Subgroups — C₄₁×#61956 #23838157

Order 10496.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3300	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3296	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3285	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3250	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3211	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#3108	C₂	1	2	yes	maximal, complemented
20	C₄₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄₁×#464	C₂	1	2	yes	maximal, complemented
23	C₄₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#559	C₂²	1	1	yes	characteristic
28	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#556	—	2	1	no	—
30	C₄₁×#556	C₂²	1	1	yes	characteristic
31	C₄₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₄₁×#555	—	2	1	no	—
33	C₄₁×#552	—	2	2	no	—
34	C₄₁×#552	C₂²	1	2	yes	complemented
35	C₄₁×#551	—	2	2	no	—
36	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
38	C₄₁×#548	C₂²	1	2	yes	—
39	C₄₁×#548	C₂²	1	2	yes	complemented
40	C₄₁×#547	—	2	1	no	—
41	C₄₁×#547	C₂²	1	1	yes	characteristic
42	C₄₁×#546	—	2	1	no	—
43	C₄₁×#546	C₂²	1	2	yes	—
44	D₄²×C₄₁	C₂²	1	1	yes	characteristic
45	C₄₁×#542	—	2	1	no	—
46	C₄₁×#538	—	2	2	no	—
47	C₄₁×#533	—	2	1	no	—
48	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
49	C₄₁×#532	C₂²	1	1	yes	characteristic
50	C₄₁×#529	—	2	2	no	—
51	C₄₁×#529	C₂²	1	1	yes	characteristic
52	C₄₁×#529	C₂²	1	2	yes	—
53	C₄₁×#529	C₂²	1	2	yes	complemented
54	C₂×#124×C₄₁	C₂²	1	2	yes	—
55	C₄₁×#518	—	2	1	no	—
56	C₄×#41×C₄₁	—	2	1	no	—
57	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
58	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
60	C₄₁×#495	C₂²	1	2	yes	—
61	C₄₁×#495	C₂²	1	2	yes	complemented
62	C₄₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₄₁×#492	C₂²	1	1	yes	characteristic
64	C₄₁×#488	C₂²	1	2	yes	—
65	C₄₁×#488	C₂²	1	2	yes	complemented
66	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#486	C₂²	1	1	yes	characteristic
68	C₄₁×#485	C₂²	1	1	yes	characteristic, complemented
69	C₄₁×#483	C₂²	1	2	yes	complemented
70	C₄₁×#482	C₂²	1	1	yes	characteristic
71	C₄₁×#480	C₂²	1	2	yes	—
72	C₄₁×#479	C₂²	1	2	yes	complemented
73	C₄₁×#479	C₂²	1	1	yes	characteristic, complemented
74	C₄₁×#479	C₂²	1	2	yes	complemented
75	C₄₁×#478	C₂²	1	2	yes	complemented
76	C₄₁×#478	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₄₁×#474	C₂²	1	1	yes	characteristic
79	C₄₁×#467	C₂²	1	2	yes	complemented
80	C₄₁×#467	C₂²	1	2	yes	complemented
81	C₄₁×#466	C₂²	1	2	yes	—
82	C₄₁×#465	C₂²	1	2	yes	—
83	C₄₁×#465	C₂²	1	2	yes	—
84	C₄₁×#465	C₂²	1	2	yes	complemented
85	C₄₁×#464	C₂²	1	2	yes	—
86	C₄₁×#464	C₂²	1	1	yes	characteristic
87	C₄₁×#464	C₂²	1	2	yes	—
88	C₄₁×#464	C₂²	1	2	yes	—
89	C₄₁×#464	C₂²	1	2	yes	complemented
90	C₄₁×#464	C₂²	1	2	yes	complemented
91	C₄₁×#464	C₂²	1	2	yes	complemented
92	C₄₁×#464	C₂²	1	2	yes	complemented
93	C₄₁×#464	C₂²	1	2	yes	complemented
94	C₄₁×#464	C₂²	1	2	yes	complemented
95	C₄₁×#463	C₂²	1	1	yes	characteristic
96	C₄₁×#463	C₂²	1	2	yes	complemented
97	C₄₁×#463	C₂²	1	2	yes	complemented
98	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
99	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
100	C₄₁×#461	C₂²	1	1	yes	characteristic
101	C₄₁×#461	C₂²	1	1	yes	characteristic, complemented
102	C₄₁×#460	C₂²	1	1	yes	characteristic
103	C₄₁×#459	C₂²	1	1	yes	characteristic
104	C₄₁×#452	C₂²	1	2	yes	complemented
105	C₄₁×#452	C₂²	1	2	yes	complemented
106	C₄₁×#452	C₂²	1	1	yes	characteristic, complemented
107	C₄₁×#451	C₂²	1	2	yes	complemented
108	C₄₁×#451	C₂²	1	2	yes	complemented
109	C₄₁×#450	C₂²	1	2	yes	—
110	C₄₁×#449	C₂²	1	1	yes	characteristic
111	C₄₁×#448	C₂²	1	2	yes	—
112	C₄₁×#448	C₂²	1	2	yes	complemented
113	C₄₁×#447	C₂²	1	2	yes	—
114	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
123	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
126	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
127	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
128	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
129	C₄₁×#431	C₂²	1	2	yes	complemented
130	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
132	C₄₁×#416	C₂²	1	2	yes	complemented
133	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
134	C₂×#102×C₄₁	C₂²	1	2	yes	—
135	C₂×#41×C₄₁	—	2	1	no	—
136	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₄₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₄₁	—	2	1	no	—
142	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
143	#135×C₄₁	—	4	4	no	—
144	C₂×Q₁₆×C₄₁	—	4	4	no	—
145	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₄₁	—	4	4	no	—
151	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
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×D₈×C₄₁	C₂³	1	2	yes	—
159	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₄₁	—	2	1	no	—
164	C₄⋊Q₈×C₄₁	—	2	1	no	—
165	C₄⋊Q₈×C₄₁	—	2	1	no	—
166	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
169	#127×C₄₁	C₂³	1	1	yes	characteristic
170	#126×C₄₁	—	2	2	no	—
171	#126×C₄₁	—	2	2	no	—
172	#126×C₄₁	—	2	2	no	—
173	#126×C₄₁	—	2	2	no	—
174	#126×C₄₁	—	2	1	no	—
175	#126×C₄₁	—	2	2	no	—
176	#125×C₄₁	—	2	2	no	—
177	#125×C₄₁	—	2	2	no	—
178	#125×C₄₁	—	2	1	no	—
179	#125×C₄₁	C₂³	1	1	yes	characteristic
180	#125×C₄₁	C₂³	1	2	yes	—
181	#124×C₄₁	—	2	1	no	—
182	#124×C₄₁	—	2	2	no	—
183	#124×C₄₁	—	2	2	no	—
184	#124×C₄₁	—	2	2	no	—
185	#124×C₄₁	—	2	2	no	—
186	#124×C₄₁	C₂³	1	1	yes	characteristic
187	#124×C₄₁	C₂³	1	2	yes	—
188	#124×C₄₁	C₂³	1	2	yes	—
189	#124×C₄₁	C₂³	1	2	yes	—
190	#124×C₄₁	C₂³	1	2	yes	—
191	#123×C₄₁	—	2	2	no	—
192	#123×C₄₁	—	2	1	no	—
193	#123×C₄₁	—	2	2	no	—
194	#123×C₄₁	—	2	2	no	—
195	#123×C₄₁	—	2	2	no	—
196	#123×C₄₁	—	2	2	no	—
197	#123×C₄₁	—	2	2	no	—
198	C₂²⋊Q₈×C₄₁	—	2	1	no	—
199	C₂²⋊Q₈×C₄₁	—	2	1	no	—
200	C₂²⋊Q₈×C₄₁	—	2	1	no	—
201	C₂²⋊Q₈×C₄₁	—	2	1	no	—
202	C₂²⋊Q₈×C₄₁	—	2	2	no	—
203	C₂²⋊Q₈×C₄₁	—	2	2	no	—
204	C₂²⋊Q₈×C₄₁	—	2	2	no	—
205	C₂²⋊Q₈×C₄₁	—	2	2	no	—
206	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
210	#121×C₄₁	—	2	2	no	—
211	#121×C₄₁	—	2	2	no	—
212	#121×C₄₁	—	2	1	no	—
213	#121×C₄₁	—	2	1	no	—
214	#121×C₄₁	—	2	1	no	—
215	#121×C₄₁	—	2	2	no	—
216	#121×C₄₁	C₂³	1	2	yes	—
217	#121×C₄₁	C₂³	1	1	yes	characteristic
218	#121×C₄₁	C₂³	1	2	yes	—
219	#120×C₄₁	—	2	2	no	—
220	#120×C₄₁	—	2	2	no	—
221	C₄×Q₈×C₄₁	—	2	1	no	—
222	C₄×Q₈×C₄₁	—	2	2	no	—
223	C₄×Q₈×C₄₁	—	2	2	no	—
224	C₄×Q₈×C₄₁	—	2	1	no	—
225	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
226	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₄₁	—	2	1	no	—
235	C₄×D₄×C₄₁	—	2	1	no	—
236	C₄×D₄×C₄₁	—	2	2	no	—
237	C₄×D₄×C₄₁	—	2	1	no	—
238	C₄×D₄×C₄₁	—	2	1	no	—
239	C₄×D₄×C₄₁	—	2	2	no	—
240	C₄×D₄×C₄₁	—	2	1	no	—
241	C₄×D₄×C₄₁	—	2	1	no	—
242	C₄×D₄×C₄₁	—	2	2	no	—
243	C₄×D₄×C₄₁	—	2	2	no	—
244	C₄×D₄×C₄₁	—	2	1	no	—
245	C₄×D₄×C₄₁	—	2	1	no	—
246	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
247	C₄×D₄×C₄₁	D₄	1	2	yes	—
248	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₄₁	C₂³	1	2	yes	—
252	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₄₁	C₂³	1	2	yes	—
254	#117×C₄₁	—	2	1	no	—
255	#117×C₄₁	—	2	1	no	—
256	#117×C₄₁	—	2	1	no	—
257	#117×C₄₁	—	2	2	no	—
258	#117×C₄₁	—	2	1	no	—
259	#117×C₄₁	—	2	1	no	—
260	#117×C₄₁	—	2	2	no	—
261	#117×C₄₁	—	2	2	no	—
262	#117×C₄₁	D₄	1	2	yes	—
263	#117×C₄₁	D₄	1	1	yes	characteristic
264	#117×C₄₁	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
266	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
270	C₂×C₄²×C₄₁	—	2	2	no	—
271	C₂×C₄²×C₄₁	—	2	1	no	—
272	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
273	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
274	#107×C₄₁	C₂³	1	1	yes	characteristic
275	#107×C₄₁	C₂³	1	2	yes	—
276	#107×C₄₁	C₂³	1	1	yes	characteristic
277	#106×C₄₁	C₂³	1	1	yes	characteristic
278	#106×C₄₁	C₂³	1	1	yes	characteristic
279	#106×C₄₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
287	#103×C₄₁	C₂³	1	1	yes	characteristic
288	#103×C₄₁	C₂³	1	2	yes	—
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	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	1	yes	characteristic
298	#102×C₄₁	C₂³	1	1	yes	characteristic
299	#102×C₄₁	C₂³	1	2	yes	—
300	#102×C₄₁	C₂³	1	2	yes	—
301	#102×C₄₁	C₂³	1	2	yes	—
302	#102×C₄₁	C₂³	1	2	yes	—
303	#102×C₄₁	C₂³	1	1	yes	characteristic
304	#102×C₄₁	C₂³	1	1	yes	characteristic
305	#102×C₄₁	C₂³	1	2	yes	—
306	#102×C₄₁	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₁	C₂³	1	2	yes	—
314	C₄×C₈×C₄₁	C₂³	1	2	yes	—
315	C₂⁴×C₄₁	—	2	2	no	—
316	#41×C₄₁	—	2	4	no	—
317	#41×C₄₁	—	2	2	no	—
318	#41×C₄₁	—	4	1	no	—
319	#41×C₄₁	—	4	2	no	—
320	#41×C₄₁	—	4	2	no	—
321	#41×C₄₁	—	4	4	no	—
322	C₂×Q₈×C₄₁	—	2	2	no	—
323	C₂×Q₈×C₄₁	—	2	1	no	—
324	C₂×Q₈×C₄₁	—	2	2	no	—
325	C₂×Q₈×C₄₁	—	2	4	no	—
326	C₂×Q₈×C₄₁	—	4	2	no	—
327	C₂×Q₈×C₄₁	—	4	2	no	—
328	C₂×Q₈×C₄₁	—	4	2	no	—
329	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₄₁	—	2	2	no	—
335	C₂×D₄×C₄₁	—	2	1	no	—
336	C₂×D₄×C₄₁	—	2	2	no	—
337	C₂×D₄×C₄₁	—	2	1	no	—
338	C₂×D₄×C₄₁	—	2	2	no	—
339	C₂×D₄×C₄₁	—	2	1	no	—
340	C₂×D₄×C₄₁	—	2	1	no	—
341	C₂×D₄×C₄₁	—	2	2	no	—
342	C₂×D₄×C₄₁	—	4	2	no	—
343	C₂×D₄×C₄₁	—	4	2	no	—
344	C₂×D₄×C₄₁	—	4	4	no	—
345	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₄₁	—	2	2	no	—
351	C₂²×C₄×C₄₁	—	2	2	no	—
352	C₂²×C₄×C₄₁	—	2	2	no	—
353	C₂²×C₄×C₄₁	—	2	1	no	—
354	C₂²×C₄×C₄₁	—	2	1	no	—
355	C₂²×C₄×C₄₁	—	2	1	no	—
356	C₂²×C₄×C₄₁	—	2	1	no	—
357	C₂²×C₄×C₄₁	—	2	2	no	—
358	C₂²×C₄×C₄₁	—	2	2	no	—
359	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
365	Q₁₆×C₄₁	—	2	2	no	—
366	Q₁₆×C₄₁	—	2	4	no	—
367	Q₁₆×C₄₁	—	4	2	no	—
368	Q₁₆×C₄₁	—	4	2	no	—
369	Q₁₆×C₄₁	—	4	2	no	—
370	SD₁₆×C₄₁	—	2	2	no	—
371	SD₁₆×C₄₁	—	2	4	no	—
372	SD₁₆×C₄₁	—	4	2	no	—
373	SD₁₆×C₄₁	—	4	2	no	—
374	SD₁₆×C₄₁	—	4	1	no	—
375	SD₁₆×C₄₁	—	4	2	no	—
376	SD₁₆×C₄₁	—	4	2	no	—
377	D₈×C₄₁	—	4	1	no	—
378	D₈×C₄₁	—	4	2	no	—
379	C₂×C₈×C₄₁	—	4	2	no	—
380	C₂×C₈×C₄₁	—	4	2	no	—
381	C₂×C₈×C₄₁	—	4	2	no	—
382	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₄₁	—	2	1	no	—
389	C₄⋊C₄×C₄₁	—	2	2	no	—
390	C₄⋊C₄×C₄₁	—	2	2	no	—
391	C₄⋊C₄×C₄₁	—	2	2	no	—
392	C₄⋊C₄×C₄₁	—	2	2	no	—
393	C₄⋊C₄×C₄₁	—	2	1	no	—
394	C₄⋊C₄×C₄₁	—	2	1	no	—
395	C₄⋊C₄×C₄₁	—	2	1	no	—
396	C₄⋊C₄×C₄₁	—	2	1	no	—
397	C₄⋊C₄×C₄₁	—	2	1	no	—
398	C₄⋊C₄×C₄₁	—	2	2	no	—
399	C₄⋊C₄×C₄₁	—	2	2	no	—
400	C₄⋊C₄×C₄₁	—	2	1	no	—
401	C₄⋊C₄×C₄₁	—	2	2	no	—
402	C₄⋊C₄×C₄₁	—	2	1	no	—
403	C₄⋊C₄×C₄₁	—	2	2	no	—
404	C₄⋊C₄×C₄₁	—	2	1	no	—
405	C₄⋊C₄×C₄₁	—	2	2	no	—
406	C₄⋊C₄×C₄₁	—	2	1	no	—
407	C₄⋊C₄×C₄₁	—	2	2	no	—
408	C₄⋊C₄×C₄₁	—	2	1	no	—
409	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
418	C₂²⋊C₄×C₄₁	—	2	2	no	—
419	C₂²⋊C₄×C₄₁	—	2	2	no	—
420	C₂²⋊C₄×C₄₁	—	2	2	no	—
421	C₂²⋊C₄×C₄₁	—	2	1	no	—
422	C₂²⋊C₄×C₄₁	—	2	1	no	—
423	C₂²⋊C₄×C₄₁	—	2	2	no	—
424	C₂²⋊C₄×C₄₁	—	2	1	no	—
425	C₂²⋊C₄×C₄₁	—	2	1	no	—
426	C₂²⋊C₄×C₄₁	—	2	1	no	—
427	C₂²⋊C₄×C₄₁	—	2	2	no	—
428	C₂²⋊C₄×C₄₁	—	2	2	no	—
429	C₂²⋊C₄×C₄₁	—	2	2	no	—
430	C₂²⋊C₄×C₄₁	—	2	2	no	—
431	C₂²⋊C₄×C₄₁	—	2	2	no	—
432	C₂²⋊C₄×C₄₁	—	2	2	no	—
433	C₂²⋊C₄×C₄₁	—	2	1	no	—
434	C₂²⋊C₄×C₄₁	—	2	1	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	2	no	—
440	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
443	C₄²×C₄₁	—	2	1	no	—
444	C₄²×C₄₁	—	2	1	no	—
445	C₄²×C₄₁	—	2	2	no	—
446	C₄²×C₄₁	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₄₁	C₂×D₄	1	2	yes	—
454	C₄²×C₄₁	C₂×D₄	1	2	yes	—
455	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₄₁	C₂⁴	1	2	yes	—
457	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₄₁	—	2	1	no	—
459	C₂³×C₄₁	—	2	1	no	—
460	C₂³×C₄₁	—	2	2	no	—
461	C₂³×C₄₁	—	4	4	no	—
462	C₂³×C₄₁	—	8	2	no	—
463	C₂³×C₄₁	—	8	2	no	—
464	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
465	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
466	Q₈×C₄₁	—	2	2	no	—
467	Q₈×C₄₁	—	2	1	no	—
468	Q₈×C₄₁	—	2	2	no	—
469	Q₈×C₄₁	—	2	2	no	—
470	Q₈×C₄₁	—	2	1	no	—
471	Q₈×C₄₁	—	2	2	no	—
472	Q₈×C₄₁	—	2	1	no	—
473	Q₈×C₄₁	—	2	2	no	—
474	Q₈×C₄₁	—	4	4	no	—
475	Q₈×C₄₁	—	4	2	no	—
476	Q₈×C₄₁	—	8	2	no	—
477	Q₈×C₄₁	H(5,𝔽₂)	1	2	yes	—
478	D₄×C₄₁	—	2	4	no	—
479	D₄×C₄₁	—	2	1	no	—
480	D₄×C₄₁	—	2	2	no	—
481	D₄×C₄₁	—	2	1	no	—
482	D₄×C₄₁	—	2	1	no	—
483	D₄×C₄₁	—	2	1	no	—
484	D₄×C₄₁	—	2	2	no	—
485	D₄×C₄₁	—	4	2	no	—
486	D₄×C₄₁	—	4	4	no	—
487	D₄×C₄₁	—	4	4	no	—
488	D₄×C₄₁	—	4	2	no	—
489	D₄×C₄₁	—	8	1	no	—
490	D₄×C₄₁	—	8	2	no	—
491	D₄×C₄₁	—	8	1	no	—
492	D₄×C₄₁	—	8	2	no	—
493	D₄×C₄₁	#135	1	4	yes	complemented
494	C₂×C₄×C₄₁	—	2	4	no	—
495	C₂×C₄×C₄₁	—	2	1	no	—
496	C₂×C₄×C₄₁	—	2	2	no	—
497	C₂×C₄×C₄₁	—	2	2	no	—
498	C₂×C₄×C₄₁	—	2	1	no	—
499	C₂×C₄×C₄₁	—	2	2	no	—
500	C₂×C₄×C₄₁	—	2	1	no	—
501	C₂×C₄×C₄₁	—	2	1	no	—
502	C₂×C₄×C₄₁	—	2	1	no	—
503	C₂×C₄×C₄₁	—	2	2	no	—
504	C₂×C₄×C₄₁	—	2	1	no	—
505	C₂×C₄×C₄₁	—	2	2	no	—
506	C₂×C₄×C₄₁	—	2	1	no	—
507	C₂×C₄×C₄₁	—	2	1	no	—
508	C₂×C₄×C₄₁	—	2	2	no	—
509	C₂×C₄×C₄₁	—	4	2	no	—
510	C₂×C₄×C₄₁	—	4	1	no	—
511	C₂×C₄×C₄₁	—	4	2	no	—
512	C₂×C₄×C₄₁	—	4	4	no	—
513	C₂×C₄×C₄₁	—	4	2	no	—
514	C₂×C₄×C₄₁	—	4	4	no	—
515	C₂×C₄×C₄₁	—	4	2	no	—
516	C₂×C₄×C₄₁	—	4	2	no	—
517	C₂×C₄×C₄₁	—	8	2	no	—
518	C₂×C₄×C₄₁	—	8	2	no	—
519	C₂×C₄×C₄₁	—	8	2	no	—
520	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
529	C₈×C₄₁	—	2	2	no	—
530	C₈×C₄₁	—	2	1	no	—
531	C₈×C₄₁	—	2	2	no	—
532	C₈×C₄₁	—	2	1	no	—
533	C₈×C₄₁	—	2	1	no	—
534	C₈×C₄₁	—	2	1	no	—
535	#61956	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
536	C₂²×C₄₁	—	2	2	no	—
537	C₂²×C₄₁	—	2	2	no	—
538	C₂²×C₄₁	—	2	1	no	—
539	C₂²×C₄₁	—	2	1	no	—
540	C₂²×C₄₁	—	2	1	no	—
541	C₂²×C₄₁	—	4	1	no	—
542	C₂²×C₄₁	—	4	2	no	—
543	C₂²×C₄₁	—	4	1	no	—
544	C₂²×C₄₁	—	4	1	no	—
545	C₂²×C₄₁	—	4	2	no	—
546	C₂²×C₄₁	—	4	1	no	—
547	C₂²×C₄₁	—	4	1	no	—
548	C₂²×C₄₁	—	4	1	no	—
549	C₂²×C₄₁	—	4	2	no	—
550	C₂²×C₄₁	—	16	4	no	—
551	C₂²×C₄₁	C₂×#135	1	4	yes	—
552	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
553	C₄×C₄₁	—	2	1	no	—
554	C₄×C₄₁	—	2	2	no	—
555	C₄×C₄₁	—	2	1	no	—
556	C₄×C₄₁	—	2	1	no	—
557	C₄×C₄₁	—	2	2	no	—
558	C₄×C₄₁	—	2	2	no	—
559	C₄×C₄₁	—	2	1	no	—
560	C₄×C₄₁	—	2	2	no	—
561	C₄×C₄₁	—	4	1	no	—
562	C₄×C₄₁	—	4	1	no	—
563	C₄×C₄₁	—	4	2	no	—
564	C₄×C₄₁	—	4	2	no	—
565	C₄×C₄₁	—	4	1	no	—
566	C₄×C₄₁	—	4	1	no	—
567	C₄×C₄₁	—	4	1	no	—
568	C₄×C₄₁	—	4	2	no	—
569	C₄×C₄₁	C₂×#135	1	2	yes	—
570	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
571	C₄×C₄₁	#585	1	1	yes	characteristic
572	#3514	C₂×C₄₁	1	1	yes	characteristic, complemented
573	#3482	C₂×C₄₁	1	1	yes	characteristic, complemented
574	#3394	C₂×C₄₁	1	1	yes	characteristic, complemented
575	#3393	C₂×C₄₁	1	1	yes	characteristic, complemented
576	#3365	C₂×C₄₁	1	1	yes	characteristic, complemented
577	#3364	C₂×C₄₁	1	1	yes	characteristic, complemented
578	#3300	C₂×C₄₁	1	2	yes	complemented
579	#3298	C₂×C₄₁	1	1	yes	characteristic, complemented
580	#3296	C₂×C₄₁	1	2	yes	complemented
581	#3294	C₂×C₄₁	1	1	yes	characteristic, complemented
582	D₄×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
583	#3285	C₂×C₄₁	1	2	yes	complemented
584	#3282	C₂×C₄₁	1	2	yes	complemented
585	D₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
586	#3250	C₂×C₄₁	1	2	yes	complemented
587	#3248	C₂×C₄₁	1	1	yes	characteristic, complemented
588	#3211	C₂×C₄₁	1	2	yes	complemented
589	#3210	C₂×C₄₁	1	1	yes	characteristic, complemented
590	#3108	C₂×C₄₁	1	2	yes	complemented
591	#3102	C₂×C₄₁	1	1	yes	characteristic, complemented
592	#3035	C₂×C₄₁	1	1	yes	characteristic, complemented
593	C₂×#464	C₂×C₄₁	1	2	yes	complemented
594	#2988	C₂×C₄₁	1	1	yes	characteristic, complemented
595	C₂×C₄₁	—	2	4	no	—
596	C₂×C₄₁	—	4	1	no	—
597	C₂×C₄₁	—	8	1	no	—
598	C₂×C₄₁	—	8	2	no	—
599	C₂×C₄₁	—	8	1	no	—
600	C₂×C₄₁	#3488	1	1	yes	characteristic
601	C₂×C₄₁	C₂²×#135	1	1	yes	characteristic
602	C₂×C₄₁	#3586	1	1	yes	characteristic
603	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
604	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
605	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
606	#559	C₂²×C₄₁	1	1	yes	characteristic
607	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
608	#556	—	2	1	no	—
609	#556	C₂²×C₄₁	1	1	yes	characteristic
610	#556	C₂²×C₄₁	1	1	yes	characteristic, complemented
611	#555	—	2	1	no	—
612	#552	—	2	2	no	—
613	#552	C₂²×C₄₁	1	2	yes	complemented
614	#551	—	2	2	no	—
615	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
616	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
617	#548	C₂²×C₄₁	1	2	yes	—
618	#548	C₂²×C₄₁	1	2	yes	complemented
619	#547	—	2	1	no	—
620	#547	C₂²×C₄₁	1	1	yes	characteristic
621	#546	—	2	1	no	—
622	#546	C₂²×C₄₁	1	2	yes	—
623	D₄²	C₂²×C₄₁	1	1	yes	characteristic
624	#542	—	2	1	no	—
625	#538	—	2	2	no	—
626	#533	—	2	1	no	—
627	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
628	#532	C₂²×C₄₁	1	1	yes	characteristic
629	#529	—	2	2	no	—
630	#529	C₂²×C₄₁	1	1	yes	characteristic
631	#529	C₂²×C₄₁	1	2	yes	—
632	#529	C₂²×C₄₁	1	2	yes	complemented
633	C₂×#124	C₂²×C₄₁	1	2	yes	—
634	#518	—	2	1	no	—
635	C₄×#41	—	2	1	no	—
636	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
637	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic, complemented
638	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
639	#495	C₂²×C₄₁	1	2	yes	—
640	#495	C₂²×C₄₁	1	2	yes	complemented
641	#494	C₂²×C₄₁	1	1	yes	characteristic, complemented
642	#492	C₂²×C₄₁	1	1	yes	characteristic
643	#488	C₂²×C₄₁	1	2	yes	—
644	#488	C₂²×C₄₁	1	2	yes	complemented
645	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
646	#486	C₂²×C₄₁	1	1	yes	characteristic
647	#485	C₂²×C₄₁	1	1	yes	characteristic, complemented
648	#483	C₂²×C₄₁	1	2	yes	complemented
649	#482	C₂²×C₄₁	1	1	yes	characteristic
650	#480	C₂²×C₄₁	1	2	yes	—
651	#479	C₂²×C₄₁	1	1	yes	characteristic, complemented
652	#479	C₂²×C₄₁	1	2	yes	complemented
653	#479	C₂²×C₄₁	1	2	yes	complemented
654	#478	C₂²×C₄₁	1	1	yes	characteristic, complemented
655	#478	C₂²×C₄₁	1	2	yes	complemented
656	#475	C₂²×C₄₁	1	1	yes	characteristic, complemented
657	#474	C₂²×C₄₁	1	1	yes	characteristic
658	#467	C₂²×C₄₁	1	2	yes	complemented
659	#467	C₂²×C₄₁	1	2	yes	complemented
660	#466	C₂²×C₄₁	1	2	yes	—
661	#465	C₂²×C₄₁	1	2	yes	—
662	#465	C₂²×C₄₁	1	2	yes	—
663	#465	C₂²×C₄₁	1	2	yes	complemented
664	#464	C₂²×C₄₁	1	1	yes	characteristic
665	#464	C₂²×C₄₁	1	2	yes	—
666	#464	C₂²×C₄₁	1	2	yes	—
667	#464	C₂²×C₄₁	1	2	yes	—
668	#464	C₂²×C₄₁	1	2	yes	complemented
669	#464	C₂²×C₄₁	1	2	yes	complemented
670	#464	C₂²×C₄₁	1	2	yes	complemented
671	#464	C₂²×C₄₁	1	2	yes	complemented
672	#464	C₂²×C₄₁	1	2	yes	complemented
673	#464	C₂²×C₄₁	1	2	yes	complemented
674	#463	C₂²×C₄₁	1	1	yes	characteristic
675	#463	C₂²×C₄₁	1	2	yes	complemented
676	#463	C₂²×C₄₁	1	2	yes	complemented
677	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
678	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
679	#461	C₂²×C₄₁	1	1	yes	characteristic
680	#461	C₂²×C₄₁	1	1	yes	characteristic, complemented
681	#460	C₂²×C₄₁	1	1	yes	characteristic
682	#459	C₂²×C₄₁	1	1	yes	characteristic
683	#452	C₂²×C₄₁	1	1	yes	characteristic, complemented
684	#452	C₂²×C₄₁	1	2	yes	complemented
685	#452	C₂²×C₄₁	1	2	yes	complemented
686	#451	C₂²×C₄₁	1	2	yes	complemented
687	#451	C₂²×C₄₁	1	2	yes	complemented
688	#450	C₂²×C₄₁	1	2	yes	—
689	#449	C₂²×C₄₁	1	1	yes	characteristic
690	#448	C₂²×C₄₁	1	2	yes	—
691	#448	C₂²×C₄₁	1	2	yes	complemented
692	#447	C₂²×C₄₁	1	2	yes	—
693	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
694	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
695	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
696	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
700	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
702	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
703	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
704	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
705	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
706	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
707	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
708	#431	C₂²×C₄₁	1	2	yes	complemented
709	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
710	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
711	#416	C₂²×C₄₁	1	2	yes	complemented
712	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
713	C₂×#102	C₂²×C₄₁	1	2	yes	—
714	C₄₁	#61956	1	1	yes	characteristic, direct product factor, Sylow
715	C₂×#41	—	2	1	no	—
716	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
717	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
718	C₂×#41	C₂³×C₄₁	1	2	yes	—
719	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
720	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
723	#135	—	4	4	no	—
724	C₂×Q₁₆	—	4	4	no	—
725	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
730	C₂×SD₁₆	—	4	4	no	—
731	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₄₁	1	2	yes	—
739	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
740	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
741	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
742	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
749	#127	C₂³×C₄₁	1	1	yes	characteristic
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	1	no	—
755	#126	—	2	2	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	1	no	—
759	#125	C₂³×C₄₁	1	1	yes	characteristic
760	#125	C₂³×C₄₁	1	2	yes	—
761	#124	—	2	1	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	C₂³×C₄₁	1	1	yes	characteristic
767	#124	C₂³×C₄₁	1	2	yes	—
768	#124	C₂³×C₄₁	1	2	yes	—
769	#124	C₂³×C₄₁	1	2	yes	—
770	#124	C₂³×C₄₁	1	2	yes	—
771	#123	—	2	2	no	—
772	#123	—	2	1	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
788	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	C₂³×C₄₁	1	2	yes	—
797	#121	C₂³×C₄₁	1	1	yes	characteristic
798	#121	C₂³×C₄₁	1	2	yes	—
799	#120	—	2	2	no	—
800	#120	—	2	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	—	2	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
810	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
812	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
827	C₄×D₄	D₄×C₄₁	1	2	yes	—
828	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₄₁	1	2	yes	—
832	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₄₁	1	2	yes	—
834	#117	—	2	1	no	—
835	#117	—	2	1	no	—
836	#117	—	2	1	no	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	2	no	—
841	#117	—	2	2	no	—
842	#117	D₄×C₄₁	1	2	yes	—
843	#117	D₄×C₄₁	1	1	yes	characteristic
844	#117	C₂³×C₄₁	1	1	yes	characteristic
845	C₂×C₄⋊C₄	—	2	2	no	—
846	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₄²	—	2	2	no	—
851	C₂×C₄²	—	2	1	no	—
852	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
853	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
854	#107	C₂³×C₄₁	1	1	yes	characteristic
855	#107	C₂³×C₄₁	1	2	yes	—
856	#107	C₂³×C₄₁	1	1	yes	characteristic
857	#106	C₂³×C₄₁	1	1	yes	characteristic
858	#106	C₂³×C₄₁	1	1	yes	characteristic
859	#106	C₂³×C₄₁	1	2	yes	—
860	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
861	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
867	#103	C₂³×C₄₁	1	1	yes	characteristic
868	#103	C₂³×C₄₁	1	2	yes	—
869	#103	C₂³×C₄₁	1	2	yes	—
870	#103	C₂³×C₄₁	1	2	yes	—
871	#103	C₂³×C₄₁	1	2	yes	—
872	#103	C₂³×C₄₁	1	1	yes	characteristic
873	#103	C₂³×C₄₁	1	1	yes	characteristic
874	#103	C₂³×C₄₁	1	2	yes	—
875	#103	C₂³×C₄₁	1	2	yes	—
876	#103	C₂³×C₄₁	1	2	yes	—
877	#103	C₂³×C₄₁	1	1	yes	characteristic
878	#102	C₂³×C₄₁	1	1	yes	characteristic
879	#102	C₂³×C₄₁	1	2	yes	—
880	#102	C₂³×C₄₁	1	2	yes	—
881	#102	C₂³×C₄₁	1	2	yes	—
882	#102	C₂³×C₄₁	1	2	yes	—
883	#102	C₂³×C₄₁	1	1	yes	characteristic
884	#102	C₂³×C₄₁	1	1	yes	characteristic
885	#102	C₂³×C₄₁	1	2	yes	—
886	#102	C₂³×C₄₁	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₄₁	1	2	yes	—
894	C₄×C₈	C₂³×C₄₁	1	2	yes	—
895	C₂⁴	—	2	2	no	—
896	#41	—	2	4	no	—
897	#41	—	2	2	no	—
898	#41	—	4	1	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	4	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	4	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	2	no	—
909	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	4	no	—
925	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
926	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
929	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
940	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
941	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
942	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
945	Q₁₆	—	2	2	no	—
946	Q₁₆	—	2	4	no	—
947	Q₁₆	—	4	2	no	—
948	Q₁₆	—	4	2	no	—
949	Q₁₆	—	4	2	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	2	4	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	1	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	D₈	—	4	1	no	—
958	D₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	—	4	2	no	—
961	C₂×C₈	—	4	2	no	—
962	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
966	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1021	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1032	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1033	C₄²	C₂×D₄×C₄₁	1	2	yes	—
1034	C₄²	C₂×D₄×C₄₁	1	2	yes	—
1035	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₄₁	1	2	yes	—
1037	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1045	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	4	4	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	H(5,𝔽₂)×C₄₁	1	2	yes	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	1	no	—
1073	D₄	#135×C₄₁	1	4	yes	complemented
1074	C₂×C₄	—	2	4	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	16	4	no	—
1130	C₂²	C₂×#135×C₄₁	1	4	yes	—
1131	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	C₂×#135×C₄₁	1	2	yes	—
1149	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1150	C₄	C₄₁×#585	1	1	yes	characteristic
1151	C₂	—	2	4	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₄₁×#3488	1	1	yes	characteristic
1157	C₂	C₂²×#135×C₄₁	1	1	yes	characteristic
1158	C₂	C₄₁×#3586	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 ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3514	C₂	semidirect
2. C₄₁×#3482	C₂	semidirect
3. C₄₁×#3394	C₂	semidirect
4. C₄₁×#3393	C₂	semidirect
5. C₄₁×#3365	C₂	semidirect
6. C₄₁×#3364	C₂	semidirect
7. C₄₁×#3300	C₂	semidirect
8. C₄₁×#3298	C₂	semidirect
9. C₄₁×#3296	C₂	semidirect
10. C₄₁×#3294	C₂	semidirect
11. D₄×Q₁₆×C₄₁	C₂	semidirect
12. C₄₁×#3285	C₂	semidirect
13. C₄₁×#3282	C₂	semidirect
14. D₄×SD₁₆×C₄₁	C₂	semidirect
15. C₄₁×#3250	C₂	semidirect
16. C₄₁×#3248	C₂	semidirect
17. C₄₁×#3211	C₂	semidirect
18. C₄₁×#3210	C₂	semidirect
19. C₄₁×#3108	C₂	semidirect
20. C₄₁×#3102	C₂	semidirect
21. C₄₁×#3035	C₂	semidirect
22. C₂×C₄₁×#464	C₂	semidirect
23. C₄₁×#2988	C₂	semidirect
24. C₂×#135×C₄₁	C₂²	semidirect
25. C₂²×Q₁₆×C₄₁	C₂²	semidirect
28. C₄₁×#557	C₂²	semidirect
31. C₄₁×#556	C₂²	semidirect
34. C₄₁×#552	C₂²	semidirect
39. C₄₁×#548	C₂²	semidirect
48. C₄₁×#533	C₂²	semidirect
53. C₄₁×#529	C₂²	semidirect
58. C₄×#41×C₄₁	C₂²	semidirect
59. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
61. C₄₁×#495	C₂²	semidirect
62. C₄₁×#494	C₂²	semidirect
65. C₄₁×#488	C₂²	semidirect
66. C₄₁×#487	C₂²	semidirect
68. C₄₁×#485	C₂²	semidirect
69. C₄₁×#483	C₂²	semidirect
72. C₄₁×#479	C₂²	semidirect
73. C₄₁×#479	C₂²	semidirect
74. C₄₁×#479	C₂²	semidirect
75. C₄₁×#478	C₂²	semidirect
76. C₄₁×#478	C₂²	semidirect
77. C₄₁×#475	C₂²	semidirect
79. C₄₁×#467	C₂²	semidirect
80. C₄₁×#467	C₂²	semidirect
84. C₄₁×#465	C₂²	semidirect
89. C₄₁×#464	C₂²	semidirect
90. C₄₁×#464	C₂²	semidirect
91. C₄₁×#464	C₂²	semidirect
92. C₄₁×#464	C₂²	semidirect
93. C₄₁×#464	C₂²	semidirect
94. C₄₁×#464	C₂²	semidirect
96. C₄₁×#463	C₂²	semidirect
97. C₄₁×#463	C₂²	semidirect
98. C₄₁×#462	C₂²	semidirect
99. C₄₁×#462	C₂²	semidirect
101. C₄₁×#461	C₂²	semidirect
104. C₄₁×#452	C₂²	semidirect
105. C₄₁×#452	C₂²	semidirect
106. C₄₁×#452	C₂²	semidirect
107. C₄₁×#451	C₂²	semidirect
108. C₄₁×#451	C₂²	semidirect
112. C₄₁×#448	C₂²	semidirect
114. C₈×Q₈×C₄₁	C₂²	semidirect
115. C₈×Q₈×C₄₁	C₂²	semidirect
116. C₄×Q₁₆×C₄₁	C₂²	semidirect
117. C₄×Q₁₆×C₄₁	C₂²	semidirect
118. C₄×Q₁₆×C₄₁	C₂²	semidirect
120. C₄×SD₁₆×C₄₁	C₂²	semidirect
121. C₄×SD₁₆×C₄₁	C₂²	semidirect
122. C₄×SD₁₆×C₄₁	C₂²	semidirect
126. C₈×D₄×C₄₁	C₂²	semidirect
127. C₈×D₄×C₄₁	C₂²	semidirect
128. C₄₁×#431	C₂²	semidirect
129. C₄₁×#431	C₂²	semidirect
130. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
131. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
132. C₄₁×#416	C₂²	semidirect
133. C₂×#103×C₄₁	C₂²	semidirect
493. D₄×C₄₁	#135	semidirect
535. #61956	C₄₁	direct (N × H)
572. #3514	C₂×C₄₁	semidirect
573. #3482	C₂×C₄₁	semidirect
574. #3394	C₂×C₄₁	semidirect
575. #3393	C₂×C₄₁	semidirect
576. #3365	C₂×C₄₁	semidirect
577. #3364	C₂×C₄₁	semidirect
578. #3300	C₂×C₄₁	semidirect
579. #3298	C₂×C₄₁	semidirect
580. #3296	C₂×C₄₁	semidirect
581. #3294	C₂×C₄₁	semidirect
582. D₄×Q₁₆	C₂×C₄₁	semidirect
583. #3285	C₂×C₄₁	semidirect
584. #3282	C₂×C₄₁	semidirect
585. D₄×SD₁₆	C₂×C₄₁	semidirect
586. #3250	C₂×C₄₁	semidirect
587. #3248	C₂×C₄₁	semidirect
588. #3211	C₂×C₄₁	semidirect
589. #3210	C₂×C₄₁	semidirect
590. #3108	C₂×C₄₁	semidirect
591. #3102	C₂×C₄₁	semidirect
592. #3035	C₂×C₄₁	semidirect
593. C₂×#464	C₂×C₄₁	semidirect
594. #2988	C₂×C₄₁	semidirect
603. C₂×#135	C₂²×C₄₁	semidirect
604. C₂²×Q₁₆	C₂²×C₄₁	semidirect
607. #557	C₂²×C₄₁	semidirect
610. #556	C₂²×C₄₁	semidirect
613. #552	C₂²×C₄₁	semidirect
618. #548	C₂²×C₄₁	semidirect
627. #533	C₂²×C₄₁	semidirect
632. #529	C₂²×C₄₁	semidirect
637. C₄×#41	C₂²×C₄₁	semidirect
638. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
640. #495	C₂²×C₄₁	semidirect
641. #494	C₂²×C₄₁	semidirect
644. #488	C₂²×C₄₁	semidirect
645. #487	C₂²×C₄₁	semidirect
647. #485	C₂²×C₄₁	semidirect
648. #483	C₂²×C₄₁	semidirect
651. #479	C₂²×C₄₁	semidirect
652. #479	C₂²×C₄₁	semidirect
653. #479	C₂²×C₄₁	semidirect
654. #478	C₂²×C₄₁	semidirect
655. #478	C₂²×C₄₁	semidirect
656. #475	C₂²×C₄₁	semidirect
658. #467	C₂²×C₄₁	semidirect
659. #467	C₂²×C₄₁	semidirect
663. #465	C₂²×C₄₁	semidirect
668. #464	C₂²×C₄₁	semidirect
669. #464	C₂²×C₄₁	semidirect
670. #464	C₂²×C₄₁	semidirect
671. #464	C₂²×C₄₁	semidirect
672. #464	C₂²×C₄₁	semidirect
673. #464	C₂²×C₄₁	semidirect
675. #463	C₂²×C₄₁	semidirect
676. #463	C₂²×C₄₁	semidirect
677. #462	C₂²×C₄₁	semidirect
678. #462	C₂²×C₄₁	semidirect
680. #461	C₂²×C₄₁	semidirect
683. #452	C₂²×C₄₁	semidirect
684. #452	C₂²×C₄₁	semidirect
685. #452	C₂²×C₄₁	semidirect
686. #451	C₂²×C₄₁	semidirect
687. #451	C₂²×C₄₁	semidirect
691. #448	C₂²×C₄₁	semidirect
693. C₈×Q₈	C₂²×C₄₁	semidirect
694. C₈×Q₈	C₂²×C₄₁	semidirect
695. C₄×Q₁₆	C₂²×C₄₁	semidirect
696. C₄×Q₁₆	C₂²×C₄₁	semidirect
697. C₄×Q₁₆	C₂²×C₄₁	semidirect
699. C₄×SD₁₆	C₂²×C₄₁	semidirect
700. C₄×SD₁₆	C₂²×C₄₁	semidirect
701. C₄×SD₁₆	C₂²×C₄₁	semidirect
705. C₈×D₄	C₂²×C₄₁	semidirect
706. C₈×D₄	C₂²×C₄₁	semidirect
707. #431	C₂²×C₄₁	semidirect
708. #431	C₂²×C₄₁	semidirect
709. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
710. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
711. #416	C₂²×C₄₁	semidirect
712. C₂×#103	C₂²×C₄₁	semidirect
714. C₄₁	#61956	direct (N × H)
1073. 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×#3514	2
C₄₁×#3482	2
C₄₁×#3394	2
C₄₁×#3393	2
C₄₁×#3365	2
C₄₁×#3364	2
C₄₁×#3300	2
C₄₁×#3298	2
C₄₁×#3296	2
C₄₁×#3294	2
D₄×Q₁₆×C₄₁	2
C₄₁×#3285	2
C₄₁×#3282	2
D₄×SD₁₆×C₄₁	2
C₄₁×#3250	2
C₄₁×#3248	2
C₄₁×#3211	2
C₄₁×#3210	2
C₄₁×#3108	2
C₄₁×#3102	2
C₄₁×#3035	2
C₂×C₄₁×#464	2
C₄₁×#2988	2
#61956	41

Subgroups — C41×#61956 #23838157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61956 #23838157