Subgroups — C₄₁×#61567 #23837768

Order 10496.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3301	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3297	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3282	C₂	1	2	yes	maximal, complemented
12	D₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3280	C₂	1	2	yes	maximal, complemented
14	D₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3191	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3188	C₂	1	2	yes	maximal, complemented
19	C₄₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3002	C₂	1	2	yes	maximal, complemented
22	C₂×C₄₁×#449	C₂	1	2	yes	maximal, complemented
23	C₄₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₄₁	C₂²	1	2	yes	complemented
25	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
26	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
27	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
28	C₂²×D₈×C₄₁	C₂²	1	2	yes	complemented
29	C₄₁×#555	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#554	C₂²	1	1	yes	characteristic
31	C₄₁×#553	—	2	1	no	—
32	C₄₁×#553	C₂²	1	2	yes	complemented
33	C₄₁×#550	C₂²	1	1	yes	characteristic, complemented
34	C₄₁×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#548	C₂²	1	2	yes	complemented
37	C₄₁×#547	—	2	1	no	—
38	C₄₁×#547	C₂²	1	1	yes	characteristic, complemented
39	C₄₁×#546	—	2	2	no	—
40	C₄₁×#546	—	2	2	no	—
41	C₄₁×#546	C₂²	1	2	yes	complemented
42	C₄₁×#546	C₂²	1	2	yes	complemented
43	D₄²×C₄₁	—	2	1	no	—
44	D₄²×C₄₁	—	2	1	no	—
45	D₄²×C₄₁	C₂²	1	1	yes	characteristic
46	D₄²×C₄₁	C₂²	1	1	yes	characteristic
47	C₄₁×#540	—	2	1	no	—
48	C₄₁×#538	—	2	2	no	—
49	C₄₁×#532	—	2	1	no	—
50	C₄₁×#532	C₂²	1	1	yes	characteristic, complemented
51	C₄₁×#532	C₂²	1	1	yes	characteristic, complemented
52	C₄₁×#529	C₂²	1	1	yes	characteristic, complemented
53	C₄₁×#525	—	2	2	no	—
54	C₄₁×#525	C₂²	1	2	yes	complemented
55	C₄₁×#525	C₂²	1	2	yes	complemented
56	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
57	C₄₁×#518	—	2	1	no	—
58	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×D₄×C₄₁	—	2	1	no	—
60	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
61	C₄₁×#495	C₂²	1	2	yes	complemented
62	C₄₁×#493	C₂²	1	1	yes	characteristic, complemented
63	C₄₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₄₁×#488	C₂²	1	2	yes	complemented
65	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₄₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#485	C₂²	1	2	yes	complemented
68	C₄₁×#485	C₂²	1	1	yes	characteristic, complemented
69	C₄₁×#484	C₂²	1	2	yes	complemented
70	C₄₁×#482	C₂²	1	2	yes	complemented
71	C₄₁×#482	C₂²	1	1	yes	characteristic, complemented
72	C₄₁×#482	C₂²	1	2	yes	complemented
73	C₄₁×#481	C₂²	1	2	yes	complemented
74	C₄₁×#479	C₂²	1	1	yes	characteristic, complemented
75	C₄₁×#478	C₂²	1	1	yes	characteristic, complemented
76	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#476	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#467	C₂²	1	2	yes	complemented
79	C₄₁×#466	C₂²	1	2	yes	complemented
80	C₄₁×#466	C₂²	1	2	yes	complemented
81	C₄₁×#466	C₂²	1	2	yes	complemented
82	C₄₁×#465	C₂²	1	2	yes	complemented
83	C₄₁×#465	C₂²	1	2	yes	complemented
84	C₄₁×#465	C₂²	1	2	yes	complemented
85	C₄₁×#465	C₂²	1	2	yes	complemented
86	C₄₁×#464	C₂²	1	1	yes	characteristic, complemented
87	C₄₁×#463	C₂²	1	2	yes	complemented
88	C₄₁×#463	C₂²	1	2	yes	complemented
89	C₄₁×#463	C₂²	1	1	yes	characteristic, complemented
90	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
92	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
93	C₄₁×#460	C₂²	1	1	yes	characteristic, complemented
94	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
95	C₄₁×#459	C₂²	1	1	yes	characteristic, complemented
96	C₄₁×#452	C₂²	1	1	yes	characteristic, complemented
97	C₄₁×#452	C₂²	1	2	yes	complemented
98	C₄₁×#452	C₂²	1	2	yes	complemented
99	C₄₁×#451	C₂²	1	2	yes	complemented
100	C₄₁×#450	C₂²	1	2	yes	complemented
101	C₄₁×#450	C₂²	1	2	yes	complemented
102	C₄₁×#449	C₂²	1	1	yes	characteristic
103	C₄₁×#449	C₂²	1	2	yes	complemented
104	C₄₁×#449	C₂²	1	2	yes	complemented
105	C₄₁×#449	C₂²	1	2	yes	complemented
106	C₄₁×#449	C₂²	1	2	yes	complemented
107	C₄₁×#449	C₂²	1	2	yes	complemented
108	C₄₁×#449	C₂²	1	2	yes	complemented
109	C₄₁×#449	C₂²	1	2	yes	complemented
110	C₄₁×#449	C₂²	1	2	yes	complemented
111	C₄₁×#449	C₂²	1	2	yes	complemented
112	C₄₁×#448	C₂²	1	2	yes	complemented
113	C₄₁×#447	C₂²	1	2	yes	complemented
114	C₄₁×#447	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
120	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
124	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
125	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
127	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
128	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
129	C₄₁×#416	C₂²	1	2	yes	complemented
130	C₄₁×#416	C₂²	1	2	yes	complemented
131	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
132	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₄₁	—	2	2	no	—
136	C₂×#41×C₄₁	—	2	2	no	—
137	C₂×#41×C₄₁	—	2	1	no	—
138	C₂×#41×C₄₁	—	4	4	no	—
139	C₂×#41×C₄₁	—	4	4	no	—
140	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₄₁	C₂³	1	2	yes	—
142	C₂×#41×C₄₁	C₂³	1	2	yes	—
143	C₂×#41×C₄₁	C₂³	1	2	yes	—
144	C₂×#41×C₄₁	C₂³	1	2	yes	—
145	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₄₁	—	2	2	no	—
147	C₂²×D₄×C₄₁	—	2	2	no	—
148	C₂²×D₄×C₄₁	—	2	1	no	—
149	C₂²×D₄×C₄₁	—	2	1	no	—
150	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
151	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
152	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
153	C₂³×C₄×C₄₁	—	2	2	no	—
154	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
155	#135×C₄₁	—	4	4	no	—
156	#135×C₄₁	—	4	4	no	—
157	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₄₁	—	4	4	no	—
160	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
167	C₂×D₈×C₄₁	—	4	4	no	—
168	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
169	C₂×D₈×C₄₁	C₂³	1	2	yes	—
170	C₂×D₈×C₄₁	C₂³	1	2	yes	—
171	C₂×D₈×C₄₁	C₂³	1	2	yes	—
172	C₂×D₈×C₄₁	C₂³	1	2	yes	—
173	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
174	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
175	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
176	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
177	C₄⋊Q₈×C₄₁	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
183	#127×C₄₁	C₂³	1	1	yes	characteristic
184	#126×C₄₁	—	2	2	no	—
185	#126×C₄₁	—	2	1	no	—
186	#125×C₄₁	—	2	1	no	—
187	#125×C₄₁	C₂³	1	1	yes	characteristic
188	#124×C₄₁	—	2	2	no	—
189	#124×C₄₁	—	2	2	no	—
190	#124×C₄₁	—	2	1	no	—
191	#124×C₄₁	C₂³	1	1	yes	characteristic
192	#124×C₄₁	C₂³	1	2	yes	—
193	#123×C₄₁	—	2	2	no	—
194	#123×C₄₁	—	2	2	no	—
195	#123×C₄₁	—	2	1	no	—
196	#123×C₄₁	—	2	2	no	—
197	#123×C₄₁	—	2	2	no	—
198	#123×C₄₁	—	2	2	no	—
199	#123×C₄₁	—	2	2	no	—
200	C₂²⋊Q₈×C₄₁	—	2	2	no	—
201	C₂²⋊Q₈×C₄₁	—	2	2	no	—
202	C₂²⋊Q₈×C₄₁	—	2	2	no	—
203	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
204	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
207	#121×C₄₁	—	2	2	no	—
208	#121×C₄₁	—	2	1	no	—
209	#121×C₄₁	—	2	2	no	—
210	#121×C₄₁	—	2	1	no	—
211	#121×C₄₁	—	2	2	no	—
212	#121×C₄₁	—	2	2	no	—
213	#121×C₄₁	—	2	1	no	—
214	#121×C₄₁	—	2	1	no	—
215	#121×C₄₁	—	2	1	no	—
216	#121×C₄₁	—	2	1	no	—
217	#121×C₄₁	—	2	1	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	C₂³	1	1	yes	characteristic
223	#121×C₄₁	C₂³	1	2	yes	—
224	#121×C₄₁	C₂³	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	#120×C₄₁	—	2	2	no	—
230	#120×C₄₁	—	2	2	no	—
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	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₄₁	—	2	1	no	—
239	C₄×D₄×C₄₁	—	2	1	no	—
240	C₄×D₄×C₄₁	—	2	2	no	—
241	C₄×D₄×C₄₁	—	2	1	no	—
242	C₄×D₄×C₄₁	—	2	1	no	—
243	C₄×D₄×C₄₁	—	2	2	no	—
244	C₄×D₄×C₄₁	—	2	2	no	—
245	C₄×D₄×C₄₁	—	2	2	no	—
246	C₄×D₄×C₄₁	—	2	1	no	—
247	C₄×D₄×C₄₁	—	2	1	no	—
248	C₄×D₄×C₄₁	—	2	1	no	—
249	C₄×D₄×C₄₁	—	2	2	no	—
250	C₄×D₄×C₄₁	—	2	2	no	—
251	C₄×D₄×C₄₁	—	2	1	no	—
252	C₄×D₄×C₄₁	—	2	1	no	—
253	C₄×D₄×C₄₁	—	2	1	no	—
254	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
255	C₄×D₄×C₄₁	D₄	1	2	yes	—
256	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
257	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₄₁	C₂³	1	2	yes	—
261	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₄₁	C₂³	1	2	yes	—
263	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
264	#117×C₄₁	—	2	1	no	—
265	#117×C₄₁	—	2	1	no	—
266	#117×C₄₁	—	2	1	no	—
267	#117×C₄₁	C₂³	1	1	yes	characteristic
268	#117×C₄₁	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
276	C₂×C₄²×C₄₁	—	2	1	no	—
277	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
278	#107×C₄₁	C₂³	1	1	yes	characteristic
279	#107×C₄₁	C₂³	1	2	yes	—
280	#107×C₄₁	C₂³	1	1	yes	characteristic
281	#106×C₄₁	C₂³	1	2	yes	—
282	#106×C₄₁	C₂³	1	1	yes	characteristic
283	#106×C₄₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
288	#103×C₄₁	C₂³	1	1	yes	characteristic
289	#103×C₄₁	C₂³	1	2	yes	—
290	#103×C₄₁	C₂³	1	2	yes	—
291	#103×C₄₁	C₂³	1	2	yes	—
292	#103×C₄₁	C₂³	1	1	yes	characteristic
293	#103×C₄₁	C₂³	1	2	yes	—
294	#103×C₄₁	C₂³	1	2	yes	—
295	#103×C₄₁	C₂³	1	1	yes	characteristic
296	#103×C₄₁	C₂³	1	1	yes	characteristic
297	#102×C₄₁	C₂³	1	1	yes	characteristic
298	#102×C₄₁	C₂³	1	2	yes	—
299	#102×C₄₁	C₂³	1	2	yes	—
300	#102×C₄₁	C₂³	1	2	yes	—
301	#102×C₄₁	C₂³	1	1	yes	characteristic
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	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
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	2	no	—
320	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
321	#41×C₄₁	—	2	2	no	—
322	#41×C₄₁	—	2	2	no	—
323	#41×C₄₁	—	2	4	no	—
324	#41×C₄₁	—	2	4	no	—
325	#41×C₄₁	—	4	2	no	—
326	#41×C₄₁	—	4	2	no	—
327	#41×C₄₁	—	4	2	no	—
328	#41×C₄₁	—	4	2	no	—
329	#41×C₄₁	—	4	8	no	—
330	#41×C₄₁	—	4	2	no	—
331	#41×C₄₁	—	4	2	no	—
332	#41×C₄₁	—	4	8	no	—
333	#41×C₄₁	—	8	2	no	—
334	C₂×Q₈×C₄₁	—	2	2	no	—
335	C₂×Q₈×C₄₁	—	2	1	no	—
336	C₂×Q₈×C₄₁	—	2	4	no	—
337	C₂×Q₈×C₄₁	—	4	2	no	—
338	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
339	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₄₁	—	2	1	no	—
342	C₂×D₄×C₄₁	—	2	4	no	—
343	C₂×D₄×C₄₁	—	2	4	no	—
344	C₂×D₄×C₄₁	—	2	2	no	—
345	C₂×D₄×C₄₁	—	2	2	no	—
346	C₂×D₄×C₄₁	—	2	2	no	—
347	C₂×D₄×C₄₁	—	2	1	no	—
348	C₂×D₄×C₄₁	—	2	2	no	—
349	C₂×D₄×C₄₁	—	2	2	no	—
350	C₂×D₄×C₄₁	—	2	2	no	—
351	C₂×D₄×C₄₁	—	2	2	no	—
352	C₂×D₄×C₄₁	—	2	2	no	—
353	C₂×D₄×C₄₁	—	2	2	no	—
354	C₂×D₄×C₄₁	—	2	2	no	—
355	C₂×D₄×C₄₁	—	2	1	no	—
356	C₂×D₄×C₄₁	—	2	1	no	—
357	C₂×D₄×C₄₁	—	2	2	no	—
358	C₂×D₄×C₄₁	—	2	1	no	—
359	C₂×D₄×C₄₁	—	2	1	no	—
360	C₂×D₄×C₄₁	—	2	2	no	—
361	C₂×D₄×C₄₁	—	4	2	no	—
362	C₂×D₄×C₄₁	—	4	2	no	—
363	C₂×D₄×C₄₁	—	4	2	no	—
364	C₂×D₄×C₄₁	—	4	8	no	—
365	C₂×D₄×C₄₁	—	4	4	no	—
366	C₂×D₄×C₄₁	—	4	4	no	—
367	C₂×D₄×C₄₁	—	8	4	no	—
368	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
372	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
374	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₄₁	—	2	1	no	—
376	C₂²×C₄×C₄₁	—	2	2	no	—
377	C₂²×C₄×C₄₁	—	2	2	no	—
378	C₂²×C₄×C₄₁	—	2	1	no	—
379	C₂²×C₄×C₄₁	—	2	2	no	—
380	C₂²×C₄×C₄₁	—	2	1	no	—
381	C₂²×C₄×C₄₁	—	2	2	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	—	4	2	no	—
387	C₂²×C₄×C₄₁	—	4	2	no	—
388	C₂²×C₄×C₄₁	—	4	8	no	—
389	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
392	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
393	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
394	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
397	Q₁₆×C₄₁	—	2	2	no	—
398	Q₁₆×C₄₁	—	4	2	no	—
399	SD₁₆×C₄₁	—	2	2	no	—
400	SD₁₆×C₄₁	—	2	4	no	—
401	SD₁₆×C₄₁	—	2	2	no	—
402	SD₁₆×C₄₁	—	4	2	no	—
403	SD₁₆×C₄₁	—	4	2	no	—
404	SD₁₆×C₄₁	—	4	2	no	—
405	SD₁₆×C₄₁	—	4	2	no	—
406	D₈×C₄₁	—	2	2	no	—
407	D₈×C₄₁	—	2	4	no	—
408	D₈×C₄₁	—	4	2	no	—
409	D₈×C₄₁	—	4	2	no	—
410	D₈×C₄₁	—	4	2	no	—
411	C₂×C₈×C₄₁	—	4	2	no	—
412	C₂×C₈×C₄₁	—	4	2	no	—
413	C₂×C₈×C₄₁	—	4	2	no	—
414	C₂×C₈×C₄₁	—	4	2	no	—
415	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
418	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
419	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₄₁	—	2	1	no	—
422	C₄⋊C₄×C₄₁	—	2	2	no	—
423	C₄⋊C₄×C₄₁	—	2	2	no	—
424	C₄⋊C₄×C₄₁	—	2	1	no	—
425	C₄⋊C₄×C₄₁	—	2	1	no	—
426	C₄⋊C₄×C₄₁	—	2	1	no	—
427	C₄⋊C₄×C₄₁	—	2	1	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	—	2	2	no	—
432	C₄⋊C₄×C₄₁	—	2	2	no	—
433	C₄⋊C₄×C₄₁	—	2	1	no	—
434	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
439	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄×C₄₁	—	2	2	no	—
443	C₂²⋊C₄×C₄₁	—	2	2	no	—
444	C₂²⋊C₄×C₄₁	—	2	1	no	—
445	C₂²⋊C₄×C₄₁	—	2	2	no	—
446	C₂²⋊C₄×C₄₁	—	2	1	no	—
447	C₂²⋊C₄×C₄₁	—	2	2	no	—
448	C₂²⋊C₄×C₄₁	—	2	1	no	—
449	C₂²⋊C₄×C₄₁	—	2	1	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	1	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	—	2	1	no	—
462	C₂²⋊C₄×C₄₁	—	2	2	no	—
463	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
467	C₄²×C₄₁	—	2	1	no	—
468	C₄²×C₄₁	—	2	1	no	—
469	C₄²×C₄₁	—	2	1	no	—
470	C₄²×C₄₁	—	2	2	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	4	no	—
478	C₂³×C₄₁	—	2	1	no	—
479	C₂³×C₄₁	—	2	2	no	—
480	C₂³×C₄₁	—	2	2	no	—
481	C₂³×C₄₁	—	4	2	no	—
482	C₂³×C₄₁	—	4	2	no	—
483	C₂³×C₄₁	—	4	4	no	—
484	C₂³×C₄₁	—	4	4	no	—
485	C₂³×C₄₁	—	4	4	no	—
486	C₂³×C₄₁	—	8	2	no	—
487	C₂³×C₄₁	—	8	2	no	—
488	C₂³×C₄₁	—	8	2	no	—
489	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
490	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
491	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
492	Q₈×C₄₁	—	2	1	no	—
493	Q₈×C₄₁	—	2	1	no	—
494	Q₈×C₄₁	—	2	1	no	—
495	Q₈×C₄₁	—	2	2	no	—
496	Q₈×C₄₁	—	2	2	no	—
497	Q₈×C₄₁	—	4	4	no	—
498	Q₈×C₄₁	—	8	1	no	—
499	Q₈×C₄₁	H(5,𝔽₂)	1	2	yes	—
500	D₄×C₄₁	—	2	4	no	—
501	D₄×C₄₁	—	2	4	no	—
502	D₄×C₄₁	—	2	2	no	—
503	D₄×C₄₁	—	2	1	no	—
504	D₄×C₄₁	—	2	1	no	—
505	D₄×C₄₁	—	2	2	no	—
506	D₄×C₄₁	—	2	2	no	—
507	D₄×C₄₁	—	2	2	no	—
508	D₄×C₄₁	—	2	2	no	—
509	D₄×C₄₁	—	2	1	no	—
510	D₄×C₄₁	—	4	4	no	—
511	D₄×C₄₁	—	4	4	no	—
512	D₄×C₄₁	—	4	4	no	—
513	D₄×C₄₁	—	4	4	no	—
514	D₄×C₄₁	—	4	2	no	—
515	D₄×C₄₁	—	4	4	no	—
516	D₄×C₄₁	—	4	4	no	—
517	D₄×C₄₁	—	4	4	no	—
518	D₄×C₄₁	—	4	2	no	—
519	D₄×C₄₁	—	4	2	no	—
520	D₄×C₄₁	—	8	1	no	—
521	D₄×C₄₁	—	8	2	no	—
522	D₄×C₄₁	—	8	1	no	—
523	D₄×C₄₁	—	8	2	no	—
524	D₄×C₄₁	—	8	2	no	—
525	D₄×C₄₁	—	8	2	no	—
526	D₄×C₄₁	—	8	2	no	—
527	D₄×C₄₁	#135	1	4	yes	complemented
528	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
529	C₂×C₄×C₄₁	—	2	4	no	—
530	C₂×C₄×C₄₁	—	2	1	no	—
531	C₂×C₄×C₄₁	—	2	2	no	—
532	C₂×C₄×C₄₁	—	2	2	no	—
533	C₂×C₄×C₄₁	—	2	2	no	—
534	C₂×C₄×C₄₁	—	2	2	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	1	no	—
539	C₂×C₄×C₄₁	—	2	1	no	—
540	C₂×C₄×C₄₁	—	2	1	no	—
541	C₂×C₄×C₄₁	—	2	1	no	—
542	C₂×C₄×C₄₁	—	2	2	no	—
543	C₂×C₄×C₄₁	—	2	1	no	—
544	C₂×C₄×C₄₁	—	2	2	no	—
545	C₂×C₄×C₄₁	—	4	2	no	—
546	C₂×C₄×C₄₁	—	4	2	no	—
547	C₂×C₄×C₄₁	—	4	2	no	—
548	C₂×C₄×C₄₁	—	4	1	no	—
549	C₂×C₄×C₄₁	—	4	4	no	—
550	C₂×C₄×C₄₁	—	4	4	no	—
551	C₂×C₄×C₄₁	—	4	4	no	—
552	C₂×C₄×C₄₁	—	4	4	no	—
553	C₂×C₄×C₄₁	—	4	2	no	—
554	C₂×C₄×C₄₁	—	4	2	no	—
555	C₂×C₄×C₄₁	—	8	1	no	—
556	C₂×C₄×C₄₁	—	8	2	no	—
557	C₂×C₄×C₄₁	—	8	2	no	—
558	C₂×C₄×C₄₁	—	8	2	no	—
559	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
562	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
565	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
567	C₈×C₄₁	—	2	1	no	—
568	C₈×C₄₁	—	2	2	no	—
569	C₈×C₄₁	—	2	1	no	—
570	C₈×C₄₁	—	2	1	no	—
571	C₈×C₄₁	—	2	2	no	—
572	C₈×C₄₁	—	2	1	no	—
573	#61567	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
574	C₂²×C₄₁	—	2	2	no	—
575	C₂²×C₄₁	—	2	2	no	—
576	C₂²×C₄₁	—	2	1	no	—
577	C₂²×C₄₁	—	2	2	no	—
578	C₂²×C₄₁	—	2	1	no	—
579	C₂²×C₄₁	—	2	2	no	—
580	C₂²×C₄₁	—	2	2	no	—
581	C₂²×C₄₁	—	2	1	no	—
582	C₂²×C₄₁	—	2	2	no	—
583	C₂²×C₄₁	—	4	1	no	—
584	C₂²×C₄₁	—	4	1	no	—
585	C₂²×C₄₁	—	4	2	no	—
586	C₂²×C₄₁	—	4	1	no	—
587	C₂²×C₄₁	—	4	2	no	—
588	C₂²×C₄₁	—	4	2	no	—
589	C₂²×C₄₁	—	4	2	no	—
590	C₂²×C₄₁	—	4	1	no	—
591	C₂²×C₄₁	—	4	1	no	—
592	C₂²×C₄₁	—	4	2	no	—
593	C₂²×C₄₁	—	4	2	no	—
594	C₂²×C₄₁	—	8	4	no	—
595	C₂²×C₄₁	—	8	8	no	—
596	C₂²×C₄₁	—	16	4	no	—
597	C₂²×C₄₁	C₂×#135	1	4	yes	—
598	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
599	C₄×C₄₁	—	2	1	no	—
600	C₄×C₄₁	—	2	1	no	—
601	C₄×C₄₁	—	2	1	no	—
602	C₄×C₄₁	—	2	2	no	—
603	C₄×C₄₁	—	2	2	no	—
604	C₄×C₄₁	—	2	2	no	—
605	C₄×C₄₁	—	2	1	no	—
606	C₄×C₄₁	—	4	1	no	—
607	C₄×C₄₁	—	4	2	no	—
608	C₄×C₄₁	—	4	1	no	—
609	C₄×C₄₁	—	4	2	no	—
610	C₄×C₄₁	—	4	1	no	—
611	C₄×C₄₁	—	4	1	no	—
612	C₄×C₄₁	—	4	1	no	—
613	C₄×C₄₁	C₂×#135	1	2	yes	—
614	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	#3519	C₂×C₄₁	1	1	yes	characteristic, complemented
617	D₄×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
618	#3305	C₂×C₄₁	1	1	yes	characteristic, complemented
619	#3303	C₂×C₄₁	1	1	yes	characteristic, complemented
620	#3301	C₂×C₄₁	1	2	yes	complemented
621	#3299	C₂×C₄₁	1	1	yes	characteristic, complemented
622	#3297	C₂×C₄₁	1	2	yes	complemented
623	#3295	C₂×C₄₁	1	1	yes	characteristic, complemented
624	#3287	C₂×C₄₁	1	1	yes	characteristic, complemented
625	#3284	C₂×C₄₁	1	1	yes	characteristic, complemented
626	#3282	C₂×C₄₁	1	2	yes	complemented
627	D₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
628	#3280	C₂×C₄₁	1	2	yes	complemented
629	D₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
630	#3212	C₂×C₄₁	1	1	yes	characteristic, complemented
631	#3207	C₂×C₄₁	1	1	yes	characteristic, complemented
632	#3191	C₂×C₄₁	1	2	yes	complemented
633	#3188	C₂×C₄₁	1	2	yes	complemented
634	#3106	C₂×C₄₁	1	1	yes	characteristic, complemented
635	#3102	C₂×C₄₁	1	1	yes	characteristic, complemented
636	#3002	C₂×C₄₁	1	2	yes	complemented
637	C₂×#449	C₂×C₄₁	1	2	yes	complemented
638	#2972	C₂×C₄₁	1	1	yes	characteristic, complemented
639	C₂×C₄₁	—	2	4	no	—
640	C₂×C₄₁	—	4	2	no	—
641	C₂×C₄₁	—	4	1	no	—
642	C₂×C₄₁	—	4	2	no	—
643	C₂×C₄₁	—	8	2	no	—
644	C₂×C₄₁	—	8	2	no	—
645	C₂×C₄₁	—	8	1	no	—
646	C₂×C₄₁	#3484	1	1	yes	characteristic
647	C₂×C₄₁	C₂²×#135	1	1	yes	characteristic
648	C₂×C₄₁	#3585	1	1	yes	characteristic
649	C₂²×#41	C₂²×C₄₁	1	2	yes	complemented
650	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
651	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
652	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
653	C₂²×D₈	C₂²×C₄₁	1	2	yes	complemented
654	#555	C₂²×C₄₁	1	1	yes	characteristic, complemented
655	#554	C₂²×C₄₁	1	1	yes	characteristic
656	#553	—	2	1	no	—
657	#553	C₂²×C₄₁	1	2	yes	complemented
658	#550	C₂²×C₄₁	1	1	yes	characteristic, complemented
659	#550	C₂²×C₄₁	1	1	yes	characteristic, complemented
660	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
661	#548	C₂²×C₄₁	1	2	yes	complemented
662	#547	—	2	1	no	—
663	#547	C₂²×C₄₁	1	1	yes	characteristic, complemented
664	#546	—	2	2	no	—
665	#546	—	2	2	no	—
666	#546	C₂²×C₄₁	1	2	yes	complemented
667	#546	C₂²×C₄₁	1	2	yes	complemented
668	D₄²	—	2	1	no	—
669	D₄²	—	2	1	no	—
670	D₄²	C₂²×C₄₁	1	1	yes	characteristic
671	D₄²	C₂²×C₄₁	1	1	yes	characteristic
672	#540	—	2	1	no	—
673	#538	—	2	2	no	—
674	#532	—	2	1	no	—
675	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
676	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
677	#529	C₂²×C₄₁	1	1	yes	characteristic, complemented
678	#525	—	2	2	no	—
679	#525	C₂²×C₄₁	1	2	yes	complemented
680	#525	C₂²×C₄₁	1	2	yes	complemented
681	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
682	#518	—	2	1	no	—
683	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic, complemented
684	C₂×C₄×D₄	—	2	1	no	—
685	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
686	#495	C₂²×C₄₁	1	2	yes	complemented
687	#493	C₂²×C₄₁	1	1	yes	characteristic, complemented
688	#492	C₂²×C₄₁	1	1	yes	characteristic, complemented
689	#488	C₂²×C₄₁	1	2	yes	complemented
690	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
691	#486	C₂²×C₄₁	1	1	yes	characteristic, complemented
692	#485	C₂²×C₄₁	1	1	yes	characteristic, complemented
693	#485	C₂²×C₄₁	1	2	yes	complemented
694	#484	C₂²×C₄₁	1	2	yes	complemented
695	#482	C₂²×C₄₁	1	1	yes	characteristic, complemented
696	#482	C₂²×C₄₁	1	2	yes	complemented
697	#482	C₂²×C₄₁	1	2	yes	complemented
698	#481	C₂²×C₄₁	1	2	yes	complemented
699	#479	C₂²×C₄₁	1	1	yes	characteristic, complemented
700	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
701	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
702	#476	C₂²×C₄₁	1	1	yes	characteristic, complemented
703	#467	C₂²×C₄₁	1	2	yes	complemented
704	#466	C₂²×C₄₁	1	2	yes	complemented
705	#466	C₂²×C₄₁	1	2	yes	complemented
706	#466	C₂²×C₄₁	1	2	yes	complemented
707	#465	C₂²×C₄₁	1	2	yes	complemented
708	#465	C₂²×C₄₁	1	2	yes	complemented
709	#465	C₂²×C₄₁	1	2	yes	complemented
710	#465	C₂²×C₄₁	1	2	yes	complemented
711	#464	C₂²×C₄₁	1	1	yes	characteristic, complemented
712	#463	C₂²×C₄₁	1	1	yes	characteristic, complemented
713	#463	C₂²×C₄₁	1	2	yes	complemented
714	#463	C₂²×C₄₁	1	2	yes	complemented
715	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
716	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
717	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
718	#460	C₂²×C₄₁	1	1	yes	characteristic, complemented
719	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
720	#459	C₂²×C₄₁	1	1	yes	characteristic, complemented
721	#452	C₂²×C₄₁	1	1	yes	characteristic, complemented
722	#452	C₂²×C₄₁	1	2	yes	complemented
723	#452	C₂²×C₄₁	1	2	yes	complemented
724	#451	C₂²×C₄₁	1	2	yes	complemented
725	#450	C₂²×C₄₁	1	2	yes	complemented
726	#450	C₂²×C₄₁	1	2	yes	complemented
727	#449	C₂²×C₄₁	1	1	yes	characteristic
728	#449	C₂²×C₄₁	1	2	yes	complemented
729	#449	C₂²×C₄₁	1	2	yes	complemented
730	#449	C₂²×C₄₁	1	2	yes	complemented
731	#449	C₂²×C₄₁	1	2	yes	complemented
732	#449	C₂²×C₄₁	1	2	yes	complemented
733	#449	C₂²×C₄₁	1	2	yes	complemented
734	#449	C₂²×C₄₁	1	2	yes	complemented
735	#449	C₂²×C₄₁	1	2	yes	complemented
736	#449	C₂²×C₄₁	1	2	yes	complemented
737	#448	C₂²×C₄₁	1	2	yes	complemented
738	#447	C₂²×C₄₁	1	2	yes	complemented
739	#447	C₂²×C₄₁	1	2	yes	complemented
740	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
741	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
742	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
743	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
744	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
745	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
746	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
747	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
748	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
749	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
750	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
751	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
752	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
753	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
754	#416	C₂²×C₄₁	1	2	yes	complemented
755	#416	C₂²×C₄₁	1	2	yes	complemented
756	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
757	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
758	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
759	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
760	C₄₁	#61567	1	1	yes	characteristic, direct product factor, Sylow
761	C₂×#41	—	2	2	no	—
762	C₂×#41	—	2	2	no	—
763	C₂×#41	—	2	1	no	—
764	C₂×#41	—	4	4	no	—
765	C₂×#41	—	4	4	no	—
766	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
767	C₂×#41	C₂³×C₄₁	1	2	yes	—
768	C₂×#41	C₂³×C₄₁	1	2	yes	—
769	C₂×#41	C₂³×C₄₁	1	2	yes	—
770	C₂×#41	C₂³×C₄₁	1	2	yes	—
771	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
772	C₂²×D₄	—	2	2	no	—
773	C₂²×D₄	—	2	2	no	—
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	—	2	1	no	—
776	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
777	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
778	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
779	C₂³×C₄	—	2	2	no	—
780	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
781	#135	—	4	4	no	—
782	#135	—	4	4	no	—
783	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
784	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
785	C₂×SD₁₆	—	4	4	no	—
786	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
787	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
788	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
789	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
790	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
793	C₂×D₈	—	4	4	no	—
794	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
795	C₂×D₈	C₂³×C₄₁	1	2	yes	—
796	C₂×D₈	C₂³×C₄₁	1	2	yes	—
797	C₂×D₈	C₂³×C₄₁	1	2	yes	—
798	C₂×D₈	C₂³×C₄₁	1	2	yes	—
799	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
800	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
801	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
802	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
803	C₄⋊Q₈	—	2	1	no	—
804	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
805	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
806	#127	—	2	1	no	—
807	#127	—	2	1	no	—
808	#127	C₂³×C₄₁	1	1	yes	characteristic
809	#127	C₂³×C₄₁	1	1	yes	characteristic
810	#126	—	2	2	no	—
811	#126	—	2	1	no	—
812	#125	—	2	1	no	—
813	#125	C₂³×C₄₁	1	1	yes	characteristic
814	#124	—	2	2	no	—
815	#124	—	2	2	no	—
816	#124	—	2	1	no	—
817	#124	C₂³×C₄₁	1	1	yes	characteristic
818	#124	C₂³×C₄₁	1	2	yes	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	1	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
831	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
833	#121	—	2	2	no	—
834	#121	—	2	1	no	—
835	#121	—	2	2	no	—
836	#121	—	2	1	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	1	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	1	no	—
843	#121	—	2	1	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	C₂³×C₄₁	1	1	yes	characteristic
849	#121	C₂³×C₄₁	1	2	yes	—
850	#121	C₂³×C₄₁	1	2	yes	—
851	#121	C₂³×C₄₁	1	2	yes	—
852	#121	C₂³×C₄₁	1	2	yes	—
853	#121	C₂³×C₄₁	1	2	yes	—
854	#121	C₂³×C₄₁	1	2	yes	—
855	#120	—	2	2	no	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
862	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
863	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	—	2	2	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	2	no	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
881	C₄×D₄	D₄×C₄₁	1	2	yes	—
882	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
883	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
884	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
885	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
886	C₄×D₄	C₂³×C₄₁	1	2	yes	—
887	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₄₁	1	2	yes	—
889	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
890	#117	—	2	1	no	—
891	#117	—	2	1	no	—
892	#117	—	2	1	no	—
893	#117	C₂³×C₄₁	1	1	yes	characteristic
894	#117	C₂³×C₄₁	1	2	yes	—
895	C₂×C₄⋊C₄	—	2	1	no	—
896	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
898	C₂×C₂²⋊C₄	—	2	2	no	—
899	C₂×C₂²⋊C₄	—	2	2	no	—
900	C₂×C₂²⋊C₄	—	2	2	no	—
901	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
902	C₂×C₄²	—	2	1	no	—
903	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
904	#107	C₂³×C₄₁	1	1	yes	characteristic
905	#107	C₂³×C₄₁	1	2	yes	—
906	#107	C₂³×C₄₁	1	1	yes	characteristic
907	#106	C₂³×C₄₁	1	2	yes	—
908	#106	C₂³×C₄₁	1	1	yes	characteristic
909	#106	C₂³×C₄₁	1	1	yes	characteristic
910	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
911	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
912	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
913	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
914	#103	C₂³×C₄₁	1	1	yes	characteristic
915	#103	C₂³×C₄₁	1	2	yes	—
916	#103	C₂³×C₄₁	1	2	yes	—
917	#103	C₂³×C₄₁	1	2	yes	—
918	#103	C₂³×C₄₁	1	1	yes	characteristic
919	#103	C₂³×C₄₁	1	2	yes	—
920	#103	C₂³×C₄₁	1	2	yes	—
921	#103	C₂³×C₄₁	1	1	yes	characteristic
922	#103	C₂³×C₄₁	1	1	yes	characteristic
923	#102	C₂³×C₄₁	1	1	yes	characteristic
924	#102	C₂³×C₄₁	1	2	yes	—
925	#102	C₂³×C₄₁	1	2	yes	—
926	#102	C₂³×C₄₁	1	2	yes	—
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	1	yes	characteristic
931	#102	C₂³×C₄₁	1	2	yes	—
932	#102	C₂³×C₄₁	1	2	yes	—
933	#102	C₂³×C₄₁	1	1	yes	characteristic
934	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
935	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
936	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
940	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
941	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
942	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
943	C₄×C₈	C₂³×C₄₁	1	2	yes	—
944	C₂⁴	—	2	2	no	—
945	C₂⁴	—	2	2	no	—
946	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
947	#41	—	2	2	no	—
948	#41	—	2	2	no	—
949	#41	—	2	4	no	—
950	#41	—	2	4	no	—
951	#41	—	4	2	no	—
952	#41	—	4	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	2	no	—
955	#41	—	4	8	no	—
956	#41	—	4	2	no	—
957	#41	—	4	2	no	—
958	#41	—	4	8	no	—
959	#41	—	8	2	no	—
960	C₂×Q₈	—	2	2	no	—
961	C₂×Q₈	—	2	1	no	—
962	C₂×Q₈	—	2	4	no	—
963	C₂×Q₈	—	4	2	no	—
964	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
965	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
966	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	4	no	—
969	C₂×D₄	—	2	4	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	1	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	2	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	4	2	no	—
988	C₂×D₄	—	4	2	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	4	8	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	—	4	4	no	—
993	C₂×D₄	—	8	4	no	—
994	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
995	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
996	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
997	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
998	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
999	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
1000	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	4	2	no	—
1013	C₂²×C₄	—	4	2	no	—
1014	C₂²×C₄	—	4	8	no	—
1015	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1016	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1017	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1018	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1019	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
1020	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1022	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
1023	Q₁₆	—	2	2	no	—
1024	Q₁₆	—	4	2	no	—
1025	SD₁₆	—	2	2	no	—
1026	SD₁₆	—	2	4	no	—
1027	SD₁₆	—	2	2	no	—
1028	SD₁₆	—	4	2	no	—
1029	SD₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	D₈	—	2	2	no	—
1033	D₈	—	2	4	no	—
1034	D₈	—	4	2	no	—
1035	D₈	—	4	2	no	—
1036	D₈	—	4	2	no	—
1037	C₂×C₈	—	4	2	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	—	4	2	no	—
1040	C₂×C₈	—	4	2	no	—
1041	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1044	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
1045	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1046	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1063	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1064	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1099	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1100	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1101	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	4	no	—
1104	C₂³	—	2	1	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	4	2	no	—
1108	C₂³	—	4	2	no	—
1109	C₂³	—	4	4	no	—
1110	C₂³	—	4	4	no	—
1111	C₂³	—	4	4	no	—
1112	C₂³	—	8	2	no	—
1113	C₂³	—	8	2	no	—
1114	C₂³	—	8	2	no	—
1115	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1116	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1117	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	2	2	no	—
1122	Q₈	—	2	2	no	—
1123	Q₈	—	4	4	no	—
1124	Q₈	—	8	1	no	—
1125	Q₈	H(5,𝔽₂)×C₄₁	1	2	yes	—
1126	D₄	—	2	4	no	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	1	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	2	no	—
1132	D₄	—	2	2	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	1	no	—
1136	D₄	—	4	4	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	4	no	—
1144	D₄	—	4	2	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	1	no	—
1148	D₄	—	8	1	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	2	no	—
1151	D₄	—	8	2	no	—
1152	D₄	—	8	2	no	—
1153	D₄	#135×C₄₁	1	4	yes	complemented
1154	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
1155	C₂×C₄	—	2	4	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	4	2	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	4	no	—
1176	C₂×C₄	—	4	4	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	4	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1188	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1191	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1192	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1193	C₈	—	2	1	no	—
1194	C₈	—	2	2	no	—
1195	C₈	—	2	1	no	—
1196	C₈	—	2	1	no	—
1197	C₈	—	2	2	no	—
1198	C₈	—	2	1	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	8	4	no	—
1220	C₂²	—	8	8	no	—
1221	C₂²	—	16	4	no	—
1222	C₂²	C₂×#135×C₄₁	1	4	yes	—
1223	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	2	2	no	—
1230	C₄	—	2	2	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	2	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	C₂×#135×C₄₁	1	2	yes	—
1239	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1240	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1241	C₂	—	2	4	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	2	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	8	2	no	—
1246	C₂	—	8	1	no	—
1247	C₂	—	8	2	no	—
1248	C₂	C₄₁×#3484	1	1	yes	characteristic
1249	C₂	C₂²×#135×C₄₁	1	1	yes	characteristic
1250	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 ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3519	C₂	semidirect
2. D₄×#41×C₄₁	C₂	semidirect
3. C₄₁×#3305	C₂	semidirect
4. C₄₁×#3303	C₂	semidirect
5. C₄₁×#3301	C₂	semidirect
6. C₄₁×#3299	C₂	semidirect
7. C₄₁×#3297	C₂	semidirect
8. C₄₁×#3295	C₂	semidirect
9. C₄₁×#3287	C₂	semidirect
10. C₄₁×#3284	C₂	semidirect
11. C₄₁×#3282	C₂	semidirect
12. D₄×SD₁₆×C₄₁	C₂	semidirect
13. C₄₁×#3280	C₂	semidirect
14. D₄×D₈×C₄₁	C₂	semidirect
15. C₄₁×#3212	C₂	semidirect
16. C₄₁×#3207	C₂	semidirect
17. C₄₁×#3191	C₂	semidirect
18. C₄₁×#3188	C₂	semidirect
19. C₄₁×#3106	C₂	semidirect
20. C₄₁×#3102	C₂	semidirect
21. C₄₁×#3002	C₂	semidirect
22. C₂×C₄₁×#449	C₂	semidirect
23. C₄₁×#2972	C₂	semidirect
24. C₂²×#41×C₄₁	C₂²	semidirect
25. C₂×#135×C₄₁	C₂²	semidirect
26. C₂×#135×C₄₁	C₂²	semidirect
27. C₂²×SD₁₆×C₄₁	C₂²	semidirect
28. C₂²×D₈×C₄₁	C₂²	semidirect
29. C₄₁×#555	C₂²	semidirect
32. C₄₁×#553	C₂²	semidirect
33. C₄₁×#550	C₂²	semidirect
34. C₄₁×#550	C₂²	semidirect
36. C₄₁×#548	C₂²	semidirect
38. C₄₁×#547	C₂²	semidirect
41. C₄₁×#546	C₂²	semidirect
42. C₄₁×#546	C₂²	semidirect
50. C₄₁×#532	C₂²	semidirect
51. C₄₁×#532	C₂²	semidirect
52. C₄₁×#529	C₂²	semidirect
54. C₄₁×#525	C₂²	semidirect
55. C₄₁×#525	C₂²	semidirect
56. C₂×#121×C₄₁	C₂²	semidirect
58. C₄×#41×C₄₁	C₂²	semidirect
61. C₄₁×#495	C₂²	semidirect
62. C₄₁×#493	C₂²	semidirect
63. C₄₁×#492	C₂²	semidirect
64. C₄₁×#488	C₂²	semidirect
65. C₄₁×#487	C₂²	semidirect
66. C₄₁×#486	C₂²	semidirect
67. C₄₁×#485	C₂²	semidirect
68. C₄₁×#485	C₂²	semidirect
69. C₄₁×#484	C₂²	semidirect
70. C₄₁×#482	C₂²	semidirect
71. C₄₁×#482	C₂²	semidirect
72. C₄₁×#482	C₂²	semidirect
73. C₄₁×#481	C₂²	semidirect
74. C₄₁×#479	C₂²	semidirect
75. C₄₁×#478	C₂²	semidirect
76. C₄₁×#477	C₂²	semidirect
77. C₄₁×#476	C₂²	semidirect
78. C₄₁×#467	C₂²	semidirect
79. C₄₁×#466	C₂²	semidirect
80. C₄₁×#466	C₂²	semidirect
81. C₄₁×#466	C₂²	semidirect
82. C₄₁×#465	C₂²	semidirect
83. C₄₁×#465	C₂²	semidirect
84. C₄₁×#465	C₂²	semidirect
85. C₄₁×#465	C₂²	semidirect
86. C₄₁×#464	C₂²	semidirect
87. C₄₁×#463	C₂²	semidirect
88. C₄₁×#463	C₂²	semidirect
89. C₄₁×#463	C₂²	semidirect
90. C₄₁×#462	C₂²	semidirect
91. C₄₁×#461	C₂²	semidirect
92. C₄₁×#460	C₂²	semidirect
93. C₄₁×#460	C₂²	semidirect
94. C₄₁×#459	C₂²	semidirect
95. C₄₁×#459	C₂²	semidirect
96. C₄₁×#452	C₂²	semidirect
97. C₄₁×#452	C₂²	semidirect
98. C₄₁×#452	C₂²	semidirect
99. C₄₁×#451	C₂²	semidirect
100. C₄₁×#450	C₂²	semidirect
101. C₄₁×#450	C₂²	semidirect
103. C₄₁×#449	C₂²	semidirect
104. C₄₁×#449	C₂²	semidirect
105. C₄₁×#449	C₂²	semidirect
106. C₄₁×#449	C₂²	semidirect
107. C₄₁×#449	C₂²	semidirect
108. C₄₁×#449	C₂²	semidirect
109. C₄₁×#449	C₂²	semidirect
110. C₄₁×#449	C₂²	semidirect
111. C₄₁×#449	C₂²	semidirect
112. C₄₁×#448	C₂²	semidirect
113. C₄₁×#447	C₂²	semidirect
114. C₄₁×#447	C₂²	semidirect
115. C₄×Q₁₆×C₄₁	C₂²	semidirect
116. C₄×SD₁₆×C₄₁	C₂²	semidirect
117. C₄×SD₁₆×C₄₁	C₂²	semidirect
118. C₄×SD₁₆×C₄₁	C₂²	semidirect
119. C₄×D₈×C₄₁	C₂²	semidirect
120. C₄×D₈×C₄₁	C₂²	semidirect
123. C₈×D₄×C₄₁	C₂²	semidirect
124. C₈×D₄×C₄₁	C₂²	semidirect
125. C₈×D₄×C₄₁	C₂²	semidirect
126. C₈×D₄×C₄₁	C₂²	semidirect
127. C₄₁×#431	C₂²	semidirect
128. C₄₁×#431	C₂²	semidirect
129. C₄₁×#416	C₂²	semidirect
130. C₄₁×#416	C₂²	semidirect
131. C₂×#103×C₄₁	C₂²	semidirect
132. C₂×#102×C₄₁	C₂²	semidirect
133. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
527. D₄×C₄₁	#135	semidirect
573. #61567	C₄₁	direct (N × H)
616. #3519	C₂×C₄₁	semidirect
617. D₄×#41	C₂×C₄₁	semidirect
618. #3305	C₂×C₄₁	semidirect
619. #3303	C₂×C₄₁	semidirect
620. #3301	C₂×C₄₁	semidirect
621. #3299	C₂×C₄₁	semidirect
622. #3297	C₂×C₄₁	semidirect
623. #3295	C₂×C₄₁	semidirect
624. #3287	C₂×C₄₁	semidirect
625. #3284	C₂×C₄₁	semidirect
626. #3282	C₂×C₄₁	semidirect
627. D₄×SD₁₆	C₂×C₄₁	semidirect
628. #3280	C₂×C₄₁	semidirect
629. D₄×D₈	C₂×C₄₁	semidirect
630. #3212	C₂×C₄₁	semidirect
631. #3207	C₂×C₄₁	semidirect
632. #3191	C₂×C₄₁	semidirect
633. #3188	C₂×C₄₁	semidirect
634. #3106	C₂×C₄₁	semidirect
635. #3102	C₂×C₄₁	semidirect
636. #3002	C₂×C₄₁	semidirect
637. C₂×#449	C₂×C₄₁	semidirect
638. #2972	C₂×C₄₁	semidirect
649. C₂²×#41	C₂²×C₄₁	semidirect
650. C₂×#135	C₂²×C₄₁	semidirect
651. C₂×#135	C₂²×C₄₁	semidirect
652. C₂²×SD₁₆	C₂²×C₄₁	semidirect
653. C₂²×D₈	C₂²×C₄₁	semidirect
654. #555	C₂²×C₄₁	semidirect
657. #553	C₂²×C₄₁	semidirect
658. #550	C₂²×C₄₁	semidirect
659. #550	C₂²×C₄₁	semidirect
661. #548	C₂²×C₄₁	semidirect
663. #547	C₂²×C₄₁	semidirect
666. #546	C₂²×C₄₁	semidirect
667. #546	C₂²×C₄₁	semidirect
675. #532	C₂²×C₄₁	semidirect
676. #532	C₂²×C₄₁	semidirect
677. #529	C₂²×C₄₁	semidirect
679. #525	C₂²×C₄₁	semidirect
680. #525	C₂²×C₄₁	semidirect
681. C₂×#121	C₂²×C₄₁	semidirect
683. C₄×#41	C₂²×C₄₁	semidirect
686. #495	C₂²×C₄₁	semidirect
687. #493	C₂²×C₄₁	semidirect
688. #492	C₂²×C₄₁	semidirect
689. #488	C₂²×C₄₁	semidirect
690. #487	C₂²×C₄₁	semidirect
691. #486	C₂²×C₄₁	semidirect
692. #485	C₂²×C₄₁	semidirect
693. #485	C₂²×C₄₁	semidirect
694. #484	C₂²×C₄₁	semidirect
695. #482	C₂²×C₄₁	semidirect
696. #482	C₂²×C₄₁	semidirect
697. #482	C₂²×C₄₁	semidirect
698. #481	C₂²×C₄₁	semidirect
699. #479	C₂²×C₄₁	semidirect
700. #478	C₂²×C₄₁	semidirect
701. #477	C₂²×C₄₁	semidirect
702. #476	C₂²×C₄₁	semidirect
703. #467	C₂²×C₄₁	semidirect
704. #466	C₂²×C₄₁	semidirect
705. #466	C₂²×C₄₁	semidirect
706. #466	C₂²×C₄₁	semidirect
707. #465	C₂²×C₄₁	semidirect
708. #465	C₂²×C₄₁	semidirect
709. #465	C₂²×C₄₁	semidirect
710. #465	C₂²×C₄₁	semidirect
711. #464	C₂²×C₄₁	semidirect
712. #463	C₂²×C₄₁	semidirect
713. #463	C₂²×C₄₁	semidirect
714. #463	C₂²×C₄₁	semidirect
715. #462	C₂²×C₄₁	semidirect
716. #461	C₂²×C₄₁	semidirect
717. #460	C₂²×C₄₁	semidirect
718. #460	C₂²×C₄₁	semidirect
719. #459	C₂²×C₄₁	semidirect
720. #459	C₂²×C₄₁	semidirect
721. #452	C₂²×C₄₁	semidirect
722. #452	C₂²×C₄₁	semidirect
723. #452	C₂²×C₄₁	semidirect
724. #451	C₂²×C₄₁	semidirect
725. #450	C₂²×C₄₁	semidirect
726. #450	C₂²×C₄₁	semidirect
728. #449	C₂²×C₄₁	semidirect
729. #449	C₂²×C₄₁	semidirect
730. #449	C₂²×C₄₁	semidirect
731. #449	C₂²×C₄₁	semidirect
732. #449	C₂²×C₄₁	semidirect
733. #449	C₂²×C₄₁	semidirect
734. #449	C₂²×C₄₁	semidirect
735. #449	C₂²×C₄₁	semidirect
736. #449	C₂²×C₄₁	semidirect
737. #448	C₂²×C₄₁	semidirect
738. #447	C₂²×C₄₁	semidirect
739. #447	C₂²×C₄₁	semidirect
740. C₄×Q₁₆	C₂²×C₄₁	semidirect
741. C₄×SD₁₆	C₂²×C₄₁	semidirect
742. C₄×SD₁₆	C₂²×C₄₁	semidirect
743. C₄×SD₁₆	C₂²×C₄₁	semidirect
744. C₄×D₈	C₂²×C₄₁	semidirect
745. C₄×D₈	C₂²×C₄₁	semidirect
748. C₈×D₄	C₂²×C₄₁	semidirect
749. C₈×D₄	C₂²×C₄₁	semidirect
750. C₈×D₄	C₂²×C₄₁	semidirect
751. C₈×D₄	C₂²×C₄₁	semidirect
752. #431	C₂²×C₄₁	semidirect
753. #431	C₂²×C₄₁	semidirect
754. #416	C₂²×C₄₁	semidirect
755. #416	C₂²×C₄₁	semidirect
756. C₂×#103	C₂²×C₄₁	semidirect
757. C₂×#102	C₂²×C₄₁	semidirect
758. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
759. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
760. C₄₁	#61567	direct (N × H)
1153. D₄	#135×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3519	2
D₄×#41×C₄₁	2
C₄₁×#3305	2
C₄₁×#3303	2
C₄₁×#3301	2
C₄₁×#3299	2
C₄₁×#3297	2
C₄₁×#3295	2
C₄₁×#3287	2
C₄₁×#3284	2
C₄₁×#3282	2
D₄×SD₁₆×C₄₁	2
C₄₁×#3280	2
D₄×D₈×C₄₁	2
C₄₁×#3212	2
C₄₁×#3207	2
C₄₁×#3191	2
C₄₁×#3188	2
C₄₁×#3106	2
C₄₁×#3102	2
C₄₁×#3002	2
C₂×C₄₁×#449	2
C₄₁×#2972	2
#61567	41

Subgroups — C41×#61567 #23837768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61567 #23837768