Subgroups — C₂×C₄₁×#2456 #23810854

Order 10496.

4282 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2456	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄₁×#396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#392	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#392	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₁×#388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₁×#387	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#123×C₄₁	—	2	8	no	—
27	C₂×#123×C₄₁	C₂²	1	8	yes	complemented
28	C₂×#121×C₄₁	—	2	8	no	—
29	C₂×#121×C₄₁	C₂²	1	8	yes	complemented
30	C₂×C₄×D₄×C₄₁	—	2	8	no	—
31	C₂×C₄×D₄×C₄₁	—	2	8	no	—
32	C₂×C₄×D₄×C₄₁	C₂²	1	8	yes	complemented
33	C₂×C₄×D₄×C₄₁	C₂²	1	8	yes	complemented
34	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
54	C₄₁×#396	C₂²	1	8	yes	complemented
55	C₄₁×#392	C₂²	1	8	yes	complemented
56	C₄₁×#392	C₂²	1	8	yes	complemented
57	C₄₁×#392	C₂²	1	8	yes	complemented
58	C₄₁×#390	C₂²	1	8	yes	complemented
59	C₄₁×#388	C₂²	1	8	yes	complemented
60	C₄₁×#388	C₂²	1	8	yes	complemented
61	C₄₁×#387	C₂²	1	8	yes	complemented
62	C₄₁×#386	C₂²	1	8	yes	complemented
63	C₄₁×#386	C₂²	1	8	yes	complemented
64	C₄₁×#385	C₂²	1	8	yes	complemented
65	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
66	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
67	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
68	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
69	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
70	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
71	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
72	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
73	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
74	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₄₁	—	2	4	no	—
76	C₂²×D₄×C₄₁	—	2	4	no	—
77	C₂²×D₄×C₄₁	—	2	4	no	—
78	C₂²×D₄×C₄₁	—	2	4	no	—
79	C₂²×D₄×C₄₁	—	2	4	no	—
80	C₂²×D₄×C₄₁	—	2	4	no	—
81	C₂²×D₄×C₄₁	—	2	4	no	—
82	C₂²×D₄×C₄₁	—	2	4	no	—
83	C₂²×D₄×C₄₁	—	2	4	no	—
84	C₂²×D₄×C₄₁	—	2	4	no	—
85	C₂²×D₄×C₄₁	—	2	4	no	—
86	C₂²×D₄×C₄₁	—	2	4	no	—
87	C₂²×D₄×C₄₁	—	2	4	no	—
88	C₂²×D₄×C₄₁	—	4	2	no	—
89	C₂²×D₄×C₄₁	—	4	2	no	—
90	C₂²×D₄×C₄₁	—	4	2	no	—
91	C₂²×D₄×C₄₁	—	4	2	no	—
92	C₂²×D₄×C₄₁	—	4	2	no	—
93	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
94	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
95	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
96	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
97	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
98	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
99	C₂³×C₄×C₄₁	—	2	4	no	—
100	C₂³×C₄×C₄₁	—	2	4	no	—
101	C₂³×C₄×C₄₁	—	2	4	no	—
102	C₂³×C₄×C₄₁	—	2	4	no	—
103	C₂³×C₄×C₄₁	—	2	4	no	—
104	C₂³×C₄×C₄₁	—	2	4	no	—
105	C₂³×C₄×C₄₁	—	4	2	no	—
106	C₂³×C₄×C₄₁	—	4	2	no	—
107	C₂³×C₄×C₄₁	—	4	2	no	—
108	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
114	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
115	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
116	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
122	#123×C₄₁	—	2	32	no	—
123	#121×C₄₁	—	2	32	no	—
124	C₄×D₄×C₄₁	—	2	32	no	—
125	C₄×D₄×C₄₁	—	2	32	no	—
126	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
127	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
128	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
129	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
130	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	complemented
131	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
137	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
138	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
139	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
140	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
141	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
142	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
144	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
145	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
146	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
147	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
148	C₂×C₂²⋊C₄×C₄₁	D₄	1	8	yes	complemented
149	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
162	C₂×C₄²×C₄₁	—	2	4	no	—
163	C₂×C₄²×C₄₁	—	2	4	no	—
164	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
165	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
166	#95×C₄₁	C₂³	1	4	yes	—
167	#95×C₄₁	C₂³	1	4	yes	—
168	#95×C₄₁	C₂³	1	4	yes	—
169	#95×C₄₁	C₂³	1	4	yes	—
170	#95×C₄₁	C₂³	1	4	yes	—
171	#95×C₄₁	C₂³	1	4	yes	—
172	C₂⁴×C₄₁	—	2	2	no	—
173	C₂⁴×C₄₁	—	2	2	no	—
174	C₂⁴×C₄₁	—	2	2	no	—
175	C₂⁴×C₄₁	—	2	2	no	—
176	C₂⁴×C₄₁	—	2	2	no	—
177	C₂⁴×C₄₁	—	2	2	no	—
178	C₂⁴×C₄₁	—	2	2	no	—
179	C₂⁴×C₄₁	—	2	2	no	—
180	C₂⁴×C₄₁	—	2	2	no	—
181	C₂⁴×C₄₁	—	2	2	no	—
182	C₂⁴×C₄₁	—	2	2	no	—
183	C₂⁴×C₄₁	—	2	2	no	—
184	C₂⁴×C₄₁	—	2	2	no	—
185	C₂⁴×C₄₁	—	2	2	no	—
186	C₂⁴×C₄₁	—	2	2	no	—
187	C₂⁴×C₄₁	—	2	2	no	—
188	C₂⁴×C₄₁	—	2	2	no	—
189	C₂⁴×C₄₁	—	2	2	no	—
190	C₂⁴×C₄₁	—	2	2	no	—
191	C₂⁴×C₄₁	—	2	2	no	—
192	C₂⁴×C₄₁	—	2	2	no	—
193	C₂⁴×C₄₁	—	2	2	no	—
194	C₂⁴×C₄₁	—	2	2	no	—
195	C₂⁴×C₄₁	—	2	2	no	—
196	C₂⁴×C₄₁	—	2	2	no	—
197	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
198	C₂⁴×C₄₁	#41	1	4	yes	—
199	C₂⁴×C₄₁	#41	1	4	yes	—
200	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
201	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
202	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
203	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
204	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
205	C₂×D₄×C₄₁	—	2	32	no	—
206	C₂×D₄×C₄₁	—	2	32	no	—
207	C₂×D₄×C₄₁	—	2	8	no	—
208	C₂×D₄×C₄₁	—	2	8	no	—
209	C₂×D₄×C₄₁	—	2	8	no	—
210	C₂×D₄×C₄₁	—	2	8	no	—
211	C₂×D₄×C₄₁	—	2	8	no	—
212	C₂×D₄×C₄₁	—	2	8	no	—
213	C₂×D₄×C₄₁	—	2	8	no	—
214	C₂×D₄×C₄₁	—	2	8	no	—
215	C₂×D₄×C₄₁	—	2	8	no	—
216	C₂×D₄×C₄₁	—	2	8	no	—
217	C₂×D₄×C₄₁	—	2	8	no	—
218	C₂×D₄×C₄₁	—	2	8	no	—
219	C₂×D₄×C₄₁	—	2	8	no	—
220	C₂×D₄×C₄₁	—	4	4	no	—
221	C₂×D₄×C₄₁	—	4	4	no	—
222	C₂×D₄×C₄₁	—	4	4	no	—
223	C₂×D₄×C₄₁	—	4	4	no	—
224	C₂×D₄×C₄₁	—	4	4	no	—
225	C₂×D₄×C₄₁	—	4	16	no	—
226	C₂×D₄×C₄₁	—	4	16	no	—
227	C₂×D₄×C₄₁	—	4	16	no	—
228	C₂×D₄×C₄₁	—	4	16	no	—
229	C₂²×C₄×C₄₁	—	2	2	no	—
230	C₂²×C₄×C₄₁	—	2	2	no	—
231	C₂²×C₄×C₄₁	—	2	2	no	—
232	C₂²×C₄×C₄₁	—	2	2	no	—
233	C₂²×C₄×C₄₁	—	2	2	no	—
234	C₂²×C₄×C₄₁	—	2	2	no	—
235	C₂²×C₄×C₄₁	—	2	2	no	—
236	C₂²×C₄×C₄₁	—	2	2	no	—
237	C₂²×C₄×C₄₁	—	2	2	no	—
238	C₂²×C₄×C₄₁	—	2	2	no	—
239	C₂²×C₄×C₄₁	—	2	2	no	—
240	C₂²×C₄×C₄₁	—	2	2	no	—
241	C₂²×C₄×C₄₁	—	2	2	no	—
242	C₂²×C₄×C₄₁	—	2	2	no	—
243	C₂²×C₄×C₄₁	—	2	2	no	—
244	C₂²×C₄×C₄₁	—	2	2	no	—
245	C₂²×C₄×C₄₁	—	2	2	no	—
246	C₂²×C₄×C₄₁	—	2	8	no	—
247	C₂²×C₄×C₄₁	—	2	2	no	—
248	C₂²×C₄×C₄₁	—	2	2	no	—
249	C₂²×C₄×C₄₁	—	2	2	no	—
250	C₂²×C₄×C₄₁	—	2	2	no	—
251	C₂²×C₄×C₄₁	—	2	2	no	—
252	C₂²×C₄×C₄₁	—	2	2	no	—
253	C₂²×C₄×C₄₁	—	2	2	no	—
254	C₂²×C₄×C₄₁	—	2	2	no	—
255	C₂²×C₄×C₄₁	—	2	2	no	—
256	C₂²×C₄×C₄₁	—	2	2	no	—
257	C₂²×C₄×C₄₁	—	2	8	no	—
258	C₂²×C₄×C₄₁	—	2	8	no	—
259	C₂²×C₄×C₄₁	—	2	8	no	—
260	C₂²×C₄×C₄₁	—	2	8	no	—
261	C₂²×C₄×C₄₁	—	2	8	no	—
262	C₂²×C₄×C₄₁	—	4	4	no	—
263	C₂²×C₄×C₄₁	—	4	4	no	—
264	C₂²×C₄×C₄₁	—	4	4	no	—
265	C₂²×C₄×C₄₁	—	4	16	no	—
266	C₂²×C₄×C₄₁	—	4	16	no	—
267	C₂²×C₄×C₄₁	—	4	16	no	—
268	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
269	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
270	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
271	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
272	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
273	C₂²×C₄×C₄₁	#41	1	4	yes	—
274	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₄₁	—	2	8	no	—
286	C₄⋊C₄×C₄₁	—	2	8	no	—
287	C₄⋊C₄×C₄₁	—	2	8	no	—
288	C₄⋊C₄×C₄₁	—	4	4	no	—
289	C₄⋊C₄×C₄₁	C₂×D₄	1	16	yes	complemented
290	C₂²⋊C₄×C₄₁	—	2	8	no	—
291	C₂²⋊C₄×C₄₁	—	2	8	no	—
292	C₂²⋊C₄×C₄₁	—	2	8	no	—
293	C₂²⋊C₄×C₄₁	—	2	8	no	—
294	C₂²⋊C₄×C₄₁	—	2	8	no	—
295	C₂²⋊C₄×C₄₁	—	2	8	no	—
296	C₂²⋊C₄×C₄₁	—	2	8	no	—
297	C₂²⋊C₄×C₄₁	—	2	8	no	—
298	C₂²⋊C₄×C₄₁	—	2	8	no	—
299	C₂²⋊C₄×C₄₁	—	4	4	no	—
300	C₂²⋊C₄×C₄₁	—	4	4	no	—
301	C₂²⋊C₄×C₄₁	—	4	4	no	—
302	C₂²⋊C₄×C₄₁	C₂×D₄	1	16	yes	complemented
303	C₄²×C₄₁	—	2	8	no	—
304	C₄²×C₄₁	—	2	8	no	—
305	C₂³×C₄₁	—	2	8	no	—
306	C₂³×C₄₁	—	2	8	no	—
307	C₂³×C₄₁	—	2	8	no	—
308	C₂³×C₄₁	—	2	8	no	—
309	C₂³×C₄₁	—	2	8	no	—
310	C₂³×C₄₁	—	2	8	no	—
311	C₂³×C₄₁	—	2	8	no	—
312	C₂³×C₄₁	—	2	8	no	—
313	C₂³×C₄₁	—	2	8	no	—
314	C₂³×C₄₁	—	2	2	no	—
315	C₂³×C₄₁	—	2	2	no	—
316	C₂³×C₄₁	—	2	2	no	—
317	C₂³×C₄₁	—	2	2	no	—
318	C₂³×C₄₁	—	2	2	no	—
319	C₂³×C₄₁	—	2	2	no	—
320	C₂³×C₄₁	—	2	2	no	—
321	C₂³×C₄₁	—	2	2	no	—
322	C₂³×C₄₁	—	2	2	no	—
323	C₂³×C₄₁	—	2	2	no	—
324	C₂³×C₄₁	—	2	2	no	—
325	C₂³×C₄₁	—	2	2	no	—
326	C₂³×C₄₁	—	2	2	no	—
327	C₂³×C₄₁	—	2	2	no	—
328	C₂³×C₄₁	—	2	2	no	—
329	C₂³×C₄₁	—	2	2	no	—
330	C₂³×C₄₁	—	2	2	no	—
331	C₂³×C₄₁	—	2	2	no	—
332	C₂³×C₄₁	—	2	2	no	—
333	C₂³×C₄₁	—	2	2	no	—
334	C₂³×C₄₁	—	2	2	no	—
335	C₂³×C₄₁	—	2	2	no	—
336	C₂³×C₄₁	—	2	2	no	—
337	C₂³×C₄₁	—	2	2	no	—
338	C₂³×C₄₁	—	2	2	no	—
339	C₂³×C₄₁	—	4	4	no	—
340	C₂³×C₄₁	—	4	4	no	—
341	C₂³×C₄₁	—	4	4	no	—
342	C₂³×C₄₁	—	4	4	no	—
343	C₂³×C₄₁	—	4	4	no	—
344	C₂³×C₄₁	—	4	4	no	—
345	C₂³×C₄₁	—	4	4	no	—
346	C₂³×C₄₁	—	4	4	no	—
347	C₂³×C₄₁	—	4	4	no	—
348	C₂³×C₄₁	—	4	4	no	—
349	C₂³×C₄₁	—	4	4	no	—
350	C₂³×C₄₁	—	4	4	no	—
351	C₂³×C₄₁	—	4	4	no	—
352	C₂³×C₄₁	—	4	4	no	—
353	C₂³×C₄₁	—	4	4	no	—
354	C₂³×C₄₁	—	4	4	no	—
355	C₂³×C₄₁	—	4	4	no	—
356	C₂³×C₄₁	—	4	4	no	—
357	C₂³×C₄₁	—	4	4	no	—
358	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
359	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
360	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
361	C₂³×C₄₁	C₂×#41	1	4	yes	—
362	C₂³×C₄₁	C₂×#41	1	4	yes	—
363	C₂³×C₄₁	C₂×#41	1	2	yes	—
364	C₂³×C₄₁	C₂×#41	1	2	yes	—
365	C₂³×C₄₁	C₂×#41	1	2	yes	—
366	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
367	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
368	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
369	D₄×C₄₁	—	2	32	no	—
370	D₄×C₄₁	—	2	32	no	—
371	D₄×C₄₁	—	4	16	no	—
372	D₄×C₄₁	—	4	16	no	—
373	D₄×C₄₁	—	4	16	no	—
374	D₄×C₄₁	—	4	16	no	—
375	C₂×C₄×C₄₁	—	2	8	no	—
376	C₂×C₄×C₄₁	—	2	8	no	—
377	C₂×C₄×C₄₁	—	2	8	no	—
378	C₂×C₄×C₄₁	—	2	8	no	—
379	C₂×C₄×C₄₁	—	2	8	no	—
380	C₂×C₄×C₄₁	—	2	8	no	—
381	C₂×C₄×C₄₁	—	2	2	no	—
382	C₂×C₄×C₄₁	—	2	2	no	—
383	C₂×C₄×C₄₁	—	2	2	no	—
384	C₂×C₄×C₄₁	—	2	2	no	—
385	C₂×C₄×C₄₁	—	2	2	no	—
386	C₂×C₄×C₄₁	—	2	2	no	—
387	C₂×C₄×C₄₁	—	2	2	no	—
388	C₂×C₄×C₄₁	—	2	2	no	—
389	C₂×C₄×C₄₁	—	2	2	no	—
390	C₂×C₄×C₄₁	—	2	2	no	—
391	C₂×C₄×C₄₁	—	2	2	no	—
392	C₂×C₄×C₄₁	—	2	2	no	—
393	C₂×C₄×C₄₁	—	2	2	no	—
394	C₂×C₄×C₄₁	—	2	2	no	—
395	C₂×C₄×C₄₁	—	2	2	no	—
396	C₂×C₄×C₄₁	—	2	2	no	—
397	C₂×C₄×C₄₁	—	2	2	no	—
398	C₂×C₄×C₄₁	—	2	2	no	—
399	C₂×C₄×C₄₁	—	2	2	no	—
400	C₂×C₄×C₄₁	—	2	2	no	—
401	C₂×C₄×C₄₁	—	2	2	no	—
402	C₂×C₄×C₄₁	—	2	2	no	—
403	C₂×C₄×C₄₁	—	2	2	no	—
404	C₂×C₄×C₄₁	—	2	2	no	—
405	C₂×C₄×C₄₁	—	2	2	no	—
406	C₂×C₄×C₄₁	—	2	2	no	—
407	C₂×C₄×C₄₁	—	2	2	no	—
408	C₂×C₄×C₄₁	—	4	16	no	—
409	C₂×C₄×C₄₁	—	4	16	no	—
410	C₂×C₄×C₄₁	—	4	16	no	—
411	C₂×C₄×C₄₁	—	4	4	no	—
412	C₂×C₄×C₄₁	—	4	4	no	—
413	C₂×C₄×C₄₁	—	4	4	no	—
414	C₂×C₄×C₄₁	—	4	4	no	—
415	C₂×C₄×C₄₁	—	4	4	no	—
416	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
417	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
418	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
419	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
420	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
421	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
422	C₂×#2456	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
423	C₂²×C₄₁	—	2	4	no	—
424	C₂²×C₄₁	—	2	4	no	—
425	C₂²×C₄₁	—	2	4	no	—
426	C₂²×C₄₁	—	2	4	no	—
427	C₂²×C₄₁	—	2	4	no	—
428	C₂²×C₄₁	—	2	4	no	—
429	C₂²×C₄₁	—	2	4	no	—
430	C₂²×C₄₁	—	2	4	no	—
431	C₂²×C₄₁	—	2	4	no	—
432	C₂²×C₄₁	—	4	2	no	—
433	C₂²×C₄₁	—	4	2	no	—
434	C₂²×C₄₁	—	4	2	no	—
435	C₂²×C₄₁	—	4	2	no	—
436	C₂²×C₄₁	—	4	2	no	—
437	C₂²×C₄₁	—	4	2	no	—
438	C₂²×C₄₁	—	4	2	no	—
439	C₂²×C₄₁	—	4	2	no	—
440	C₂²×C₄₁	—	4	2	no	—
441	C₂²×C₄₁	—	4	2	no	—
442	C₂²×C₄₁	—	4	2	no	—
443	C₂²×C₄₁	—	4	2	no	—
444	C₂²×C₄₁	—	4	16	no	—
445	C₂²×C₄₁	—	4	16	no	—
446	C₂²×C₄₁	—	4	16	no	—
447	C₂²×C₄₁	—	4	2	no	—
448	C₂²×C₄₁	—	4	2	no	—
449	C₂²×C₄₁	—	4	2	no	—
450	C₂²×C₄₁	—	4	2	no	—
451	C₂²×C₄₁	—	4	2	no	—
452	C₂²×C₄₁	—	4	2	no	—
453	C₂²×C₄₁	—	4	2	no	—
454	C₂²×C₄₁	—	8	8	no	—
455	C₂²×C₄₁	#525	1	4	yes	—
456	C₂²×C₄₁	#525	1	4	yes	—
457	C₂²×C₄₁	#538	1	4	yes	—
458	C₂²×C₄₁	D₄²	1	4	yes	—
459	C₂²×C₄₁	#546	1	4	yes	—
460	C₂²×C₄₁	#550	1	4	yes	—
461	C₂²×C₄₁	#553	1	4	yes	—
462	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
463	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
464	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
465	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
466	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
467	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₄×C₄₁	—	2	4	no	—
470	C₄×C₄₁	—	2	4	no	—
471	C₄×C₄₁	—	2	4	no	—
472	C₄×C₄₁	—	2	4	no	—
473	C₄×C₄₁	—	2	4	no	—
474	C₄×C₄₁	—	2	4	no	—
475	C₄×C₄₁	—	4	2	no	—
476	C₄×C₄₁	—	4	2	no	—
477	C₄×C₄₁	—	4	2	no	—
478	C₄×C₄₁	—	4	2	no	—
479	C₄×C₄₁	—	4	2	no	—
480	C₂²×#123	C₂×C₄₁	1	1	yes	characteristic, complemented
481	C₂²×#121	C₂×C₄₁	1	1	yes	characteristic, complemented
482	C₂²×C₄×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
483	C₂²×C₄×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
484	#2456	C₂×C₄₁	1	16	yes	direct product factor
485	C₂×#396	C₂×C₄₁	1	1	yes	characteristic, complemented
486	C₂×#392	C₂×C₄₁	1	1	yes	characteristic, complemented
487	C₂×#392	C₂×C₄₁	1	1	yes	characteristic, complemented
488	C₂×#392	C₂×C₄₁	1	1	yes	characteristic, complemented
489	C₂×#390	C₂×C₄₁	1	1	yes	characteristic, complemented
490	C₂×#388	C₂×C₄₁	1	1	yes	characteristic, complemented
491	C₂×#388	C₂×C₄₁	1	1	yes	characteristic, complemented
492	C₂×#387	C₂×C₄₁	1	1	yes	characteristic, complemented
493	C₂×#386	C₂×C₄₁	1	1	yes	characteristic, complemented
494	C₂×#386	C₂×C₄₁	1	1	yes	characteristic, complemented
495	C₂×#385	C₂×C₄₁	1	1	yes	characteristic, complemented
496	C₂×C₄₁	—	4	4	no	—
497	C₂×C₄₁	—	4	4	no	—
498	C₂×C₄₁	—	4	4	no	—
499	C₂×C₄₁	—	8	2	no	—
500	C₂×C₄₁	#2456	1	8	yes	direct product factor
501	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
502	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
503	C₂×C₄₁	C₂×#538	1	1	yes	characteristic
504	C₂×C₄₁	C₂×D₄²	1	1	yes	characteristic
505	C₂×C₄₁	C₂×#546	1	1	yes	characteristic
506	C₂×C₄₁	C₂×#550	1	1	yes	characteristic
507	C₂×C₄₁	C₂×#553	1	1	yes	characteristic
508	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
509	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
510	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
511	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
512	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
513	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
514	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
515	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
516	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
517	C₂×#123	—	2	8	no	—
518	C₂×#123	C₂²×C₄₁	1	8	yes	complemented
519	C₂×#121	—	2	8	no	—
520	C₂×#121	C₂²×C₄₁	1	8	yes	complemented
521	C₂×C₄×D₄	—	2	8	no	—
522	C₂×C₄×D₄	—	2	8	no	—
523	C₂×C₄×D₄	C₂²×C₄₁	1	8	yes	complemented
524	C₂×C₄×D₄	C₂²×C₄₁	1	8	yes	complemented
525	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
526	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
527	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
528	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
529	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
530	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
531	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
532	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
533	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
534	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
535	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
536	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
537	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
538	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
539	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
540	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
541	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
542	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
543	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
544	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
545	#396	C₂²×C₄₁	1	8	yes	complemented
546	#392	C₂²×C₄₁	1	8	yes	complemented
547	#392	C₂²×C₄₁	1	8	yes	complemented
548	#392	C₂²×C₄₁	1	8	yes	complemented
549	#390	C₂²×C₄₁	1	8	yes	complemented
550	#388	C₂²×C₄₁	1	8	yes	complemented
551	#388	C₂²×C₄₁	1	8	yes	complemented
552	#387	C₂²×C₄₁	1	8	yes	complemented
553	#386	C₂²×C₄₁	1	8	yes	complemented
554	#386	C₂²×C₄₁	1	8	yes	complemented
555	#385	C₂²×C₄₁	1	8	yes	complemented
556	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
557	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
558	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
559	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
560	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
561	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
562	C₄₁	C₂×#2456	1	1	yes	characteristic, direct product factor, Sylow
563	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
564	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
565	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
566	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
567	C₂²×D₄	—	2	4	no	—
568	C₂²×D₄	—	2	4	no	—
569	C₂²×D₄	—	2	4	no	—
570	C₂²×D₄	—	2	4	no	—
571	C₂²×D₄	—	2	4	no	—
572	C₂²×D₄	—	2	4	no	—
573	C₂²×D₄	—	2	4	no	—
574	C₂²×D₄	—	2	4	no	—
575	C₂²×D₄	—	2	4	no	—
576	C₂²×D₄	—	2	4	no	—
577	C₂²×D₄	—	2	4	no	—
578	C₂²×D₄	—	2	4	no	—
579	C₂²×D₄	—	2	4	no	—
580	C₂²×D₄	—	4	2	no	—
581	C₂²×D₄	—	4	2	no	—
582	C₂²×D₄	—	4	2	no	—
583	C₂²×D₄	—	4	2	no	—
584	C₂²×D₄	—	4	2	no	—
585	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
586	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
587	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
588	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
589	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
590	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
591	C₂³×C₄	—	2	4	no	—
592	C₂³×C₄	—	2	4	no	—
593	C₂³×C₄	—	2	4	no	—
594	C₂³×C₄	—	2	4	no	—
595	C₂³×C₄	—	2	4	no	—
596	C₂³×C₄	—	2	4	no	—
597	C₂³×C₄	—	4	2	no	—
598	C₂³×C₄	—	4	2	no	—
599	C₂³×C₄	—	4	2	no	—
600	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
606	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
607	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
608	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
614	#123	—	2	32	no	—
615	#121	—	2	32	no	—
616	C₄×D₄	—	2	32	no	—
617	C₄×D₄	—	2	32	no	—
618	C₂×C₄⋊C₄	—	2	4	no	—
619	C₂×C₄⋊C₄	—	2	4	no	—
620	C₂×C₄⋊C₄	—	2	4	no	—
621	C₂×C₄⋊C₄	—	4	2	no	—
622	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	complemented
623	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
624	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
625	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
626	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
627	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
628	C₂×C₂²⋊C₄	—	2	4	no	—
629	C₂×C₂²⋊C₄	—	2	4	no	—
630	C₂×C₂²⋊C₄	—	2	4	no	—
631	C₂×C₂²⋊C₄	—	2	4	no	—
632	C₂×C₂²⋊C₄	—	2	4	no	—
633	C₂×C₂²⋊C₄	—	2	4	no	—
634	C₂×C₂²⋊C₄	—	2	4	no	—
635	C₂×C₂²⋊C₄	—	2	4	no	—
636	C₂×C₂²⋊C₄	—	2	4	no	—
637	C₂×C₂²⋊C₄	—	4	2	no	—
638	C₂×C₂²⋊C₄	—	4	2	no	—
639	C₂×C₂²⋊C₄	—	4	2	no	—
640	C₂×C₂²⋊C₄	D₄×C₄₁	1	8	yes	complemented
641	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
654	C₂×C₄²	—	2	4	no	—
655	C₂×C₄²	—	2	4	no	—
656	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
657	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
658	#95	C₂³×C₄₁	1	4	yes	—
659	#95	C₂³×C₄₁	1	4	yes	—
660	#95	C₂³×C₄₁	1	4	yes	—
661	#95	C₂³×C₄₁	1	4	yes	—
662	#95	C₂³×C₄₁	1	4	yes	—
663	#95	C₂³×C₄₁	1	4	yes	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	2	2	no	—
667	C₂⁴	—	2	2	no	—
668	C₂⁴	—	2	2	no	—
669	C₂⁴	—	2	2	no	—
670	C₂⁴	—	2	2	no	—
671	C₂⁴	—	2	2	no	—
672	C₂⁴	—	2	2	no	—
673	C₂⁴	—	2	2	no	—
674	C₂⁴	—	2	2	no	—
675	C₂⁴	—	2	2	no	—
676	C₂⁴	—	2	2	no	—
677	C₂⁴	—	2	2	no	—
678	C₂⁴	—	2	2	no	—
679	C₂⁴	—	2	2	no	—
680	C₂⁴	—	2	2	no	—
681	C₂⁴	—	2	2	no	—
682	C₂⁴	—	2	2	no	—
683	C₂⁴	—	2	2	no	—
684	C₂⁴	—	2	2	no	—
685	C₂⁴	—	2	2	no	—
686	C₂⁴	—	2	2	no	—
687	C₂⁴	—	2	2	no	—
688	C₂⁴	—	2	2	no	—
689	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
690	C₂⁴	#41×C₄₁	1	4	yes	—
691	C₂⁴	#41×C₄₁	1	4	yes	—
692	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
693	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
694	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
695	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
696	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
697	C₂×D₄	—	2	32	no	—
698	C₂×D₄	—	2	32	no	—
699	C₂×D₄	—	2	8	no	—
700	C₂×D₄	—	2	8	no	—
701	C₂×D₄	—	2	8	no	—
702	C₂×D₄	—	2	8	no	—
703	C₂×D₄	—	2	8	no	—
704	C₂×D₄	—	2	8	no	—
705	C₂×D₄	—	2	8	no	—
706	C₂×D₄	—	2	8	no	—
707	C₂×D₄	—	2	8	no	—
708	C₂×D₄	—	2	8	no	—
709	C₂×D₄	—	2	8	no	—
710	C₂×D₄	—	2	8	no	—
711	C₂×D₄	—	2	8	no	—
712	C₂×D₄	—	4	4	no	—
713	C₂×D₄	—	4	4	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	—	4	4	no	—
717	C₂×D₄	—	4	16	no	—
718	C₂×D₄	—	4	16	no	—
719	C₂×D₄	—	4	16	no	—
720	C₂×D₄	—	4	16	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	8	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	8	no	—
750	C₂²×C₄	—	2	8	no	—
751	C₂²×C₄	—	2	8	no	—
752	C₂²×C₄	—	2	8	no	—
753	C₂²×C₄	—	2	8	no	—
754	C₂²×C₄	—	4	4	no	—
755	C₂²×C₄	—	4	4	no	—
756	C₂²×C₄	—	4	4	no	—
757	C₂²×C₄	—	4	16	no	—
758	C₂²×C₄	—	4	16	no	—
759	C₂²×C₄	—	4	16	no	—
760	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
761	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
762	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
763	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
764	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
765	C₂²×C₄	#41×C₄₁	1	4	yes	—
766	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
777	C₄⋊C₄	—	2	8	no	—
778	C₄⋊C₄	—	2	8	no	—
779	C₄⋊C₄	—	2	8	no	—
780	C₄⋊C₄	—	4	4	no	—
781	C₄⋊C₄	C₂×D₄×C₄₁	1	16	yes	complemented
782	C₂²⋊C₄	—	2	8	no	—
783	C₂²⋊C₄	—	2	8	no	—
784	C₂²⋊C₄	—	2	8	no	—
785	C₂²⋊C₄	—	2	8	no	—
786	C₂²⋊C₄	—	2	8	no	—
787	C₂²⋊C₄	—	2	8	no	—
788	C₂²⋊C₄	—	2	8	no	—
789	C₂²⋊C₄	—	2	8	no	—
790	C₂²⋊C₄	—	2	8	no	—
791	C₂²⋊C₄	—	4	4	no	—
792	C₂²⋊C₄	—	4	4	no	—
793	C₂²⋊C₄	—	4	4	no	—
794	C₂²⋊C₄	C₂×D₄×C₄₁	1	16	yes	complemented
795	C₄²	—	2	8	no	—
796	C₄²	—	2	8	no	—
797	C₂³	—	2	8	no	—
798	C₂³	—	2	8	no	—
799	C₂³	—	2	8	no	—
800	C₂³	—	2	8	no	—
801	C₂³	—	2	8	no	—
802	C₂³	—	2	8	no	—
803	C₂³	—	2	8	no	—
804	C₂³	—	2	8	no	—
805	C₂³	—	2	8	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	4	4	no	—
832	C₂³	—	4	4	no	—
833	C₂³	—	4	4	no	—
834	C₂³	—	4	4	no	—
835	C₂³	—	4	4	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	4	4	no	—
840	C₂³	—	4	4	no	—
841	C₂³	—	4	4	no	—
842	C₂³	—	4	4	no	—
843	C₂³	—	4	4	no	—
844	C₂³	—	4	4	no	—
845	C₂³	—	4	4	no	—
846	C₂³	—	4	4	no	—
847	C₂³	—	4	4	no	—
848	C₂³	—	4	4	no	—
849	C₂³	—	4	4	no	—
850	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
851	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
852	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
853	C₂³	C₂×#41×C₄₁	1	4	yes	—
854	C₂³	C₂×#41×C₄₁	1	4	yes	—
855	C₂³	C₂×#41×C₄₁	1	2	yes	—
856	C₂³	C₂×#41×C₄₁	1	2	yes	—
857	C₂³	C₂×#41×C₄₁	1	2	yes	—
858	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
859	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
860	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
861	D₄	—	2	32	no	—
862	D₄	—	2	32	no	—
863	D₄	—	4	16	no	—
864	D₄	—	4	16	no	—
865	D₄	—	4	16	no	—
866	D₄	—	4	16	no	—
867	C₂×C₄	—	2	8	no	—
868	C₂×C₄	—	2	8	no	—
869	C₂×C₄	—	2	8	no	—
870	C₂×C₄	—	2	8	no	—
871	C₂×C₄	—	2	8	no	—
872	C₂×C₄	—	2	8	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	4	16	no	—
901	C₂×C₄	—	4	16	no	—
902	C₂×C₄	—	4	16	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
909	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
910	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
911	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
912	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
913	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
914	C₂²	—	2	4	no	—
915	C₂²	—	2	4	no	—
916	C₂²	—	2	4	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	16	no	—
936	C₂²	—	4	16	no	—
937	C₂²	—	4	16	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	8	8	no	—
946	C₂²	C₄₁×#525	1	4	yes	—
947	C₂²	C₄₁×#525	1	4	yes	—
948	C₂²	C₄₁×#538	1	4	yes	—
949	C₂²	D₄²×C₄₁	1	4	yes	—
950	C₂²	C₄₁×#546	1	4	yes	—
951	C₂²	C₄₁×#550	1	4	yes	—
952	C₂²	C₄₁×#553	1	4	yes	—
953	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
954	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
955	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
956	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
957	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
958	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
959	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
960	C₄	—	2	4	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	4	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	4	no	—
965	C₄	—	2	4	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₂	—	4	4	no	—
972	C₂	—	4	4	no	—
973	C₂	—	4	4	no	—
974	C₂	—	8	2	no	—
975	C₂	C₄₁×#2456	1	8	yes	direct product factor
976	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
977	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
978	C₂	C₂×C₄₁×#538	1	1	yes	characteristic
979	C₂	C₂×D₄²×C₄₁	1	1	yes	characteristic
980	C₂	C₂×C₄₁×#546	1	1	yes	characteristic
981	C₂	C₂×C₄₁×#550	1	1	yes	characteristic
982	C₂	C₂×C₄₁×#553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#123×C₄₁	C₂	semidirect
2. C₂²×#121×C₄₁	C₂	semidirect
3. C₂²×C₄×D₄×C₄₁	C₂	semidirect
4. C₂²×C₄×D₄×C₄₁	C₂	semidirect
5. C₄₁×#2456	C₂	direct (N × H)
6. C₂×C₄₁×#396	C₂	semidirect
7. C₂×C₄₁×#392	C₂	semidirect
8. C₂×C₄₁×#392	C₂	semidirect
9. C₂×C₄₁×#392	C₂	semidirect
10. C₂×C₄₁×#390	C₂	semidirect
11. C₂×C₄₁×#388	C₂	semidirect
12. C₂×C₄₁×#388	C₂	semidirect
13. C₂×C₄₁×#387	C₂	semidirect
14. C₂×C₄₁×#386	C₂	semidirect
15. C₂×C₄₁×#386	C₂	semidirect
16. C₂×C₄₁×#385	C₂	semidirect
27. C₂×#123×C₄₁	C₂²	semidirect
29. C₂×#121×C₄₁	C₂²	semidirect
32. C₂×C₄×D₄×C₄₁	C₂²	semidirect
33. C₂×C₄×D₄×C₄₁	C₂²	semidirect
54. C₄₁×#396	C₂²	semidirect
55. C₄₁×#392	C₂²	semidirect
56. C₄₁×#392	C₂²	semidirect
57. C₄₁×#392	C₂²	semidirect
58. C₄₁×#390	C₂²	semidirect
59. C₄₁×#388	C₂²	semidirect
60. C₄₁×#388	C₂²	semidirect
61. C₄₁×#387	C₂²	semidirect
62. C₄₁×#386	C₂²	semidirect
63. C₄₁×#386	C₂²	semidirect
64. C₄₁×#385	C₂²	semidirect
130. C₂×C₄⋊C₄×C₄₁	D₄	semidirect
148. C₂×C₂²⋊C₄×C₄₁	D₄	semidirect
289. C₄⋊C₄×C₄₁	C₂×D₄	semidirect
302. C₂²⋊C₄×C₄₁	C₂×D₄	semidirect
422. C₂×#2456	C₄₁	direct (N × H)
480. C₂²×#123	C₂×C₄₁	semidirect
481. C₂²×#121	C₂×C₄₁	semidirect
482. C₂²×C₄×D₄	C₂×C₄₁	semidirect
483. C₂²×C₄×D₄	C₂×C₄₁	semidirect
484. #2456	C₂×C₄₁	direct (N × H)
485. C₂×#396	C₂×C₄₁	semidirect
486. C₂×#392	C₂×C₄₁	semidirect
487. C₂×#392	C₂×C₄₁	semidirect
488. C₂×#392	C₂×C₄₁	semidirect
489. C₂×#390	C₂×C₄₁	semidirect
490. C₂×#388	C₂×C₄₁	semidirect
491. C₂×#388	C₂×C₄₁	semidirect
492. C₂×#387	C₂×C₄₁	semidirect
493. C₂×#386	C₂×C₄₁	semidirect
494. C₂×#386	C₂×C₄₁	semidirect
495. C₂×#385	C₂×C₄₁	semidirect
500. C₂×C₄₁	#2456	direct (N × H)
518. C₂×#123	C₂²×C₄₁	semidirect
520. C₂×#121	C₂²×C₄₁	semidirect
523. C₂×C₄×D₄	C₂²×C₄₁	semidirect
524. C₂×C₄×D₄	C₂²×C₄₁	semidirect
545. #396	C₂²×C₄₁	semidirect
546. #392	C₂²×C₄₁	semidirect
547. #392	C₂²×C₄₁	semidirect
548. #392	C₂²×C₄₁	semidirect
549. #390	C₂²×C₄₁	semidirect
550. #388	C₂²×C₄₁	semidirect
551. #388	C₂²×C₄₁	semidirect
552. #387	C₂²×C₄₁	semidirect
553. #386	C₂²×C₄₁	semidirect
554. #386	C₂²×C₄₁	semidirect
555. #385	C₂²×C₄₁	semidirect
562. C₄₁	C₂×#2456	direct (N × H)
622. C₂×C₄⋊C₄	D₄×C₄₁	semidirect
640. C₂×C₂²⋊C₄	D₄×C₄₁	semidirect
781. C₄⋊C₄	C₂×D₄×C₄₁	semidirect
794. C₂²⋊C₄	C₂×D₄×C₄₁	semidirect
975. C₂	C₄₁×#2456	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#123×C₄₁	2
C₂²×#121×C₄₁	2
C₂²×C₄×D₄×C₄₁	2
C₄₁×#2456	2
C₂×C₄₁×#396	2
C₂×C₄₁×#392	2
C₂×C₄₁×#390	2
C₂×C₄₁×#388	2
C₂×C₄₁×#387	2
C₂×C₄₁×#386	2
C₂×C₄₁×#385	2
C₂×#2456	41

Subgroups — C2×C41×#2456 #23810854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2456 #23810854