Subgroups — C₂×C₄₁×#3401 #23837599

Order 10496.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3401	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#496	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₁₆×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×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#559	—	2	4	no	—
27	C₄₁×#559	C₂²	1	8	yes	complemented
28	C₄₁×#556	—	2	4	no	—
29	C₄₁×#556	C₂²	1	8	yes	complemented
30	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#126×C₄₁	—	2	1	no	—
33	C₂×#126×C₄₁	—	2	1	no	—
34	C₂×#124×C₄₁	—	2	1	no	—
35	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#123×C₄₁	—	2	1	no	—
40	C₂×#123×C₄₁	—	2	1	no	—
41	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
42	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₄₁	—	2	1	no	—
47	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
50	C₂×#117×C₄₁	—	2	1	no	—
51	C₄₁×#497	C₂²	1	8	yes	complemented
52	C₄₁×#496	C₂²	1	8	yes	—
53	C₄₁×#495	C₂²	1	8	yes	complemented
54	C₄₁×#464	C₂²	1	8	yes	complemented
55	C₄₁×#464	C₂²	1	8	yes	complemented
56	C₄₁×#463	C₂²	1	8	yes	complemented
57	C₄₁×#463	C₂²	1	8	yes	complemented
58	C₄₁×#461	C₂²	1	8	yes	complemented
59	C₄₁×#460	C₂²	1	8	yes	complemented
60	C₄₁×#446	C₂²	1	8	yes	complemented
61	C₄₁×#442	C₂²	1	8	yes	complemented
62	C₄₁×#441	C₂²	1	8	yes	complemented
63	C₄×SD₁₆×C₄₁	C₂²	1	8	yes	complemented
64	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
66	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
67	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
68	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
69	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
70	C₂×#103×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×#102×C₄₁	C₂²	1	1	yes	characteristic
74	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
75	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
78	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₄₁	—	2	1	no	—
82	C₂²×D₄×C₄₁	—	2	1	no	—
83	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₁	—	2	1	no	—
87	C₂³×C₄×C₄₁	—	2	1	no	—
88	C₂³×C₄×C₄₁	—	2	1	no	—
89	C₂×Q₁₆×C₄₁	—	2	4	no	—
90	C₂×Q₁₆×C₄₁	—	4	2	no	—
91	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
92	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₄₁	—	2	4	no	—
94	C₂×SD₁₆×C₄₁	—	4	2	no	—
95	C₂×SD₁₆×C₄₁	—	4	2	no	—
96	C₂×SD₁₆×C₄₁	—	4	2	no	—
97	C₂×SD₁₆×C₄₁	—	4	2	no	—
98	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
103	C₂×D₈×C₄₁	—	2	4	no	—
104	C₂×D₈×C₄₁	—	4	2	no	—
105	C₂×D₈×C₄₁	C₂³	1	4	yes	—
106	C₂×D₈×C₄₁	C₂³	1	4	yes	—
107	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₄₁	—	2	2	no	—
112	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
113	#127×C₄₁	—	2	2	no	—
114	#127×C₄₁	C₂³	1	4	yes	—
115	#126×C₄₁	—	2	8	no	—
116	#126×C₄₁	—	2	8	no	—
117	#124×C₄₁	—	2	8	no	—
118	#124×C₄₁	—	2	2	no	—
119	#124×C₄₁	—	2	2	no	—
120	#124×C₄₁	—	2	2	no	—
121	#124×C₄₁	—	2	2	no	—
122	#124×C₄₁	C₂³	1	4	yes	—
123	#124×C₄₁	C₂³	1	4	yes	—
124	#124×C₄₁	C₂³	1	4	yes	—
125	#124×C₄₁	C₂³	1	4	yes	—
126	#123×C₄₁	—	2	8	no	—
127	#123×C₄₁	—	2	8	no	—
128	C₂²⋊Q₈×C₄₁	—	2	8	no	—
129	C₄×Q₈×C₄₁	—	2	2	no	—
130	C₄×Q₈×C₄₁	—	2	2	no	—
131	C₄×Q₈×C₄₁	—	2	2	no	—
132	C₄×Q₈×C₄₁	D₄	1	4	yes	—
133	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
134	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
135	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
136	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
137	C₄×D₄×C₄₁	—	2	8	no	—
138	C₄×D₄×C₄₁	—	2	2	no	—
139	C₄×D₄×C₄₁	—	2	2	no	—
140	C₄×D₄×C₄₁	—	2	2	no	—
141	C₄×D₄×C₄₁	C₂³	1	4	yes	—
142	C₄×D₄×C₄₁	C₂³	1	4	yes	—
143	C₄×D₄×C₄₁	C₂³	1	4	yes	—
144	#117×C₄₁	—	2	8	no	—
145	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
146	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
147	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
148	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
149	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
150	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
166	C₂×C₄²×C₄₁	—	2	1	no	—
167	C₂×C₄²×C₄₁	—	2	1	no	—
168	C₂×C₄²×C₄₁	—	2	1	no	—
169	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
172	#106×C₄₁	C₂³	1	4	yes	—
173	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
174	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
175	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
176	#103×C₄₁	C₂³	1	4	yes	—
177	#103×C₄₁	C₂³	1	4	yes	—
178	#103×C₄₁	C₂³	1	4	yes	—
179	#102×C₄₁	C₂³	1	4	yes	—
180	#102×C₄₁	C₂³	1	4	yes	—
181	#102×C₄₁	C₂³	1	4	yes	—
182	#97×C₄₁	C₂³	1	4	yes	—
183	#97×C₄₁	C₂³	1	4	yes	—
184	C₄×C₈×C₄₁	C₂³	1	4	yes	—
185	C₂⁴×C₄₁	—	2	1	no	—
186	C₂⁴×C₄₁	—	2	1	no	—
187	C₂⁴×C₄₁	—	2	1	no	—
188	C₂×Q₈×C₄₁	—	2	1	no	—
189	C₂×Q₈×C₄₁	—	2	1	no	—
190	C₂×Q₈×C₄₁	—	2	1	no	—
191	C₂×Q₈×C₄₁	—	2	2	no	—
192	C₂×Q₈×C₄₁	—	2	2	no	—
193	C₂×Q₈×C₄₁	—	2	2	no	—
194	C₂×Q₈×C₄₁	—	2	2	no	—
195	C₂×Q₈×C₄₁	—	2	2	no	—
196	C₂×Q₈×C₄₁	—	2	2	no	—
197	C₂×Q₈×C₄₁	—	4	2	no	—
198	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
199	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
200	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
201	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
202	C₂×D₄×C₄₁	—	2	1	no	—
203	C₂×D₄×C₄₁	—	2	1	no	—
204	C₂×D₄×C₄₁	—	2	1	no	—
205	C₂×D₄×C₄₁	—	2	4	no	—
206	C₂×D₄×C₄₁	—	2	4	no	—
207	C₂×D₄×C₄₁	—	2	2	no	—
208	C₂×D₄×C₄₁	—	2	2	no	—
209	C₂×D₄×C₄₁	—	2	2	no	—
210	C₂×D₄×C₄₁	—	2	2	no	—
211	C₂×D₄×C₄₁	—	2	2	no	—
212	C₂×D₄×C₄₁	—	2	2	no	—
213	C₂×D₄×C₄₁	—	4	4	no	—
214	C₂×D₄×C₄₁	—	8	2	no	—
215	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
216	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
217	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₄₁	—	2	1	no	—
219	C₂²×C₄×C₄₁	—	2	1	no	—
220	C₂²×C₄×C₄₁	—	2	1	no	—
221	C₂²×C₄×C₄₁	—	2	1	no	—
222	C₂²×C₄×C₄₁	—	2	1	no	—
223	C₂²×C₄×C₄₁	—	2	4	no	—
224	C₂²×C₄×C₄₁	—	2	4	no	—
225	C₂²×C₄×C₄₁	—	2	4	no	—
226	C₂²×C₄×C₄₁	—	4	4	no	—
227	C₂²×C₄×C₄₁	—	8	2	no	—
228	C₂²×C₄×C₄₁	—	8	2	no	—
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	1	yes	characteristic
233	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₄₁	—	2	8	no	—
237	Q₁₆×C₄₁	—	4	4	no	—
238	SD₁₆×C₄₁	—	2	8	no	—
239	SD₁₆×C₄₁	—	4	4	no	—
240	SD₁₆×C₄₁	—	4	4	no	—
241	SD₁₆×C₄₁	—	4	4	no	—
242	SD₁₆×C₄₁	—	4	4	no	—
243	D₈×C₄₁	—	2	8	no	—
244	D₈×C₄₁	—	4	4	no	—
245	C₂×C₈×C₄₁	—	2	2	no	—
246	C₂×C₈×C₄₁	—	2	2	no	—
247	C₂×C₈×C₄₁	—	2	2	no	—
248	C₂×C₈×C₄₁	#41	1	4	yes	—
249	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
250	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
251	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
252	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₄₁	—	2	4	no	—
254	C₄⋊C₄×C₄₁	—	2	4	no	—
255	C₄⋊C₄×C₄₁	—	2	4	no	—
256	C₄⋊C₄×C₄₁	—	2	4	no	—
257	C₄⋊C₄×C₄₁	—	2	4	no	—
258	C₄⋊C₄×C₄₁	—	2	1	no	—
259	C₄⋊C₄×C₄₁	—	2	1	no	—
260	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
262	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₄₁	—	2	4	no	—
271	C₂²⋊C₄×C₄₁	—	2	4	no	—
272	C₂²⋊C₄×C₄₁	—	2	4	no	—
273	C₂²⋊C₄×C₄₁	—	2	4	no	—
274	C₂²⋊C₄×C₄₁	—	2	4	no	—
275	C₂²⋊C₄×C₄₁	—	2	4	no	—
276	C₄²×C₄₁	—	2	4	no	—
277	C₄²×C₄₁	—	2	4	no	—
278	C₄²×C₄₁	—	2	4	no	—
279	C₄²×C₄₁	C₂×D₄	1	2	yes	—
280	C₄²×C₄₁	C₂×D₄	1	2	yes	—
281	C₄²×C₄₁	C₂×D₄	1	2	yes	—
282	C₄²×C₄₁	C₂⁴	1	2	yes	—
283	C₄²×C₄₁	C₂⁴	1	2	yes	—
284	C₄²×C₄₁	C₂⁴	1	2	yes	—
285	C₂³×C₄₁	—	2	2	no	—
286	C₂³×C₄₁	—	2	2	no	—
287	C₂³×C₄₁	—	2	2	no	—
288	C₂³×C₄₁	—	4	2	no	—
289	C₂³×C₄₁	—	4	2	no	—
290	C₂³×C₄₁	—	4	2	no	—
291	C₂³×C₄₁	—	4	2	no	—
292	C₂³×C₄₁	—	4	2	no	—
293	C₂³×C₄₁	—	4	2	no	—
294	C₂³×C₄₁	—	4	2	no	—
295	C₂³×C₄₁	—	4	2	no	—
296	C₂³×C₄₁	—	4	2	no	—
297	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₄₁	—	2	2	no	—
299	Q₈×C₄₁	—	2	2	no	—
300	Q₈×C₄₁	—	2	2	no	—
301	Q₈×C₄₁	—	2	2	no	—
302	Q₈×C₄₁	—	2	2	no	—
303	Q₈×C₄₁	—	2	2	no	—
304	Q₈×C₄₁	—	4	4	no	—
305	Q₈×C₄₁	—	4	2	no	—
306	Q₈×C₄₁	—	4	2	no	—
307	Q₈×C₄₁	—	4	2	no	—
308	D₄×C₄₁	—	2	2	no	—
309	D₄×C₄₁	—	2	2	no	—
310	D₄×C₄₁	—	2	2	no	—
311	D₄×C₄₁	—	2	2	no	—
312	D₄×C₄₁	—	2	2	no	—
313	D₄×C₄₁	—	2	2	no	—
314	D₄×C₄₁	—	4	8	no	—
315	D₄×C₄₁	—	4	2	no	—
316	D₄×C₄₁	—	4	2	no	—
317	D₄×C₄₁	—	4	2	no	—
318	D₄×C₄₁	—	8	4	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	—	2	2	no	—
324	C₂×C₄×C₄₁	—	2	2	no	—
325	C₂×C₄×C₄₁	—	2	2	no	—
326	C₂×C₄×C₄₁	—	2	2	no	—
327	C₂×C₄×C₄₁	—	2	2	no	—
328	C₂×C₄×C₄₁	—	2	2	no	—
329	C₂×C₄×C₄₁	—	2	2	no	—
330	C₂×C₄×C₄₁	—	4	8	no	—
331	C₂×C₄×C₄₁	—	4	2	no	—
332	C₂×C₄×C₄₁	—	4	2	no	—
333	C₂×C₄×C₄₁	—	4	2	no	—
334	C₂×C₄×C₄₁	—	4	2	no	—
335	C₂×C₄×C₄₁	—	4	2	no	—
336	C₂×C₄×C₄₁	—	8	4	no	—
337	C₂×C₄×C₄₁	—	8	4	no	—
338	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
346	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
347	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
348	C₈×C₄₁	—	2	2	no	—
349	C₈×C₄₁	—	2	2	no	—
350	C₈×C₄₁	—	2	2	no	—
351	C₈×C₄₁	C₂×#41	1	4	yes	—
352	C₂×#3401	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	4	2	no	—
359	C₂²×C₄₁	—	4	2	no	—
360	C₂²×C₄₁	—	4	2	no	—
361	C₂²×C₄₁	—	4	2	no	—
362	C₂²×C₄₁	—	8	4	no	—
363	C₂²×C₄₁	—	8	4	no	—
364	C₂²×C₄₁	—	8	4	no	—
365	C₂²×C₄₁	#550	1	2	yes	—
366	C₂²×C₄₁	#575	1	2	yes	—
367	C₂²×C₄₁	#577	1	2	yes	—
368	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
369	C₄×C₄₁	—	2	2	no	—
370	C₄×C₄₁	—	2	2	no	—
371	C₄×C₄₁	—	2	2	no	—
372	C₄×C₄₁	—	2	2	no	—
373	C₄×C₄₁	—	2	2	no	—
374	C₄×C₄₁	—	2	2	no	—
375	C₄×C₄₁	—	4	2	no	—
376	C₄×C₄₁	—	4	2	no	—
377	C₄×C₄₁	—	4	2	no	—
378	C₄×C₄₁	—	4	2	no	—
379	C₄×C₄₁	—	4	2	no	—
380	C₄×C₄₁	#550	1	2	yes	—
381	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
382	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂×#559	C₂×C₄₁	1	1	yes	characteristic, complemented
384	C₂×#556	C₂×C₄₁	1	1	yes	characteristic, complemented
385	#3401	C₂×C₄₁	1	16	yes	direct product factor
386	C₂×#497	C₂×C₄₁	1	1	yes	characteristic, complemented
387	C₂×#496	C₂×C₄₁	1	1	yes	characteristic
388	C₂×#495	C₂×C₄₁	1	1	yes	characteristic, complemented
389	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
390	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
391	C₂×#460	C₂×C₄₁	1	1	yes	characteristic, complemented
392	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
393	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
394	C₂×#461	C₂×C₄₁	1	1	yes	characteristic, complemented
395	C₂×#446	C₂×C₄₁	1	1	yes	characteristic, complemented
396	C₂×#442	C₂×C₄₁	1	1	yes	characteristic, complemented
397	C₂×#441	C₂×C₄₁	1	1	yes	characteristic, complemented
398	C₂×C₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
399	C₂×C₄₁	—	8	2	no	—
400	C₂×C₄₁	—	8	2	no	—
401	C₂×C₄₁	—	8	2	no	—
402	C₂×C₄₁	#3401	1	4	yes	direct product factor
403	C₂×C₄₁	C₂×#550	1	1	yes	characteristic
404	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
405	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
406	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
407	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
408	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
409	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
410	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
411	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
412	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
413	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
414	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
415	#559	—	2	4	no	—
416	#559	C₂²×C₄₁	1	8	yes	complemented
417	#556	—	2	4	no	—
418	#556	C₂²×C₄₁	1	8	yes	complemented
419	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
420	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
421	C₂×#126	—	2	1	no	—
422	C₂×#126	—	2	1	no	—
423	C₂×#124	—	2	1	no	—
424	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
425	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
426	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
427	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
428	C₂×#123	—	2	1	no	—
429	C₂×#123	—	2	1	no	—
430	C₂×C₂²⋊Q₈	—	2	1	no	—
431	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
432	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
433	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
434	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
435	C₂×C₄×D₄	—	2	1	no	—
436	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
439	C₂×#117	—	2	1	no	—
440	#497	C₂²×C₄₁	1	8	yes	complemented
441	#496	C₂²×C₄₁	1	8	yes	—
442	#495	C₂²×C₄₁	1	8	yes	complemented
443	#464	C₂²×C₄₁	1	8	yes	complemented
444	#464	C₂²×C₄₁	1	8	yes	complemented
445	#463	C₂²×C₄₁	1	8	yes	complemented
446	#463	C₂²×C₄₁	1	8	yes	complemented
447	#461	C₂²×C₄₁	1	8	yes	complemented
448	#460	C₂²×C₄₁	1	8	yes	complemented
449	#446	C₂²×C₄₁	1	8	yes	complemented
450	#442	C₂²×C₄₁	1	8	yes	complemented
451	#441	C₂²×C₄₁	1	8	yes	complemented
452	C₄×SD₁₆	C₂²×C₄₁	1	8	yes	complemented
453	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
454	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
455	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
456	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
457	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
458	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
459	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
460	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
461	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
462	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
463	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
464	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
465	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
466	C₄₁	C₂×#3401	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
468	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
470	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	—	2	1	no	—
479	C₂×Q₁₆	—	2	4	no	—
480	C₂×Q₁₆	—	4	2	no	—
481	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
482	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
483	C₂×SD₁₆	—	2	4	no	—
484	C₂×SD₁₆	—	4	2	no	—
485	C₂×SD₁₆	—	4	2	no	—
486	C₂×SD₁₆	—	4	2	no	—
487	C₂×SD₁₆	—	4	2	no	—
488	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
489	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
490	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
491	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
492	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
493	C₂×D₈	—	2	4	no	—
494	C₂×D₈	—	4	2	no	—
495	C₂×D₈	C₂³×C₄₁	1	4	yes	—
496	C₂×D₈	C₂³×C₄₁	1	4	yes	—
497	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
501	C₄⋊Q₈	—	2	2	no	—
502	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
503	#127	—	2	2	no	—
504	#127	C₂³×C₄₁	1	4	yes	—
505	#126	—	2	8	no	—
506	#126	—	2	8	no	—
507	#124	—	2	8	no	—
508	#124	—	2	2	no	—
509	#124	—	2	2	no	—
510	#124	—	2	2	no	—
511	#124	—	2	2	no	—
512	#124	C₂³×C₄₁	1	4	yes	—
513	#124	C₂³×C₄₁	1	4	yes	—
514	#124	C₂³×C₄₁	1	4	yes	—
515	#124	C₂³×C₄₁	1	4	yes	—
516	#123	—	2	8	no	—
517	#123	—	2	8	no	—
518	C₂²⋊Q₈	—	2	8	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	D₄×C₄₁	1	4	yes	—
523	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
524	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
525	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
526	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	C₂³×C₄₁	1	4	yes	—
532	C₄×D₄	C₂³×C₄₁	1	4	yes	—
533	C₄×D₄	C₂³×C₄₁	1	4	yes	—
534	#117	—	2	8	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
541	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
542	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
562	#106	C₂³×C₄₁	1	4	yes	—
563	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
564	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
565	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
566	#103	C₂³×C₄₁	1	4	yes	—
567	#103	C₂³×C₄₁	1	4	yes	—
568	#103	C₂³×C₄₁	1	4	yes	—
569	#102	C₂³×C₄₁	1	4	yes	—
570	#102	C₂³×C₄₁	1	4	yes	—
571	#102	C₂³×C₄₁	1	4	yes	—
572	#97	C₂³×C₄₁	1	4	yes	—
573	#97	C₂³×C₄₁	1	4	yes	—
574	C₄×C₈	C₂³×C₄₁	1	4	yes	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	—	2	1	no	—
577	C₂⁴	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	4	2	no	—
588	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
589	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
590	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	8	2	no	—
605	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
606	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
607	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	4	4	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	—	8	2	no	—
619	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
626	Q₁₆	—	2	8	no	—
627	Q₁₆	—	4	4	no	—
628	SD₁₆	—	2	8	no	—
629	SD₁₆	—	4	4	no	—
630	SD₁₆	—	4	4	no	—
631	SD₁₆	—	4	4	no	—
632	SD₁₆	—	4	4	no	—
633	D₈	—	2	8	no	—
634	D₈	—	4	4	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	2	no	—
638	C₂×C₈	#41×C₄₁	1	4	yes	—
639	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
640	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
641	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
642	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
651	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
652	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
653	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	C₂×D₄×C₄₁	1	2	yes	—
670	C₄²	C₂×D₄×C₄₁	1	2	yes	—
671	C₄²	C₂×D₄×C₄₁	1	2	yes	—
672	C₄²	C₂⁴×C₄₁	1	2	yes	—
673	C₄²	C₂⁴×C₄₁	1	2	yes	—
674	C₄²	C₂⁴×C₄₁	1	2	yes	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	4	4	no	—
695	Q₈	—	4	2	no	—
696	Q₈	—	4	2	no	—
697	Q₈	—	4	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	2	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	4	8	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	8	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	—	8	4	no	—
728	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
735	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
736	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
737	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	C₂×#41×C₄₁	1	4	yes	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	8	4	no	—
752	C₂²	—	8	4	no	—
753	C₂²	—	8	4	no	—
754	C₂²	C₄₁×#550	1	2	yes	—
755	C₂²	C₄₁×#575	1	2	yes	—
756	C₂²	C₄₁×#577	1	2	yes	—
757	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	C₄₁×#550	1	2	yes	—
770	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
771	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
772	C₂	—	8	2	no	—
773	C₂	—	8	2	no	—
774	C₂	—	8	2	no	—
775	C₂	C₄₁×#3401	1	4	yes	direct product factor
776	C₂	C₂×C₄₁×#550	1	1	yes	characteristic
777	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
778	C₂	C₂×C₄₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₂×C₄₁×#496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#559	C₂	semidirect
2. C₂×C₄₁×#556	C₂	semidirect
3. C₄₁×#3401	C₂	direct (N × H)
4. C₂×C₄₁×#497	C₂	semidirect
6. C₂×C₄₁×#495	C₂	semidirect
7. C₂×C₄₁×#464	C₂	semidirect
8. C₂×C₄₁×#464	C₂	semidirect
9. C₂×C₄₁×#460	C₂	semidirect
10. C₂×C₄₁×#463	C₂	semidirect
11. C₂×C₄₁×#463	C₂	semidirect
12. C₂×C₄₁×#461	C₂	semidirect
13. C₂×C₄₁×#446	C₂	semidirect
14. C₂×C₄₁×#442	C₂	semidirect
15. C₂×C₄₁×#441	C₂	semidirect
16. C₂×C₄×SD₁₆×C₄₁	C₂	semidirect
27. C₄₁×#559	C₂²	semidirect
29. C₄₁×#556	C₂²	semidirect
51. C₄₁×#497	C₂²	semidirect
53. C₄₁×#495	C₂²	semidirect
54. C₄₁×#464	C₂²	semidirect
55. C₄₁×#464	C₂²	semidirect
56. C₄₁×#463	C₂²	semidirect
57. C₄₁×#463	C₂²	semidirect
58. C₄₁×#461	C₂²	semidirect
59. C₄₁×#460	C₂²	semidirect
60. C₄₁×#446	C₂²	semidirect
61. C₄₁×#442	C₂²	semidirect
62. C₄₁×#441	C₂²	semidirect
63. C₄×SD₁₆×C₄₁	C₂²	semidirect
352. C₂×#3401	C₄₁	direct (N × H)
383. C₂×#559	C₂×C₄₁	semidirect
384. C₂×#556	C₂×C₄₁	semidirect
385. #3401	C₂×C₄₁	direct (N × H)
386. C₂×#497	C₂×C₄₁	semidirect
388. C₂×#495	C₂×C₄₁	semidirect
389. C₂×#464	C₂×C₄₁	semidirect
390. C₂×#464	C₂×C₄₁	semidirect
391. C₂×#460	C₂×C₄₁	semidirect
392. C₂×#463	C₂×C₄₁	semidirect
393. C₂×#463	C₂×C₄₁	semidirect
394. C₂×#461	C₂×C₄₁	semidirect
395. C₂×#446	C₂×C₄₁	semidirect
396. C₂×#442	C₂×C₄₁	semidirect
397. C₂×#441	C₂×C₄₁	semidirect
398. C₂×C₄×SD₁₆	C₂×C₄₁	semidirect
402. C₂×C₄₁	#3401	direct (N × H)
416. #559	C₂²×C₄₁	semidirect
418. #556	C₂²×C₄₁	semidirect
440. #497	C₂²×C₄₁	semidirect
442. #495	C₂²×C₄₁	semidirect
443. #464	C₂²×C₄₁	semidirect
444. #464	C₂²×C₄₁	semidirect
445. #463	C₂²×C₄₁	semidirect
446. #463	C₂²×C₄₁	semidirect
447. #461	C₂²×C₄₁	semidirect
448. #460	C₂²×C₄₁	semidirect
449. #446	C₂²×C₄₁	semidirect
450. #442	C₂²×C₄₁	semidirect
451. #441	C₂²×C₄₁	semidirect
452. C₄×SD₁₆	C₂²×C₄₁	semidirect
466. C₄₁	C₂×#3401	direct (N × H)
775. C₂	C₄₁×#3401	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×#559	2
C₂×C₄₁×#556	2
C₄₁×#3401	2
C₂×C₄₁×#497	2
C₂×C₄₁×#496	2
C₂×C₄₁×#495	2
C₂×C₄₁×#464	2
C₂×C₄₁×#460	2
C₂×C₄₁×#463	2
C₂×C₄₁×#461	2
C₂×C₄₁×#446	2
C₂×C₄₁×#442	2
C₂×C₄₁×#441	2
C₂×C₄×SD₁₆×C₄₁	2
C₂×#3401	41

Subgroups — C2×C41×#3401 #23837599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3401 #23837599