Subgroups — C₄₁×#34471 #23810672

Order 10496.

3112 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2377	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2375	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2358	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₂²⋊C₄×C₄₁	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#2333	C₂	1	2	yes	maximal, complemented
14	C₄₁×#2328	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2321	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2321	C₂	1	2	yes	maximal, complemented
18	C₄₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2309	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#2308	C₂	1	2	yes	maximal, complemented
21	C₄×#121×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
26	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
27	D₄²×C₄₁	C₄	1	16	yes	complemented
28	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#121×C₄₁	C₂²	1	2	yes	—
32	C₂×#120×C₄₁	C₂²	1	2	yes	—
33	C₂×#120×C₄₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
37	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
39	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
40	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic, complemented
44	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
47	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
48	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
50	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic, complemented
51	C₄₁×#390	C₂²	1	1	yes	characteristic
52	C₄₁×#390	C₂²	1	1	yes	characteristic
53	C₄₁×#390	C₂²	1	1	yes	characteristic
54	C₄₁×#390	C₂²	1	1	yes	characteristic
55	C₄₁×#390	C₂²	1	2	yes	complemented
56	C₄₁×#390	C₂²	1	1	yes	characteristic, complemented
57	C₄₁×#390	C₂²	1	1	yes	characteristic, complemented
58	C₄₁×#390	C₂²	1	2	yes	complemented
59	C₄₁×#390	C₂²	1	1	yes	characteristic, complemented
60	C₄₁×#390	C₂²	1	2	yes	complemented
61	C₄₁×#390	C₂²	1	2	yes	complemented
62	C₄₁×#390	C₂²	1	1	yes	characteristic, complemented
63	C₄₁×#390	C₂²	1	2	yes	complemented
64	C₄₁×#390	C₂²	1	2	yes	complemented
65	C₄₁×#390	C₂²	1	2	yes	complemented
66	C₄₁×#389	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#389	C₂²	1	1	yes	characteristic, complemented
68	C₄₁×#388	C₂²	1	1	yes	characteristic, complemented
69	C₄₁×#388	C₂²	1	1	yes	characteristic, complemented
70	C₄₁×#388	C₂²	1	2	yes	complemented
71	C₄₁×#388	C₂²	1	2	yes	complemented
72	C₄₁×#388	C₂²	1	2	yes	complemented
73	C₄₁×#388	C₂²	1	2	yes	complemented
74	C₄₁×#388	C₂²	1	2	yes	complemented
75	C₄₁×#388	C₂²	1	2	yes	complemented
76	C₄₁×#388	C₂²	1	2	yes	complemented
77	C₄₁×#388	C₂²	1	2	yes	complemented
78	C₄₁×#388	C₂²	1	2	yes	complemented
79	C₄₁×#387	C₂²	1	1	yes	characteristic, complemented
80	C₄₁×#387	C₂²	1	1	yes	characteristic, complemented
81	C₄₁×#387	C₂²	1	2	yes	complemented
82	C₄₁×#386	C₂²	1	1	yes	characteristic
83	C₄₁×#386	C₂²	1	1	yes	characteristic
84	C₄₁×#386	C₂²	1	2	yes	—
85	C₄₁×#386	C₂²	1	2	yes	complemented
86	C₄₁×#386	C₂²	1	2	yes	complemented
87	C₄₁×#386	C₂²	1	2	yes	complemented
88	C₄₁×#386	C₂²	1	2	yes	complemented
89	C₄₁×#386	C₂²	1	2	yes	complemented
90	C₄₁×#386	C₂²	1	2	yes	complemented
91	C₄₁×#386	C₂²	1	2	yes	complemented
92	C₄₁×#386	C₂²	1	2	yes	complemented
93	C₄₁×#386	C₂²	1	2	yes	complemented
94	C₄₁×#386	C₂²	1	2	yes	complemented
95	C₄₁×#386	C₂²	1	2	yes	complemented
96	C₄₁×#386	C₂²	1	2	yes	complemented
97	C₄₁×#386	C₂²	1	2	yes	complemented
98	C₄₁×#386	C₂²	1	2	yes	complemented
99	C₄₁×#385	C₂²	1	1	yes	characteristic, complemented
100	C₄₁×#385	C₂²	1	1	yes	characteristic, complemented
101	C₄₁×#385	C₂²	1	2	yes	complemented
102	C₄₁×#385	C₂²	1	2	yes	complemented
103	C₄₁×#382	C₂²	1	1	yes	characteristic, complemented
104	C₄₁×#381	C₂²	1	2	yes	complemented
105	C₄₁×#381	C₂²	1	2	yes	complemented
106	C₄₁×#380	C₂²	1	1	yes	characteristic, complemented
107	C₄₁×#380	C₂²	1	2	yes	complemented
108	C₄₁×#380	C₂²	1	1	yes	characteristic, complemented
109	C₄₁×#379	C₂²	1	2	yes	complemented
110	C₄₁×#379	C₂²	1	2	yes	complemented
111	C₄₁×#379	C₂²	1	2	yes	complemented
112	C₄₁×#379	C₂²	1	2	yes	complemented
113	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
123	C₄₁×#376	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₄₁	C₂³	1	2	yes	—
125	C₂⁵×C₄₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₄₁	—	4	2	no	—
127	C₂²×D₄×C₄₁	—	4	2	no	—
128	C₂²×D₄×C₄₁	—	4	2	no	—
129	C₂²×D₄×C₄₁	—	4	2	no	—
130	C₂²×D₄×C₄₁	—	4	4	no	—
131	C₂²×D₄×C₄₁	—	4	4	no	—
132	C₂²×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
133	C₂²×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
134	C₂²×D₄×C₄₁	C₂×C₄	1	16	yes	complemented
135	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
138	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
142	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
143	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
150	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
151	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
152	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
153	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
154	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
155	#127×C₄₁	C₂×C₄	1	8	yes	complemented
156	#121×C₄₁	C₂×C₄	1	8	yes	complemented
157	#121×C₄₁	C₂×C₄	1	8	yes	complemented
158	#121×C₄₁	C₂×C₄	1	16	yes	complemented
159	#120×C₄₁	C₂×C₄	1	16	yes	complemented
160	#120×C₄₁	C₂×C₄	1	16	yes	complemented
161	C₄×D₄×C₄₁	—	4	2	no	—
162	C₄×D₄×C₄₁	—	4	2	no	—
163	C₄×D₄×C₄₁	—	4	2	no	—
164	C₄×D₄×C₄₁	—	4	2	no	—
165	C₄×D₄×C₄₁	—	4	4	no	—
166	C₄×D₄×C₄₁	—	4	4	no	—
167	C₄×D₄×C₄₁	—	4	4	no	—
168	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
169	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
170	#117×C₄₁	—	4	2	no	—
171	#117×C₄₁	—	4	2	no	—
172	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
173	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
187	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
188	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
189	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
190	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
224	C₂×C₄²×C₄₁	—	4	2	no	—
225	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
232	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
233	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
234	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
235	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
236	#95×C₄₁	C₂³	1	1	yes	characteristic
237	#95×C₄₁	C₂³	1	1	yes	characteristic
238	#95×C₄₁	C₂³	1	1	yes	characteristic
239	#95×C₄₁	C₂³	1	1	yes	characteristic
240	#95×C₄₁	C₂³	1	1	yes	characteristic
241	#95×C₄₁	C₂³	1	1	yes	characteristic
242	#95×C₄₁	C₂³	1	2	yes	—
243	#95×C₄₁	C₂³	1	2	yes	—
244	#95×C₄₁	C₂³	1	2	yes	—
245	#95×C₄₁	C₂³	1	2	yes	—
246	#95×C₄₁	C₂³	1	2	yes	—
247	#95×C₄₁	C₂³	1	2	yes	—
248	#95×C₄₁	C₂³	1	1	yes	characteristic
249	#95×C₄₁	C₂³	1	1	yes	characteristic
250	#95×C₄₁	C₂³	1	1	yes	characteristic
251	#95×C₄₁	C₂³	1	2	yes	—
252	#95×C₄₁	C₂³	1	1	yes	characteristic
253	#95×C₄₁	C₂³	1	2	yes	—
254	#95×C₄₁	C₂³	1	2	yes	—
255	C₂⁴×C₄₁	—	2	4	no	—
256	C₂⁴×C₄₁	—	2	4	no	—
257	C₂⁴×C₄₁	—	4	2	no	—
258	C₂⁴×C₄₁	—	4	2	no	—
259	C₂⁴×C₄₁	—	4	2	no	—
260	C₂⁴×C₄₁	—	4	2	no	—
261	C₂⁴×C₄₁	—	4	2	no	—
262	C₂⁴×C₄₁	—	4	2	no	—
263	C₂⁴×C₄₁	—	4	2	no	—
264	C₂⁴×C₄₁	—	4	2	no	—
265	C₂⁴×C₄₁	—	4	2	no	—
266	C₂⁴×C₄₁	—	4	2	no	—
267	C₂⁴×C₄₁	C₂²×C₄	1	8	yes	—
268	C₂⁴×C₄₁	C₂²×C₄	1	8	yes	—
269	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
270	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
271	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
272	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
273	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
274	C₂×D₄×C₄₁	—	2	4	no	—
275	C₂×D₄×C₄₁	—	2	4	no	—
276	C₂×D₄×C₄₁	—	2	2	no	—
277	C₂×D₄×C₄₁	—	2	2	no	—
278	C₂×D₄×C₄₁	—	2	2	no	—
279	C₂×D₄×C₄₁	—	2	2	no	—
280	C₂×D₄×C₄₁	—	2	2	no	—
281	C₂×D₄×C₄₁	—	2	2	no	—
282	C₂×D₄×C₄₁	—	2	2	no	—
283	C₂×D₄×C₄₁	—	2	2	no	—
284	C₂×D₄×C₄₁	—	4	16	no	—
285	C₂×D₄×C₄₁	—	4	16	no	—
286	C₂×D₄×C₄₁	—	4	2	no	—
287	C₂×D₄×C₄₁	—	4	2	no	—
288	C₂×D₄×C₄₁	—	4	2	no	—
289	C₂×D₄×C₄₁	—	4	2	no	—
290	C₂×D₄×C₄₁	—	4	2	no	—
291	C₂×D₄×C₄₁	—	4	2	no	—
292	C₂×D₄×C₄₁	—	4	2	no	—
293	C₂×D₄×C₄₁	—	4	2	no	—
294	C₂×D₄×C₄₁	—	4	2	no	—
295	C₂×D₄×C₄₁	—	4	2	no	—
296	C₂×D₄×C₄₁	—	4	32	no	—
297	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
298	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
299	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
300	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
301	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
302	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
303	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
304	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
305	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
306	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
307	C₂²×C₄×C₄₁	—	2	2	no	—
308	C₂²×C₄×C₄₁	—	2	2	no	—
309	C₂²×C₄×C₄₁	—	2	2	no	—
310	C₂²×C₄×C₄₁	—	2	2	no	—
311	C₂²×C₄×C₄₁	—	2	2	no	—
312	C₂²×C₄×C₄₁	—	2	2	no	—
313	C₂²×C₄×C₄₁	—	2	4	no	—
314	C₂²×C₄×C₄₁	—	2	2	no	—
315	C₂²×C₄×C₄₁	—	2	4	no	—
316	C₂²×C₄×C₄₁	—	4	1	no	—
317	C₂²×C₄×C₄₁	—	4	1	no	—
318	C₂²×C₄×C₄₁	—	4	1	no	—
319	C₂²×C₄×C₄₁	—	4	2	no	—
320	C₂²×C₄×C₄₁	—	4	2	no	—
321	C₂²×C₄×C₄₁	—	4	2	no	—
322	C₂²×C₄×C₄₁	—	4	2	no	—
323	C₂²×C₄×C₄₁	—	4	2	no	—
324	C₂²×C₄×C₄₁	—	4	2	no	—
325	C₂²×C₄×C₄₁	—	4	2	no	—
326	C₂²×C₄×C₄₁	—	4	2	no	—
327	C₂²×C₄×C₄₁	—	4	2	no	—
328	C₂²×C₄×C₄₁	—	4	2	no	—
329	C₂²×C₄×C₄₁	—	4	2	no	—
330	C₂²×C₄×C₄₁	—	4	2	no	—
331	C₂²×C₄×C₄₁	—	4	2	no	—
332	C₂²×C₄×C₄₁	—	4	2	no	—
333	C₂²×C₄×C₄₁	—	4	2	no	—
334	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
335	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
336	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
337	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
355	C₄⋊C₄×C₄₁	—	2	2	no	—
356	C₄⋊C₄×C₄₁	—	2	2	no	—
357	C₄⋊C₄×C₄₁	—	2	2	no	—
358	C₄⋊C₄×C₄₁	—	2	2	no	—
359	C₄⋊C₄×C₄₁	—	2	2	no	—
360	C₄⋊C₄×C₄₁	—	4	2	no	—
361	C₄⋊C₄×C₄₁	—	4	1	no	—
362	C₄⋊C₄×C₄₁	—	4	1	no	—
363	C₄⋊C₄×C₄₁	—	4	1	no	—
364	C₄⋊C₄×C₄₁	—	4	2	no	—
365	C₄⋊C₄×C₄₁	—	4	2	no	—
366	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
367	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
368	C₂²⋊C₄×C₄₁	—	2	2	no	—
369	C₂²⋊C₄×C₄₁	—	2	4	no	—
370	C₂²⋊C₄×C₄₁	—	2	2	no	—
371	C₂²⋊C₄×C₄₁	—	2	2	no	—
372	C₂²⋊C₄×C₄₁	—	2	4	no	—
373	C₂²⋊C₄×C₄₁	—	2	4	no	—
374	C₂²⋊C₄×C₄₁	—	4	2	no	—
375	C₂²⋊C₄×C₄₁	—	4	2	no	—
376	C₂²⋊C₄×C₄₁	—	4	2	no	—
377	C₂²⋊C₄×C₄₁	—	4	2	no	—
378	C₂²⋊C₄×C₄₁	—	4	2	no	—
379	C₂²⋊C₄×C₄₁	—	4	2	no	—
380	C₂²⋊C₄×C₄₁	—	4	2	no	—
381	C₂²⋊C₄×C₄₁	—	4	2	no	—
382	C₂²⋊C₄×C₄₁	—	4	2	no	—
383	C₂²⋊C₄×C₄₁	—	4	2	no	—
384	C₂²⋊C₄×C₄₁	—	4	2	no	—
385	C₂²⋊C₄×C₄₁	—	4	2	no	—
386	C₂²⋊C₄×C₄₁	—	4	1	no	—
387	C₂²⋊C₄×C₄₁	—	4	1	no	—
388	C₂²⋊C₄×C₄₁	—	4	1	no	—
389	C₂²⋊C₄×C₄₁	—	4	2	no	—
390	C₂²⋊C₄×C₄₁	—	4	2	no	—
391	C₂²⋊C₄×C₄₁	—	4	2	no	—
392	C₂²⋊C₄×C₄₁	—	4	2	no	—
393	C₂²⋊C₄×C₄₁	—	4	2	no	—
394	C₂²⋊C₄×C₄₁	—	4	2	no	—
395	C₂²⋊C₄×C₄₁	—	4	2	no	—
396	C₂²⋊C₄×C₄₁	—	4	2	no	—
397	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
398	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
399	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
400	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
401	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
402	C₄²×C₄₁	—	2	2	no	—
403	C₄²×C₄₁	—	2	2	no	—
404	C₄²×C₄₁	—	2	2	no	—
405	C₄²×C₄₁	—	2	2	no	—
406	C₄²×C₄₁	—	4	1	no	—
407	C₄²×C₄₁	—	4	1	no	—
408	C₄²×C₄₁	—	4	2	no	—
409	C₄²×C₄₁	—	4	2	no	—
410	C₄²×C₄₁	—	4	2	no	—
411	C₄²×C₄₁	—	4	2	no	—
412	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
413	C₂³×C₄₁	—	2	1	no	—
414	C₂³×C₄₁	—	2	1	no	—
415	C₂³×C₄₁	—	2	1	no	—
416	C₂³×C₄₁	—	2	1	no	—
417	C₂³×C₄₁	—	2	1	no	—
418	C₂³×C₄₁	—	2	2	no	—
419	C₂³×C₄₁	—	2	2	no	—
420	C₂³×C₄₁	—	2	1	no	—
421	C₂³×C₄₁	—	2	1	no	—
422	C₂³×C₄₁	—	2	2	no	—
423	C₂³×C₄₁	—	2	2	no	—
424	C₂³×C₄₁	—	2	2	no	—
425	C₂³×C₄₁	—	2	2	no	—
426	C₂³×C₄₁	—	2	2	no	—
427	C₂³×C₄₁	—	2	2	no	—
428	C₂³×C₄₁	—	2	2	no	—
429	C₂³×C₄₁	—	2	2	no	—
430	C₂³×C₄₁	—	2	2	no	—
431	C₂³×C₄₁	—	2	2	no	—
432	C₂³×C₄₁	—	2	2	no	—
433	C₂³×C₄₁	—	2	2	no	—
434	C₂³×C₄₁	—	2	1	no	—
435	C₂³×C₄₁	—	2	1	no	—
436	C₂³×C₄₁	—	2	2	no	—
437	C₂³×C₄₁	—	2	2	no	—
438	C₂³×C₄₁	—	2	1	no	—
439	C₂³×C₄₁	—	2	2	no	—
440	C₂³×C₄₁	—	2	2	no	—
441	C₂³×C₄₁	—	2	16	no	—
442	C₂³×C₄₁	—	4	8	no	—
443	C₂³×C₄₁	—	4	8	no	—
444	C₂³×C₄₁	—	4	8	no	—
445	C₂³×C₄₁	—	4	8	no	—
446	C₂³×C₄₁	—	4	8	no	—
447	C₂³×C₄₁	—	8	4	no	—
448	C₂³×C₄₁	—	8	4	no	—
449	C₂³×C₄₁	—	8	4	no	—
450	C₂³×C₄₁	—	8	4	no	—
451	C₂³×C₄₁	—	8	4	no	—
452	C₂³×C₄₁	—	8	4	no	—
453	C₂³×C₄₁	—	8	4	no	—
454	C₂³×C₄₁	—	8	4	no	—
455	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
456	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
457	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
458	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
459	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
460	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
461	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
462	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
463	D₄×C₄₁	—	2	8	no	—
464	D₄×C₄₁	—	2	16	no	—
465	D₄×C₄₁	—	2	8	no	—
466	D₄×C₄₁	—	2	8	no	—
467	D₄×C₄₁	—	2	8	no	—
468	D₄×C₄₁	—	4	8	no	—
469	D₄×C₄₁	—	4	8	no	—
470	D₄×C₄₁	—	4	8	no	—
471	D₄×C₄₁	—	4	8	no	—
472	D₄×C₄₁	—	4	8	no	—
473	C₂×C₄×C₄₁	—	2	1	no	—
474	C₂×C₄×C₄₁	—	2	1	no	—
475	C₂×C₄×C₄₁	—	2	1	no	—
476	C₂×C₄×C₄₁	—	2	1	no	—
477	C₂×C₄×C₄₁	—	2	1	no	—
478	C₂×C₄×C₄₁	—	2	2	no	—
479	C₂×C₄×C₄₁	—	2	2	no	—
480	C₂×C₄×C₄₁	—	2	1	no	—
481	C₂×C₄×C₄₁	—	2	1	no	—
482	C₂×C₄×C₄₁	—	2	1	no	—
483	C₂×C₄×C₄₁	—	2	1	no	—
484	C₂×C₄×C₄₁	—	2	1	no	—
485	C₂×C₄×C₄₁	—	2	8	no	—
486	C₂×C₄×C₄₁	—	2	8	no	—
487	C₂×C₄×C₄₁	—	2	1	no	—
488	C₂×C₄×C₄₁	—	2	1	no	—
489	C₂×C₄×C₄₁	—	2	1	no	—
490	C₂×C₄×C₄₁	—	2	1	no	—
491	C₂×C₄×C₄₁	—	2	1	no	—
492	C₂×C₄×C₄₁	—	2	1	no	—
493	C₂×C₄×C₄₁	—	2	1	no	—
494	C₂×C₄×C₄₁	—	2	1	no	—
495	C₂×C₄×C₄₁	—	2	2	no	—
496	C₂×C₄×C₄₁	—	2	2	no	—
497	C₂×C₄×C₄₁	—	2	2	no	—
498	C₂×C₄×C₄₁	—	2	2	no	—
499	C₂×C₄×C₄₁	—	2	2	no	—
500	C₂×C₄×C₄₁	—	2	2	no	—
501	C₂×C₄×C₄₁	—	2	1	no	—
502	C₂×C₄×C₄₁	—	2	1	no	—
503	C₂×C₄×C₄₁	—	2	2	no	—
504	C₂×C₄×C₄₁	—	2	1	no	—
505	C₂×C₄×C₄₁	—	2	2	no	—
506	C₂×C₄×C₄₁	—	2	1	no	—
507	C₂×C₄×C₄₁	—	2	1	no	—
508	C₂×C₄×C₄₁	—	2	1	no	—
509	C₂×C₄×C₄₁	—	2	1	no	—
510	C₂×C₄×C₄₁	—	2	2	no	—
511	C₂×C₄×C₄₁	—	2	2	no	—
512	C₂×C₄×C₄₁	—	2	1	no	—
513	C₂×C₄×C₄₁	—	2	1	no	—
514	C₂×C₄×C₄₁	—	2	2	no	—
515	C₂×C₄×C₄₁	—	2	1	no	—
516	C₂×C₄×C₄₁	—	2	1	no	—
517	C₂×C₄×C₄₁	—	2	2	no	—
518	C₂×C₄×C₄₁	—	2	1	no	—
519	C₂×C₄×C₄₁	—	2	1	no	—
520	C₂×C₄×C₄₁	—	4	8	no	—
521	C₂×C₄×C₄₁	—	4	4	no	—
522	C₂×C₄×C₄₁	—	4	4	no	—
523	C₂×C₄×C₄₁	—	8	4	no	—
524	C₂×C₄×C₄₁	—	8	4	no	—
525	C₂×C₄×C₄₁	—	8	4	no	—
526	C₂×C₄×C₄₁	—	8	4	no	—
527	C₂×C₄×C₄₁	—	8	4	no	—
528	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
529	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
530	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
531	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
532	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
533	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
534	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
535	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
536	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
537	#34471	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂²×C₄₁	—	2	2	no	—
539	C₂²×C₄₁	—	2	2	no	—
540	C₂²×C₄₁	—	2	2	no	—
541	C₂²×C₄₁	—	2	2	no	—
542	C₂²×C₄₁	—	2	2	no	—
543	C₂²×C₄₁	—	2	2	no	—
544	C₂²×C₄₁	—	2	2	no	—
545	C₂²×C₄₁	—	2	4	no	—
546	C₂²×C₄₁	—	2	2	no	—
547	C₂²×C₄₁	—	2	4	no	—
548	C₂²×C₄₁	—	2	4	no	—
549	C₂²×C₄₁	—	2	4	no	—
550	C₂²×C₄₁	—	2	4	no	—
551	C₂²×C₄₁	—	2	4	no	—
552	C₂²×C₄₁	—	2	4	no	—
553	C₂²×C₄₁	—	2	4	no	—
554	C₂²×C₄₁	—	2	2	no	—
555	C₂²×C₄₁	—	2	4	no	—
556	C₂²×C₄₁	—	4	2	no	—
557	C₂²×C₄₁	—	4	2	no	—
558	C₂²×C₄₁	—	4	1	no	—
559	C₂²×C₄₁	—	4	2	no	—
560	C₂²×C₄₁	—	4	2	no	—
561	C₂²×C₄₁	—	4	2	no	—
562	C₂²×C₄₁	—	4	1	no	—
563	C₂²×C₄₁	—	4	2	no	—
564	C₂²×C₄₁	—	4	2	no	—
565	C₂²×C₄₁	—	4	2	no	—
566	C₂²×C₄₁	—	4	1	no	—
567	C₂²×C₄₁	—	4	2	no	—
568	C₂²×C₄₁	—	4	2	no	—
569	C₂²×C₄₁	—	4	2	no	—
570	C₂²×C₄₁	—	4	1	no	—
571	C₂²×C₄₁	—	4	2	no	—
572	C₂²×C₄₁	—	8	16	no	—
573	C₂²×C₄₁	—	8	16	no	—
574	C₂²×C₄₁	#518	1	4	yes	—
575	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
576	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂²×C₄₁	#585	1	1	yes	characteristic
582	C₄×C₄₁	—	2	2	no	—
583	C₄×C₄₁	—	2	2	no	—
584	C₄×C₄₁	—	2	2	no	—
585	C₄×C₄₁	—	2	4	no	—
586	C₄×C₄₁	—	2	2	no	—
587	C₄×C₄₁	—	2	2	no	—
588	C₄×C₄₁	—	4	1	no	—
589	C₄×C₄₁	—	4	1	no	—
590	C₄×C₄₁	—	4	2	no	—
591	C₄×C₄₁	—	4	1	no	—
592	C₄×C₄₁	—	4	1	no	—
593	C₄×C₄₁	—	4	1	no	—
594	C₄×C₄₁	—	4	2	no	—
595	C₄×C₄₁	—	4	1	no	—
596	C₄×C₄₁	—	4	2	no	—
597	C₄×C₄₁	—	4	2	no	—
598	C₄×C₄₁	—	4	1	no	—
599	C₄×C₄₁	#518	1	4	yes	—
600	C₂×D₄²	C₂×C₄₁	1	1	yes	characteristic
601	#2377	C₂×C₄₁	1	2	yes	complemented
602	#2375	C₂×C₄₁	1	2	yes	complemented
603	#2366	C₂×C₄₁	1	1	yes	characteristic, complemented
604	#2363	C₂×C₄₁	1	1	yes	characteristic, complemented
605	#2361	C₂×C₄₁	1	1	yes	characteristic, complemented
606	#2358	C₂×C₄₁	1	2	yes	complemented
607	#2357	C₂×C₄₁	1	1	yes	characteristic, complemented
608	#2352	C₂×C₄₁	1	1	yes	characteristic, complemented
609	D₄×C₂²⋊C₄	C₂×C₄₁	1	2	yes	complemented
610	D₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
611	D₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
612	#2333	C₂×C₄₁	1	2	yes	complemented
613	#2328	C₂×C₄₁	1	1	yes	characteristic, complemented
614	#2324	C₂×C₄₁	1	1	yes	characteristic, complemented
615	#2321	C₂×C₄₁	1	2	yes	complemented
616	#2321	C₂×C₄₁	1	2	yes	complemented
617	#2319	C₂×C₄₁	1	1	yes	characteristic, complemented
618	#2309	C₂×C₄₁	1	1	yes	characteristic, complemented
619	#2308	C₂×C₄₁	1	2	yes	complemented
620	C₄×#121	C₂×C₄₁	1	1	yes	characteristic, complemented
621	C₂×#390	C₂×C₄₁	1	1	yes	characteristic, complemented
622	#2290	C₂×C₄₁	1	1	yes	characteristic, complemented
623	C₂×C₄₁	—	2	4	no	—
624	C₂×C₄₁	—	4	4	no	—
625	C₂×C₄₁	—	4	4	no	—
626	C₂×C₄₁	—	4	2	no	—
627	C₂×C₄₁	—	4	4	no	—
628	C₂×C₄₁	C₂×#518	1	1	yes	characteristic
629	C₂×C₄₁	C₂×#518	1	1	yes	characteristic
630	C₂×C₄₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
631	C₂×C₄₁	#3537	1	1	yes	characteristic
632	C₂×C₄₁	#3542	1	1	yes	characteristic
633	C₂×C₄₁	#3543	1	1	yes	characteristic
634	C₂×C₄₁	#3558	1	1	yes	characteristic
635	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
636	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
637	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
638	D₄²	C₄×C₄₁	1	16	yes	complemented
639	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
640	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
641	C₂×#121	C₂²×C₄₁	1	2	yes	—
642	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
643	C₂×#120	C₂²×C₄₁	1	2	yes	—
644	C₂×#120	C₂²×C₄₁	1	2	yes	—
645	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
646	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
647	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
648	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
649	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
650	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
651	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
652	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
653	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
654	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic, complemented
655	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic, complemented
656	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
657	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
658	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
659	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
660	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
661	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic, complemented
662	#390	C₂²×C₄₁	1	1	yes	characteristic
663	#390	C₂²×C₄₁	1	1	yes	characteristic
664	#390	C₂²×C₄₁	1	1	yes	characteristic
665	#390	C₂²×C₄₁	1	1	yes	characteristic
666	#390	C₂²×C₄₁	1	2	yes	complemented
667	#390	C₂²×C₄₁	1	1	yes	characteristic, complemented
668	#390	C₂²×C₄₁	1	2	yes	complemented
669	#390	C₂²×C₄₁	1	1	yes	characteristic, complemented
670	#390	C₂²×C₄₁	1	2	yes	complemented
671	#390	C₂²×C₄₁	1	2	yes	complemented
672	#390	C₂²×C₄₁	1	2	yes	complemented
673	#390	C₂²×C₄₁	1	1	yes	characteristic, complemented
674	#390	C₂²×C₄₁	1	2	yes	complemented
675	#390	C₂²×C₄₁	1	1	yes	characteristic, complemented
676	#390	C₂²×C₄₁	1	2	yes	complemented
677	#389	C₂²×C₄₁	1	1	yes	characteristic, complemented
678	#389	C₂²×C₄₁	1	1	yes	characteristic, complemented
679	#388	C₂²×C₄₁	1	2	yes	complemented
680	#388	C₂²×C₄₁	1	2	yes	complemented
681	#388	C₂²×C₄₁	1	1	yes	characteristic, complemented
682	#388	C₂²×C₄₁	1	2	yes	complemented
683	#388	C₂²×C₄₁	1	2	yes	complemented
684	#388	C₂²×C₄₁	1	2	yes	complemented
685	#388	C₂²×C₄₁	1	2	yes	complemented
686	#388	C₂²×C₄₁	1	2	yes	complemented
687	#388	C₂²×C₄₁	1	2	yes	complemented
688	#388	C₂²×C₄₁	1	1	yes	characteristic, complemented
689	#388	C₂²×C₄₁	1	2	yes	complemented
690	#387	C₂²×C₄₁	1	1	yes	characteristic, complemented
691	#387	C₂²×C₄₁	1	2	yes	complemented
692	#387	C₂²×C₄₁	1	1	yes	characteristic, complemented
693	#386	C₂²×C₄₁	1	1	yes	characteristic
694	#386	C₂²×C₄₁	1	2	yes	—
695	#386	C₂²×C₄₁	1	1	yes	characteristic
696	#386	C₂²×C₄₁	1	2	yes	complemented
697	#386	C₂²×C₄₁	1	2	yes	complemented
698	#386	C₂²×C₄₁	1	2	yes	complemented
699	#386	C₂²×C₄₁	1	2	yes	complemented
700	#386	C₂²×C₄₁	1	2	yes	complemented
701	#386	C₂²×C₄₁	1	2	yes	complemented
702	#386	C₂²×C₄₁	1	2	yes	complemented
703	#386	C₂²×C₄₁	1	2	yes	complemented
704	#386	C₂²×C₄₁	1	2	yes	complemented
705	#386	C₂²×C₄₁	1	2	yes	complemented
706	#386	C₂²×C₄₁	1	2	yes	complemented
707	#386	C₂²×C₄₁	1	2	yes	complemented
708	#386	C₂²×C₄₁	1	2	yes	complemented
709	#386	C₂²×C₄₁	1	2	yes	complemented
710	#385	C₂²×C₄₁	1	1	yes	characteristic, complemented
711	#385	C₂²×C₄₁	1	2	yes	complemented
712	#385	C₂²×C₄₁	1	2	yes	complemented
713	#385	C₂²×C₄₁	1	1	yes	characteristic, complemented
714	#382	C₂²×C₄₁	1	1	yes	characteristic, complemented
715	#381	C₂²×C₄₁	1	2	yes	complemented
716	#381	C₂²×C₄₁	1	2	yes	complemented
717	#380	C₂²×C₄₁	1	2	yes	complemented
718	#380	C₂²×C₄₁	1	1	yes	characteristic, complemented
719	#380	C₂²×C₄₁	1	1	yes	characteristic, complemented
720	#379	C₂²×C₄₁	1	2	yes	complemented
721	#379	C₂²×C₄₁	1	2	yes	complemented
722	#379	C₂²×C₄₁	1	2	yes	complemented
723	#379	C₂²×C₄₁	1	2	yes	complemented
724	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
725	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
726	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
727	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
728	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
729	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
730	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
731	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
732	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
733	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
734	#376	C₂²×C₄₁	1	1	yes	characteristic, complemented
735	C₄₁	#34471	1	1	yes	characteristic, direct product factor, Sylow
736	C₂⁵	C₂³×C₄₁	1	2	yes	—
737	C₂⁵	C₂³×C₄₁	1	2	yes	—
738	C₂²×D₄	—	4	2	no	—
739	C₂²×D₄	—	4	2	no	—
740	C₂²×D₄	—	4	2	no	—
741	C₂²×D₄	—	4	2	no	—
742	C₂²×D₄	—	4	4	no	—
743	C₂²×D₄	—	4	4	no	—
744	C₂²×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
745	C₂²×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
746	C₂²×D₄	C₂×C₄×C₄₁	1	16	yes	complemented
747	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
748	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
750	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
751	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
752	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
753	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
754	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
755	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
756	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
757	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
758	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
759	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
760	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
761	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
762	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
763	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
764	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
765	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
766	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
767	#127	C₂×C₄×C₄₁	1	8	yes	complemented
768	#121	C₂×C₄×C₄₁	1	8	yes	complemented
769	#121	C₂×C₄×C₄₁	1	8	yes	complemented
770	#121	C₂×C₄×C₄₁	1	16	yes	complemented
771	#120	C₂×C₄×C₄₁	1	16	yes	complemented
772	#120	C₂×C₄×C₄₁	1	16	yes	complemented
773	C₄×D₄	—	4	2	no	—
774	C₄×D₄	—	4	2	no	—
775	C₄×D₄	—	4	2	no	—
776	C₄×D₄	—	4	2	no	—
777	C₄×D₄	—	4	4	no	—
778	C₄×D₄	—	4	4	no	—
779	C₄×D₄	—	4	4	no	—
780	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
781	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
782	#117	—	4	2	no	—
783	#117	—	4	2	no	—
784	C₂×C₄⋊C₄	—	4	2	no	—
785	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
791	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
793	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
794	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
795	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
798	C₂×C₂²⋊C₄	—	4	4	no	—
799	C₂×C₂²⋊C₄	—	4	4	no	—
800	C₂×C₂²⋊C₄	—	4	4	no	—
801	C₂×C₂²⋊C₄	—	4	4	no	—
802	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
803	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
804	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
808	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
819	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
821	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
829	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
830	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
831	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
832	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
833	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
834	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
835	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
836	C₂×C₄²	—	4	2	no	—
837	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
838	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
839	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
841	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
842	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
843	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
844	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
845	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
846	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
847	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
848	#95	C₂³×C₄₁	1	1	yes	characteristic
849	#95	C₂³×C₄₁	1	1	yes	characteristic
850	#95	C₂³×C₄₁	1	1	yes	characteristic
851	#95	C₂³×C₄₁	1	1	yes	characteristic
852	#95	C₂³×C₄₁	1	1	yes	characteristic
853	#95	C₂³×C₄₁	1	1	yes	characteristic
854	#95	C₂³×C₄₁	1	2	yes	—
855	#95	C₂³×C₄₁	1	2	yes	—
856	#95	C₂³×C₄₁	1	2	yes	—
857	#95	C₂³×C₄₁	1	2	yes	—
858	#95	C₂³×C₄₁	1	2	yes	—
859	#95	C₂³×C₄₁	1	2	yes	—
860	#95	C₂³×C₄₁	1	1	yes	characteristic
861	#95	C₂³×C₄₁	1	1	yes	characteristic
862	#95	C₂³×C₄₁	1	1	yes	characteristic
863	#95	C₂³×C₄₁	1	2	yes	—
864	#95	C₂³×C₄₁	1	1	yes	characteristic
865	#95	C₂³×C₄₁	1	2	yes	—
866	#95	C₂³×C₄₁	1	2	yes	—
867	C₂⁴	—	2	4	no	—
868	C₂⁴	—	2	4	no	—
869	C₂⁴	—	4	2	no	—
870	C₂⁴	—	4	2	no	—
871	C₂⁴	—	4	2	no	—
872	C₂⁴	—	4	2	no	—
873	C₂⁴	—	4	2	no	—
874	C₂⁴	—	4	2	no	—
875	C₂⁴	—	4	2	no	—
876	C₂⁴	—	4	2	no	—
877	C₂⁴	—	4	2	no	—
878	C₂⁴	—	4	2	no	—
879	C₂⁴	C₂²×C₄×C₄₁	1	8	yes	—
880	C₂⁴	C₂²×C₄×C₄₁	1	8	yes	—
881	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
882	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
883	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
884	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
885	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
886	C₂×D₄	—	2	4	no	—
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	4	16	no	—
897	C₂×D₄	—	4	16	no	—
898	C₂×D₄	—	4	2	no	—
899	C₂×D₄	—	4	2	no	—
900	C₂×D₄	—	4	2	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	2	no	—
904	C₂×D₄	—	4	2	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	32	no	—
909	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
910	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
911	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
912	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
913	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
914	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
915	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
916	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
917	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
918	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	4	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	4	no	—
928	C₂²×C₄	—	4	1	no	—
929	C₂²×C₄	—	4	1	no	—
930	C₂²×C₄	—	4	2	no	—
931	C₂²×C₄	—	4	2	no	—
932	C₂²×C₄	—	4	1	no	—
933	C₂²×C₄	—	4	2	no	—
934	C₂²×C₄	—	4	2	no	—
935	C₂²×C₄	—	4	2	no	—
936	C₂²×C₄	—	4	2	no	—
937	C₂²×C₄	—	4	2	no	—
938	C₂²×C₄	—	4	2	no	—
939	C₂²×C₄	—	4	2	no	—
940	C₂²×C₄	—	4	2	no	—
941	C₂²×C₄	—	4	2	no	—
942	C₂²×C₄	—	4	2	no	—
943	C₂²×C₄	—	4	2	no	—
944	C₂²×C₄	—	4	2	no	—
945	C₂²×C₄	—	4	2	no	—
946	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
947	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
948	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
949	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
957	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
960	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	4	2	no	—
973	C₄⋊C₄	—	4	1	no	—
974	C₄⋊C₄	—	4	1	no	—
975	C₄⋊C₄	—	4	2	no	—
976	C₄⋊C₄	—	4	2	no	—
977	C₄⋊C₄	—	4	1	no	—
978	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
979	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	2	4	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	4	1	no	—
997	C₂²⋊C₄	—	4	1	no	—
998	C₂²⋊C₄	—	4	2	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	—	4	2	no	—
1001	C₂²⋊C₄	—	4	2	no	—
1002	C₂²⋊C₄	—	4	2	no	—
1003	C₂²⋊C₄	—	4	2	no	—
1004	C₂²⋊C₄	—	4	2	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	1	no	—
1009	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
1010	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
1011	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
1012	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
1013	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	4	1	no	—
1019	C₄²	—	4	1	no	—
1020	C₄²	—	4	2	no	—
1021	C₄²	—	4	2	no	—
1022	C₄²	—	4	2	no	—
1023	C₄²	—	4	2	no	—
1024	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	2	no	—
1053	C₂³	—	2	16	no	—
1054	C₂³	—	4	8	no	—
1055	C₂³	—	4	8	no	—
1056	C₂³	—	4	8	no	—
1057	C₂³	—	4	8	no	—
1058	C₂³	—	4	8	no	—
1059	C₂³	—	8	4	no	—
1060	C₂³	—	8	4	no	—
1061	C₂³	—	8	4	no	—
1062	C₂³	—	8	4	no	—
1063	C₂³	—	8	4	no	—
1064	C₂³	—	8	4	no	—
1065	C₂³	—	8	4	no	—
1066	C₂³	—	8	4	no	—
1067	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
1068	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
1069	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
1070	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
1071	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
1072	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
1073	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
1074	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
1075	D₄	—	2	8	no	—
1076	D₄	—	2	16	no	—
1077	D₄	—	2	8	no	—
1078	D₄	—	2	8	no	—
1079	D₄	—	2	8	no	—
1080	D₄	—	4	8	no	—
1081	D₄	—	4	8	no	—
1082	D₄	—	4	8	no	—
1083	D₄	—	4	8	no	—
1084	D₄	—	4	8	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	8	no	—
1098	C₂×C₄	—	2	8	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	4	8	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	8	4	no	—
1136	C₂×C₄	—	8	4	no	—
1137	C₂×C₄	—	8	4	no	—
1138	C₂×C₄	—	8	4	no	—
1139	C₂×C₄	—	8	4	no	—
1140	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1141	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1142	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1143	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1144	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
1145	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1146	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1147	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1148	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	4	no	—
1160	C₂²	—	2	4	no	—
1161	C₂²	—	2	4	no	—
1162	C₂²	—	2	4	no	—
1163	C₂²	—	2	4	no	—
1164	C₂²	—	2	4	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	4	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	8	16	no	—
1184	C₂²	—	8	16	no	—
1185	C₂²	C₄₁×#518	1	4	yes	—
1186	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
1187	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1188	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1189	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1190	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1191	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1192	C₂²	C₄₁×#585	1	1	yes	characteristic
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	4	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	2	no	—
1210	C₄	C₄₁×#518	1	4	yes	—
1211	C₂	—	2	4	no	—
1212	C₂	—	4	2	no	—
1213	C₂	—	4	4	no	—
1214	C₂	—	4	4	no	—
1215	C₂	—	4	4	no	—
1216	C₂	C₂×C₄₁×#518	1	1	yes	characteristic
1217	C₂	C₂×C₄₁×#518	1	1	yes	characteristic
1218	C₂	C₄×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1219	C₂	C₄₁×#3537	1	1	yes	characteristic
1220	C₂	C₄₁×#3542	1	1	yes	characteristic
1221	C₂	C₄₁×#3543	1	1	yes	characteristic
1222	C₂	C₄₁×#3558	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂×D₄²×C₄₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2377	C₂	semidirect
3. C₄₁×#2375	C₂	semidirect
4. C₄₁×#2366	C₂	semidirect
5. C₄₁×#2363	C₂	semidirect
6. C₄₁×#2361	C₂	semidirect
7. C₄₁×#2358	C₂	semidirect
8. C₄₁×#2357	C₂	semidirect
9. C₄₁×#2352	C₂	semidirect
10. D₄×C₂²⋊C₄×C₄₁	C₂	semidirect
11. D₄×C₂²⋊C₄×C₄₁	C₂	semidirect
12. D₄×C₂²⋊C₄×C₄₁	C₂	semidirect
13. C₄₁×#2333	C₂	semidirect
14. C₄₁×#2328	C₂	semidirect
15. C₄₁×#2324	C₂	semidirect
16. C₄₁×#2321	C₂	semidirect
17. C₄₁×#2321	C₂	semidirect
18. C₄₁×#2319	C₂	semidirect
19. C₄₁×#2309	C₂	semidirect
20. C₄₁×#2308	C₂	semidirect
21. C₄×#121×C₄₁	C₂	semidirect
22. C₂×C₄₁×#390	C₂	semidirect
23. C₄₁×#2290	C₂	semidirect
27. D₄²×C₄₁	C₄	semidirect
36. C₂×C₄×D₄×C₄₁	C₂²	semidirect
37. C₂×C₄×D₄×C₄₁	C₂²	semidirect
38. C₂×C₄×D₄×C₄₁	C₂²	semidirect
39. C₂×C₄×D₄×C₄₁	C₂²	semidirect
40. C₂×C₄×D₄×C₄₁	C₂²	semidirect
41. C₂×C₄×D₄×C₄₁	C₂²	semidirect
42. C₂×C₄×D₄×C₄₁	C₂²	semidirect
43. C₂×#117×C₄₁	C₂²	semidirect
44. C₂×#117×C₄₁	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
46. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
47. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
50. C₂²×C₄²×C₄₁	C₂²	semidirect
55. C₄₁×#390	C₂²	semidirect
56. C₄₁×#390	C₂²	semidirect
57. C₄₁×#390	C₂²	semidirect
58. C₄₁×#390	C₂²	semidirect
59. C₄₁×#390	C₂²	semidirect
60. C₄₁×#390	C₂²	semidirect
61. C₄₁×#390	C₂²	semidirect
62. C₄₁×#390	C₂²	semidirect
63. C₄₁×#390	C₂²	semidirect
64. C₄₁×#390	C₂²	semidirect
65. C₄₁×#390	C₂²	semidirect
66. C₄₁×#389	C₂²	semidirect
67. C₄₁×#389	C₂²	semidirect
68. C₄₁×#388	C₂²	semidirect
69. C₄₁×#388	C₂²	semidirect
70. C₄₁×#388	C₂²	semidirect
71. C₄₁×#388	C₂²	semidirect
72. C₄₁×#388	C₂²	semidirect
73. C₄₁×#388	C₂²	semidirect
74. C₄₁×#388	C₂²	semidirect
75. C₄₁×#388	C₂²	semidirect
76. C₄₁×#388	C₂²	semidirect
77. C₄₁×#388	C₂²	semidirect
78. C₄₁×#388	C₂²	semidirect
79. C₄₁×#387	C₂²	semidirect
80. C₄₁×#387	C₂²	semidirect
81. C₄₁×#387	C₂²	semidirect
85. C₄₁×#386	C₂²	semidirect
86. C₄₁×#386	C₂²	semidirect
87. C₄₁×#386	C₂²	semidirect
88. C₄₁×#386	C₂²	semidirect
89. C₄₁×#386	C₂²	semidirect
90. C₄₁×#386	C₂²	semidirect
91. C₄₁×#386	C₂²	semidirect
92. C₄₁×#386	C₂²	semidirect
93. C₄₁×#386	C₂²	semidirect
94. C₄₁×#386	C₂²	semidirect
95. C₄₁×#386	C₂²	semidirect
96. C₄₁×#386	C₂²	semidirect
97. C₄₁×#386	C₂²	semidirect
98. C₄₁×#386	C₂²	semidirect
99. C₄₁×#385	C₂²	semidirect
100. C₄₁×#385	C₂²	semidirect
101. C₄₁×#385	C₂²	semidirect
102. C₄₁×#385	C₂²	semidirect
103. C₄₁×#382	C₂²	semidirect
104. C₄₁×#381	C₂²	semidirect
105. C₄₁×#381	C₂²	semidirect
106. C₄₁×#380	C₂²	semidirect
107. C₄₁×#380	C₂²	semidirect
108. C₄₁×#380	C₂²	semidirect
109. C₄₁×#379	C₂²	semidirect
110. C₄₁×#379	C₂²	semidirect
111. C₄₁×#379	C₂²	semidirect
112. C₄₁×#379	C₂²	semidirect
113. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
114. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
115. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
116. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
117. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
123. C₄₁×#376	C₂²	semidirect
132. C₂²×D₄×C₄₁	C₂×C₄	semidirect
133. C₂²×D₄×C₄₁	C₂×C₄	semidirect
134. C₂²×D₄×C₄₁	C₂×C₄	semidirect
155. #127×C₄₁	C₂×C₄	semidirect
156. #121×C₄₁	C₂×C₄	semidirect
157. #121×C₄₁	C₂×C₄	semidirect
158. #121×C₄₁	C₂×C₄	semidirect
159. #120×C₄₁	C₂×C₄	semidirect
160. #120×C₄₁	C₂×C₄	semidirect
168. C₄×D₄×C₄₁	C₂×C₄	semidirect
169. C₄×D₄×C₄₁	C₂×C₄	semidirect
537. #34471	C₄₁	direct (N × H)
601. #2377	C₂×C₄₁	semidirect
602. #2375	C₂×C₄₁	semidirect
603. #2366	C₂×C₄₁	semidirect
604. #2363	C₂×C₄₁	semidirect
605. #2361	C₂×C₄₁	semidirect
606. #2358	C₂×C₄₁	semidirect
607. #2357	C₂×C₄₁	semidirect
608. #2352	C₂×C₄₁	semidirect
609. D₄×C₂²⋊C₄	C₂×C₄₁	semidirect
610. D₄×C₂²⋊C₄	C₂×C₄₁	semidirect
611. D₄×C₂²⋊C₄	C₂×C₄₁	semidirect
612. #2333	C₂×C₄₁	semidirect
613. #2328	C₂×C₄₁	semidirect
614. #2324	C₂×C₄₁	semidirect
615. #2321	C₂×C₄₁	semidirect
616. #2321	C₂×C₄₁	semidirect
617. #2319	C₂×C₄₁	semidirect
618. #2309	C₂×C₄₁	semidirect
619. #2308	C₂×C₄₁	semidirect
620. C₄×#121	C₂×C₄₁	semidirect
621. C₂×#390	C₂×C₄₁	semidirect
622. #2290	C₂×C₄₁	semidirect
638. D₄²	C₄×C₄₁	semidirect
647. C₂×C₄×D₄	C₂²×C₄₁	semidirect
648. C₂×C₄×D₄	C₂²×C₄₁	semidirect
649. C₂×C₄×D₄	C₂²×C₄₁	semidirect
650. C₂×C₄×D₄	C₂²×C₄₁	semidirect
651. C₂×C₄×D₄	C₂²×C₄₁	semidirect
652. C₂×C₄×D₄	C₂²×C₄₁	semidirect
653. C₂×C₄×D₄	C₂²×C₄₁	semidirect
654. C₂×#117	C₂²×C₄₁	semidirect
655. C₂×#117	C₂²×C₄₁	semidirect
656. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
657. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
658. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
659. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
660. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
661. C₂²×C₄²	C₂²×C₄₁	semidirect
666. #390	C₂²×C₄₁	semidirect
667. #390	C₂²×C₄₁	semidirect
668. #390	C₂²×C₄₁	semidirect
669. #390	C₂²×C₄₁	semidirect
670. #390	C₂²×C₄₁	semidirect
671. #390	C₂²×C₄₁	semidirect
672. #390	C₂²×C₄₁	semidirect
673. #390	C₂²×C₄₁	semidirect
674. #390	C₂²×C₄₁	semidirect
675. #390	C₂²×C₄₁	semidirect
676. #390	C₂²×C₄₁	semidirect
677. #389	C₂²×C₄₁	semidirect
678. #389	C₂²×C₄₁	semidirect
679. #388	C₂²×C₄₁	semidirect
680. #388	C₂²×C₄₁	semidirect
681. #388	C₂²×C₄₁	semidirect
682. #388	C₂²×C₄₁	semidirect
683. #388	C₂²×C₄₁	semidirect
684. #388	C₂²×C₄₁	semidirect
685. #388	C₂²×C₄₁	semidirect
686. #388	C₂²×C₄₁	semidirect
687. #388	C₂²×C₄₁	semidirect
688. #388	C₂²×C₄₁	semidirect
689. #388	C₂²×C₄₁	semidirect
690. #387	C₂²×C₄₁	semidirect
691. #387	C₂²×C₄₁	semidirect
692. #387	C₂²×C₄₁	semidirect
696. #386	C₂²×C₄₁	semidirect
697. #386	C₂²×C₄₁	semidirect
698. #386	C₂²×C₄₁	semidirect
699. #386	C₂²×C₄₁	semidirect
700. #386	C₂²×C₄₁	semidirect
701. #386	C₂²×C₄₁	semidirect
702. #386	C₂²×C₄₁	semidirect
703. #386	C₂²×C₄₁	semidirect
704. #386	C₂²×C₄₁	semidirect
705. #386	C₂²×C₄₁	semidirect
706. #386	C₂²×C₄₁	semidirect
707. #386	C₂²×C₄₁	semidirect
708. #386	C₂²×C₄₁	semidirect
709. #386	C₂²×C₄₁	semidirect
710. #385	C₂²×C₄₁	semidirect
711. #385	C₂²×C₄₁	semidirect
712. #385	C₂²×C₄₁	semidirect
713. #385	C₂²×C₄₁	semidirect
714. #382	C₂²×C₄₁	semidirect
715. #381	C₂²×C₄₁	semidirect
716. #381	C₂²×C₄₁	semidirect
717. #380	C₂²×C₄₁	semidirect
718. #380	C₂²×C₄₁	semidirect
719. #380	C₂²×C₄₁	semidirect
720. #379	C₂²×C₄₁	semidirect
721. #379	C₂²×C₄₁	semidirect
722. #379	C₂²×C₄₁	semidirect
723. #379	C₂²×C₄₁	semidirect
724. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
725. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
726. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
727. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
728. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
729. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
730. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
731. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
732. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
733. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
734. #376	C₂²×C₄₁	semidirect
735. C₄₁	#34471	direct (N × H)
744. C₂²×D₄	C₂×C₄×C₄₁	semidirect
745. C₂²×D₄	C₂×C₄×C₄₁	semidirect
746. C₂²×D₄	C₂×C₄×C₄₁	semidirect
767. #127	C₂×C₄×C₄₁	semidirect
768. #121	C₂×C₄×C₄₁	semidirect
769. #121	C₂×C₄×C₄₁	semidirect
770. #121	C₂×C₄×C₄₁	semidirect
771. #120	C₂×C₄×C₄₁	semidirect
772. #120	C₂×C₄×C₄₁	semidirect
780. C₄×D₄	C₂×C₄×C₄₁	semidirect
781. C₄×D₄	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₄₁	2
C₄₁×#2377	2
C₄₁×#2375	2
C₄₁×#2366	2
C₄₁×#2363	2
C₄₁×#2361	2
C₄₁×#2358	2
C₄₁×#2357	2
C₄₁×#2352	2
D₄×C₂²⋊C₄×C₄₁	2
C₄₁×#2333	2
C₄₁×#2328	2
C₄₁×#2324	2
C₄₁×#2321	2
C₄₁×#2319	2
C₄₁×#2309	2
C₄₁×#2308	2
C₄×#121×C₄₁	2
C₂×C₄₁×#390	2
C₄₁×#2290	2
#34471	41

Subgroups — C41×#34471 #23810672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34471 #23810672