Subgroups — C₂×C₄₁×#3111 #23836744

Order 10496.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3111	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#449	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#529	—	2	4	no	—
23	C₄₁×#529	C₂²	1	8	yes	complemented
24	C₂×#126×C₄₁	—	2	1	no	—
25	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#123×C₄₁	—	2	1	no	—
28	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
30	C₄×#41×C₄₁	—	2	4	no	—
31	C₄×#41×C₄₁	C₂²	1	8	yes	complemented
32	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₁	—	2	1	no	—
36	C₂×C₄×D₄×C₄₁	—	2	1	no	—
37	C₂×C₄×D₄×C₄₁	—	2	1	no	—
38	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#117×C₄₁	—	2	1	no	—
42	C₂×#117×C₄₁	—	2	1	no	—
43	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₄₁	—	2	1	no	—
45	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
46	C₄₁×#485	C₂²	1	8	yes	complemented
47	C₄₁×#482	C₂²	1	8	yes	complemented
48	C₄₁×#479	C₂²	1	8	yes	complemented
49	C₄₁×#478	C₂²	1	8	yes	complemented
50	C₄₁×#464	C₂²	1	8	yes	complemented
51	C₄₁×#463	C₂²	1	8	yes	complemented
52	C₄₁×#452	C₂²	1	8	yes	complemented
53	C₄₁×#449	C₂²	1	8	yes	—
54	C₄₁×#442	C₂²	1	8	yes	complemented
55	C₄₁×#441	C₂²	1	8	yes	complemented
56	C₄₁×#440	C₂²	1	8	yes	complemented
57	C₄₁×#440	C₂²	1	8	yes	complemented
58	C₄₁×#432	C₂²	1	8	yes	complemented
59	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
60	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
61	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
62	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
65	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
66	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
67	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
68	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
69	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
70	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
71	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
72	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
73	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
75	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
76	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
77	C₂×#41×C₄₁	—	2	4	no	—
78	C₂×#41×C₄₁	—	2	4	no	—
79	C₂×#41×C₄₁	—	2	2	no	—
80	C₂×#41×C₄₁	C₂³	1	4	yes	—
81	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₄₁	—	2	1	no	—
84	C₂²×D₄×C₄₁	—	2	1	no	—
85	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₁	—	2	1	no	—
88	C₂³×C₄×C₄₁	—	2	1	no	—
89	C₂³×C₄×C₄₁	—	2	1	no	—
90	C₂³×C₄×C₄₁	—	2	1	no	—
91	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
94	C₂×Q₁₆×C₄₁	—	2	4	no	—
95	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
96	C₂×SD₁₆×C₄₁	—	2	4	no	—
97	C₂×SD₁₆×C₄₁	—	2	4	no	—
98	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
100	C₂×D₈×C₄₁	—	2	4	no	—
101	C₂×D₈×C₄₁	C₂³	1	4	yes	—
102	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
106	#126×C₄₁	—	2	8	no	—
107	#125×C₄₁	—	2	2	no	—
108	#125×C₄₁	C₂³	1	4	yes	—
109	#124×C₄₁	—	2	2	no	—
110	#124×C₄₁	C₂³	1	4	yes	—
111	#123×C₄₁	—	2	8	no	—
112	C₂²⋊Q₈×C₄₁	—	2	2	no	—
113	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
114	#121×C₄₁	—	2	2	no	—
115	#121×C₄₁	C₂³	1	4	yes	—
116	C₄×Q₈×C₄₁	—	2	2	no	—
117	C₄×Q₈×C₄₁	—	2	2	no	—
118	C₄×Q₈×C₄₁	—	2	2	no	—
119	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
120	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
121	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
122	C₄×D₄×C₄₁	—	2	8	no	—
123	C₄×D₄×C₄₁	—	2	8	no	—
124	C₄×D₄×C₄₁	—	2	8	no	—
125	C₄×D₄×C₄₁	—	2	2	no	—
126	C₄×D₄×C₄₁	—	2	2	no	—
127	C₄×D₄×C₄₁	—	2	2	no	—
128	C₄×D₄×C₄₁	C₂³	1	4	yes	—
129	C₄×D₄×C₄₁	C₂³	1	4	yes	—
130	C₄×D₄×C₄₁	C₂³	1	4	yes	—
131	#117×C₄₁	—	2	2	no	—
132	#117×C₄₁	—	2	8	no	—
133	#117×C₄₁	—	2	8	no	—
134	#117×C₄₁	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
136	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
137	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
138	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
139	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
140	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
141	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
153	C₂×C₄²×C₄₁	—	2	1	no	—
154	C₂×C₄²×C₄₁	—	2	1	no	—
155	C₂×C₄²×C₄₁	—	2	1	no	—
156	C₂×C₄²×C₄₁	—	2	1	no	—
157	C₂×C₄²×C₄₁	—	2	8	no	—
158	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₄₁	D₄	1	4	yes	—
161	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
164	#107×C₄₁	C₂³	1	4	yes	—
165	#107×C₄₁	C₂³	1	4	yes	—
166	#106×C₄₁	C₂³	1	4	yes	—
167	#106×C₄₁	C₂³	1	4	yes	—
168	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
169	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
170	#103×C₄₁	C₂³	1	4	yes	—
171	#103×C₄₁	C₂³	1	4	yes	—
172	#103×C₄₁	C₂³	1	4	yes	—
173	#103×C₄₁	C₂³	1	4	yes	—
174	#102×C₄₁	C₂³	1	4	yes	—
175	#102×C₄₁	C₂³	1	4	yes	—
176	#102×C₄₁	C₂³	1	4	yes	—
177	#102×C₄₁	C₂³	1	4	yes	—
178	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
179	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
180	#97×C₄₁	C₂³	1	4	yes	—
181	#97×C₄₁	C₂³	1	4	yes	—
182	C₂⁴×C₄₁	—	2	1	no	—
183	C₂⁴×C₄₁	—	2	1	no	—
184	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
185	#41×C₄₁	—	2	16	no	—
186	#41×C₄₁	—	2	8	no	—
187	#41×C₄₁	—	2	8	no	—
188	C₂×Q₈×C₄₁	—	2	1	no	—
189	C₂×Q₈×C₄₁	—	2	1	no	—
190	C₂×Q₈×C₄₁	—	2	2	no	—
191	C₂×Q₈×C₄₁	—	2	2	no	—
192	C₂×Q₈×C₄₁	—	2	2	no	—
193	C₂×Q₈×C₄₁	#41	1	4	yes	—
194	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
195	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
196	C₂×D₄×C₄₁	—	2	8	no	—
197	C₂×D₄×C₄₁	—	2	4	no	—
198	C₂×D₄×C₄₁	—	2	4	no	—
199	C₂×D₄×C₄₁	—	2	1	no	—
200	C₂×D₄×C₄₁	—	2	1	no	—
201	C₂×D₄×C₄₁	—	2	2	no	—
202	C₂×D₄×C₄₁	—	2	2	no	—
203	C₂×D₄×C₄₁	—	2	2	no	—
204	C₂×D₄×C₄₁	—	4	4	no	—
205	C₂×D₄×C₄₁	#41	1	4	yes	—
206	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
207	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₄₁	—	2	8	no	—
209	C₂²×C₄×C₄₁	—	2	1	no	—
210	C₂²×C₄×C₄₁	—	2	4	no	—
211	C₂²×C₄×C₄₁	—	2	2	no	—
212	C₂²×C₄×C₄₁	—	2	2	no	—
213	C₂²×C₄×C₄₁	—	2	1	no	—
214	C₂²×C₄×C₄₁	—	2	1	no	—
215	C₂²×C₄×C₄₁	—	2	1	no	—
216	C₂²×C₄×C₄₁	—	2	1	no	—
217	C₂²×C₄×C₄₁	—	2	1	no	—
218	C₂²×C₄×C₄₁	—	2	4	no	—
219	C₂²×C₄×C₄₁	—	2	4	no	—
220	C₂²×C₄×C₄₁	—	2	4	no	—
221	C₂²×C₄×C₄₁	—	4	2	no	—
222	C₂²×C₄×C₄₁	—	4	2	no	—
223	C₂²×C₄×C₄₁	—	4	4	no	—
224	C₂²×C₄×C₄₁	—	4	4	no	—
225	C₂²×C₄×C₄₁	—	4	4	no	—
226	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₄₁	—	2	8	no	—
237	SD₁₆×C₄₁	—	2	8	no	—
238	SD₁₆×C₄₁	—	2	8	no	—
239	D₈×C₄₁	—	2	8	no	—
240	C₂×C₈×C₄₁	—	2	2	no	—
241	C₂×C₈×C₄₁	—	2	2	no	—
242	C₂×C₈×C₄₁	—	2	2	no	—
243	C₂×C₈×C₄₁	—	2	2	no	—
244	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
245	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
246	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
247	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
248	C₄⋊C₄×C₄₁	—	2	4	no	—
249	C₄⋊C₄×C₄₁	—	2	4	no	—
250	C₄⋊C₄×C₄₁	—	2	4	no	—
251	C₄⋊C₄×C₄₁	—	2	4	no	—
252	C₄⋊C₄×C₄₁	—	2	4	no	—
253	C₄⋊C₄×C₄₁	—	2	4	no	—
254	C₄⋊C₄×C₄₁	—	2	1	no	—
255	C₄⋊C₄×C₄₁	—	2	1	no	—
256	C₄⋊C₄×C₄₁	—	2	1	no	—
257	C₄⋊C₄×C₄₁	—	2	1	no	—
258	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₄₁	—	2	4	no	—
263	C₂²⋊C₄×C₄₁	—	2	4	no	—
264	C₂²⋊C₄×C₄₁	—	2	4	no	—
265	C₂²⋊C₄×C₄₁	—	2	4	no	—
266	C₂²⋊C₄×C₄₁	—	2	4	no	—
267	C₂²⋊C₄×C₄₁	—	2	4	no	—
268	C₂²⋊C₄×C₄₁	—	2	4	no	—
269	C₂²⋊C₄×C₄₁	—	2	4	no	—
270	C₄²×C₄₁	—	2	4	no	—
271	C₄²×C₄₁	—	2	4	no	—
272	C₄²×C₄₁	—	2	4	no	—
273	C₄²×C₄₁	—	2	4	no	—
274	C₄²×C₄₁	C₂×D₄	1	4	yes	—
275	C₄²×C₄₁	C₂×D₄	1	4	yes	—
276	C₄²×C₄₁	C₂×D₄	1	2	yes	—
277	C₄²×C₄₁	C₂×D₄	1	2	yes	—
278	C₄²×C₄₁	C₂⁴	1	2	yes	—
279	C₄²×C₄₁	C₂⁴	1	2	yes	—
280	C₂³×C₄₁	—	2	2	no	—
281	C₂³×C₄₁	—	2	4	no	—
282	C₂³×C₄₁	—	2	2	no	—
283	C₂³×C₄₁	—	2	2	no	—
284	C₂³×C₄₁	—	2	2	no	—
285	C₂³×C₄₁	—	2	2	no	—
286	C₂³×C₄₁	—	4	2	no	—
287	C₂³×C₄₁	—	4	2	no	—
288	C₂³×C₄₁	—	4	2	no	—
289	C₂³×C₄₁	—	4	2	no	—
290	C₂³×C₄₁	—	4	2	no	—
291	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
292	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₄₁	—	2	4	no	—
294	Q₈×C₄₁	—	2	2	no	—
295	Q₈×C₄₁	—	2	2	no	—
296	Q₈×C₄₁	—	2	2	no	—
297	Q₈×C₄₁	—	4	2	no	—
298	Q₈×C₄₁	C₂×#41	1	4	yes	—
299	D₄×C₄₁	—	2	16	no	—
300	D₄×C₄₁	—	2	4	no	—
301	D₄×C₄₁	—	2	2	no	—
302	D₄×C₄₁	—	2	2	no	—
303	D₄×C₄₁	—	2	2	no	—
304	D₄×C₄₁	—	4	8	no	—
305	D₄×C₄₁	—	4	2	no	—
306	D₄×C₄₁	C₂×#41	1	4	yes	—
307	C₂×C₄×C₄₁	—	2	16	no	—
308	C₂×C₄×C₄₁	—	2	2	no	—
309	C₂×C₄×C₄₁	—	2	4	no	—
310	C₂×C₄×C₄₁	—	2	2	no	—
311	C₂×C₄×C₄₁	—	2	2	no	—
312	C₂×C₄×C₄₁	—	2	2	no	—
313	C₂×C₄×C₄₁	—	2	2	no	—
314	C₂×C₄×C₄₁	—	2	2	no	—
315	C₂×C₄×C₄₁	—	2	4	no	—
316	C₂×C₄×C₄₁	—	2	2	no	—
317	C₂×C₄×C₄₁	—	2	2	no	—
318	C₂×C₄×C₄₁	—	2	2	no	—
319	C₂×C₄×C₄₁	—	2	2	no	—
320	C₂×C₄×C₄₁	—	2	2	no	—
321	C₂×C₄×C₄₁	—	2	2	no	—
322	C₂×C₄×C₄₁	—	2	2	no	—
323	C₂×C₄×C₄₁	—	4	4	no	—
324	C₂×C₄×C₄₁	—	4	4	no	—
325	C₂×C₄×C₄₁	—	4	8	no	—
326	C₂×C₄×C₄₁	—	4	8	no	—
327	C₂×C₄×C₄₁	—	4	8	no	—
328	C₂×C₄×C₄₁	—	4	2	no	—
329	C₂×C₄×C₄₁	—	4	2	no	—
330	C₂×C₄×C₄₁	—	4	2	no	—
331	C₂×C₄×C₄₁	—	4	2	no	—
332	C₂×C₄×C₄₁	—	4	2	no	—
333	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
340	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
341	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
342	C₈×C₄₁	—	2	2	no	—
343	C₈×C₄₁	—	2	2	no	—
344	C₈×C₄₁	—	2	2	no	—
345	C₈×C₄₁	—	2	2	no	—
346	C₂×#3111	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
347	C₂²×C₄₁	—	2	2	no	—
348	C₂²×C₄₁	—	2	4	no	—
349	C₂²×C₄₁	—	2	2	no	—
350	C₂²×C₄₁	—	2	2	no	—
351	C₂²×C₄₁	—	4	4	no	—
352	C₂²×C₄₁	—	4	8	no	—
353	C₂²×C₄₁	—	4	2	no	—
354	C₂²×C₄₁	—	4	2	no	—
355	C₂²×C₄₁	—	4	2	no	—
356	C₂²×C₄₁	—	4	2	no	—
357	C₂²×C₄₁	—	4	2	no	—
358	C₂²×C₄₁	—	8	4	no	—
359	C₂²×C₄₁	#525	1	2	yes	—
360	C₂²×C₄₁	#575	1	2	yes	—
361	C₂²×C₄₁	#575	1	2	yes	—
362	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
363	C₄×C₄₁	—	2	2	no	—
364	C₄×C₄₁	—	2	4	no	—
365	C₄×C₄₁	—	2	2	no	—
366	C₄×C₄₁	—	2	2	no	—
367	C₄×C₄₁	—	2	2	no	—
368	C₄×C₄₁	—	2	2	no	—
369	C₄×C₄₁	—	4	2	no	—
370	C₄×C₄₁	—	4	2	no	—
371	C₄×C₄₁	—	4	2	no	—
372	C₄×C₄₁	—	4	2	no	—
373	C₄×C₄₁	—	4	2	no	—
374	C₄×C₄₁	#525	1	2	yes	—
375	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
376	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
377	C₂×#529	C₂×C₄₁	1	1	yes	characteristic, complemented
378	C₂×C₄×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
379	#3111	C₂×C₄₁	1	16	yes	direct product factor
380	C₂×#485	C₂×C₄₁	1	1	yes	characteristic, complemented
381	C₂×#482	C₂×C₄₁	1	1	yes	characteristic, complemented
382	C₂×#479	C₂×C₄₁	1	1	yes	characteristic, complemented
383	C₂×#478	C₂×C₄₁	1	1	yes	characteristic, complemented
384	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
385	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
386	C₂×#452	C₂×C₄₁	1	1	yes	characteristic, complemented
387	C₂×#449	C₂×C₄₁	1	1	yes	characteristic
388	C₂×#442	C₂×C₄₁	1	1	yes	characteristic, complemented
389	C₂×#441	C₂×C₄₁	1	1	yes	characteristic, complemented
390	C₂×#440	C₂×C₄₁	1	1	yes	characteristic, complemented
391	C₂×#440	C₂×C₄₁	1	1	yes	characteristic, complemented
392	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
393	C₂×C₄₁	—	4	2	no	—
394	C₂×C₄₁	—	4	4	no	—
395	C₂×C₄₁	—	8	2	no	—
396	C₂×C₄₁	#3111	1	4	yes	direct product factor
397	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
398	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
399	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
400	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
401	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
402	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
403	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
404	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
405	#529	—	2	4	no	—
406	#529	C₂²×C₄₁	1	8	yes	complemented
407	C₂×#126	—	2	1	no	—
408	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
409	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
410	C₂×#123	—	2	1	no	—
411	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
412	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
413	C₄×#41	—	2	4	no	—
414	C₄×#41	C₂²×C₄₁	1	8	yes	complemented
415	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
418	C₂×C₄×D₄	—	2	1	no	—
419	C₂×C₄×D₄	—	2	1	no	—
420	C₂×C₄×D₄	—	2	1	no	—
421	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
424	C₂×#117	—	2	1	no	—
425	C₂×#117	—	2	1	no	—
426	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
427	C₂²×C₄²	—	2	1	no	—
428	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
429	#485	C₂²×C₄₁	1	8	yes	complemented
430	#482	C₂²×C₄₁	1	8	yes	complemented
431	#479	C₂²×C₄₁	1	8	yes	complemented
432	#478	C₂²×C₄₁	1	8	yes	complemented
433	#464	C₂²×C₄₁	1	8	yes	complemented
434	#463	C₂²×C₄₁	1	8	yes	complemented
435	#452	C₂²×C₄₁	1	8	yes	complemented
436	#449	C₂²×C₄₁	1	8	yes	—
437	#442	C₂²×C₄₁	1	8	yes	complemented
438	#441	C₂²×C₄₁	1	8	yes	complemented
439	#440	C₂²×C₄₁	1	8	yes	complemented
440	#440	C₂²×C₄₁	1	8	yes	complemented
441	#432	C₂²×C₄₁	1	8	yes	complemented
442	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
443	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
444	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
445	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
446	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
447	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
448	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
449	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
450	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
451	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
452	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
453	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
454	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
455	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
456	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
457	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
458	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
459	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
460	C₄₁	C₂×#3111	1	1	yes	characteristic, direct product factor, Sylow
461	C₂×#41	—	2	4	no	—
462	C₂×#41	—	2	4	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	C₂³×C₄₁	1	4	yes	—
465	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	—	2	1	no	—
475	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
476	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
478	C₂×Q₁₆	—	2	4	no	—
479	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
480	C₂×SD₁₆	—	2	4	no	—
481	C₂×SD₁₆	—	2	4	no	—
482	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
484	C₂×D₈	—	2	4	no	—
485	C₂×D₈	C₂³×C₄₁	1	4	yes	—
486	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
490	#126	—	2	8	no	—
491	#125	—	2	2	no	—
492	#125	C₂³×C₄₁	1	4	yes	—
493	#124	—	2	2	no	—
494	#124	C₂³×C₄₁	1	4	yes	—
495	#123	—	2	8	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
498	#121	—	2	2	no	—
499	#121	C₂³×C₄₁	1	4	yes	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
504	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
505	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	8	no	—
508	C₄×D₄	—	2	8	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	C₂³×C₄₁	1	4	yes	—
513	C₄×D₄	C₂³×C₄₁	1	4	yes	—
514	C₄×D₄	C₂³×C₄₁	1	4	yes	—
515	#117	—	2	2	no	—
516	#117	—	2	8	no	—
517	#117	—	2	8	no	—
518	#117	C₂³×C₄₁	1	4	yes	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₄²	—	2	1	no	—
538	C₂×C₄²	—	2	1	no	—
539	C₂×C₄²	—	2	1	no	—
540	C₂×C₄²	—	2	1	no	—
541	C₂×C₄²	—	2	8	no	—
542	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
543	C₂×C₄²	D₄×C₄₁	1	4	yes	—
544	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
548	#107	C₂³×C₄₁	1	4	yes	—
549	#107	C₂³×C₄₁	1	4	yes	—
550	#106	C₂³×C₄₁	1	4	yes	—
551	#106	C₂³×C₄₁	1	4	yes	—
552	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
553	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
554	#103	C₂³×C₄₁	1	4	yes	—
555	#103	C₂³×C₄₁	1	4	yes	—
556	#103	C₂³×C₄₁	1	4	yes	—
557	#103	C₂³×C₄₁	1	4	yes	—
558	#102	C₂³×C₄₁	1	4	yes	—
559	#102	C₂³×C₄₁	1	4	yes	—
560	#102	C₂³×C₄₁	1	4	yes	—
561	#102	C₂³×C₄₁	1	4	yes	—
562	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
563	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
564	#97	C₂³×C₄₁	1	4	yes	—
565	#97	C₂³×C₄₁	1	4	yes	—
566	C₂⁴	—	2	1	no	—
567	C₂⁴	—	2	1	no	—
568	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
569	#41	—	2	16	no	—
570	#41	—	2	8	no	—
571	#41	—	2	8	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	#41×C₄₁	1	4	yes	—
578	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
579	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
580	C₂×D₄	—	2	8	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	#41×C₄₁	1	4	yes	—
590	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
591	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
592	C₂²×C₄	—	2	8	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
615	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
617	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
618	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
620	Q₁₆	—	2	8	no	—
621	SD₁₆	—	2	8	no	—
622	SD₁₆	—	2	8	no	—
623	D₈	—	2	8	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	2	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
629	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
630	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
631	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	C₂×D₄×C₄₁	1	4	yes	—
659	C₄²	C₂×D₄×C₄₁	1	4	yes	—
660	C₄²	C₂×D₄×C₄₁	1	2	yes	—
661	C₄²	C₂×D₄×C₄₁	1	2	yes	—
662	C₄²	C₂⁴×C₄₁	1	2	yes	—
663	C₄²	C₂⁴×C₄₁	1	2	yes	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
676	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
677	Q₈	—	2	4	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	4	2	no	—
682	Q₈	C₂×#41×C₄₁	1	4	yes	—
683	D₄	—	2	16	no	—
684	D₄	—	2	4	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	4	8	no	—
689	D₄	—	4	2	no	—
690	D₄	C₂×#41×C₄₁	1	4	yes	—
691	C₂×C₄	—	2	16	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	8	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
721	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
723	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
724	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
725	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
726	C₈	—	2	2	no	—
727	C₈	—	2	2	no	—
728	C₈	—	2	2	no	—
729	C₈	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	8	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	8	4	no	—
742	C₂²	C₄₁×#525	1	2	yes	—
743	C₂²	C₄₁×#575	1	2	yes	—
744	C₂²	C₄₁×#575	1	2	yes	—
745	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	C₄₁×#525	1	2	yes	—
758	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
759	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
760	C₂	—	4	2	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	C₄₁×#3111	1	4	yes	direct product factor
764	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
765	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
766	C₂	C₂×C₄₁×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₂×C₄₁×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#529	C₂	semidirect
2. C₂×C₄×#41×C₄₁	C₂	semidirect
3. C₄₁×#3111	C₂	direct (N × H)
4. C₂×C₄₁×#485	C₂	semidirect
5. C₂×C₄₁×#482	C₂	semidirect
6. C₂×C₄₁×#479	C₂	semidirect
7. C₂×C₄₁×#478	C₂	semidirect
8. C₂×C₄₁×#464	C₂	semidirect
9. C₂×C₄₁×#463	C₂	semidirect
10. C₂×C₄₁×#452	C₂	semidirect
12. C₂×C₄₁×#442	C₂	semidirect
13. C₂×C₄₁×#441	C₂	semidirect
14. C₂×C₄₁×#440	C₂	semidirect
15. C₂×C₄₁×#440	C₂	semidirect
16. C₂×C₄₁×#432	C₂	semidirect
23. C₄₁×#529	C₂²	semidirect
31. C₄×#41×C₄₁	C₂²	semidirect
46. C₄₁×#485	C₂²	semidirect
47. C₄₁×#482	C₂²	semidirect
48. C₄₁×#479	C₂²	semidirect
49. C₄₁×#478	C₂²	semidirect
50. C₄₁×#464	C₂²	semidirect
51. C₄₁×#463	C₂²	semidirect
52. C₄₁×#452	C₂²	semidirect
54. C₄₁×#442	C₂²	semidirect
55. C₄₁×#441	C₂²	semidirect
56. C₄₁×#440	C₂²	semidirect
57. C₄₁×#440	C₂²	semidirect
58. C₄₁×#432	C₂²	semidirect
346. C₂×#3111	C₄₁	direct (N × H)
377. C₂×#529	C₂×C₄₁	semidirect
378. C₂×C₄×#41	C₂×C₄₁	semidirect
379. #3111	C₂×C₄₁	direct (N × H)
380. C₂×#485	C₂×C₄₁	semidirect
381. C₂×#482	C₂×C₄₁	semidirect
382. C₂×#479	C₂×C₄₁	semidirect
383. C₂×#478	C₂×C₄₁	semidirect
384. C₂×#464	C₂×C₄₁	semidirect
385. C₂×#463	C₂×C₄₁	semidirect
386. C₂×#452	C₂×C₄₁	semidirect
388. C₂×#442	C₂×C₄₁	semidirect
389. C₂×#441	C₂×C₄₁	semidirect
390. C₂×#440	C₂×C₄₁	semidirect
391. C₂×#440	C₂×C₄₁	semidirect
392. C₂×#432	C₂×C₄₁	semidirect
396. C₂×C₄₁	#3111	direct (N × H)
406. #529	C₂²×C₄₁	semidirect
414. C₄×#41	C₂²×C₄₁	semidirect
429. #485	C₂²×C₄₁	semidirect
430. #482	C₂²×C₄₁	semidirect
431. #479	C₂²×C₄₁	semidirect
432. #478	C₂²×C₄₁	semidirect
433. #464	C₂²×C₄₁	semidirect
434. #463	C₂²×C₄₁	semidirect
435. #452	C₂²×C₄₁	semidirect
437. #442	C₂²×C₄₁	semidirect
438. #441	C₂²×C₄₁	semidirect
439. #440	C₂²×C₄₁	semidirect
440. #440	C₂²×C₄₁	semidirect
441. #432	C₂²×C₄₁	semidirect
460. C₄₁	C₂×#3111	direct (N × H)
763. C₂	C₄₁×#3111	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#529	2
C₂×C₄×#41×C₄₁	2
C₄₁×#3111	2
C₂×C₄₁×#485	2
C₂×C₄₁×#482	2
C₂×C₄₁×#479	2
C₂×C₄₁×#478	2
C₂×C₄₁×#464	2
C₂×C₄₁×#463	2
C₂×C₄₁×#452	2
C₂×C₄₁×#449	2
C₂×C₄₁×#442	2
C₂×C₄₁×#441	2
C₂×C₄₁×#440	2
C₂×C₄₁×#432	2
C₂×#3111	41

Subgroups — C2×C41×#3111 #23836744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3111 #23836744