Subgroups — C₄₁×#34962 #23811163

Order 10496.

2198 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2593	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#2586	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2574	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2572	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2555	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2554	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2518	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2467	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2459	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2456	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2396	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#2392	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#2388	C₂	1	2	yes	maximal, complemented
14	C₄×#126×C₄₁	C₂	1	2	yes	maximal, complemented
15	C₄×#124×C₄₁	C₂	1	2	yes	maximal, complemented
16	C₄×#123×C₄₁	C₂	1	2	yes	maximal, complemented
17	C₄×#121×C₄₁	C₂	1	2	yes	maximal, complemented
18	C₄₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₄₁	C₂	1	2	yes	maximal, complemented
20	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#126×C₄₁	C₂²	1	2	yes	—
22	C₂×#124×C₄₁	C₂²	1	2	yes	—
23	C₂×#123×C₄₁	C₂²	1	2	yes	—
24	C₂×#121×C₄₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
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×#117×C₄₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
35	C₄₁×#400	C₂²	1	1	yes	characteristic
36	C₄₁×#399	C₂²	1	1	yes	characteristic
37	C₄₁×#398	C₂²	1	2	yes	—
38	C₄₁×#398	C₂²	1	1	yes	characteristic
39	C₄₁×#397	C₂²	1	1	yes	characteristic
40	C₄₁×#396	C₂²	1	2	yes	—
41	C₄₁×#396	C₂²	1	2	yes	—
42	C₄₁×#395	C₂²	1	1	yes	characteristic
43	C₄₁×#395	C₂²	1	2	yes	—
44	C₄₁×#394	C₂²	1	2	yes	—
45	C₄₁×#394	C₂²	1	1	yes	characteristic
46	C₄₁×#394	C₂²	1	2	yes	—
47	C₄₁×#394	C₂²	1	2	yes	—
48	C₄₁×#394	C₂²	1	2	yes	—
49	C₄₁×#393	C₂²	1	2	yes	—
50	C₄₁×#393	C₂²	1	1	yes	characteristic
51	C₄₁×#392	C₂²	1	2	yes	—
52	C₄₁×#392	C₂²	1	2	yes	—
53	C₄₁×#392	C₂²	1	2	yes	—
54	C₄₁×#392	C₂²	1	1	yes	characteristic
55	C₄₁×#391	C₂²	1	1	yes	characteristic
56	C₄₁×#391	C₂²	1	1	yes	characteristic
57	C₄₁×#391	C₂²	1	2	yes	—
58	C₄₁×#390	C₂²	1	1	yes	characteristic
59	C₄₁×#390	C₂²	1	1	yes	characteristic
60	C₄₁×#390	C₂²	1	2	yes	—
61	C₄₁×#390	C₂²	1	2	yes	—
62	C₄₁×#389	C₂²	1	2	yes	—
63	C₄₁×#388	C₂²	1	2	yes	—
64	C₄₁×#388	C₂²	1	2	yes	—
65	C₄₁×#388	C₂²	1	2	yes	—
66	C₄₁×#388	C₂²	1	2	yes	—
67	C₄₁×#388	C₂²	1	2	yes	—
68	C₄₁×#388	C₂²	1	2	yes	—
69	C₄₁×#388	C₂²	1	2	yes	—
70	C₄₁×#388	C₂²	1	2	yes	—
71	C₄₁×#388	C₂²	1	2	yes	—
72	C₄₁×#388	C₂²	1	2	yes	—
73	C₄₁×#388	C₂²	1	2	yes	—
74	C₄₁×#387	C₂²	1	2	yes	—
75	C₄₁×#387	C₂²	1	2	yes	—
76	C₄₁×#387	C₂²	1	2	yes	—
77	C₄₁×#387	C₂²	1	2	yes	—
78	C₄₁×#387	C₂²	1	2	yes	—
79	C₄₁×#386	C₂²	1	2	yes	—
80	C₄₁×#386	C₂²	1	2	yes	—
81	C₄₁×#386	C₂²	1	2	yes	—
82	C₄₁×#386	C₂²	1	2	yes	—
83	C₄₁×#386	C₂²	1	2	yes	—
84	C₄₁×#385	C₂²	1	2	yes	—
85	C₄₁×#383	C₂²	1	2	yes	—
86	C₄₁×#382	C₂²	1	2	yes	—
87	C₄₁×#381	C₂²	1	2	yes	—
88	C₄₁×#380	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
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	2	yes	—
105	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
106	C₄³×C₄₁	C₂²	1	2	yes	—
107	C₂×#41×C₄₁	—	2	4	no	—
108	C₂×#41×C₄₁	—	4	2	no	—
109	C₂×#41×C₄₁	—	4	2	no	—
110	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
116	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
117	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
119	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
120	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
121	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
122	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
124	#126×C₄₁	—	2	8	no	—
125	#124×C₄₁	—	2	8	no	—
126	#123×C₄₁	—	2	8	no	—
127	#121×C₄₁	—	2	8	no	—
128	C₄×Q₈×C₄₁	—	4	2	no	—
129	C₄×D₄×C₄₁	—	2	8	no	—
130	C₄×D₄×C₄₁	—	2	8	no	—
131	C₄×D₄×C₄₁	—	2	8	no	—
132	C₄×D₄×C₄₁	—	4	4	no	—
133	C₄×D₄×C₄₁	—	4	2	no	—
134	C₄×D₄×C₄₁	—	4	4	no	—
135	#117×C₄₁	—	4	2	no	—
136	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
147	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
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	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
173	C₂×C₄²×C₄₁	—	4	2	no	—
174	C₂×C₄²×C₄₁	—	4	4	no	—
175	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
177	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
178	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
179	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
180	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
184	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
185	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
188	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
189	#95×C₄₁	C₂³	1	2	yes	—
190	#95×C₄₁	C₂³	1	2	yes	—
191	#95×C₄₁	C₂³	1	2	yes	—
192	#95×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	1	yes	characteristic
206	#95×C₄₁	C₂³	1	1	yes	characteristic
207	#95×C₄₁	C₂³	1	2	yes	—
208	#95×C₄₁	C₂³	1	1	yes	characteristic
209	#95×C₄₁	C₂³	1	2	yes	—
210	#95×C₄₁	C₂³	1	1	yes	characteristic
211	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
212	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
214	#41×C₄₁	—	4	16	no	—
215	C₂×Q₈×C₄₁	—	2	4	no	—
216	C₂×Q₈×C₄₁	—	2	2	no	—
217	C₂×Q₈×C₄₁	—	4	1	no	—
218	C₂×Q₈×C₄₁	—	4	1	no	—
219	C₂×Q₈×C₄₁	—	4	1	no	—
220	C₂×D₄×C₄₁	—	2	4	no	—
221	C₂×D₄×C₄₁	—	2	4	no	—
222	C₂×D₄×C₄₁	—	2	4	no	—
223	C₂×D₄×C₄₁	—	2	4	no	—
224	C₂×D₄×C₄₁	—	2	4	no	—
225	C₂×D₄×C₄₁	—	2	4	no	—
226	C₂×D₄×C₄₁	—	2	4	no	—
227	C₂×D₄×C₄₁	—	2	4	no	—
228	C₂×D₄×C₄₁	—	2	4	no	—
229	C₂×D₄×C₄₁	—	2	2	no	—
230	C₂×D₄×C₄₁	—	4	2	no	—
231	C₂×D₄×C₄₁	—	4	2	no	—
232	C₂×D₄×C₄₁	—	4	1	no	—
233	C₂×D₄×C₄₁	—	4	1	no	—
234	C₂×D₄×C₄₁	—	4	1	no	—
235	C₂×D₄×C₄₁	—	4	2	no	—
236	C₂×D₄×C₄₁	—	4	2	no	—
237	C₂²×C₄×C₄₁	—	2	2	no	—
238	C₂²×C₄×C₄₁	—	2	2	no	—
239	C₂²×C₄×C₄₁	—	2	4	no	—
240	C₂²×C₄×C₄₁	—	2	4	no	—
241	C₂²×C₄×C₄₁	—	2	4	no	—
242	C₂²×C₄×C₄₁	—	2	4	no	—
243	C₂²×C₄×C₄₁	—	2	4	no	—
244	C₂²×C₄×C₄₁	—	2	4	no	—
245	C₂²×C₄×C₄₁	—	2	4	no	—
246	C₂²×C₄×C₄₁	—	2	4	no	—
247	C₂²×C₄×C₄₁	—	2	4	no	—
248	C₂²×C₄×C₄₁	—	2	4	no	—
249	C₂²×C₄×C₄₁	—	2	4	no	—
250	C₂²×C₄×C₄₁	—	2	4	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	#41	1	4	yes	—
255	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
268	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₄₁	—	2	4	no	—
272	C₄⋊C₄×C₄₁	—	2	4	no	—
273	C₄⋊C₄×C₄₁	—	2	4	no	—
274	C₄⋊C₄×C₄₁	—	2	4	no	—
275	C₄⋊C₄×C₄₁	—	2	4	no	—
276	C₄⋊C₄×C₄₁	—	2	4	no	—
277	C₄⋊C₄×C₄₁	—	4	1	no	—
278	C₄⋊C₄×C₄₁	—	4	1	no	—
279	C₄⋊C₄×C₄₁	—	4	2	no	—
280	C₄⋊C₄×C₄₁	—	4	2	no	—
281	C₄⋊C₄×C₄₁	—	4	1	no	—
282	C₄⋊C₄×C₄₁	—	4	2	no	—
283	C₄⋊C₄×C₄₁	—	4	1	no	—
284	C₄⋊C₄×C₄₁	#41	1	8	yes	complemented
285	C₂²⋊C₄×C₄₁	—	2	4	no	—
286	C₂²⋊C₄×C₄₁	—	2	4	no	—
287	C₂²⋊C₄×C₄₁	—	2	4	no	—
288	C₂²⋊C₄×C₄₁	—	2	4	no	—
289	C₂²⋊C₄×C₄₁	—	2	4	no	—
290	C₂²⋊C₄×C₄₁	—	2	4	no	—
291	C₂²⋊C₄×C₄₁	—	2	4	no	—
292	C₂²⋊C₄×C₄₁	—	2	4	no	—
293	C₂²⋊C₄×C₄₁	—	2	4	no	—
294	C₂²⋊C₄×C₄₁	—	2	4	no	—
295	C₂²⋊C₄×C₄₁	—	2	4	no	—
296	C₂²⋊C₄×C₄₁	—	2	4	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	1	no	—
301	C₂²⋊C₄×C₄₁	—	4	1	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	#41	1	8	yes	complemented
308	C₄²×C₄₁	—	2	4	no	—
309	C₄²×C₄₁	—	2	4	no	—
310	C₄²×C₄₁	—	2	4	no	—
311	C₄²×C₄₁	—	2	4	no	—
312	C₄²×C₄₁	—	2	4	no	—
313	C₄²×C₄₁	—	2	4	no	—
314	C₄²×C₄₁	—	2	4	no	—
315	C₄²×C₄₁	—	2	2	no	—
316	C₄²×C₄₁	—	2	2	no	—
317	C₄²×C₄₁	—	2	4	no	—
318	C₄²×C₄₁	—	4	1	no	—
319	C₄²×C₄₁	—	4	1	no	—
320	C₄²×C₄₁	—	4	2	no	—
321	C₄²×C₄₁	—	4	2	no	—
322	C₂³×C₄₁	—	2	2	no	—
323	C₂³×C₄₁	—	2	2	no	—
324	C₂³×C₄₁	—	2	2	no	—
325	C₂³×C₄₁	—	2	2	no	—
326	C₂³×C₄₁	—	2	2	no	—
327	C₂³×C₄₁	—	2	2	no	—
328	C₂³×C₄₁	—	2	1	no	—
329	C₂³×C₄₁	—	2	2	no	—
330	C₂³×C₄₁	—	2	2	no	—
331	C₂³×C₄₁	—	2	1	no	—
332	C₂³×C₄₁	—	2	2	no	—
333	C₂³×C₄₁	—	2	2	no	—
334	C₂³×C₄₁	—	2	2	no	—
335	C₂³×C₄₁	—	2	2	no	—
336	C₂³×C₄₁	—	2	2	no	—
337	C₂³×C₄₁	—	2	2	no	—
338	C₂³×C₄₁	—	2	2	no	—
339	C₂³×C₄₁	C₂×#41	1	2	yes	—
340	C₂³×C₄₁	C₂×#41	1	4	yes	—
341	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
342	Q₈×C₄₁	—	4	4	no	—
343	Q₈×C₄₁	—	4	4	no	—
344	D₄×C₄₁	—	2	16	no	—
345	D₄×C₄₁	—	4	8	no	—
346	D₄×C₄₁	—	4	8	no	—
347	D₄×C₄₁	—	4	4	no	—
348	D₄×C₄₁	—	4	4	no	—
349	D₄×C₄₁	—	4	8	no	—
350	C₂×C₄×C₄₁	—	2	2	no	—
351	C₂×C₄×C₄₁	—	2	2	no	—
352	C₂×C₄×C₄₁	—	2	2	no	—
353	C₂×C₄×C₄₁	—	2	2	no	—
354	C₂×C₄×C₄₁	—	2	2	no	—
355	C₂×C₄×C₄₁	—	2	2	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	1	no	—
361	C₂×C₄×C₄₁	—	2	1	no	—
362	C₂×C₄×C₄₁	—	2	8	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	2	no	—
367	C₂×C₄×C₄₁	—	2	2	no	—
368	C₂×C₄×C₄₁	—	2	2	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	1	no	—
378	C₂×C₄×C₄₁	—	2	2	no	—
379	C₂×C₄×C₄₁	—	2	1	no	—
380	C₂×C₄×C₄₁	—	2	1	no	—
381	C₂×C₄×C₄₁	—	2	1	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	—	4	8	no	—
387	C₂×C₄×C₄₁	—	4	8	no	—
388	C₂×C₄×C₄₁	—	4	8	no	—
389	C₂×C₄×C₄₁	—	4	8	no	—
390	C₂×C₄×C₄₁	—	4	8	no	—
391	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
392	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
393	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
394	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
395	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
396	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
397	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
398	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
399	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
400	#34962	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂²×C₄₁	—	2	4	no	—
402	C₂²×C₄₁	—	2	4	no	—
403	C₂²×C₄₁	—	2	2	no	—
404	C₂²×C₄₁	—	2	4	no	—
405	C₂²×C₄₁	—	2	4	no	—
406	C₂²×C₄₁	—	4	2	no	—
407	C₂²×C₄₁	—	4	2	no	—
408	C₂²×C₄₁	—	4	2	no	—
409	C₂²×C₄₁	—	4	2	no	—
410	C₂²×C₄₁	—	4	1	no	—
411	C₂²×C₄₁	—	4	1	no	—
412	C₂²×C₄₁	—	4	2	no	—
413	C₂²×C₄₁	—	4	2	no	—
414	C₂²×C₄₁	—	4	2	no	—
415	C₂²×C₄₁	—	4	2	no	—
416	C₂²×C₄₁	—	4	2	no	—
417	C₂²×C₄₁	—	4	2	no	—
418	C₂²×C₄₁	—	4	2	no	—
419	C₂²×C₄₁	—	4	2	no	—
420	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
421	C₂²×C₄₁	C₂²×#41	1	2	yes	—
422	C₂²×C₄₁	C₂²×#41	1	2	yes	—
423	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	C₄×C₄₁	—	2	4	no	—
426	C₄×C₄₁	—	2	2	no	—
427	C₄×C₄₁	—	2	4	no	—
428	C₄×C₄₁	—	2	4	no	—
429	C₄×C₄₁	—	2	4	no	—
430	C₄×C₄₁	—	2	4	no	—
431	C₄×C₄₁	—	4	2	no	—
432	C₄×C₄₁	—	4	2	no	—
433	C₄×C₄₁	—	4	2	no	—
434	C₄×C₄₁	—	4	2	no	—
435	C₄×C₄₁	—	4	1	no	—
436	C₄×C₄₁	—	4	1	no	—
437	C₄×C₄₁	—	4	2	no	—
438	C₄×C₄₁	—	4	1	no	—
439	C₄×C₄₁	—	4	1	no	—
440	C₄×C₄₁	#538	1	4	yes	—
441	#2593	C₂×C₄₁	1	1	yes	characteristic, complemented
442	#2586	C₂×C₄₁	1	1	yes	characteristic, complemented
443	#2574	C₂×C₄₁	1	2	yes	complemented
444	#2572	C₂×C₄₁	1	1	yes	characteristic, complemented
445	#2555	C₂×C₄₁	1	1	yes	characteristic, complemented
446	#2554	C₂×C₄₁	1	2	yes	complemented
447	#2518	C₂×C₄₁	1	2	yes	complemented
448	#2467	C₂×C₄₁	1	2	yes	complemented
449	#2459	C₂×C₄₁	1	2	yes	complemented
450	#2456	C₂×C₄₁	1	2	yes	complemented
451	#2396	C₂×C₄₁	1	1	yes	characteristic, complemented
452	#2392	C₂×C₄₁	1	1	yes	characteristic, complemented
453	#2388	C₂×C₄₁	1	2	yes	complemented
454	C₄×#126	C₂×C₄₁	1	2	yes	complemented
455	C₄×#124	C₂×C₄₁	1	2	yes	complemented
456	C₄×#123	C₂×C₄₁	1	2	yes	complemented
457	C₄×#121	C₂×C₄₁	1	2	yes	complemented
458	#2297	C₂×C₄₁	1	1	yes	characteristic, complemented
459	C₄²×D₄	C₂×C₄₁	1	2	yes	complemented
460	C₂×C₄₁	—	4	2	no	—
461	C₂×C₄₁	—	4	4	no	—
462	C₂×C₄₁	—	8	2	no	—
463	C₂×C₄₁	#3444	1	2	yes	—
464	C₂×C₄₁	C₂×#538	1	1	yes	characteristic
465	C₂×C₄₁	#3481	1	2	yes	—
466	C₂×C₄₁	#3481	1	1	yes	characteristic
467	C₂×C₄₁	#3483	1	1	yes	characteristic
468	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
469	C₂×#126	C₂²×C₄₁	1	2	yes	—
470	C₂×#124	C₂²×C₄₁	1	2	yes	—
471	C₂×#123	C₂²×C₄₁	1	2	yes	—
472	C₂×#121	C₂²×C₄₁	1	2	yes	—
473	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
474	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
475	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
476	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
477	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
478	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
479	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
480	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
481	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
482	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
483	#400	C₂²×C₄₁	1	1	yes	characteristic
484	#399	C₂²×C₄₁	1	1	yes	characteristic
485	#398	C₂²×C₄₁	1	2	yes	—
486	#398	C₂²×C₄₁	1	1	yes	characteristic
487	#397	C₂²×C₄₁	1	1	yes	characteristic
488	#396	C₂²×C₄₁	1	2	yes	—
489	#396	C₂²×C₄₁	1	2	yes	—
490	#395	C₂²×C₄₁	1	2	yes	—
491	#395	C₂²×C₄₁	1	1	yes	characteristic
492	#394	C₂²×C₄₁	1	1	yes	characteristic
493	#394	C₂²×C₄₁	1	2	yes	—
494	#394	C₂²×C₄₁	1	2	yes	—
495	#394	C₂²×C₄₁	1	2	yes	—
496	#394	C₂²×C₄₁	1	2	yes	—
497	#393	C₂²×C₄₁	1	2	yes	—
498	#393	C₂²×C₄₁	1	1	yes	characteristic
499	#392	C₂²×C₄₁	1	2	yes	—
500	#392	C₂²×C₄₁	1	2	yes	—
501	#392	C₂²×C₄₁	1	2	yes	—
502	#392	C₂²×C₄₁	1	1	yes	characteristic
503	#391	C₂²×C₄₁	1	1	yes	characteristic
504	#391	C₂²×C₄₁	1	1	yes	characteristic
505	#391	C₂²×C₄₁	1	2	yes	—
506	#390	C₂²×C₄₁	1	1	yes	characteristic
507	#390	C₂²×C₄₁	1	2	yes	—
508	#390	C₂²×C₄₁	1	2	yes	—
509	#390	C₂²×C₄₁	1	1	yes	characteristic
510	#389	C₂²×C₄₁	1	2	yes	—
511	#388	C₂²×C₄₁	1	2	yes	—
512	#388	C₂²×C₄₁	1	2	yes	—
513	#388	C₂²×C₄₁	1	2	yes	—
514	#388	C₂²×C₄₁	1	2	yes	—
515	#388	C₂²×C₄₁	1	2	yes	—
516	#388	C₂²×C₄₁	1	2	yes	—
517	#388	C₂²×C₄₁	1	2	yes	—
518	#388	C₂²×C₄₁	1	2	yes	—
519	#388	C₂²×C₄₁	1	2	yes	—
520	#388	C₂²×C₄₁	1	2	yes	—
521	#388	C₂²×C₄₁	1	2	yes	—
522	#387	C₂²×C₄₁	1	2	yes	—
523	#387	C₂²×C₄₁	1	2	yes	—
524	#387	C₂²×C₄₁	1	2	yes	—
525	#387	C₂²×C₄₁	1	2	yes	—
526	#387	C₂²×C₄₁	1	2	yes	—
527	#386	C₂²×C₄₁	1	2	yes	—
528	#386	C₂²×C₄₁	1	2	yes	—
529	#386	C₂²×C₄₁	1	2	yes	—
530	#386	C₂²×C₄₁	1	2	yes	—
531	#386	C₂²×C₄₁	1	2	yes	—
532	#385	C₂²×C₄₁	1	2	yes	—
533	#383	C₂²×C₄₁	1	2	yes	—
534	#382	C₂²×C₄₁	1	2	yes	—
535	#381	C₂²×C₄₁	1	2	yes	—
536	#380	C₂²×C₄₁	1	2	yes	—
537	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
539	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
540	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
541	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
542	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
543	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
548	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
549	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
551	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
552	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
553	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
554	C₄³	C₂²×C₄₁	1	2	yes	—
555	C₄₁	#34962	1	1	yes	characteristic, direct product factor, Sylow
556	C₂×#41	—	2	4	no	—
557	C₂×#41	—	4	2	no	—
558	C₂×#41	—	4	2	no	—
559	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
560	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
562	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
564	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
565	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
566	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
568	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
569	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
570	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
571	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
572	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
573	#126	—	2	8	no	—
574	#124	—	2	8	no	—
575	#123	—	2	8	no	—
576	#121	—	2	8	no	—
577	C₄×Q₈	—	4	2	no	—
578	C₄×D₄	—	2	8	no	—
579	C₄×D₄	—	2	8	no	—
580	C₄×D₄	—	2	8	no	—
581	C₄×D₄	—	4	4	no	—
582	C₄×D₄	—	4	2	no	—
583	C₄×D₄	—	4	4	no	—
584	#117	—	4	2	no	—
585	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
622	C₂×C₄²	—	4	2	no	—
623	C₂×C₄²	—	4	4	no	—
624	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
627	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
628	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
629	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
630	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
631	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
632	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
633	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
634	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
637	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
638	#95	C₂³×C₄₁	1	2	yes	—
639	#95	C₂³×C₄₁	1	2	yes	—
640	#95	C₂³×C₄₁	1	2	yes	—
641	#95	C₂³×C₄₁	1	2	yes	—
642	#95	C₂³×C₄₁	1	2	yes	—
643	#95	C₂³×C₄₁	1	2	yes	—
644	#95	C₂³×C₄₁	1	2	yes	—
645	#95	C₂³×C₄₁	1	2	yes	—
646	#95	C₂³×C₄₁	1	2	yes	—
647	#95	C₂³×C₄₁	1	2	yes	—
648	#95	C₂³×C₄₁	1	2	yes	—
649	#95	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	1	yes	characteristic
655	#95	C₂³×C₄₁	1	1	yes	characteristic
656	#95	C₂³×C₄₁	1	2	yes	—
657	#95	C₂³×C₄₁	1	1	yes	characteristic
658	#95	C₂³×C₄₁	1	2	yes	—
659	#95	C₂³×C₄₁	1	1	yes	characteristic
660	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
661	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
662	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
663	#41	—	4	16	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	4	1	no	—
667	C₂×Q₈	—	4	1	no	—
668	C₂×Q₈	—	4	1	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂×D₄	—	4	1	no	—
682	C₂×D₄	—	4	1	no	—
683	C₂×D₄	—	4	1	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	4	no	—
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	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	#41×C₄₁	1	4	yes	—
704	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	4	1	no	—
727	C₄⋊C₄	—	4	1	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	1	no	—
733	C₄⋊C₄	#41×C₄₁	1	8	yes	complemented
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	4	1	no	—
750	C₂²⋊C₄	—	4	1	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	#41×C₄₁	1	8	yes	complemented
757	C₄²	—	2	4	no	—
758	C₄²	—	2	4	no	—
759	C₄²	—	2	4	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	4	no	—
767	C₄²	—	4	1	no	—
768	C₄²	—	4	1	no	—
769	C₄²	—	4	2	no	—
770	C₄²	—	4	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	C₂×#41×C₄₁	1	2	yes	—
789	C₂³	C₂×#41×C₄₁	1	4	yes	—
790	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
791	Q₈	—	4	4	no	—
792	Q₈	—	4	4	no	—
793	D₄	—	2	16	no	—
794	D₄	—	4	8	no	—
795	D₄	—	4	8	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	8	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	2	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	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	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	—	4	8	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	—	4	8	no	—
839	C₂×C₄	—	4	8	no	—
840	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
841	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
842	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
843	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
844	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
845	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
846	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
847	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
848	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
849	C₂²	—	2	4	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
869	C₂²	C₂²×#41×C₄₁	1	2	yes	—
870	C₂²	C₂²×#41×C₄₁	1	2	yes	—
871	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
872	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
873	C₄	—	2	4	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	4	no	—
876	C₄	—	2	4	no	—
877	C₄	—	2	4	no	—
878	C₄	—	2	4	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	C₄₁×#538	1	4	yes	—
889	C₂	—	4	2	no	—
890	C₂	—	4	4	no	—
891	C₂	—	8	2	no	—
892	C₂	C₄₁×#3444	1	2	yes	—
893	C₂	C₂×C₄₁×#538	1	1	yes	characteristic
894	C₂	C₄₁×#3481	1	2	yes	—
895	C₂	C₄₁×#3481	1	1	yes	characteristic
896	C₂	C₄₁×#3483	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2593	C₂	semidirect
2. C₄₁×#2586	C₂	semidirect
3. C₄₁×#2574	C₂	semidirect
4. C₄₁×#2572	C₂	semidirect
5. C₄₁×#2555	C₂	semidirect
6. C₄₁×#2554	C₂	semidirect
7. C₄₁×#2518	C₂	semidirect
8. C₄₁×#2467	C₂	semidirect
9. C₄₁×#2459	C₂	semidirect
10. C₄₁×#2456	C₂	semidirect
11. C₄₁×#2396	C₂	semidirect
12. C₄₁×#2392	C₂	semidirect
13. C₄₁×#2388	C₂	semidirect
14. C₄×#126×C₄₁	C₂	semidirect
15. C₄×#124×C₄₁	C₂	semidirect
16. C₄×#123×C₄₁	C₂	semidirect
17. C₄×#121×C₄₁	C₂	semidirect
18. C₄₁×#2297	C₂	semidirect
19. C₄²×D₄×C₄₁	C₂	semidirect
284. C₄⋊C₄×C₄₁	#41	semidirect
307. C₂²⋊C₄×C₄₁	#41	semidirect
400. #34962	C₄₁	direct (N × H)
441. #2593	C₂×C₄₁	semidirect
442. #2586	C₂×C₄₁	semidirect
443. #2574	C₂×C₄₁	semidirect
444. #2572	C₂×C₄₁	semidirect
445. #2555	C₂×C₄₁	semidirect
446. #2554	C₂×C₄₁	semidirect
447. #2518	C₂×C₄₁	semidirect
448. #2467	C₂×C₄₁	semidirect
449. #2459	C₂×C₄₁	semidirect
450. #2456	C₂×C₄₁	semidirect
451. #2396	C₂×C₄₁	semidirect
452. #2392	C₂×C₄₁	semidirect
453. #2388	C₂×C₄₁	semidirect
454. C₄×#126	C₂×C₄₁	semidirect
455. C₄×#124	C₂×C₄₁	semidirect
456. C₄×#123	C₂×C₄₁	semidirect
457. C₄×#121	C₂×C₄₁	semidirect
458. #2297	C₂×C₄₁	semidirect
459. C₄²×D₄	C₂×C₄₁	semidirect
555. C₄₁	#34962	direct (N × H)
733. C₄⋊C₄	#41×C₄₁	semidirect
756. C₂²⋊C₄	#41×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#2593	2
C₄₁×#2586	2
C₄₁×#2574	2
C₄₁×#2572	2
C₄₁×#2555	2
C₄₁×#2554	2
C₄₁×#2518	2
C₄₁×#2467	2
C₄₁×#2459	2
C₄₁×#2456	2
C₄₁×#2396	2
C₄₁×#2392	2
C₄₁×#2388	2
C₄×#126×C₄₁	2
C₄×#124×C₄₁	2
C₄×#123×C₄₁	2
C₄×#121×C₄₁	2
C₄₁×#2297	2
C₄²×D₄×C₄₁	2
#34962	41

Subgroups — C41×#34962 #23811163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34962 #23811163