Subgroups — C₂×C₄₁×#2449 #23810852

Order 10496.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2449	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄₁×#399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#398	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#396	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#395	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₁×#386	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄₁×#386	C₂	1	1	yes	maximal, characteristic
14	C₂×C₄₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₄₁	—	2	8	no	—
24	C₂×C₂²⋊Q₈×C₄₁	—	2	8	no	—
25	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	8	yes	complemented
26	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	8	yes	complemented
27	C₂×C₄×D₄×C₄₁	—	2	8	no	—
28	C₂×C₄×D₄×C₄₁	C₂²	1	8	yes	—
29	C₂²×C₄⋊C₄×C₄₁	—	2	8	no	—
30	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₄₁	C₂²	1	8	yes	complemented
43	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
52	C₄₁×#399	C₂²	1	8	yes	complemented
53	C₄₁×#398	C₂²	1	8	yes	complemented
54	C₄₁×#396	C₂²	1	8	yes	complemented
55	C₄₁×#395	C₂²	1	8	yes	complemented
56	C₄₁×#389	C₂²	1	8	yes	complemented
57	C₄₁×#387	C₂²	1	8	yes	complemented
58	C₄₁×#386	C₂²	1	8	yes	—
59	C₄₁×#386	C₂²	1	8	yes	—
60	C₄₁×#385	C₂²	1	8	yes	complemented
61	C₄₁×#385	C₂²	1	8	yes	complemented
62	C₄₁×#385	C₂²	1	8	yes	complemented
63	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
64	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
65	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
66	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
67	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
68	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
69	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
70	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
71	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
72	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₄₁	—	2	4	no	—
74	C₂²×Q₈×C₄₁	—	2	4	no	—
75	C₂²×Q₈×C₄₁	—	4	2	no	—
76	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
77	C₂²×D₄×C₄₁	—	2	4	no	—
78	C₂²×D₄×C₄₁	—	2	4	no	—
79	C₂²×D₄×C₄₁	Q₈	1	8	yes	complemented
80	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
81	C₂³×C₄×C₄₁	—	2	4	no	—
82	C₂³×C₄×C₄₁	—	2	4	no	—
83	C₂³×C₄×C₄₁	—	2	4	no	—
84	C₂³×C₄×C₄₁	—	2	4	no	—
85	C₂³×C₄×C₄₁	—	2	4	no	—
86	C₂³×C₄×C₄₁	—	2	4	no	—
87	C₂³×C₄×C₄₁	—	2	4	no	—
88	C₂³×C₄×C₄₁	—	2	4	no	—
89	C₂³×C₄×C₄₁	—	2	4	no	—
90	C₂³×C₄×C₄₁	—	4	2	no	—
91	C₂³×C₄×C₄₁	—	4	2	no	—
92	C₂³×C₄×C₄₁	—	4	2	no	—
93	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
94	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
101	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
102	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
103	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂²⋊Q₈×C₄₁	—	2	32	no	—
111	C₂²⋊Q₈×C₄₁	—	2	32	no	—
112	C₄×D₄×C₄₁	—	2	32	no	—
113	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
114	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
116	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
117	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
118	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
119	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
120	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
121	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
122	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
123	C₂×C₄⋊C₄×C₄₁	—	2	32	no	—
124	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
125	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	complemented
126	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
139	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
140	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
141	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
142	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
144	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
145	C₂×C₂²⋊C₄×C₄₁	D₄	1	8	yes	—
146	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
154	C₂×C₄²×C₄₁	—	2	4	no	—
155	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
156	#95×C₄₁	C₂³	1	4	yes	—
157	#95×C₄₁	C₂³	1	4	yes	—
158	#95×C₄₁	C₂³	1	4	yes	—
159	#95×C₄₁	C₂³	1	4	yes	—
160	#95×C₄₁	C₂³	1	4	yes	—
161	#95×C₄₁	C₂³	1	4	yes	—
162	#95×C₄₁	C₂³	1	4	yes	—
163	#95×C₄₁	C₂³	1	4	yes	—
164	C₂⁴×C₄₁	—	2	2	no	—
165	C₂⁴×C₄₁	—	2	2	no	—
166	C₂⁴×C₄₁	—	2	2	no	—
167	C₂⁴×C₄₁	—	2	2	no	—
168	C₂⁴×C₄₁	—	2	2	no	—
169	C₂⁴×C₄₁	—	2	2	no	—
170	C₂⁴×C₄₁	—	2	2	no	—
171	C₂⁴×C₄₁	—	2	2	no	—
172	C₂⁴×C₄₁	—	2	2	no	—
173	C₂⁴×C₄₁	—	2	2	no	—
174	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
175	C₂⁴×C₄₁	C₂×Q₈	1	4	yes	—
176	C₂⁴×C₄₁	C₂×Q₈	1	4	yes	—
177	C₂⁴×C₄₁	#41	1	4	yes	—
178	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
179	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
180	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
181	C₂×Q₈×C₄₁	—	2	8	no	—
182	C₂×Q₈×C₄₁	—	2	8	no	—
183	C₂×Q₈×C₄₁	—	4	4	no	—
184	C₂×Q₈×C₄₁	—	4	16	no	—
185	C₂×D₄×C₄₁	—	2	32	no	—
186	C₂×D₄×C₄₁	—	2	8	no	—
187	C₂×D₄×C₄₁	—	2	8	no	—
188	C₂×D₄×C₄₁	C₂×Q₈	1	16	yes	complemented
189	C₂²×C₄×C₄₁	—	2	32	no	—
190	C₂²×C₄×C₄₁	—	2	2	no	—
191	C₂²×C₄×C₄₁	—	2	2	no	—
192	C₂²×C₄×C₄₁	—	2	2	no	—
193	C₂²×C₄×C₄₁	—	2	2	no	—
194	C₂²×C₄×C₄₁	—	2	2	no	—
195	C₂²×C₄×C₄₁	—	2	2	no	—
196	C₂²×C₄×C₄₁	—	2	8	no	—
197	C₂²×C₄×C₄₁	—	2	2	no	—
198	C₂²×C₄×C₄₁	—	2	2	no	—
199	C₂²×C₄×C₄₁	—	2	2	no	—
200	C₂²×C₄×C₄₁	—	2	2	no	—
201	C₂²×C₄×C₄₁	—	2	2	no	—
202	C₂²×C₄×C₄₁	—	2	2	no	—
203	C₂²×C₄×C₄₁	—	2	2	no	—
204	C₂²×C₄×C₄₁	—	2	2	no	—
205	C₂²×C₄×C₄₁	—	2	8	no	—
206	C₂²×C₄×C₄₁	—	2	8	no	—
207	C₂²×C₄×C₄₁	—	2	2	no	—
208	C₂²×C₄×C₄₁	—	2	2	no	—
209	C₂²×C₄×C₄₁	—	2	2	no	—
210	C₂²×C₄×C₄₁	—	2	2	no	—
211	C₂²×C₄×C₄₁	—	2	2	no	—
212	C₂²×C₄×C₄₁	—	2	2	no	—
213	C₂²×C₄×C₄₁	—	2	2	no	—
214	C₂²×C₄×C₄₁	—	2	2	no	—
215	C₂²×C₄×C₄₁	—	2	8	no	—
216	C₂²×C₄×C₄₁	—	2	8	no	—
217	C₂²×C₄×C₄₁	—	2	2	no	—
218	C₂²×C₄×C₄₁	—	2	2	no	—
219	C₂²×C₄×C₄₁	—	2	2	no	—
220	C₂²×C₄×C₄₁	—	2	2	no	—
221	C₂²×C₄×C₄₁	—	2	2	no	—
222	C₂²×C₄×C₄₁	—	2	2	no	—
223	C₂²×C₄×C₄₁	—	2	2	no	—
224	C₂²×C₄×C₄₁	—	2	2	no	—
225	C₂²×C₄×C₄₁	—	2	2	no	—
226	C₂²×C₄×C₄₁	—	2	2	no	—
227	C₂²×C₄×C₄₁	—	2	8	no	—
228	C₂²×C₄×C₄₁	—	2	8	no	—
229	C₂²×C₄×C₄₁	—	2	8	no	—
230	C₂²×C₄×C₄₁	—	2	8	no	—
231	C₂²×C₄×C₄₁	—	4	4	no	—
232	C₂²×C₄×C₄₁	—	4	4	no	—
233	C₂²×C₄×C₄₁	—	4	4	no	—
234	C₂²×C₄×C₄₁	—	4	16	no	—
235	C₂²×C₄×C₄₁	—	4	16	no	—
236	C₂²×C₄×C₄₁	—	4	16	no	—
237	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
238	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
243	C₂²×C₄×C₄₁	#41	1	4	yes	—
244	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₄₁	—	2	8	no	—
258	C₄⋊C₄×C₄₁	—	2	8	no	—
259	C₄⋊C₄×C₄₁	—	2	8	no	—
260	C₄⋊C₄×C₄₁	—	2	8	no	—
261	C₄⋊C₄×C₄₁	—	2	8	no	—
262	C₄⋊C₄×C₄₁	—	2	8	no	—
263	C₄⋊C₄×C₄₁	—	2	8	no	—
264	C₄⋊C₄×C₄₁	—	2	8	no	—
265	C₄⋊C₄×C₄₁	—	2	8	no	—
266	C₄⋊C₄×C₄₁	—	2	8	no	—
267	C₄⋊C₄×C₄₁	—	4	4	no	—
268	C₄⋊C₄×C₄₁	C₂×D₄	1	16	yes	complemented
269	C₂²⋊C₄×C₄₁	—	2	8	no	—
270	C₂²⋊C₄×C₄₁	—	2	8	no	—
271	C₂²⋊C₄×C₄₁	—	2	8	no	—
272	C₂²⋊C₄×C₄₁	—	2	8	no	—
273	C₂²⋊C₄×C₄₁	—	2	8	no	—
274	C₂²⋊C₄×C₄₁	—	2	8	no	—
275	C₂²⋊C₄×C₄₁	—	4	4	no	—
276	C₂²⋊C₄×C₄₁	C₂×D₄	1	16	yes	—
277	C₄²×C₄₁	—	2	8	no	—
278	C₂³×C₄₁	—	2	8	no	—
279	C₂³×C₄₁	—	2	8	no	—
280	C₂³×C₄₁	—	2	8	no	—
281	C₂³×C₄₁	—	2	8	no	—
282	C₂³×C₄₁	—	2	8	no	—
283	C₂³×C₄₁	—	2	8	no	—
284	C₂³×C₄₁	—	2	2	no	—
285	C₂³×C₄₁	—	2	2	no	—
286	C₂³×C₄₁	—	2	2	no	—
287	C₂³×C₄₁	—	2	2	no	—
288	C₂³×C₄₁	—	2	8	no	—
289	C₂³×C₄₁	—	2	8	no	—
290	C₂³×C₄₁	—	2	8	no	—
291	C₂³×C₄₁	—	2	2	no	—
292	C₂³×C₄₁	—	2	2	no	—
293	C₂³×C₄₁	—	2	2	no	—
294	C₂³×C₄₁	—	2	2	no	—
295	C₂³×C₄₁	—	2	2	no	—
296	C₂³×C₄₁	—	2	2	no	—
297	C₂³×C₄₁	—	4	4	no	—
298	C₂³×C₄₁	—	4	4	no	—
299	C₂³×C₄₁	—	4	4	no	—
300	C₂³×C₄₁	—	4	4	no	—
301	C₂³×C₄₁	C₂²⋊Q₈	1	16	yes	complemented
302	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
303	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
304	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
305	C₂³×C₄₁	C₂²×Q₈	1	4	yes	—
306	C₂³×C₄₁	C₂²×Q₈	1	4	yes	—
307	C₂³×C₄₁	C₂²×Q₈	1	2	yes	—
308	C₂³×C₄₁	C₂×#41	1	4	yes	—
309	C₂³×C₄₁	C₂×#41	1	2	yes	—
310	C₂³×C₄₁	C₂×#41	1	2	yes	—
311	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
312	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
313	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
314	Q₈×C₄₁	—	4	16	no	—
315	D₄×C₄₁	—	2	32	no	—
316	C₂×C₄×C₄₁	—	2	32	no	—
317	C₂×C₄×C₄₁	—	2	8	no	—
318	C₂×C₄×C₄₁	—	2	8	no	—
319	C₂×C₄×C₄₁	—	2	8	no	—
320	C₂×C₄×C₄₁	—	2	8	no	—
321	C₂×C₄×C₄₁	—	2	8	no	—
322	C₂×C₄×C₄₁	—	2	8	no	—
323	C₂×C₄×C₄₁	—	2	8	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	—	2	2	no	—
331	C₂×C₄×C₄₁	—	2	2	no	—
332	C₂×C₄×C₄₁	—	2	2	no	—
333	C₂×C₄×C₄₁	—	2	2	no	—
334	C₂×C₄×C₄₁	—	2	2	no	—
335	C₂×C₄×C₄₁	—	2	2	no	—
336	C₂×C₄×C₄₁	—	2	2	no	—
337	C₂×C₄×C₄₁	—	2	2	no	—
338	C₂×C₄×C₄₁	—	2	2	no	—
339	C₂×C₄×C₄₁	—	2	2	no	—
340	C₂×C₄×C₄₁	—	2	2	no	—
341	C₂×C₄×C₄₁	—	2	2	no	—
342	C₂×C₄×C₄₁	—	2	2	no	—
343	C₂×C₄×C₄₁	—	2	2	no	—
344	C₂×C₄×C₄₁	—	2	2	no	—
345	C₂×C₄×C₄₁	—	2	2	no	—
346	C₂×C₄×C₄₁	—	2	2	no	—
347	C₂×C₄×C₄₁	—	2	2	no	—
348	C₂×C₄×C₄₁	—	2	2	no	—
349	C₂×C₄×C₄₁	—	2	2	no	—
350	C₂×C₄×C₄₁	—	2	2	no	—
351	C₂×C₄×C₄₁	—	2	2	no	—
352	C₂×C₄×C₄₁	—	2	2	no	—
353	C₂×C₄×C₄₁	—	2	2	no	—
354	C₂×C₄×C₄₁	—	2	2	no	—
355	C₂×C₄×C₄₁	—	2	2	no	—
356	C₂×C₄×C₄₁	—	4	16	no	—
357	C₂×C₄×C₄₁	—	4	16	no	—
358	C₂×C₄×C₄₁	—	4	16	no	—
359	C₂×C₄×C₄₁	—	4	4	no	—
360	C₂×C₄×C₄₁	—	4	4	no	—
361	C₂×C₄×C₄₁	—	4	4	no	—
362	C₂×C₄×C₄₁	—	4	4	no	—
363	C₂×C₄×C₄₁	—	4	4	no	—
364	C₂×C₄×C₄₁	—	4	4	no	—
365	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
366	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
368	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
369	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₄₁	C₂²×Q₈	1	4	yes	—
371	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
372	C₂×#2449	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
373	C₂²×C₄₁	—	2	4	no	—
374	C₂²×C₄₁	—	2	4	no	—
375	C₂²×C₄₁	—	2	4	no	—
376	C₂²×C₄₁	—	2	4	no	—
377	C₂²×C₄₁	—	2	4	no	—
378	C₂²×C₄₁	—	2	4	no	—
379	C₂²×C₄₁	—	2	32	no	—
380	C₂²×C₄₁	—	2	4	no	—
381	C₂²×C₄₁	—	2	4	no	—
382	C₂²×C₄₁	—	2	4	no	—
383	C₂²×C₄₁	—	4	2	no	—
384	C₂²×C₄₁	—	4	2	no	—
385	C₂²×C₄₁	—	4	2	no	—
386	C₂²×C₄₁	—	4	2	no	—
387	C₂²×C₄₁	—	4	16	no	—
388	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	4	yes	—
389	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	8	yes	complemented
390	C₂²×C₄₁	#525	1	4	yes	—
391	C₂²×C₄₁	#539	1	4	yes	—
392	C₂²×C₄₁	D₄²	1	4	yes	—
393	C₂²×C₄₁	#547	1	4	yes	—
394	C₂²×C₄₁	D₄×Q₈	1	4	yes	—
395	C₂²×C₄₁	#554	1	4	yes	—
396	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
397	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
398	C₂²×C₄₁	C₂³×Q₈	1	1	yes	characteristic
399	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
401	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
403	C₄×C₄₁	—	2	4	no	—
404	C₄×C₄₁	—	2	4	no	—
405	C₄×C₄₁	—	2	4	no	—
406	C₄×C₄₁	—	2	4	no	—
407	C₄×C₄₁	—	2	4	no	—
408	C₄×C₄₁	—	2	4	no	—
409	C₄×C₄₁	—	2	4	no	—
410	C₄×C₄₁	—	4	2	no	—
411	C₄×C₄₁	—	4	2	no	—
412	C₄×C₄₁	—	4	2	no	—
413	C₄×C₄₁	—	4	2	no	—
414	C₄×C₄₁	—	4	2	no	—
415	C₄×C₄₁	—	4	2	no	—
416	C₂²×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
417	C₂²×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
418	C₂²×C₄×D₄	C₂×C₄₁	1	1	yes	characteristic
419	C₂³×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
420	#2449	C₂×C₄₁	1	16	yes	direct product factor
421	C₂×#399	C₂×C₄₁	1	1	yes	characteristic, complemented
422	C₂×#398	C₂×C₄₁	1	1	yes	characteristic, complemented
423	C₂×#396	C₂×C₄₁	1	1	yes	characteristic, complemented
424	C₂×#395	C₂×C₄₁	1	1	yes	characteristic, complemented
425	C₂×#389	C₂×C₄₁	1	1	yes	characteristic, complemented
426	C₂×#387	C₂×C₄₁	1	1	yes	characteristic, complemented
427	C₂×#386	C₂×C₄₁	1	1	yes	characteristic
428	C₂×#386	C₂×C₄₁	1	1	yes	characteristic
429	C₂×#385	C₂×C₄₁	1	1	yes	characteristic, complemented
430	C₂×#385	C₂×C₄₁	1	1	yes	characteristic, complemented
431	C₂×#385	C₂×C₄₁	1	1	yes	characteristic, complemented
432	C₂×C₄₁	—	2	8	no	—
433	C₂×C₄₁	—	4	4	no	—
434	C₂×C₄₁	#2449	1	8	yes	direct product factor
435	C₂×C₄₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
436	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
437	C₂×C₄₁	C₂×#539	1	1	yes	characteristic
438	C₂×C₄₁	C₂×D₄²	1	1	yes	characteristic
439	C₂×C₄₁	C₂×#547	1	1	yes	characteristic
440	C₂×C₄₁	C₂×D₄×Q₈	1	1	yes	characteristic
441	C₂×C₄₁	C₂×#554	1	1	yes	characteristic
442	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
443	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
444	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
445	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
446	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
447	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
448	C₂×C₂²⋊Q₈	—	2	8	no	—
449	C₂×C₂²⋊Q₈	—	2	8	no	—
450	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	8	yes	complemented
451	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	8	yes	complemented
452	C₂×C₄×D₄	—	2	8	no	—
453	C₂×C₄×D₄	C₂²×C₄₁	1	8	yes	—
454	C₂²×C₄⋊C₄	—	2	8	no	—
455	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
456	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
457	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
458	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
459	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
460	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
461	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
462	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
463	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
464	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
465	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
466	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
467	C₂²×C₄⋊C₄	C₂²×C₄₁	1	8	yes	complemented
468	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
469	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
470	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
471	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
472	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
473	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
474	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
475	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
476	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
477	#399	C₂²×C₄₁	1	8	yes	complemented
478	#398	C₂²×C₄₁	1	8	yes	complemented
479	#396	C₂²×C₄₁	1	8	yes	complemented
480	#395	C₂²×C₄₁	1	8	yes	complemented
481	#389	C₂²×C₄₁	1	8	yes	complemented
482	#387	C₂²×C₄₁	1	8	yes	complemented
483	#386	C₂²×C₄₁	1	8	yes	—
484	#386	C₂²×C₄₁	1	8	yes	—
485	#385	C₂²×C₄₁	1	8	yes	complemented
486	#385	C₂²×C₄₁	1	8	yes	complemented
487	#385	C₂²×C₄₁	1	8	yes	complemented
488	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
489	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
490	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
491	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
492	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
493	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
494	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
495	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
496	C₄₁	C₂×#2449	1	1	yes	characteristic, direct product factor, Sylow
497	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
498	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
499	C₂²×Q₈	—	2	4	no	—
500	C₂²×Q₈	—	2	4	no	—
501	C₂²×Q₈	—	4	2	no	—
502	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
503	C₂²×D₄	—	2	4	no	—
504	C₂²×D₄	—	2	4	no	—
505	C₂²×D₄	Q₈×C₄₁	1	8	yes	complemented
506	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
507	C₂³×C₄	—	2	4	no	—
508	C₂³×C₄	—	2	4	no	—
509	C₂³×C₄	—	2	4	no	—
510	C₂³×C₄	—	2	4	no	—
511	C₂³×C₄	—	2	4	no	—
512	C₂³×C₄	—	2	4	no	—
513	C₂³×C₄	—	2	4	no	—
514	C₂³×C₄	—	2	4	no	—
515	C₂³×C₄	—	2	4	no	—
516	C₂³×C₄	—	4	2	no	—
517	C₂³×C₄	—	4	2	no	—
518	C₂³×C₄	—	4	2	no	—
519	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
526	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
527	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
528	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
529	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
536	C₂²⋊Q₈	—	2	32	no	—
537	C₂²⋊Q₈	—	2	32	no	—
538	C₄×D₄	—	2	32	no	—
539	C₂×C₄⋊C₄	—	2	4	no	—
540	C₂×C₄⋊C₄	—	2	4	no	—
541	C₂×C₄⋊C₄	—	2	4	no	—
542	C₂×C₄⋊C₄	—	2	4	no	—
543	C₂×C₄⋊C₄	—	2	4	no	—
544	C₂×C₄⋊C₄	—	2	4	no	—
545	C₂×C₄⋊C₄	—	2	4	no	—
546	C₂×C₄⋊C₄	—	2	4	no	—
547	C₂×C₄⋊C₄	—	2	4	no	—
548	C₂×C₄⋊C₄	—	2	4	no	—
549	C₂×C₄⋊C₄	—	2	32	no	—
550	C₂×C₄⋊C₄	—	4	2	no	—
551	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	complemented
552	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
554	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
555	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
558	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
559	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
560	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
563	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	—	2	4	no	—
567	C₂×C₂²⋊C₄	—	2	4	no	—
568	C₂×C₂²⋊C₄	—	2	4	no	—
569	C₂×C₂²⋊C₄	—	2	4	no	—
570	C₂×C₂²⋊C₄	—	4	2	no	—
571	C₂×C₂²⋊C₄	D₄×C₄₁	1	8	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
580	C₂×C₄²	—	2	4	no	—
581	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
582	#95	C₂³×C₄₁	1	4	yes	—
583	#95	C₂³×C₄₁	1	4	yes	—
584	#95	C₂³×C₄₁	1	4	yes	—
585	#95	C₂³×C₄₁	1	4	yes	—
586	#95	C₂³×C₄₁	1	4	yes	—
587	#95	C₂³×C₄₁	1	4	yes	—
588	#95	C₂³×C₄₁	1	4	yes	—
589	#95	C₂³×C₄₁	1	4	yes	—
590	C₂⁴	—	2	2	no	—
591	C₂⁴	—	2	2	no	—
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	2	no	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	2	no	—
598	C₂⁴	—	2	2	no	—
599	C₂⁴	—	2	2	no	—
600	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
601	C₂⁴	C₂×Q₈×C₄₁	1	4	yes	—
602	C₂⁴	C₂×Q₈×C₄₁	1	4	yes	—
603	C₂⁴	#41×C₄₁	1	4	yes	—
604	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
605	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
606	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
607	C₂×Q₈	—	2	8	no	—
608	C₂×Q₈	—	2	8	no	—
609	C₂×Q₈	—	4	4	no	—
610	C₂×Q₈	—	4	16	no	—
611	C₂×D₄	—	2	32	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	8	no	—
614	C₂×D₄	C₂×Q₈×C₄₁	1	16	yes	complemented
615	C₂²×C₄	—	2	32	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	8	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	8	no	—
632	C₂²×C₄	—	2	8	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	8	no	—
642	C₂²×C₄	—	2	8	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	8	no	—
654	C₂²×C₄	—	2	8	no	—
655	C₂²×C₄	—	2	8	no	—
656	C₂²×C₄	—	2	8	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	—	4	4	no	—
659	C₂²×C₄	—	4	4	no	—
660	C₂²×C₄	—	4	16	no	—
661	C₂²×C₄	—	4	16	no	—
662	C₂²×C₄	—	4	16	no	—
663	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
664	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
665	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
666	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
667	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
668	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
669	C₂²×C₄	#41×C₄₁	1	4	yes	—
670	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
683	C₄⋊C₄	—	2	8	no	—
684	C₄⋊C₄	—	2	8	no	—
685	C₄⋊C₄	—	2	8	no	—
686	C₄⋊C₄	—	2	8	no	—
687	C₄⋊C₄	—	2	8	no	—
688	C₄⋊C₄	—	2	8	no	—
689	C₄⋊C₄	—	2	8	no	—
690	C₄⋊C₄	—	2	8	no	—
691	C₄⋊C₄	—	2	8	no	—
692	C₄⋊C₄	—	2	8	no	—
693	C₄⋊C₄	—	4	4	no	—
694	C₄⋊C₄	C₂×D₄×C₄₁	1	16	yes	complemented
695	C₂²⋊C₄	—	2	8	no	—
696	C₂²⋊C₄	—	2	8	no	—
697	C₂²⋊C₄	—	2	8	no	—
698	C₂²⋊C₄	—	2	8	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	8	no	—
701	C₂²⋊C₄	—	4	4	no	—
702	C₂²⋊C₄	C₂×D₄×C₄₁	1	16	yes	—
703	C₄²	—	2	8	no	—
704	C₂³	—	2	8	no	—
705	C₂³	—	2	8	no	—
706	C₂³	—	2	8	no	—
707	C₂³	—	2	8	no	—
708	C₂³	—	2	8	no	—
709	C₂³	—	2	8	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	8	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	8	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	4	no	—
724	C₂³	—	4	4	no	—
725	C₂³	—	4	4	no	—
726	C₂³	—	4	4	no	—
727	C₂³	C₂²⋊Q₈×C₄₁	1	16	yes	complemented
728	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
729	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
730	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
731	C₂³	C₂²×Q₈×C₄₁	1	4	yes	—
732	C₂³	C₂²×Q₈×C₄₁	1	4	yes	—
733	C₂³	C₂²×Q₈×C₄₁	1	2	yes	—
734	C₂³	C₂×#41×C₄₁	1	4	yes	—
735	C₂³	C₂×#41×C₄₁	1	2	yes	—
736	C₂³	C₂×#41×C₄₁	1	2	yes	—
737	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
738	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
739	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
740	Q₈	—	4	16	no	—
741	D₄	—	2	32	no	—
742	C₂×C₄	—	2	32	no	—
743	C₂×C₄	—	2	8	no	—
744	C₂×C₄	—	2	8	no	—
745	C₂×C₄	—	2	8	no	—
746	C₂×C₄	—	2	8	no	—
747	C₂×C₄	—	2	8	no	—
748	C₂×C₄	—	2	8	no	—
749	C₂×C₄	—	2	8	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	4	16	no	—
783	C₂×C₄	—	4	16	no	—
784	C₂×C₄	—	4	16	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
792	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
793	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
794	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
795	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
796	C₂×C₄	C₂²×Q₈×C₄₁	1	4	yes	—
797	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	4	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	32	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	16	no	—
813	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	4	yes	—
814	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	8	yes	complemented
815	C₂²	C₄₁×#525	1	4	yes	—
816	C₂²	C₄₁×#539	1	4	yes	—
817	C₂²	D₄²×C₄₁	1	4	yes	—
818	C₂²	C₄₁×#547	1	4	yes	—
819	C₂²	D₄×Q₈×C₄₁	1	4	yes	—
820	C₂²	C₄₁×#554	1	4	yes	—
821	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
822	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
823	C₂²	C₂³×Q₈×C₄₁	1	1	yes	characteristic
824	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
825	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
826	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
827	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
828	C₄	—	2	4	no	—
829	C₄	—	2	4	no	—
830	C₄	—	2	4	no	—
831	C₄	—	2	4	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	4	no	—
834	C₄	—	2	4	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₂	—	2	8	no	—
842	C₂	—	4	4	no	—
843	C₂	C₄₁×#2449	1	8	yes	direct product factor
844	C₂	C₂²×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
845	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
846	C₂	C₂×C₄₁×#539	1	1	yes	characteristic
847	C₂	C₂×D₄²×C₄₁	1	1	yes	characteristic
848	C₂	C₂×C₄₁×#547	1	1	yes	characteristic
849	C₂	C₂×D₄×Q₈×C₄₁	1	1	yes	characteristic
850	C₂	C₂×C₄₁×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊Q₈×C₄₁	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₄₁	C₂	semidirect
4. C₂³×C₄⋊C₄×C₄₁	C₂	semidirect
5. C₄₁×#2449	C₂	direct (N × H)
6. C₂×C₄₁×#399	C₂	semidirect
7. C₂×C₄₁×#398	C₂	semidirect
8. C₂×C₄₁×#396	C₂	semidirect
9. C₂×C₄₁×#395	C₂	semidirect
10. C₂×C₄₁×#389	C₂	semidirect
11. C₂×C₄₁×#387	C₂	semidirect
14. C₂×C₄₁×#385	C₂	semidirect
15. C₂×C₄₁×#385	C₂	semidirect
16. C₂×C₄₁×#385	C₂	semidirect
25. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
42. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
52. C₄₁×#399	C₂²	semidirect
53. C₄₁×#398	C₂²	semidirect
54. C₄₁×#396	C₂²	semidirect
55. C₄₁×#395	C₂²	semidirect
56. C₄₁×#389	C₂²	semidirect
57. C₄₁×#387	C₂²	semidirect
60. C₄₁×#385	C₂²	semidirect
61. C₄₁×#385	C₂²	semidirect
62. C₄₁×#385	C₂²	semidirect
79. C₂²×D₄×C₄₁	Q₈	semidirect
125. C₂×C₄⋊C₄×C₄₁	D₄	semidirect
188. C₂×D₄×C₄₁	C₂×Q₈	semidirect
268. C₄⋊C₄×C₄₁	C₂×D₄	semidirect
301. C₂³×C₄₁	C₂²⋊Q₈	semidirect
372. C₂×#2449	C₄₁	direct (N × H)
389. C₂²×C₄₁	C₂×C₂²⋊Q₈	semidirect
416. C₂²×C₂²⋊Q₈	C₂×C₄₁	semidirect
417. C₂²×C₂²⋊Q₈	C₂×C₄₁	semidirect
419. C₂³×C₄⋊C₄	C₂×C₄₁	semidirect
420. #2449	C₂×C₄₁	direct (N × H)
421. C₂×#399	C₂×C₄₁	semidirect
422. C₂×#398	C₂×C₄₁	semidirect
423. C₂×#396	C₂×C₄₁	semidirect
424. C₂×#395	C₂×C₄₁	semidirect
425. C₂×#389	C₂×C₄₁	semidirect
426. C₂×#387	C₂×C₄₁	semidirect
429. C₂×#385	C₂×C₄₁	semidirect
430. C₂×#385	C₂×C₄₁	semidirect
431. C₂×#385	C₂×C₄₁	semidirect
434. C₂×C₄₁	#2449	direct (N × H)
450. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
451. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
467. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
477. #399	C₂²×C₄₁	semidirect
478. #398	C₂²×C₄₁	semidirect
479. #396	C₂²×C₄₁	semidirect
480. #395	C₂²×C₄₁	semidirect
481. #389	C₂²×C₄₁	semidirect
482. #387	C₂²×C₄₁	semidirect
485. #385	C₂²×C₄₁	semidirect
486. #385	C₂²×C₄₁	semidirect
487. #385	C₂²×C₄₁	semidirect
496. C₄₁	C₂×#2449	direct (N × H)
505. C₂²×D₄	Q₈×C₄₁	semidirect
551. C₂×C₄⋊C₄	D₄×C₄₁	semidirect
614. C₂×D₄	C₂×Q₈×C₄₁	semidirect
694. C₄⋊C₄	C₂×D₄×C₄₁	semidirect
727. C₂³	C₂²⋊Q₈×C₄₁	semidirect
814. C₂²	C₂×C₂²⋊Q₈×C₄₁	semidirect
843. C₂	C₄₁×#2449	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₄₁	2
C₂²×C₄×D₄×C₄₁	2
C₂³×C₄⋊C₄×C₄₁	2
C₄₁×#2449	2
C₂×C₄₁×#399	2
C₂×C₄₁×#398	2
C₂×C₄₁×#396	2
C₂×C₄₁×#395	2
C₂×C₄₁×#389	2
C₂×C₄₁×#387	2
C₂×C₄₁×#386	2
C₂×C₄₁×#385	2
C₂×#2449	41

Subgroups — C2×C41×#2449 #23810852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2449 #23810852