Subgroups — C₄₁×#21874 #23798075

Order 10496.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#525	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1996	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1964	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1898	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1799	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₄₁	C₄	1	1	yes	characteristic, complemented
9	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₄₁×#525	—	2	1	no	—
11	C₄₁×#525	—	2	1	no	—
12	C₄₁×#525	—	2	1	no	—
13	C₄₁×#525	—	2	1	no	—
14	C₄₁×#525	—	2	1	no	—
15	C₄₁×#525	—	2	1	no	—
16	C₄₁×#525	—	2	1	no	—
17	C₄₁×#525	—	2	1	no	—
18	C₂×#123×C₄₁	C₄	1	2	yes	complemented
19	C₂×C₂²⋊Q₈×C₄₁	C₄	1	1	yes	characteristic, complemented
20	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#121×C₄₁	C₄	1	1	yes	characteristic, complemented
22	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#120×C₄₁	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₄₁	C₄	1	2	yes	complemented
25	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
26	C₂×#117×C₄₁	—	2	1	no	—
27	C₂×#117×C₄₁	C₄	1	1	yes	characteristic, complemented
28	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
29	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₂×#99×C₄₁	C₂²	1	8	yes	—
31	C₄₁×#381	—	2	1	no	—
32	C₄₁×#380	—	2	1	no	—
33	C₄₁×#380	—	2	1	no	—
34	C₄₁×#380	—	2	1	no	—
35	C₄₁×#380	C₂²	1	2	yes	—
36	C₄₁×#380	C₂²	1	2	yes	—
37	C₄₁×#380	C₂²	1	2	yes	—
38	C₄₁×#379	C₂²	1	2	yes	—
39	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
41	C₂×#95×C₄₁	—	2	1	no	—
42	C₄₁×#342	C₂²	1	8	yes	—
43	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
44	C₂×#41×C₄₁	—	2	1	no	—
45	C₂×#41×C₄₁	—	2	1	no	—
46	C₂×#41×C₄₁	—	2	1	no	—
47	C₂×#41×C₄₁	—	2	1	no	—
48	C₂×#41×C₄₁	—	4	4	no	—
49	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
52	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₁	—	2	2	no	—
55	C₂³×C₄×C₄₁	—	4	4	no	—
56	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	complemented
61	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
71	#123×C₄₁	—	2	2	no	—
72	#123×C₄₁	—	2	2	no	—
73	#123×C₄₁	—	2	2	no	—
74	#123×C₄₁	—	2	2	no	—
75	C₂²⋊Q₈×C₄₁	—	2	1	no	—
76	C₂²⋊Q₈×C₄₁	—	2	1	no	—
77	C₂²⋊Q₈×C₄₁	—	2	1	no	—
78	C₂²⋊Q₈×C₄₁	—	2	1	no	—
79	C₂²⋊Q₈×C₄₁	—	2	1	no	—
80	C₂²⋊Q₈×C₄₁	—	2	1	no	—
81	C₂²⋊Q₈×C₄₁	—	2	1	no	—
82	C₂²⋊Q₈×C₄₁	—	2	1	no	—
83	#121×C₄₁	—	2	1	no	—
84	#121×C₄₁	—	2	1	no	—
85	#121×C₄₁	—	2	1	no	—
86	#121×C₄₁	—	2	1	no	—
87	#121×C₄₁	—	2	1	no	—
88	#121×C₄₁	—	2	1	no	—
89	#121×C₄₁	—	2	1	no	—
90	#121×C₄₁	—	2	1	no	—
91	#120×C₄₁	—	2	2	no	—
92	#120×C₄₁	—	2	2	no	—
93	#120×C₄₁	—	2	2	no	—
94	#120×C₄₁	—	2	2	no	—
95	C₄×D₄×C₄₁	—	2	2	no	—
96	C₄×D₄×C₄₁	—	2	2	no	—
97	C₄×D₄×C₄₁	—	2	2	no	—
98	C₄×D₄×C₄₁	—	2	2	no	—
99	C₄×D₄×C₄₁	—	2	2	no	—
100	C₄×D₄×C₄₁	—	2	2	no	—
101	C₄×D₄×C₄₁	—	2	2	no	—
102	C₄×D₄×C₄₁	—	2	2	no	—
103	#117×C₄₁	—	2	1	no	—
104	#117×C₄₁	—	2	1	no	—
105	#117×C₄₁	—	2	1	no	—
106	#117×C₄₁	—	2	1	no	—
107	#117×C₄₁	—	4	4	no	—
108	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
109	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
110	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
111	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
112	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
114	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	complemented
115	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	complemented
116	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
117	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
118	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
119	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
120	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
121	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
122	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	complemented
123	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	complemented
124	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
127	C₂×C₄²×C₄₁	—	2	2	no	—
128	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	complemented
129	#99×C₄₁	—	4	8	no	—
130	#95×C₄₁	—	2	2	no	—
131	#95×C₄₁	—	2	2	no	—
132	#95×C₄₁	—	2	2	no	—
133	#95×C₄₁	—	2	2	no	—
134	C₂⁴×C₄₁	—	2	2	no	—
135	C₂⁴×C₄₁	—	2	2	no	—
136	C₂⁴×C₄₁	—	4	2	no	—
137	C₂⁴×C₄₁	—	4	2	no	—
138	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
139	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
140	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
141	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
145	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
146	#41×C₄₁	—	4	4	no	—
147	#41×C₄₁	—	4	4	no	—
148	#41×C₄₁	—	4	4	no	—
149	#41×C₄₁	—	4	4	no	—
150	C₂×Q₈×C₄₁	—	2	1	no	—
151	C₂×Q₈×C₄₁	—	2	1	no	—
152	C₂×Q₈×C₄₁	—	4	2	no	—
153	C₂×D₄×C₄₁	—	2	2	no	—
154	C₂×D₄×C₄₁	—	2	2	no	—
155	C₂×D₄×C₄₁	—	2	2	no	—
156	C₂×D₄×C₄₁	—	2	2	no	—
157	C₂×D₄×C₄₁	—	2	2	no	—
158	C₂×D₄×C₄₁	—	2	2	no	—
159	C₂×D₄×C₄₁	—	2	4	no	—
160	C₂×D₄×C₄₁	—	2	4	no	—
161	C₂×D₄×C₄₁	—	2	1	no	—
162	C₂×D₄×C₄₁	—	2	1	no	—
163	C₂×D₄×C₄₁	—	4	2	no	—
164	C₂×D₄×C₄₁	—	4	4	no	—
165	C₂×D₄×C₄₁	—	4	4	no	—
166	C₂²×C₄×C₄₁	—	2	4	no	—
167	C₂²×C₄×C₄₁	—	2	4	no	—
168	C₂²×C₄×C₄₁	—	2	4	no	—
169	C₂²×C₄×C₄₁	—	2	2	no	—
170	C₂²×C₄×C₄₁	—	2	2	no	—
171	C₂²×C₄×C₄₁	—	2	4	no	—
172	C₂²×C₄×C₄₁	—	2	4	no	—
173	C₂²×C₄×C₄₁	—	4	2	no	—
174	C₂²×C₄×C₄₁	—	4	2	no	—
175	C₂²×C₄×C₄₁	—	4	2	no	—
176	C₂²×C₄×C₄₁	—	4	2	no	—
177	C₂²×C₄×C₄₁	—	4	2	no	—
178	C₂²×C₄×C₄₁	—	4	2	no	—
179	C₂²×C₄×C₄₁	—	4	2	no	—
180	C₂²×C₄×C₄₁	—	4	2	no	—
181	C₂²×C₄×C₄₁	—	4	2	no	—
182	C₂²×C₄×C₄₁	—	4	2	no	—
183	C₂²×C₄×C₄₁	—	4	2	no	—
184	C₂²×C₄×C₄₁	—	4	4	no	—
185	C₂²×C₄×C₄₁	—	4	4	no	—
186	C₂²×C₄×C₄₁	—	4	4	no	—
187	C₂²×C₄×C₄₁	—	4	4	no	—
188	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
202	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
205	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
208	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
209	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
219	C₄⋊C₄×C₄₁	—	2	1	no	—
220	C₄⋊C₄×C₄₁	—	2	1	no	—
221	C₄⋊C₄×C₄₁	—	2	1	no	—
222	C₄⋊C₄×C₄₁	—	2	1	no	—
223	C₄⋊C₄×C₄₁	—	2	2	no	—
224	C₄⋊C₄×C₄₁	—	2	2	no	—
225	C₄⋊C₄×C₄₁	—	2	2	no	—
226	C₄⋊C₄×C₄₁	—	2	2	no	—
227	C₄⋊C₄×C₄₁	—	4	4	no	—
228	C₄⋊C₄×C₄₁	—	4	4	no	—
229	C₄⋊C₄×C₄₁	—	4	4	no	—
230	C₂²⋊C₄×C₄₁	—	2	2	no	—
231	C₂²⋊C₄×C₄₁	—	2	2	no	—
232	C₂²⋊C₄×C₄₁	—	2	2	no	—
233	C₂²⋊C₄×C₄₁	—	2	2	no	—
234	C₂²⋊C₄×C₄₁	—	2	2	no	—
235	C₂²⋊C₄×C₄₁	—	2	2	no	—
236	C₂²⋊C₄×C₄₁	—	2	2	no	—
237	C₂²⋊C₄×C₄₁	—	2	2	no	—
238	C₂²⋊C₄×C₄₁	—	2	2	no	—
239	C₂²⋊C₄×C₄₁	—	2	2	no	—
240	C₂²⋊C₄×C₄₁	—	2	4	no	—
241	C₂²⋊C₄×C₄₁	—	2	8	no	—
242	C₂²⋊C₄×C₄₁	—	2	4	no	—
243	C₂²⋊C₄×C₄₁	—	4	4	no	—
244	C₂²⋊C₄×C₄₁	—	4	4	no	—
245	C₂²⋊C₄×C₄₁	—	4	4	no	—
246	C₄²×C₄₁	—	2	2	no	—
247	C₄²×C₄₁	—	2	2	no	—
248	C₄²×C₄₁	—	4	4	no	—
249	C₂³×C₄₁	—	2	1	no	—
250	C₂³×C₄₁	—	2	1	no	—
251	C₂³×C₄₁	—	2	2	no	—
252	C₂³×C₄₁	—	2	2	no	—
253	C₂³×C₄₁	—	2	2	no	—
254	C₂³×C₄₁	—	2	2	no	—
255	C₂³×C₄₁	—	2	1	no	—
256	C₂³×C₄₁	—	2	1	no	—
257	C₂³×C₄₁	—	2	2	no	—
258	C₂³×C₄₁	—	2	2	no	—
259	C₂³×C₄₁	—	2	2	no	—
260	C₂³×C₄₁	—	2	2	no	—
261	C₂³×C₄₁	—	2	2	no	—
262	C₂³×C₄₁	—	2	2	no	—
263	C₂³×C₄₁	—	2	2	no	—
264	C₂³×C₄₁	—	2	4	no	—
265	C₂³×C₄₁	—	4	1	no	—
266	C₂³×C₄₁	—	4	1	no	—
267	C₂³×C₄₁	—	4	1	no	—
268	C₂³×C₄₁	—	4	1	no	—
269	C₂³×C₄₁	—	4	1	no	—
270	C₂³×C₄₁	—	4	1	no	—
271	C₂³×C₄₁	—	4	1	no	—
272	C₂³×C₄₁	—	4	1	no	—
273	C₂³×C₄₁	—	4	8	no	—
274	C₂³×C₄₁	—	4	8	no	—
275	C₂³×C₄₁	—	4	2	no	—
276	C₂³×C₄₁	—	4	2	no	—
277	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
282	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
283	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
284	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
285	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
286	Q₈×C₄₁	—	4	2	no	—
287	Q₈×C₄₁	—	4	2	no	—
288	D₄×C₄₁	—	4	2	no	—
289	D₄×C₄₁	—	4	4	no	—
290	D₄×C₄₁	—	4	4	no	—
291	D₄×C₄₁	—	4	2	no	—
292	D₄×C₄₁	—	4	2	no	—
293	D₄×C₄₁	—	4	4	no	—
294	D₄×C₄₁	—	4	4	no	—
295	D₄×C₄₁	—	4	4	no	—
296	D₄×C₄₁	—	4	2	no	—
297	C₂×C₄×C₄₁	—	2	2	no	—
298	C₂×C₄×C₄₁	—	2	2	no	—
299	C₂×C₄×C₄₁	—	2	2	no	—
300	C₂×C₄×C₄₁	—	2	2	no	—
301	C₂×C₄×C₄₁	—	2	2	no	—
302	C₂×C₄×C₄₁	—	2	2	no	—
303	C₂×C₄×C₄₁	—	2	2	no	—
304	C₂×C₄×C₄₁	—	2	2	no	—
305	C₂×C₄×C₄₁	—	2	2	no	—
306	C₂×C₄×C₄₁	—	2	2	no	—
307	C₂×C₄×C₄₁	—	2	2	no	—
308	C₂×C₄×C₄₁	—	2	2	no	—
309	C₂×C₄×C₄₁	—	2	2	no	—
310	C₂×C₄×C₄₁	—	2	2	no	—
311	C₂×C₄×C₄₁	—	2	2	no	—
312	C₂×C₄×C₄₁	—	2	2	no	—
313	C₂×C₄×C₄₁	—	2	2	no	—
314	C₂×C₄×C₄₁	—	2	2	no	—
315	C₂×C₄×C₄₁	—	2	4	no	—
316	C₂×C₄×C₄₁	—	4	1	no	—
317	C₂×C₄×C₄₁	—	4	1	no	—
318	C₂×C₄×C₄₁	—	4	1	no	—
319	C₂×C₄×C₄₁	—	4	1	no	—
320	C₂×C₄×C₄₁	—	4	1	no	—
321	C₂×C₄×C₄₁	—	4	1	no	—
322	C₂×C₄×C₄₁	—	4	1	no	—
323	C₂×C₄×C₄₁	—	4	1	no	—
324	C₂×C₄×C₄₁	—	4	1	no	—
325	C₂×C₄×C₄₁	—	4	1	no	—
326	C₂×C₄×C₄₁	—	4	1	no	—
327	C₂×C₄×C₄₁	—	4	1	no	—
328	C₂×C₄×C₄₁	—	4	4	no	—
329	C₂×C₄×C₄₁	—	4	4	no	—
330	C₂×C₄×C₄₁	—	4	2	no	—
331	C₂×C₄×C₄₁	—	4	2	no	—
332	C₂×C₄×C₄₁	—	4	4	no	—
333	C₂×C₄×C₄₁	—	4	4	no	—
334	C₂×C₄×C₄₁	—	4	4	no	—
335	C₂×C₄×C₄₁	—	4	4	no	—
336	C₂×C₄×C₄₁	—	4	4	no	—
337	C₂×C₄×C₄₁	—	4	4	no	—
338	C₂×C₄×C₄₁	—	8	8	no	—
339	C₂×C₄×C₄₁	#99	1	4	yes	complemented
340	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
341	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
344	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	#21874	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₂²×C₄₁	—	2	4	no	—
350	C₂²×C₄₁	—	2	4	no	—
351	C₂²×C₄₁	—	2	1	no	—
352	C₂²×C₄₁	—	2	1	no	—
353	C₂²×C₄₁	—	2	1	no	—
354	C₂²×C₄₁	—	2	1	no	—
355	C₂²×C₄₁	—	2	1	no	—
356	C₂²×C₄₁	—	2	1	no	—
357	C₂²×C₄₁	—	2	1	no	—
358	C₂²×C₄₁	—	2	1	no	—
359	C₂²×C₄₁	—	2	1	no	—
360	C₂²×C₄₁	—	2	1	no	—
361	C₂²×C₄₁	—	2	1	no	—
362	C₂²×C₄₁	—	2	1	no	—
363	C₂²×C₄₁	—	2	1	no	—
364	C₂²×C₄₁	—	2	1	no	—
365	C₂²×C₄₁	—	2	1	no	—
366	C₂²×C₄₁	—	2	1	no	—
367	C₂²×C₄₁	—	4	2	no	—
368	C₂²×C₄₁	—	4	2	no	—
369	C₂²×C₄₁	—	4	4	no	—
370	C₂²×C₄₁	—	4	4	no	—
371	C₂²×C₄₁	—	4	4	no	—
372	C₂²×C₄₁	—	4	4	no	—
373	C₂²×C₄₁	—	4	2	no	—
374	C₂²×C₄₁	—	4	2	no	—
375	C₂²×C₄₁	—	4	2	no	—
376	C₂²×C₄₁	—	4	2	no	—
377	C₂²×C₄₁	—	4	2	no	—
378	C₂²×C₄₁	—	8	4	no	—
379	C₂²×C₄₁	C₂×#99	1	2	yes	—
380	C₂²×C₄₁	#410	1	2	yes	—
381	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
382	C₂²×C₄₁	#520	1	2	yes	—
383	C₂²×C₄₁	#535	1	1	yes	characteristic
384	C₂²×C₄₁	#536	1	1	yes	characteristic
385	C₂²×C₄₁	#537	1	2	yes	—
386	C₄×C₄₁	—	2	1	no	—
387	C₄×C₄₁	—	2	1	no	—
388	C₄×C₄₁	—	2	1	no	—
389	C₄×C₄₁	—	2	1	no	—
390	C₄×C₄₁	—	2	1	no	—
391	C₄×C₄₁	—	2	1	no	—
392	C₄×C₄₁	—	4	2	no	—
393	C₄×C₄₁	—	4	2	no	—
394	C₄×C₄₁	—	4	2	no	—
395	C₄×C₄₁	—	8	4	no	—
396	C₄×C₄₁	—	8	4	no	—
397	C₄×C₄₁	C₂×#99	1	2	yes	—
398	C₄×C₄₁	C₂×#99	1	2	yes	—
399	C₂×#525	C₂×C₄₁	1	1	yes	characteristic
400	#2280	C₂×C₄₁	1	1	yes	characteristic, complemented
401	C₂×#380	C₂×C₄₁	1	1	yes	characteristic, complemented
402	#1996	C₂×C₄₁	1	2	yes	complemented
403	#1964	C₂×C₄₁	1	2	yes	complemented
404	#1898	C₂×C₄₁	1	4	yes	complemented
405	#1799	C₂×C₄₁	1	4	yes	complemented
406	C₂×C₄₁	—	2	1	no	—
407	C₂×C₄₁	—	2	2	no	—
408	C₂×C₄₁	—	2	1	no	—
409	C₂×C₄₁	—	2	2	no	—
410	C₂×C₄₁	—	2	2	no	—
411	C₂×C₄₁	—	2	2	no	—
412	C₂×C₄₁	—	4	1	no	—
413	C₂×C₄₁	—	4	1	no	—
414	C₂×C₄₁	—	8	2	no	—
415	C₂×C₄₁	#2311	1	1	yes	characteristic
416	C₂×C₄₁	C₂²×#99	1	1	yes	characteristic
417	C₂×C₄₁	C₂×#410	1	1	yes	characteristic
418	C₂²×#41	C₄×C₄₁	1	1	yes	characteristic, complemented
419	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
420	#525	—	2	1	no	—
421	#525	—	2	1	no	—
422	#525	—	2	1	no	—
423	#525	—	2	1	no	—
424	#525	—	2	1	no	—
425	#525	—	2	1	no	—
426	#525	—	2	1	no	—
427	#525	—	2	1	no	—
428	C₂×#123	C₄×C₄₁	1	2	yes	complemented
429	C₂×C₂²⋊Q₈	C₄×C₄₁	1	1	yes	characteristic, complemented
430	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
431	C₂×#121	C₄×C₄₁	1	1	yes	characteristic, complemented
432	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
433	C₂×#120	C₂²×C₄₁	1	2	yes	—
434	C₂×C₄×D₄	C₄×C₄₁	1	2	yes	complemented
435	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
436	C₂×#117	—	2	1	no	—
437	C₂×#117	C₄×C₄₁	1	1	yes	characteristic, complemented
438	C₂²×C₄⋊C₄	—	2	1	no	—
439	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
440	C₂×#99	C₂²×C₄₁	1	8	yes	—
441	#381	—	2	1	no	—
442	#380	—	2	1	no	—
443	#380	—	2	1	no	—
444	#380	—	2	1	no	—
445	#380	C₂²×C₄₁	1	2	yes	—
446	#380	C₂²×C₄₁	1	2	yes	—
447	#380	C₂²×C₄₁	1	2	yes	—
448	#379	C₂²×C₄₁	1	2	yes	—
449	C₄×C₂²⋊C₄	—	2	1	no	—
450	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
451	C₂×#95	—	2	1	no	—
452	#342	C₂²×C₄₁	1	8	yes	—
453	C₄₁	#21874	1	1	yes	characteristic, direct product factor, Sylow
454	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	4	4	no	—
460	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
461	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
462	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
463	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
464	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
465	C₂³×C₄	—	2	2	no	—
466	C₂³×C₄	—	4	4	no	—
467	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
468	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
469	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
470	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
471	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	complemented
472	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
473	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
474	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
475	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
476	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
477	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
478	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
479	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
482	#123	—	2	2	no	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	#123	—	2	2	no	—
486	C₂²⋊Q₈	—	2	1	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	—	2	1	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	#121	—	2	1	no	—
495	#121	—	2	1	no	—
496	#121	—	2	1	no	—
497	#121	—	2	1	no	—
498	#121	—	2	1	no	—
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#120	—	2	2	no	—
503	#120	—	2	2	no	—
504	#120	—	2	2	no	—
505	#120	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	#117	—	2	1	no	—
515	#117	—	2	1	no	—
516	#117	—	2	1	no	—
517	#117	—	2	1	no	—
518	#117	—	4	4	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	—	4	4	no	—
523	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
524	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
525	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	complemented
526	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	complemented
527	C₂×C₂²⋊C₄	—	2	2	no	—
528	C₂×C₂²⋊C₄	—	2	2	no	—
529	C₂×C₂²⋊C₄	—	2	2	no	—
530	C₂×C₂²⋊C₄	—	4	4	no	—
531	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	complemented
534	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	complemented
535	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
538	C₂×C₄²	—	2	2	no	—
539	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	complemented
540	#99	—	4	8	no	—
541	#95	—	2	2	no	—
542	#95	—	2	2	no	—
543	#95	—	2	2	no	—
544	#95	—	2	2	no	—
545	C₂⁴	—	2	2	no	—
546	C₂⁴	—	2	2	no	—
547	C₂⁴	—	4	2	no	—
548	C₂⁴	—	4	2	no	—
549	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
550	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
551	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
552	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
553	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
554	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
555	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
556	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
557	#41	—	4	4	no	—
558	#41	—	4	4	no	—
559	#41	—	4	4	no	—
560	#41	—	4	4	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	4	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	4	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	4	4	no	—
598	C₂²×C₄	—	4	4	no	—
599	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
600	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
601	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
602	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
603	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
604	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
605	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
606	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
607	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
608	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
609	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
610	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
611	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
612	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
613	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
614	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
615	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
616	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
617	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
618	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
619	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
620	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
621	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
628	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	4	4	no	—
639	C₄⋊C₄	—	4	4	no	—
640	C₄⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	—	4	4	no	—
656	C₂²⋊C₄	—	4	4	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	4	4	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	8	no	—
685	C₂³	—	4	8	no	—
686	C₂³	—	4	2	no	—
687	C₂³	—	4	2	no	—
688	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
689	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
690	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
691	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
692	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
693	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
694	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
695	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
696	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
697	Q₈	—	4	2	no	—
698	Q₈	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	2	no	—
704	D₄	—	4	4	no	—
705	D₄	—	4	4	no	—
706	D₄	—	4	4	no	—
707	D₄	—	4	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	4	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	4	4	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	—	8	8	no	—
750	C₂×C₄	#99×C₄₁	1	4	yes	complemented
751	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
752	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
753	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
754	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
755	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
756	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
757	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
758	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
759	C₂²	—	2	4	no	—
760	C₂²	—	2	4	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	8	4	no	—
789	C₂²	C₂×#99×C₄₁	1	2	yes	—
790	C₂²	C₄₁×#410	1	2	yes	—
791	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
792	C₂²	C₄₁×#520	1	2	yes	—
793	C₂²	C₄₁×#535	1	1	yes	characteristic
794	C₂²	C₄₁×#536	1	1	yes	characteristic
795	C₂²	C₄₁×#537	1	2	yes	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	1	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₄	—	8	4	no	—
806	C₄	—	8	4	no	—
807	C₄	C₂×#99×C₄₁	1	2	yes	—
808	C₄	C₂×#99×C₄₁	1	2	yes	—
809	C₂	—	2	1	no	—
810	C₂	—	2	2	no	—
811	C₂	—	2	1	no	—
812	C₂	—	2	2	no	—
813	C₂	—	2	2	no	—
814	C₂	—	2	2	no	—
815	C₂	—	4	1	no	—
816	C₂	—	4	1	no	—
817	C₂	—	8	2	no	—
818	C₂	C₄₁×#2311	1	1	yes	characteristic
819	C₂	C₂²×#99×C₄₁	1	1	yes	characteristic
820	C₂	C₂×C₄₁×#410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂⁴	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#525	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂⁴×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2280	C₂	semidirect
3. C₂×C₄₁×#380	C₂	semidirect
4. C₄₁×#1996	C₂	semidirect
5. C₄₁×#1964	C₂	semidirect
6. C₄₁×#1898	C₂	semidirect
7. C₄₁×#1799	C₂	semidirect
8. C₂²×#41×C₄₁	C₄	semidirect
18. C₂×#123×C₄₁	C₄	semidirect
19. C₂×C₂²⋊Q₈×C₄₁	C₄	semidirect
21. C₂×#121×C₄₁	C₄	semidirect
24. C₂×C₄×D₄×C₄₁	C₄	semidirect
27. C₂×#117×C₄₁	C₄	semidirect
49. C₂²×Q₈×C₄₁	C₂×C₄	semidirect
52. C₂²×D₄×C₄₁	C₂×C₄	semidirect
60. C₂³×C₄×C₄₁	C₂×C₄	semidirect
112. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
113. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
114. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
115. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
122. C₂×C₂²⋊C₄×C₄₁	C₂×C₄	semidirect
123. C₂×C₂²⋊C₄×C₄₁	C₂×C₄	semidirect
128. C₂×C₄²×C₄₁	C₂×C₄	semidirect
339. C₂×C₄×C₄₁	#99	semidirect
348. #21874	C₄₁	direct (N × H)
400. #2280	C₂×C₄₁	semidirect
401. C₂×#380	C₂×C₄₁	semidirect
402. #1996	C₂×C₄₁	semidirect
403. #1964	C₂×C₄₁	semidirect
404. #1898	C₂×C₄₁	semidirect
405. #1799	C₂×C₄₁	semidirect
418. C₂²×#41	C₄×C₄₁	semidirect
428. C₂×#123	C₄×C₄₁	semidirect
429. C₂×C₂²⋊Q₈	C₄×C₄₁	semidirect
431. C₂×#121	C₄×C₄₁	semidirect
434. C₂×C₄×D₄	C₄×C₄₁	semidirect
437. C₂×#117	C₄×C₄₁	semidirect
453. C₄₁	#21874	direct (N × H)
460. C₂²×Q₈	C₂×C₄×C₄₁	semidirect
463. C₂²×D₄	C₂×C₄×C₄₁	semidirect
471. C₂³×C₄	C₂×C₄×C₄₁	semidirect
523. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
524. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
525. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
526. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
533. C₂×C₂²⋊C₄	C₂×C₄×C₄₁	semidirect
534. C₂×C₂²⋊C₄	C₂×C₄×C₄₁	semidirect
539. C₂×C₄²	C₂×C₄×C₄₁	semidirect
750. C₂×C₄	#99×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×#525	2
C₄₁×#2280	2
C₂×C₄₁×#380	2
C₄₁×#1996	2
C₄₁×#1964	2
C₄₁×#1898	2
C₄₁×#1799	2
#21874	41

Subgroups — C41×#21874 #23798075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21874 #23798075