Subgroups — C₄₁×#60571 #23836772

Order 10496.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×H(5,𝔽₂)×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3125	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3123	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3120	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3118	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3107	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3105	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3102	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3101	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3042	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3012	C₂	1	1	yes	maximal, characteristic
18	C₄₁×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#137×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#135×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#137×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#544	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#542	—	2	1	no	—
31	C₄₁×#542	C₂²	1	2	yes	complemented
32	C₄₁×#541	—	2	1	no	—
33	C₄₁×#541	C₂²	1	2	yes	complemented
34	C₄₁×#539	—	2	2	no	—
35	C₄₁×#537	C₂²	1	1	yes	characteristic
36	C₄₁×#536	C₂²	1	1	yes	characteristic
37	C₄₁×#536	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#533	—	2	1	no	—
39	C₄₁×#533	C₂²	1	2	yes	complemented
40	C₄₁×#529	—	2	2	no	—
41	C₄₁×#529	—	2	1	no	—
42	C₄₁×#529	C₂²	1	2	yes	complemented
43	C₄₁×#520	—	2	1	no	—
44	C₄₁×#520	C₂²	1	1	yes	characteristic
45	C₄₁×#520	C₂²	1	2	yes	—
46	C₄₁×#520	C₂²	1	1	yes	characteristic
47	C₄₁×#518	—	2	2	no	—
48	C₄₁×#518	—	2	1	no	—
49	C₄₁×#518	C₂²	1	1	yes	characteristic
50	C₄₁×#518	C₂²	1	2	yes	—
51	C₄×#41×C₄₁	—	2	1	no	—
52	C₄×#41×C₄₁	C₂²	1	2	yes	—
53	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₄₁	—	2	1	no	—
58	C₂×C₄×D₄×C₄₁	—	2	2	no	—
59	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
60	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
61	C₄₁×#485	C₂²	1	2	yes	complemented
62	C₄₁×#485	C₂²	1	2	yes	complemented
63	C₄₁×#485	C₂²	1	2	yes	complemented
64	C₄₁×#484	C₂²	1	2	yes	complemented
65	C₄₁×#483	C₂²	1	2	yes	complemented
66	C₄₁×#483	C₂²	1	2	yes	complemented
67	C₄₁×#482	C₂²	1	2	yes	complemented
68	C₄₁×#481	C₂²	1	2	yes	complemented
69	C₄₁×#479	C₂²	1	2	yes	complemented
70	C₄₁×#478	C₂²	1	2	yes	complemented
71	C₄₁×#478	C₂²	1	2	yes	complemented
72	C₄₁×#478	C₂²	1	2	yes	complemented
73	C₄₁×#476	C₂²	1	2	yes	complemented
74	C₄₁×#476	C₂²	1	2	yes	complemented
75	C₄₁×#475	C₂²	1	2	yes	complemented
76	C₄₁×#474	C₂²	1	2	yes	complemented
77	C₄₁×#464	C₂²	1	2	yes	complemented
78	C₄₁×#463	C₂²	1	2	yes	complemented
79	C₄₁×#463	C₂²	1	2	yes	complemented
80	C₄₁×#463	C₂²	1	2	yes	complemented
81	C₄₁×#462	C₂²	1	2	yes	complemented
82	C₄₁×#461	C₂²	1	2	yes	complemented
83	C₄₁×#461	C₂²	1	2	yes	complemented
84	C₄₁×#461	C₂²	1	2	yes	complemented
85	C₄₁×#452	C₂²	1	2	yes	—
86	C₄₁×#452	C₂²	1	2	yes	—
87	C₄₁×#452	C₂²	1	2	yes	—
88	C₄₁×#450	C₂²	1	2	yes	—
89	C₄₁×#450	C₂²	1	2	yes	—
90	C₄₁×#450	C₂²	1	2	yes	—
91	C₄₁×#449	C₂²	1	2	yes	—
92	C₄₁×#447	C₂²	1	2	yes	—
93	C₄₁×#442	C₂²	1	2	yes	complemented
94	C₄₁×#441	C₂²	1	2	yes	complemented
95	C₄₁×#440	C₂²	1	2	yes	complemented
96	C₄₁×#440	C₂²	1	2	yes	complemented
97	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
98	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
100	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
108	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
110	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
111	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
113	C₄₁×#433	C₂²	1	2	yes	complemented
114	C₄₁×#433	C₂²	1	2	yes	complemented
115	C₄₁×#431	C₂²	1	2	yes	complemented
116	C₄₁×#431	C₂²	1	2	yes	complemented
117	C₄₁×#428	C₂²	1	1	yes	characteristic, complemented
118	C₄₁×#428	C₂²	1	1	yes	characteristic, complemented
119	C₄₁×#427	C₂²	1	1	yes	characteristic, complemented
120	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic, complemented
121	C₄₁×#424	C₂²	1	1	yes	characteristic, complemented
122	C₄₁×#424	C₂²	1	1	yes	characteristic, complemented
123	C₄₁×#419	C₂²	1	1	yes	characteristic, complemented
124	C₄₁×#418	C₂²	1	1	yes	characteristic
125	C₄₁×#417	C₂²	1	1	yes	characteristic
126	C₄₁×#417	C₂²	1	1	yes	characteristic, complemented
127	C₄₁×#416	C₂²	1	1	yes	characteristic
128	C₄₁×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
131	C₄₁×#408	C₂²	1	1	yes	characteristic
132	C₄₁×#408	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₄₁	—	2	4	no	—
136	H(5,𝔽₂)×C₄₁	—	2	4	no	—
137	C₂×#41×C₄₁	—	2	1	no	—
138	C₂×#41×C₄₁	C₂³	1	2	yes	—
139	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
140	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₄₁	—	2	2	no	—
144	C₂²×D₄×C₄₁	—	2	1	no	—
145	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₄₁	—	2	1	no	—
148	C₂³×C₄×C₄₁	—	2	2	no	—
149	#137×C₄₁	—	2	4	no	—
150	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
151	#135×C₄₁	—	2	4	no	—
152	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
153	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₄₁	—	2	4	no	—
155	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
161	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
162	C₂×D₈×C₄₁	C₂³	1	2	yes	—
163	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₄₁	—	2	1	no	—
168	C₄⋊Q₈×C₄₁	—	2	1	no	—
169	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
171	#126×C₄₁	—	2	2	no	—
172	#126×C₄₁	—	2	2	no	—
173	#126×C₄₁	—	2	2	no	—
174	#126×C₄₁	—	2	2	no	—
175	#125×C₄₁	—	2	2	no	—
176	#125×C₄₁	—	2	1	no	—
177	#125×C₄₁	—	2	2	no	—
178	#125×C₄₁	—	2	2	no	—
179	#125×C₄₁	C₂³	1	2	yes	—
180	#124×C₄₁	—	2	1	no	—
181	#124×C₄₁	—	2	2	no	—
182	#124×C₄₁	C₂³	1	2	yes	—
183	#123×C₄₁	—	2	2	no	—
184	#123×C₄₁	—	2	2	no	—
185	#123×C₄₁	—	2	2	no	—
186	#123×C₄₁	—	2	2	no	—
187	C₂²⋊Q₈×C₄₁	—	2	1	no	—
188	C₂²⋊Q₈×C₄₁	—	2	2	no	—
189	C₂²⋊Q₈×C₄₁	—	2	1	no	—
190	C₂²⋊Q₈×C₄₁	—	2	1	no	—
191	C₂²⋊Q₈×C₄₁	—	2	2	no	—
192	C₂²⋊Q₈×C₄₁	—	2	2	no	—
193	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
196	#121×C₄₁	—	2	2	no	—
197	#121×C₄₁	—	2	1	no	—
198	#121×C₄₁	C₂³	1	2	yes	—
199	C₄×Q₈×C₄₁	—	2	1	no	—
200	C₄×Q₈×C₄₁	—	2	1	no	—
201	C₄×Q₈×C₄₁	—	2	1	no	—
202	C₄×Q₈×C₄₁	—	2	2	no	—
203	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
204	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
205	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
206	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
212	C₄×D₄×C₄₁	—	2	2	no	—
213	C₄×D₄×C₄₁	—	2	1	no	—
214	C₄×D₄×C₄₁	—	2	1	no	—
215	C₄×D₄×C₄₁	—	2	2	no	—
216	C₄×D₄×C₄₁	—	2	1	no	—
217	C₄×D₄×C₄₁	—	2	2	no	—
218	C₄×D₄×C₄₁	—	2	1	no	—
219	C₄×D₄×C₄₁	—	2	1	no	—
220	C₄×D₄×C₄₁	—	2	2	no	—
221	C₄×D₄×C₄₁	—	2	1	no	—
222	C₄×D₄×C₄₁	—	2	2	no	—
223	C₄×D₄×C₄₁	—	2	2	no	—
224	C₄×D₄×C₄₁	—	2	1	no	—
225	C₄×D₄×C₄₁	—	2	2	no	—
226	C₄×D₄×C₄₁	—	2	2	no	—
227	C₄×D₄×C₄₁	—	2	2	no	—
228	C₄×D₄×C₄₁	—	2	1	no	—
229	C₄×D₄×C₄₁	—	2	2	no	—
230	C₄×D₄×C₄₁	—	2	1	no	—
231	C₄×D₄×C₄₁	—	2	2	no	—
232	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
233	C₄×D₄×C₄₁	D₄	1	2	yes	—
234	C₄×D₄×C₄₁	D₄	1	2	yes	—
235	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
236	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₄₁	C₂³	1	2	yes	—
238	C₄×D₄×C₄₁	C₂³	1	2	yes	—
239	C₄×D₄×C₄₁	C₂³	1	2	yes	—
240	C₄×D₄×C₄₁	C₂³	1	2	yes	—
241	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₄₁	C₂³	1	2	yes	—
243	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
245	#117×C₄₁	—	2	2	no	—
246	#117×C₄₁	—	2	2	no	—
247	#117×C₄₁	—	2	1	no	—
248	#117×C₄₁	—	2	1	no	—
249	#117×C₄₁	—	2	2	no	—
250	#117×C₄₁	—	2	1	no	—
251	#117×C₄₁	—	2	2	no	—
252	#117×C₄₁	C₂³	1	1	yes	characteristic
253	#117×C₄₁	C₂³	1	2	yes	—
254	#117×C₄₁	C₂³	1	1	yes	characteristic
255	#117×C₄₁	C₂³	1	1	yes	characteristic
256	#117×C₄₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
260	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
268	C₂×C₄²×C₄₁	—	2	1	no	—
269	C₂×C₄²×C₄₁	—	2	1	no	—
270	C₂×C₄²×C₄₁	—	2	2	no	—
271	C₂×C₄²×C₄₁	—	2	1	no	—
272	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
274	#107×C₄₁	C₂³	1	1	yes	characteristic
275	#107×C₄₁	C₂³	1	1	yes	characteristic
276	#107×C₄₁	C₂³	1	2	yes	—
277	#107×C₄₁	C₂³	1	2	yes	—
278	#106×C₄₁	C₂³	1	2	yes	—
279	#106×C₄₁	C₂³	1	2	yes	—
280	#106×C₄₁	C₂³	1	1	yes	characteristic
281	#106×C₄₁	C₂³	1	1	yes	characteristic
282	#106×C₄₁	C₂³	1	2	yes	—
283	#106×C₄₁	C₂³	1	2	yes	—
284	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
287	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
288	#103×C₄₁	C₂³	1	2	yes	—
289	#103×C₄₁	C₂³	1	2	yes	—
290	#103×C₄₁	C₂³	1	1	yes	characteristic
291	#103×C₄₁	C₂³	1	1	yes	characteristic
292	#103×C₄₁	C₂³	1	1	yes	characteristic
293	#103×C₄₁	C₂³	1	1	yes	characteristic
294	#103×C₄₁	C₂³	1	2	yes	—
295	#103×C₄₁	C₂³	1	2	yes	—
296	#103×C₄₁	C₂³	1	2	yes	—
297	#103×C₄₁	C₂³	1	2	yes	—
298	#102×C₄₁	C₂³	1	2	yes	—
299	#102×C₄₁	C₂³	1	2	yes	—
300	#102×C₄₁	C₂³	1	1	yes	characteristic
301	#102×C₄₁	C₂³	1	1	yes	characteristic
302	#102×C₄₁	C₂³	1	1	yes	characteristic
303	#102×C₄₁	C₂³	1	1	yes	characteristic
304	#102×C₄₁	C₂³	1	2	yes	—
305	#102×C₄₁	C₂³	1	2	yes	—
306	#102×C₄₁	C₂³	1	2	yes	—
307	#102×C₄₁	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
312	#97×C₄₁	C₂³	1	2	yes	—
313	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₄₁	C₂³	1	2	yes	—
318	C₂⁴×C₄₁	—	2	2	no	—
319	C₂⁴×C₄₁	—	2	1	no	—
320	#41×C₄₁	—	2	8	no	—
321	#41×C₄₁	—	2	4	no	—
322	#41×C₄₁	—	2	4	no	—
323	#41×C₄₁	—	2	2	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	#41	1	4	yes	—
329	C₂×Q₈×C₄₁	—	2	1	no	—
330	C₂×Q₈×C₄₁	—	2	2	no	—
331	C₂×Q₈×C₄₁	—	2	2	no	—
332	C₂×Q₈×C₄₁	—	2	2	no	—
333	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
336	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₄₁	—	2	16	no	—
338	C₂×D₄×C₄₁	—	2	8	no	—
339	C₂×D₄×C₄₁	—	2	2	no	—
340	C₂×D₄×C₄₁	—	2	1	no	—
341	C₂×D₄×C₄₁	—	2	4	no	—
342	C₂×D₄×C₄₁	—	2	4	no	—
343	C₂×D₄×C₄₁	—	2	1	no	—
344	C₂×D₄×C₄₁	—	2	2	no	—
345	C₂×D₄×C₄₁	—	2	2	no	—
346	C₂×D₄×C₄₁	—	2	1	no	—
347	C₂×D₄×C₄₁	—	2	2	no	—
348	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₄₁	#41	1	4	yes	—
351	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₄₁	—	2	2	no	—
355	C₂²×C₄×C₄₁	—	2	1	no	—
356	C₂²×C₄×C₄₁	—	2	1	no	—
357	C₂²×C₄×C₄₁	—	2	1	no	—
358	C₂²×C₄×C₄₁	—	2	2	no	—
359	C₂²×C₄×C₄₁	—	2	1	no	—
360	C₂²×C₄×C₄₁	—	2	1	no	—
361	C₂²×C₄×C₄₁	—	2	1	no	—
362	C₂²×C₄×C₄₁	—	2	1	no	—
363	C₂²×C₄×C₄₁	—	2	2	no	—
364	C₂²×C₄×C₄₁	—	2	1	no	—
365	C₂²×C₄×C₄₁	—	2	2	no	—
366	C₂²×C₄×C₄₁	—	2	1	no	—
367	C₂²×C₄×C₄₁	—	2	2	no	—
368	C₂²×C₄×C₄₁	—	2	2	no	—
369	C₂²×C₄×C₄₁	—	2	2	no	—
370	C₂²×C₄×C₄₁	—	8	2	no	—
371	C₂²×C₄×C₄₁	—	8	4	no	—
372	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
378	Q₁₆×C₄₁	—	2	2	no	—
379	Q₁₆×C₄₁	—	2	4	no	—
380	SD₁₆×C₄₁	—	2	2	no	—
381	SD₁₆×C₄₁	—	2	4	no	—
382	SD₁₆×C₄₁	—	2	4	no	—
383	SD₁₆×C₄₁	—	2	2	no	—
384	SD₁₆×C₄₁	—	2	4	no	—
385	SD₁₆×C₄₁	—	2	4	no	—
386	D₈×C₄₁	—	2	2	no	—
387	D₈×C₄₁	—	2	4	no	—
388	M₁₆×C₄₁	—	2	2	no	—
389	M₁₆×C₄₁	—	2	2	no	—
390	C₂×C₈×C₄₁	—	2	2	no	—
391	C₂×C₈×C₄₁	—	2	2	no	—
392	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
397	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₄₁	—	2	1	no	—
399	C₄⋊C₄×C₄₁	—	2	2	no	—
400	C₄⋊C₄×C₄₁	—	2	2	no	—
401	C₄⋊C₄×C₄₁	—	2	1	no	—
402	C₄⋊C₄×C₄₁	—	2	2	no	—
403	C₄⋊C₄×C₄₁	—	2	2	no	—
404	C₄⋊C₄×C₄₁	—	2	1	no	—
405	C₄⋊C₄×C₄₁	—	2	1	no	—
406	C₄⋊C₄×C₄₁	—	2	1	no	—
407	C₄⋊C₄×C₄₁	—	2	1	no	—
408	C₄⋊C₄×C₄₁	—	2	2	no	—
409	C₄⋊C₄×C₄₁	—	2	2	no	—
410	C₄⋊C₄×C₄₁	—	2	2	no	—
411	C₄⋊C₄×C₄₁	—	2	2	no	—
412	C₄⋊C₄×C₄₁	—	2	2	no	—
413	C₄⋊C₄×C₄₁	—	2	2	no	—
414	C₄⋊C₄×C₄₁	—	2	2	no	—
415	C₄⋊C₄×C₄₁	—	2	2	no	—
416	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
426	C₂²⋊C₄×C₄₁	—	2	2	no	—
427	C₂²⋊C₄×C₄₁	—	2	1	no	—
428	C₂²⋊C₄×C₄₁	—	2	2	no	—
429	C₂²⋊C₄×C₄₁	—	2	2	no	—
430	C₂²⋊C₄×C₄₁	—	2	1	no	—
431	C₂²⋊C₄×C₄₁	—	2	2	no	—
432	C₂²⋊C₄×C₄₁	—	2	1	no	—
433	C₂²⋊C₄×C₄₁	—	2	2	no	—
434	C₂²⋊C₄×C₄₁	—	2	2	no	—
435	C₂²⋊C₄×C₄₁	—	2	2	no	—
436	C₂²⋊C₄×C₄₁	—	2	2	no	—
437	C₂²⋊C₄×C₄₁	—	2	2	no	—
438	C₂²⋊C₄×C₄₁	—	2	1	no	—
439	C₂²⋊C₄×C₄₁	—	2	1	no	—
440	C₂²⋊C₄×C₄₁	—	2	1	no	—
441	C₂²⋊C₄×C₄₁	—	2	2	no	—
442	C₂²⋊C₄×C₄₁	—	2	2	no	—
443	C₂²⋊C₄×C₄₁	—	2	2	no	—
444	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
447	C₄²×C₄₁	—	2	1	no	—
448	C₄²×C₄₁	—	2	2	no	—
449	C₄²×C₄₁	—	2	2	no	—
450	C₄²×C₄₁	—	2	1	no	—
451	C₄²×C₄₁	—	2	1	no	—
452	C₄²×C₄₁	—	2	1	no	—
453	C₄²×C₄₁	—	2	2	no	—
454	C₄²×C₄₁	—	2	1	no	—
455	C₄²×C₄₁	—	2	2	no	—
456	C₄²×C₄₁	—	2	1	no	—
457	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₄₁	C₂×D₄	1	2	yes	—
459	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₄₁	C₂×D₄	1	2	yes	—
461	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
462	C₄²×C₄₁	C₂⁴	1	2	yes	—
463	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
464	C₂³×C₄₁	—	2	8	no	—
465	C₂³×C₄₁	—	2	2	no	—
466	C₂³×C₄₁	—	2	1	no	—
467	C₂³×C₄₁	—	2	4	no	—
468	C₂³×C₄₁	—	2	1	no	—
469	C₂³×C₄₁	—	8	1	no	—
470	C₂³×C₄₁	—	8	2	no	—
471	C₂³×C₄₁	—	8	1	no	—
472	C₂³×C₄₁	—	8	2	no	—
473	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
474	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
475	Q₈×C₄₁	—	2	2	no	—
476	Q₈×C₄₁	—	2	1	no	—
477	Q₈×C₄₁	—	2	2	no	—
478	Q₈×C₄₁	—	2	1	no	—
479	Q₈×C₄₁	—	2	2	no	—
480	Q₈×C₄₁	—	2	1	no	—
481	Q₈×C₄₁	—	4	2	no	—
482	Q₈×C₄₁	—	8	2	no	—
483	Q₈×C₄₁	C₂×#41	1	2	yes	—
484	D₄×C₄₁	—	2	8	no	—
485	D₄×C₄₁	—	2	8	no	—
486	D₄×C₄₁	—	2	4	no	—
487	D₄×C₄₁	—	2	4	no	—
488	D₄×C₄₁	—	2	2	no	—
489	D₄×C₄₁	—	2	4	no	—
490	D₄×C₄₁	—	2	2	no	—
491	D₄×C₄₁	—	2	1	no	—
492	D₄×C₄₁	—	2	1	no	—
493	D₄×C₄₁	—	2	1	no	—
494	D₄×C₄₁	—	4	2	no	—
495	D₄×C₄₁	—	8	2	no	—
496	D₄×C₄₁	C₂×#41	1	2	yes	—
497	D₄×C₄₁	C₂×#41	1	4	yes	—
498	C₂×C₄×C₄₁	—	2	8	no	—
499	C₂×C₄×C₄₁	—	2	1	no	—
500	C₂×C₄×C₄₁	—	2	4	no	—
501	C₂×C₄×C₄₁	—	2	2	no	—
502	C₂×C₄×C₄₁	—	2	4	no	—
503	C₂×C₄×C₄₁	—	2	2	no	—
504	C₂×C₄×C₄₁	—	2	2	no	—
505	C₂×C₄×C₄₁	—	2	1	no	—
506	C₂×C₄×C₄₁	—	2	1	no	—
507	C₂×C₄×C₄₁	—	2	2	no	—
508	C₂×C₄×C₄₁	—	2	1	no	—
509	C₂×C₄×C₄₁	—	2	1	no	—
510	C₂×C₄×C₄₁	—	2	2	no	—
511	C₂×C₄×C₄₁	—	2	1	no	—
512	C₂×C₄×C₄₁	—	2	2	no	—
513	C₂×C₄×C₄₁	—	4	1	no	—
514	C₂×C₄×C₄₁	—	4	2	no	—
515	C₂×C₄×C₄₁	—	4	2	no	—
516	C₂×C₄×C₄₁	—	4	2	no	—
517	C₂×C₄×C₄₁	—	4	2	no	—
518	C₂×C₄×C₄₁	—	4	4	no	—
519	C₂×C₄×C₄₁	—	4	2	no	—
520	C₂×C₄×C₄₁	—	8	1	no	—
521	C₂×C₄×C₄₁	—	8	1	no	—
522	C₂×C₄×C₄₁	—	8	2	no	—
523	C₂×C₄×C₄₁	—	8	2	no	—
524	C₂×C₄×C₄₁	—	8	2	no	—
525	C₂×C₄×C₄₁	—	8	2	no	—
526	C₂×C₄×C₄₁	—	8	1	no	—
527	C₂×C₄×C₄₁	—	8	1	no	—
528	C₂×C₄×C₄₁	—	8	2	no	—
529	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
538	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
539	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
540	C₈×C₄₁	—	2	1	no	—
541	C₈×C₄₁	—	2	1	no	—
542	C₈×C₄₁	—	2	1	no	—
543	C₈×C₄₁	—	2	1	no	—
544	C₈×C₄₁	—	2	2	no	—
545	C₈×C₄₁	—	2	2	no	—
546	#60571	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
547	C₂²×C₄₁	—	2	1	no	—
548	C₂²×C₄₁	—	2	1	no	—
549	C₂²×C₄₁	—	2	2	no	—
550	C₂²×C₄₁	—	2	2	no	—
551	C₂²×C₄₁	—	2	4	no	—
552	C₂²×C₄₁	—	2	2	no	—
553	C₂²×C₄₁	—	2	2	no	—
554	C₂²×C₄₁	—	4	2	no	—
555	C₂²×C₄₁	—	4	1	no	—
556	C₂²×C₄₁	—	4	2	no	—
557	C₂²×C₄₁	—	4	1	no	—
558	C₂²×C₄₁	—	4	1	no	—
559	C₂²×C₄₁	—	4	1	no	—
560	C₂²×C₄₁	—	4	1	no	—
561	C₂²×C₄₁	—	8	4	no	—
562	C₂²×C₄₁	—	8	8	no	—
563	C₂²×C₄₁	#525	1	2	yes	—
564	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
565	C₄×C₄₁	—	2	1	no	—
566	C₄×C₄₁	—	2	1	no	—
567	C₄×C₄₁	—	2	2	no	—
568	C₄×C₄₁	—	2	2	no	—
569	C₄×C₄₁	—	2	2	no	—
570	C₄×C₄₁	—	2	1	no	—
571	C₄×C₄₁	—	2	2	no	—
572	C₄×C₄₁	—	4	1	no	—
573	C₄×C₄₁	—	4	2	no	—
574	C₄×C₄₁	—	4	1	no	—
575	C₄×C₄₁	—	4	1	no	—
576	C₄×C₄₁	—	4	2	no	—
577	C₄×C₄₁	—	4	1	no	—
578	C₄×C₄₁	—	4	2	no	—
579	C₄×C₄₁	—	4	1	no	—
580	C₄×C₄₁	#525	1	2	yes	—
581	C₄×C₄₁	#577	1	2	yes	—
582	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
583	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
584	#3461	C₂×C₄₁	1	1	yes	characteristic, complemented
585	C₄×H(5,𝔽₂)	C₂×C₄₁	1	1	yes	characteristic, complemented
586	#3125	C₂×C₄₁	1	2	yes	complemented
587	#3123	C₂×C₄₁	1	2	yes	complemented
588	#3120	C₂×C₄₁	1	2	yes	complemented
589	#3118	C₂×C₄₁	1	2	yes	complemented
590	#3107	C₂×C₄₁	1	2	yes	complemented
591	#3105	C₂×C₄₁	1	2	yes	complemented
592	#3102	C₂×C₄₁	1	2	yes	complemented
593	#3101	C₂×C₄₁	1	2	yes	complemented
594	#3099	C₂×C₄₁	1	1	yes	characteristic, complemented
595	#3097	C₂×C₄₁	1	1	yes	characteristic, complemented
596	#3084	C₂×C₄₁	1	1	yes	characteristic, complemented
597	#3081	C₂×C₄₁	1	1	yes	characteristic, complemented
598	#3046	C₂×C₄₁	1	1	yes	characteristic, complemented
599	#3042	C₂×C₄₁	1	1	yes	characteristic, complemented
600	#3012	C₂×C₄₁	1	1	yes	characteristic
601	#3009	C₂×C₄₁	1	1	yes	characteristic, complemented
602	C₄×#137	C₂×C₄₁	1	1	yes	characteristic, complemented
603	C₄×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic, complemented
604	C₄×#135	C₂×C₄₁	1	1	yes	characteristic, complemented
605	C₂×C₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
606	#2922	C₂×C₄₁	1	1	yes	characteristic, complemented
607	C₂×C₄₁	—	2	2	no	—
608	C₂×C₄₁	—	4	2	no	—
609	C₂×C₄₁	—	4	4	no	—
610	C₂×C₄₁	—	4	2	no	—
611	C₂×C₄₁	—	8	1	no	—
612	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
613	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
614	C₂×C₄₁	#3584	1	1	yes	characteristic
615	C₂×H(5,𝔽₂)	C₂²×C₄₁	1	1	yes	characteristic
616	C₂×#137	C₂²×C₄₁	1	1	yes	characteristic
617	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	1	yes	characteristic
618	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
619	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
620	#544	C₂²×C₄₁	1	1	yes	characteristic, complemented
621	#542	—	2	1	no	—
622	#542	C₂²×C₄₁	1	2	yes	complemented
623	#541	—	2	1	no	—
624	#541	C₂²×C₄₁	1	2	yes	complemented
625	#539	—	2	2	no	—
626	#537	C₂²×C₄₁	1	1	yes	characteristic
627	#536	C₂²×C₄₁	1	1	yes	characteristic
628	#536	C₂²×C₄₁	1	1	yes	characteristic, complemented
629	#533	—	2	1	no	—
630	#533	C₂²×C₄₁	1	2	yes	complemented
631	#529	—	2	2	no	—
632	#529	—	2	1	no	—
633	#529	C₂²×C₄₁	1	2	yes	complemented
634	#520	—	2	1	no	—
635	#520	C₂²×C₄₁	1	1	yes	characteristic
636	#520	C₂²×C₄₁	1	2	yes	—
637	#520	C₂²×C₄₁	1	1	yes	characteristic
638	#518	—	2	2	no	—
639	#518	—	2	1	no	—
640	#518	C₂²×C₄₁	1	1	yes	characteristic
641	#518	C₂²×C₄₁	1	2	yes	—
642	C₄×#41	—	2	1	no	—
643	C₄×#41	C₂²×C₄₁	1	2	yes	—
644	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
645	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
646	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic, complemented
647	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
648	C₂×C₄×D₄	—	2	1	no	—
649	C₂×C₄×D₄	—	2	2	no	—
650	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
651	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
652	#485	C₂²×C₄₁	1	2	yes	complemented
653	#485	C₂²×C₄₁	1	2	yes	complemented
654	#485	C₂²×C₄₁	1	2	yes	complemented
655	#484	C₂²×C₄₁	1	2	yes	complemented
656	#483	C₂²×C₄₁	1	2	yes	complemented
657	#483	C₂²×C₄₁	1	2	yes	complemented
658	#482	C₂²×C₄₁	1	2	yes	complemented
659	#481	C₂²×C₄₁	1	2	yes	complemented
660	#479	C₂²×C₄₁	1	2	yes	complemented
661	#478	C₂²×C₄₁	1	2	yes	complemented
662	#478	C₂²×C₄₁	1	2	yes	complemented
663	#478	C₂²×C₄₁	1	2	yes	complemented
664	#476	C₂²×C₄₁	1	2	yes	complemented
665	#476	C₂²×C₄₁	1	2	yes	complemented
666	#475	C₂²×C₄₁	1	2	yes	complemented
667	#474	C₂²×C₄₁	1	2	yes	complemented
668	#464	C₂²×C₄₁	1	2	yes	complemented
669	#463	C₂²×C₄₁	1	2	yes	complemented
670	#463	C₂²×C₄₁	1	2	yes	complemented
671	#463	C₂²×C₄₁	1	2	yes	complemented
672	#462	C₂²×C₄₁	1	2	yes	complemented
673	#461	C₂²×C₄₁	1	2	yes	complemented
674	#461	C₂²×C₄₁	1	2	yes	complemented
675	#461	C₂²×C₄₁	1	2	yes	complemented
676	#452	C₂²×C₄₁	1	2	yes	—
677	#452	C₂²×C₄₁	1	2	yes	—
678	#452	C₂²×C₄₁	1	2	yes	—
679	#450	C₂²×C₄₁	1	2	yes	—
680	#450	C₂²×C₄₁	1	2	yes	—
681	#450	C₂²×C₄₁	1	2	yes	—
682	#449	C₂²×C₄₁	1	2	yes	—
683	#447	C₂²×C₄₁	1	2	yes	—
684	#442	C₂²×C₄₁	1	2	yes	complemented
685	#441	C₂²×C₄₁	1	2	yes	complemented
686	#440	C₂²×C₄₁	1	2	yes	complemented
687	#440	C₂²×C₄₁	1	2	yes	complemented
688	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
689	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
690	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
692	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
694	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
695	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
696	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
697	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
701	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
702	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
703	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
704	#433	C₂²×C₄₁	1	2	yes	complemented
705	#433	C₂²×C₄₁	1	2	yes	complemented
706	#431	C₂²×C₄₁	1	2	yes	complemented
707	#431	C₂²×C₄₁	1	2	yes	complemented
708	#428	C₂²×C₄₁	1	1	yes	characteristic, complemented
709	#428	C₂²×C₄₁	1	1	yes	characteristic, complemented
710	#427	C₂²×C₄₁	1	1	yes	characteristic, complemented
711	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic, complemented
712	#424	C₂²×C₄₁	1	1	yes	characteristic, complemented
713	#424	C₂²×C₄₁	1	1	yes	characteristic, complemented
714	#419	C₂²×C₄₁	1	1	yes	characteristic, complemented
715	#418	C₂²×C₄₁	1	1	yes	characteristic
716	#417	C₂²×C₄₁	1	1	yes	characteristic
717	#417	C₂²×C₄₁	1	1	yes	characteristic, complemented
718	#416	C₂²×C₄₁	1	1	yes	characteristic
719	#416	C₂²×C₄₁	1	1	yes	characteristic, complemented
720	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic, complemented
721	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
722	#408	C₂²×C₄₁	1	1	yes	characteristic
723	#408	C₂²×C₄₁	1	1	yes	characteristic
724	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
725	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
726	C₄₁	#60571	1	1	yes	characteristic, direct product factor, Sylow
727	H(5,𝔽₂)	—	2	4	no	—
728	H(5,𝔽₂)	—	2	4	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	C₂³×C₄₁	1	2	yes	—
731	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
732	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
733	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
734	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
735	C₂²×D₄	—	2	2	no	—
736	C₂²×D₄	—	2	1	no	—
737	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
738	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
739	C₂³×C₄	—	2	1	no	—
740	C₂³×C₄	—	2	2	no	—
741	#137	—	2	4	no	—
742	AGL(1,ℤ/8)	—	2	4	no	—
743	#135	—	2	4	no	—
744	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
745	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
746	C₂×SD₁₆	—	2	4	no	—
747	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
751	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
753	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
754	C₂×D₈	C₂³×C₄₁	1	2	yes	—
755	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
756	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
757	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
758	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
759	C₄⋊Q₈	—	2	1	no	—
760	C₄⋊Q₈	—	2	1	no	—
761	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
762	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#126	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	—	2	1	no	—
769	#125	—	2	2	no	—
770	#125	—	2	2	no	—
771	#125	C₂³×C₄₁	1	2	yes	—
772	#124	—	2	1	no	—
773	#124	—	2	2	no	—
774	#124	C₂³×C₄₁	1	2	yes	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
788	#121	—	2	2	no	—
789	#121	—	2	1	no	—
790	#121	C₂³×C₄₁	1	2	yes	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	2	no	—
795	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
796	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
798	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
799	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
802	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
825	C₄×D₄	D₄×C₄₁	1	2	yes	—
826	C₄×D₄	D₄×C₄₁	1	2	yes	—
827	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₄₁	1	2	yes	—
830	C₄×D₄	C₂³×C₄₁	1	2	yes	—
831	C₄×D₄	C₂³×C₄₁	1	2	yes	—
832	C₄×D₄	C₂³×C₄₁	1	2	yes	—
833	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₄₁	1	2	yes	—
835	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
837	#117	—	2	2	no	—
838	#117	—	2	2	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	2	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	C₂³×C₄₁	1	1	yes	characteristic
845	#117	C₂³×C₄₁	1	2	yes	—
846	#117	C₂³×C₄₁	1	1	yes	characteristic
847	#117	C₂³×C₄₁	1	1	yes	characteristic
848	#117	C₂³×C₄₁	1	2	yes	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	—	2	2	no	—
852	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
853	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
854	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	—	2	1	no	—
862	C₂×C₄²	—	2	2	no	—
863	C₂×C₄²	—	2	1	no	—
864	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
865	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
866	#107	C₂³×C₄₁	1	1	yes	characteristic
867	#107	C₂³×C₄₁	1	1	yes	characteristic
868	#107	C₂³×C₄₁	1	2	yes	—
869	#107	C₂³×C₄₁	1	2	yes	—
870	#106	C₂³×C₄₁	1	2	yes	—
871	#106	C₂³×C₄₁	1	2	yes	—
872	#106	C₂³×C₄₁	1	1	yes	characteristic
873	#106	C₂³×C₄₁	1	1	yes	characteristic
874	#106	C₂³×C₄₁	1	2	yes	—
875	#106	C₂³×C₄₁	1	2	yes	—
876	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
877	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
878	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
879	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
880	#103	C₂³×C₄₁	1	2	yes	—
881	#103	C₂³×C₄₁	1	2	yes	—
882	#103	C₂³×C₄₁	1	1	yes	characteristic
883	#103	C₂³×C₄₁	1	1	yes	characteristic
884	#103	C₂³×C₄₁	1	1	yes	characteristic
885	#103	C₂³×C₄₁	1	1	yes	characteristic
886	#103	C₂³×C₄₁	1	2	yes	—
887	#103	C₂³×C₄₁	1	2	yes	—
888	#103	C₂³×C₄₁	1	2	yes	—
889	#103	C₂³×C₄₁	1	2	yes	—
890	#102	C₂³×C₄₁	1	2	yes	—
891	#102	C₂³×C₄₁	1	2	yes	—
892	#102	C₂³×C₄₁	1	1	yes	characteristic
893	#102	C₂³×C₄₁	1	1	yes	characteristic
894	#102	C₂³×C₄₁	1	1	yes	characteristic
895	#102	C₂³×C₄₁	1	1	yes	characteristic
896	#102	C₂³×C₄₁	1	2	yes	—
897	#102	C₂³×C₄₁	1	2	yes	—
898	#102	C₂³×C₄₁	1	2	yes	—
899	#102	C₂³×C₄₁	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
904	#97	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	C₄×C₈	C₂³×C₄₁	1	2	yes	—
910	C₂⁴	—	2	2	no	—
911	C₂⁴	—	2	1	no	—
912	#41	—	2	8	no	—
913	#41	—	2	4	no	—
914	#41	—	2	4	no	—
915	#41	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	#41×C₄₁	1	4	yes	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	—	2	2	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
927	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
929	C₂×D₄	—	2	16	no	—
930	C₂×D₄	—	2	8	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	4	no	—
934	C₂×D₄	—	2	4	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
941	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
942	C₂×D₄	#41×C₄₁	1	4	yes	—
943	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	8	2	no	—
963	C₂²×C₄	—	8	4	no	—
964	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
965	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
966	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
967	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
970	Q₁₆	—	2	2	no	—
971	Q₁₆	—	2	4	no	—
972	SD₁₆	—	2	2	no	—
973	SD₁₆	—	2	4	no	—
974	SD₁₆	—	2	4	no	—
975	SD₁₆	—	2	2	no	—
976	SD₁₆	—	2	4	no	—
977	SD₁₆	—	2	4	no	—
978	D₈	—	2	2	no	—
979	D₈	—	2	4	no	—
980	M₁₆	—	2	2	no	—
981	M₁₆	—	2	2	no	—
982	C₂×C₈	—	2	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
989	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1010	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1011	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1013	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1014	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1037	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1038	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	2	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₄₁	1	2	yes	—
1051	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1052	C₄²	C₂×D₄×C₄₁	1	2	yes	—
1053	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₄₁	1	2	yes	—
1056	C₂³	—	2	8	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	8	1	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	—	8	2	no	—
1065	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1066	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	2	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	4	2	no	—
1074	Q₈	—	8	2	no	—
1075	Q₈	C₂×#41×C₄₁	1	2	yes	—
1076	D₄	—	2	8	no	—
1077	D₄	—	2	8	no	—
1078	D₄	—	2	4	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	4	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	C₂×#41×C₄₁	1	2	yes	—
1089	D₄	C₂×#41×C₄₁	1	4	yes	—
1090	C₂×C₄	—	2	8	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	4	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	4	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	4	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	1	no	—
1116	C₂×C₄	—	8	1	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1123	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1127	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1128	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1129	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
1130	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
1131	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	2	no	—
1137	C₈	—	2	2	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	4	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	8	4	no	—
1153	C₂²	—	8	8	no	—
1154	C₂²	C₄₁×#525	1	2	yes	—
1155	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	2	no	—
1171	C₄	C₄₁×#525	1	2	yes	—
1172	C₄	C₄₁×#577	1	2	yes	—
1173	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
1174	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	4	4	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
1181	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
1182	C₂	C₄₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
socle	C₂²×C₄₁	C₂³×D₄
prime radical	C₄₁×#3012	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3461	C₂	semidirect
2. C₄×H(5,𝔽₂)×C₄₁	C₂	semidirect
3. C₄₁×#3125	C₂	semidirect
4. C₄₁×#3123	C₂	semidirect
5. C₄₁×#3120	C₂	semidirect
6. C₄₁×#3118	C₂	semidirect
7. C₄₁×#3107	C₂	semidirect
8. C₄₁×#3105	C₂	semidirect
9. C₄₁×#3102	C₂	semidirect
10. C₄₁×#3101	C₂	semidirect
11. C₄₁×#3099	C₂	semidirect
12. C₄₁×#3097	C₂	semidirect
13. C₄₁×#3084	C₂	semidirect
14. C₄₁×#3081	C₂	semidirect
15. C₄₁×#3046	C₂	semidirect
16. C₄₁×#3042	C₂	semidirect
18. C₄₁×#3009	C₂	semidirect
19. C₄×#137×C₄₁	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₄₁	C₂	semidirect
21. C₄×#135×C₄₁	C₂	semidirect
22. C₂×C₄×SD₁₆×C₄₁	C₂	semidirect
23. C₄₁×#2922	C₂	semidirect
29. C₄₁×#544	C₂²	semidirect
31. C₄₁×#542	C₂²	semidirect
33. C₄₁×#541	C₂²	semidirect
37. C₄₁×#536	C₂²	semidirect
39. C₄₁×#533	C₂²	semidirect
42. C₄₁×#529	C₂²	semidirect
55. C₄×#41×C₄₁	C₂²	semidirect
56. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
61. C₄₁×#485	C₂²	semidirect
62. C₄₁×#485	C₂²	semidirect
63. C₄₁×#485	C₂²	semidirect
64. C₄₁×#484	C₂²	semidirect
65. C₄₁×#483	C₂²	semidirect
66. C₄₁×#483	C₂²	semidirect
67. C₄₁×#482	C₂²	semidirect
68. C₄₁×#481	C₂²	semidirect
69. C₄₁×#479	C₂²	semidirect
70. C₄₁×#478	C₂²	semidirect
71. C₄₁×#478	C₂²	semidirect
72. C₄₁×#478	C₂²	semidirect
73. C₄₁×#476	C₂²	semidirect
74. C₄₁×#476	C₂²	semidirect
75. C₄₁×#475	C₂²	semidirect
76. C₄₁×#474	C₂²	semidirect
77. C₄₁×#464	C₂²	semidirect
78. C₄₁×#463	C₂²	semidirect
79. C₄₁×#463	C₂²	semidirect
80. C₄₁×#463	C₂²	semidirect
81. C₄₁×#462	C₂²	semidirect
82. C₄₁×#461	C₂²	semidirect
83. C₄₁×#461	C₂²	semidirect
84. C₄₁×#461	C₂²	semidirect
93. C₄₁×#442	C₂²	semidirect
94. C₄₁×#441	C₂²	semidirect
95. C₄₁×#440	C₂²	semidirect
96. C₄₁×#440	C₂²	semidirect
97. C₄×Q₁₆×C₄₁	C₂²	semidirect
98. C₄×Q₁₆×C₄₁	C₂²	semidirect
99. C₄×Q₁₆×C₄₁	C₂²	semidirect
100. C₄×SD₁₆×C₄₁	C₂²	semidirect
101. C₄×SD₁₆×C₄₁	C₂²	semidirect
102. C₄×SD₁₆×C₄₁	C₂²	semidirect
103. C₄×SD₁₆×C₄₁	C₂²	semidirect
104. C₄×SD₁₆×C₄₁	C₂²	semidirect
105. C₄×SD₁₆×C₄₁	C₂²	semidirect
106. C₄×SD₁₆×C₄₁	C₂²	semidirect
107. C₄×SD₁₆×C₄₁	C₂²	semidirect
108. C₄×SD₁₆×C₄₁	C₂²	semidirect
109. C₄×SD₁₆×C₄₁	C₂²	semidirect
110. C₄×D₈×C₄₁	C₂²	semidirect
111. C₄×D₈×C₄₁	C₂²	semidirect
112. C₄×D₈×C₄₁	C₂²	semidirect
113. C₄₁×#433	C₂²	semidirect
114. C₄₁×#433	C₂²	semidirect
115. C₄₁×#431	C₂²	semidirect
116. C₄₁×#431	C₂²	semidirect
117. C₄₁×#428	C₂²	semidirect
118. C₄₁×#428	C₂²	semidirect
119. C₄₁×#427	C₂²	semidirect
120. C₂×#106×C₄₁	C₂²	semidirect
121. C₄₁×#424	C₂²	semidirect
122. C₄₁×#424	C₂²	semidirect
123. C₄₁×#419	C₂²	semidirect
126. C₄₁×#417	C₂²	semidirect
128. C₄₁×#416	C₂²	semidirect
129. C₂×#103×C₄₁	C₂²	semidirect
133. C₄×M₁₆×C₄₁	C₂²	semidirect
134. C₂×C₄×C₈×C₄₁	C₂²	semidirect
546. #60571	C₄₁	direct (N × H)
584. #3461	C₂×C₄₁	semidirect
585. C₄×H(5,𝔽₂)	C₂×C₄₁	semidirect
586. #3125	C₂×C₄₁	semidirect
587. #3123	C₂×C₄₁	semidirect
588. #3120	C₂×C₄₁	semidirect
589. #3118	C₂×C₄₁	semidirect
590. #3107	C₂×C₄₁	semidirect
591. #3105	C₂×C₄₁	semidirect
592. #3102	C₂×C₄₁	semidirect
593. #3101	C₂×C₄₁	semidirect
594. #3099	C₂×C₄₁	semidirect
595. #3097	C₂×C₄₁	semidirect
596. #3084	C₂×C₄₁	semidirect
597. #3081	C₂×C₄₁	semidirect
598. #3046	C₂×C₄₁	semidirect
599. #3042	C₂×C₄₁	semidirect
601. #3009	C₂×C₄₁	semidirect
602. C₄×#137	C₂×C₄₁	semidirect
603. C₄×AGL(1,ℤ/8)	C₂×C₄₁	semidirect
604. C₄×#135	C₂×C₄₁	semidirect
605. C₂×C₄×SD₁₆	C₂×C₄₁	semidirect
606. #2922	C₂×C₄₁	semidirect
620. #544	C₂²×C₄₁	semidirect
622. #542	C₂²×C₄₁	semidirect
624. #541	C₂²×C₄₁	semidirect
628. #536	C₂²×C₄₁	semidirect
630. #533	C₂²×C₄₁	semidirect
633. #529	C₂²×C₄₁	semidirect
646. C₄×#41	C₂²×C₄₁	semidirect
647. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
652. #485	C₂²×C₄₁	semidirect
653. #485	C₂²×C₄₁	semidirect
654. #485	C₂²×C₄₁	semidirect
655. #484	C₂²×C₄₁	semidirect
656. #483	C₂²×C₄₁	semidirect
657. #483	C₂²×C₄₁	semidirect
658. #482	C₂²×C₄₁	semidirect
659. #481	C₂²×C₄₁	semidirect
660. #479	C₂²×C₄₁	semidirect
661. #478	C₂²×C₄₁	semidirect
662. #478	C₂²×C₄₁	semidirect
663. #478	C₂²×C₄₁	semidirect
664. #476	C₂²×C₄₁	semidirect
665. #476	C₂²×C₄₁	semidirect
666. #475	C₂²×C₄₁	semidirect
667. #474	C₂²×C₄₁	semidirect
668. #464	C₂²×C₄₁	semidirect
669. #463	C₂²×C₄₁	semidirect
670. #463	C₂²×C₄₁	semidirect
671. #463	C₂²×C₄₁	semidirect
672. #462	C₂²×C₄₁	semidirect
673. #461	C₂²×C₄₁	semidirect
674. #461	C₂²×C₄₁	semidirect
675. #461	C₂²×C₄₁	semidirect
684. #442	C₂²×C₄₁	semidirect
685. #441	C₂²×C₄₁	semidirect
686. #440	C₂²×C₄₁	semidirect
687. #440	C₂²×C₄₁	semidirect
688. C₄×Q₁₆	C₂²×C₄₁	semidirect
689. C₄×Q₁₆	C₂²×C₄₁	semidirect
690. C₄×Q₁₆	C₂²×C₄₁	semidirect
691. C₄×SD₁₆	C₂²×C₄₁	semidirect
692. C₄×SD₁₆	C₂²×C₄₁	semidirect
693. C₄×SD₁₆	C₂²×C₄₁	semidirect
694. C₄×SD₁₆	C₂²×C₄₁	semidirect
695. C₄×SD₁₆	C₂²×C₄₁	semidirect
696. C₄×SD₁₆	C₂²×C₄₁	semidirect
697. C₄×SD₁₆	C₂²×C₄₁	semidirect
698. C₄×SD₁₆	C₂²×C₄₁	semidirect
699. C₄×SD₁₆	C₂²×C₄₁	semidirect
700. C₄×SD₁₆	C₂²×C₄₁	semidirect
701. C₄×D₈	C₂²×C₄₁	semidirect
702. C₄×D₈	C₂²×C₄₁	semidirect
703. C₄×D₈	C₂²×C₄₁	semidirect
704. #433	C₂²×C₄₁	semidirect
705. #433	C₂²×C₄₁	semidirect
706. #431	C₂²×C₄₁	semidirect
707. #431	C₂²×C₄₁	semidirect
708. #428	C₂²×C₄₁	semidirect
709. #428	C₂²×C₄₁	semidirect
710. #427	C₂²×C₄₁	semidirect
711. C₂×#106	C₂²×C₄₁	semidirect
712. #424	C₂²×C₄₁	semidirect
713. #424	C₂²×C₄₁	semidirect
714. #419	C₂²×C₄₁	semidirect
717. #417	C₂²×C₄₁	semidirect
719. #416	C₂²×C₄₁	semidirect
720. C₂×#103	C₂²×C₄₁	semidirect
724. C₄×M₁₆	C₂²×C₄₁	semidirect
725. C₂×C₄×C₈	C₂²×C₄₁	semidirect
726. C₄₁	#60571	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3461	2
C₄×H(5,𝔽₂)×C₄₁	2
C₄₁×#3125	2
C₄₁×#3123	2
C₄₁×#3120	2
C₄₁×#3118	2
C₄₁×#3107	2
C₄₁×#3105	2
C₄₁×#3102	2
C₄₁×#3101	2
C₄₁×#3099	2
C₄₁×#3097	2
C₄₁×#3084	2
C₄₁×#3081	2
C₄₁×#3046	2
C₄₁×#3042	2
C₄₁×#3012	2
C₄₁×#3009	2
C₄×#137×C₄₁	2
C₄×AGL(1,ℤ/8)×C₄₁	2
C₄×#135×C₄₁	2
C₂×C₄×SD₁₆×C₄₁	2
C₄₁×#2922	2
#60571	41

Subgroups — C41×#60571 #23836772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#60571 #23836772