Subgroups — C₄₁×#34510 #23810711

Order 10496.

2148 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#559	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2380	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2379	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2372	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2359	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2356	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2353	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2352	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2337	C₂	1	2	yes	maximal, complemented
12	C₄₁×#2337	C₂	1	2	yes	maximal, complemented
13	C₄₁×#2335	C₂	1	2	yes	maximal, complemented
14	C₄₁×#2328	C₂	1	1	yes	maximal, characteristic
15	C₄₁×#2322	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2320	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2318	C₂	1	2	yes	maximal, complemented
18	C₄×#123×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2290	C₂	1	2	yes	maximal, complemented
20	C₄₁×#559	C₄	1	16	yes	complemented
21	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#124×C₄₁	C₂²	1	2	yes	—
23	C₂×#124×C₄₁	C₂²	1	2	yes	—
24	C₂×#123×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#123×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#123×C₄₁	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
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	2	yes	—
33	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
35	C₄₁×#391	C₂²	1	2	yes	—
36	C₄₁×#391	C₂²	1	2	yes	—
37	C₄₁×#391	C₂²	1	2	yes	—
38	C₄₁×#391	C₂²	1	2	yes	—
39	C₄₁×#390	C₂²	1	1	yes	characteristic
40	C₄₁×#390	C₂²	1	1	yes	characteristic
41	C₄₁×#389	C₂²	1	2	yes	—
42	C₄₁×#389	C₂²	1	2	yes	—
43	C₄₁×#388	C₂²	1	2	yes	—
44	C₄₁×#388	C₂²	1	2	yes	—
45	C₄₁×#388	C₂²	1	2	yes	—
46	C₄₁×#388	C₂²	1	2	yes	—
47	C₄₁×#388	C₂²	1	2	yes	—
48	C₄₁×#388	C₂²	1	2	yes	—
49	C₄₁×#388	C₂²	1	2	yes	—
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×#387	C₂²	1	2	yes	—
56	C₄₁×#387	C₂²	1	2	yes	—
57	C₄₁×#387	C₂²	1	2	yes	—
58	C₄₁×#387	C₂²	1	2	yes	—
59	C₄₁×#387	C₂²	1	2	yes	—
60	C₄₁×#387	C₂²	1	2	yes	—
61	C₄₁×#387	C₂²	1	2	yes	—
62	C₄₁×#387	C₂²	1	2	yes	—
63	C₄₁×#386	C₂²	1	2	yes	—
64	C₄₁×#386	C₂²	1	2	yes	—
65	C₄₁×#386	C₂²	1	1	yes	characteristic
66	C₄₁×#386	C₂²	1	2	yes	—
67	C₄₁×#386	C₂²	1	2	yes	—
68	C₄₁×#386	C₂²	1	1	yes	characteristic
69	C₄₁×#386	C₂²	1	2	yes	—
70	C₄₁×#386	C₂²	1	2	yes	—
71	C₄₁×#386	C₂²	1	2	yes	—
72	C₄₁×#386	C₂²	1	2	yes	—
73	C₄₁×#386	C₂²	1	2	yes	—
74	C₄₁×#385	C₂²	1	2	yes	—
75	C₄₁×#385	C₂²	1	2	yes	—
76	C₄₁×#385	C₂²	1	1	yes	characteristic
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×#383	C₂²	1	2	yes	—
82	C₄₁×#383	C₂²	1	2	yes	—
83	C₄₁×#383	C₂²	1	2	yes	—
84	C₄₁×#382	C₂²	1	2	yes	—
85	C₄₁×#382	C₂²	1	1	yes	characteristic
86	C₄₁×#382	C₂²	1	2	yes	—
87	C₄₁×#381	C₂²	1	1	yes	characteristic
88	C₄₁×#381	C₂²	1	1	yes	characteristic
89	C₄₁×#380	C₂²	1	2	yes	—
90	C₄₁×#380	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	2	yes	—
94	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
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	1	yes	characteristic
98	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
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	C₄₁×#376	C₂²	1	2	yes	—
105	C₄₁×#376	C₂²	1	2	yes	—
106	C₄₁×#376	C₂²	1	1	yes	characteristic
107	C₂×#95×C₄₁	C₂²	1	2	yes	—
108	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
113	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
122	#127×C₄₁	C₂×C₄	1	8	yes	—
123	#124×C₄₁	C₂×C₄	1	16	yes	complemented
124	#124×C₄₁	C₂×C₄	1	16	yes	complemented
125	#123×C₄₁	C₂×C₄	1	8	yes	complemented
126	#123×C₄₁	C₂×C₄	1	8	yes	complemented
127	#123×C₄₁	C₂×C₄	1	16	yes	complemented
128	C₄×Q₈×C₄₁	C₂×C₄	1	16	yes	complemented
129	C₄×D₄×C₄₁	—	4	2	no	—
130	C₄×D₄×C₄₁	—	4	2	no	—
131	C₄×D₄×C₄₁	C₂×C₄	1	16	yes	complemented
132	C₄×D₄×C₄₁	C₂×C₄	1	16	yes	complemented
133	#117×C₄₁	—	4	4	no	—
134	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
135	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
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	1	yes	characteristic
139	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	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×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
166	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
169	C₂×C₄²×C₄₁	—	4	2	no	—
170	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
171	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
175	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
177	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
182	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
183	#95×C₄₁	C₂³	1	2	yes	—
184	#95×C₄₁	C₂³	1	2	yes	—
185	#95×C₄₁	C₂³	1	2	yes	—
186	#95×C₄₁	C₂³	1	2	yes	—
187	#95×C₄₁	C₂³	1	2	yes	—
188	#95×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	2	yes	—
206	#95×C₄₁	C₂³	1	2	yes	—
207	#95×C₄₁	C₂³	1	2	yes	—
208	#95×C₄₁	C₂³	1	2	yes	—
209	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
210	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
211	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
212	C₂×Q₈×C₄₁	—	4	2	no	—
213	C₂×Q₈×C₄₁	—	4	2	no	—
214	C₂×Q₈×C₄₁	C₂²×C₄	1	8	yes	—
215	C₂×D₄×C₄₁	—	4	1	no	—
216	C₂×D₄×C₄₁	—	4	1	no	—
217	C₂×D₄×C₄₁	—	4	1	no	—
218	C₂×D₄×C₄₁	—	4	1	no	—
219	C₂×D₄×C₄₁	—	4	2	no	—
220	C₂×D₄×C₄₁	—	4	2	no	—
221	C₂×D₄×C₄₁	—	4	2	no	—
222	C₂×D₄×C₄₁	—	4	2	no	—
223	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
224	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
225	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
226	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
227	C₂²×C₄×C₄₁	—	2	2	no	—
228	C₂²×C₄×C₄₁	—	2	2	no	—
229	C₂²×C₄×C₄₁	—	4	1	no	—
230	C₂²×C₄×C₄₁	—	4	1	no	—
231	C₂²×C₄×C₄₁	—	4	1	no	—
232	C₂²×C₄×C₄₁	—	4	2	no	—
233	C₂²×C₄×C₄₁	—	4	1	no	—
234	C₂²×C₄×C₄₁	—	4	2	no	—
235	C₂²×C₄×C₄₁	—	4	2	no	—
236	C₂²×C₄×C₄₁	—	4	1	no	—
237	C₂²×C₄×C₄₁	—	4	2	no	—
238	C₂²×C₄×C₄₁	—	4	1	no	—
239	C₂²×C₄×C₄₁	—	4	2	no	—
240	C₂²×C₄×C₄₁	—	4	2	no	—
241	C₂²×C₄×C₄₁	—	4	2	no	—
242	C₂²×C₄×C₄₁	—	4	2	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	C₂²×C₄	1	4	yes	—
248	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
249	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
250	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
260	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
266	C₄⋊C₄×C₄₁	—	2	4	no	—
267	C₄⋊C₄×C₄₁	—	4	2	no	—
268	C₄⋊C₄×C₄₁	—	4	2	no	—
269	C₄⋊C₄×C₄₁	—	4	2	no	—
270	C₄⋊C₄×C₄₁	—	4	2	no	—
271	C₄⋊C₄×C₄₁	—	4	2	no	—
272	C₄⋊C₄×C₄₁	—	4	2	no	—
273	C₄⋊C₄×C₄₁	—	4	2	no	—
274	C₄⋊C₄×C₄₁	—	4	1	no	—
275	C₄⋊C₄×C₄₁	—	4	1	no	—
276	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
277	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
278	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
279	C₂²⋊C₄×C₄₁	—	2	4	no	—
280	C₂²⋊C₄×C₄₁	—	4	2	no	—
281	C₂²⋊C₄×C₄₁	—	4	2	no	—
282	C₂²⋊C₄×C₄₁	—	4	1	no	—
283	C₂²⋊C₄×C₄₁	—	4	2	no	—
284	C₂²⋊C₄×C₄₁	—	4	2	no	—
285	C₂²⋊C₄×C₄₁	—	4	2	no	—
286	C₂²⋊C₄×C₄₁	—	4	2	no	—
287	C₂²⋊C₄×C₄₁	—	4	2	no	—
288	C₂²⋊C₄×C₄₁	—	4	1	no	—
289	C₂²⋊C₄×C₄₁	—	4	2	no	—
290	C₂²⋊C₄×C₄₁	—	4	2	no	—
291	C₂²⋊C₄×C₄₁	—	4	1	no	—
292	C₂²⋊C₄×C₄₁	—	4	1	no	—
293	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
294	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
295	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
296	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
297	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
298	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
299	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
300	C₄²×C₄₁	—	2	4	no	—
301	C₄²×C₄₁	—	2	2	no	—
302	C₄²×C₄₁	—	4	2	no	—
303	C₄²×C₄₁	—	4	2	no	—
304	C₄²×C₄₁	—	4	2	no	—
305	C₄²×C₄₁	—	4	2	no	—
306	C₄²×C₄₁	—	4	2	no	—
307	C₄²×C₄₁	—	4	2	no	—
308	C₄²×C₄₁	—	4	1	no	—
309	C₄²×C₄₁	—	4	2	no	—
310	C₄²×C₄₁	C₂²×C₄	1	8	yes	—
311	C₄²×C₄₁	C₂²×C₄	1	8	yes	—
312	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
313	C₂³×C₄₁	—	2	2	no	—
314	C₂³×C₄₁	—	2	1	no	—
315	C₂³×C₄₁	—	2	1	no	—
316	C₂³×C₄₁	—	2	2	no	—
317	C₂³×C₄₁	—	2	2	no	—
318	C₂³×C₄₁	—	2	2	no	—
319	C₂³×C₄₁	—	2	2	no	—
320	C₂³×C₄₁	—	2	2	no	—
321	C₂³×C₄₁	—	2	2	no	—
322	C₂³×C₄₁	—	2	1	no	—
323	C₂³×C₄₁	—	2	1	no	—
324	C₂³×C₄₁	—	2	2	no	—
325	C₂³×C₄₁	—	2	2	no	—
326	C₂³×C₄₁	—	2	2	no	—
327	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
328	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
329	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
330	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
331	Q₈×C₄₁	—	4	8	no	—
332	D₄×C₄₁	—	4	8	no	—
333	D₄×C₄₁	—	4	8	no	—
334	D₄×C₄₁	—	4	4	no	—
335	D₄×C₄₁	—	4	4	no	—
336	C₂×C₄×C₄₁	—	2	2	no	—
337	C₂×C₄×C₄₁	—	2	1	no	—
338	C₂×C₄×C₄₁	—	2	2	no	—
339	C₂×C₄×C₄₁	—	2	2	no	—
340	C₂×C₄×C₄₁	—	2	2	no	—
341	C₂×C₄×C₄₁	—	2	2	no	—
342	C₂×C₄×C₄₁	—	2	2	no	—
343	C₂×C₄×C₄₁	—	2	2	no	—
344	C₂×C₄×C₄₁	—	2	1	no	—
345	C₂×C₄×C₄₁	—	2	2	no	—
346	C₂×C₄×C₄₁	—	2	2	no	—
347	C₂×C₄×C₄₁	—	2	2	no	—
348	C₂×C₄×C₄₁	—	2	2	no	—
349	C₂×C₄×C₄₁	—	2	2	no	—
350	C₂×C₄×C₄₁	—	2	1	no	—
351	C₂×C₄×C₄₁	—	2	1	no	—
352	C₂×C₄×C₄₁	—	2	2	no	—
353	C₂×C₄×C₄₁	—	2	2	no	—
354	C₂×C₄×C₄₁	—	2	1	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	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	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	—	4	4	no	—
374	C₂×C₄×C₄₁	—	4	4	no	—
375	C₂×C₄×C₄₁	—	4	8	no	—
376	C₂×C₄×C₄₁	—	4	4	no	—
377	C₂×C₄×C₄₁	—	4	4	no	—
378	C₂×C₄×C₄₁	—	8	2	no	—
379	C₂×C₄×C₄₁	—	8	2	no	—
380	C₂×C₄×C₄₁	—	8	4	no	—
381	C₂×C₄×C₄₁	—	8	4	no	—
382	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
383	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
384	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
385	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
386	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
387	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
388	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
389	#34510	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂²×C₄₁	—	2	4	no	—
391	C₂²×C₄₁	—	2	4	no	—
392	C₂²×C₄₁	—	2	4	no	—
393	C₂²×C₄₁	—	2	4	no	—
394	C₂²×C₄₁	—	2	4	no	—
395	C₂²×C₄₁	—	2	2	no	—
396	C₂²×C₄₁	—	2	2	no	—
397	C₂²×C₄₁	—	4	1	no	—
398	C₂²×C₄₁	—	4	1	no	—
399	C₂²×C₄₁	—	4	2	no	—
400	C₂²×C₄₁	—	4	1	no	—
401	C₂²×C₄₁	—	4	2	no	—
402	C₂²×C₄₁	—	4	1	no	—
403	C₂²×C₄₁	—	4	2	no	—
404	C₂²×C₄₁	—	4	2	no	—
405	C₂²×C₄₁	—	4	2	no	—
406	C₂²×C₄₁	—	4	2	no	—
407	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
408	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂²×C₄₁	#585	1	2	yes	—
410	C₂²×C₄₁	#585	1	2	yes	—
411	C₂²×C₄₁	#585	1	1	yes	characteristic
412	C₄×C₄₁	—	2	4	no	—
413	C₄×C₄₁	—	2	4	no	—
414	C₄×C₄₁	—	2	4	no	—
415	C₄×C₄₁	—	2	4	no	—
416	C₄×C₄₁	—	2	4	no	—
417	C₄×C₄₁	—	2	2	no	—
418	C₄×C₄₁	—	2	2	no	—
419	C₄×C₄₁	—	4	1	no	—
420	C₄×C₄₁	—	4	2	no	—
421	C₄×C₄₁	—	4	1	no	—
422	C₄×C₄₁	—	4	2	no	—
423	C₄×C₄₁	—	4	2	no	—
424	C₄×C₄₁	—	4	1	no	—
425	C₄×C₄₁	—	4	2	no	—
426	C₄×C₄₁	—	4	2	no	—
427	C₄×C₄₁	—	4	2	no	—
428	C₂×#559	C₂×C₄₁	1	1	yes	characteristic
429	#2380	C₂×C₄₁	1	1	yes	characteristic
430	#2379	C₂×C₄₁	1	2	yes	complemented
431	#2376	C₂×C₄₁	1	1	yes	characteristic, complemented
432	#2374	C₂×C₄₁	1	1	yes	characteristic, complemented
433	#2372	C₂×C₄₁	1	2	yes	complemented
434	#2359	C₂×C₄₁	1	2	yes	complemented
435	#2356	C₂×C₄₁	1	2	yes	complemented
436	#2353	C₂×C₄₁	1	2	yes	complemented
437	#2352	C₂×C₄₁	1	2	yes	complemented
438	#2337	C₂×C₄₁	1	2	yes	complemented
439	#2337	C₂×C₄₁	1	2	yes	complemented
440	#2335	C₂×C₄₁	1	2	yes	complemented
441	#2328	C₂×C₄₁	1	1	yes	characteristic
442	#2322	C₂×C₄₁	1	1	yes	characteristic, complemented
443	#2320	C₂×C₄₁	1	2	yes	complemented
444	#2318	C₂×C₄₁	1	2	yes	complemented
445	C₄×#123	C₂×C₄₁	1	1	yes	characteristic, complemented
446	#2290	C₂×C₄₁	1	2	yes	complemented
447	C₂×C₄₁	—	4	2	no	—
448	C₂×C₄₁	—	4	2	no	—
449	C₂×C₄₁	—	4	4	no	—
450	C₂×C₄₁	#3428	1	2	yes	—
451	C₂×C₄₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₄₁	#3533	1	1	yes	characteristic
453	C₂×C₄₁	#3540	1	1	yes	characteristic
454	C₂×C₄₁	#3566	1	2	yes	—
455	#559	C₄×C₄₁	1	16	yes	complemented
456	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
457	C₂×#124	C₂²×C₄₁	1	2	yes	—
458	C₂×#124	C₂²×C₄₁	1	2	yes	—
459	C₂×#123	C₂²×C₄₁	1	1	yes	characteristic
460	C₂×#123	C₂²×C₄₁	1	2	yes	—
461	C₂×#123	C₂²×C₄₁	1	1	yes	characteristic
462	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
463	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
464	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
465	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
466	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
467	C₂×#117	C₂²×C₄₁	1	2	yes	—
468	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
469	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
470	#391	C₂²×C₄₁	1	2	yes	—
471	#391	C₂²×C₄₁	1	2	yes	—
472	#391	C₂²×C₄₁	1	2	yes	—
473	#391	C₂²×C₄₁	1	2	yes	—
474	#390	C₂²×C₄₁	1	1	yes	characteristic
475	#390	C₂²×C₄₁	1	1	yes	characteristic
476	#389	C₂²×C₄₁	1	2	yes	—
477	#389	C₂²×C₄₁	1	2	yes	—
478	#388	C₂²×C₄₁	1	2	yes	—
479	#388	C₂²×C₄₁	1	2	yes	—
480	#388	C₂²×C₄₁	1	2	yes	—
481	#388	C₂²×C₄₁	1	2	yes	—
482	#388	C₂²×C₄₁	1	2	yes	—
483	#388	C₂²×C₄₁	1	2	yes	—
484	#388	C₂²×C₄₁	1	2	yes	—
485	#388	C₂²×C₄₁	1	2	yes	—
486	#388	C₂²×C₄₁	1	2	yes	—
487	#388	C₂²×C₄₁	1	2	yes	—
488	#388	C₂²×C₄₁	1	2	yes	—
489	#388	C₂²×C₄₁	1	2	yes	—
490	#387	C₂²×C₄₁	1	2	yes	—
491	#387	C₂²×C₄₁	1	2	yes	—
492	#387	C₂²×C₄₁	1	2	yes	—
493	#387	C₂²×C₄₁	1	2	yes	—
494	#387	C₂²×C₄₁	1	2	yes	—
495	#387	C₂²×C₄₁	1	2	yes	—
496	#387	C₂²×C₄₁	1	2	yes	—
497	#387	C₂²×C₄₁	1	2	yes	—
498	#386	C₂²×C₄₁	1	2	yes	—
499	#386	C₂²×C₄₁	1	2	yes	—
500	#386	C₂²×C₄₁	1	1	yes	characteristic
501	#386	C₂²×C₄₁	1	2	yes	—
502	#386	C₂²×C₄₁	1	2	yes	—
503	#386	C₂²×C₄₁	1	2	yes	—
504	#386	C₂²×C₄₁	1	2	yes	—
505	#386	C₂²×C₄₁	1	2	yes	—
506	#386	C₂²×C₄₁	1	2	yes	—
507	#386	C₂²×C₄₁	1	1	yes	characteristic
508	#386	C₂²×C₄₁	1	2	yes	—
509	#385	C₂²×C₄₁	1	2	yes	—
510	#385	C₂²×C₄₁	1	2	yes	—
511	#385	C₂²×C₄₁	1	1	yes	characteristic
512	#385	C₂²×C₄₁	1	2	yes	—
513	#385	C₂²×C₄₁	1	2	yes	—
514	#385	C₂²×C₄₁	1	2	yes	—
515	#385	C₂²×C₄₁	1	1	yes	characteristic
516	#383	C₂²×C₄₁	1	2	yes	—
517	#383	C₂²×C₄₁	1	2	yes	—
518	#383	C₂²×C₄₁	1	2	yes	—
519	#382	C₂²×C₄₁	1	2	yes	—
520	#382	C₂²×C₄₁	1	1	yes	characteristic
521	#382	C₂²×C₄₁	1	2	yes	—
522	#381	C₂²×C₄₁	1	1	yes	characteristic
523	#381	C₂²×C₄₁	1	1	yes	characteristic
524	#380	C₂²×C₄₁	1	2	yes	—
525	#380	C₂²×C₄₁	1	2	yes	—
526	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
527	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
528	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
530	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
532	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
533	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
534	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
535	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
536	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
537	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
539	#376	C₂²×C₄₁	1	2	yes	—
540	#376	C₂²×C₄₁	1	1	yes	characteristic
541	#376	C₂²×C₄₁	1	2	yes	—
542	C₂×#95	C₂²×C₄₁	1	2	yes	—
543	C₄₁	#34510	1	1	yes	characteristic, direct product factor, Sylow
544	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
545	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
548	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
549	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
553	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
554	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
557	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
558	#127	C₂×C₄×C₄₁	1	8	yes	—
559	#124	C₂×C₄×C₄₁	1	16	yes	complemented
560	#124	C₂×C₄×C₄₁	1	16	yes	complemented
561	#123	C₂×C₄×C₄₁	1	8	yes	complemented
562	#123	C₂×C₄×C₄₁	1	16	yes	complemented
563	#123	C₂×C₄×C₄₁	1	8	yes	complemented
564	C₄×Q₈	C₂×C₄×C₄₁	1	16	yes	complemented
565	C₄×D₄	—	4	2	no	—
566	C₄×D₄	—	4	2	no	—
567	C₄×D₄	C₂×C₄×C₄₁	1	16	yes	complemented
568	C₄×D₄	C₂×C₄×C₄₁	1	16	yes	complemented
569	#117	—	4	4	no	—
570	C₂×C₄⋊C₄	—	4	2	no	—
571	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
598	C₂×C₂²⋊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	1	yes	characteristic
603	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
605	C₂×C₄²	—	4	2	no	—
606	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
607	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
609	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
610	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
611	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
612	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
614	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
615	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
616	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
617	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
618	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
619	#95	C₂³×C₄₁	1	2	yes	—
620	#95	C₂³×C₄₁	1	2	yes	—
621	#95	C₂³×C₄₁	1	2	yes	—
622	#95	C₂³×C₄₁	1	2	yes	—
623	#95	C₂³×C₄₁	1	2	yes	—
624	#95	C₂³×C₄₁	1	2	yes	—
625	#95	C₂³×C₄₁	1	2	yes	—
626	#95	C₂³×C₄₁	1	2	yes	—
627	#95	C₂³×C₄₁	1	2	yes	—
628	#95	C₂³×C₄₁	1	2	yes	—
629	#95	C₂³×C₄₁	1	2	yes	—
630	#95	C₂³×C₄₁	1	2	yes	—
631	#95	C₂³×C₄₁	1	2	yes	—
632	#95	C₂³×C₄₁	1	2	yes	—
633	#95	C₂³×C₄₁	1	2	yes	—
634	#95	C₂³×C₄₁	1	2	yes	—
635	#95	C₂³×C₄₁	1	2	yes	—
636	#95	C₂³×C₄₁	1	2	yes	—
637	#95	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	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
646	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
647	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
648	C₂×Q₈	—	4	2	no	—
649	C₂×Q₈	—	4	2	no	—
650	C₂×Q₈	C₂²×C₄×C₄₁	1	8	yes	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	1	no	—
653	C₂×D₄	—	4	1	no	—
654	C₂×D₄	—	4	1	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
660	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
661	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
662	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
684	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
685	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
686	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	1	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
713	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
714	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	—	4	1	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	1	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	1	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
730	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
731	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
732	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
733	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
734	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
735	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	4	2	no	—
739	C₄²	—	4	2	no	—
740	C₄²	—	4	2	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₄²	—	4	1	no	—
746	C₄²	C₂²×C₄×C₄₁	1	8	yes	—
747	C₄²	C₂²×C₄×C₄₁	1	8	yes	—
748	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
764	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
765	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
766	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
767	Q₈	—	4	8	no	—
768	D₄	—	4	8	no	—
769	D₄	—	4	8	no	—
770	D₄	—	4	4	no	—
771	D₄	—	4	4	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	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	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	—	8	4	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
819	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
820	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
821	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
822	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
823	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
824	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	1	no	—
842	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
843	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
844	C₂²	C₄₁×#585	1	1	yes	characteristic
845	C₂²	C₄₁×#585	1	2	yes	—
846	C₂²	C₄₁×#585	1	2	yes	—
847	C₄	—	2	4	no	—
848	C₄	—	2	4	no	—
849	C₄	—	2	4	no	—
850	C₄	—	2	4	no	—
851	C₄	—	2	4	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₂	—	4	4	no	—
864	C₂	—	4	2	no	—
865	C₂	—	4	2	no	—
866	C₂	C₄₁×#3428	1	2	yes	—
867	C₂	C₄×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
868	C₂	C₄₁×#3533	1	1	yes	characteristic
869	C₂	C₄₁×#3540	1	1	yes	characteristic
870	C₂	C₄₁×#3566	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂×#127×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
3. C₄₁×#2379	C₂	semidirect
4. C₄₁×#2376	C₂	semidirect
5. C₄₁×#2374	C₂	semidirect
6. C₄₁×#2372	C₂	semidirect
7. C₄₁×#2359	C₂	semidirect
8. C₄₁×#2356	C₂	semidirect
9. C₄₁×#2353	C₂	semidirect
10. C₄₁×#2352	C₂	semidirect
11. C₄₁×#2337	C₂	semidirect
12. C₄₁×#2337	C₂	semidirect
13. C₄₁×#2335	C₂	semidirect
15. C₄₁×#2322	C₂	semidirect
16. C₄₁×#2320	C₂	semidirect
17. C₄₁×#2318	C₂	semidirect
18. C₄×#123×C₄₁	C₂	semidirect
19. C₄₁×#2290	C₂	semidirect
20. C₄₁×#559	C₄	semidirect
123. #124×C₄₁	C₂×C₄	semidirect
124. #124×C₄₁	C₂×C₄	semidirect
125. #123×C₄₁	C₂×C₄	semidirect
126. #123×C₄₁	C₂×C₄	semidirect
127. #123×C₄₁	C₂×C₄	semidirect
128. C₄×Q₈×C₄₁	C₂×C₄	semidirect
131. C₄×D₄×C₄₁	C₂×C₄	semidirect
132. C₄×D₄×C₄₁	C₂×C₄	semidirect
389. #34510	C₄₁	direct (N × H)
430. #2379	C₂×C₄₁	semidirect
431. #2376	C₂×C₄₁	semidirect
432. #2374	C₂×C₄₁	semidirect
433. #2372	C₂×C₄₁	semidirect
434. #2359	C₂×C₄₁	semidirect
435. #2356	C₂×C₄₁	semidirect
436. #2353	C₂×C₄₁	semidirect
437. #2352	C₂×C₄₁	semidirect
438. #2337	C₂×C₄₁	semidirect
439. #2337	C₂×C₄₁	semidirect
440. #2335	C₂×C₄₁	semidirect
442. #2322	C₂×C₄₁	semidirect
443. #2320	C₂×C₄₁	semidirect
444. #2318	C₂×C₄₁	semidirect
445. C₄×#123	C₂×C₄₁	semidirect
446. #2290	C₂×C₄₁	semidirect
455. #559	C₄×C₄₁	semidirect
543. C₄₁	#34510	direct (N × H)
559. #124	C₂×C₄×C₄₁	semidirect
560. #124	C₂×C₄×C₄₁	semidirect
561. #123	C₂×C₄×C₄₁	semidirect
562. #123	C₂×C₄×C₄₁	semidirect
563. #123	C₂×C₄×C₄₁	semidirect
564. C₄×Q₈	C₂×C₄×C₄₁	semidirect
567. C₄×D₄	C₂×C₄×C₄₁	semidirect
568. C₄×D₄	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#559	2
C₄₁×#2380	2
C₄₁×#2379	2
C₄₁×#2376	2
C₄₁×#2374	2
C₄₁×#2372	2
C₄₁×#2359	2
C₄₁×#2356	2
C₄₁×#2353	2
C₄₁×#2352	2
C₄₁×#2337	2
C₄₁×#2335	2
C₄₁×#2328	2
C₄₁×#2322	2
C₄₁×#2320	2
C₄₁×#2318	2
C₄×#123×C₄₁	2
C₄₁×#2290	2
#34510	41

Subgroups — C41×#34510 #23810711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34510 #23810711