Subgroups — C₄₁×#61438 #23837639

Order 10496.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3475	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3344	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3314	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3312	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3266	C₂	1	2	yes	maximal, complemented
15	C₄₁×#3172	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#3108	C₂	1	2	yes	maximal, complemented
18	C₄₁×#3107	C₂	1	2	yes	maximal, complemented
19	C₄₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137×C₄₁	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₄₁	C₂²	1	2	yes	—
25	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
26	Q₈²×C₄₁	C₂²	1	1	yes	characteristic, complemented
27	C₄₁×#557	—	2	1	no	—
28	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#556	C₂²	1	1	yes	characteristic
30	C₄₁×#555	C₂²	1	1	yes	characteristic
31	C₄₁×#554	—	2	2	no	—
32	C₄₁×#554	—	2	1	no	—
33	C₄₁×#554	C₂²	1	1	yes	characteristic
34	C₄₁×#554	C₂²	1	2	yes	—
35	C₄₁×#554	C₂²	1	1	yes	characteristic, complemented
36	C₄₁×#553	—	2	1	no	—
37	C₄₁×#552	—	2	1	no	—
38	C₄₁×#552	C₂²	1	2	yes	—
39	C₄₁×#551	—	2	2	no	—
40	D₄×Q₈×C₄₁	C₂²	1	2	yes	—
41	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
42	C₄₁×#547	C₂²	1	1	yes	characteristic
43	C₄₁×#546	C₂²	1	2	yes	—
44	C₄₁×#533	—	2	1	no	—
45	C₄₁×#533	—	2	2	no	—
46	C₄₁×#533	C₂²	1	1	yes	characteristic
47	C₄₁×#533	C₂²	1	1	yes	characteristic
48	C₄₁×#533	C₂²	1	2	yes	complemented
49	C₄₁×#529	—	2	2	no	—
50	C₄₁×#529	C₂²	1	2	yes	—
51	C₄₁×#525	—	2	1	no	—
52	C₄×#41×C₄₁	—	2	1	no	—
53	C₄×#41×C₄₁	C₂²	1	2	yes	—
54	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
58	C₂×#117×C₄₁	—	2	1	no	—
59	C₄₁×#501	C₂²	1	2	yes	complemented
60	C₄₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₄₁×#497	C₂²	1	2	yes	—
62	C₄₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₄₁×#491	C₂²	1	2	yes	complemented
64	C₄₁×#489	C₂²	1	2	yes	—
65	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₄₁×#485	C₂²	1	2	yes	complemented
68	C₄₁×#485	C₂²	1	2	yes	complemented
69	C₄₁×#484	C₂²	1	2	yes	—
70	C₄₁×#483	C₂²	1	2	yes	—
71	C₄₁×#483	C₂²	1	2	yes	complemented
72	C₄₁×#480	C₂²	1	2	yes	—
73	C₄₁×#479	C₂²	1	2	yes	complemented
74	C₄₁×#479	C₂²	1	2	yes	complemented
75	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
76	C₄₁×#477	C₂²	1	1	yes	characteristic, complemented
77	C₄₁×#476	C₂²	1	1	yes	characteristic
78	C₄₁×#476	C₂²	1	1	yes	characteristic
79	C₄₁×#475	C₂²	1	2	yes	complemented
80	C₄₁×#474	C₂²	1	2	yes	—
81	C₄₁×#470	C₂²	1	2	yes	complemented
82	C₄₁×#470	C₂²	1	2	yes	complemented
83	C₄₁×#468	C₂²	1	2	yes	—
84	C₄₁×#468	C₂²	1	2	yes	—
85	C₄₁×#467	C₂²	1	2	yes	—
86	C₄₁×#467	C₂²	1	2	yes	—
87	C₄₁×#464	C₂²	1	2	yes	—
88	C₄₁×#464	C₂²	1	2	yes	—
89	C₄₁×#462	C₂²	1	2	yes	complemented
90	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₄₁×#462	C₂²	1	1	yes	characteristic, complemented
92	C₄₁×#461	C₂²	1	1	yes	characteristic
93	C₄₁×#461	C₂²	1	1	yes	characteristic
94	C₄₁×#461	C₂²	1	2	yes	—
95	C₄₁×#452	C₂²	1	2	yes	—
96	C₄₁×#452	C₂²	1	2	yes	—
97	C₄₁×#451	C₂²	1	2	yes	—
98	C₄₁×#451	C₂²	1	2	yes	complemented
99	C₄₁×#450	C₂²	1	2	yes	—
100	C₄₁×#448	C₂²	1	2	yes	—
101	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₄₁×#446	C₂²	1	1	yes	characteristic, complemented
103	C₄₁×#441	C₂²	1	2	yes	complemented
104	C₄₁×#441	C₂²	1	2	yes	complemented
105	C₄₁×#440	C₂²	1	2	yes	—
106	C₄₁×#440	C₂²	1	2	yes	—
107	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
108	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
109	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
110	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
121	C₄₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₄₁×#436	C₂²	1	1	yes	characteristic, complemented
123	C₄₁×#435	C₂²	1	2	yes	—
124	C₄₁×#435	C₂²	1	2	yes	—
125	C₄₁×#431	C₂²	1	1	yes	characteristic
126	C₄₁×#431	C₂²	1	2	yes	complemented
127	C₄₁×#428	C₂²	1	2	yes	complemented
128	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
129	C₄₁×#419	C₂²	1	2	yes	complemented
130	C₄₁×#417	C₂²	1	2	yes	—
131	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
132	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₄₁	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
136	C₂×#41×C₄₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₄₁	—	2	1	no	—
141	#137×C₄₁	—	2	8	no	—
142	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₄₁	—	2	4	no	—
147	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₄₁	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
154	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₄₁	—	2	2	no	—
158	C₄⋊Q₈×C₄₁	—	2	1	no	—
159	C₄⋊Q₈×C₄₁	—	2	1	no	—
160	C₄⋊Q₈×C₄₁	—	2	2	no	—
161	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
167	#126×C₄₁	—	2	2	no	—
168	#126×C₄₁	—	2	2	no	—
169	#126×C₄₁	—	2	2	no	—
170	#125×C₄₁	—	2	2	no	—
171	#125×C₄₁	—	2	1	no	—
172	#125×C₄₁	—	2	2	no	—
173	#125×C₄₁	—	2	2	no	—
174	#125×C₄₁	—	2	1	no	—
175	#125×C₄₁	—	2	1	no	—
176	#125×C₄₁	—	2	1	no	—
177	#125×C₄₁	—	2	2	no	—
178	#125×C₄₁	C₂³	1	2	yes	—
179	#124×C₄₁	—	2	2	no	—
180	#124×C₄₁	C₂³	1	2	yes	—
181	#123×C₄₁	—	2	2	no	—
182	#123×C₄₁	—	2	2	no	—
183	#123×C₄₁	—	2	2	no	—
184	#123×C₄₁	—	2	2	no	—
185	C₂²⋊Q₈×C₄₁	—	2	1	no	—
186	C₂²⋊Q₈×C₄₁	—	2	1	no	—
187	C₂²⋊Q₈×C₄₁	—	2	1	no	—
188	C₂²⋊Q₈×C₄₁	—	2	1	no	—
189	C₂²⋊Q₈×C₄₁	—	2	2	no	—
190	C₂²⋊Q₈×C₄₁	—	2	2	no	—
191	C₂²⋊Q₈×C₄₁	—	2	2	no	—
192	C₂²⋊Q₈×C₄₁	—	2	2	no	—
193	C₂²⋊Q₈×C₄₁	—	2	2	no	—
194	C₂²⋊Q₈×C₄₁	—	2	2	no	—
195	C₂²⋊Q₈×C₄₁	—	2	2	no	—
196	C₂²⋊Q₈×C₄₁	—	2	2	no	—
197	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
202	#121×C₄₁	—	2	1	no	—
203	#121×C₄₁	—	2	1	no	—
204	#121×C₄₁	—	2	2	no	—
205	#121×C₄₁	C₂³	1	2	yes	—
206	#120×C₄₁	—	2	2	no	—
207	C₄×Q₈×C₄₁	—	2	1	no	—
208	C₄×Q₈×C₄₁	—	2	1	no	—
209	C₄×Q₈×C₄₁	—	2	1	no	—
210	C₄×Q₈×C₄₁	—	2	1	no	—
211	C₄×Q₈×C₄₁	—	2	2	no	—
212	C₄×Q₈×C₄₁	—	2	2	no	—
213	C₄×Q₈×C₄₁	—	2	1	no	—
214	C₄×Q₈×C₄₁	—	2	1	no	—
215	C₄×Q₈×C₄₁	—	2	2	no	—
216	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
217	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
233	C₄×D₄×C₄₁	—	2	2	no	—
234	C₄×D₄×C₄₁	—	2	1	no	—
235	C₄×D₄×C₄₁	—	2	1	no	—
236	C₄×D₄×C₄₁	D₄	1	2	yes	—
237	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
238	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₄₁	C₂³	1	2	yes	—
243	C₄×D₄×C₄₁	C₂³	1	2	yes	—
244	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
245	#117×C₄₁	—	2	1	no	—
246	#117×C₄₁	—	2	1	no	—
247	#117×C₄₁	—	2	2	no	—
248	#117×C₄₁	—	2	1	no	—
249	#117×C₄₁	—	2	1	no	—
250	#117×C₄₁	—	2	2	no	—
251	#117×C₄₁	—	2	2	no	—
252	#117×C₄₁	—	2	2	no	—
253	#117×C₄₁	D₄	1	1	yes	characteristic
254	#117×C₄₁	D₄	1	2	yes	—
255	#117×C₄₁	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
258	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
265	C₂×C₄²×C₄₁	—	2	1	no	—
266	C₂×C₄²×C₄₁	—	2	2	no	—
267	C₂×C₄²×C₄₁	—	2	2	no	—
268	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
270	#107×C₄₁	C₂³	1	2	yes	—
271	#107×C₄₁	C₂³	1	2	yes	—
272	#107×C₄₁	C₂³	1	2	yes	—
273	#107×C₄₁	C₂³	1	2	yes	—
274	#106×C₄₁	C₂³	1	1	yes	characteristic
275	#106×C₄₁	C₂³	1	2	yes	—
276	#106×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	1	yes	characteristic
281	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
284	#103×C₄₁	C₂³	1	1	yes	characteristic
285	#103×C₄₁	C₂³	1	1	yes	characteristic
286	#103×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	2	yes	—
293	#103×C₄₁	C₂³	1	2	yes	—
294	#103×C₄₁	C₂³	1	2	yes	—
295	#103×C₄₁	C₂³	1	2	yes	—
296	#103×C₄₁	C₂³	1	2	yes	—
297	#103×C₄₁	C₂³	1	2	yes	—
298	#102×C₄₁	C₂³	1	1	yes	characteristic
299	#102×C₄₁	C₂³	1	1	yes	characteristic
300	#102×C₄₁	C₂³	1	1	yes	characteristic
301	#102×C₄₁	C₂³	1	1	yes	characteristic
302	#102×C₄₁	C₂³	1	2	yes	—
303	#102×C₄₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
307	#97×C₄₁	C₂³	1	2	yes	—
308	#97×C₄₁	C₂³	1	2	yes	—
309	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
310	C₄×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	C₂⁴×C₄₁	—	2	1	no	—
315	#41×C₄₁	—	2	4	no	—
316	#41×C₄₁	—	2	4	no	—
317	#41×C₄₁	—	4	2	no	—
318	C₂×Q₈×C₄₁	—	2	2	no	—
319	C₂×Q₈×C₄₁	—	2	1	no	—
320	C₂×Q₈×C₄₁	—	2	1	no	—
321	C₂×Q₈×C₄₁	—	2	2	no	—
322	C₂×Q₈×C₄₁	—	2	1	no	—
323	C₂×Q₈×C₄₁	—	2	2	no	—
324	C₂×Q₈×C₄₁	—	2	4	no	—
325	C₂×Q₈×C₄₁	—	4	1	no	—
326	C₂×Q₈×C₄₁	—	4	2	no	—
327	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₄₁	—	2	2	no	—
333	C₂×D₄×C₄₁	—	2	2	no	—
334	C₂×D₄×C₄₁	—	2	2	no	—
335	C₂×D₄×C₄₁	—	2	1	no	—
336	C₂×D₄×C₄₁	—	4	1	no	—
337	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₄₁	—	2	2	no	—
342	C₂²×C₄×C₄₁	—	2	1	no	—
343	C₂²×C₄×C₄₁	—	2	1	no	—
344	C₂²×C₄×C₄₁	—	2	2	no	—
345	C₂²×C₄×C₄₁	—	2	1	no	—
346	C₂²×C₄×C₄₁	—	2	2	no	—
347	C₂²×C₄×C₄₁	—	2	1	no	—
348	C₂²×C₄×C₄₁	—	2	1	no	—
349	C₂²×C₄×C₄₁	—	2	1	no	—
350	C₂²×C₄×C₄₁	—	2	1	no	—
351	C₂²×C₄×C₄₁	—	2	2	no	—
352	C₂²×C₄×C₄₁	—	4	4	no	—
353	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
354	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
359	Q₁₆×C₄₁	—	2	4	no	—
360	Q₁₆×C₄₁	—	2	4	no	—
361	Q₁₆×C₄₁	—	4	2	no	—
362	Q₁₆×C₄₁	—	4	2	no	—
363	SD₁₆×C₄₁	—	2	2	no	—
364	SD₁₆×C₄₁	—	2	2	no	—
365	SD₁₆×C₄₁	—	2	4	no	—
366	SD₁₆×C₄₁	—	2	2	no	—
367	SD₁₆×C₄₁	—	4	2	no	—
368	SD₁₆×C₄₁	#41	1	4	yes	complemented
369	M₁₆×C₄₁	—	2	4	no	—
370	M₁₆×C₄₁	—	4	2	no	—
371	C₂×C₈×C₄₁	—	2	2	no	—
372	C₂×C₈×C₄₁	—	4	1	no	—
373	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
377	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
378	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₄₁	—	2	1	no	—
380	C₄⋊C₄×C₄₁	—	2	1	no	—
381	C₄⋊C₄×C₄₁	—	2	1	no	—
382	C₄⋊C₄×C₄₁	—	2	2	no	—
383	C₄⋊C₄×C₄₁	—	2	2	no	—
384	C₄⋊C₄×C₄₁	—	2	2	no	—
385	C₄⋊C₄×C₄₁	—	2	1	no	—
386	C₄⋊C₄×C₄₁	—	2	1	no	—
387	C₄⋊C₄×C₄₁	—	2	2	no	—
388	C₄⋊C₄×C₄₁	—	2	2	no	—
389	C₄⋊C₄×C₄₁	—	2	1	no	—
390	C₄⋊C₄×C₄₁	—	2	1	no	—
391	C₄⋊C₄×C₄₁	—	2	2	no	—
392	C₄⋊C₄×C₄₁	—	2	1	no	—
393	C₄⋊C₄×C₄₁	—	2	2	no	—
394	C₄⋊C₄×C₄₁	—	2	1	no	—
395	C₄⋊C₄×C₄₁	—	2	2	no	—
396	C₄⋊C₄×C₄₁	—	2	1	no	—
397	C₄⋊C₄×C₄₁	—	2	2	no	—
398	C₄⋊C₄×C₄₁	—	2	2	no	—
399	C₄⋊C₄×C₄₁	—	2	2	no	—
400	C₄⋊C₄×C₄₁	—	2	2	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	2	no	—
405	C₄⋊C₄×C₄₁	—	2	2	no	—
406	C₄⋊C₄×C₄₁	—	2	1	no	—
407	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
417	C₂²⋊C₄×C₄₁	—	2	2	no	—
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	2	no	—
422	C₂²⋊C₄×C₄₁	—	2	2	no	—
423	C₂²⋊C₄×C₄₁	—	2	1	no	—
424	C₂²⋊C₄×C₄₁	—	2	2	no	—
425	C₂²⋊C₄×C₄₁	—	2	2	no	—
426	C₂²⋊C₄×C₄₁	—	2	1	no	—
427	C₂²⋊C₄×C₄₁	—	2	1	no	—
428	C₂²⋊C₄×C₄₁	—	2	1	no	—
429	C₂²⋊C₄×C₄₁	—	2	2	no	—
430	C₂²⋊C₄×C₄₁	—	2	2	no	—
431	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
434	C₄²×C₄₁	—	2	2	no	—
435	C₄²×C₄₁	—	2	2	no	—
436	C₄²×C₄₁	—	2	2	no	—
437	C₄²×C₄₁	—	2	1	no	—
438	C₄²×C₄₁	—	2	2	no	—
439	C₄²×C₄₁	—	2	1	no	—
440	C₄²×C₄₁	—	2	1	no	—
441	C₄²×C₄₁	—	2	2	no	—
442	C₄²×C₄₁	—	2	1	no	—
443	C₄²×C₄₁	—	2	2	no	—
444	C₄²×C₄₁	C₂×D₄	1	2	yes	—
445	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₄₁	C₂×D₄	1	2	yes	—
447	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
449	C₄²×C₄₁	C₂⁴	1	2	yes	—
450	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
451	C₂³×C₄₁	—	2	1	no	—
452	C₂³×C₄₁	—	2	1	no	—
453	C₂³×C₄₁	—	4	2	no	—
454	C₂³×C₄₁	—	4	2	no	—
455	C₂³×C₄₁	—	8	1	no	—
456	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
457	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₄₁	—	2	2	no	—
459	Q₈×C₄₁	—	2	1	no	—
460	Q₈×C₄₁	—	2	1	no	—
461	Q₈×C₄₁	—	2	2	no	—
462	Q₈×C₄₁	—	2	2	no	—
463	Q₈×C₄₁	—	2	2	no	—
464	Q₈×C₄₁	—	2	1	no	—
465	Q₈×C₄₁	—	2	2	no	—
466	Q₈×C₄₁	—	4	4	no	—
467	Q₈×C₄₁	—	4	2	no	—
468	Q₈×C₄₁	—	8	2	no	—
469	Q₈×C₄₁	—	8	1	no	—
470	Q₈×C₄₁	—	8	1	no	—
471	Q₈×C₄₁	C₂×#41	1	2	yes	—
472	D₄×C₄₁	—	2	4	no	—
473	D₄×C₄₁	—	2	2	no	—
474	D₄×C₄₁	—	2	1	no	—
475	D₄×C₄₁	—	2	1	no	—
476	D₄×C₄₁	—	2	1	no	—
477	D₄×C₄₁	—	4	2	no	—
478	D₄×C₄₁	—	4	4	no	—
479	D₄×C₄₁	—	8	2	no	—
480	D₄×C₄₁	C₂×#41	1	2	yes	—
481	C₂×C₄×C₄₁	—	2	1	no	—
482	C₂×C₄×C₄₁	—	2	4	no	—
483	C₂×C₄×C₄₁	—	2	1	no	—
484	C₂×C₄×C₄₁	—	2	2	no	—
485	C₂×C₄×C₄₁	—	2	1	no	—
486	C₂×C₄×C₄₁	—	2	2	no	—
487	C₂×C₄×C₄₁	—	2	1	no	—
488	C₂×C₄×C₄₁	—	2	1	no	—
489	C₂×C₄×C₄₁	—	2	2	no	—
490	C₂×C₄×C₄₁	—	2	2	no	—
491	C₂×C₄×C₄₁	—	2	1	no	—
492	C₂×C₄×C₄₁	—	2	2	no	—
493	C₂×C₄×C₄₁	—	2	2	no	—
494	C₂×C₄×C₄₁	—	2	1	no	—
495	C₂×C₄×C₄₁	—	2	1	no	—
496	C₂×C₄×C₄₁	—	4	2	no	—
497	C₂×C₄×C₄₁	—	4	1	no	—
498	C₂×C₄×C₄₁	—	4	2	no	—
499	C₂×C₄×C₄₁	—	4	4	no	—
500	C₂×C₄×C₄₁	—	4	4	no	—
501	C₂×C₄×C₄₁	—	4	2	no	—
502	C₂×C₄×C₄₁	—	4	2	no	—
503	C₂×C₄×C₄₁	—	4	2	no	—
504	C₂×C₄×C₄₁	—	4	2	no	—
505	C₂×C₄×C₄₁	—	4	2	no	—
506	C₂×C₄×C₄₁	—	8	2	no	—
507	C₂×C₄×C₄₁	—	8	1	no	—
508	C₂×C₄×C₄₁	—	8	2	no	—
509	C₂×C₄×C₄₁	#137	1	4	yes	complemented
510	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
519	C₈×C₄₁	—	2	1	no	—
520	C₈×C₄₁	—	2	2	no	—
521	C₈×C₄₁	—	2	1	no	—
522	C₈×C₄₁	—	2	1	no	—
523	C₈×C₄₁	—	2	2	no	—
524	C₈×C₄₁	C₂×#41	1	2	yes	—
525	#61438	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
526	C₂²×C₄₁	—	2	1	no	—
527	C₂²×C₄₁	—	2	1	no	—
528	C₂²×C₄₁	—	2	2	no	—
529	C₂²×C₄₁	—	2	2	no	—
530	C₂²×C₄₁	—	2	2	no	—
531	C₂²×C₄₁	—	2	2	no	—
532	C₂²×C₄₁	—	4	1	no	—
533	C₂²×C₄₁	—	4	1	no	—
534	C₂²×C₄₁	—	4	1	no	—
535	C₂²×C₄₁	—	4	1	no	—
536	C₂²×C₄₁	—	4	1	no	—
537	C₂²×C₄₁	—	8	4	no	—
538	C₂²×C₄₁	C₂×#137	1	2	yes	—
539	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
540	C₄×C₄₁	—	2	1	no	—
541	C₄×C₄₁	—	2	2	no	—
542	C₄×C₄₁	—	2	1	no	—
543	C₄×C₄₁	—	2	2	no	—
544	C₄×C₄₁	—	2	1	no	—
545	C₄×C₄₁	—	2	2	no	—
546	C₄×C₄₁	—	2	2	no	—
547	C₄×C₄₁	—	4	1	no	—
548	C₄×C₄₁	—	4	2	no	—
549	C₄×C₄₁	—	4	1	no	—
550	C₄×C₄₁	—	4	2	no	—
551	C₄×C₄₁	—	4	2	no	—
552	C₄×C₄₁	—	4	1	no	—
553	C₄×C₄₁	—	4	2	no	—
554	C₄×C₄₁	—	4	1	no	—
555	C₄×C₄₁	—	4	1	no	—
556	C₄×C₄₁	C₂×#137	1	2	yes	—
557	C₄×C₄₁	C₂×#137	1	2	yes	—
558	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
559	C₄×C₄₁	#585	1	1	yes	characteristic
560	Q₈×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
561	#3475	C₂×C₄₁	1	1	yes	characteristic
562	#3398	C₂×C₄₁	1	1	yes	characteristic, complemented
563	#3385	C₂×C₄₁	1	1	yes	characteristic, complemented
564	#3372	C₂×C₄₁	1	1	yes	characteristic, complemented
565	#3369	C₂×C₄₁	1	1	yes	characteristic, complemented
566	#3357	C₂×C₄₁	1	1	yes	characteristic, complemented
567	#3344	C₂×C₄₁	1	2	yes	complemented
568	#3331	C₂×C₄₁	1	1	yes	characteristic, complemented
569	#3329	C₂×C₄₁	1	1	yes	characteristic, complemented
570	#3314	C₂×C₄₁	1	2	yes	complemented
571	#3312	C₂×C₄₁	1	2	yes	complemented
572	#3276	C₂×C₄₁	1	1	yes	characteristic, complemented
573	#3266	C₂×C₄₁	1	2	yes	complemented
574	#3172	C₂×C₄₁	1	2	yes	complemented
575	#3170	C₂×C₄₁	1	1	yes	characteristic, complemented
576	#3108	C₂×C₄₁	1	2	yes	complemented
577	#3107	C₂×C₄₁	1	2	yes	complemented
578	#3104	C₂×C₄₁	1	1	yes	characteristic, complemented
579	#3101	C₂×C₄₁	1	1	yes	characteristic, complemented
580	#2965	C₂×C₄₁	1	1	yes	characteristic, complemented
581	C₄×#137	C₂×C₄₁	1	2	yes	complemented
582	C₂×C₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
583	C₂×C₄₁	—	2	2	no	—
584	C₂×C₄₁	—	4	2	no	—
585	C₂×C₄₁	—	4	2	no	—
586	C₂×C₄₁	—	8	1	no	—
587	C₂×C₄₁	D₄×#41	1	1	yes	characteristic
588	C₂×C₄₁	C₂²×#137	1	1	yes	characteristic
589	C₂×C₄₁	#3584	1	1	yes	characteristic
590	C₂×#137	C₂²×C₄₁	1	2	yes	—
591	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
592	Q₈²	C₂²×C₄₁	1	1	yes	characteristic, complemented
593	#557	—	2	1	no	—
594	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
595	#556	C₂²×C₄₁	1	1	yes	characteristic
596	#555	C₂²×C₄₁	1	1	yes	characteristic
597	#554	—	2	2	no	—
598	#554	—	2	1	no	—
599	#554	C₂²×C₄₁	1	1	yes	characteristic
600	#554	C₂²×C₄₁	1	2	yes	—
601	#554	C₂²×C₄₁	1	1	yes	characteristic, complemented
602	#553	—	2	1	no	—
603	#552	—	2	1	no	—
604	#552	C₂²×C₄₁	1	2	yes	—
605	#551	—	2	2	no	—
606	D₄×Q₈	C₂²×C₄₁	1	2	yes	—
607	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
608	#547	C₂²×C₄₁	1	1	yes	characteristic
609	#546	C₂²×C₄₁	1	2	yes	—
610	#533	—	2	1	no	—
611	#533	—	2	2	no	—
612	#533	C₂²×C₄₁	1	1	yes	characteristic
613	#533	C₂²×C₄₁	1	1	yes	characteristic
614	#533	C₂²×C₄₁	1	2	yes	complemented
615	#529	—	2	2	no	—
616	#529	C₂²×C₄₁	1	2	yes	—
617	#525	—	2	1	no	—
618	C₄×#41	—	2	1	no	—
619	C₄×#41	C₂²×C₄₁	1	2	yes	—
620	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
621	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
622	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
623	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
624	C₂×#117	—	2	1	no	—
625	#501	C₂²×C₄₁	1	2	yes	complemented
626	#500	C₂²×C₄₁	1	1	yes	characteristic, complemented
627	#497	C₂²×C₄₁	1	2	yes	—
628	#494	C₂²×C₄₁	1	1	yes	characteristic, complemented
629	#491	C₂²×C₄₁	1	2	yes	complemented
630	#489	C₂²×C₄₁	1	2	yes	—
631	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
632	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
633	#485	C₂²×C₄₁	1	2	yes	complemented
634	#485	C₂²×C₄₁	1	2	yes	complemented
635	#484	C₂²×C₄₁	1	2	yes	—
636	#483	C₂²×C₄₁	1	2	yes	—
637	#483	C₂²×C₄₁	1	2	yes	complemented
638	#480	C₂²×C₄₁	1	2	yes	—
639	#479	C₂²×C₄₁	1	2	yes	complemented
640	#479	C₂²×C₄₁	1	2	yes	complemented
641	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
642	#477	C₂²×C₄₁	1	1	yes	characteristic, complemented
643	#476	C₂²×C₄₁	1	1	yes	characteristic
644	#476	C₂²×C₄₁	1	1	yes	characteristic
645	#475	C₂²×C₄₁	1	2	yes	complemented
646	#474	C₂²×C₄₁	1	2	yes	—
647	#470	C₂²×C₄₁	1	2	yes	complemented
648	#470	C₂²×C₄₁	1	2	yes	complemented
649	#468	C₂²×C₄₁	1	2	yes	—
650	#468	C₂²×C₄₁	1	2	yes	—
651	#467	C₂²×C₄₁	1	2	yes	—
652	#467	C₂²×C₄₁	1	2	yes	—
653	#464	C₂²×C₄₁	1	2	yes	—
654	#464	C₂²×C₄₁	1	2	yes	—
655	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
656	#462	C₂²×C₄₁	1	1	yes	characteristic, complemented
657	#462	C₂²×C₄₁	1	2	yes	complemented
658	#461	C₂²×C₄₁	1	1	yes	characteristic
659	#461	C₂²×C₄₁	1	1	yes	characteristic
660	#461	C₂²×C₄₁	1	2	yes	—
661	#452	C₂²×C₄₁	1	2	yes	—
662	#452	C₂²×C₄₁	1	2	yes	—
663	#451	C₂²×C₄₁	1	2	yes	—
664	#451	C₂²×C₄₁	1	2	yes	complemented
665	#450	C₂²×C₄₁	1	2	yes	—
666	#448	C₂²×C₄₁	1	2	yes	—
667	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
668	#446	C₂²×C₄₁	1	1	yes	characteristic, complemented
669	#441	C₂²×C₄₁	1	2	yes	complemented
670	#441	C₂²×C₄₁	1	2	yes	complemented
671	#440	C₂²×C₄₁	1	2	yes	—
672	#440	C₂²×C₄₁	1	2	yes	—
673	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
674	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
675	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
676	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
677	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
680	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
681	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
686	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
687	#436	C₂²×C₄₁	1	1	yes	characteristic, complemented
688	#436	C₂²×C₄₁	1	1	yes	characteristic, complemented
689	#435	C₂²×C₄₁	1	2	yes	—
690	#435	C₂²×C₄₁	1	2	yes	—
691	#431	C₂²×C₄₁	1	1	yes	characteristic
692	#431	C₂²×C₄₁	1	2	yes	complemented
693	#428	C₂²×C₄₁	1	2	yes	complemented
694	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
695	#419	C₂²×C₄₁	1	2	yes	complemented
696	#417	C₂²×C₄₁	1	2	yes	—
697	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
698	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
699	C₄×M₁₆	C₂²×C₄₁	1	2	yes	complemented
700	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
701	C₄₁	#61438	1	1	yes	characteristic, direct product factor, Sylow
702	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
703	C₂×#41	C₂³×C₄₁	1	2	yes	—
704	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
705	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
706	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
707	C₂³×C₄	—	2	1	no	—
708	#137	—	2	8	no	—
709	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
712	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
713	C₂×SD₁₆	—	2	4	no	—
714	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₄₁	1	1	yes	characteristic
720	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
721	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
722	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
723	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
724	C₄⋊Q₈	—	2	2	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	—	2	1	no	—
727	C₄⋊Q₈	—	2	2	no	—
728	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
731	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
732	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	—	2	2	no	—
740	#125	—	2	2	no	—
741	#125	—	2	1	no	—
742	#125	—	2	1	no	—
743	#125	—	2	1	no	—
744	#125	—	2	2	no	—
745	#125	C₂³×C₄₁	1	2	yes	—
746	#124	—	2	2	no	—
747	#124	C₂³×C₄₁	1	2	yes	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
766	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
769	#121	—	2	1	no	—
770	#121	—	2	1	no	—
771	#121	—	2	2	no	—
772	#121	C₂³×C₄₁	1	2	yes	—
773	#120	—	2	2	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	—	2	2	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	2	no	—
783	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
789	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
790	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
791	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
792	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
793	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	D₄×C₄₁	1	2	yes	—
804	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₄₁	1	2	yes	—
810	C₄×D₄	C₂³×C₄₁	1	2	yes	—
811	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	—	2	2	no	—
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	—	2	2	no	—
818	#117	—	2	2	no	—
819	#117	—	2	2	no	—
820	#117	D₄×C₄₁	1	1	yes	characteristic
821	#117	D₄×C₄₁	1	2	yes	—
822	#117	C₂³×C₄₁	1	2	yes	—
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	—	2	2	no	—
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
830	C₂×C₂²⋊C₄	—	2	1	no	—
831	C₂×C₂²⋊C₄	—	2	2	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	—	2	2	no	—
834	C₂×C₄²	—	2	2	no	—
835	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
836	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
837	#107	C₂³×C₄₁	1	2	yes	—
838	#107	C₂³×C₄₁	1	2	yes	—
839	#107	C₂³×C₄₁	1	2	yes	—
840	#107	C₂³×C₄₁	1	2	yes	—
841	#106	C₂³×C₄₁	1	1	yes	characteristic
842	#106	C₂³×C₄₁	1	1	yes	characteristic
843	#106	C₂³×C₄₁	1	1	yes	characteristic
844	#106	C₂³×C₄₁	1	1	yes	characteristic
845	#106	C₂³×C₄₁	1	2	yes	—
846	#106	C₂³×C₄₁	1	2	yes	—
847	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
850	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
851	#103	C₂³×C₄₁	1	1	yes	characteristic
852	#103	C₂³×C₄₁	1	1	yes	characteristic
853	#103	C₂³×C₄₁	1	1	yes	characteristic
854	#103	C₂³×C₄₁	1	1	yes	characteristic
855	#103	C₂³×C₄₁	1	2	yes	—
856	#103	C₂³×C₄₁	1	2	yes	—
857	#103	C₂³×C₄₁	1	2	yes	—
858	#103	C₂³×C₄₁	1	2	yes	—
859	#103	C₂³×C₄₁	1	2	yes	—
860	#103	C₂³×C₄₁	1	2	yes	—
861	#103	C₂³×C₄₁	1	2	yes	—
862	#103	C₂³×C₄₁	1	2	yes	—
863	#103	C₂³×C₄₁	1	2	yes	—
864	#103	C₂³×C₄₁	1	2	yes	—
865	#102	C₂³×C₄₁	1	1	yes	characteristic
866	#102	C₂³×C₄₁	1	1	yes	characteristic
867	#102	C₂³×C₄₁	1	1	yes	characteristic
868	#102	C₂³×C₄₁	1	1	yes	characteristic
869	#102	C₂³×C₄₁	1	2	yes	—
870	#102	C₂³×C₄₁	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
874	#97	C₂³×C₄₁	1	2	yes	—
875	#97	C₂³×C₄₁	1	2	yes	—
876	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
880	C₄×C₈	C₂³×C₄₁	1	2	yes	—
881	C₂⁴	—	2	1	no	—
882	#41	—	2	4	no	—
883	#41	—	2	4	no	—
884	#41	—	4	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	2	no	—
891	C₂×Q₈	—	2	4	no	—
892	C₂×Q₈	—	4	1	no	—
893	C₂×Q₈	—	4	2	no	—
894	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
896	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
898	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	4	1	no	—
904	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
905	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
906	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
907	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	4	4	no	—
920	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
921	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
922	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
923	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
926	Q₁₆	—	2	4	no	—
927	Q₁₆	—	2	4	no	—
928	Q₁₆	—	4	2	no	—
929	Q₁₆	—	4	2	no	—
930	SD₁₆	—	2	2	no	—
931	SD₁₆	—	2	2	no	—
932	SD₁₆	—	2	4	no	—
933	SD₁₆	—	2	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	#41×C₄₁	1	4	yes	complemented
936	M₁₆	—	2	4	no	—
937	M₁₆	—	4	2	no	—
938	C₂×C₈	—	2	2	no	—
939	C₂×C₈	—	4	1	no	—
940	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
944	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
945	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	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	C₂×D₄×C₄₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
977	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	C₂×D₄×C₄₁	1	2	yes	—
1012	C₄²	C₂×D₄×C₄₁	1	2	yes	—
1013	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1014	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
1017	C₄²	C₂⁴×C₄₁	1	2	yes	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	4	2	no	—
1021	C₂³	—	4	2	no	—
1022	C₂³	—	8	1	no	—
1023	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
1024	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	2	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	4	4	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	2	no	—
1036	Q₈	—	8	1	no	—
1037	Q₈	—	8	1	no	—
1038	Q₈	C₂×#41×C₄₁	1	2	yes	—
1039	D₄	—	2	4	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	8	2	no	—
1047	D₄	C₂×#41×C₄₁	1	2	yes	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	4	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	4	1	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	4	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	#137×C₄₁	1	4	yes	complemented
1077	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
1085	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
1086	C₈	—	2	1	no	—
1087	C₈	—	2	2	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	2	no	—
1091	C₈	C₂×#41×C₄₁	1	2	yes	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	8	4	no	—
1104	C₂²	C₂×#137×C₄₁	1	2	yes	—
1105	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	C₂×#137×C₄₁	1	2	yes	—
1123	C₄	C₂×#137×C₄₁	1	2	yes	—
1124	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
1125	C₄	C₄₁×#585	1	1	yes	characteristic
1126	C₂	—	2	2	no	—
1127	C₂	—	4	2	no	—
1128	C₂	—	4	2	no	—
1129	C₂	—	8	1	no	—
1130	C₂	D₄×#41×C₄₁	1	1	yes	characteristic
1131	C₂	C₂²×#137×C₄₁	1	1	yes	characteristic
1132	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×#3475	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. Q₈×#41×C₄₁	C₂	semidirect
3. C₄₁×#3398	C₂	semidirect
4. C₄₁×#3385	C₂	semidirect
5. C₄₁×#3372	C₂	semidirect
6. C₄₁×#3369	C₂	semidirect
7. C₄₁×#3357	C₂	semidirect
8. C₄₁×#3344	C₂	semidirect
9. C₄₁×#3331	C₂	semidirect
10. C₄₁×#3329	C₂	semidirect
11. C₄₁×#3314	C₂	semidirect
12. C₄₁×#3312	C₂	semidirect
13. C₄₁×#3276	C₂	semidirect
14. C₄₁×#3266	C₂	semidirect
15. C₄₁×#3172	C₂	semidirect
16. C₄₁×#3170	C₂	semidirect
17. C₄₁×#3108	C₂	semidirect
18. C₄₁×#3107	C₂	semidirect
19. C₄₁×#3104	C₂	semidirect
20. C₄₁×#3101	C₂	semidirect
21. C₄₁×#2965	C₂	semidirect
22. C₄×#137×C₄₁	C₂	semidirect
23. C₂×C₄×SD₁₆×C₄₁	C₂	semidirect
26. Q₈²×C₄₁	C₂²	semidirect
28. C₄₁×#557	C₂²	semidirect
35. C₄₁×#554	C₂²	semidirect
41. D₄×Q₈×C₄₁	C₂²	semidirect
48. C₄₁×#533	C₂²	semidirect
56. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
59. C₄₁×#501	C₂²	semidirect
60. C₄₁×#500	C₂²	semidirect
62. C₄₁×#494	C₂²	semidirect
63. C₄₁×#491	C₂²	semidirect
65. C₄₁×#487	C₂²	semidirect
66. C₄₁×#487	C₂²	semidirect
67. C₄₁×#485	C₂²	semidirect
68. C₄₁×#485	C₂²	semidirect
71. C₄₁×#483	C₂²	semidirect
73. C₄₁×#479	C₂²	semidirect
74. C₄₁×#479	C₂²	semidirect
75. C₄₁×#477	C₂²	semidirect
76. C₄₁×#477	C₂²	semidirect
79. C₄₁×#475	C₂²	semidirect
81. C₄₁×#470	C₂²	semidirect
82. C₄₁×#470	C₂²	semidirect
89. C₄₁×#462	C₂²	semidirect
90. C₄₁×#462	C₂²	semidirect
91. C₄₁×#462	C₂²	semidirect
98. C₄₁×#451	C₂²	semidirect
101. C₄₁×#446	C₂²	semidirect
102. C₄₁×#446	C₂²	semidirect
103. C₄₁×#441	C₂²	semidirect
104. C₄₁×#441	C₂²	semidirect
107. C₄×Q₁₆×C₄₁	C₂²	semidirect
108. C₄×Q₁₆×C₄₁	C₂²	semidirect
109. C₄×Q₁₆×C₄₁	C₂²	semidirect
110. C₄×Q₁₆×C₄₁	C₂²	semidirect
121. C₄₁×#436	C₂²	semidirect
122. C₄₁×#436	C₂²	semidirect
126. C₄₁×#431	C₂²	semidirect
127. C₄₁×#428	C₂²	semidirect
129. C₄₁×#419	C₂²	semidirect
133. C₄×M₁₆×C₄₁	C₂²	semidirect
368. SD₁₆×C₄₁	#41	semidirect
509. C₂×C₄×C₄₁	#137	semidirect
525. #61438	C₄₁	direct (N × H)
560. Q₈×#41	C₂×C₄₁	semidirect
562. #3398	C₂×C₄₁	semidirect
563. #3385	C₂×C₄₁	semidirect
564. #3372	C₂×C₄₁	semidirect
565. #3369	C₂×C₄₁	semidirect
566. #3357	C₂×C₄₁	semidirect
567. #3344	C₂×C₄₁	semidirect
568. #3331	C₂×C₄₁	semidirect
569. #3329	C₂×C₄₁	semidirect
570. #3314	C₂×C₄₁	semidirect
571. #3312	C₂×C₄₁	semidirect
572. #3276	C₂×C₄₁	semidirect
573. #3266	C₂×C₄₁	semidirect
574. #3172	C₂×C₄₁	semidirect
575. #3170	C₂×C₄₁	semidirect
576. #3108	C₂×C₄₁	semidirect
577. #3107	C₂×C₄₁	semidirect
578. #3104	C₂×C₄₁	semidirect
579. #3101	C₂×C₄₁	semidirect
580. #2965	C₂×C₄₁	semidirect
581. C₄×#137	C₂×C₄₁	semidirect
582. C₂×C₄×SD₁₆	C₂×C₄₁	semidirect
592. Q₈²	C₂²×C₄₁	semidirect
594. #557	C₂²×C₄₁	semidirect
601. #554	C₂²×C₄₁	semidirect
607. D₄×Q₈	C₂²×C₄₁	semidirect
614. #533	C₂²×C₄₁	semidirect
622. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
625. #501	C₂²×C₄₁	semidirect
626. #500	C₂²×C₄₁	semidirect
628. #494	C₂²×C₄₁	semidirect
629. #491	C₂²×C₄₁	semidirect
631. #487	C₂²×C₄₁	semidirect
632. #487	C₂²×C₄₁	semidirect
633. #485	C₂²×C₄₁	semidirect
634. #485	C₂²×C₄₁	semidirect
637. #483	C₂²×C₄₁	semidirect
639. #479	C₂²×C₄₁	semidirect
640. #479	C₂²×C₄₁	semidirect
641. #477	C₂²×C₄₁	semidirect
642. #477	C₂²×C₄₁	semidirect
645. #475	C₂²×C₄₁	semidirect
647. #470	C₂²×C₄₁	semidirect
648. #470	C₂²×C₄₁	semidirect
655. #462	C₂²×C₄₁	semidirect
656. #462	C₂²×C₄₁	semidirect
657. #462	C₂²×C₄₁	semidirect
664. #451	C₂²×C₄₁	semidirect
667. #446	C₂²×C₄₁	semidirect
668. #446	C₂²×C₄₁	semidirect
669. #441	C₂²×C₄₁	semidirect
670. #441	C₂²×C₄₁	semidirect
673. C₄×Q₁₆	C₂²×C₄₁	semidirect
674. C₄×Q₁₆	C₂²×C₄₁	semidirect
675. C₄×Q₁₆	C₂²×C₄₁	semidirect
676. C₄×Q₁₆	C₂²×C₄₁	semidirect
687. #436	C₂²×C₄₁	semidirect
688. #436	C₂²×C₄₁	semidirect
692. #431	C₂²×C₄₁	semidirect
693. #428	C₂²×C₄₁	semidirect
695. #419	C₂²×C₄₁	semidirect
699. C₄×M₁₆	C₂²×C₄₁	semidirect
701. C₄₁	#61438	direct (N × H)
935. SD₁₆	#41×C₄₁	semidirect
1076. C₂×C₄	#137×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#41×C₄₁	2
C₄₁×#3475	2
C₄₁×#3398	2
C₄₁×#3385	2
C₄₁×#3372	2
C₄₁×#3369	2
C₄₁×#3357	2
C₄₁×#3344	2
C₄₁×#3331	2
C₄₁×#3329	2
C₄₁×#3314	2
C₄₁×#3312	2
C₄₁×#3276	2
C₄₁×#3266	2
C₄₁×#3172	2
C₄₁×#3170	2
C₄₁×#3108	2
C₄₁×#3107	2
C₄₁×#3104	2
C₄₁×#3101	2
C₄₁×#2965	2
C₄×#137×C₄₁	2
C₂×C₄×SD₁₆×C₄₁	2
#61438	41

Subgroups — C41×#61438 #23837639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61438 #23837639