	no	—
236	C₃×C₄×D₅	—	2	8	no	—
237	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
238	C₃×C₄×D₅	C₂⁴	1	4	yes	—
239	C₃×Dic₁₀	—	2	1	no	—
240	C₃×Dic₁₀	C₂×D₄	1	4	yes	—
241	C₃×Dic₁₀	C₂⁴	1	2	yes	—
242	C₃×C₅×C₈	C₂⁴	1	4	yes	—
243	C₃×#168	C₂⁴	1	2	yes	—
244	C₃×#168	C₂⁴	1	2	yes	—
245	C₃×H(5,𝔽₂)	—	5	8	no	—
246	C₃×H(5,𝔽₂)	—	5	8	no	—
247	C₃×H(5,𝔽₂)	—	10	4	no	—
248	C₃×H(5,𝔽₂)	—	10	4	no	—
249	C₂×C₃×#41	—	5	1	no	—
250	C₂×C₃×#41	—	5	2	no	—
251	C₂×C₃×#41	—	5	2	no	—
252	C₂×C₃×#41	—	5	1	no	—
253	C₂×C₃×#41	—	10	1	no	—
254	C₂×C₃×#41	—	10	1	no	—
255	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic, complemented
256	C₂²×C₃×D₄	—	5	2	no	—
257	C₂²×C₃×D₄	—	5	2	no	—
258	C₂²×C₃×D₄	—	5	1	no	—
259	C₂²×C₃×D₄	—	10	1	no	—
260	C₂²×C₃×D₄	—	10	2	no	—
261	C₂²×C₃×D₄	—	10	1	no	—
262	C₂²×C₃×D₄	—	10	2	no	—
263	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
264	C₃×AGL(1,ℤ/8)	—	5	16	no	—
265	C₃×AGL(1,ℤ/8)	—	5	16	no	—
266	C₃×AGL(1,ℤ/8)	—	5	8	no	—
267	C₃×AGL(1,ℤ/8)	C₂×D₅	1	8	yes	complemented
268	C₃×#135	—	5	8	no	—
269	C₃×#135	—	5	16	no	—
270	C₂×C₃×Q₁₆	—	5	1	no	—
271	C₂×C₃×SD₁₆	—	5	1	no	—
272	C₂×C₃×SD₁₆	—	5	1	no	—
273	C₂×C₃×SD₁₆	—	5	2	no	—
274	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
275	C₂×C₃×D₈	—	5	2	no	—
276	C₂×C₃×D₈	—	5	1	no	—
277	C₂×C₃×D₈	—	5	2	no	—
278	C₂×C₃×D₈	—	5	8	no	—
279	C₂×C₃×D₈	—	5	16	no	—
280	C₂×C₃×D₈	—	5	2	no	—
281	C₂×C₃×D₈	C₂×D₅	1	2	yes	complemented
282	C₃×#131	—	5	8	no	—
283	C₂×C₃×M₁₆	—	5	2	no	—
284	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
285	C₂²×C₃×C₈	—	5	1	no	—
286	C₂²×C₃×C₈	—	5	2	no	—
287	C₂⁴×C₅	—	2	1	no	—
288	C₂³×D₅	—	2	1	no	—
289	C₂³×D₅	—	2	2	no	—
290	C₂³×D₅	—	2	2	no	—
291	C₅×#41	—	2	2	no	—
292	C₅×#41	C₂³×C₃	1	4	yes	complemented
293	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₅×D₄	—	2	1	no	—
295	C₂×C₅×D₄	—	2	1	no	—
296	C₂×C₅×D₄	—	2	2	no	—
297	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
299	C₂×C₅×D₄	C₂³×C₃	1	4	yes	complemented
300	C₂²×C₄×C₅	—	2	1	no	—
301	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₂²⋊D₅	—	2	1	no	—
303	C₂×C₂²⋊D₅	—	2	2	no	—
304	C₂×C₂²⋊D₅	—	2	16	no	—
305	C₂×C₂²⋊D₅	—	2	2	no	—
306	C₂×C₂²⋊D₅	—	2	2	no	—
307	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
308	C₂²×Dic₅	—	2	2	no	—
309	#713	—	2	4	no	—
310	#713	C₂³×C₃	1	8	yes	complemented
311	#711	—	2	4	no	—
312	#711	—	2	8	no	—
313	#711	C₂³×C₃	1	8	yes	complemented
314	D₄×D₅	—	2	16	no	—
315	D₄×D₅	—	2	8	no	—
316	D₄×D₅	—	2	4	no	—
317	D₄×D₅	—	2	4	no	—
318	D₄×D₅	C₂³×C₃	1	8	yes	complemented
319	D₄×D₅	C₂³×C₃	1	8	yes	complemented
320	#709	—	2	2	no	—
321	#709	—	2	8	no	—
322	#709	C₃×D₄	1	4	yes	—
323	#709	C₂³×C₃	1	4	yes	—
324	#709	C₂³×C₃	1	4	yes	complemented
325	C₂×D₂₀	—	2	2	no	—
326	C₂×D₂₀	—	2	1	no	—
327	C₂×D₂₀	—	2	2	no	—
328	C₂×D₂₀	—	2	8	no	—
329	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
330	C₂×D₂₀	C₂³×C₃	1	2	yes	—
331	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
332	C₂×D₂₀	C₂³×C₃	1	4	yes	complemented
333	C₂×C₄×D₅	—	2	1	no	—
334	C₂×C₄×D₅	—	2	2	no	—
335	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
336	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
337	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
338	C₅×SD₁₆	C₂³×C₃	1	8	yes	complemented
339	C₅×D₈	C₂³×C₃	1	8	yes	complemented
340	C₅×M₁₆	C₂³×C₃	1	4	yes	complemented
341	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
342	#689	C₂³×C₃	1	4	yes	complemented
343	#688	C₂³×C₃	1	4	yes	complemented
344	#687	C₂³×C₃	1	4	yes	complemented
345	#686	C₂³×C₃	1	4	yes	complemented
346	#686	C₂³×C₃	1	8	yes	complemented
347	#686	C₂³×C₃	1	8	yes	complemented
348	C₂×#168	C₂³×C₃	1	1	yes	characteristic
349	C₂×#168	C₂³×C₃	1	1	yes	characteristic
350	C₂×#168	C₂³×C₃	1	4	yes	complemented
351	D₄₀	C₂³×C₃	1	8	yes	complemented
352	#677	C₂³×C₃	1	8	yes	complemented
353	#676	C₂³×C₃	1	8	yes	complemented
354	C₈×D₅	C₂³×C₃	1	8	yes	complemented
355	C₂×H(5,𝔽₂)	—	5	1	no	—
356	C₂×H(5,𝔽₂)	—	5	1	no	—
357	#576	—	5	16	no	—
358	C₂×AGL(1,ℤ/8)	—	5	2	no	—
359	C₂×AGL(1,ℤ/8)	—	5	2	no	—
360	C₂×AGL(1,ℤ/8)	—	5	1	no	—
361	C₂×AGL(1,ℤ/8)	C₃×D₅	1	1	yes	characteristic, complemented
362	C₂×#135	—	5	1	no	—
363	C₂×#135	—	5	2	no	—
364	C₂²×D₈	—	5	1	no	—
365	C₂²×D₈	—	5	2	no	—
366	C₂×#131	—	5	1	no	—
367	C₂²×C₃×C₅	—	2	2	no	—
368	C₂²×C₃×C₅	—	2	4	no	—
369	C₂²×C₃×C₅	—	2	2	no	—
370	C₂²×C₃×C₅	—	4	2	no	—
371	C₂²×C₃×C₅	—	4	4	no	—
372	C₂²×C₃×C₅	—	8	4	no	—
373	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
374	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₃×D₅	—	2	4	no	—
376	C₂×C₃×D₅	—	2	4	no	—
377	C₂×C₃×D₅	—	2	2	no	—
378	C₂×C₃×D₅	—	4	4	no	—
379	C₂×C₃×D₅	—	4	2	no	—
380	C₂×C₃×D₅	—	8	8	no	—
381	C₂×C₃×D₅	—	8	8	no	—
382	C₂×C₃×D₅	—	8	4	no	—
383	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
384	C₃×C₄×C₅	—	2	2	no	—
385	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
386	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
387	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
388	C₃×Dic₅	—	2	2	no	—
389	C₃×Dic₅	C₂²×D₄	1	4	yes	—
390	C₂⁴×C₃	—	2	1	no	—
391	C₂⁴×C₃	—	10	2	no	—
392	C₂⁴×C₃	—	10	2	no	—
393	C₂⁴×C₃	—	10	1	no	—
394	C₃×#41	—	2	2	no	—
395	C₃×#41	—	5	4	no	—
396	C₃×#41	—	5	4	no	—
397	C₃×#41	—	5	8	no	—
398	C₃×#41	—	5	8	no	—
399	C₃×#41	—	5	4	no	—
400	C₃×#41	—	10	8	no	—
401	C₃×#41	—	10	4	no	—
402	C₃×#41	—	10	4	no	—
403	C₃×#41	—	10	8	no	—
404	C₃×#41	—	10	2	no	—
405	C₃×#41	C₂²×D₅	1	4	yes	complemented
406	C₂×C₃×Q₈	—	5	1	no	—
407	C₂×C₃×Q₈	—	5	1	no	—
408	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
409	C₂×C₃×D₄	—	2	1	no	—
410	C₂×C₃×D₄	—	2	1	no	—
411	C₂×C₃×D₄	—	2	2	no	—
412	C₂×C₃×D₄	—	5	2	no	—
413	C₂×C₃×D₄	—	5	8	no	—
414	C₂×C₃×D₄	—	5	8	no	—
415	C₂×C₃×D₄	—	5	1	no	—
416	C₂×C₃×D₄	—	5	2	no	—
417	C₂×C₃×D₄	—	5	1	no	—
418	C₂×C₃×D₄	—	5	4	no	—
419	C₂×C₃×D₄	—	10	8	no	—
420	C₂×C₃×D₄	—	10	2	no	—
421	C₂×C₃×D₄	—	10	4	no	—
422	C₂×C₃×D₄	—	10	4	no	—
423	C₂×C₃×D₄	—	10	2	no	—
424	C₂×C₃×D₄	—	10	2	no	—
425	C₂×C₃×D₄	—	10	16	no	—
426	C₂×C₃×D₄	—	10	8	no	—
427	C₂×C₃×D₄	—	10	16	no	—
428	C₂×C₃×D₄	—	10	2	no	—
429	C₂×C₃×D₄	—	10	1	no	—
430	C₂×C₃×D₄	—	10	1	no	—
431	C₂×C₃×D₄	—	10	2	no	—
432	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
433	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
434	C₂×C₃×D₄	C₂²×D₅	1	4	yes	complemented
435	C₂²×C₃×C₄	—	2	1	no	—
436	C₂²×C₃×C₄	—	5	2	no	—
437	C₂²×C₃×C₄	—	10	2	no	—
438	C₂²×C₃×C₄	—	10	2	no	—
439	C₂²×C₃×C₄	—	10	1	no	—
440	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
441	C₃×Q₁₆	—	5	4	no	—
442	C₃×SD₁₆	—	5	4	no	—
443	C₃×SD₁₆	—	5	4	no	—
444	C₃×SD₁₆	—	5	8	no	—
445	C₃×SD₁₆	C₂²×D₅	1	8	yes	complemented
446	C₃×D₈	—	5	8	no	—
447	C₃×D₈	—	5	4	no	—
448	C₃×D₈	—	5	8	no	—
449	C₃×D₈	—	5	8	no	—
450	C₃×D₈	C₂²×D₅	1	8	yes	complemented
451	C₃×M₁₆	—	5	8	no	—
452	C₃×M₁₆	C₂²×D₅	1	4	yes	complemented
453	C₂×C₃×C₈	—	5	1	no	—
454	C₂×C₃×C₈	—	5	1	no	—
455	C₂×C₃×C₈	—	5	4	no	—
456	C₂×C₃×C₈	—	5	8	no	—
457	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
458	C₂³×C₅	—	2	2	no	—
459	C₂³×C₅	—	2	1	no	—
460	C₂³×C₅	—	2	4	no	—
461	C₂³×C₅	—	8	2	no	—
462	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
463	C₂²×D₅	—	2	2	no	—
464	C₂²×D₅	—	2	1	no	—
465	C₂²×D₅	—	2	4	no	—
466	C₂²×D₅	—	2	8	no	—
467	C₂²×D₅	—	2	8	no	—
468	C₂²×D₅	—	8	4	no	—
469	C₂²×D₅	—	8	4	no	—
470	C₂²×D₅	—	8	2	no	—
471	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
472	C₅×Q₈	—	2	1	no	—
473	C₅×Q₈	C₂⁴×C₃	1	2	yes	—
474	C₅×D₄	—	2	4	no	—
475	C₅×D₄	—	2	1	no	—
476	C₅×D₄	—	2	2	no	—
477	C₅×D₄	—	2	4	no	—
478	C₅×D₄	C₂⁴×C₃	1	4	yes	—
479	C₅×D₄	C₂⁴×C₃	1	2	yes	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	4	no	—
482	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
483	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
484	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
485	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
486	C₂²⋊D₅	—	2	4	no	—
487	C₂²⋊D₅	—	2	8	no	—
488	C₂²⋊D₅	—	2	8	no	—
489	C₂²⋊D₅	—	2	8	no	—
490	C₂²⋊D₅	C₂×C₃×D₄	1	8	yes	—
491	C₂×Dic₅	—	2	1	no	—
492	C₂×Dic₅	—	2	8	no	—
493	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
494	D₂₀	—	2	8	no	—
495	D₂₀	—	2	4	no	—
496	D₂₀	—	2	2	no	—
497	D₂₀	—	2	1	no	—
498	D₂₀	C₂×C₃×D₄	1	4	yes	—
499	D₂₀	C₂⁴×C₃	1	4	yes	—
500	D₂₀	C₂⁴×C₃	1	2	yes	—
501	C₄×D₅	—	2	4	no	—
502	C₄×D₅	—	2	8	no	—
503	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
504	C₄×D₅	C₂⁴×C₃	1	4	yes	—
505	Dic₁₀	—	2	1	no	—
506	Dic₁₀	C₂×C₃×D₄	1	4	yes	—
507	Dic₁₀	C₂⁴×C₃	1	2	yes	—
508	C₅×C₈	C₂⁴×C₃	1	4	yes	—
509	#168	C₂⁴×C₃	1	2	yes	—
510	#168	C₂⁴×C₃	1	2	yes	—
511	H(5,𝔽₂)	—	5	8	no	—
512	H(5,𝔽₂)	—	5	8	no	—
513	H(5,𝔽₂)	—	10	4	no	—
514	H(5,𝔽₂)	—	10	4	no	—
515	C₂×#41	—	5	1	no	—
516	C₂×#41	—	5	2	no	—
517	C₂×#41	—	5	2	no	—
518	C₂×#41	—	5	1	no	—
519	C₂×#41	—	10	1	no	—
520	C₂×#41	—	10	1	no	—
521	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic, complemented
522	C₂²×D₄	—	5	2	no	—
523	C₂²×D₄	—	5	2	no	—
524	C₂²×D₄	—	5	1	no	—
525	C₂²×D₄	—	10	1	no	—
526	C₂²×D₄	—	10	2	no	—
527	C₂²×D₄	—	10	1	no	—
528	C₂²×D₄	—	10	2	no	—
529	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
530	AGL(1,ℤ/8)	—	5	16	no	—
531	AGL(1,ℤ/8)	—	5	16	no	—
532	AGL(1,ℤ/8)	—	5	8	no	—
533	AGL(1,ℤ/8)	C₂×C₃×D₅	1	8	yes	complemented
534	#135	—	5	8	no	—
535	#135	—	5	16	no	—
536	C₂×Q₁₆	—	5	1	no	—
537	C₂×SD₁₆	—	5	1	no	—
538	C₂×SD₁₆	—	5	1	no	—
539	C₂×SD₁₆	—	5	2	no	—
540	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
541	C₂×D₈	—	5	2	no	—
542	C₂×D₈	—	5	1	no	—
543	C₂×D₈	—	5	2	no	—
544	C₂×D₈	—	5	8	no	—
545	C₂×D₈	—	5	16	no	—
546	C₂×D₈	—	5	2	no	—
547	C₂×D₈	C₂×C₃×D₅	1	2	yes	complemented
548	#131	—	5	8	no	—
549	C₂×M₁₆	—	5	2	no	—
550	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
551	C₂²×C₈	—	5	1	no	—
552	C₂²×C₈	—	5	2	no	—
553	C₂×C₃×C₅	—	2	2	no	—
554	C₂×C₃×C₅	—	4	2	no	—
555	C₂×C₃×C₅	—	4	4	no	—
556	C₂×C₃×C₅	#576	1	2	yes	complemented
557	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
558	C₃×D₅	—	2	4	no	—
559	C₃×D₅	—	4	4	no	—
560	C₃×D₅	—	4	2	no	—
561	C₂³×C₃	—	2	1	no	—
562	C₂³×C₃	—	2	2	no	—
563	C₂³×C₃	—	2	4	no	—
564	C₂³×C₃	—	5	2	no	—
565	C₂³×C₃	—	8	2	no	—
566	C₂³×C₃	—	10	8	no	—
567	C₂³×C₃	—	10	8	no	—
568	C₂³×C₃	—	10	2	no	—
569	C₂³×C₃	—	10	1	no	—
570	C₂³×C₃	—	10	4	no	—
571	C₂³×C₃	—	40	2	no	—
572	C₂³×C₃	—	40	4	no	—
573	C₂³×C₃	—	40	4	no	—
574	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
575	C₃×Q₈	—	2	1	no	—
576	C₃×Q₈	—	5	4	no	—
577	C₃×Q₈	—	5	2	no	—
578	C₃×Q₈	—	10	1	no	—
579	C₃×Q₈	C₂³×D₅	1	2	yes	—
580	C₃×D₄	—	2	4	no	—
581	C₃×D₄	—	2	2	no	—
582	C₃×D₄	—	2	4	no	—
583	C₃×D₄	—	2	1	no	—
584	C₃×D₄	—	5	8	no	—
585	C₃×D₄	—	5	4	no	—
586	C₃×D₄	—	5	4	no	—
587	C₃×D₄	—	5	2	no	—
588	C₃×D₄	—	10	8	no	—
589	C₃×D₄	—	10	8	no	—
590	C₃×D₄	—	10	8	no	—
591	C₃×D₄	—	10	8	no	—
592	C₃×D₄	—	10	4	no	—
593	C₃×D₄	—	10	4	no	—
594	C₃×D₄	—	10	2	no	—
595	C₃×D₄	—	10	1	no	—
596	C₃×D₄	C₂³×D₅	1	4	yes	—
597	C₃×D₄	C₂³×D₅	1	2	yes	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	4	no	—
600	C₂×C₃×C₄	—	5	2	no	—
601	C₂×C₃×C₄	—	5	4	no	—
602	C₂×C₃×C₄	—	5	4	no	—
603	C₂×C₃×C₄	—	10	8	no	—
604	C₂×C₃×C₄	—	10	8	no	—
605	C₂×C₃×C₄	—	10	1	no	—
606	C₂×C₃×C₄	—	10	4	no	—
607	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
608	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
609	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
610	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
611	C₃×C₈	—	5	2	no	—
612	C₃×C₈	—	5	2	no	—
613	C₃×C₈	C₂³×D₅	1	4	yes	—
614	C₂²×C₅	—	2	2	no	—
615	C₂²×C₅	—	2	4	no	—
616	C₂²×C₅	—	2	2	no	—
617	C₂²×C₅	—	4	2	no	—
618	C₂²×C₅	—	4	4	no	—
619	C₂²×C₅	—	8	4	no	—
620	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
621	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
622	C₂×D₅	—	2	4	no	—
623	C₂×D₅	—	2	4	no	—
624	C₂×D₅	—	2	2	no	—
625	C₂×D₅	—	4	4	no	—
626	C₂×D₅	—	4	2	no	—
627	C₂×D₅	—	8	8	no	—
628	C₂×D₅	—	8	8	no	—
629	C₂×D₅	—	8	4	no	—
630	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
631	C₄×C₅	—	2	2	no	—
632	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
633	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
634	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
635	Dic₅	—	2	2	no	—
636	Dic₅	C₂²×C₃×D₄	1	4	yes	—
637	C₂⁴	—	2	1	no	—
638	C₂⁴	—	10	2	no	—
639	C₂⁴	—	10	2	no	—
640	C₂⁴	—	10	1	no	—
641	#41	—	2	2	no	—
642	#41	—	5	4	no	—
643	#41	—	5	4	no	—
644	#41	—	5	8	no	—
645	#41	—	5	8	no	—
646	#41	—	5	4	no	—
647	#41	—	10	8	no	—
648	#41	—	10	4	no	—
649	#41	—	10	4	no	—
650	#41	—	10	8	no	—
651	#41	—	10	2	no	—
652	#41	C₂²×C₃×D₅	1	4	yes	complemented
653	C₂×Q₈	—	5	1	no	—
654	C₂×Q₈	—	5	1	no	—
655	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	5	2	no	—
660	C₂×D₄	—	5	8	no	—
661	C₂×D₄	—	5	8	no	—
662	C₂×D₄	—	5	1	no	—
663	C₂×D₄	—	5	2	no	—
664	C₂×D₄	—	5	1	no	—
665	C₂×D₄	—	5	4	no	—
666	C₂×D₄	—	10	8	no	—
667	C₂×D₄	—	10	2	no	—
668	C₂×D₄	—	10	4	no	—
669	C₂×D₄	—	10	4	no	—
670	C₂×D₄	—	10	2	no	—
671	C₂×D₄	—	10	2	no	—
672	C₂×D₄	—	10	16	no	—
673	C₂×D₄	—	10	8	no	—
674	C₂×D₄	—	10	16	no	—
675	C₂×D₄	—	10	2	no	—
676	C₂×D₄	—	10	1	no	—
677	C₂×D₄	—	10	1	no	—
678	C₂×D₄	—	10	2	no	—
679	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
680	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
681	C₂×D₄	C₂²×C₃×D₅	1	4	yes	complemented
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	5	2	no	—
684	C₂²×C₄	—	10	2	no	—
685	C₂²×C₄	—	10	2	no	—
686	C₂²×C₄	—	10	1	no	—
687	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
688	Q₁₆	—	5	4	no	—
689	SD₁₆	—	5	4	no	—
690	SD₁₆	—	5	4	no	—
691	SD₁₆	—	5	8	no	—
692	SD₁₆	C₂²×C₃×D₅	1	8	yes	complemented
693	D₈	—	5	8	no	—
694	D₈	—	5	4	no	—
695	D₈	—	5	8	no	—
696	D₈	—	5	8	no	—
697	D₈	C₂²×C₃×D₅	1	8	yes	complemented
698	M₁₆	—	5	8	no	—
699	M₁₆	C₂²×C₃×D₅	1	4	yes	complemented
700	C₂×C₈	—	5	1	no	—
701	C₂×C₈	—	5	1	no	—
702	C₂×C₈	—	5	4	no	—
703	C₂×C₈	—	5	8	no	—
704	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
705	C₃×C₅	C₂×#576	1	1	yes	characteristic, complemented, Hall
706	C₂²×C₃	—	2	2	no	—
707	C₂²×C₃	—	2	2	no	—
708	C₂²×C₃	—	2	4	no	—
709	C₂²×C₃	—	4	4	no	—
710	C₂²×C₃	—	4	2	no	—
711	C₂²×C₃	—	5	4	no	—
712	C₂²×C₃	—	8	4	no	—
713	C₂²×C₃	—	10	4	no	—
714	C₂²×C₃	—	10	4	no	—
715	C₂²×C₃	—	10	2	no	—
716	C₂²×C₃	—	20	4	no	—
717	C₂²×C₃	—	20	2	no	—
718	C₂²×C₃	—	40	4	no	—
719	C₂²×C₃	—	40	8	no	—
720	C₂²×C₃	—	40	8	no	—
721	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
722	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
723	C₃×C₄	—	2	2	no	—
724	C₃×C₄	—	5	4	no	—
725	C₃×C₄	—	10	2	no	—
726	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
727	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
728	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
729	C₂×C₅	—	2	2	no	—
730	C₂×C₅	—	4	2	no	—
731	C₂×C₅	—	4	4	no	—
732	C₂×C₅	C₃×#576	1	2	yes	complemented
733	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
734	D₅	—	2	4	no	—
735	D₅	—	4	4	no	—
736	D₅	—	4	2	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	4	no	—
740	C₂³	—	5	2	no	—
741	C₂³	—	8	2	no	—
742	C₂³	—	10	8	no	—
743	C₂³	—	10	8	no	—
744	C₂³	—	10	2	no	—
745	C₂³	—	10	1	no	—
746	C₂³	—	10	4	no	—
747	C₂³	—	40	2	no	—
748	C₂³	—	40	4	no	—
749	C₂³	—	40	4	no	—
750	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
751	Q₈	—	2	1	no	—
752	Q₈	—	5	4	no	—
753	Q₈	—	5	2	no	—
754	Q₈	—	10	1	no	—
755	Q₈	C₂³×C₃×D₅	1	2	yes	—
756	D₄	—	2	4	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	4	no	—
759	D₄	—	2	1	no	—
760	D₄	—	5	8	no	—
761	D₄	—	5	4	no	—
762	D₄	—	5	4	no	—
763	D₄	—	5	2	no	—
764	D₄	—	10	8	no	—
765	D₄	—	10	8	no	—
766	D₄	—	10	8	no	—
767	D₄	—	10	8	no	—
768	D₄	—	10	4	no	—
769	D₄	—	10	4	no	—
770	D₄	—	10	1	no	—
771	D₄	—	10	2	no	—
772	D₄	C₂³×C₃×D₅	1	4	yes	—
773	D₄	C₂³×C₃×D₅	1	2	yes	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	5	2	no	—
777	C₂×C₄	—	5	4	no	—
778	C₂×C₄	—	5	4	no	—
779	C₂×C₄	—	10	8	no	—
780	C₂×C₄	—	10	8	no	—
781	C₂×C₄	—	10	1	no	—
782	C₂×C₄	—	10	4	no	—
783	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
784	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
785	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
786	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
787	C₈	—	5	2	no	—
788	C₈	—	5	2	no	—
789	C₈	C₂³×C₃×D₅	1	4	yes	—
790	C₂×C₃	—	2	2	no	—
791	C₂×C₃	—	4	4	no	—
792	C₂×C₃	—	4	2	no	—
793	C₂×C₃	—	10	4	no	—
794	C₂×C₃	—	20	4	no	—
795	C₂×C₃	—	20	2	no	—
796	C₂×C₃	#66108	1	2	yes	direct product factor
797	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
798	C₅	C₂×C₃×#576	1	1	yes	characteristic, complemented, Sylow
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	5	4	no	—
805	C₂²	—	8	4	no	—
806	C₂²	—	10	4	no	—
807	C₂²	—	10	4	no	—
808	C₂²	—	10	2	no	—
809	C₂²	—	20	4	no	—
810	C₂²	—	20	2	no	—
811	C₂²	—	40	4	no	—
812	C₂²	—	40	8	no	—
813	C₂²	—	40	8	no	—
814	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
815	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
816	C₄	—	2	2	no	—
817	C₄	—	5	4	no	—
818	C₄	—	10	2	no	—
819	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
820	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
821	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
822	C₃	C₂×#66108	1	1	yes	characteristic, direct product factor, Sylow
823	C₂	—	2	2	no	—
824	C₂	—	4	4	no	—
825	C₂	—	4	2	no	—
826	C₂	—	10	4	no	—
827	C₂	—	20	4	no	—
828	C₂	—	20	2	no	—
829	C₂	C₃×#66108	1	2	yes	direct product factor
830	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×AGL(1,ℤ/8)	D₅
hypocenter	C₅	C₂×C₃×#576
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4149	C₂	semidirect
2. C₂×C₃×#4144	C₂	semidirect
3. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
4. C₂×C₃×#4096	C₂	semidirect
5. C₂²×C₃×#686	C₂	semidirect
6. C₃×#66108	C₂	direct (N × H)
7. C₂×C₃×#4062	C₂	semidirect
8. C₂×C₃×#4060	C₂	semidirect
9. C₂×C₃×#4057	C₂	semidirect
10. C₂×C₃×D₅×D₈	C₂	semidirect
11. C₂×C₃×#4054	C₂	semidirect
12. C₂×C₃×#4053	C₂	semidirect
13. C₂×#66108	C₃	direct (N × H)
14. C₂×C₃×C₅×#41	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₃×#4149	C₂²	semidirect
19. C₂×C₃×#713	C₂²	semidirect
21. C₃×#4144	C₂²	semidirect
23. C₂×C₃×#711	C₂²	semidirect
26. C₂×C₃×D₄×D₅	C₂²	semidirect
27. C₂×C₃×D₄×D₅	C₂²	semidirect
30. C₂×C₃×#709	C₂²	semidirect
32. C₂²×C₃×D₂₀	C₂²	semidirect
33. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
34. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
35. C₂×C₃×C₅×D₈	C₂²	semidirect
36. C₂×C₃×C₅×M₁₆	C₂²	semidirect
37. C₃×#4096	C₂²	semidirect
38. C₂×C₃×#689	C₂²	semidirect
39. C₂×C₃×#688	C₂²	semidirect
40. C₂×C₃×#687	C₂²	semidirect
41. C₂×C₃×#686	C₂²	semidirect
42. C₂×C₃×#686	C₂²	semidirect
43. C₂×C₃×#686	C₂²	semidirect
44. C₂×C₃×#686	C₂²	semidirect
45. C₂²×C₃×#168	C₂²	semidirect
46. C₃×#4062	C₂²	semidirect
47. C₃×#4060	C₂²	semidirect
48. C₃×#4057	C₂²	semidirect
49. C₃×D₅×D₈	C₂²	semidirect
50. C₃×#4054	C₂²	semidirect
51. C₃×#4053	C₂²	semidirect
52. C₂×C₃×D₄₀	C₂²	semidirect
53. C₂×C₃×#677	C₂²	semidirect
54. C₂×C₃×#676	C₂²	semidirect
55. C₂×C₃×C₈×D₅	C₂²	semidirect
57. C₂×#4149	C₂×C₃	semidirect
58. C₂×#4144	C₂×C₃	semidirect
59. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
60. C₂×#4096	C₂×C₃	semidirect
61. C₂²×#686	C₂×C₃	semidirect
62. #66108	C₂×C₃	direct (N × H)
63. C₂×#4062	C₂×C₃	semidirect
64. C₂×#4060	C₂×C₃	semidirect
65. C₂×#4057	C₂×C₃	semidirect
66. C₂×D₅×D₈	C₂×C₃	semidirect
67. C₂×#4054	C₂×C₃	semidirect
68. C₂×#4053	C₂×C₃	semidirect
74. C₃×C₅×#41	C₂³	semidirect
81. C₂×C₃×C₅×D₄	C₂³	semidirect
92. C₃×#713	C₂³	semidirect
95. C₃×#711	C₂³	semidirect
100. C₃×D₄×D₅	C₂³	semidirect
101. C₃×D₄×D₅	C₂³	semidirect
106. C₃×#709	C₂³	semidirect
114. C₂×C₃×D₂₀	C₂³	semidirect
120. C₃×C₅×SD₁₆	C₂³	semidirect
121. C₃×C₅×D₈	C₂³	semidirect
122. C₃×C₅×M₁₆	C₂³	semidirect
124. C₃×#689	C₂³	semidirect
125. C₃×#688	C₂³	semidirect
126. C₃×#687	C₂³	semidirect
127. C₃×#686	C₂³	semidirect
128. C₃×#686	C₂³	semidirect
129. C₃×#686	C₂³	semidirect
132. C₂×C₃×#168	C₂³	semidirect
133. C₃×D₄₀	C₂³	semidirect
134. C₃×#677	C₂³	semidirect
135. C₃×#676	C₂³	semidirect
136. C₃×C₈×D₅	C₂³	semidirect
143. C₂×C₃×AGL(1,ℤ/8)	D₅	semidirect
149. C₂×C₅×#41	C₂²×C₃	semidirect
150. C₂²×C₅×D₄	C₂²×C₃	semidirect
153. #4149	C₂²×C₃	semidirect
154. C₂×#713	C₂²×C₃	semidirect
156. #4144	C₂²×C₃	semidirect
158. C₂×#711	C₂²×C₃	semidirect
161. C₂×D₄×D₅	C₂²×C₃	semidirect
162. C₂×D₄×D₅	C₂²×C₃	semidirect
165. C₂×#709	C₂²×C₃	semidirect
167. C₂²×D₂₀	C₂²×C₃	semidirect
168. C₅×AGL(1,ℤ/8)	C₂²×C₃	semidirect
169. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
170. C₂×C₅×D₈	C₂²×C₃	semidirect
171. C₂×C₅×M₁₆	C₂²×C₃	semidirect
172. #4096	C₂²×C₃	semidirect
173. C₂×#689	C₂²×C₃	semidirect
174. C₂×#688	C₂²×C₃	semidirect
175. C₂×#687	C₂²×C₃	semidirect
176. C₂×#686	C₂²×C₃	semidirect
177. C₂×#686	C₂²×C₃	semidirect
178. C₂×#686	C₂²×C₃	semidirect
179. C₂×#686	C₂²×C₃	semidirect
180. C₂²×#168	C₂²×C₃	semidirect
181. #4062	C₂²×C₃	semidirect
182. #4060	C₂²×C₃	semidirect
183. #4057	C₂²×C₃	semidirect
184. D₅×D₈	C₂²×C₃	semidirect
185. #4054	C₂²×C₃	semidirect
186. #4053	C₂²×C₃	semidirect
187. C₂×D₄₀	C₂²×C₃	semidirect
188. C₂×#677	C₂²×C₃	semidirect
189. C₂×#676	C₂²×C₃	semidirect
190. C₂×C₈×D₅	C₂²×C₃	semidirect
255. C₂×C₃×#41	C₂×D₅	semidirect
263. C₂²×C₃×D₄	C₂×D₅	semidirect
267. C₃×AGL(1,ℤ/8)	C₂×D₅	semidirect
274. C₂×C₃×SD₁₆	C₂×D₅	semidirect
281. C₂×C₃×D₈	C₂×D₅	semidirect
284. C₂×C₃×M₁₆	C₂×D₅	semidirect
292. C₅×#41	C₂³×C₃	semidirect
299. C₂×C₅×D₄	C₂³×C₃	semidirect
310. #713	C₂³×C₃	semidirect
313. #711	C₂³×C₃	semidirect
318. D₄×D₅	C₂³×C₃	semidirect
319. D₄×D₅	C₂³×C₃	semidirect
324. #709	C₂³×C₃	semidirect
332. C₂×D₂₀	C₂³×C₃	semidirect
338. C₅×SD₁₆	C₂³×C₃	semidirect
339. C₅×D₈	C₂³×C₃	semidirect
340. C₅×M₁₆	C₂³×C₃	semidirect
342. #689	C₂³×C₃	semidirect
343. #688	C₂³×C₃	semidirect
344. #687	C₂³×C₃	semidirect
345. #686	C₂³×C₃	semidirect
346. #686	C₂³×C₃	semidirect
347. #686	C₂³×C₃	semidirect
350. C₂×#168	C₂³×C₃	semidirect
351. D₄₀	C₂³×C₃	semidirect
352. #677	C₂³×C₃	semidirect
353. #676	C₂³×C₃	semidirect
354. C₈×D₅	C₂³×C₃	semidirect
361. C₂×AGL(1,ℤ/8)	C₃×D₅	semidirect
405. C₃×#41	C₂²×D₅	semidirect
434. C₂×C₃×D₄	C₂²×D₅	semidirect
445. C₃×SD₁₆	C₂²×D₅	semidirect
450. C₃×D₈	C₂²×D₅	semidirect
452. C₃×M₁₆	C₂²×D₅	semidirect
521. C₂×#41	C₂×C₃×D₅	semidirect
529. C₂²×D₄	C₂×C₃×D₅	semidirect
533. AGL(1,ℤ/8)	C₂×C₃×D₅	semidirect
540. C₂×SD₁₆	C₂×C₃×D₅	semidirect
547. C₂×D₈	C₂×C₃×D₅	semidirect
550. C₂×M₁₆	C₂×C₃×D₅	semidirect
556. C₂×C₃×C₅	#576	semidirect
652. #41	C₂²×C₃×D₅	semidirect
681. C₂×D₄	C₂²×C₃×D₅	semidirect
692. SD₁₆	C₂²×C₃×D₅	semidirect
697. D₈	C₂²×C₃×D₅	semidirect
699. M₁₆	C₂²×C₃×D₅	semidirect
705. C₃×C₅	C₂×#576	semidirect
732. C₂×C₅	C₃×#576	semidirect
796. C₂×C₃	#66108	direct (N × H)
798. C₅	C₂×C₃×#576	semidirect
822. C₃	C₂×#66108	direct (N × H)
829. C₂	C₃×#66108	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4149	2
C₂×C₃×#4144	2
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₂×C₃×#4096	2
C₂²×C₃×#686	2
C₃×#66108	2
C₂×C₃×#4062	2
C₂×C₃×#4060	2
C₂×C₃×#4057	2
C₂×C₃×D₅×D₈	2
C₂×C₃×#4054	2
C₂×C₃×#4053	2
C₂×#66108	3
C₂×C₃×#576	5

Subgroups — C2×C3×#66108 #14509961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66108 #14509961