Subgroups — C₄₁×#34438 #23810639

Order 10496.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#535	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×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2366	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2364	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2358	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#2333	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2328	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#2325	C₂	1	2	yes	maximal, complemented
18	C₄₁×#2321	C₂	1	2	yes	maximal, complemented
19	C₄₁×#2321	C₂	1	2	yes	maximal, complemented
20	C₄₁×#2314	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#127×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#124×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2298	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#535	C₄	1	16	yes	complemented
27	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#121×C₄₁	C₂²	1	2	yes	—
32	C₂×#121×C₄₁	C₂²	1	2	yes	—
33	C₂×#120×C₄₁	C₂²	1	2	yes	—
34	C₂×#120×C₄₁	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
47	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
49	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
50	C₄₁×#391	C₂²	1	1	yes	characteristic, complemented
51	C₄₁×#391	C₂²	1	1	yes	characteristic, complemented
52	C₄₁×#390	C₂²	1	1	yes	characteristic
53	C₄₁×#390	C₂²	1	1	yes	characteristic
54	C₄₁×#390	C₂²	1	2	yes	—
55	C₄₁×#390	C₂²	1	2	yes	—
56	C₄₁×#390	C₂²	1	1	yes	characteristic
57	C₄₁×#390	C₂²	1	1	yes	characteristic
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×#388	C₂²	1	1	yes	characteristic
65	C₄₁×#388	C₂²	1	1	yes	characteristic
66	C₄₁×#388	C₂²	1	1	yes	characteristic
67	C₄₁×#388	C₂²	1	1	yes	characteristic
68	C₄₁×#388	C₂²	1	2	yes	—
69	C₄₁×#388	C₂²	1	2	yes	—
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×#387	C₂²	1	1	yes	characteristic, complemented
79	C₄₁×#387	C₂²	1	1	yes	characteristic, complemented
80	C₄₁×#387	C₂²	1	1	yes	characteristic, complemented
81	C₄₁×#387	C₂²	1	1	yes	characteristic, complemented
82	C₄₁×#387	C₂²	1	2	yes	complemented
83	C₄₁×#387	C₂²	1	2	yes	complemented
84	C₄₁×#386	C₂²	1	2	yes	—
85	C₄₁×#386	C₂²	1	2	yes	—
86	C₄₁×#386	C₂²	1	2	yes	—
87	C₄₁×#386	C₂²	1	2	yes	—
88	C₄₁×#386	C₂²	1	2	yes	—
89	C₄₁×#386	C₂²	1	2	yes	—
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×#385	C₂²	1	2	yes	complemented
99	C₄₁×#385	C₂²	1	2	yes	complemented
100	C₄₁×#385	C₂²	1	2	yes	complemented
101	C₄₁×#385	C₂²	1	2	yes	complemented
102	C₄₁×#384	C₂²	1	1	yes	characteristic, complemented
103	C₄₁×#382	C₂²	1	1	yes	characteristic, complemented
104	C₄₁×#381	C₂²	1	2	yes	complemented
105	C₄₁×#380	C₂²	1	1	yes	characteristic
106	C₄₁×#380	C₂²	1	1	yes	characteristic
107	C₄₁×#380	C₂²	1	2	yes	complemented
108	C₄₁×#379	C₂²	1	2	yes	—
109	C₄₁×#379	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
117	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
118	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
119	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
121	C₄₁×#376	C₂²	1	1	yes	characteristic, complemented
122	C₂×#95×C₄₁	C₂²	1	2	yes	complemented
123	C₄³×C₄₁	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₄₁	C₂³	1	2	yes	—
125	C₂×#41×C₄₁	—	4	2	no	—
126	C₂×#41×C₄₁	—	4	2	no	—
127	C₂×#41×C₄₁	C₂×C₄	1	8	yes	complemented
128	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₄₁	—	4	2	no	—
130	C₂²×D₄×C₄₁	—	4	2	no	—
131	C₂²×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
132	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
136	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
137	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
138	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
146	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
147	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
148	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
149	#127×C₄₁	C₂×C₄	1	8	yes	complemented
150	#127×C₄₁	C₂×C₄	1	8	yes	complemented
151	#124×C₄₁	C₂×C₄	1	8	yes	complemented
152	#124×C₄₁	C₂×C₄	1	8	yes	complemented
153	#121×C₄₁	C₂×C₄	1	16	yes	complemented
154	#121×C₄₁	C₂×C₄	1	16	yes	complemented
155	#120×C₄₁	C₂×C₄	1	16	yes	complemented
156	#120×C₄₁	C₂×C₄	1	16	yes	complemented
157	C₄×Q₈×C₄₁	—	4	2	no	—
158	C₄×Q₈×C₄₁	—	4	2	no	—
159	C₄×D₄×C₄₁	—	4	4	no	—
160	C₄×D₄×C₄₁	—	4	2	no	—
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	2	no	—
166	C₄×D₄×C₄₁	—	4	4	no	—
167	C₄×D₄×C₄₁	—	4	4	no	—
168	C₄×D₄×C₄₁	—	4	4	no	—
169	#117×C₄₁	C₂×C₄	1	8	yes	complemented
170	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
177	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
185	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
186	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
209	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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×C₄²×C₄₁	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
223	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
224	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
225	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
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	#95×C₄₁	C₂³	1	1	yes	characteristic
231	#95×C₄₁	C₂³	1	2	yes	—
232	#95×C₄₁	C₂³	1	2	yes	—
233	#95×C₄₁	C₂³	1	2	yes	—
234	#95×C₄₁	C₂³	1	1	yes	characteristic
235	#95×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	1	yes	characteristic
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	2	yes	—
249	#95×C₄₁	C₂³	1	2	yes	—
250	#95×C₄₁	C₂³	1	1	yes	characteristic
251	#95×C₄₁	C₂³	1	1	yes	characteristic
252	C₂⁴×C₄₁	—	4	2	no	—
253	C₂⁴×C₄₁	—	4	2	no	—
254	C₂⁴×C₄₁	—	4	2	no	—
255	C₂⁴×C₄₁	—	4	2	no	—
256	C₂⁴×C₄₁	—	4	2	no	—
257	C₂⁴×C₄₁	—	4	2	no	—
258	C₂⁴×C₄₁	C₂²×C₄	1	8	yes	—
259	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
261	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
262	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
263	#41×C₄₁	—	4	16	no	—
264	C₂×Q₈×C₄₁	—	2	2	no	—
265	C₂×Q₈×C₄₁	—	2	2	no	—
266	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₄₁	—	2	2	no	—
268	C₂×D₄×C₄₁	—	2	2	no	—
269	C₂×D₄×C₄₁	—	2	2	no	—
270	C₂×D₄×C₄₁	—	2	2	no	—
271	C₂×D₄×C₄₁	—	2	2	no	—
272	C₂×D₄×C₄₁	—	2	2	no	—
273	C₂×D₄×C₄₁	—	4	16	no	—
274	C₂×D₄×C₄₁	—	4	2	no	—
275	C₂×D₄×C₄₁	—	4	2	no	—
276	C₂×D₄×C₄₁	—	4	2	no	—
277	C₂×D₄×C₄₁	—	4	2	no	—
278	C₂×D₄×C₄₁	—	4	2	no	—
279	C₂×D₄×C₄₁	—	4	2	no	—
280	C₂×D₄×C₄₁	—	4	2	no	—
281	C₂×D₄×C₄₁	—	4	2	no	—
282	C₂×D₄×C₄₁	—	4	2	no	—
283	C₂×D₄×C₄₁	—	4	2	no	—
284	C₂×D₄×C₄₁	—	4	2	no	—
285	C₂×D₄×C₄₁	—	4	2	no	—
286	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
287	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
288	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
289	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
290	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
291	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
292	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
293	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
294	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
295	C₂²×C₄×C₄₁	—	2	2	no	—
296	C₂²×C₄×C₄₁	—	2	2	no	—
297	C₂²×C₄×C₄₁	—	2	4	no	—
298	C₂²×C₄×C₄₁	—	2	4	no	—
299	C₂²×C₄×C₄₁	—	2	4	no	—
300	C₂²×C₄×C₄₁	—	4	2	no	—
301	C₂²×C₄×C₄₁	—	4	2	no	—
302	C₂²×C₄×C₄₁	—	4	2	no	—
303	C₂²×C₄×C₄₁	—	4	2	no	—
304	C₂²×C₄×C₄₁	—	4	2	no	—
305	C₂²×C₄×C₄₁	—	4	2	no	—
306	C₂²×C₄×C₄₁	—	4	2	no	—
307	C₂²×C₄×C₄₁	—	4	2	no	—
308	C₂²×C₄×C₄₁	—	4	2	no	—
309	C₂²×C₄×C₄₁	—	4	2	no	—
310	C₂²×C₄×C₄₁	—	4	2	no	—
311	C₂²×C₄×C₄₁	—	4	2	no	—
312	C₂²×C₄×C₄₁	—	4	2	no	—
313	C₂²×C₄×C₄₁	—	4	2	no	—
314	C₂²×C₄×C₄₁	—	4	2	no	—
315	C₂²×C₄×C₄₁	—	4	2	no	—
316	C₂²×C₄×C₄₁	—	4	2	no	—
317	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
318	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
319	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
338	C₄⋊C₄×C₄₁	—	2	2	no	—
339	C₄⋊C₄×C₄₁	—	2	2	no	—
340	C₄⋊C₄×C₄₁	—	2	2	no	—
341	C₄⋊C₄×C₄₁	—	2	2	no	—
342	C₄⋊C₄×C₄₁	—	2	2	no	—
343	C₄⋊C₄×C₄₁	—	2	2	no	—
344	C₄⋊C₄×C₄₁	—	4	1	no	—
345	C₄⋊C₄×C₄₁	—	4	1	no	—
346	C₄⋊C₄×C₄₁	—	4	2	no	—
347	C₄⋊C₄×C₄₁	—	4	2	no	—
348	C₄⋊C₄×C₄₁	—	4	2	no	—
349	C₄⋊C₄×C₄₁	—	4	2	no	—
350	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
351	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
352	C₂²⋊C₄×C₄₁	—	2	2	no	—
353	C₂²⋊C₄×C₄₁	—	2	2	no	—
354	C₂²⋊C₄×C₄₁	—	2	4	no	—
355	C₂²⋊C₄×C₄₁	—	2	4	no	—
356	C₂²⋊C₄×C₄₁	—	2	4	no	—
357	C₂²⋊C₄×C₄₁	—	4	2	no	—
358	C₂²⋊C₄×C₄₁	—	4	2	no	—
359	C₂²⋊C₄×C₄₁	—	4	2	no	—
360	C₂²⋊C₄×C₄₁	—	4	2	no	—
361	C₂²⋊C₄×C₄₁	—	4	2	no	—
362	C₂²⋊C₄×C₄₁	—	4	1	no	—
363	C₂²⋊C₄×C₄₁	—	4	1	no	—
364	C₂²⋊C₄×C₄₁	—	4	2	no	—
365	C₂²⋊C₄×C₄₁	—	4	2	no	—
366	C₂²⋊C₄×C₄₁	—	4	2	no	—
367	C₂²⋊C₄×C₄₁	—	4	2	no	—
368	C₂²⋊C₄×C₄₁	—	4	2	no	—
369	C₂²⋊C₄×C₄₁	—	4	2	no	—
370	C₂²⋊C₄×C₄₁	—	4	2	no	—
371	C₂²⋊C₄×C₄₁	—	4	2	no	—
372	C₂²⋊C₄×C₄₁	—	4	2	no	—
373	C₂²⋊C₄×C₄₁	—	4	2	no	—
374	C₂²⋊C₄×C₄₁	—	4	2	no	—
375	C₂²⋊C₄×C₄₁	—	4	2	no	—
376	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
377	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
378	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
379	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
380	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
381	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
382	C₄²×C₄₁	—	2	2	no	—
383	C₄²×C₄₁	—	2	2	no	—
384	C₄²×C₄₁	—	2	2	no	—
385	C₄²×C₄₁	—	2	2	no	—
386	C₄²×C₄₁	—	2	2	no	—
387	C₄²×C₄₁	—	2	2	no	—
388	C₄²×C₄₁	—	4	1	no	—
389	C₄²×C₄₁	—	4	1	no	—
390	C₄²×C₄₁	—	4	2	no	—
391	C₄²×C₄₁	—	4	2	no	—
392	C₄²×C₄₁	—	4	2	no	—
393	C₄²×C₄₁	—	4	2	no	—
394	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
395	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
396	C₂³×C₄₁	—	2	1	no	—
397	C₂³×C₄₁	—	2	1	no	—
398	C₂³×C₄₁	—	2	2	no	—
399	C₂³×C₄₁	—	2	2	no	—
400	C₂³×C₄₁	—	2	2	no	—
401	C₂³×C₄₁	—	2	2	no	—
402	C₂³×C₄₁	—	2	2	no	—
403	C₂³×C₄₁	—	2	2	no	—
404	C₂³×C₄₁	—	2	2	no	—
405	C₂³×C₄₁	—	2	2	no	—
406	C₂³×C₄₁	—	2	2	no	—
407	C₂³×C₄₁	—	2	2	no	—
408	C₂³×C₄₁	—	2	2	no	—
409	C₂³×C₄₁	—	2	2	no	—
410	C₂³×C₄₁	—	2	1	no	—
411	C₂³×C₄₁	—	2	1	no	—
412	C₂³×C₄₁	—	2	2	no	—
413	C₂³×C₄₁	—	2	2	no	—
414	C₂³×C₄₁	—	2	2	no	—
415	C₂³×C₄₁	—	2	1	no	—
416	C₂³×C₄₁	—	2	1	no	—
417	C₂³×C₄₁	—	2	2	no	—
418	C₂³×C₄₁	—	2	2	no	—
419	C₂³×C₄₁	—	2	2	no	—
420	C₂³×C₄₁	—	4	8	no	—
421	C₂³×C₄₁	—	4	8	no	—
422	C₂³×C₄₁	—	4	8	no	—
423	C₂³×C₄₁	—	8	4	no	—
424	C₂³×C₄₁	—	8	4	no	—
425	C₂³×C₄₁	—	8	4	no	—
426	C₂³×C₄₁	—	8	4	no	—
427	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
428	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
429	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
430	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
431	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
432	Q₈×C₄₁	—	2	8	no	—
433	D₄×C₄₁	—	2	8	no	—
434	D₄×C₄₁	—	2	8	no	—
435	D₄×C₄₁	—	2	8	no	—
436	D₄×C₄₁	—	4	8	no	—
437	D₄×C₄₁	—	4	8	no	—
438	D₄×C₄₁	—	4	8	no	—
439	D₄×C₄₁	—	4	8	no	—
440	D₄×C₄₁	—	4	8	no	—
441	D₄×C₄₁	—	4	8	no	—
442	C₂×C₄×C₄₁	—	2	1	no	—
443	C₂×C₄×C₄₁	—	2	1	no	—
444	C₂×C₄×C₄₁	—	2	1	no	—
445	C₂×C₄×C₄₁	—	2	1	no	—
446	C₂×C₄×C₄₁	—	2	1	no	—
447	C₂×C₄×C₄₁	—	2	1	no	—
448	C₂×C₄×C₄₁	—	2	1	no	—
449	C₂×C₄×C₄₁	—	2	2	no	—
450	C₂×C₄×C₄₁	—	2	2	no	—
451	C₂×C₄×C₄₁	—	2	1	no	—
452	C₂×C₄×C₄₁	—	2	1	no	—
453	C₂×C₄×C₄₁	—	2	1	no	—
454	C₂×C₄×C₄₁	—	2	1	no	—
455	C₂×C₄×C₄₁	—	2	1	no	—
456	C₂×C₄×C₄₁	—	2	1	no	—
457	C₂×C₄×C₄₁	—	2	1	no	—
458	C₂×C₄×C₄₁	—	2	8	no	—
459	C₂×C₄×C₄₁	—	2	1	no	—
460	C₂×C₄×C₄₁	—	2	1	no	—
461	C₂×C₄×C₄₁	—	2	1	no	—
462	C₂×C₄×C₄₁	—	2	1	no	—
463	C₂×C₄×C₄₁	—	2	1	no	—
464	C₂×C₄×C₄₁	—	2	1	no	—
465	C₂×C₄×C₄₁	—	2	1	no	—
466	C₂×C₄×C₄₁	—	2	2	no	—
467	C₂×C₄×C₄₁	—	2	2	no	—
468	C₂×C₄×C₄₁	—	2	2	no	—
469	C₂×C₄×C₄₁	—	2	2	no	—
470	C₂×C₄×C₄₁	—	2	2	no	—
471	C₂×C₄×C₄₁	—	2	2	no	—
472	C₂×C₄×C₄₁	—	2	1	no	—
473	C₂×C₄×C₄₁	—	2	1	no	—
474	C₂×C₄×C₄₁	—	2	2	no	—
475	C₂×C₄×C₄₁	—	2	2	no	—
476	C₂×C₄×C₄₁	—	2	2	no	—
477	C₂×C₄×C₄₁	—	2	1	no	—
478	C₂×C₄×C₄₁	—	2	2	no	—
479	C₂×C₄×C₄₁	—	2	1	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	2	no	—
486	C₂×C₄×C₄₁	—	2	1	no	—
487	C₂×C₄×C₄₁	—	2	2	no	—
488	C₂×C₄×C₄₁	—	2	1	no	—
489	C₂×C₄×C₄₁	—	4	8	no	—
490	C₂×C₄×C₄₁	—	8	4	no	—
491	C₂×C₄×C₄₁	—	8	4	no	—
492	C₂×C₄×C₄₁	—	8	4	no	—
493	C₂×C₄×C₄₁	—	8	4	no	—
494	C₂×C₄×C₄₁	—	8	4	no	—
495	C₂×C₄×C₄₁	—	8	4	no	—
496	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
497	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
498	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
499	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
500	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
501	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
502	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
503	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
504	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
505	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
506	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
507	#34438	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
508	C₂²×C₄₁	—	2	2	no	—
509	C₂²×C₄₁	—	2	4	no	—
510	C₂²×C₄₁	—	2	4	no	—
511	C₂²×C₄₁	—	2	4	no	—
512	C₂²×C₄₁	—	2	4	no	—
513	C₂²×C₄₁	—	2	4	no	—
514	C₂²×C₄₁	—	2	4	no	—
515	C₂²×C₄₁	—	2	4	no	—
516	C₂²×C₄₁	—	2	4	no	—
517	C₂²×C₄₁	—	2	4	no	—
518	C₂²×C₄₁	—	2	2	no	—
519	C₂²×C₄₁	—	2	2	no	—
520	C₂²×C₄₁	—	4	2	no	—
521	C₂²×C₄₁	—	4	2	no	—
522	C₂²×C₄₁	—	4	2	no	—
523	C₂²×C₄₁	—	4	1	no	—
524	C₂²×C₄₁	—	4	2	no	—
525	C₂²×C₄₁	—	4	2	no	—
526	C₂²×C₄₁	—	4	2	no	—
527	C₂²×C₄₁	—	4	1	no	—
528	C₂²×C₄₁	—	4	2	no	—
529	C₂²×C₄₁	—	4	2	no	—
530	C₂²×C₄₁	—	4	2	no	—
531	C₂²×C₄₁	—	4	1	no	—
532	C₂²×C₄₁	—	4	2	no	—
533	C₂²×C₄₁	—	4	2	no	—
534	C₂²×C₄₁	—	4	2	no	—
535	C₂²×C₄₁	—	4	1	no	—
536	C₂²×C₄₁	—	8	16	no	—
537	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
538	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
542	C₂²×C₄₁	#585	1	1	yes	characteristic
543	C₂²×C₄₁	#585	1	1	yes	characteristic
544	C₄×C₄₁	—	2	2	no	—
545	C₄×C₄₁	—	2	4	no	—
546	C₄×C₄₁	—	2	2	no	—
547	C₄×C₄₁	—	2	2	no	—
548	C₄×C₄₁	—	2	2	no	—
549	C₄×C₄₁	—	2	2	no	—
550	C₄×C₄₁	—	2	2	no	—
551	C₄×C₄₁	—	2	2	no	—
552	C₄×C₄₁	—	4	2	no	—
553	C₄×C₄₁	—	4	1	no	—
554	C₄×C₄₁	—	4	2	no	—
555	C₄×C₄₁	—	4	1	no	—
556	C₄×C₄₁	—	4	2	no	—
557	C₄×C₄₁	—	4	1	no	—
558	C₄×C₄₁	—	4	1	no	—
559	C₄×C₄₁	—	4	2	no	—
560	C₄×C₄₁	—	4	1	no	—
561	C₄×C₄₁	—	4	1	no	—
562	C₄×C₄₁	#518	1	4	yes	—
563	C₂×#535	C₂×C₄₁	1	1	yes	characteristic
564	#2377	C₂×C₄₁	1	2	yes	complemented
565	#2375	C₂×C₄₁	1	2	yes	complemented
566	#2367	C₂×C₄₁	1	1	yes	characteristic, complemented
567	#2367	C₂×C₄₁	1	1	yes	characteristic, complemented
568	#2366	C₂×C₄₁	1	1	yes	characteristic, complemented
569	#2366	C₂×C₄₁	1	1	yes	characteristic, complemented
570	#2364	C₂×C₄₁	1	2	yes	complemented
571	#2358	C₂×C₄₁	1	2	yes	complemented
572	#2341	C₂×C₄₁	1	1	yes	characteristic, complemented
573	#2339	C₂×C₄₁	1	1	yes	characteristic, complemented
574	D₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
575	D₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
576	#2333	C₂×C₄₁	1	2	yes	complemented
577	#2328	C₂×C₄₁	1	1	yes	characteristic, complemented
578	#2326	C₂×C₄₁	1	1	yes	characteristic, complemented
579	#2325	C₂×C₄₁	1	2	yes	complemented
580	#2321	C₂×C₄₁	1	2	yes	complemented
581	#2321	C₂×C₄₁	1	2	yes	complemented
582	#2314	C₂×C₄₁	1	1	yes	characteristic, complemented
583	C₄×#127	C₂×C₄₁	1	1	yes	characteristic, complemented
584	C₄×#124	C₂×C₄₁	1	1	yes	characteristic, complemented
585	#2298	C₂×C₄₁	1	1	yes	characteristic, complemented
586	C₂×C₄₁	—	4	4	no	—
587	C₂×C₄₁	—	4	4	no	—
588	C₂×C₄₁	—	4	4	no	—
589	C₂×C₄₁	—	4	2	no	—
590	C₂×C₄₁	C₂×#518	1	1	yes	characteristic
591	C₂×C₄₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂×C₄₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂×C₄₁	#3543	1	1	yes	characteristic
594	C₂×C₄₁	#3546	1	1	yes	characteristic
595	C₂×C₄₁	#3558	1	1	yes	characteristic
596	C₂×C₄₁	#3562	1	1	yes	characteristic
597	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
598	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
599	#535	C₄×C₄₁	1	16	yes	complemented
600	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
601	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
602	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
603	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
604	C₂×#121	C₂²×C₄₁	1	2	yes	—
605	C₂×#121	C₂²×C₄₁	1	2	yes	—
606	C₂×#120	C₂²×C₄₁	1	2	yes	—
607	C₂×#120	C₂²×C₄₁	1	2	yes	—
608	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
609	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
610	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
611	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
615	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
616	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
617	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
618	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
619	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
620	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
621	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
622	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
623	#391	C₂²×C₄₁	1	1	yes	characteristic, complemented
624	#391	C₂²×C₄₁	1	1	yes	characteristic, complemented
625	#390	C₂²×C₄₁	1	1	yes	characteristic
626	#390	C₂²×C₄₁	1	2	yes	—
627	#390	C₂²×C₄₁	1	2	yes	—
628	#390	C₂²×C₄₁	1	1	yes	characteristic
629	#390	C₂²×C₄₁	1	1	yes	characteristic
630	#390	C₂²×C₄₁	1	1	yes	characteristic
631	#390	C₂²×C₄₁	1	2	yes	complemented
632	#390	C₂²×C₄₁	1	1	yes	characteristic, complemented
633	#390	C₂²×C₄₁	1	2	yes	complemented
634	#390	C₂²×C₄₁	1	2	yes	complemented
635	#390	C₂²×C₄₁	1	1	yes	characteristic, complemented
636	#390	C₂²×C₄₁	1	2	yes	complemented
637	#388	C₂²×C₄₁	1	2	yes	—
638	#388	C₂²×C₄₁	1	2	yes	—
639	#388	C₂²×C₄₁	1	1	yes	characteristic
640	#388	C₂²×C₄₁	1	1	yes	characteristic
641	#388	C₂²×C₄₁	1	1	yes	characteristic
642	#388	C₂²×C₄₁	1	1	yes	characteristic
643	#388	C₂²×C₄₁	1	2	yes	complemented
644	#388	C₂²×C₄₁	1	2	yes	complemented
645	#388	C₂²×C₄₁	1	2	yes	complemented
646	#388	C₂²×C₄₁	1	2	yes	complemented
647	#388	C₂²×C₄₁	1	2	yes	complemented
648	#388	C₂²×C₄₁	1	2	yes	complemented
649	#388	C₂²×C₄₁	1	2	yes	complemented
650	#388	C₂²×C₄₁	1	2	yes	complemented
651	#387	C₂²×C₄₁	1	2	yes	complemented
652	#387	C₂²×C₄₁	1	2	yes	complemented
653	#387	C₂²×C₄₁	1	1	yes	characteristic, complemented
654	#387	C₂²×C₄₁	1	1	yes	characteristic, complemented
655	#387	C₂²×C₄₁	1	1	yes	characteristic, complemented
656	#387	C₂²×C₄₁	1	1	yes	characteristic, complemented
657	#386	C₂²×C₄₁	1	2	yes	—
658	#386	C₂²×C₄₁	1	2	yes	—
659	#386	C₂²×C₄₁	1	2	yes	—
660	#386	C₂²×C₄₁	1	2	yes	—
661	#386	C₂²×C₄₁	1	2	yes	—
662	#386	C₂²×C₄₁	1	2	yes	—
663	#386	C₂²×C₄₁	1	2	yes	complemented
664	#386	C₂²×C₄₁	1	2	yes	complemented
665	#386	C₂²×C₄₁	1	2	yes	complemented
666	#386	C₂²×C₄₁	1	2	yes	complemented
667	#386	C₂²×C₄₁	1	2	yes	complemented
668	#386	C₂²×C₄₁	1	2	yes	complemented
669	#386	C₂²×C₄₁	1	2	yes	complemented
670	#386	C₂²×C₄₁	1	2	yes	complemented
671	#385	C₂²×C₄₁	1	2	yes	complemented
672	#385	C₂²×C₄₁	1	2	yes	complemented
673	#385	C₂²×C₄₁	1	2	yes	complemented
674	#385	C₂²×C₄₁	1	2	yes	complemented
675	#384	C₂²×C₄₁	1	1	yes	characteristic, complemented
676	#382	C₂²×C₄₁	1	1	yes	characteristic, complemented
677	#381	C₂²×C₄₁	1	2	yes	complemented
678	#380	C₂²×C₄₁	1	1	yes	characteristic
679	#380	C₂²×C₄₁	1	1	yes	characteristic
680	#380	C₂²×C₄₁	1	2	yes	complemented
681	#379	C₂²×C₄₁	1	2	yes	—
682	#379	C₂²×C₄₁	1	2	yes	—
683	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
684	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
685	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
686	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
687	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
688	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
689	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
690	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
691	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
692	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
693	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
694	#376	C₂²×C₄₁	1	1	yes	characteristic, complemented
695	C₂×#95	C₂²×C₄₁	1	2	yes	complemented
696	C₄³	C₂²×C₄₁	1	1	yes	characteristic, complemented
697	C₄₁	#34438	1	1	yes	characteristic, direct product factor, Sylow
698	C₂⁵	C₂³×C₄₁	1	2	yes	—
699	C₂×#41	—	4	2	no	—
700	C₂×#41	—	4	2	no	—
701	C₂×#41	C₂×C₄×C₄₁	1	8	yes	complemented
702	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
703	C₂²×D₄	—	4	2	no	—
704	C₂²×D₄	—	4	2	no	—
705	C₂²×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
706	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
707	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
708	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
709	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
710	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
711	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
712	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
713	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
714	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
715	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
716	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
717	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
718	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
719	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
720	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
721	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
722	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
723	#127	C₂×C₄×C₄₁	1	8	yes	complemented
724	#127	C₂×C₄×C₄₁	1	8	yes	complemented
725	#124	C₂×C₄×C₄₁	1	8	yes	complemented
726	#124	C₂×C₄×C₄₁	1	8	yes	complemented
727	#121	C₂×C₄×C₄₁	1	16	yes	complemented
728	#121	C₂×C₄×C₄₁	1	16	yes	complemented
729	#120	C₂×C₄×C₄₁	1	16	yes	complemented
730	#120	C₂×C₄×C₄₁	1	16	yes	complemented
731	C₄×Q₈	—	4	2	no	—
732	C₄×Q₈	—	4	2	no	—
733	C₄×D₄	—	4	4	no	—
734	C₄×D₄	—	4	2	no	—
735	C₄×D₄	—	4	2	no	—
736	C₄×D₄	—	4	2	no	—
737	C₄×D₄	—	4	2	no	—
738	C₄×D₄	—	4	2	no	—
739	C₄×D₄	—	4	2	no	—
740	C₄×D₄	—	4	4	no	—
741	C₄×D₄	—	4	4	no	—
742	C₄×D₄	—	4	4	no	—
743	#117	C₂×C₄×C₄₁	1	8	yes	complemented
744	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
758	C₂×C₂²⋊C₄	—	4	4	no	—
759	C₂×C₂²⋊C₄	—	4	4	no	—
760	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
781	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
790	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
791	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
792	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
797	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
798	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
799	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
800	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
802	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
803	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
804	#95	C₂³×C₄₁	1	1	yes	characteristic
805	#95	C₂³×C₄₁	1	2	yes	—
806	#95	C₂³×C₄₁	1	2	yes	—
807	#95	C₂³×C₄₁	1	2	yes	—
808	#95	C₂³×C₄₁	1	1	yes	characteristic
809	#95	C₂³×C₄₁	1	1	yes	characteristic
810	#95	C₂³×C₄₁	1	1	yes	characteristic
811	#95	C₂³×C₄₁	1	1	yes	characteristic
812	#95	C₂³×C₄₁	1	1	yes	characteristic
813	#95	C₂³×C₄₁	1	1	yes	characteristic
814	#95	C₂³×C₄₁	1	1	yes	characteristic
815	#95	C₂³×C₄₁	1	1	yes	characteristic
816	#95	C₂³×C₄₁	1	1	yes	characteristic
817	#95	C₂³×C₄₁	1	2	yes	—
818	#95	C₂³×C₄₁	1	2	yes	—
819	#95	C₂³×C₄₁	1	2	yes	—
820	#95	C₂³×C₄₁	1	2	yes	—
821	#95	C₂³×C₄₁	1	2	yes	—
822	#95	C₂³×C₄₁	1	2	yes	—
823	#95	C₂³×C₄₁	1	2	yes	—
824	#95	C₂³×C₄₁	1	1	yes	characteristic
825	#95	C₂³×C₄₁	1	1	yes	characteristic
826	C₂⁴	—	4	2	no	—
827	C₂⁴	—	4	2	no	—
828	C₂⁴	—	4	2	no	—
829	C₂⁴	—	4	2	no	—
830	C₂⁴	—	4	2	no	—
831	C₂⁴	—	4	2	no	—
832	C₂⁴	C₂²×C₄×C₄₁	1	8	yes	—
833	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
834	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
835	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
836	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
837	#41	—	4	16	no	—
838	C₂×Q₈	—	2	2	no	—
839	C₂×Q₈	—	2	2	no	—
840	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	4	16	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	—	4	2	no	—
853	C₂×D₄	—	4	2	no	—
854	C₂×D₄	—	4	2	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂×D₄	—	4	2	no	—
858	C₂×D₄	—	4	2	no	—
859	C₂×D₄	—	4	2	no	—
860	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
861	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
862	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
863	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
864	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
865	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
866	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
867	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
868	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	4	no	—
872	C₂²×C₄	—	2	4	no	—
873	C₂²×C₄	—	2	4	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	4	2	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	—	4	2	no	—
891	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
892	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
893	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
901	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
907	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	2	no	—
922	C₄⋊C₄	—	4	1	no	—
923	C₄⋊C₄	—	4	1	no	—
924	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
925	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	4	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	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	—	4	1	no	—
947	C₂²⋊C₄	—	4	1	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
951	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
952	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
953	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
955	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	4	2	no	—
963	C₄²	—	4	2	no	—
964	C₄²	—	4	2	no	—
965	C₄²	—	4	2	no	—
966	C₄²	—	4	1	no	—
967	C₄²	—	4	1	no	—
968	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
969	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	2	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	2	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	2	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	4	8	no	—
995	C₂³	—	4	8	no	—
996	C₂³	—	4	8	no	—
997	C₂³	—	8	4	no	—
998	C₂³	—	8	4	no	—
999	C₂³	—	8	4	no	—
1000	C₂³	—	8	4	no	—
1001	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
1002	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
1003	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
1004	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
1005	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
1006	Q₈	—	2	8	no	—
1007	D₄	—	2	8	no	—
1008	D₄	—	2	8	no	—
1009	D₄	—	2	8	no	—
1010	D₄	—	4	8	no	—
1011	D₄	—	4	8	no	—
1012	D₄	—	4	8	no	—
1013	D₄	—	4	8	no	—
1014	D₄	—	4	8	no	—
1015	D₄	—	4	8	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	8	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	4	8	no	—
1064	C₂×C₄	—	8	4	no	—
1065	C₂×C₄	—	8	4	no	—
1066	C₂×C₄	—	8	4	no	—
1067	C₂×C₄	—	8	4	no	—
1068	C₂×C₄	—	8	4	no	—
1069	C₂×C₄	—	8	4	no	—
1070	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1071	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1072	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1073	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1074	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
1075	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1076	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
1077	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1078	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1079	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1080	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	4	no	—
1083	C₂²	—	2	4	no	—
1084	C₂²	—	2	4	no	—
1085	C₂²	—	2	4	no	—
1086	C₂²	—	2	4	no	—
1087	C₂²	—	2	4	no	—
1088	C₂²	—	2	4	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	2	4	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	8	16	no	—
1110	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
1111	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1112	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1113	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1114	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1115	C₂²	C₄₁×#585	1	1	yes	characteristic
1116	C₂²	C₄₁×#585	1	1	yes	characteristic
1117	C₄	—	2	2	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	4	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	C₄₁×#518	1	4	yes	—
1136	C₂	—	4	2	no	—
1137	C₂	—	4	4	no	—
1138	C₂	—	4	4	no	—
1139	C₂	—	4	4	no	—
1140	C₂	C₂×C₄₁×#518	1	1	yes	characteristic
1141	C₂	C₄×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1142	C₂	C₄×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1143	C₂	C₄₁×#3543	1	1	yes	characteristic
1144	C₂	C₄₁×#3546	1	1	yes	characteristic
1145	C₂	C₄₁×#3558	1	1	yes	characteristic
1146	C₂	C₄₁×#3562	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×C₄₁×#535	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×#2367	C₂	semidirect
5. C₄₁×#2367	C₂	semidirect
6. C₄₁×#2366	C₂	semidirect
7. C₄₁×#2366	C₂	semidirect
8. C₄₁×#2364	C₂	semidirect
9. C₄₁×#2358	C₂	semidirect
10. C₄₁×#2341	C₂	semidirect
11. C₄₁×#2339	C₂	semidirect
12. D₄×C₂²⋊C₄×C₄₁	C₂	semidirect
13. D₄×C₂²⋊C₄×C₄₁	C₂	semidirect
14. C₄₁×#2333	C₂	semidirect
15. C₄₁×#2328	C₂	semidirect
16. C₄₁×#2326	C₂	semidirect
17. C₄₁×#2325	C₂	semidirect
18. C₄₁×#2321	C₂	semidirect
19. C₄₁×#2321	C₂	semidirect
20. C₄₁×#2314	C₂	semidirect
21. C₄×#127×C₄₁	C₂	semidirect
22. C₄×#124×C₄₁	C₂	semidirect
23. C₄₁×#2298	C₂	semidirect
26. C₄₁×#535	C₄	semidirect
35. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
36. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
41. C₂×C₄×D₄×C₄₁	C₂²	semidirect
42. C₂×C₄×D₄×C₄₁	C₂²	semidirect
43. C₂×C₄×D₄×C₄₁	C₂²	semidirect
44. C₂×C₄×D₄×C₄₁	C₂²	semidirect
45. C₂×C₄×D₄×C₄₁	C₂²	semidirect
46. C₂×C₄×D₄×C₄₁	C₂²	semidirect
50. C₄₁×#391	C₂²	semidirect
51. C₄₁×#391	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
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×#387	C₂²	semidirect
79. C₄₁×#387	C₂²	semidirect
80. C₄₁×#387	C₂²	semidirect
81. C₄₁×#387	C₂²	semidirect
82. C₄₁×#387	C₂²	semidirect
83. C₄₁×#387	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×#385	C₂²	semidirect
99. C₄₁×#385	C₂²	semidirect
100. C₄₁×#385	C₂²	semidirect
101. C₄₁×#385	C₂²	semidirect
102. C₄₁×#384	C₂²	semidirect
103. C₄₁×#382	C₂²	semidirect
104. C₄₁×#381	C₂²	semidirect
107. C₄₁×#380	C₂²	semidirect
110. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
111. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
112. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
113. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
116. C₄×C₂²⋊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. C₄₁×#376	C₂²	semidirect
122. C₂×#95×C₄₁	C₂²	semidirect
123. C₄³×C₄₁	C₂²	semidirect
127. C₂×#41×C₄₁	C₂×C₄	semidirect
131. C₂²×D₄×C₄₁	C₂×C₄	semidirect
149. #127×C₄₁	C₂×C₄	semidirect
150. #127×C₄₁	C₂×C₄	semidirect
151. #124×C₄₁	C₂×C₄	semidirect
152. #124×C₄₁	C₂×C₄	semidirect
153. #121×C₄₁	C₂×C₄	semidirect
154. #121×C₄₁	C₂×C₄	semidirect
155. #120×C₄₁	C₂×C₄	semidirect
156. #120×C₄₁	C₂×C₄	semidirect
169. #117×C₄₁	C₂×C₄	semidirect
507. #34438	C₄₁	direct (N × H)
564. #2377	C₂×C₄₁	semidirect
565. #2375	C₂×C₄₁	semidirect
566. #2367	C₂×C₄₁	semidirect
567. #2367	C₂×C₄₁	semidirect
568. #2366	C₂×C₄₁	semidirect
569. #2366	C₂×C₄₁	semidirect
570. #2364	C₂×C₄₁	semidirect
571. #2358	C₂×C₄₁	semidirect
572. #2341	C₂×C₄₁	semidirect
573. #2339	C₂×C₄₁	semidirect
574. D₄×C₂²⋊C₄	C₂×C₄₁	semidirect
575. D₄×C₂²⋊C₄	C₂×C₄₁	semidirect
576. #2333	C₂×C₄₁	semidirect
577. #2328	C₂×C₄₁	semidirect
578. #2326	C₂×C₄₁	semidirect
579. #2325	C₂×C₄₁	semidirect
580. #2321	C₂×C₄₁	semidirect
581. #2321	C₂×C₄₁	semidirect
582. #2314	C₂×C₄₁	semidirect
583. C₄×#127	C₂×C₄₁	semidirect
584. C₄×#124	C₂×C₄₁	semidirect
585. #2298	C₂×C₄₁	semidirect
599. #535	C₄×C₄₁	semidirect
608. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
609. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
614. C₂×C₄×D₄	C₂²×C₄₁	semidirect
615. C₂×C₄×D₄	C₂²×C₄₁	semidirect
616. C₂×C₄×D₄	C₂²×C₄₁	semidirect
617. C₂×C₄×D₄	C₂²×C₄₁	semidirect
618. C₂×C₄×D₄	C₂²×C₄₁	semidirect
619. C₂×C₄×D₄	C₂²×C₄₁	semidirect
623. #391	C₂²×C₄₁	semidirect
624. #391	C₂²×C₄₁	semidirect
631. #390	C₂²×C₄₁	semidirect
632. #390	C₂²×C₄₁	semidirect
633. #390	C₂²×C₄₁	semidirect
634. #390	C₂²×C₄₁	semidirect
635. #390	C₂²×C₄₁	semidirect
636. #390	C₂²×C₄₁	semidirect
643. #388	C₂²×C₄₁	semidirect
644. #388	C₂²×C₄₁	semidirect
645. #388	C₂²×C₄₁	semidirect
646. #388	C₂²×C₄₁	semidirect
647. #388	C₂²×C₄₁	semidirect
648. #388	C₂²×C₄₁	semidirect
649. #388	C₂²×C₄₁	semidirect
650. #388	C₂²×C₄₁	semidirect
651. #387	C₂²×C₄₁	semidirect
652. #387	C₂²×C₄₁	semidirect
653. #387	C₂²×C₄₁	semidirect
654. #387	C₂²×C₄₁	semidirect
655. #387	C₂²×C₄₁	semidirect
656. #387	C₂²×C₄₁	semidirect
663. #386	C₂²×C₄₁	semidirect
664. #386	C₂²×C₄₁	semidirect
665. #386	C₂²×C₄₁	semidirect
666. #386	C₂²×C₄₁	semidirect
667. #386	C₂²×C₄₁	semidirect
668. #386	C₂²×C₄₁	semidirect
669. #386	C₂²×C₄₁	semidirect
670. #386	C₂²×C₄₁	semidirect
671. #385	C₂²×C₄₁	semidirect
672. #385	C₂²×C₄₁	semidirect
673. #385	C₂²×C₄₁	semidirect
674. #385	C₂²×C₄₁	semidirect
675. #384	C₂²×C₄₁	semidirect
676. #382	C₂²×C₄₁	semidirect
677. #381	C₂²×C₄₁	semidirect
680. #380	C₂²×C₄₁	semidirect
683. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
684. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
685. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
686. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
689. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
690. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
691. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
692. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
693. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
694. #376	C₂²×C₄₁	semidirect
695. C₂×#95	C₂²×C₄₁	semidirect
696. C₄³	C₂²×C₄₁	semidirect
697. C₄₁	#34438	direct (N × H)
701. C₂×#41	C₂×C₄×C₄₁	semidirect
705. C₂²×D₄	C₂×C₄×C₄₁	semidirect
723. #127	C₂×C₄×C₄₁	semidirect
724. #127	C₂×C₄×C₄₁	semidirect
725. #124	C₂×C₄×C₄₁	semidirect
726. #124	C₂×C₄×C₄₁	semidirect
727. #121	C₂×C₄×C₄₁	semidirect
728. #121	C₂×C₄×C₄₁	semidirect
729. #120	C₂×C₄×C₄₁	semidirect
730. #120	C₂×C₄×C₄₁	semidirect
743. #117	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×C₄₁×#535	2
C₄₁×#2377	2
C₄₁×#2375	2
C₄₁×#2367	2
C₄₁×#2366	2
C₄₁×#2364	2
C₄₁×#2358	2
C₄₁×#2341	2
C₄₁×#2339	2
D₄×C₂²⋊C₄×C₄₁	2
C₄₁×#2333	2
C₄₁×#2328	2
C₄₁×#2326	2
C₄₁×#2325	2
C₄₁×#2321	2
C₄₁×#2314	2
C₄×#127×C₄₁	2
C₄×#124×C₄₁	2
C₄₁×#2298	2
#34438	41

Subgroups — C41×#34438 #23810639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34438 #23810639