Subgroups — C₄₁×#24364 #23800565

Order 10496.

1512 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2431	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2014	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1893	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#135×C₄₁	—	2	4	no	—
19	C₂×#135×C₄₁	—	2	4	no	—
20	C₂×#135×C₄₁	—	2	4	no	—
21	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂³×C₈×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×#121×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#463	—	2	4	no	—
34	C₄₁×#459	—	2	4	no	—
35	C₄₁×#449	—	2	4	no	—
36	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
44	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
47	C₄₁×#392	—	2	1	no	—
48	C₄₁×#392	—	2	1	no	—
49	C₄₁×#391	C₂²	1	1	yes	characteristic
50	C₄₁×#391	C₂²	1	1	yes	characteristic
51	C₄₁×#391	C₂²	1	1	yes	characteristic
52	C₄₁×#390	C₂²	1	1	yes	characteristic
53	C₄₁×#386	—	2	1	no	—
54	C₄₁×#386	—	2	1	no	—
55	C₄₁×#386	—	2	1	no	—
56	C₄₁×#386	—	2	1	no	—
57	C₄₁×#381	—	2	1	no	—
58	C₄₁×#380	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
60	C₂×#95×C₄₁	—	2	1	no	—
61	C₄₁×#340	C₂²	1	1	yes	characteristic
62	C₄₁×#340	C₂²	1	1	yes	characteristic
63	C₄₁×#336	C₂²	1	1	yes	characteristic
64	C₄₁×#336	C₂²	1	1	yes	characteristic
65	C₂×#41×C₄₁	—	2	2	no	—
66	C₂×#41×C₄₁	—	2	2	no	—
67	C₂×#41×C₄₁	—	2	2	no	—
68	C₂×#41×C₄₁	—	2	2	no	—
69	C₂×#41×C₄₁	—	2	2	no	—
70	C₂×#41×C₄₁	—	2	2	no	—
71	C₂×#41×C₄₁	—	2	2	no	—
72	C₂×#41×C₄₁	—	4	1	no	—
73	C₂×#41×C₄₁	—	4	1	no	—
74	C₂×#41×C₄₁	—	4	1	no	—
75	C₂×#41×C₄₁	—	4	1	no	—
76	C₂×#41×C₄₁	D₄	1	4	yes	complemented
77	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₄₁	—	2	1	no	—
80	C₂²×D₄×C₄₁	—	2	1	no	—
81	C₂²×D₄×C₄₁	—	2	1	no	—
82	C₂²×D₄×C₄₁	—	2	1	no	—
83	C₂²×D₄×C₄₁	—	2	1	no	—
84	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₁	—	2	1	no	—
88	C₂³×C₄×C₄₁	—	2	1	no	—
89	C₂³×C₄×C₄₁	—	2	1	no	—
90	C₂³×C₄×C₄₁	—	2	1	no	—
91	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
92	#135×C₄₁	—	2	32	no	—
93	C₂×Q₁₆×C₄₁	—	2	2	no	—
94	C₂×Q₁₆×C₄₁	—	2	2	no	—
95	C₂×Q₁₆×C₄₁	—	2	2	no	—
96	C₂×SD₁₆×C₄₁	—	2	2	no	—
97	C₂×SD₁₆×C₄₁	—	2	2	no	—
98	C₂×SD₁₆×C₄₁	—	2	2	no	—
99	C₂×SD₁₆×C₄₁	—	2	2	no	—
100	C₂×SD₁₆×C₄₁	—	2	2	no	—
101	C₂×SD₁₆×C₄₁	—	2	2	no	—
102	C₂×SD₁₆×C₄₁	—	4	1	no	—
103	C₂×SD₁₆×C₄₁	—	4	1	no	—
104	C₂×SD₁₆×C₄₁	D₄	1	4	yes	complemented
105	C₂×D₈×C₄₁	—	2	2	no	—
106	C₂×D₈×C₄₁	—	2	2	no	—
107	C₂×D₈×C₄₁	—	2	2	no	—
108	C₂×D₈×C₄₁	—	2	2	no	—
109	C₂×D₈×C₄₁	—	2	2	no	—
110	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
111	C₂²×C₈×C₄₁	—	2	2	no	—
112	C₂²×C₈×C₄₁	—	2	2	no	—
113	C₂²×C₈×C₄₁	—	2	2	no	—
114	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
118	#127×C₄₁	—	2	2	no	—
119	#127×C₄₁	—	4	1	no	—
120	#124×C₄₁	—	2	2	no	—
121	#124×C₄₁	—	4	1	no	—
122	#121×C₄₁	—	2	2	no	—
123	#121×C₄₁	—	2	2	no	—
124	C₄×D₄×C₄₁	—	2	2	no	—
125	C₄×D₄×C₄₁	—	2	2	no	—
126	C₄×D₄×C₄₁	—	4	1	no	—
127	C₄×D₄×C₄₁	—	4	1	no	—
128	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
141	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
143	C₄⋊C₈×C₄₁	—	2	2	no	—
144	C₄⋊C₈×C₄₁	—	2	2	no	—
145	#103×C₄₁	—	2	2	no	—
146	#103×C₄₁	—	2	2	no	—
147	#103×C₄₁	—	4	1	no	—
148	#102×C₄₁	—	2	2	no	—
149	#102×C₄₁	—	2	2	no	—
150	#102×C₄₁	—	2	2	no	—
151	#102×C₄₁	—	2	2	no	—
152	#102×C₄₁	—	4	1	no	—
153	C₂²⋊C₈×C₄₁	—	2	2	no	—
154	#95×C₄₁	—	2	1	no	—
155	#95×C₄₁	—	2	1	no	—
156	#95×C₄₁	—	2	1	no	—
157	#95×C₄₁	—	2	1	no	—
158	#95×C₄₁	—	2	1	no	—
159	#95×C₄₁	—	2	1	no	—
160	#95×C₄₁	—	2	1	no	—
161	#95×C₄₁	D₄	1	1	yes	characteristic
162	#95×C₄₁	D₄	1	1	yes	characteristic
163	C₂⁴×C₄₁	—	2	1	no	—
164	C₂⁴×C₄₁	—	2	1	no	—
165	C₂⁴×C₄₁	—	2	1	no	—
166	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
167	#41×C₄₁	—	2	8	no	—
168	#41×C₄₁	—	2	8	no	—
169	#41×C₄₁	—	4	4	no	—
170	#41×C₄₁	—	4	4	no	—
171	#41×C₄₁	—	4	4	no	—
172	#41×C₄₁	—	4	4	no	—
173	#41×C₄₁	—	4	4	no	—
174	#41×C₄₁	—	4	4	no	—
175	C₂×Q₈×C₄₁	—	2	1	no	—
176	C₂×Q₈×C₄₁	—	2	1	no	—
177	C₂×Q₈×C₄₁	—	2	1	no	—
178	C₂×Q₈×C₄₁	—	2	1	no	—
179	C₂×Q₈×C₄₁	—	2	1	no	—
180	C₂×Q₈×C₄₁	—	2	1	no	—
181	C₂×Q₈×C₄₁	—	2	1	no	—
182	C₂×Q₈×C₄₁	—	2	1	no	—
183	C₂×Q₈×C₄₁	—	2	1	no	—
184	C₂×Q₈×C₄₁	—	2	1	no	—
185	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
186	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
187	C₂×D₄×C₄₁	—	2	4	no	—
188	C₂×D₄×C₄₁	—	2	1	no	—
189	C₂×D₄×C₄₁	—	2	1	no	—
190	C₂×D₄×C₄₁	—	2	1	no	—
191	C₂×D₄×C₄₁	—	2	1	no	—
192	C₂×D₄×C₄₁	—	2	1	no	—
193	C₂×D₄×C₄₁	—	2	1	no	—
194	C₂×D₄×C₄₁	—	2	1	no	—
195	C₂×D₄×C₄₁	—	2	1	no	—
196	C₂×D₄×C₄₁	—	2	1	no	—
197	C₂×D₄×C₄₁	—	2	1	no	—
198	C₂×D₄×C₄₁	—	2	1	no	—
199	C₂×D₄×C₄₁	—	2	1	no	—
200	C₂×D₄×C₄₁	—	2	1	no	—
201	C₂×D₄×C₄₁	—	2	1	no	—
202	C₂×D₄×C₄₁	—	4	2	no	—
203	C₂×D₄×C₄₁	—	4	2	no	—
204	C₂×D₄×C₄₁	—	4	2	no	—
205	C₂×D₄×C₄₁	—	4	2	no	—
206	C₂×D₄×C₄₁	—	4	2	no	—
207	C₂×D₄×C₄₁	—	4	2	no	—
208	C₂×D₄×C₄₁	—	4	2	no	—
209	C₂×D₄×C₄₁	—	4	2	no	—
210	C₂×D₄×C₄₁	—	4	2	no	—
211	C₂×D₄×C₄₁	—	4	2	no	—
212	C₂×D₄×C₄₁	—	8	1	no	—
213	C₂×D₄×C₄₁	—	8	1	no	—
214	C₂×D₄×C₄₁	—	8	1	no	—
215	C₂×D₄×C₄₁	—	8	1	no	—
216	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₄₁	—	2	1	no	—
221	C₂²×C₄×C₄₁	—	2	1	no	—
222	C₂²×C₄×C₄₁	—	2	1	no	—
223	C₂²×C₄×C₄₁	—	2	1	no	—
224	C₂²×C₄×C₄₁	—	2	1	no	—
225	C₂²×C₄×C₄₁	—	2	1	no	—
226	C₂²×C₄×C₄₁	—	2	4	no	—
227	C₂²×C₄×C₄₁	—	2	1	no	—
228	C₂²×C₄×C₄₁	—	2	1	no	—
229	C₂²×C₄×C₄₁	—	2	1	no	—
230	C₂²×C₄×C₄₁	—	4	2	no	—
231	C₂²×C₄×C₄₁	—	4	2	no	—
232	C₂²×C₄×C₄₁	—	4	2	no	—
233	C₂²×C₄×C₄₁	—	4	2	no	—
234	C₂²×C₄×C₄₁	—	4	2	no	—
235	C₂²×C₄×C₄₁	—	4	2	no	—
236	C₂²×C₄×C₄₁	—	4	2	no	—
237	C₂²×C₄×C₄₁	—	4	2	no	—
238	C₂²×C₄×C₄₁	—	4	2	no	—
239	C₂²×C₄×C₄₁	—	8	1	no	—
240	C₂²×C₄×C₄₁	—	8	1	no	—
241	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₄₁	#41	1	2	yes	—
248	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
249	Q₁₆×C₄₁	—	2	8	no	—
250	SD₁₆×C₄₁	—	2	8	no	—
251	SD₁₆×C₄₁	—	2	8	no	—
252	SD₁₆×C₄₁	—	4	4	no	—
253	D₈×C₄₁	—	2	8	no	—
254	D₈×C₄₁	—	4	4	no	—
255	C₂×C₈×C₄₁	—	2	8	no	—
256	C₂×C₈×C₄₁	—	2	1	no	—
257	C₂×C₈×C₄₁	—	2	1	no	—
258	C₂×C₈×C₄₁	—	2	1	no	—
259	C₂×C₈×C₄₁	—	2	1	no	—
260	C₂×C₈×C₄₁	—	2	1	no	—
261	C₂×C₈×C₄₁	—	2	1	no	—
262	C₂×C₈×C₄₁	—	2	1	no	—
263	C₂×C₈×C₄₁	—	2	1	no	—
264	C₂×C₈×C₄₁	—	2	1	no	—
265	C₂×C₈×C₄₁	—	2	1	no	—
266	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
267	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
268	C₄⋊C₄×C₄₁	—	2	1	no	—
269	C₄⋊C₄×C₄₁	—	2	1	no	—
270	C₄⋊C₄×C₄₁	—	2	1	no	—
271	C₄⋊C₄×C₄₁	—	2	1	no	—
272	C₄⋊C₄×C₄₁	—	2	1	no	—
273	C₄⋊C₄×C₄₁	—	2	1	no	—
274	C₂²⋊C₄×C₄₁	—	2	2	no	—
275	C₂²⋊C₄×C₄₁	—	4	1	no	—
276	C₂²⋊C₄×C₄₁	—	4	2	no	—
277	C₂²⋊C₄×C₄₁	—	4	2	no	—
278	C₂²⋊C₄×C₄₁	—	4	2	no	—
279	C₂²⋊C₄×C₄₁	—	4	2	no	—
280	C₂²⋊C₄×C₄₁	—	4	2	no	—
281	C₂²⋊C₄×C₄₁	—	8	1	no	—
282	C₂²⋊C₄×C₄₁	—	8	1	no	—
283	C₂²⋊C₄×C₄₁	—	8	1	no	—
284	C₄²×C₄₁	—	2	1	no	—
285	C₄²×C₄₁	—	2	1	no	—
286	C₄²×C₄₁	—	2	1	no	—
287	C₄²×C₄₁	—	2	1	no	—
288	C₂³×C₄₁	—	2	2	no	—
289	C₂³×C₄₁	—	2	2	no	—
290	C₂³×C₄₁	—	2	2	no	—
291	C₂³×C₄₁	—	2	1	no	—
292	C₂³×C₄₁	—	2	1	no	—
293	C₂³×C₄₁	—	2	1	no	—
294	C₂³×C₄₁	—	2	1	no	—
295	C₂³×C₄₁	—	2	1	no	—
296	C₂³×C₄₁	—	2	1	no	—
297	C₂³×C₄₁	—	2	2	no	—
298	C₂³×C₄₁	—	4	1	no	—
299	C₂³×C₄₁	—	4	1	no	—
300	C₂³×C₄₁	—	4	1	no	—
301	C₂³×C₄₁	—	4	1	no	—
302	C₂³×C₄₁	—	4	1	no	—
303	C₂³×C₄₁	—	4	1	no	—
304	C₂³×C₄₁	—	4	1	no	—
305	C₂³×C₄₁	—	4	1	no	—
306	C₂³×C₄₁	—	4	1	no	—
307	C₂³×C₄₁	—	4	1	no	—
308	C₂³×C₄₁	—	4	1	no	—
309	C₂³×C₄₁	—	4	1	no	—
310	C₂³×C₄₁	—	4	1	no	—
311	C₂³×C₄₁	—	4	1	no	—
312	C₂³×C₄₁	—	4	1	no	—
313	C₂³×C₄₁	—	4	1	no	—
314	C₂³×C₄₁	—	4	1	no	—
315	C₂³×C₄₁	#121	1	2	yes	—
316	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₄₁	—	2	2	no	—
318	Q₈×C₄₁	—	2	2	no	—
319	Q₈×C₄₁	—	2	2	no	—
320	Q₈×C₄₁	—	2	2	no	—
321	Q₈×C₄₁	—	4	1	no	—
322	Q₈×C₄₁	—	4	1	no	—
323	Q₈×C₄₁	—	4	1	no	—
324	Q₈×C₄₁	—	4	1	no	—
325	D₄×C₄₁	—	2	2	no	—
326	D₄×C₄₁	—	2	2	no	—
327	D₄×C₄₁	—	2	2	no	—
328	D₄×C₄₁	—	2	2	no	—
329	D₄×C₄₁	—	2	2	no	—
330	D₄×C₄₁	—	4	8	no	—
331	D₄×C₄₁	—	4	8	no	—
332	D₄×C₄₁	—	4	1	no	—
333	D₄×C₄₁	—	4	1	no	—
334	D₄×C₄₁	—	4	1	no	—
335	D₄×C₄₁	—	4	1	no	—
336	D₄×C₄₁	—	4	1	no	—
337	D₄×C₄₁	—	4	1	no	—
338	D₄×C₄₁	—	8	4	no	—
339	D₄×C₄₁	—	8	4	no	—
340	D₄×C₄₁	—	8	4	no	—
341	D₄×C₄₁	#120	1	4	yes	—
342	C₂×C₄×C₄₁	—	2	1	no	—
343	C₂×C₄×C₄₁	—	2	1	no	—
344	C₂×C₄×C₄₁	—	2	1	no	—
345	C₂×C₄×C₄₁	—	2	1	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	2	no	—
351	C₂×C₄×C₄₁	—	2	1	no	—
352	C₂×C₄×C₄₁	—	2	1	no	—
353	C₂×C₄×C₄₁	—	2	1	no	—
354	C₂×C₄×C₄₁	—	2	2	no	—
355	C₂×C₄×C₄₁	—	2	1	no	—
356	C₂×C₄×C₄₁	—	2	1	no	—
357	C₂×C₄×C₄₁	—	2	1	no	—
358	C₂×C₄×C₄₁	—	2	1	no	—
359	C₂×C₄×C₄₁	—	2	1	no	—
360	C₂×C₄×C₄₁	—	2	1	no	—
361	C₂×C₄×C₄₁	—	4	8	no	—
362	C₂×C₄×C₄₁	—	4	8	no	—
363	C₂×C₄×C₄₁	—	4	1	no	—
364	C₂×C₄×C₄₁	—	4	1	no	—
365	C₂×C₄×C₄₁	—	4	1	no	—
366	C₂×C₄×C₄₁	—	4	1	no	—
367	C₂×C₄×C₄₁	—	4	1	no	—
368	C₂×C₄×C₄₁	—	4	1	no	—
369	C₂×C₄×C₄₁	—	4	1	no	—
370	C₂×C₄×C₄₁	—	4	1	no	—
371	C₂×C₄×C₄₁	—	4	1	no	—
372	C₂×C₄×C₄₁	—	4	1	no	—
373	C₂×C₄×C₄₁	—	4	1	no	—
374	C₂×C₄×C₄₁	—	4	1	no	—
375	C₂×C₄×C₄₁	—	4	1	no	—
376	C₂×C₄×C₄₁	—	8	4	no	—
377	C₂×C₄×C₄₁	—	8	4	no	—
378	C₂×C₄×C₄₁	#121	1	2	yes	—
379	C₂×C₄×C₄₁	#135	1	2	yes	complemented
380	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
384	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
385	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
386	C₈×C₄₁	—	2	2	no	—
387	C₈×C₄₁	—	2	2	no	—
388	C₈×C₄₁	—	4	1	no	—
389	C₈×C₄₁	—	4	1	no	—
390	#24364	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂²×C₄₁	—	2	2	no	—
392	C₂²×C₄₁	—	2	4	no	—
393	C₂²×C₄₁	—	2	2	no	—
394	C₂²×C₄₁	—	2	2	no	—
395	C₂²×C₄₁	—	4	1	no	—
396	C₂²×C₄₁	—	4	2	no	—
397	C₂²×C₄₁	—	4	2	no	—
398	C₂²×C₄₁	—	4	1	no	—
399	C₂²×C₄₁	—	4	2	no	—
400	C₂²×C₄₁	—	4	1	no	—
401	C₂²×C₄₁	—	4	1	no	—
402	C₂²×C₄₁	—	4	2	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	—	4	2	no	—
408	C₂²×C₄₁	—	8	1	no	—
409	C₂²×C₄₁	—	8	1	no	—
410	C₂²×C₄₁	—	8	1	no	—
411	C₂²×C₄₁	—	8	1	no	—
412	C₂²×C₄₁	—	8	1	no	—
413	C₂²×C₄₁	—	8	1	no	—
414	C₂²×C₄₁	—	8	1	no	—
415	C₂²×C₄₁	—	8	1	no	—
416	C₂²×C₄₁	—	8	1	no	—
417	C₂²×C₄₁	—	8	1	no	—
418	C₂²×C₄₁	—	8	1	no	—
419	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
420	C₂²×C₄₁	D₄²	1	1	yes	characteristic
421	C₂²×C₄₁	D₄²	1	1	yes	characteristic
422	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
423	C₂²×C₄₁	#575	1	1	yes	characteristic
424	C₂²×C₄₁	#576	1	1	yes	characteristic
425	C₂²×C₄₁	#577	1	1	yes	characteristic
426	C₄×C₄₁	—	2	2	no	—
427	C₄×C₄₁	—	2	2	no	—
428	C₄×C₄₁	—	4	2	no	—
429	C₄×C₄₁	—	4	2	no	—
430	C₄×C₄₁	—	4	1	no	—
431	C₄×C₄₁	—	4	1	no	—
432	C₄×C₄₁	—	4	1	no	—
433	C₄×C₄₁	—	8	1	no	—
434	C₄×C₄₁	—	8	1	no	—
435	C₄×C₄₁	—	8	1	no	—
436	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
437	C₄×C₄₁	#534	1	1	yes	characteristic
438	C₄×C₄₁	#546	1	1	yes	characteristic
439	C₄×C₄₁	#546	1	1	yes	characteristic
440	C₂²×#135	C₂×C₄₁	1	1	yes	characteristic, complemented
441	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
442	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
443	C₂×#449	C₂×C₄₁	1	1	yes	characteristic, complemented
444	#2431	C₂×C₄₁	1	1	yes	characteristic, complemented
445	#2339	C₂×C₄₁	1	1	yes	characteristic, complemented
446	#2056	C₂×C₄₁	1	1	yes	characteristic, complemented
447	#2055	C₂×C₄₁	1	1	yes	characteristic, complemented
448	#2015	C₂×C₄₁	1	1	yes	characteristic, complemented
449	#2014	C₂×C₄₁	1	1	yes	characteristic, complemented
450	#1893	C₂×C₄₁	1	1	yes	characteristic, complemented
451	#1879	C₂×C₄₁	1	1	yes	characteristic, complemented
452	#1877	C₂×C₄₁	1	1	yes	characteristic, complemented
453	#1850	C₂×C₄₁	1	1	yes	characteristic, complemented
454	#1788	C₂×C₄₁	1	1	yes	characteristic, complemented
455	C₂×C₄₁	—	4	2	no	—
456	C₂×C₄₁	—	4	4	no	—
457	C₂×C₄₁	—	8	2	no	—
458	C₂×C₄₁	—	16	1	no	—
459	C₂×C₄₁	#2410	1	1	yes	characteristic
460	C₂×C₄₁	#3035	1	1	yes	characteristic
461	C₂×C₄₁	#3045	1	1	yes	characteristic
462	C₂×C₄₁	#3267	1	1	yes	characteristic
463	C₂×C₄₁	#3268	1	1	yes	characteristic
464	C₂×C₄₁	#3280	1	1	yes	characteristic
465	C₂×C₄₁	#3284	1	1	yes	characteristic
466	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
467	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
468	C₂×#135	—	2	4	no	—
469	C₂×#135	—	2	4	no	—
470	C₂×#135	—	2	4	no	—
471	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
472	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
473	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
474	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
475	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
476	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
477	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
478	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
479	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
480	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
481	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
482	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
483	#463	—	2	4	no	—
484	#459	—	2	4	no	—
485	#449	—	2	4	no	—
486	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
487	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
488	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
489	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
490	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
491	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
492	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
493	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
494	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
495	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
496	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
497	#392	—	2	1	no	—
498	#392	—	2	1	no	—
499	#391	C₂²×C₄₁	1	1	yes	characteristic
500	#391	C₂²×C₄₁	1	1	yes	characteristic
501	#391	C₂²×C₄₁	1	1	yes	characteristic
502	#390	C₂²×C₄₁	1	1	yes	characteristic
503	#386	—	2	1	no	—
504	#386	—	2	1	no	—
505	#386	—	2	1	no	—
506	#386	—	2	1	no	—
507	#381	—	2	1	no	—
508	#380	C₂²×C₄₁	1	1	yes	characteristic
509	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
510	C₂×#95	—	2	1	no	—
511	#340	C₂²×C₄₁	1	1	yes	characteristic
512	#340	C₂²×C₄₁	1	1	yes	characteristic
513	#336	C₂²×C₄₁	1	1	yes	characteristic
514	#336	C₂²×C₄₁	1	1	yes	characteristic
515	C₄₁	#24364	1	1	yes	characteristic, direct product factor, Sylow
516	C₂×#41	—	2	2	no	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	2	no	—
523	C₂×#41	—	4	1	no	—
524	C₂×#41	—	4	1	no	—
525	C₂×#41	—	4	1	no	—
526	C₂×#41	—	4	1	no	—
527	C₂×#41	D₄×C₄₁	1	4	yes	complemented
528	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
529	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	—	2	1	no	—
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
536	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
538	C₂³×C₄	—	2	1	no	—
539	C₂³×C₄	—	2	1	no	—
540	C₂³×C₄	—	2	1	no	—
541	C₂³×C₄	—	2	1	no	—
542	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
543	#135	—	2	32	no	—
544	C₂×Q₁₆	—	2	2	no	—
545	C₂×Q₁₆	—	2	2	no	—
546	C₂×Q₁₆	—	2	2	no	—
547	C₂×SD₁₆	—	2	2	no	—
548	C₂×SD₁₆	—	2	2	no	—
549	C₂×SD₁₆	—	2	2	no	—
550	C₂×SD₁₆	—	2	2	no	—
551	C₂×SD₁₆	—	2	2	no	—
552	C₂×SD₁₆	—	2	2	no	—
553	C₂×SD₁₆	—	4	1	no	—
554	C₂×SD₁₆	—	4	1	no	—
555	C₂×SD₁₆	D₄×C₄₁	1	4	yes	complemented
556	C₂×D₈	—	2	2	no	—
557	C₂×D₈	—	2	2	no	—
558	C₂×D₈	—	2	2	no	—
559	C₂×D₈	—	2	2	no	—
560	C₂×D₈	—	2	2	no	—
561	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
562	C₂²×C₈	—	2	2	no	—
563	C₂²×C₈	—	2	2	no	—
564	C₂²×C₈	—	2	2	no	—
565	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
566	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
567	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
568	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
569	#127	—	2	2	no	—
570	#127	—	4	1	no	—
571	#124	—	2	2	no	—
572	#124	—	4	1	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	4	1	no	—
578	C₄×D₄	—	4	1	no	—
579	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
594	C₄⋊C₈	—	2	2	no	—
595	C₄⋊C₈	—	2	2	no	—
596	#103	—	2	2	no	—
597	#103	—	2	2	no	—
598	#103	—	4	1	no	—
599	#102	—	2	2	no	—
600	#102	—	2	2	no	—
601	#102	—	2	2	no	—
602	#102	—	2	2	no	—
603	#102	—	4	1	no	—
604	C₂²⋊C₈	—	2	2	no	—
605	#95	—	2	1	no	—
606	#95	—	2	1	no	—
607	#95	—	2	1	no	—
608	#95	—	2	1	no	—
609	#95	—	2	1	no	—
610	#95	—	2	1	no	—
611	#95	—	2	1	no	—
612	#95	D₄×C₄₁	1	1	yes	characteristic
613	#95	D₄×C₄₁	1	1	yes	characteristic
614	C₂⁴	—	2	1	no	—
615	C₂⁴	—	2	1	no	—
616	C₂⁴	—	2	1	no	—
617	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
618	#41	—	2	8	no	—
619	#41	—	2	8	no	—
620	#41	—	4	4	no	—
621	#41	—	4	4	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	#41	—	4	4	no	—
625	#41	—	4	4	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	1	no	—
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	1	no	—
635	C₂×Q₈	—	2	1	no	—
636	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
637	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	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	—	4	2	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	2	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂×D₄	—	8	1	no	—
664	C₂×D₄	—	8	1	no	—
665	C₂×D₄	—	8	1	no	—
666	C₂×D₄	—	8	1	no	—
667	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
668	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
669	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
670	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	8	1	no	—
691	C₂²×C₄	—	8	1	no	—
692	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
697	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
698	C₂²×C₄	#41×C₄₁	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
700	Q₁₆	—	2	8	no	—
701	SD₁₆	—	2	8	no	—
702	SD₁₆	—	2	8	no	—
703	SD₁₆	—	4	4	no	—
704	D₈	—	2	8	no	—
705	D₈	—	4	4	no	—
706	C₂×C₈	—	2	8	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	2	1	no	—
711	C₂×C₈	—	2	1	no	—
712	C₂×C₈	—	2	1	no	—
713	C₂×C₈	—	2	1	no	—
714	C₂×C₈	—	2	1	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	—	2	1	no	—
717	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
718	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	4	1	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	8	1	no	—
733	C₂²⋊C₄	—	8	1	no	—
734	C₂²⋊C₄	—	8	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	2	1	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	1	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	1	no	—
760	C₂³	—	4	1	no	—
761	C₂³	—	4	1	no	—
762	C₂³	—	4	1	no	—
763	C₂³	—	4	1	no	—
764	C₂³	—	4	1	no	—
765	C₂³	—	4	1	no	—
766	C₂³	#121×C₄₁	1	2	yes	—
767	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	4	1	no	—
773	Q₈	—	4	1	no	—
774	Q₈	—	4	1	no	—
775	Q₈	—	4	1	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	8	no	—
783	D₄	—	4	1	no	—
784	D₄	—	4	1	no	—
785	D₄	—	4	1	no	—
786	D₄	—	4	1	no	—
787	D₄	—	4	1	no	—
788	D₄	—	4	1	no	—
789	D₄	—	8	4	no	—
790	D₄	—	8	4	no	—
791	D₄	—	8	4	no	—
792	D₄	#120×C₄₁	1	4	yes	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	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	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	8	4	no	—
828	C₂×C₄	—	8	4	no	—
829	C₂×C₄	#121×C₄₁	1	2	yes	—
830	C₂×C₄	#135×C₄₁	1	2	yes	complemented
831	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
834	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
835	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
836	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
837	C₈	—	2	2	no	—
838	C₈	—	2	2	no	—
839	C₈	—	4	1	no	—
840	C₈	—	4	1	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	4	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	1	no	—
859	C₂²	—	8	1	no	—
860	C₂²	—	8	1	no	—
861	C₂²	—	8	1	no	—
862	C₂²	—	8	1	no	—
863	C₂²	—	8	1	no	—
864	C₂²	—	8	1	no	—
865	C₂²	—	8	1	no	—
866	C₂²	—	8	1	no	—
867	C₂²	—	8	1	no	—
868	C₂²	—	8	1	no	—
869	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
870	C₂²	D₄²×C₄₁	1	1	yes	characteristic
871	C₂²	D₄²×C₄₁	1	1	yes	characteristic
872	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
873	C₂²	C₄₁×#575	1	1	yes	characteristic
874	C₂²	C₄₁×#576	1	1	yes	characteristic
875	C₂²	C₄₁×#577	1	1	yes	characteristic
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	8	1	no	—
884	C₄	—	8	1	no	—
885	C₄	—	8	1	no	—
886	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
887	C₄	C₄₁×#534	1	1	yes	characteristic
888	C₄	C₄₁×#546	1	1	yes	characteristic
889	C₄	C₄₁×#546	1	1	yes	characteristic
890	C₂	—	4	2	no	—
891	C₂	—	4	4	no	—
892	C₂	—	8	2	no	—
893	C₂	—	16	1	no	—
894	C₂	C₄₁×#2410	1	1	yes	characteristic
895	C₂	C₄₁×#3035	1	1	yes	characteristic
896	C₂	C₄₁×#3045	1	1	yes	characteristic
897	C₂	C₄₁×#3267	1	1	yes	characteristic
898	C₂	C₄₁×#3268	1	1	yes	characteristic
899	C₂	C₄₁×#3280	1	1	yes	characteristic
900	C₂	C₄₁×#3284	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₄₁	C₂	semidirect
2. C₂×C₄₁×#463	C₂	semidirect
3. C₂×C₄₁×#459	C₂	semidirect
4. C₂×C₄₁×#449	C₂	semidirect
5. C₄₁×#2431	C₂	semidirect
6. C₄₁×#2339	C₂	semidirect
7. C₄₁×#2056	C₂	semidirect
8. C₄₁×#2055	C₂	semidirect
9. C₄₁×#2015	C₂	semidirect
10. C₄₁×#2014	C₂	semidirect
11. C₄₁×#1893	C₂	semidirect
12. C₄₁×#1879	C₂	semidirect
13. C₄₁×#1877	C₂	semidirect
14. C₄₁×#1850	C₂	semidirect
15. C₄₁×#1788	C₂	semidirect
76. C₂×#41×C₄₁	D₄	semidirect
104. C₂×SD₁₆×C₄₁	D₄	semidirect
110. C₂×D₈×C₄₁	D₄	semidirect
379. C₂×C₄×C₄₁	#135	semidirect
390. #24364	C₄₁	direct (N × H)
440. C₂²×#135	C₂×C₄₁	semidirect
441. C₂×#463	C₂×C₄₁	semidirect
442. C₂×#459	C₂×C₄₁	semidirect
443. C₂×#449	C₂×C₄₁	semidirect
444. #2431	C₂×C₄₁	semidirect
445. #2339	C₂×C₄₁	semidirect
446. #2056	C₂×C₄₁	semidirect
447. #2055	C₂×C₄₁	semidirect
448. #2015	C₂×C₄₁	semidirect
449. #2014	C₂×C₄₁	semidirect
450. #1893	C₂×C₄₁	semidirect
451. #1879	C₂×C₄₁	semidirect
452. #1877	C₂×C₄₁	semidirect
453. #1850	C₂×C₄₁	semidirect
454. #1788	C₂×C₄₁	semidirect
515. C₄₁	#24364	direct (N × H)
527. C₂×#41	D₄×C₄₁	semidirect
555. C₂×SD₁₆	D₄×C₄₁	semidirect
561. C₂×D₈	D₄×C₄₁	semidirect
830. C₂×C₄	#135×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₄₁	2
C₂×C₄₁×#463	2
C₂×C₄₁×#459	2
C₂×C₄₁×#449	2
C₄₁×#2431	2
C₄₁×#2339	2
C₄₁×#2056	2
C₄₁×#2055	2
C₄₁×#2015	2
C₄₁×#2014	2
C₄₁×#1893	2
C₄₁×#1879	2
C₄₁×#1877	2
C₄₁×#1850	2
C₄₁×#1788	2
#24364	41

Subgroups — C41×#24364 #23800565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24364 #23800565