Subgroups — C₂×C₃×#66109 #14510031

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4150	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×#687	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66109	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4061	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×D₅×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4058	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4057	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#4055	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#66109	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
16	C₂²×C₃×C₂²⋊D₅	—	2	2	no	—
17	C₃×#4150	—	2	4	no	—
18	C₃×#4150	C₂²	1	8	yes	complemented
19	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	complemented
20	C₃×#4144	—	2	4	no	—
21	C₃×#4144	C₂²	1	8	yes	complemented
22	C₂×C₃×#711	—	2	2	no	—
23	C₂×C₃×#711	—	2	1	no	—
24	C₂×C₃×#711	C₂²	1	2	yes	—
25	C₂×C₃×#711	C₂²	1	2	yes	complemented
26	C₂×C₃×D₄×D₅	—	2	1	no	—
27	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
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
31	C₂²×C₃×Dic₁₀	—	2	1	no	—
32	C₂²×C₃×Dic₁₀	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	2	yes	complemented
41	C₂×C₃×#687	C₂²	1	2	yes	complemented
42	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×#687	C₂²	1	8	yes	complemented
44	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₃×#168	C₂²	1	1	yes	characteristic, complemented
46	C₃×#4061	C₂²	1	16	yes	complemented
47	C₃×D₅×SD₁₆	C₂²	1	16	yes	complemented
48	C₃×#4058	C₂²	1	16	yes	complemented
49	C₃×#4057	C₂²	1	16	yes	complemented
50	C₃×#4055	C₂²	1	8	yes	complemented
51	C₃×#4053	C₂²	1	8	yes	complemented
52	C₂×C₃×Dic₂₀	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×#577	—	5	1	no	maximal, Hall
57	C₂×#4150	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×#687	C₂×C₃	1	1	yes	characteristic, complemented
62	#66109	C₂×C₃	1	16	yes	direct product factor
63	C₂×#4061	C₂×C₃	1	2	yes	complemented
64	C₂×D₅×SD₁₆	C₂×C₃	1	2	yes	complemented
65	C₂×#4058	C₂×C₃	1	2	yes	complemented
66	C₂×#4057	C₂×C₃	1	2	yes	complemented
67	C₂×#4055	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	2	no	—
71	C₃×C₅×#41	—	2	2	no	—
72	C₃×C₅×#41	C₂³	1	4	yes	complemented
73	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×D₄	—	2	1	no	—
75	C₂×C₃×C₅×D₄	—	2	1	no	—
76	C₂×C₃×C₅×D₄	—	2	2	no	—
77	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
79	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
80	C₂²×C₃×C₄×C₅	—	2	1	no	—
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
83	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
84	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
85	C₂×C₃×C₂²⋊D₅	—	2	16	no	—
86	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
87	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
88	C₂²×C₃×Dic₅	—	2	1	no	—
89	C₂²×C₃×Dic₅	—	2	2	no	—
90	C₂²×C₃×Dic₅	—	2	2	no	—
91	C₃×Q₈×D₅	—	2	4	no	—
92	C₃×Q₈×D₅	C₂³	1	8	yes	complemented
93	C₃×#711	—	2	16	no	—
94	C₃×#711	—	2	4	no	—
95	C₃×#711	—	2	4	no	—
96	C₃×#711	—	2	8	no	—
97	C₃×#711	C₂³	1	8	yes	—
98	C₃×#711	C₂³	1	8	yes	complemented
99	C₃×D₄×D₅	—	2	8	no	—
100	C₃×D₄×D₅	—	2	4	no	—
101	C₃×D₄×D₅	C₂³	1	8	yes	—
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	—
107	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
108	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₄×D₅	—	2	2	no	—
110	C₂×C₃×C₄×D₅	—	2	1	no	—
111	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
112	C₂×C₃×Dic₁₀	—	2	1	no	—
113	C₂×C₃×Dic₁₀	—	2	2	no	—
114	C₂×C₃×Dic₁₀	—	2	2	no	—
115	C₂×C₃×Dic₁₀	—	2	8	no	—
116	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
117	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
118	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
119	C₂×C₃×Dic₁₀	C₂³	1	4	yes	complemented
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	8	yes	complemented
127	C₃×#687	C₂³	1	8	yes	complemented
128	C₃×#687	C₂³	1	4	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×Dic₂₀	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×C₃×2₋¹⁺⁴	—	5	1	no	—
138	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
139	C₃×#577	—	5	16	no	—
140	C₂×C₃×#137	—	5	2	no	—
141	C₂×C₃×#137	—	5	1	no	—
142	C₂×C₃×AGL(1,ℤ/8)	—	5	2	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×SD₁₆	—	5	1	no	—
147	C₂²×C₃×SD₁₆	—	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
151	C₂²×C₂²⋊D₅	—	2	2	no	—
152	#4150	—	2	4	no	—
153	#4150	C₂²×C₃	1	8	yes	complemented
154	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	complemented
155	#4144	—	2	4	no	—
156	#4144	C₂²×C₃	1	8	yes	complemented
157	C₂×#711	—	2	2	no	—
158	C₂×#711	—	2	1	no	—
159	C₂×#711	C₂²×C₃	1	2	yes	—
160	C₂×#711	C₂²×C₃	1	2	yes	complemented
161	C₂×D₄×D₅	—	2	1	no	—
162	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
163	C₂×#709	—	2	1	no	—
164	C₂×#709	C₂²×C₃	1	1	yes	characteristic
165	C₂×#709	C₂²×C₃	1	1	yes	characteristic
166	C₂²×Dic₁₀	—	2	1	no	—
167	C₂²×Dic₁₀	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	2	yes	complemented
176	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₂×#687	C₂²×C₃	1	2	yes	complemented
178	C₂×#687	C₂²×C₃	1	8	yes	complemented
179	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
180	C₂²×#168	C₂²×C₃	1	1	yes	characteristic, complemented
181	#4061	C₂²×C₃	1	16	yes	complemented
182	D₅×SD₁₆	C₂²×C₃	1	16	yes	complemented
183	#4058	C₂²×C₃	1	16	yes	complemented
184	#4057	C₂²×C₃	1	16	yes	complemented
185	#4055	C₂²×C₃	1	8	yes	complemented
186	#4053	C₂²×C₃	1	8	yes	complemented
187	C₂×Dic₂₀	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×#577	—	5	1	no	Sylow
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	—	2	2	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	1	no	—
198	C₂²×C₃×D₅	—	2	8	no	—
199	C₂²×C₃×D₅	—	8	4	no	—
200	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
201	C₃×C₅×Q₈	—	2	1	no	—
202	C₃×C₅×Q₈	C₂⁴	1	2	yes	—
203	C₃×C₅×D₄	—	2	4	no	—
204	C₃×C₅×D₄	—	2	2	no	—
205	C₃×C₅×D₄	—	2	4	no	—
206	C₃×C₅×D₄	—	2	1	no	—
207	C₃×C₅×D₄	C₂⁴	1	2	yes	—
208	C₃×C₅×D₄	C₂⁴	1	4	yes	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	4	no	—
211	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
212	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
213	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
215	C₃×C₂²⋊D₅	—	2	4	no	—
216	C₃×C₂²⋊D₅	—	2	8	no	—
217	C₃×C₂²⋊D₅	—	2	8	no	—
218	C₃×C₂²⋊D₅	—	2	8	no	—
219	C₃×C₂²⋊D₅	C₂×D₄	1	8	yes	—
220	C₂×C₃×Dic₅	—	2	2	no	—
221	C₂×C₃×Dic₅	—	2	4	no	—
222	C₂×C₃×Dic₅	—	2	1	no	—
223	C₂×C₃×Dic₅	—	2	8	no	—
224	C₂×C₃×Dic₅	—	2	8	no	—
225	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
226	C₃×D₂₀	—	2	1	no	—
227	C₃×D₂₀	C₂×D₄	1	4	yes	—
228	C₃×D₂₀	C₂⁴	1	2	yes	—
229	C₃×C₄×D₅	—	2	8	no	—
230	C₃×C₄×D₅	—	2	4	no	—
231	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
232	C₃×C₄×D₅	C₂⁴	1	4	yes	—
233	C₃×Dic₁₀	—	2	4	no	—
234	C₃×Dic₁₀	—	2	2	no	—
235	C₃×Dic₁₀	—	2	1	no	—
236	C₃×Dic₁₀	—	2	8	no	—
237	C₃×Dic₁₀	C₂×D₄	1	4	yes	—
238	C₃×Dic₁₀	C₂⁴	1	4	yes	—
239	C₃×Dic₁₀	C₂⁴	1	2	yes	—
240	C₃×C₅×C₈	C₂⁴	1	4	yes	—
241	C₃×#168	C₂⁴	1	2	yes	—
242	C₃×#168	C₂⁴	1	2	yes	—
243	C₃×2₋¹⁺⁴	—	5	8	no	—
244	C₃×2₋¹⁺⁴	—	10	4	no	—
245	C₃×H(5,𝔽₂)	—	5	8	no	—
246	C₃×H(5,𝔽₂)	—	10	4	no	—
247	C₂×C₃×#41	—	5	1	no	—
248	C₂×C₃×#41	—	5	2	no	—
249	C₂×C₃×#41	—	5	2	no	—
250	C₂×C₃×#41	—	5	1	no	—
251	C₂×C₃×#41	—	10	1	no	—
252	C₂×C₃×#41	—	10	2	no	—
253	C₂×C₃×#41	—	10	1	no	—
254	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic, complemented
255	C₂²×C₃×Q₈	—	5	2	no	—
256	C₂²×C₃×Q₈	—	5	1	no	—
257	C₂²×C₃×Q₈	—	10	1	no	—
258	C₂²×C₃×D₄	—	5	2	no	—
259	C₂²×C₃×D₄	—	10	1	no	—
260	C₂²×C₃×D₄	—	10	2	no	—
261	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
262	C₃×#137	—	5	16	no	—
263	C₃×#137	—	5	8	no	—
264	C₃×AGL(1,ℤ/8)	—	5	16	no	—
265	C₃×AGL(1,ℤ/8)	C₂×D₅	1	8	yes	complemented
266	C₃×#135	—	5	8	no	—
267	C₃×#135	—	5	16	no	—
268	C₂×C₃×Q₁₆	—	5	1	no	—
269	C₂×C₃×Q₁₆	—	5	2	no	—
270	C₂×C₃×SD₁₆	—	5	1	no	—
271	C₂×C₃×SD₁₆	—	5	2	no	—
272	C₂×C₃×SD₁₆	—	5	2	no	—
273	C₂×C₃×SD₁₆	—	5	8	no	—
274	C₂×C₃×SD₁₆	—	5	1	no	—
275	C₂×C₃×SD₁₆	—	5	16	no	—
276	C₂×C₃×SD₁₆	—	5	2	no	—
277	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
278	C₂×C₃×D₈	—	5	1	no	—
279	C₂×C₃×D₈	C₂×D₅	1	2	yes	complemented
280	C₃×#131	—	5	8	no	—
281	C₂×C₃×M₁₆	—	5	2	no	—
282	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
283	C₂²×C₃×C₈	—	5	1	no	—
284	C₂²×C₃×C₈	—	5	2	no	—
285	C₂⁴×C₅	—	2	1	no	—
286	C₂³×D₅	—	2	2	no	—
287	C₅×#41	—	2	2	no	—
288	C₅×#41	C₂³×C₃	1	4	yes	complemented
289	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₅×D₄	—	2	1	no	—
291	C₂×C₅×D₄	—	2	1	no	—
292	C₂×C₅×D₄	—	2	2	no	—
293	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
295	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
296	C₂²×C₄×C₅	—	2	1	no	—
297	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₂²⋊D₅	—	2	1	no	—
299	C₂×C₂²⋊D₅	—	2	2	no	—
300	C₂×C₂²⋊D₅	—	2	2	no	—
301	C₂×C₂²⋊D₅	—	2	16	no	—
302	C₂×C₂²⋊D₅	—	2	2	no	—
303	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
304	C₂²×Dic₅	—	2	1	no	—
305	C₂²×Dic₅	—	2	2	no	—
306	C₂²×Dic₅	—	2	2	no	—
307	Q₈×D₅	—	2	4	no	—
308	Q₈×D₅	C₂³×C₃	1	8	yes	complemented
309	#711	—	2	16	no	—
310	#711	—	2	4	no	—
311	#711	—	2	4	no	—
312	#711	—	2	8	no	—
313	#711	C₂³×C₃	1	8	yes	—
314	#711	C₂³×C₃	1	8	yes	complemented
315	D₄×D₅	—	2	8	no	—
316	D₄×D₅	—	2	4	no	—
317	D₄×D₅	C₂³×C₃	1	8	yes	—
318	#709	—	2	2	no	—
319	#709	—	2	8	no	—
320	#709	C₃×D₄	1	4	yes	—
321	#709	C₂³×C₃	1	4	yes	—
322	#709	C₂³×C₃	1	4	yes	—
323	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
324	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
325	C₂×C₄×D₅	—	2	2	no	—
326	C₂×C₄×D₅	—	2	1	no	—
327	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
328	C₂×Dic₁₀	—	2	1	no	—
329	C₂×Dic₁₀	—	2	2	no	—
330	C₂×Dic₁₀	—	2	2	no	—
331	C₂×Dic₁₀	—	2	8	no	—
332	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
333	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
334	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
335	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
336	C₅×SD₁₆	C₂³×C₃	1	8	yes	complemented
337	C₅×D₈	C₂³×C₃	1	8	yes	complemented
338	C₅×M₁₆	C₂³×C₃	1	4	yes	complemented
339	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
340	#689	C₂³×C₃	1	4	yes	complemented
341	#688	C₂³×C₃	1	4	yes	complemented
342	#687	C₂³×C₃	1	4	yes	complemented
343	#687	C₂³×C₃	1	8	yes	complemented
344	#687	C₂³×C₃	1	8	yes	complemented
345	#686	C₂³×C₃	1	4	yes	complemented
346	C₂×#168	C₂³×C₃	1	1	yes	characteristic
347	C₂×#168	C₂³×C₃	1	1	yes	characteristic
348	C₂×#168	C₂³×C₃	1	4	yes	complemented
349	Dic₂₀	C₂³×C₃	1	8	yes	complemented
350	#677	C₂³×C₃	1	8	yes	complemented
351	#676	C₂³×C₃	1	8	yes	complemented
352	C₈×D₅	C₂³×C₃	1	8	yes	complemented
353	C₂×2₋¹⁺⁴	—	5	1	no	—
354	C₂×H(5,𝔽₂)	—	5	1	no	—
355	#577	—	5	16	no	—
356	C₂×#137	—	5	2	no	—
357	C₂×#137	—	5	1	no	—
358	C₂×AGL(1,ℤ/8)	—	5	2	no	—
359	C₂×AGL(1,ℤ/8)	C₃×D₅	1	1	yes	characteristic, complemented
360	C₂×#135	—	5	1	no	—
361	C₂×#135	—	5	2	no	—
362	C₂²×SD₁₆	—	5	1	no	—
363	C₂²×SD₁₆	—	5	2	no	—
364	C₂×#131	—	5	1	no	—
365	C₂²×C₃×C₅	—	2	2	no	—
366	C₂²×C₃×C₅	—	2	2	no	—
367	C₂²×C₃×C₅	—	2	4	no	—
368	C₂²×C₃×C₅	—	4	4	no	—
369	C₂²×C₃×C₅	—	4	2	no	—
370	C₂²×C₃×C₅	—	8	4	no	—
371	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
372	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₃×D₅	—	2	4	no	—
374	C₂×C₃×D₅	—	2	2	no	—
375	C₂×C₃×D₅	—	4	2	no	—
376	C₂×C₃×D₅	—	8	8	no	—
377	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
378	C₃×C₄×C₅	—	2	2	no	—
379	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
380	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
381	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
382	C₃×Dic₅	—	2	4	no	—
383	C₃×Dic₅	—	2	2	no	—
384	C₃×Dic₅	C₂²×D₄	1	4	yes	—
385	C₂⁴×C₃	—	2	1	no	—
386	C₂⁴×C₃	—	10	2	no	—
387	C₃×#41	—	2	2	no	—
388	C₃×#41	—	5	4	no	—
389	C₃×#41	—	5	4	no	—
390	C₃×#41	—	5	8	no	—
391	C₃×#41	—	5	8	no	—
392	C₃×#41	—	5	4	no	—
393	C₃×#41	—	10	8	no	—
394	C₃×#41	—	10	4	no	—
395	C₃×#41	—	10	4	no	—
396	C₃×#41	—	10	16	no	—
397	C₃×#41	—	10	8	no	—
398	C₃×#41	—	10	2	no	—
399	C₃×#41	C₂²×D₅	1	4	yes	complemented
400	C₂×C₃×Q₈	—	5	1	no	—
401	C₂×C₃×Q₈	—	5	8	no	—
402	C₂×C₃×Q₈	—	5	2	no	—
403	C₂×C₃×Q₈	—	5	1	no	—
404	C₂×C₃×Q₈	—	5	4	no	—
405	C₂×C₃×Q₈	—	10	2	no	—
406	C₂×C₃×Q₈	—	10	8	no	—
407	C₂×C₃×Q₈	—	10	4	no	—
408	C₂×C₃×Q₈	—	10	1	no	—
409	C₂×C₃×Q₈	—	10	2	no	—
410	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
411	C₂×C₃×D₄	—	2	1	no	—
412	C₂×C₃×D₄	—	2	1	no	—
413	C₂×C₃×D₄	—	2	2	no	—
414	C₂×C₃×D₄	—	5	2	no	—
415	C₂×C₃×D₄	—	5	8	no	—
416	C₂×C₃×D₄	—	5	1	no	—
417	C₂×C₃×D₄	—	5	1	no	—
418	C₂×C₃×D₄	—	10	4	no	—
419	C₂×C₃×D₄	—	10	2	no	—
420	C₂×C₃×D₄	—	10	8	no	—
421	C₂×C₃×D₄	—	10	16	no	—
422	C₂×C₃×D₄	—	10	2	no	—
423	C₂×C₃×D₄	—	10	2	no	—
424	C₂×C₃×D₄	—	10	1	no	—
425	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
426	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
427	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
428	C₂²×C₃×C₄	—	2	1	no	—
429	C₂²×C₃×C₄	—	5	2	no	—
430	C₂²×C₃×C₄	—	10	2	no	—
431	C₂²×C₃×C₄	—	10	2	no	—
432	C₂²×C₃×C₄	—	10	2	no	—
433	C₂²×C₃×C₄	—	10	1	no	—
434	C₂²×C₃×C₄	—	10	1	no	—
435	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
436	C₃×Q₁₆	—	5	4	no	—
437	C₃×Q₁₆	—	5	8	no	—
438	C₃×SD₁₆	—	5	4	no	—
439	C₃×SD₁₆	—	5	8	no	—
440	C₃×SD₁₆	—	5	8	no	—
441	C₃×SD₁₆	—	5	4	no	—
442	C₃×SD₁₆	—	5	8	no	—
443	C₃×SD₁₆	C₂²×D₅	1	8	yes	complemented
444	C₃×D₈	—	5	4	no	—
445	C₃×D₈	C₂²×D₅	1	8	yes	complemented
446	C₃×M₁₆	—	5	8	no	—
447	C₃×M₁₆	C₂²×D₅	1	4	yes	complemented
448	C₂×C₃×C₈	—	5	1	no	—
449	C₂×C₃×C₈	—	5	1	no	—
450	C₂×C₃×C₈	—	5	4	no	—
451	C₂×C₃×C₈	—	5	8	no	—
452	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
453	C₂³×C₅	—	2	1	no	—
454	C₂³×C₅	—	2	2	no	—
455	C₂³×C₅	—	2	4	no	—
456	C₂³×C₅	—	8	2	no	—
457	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
458	C₂²×D₅	—	2	1	no	—
459	C₂²×D₅	—	2	8	no	—
460	C₂²×D₅	—	8	4	no	—
461	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
462	C₅×Q₈	—	2	1	no	—
463	C₅×Q₈	C₂⁴×C₃	1	2	yes	—
464	C₅×D₄	—	2	4	no	—
465	C₅×D₄	—	2	2	no	—
466	C₅×D₄	—	2	4	no	—
467	C₅×D₄	—	2	1	no	—
468	C₅×D₄	C₂⁴×C₃	1	2	yes	—
469	C₅×D₄	C₂⁴×C₃	1	4	yes	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	2	4	no	—
472	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
473	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
474	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
475	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
476	C₂²⋊D₅	—	2	4	no	—
477	C₂²⋊D₅	—	2	8	no	—
478	C₂²⋊D₅	—	2	8	no	—
479	C₂²⋊D₅	—	2	8	no	—
480	C₂²⋊D₅	C₂×C₃×D₄	1	8	yes	—
481	C₂×Dic₅	—	2	2	no	—
482	C₂×Dic₅	—	2	4	no	—
483	C₂×Dic₅	—	2	1	no	—
484	C₂×Dic₅	—	2	8	no	—
485	C₂×Dic₅	—	2	8	no	—
486	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
487	D₂₀	—	2	1	no	—
488	D₂₀	C₂×C₃×D₄	1	4	yes	—
489	D₂₀	C₂⁴×C₃	1	2	yes	—
490	C₄×D₅	—	2	8	no	—
491	C₄×D₅	—	2	4	no	—
492	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
493	C₄×D₅	C₂⁴×C₃	1	4	yes	—
494	Dic₁₀	—	2	4	no	—
495	Dic₁₀	—	2	2	no	—
496	Dic₁₀	—	2	1	no	—
497	Dic₁₀	—	2	8	no	—
498	Dic₁₀	C₂×C₃×D₄	1	4	yes	—
499	Dic₁₀	C₂⁴×C₃	1	4	yes	—
500	Dic₁₀	C₂⁴×C₃	1	2	yes	—
501	C₅×C₈	C₂⁴×C₃	1	4	yes	—
502	#168	C₂⁴×C₃	1	2	yes	—
503	#168	C₂⁴×C₃	1	2	yes	—
504	2₋¹⁺⁴	—	5	8	no	—
505	2₋¹⁺⁴	—	10	4	no	—
506	H(5,𝔽₂)	—	5	8	no	—
507	H(5,𝔽₂)	—	10	4	no	—
508	C₂×#41	—	5	1	no	—
509	C₂×#41	—	5	2	no	—
510	C₂×#41	—	5	2	no	—
511	C₂×#41	—	5	1	no	—
512	C₂×#41	—	10	1	no	—
513	C₂×#41	—	10	2	no	—
514	C₂×#41	—	10	1	no	—
515	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic, complemented
516	C₂²×Q₈	—	5	2	no	—
517	C₂²×Q₈	—	5	1	no	—
518	C₂²×Q₈	—	10	1	no	—
519	C₂²×D₄	—	5	2	no	—
520	C₂²×D₄	—	10	1	no	—
521	C₂²×D₄	—	10	2	no	—
522	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
523	#137	—	5	16	no	—
524	#137	—	5	8	no	—
525	AGL(1,ℤ/8)	—	5	16	no	—
526	AGL(1,ℤ/8)	C₂×C₃×D₅	1	8	yes	complemented
527	#135	—	5	8	no	—
528	#135	—	5	16	no	—
529	C₂×Q₁₆	—	5	1	no	—
530	C₂×Q₁₆	—	5	2	no	—
531	C₂×SD₁₆	—	5	1	no	—
532	C₂×SD₁₆	—	5	2	no	—
533	C₂×SD₁₆	—	5	2	no	—
534	C₂×SD₁₆	—	5	8	no	—
535	C₂×SD₁₆	—	5	1	no	—
536	C₂×SD₁₆	—	5	16	no	—
537	C₂×SD₁₆	—	5	2	no	—
538	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
539	C₂×D₈	—	5	1	no	—
540	C₂×D₈	C₂×C₃×D₅	1	2	yes	complemented
541	#131	—	5	8	no	—
542	C₂×M₁₆	—	5	2	no	—
543	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
544	C₂²×C₈	—	5	1	no	—
545	C₂²×C₈	—	5	2	no	—
546	C₂×C₃×C₅	—	2	2	no	—
547	C₂×C₃×C₅	—	4	4	no	—
548	C₂×C₃×C₅	—	4	2	no	—
549	C₂×C₃×C₅	#577	1	2	yes	complemented
550	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
551	C₃×D₅	—	2	4	no	—
552	C₃×D₅	—	4	2	no	—
553	C₂³×C₃	—	2	1	no	—
554	C₂³×C₃	—	2	2	no	—
555	C₂³×C₃	—	2	4	no	—
556	C₂³×C₃	—	5	2	no	—
557	C₂³×C₃	—	8	2	no	—
558	C₂³×C₃	—	10	8	no	—
559	C₂³×C₃	—	10	1	no	—
560	C₂³×C₃	—	40	4	no	—
561	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
562	C₃×Q₈	—	2	1	no	—
563	C₃×Q₈	—	5	4	no	—
564	C₃×Q₈	—	5	4	no	—
565	C₃×Q₈	—	5	2	no	—
566	C₃×Q₈	—	10	8	no	—
567	C₃×Q₈	—	10	4	no	—
568	C₃×Q₈	—	10	2	no	—
569	C₃×Q₈	—	10	1	no	—
570	C₃×Q₈	C₂³×D₅	1	2	yes	—
571	C₃×D₄	—	2	4	no	—
572	C₃×D₄	—	2	4	no	—
573	C₃×D₄	—	2	2	no	—
574	C₃×D₄	—	2	1	no	—
575	C₃×D₄	—	5	8	no	—
576	C₃×D₄	—	5	4	no	—
577	C₃×D₄	—	5	2	no	—
578	C₃×D₄	—	10	8	no	—
579	C₃×D₄	—	10	8	no	—
580	C₃×D₄	—	10	8	no	—
581	C₃×D₄	—	10	4	no	—
582	C₃×D₄	—	10	1	no	—
583	C₃×D₄	C₂³×D₅	1	2	yes	—
584	C₃×D₄	C₂³×D₅	1	4	yes	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	4	no	—
587	C₂×C₃×C₄	—	5	2	no	—
588	C₂×C₃×C₄	—	5	4	no	—
589	C₂×C₃×C₄	—	5	4	no	—
590	C₂×C₃×C₄	—	10	8	no	—
591	C₂×C₃×C₄	—	10	8	no	—
592	C₂×C₃×C₄	—	10	8	no	—
593	C₂×C₃×C₄	—	10	4	no	—
594	C₂×C₃×C₄	—	10	1	no	—
595	C₂×C₃×C₄	—	10	2	no	—
596	C₂×C₃×C₄	—	10	4	no	—
597	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
598	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
599	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
600	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
601	C₃×C₈	—	5	2	no	—
602	C₃×C₈	—	5	2	no	—
603	C₃×C₈	C₂³×D₅	1	4	yes	—
604	C₂²×C₅	—	2	2	no	—
605	C₂²×C₅	—	2	2	no	—
606	C₂²×C₅	—	2	4	no	—
607	C₂²×C₅	—	4	4	no	—
608	C₂²×C₅	—	4	2	no	—
609	C₂²×C₅	—	8	4	no	—
610	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
611	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
612	C₂×D₅	—	2	4	no	—
613	C₂×D₅	—	2	2	no	—
614	C₂×D₅	—	4	2	no	—
615	C₂×D₅	—	8	8	no	—
616	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
617	C₄×C₅	—	2	2	no	—
618	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
619	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
620	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
621	Dic₅	—	2	4	no	—
622	Dic₅	—	2	2	no	—
623	Dic₅	C₂²×C₃×D₄	1	4	yes	—
624	C₂⁴	—	2	1	no	—
625	C₂⁴	—	10	2	no	—
626	#41	—	2	2	no	—
627	#41	—	5	4	no	—
628	#41	—	5	4	no	—
629	#41	—	5	8	no	—
630	#41	—	5	8	no	—
631	#41	—	5	4	no	—
632	#41	—	10	8	no	—
633	#41	—	10	4	no	—
634	#41	—	10	4	no	—
635	#41	—	10	16	no	—
636	#41	—	10	8	no	—
637	#41	—	10	2	no	—
638	#41	C₂²×C₃×D₅	1	4	yes	complemented
639	C₂×Q₈	—	5	1	no	—
640	C₂×Q₈	—	5	8	no	—
641	C₂×Q₈	—	5	2	no	—
642	C₂×Q₈	—	5	4	no	—
643	C₂×Q₈	—	5	1	no	—
644	C₂×Q₈	—	10	2	no	—
645	C₂×Q₈	—	10	8	no	—
646	C₂×Q₈	—	10	4	no	—
647	C₂×Q₈	—	10	1	no	—
648	C₂×Q₈	—	10	2	no	—
649	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	5	2	no	—
654	C₂×D₄	—	5	8	no	—
655	C₂×D₄	—	5	1	no	—
656	C₂×D₄	—	5	1	no	—
657	C₂×D₄	—	10	4	no	—
658	C₂×D₄	—	10	2	no	—
659	C₂×D₄	—	10	8	no	—
660	C₂×D₄	—	10	16	no	—
661	C₂×D₄	—	10	2	no	—
662	C₂×D₄	—	10	2	no	—
663	C₂×D₄	—	10	1	no	—
664	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
665	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
666	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	5	2	no	—
669	C₂²×C₄	—	10	2	no	—
670	C₂²×C₄	—	10	2	no	—
671	C₂²×C₄	—	10	2	no	—
672	C₂²×C₄	—	10	1	no	—
673	C₂²×C₄	—	10	1	no	—
674	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
675	Q₁₆	—	5	4	no	—
676	Q₁₆	—	5	8	no	—
677	SD₁₆	—	5	4	no	—
678	SD₁₆	—	5	8	no	—
679	SD₁₆	—	5	8	no	—
680	SD₁₆	—	5	4	no	—
681	SD₁₆	—	5	8	no	—
682	SD₁₆	C₂²×C₃×D₅	1	8	yes	complemented
683	D₈	—	5	4	no	—
684	D₈	C₂²×C₃×D₅	1	8	yes	complemented
685	M₁₆	—	5	8	no	—
686	M₁₆	C₂²×C₃×D₅	1	4	yes	complemented
687	C₂×C₈	—	5	1	no	—
688	C₂×C₈	—	5	1	no	—
689	C₂×C₈	—	5	4	no	—
690	C₂×C₈	—	5	8	no	—
691	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
692	C₃×C₅	C₂×#577	1	1	yes	characteristic, complemented, Hall
693	C₂²×C₃	—	2	2	no	—
694	C₂²×C₃	—	2	2	no	—
695	C₂²×C₃	—	2	4	no	—
696	C₂²×C₃	—	4	2	no	—
697	C₂²×C₃	—	4	4	no	—
698	C₂²×C₃	—	5	4	no	—
699	C₂²×C₃	—	8	4	no	—
700	C₂²×C₃	—	10	4	no	—
701	C₂²×C₃	—	10	2	no	—
702	C₂²×C₃	—	20	2	no	—
703	C₂²×C₃	—	40	8	no	—
704	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
705	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
706	C₃×C₄	—	2	2	no	—
707	C₃×C₄	—	5	4	no	—
708	C₃×C₄	—	10	2	no	—
709	C₃×C₄	—	10	4	no	—
710	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
711	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
712	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
713	C₂×C₅	—	2	2	no	—
714	C₂×C₅	—	4	4	no	—
715	C₂×C₅	—	4	2	no	—
716	C₂×C₅	C₃×#577	1	2	yes	complemented
717	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
718	D₅	—	2	4	no	—
719	D₅	—	4	2	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	5	2	no	—
724	C₂³	—	8	2	no	—
725	C₂³	—	10	8	no	—
726	C₂³	—	10	1	no	—
727	C₂³	—	40	4	no	—
728	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
729	Q₈	—	2	1	no	—
730	Q₈	—	5	4	no	—
731	Q₈	—	5	4	no	—
732	Q₈	—	5	2	no	—
733	Q₈	—	10	8	no	—
734	Q₈	—	10	4	no	—
735	Q₈	—	10	2	no	—
736	Q₈	—	10	1	no	—
737	Q₈	C₂³×C₃×D₅	1	2	yes	—
738	D₄	—	2	4	no	—
739	D₄	—	2	4	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	1	no	—
742	D₄	—	5	8	no	—
743	D₄	—	5	4	no	—
744	D₄	—	5	2	no	—
745	D₄	—	10	8	no	—
746	D₄	—	10	8	no	—
747	D₄	—	10	8	no	—
748	D₄	—	10	4	no	—
749	D₄	—	10	1	no	—
750	D₄	C₂³×C₃×D₅	1	2	yes	—
751	D₄	C₂³×C₃×D₅	1	4	yes	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	5	2	no	—
755	C₂×C₄	—	5	4	no	—
756	C₂×C₄	—	5	4	no	—
757	C₂×C₄	—	10	8	no	—
758	C₂×C₄	—	10	8	no	—
759	C₂×C₄	—	10	8	no	—
760	C₂×C₄	—	10	1	no	—
761	C₂×C₄	—	10	2	no	—
762	C₂×C₄	—	10	4	no	—
763	C₂×C₄	—	10	4	no	—
764	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
765	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
766	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
767	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
768	C₈	—	5	2	no	—
769	C₈	—	5	2	no	—
770	C₈	C₂³×C₃×D₅	1	4	yes	—
771	C₂×C₃	—	2	2	no	—
772	C₂×C₃	—	4	4	no	—
773	C₂×C₃	—	4	2	no	—
774	C₂×C₃	—	10	4	no	—
775	C₂×C₃	—	20	2	no	—
776	C₂×C₃	#66109	1	2	yes	direct product factor
777	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
778	C₅	C₂×C₃×#577	1	1	yes	characteristic, complemented, Sylow
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	4	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	5	4	no	—
785	C₂²	—	8	4	no	—
786	C₂²	—	10	4	no	—
787	C₂²	—	10	2	no	—
788	C₂²	—	20	2	no	—
789	C₂²	—	40	8	no	—
790	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
791	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
792	C₄	—	2	2	no	—
793	C₄	—	5	4	no	—
794	C₄	—	10	2	no	—
795	C₄	—	10	4	no	—
796	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
797	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
798	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
799	C₃	C₂×#66109	1	1	yes	characteristic, direct product factor, Sylow
800	C₂	—	2	2	no	—
801	C₂	—	4	4	no	—
802	C₂	—	4	2	no	—
803	C₂	—	10	4	no	—
804	C₂	—	20	2	no	—
805	C₂	C₃×#66109	1	2	yes	direct product factor
806	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×#577
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×#4150	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×#687	C₂	semidirect
6. C₃×#66109	C₂	direct (N × H)
7. C₂×C₃×#4061	C₂	semidirect
8. C₂×C₃×D₅×SD₁₆	C₂	semidirect
9. C₂×C₃×#4058	C₂	semidirect
10. C₂×C₃×#4057	C₂	semidirect
11. C₂×C₃×#4055	C₂	semidirect
12. C₂×C₃×#4053	C₂	semidirect
13. C₂×#66109	C₃	direct (N × H)
14. C₂×C₃×C₅×#41	C₂²	semidirect
18. C₃×#4150	C₂²	semidirect
19. C₂×C₃×Q₈×D₅	C₂²	semidirect
21. C₃×#4144	C₂²	semidirect
25. C₂×C₃×#711	C₂²	semidirect
32. C₂²×C₃×Dic₁₀	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×#687	C₂²	semidirect
42. C₂×C₃×#687	C₂²	semidirect
43. C₂×C₃×#687	C₂²	semidirect
44. C₂×C₃×#686	C₂²	semidirect
45. C₂²×C₃×#168	C₂²	semidirect
46. C₃×#4061	C₂²	semidirect
47. C₃×D₅×SD₁₆	C₂²	semidirect
48. C₃×#4058	C₂²	semidirect
49. C₃×#4057	C₂²	semidirect
50. C₃×#4055	C₂²	semidirect
51. C₃×#4053	C₂²	semidirect
52. C₂×C₃×Dic₂₀	C₂²	semidirect
53. C₂×C₃×#677	C₂²	semidirect
54. C₂×C₃×#676	C₂²	semidirect
55. C₂×C₃×C₈×D₅	C₂²	semidirect
57. C₂×#4150	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×#687	C₂×C₃	semidirect
62. #66109	C₂×C₃	direct (N × H)
63. C₂×#4061	C₂×C₃	semidirect
64. C₂×D₅×SD₁₆	C₂×C₃	semidirect
65. C₂×#4058	C₂×C₃	semidirect
66. C₂×#4057	C₂×C₃	semidirect
67. C₂×#4055	C₂×C₃	semidirect
68. C₂×#4053	C₂×C₃	semidirect
72. C₃×C₅×#41	C₂³	semidirect
92. C₃×Q₈×D₅	C₂³	semidirect
98. C₃×#711	C₂³	semidirect
119. C₂×C₃×Dic₁₀	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×#687	C₂³	semidirect
128. C₃×#687	C₂³	semidirect
129. C₃×#686	C₂³	semidirect
132. C₂×C₃×#168	C₂³	semidirect
133. C₃×Dic₂₀	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
153. #4150	C₂²×C₃	semidirect
154. C₂×Q₈×D₅	C₂²×C₃	semidirect
156. #4144	C₂²×C₃	semidirect
160. C₂×#711	C₂²×C₃	semidirect
167. C₂²×Dic₁₀	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×#687	C₂²×C₃	semidirect
177. C₂×#687	C₂²×C₃	semidirect
178. C₂×#687	C₂²×C₃	semidirect
179. C₂×#686	C₂²×C₃	semidirect
180. C₂²×#168	C₂²×C₃	semidirect
181. #4061	C₂²×C₃	semidirect
182. D₅×SD₁₆	C₂²×C₃	semidirect
183. #4058	C₂²×C₃	semidirect
184. #4057	C₂²×C₃	semidirect
185. #4055	C₂²×C₃	semidirect
186. #4053	C₂²×C₃	semidirect
187. C₂×Dic₂₀	C₂²×C₃	semidirect
188. C₂×#677	C₂²×C₃	semidirect
189. C₂×#676	C₂²×C₃	semidirect
190. C₂×C₈×D₅	C₂²×C₃	semidirect
254. C₂×C₃×#41	C₂×D₅	semidirect
265. C₃×AGL(1,ℤ/8)	C₂×D₅	semidirect
277. C₂×C₃×SD₁₆	C₂×D₅	semidirect
279. C₂×C₃×D₈	C₂×D₅	semidirect
282. C₂×C₃×M₁₆	C₂×D₅	semidirect
288. C₅×#41	C₂³×C₃	semidirect
308. Q₈×D₅	C₂³×C₃	semidirect
314. #711	C₂³×C₃	semidirect
335. C₂×Dic₁₀	C₂³×C₃	semidirect
336. C₅×SD₁₆	C₂³×C₃	semidirect
337. C₅×D₈	C₂³×C₃	semidirect
338. C₅×M₁₆	C₂³×C₃	semidirect
340. #689	C₂³×C₃	semidirect
341. #688	C₂³×C₃	semidirect
342. #687	C₂³×C₃	semidirect
343. #687	C₂³×C₃	semidirect
344. #687	C₂³×C₃	semidirect
345. #686	C₂³×C₃	semidirect
348. C₂×#168	C₂³×C₃	semidirect
349. Dic₂₀	C₂³×C₃	semidirect
350. #677	C₂³×C₃	semidirect
351. #676	C₂³×C₃	semidirect
352. C₈×D₅	C₂³×C₃	semidirect
359. C₂×AGL(1,ℤ/8)	C₃×D₅	semidirect
399. C₃×#41	C₂²×D₅	semidirect
443. C₃×SD₁₆	C₂²×D₅	semidirect
445. C₃×D₈	C₂²×D₅	semidirect
447. C₃×M₁₆	C₂²×D₅	semidirect
515. C₂×#41	C₂×C₃×D₅	semidirect
526. AGL(1,ℤ/8)	C₂×C₃×D₅	semidirect
538. C₂×SD₁₆	C₂×C₃×D₅	semidirect
540. C₂×D₈	C₂×C₃×D₅	semidirect
543. C₂×M₁₆	C₂×C₃×D₅	semidirect
549. C₂×C₃×C₅	#577	semidirect
638. #41	C₂²×C₃×D₅	semidirect
682. SD₁₆	C₂²×C₃×D₅	semidirect
684. D₈	C₂²×C₃×D₅	semidirect
686. M₁₆	C₂²×C₃×D₅	semidirect
692. C₃×C₅	C₂×#577	semidirect
716. C₂×C₅	C₃×#577	semidirect
776. C₂×C₃	#66109	direct (N × H)
778. C₅	C₂×C₃×#577	semidirect
799. C₃	C₂×#66109	direct (N × H)
805. C₂	C₃×#66109	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×#4150	2
C₂×C₃×#4144	2
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₂×C₃×#4096	2
C₂²×C₃×#687	2
C₃×#66109	2
C₂×C₃×#4061	2
C₂×C₃×D₅×SD₁₆	2
C₂×C₃×#4058	2
C₂×C₃×#4057	2
C₂×C₃×#4055	2
C₂×C₃×#4053	2
C₂×#66109	3
C₂×C₃×#577	5

Subgroups — C2×C3×#66109 #14510031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66109 #14510031