Subgroups — C₄₁×#34457 #23810658

Order 10496.

2500 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#551	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2383	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2360	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2359	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2358	C₂	1	1	yes	maximal, characteristic
8	D₄×C₄⋊C₄×C₄₁	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2343	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2342	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2334	C₂	1	2	yes	maximal, complemented
12	C₄₁×#2329	C₂	1	2	yes	maximal, complemented
13	C₄₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#2322	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2322	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2318	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2317	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₄₁	C₂	1	1	yes	maximal, characteristic
19	C₂×C₄₁×#385	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#551	C₄	1	16	yes	complemented
22	C₂×#126×C₄₁	C₂²	1	2	yes	—
23	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#123×C₄₁	C₂²	1	2	yes	—
25	C₂×#123×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
27	C₂×#120×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
33	C₂×#117×C₄₁	C₂²	1	2	yes	—
34	C₂×#117×C₄₁	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
39	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
40	C₄₁×#391	C₂²	1	1	yes	characteristic, complemented
41	C₄₁×#391	C₂²	1	2	yes	complemented
42	C₄₁×#390	C₂²	1	1	yes	characteristic
43	C₄₁×#389	C₂²	1	2	yes	complemented
44	C₄₁×#389	C₂²	1	2	yes	complemented
45	C₄₁×#389	C₂²	1	2	yes	complemented
46	C₄₁×#389	C₂²	1	2	yes	complemented
47	C₄₁×#389	C₂²	1	2	yes	complemented
48	C₄₁×#389	C₂²	1	2	yes	complemented
49	C₄₁×#389	C₂²	1	2	yes	complemented
50	C₄₁×#388	C₂²	1	2	yes	—
51	C₄₁×#388	C₂²	1	2	yes	—
52	C₄₁×#388	C₂²	1	2	yes	—
53	C₄₁×#388	C₂²	1	2	yes	—
54	C₄₁×#388	C₂²	1	2	yes	—
55	C₄₁×#388	C₂²	1	2	yes	complemented
56	C₄₁×#388	C₂²	1	2	yes	complemented
57	C₄₁×#388	C₂²	1	2	yes	complemented
58	C₄₁×#387	C₂²	1	2	yes	complemented
59	C₄₁×#387	C₂²	1	2	yes	complemented
60	C₄₁×#387	C₂²	1	2	yes	complemented
61	C₄₁×#387	C₂²	1	2	yes	complemented
62	C₄₁×#387	C₂²	1	2	yes	complemented
63	C₄₁×#387	C₂²	1	2	yes	complemented
64	C₄₁×#387	C₂²	1	2	yes	complemented
65	C₄₁×#387	C₂²	1	2	yes	complemented
66	C₄₁×#386	C₂²	1	2	yes	—
67	C₄₁×#386	C₂²	1	1	yes	characteristic
68	C₄₁×#386	C₂²	1	2	yes	—
69	C₄₁×#386	C₂²	1	1	yes	characteristic
70	C₄₁×#385	C₂²	1	2	yes	—
71	C₄₁×#385	C₂²	1	2	yes	—
72	C₄₁×#385	C₂²	1	2	yes	—
73	C₄₁×#385	C₂²	1	2	yes	—
74	C₄₁×#385	C₂²	1	2	yes	—
75	C₄₁×#385	C₂²	1	2	yes	—
76	C₄₁×#385	C₂²	1	2	yes	—
77	C₄₁×#385	C₂²	1	2	yes	—
78	C₄₁×#385	C₂²	1	2	yes	—
79	C₄₁×#385	C₂²	1	1	yes	characteristic
80	C₄₁×#385	C₂²	1	2	yes	—
81	C₄₁×#385	C₂²	1	2	yes	—
82	C₄₁×#385	C₂²	1	2	yes	—
83	C₄₁×#385	C₂²	1	1	yes	characteristic, complemented
84	C₄₁×#385	C₂²	1	2	yes	complemented
85	C₄₁×#385	C₂²	1	2	yes	complemented
86	C₄₁×#384	C₂²	1	1	yes	characteristic, complemented
87	C₄₁×#384	C₂²	1	2	yes	complemented
88	C₄₁×#383	C₂²	1	2	yes	complemented
89	C₄₁×#382	C₂²	1	2	yes	complemented
90	C₄₁×#382	C₂²	1	2	yes	complemented
91	C₄₁×#381	C₂²	1	2	yes	—
92	C₄₁×#381	C₂²	1	1	yes	characteristic, complemented
93	C₄₁×#380	C₂²	1	2	yes	—
94	C₄₁×#380	C₂²	1	2	yes	complemented
95	C₄₁×#379	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
105	C₄₁×#376	C₂²	1	1	yes	characteristic, complemented
106	C₂×#95×C₄₁	C₂²	1	2	yes	—
107	C₂×#95×C₄₁	C₂²	1	2	yes	—
108	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₄₁	—	4	2	no	—
113	C₂³×C₄×C₄₁	—	4	4	no	—
114	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
115	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
116	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
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	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
124	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
125	#126×C₄₁	C₂×C₄	1	16	yes	complemented
126	#124×C₄₁	C₂×C₄	1	8	yes	complemented
127	#123×C₄₁	C₂×C₄	1	8	yes	complemented
128	#123×C₄₁	C₂×C₄	1	16	yes	complemented
129	C₂²⋊Q₈×C₄₁	C₂×C₄	1	16	yes	complemented
130	#120×C₄₁	C₂×C₄	1	8	yes	—
131	C₄×Q₈×C₄₁	—	4	2	no	—
132	C₄×D₄×C₄₁	—	4	2	no	—
133	C₄×D₄×C₄₁	—	4	4	no	—
134	C₄×D₄×C₄₁	—	4	4	no	—
135	C₄×D₄×C₄₁	C₂×C₄	1	16	yes	complemented
136	#117×C₄₁	—	4	4	no	—
137	#117×C₄₁	C₂×C₄	1	16	yes	complemented
138	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
139	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
140	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
141	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
162	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	16	yes	complemented
163	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
185	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
186	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
188	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
189	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
191	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
193	#95×C₄₁	C₂³	1	2	yes	—
194	#95×C₄₁	C₂³	1	2	yes	—
195	#95×C₄₁	C₂³	1	2	yes	—
196	#95×C₄₁	C₂³	1	2	yes	—
197	#95×C₄₁	C₂³	1	2	yes	—
198	#95×C₄₁	C₂³	1	2	yes	—
199	#95×C₄₁	C₂³	1	2	yes	—
200	#95×C₄₁	C₂³	1	2	yes	—
201	#95×C₄₁	C₂³	1	2	yes	—
202	#95×C₄₁	C₂³	1	2	yes	—
203	#95×C₄₁	C₂³	1	2	yes	—
204	#95×C₄₁	C₂³	1	2	yes	—
205	#95×C₄₁	C₂³	1	2	yes	—
206	#95×C₄₁	C₂³	1	2	yes	—
207	#95×C₄₁	C₂³	1	2	yes	—
208	#95×C₄₁	C₂³	1	2	yes	—
209	#95×C₄₁	C₂³	1	2	yes	—
210	#95×C₄₁	C₂³	1	2	yes	—
211	#95×C₄₁	C₂³	1	2	yes	—
212	#95×C₄₁	C₂³	1	2	yes	—
213	#95×C₄₁	C₂³	1	2	yes	—
214	#95×C₄₁	C₂³	1	2	yes	—
215	C₂⁴×C₄₁	—	2	4	no	—
216	C₂⁴×C₄₁	—	2	4	no	—
217	C₂⁴×C₄₁	—	4	1	no	—
218	C₂⁴×C₄₁	—	4	1	no	—
219	C₂⁴×C₄₁	C₂²×C₄	1	4	yes	—
220	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₄₁	—	4	1	no	—
224	C₂×Q₈×C₄₁	—	4	1	no	—
225	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	complemented
226	C₂×D₄×C₄₁	—	2	4	no	—
227	C₂×D₄×C₄₁	—	2	4	no	—
228	C₂×D₄×C₄₁	—	4	1	no	—
229	C₂×D₄×C₄₁	—	4	1	no	—
230	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
231	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
232	C₂²×C₄×C₄₁	—	2	4	no	—
233	C₂²×C₄×C₄₁	—	2	4	no	—
234	C₂²×C₄×C₄₁	—	2	4	no	—
235	C₂²×C₄×C₄₁	—	2	4	no	—
236	C₂²×C₄×C₄₁	—	2	4	no	—
237	C₂²×C₄×C₄₁	—	2	4	no	—
238	C₂²×C₄×C₄₁	—	2	4	no	—
239	C₂²×C₄×C₄₁	—	2	2	no	—
240	C₂²×C₄×C₄₁	—	2	2	no	—
241	C₂²×C₄×C₄₁	—	4	2	no	—
242	C₂²×C₄×C₄₁	—	4	1	no	—
243	C₂²×C₄×C₄₁	—	4	2	no	—
244	C₂²×C₄×C₄₁	—	4	2	no	—
245	C₂²×C₄×C₄₁	—	4	2	no	—
246	C₂²×C₄×C₄₁	—	4	2	no	—
247	C₂²×C₄×C₄₁	—	4	2	no	—
248	C₂²×C₄×C₄₁	—	4	1	no	—
249	C₂²×C₄×C₄₁	—	4	2	no	—
250	C₂²×C₄×C₄₁	—	4	1	no	—
251	C₂²×C₄×C₄₁	—	4	2	no	—
252	C₂²×C₄×C₄₁	—	4	2	no	—
253	C₂²×C₄×C₄₁	—	4	2	no	—
254	C₂²×C₄×C₄₁	—	4	1	no	—
255	C₂²×C₄×C₄₁	—	4	2	no	—
256	C₂²×C₄×C₄₁	—	4	2	no	—
257	C₂²×C₄×C₄₁	—	4	2	no	—
258	C₂²×C₄×C₄₁	—	4	16	no	—
259	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
260	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
261	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	complemented
262	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₄₁	C₂⁴	1	2	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	1	yes	characteristic
278	C₄⋊C₄×C₄₁	—	2	4	no	—
279	C₄⋊C₄×C₄₁	—	2	4	no	—
280	C₄⋊C₄×C₄₁	—	4	2	no	—
281	C₄⋊C₄×C₄₁	—	4	2	no	—
282	C₄⋊C₄×C₄₁	—	4	2	no	—
283	C₄⋊C₄×C₄₁	—	4	2	no	—
284	C₄⋊C₄×C₄₁	—	4	2	no	—
285	C₄⋊C₄×C₄₁	—	4	2	no	—
286	C₄⋊C₄×C₄₁	—	4	2	no	—
287	C₄⋊C₄×C₄₁	—	4	2	no	—
288	C₄⋊C₄×C₄₁	—	4	2	no	—
289	C₄⋊C₄×C₄₁	—	4	2	no	—
290	C₄⋊C₄×C₄₁	—	4	1	no	—
291	C₄⋊C₄×C₄₁	—	4	2	no	—
292	C₄⋊C₄×C₄₁	—	4	2	no	—
293	C₄⋊C₄×C₄₁	—	4	1	no	—
294	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	complemented
295	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	complemented
296	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	complemented
297	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	complemented
298	C₂²⋊C₄×C₄₁	—	2	4	no	—
299	C₂²⋊C₄×C₄₁	—	2	4	no	—
300	C₂²⋊C₄×C₄₁	—	2	4	no	—
301	C₂²⋊C₄×C₄₁	—	2	4	no	—
302	C₂²⋊C₄×C₄₁	—	4	2	no	—
303	C₂²⋊C₄×C₄₁	—	4	2	no	—
304	C₂²⋊C₄×C₄₁	—	4	1	no	—
305	C₂²⋊C₄×C₄₁	—	4	1	no	—
306	C₂²⋊C₄×C₄₁	—	4	1	no	—
307	C₂²⋊C₄×C₄₁	—	4	1	no	—
308	C₂²⋊C₄×C₄₁	—	4	2	no	—
309	C₂²⋊C₄×C₄₁	—	4	2	no	—
310	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
311	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
312	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
313	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
314	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
315	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
316	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	complemented
317	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	complemented
318	C₄²×C₄₁	—	2	2	no	—
319	C₄²×C₄₁	—	4	2	no	—
320	C₄²×C₄₁	—	4	1	no	—
321	C₄²×C₄₁	—	4	2	no	—
322	C₄²×C₄₁	—	4	2	no	—
323	C₄²×C₄₁	—	4	2	no	—
324	C₄²×C₄₁	—	4	2	no	—
325	C₄²×C₄₁	—	4	2	no	—
326	C₄²×C₄₁	C₂²×C₄	1	4	yes	complemented
327	C₄²×C₄₁	C₂²×C₄	1	8	yes	complemented
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	16	no	—
333	C₂³×C₄₁	—	2	2	no	—
334	C₂³×C₄₁	—	2	2	no	—
335	C₂³×C₄₁	—	2	1	no	—
336	C₂³×C₄₁	—	2	1	no	—
337	C₂³×C₄₁	—	2	2	no	—
338	C₂³×C₄₁	—	2	2	no	—
339	C₂³×C₄₁	—	2	1	no	—
340	C₂³×C₄₁	—	2	1	no	—
341	C₂³×C₄₁	—	4	4	no	—
342	C₂³×C₄₁	—	4	4	no	—
343	C₂³×C₄₁	—	4	8	no	—
344	C₂³×C₄₁	—	4	4	no	—
345	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
346	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
347	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
348	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
349	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
350	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
351	Q₈×C₄₁	—	4	4	no	—
352	D₄×C₄₁	—	2	16	no	—
353	D₄×C₄₁	—	4	4	no	—
354	C₂×C₄×C₄₁	—	2	16	no	—
355	C₂×C₄×C₄₁	—	2	1	no	—
356	C₂×C₄×C₄₁	—	2	2	no	—
357	C₂×C₄×C₄₁	—	2	2	no	—
358	C₂×C₄×C₄₁	—	2	2	no	—
359	C₂×C₄×C₄₁	—	2	2	no	—
360	C₂×C₄×C₄₁	—	2	2	no	—
361	C₂×C₄×C₄₁	—	2	2	no	—
362	C₂×C₄×C₄₁	—	2	2	no	—
363	C₂×C₄×C₄₁	—	2	2	no	—
364	C₂×C₄×C₄₁	—	2	2	no	—
365	C₂×C₄×C₄₁	—	2	2	no	—
366	C₂×C₄×C₄₁	—	2	1	no	—
367	C₂×C₄×C₄₁	—	2	2	no	—
368	C₂×C₄×C₄₁	—	2	1	no	—
369	C₂×C₄×C₄₁	—	2	2	no	—
370	C₂×C₄×C₄₁	—	2	2	no	—
371	C₂×C₄×C₄₁	—	2	2	no	—
372	C₂×C₄×C₄₁	—	2	2	no	—
373	C₂×C₄×C₄₁	—	2	2	no	—
374	C₂×C₄×C₄₁	—	2	2	no	—
375	C₂×C₄×C₄₁	—	2	2	no	—
376	C₂×C₄×C₄₁	—	2	2	no	—
377	C₂×C₄×C₄₁	—	2	2	no	—
378	C₂×C₄×C₄₁	—	2	1	no	—
379	C₂×C₄×C₄₁	—	2	2	no	—
380	C₂×C₄×C₄₁	—	2	1	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	—	4	8	no	—
393	C₂×C₄×C₄₁	—	4	4	no	—
394	C₂×C₄×C₄₁	—	4	8	no	—
395	C₂×C₄×C₄₁	—	4	4	no	—
396	C₂×C₄×C₄₁	—	4	8	no	—
397	C₂×C₄×C₄₁	—	4	4	no	—
398	C₂×C₄×C₄₁	—	8	2	no	—
399	C₂×C₄×C₄₁	—	8	4	no	—
400	C₂×C₄×C₄₁	—	8	4	no	—
401	C₂×C₄×C₄₁	—	8	2	no	—
402	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
403	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
404	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
405	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
406	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
407	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
408	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
409	#34457	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
410	C₂²×C₄₁	—	2	4	no	—
411	C₂²×C₄₁	—	2	4	no	—
412	C₂²×C₄₁	—	2	4	no	—
413	C₂²×C₄₁	—	2	4	no	—
414	C₂²×C₄₁	—	2	4	no	—
415	C₂²×C₄₁	—	2	4	no	—
416	C₂²×C₄₁	—	2	4	no	—
417	C₂²×C₄₁	—	2	4	no	—
418	C₂²×C₄₁	—	2	2	no	—
419	C₂²×C₄₁	—	2	2	no	—
420	C₂²×C₄₁	—	4	16	no	—
421	C₂²×C₄₁	—	4	1	no	—
422	C₂²×C₄₁	—	4	1	no	—
423	C₂²×C₄₁	—	4	2	no	—
424	C₂²×C₄₁	—	4	2	no	—
425	C₂²×C₄₁	—	4	1	no	—
426	C₂²×C₄₁	—	4	1	no	—
427	C₂²×C₄₁	#520	1	8	yes	—
428	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
429	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
430	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
432	C₂²×C₄₁	#585	1	1	yes	characteristic
433	C₄×C₄₁	—	2	4	no	—
434	C₄×C₄₁	—	2	4	no	—
435	C₄×C₄₁	—	2	4	no	—
436	C₄×C₄₁	—	2	4	no	—
437	C₄×C₄₁	—	2	4	no	—
438	C₄×C₄₁	—	2	2	no	—
439	C₄×C₄₁	—	2	2	no	—
440	C₄×C₄₁	—	4	2	no	—
441	C₄×C₄₁	—	4	1	no	—
442	C₄×C₄₁	—	4	2	no	—
443	C₄×C₄₁	—	4	1	no	—
444	C₄×C₄₁	—	4	2	no	—
445	C₄×C₄₁	—	4	2	no	—
446	C₄×C₄₁	—	4	2	no	—
447	C₄×C₄₁	—	4	2	no	—
448	C₄×C₄₁	—	4	1	no	—
449	C₂×#551	C₂×C₄₁	1	1	yes	characteristic
450	#2383	C₂×C₄₁	1	2	yes	complemented
451	#2379	C₂×C₄₁	1	1	yes	characteristic, complemented
452	#2376	C₂×C₄₁	1	1	yes	characteristic, complemented
453	#2360	C₂×C₄₁	1	2	yes	complemented
454	#2359	C₂×C₄₁	1	2	yes	complemented
455	#2358	C₂×C₄₁	1	1	yes	characteristic
456	D₄×C₄⋊C₄	C₂×C₄₁	1	2	yes	complemented
457	#2343	C₂×C₄₁	1	2	yes	complemented
458	#2342	C₂×C₄₁	1	2	yes	complemented
459	#2334	C₂×C₄₁	1	2	yes	complemented
460	#2329	C₂×C₄₁	1	2	yes	complemented
461	#2326	C₂×C₄₁	1	1	yes	characteristic, complemented
462	#2322	C₂×C₄₁	1	2	yes	complemented
463	#2322	C₂×C₄₁	1	1	yes	characteristic, complemented
464	#2318	C₂×C₄₁	1	2	yes	complemented
465	#2317	C₂×C₄₁	1	2	yes	complemented
466	C₄×#120	C₂×C₄₁	1	1	yes	characteristic
467	C₂×#385	C₂×C₄₁	1	2	yes	complemented
468	C₂×C₄₁	—	2	8	no	—
469	C₂×C₄₁	—	4	2	no	—
470	C₂×C₄₁	—	4	2	no	—
471	C₂×C₄₁	C₂×#520	1	2	yes	—
472	C₂×C₄₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂×C₄₁	#3532	1	1	yes	characteristic
474	C₂×C₄₁	#3535	1	2	yes	—
475	C₂×C₄₁	#3538	1	1	yes	characteristic
476	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
477	#551	C₄×C₄₁	1	16	yes	complemented
478	C₂×#126	C₂²×C₄₁	1	2	yes	—
479	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
480	C₂×#123	C₂²×C₄₁	1	2	yes	—
481	C₂×#123	C₂²×C₄₁	1	1	yes	characteristic
482	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
483	C₂×#120	C₂²×C₄₁	1	1	yes	characteristic
484	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
485	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
486	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
487	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
488	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
489	C₂×#117	C₂²×C₄₁	1	2	yes	—
490	C₂×#117	C₂²×C₄₁	1	2	yes	—
491	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
492	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
493	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
494	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
495	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
496	#391	C₂²×C₄₁	1	1	yes	characteristic, complemented
497	#391	C₂²×C₄₁	1	2	yes	complemented
498	#390	C₂²×C₄₁	1	1	yes	characteristic
499	#389	C₂²×C₄₁	1	2	yes	complemented
500	#389	C₂²×C₄₁	1	2	yes	complemented
501	#389	C₂²×C₄₁	1	2	yes	complemented
502	#389	C₂²×C₄₁	1	2	yes	complemented
503	#389	C₂²×C₄₁	1	2	yes	complemented
504	#389	C₂²×C₄₁	1	2	yes	complemented
505	#389	C₂²×C₄₁	1	2	yes	complemented
506	#388	C₂²×C₄₁	1	2	yes	—
507	#388	C₂²×C₄₁	1	2	yes	—
508	#388	C₂²×C₄₁	1	2	yes	—
509	#388	C₂²×C₄₁	1	2	yes	—
510	#388	C₂²×C₄₁	1	2	yes	—
511	#388	C₂²×C₄₁	1	2	yes	complemented
512	#388	C₂²×C₄₁	1	2	yes	complemented
513	#388	C₂²×C₄₁	1	2	yes	complemented
514	#387	C₂²×C₄₁	1	2	yes	complemented
515	#387	C₂²×C₄₁	1	2	yes	complemented
516	#387	C₂²×C₄₁	1	2	yes	complemented
517	#387	C₂²×C₄₁	1	2	yes	complemented
518	#387	C₂²×C₄₁	1	2	yes	complemented
519	#387	C₂²×C₄₁	1	2	yes	complemented
520	#387	C₂²×C₄₁	1	2	yes	complemented
521	#387	C₂²×C₄₁	1	2	yes	complemented
522	#386	C₂²×C₄₁	1	2	yes	—
523	#386	C₂²×C₄₁	1	2	yes	—
524	#386	C₂²×C₄₁	1	1	yes	characteristic
525	#386	C₂²×C₄₁	1	1	yes	characteristic
526	#385	C₂²×C₄₁	1	2	yes	—
527	#385	C₂²×C₄₁	1	2	yes	—
528	#385	C₂²×C₄₁	1	2	yes	—
529	#385	C₂²×C₄₁	1	2	yes	—
530	#385	C₂²×C₄₁	1	2	yes	—
531	#385	C₂²×C₄₁	1	2	yes	—
532	#385	C₂²×C₄₁	1	2	yes	—
533	#385	C₂²×C₄₁	1	2	yes	—
534	#385	C₂²×C₄₁	1	2	yes	—
535	#385	C₂²×C₄₁	1	2	yes	—
536	#385	C₂²×C₄₁	1	2	yes	—
537	#385	C₂²×C₄₁	1	2	yes	—
538	#385	C₂²×C₄₁	1	1	yes	characteristic
539	#385	C₂²×C₄₁	1	1	yes	characteristic, complemented
540	#385	C₂²×C₄₁	1	2	yes	complemented
541	#385	C₂²×C₄₁	1	2	yes	complemented
542	#384	C₂²×C₄₁	1	1	yes	characteristic, complemented
543	#384	C₂²×C₄₁	1	2	yes	complemented
544	#383	C₂²×C₄₁	1	2	yes	complemented
545	#382	C₂²×C₄₁	1	2	yes	complemented
546	#382	C₂²×C₄₁	1	2	yes	complemented
547	#381	C₂²×C₄₁	1	2	yes	—
548	#381	C₂²×C₄₁	1	1	yes	characteristic, complemented
549	#380	C₂²×C₄₁	1	2	yes	—
550	#380	C₂²×C₄₁	1	2	yes	complemented
551	#379	C₂²×C₄₁	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
553	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
554	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
555	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
556	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
557	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
558	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
559	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
560	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
561	#376	C₂²×C₄₁	1	1	yes	characteristic, complemented
562	C₂×#95	C₂²×C₄₁	1	2	yes	—
563	C₂×#95	C₂²×C₄₁	1	2	yes	—
564	C₄₁	#34457	1	1	yes	characteristic, direct product factor, Sylow
565	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
568	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
569	C₂³×C₄	—	4	2	no	—
570	C₂³×C₄	—	4	4	no	—
571	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
572	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
573	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
574	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
575	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
576	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
581	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
582	#126	C₂×C₄×C₄₁	1	16	yes	complemented
583	#124	C₂×C₄×C₄₁	1	8	yes	complemented
584	#123	C₂×C₄×C₄₁	1	8	yes	complemented
585	#123	C₂×C₄×C₄₁	1	16	yes	complemented
586	C₂²⋊Q₈	C₂×C₄×C₄₁	1	16	yes	complemented
587	#120	C₂×C₄×C₄₁	1	8	yes	—
588	C₄×Q₈	—	4	2	no	—
589	C₄×D₄	—	4	2	no	—
590	C₄×D₄	—	4	4	no	—
591	C₄×D₄	—	4	4	no	—
592	C₄×D₄	C₂×C₄×C₄₁	1	16	yes	complemented
593	#117	—	4	4	no	—
594	#117	C₂×C₄×C₄₁	1	16	yes	complemented
595	C₂×C₄⋊C₄	—	4	4	no	—
596	C₂×C₄⋊C₄	—	4	2	no	—
597	C₂×C₄⋊C₄	—	4	4	no	—
598	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
618	C₂×C₂²⋊C₄	—	4	4	no	—
619	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	16	yes	complemented
620	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
642	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
643	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
644	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
645	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
646	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
648	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
650	#95	C₂³×C₄₁	1	2	yes	—
651	#95	C₂³×C₄₁	1	2	yes	—
652	#95	C₂³×C₄₁	1	2	yes	—
653	#95	C₂³×C₄₁	1	2	yes	—
654	#95	C₂³×C₄₁	1	2	yes	—
655	#95	C₂³×C₄₁	1	2	yes	—
656	#95	C₂³×C₄₁	1	2	yes	—
657	#95	C₂³×C₄₁	1	2	yes	—
658	#95	C₂³×C₄₁	1	2	yes	—
659	#95	C₂³×C₄₁	1	2	yes	—
660	#95	C₂³×C₄₁	1	2	yes	—
661	#95	C₂³×C₄₁	1	2	yes	—
662	#95	C₂³×C₄₁	1	2	yes	—
663	#95	C₂³×C₄₁	1	2	yes	—
664	#95	C₂³×C₄₁	1	2	yes	—
665	#95	C₂³×C₄₁	1	2	yes	—
666	#95	C₂³×C₄₁	1	2	yes	—
667	#95	C₂³×C₄₁	1	2	yes	—
668	#95	C₂³×C₄₁	1	2	yes	—
669	#95	C₂³×C₄₁	1	2	yes	—
670	#95	C₂³×C₄₁	1	2	yes	—
671	#95	C₂³×C₄₁	1	2	yes	—
672	C₂⁴	—	2	4	no	—
673	C₂⁴	—	2	4	no	—
674	C₂⁴	—	4	1	no	—
675	C₂⁴	—	4	1	no	—
676	C₂⁴	C₂²×C₄×C₄₁	1	4	yes	—
677	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
678	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
679	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
680	C₂×Q₈	—	4	1	no	—
681	C₂×Q₈	—	4	1	no	—
682	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	complemented
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	1	no	—
687	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
688	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	1	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	1	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	16	no	—
716	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
717	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
718	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	complemented
719	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	1	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	complemented
752	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	complemented
753	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	complemented
754	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	complemented
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	1	no	—
762	C₂²⋊C₄	—	4	1	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	1	no	—
766	C₂²⋊C₄	—	4	1	no	—
767	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
768	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
769	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
770	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
771	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
772	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
773	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	complemented
774	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	complemented
775	C₄²	—	2	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	—	4	2	no	—
779	C₄²	—	4	2	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	2	no	—
782	C₄²	—	4	1	no	—
783	C₄²	C₂²×C₄×C₄₁	1	4	yes	complemented
784	C₄²	C₂²×C₄×C₄₁	1	8	yes	complemented
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	16	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	4	no	—
800	C₂³	—	4	8	no	—
801	C₂³	—	4	4	no	—
802	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
803	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
804	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
805	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
806	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
807	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
808	Q₈	—	4	4	no	—
809	D₄	—	2	16	no	—
810	D₄	—	4	4	no	—
811	C₂×C₄	—	2	16	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	8	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	—	8	4	no	—
857	C₂×C₄	—	8	4	no	—
858	C₂×C₄	—	8	2	no	—
859	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
860	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
861	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
862	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
863	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
864	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
865	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	4	16	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	C₄₁×#520	1	8	yes	—
884	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
885	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
886	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
887	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
888	C₂²	C₄₁×#585	1	1	yes	characteristic
889	C₄	—	2	4	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₂	—	2	8	no	—
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	C₂×C₄₁×#520	1	2	yes	—
909	C₂	C₄×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
910	C₂	C₄₁×#3532	1	1	yes	characteristic
911	C₂	C₄₁×#3535	1	2	yes	—
912	C₂	C₄₁×#3538	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×#120×C₄₁	C₂²
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×#2383	C₂	semidirect
3. C₄₁×#2379	C₂	semidirect
4. C₄₁×#2376	C₂	semidirect
5. C₄₁×#2360	C₂	semidirect
6. C₄₁×#2359	C₂	semidirect
8. D₄×C₄⋊C₄×C₄₁	C₂	semidirect
9. C₄₁×#2343	C₂	semidirect
10. C₄₁×#2342	C₂	semidirect
11. C₄₁×#2334	C₂	semidirect
12. C₄₁×#2329	C₂	semidirect
13. C₄₁×#2326	C₂	semidirect
14. C₄₁×#2322	C₂	semidirect
15. C₄₁×#2322	C₂	semidirect
16. C₄₁×#2318	C₂	semidirect
17. C₄₁×#2317	C₂	semidirect
19. C₂×C₄₁×#385	C₂	semidirect
21. C₄₁×#551	C₄	semidirect
28. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
40. C₄₁×#391	C₂²	semidirect
41. C₄₁×#391	C₂²	semidirect
43. C₄₁×#389	C₂²	semidirect
44. C₄₁×#389	C₂²	semidirect
45. C₄₁×#389	C₂²	semidirect
46. C₄₁×#389	C₂²	semidirect
47. C₄₁×#389	C₂²	semidirect
48. C₄₁×#389	C₂²	semidirect
49. C₄₁×#389	C₂²	semidirect
55. C₄₁×#388	C₂²	semidirect
56. C₄₁×#388	C₂²	semidirect
57. C₄₁×#388	C₂²	semidirect
58. C₄₁×#387	C₂²	semidirect
59. C₄₁×#387	C₂²	semidirect
60. C₄₁×#387	C₂²	semidirect
61. C₄₁×#387	C₂²	semidirect
62. C₄₁×#387	C₂²	semidirect
63. C₄₁×#387	C₂²	semidirect
64. C₄₁×#387	C₂²	semidirect
65. C₄₁×#387	C₂²	semidirect
83. C₄₁×#385	C₂²	semidirect
84. C₄₁×#385	C₂²	semidirect
85. C₄₁×#385	C₂²	semidirect
86. C₄₁×#384	C₂²	semidirect
87. C₄₁×#384	C₂²	semidirect
88. C₄₁×#383	C₂²	semidirect
89. C₄₁×#382	C₂²	semidirect
90. C₄₁×#382	C₂²	semidirect
92. C₄₁×#381	C₂²	semidirect
94. C₄₁×#380	C₂²	semidirect
96. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
97. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
105. C₄₁×#376	C₂²	semidirect
125. #126×C₄₁	C₂×C₄	semidirect
126. #124×C₄₁	C₂×C₄	semidirect
127. #123×C₄₁	C₂×C₄	semidirect
128. #123×C₄₁	C₂×C₄	semidirect
129. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
135. C₄×D₄×C₄₁	C₂×C₄	semidirect
137. #117×C₄₁	C₂×C₄	semidirect
162. C₂×C₂²⋊C₄×C₄₁	C₂×C₄	semidirect
225. C₂×Q₈×C₄₁	C₂²×C₄	semidirect
261. C₂²×C₄×C₄₁	C₂²×C₄	semidirect
294. C₄⋊C₄×C₄₁	C₂²×C₄	semidirect
295. C₄⋊C₄×C₄₁	C₂²×C₄	semidirect
296. C₄⋊C₄×C₄₁	C₂²×C₄	semidirect
297. C₄⋊C₄×C₄₁	C₂²×C₄	semidirect
316. C₂²⋊C₄×C₄₁	C₂²×C₄	semidirect
317. C₂²⋊C₄×C₄₁	C₂²×C₄	semidirect
326. C₄²×C₄₁	C₂²×C₄	semidirect
327. C₄²×C₄₁	C₂²×C₄	semidirect
409. #34457	C₄₁	direct (N × H)
450. #2383	C₂×C₄₁	semidirect
451. #2379	C₂×C₄₁	semidirect
452. #2376	C₂×C₄₁	semidirect
453. #2360	C₂×C₄₁	semidirect
454. #2359	C₂×C₄₁	semidirect
456. D₄×C₄⋊C₄	C₂×C₄₁	semidirect
457. #2343	C₂×C₄₁	semidirect
458. #2342	C₂×C₄₁	semidirect
459. #2334	C₂×C₄₁	semidirect
460. #2329	C₂×C₄₁	semidirect
461. #2326	C₂×C₄₁	semidirect
462. #2322	C₂×C₄₁	semidirect
463. #2322	C₂×C₄₁	semidirect
464. #2318	C₂×C₄₁	semidirect
465. #2317	C₂×C₄₁	semidirect
467. C₂×#385	C₂×C₄₁	semidirect
477. #551	C₄×C₄₁	semidirect
484. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
493. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
496. #391	C₂²×C₄₁	semidirect
497. #391	C₂²×C₄₁	semidirect
499. #389	C₂²×C₄₁	semidirect
500. #389	C₂²×C₄₁	semidirect
501. #389	C₂²×C₄₁	semidirect
502. #389	C₂²×C₄₁	semidirect
503. #389	C₂²×C₄₁	semidirect
504. #389	C₂²×C₄₁	semidirect
505. #389	C₂²×C₄₁	semidirect
511. #388	C₂²×C₄₁	semidirect
512. #388	C₂²×C₄₁	semidirect
513. #388	C₂²×C₄₁	semidirect
514. #387	C₂²×C₄₁	semidirect
515. #387	C₂²×C₄₁	semidirect
516. #387	C₂²×C₄₁	semidirect
517. #387	C₂²×C₄₁	semidirect
518. #387	C₂²×C₄₁	semidirect
519. #387	C₂²×C₄₁	semidirect
520. #387	C₂²×C₄₁	semidirect
521. #387	C₂²×C₄₁	semidirect
539. #385	C₂²×C₄₁	semidirect
540. #385	C₂²×C₄₁	semidirect
541. #385	C₂²×C₄₁	semidirect
542. #384	C₂²×C₄₁	semidirect
543. #384	C₂²×C₄₁	semidirect
544. #383	C₂²×C₄₁	semidirect
545. #382	C₂²×C₄₁	semidirect
546. #382	C₂²×C₄₁	semidirect
548. #381	C₂²×C₄₁	semidirect
550. #380	C₂²×C₄₁	semidirect
552. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
553. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
560. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
561. #376	C₂²×C₄₁	semidirect
564. C₄₁	#34457	direct (N × H)
582. #126	C₂×C₄×C₄₁	semidirect
583. #124	C₂×C₄×C₄₁	semidirect
584. #123	C₂×C₄×C₄₁	semidirect
585. #123	C₂×C₄×C₄₁	semidirect
586. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
592. C₄×D₄	C₂×C₄×C₄₁	semidirect
594. #117	C₂×C₄×C₄₁	semidirect
619. C₂×C₂²⋊C₄	C₂×C₄×C₄₁	semidirect
682. C₂×Q₈	C₂²×C₄×C₄₁	semidirect
718. C₂²×C₄	C₂²×C₄×C₄₁	semidirect
751. C₄⋊C₄	C₂²×C₄×C₄₁	semidirect
752. C₄⋊C₄	C₂²×C₄×C₄₁	semidirect
753. C₄⋊C₄	C₂²×C₄×C₄₁	semidirect
754. C₄⋊C₄	C₂²×C₄×C₄₁	semidirect
773. C₂²⋊C₄	C₂²×C₄×C₄₁	semidirect
774. C₂²⋊C₄	C₂²×C₄×C₄₁	semidirect
783. C₄²	C₂²×C₄×C₄₁	semidirect
784. C₄²	C₂²×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×#551	2
C₄₁×#2383	2
C₄₁×#2379	2
C₄₁×#2376	2
C₄₁×#2360	2
C₄₁×#2359	2
C₄₁×#2358	2
D₄×C₄⋊C₄×C₄₁	2
C₄₁×#2343	2
C₄₁×#2342	2
C₄₁×#2334	2
C₄₁×#2329	2
C₄₁×#2326	2
C₄₁×#2322	2
C₄₁×#2318	2
C₄₁×#2317	2
C₄×#120×C₄₁	2
C₂×C₄₁×#385	2
#34457	41

Subgroups — C41×#34457 #23810658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34457 #23810658