Subgroups — C₄₁×#61208 #23837409

Order 10496.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3326	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3322	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3321	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3319	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3308	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3306	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3301	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3297	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3058	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#3010	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3008	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic, complemented
31	C₄₁×#559	—	2	1	no	—
32	C₄₁×#559	—	2	1	no	—
33	C₄₁×#556	—	2	1	no	—
34	C₄₁×#555	C₂²	1	2	yes	complemented
35	C₄₁×#553	C₂²	1	2	yes	complemented
36	C₄₁×#553	C₂²	1	2	yes	complemented
37	C₄₁×#550	—	2	1	no	—
38	C₄₁×#548	C₂²	1	2	yes	complemented
39	C₄₁×#548	C₂²	1	2	yes	complemented
40	C₄₁×#547	C₂²	1	2	yes	complemented
41	C₄₁×#546	—	2	2	no	—
42	C₄₁×#546	—	2	2	no	—
43	C₄₁×#546	C₂²	1	2	yes	complemented
44	C₄₁×#546	C₂²	1	2	yes	complemented
45	C₄₁×#538	—	2	2	no	—
46	C₄₁×#536	—	2	1	no	—
47	C₄₁×#536	C₂²	1	1	yes	characteristic
48	C₄₁×#535	—	2	1	no	—
49	C₄₁×#535	C₂²	1	1	yes	characteristic
50	C₄₁×#535	C₂²	1	1	yes	characteristic
51	C₄₁×#535	C₂²	1	1	yes	characteristic, complemented
52	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
53	C₄₁×#532	—	2	1	no	—
54	C₄₁×#532	C₂²	1	1	yes	characteristic
55	C₂×#124×C₄₁	—	2	1	no	—
56	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
57	C₄₁×#525	—	2	2	no	—
58	C₄₁×#520	C₂²	1	1	yes	characteristic
59	C₄₁×#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
62	C₄₁×#489	C₂²	1	2	yes	complemented
63	C₄₁×#489	C₂²	1	2	yes	complemented
64	C₄₁×#488	C₂²	1	2	yes	complemented
65	C₄₁×#488	C₂²	1	2	yes	complemented
66	C₄₁×#485	C₂²	1	2	yes	complemented
67	C₄₁×#485	C₂²	1	2	yes	complemented
68	C₄₁×#484	C₂²	1	2	yes	complemented
69	C₄₁×#483	C₂²	1	2	yes	complemented
70	C₄₁×#482	C₂²	1	2	yes	complemented
71	C₄₁×#482	C₂²	1	2	yes	complemented
72	C₄₁×#481	C₂²	1	2	yes	complemented
73	C₄₁×#480	C₂²	1	2	yes	complemented
74	C₄₁×#479	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#479	C₂²	1	1	yes	characteristic, complemented
76	C₄₁×#478	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#478	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
79	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
80	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
81	C₄₁×#474	C₂²	1	1	yes	characteristic, complemented
82	C₄₁×#469	C₂²	1	2	yes	complemented
83	C₄₁×#469	C₂²	1	2	yes	complemented
84	C₄₁×#468	C₂²	1	2	yes	complemented
85	C₄₁×#468	C₂²	1	2	yes	complemented
86	C₄₁×#466	C₂²	1	2	yes	complemented
87	C₄₁×#466	C₂²	1	2	yes	complemented
88	C₄₁×#465	C₂²	1	2	yes	complemented
89	C₄₁×#465	C₂²	1	2	yes	complemented
90	C₄₁×#463	C₂²	1	2	yes	complemented
91	C₄₁×#463	C₂²	1	2	yes	complemented
92	C₄₁×#463	C₂²	1	2	yes	complemented
93	C₄₁×#463	C₂²	1	2	yes	complemented
94	C₄₁×#449	C₂²	1	2	yes	—
95	C₄₁×#449	C₂²	1	2	yes	—
96	C₄₁×#449	C₂²	1	2	yes	complemented
97	C₄₁×#449	C₂²	1	2	yes	complemented
98	C₄₁×#448	C₂²	1	2	yes	complemented
99	C₄₁×#448	C₂²	1	2	yes	complemented
100	C₄₁×#447	C₂²	1	2	yes	—
101	C₄₁×#447	C₂²	1	2	yes	—
102	C₄₁×#442	C₂²	1	2	yes	complemented
103	C₄₁×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
105	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
106	C₄₁×#436	C₂²	1	2	yes	complemented
107	C₄₁×#435	C₂²	1	2	yes	complemented
108	C₄₁×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
110	C₄₁×#428	C₂²	1	1	yes	characteristic, complemented
111	C₄₁×#427	C₂²	1	1	yes	characteristic, complemented
112	C₄₁×#427	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
114	C₄₁×#419	C₂²	1	1	yes	characteristic, complemented
115	C₄₁×#419	C₂²	1	2	yes	complemented
116	C₄₁×#419	C₂²	1	1	yes	characteristic, complemented
117	C₄₁×#418	C₂²	1	1	yes	characteristic
118	C₄₁×#418	C₂²	1	1	yes	characteristic
119	C₄₁×#418	C₂²	1	1	yes	characteristic, complemented
120	C₄₁×#418	C₂²	1	2	yes	complemented
121	C₄₁×#417	C₂²	1	1	yes	characteristic
122	C₄₁×#417	C₂²	1	2	yes	complemented
123	C₄₁×#417	C₂²	1	2	yes	complemented
124	C₄₁×#416	C₂²	1	1	yes	characteristic
125	C₄₁×#416	C₂²	1	1	yes	characteristic
126	C₄₁×#416	C₂²	1	2	yes	complemented
127	C₄₁×#416	C₂²	1	2	yes	complemented
128	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
129	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
131	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
132	C₄₁×#408	C₂²	1	1	yes	characteristic
133	C₄₁×#408	C₂²	1	1	yes	characteristic, complemented
134	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴×C₄₁	—	2	4	no	—
136	2₋¹⁺⁴×C₄₁	—	4	2	no	—
137	H(5,𝔽₂)×C₄₁	—	2	4	no	—
138	H(5,𝔽₂)×C₄₁	—	4	2	no	—
139	C₂×#41×C₄₁	—	2	1	no	—
140	C₂×#41×C₄₁	—	2	1	no	—
141	C₂×#41×C₄₁	—	2	2	no	—
142	C₂×#41×C₄₁	—	2	2	no	—
143	C₂×#41×C₄₁	C₂³	1	2	yes	—
144	C₂×#41×C₄₁	C₂³	1	2	yes	—
145	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
146	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
147	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₄₁	—	2	1	no	—
149	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
151	C₂²×D₄×C₄₁	—	2	1	no	—
152	C₂²×D₄×C₄₁	—	2	2	no	—
153	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
156	C₂³×C₄×C₄₁	—	2	1	no	—
157	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
158	C₂×SD₁₆×C₄₁	—	4	2	no	—
159	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
162	C₂×D₈×C₄₁	—	4	2	no	—
163	C₂×D₈×C₄₁	C₂³	1	2	yes	—
164	C₂×D₈×C₄₁	C₂³	1	2	yes	—
165	C₂×D₈×C₄₁	C₂³	1	2	yes	—
166	#131×C₄₁	—	4	2	no	—
167	#131×C₄₁	—	4	2	no	—
168	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
171	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
172	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
175	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
176	C₄⋊Q₈×C₄₁	—	2	1	no	—
177	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
178	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
180	#127×C₄₁	—	2	1	no	—
181	#127×C₄₁	—	2	1	no	—
182	#127×C₄₁	—	2	1	no	—
183	#127×C₄₁	D₄	1	1	yes	characteristic
184	#126×C₄₁	—	2	2	no	—
185	#126×C₄₁	—	2	2	no	—
186	#125×C₄₁	C₂³	1	1	yes	characteristic
187	#125×C₄₁	C₂³	1	1	yes	characteristic
188	#124×C₄₁	—	2	1	no	—
189	#124×C₄₁	—	2	1	no	—
190	#124×C₄₁	—	2	1	no	—
191	#124×C₄₁	—	2	1	no	—
192	#124×C₄₁	—	2	2	no	—
193	#124×C₄₁	—	2	2	no	—
194	#124×C₄₁	—	2	2	no	—
195	#124×C₄₁	—	2	2	no	—
196	#124×C₄₁	—	2	1	no	—
197	#124×C₄₁	—	2	1	no	—
198	#124×C₄₁	D₄	1	1	yes	characteristic
199	#124×C₄₁	D₄	1	1	yes	characteristic
200	#124×C₄₁	C₂³	1	2	yes	—
201	#124×C₄₁	C₂³	1	2	yes	—
202	#123×C₄₁	—	2	2	no	—
203	#123×C₄₁	—	2	2	no	—
204	#123×C₄₁	—	2	2	no	—
205	#123×C₄₁	—	2	2	no	—
206	#123×C₄₁	—	2	2	no	—
207	#123×C₄₁	—	2	2	no	—
208	#123×C₄₁	—	2	2	no	—
209	C₂²⋊Q₈×C₄₁	—	2	1	no	—
210	C₂²⋊Q₈×C₄₁	—	2	1	no	—
211	C₂²⋊Q₈×C₄₁	—	2	2	no	—
212	C₂²⋊Q₈×C₄₁	—	2	2	no	—
213	C₂²⋊Q₈×C₄₁	—	2	2	no	—
214	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
216	#121×C₄₁	—	2	2	no	—
217	#121×C₄₁	—	2	2	no	—
218	#121×C₄₁	—	2	2	no	—
219	#121×C₄₁	—	2	2	no	—
220	#121×C₄₁	—	2	2	no	—
221	#121×C₄₁	—	2	2	no	—
222	#121×C₄₁	—	2	2	no	—
223	#121×C₄₁	D₄	1	2	yes	—
224	#121×C₄₁	D₄	1	2	yes	—
225	#121×C₄₁	C₂³	1	2	yes	—
226	#121×C₄₁	C₂³	1	2	yes	—
227	#121×C₄₁	C₂³	1	2	yes	—
228	#121×C₄₁	C₂³	1	2	yes	—
229	#121×C₄₁	C₂³	1	2	yes	—
230	#121×C₄₁	C₂³	1	2	yes	—
231	#120×C₄₁	—	2	2	no	—
232	#120×C₄₁	—	2	2	no	—
233	#120×C₄₁	—	2	2	no	—
234	#120×C₄₁	—	2	2	no	—
235	#120×C₄₁	—	2	2	no	—
236	C₄×Q₈×C₄₁	—	2	1	no	—
237	C₄×Q₈×C₄₁	—	2	1	no	—
238	C₄×Q₈×C₄₁	—	2	1	no	—
239	C₄×Q₈×C₄₁	—	2	1	no	—
240	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₄₁	—	2	2	no	—
243	C₄×D₄×C₄₁	—	2	1	no	—
244	C₄×D₄×C₄₁	—	2	2	no	—
245	C₄×D₄×C₄₁	—	2	1	no	—
246	C₄×D₄×C₄₁	—	2	1	no	—
247	C₄×D₄×C₄₁	—	2	1	no	—
248	C₄×D₄×C₄₁	—	2	2	no	—
249	C₄×D₄×C₄₁	—	2	2	no	—
250	C₄×D₄×C₄₁	—	2	2	no	—
251	C₄×D₄×C₄₁	—	2	2	no	—
252	C₄×D₄×C₄₁	—	2	1	no	—
253	C₄×D₄×C₄₁	—	2	1	no	—
254	C₄×D₄×C₄₁	C₂³	1	2	yes	—
255	C₄×D₄×C₄₁	C₂³	1	2	yes	—
256	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₄₁	C₂³	1	2	yes	—
259	C₄×D₄×C₄₁	C₂³	1	2	yes	—
260	#117×C₄₁	—	2	2	no	—
261	#117×C₄₁	—	2	1	no	—
262	#117×C₄₁	C₂³	1	1	yes	characteristic
263	#117×C₄₁	C₂³	1	1	yes	characteristic
264	#117×C₄₁	C₂³	1	2	yes	—
265	#117×C₄₁	C₂³	1	1	yes	characteristic
266	#117×C₄₁	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
273	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
275	C₂×C₄²×C₄₁	—	2	1	no	—
276	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
277	#107×C₄₁	C₂³	1	1	yes	characteristic
278	#107×C₄₁	C₂³	1	1	yes	characteristic
279	#107×C₄₁	C₂³	1	1	yes	characteristic
280	#107×C₄₁	C₂³	1	1	yes	characteristic
281	#107×C₄₁	C₂³	1	2	yes	—
282	#106×C₄₁	C₂³	1	1	yes	characteristic
283	#106×C₄₁	C₂³	1	1	yes	characteristic
284	#106×C₄₁	C₂³	1	1	yes	characteristic
285	#106×C₄₁	C₂³	1	1	yes	characteristic
286	#106×C₄₁	C₂³	1	2	yes	—
287	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
291	#103×C₄₁	C₂³	1	1	yes	characteristic
292	#103×C₄₁	C₂³	1	2	yes	—
293	#103×C₄₁	C₂³	1	2	yes	—
294	#103×C₄₁	C₂³	1	2	yes	—
295	#103×C₄₁	C₂³	1	2	yes	—
296	#103×C₄₁	C₂³	1	1	yes	characteristic
297	#103×C₄₁	C₂³	1	1	yes	characteristic
298	#103×C₄₁	C₂³	1	1	yes	characteristic
299	#103×C₄₁	C₂³	1	2	yes	—
300	#103×C₄₁	C₂³	1	2	yes	—
301	#103×C₄₁	C₂³	1	2	yes	—
302	#102×C₄₁	C₂³	1	2	yes	—
303	#102×C₄₁	C₂³	1	2	yes	—
304	#102×C₄₁	C₂³	1	1	yes	characteristic
305	#102×C₄₁	C₂³	1	2	yes	—
306	#102×C₄₁	C₂³	1	2	yes	—
307	#102×C₄₁	C₂³	1	1	yes	characteristic
308	#102×C₄₁	C₂³	1	1	yes	characteristic
309	#102×C₄₁	C₂³	1	1	yes	characteristic
310	#102×C₄₁	C₂³	1	2	yes	—
311	#102×C₄₁	C₂³	1	2	yes	—
312	#102×C₄₁	C₂³	1	2	yes	—
313	#102×C₄₁	C₂³	1	2	yes	—
314	#102×C₄₁	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
319	#97×C₄₁	C₂³	1	2	yes	—
320	C₄×C₈×C₄₁	C₂³	1	2	yes	—
321	C₂⁴×C₄₁	—	2	2	no	—
322	C₂⁴×C₄₁	—	2	1	no	—
323	C₂⁴×C₄₁	—	2	1	no	—
324	#41×C₄₁	—	2	2	no	—
325	#41×C₄₁	—	2	2	no	—
326	#41×C₄₁	—	2	2	no	—
327	#41×C₄₁	—	2	2	no	—
328	#41×C₄₁	—	2	2	no	—
329	#41×C₄₁	—	2	4	no	—
330	#41×C₄₁	—	2	4	no	—
331	#41×C₄₁	—	4	2	no	—
332	#41×C₄₁	—	4	2	no	—
333	#41×C₄₁	—	4	4	no	—
334	#41×C₄₁	—	4	4	no	—
335	#41×C₄₁	—	4	8	no	—
336	#41×C₄₁	—	8	4	no	—
337	#41×C₄₁	#41	1	4	yes	complemented
338	C₂×Q₈×C₄₁	—	2	1	no	—
339	C₂×Q₈×C₄₁	—	2	2	no	—
340	C₂×Q₈×C₄₁	—	2	1	no	—
341	C₂×Q₈×C₄₁	—	2	1	no	—
342	C₂×Q₈×C₄₁	—	2	4	no	—
343	C₂×Q₈×C₄₁	—	2	2	no	—
344	C₂×Q₈×C₄₁	—	2	2	no	—
345	C₂×Q₈×C₄₁	—	4	2	no	—
346	C₂×Q₈×C₄₁	—	4	4	no	—
347	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
348	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
349	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
350	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₄₁	—	2	1	no	—
352	C₂×D₄×C₄₁	—	2	4	no	—
353	C₂×D₄×C₄₁	—	2	2	no	—
354	C₂×D₄×C₄₁	—	2	2	no	—
355	C₂×D₄×C₄₁	—	2	2	no	—
356	C₂×D₄×C₄₁	—	2	2	no	—
357	C₂×D₄×C₄₁	—	2	2	no	—
358	C₂×D₄×C₄₁	—	2	2	no	—
359	C₂×D₄×C₄₁	—	2	2	no	—
360	C₂×D₄×C₄₁	—	2	2	no	—
361	C₂×D₄×C₄₁	—	2	1	no	—
362	C₂×D₄×C₄₁	—	2	2	no	—
363	C₂×D₄×C₄₁	—	2	1	no	—
364	C₂×D₄×C₄₁	—	2	2	no	—
365	C₂×D₄×C₄₁	—	2	2	no	—
366	C₂×D₄×C₄₁	—	2	2	no	—
367	C₂×D₄×C₄₁	—	2	2	no	—
368	C₂×D₄×C₄₁	—	4	2	no	—
369	C₂×D₄×C₄₁	—	4	4	no	—
370	C₂×D₄×C₄₁	—	4	8	no	—
371	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
376	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
378	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
379	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₄₁	—	2	1	no	—
381	C₂²×C₄×C₄₁	—	2	1	no	—
382	C₂²×C₄×C₄₁	—	2	2	no	—
383	C₂²×C₄×C₄₁	—	2	1	no	—
384	C₂²×C₄×C₄₁	—	2	2	no	—
385	C₂²×C₄×C₄₁	—	2	2	no	—
386	C₂²×C₄×C₄₁	—	2	2	no	—
387	C₂²×C₄×C₄₁	—	2	2	no	—
388	C₂²×C₄×C₄₁	—	2	2	no	—
389	C₂²×C₄×C₄₁	—	2	1	no	—
390	C₂²×C₄×C₄₁	—	2	1	no	—
391	C₂²×C₄×C₄₁	—	2	2	no	—
392	C₂²×C₄×C₄₁	—	8	2	no	—
393	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
398	SD₁₆×C₄₁	—	2	4	no	—
399	SD₁₆×C₄₁	—	4	2	no	—
400	SD₁₆×C₄₁	—	4	2	no	—
401	D₈×C₄₁	—	2	4	no	—
402	D₈×C₄₁	—	4	2	no	—
403	D₈×C₄₁	—	4	2	no	—
404	M₁₆×C₄₁	—	2	2	no	—
405	M₁₆×C₄₁	—	2	2	no	—
406	M₁₆×C₄₁	—	4	2	no	—
407	M₁₆×C₄₁	—	4	2	no	—
408	C₂×C₈×C₄₁	—	2	2	no	—
409	C₂×C₈×C₄₁	—	2	2	no	—
410	C₂×C₈×C₄₁	—	4	2	no	—
411	C₂×C₈×C₄₁	—	4	2	no	—
412	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
413	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
414	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₄₁	—	2	1	no	—
419	C₄⋊C₄×C₄₁	—	2	2	no	—
420	C₄⋊C₄×C₄₁	—	2	2	no	—
421	C₄⋊C₄×C₄₁	—	2	1	no	—
422	C₄⋊C₄×C₄₁	—	2	1	no	—
423	C₄⋊C₄×C₄₁	—	2	1	no	—
424	C₄⋊C₄×C₄₁	—	2	1	no	—
425	C₄⋊C₄×C₄₁	—	2	1	no	—
426	C₄⋊C₄×C₄₁	—	2	2	no	—
427	C₄⋊C₄×C₄₁	—	2	2	no	—
428	C₄⋊C₄×C₄₁	—	2	1	no	—
429	C₄⋊C₄×C₄₁	—	2	1	no	—
430	C₄⋊C₄×C₄₁	—	2	1	no	—
431	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
432	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
434	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₄₁	—	2	2	no	—
441	C₂²⋊C₄×C₄₁	—	2	2	no	—
442	C₂²⋊C₄×C₄₁	—	2	1	no	—
443	C₂²⋊C₄×C₄₁	—	2	1	no	—
444	C₂²⋊C₄×C₄₁	—	2	1	no	—
445	C₂²⋊C₄×C₄₁	—	2	2	no	—
446	C₂²⋊C₄×C₄₁	—	2	2	no	—
447	C₂²⋊C₄×C₄₁	—	2	2	no	—
448	C₂²⋊C₄×C₄₁	—	2	2	no	—
449	C₂²⋊C₄×C₄₁	—	2	2	no	—
450	C₂²⋊C₄×C₄₁	—	2	2	no	—
451	C₂²⋊C₄×C₄₁	—	2	2	no	—
452	C₂²⋊C₄×C₄₁	—	2	2	no	—
453	C₂²⋊C₄×C₄₁	—	2	2	no	—
454	C₂²⋊C₄×C₄₁	—	2	2	no	—
455	C₂²⋊C₄×C₄₁	—	2	1	no	—
456	C₂²⋊C₄×C₄₁	—	2	1	no	—
457	C₂²⋊C₄×C₄₁	—	2	2	no	—
458	C₂²⋊C₄×C₄₁	—	2	2	no	—
459	C₂²⋊C₄×C₄₁	—	2	2	no	—
460	C₂²⋊C₄×C₄₁	—	2	2	no	—
461	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
465	C₄²×C₄₁	—	2	1	no	—
466	C₄²×C₄₁	—	2	1	no	—
467	C₄²×C₄₁	—	2	1	no	—
468	C₄²×C₄₁	—	2	2	no	—
469	C₄²×C₄₁	—	2	2	no	—
470	C₄²×C₄₁	—	2	1	no	—
471	C₄²×C₄₁	—	2	1	no	—
472	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
475	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
476	C₂³×C₄₁	—	2	1	no	—
477	C₂³×C₄₁	—	2	2	no	—
478	C₂³×C₄₁	—	2	2	no	—
479	C₂³×C₄₁	—	4	4	no	—
480	C₂³×C₄₁	—	4	2	no	—
481	C₂³×C₄₁	—	4	2	no	—
482	C₂³×C₄₁	—	8	1	no	—
483	C₂³×C₄₁	—	8	1	no	—
484	C₂³×C₄₁	—	8	1	no	—
485	C₂³×C₄₁	—	8	1	no	—
486	C₂³×C₄₁	—	8	2	no	—
487	C₂³×C₄₁	—	8	2	no	—
488	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
489	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
490	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
491	Q₈×C₄₁	—	2	2	no	—
492	Q₈×C₄₁	—	2	2	no	—
493	Q₈×C₄₁	—	2	1	no	—
494	Q₈×C₄₁	—	2	2	no	—
495	Q₈×C₄₁	—	2	2	no	—
496	Q₈×C₄₁	—	4	4	no	—
497	Q₈×C₄₁	—	4	2	no	—
498	Q₈×C₄₁	—	4	2	no	—
499	Q₈×C₄₁	—	8	1	no	—
500	Q₈×C₄₁	C₂×#41	1	2	yes	—
501	D₄×C₄₁	—	2	4	no	—
502	D₄×C₄₁	—	2	4	no	—
503	D₄×C₄₁	—	2	4	no	—
504	D₄×C₄₁	—	2	2	no	—
505	D₄×C₄₁	—	2	2	no	—
506	D₄×C₄₁	—	2	2	no	—
507	D₄×C₄₁	—	2	2	no	—
508	D₄×C₄₁	—	2	1	no	—
509	D₄×C₄₁	—	2	2	no	—
510	D₄×C₄₁	—	2	2	no	—
511	D₄×C₄₁	—	4	2	no	—
512	D₄×C₄₁	—	4	2	no	—
513	D₄×C₄₁	—	4	4	no	—
514	D₄×C₄₁	—	4	4	no	—
515	D₄×C₄₁	—	4	4	no	—
516	D₄×C₄₁	—	4	2	no	—
517	D₄×C₄₁	—	4	2	no	—
518	D₄×C₄₁	—	8	2	no	—
519	D₄×C₄₁	—	8	2	no	—
520	D₄×C₄₁	—	8	2	no	—
521	D₄×C₄₁	—	8	2	no	—
522	D₄×C₄₁	—	8	2	no	—
523	D₄×C₄₁	—	8	2	no	—
524	D₄×C₄₁	C₂×#41	1	2	yes	—
525	C₂×C₄×C₄₁	—	2	1	no	—
526	C₂×C₄×C₄₁	—	2	4	no	—
527	C₂×C₄×C₄₁	—	2	2	no	—
528	C₂×C₄×C₄₁	—	2	2	no	—
529	C₂×C₄×C₄₁	—	2	2	no	—
530	C₂×C₄×C₄₁	—	2	2	no	—
531	C₂×C₄×C₄₁	—	2	1	no	—
532	C₂×C₄×C₄₁	—	2	1	no	—
533	C₂×C₄×C₄₁	—	2	1	no	—
534	C₂×C₄×C₄₁	—	2	1	no	—
535	C₂×C₄×C₄₁	—	2	2	no	—
536	C₂×C₄×C₄₁	—	2	1	no	—
537	C₂×C₄×C₄₁	—	2	1	no	—
538	C₂×C₄×C₄₁	—	2	2	no	—
539	C₂×C₄×C₄₁	—	4	1	no	—
540	C₂×C₄×C₄₁	—	4	1	no	—
541	C₂×C₄×C₄₁	—	4	4	no	—
542	C₂×C₄×C₄₁	—	4	4	no	—
543	C₂×C₄×C₄₁	—	4	4	no	—
544	C₂×C₄×C₄₁	—	4	4	no	—
545	C₂×C₄×C₄₁	—	4	2	no	—
546	C₂×C₄×C₄₁	—	8	1	no	—
547	C₂×C₄×C₄₁	—	8	1	no	—
548	C₂×C₄×C₄₁	—	8	2	no	—
549	C₂×C₄×C₄₁	—	8	1	no	—
550	C₂×C₄×C₄₁	—	8	2	no	—
551	C₂×C₄×C₄₁	—	8	2	no	—
552	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
560	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
561	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
562	C₈×C₄₁	—	2	2	no	—
563	C₈×C₄₁	—	2	1	no	—
564	C₈×C₄₁	—	2	1	no	—
565	C₈×C₄₁	—	2	1	no	—
566	C₈×C₄₁	—	2	1	no	—
567	C₈×C₄₁	—	2	2	no	—
568	#61208	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
569	C₂²×C₄₁	—	2	1	no	—
570	C₂²×C₄₁	—	2	1	no	—
571	C₂²×C₄₁	—	2	2	no	—
572	C₂²×C₄₁	—	2	2	no	—
573	C₂²×C₄₁	—	2	2	no	—
574	C₂²×C₄₁	—	2	2	no	—
575	C₂²×C₄₁	—	2	2	no	—
576	C₂²×C₄₁	—	2	2	no	—
577	C₂²×C₄₁	—	2	2	no	—
578	C₂²×C₄₁	—	4	1	no	—
579	C₂²×C₄₁	—	4	1	no	—
580	C₂²×C₄₁	—	4	2	no	—
581	C₂²×C₄₁	—	4	2	no	—
582	C₂²×C₄₁	—	4	2	no	—
583	C₂²×C₄₁	—	4	2	no	—
584	C₂²×C₄₁	—	4	2	no	—
585	C₂²×C₄₁	—	4	2	no	—
586	C₂²×C₄₁	—	8	4	no	—
587	C₂²×C₄₁	—	16	2	no	—
588	C₂²×C₄₁	—	16	4	no	—
589	C₂²×C₄₁	#546	1	2	yes	—
590	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
591	C₄×C₄₁	—	2	1	no	—
592	C₄×C₄₁	—	2	1	no	—
593	C₄×C₄₁	—	2	1	no	—
594	C₄×C₄₁	—	2	1	no	—
595	C₄×C₄₁	—	2	2	no	—
596	C₄×C₄₁	—	2	2	no	—
597	C₄×C₄₁	—	2	2	no	—
598	C₄×C₄₁	—	4	1	no	—
599	C₄×C₄₁	—	4	1	no	—
600	C₄×C₄₁	—	4	1	no	—
601	C₄×C₄₁	—	4	2	no	—
602	C₄×C₄₁	—	4	1	no	—
603	C₄×C₄₁	—	4	1	no	—
604	C₄×C₄₁	—	4	1	no	—
605	C₄×C₄₁	—	4	2	no	—
606	C₄×C₄₁	#546	1	2	yes	—
607	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
608	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
609	#3506	C₂×C₄₁	1	1	yes	characteristic, complemented
610	#3500	C₂×C₄₁	1	1	yes	characteristic, complemented
611	#3326	C₂×C₄₁	1	2	yes	complemented
612	#3322	C₂×C₄₁	1	2	yes	complemented
613	#3321	C₂×C₄₁	1	2	yes	complemented
614	#3319	C₂×C₄₁	1	2	yes	complemented
615	#3308	C₂×C₄₁	1	2	yes	complemented
616	#3306	C₂×C₄₁	1	2	yes	complemented
617	#3301	C₂×C₄₁	1	2	yes	complemented
618	#3297	C₂×C₄₁	1	2	yes	complemented
619	#3140	C₂×C₄₁	1	1	yes	characteristic, complemented
620	#3097	C₂×C₄₁	1	1	yes	characteristic, complemented
621	#3096	C₂×C₄₁	1	1	yes	characteristic, complemented
622	#3076	C₂×C₄₁	1	1	yes	characteristic, complemented
623	#3058	C₂×C₄₁	1	1	yes	characteristic, complemented
624	#3057	C₂×C₄₁	1	1	yes	characteristic, complemented
625	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
626	#3010	C₂×C₄₁	1	1	yes	characteristic, complemented
627	#3008	C₂×C₄₁	1	1	yes	characteristic, complemented
628	C₄×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic, complemented
629	#2935	C₂×C₄₁	1	1	yes	characteristic, complemented
630	#2898	C₂×C₄₁	1	1	yes	characteristic, complemented
631	#2897	C₂×C₄₁	1	1	yes	characteristic, complemented
632	C₂×C₄₁	—	2	2	no	—
633	C₂×C₄₁	—	4	2	no	—
634	C₂×C₄₁	—	4	2	no	—
635	C₂×C₄₁	—	4	2	no	—
636	C₂×C₄₁	—	8	2	no	—
637	C₂×C₄₁	—	8	2	no	—
638	C₂×C₄₁	C₂×#546	1	1	yes	characteristic
639	C₂×C₄₁	#3584	1	1	yes	characteristic
640	C₂×C₄₁	#3585	1	1	yes	characteristic
641	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	1	yes	characteristic
642	C₂×H(5,𝔽₂)	C₂²×C₄₁	1	1	yes	characteristic
643	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	1	yes	characteristic
644	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
645	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
646	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
647	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic, complemented
648	#559	—	2	1	no	—
649	#559	—	2	1	no	—
650	#556	—	2	1	no	—
651	#555	C₂²×C₄₁	1	2	yes	complemented
652	#553	C₂²×C₄₁	1	2	yes	complemented
653	#553	C₂²×C₄₁	1	2	yes	complemented
654	#550	—	2	1	no	—
655	#548	C₂²×C₄₁	1	2	yes	complemented
656	#548	C₂²×C₄₁	1	2	yes	complemented
657	#547	C₂²×C₄₁	1	2	yes	complemented
658	#546	—	2	2	no	—
659	#546	—	2	2	no	—
660	#546	C₂²×C₄₁	1	2	yes	complemented
661	#546	C₂²×C₄₁	1	2	yes	complemented
662	#538	—	2	2	no	—
663	#536	—	2	1	no	—
664	#536	C₂²×C₄₁	1	1	yes	characteristic
665	#535	—	2	1	no	—
666	#535	C₂²×C₄₁	1	1	yes	characteristic
667	#535	C₂²×C₄₁	1	1	yes	characteristic
668	#535	C₂²×C₄₁	1	1	yes	characteristic, complemented
669	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
670	#532	—	2	1	no	—
671	#532	C₂²×C₄₁	1	1	yes	characteristic
672	C₂×#124	—	2	1	no	—
673	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
674	#525	—	2	2	no	—
675	#520	C₂²×C₄₁	1	1	yes	characteristic
676	#520	C₂²×C₄₁	1	1	yes	characteristic, complemented
677	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
678	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
679	#489	C₂²×C₄₁	1	2	yes	complemented
680	#489	C₂²×C₄₁	1	2	yes	complemented
681	#488	C₂²×C₄₁	1	2	yes	complemented
682	#488	C₂²×C₄₁	1	2	yes	complemented
683	#485	C₂²×C₄₁	1	2	yes	complemented
684	#485	C₂²×C₄₁	1	2	yes	complemented
685	#484	C₂²×C₄₁	1	2	yes	complemented
686	#483	C₂²×C₄₁	1	2	yes	complemented
687	#482	C₂²×C₄₁	1	2	yes	complemented
688	#482	C₂²×C₄₁	1	2	yes	complemented
689	#481	C₂²×C₄₁	1	2	yes	complemented
690	#480	C₂²×C₄₁	1	2	yes	complemented
691	#479	C₂²×C₄₁	1	1	yes	characteristic, complemented
692	#479	C₂²×C₄₁	1	1	yes	characteristic, complemented
693	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
694	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
695	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
696	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
697	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
698	#474	C₂²×C₄₁	1	1	yes	characteristic, complemented
699	#469	C₂²×C₄₁	1	2	yes	complemented
700	#469	C₂²×C₄₁	1	2	yes	complemented
701	#468	C₂²×C₄₁	1	2	yes	complemented
702	#468	C₂²×C₄₁	1	2	yes	complemented
703	#466	C₂²×C₄₁	1	2	yes	complemented
704	#466	C₂²×C₄₁	1	2	yes	complemented
705	#465	C₂²×C₄₁	1	2	yes	complemented
706	#465	C₂²×C₄₁	1	2	yes	complemented
707	#463	C₂²×C₄₁	1	2	yes	complemented
708	#463	C₂²×C₄₁	1	2	yes	complemented
709	#463	C₂²×C₄₁	1	2	yes	complemented
710	#463	C₂²×C₄₁	1	2	yes	complemented
711	#449	C₂²×C₄₁	1	2	yes	—
712	#449	C₂²×C₄₁	1	2	yes	—
713	#449	C₂²×C₄₁	1	2	yes	complemented
714	#449	C₂²×C₄₁	1	2	yes	complemented
715	#448	C₂²×C₄₁	1	2	yes	complemented
716	#448	C₂²×C₄₁	1	2	yes	complemented
717	#447	C₂²×C₄₁	1	2	yes	—
718	#447	C₂²×C₄₁	1	2	yes	—
719	#442	C₂²×C₄₁	1	2	yes	complemented
720	#440	C₂²×C₄₁	1	2	yes	complemented
721	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
722	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
723	#436	C₂²×C₄₁	1	2	yes	complemented
724	#435	C₂²×C₄₁	1	2	yes	complemented
725	#435	C₂²×C₄₁	1	2	yes	complemented
726	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
727	#428	C₂²×C₄₁	1	1	yes	characteristic, complemented
728	#427	C₂²×C₄₁	1	1	yes	characteristic, complemented
729	#427	C₂²×C₄₁	1	1	yes	characteristic, complemented
730	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
731	#419	C₂²×C₄₁	1	1	yes	characteristic, complemented
732	#419	C₂²×C₄₁	1	1	yes	characteristic, complemented
733	#419	C₂²×C₄₁	1	2	yes	complemented
734	#418	C₂²×C₄₁	1	1	yes	characteristic
735	#418	C₂²×C₄₁	1	1	yes	characteristic
736	#418	C₂²×C₄₁	1	2	yes	complemented
737	#418	C₂²×C₄₁	1	1	yes	characteristic, complemented
738	#417	C₂²×C₄₁	1	1	yes	characteristic
739	#417	C₂²×C₄₁	1	2	yes	complemented
740	#417	C₂²×C₄₁	1	2	yes	complemented
741	#416	C₂²×C₄₁	1	1	yes	characteristic
742	#416	C₂²×C₄₁	1	1	yes	characteristic
743	#416	C₂²×C₄₁	1	2	yes	complemented
744	#416	C₂²×C₄₁	1	2	yes	complemented
745	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
746	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
747	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
748	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
749	#408	C₂²×C₄₁	1	1	yes	characteristic
750	#408	C₂²×C₄₁	1	1	yes	characteristic, complemented
751	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
752	C₄₁	#61208	1	1	yes	characteristic, direct product factor, Sylow
753	2₋¹⁺⁴	—	2	4	no	—
754	2₋¹⁺⁴	—	4	2	no	—
755	H(5,𝔽₂)	—	2	4	no	—
756	H(5,𝔽₂)	—	4	2	no	—
757	C₂×#41	—	2	1	no	—
758	C₂×#41	—	2	1	no	—
759	C₂×#41	—	2	2	no	—
760	C₂×#41	—	2	2	no	—
761	C₂×#41	C₂³×C₄₁	1	2	yes	—
762	C₂×#41	C₂³×C₄₁	1	2	yes	—
763	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
764	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
765	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
766	C₂²×Q₈	—	2	1	no	—
767	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
768	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
769	C₂²×D₄	—	2	1	no	—
770	C₂²×D₄	—	2	2	no	—
771	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
772	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
773	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
774	C₂³×C₄	—	2	1	no	—
775	AGL(1,ℤ/8)	—	2	4	no	—
776	C₂×SD₁₆	—	4	2	no	—
777	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
780	C₂×D₈	—	4	2	no	—
781	C₂×D₈	C₂³×C₄₁	1	2	yes	—
782	C₂×D₈	C₂³×C₄₁	1	2	yes	—
783	C₂×D₈	C₂³×C₄₁	1	2	yes	—
784	#131	—	4	2	no	—
785	#131	—	4	2	no	—
786	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
787	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
788	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
789	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
790	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
791	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
792	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
793	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
794	C₄⋊Q₈	—	2	1	no	—
795	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
796	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
797	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
798	#127	—	2	1	no	—
799	#127	—	2	1	no	—
800	#127	—	2	1	no	—
801	#127	D₄×C₄₁	1	1	yes	characteristic
802	#126	—	2	2	no	—
803	#126	—	2	2	no	—
804	#125	C₂³×C₄₁	1	1	yes	characteristic
805	#125	C₂³×C₄₁	1	1	yes	characteristic
806	#124	—	2	1	no	—
807	#124	—	2	1	no	—
808	#124	—	2	1	no	—
809	#124	—	2	1	no	—
810	#124	—	2	2	no	—
811	#124	—	2	2	no	—
812	#124	—	2	2	no	—
813	#124	—	2	2	no	—
814	#124	—	2	1	no	—
815	#124	—	2	1	no	—
816	#124	D₄×C₄₁	1	1	yes	characteristic
817	#124	D₄×C₄₁	1	1	yes	characteristic
818	#124	C₂³×C₄₁	1	2	yes	—
819	#124	C₂³×C₄₁	1	2	yes	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	#123	—	2	2	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	2	2	no	—
830	C₂²⋊Q₈	—	2	2	no	—
831	C₂²⋊Q₈	—	2	2	no	—
832	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	D₄×C₄₁	1	2	yes	—
842	#121	D₄×C₄₁	1	2	yes	—
843	#121	C₂³×C₄₁	1	2	yes	—
844	#121	C₂³×C₄₁	1	2	yes	—
845	#121	C₂³×C₄₁	1	2	yes	—
846	#121	C₂³×C₄₁	1	2	yes	—
847	#121	C₂³×C₄₁	1	2	yes	—
848	#121	C₂³×C₄₁	1	2	yes	—
849	#120	—	2	2	no	—
850	#120	—	2	2	no	—
851	#120	—	2	2	no	—
852	#120	—	2	2	no	—
853	#120	—	2	2	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	—	2	1	no	—
856	C₄×Q₈	—	2	1	no	—
857	C₄×Q₈	—	2	1	no	—
858	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
859	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	C₂³×C₄₁	1	2	yes	—
873	C₄×D₄	C₂³×C₄₁	1	2	yes	—
874	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
876	C₄×D₄	C₂³×C₄₁	1	2	yes	—
877	C₄×D₄	C₂³×C₄₁	1	2	yes	—
878	#117	—	2	2	no	—
879	#117	—	2	1	no	—
880	#117	C₂³×C₄₁	1	1	yes	characteristic
881	#117	C₂³×C₄₁	1	1	yes	characteristic
882	#117	C₂³×C₄₁	1	2	yes	—
883	#117	C₂³×C₄₁	1	1	yes	characteristic
884	#117	C₂³×C₄₁	1	2	yes	—
885	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
887	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
888	C₂×C₂²⋊C₄	—	2	1	no	—
889	C₂×C₂²⋊C₄	—	2	1	no	—
890	C₂×C₂²⋊C₄	—	2	1	no	—
891	C₂×C₂²⋊C₄	—	2	2	no	—
892	C₂×C₂²⋊C₄	—	2	2	no	—
893	C₂×C₄²	—	2	1	no	—
894	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
895	#107	C₂³×C₄₁	1	1	yes	characteristic
896	#107	C₂³×C₄₁	1	1	yes	characteristic
897	#107	C₂³×C₄₁	1	1	yes	characteristic
898	#107	C₂³×C₄₁	1	1	yes	characteristic
899	#107	C₂³×C₄₁	1	2	yes	—
900	#106	C₂³×C₄₁	1	1	yes	characteristic
901	#106	C₂³×C₄₁	1	1	yes	characteristic
902	#106	C₂³×C₄₁	1	1	yes	characteristic
903	#106	C₂³×C₄₁	1	1	yes	characteristic
904	#106	C₂³×C₄₁	1	2	yes	—
905	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
906	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
907	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
908	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
909	#103	C₂³×C₄₁	1	1	yes	characteristic
910	#103	C₂³×C₄₁	1	2	yes	—
911	#103	C₂³×C₄₁	1	2	yes	—
912	#103	C₂³×C₄₁	1	2	yes	—
913	#103	C₂³×C₄₁	1	2	yes	—
914	#103	C₂³×C₄₁	1	1	yes	characteristic
915	#103	C₂³×C₄₁	1	1	yes	characteristic
916	#103	C₂³×C₄₁	1	1	yes	characteristic
917	#103	C₂³×C₄₁	1	2	yes	—
918	#103	C₂³×C₄₁	1	2	yes	—
919	#103	C₂³×C₄₁	1	2	yes	—
920	#102	C₂³×C₄₁	1	2	yes	—
921	#102	C₂³×C₄₁	1	2	yes	—
922	#102	C₂³×C₄₁	1	1	yes	characteristic
923	#102	C₂³×C₄₁	1	2	yes	—
924	#102	C₂³×C₄₁	1	2	yes	—
925	#102	C₂³×C₄₁	1	1	yes	characteristic
926	#102	C₂³×C₄₁	1	1	yes	characteristic
927	#102	C₂³×C₄₁	1	1	yes	characteristic
928	#102	C₂³×C₄₁	1	2	yes	—
929	#102	C₂³×C₄₁	1	2	yes	—
930	#102	C₂³×C₄₁	1	2	yes	—
931	#102	C₂³×C₄₁	1	2	yes	—
932	#102	C₂³×C₄₁	1	2	yes	—
933	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
934	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
935	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
936	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
937	#97	C₂³×C₄₁	1	2	yes	—
938	C₄×C₈	C₂³×C₄₁	1	2	yes	—
939	C₂⁴	—	2	2	no	—
940	C₂⁴	—	2	1	no	—
941	C₂⁴	—	2	1	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	4	no	—
948	#41	—	2	4	no	—
949	#41	—	4	2	no	—
950	#41	—	4	2	no	—
951	#41	—	4	4	no	—
952	#41	—	4	4	no	—
953	#41	—	4	8	no	—
954	#41	—	8	4	no	—
955	#41	#41×C₄₁	1	4	yes	complemented
956	C₂×Q₈	—	2	1	no	—
957	C₂×Q₈	—	2	2	no	—
958	C₂×Q₈	—	2	1	no	—
959	C₂×Q₈	—	2	1	no	—
960	C₂×Q₈	—	2	4	no	—
961	C₂×Q₈	—	2	2	no	—
962	C₂×Q₈	—	2	2	no	—
963	C₂×Q₈	—	4	2	no	—
964	C₂×Q₈	—	4	4	no	—
965	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
966	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
967	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
968	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	2	4	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	4	2	no	—
987	C₂×D₄	—	4	4	no	—
988	C₂×D₄	—	4	8	no	—
989	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
990	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
991	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
992	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
993	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
994	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
995	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
996	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
997	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	8	2	no	—
1011	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1012	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1014	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1015	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1016	SD₁₆	—	2	4	no	—
1017	SD₁₆	—	4	2	no	—
1018	SD₁₆	—	4	2	no	—
1019	D₈	—	2	4	no	—
1020	D₈	—	4	2	no	—
1021	D₈	—	4	2	no	—
1022	M₁₆	—	2	2	no	—
1023	M₁₆	—	2	2	no	—
1024	M₁₆	—	4	2	no	—
1025	M₁₆	—	4	2	no	—
1026	C₂×C₈	—	2	2	no	—
1027	C₂×C₈	—	2	2	no	—
1028	C₂×C₈	—	4	2	no	—
1029	C₂×C₈	—	4	2	no	—
1030	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1031	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1032	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1033	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1034	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1035	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1050	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1055	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1080	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1081	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1082	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	2	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	1	no	—
1089	C₄²	—	2	1	no	—
1090	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1091	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1092	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1093	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	2	no	—
1096	C₂³	—	2	2	no	—
1097	C₂³	—	4	4	no	—
1098	C₂³	—	4	2	no	—
1099	C₂³	—	4	2	no	—
1100	C₂³	—	8	1	no	—
1101	C₂³	—	8	1	no	—
1102	C₂³	—	8	1	no	—
1103	C₂³	—	8	1	no	—
1104	C₂³	—	8	2	no	—
1105	C₂³	—	8	2	no	—
1106	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1107	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1108	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1109	Q₈	—	2	2	no	—
1110	Q₈	—	2	2	no	—
1111	Q₈	—	2	1	no	—
1112	Q₈	—	2	2	no	—
1113	Q₈	—	2	2	no	—
1114	Q₈	—	4	4	no	—
1115	Q₈	—	4	2	no	—
1116	Q₈	—	4	2	no	—
1117	Q₈	—	8	1	no	—
1118	Q₈	C₂×#41×C₄₁	1	2	yes	—
1119	D₄	—	2	4	no	—
1120	D₄	—	2	4	no	—
1121	D₄	—	2	4	no	—
1122	D₄	—	2	2	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	2	2	no	—
1125	D₄	—	2	2	no	—
1126	D₄	—	2	1	no	—
1127	D₄	—	2	2	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	4	4	no	—
1132	D₄	—	4	4	no	—
1133	D₄	—	4	4	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	8	2	no	—
1137	D₄	—	8	2	no	—
1138	D₄	—	8	2	no	—
1139	D₄	—	8	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	C₂×#41×C₄₁	1	2	yes	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	4	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	4	no	—
1160	C₂×C₄	—	4	4	no	—
1161	C₂×C₄	—	4	4	no	—
1162	C₂×C₄	—	4	4	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	8	2	no	—
1165	C₂×C₄	—	8	1	no	—
1166	C₂×C₄	—	8	1	no	—
1167	C₂×C₄	—	8	1	no	—
1168	C₂×C₄	—	8	2	no	—
1169	C₂×C₄	—	8	2	no	—
1170	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1171	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1172	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1173	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1174	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1175	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1177	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
1178	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1179	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1180	C₈	—	2	2	no	—
1181	C₈	—	2	1	no	—
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	2	2	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	2	no	—
1200	C₂²	—	4	2	no	—
1201	C₂²	—	4	2	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	8	4	no	—
1204	C₂²	—	16	2	no	—
1205	C₂²	—	16	4	no	—
1206	C₂²	C₄₁×#546	1	2	yes	—
1207	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1208	C₄	—	2	1	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	2	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	2	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	2	no	—
1223	C₄	C₄₁×#546	1	2	yes	—
1224	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
1225	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1226	C₂	—	2	2	no	—
1227	C₂	—	4	2	no	—
1228	C₂	—	4	2	no	—
1229	C₂	—	4	2	no	—
1230	C₂	—	8	2	no	—
1231	C₂	—	8	2	no	—
1232	C₂	C₂×C₄₁×#546	1	1	yes	characteristic
1233	C₂	C₄₁×#3584	1	1	yes	characteristic
1234	C₂	C₄₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3506	C₂	semidirect
2. C₄₁×#3500	C₂	semidirect
3. C₄₁×#3326	C₂	semidirect
4. C₄₁×#3322	C₂	semidirect
5. C₄₁×#3321	C₂	semidirect
6. C₄₁×#3319	C₂	semidirect
7. C₄₁×#3308	C₂	semidirect
8. C₄₁×#3306	C₂	semidirect
9. C₄₁×#3301	C₂	semidirect
10. C₄₁×#3297	C₂	semidirect
11. C₄₁×#3140	C₂	semidirect
12. C₄₁×#3097	C₂	semidirect
13. C₄₁×#3096	C₂	semidirect
14. C₄₁×#3076	C₂	semidirect
15. C₄₁×#3058	C₂	semidirect
16. C₄₁×#3057	C₂	semidirect
17. C₂×C₄₁×#463	C₂	semidirect
18. C₄₁×#3010	C₂	semidirect
19. C₄₁×#3008	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₄₁	C₂	semidirect
21. C₄₁×#2935	C₂	semidirect
22. C₄₁×#2898	C₂	semidirect
23. C₄₁×#2897	C₂	semidirect
27. C₂²×SD₁₆×C₄₁	C₂²	semidirect
30. C₂×#131×C₄₁	C₂²	semidirect
34. C₄₁×#555	C₂²	semidirect
35. C₄₁×#553	C₂²	semidirect
36. C₄₁×#553	C₂²	semidirect
38. C₄₁×#548	C₂²	semidirect
39. C₄₁×#548	C₂²	semidirect
40. C₄₁×#547	C₂²	semidirect
43. C₄₁×#546	C₂²	semidirect
44. C₄₁×#546	C₂²	semidirect
51. C₄₁×#535	C₂²	semidirect
52. C₄₁×#533	C₂²	semidirect
59. C₄₁×#520	C₂²	semidirect
61. C₂×C₄×D₄×C₄₁	C₂²	semidirect
62. C₄₁×#489	C₂²	semidirect
63. C₄₁×#489	C₂²	semidirect
64. C₄₁×#488	C₂²	semidirect
65. C₄₁×#488	C₂²	semidirect
66. C₄₁×#485	C₂²	semidirect
67. C₄₁×#485	C₂²	semidirect
68. C₄₁×#484	C₂²	semidirect
69. C₄₁×#483	C₂²	semidirect
70. C₄₁×#482	C₂²	semidirect
71. C₄₁×#482	C₂²	semidirect
72. C₄₁×#481	C₂²	semidirect
73. C₄₁×#480	C₂²	semidirect
74. C₄₁×#479	C₂²	semidirect
75. C₄₁×#479	C₂²	semidirect
76. C₄₁×#478	C₂²	semidirect
77. C₄₁×#478	C₂²	semidirect
78. C₄₁×#477	C₂²	semidirect
79. C₄₁×#476	C₂²	semidirect
80. C₄₁×#475	C₂²	semidirect
81. C₄₁×#474	C₂²	semidirect
82. C₄₁×#469	C₂²	semidirect
83. C₄₁×#469	C₂²	semidirect
84. C₄₁×#468	C₂²	semidirect
85. C₄₁×#468	C₂²	semidirect
86. C₄₁×#466	C₂²	semidirect
87. C₄₁×#466	C₂²	semidirect
88. C₄₁×#465	C₂²	semidirect
89. C₄₁×#465	C₂²	semidirect
90. C₄₁×#463	C₂²	semidirect
91. C₄₁×#463	C₂²	semidirect
92. C₄₁×#463	C₂²	semidirect
93. C₄₁×#463	C₂²	semidirect
96. C₄₁×#449	C₂²	semidirect
97. C₄₁×#449	C₂²	semidirect
98. C₄₁×#448	C₂²	semidirect
99. C₄₁×#448	C₂²	semidirect
102. C₄₁×#442	C₂²	semidirect
103. C₄₁×#440	C₂²	semidirect
104. C₄×SD₁₆×C₄₁	C₂²	semidirect
105. C₄×D₈×C₄₁	C₂²	semidirect
106. C₄₁×#436	C₂²	semidirect
107. C₄₁×#435	C₂²	semidirect
108. C₄₁×#435	C₂²	semidirect
109. C₈×D₄×C₄₁	C₂²	semidirect
110. C₄₁×#428	C₂²	semidirect
111. C₄₁×#427	C₂²	semidirect
112. C₄₁×#427	C₂²	semidirect
113. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
114. C₄₁×#419	C₂²	semidirect
115. C₄₁×#419	C₂²	semidirect
116. C₄₁×#419	C₂²	semidirect
119. C₄₁×#418	C₂²	semidirect
120. C₄₁×#418	C₂²	semidirect
122. C₄₁×#417	C₂²	semidirect
123. C₄₁×#417	C₂²	semidirect
126. C₄₁×#416	C₂²	semidirect
127. C₄₁×#416	C₂²	semidirect
128. C₂×#103×C₄₁	C₂²	semidirect
129. C₂×#103×C₄₁	C₂²	semidirect
131. C₂×#102×C₄₁	C₂²	semidirect
133. C₄₁×#408	C₂²	semidirect
134. C₄×M₁₆×C₄₁	C₂²	semidirect
337. #41×C₄₁	#41	semidirect
568. #61208	C₄₁	direct (N × H)
609. #3506	C₂×C₄₁	semidirect
610. #3500	C₂×C₄₁	semidirect
611. #3326	C₂×C₄₁	semidirect
612. #3322	C₂×C₄₁	semidirect
613. #3321	C₂×C₄₁	semidirect
614. #3319	C₂×C₄₁	semidirect
615. #3308	C₂×C₄₁	semidirect
616. #3306	C₂×C₄₁	semidirect
617. #3301	C₂×C₄₁	semidirect
618. #3297	C₂×C₄₁	semidirect
619. #3140	C₂×C₄₁	semidirect
620. #3097	C₂×C₄₁	semidirect
621. #3096	C₂×C₄₁	semidirect
622. #3076	C₂×C₄₁	semidirect
623. #3058	C₂×C₄₁	semidirect
624. #3057	C₂×C₄₁	semidirect
625. C₂×#463	C₂×C₄₁	semidirect
626. #3010	C₂×C₄₁	semidirect
627. #3008	C₂×C₄₁	semidirect
628. C₄×AGL(1,ℤ/8)	C₂×C₄₁	semidirect
629. #2935	C₂×C₄₁	semidirect
630. #2898	C₂×C₄₁	semidirect
631. #2897	C₂×C₄₁	semidirect
644. C₂²×SD₁₆	C₂²×C₄₁	semidirect
647. C₂×#131	C₂²×C₄₁	semidirect
651. #555	C₂²×C₄₁	semidirect
652. #553	C₂²×C₄₁	semidirect
653. #553	C₂²×C₄₁	semidirect
655. #548	C₂²×C₄₁	semidirect
656. #548	C₂²×C₄₁	semidirect
657. #547	C₂²×C₄₁	semidirect
660. #546	C₂²×C₄₁	semidirect
661. #546	C₂²×C₄₁	semidirect
668. #535	C₂²×C₄₁	semidirect
669. #533	C₂²×C₄₁	semidirect
676. #520	C₂²×C₄₁	semidirect
678. C₂×C₄×D₄	C₂²×C₄₁	semidirect
679. #489	C₂²×C₄₁	semidirect
680. #489	C₂²×C₄₁	semidirect
681. #488	C₂²×C₄₁	semidirect
682. #488	C₂²×C₄₁	semidirect
683. #485	C₂²×C₄₁	semidirect
684. #485	C₂²×C₄₁	semidirect
685. #484	C₂²×C₄₁	semidirect
686. #483	C₂²×C₄₁	semidirect
687. #482	C₂²×C₄₁	semidirect
688. #482	C₂²×C₄₁	semidirect
689. #481	C₂²×C₄₁	semidirect
690. #480	C₂²×C₄₁	semidirect
691. #479	C₂²×C₄₁	semidirect
692. #479	C₂²×C₄₁	semidirect
693. #478	C₂²×C₄₁	semidirect
694. #478	C₂²×C₄₁	semidirect
695. #477	C₂²×C₄₁	semidirect
696. #476	C₂²×C₄₁	semidirect
697. #475	C₂²×C₄₁	semidirect
698. #474	C₂²×C₄₁	semidirect
699. #469	C₂²×C₄₁	semidirect
700. #469	C₂²×C₄₁	semidirect
701. #468	C₂²×C₄₁	semidirect
702. #468	C₂²×C₄₁	semidirect
703. #466	C₂²×C₄₁	semidirect
704. #466	C₂²×C₄₁	semidirect
705. #465	C₂²×C₄₁	semidirect
706. #465	C₂²×C₄₁	semidirect
707. #463	C₂²×C₄₁	semidirect
708. #463	C₂²×C₄₁	semidirect
709. #463	C₂²×C₄₁	semidirect
710. #463	C₂²×C₄₁	semidirect
713. #449	C₂²×C₄₁	semidirect
714. #449	C₂²×C₄₁	semidirect
715. #448	C₂²×C₄₁	semidirect
716. #448	C₂²×C₄₁	semidirect
719. #442	C₂²×C₄₁	semidirect
720. #440	C₂²×C₄₁	semidirect
721. C₄×SD₁₆	C₂²×C₄₁	semidirect
722. C₄×D₈	C₂²×C₄₁	semidirect
723. #436	C₂²×C₄₁	semidirect
724. #435	C₂²×C₄₁	semidirect
725. #435	C₂²×C₄₁	semidirect
726. C₈×D₄	C₂²×C₄₁	semidirect
727. #428	C₂²×C₄₁	semidirect
728. #427	C₂²×C₄₁	semidirect
729. #427	C₂²×C₄₁	semidirect
730. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
731. #419	C₂²×C₄₁	semidirect
732. #419	C₂²×C₄₁	semidirect
733. #419	C₂²×C₄₁	semidirect
736. #418	C₂²×C₄₁	semidirect
737. #418	C₂²×C₄₁	semidirect
739. #417	C₂²×C₄₁	semidirect
740. #417	C₂²×C₄₁	semidirect
743. #416	C₂²×C₄₁	semidirect
744. #416	C₂²×C₄₁	semidirect
745. C₂×#103	C₂²×C₄₁	semidirect
746. C₂×#103	C₂²×C₄₁	semidirect
748. C₂×#102	C₂²×C₄₁	semidirect
750. #408	C₂²×C₄₁	semidirect
751. C₄×M₁₆	C₂²×C₄₁	semidirect
752. C₄₁	#61208	direct (N × H)
955. #41	#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×#3506	2
C₄₁×#3500	2
C₄₁×#3326	2
C₄₁×#3322	2
C₄₁×#3321	2
C₄₁×#3319	2
C₄₁×#3308	2
C₄₁×#3306	2
C₄₁×#3301	2
C₄₁×#3297	2
C₄₁×#3140	2
C₄₁×#3097	2
C₄₁×#3096	2
C₄₁×#3076	2
C₄₁×#3058	2
C₄₁×#3057	2
C₂×C₄₁×#463	2
C₄₁×#3010	2
C₄₁×#3008	2
C₄×AGL(1,ℤ/8)×C₄₁	2
C₄₁×#2935	2
C₄₁×#2898	2
C₄₁×#2897	2
#61208	41

Subgroups — C41×#61208 #23837409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61208 #23837409