Subgroups — C₄₁×#25378 #23801579

Order 10496.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#496	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2545	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2013	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₁	—	2	1	no	—
28	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#496	—	2	4	no	—
31	C₄₁×#463	—	2	4	no	—
32	C₄₁×#461	—	2	4	no	—
33	C₄₁×#460	—	2	4	no	—
34	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
44	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
46	C₄₁×#396	—	2	1	no	—
47	C₄₁×#396	—	2	1	no	—
48	C₄₁×#391	C₂²	1	1	yes	characteristic
49	C₄₁×#390	—	2	1	no	—
50	C₄₁×#390	C₂²	1	1	yes	characteristic
51	C₄₁×#390	C₂²	1	1	yes	characteristic
52	C₄₁×#390	C₂²	1	1	yes	characteristic
53	C₄₁×#388	—	2	1	no	—
54	C₄₁×#388	—	2	1	no	—
55	C₄₁×#386	—	2	1	no	—
56	C₄₁×#386	—	2	1	no	—
57	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
59	C₄₁×#340	C₂²	1	1	yes	characteristic
60	C₄₁×#340	C₂²	1	1	yes	characteristic
61	C₄₁×#336	C₂²	1	1	yes	characteristic
62	C₄₁×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₄₁	—	2	1	no	—
66	C₂²×D₄×C₄₁	—	2	1	no	—
67	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₁	—	2	1	no	—
71	C₂³×C₄×C₄₁	—	2	1	no	—
72	C₂×SD₁₆×C₄₁	—	2	2	no	—
73	C₂×SD₁₆×C₄₁	—	2	2	no	—
74	C₂×SD₁₆×C₄₁	—	2	2	no	—
75	C₂×SD₁₆×C₄₁	—	2	2	no	—
76	C₂×SD₁₆×C₄₁	—	2	2	no	—
77	C₂×SD₁₆×C₄₁	—	2	2	no	—
78	C₂×SD₁₆×C₄₁	—	2	2	no	—
79	C₂×SD₁₆×C₄₁	—	2	2	no	—
80	C₂×SD₁₆×C₄₁	—	4	1	no	—
81	C₂×SD₁₆×C₄₁	—	4	1	no	—
82	C₂×SD₁₆×C₄₁	—	4	1	no	—
83	C₂×SD₁₆×C₄₁	—	4	1	no	—
84	C₂×D₈×C₄₁	—	2	2	no	—
85	C₂×D₈×C₄₁	—	2	2	no	—
86	C₂×D₈×C₄₁	—	2	2	no	—
87	C₂×D₈×C₄₁	—	2	2	no	—
88	C₂×D₈×C₄₁	—	4	1	no	—
89	C₂×D₈×C₄₁	—	4	1	no	—
90	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
94	C₄⋊Q₈×C₄₁	—	2	2	no	—
95	C₄⋊Q₈×C₄₁	—	4	1	no	—
96	#127×C₄₁	—	2	2	no	—
97	#127×C₄₁	D₄	1	4	yes	—
98	#124×C₄₁	—	2	2	no	—
99	#124×C₄₁	—	2	2	no	—
100	#124×C₄₁	—	2	2	no	—
101	#124×C₄₁	—	4	1	no	—
102	C₄×Q₈×C₄₁	—	2	2	no	—
103	C₄×Q₈×C₄₁	—	2	2	no	—
104	C₄×D₄×C₄₁	—	2	2	no	—
105	C₄×D₄×C₄₁	—	2	2	no	—
106	C₄×D₄×C₄₁	—	4	1	no	—
107	C₄×D₄×C₄₁	—	4	1	no	—
108	C₄×D₄×C₄₁	—	4	4	no	—
109	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
110	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
111	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
112	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
129	C₂×C₄²×C₄₁	—	2	1	no	—
130	C₂×C₄²×C₄₁	—	2	1	no	—
131	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
134	C₄⋊C₈×C₄₁	—	2	2	no	—
135	C₄⋊C₈×C₄₁	—	2	2	no	—
136	C₄⋊C₈×C₄₁	—	2	2	no	—
137	#103×C₄₁	—	2	2	no	—
138	#103×C₄₁	—	2	2	no	—
139	#103×C₄₁	—	4	1	no	—
140	#103×C₄₁	D₄	1	4	yes	complemented
141	#102×C₄₁	—	2	2	no	—
142	#102×C₄₁	—	2	2	no	—
143	#102×C₄₁	—	2	2	no	—
144	#102×C₄₁	—	4	1	no	—
145	#97×C₄₁	—	2	2	no	—
146	#95×C₄₁	—	2	1	no	—
147	#95×C₄₁	—	2	1	no	—
148	#95×C₄₁	—	2	1	no	—
149	#95×C₄₁	D₄	1	1	yes	characteristic
150	#95×C₄₁	D₄	1	1	yes	characteristic
151	C₂⁴×C₄₁	—	2	1	no	—
152	C₂⁴×C₄₁	—	2	1	no	—
153	C₂⁴×C₄₁	—	2	1	no	—
154	C₂×Q₈×C₄₁	—	2	1	no	—
155	C₂×Q₈×C₄₁	—	2	1	no	—
156	C₂×Q₈×C₄₁	—	2	1	no	—
157	C₂×Q₈×C₄₁	—	2	1	no	—
158	C₂×Q₈×C₄₁	—	2	1	no	—
159	C₂×Q₈×C₄₁	—	2	1	no	—
160	C₂×Q₈×C₄₁	—	2	1	no	—
161	C₂×Q₈×C₄₁	—	2	1	no	—
162	C₂×Q₈×C₄₁	—	2	1	no	—
163	C₂×Q₈×C₄₁	—	2	1	no	—
164	C₂×Q₈×C₄₁	—	2	1	no	—
165	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
166	C₂×D₄×C₄₁	—	2	4	no	—
167	C₂×D₄×C₄₁	—	2	4	no	—
168	C₂×D₄×C₄₁	—	2	1	no	—
169	C₂×D₄×C₄₁	—	2	1	no	—
170	C₂×D₄×C₄₁	—	2	1	no	—
171	C₂×D₄×C₄₁	—	2	1	no	—
172	C₂×D₄×C₄₁	—	2	1	no	—
173	C₂×D₄×C₄₁	—	2	1	no	—
174	C₂×D₄×C₄₁	—	2	1	no	—
175	C₂×D₄×C₄₁	—	2	1	no	—
176	C₂×D₄×C₄₁	—	2	1	no	—
177	C₂×D₄×C₄₁	—	2	1	no	—
178	C₂×D₄×C₄₁	—	2	1	no	—
179	C₂×D₄×C₄₁	—	2	1	no	—
180	C₂×D₄×C₄₁	—	2	1	no	—
181	C₂×D₄×C₄₁	—	2	1	no	—
182	C₂×D₄×C₄₁	—	2	1	no	—
183	C₂×D₄×C₄₁	—	2	1	no	—
184	C₂×D₄×C₄₁	—	4	2	no	—
185	C₂×D₄×C₄₁	—	4	2	no	—
186	C₂×D₄×C₄₁	—	8	1	no	—
187	C₂×D₄×C₄₁	—	8	1	no	—
188	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₄₁	—	2	1	no	—
191	C₂²×C₄×C₄₁	—	2	1	no	—
192	C₂²×C₄×C₄₁	—	2	1	no	—
193	C₂²×C₄×C₄₁	—	2	1	no	—
194	C₂²×C₄×C₄₁	—	2	1	no	—
195	C₂²×C₄×C₄₁	—	4	2	no	—
196	C₂²×C₄×C₄₁	—	4	2	no	—
197	C₂²×C₄×C₄₁	—	4	2	no	—
198	C₂²×C₄×C₄₁	—	4	2	no	—
199	C₂²×C₄×C₄₁	—	8	1	no	—
200	C₂²×C₄×C₄₁	—	8	1	no	—
201	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
208	SD₁₆×C₄₁	—	4	4	no	—
209	SD₁₆×C₄₁	—	4	4	no	—
210	SD₁₆×C₄₁	—	4	4	no	—
211	SD₁₆×C₄₁	—	4	4	no	—
212	D₈×C₄₁	—	4	4	no	—
213	D₈×C₄₁	—	4	4	no	—
214	C₂×C₈×C₄₁	—	2	1	no	—
215	C₂×C₈×C₄₁	—	2	1	no	—
216	C₂×C₈×C₄₁	—	2	1	no	—
217	C₂×C₈×C₄₁	—	2	1	no	—
218	C₂×C₈×C₄₁	—	2	1	no	—
219	C₂×C₈×C₄₁	—	2	1	no	—
220	C₂×C₈×C₄₁	—	2	1	no	—
221	C₂×C₈×C₄₁	—	2	1	no	—
222	C₂×C₈×C₄₁	—	2	1	no	—
223	C₂×C₈×C₄₁	—	2	1	no	—
224	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
225	C₂×C₈×C₄₁	#41	1	2	yes	—
226	C₄⋊C₄×C₄₁	—	2	2	no	—
227	C₄⋊C₄×C₄₁	—	2	1	no	—
228	C₄⋊C₄×C₄₁	—	2	1	no	—
229	C₄⋊C₄×C₄₁	—	2	1	no	—
230	C₄⋊C₄×C₄₁	—	2	1	no	—
231	C₄⋊C₄×C₄₁	—	2	1	no	—
232	C₄⋊C₄×C₄₁	—	4	1	no	—
233	C₄⋊C₄×C₄₁	—	4	2	no	—
234	C₄⋊C₄×C₄₁	—	4	2	no	—
235	C₄⋊C₄×C₄₁	—	4	2	no	—
236	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
237	C₂²⋊C₄×C₄₁	—	4	2	no	—
238	C₂²⋊C₄×C₄₁	—	4	2	no	—
239	C₂²⋊C₄×C₄₁	—	4	2	no	—
240	C₂²⋊C₄×C₄₁	—	4	2	no	—
241	C₂²⋊C₄×C₄₁	—	4	2	no	—
242	C₂²⋊C₄×C₄₁	—	4	2	no	—
243	C₂²⋊C₄×C₄₁	—	4	2	no	—
244	C₂²⋊C₄×C₄₁	—	4	2	no	—
245	C₂²⋊C₄×C₄₁	—	4	2	no	—
246	C₂²⋊C₄×C₄₁	—	4	2	no	—
247	C₂²⋊C₄×C₄₁	—	8	1	no	—
248	C₂²⋊C₄×C₄₁	—	8	1	no	—
249	C₄²×C₄₁	—	2	1	no	—
250	C₄²×C₄₁	—	2	1	no	—
251	C₄²×C₄₁	—	2	1	no	—
252	C₄²×C₄₁	—	2	1	no	—
253	C₄²×C₄₁	—	4	2	no	—
254	C₄²×C₄₁	—	4	2	no	—
255	C₄²×C₄₁	C₂×D₄	1	2	yes	—
256	C₄²×C₄₁	#41	1	2	yes	—
257	C₂³×C₄₁	—	2	2	no	—
258	C₂³×C₄₁	—	2	2	no	—
259	C₂³×C₄₁	—	4	1	no	—
260	C₂³×C₄₁	—	4	1	no	—
261	C₂³×C₄₁	—	4	1	no	—
262	C₂³×C₄₁	—	4	1	no	—
263	C₂³×C₄₁	—	4	1	no	—
264	C₂³×C₄₁	—	4	1	no	—
265	C₂³×C₄₁	—	4	1	no	—
266	C₂³×C₄₁	—	4	1	no	—
267	C₂³×C₄₁	—	4	1	no	—
268	C₂³×C₄₁	—	4	1	no	—
269	C₂³×C₄₁	—	4	1	no	—
270	C₂³×C₄₁	—	4	1	no	—
271	C₂³×C₄₁	—	4	1	no	—
272	C₂³×C₄₁	—	4	1	no	—
273	C₂³×C₄₁	—	4	1	no	—
274	C₂³×C₄₁	—	4	1	no	—
275	C₂³×C₄₁	—	4	1	no	—
276	C₂³×C₄₁	—	4	1	no	—
277	C₂³×C₄₁	—	4	1	no	—
278	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
279	Q₈×C₄₁	—	2	2	no	—
280	Q₈×C₄₁	—	2	2	no	—
281	Q₈×C₄₁	—	4	1	no	—
282	Q₈×C₄₁	—	4	1	no	—
283	Q₈×C₄₁	—	4	1	no	—
284	Q₈×C₄₁	—	4	1	no	—
285	Q₈×C₄₁	—	4	1	no	—
286	Q₈×C₄₁	—	4	1	no	—
287	D₄×C₄₁	—	2	2	no	—
288	D₄×C₄₁	—	2	2	no	—
289	D₄×C₄₁	—	2	2	no	—
290	D₄×C₄₁	—	2	2	no	—
291	D₄×C₄₁	—	4	8	no	—
292	D₄×C₄₁	—	4	1	no	—
293	D₄×C₄₁	—	4	1	no	—
294	D₄×C₄₁	—	4	1	no	—
295	D₄×C₄₁	—	4	1	no	—
296	D₄×C₄₁	—	4	1	no	—
297	D₄×C₄₁	—	4	1	no	—
298	D₄×C₄₁	—	4	1	no	—
299	D₄×C₄₁	—	4	1	no	—
300	D₄×C₄₁	—	8	4	no	—
301	C₂×C₄×C₄₁	—	2	1	no	—
302	C₂×C₄×C₄₁	—	2	1	no	—
303	C₂×C₄×C₄₁	—	2	1	no	—
304	C₂×C₄×C₄₁	—	2	1	no	—
305	C₂×C₄×C₄₁	—	2	1	no	—
306	C₂×C₄×C₄₁	—	2	1	no	—
307	C₂×C₄×C₄₁	—	2	1	no	—
308	C₂×C₄×C₄₁	—	2	1	no	—
309	C₂×C₄×C₄₁	—	2	1	no	—
310	C₂×C₄×C₄₁	—	2	2	no	—
311	C₂×C₄×C₄₁	—	2	2	no	—
312	C₂×C₄×C₄₁	—	2	1	no	—
313	C₂×C₄×C₄₁	—	2	1	no	—
314	C₂×C₄×C₄₁	—	2	1	no	—
315	C₂×C₄×C₄₁	—	2	1	no	—
316	C₂×C₄×C₄₁	—	2	1	no	—
317	C₂×C₄×C₄₁	—	2	1	no	—
318	C₂×C₄×C₄₁	—	4	1	no	—
319	C₂×C₄×C₄₁	—	4	1	no	—
320	C₂×C₄×C₄₁	—	4	1	no	—
321	C₂×C₄×C₄₁	—	4	1	no	—
322	C₂×C₄×C₄₁	—	4	1	no	—
323	C₂×C₄×C₄₁	—	4	1	no	—
324	C₂×C₄×C₄₁	—	4	1	no	—
325	C₂×C₄×C₄₁	—	4	1	no	—
326	C₂×C₄×C₄₁	—	4	1	no	—
327	C₂×C₄×C₄₁	—	4	1	no	—
328	C₂×C₄×C₄₁	—	4	1	no	—
329	C₂×C₄×C₄₁	—	4	1	no	—
330	C₂×C₄×C₄₁	—	4	1	no	—
331	C₂×C₄×C₄₁	—	8	4	no	—
332	C₂×C₄×C₄₁	—	8	4	no	—
333	C₂×C₄×C₄₁	#121	1	2	yes	—
334	C₂×C₄×C₄₁	#121	1	2	yes	—
335	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
336	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
341	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
342	C₈×C₄₁	—	2	2	no	—
343	C₈×C₄₁	—	2	2	no	—
344	C₈×C₄₁	—	4	1	no	—
345	C₈×C₄₁	—	4	1	no	—
346	#25378	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
347	C₂²×C₄₁	—	4	2	no	—
348	C₂²×C₄₁	—	4	2	no	—
349	C₂²×C₄₁	—	4	2	no	—
350	C₂²×C₄₁	—	4	2	no	—
351	C₂²×C₄₁	—	4	2	no	—
352	C₂²×C₄₁	—	4	2	no	—
353	C₂²×C₄₁	—	8	1	no	—
354	C₂²×C₄₁	—	8	1	no	—
355	C₂²×C₄₁	—	8	1	no	—
356	C₂²×C₄₁	—	8	1	no	—
357	C₂²×C₄₁	—	8	1	no	—
358	C₂²×C₄₁	—	8	1	no	—
359	C₂²×C₄₁	—	8	1	no	—
360	C₂²×C₄₁	—	8	1	no	—
361	C₂²×C₄₁	—	8	1	no	—
362	C₂²×C₄₁	—	8	1	no	—
363	C₂²×C₄₁	—	8	1	no	—
364	C₂²×C₄₁	—	8	1	no	—
365	C₂²×C₄₁	—	8	1	no	—
366	C₂²×C₄₁	—	8	1	no	—
367	C₂²×C₄₁	—	8	1	no	—
368	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
369	C₂²×C₄₁	D₄²	1	1	yes	characteristic
370	C₂²×C₄₁	#550	1	1	yes	characteristic
371	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
372	C₂²×C₄₁	#575	1	1	yes	characteristic
373	C₂²×C₄₁	#577	1	1	yes	characteristic
374	C₂²×C₄₁	#577	1	1	yes	characteristic
375	C₄×C₄₁	—	2	2	no	—
376	C₄×C₄₁	—	2	2	no	—
377	C₄×C₄₁	—	2	2	no	—
378	C₄×C₄₁	—	4	2	no	—
379	C₄×C₄₁	—	4	1	no	—
380	C₄×C₄₁	—	4	2	no	—
381	C₄×C₄₁	—	4	1	no	—
382	C₄×C₄₁	—	4	1	no	—
383	C₄×C₄₁	—	8	1	no	—
384	C₄×C₄₁	—	8	1	no	—
385	C₄×C₄₁	—	8	1	no	—
386	C₄×C₄₁	#532	1	1	yes	characteristic
387	C₄×C₄₁	#540	1	1	yes	characteristic
388	C₄×C₄₁	D₄²	1	1	yes	characteristic
389	C₄×C₄₁	#546	1	1	yes	characteristic
390	C₂×#496	C₂×C₄₁	1	1	yes	characteristic
391	C₂×#460	C₂×C₄₁	1	1	yes	characteristic, complemented
392	C₂×#463	C₂×C₄₁	1	1	yes	characteristic, complemented
393	C₂×#461	C₂×C₄₁	1	1	yes	characteristic, complemented
394	#2545	C₂×C₄₁	1	1	yes	characteristic, complemented
395	#2366	C₂×C₄₁	1	1	yes	characteristic, complemented
396	#2055	C₂×C₄₁	1	1	yes	characteristic, complemented
397	#2054	C₂×C₄₁	1	1	yes	characteristic, complemented
398	#2013	C₂×C₄₁	1	1	yes	characteristic, complemented
399	#2012	C₂×C₄₁	1	1	yes	characteristic, complemented
400	#1983	C₂×C₄₁	1	1	yes	characteristic, complemented
401	#1940	C₂×C₄₁	1	1	yes	characteristic, complemented
402	#1879	C₂×C₄₁	1	1	yes	characteristic, complemented
403	#1877	C₂×C₄₁	1	1	yes	characteristic, complemented
404	#1763	C₂×C₄₁	1	1	yes	characteristic, complemented
405	C₂×C₄₁	—	8	2	no	—
406	C₂×C₄₁	—	8	2	no	—
407	C₂×C₄₁	—	16	1	no	—
408	C₂×C₄₁	#2428	1	1	yes	characteristic
409	C₂×C₄₁	#3036	1	1	yes	characteristic
410	C₂×C₄₁	#3042	1	1	yes	characteristic
411	C₂×C₄₁	#3265	1	1	yes	characteristic
412	C₂×C₄₁	#3271	1	1	yes	characteristic
413	C₂×C₄₁	#3397	1	1	yes	characteristic
414	C₂×C₄₁	#3401	1	1	yes	characteristic
415	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
416	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
417	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
418	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
419	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
420	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
421	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
422	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
423	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
424	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
425	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
426	C₂×C₄×D₄	—	2	1	no	—
427	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
429	#496	—	2	4	no	—
430	#463	—	2	4	no	—
431	#461	—	2	4	no	—
432	#460	—	2	4	no	—
433	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
434	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
435	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
436	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
437	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
438	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
439	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
440	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
441	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
442	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
443	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
444	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
445	#396	—	2	1	no	—
446	#396	—	2	1	no	—
447	#391	C₂²×C₄₁	1	1	yes	characteristic
448	#390	—	2	1	no	—
449	#390	C₂²×C₄₁	1	1	yes	characteristic
450	#390	C₂²×C₄₁	1	1	yes	characteristic
451	#390	C₂²×C₄₁	1	1	yes	characteristic
452	#388	—	2	1	no	—
453	#388	—	2	1	no	—
454	#386	—	2	1	no	—
455	#386	—	2	1	no	—
456	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
458	#340	C₂²×C₄₁	1	1	yes	characteristic
459	#340	C₂²×C₄₁	1	1	yes	characteristic
460	#336	C₂²×C₄₁	1	1	yes	characteristic
461	#336	C₂²×C₄₁	1	1	yes	characteristic
462	C₄₁	#25378	1	1	yes	characteristic, direct product factor, Sylow
463	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
464	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	C₂×SD₁₆	—	2	2	no	—
473	C₂×SD₁₆	—	2	2	no	—
474	C₂×SD₁₆	—	2	2	no	—
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	2	2	no	—
477	C₂×SD₁₆	—	2	2	no	—
478	C₂×SD₁₆	—	2	2	no	—
479	C₂×SD₁₆	—	2	2	no	—
480	C₂×SD₁₆	—	4	1	no	—
481	C₂×SD₁₆	—	4	1	no	—
482	C₂×SD₁₆	—	4	1	no	—
483	C₂×SD₁₆	—	4	1	no	—
484	C₂×D₈	—	2	2	no	—
485	C₂×D₈	—	2	2	no	—
486	C₂×D₈	—	2	2	no	—
487	C₂×D₈	—	2	2	no	—
488	C₂×D₈	—	4	1	no	—
489	C₂×D₈	—	4	1	no	—
490	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	—	4	1	no	—
496	#127	—	2	2	no	—
497	#127	D₄×C₄₁	1	4	yes	—
498	#124	—	2	2	no	—
499	#124	—	2	2	no	—
500	#124	—	2	2	no	—
501	#124	—	4	1	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	4	1	no	—
507	C₄×D₄	—	4	1	no	—
508	C₄×D₄	—	4	4	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
513	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
534	C₄⋊C₈	—	2	2	no	—
535	C₄⋊C₈	—	2	2	no	—
536	C₄⋊C₈	—	2	2	no	—
537	#103	—	2	2	no	—
538	#103	—	2	2	no	—
539	#103	—	4	1	no	—
540	#103	D₄×C₄₁	1	4	yes	complemented
541	#102	—	2	2	no	—
542	#102	—	2	2	no	—
543	#102	—	2	2	no	—
544	#102	—	4	1	no	—
545	#97	—	2	2	no	—
546	#95	—	2	1	no	—
547	#95	—	2	1	no	—
548	#95	—	2	1	no	—
549	#95	D₄×C₄₁	1	1	yes	characteristic
550	#95	D₄×C₄₁	1	1	yes	characteristic
551	C₂⁴	—	2	1	no	—
552	C₂⁴	—	2	1	no	—
553	C₂⁴	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	8	1	no	—
587	C₂×D₄	—	8	1	no	—
588	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
589	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	8	1	no	—
600	C₂²×C₄	—	8	1	no	—
601	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
608	SD₁₆	—	4	4	no	—
609	SD₁₆	—	4	4	no	—
610	SD₁₆	—	4	4	no	—
611	SD₁₆	—	4	4	no	—
612	D₈	—	4	4	no	—
613	D₈	—	4	4	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
625	C₂×C₈	#41×C₄₁	1	2	yes	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	4	1	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	8	1	no	—
648	C₂²⋊C₄	—	8	1	no	—
649	C₄²	—	2	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	4	2	no	—
654	C₄²	—	4	2	no	—
655	C₄²	C₂×D₄×C₄₁	1	2	yes	—
656	C₄²	#41×C₄₁	1	2	yes	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
679	Q₈	—	2	2	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	4	1	no	—
682	Q₈	—	4	1	no	—
683	Q₈	—	4	1	no	—
684	Q₈	—	4	1	no	—
685	Q₈	—	4	1	no	—
686	Q₈	—	4	1	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	4	8	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	1	no	—
700	D₄	—	8	4	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	8	4	no	—
732	C₂×C₄	—	8	4	no	—
733	C₂×C₄	#121×C₄₁	1	2	yes	—
734	C₂×C₄	#121×C₄₁	1	2	yes	—
735	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
738	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
739	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
740	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
741	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
742	C₈	—	2	2	no	—
743	C₈	—	2	2	no	—
744	C₈	—	4	1	no	—
745	C₈	—	4	1	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	—	4	2	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
768	C₂²	D₄²×C₄₁	1	1	yes	characteristic
769	C₂²	C₄₁×#550	1	1	yes	characteristic
770	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
771	C₂²	C₄₁×#575	1	1	yes	characteristic
772	C₂²	C₄₁×#577	1	1	yes	characteristic
773	C₂²	C₄₁×#577	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	—	8	1	no	—
783	C₄	—	8	1	no	—
784	C₄	—	8	1	no	—
785	C₄	C₄₁×#532	1	1	yes	characteristic
786	C₄	C₄₁×#540	1	1	yes	characteristic
787	C₄	D₄²×C₄₁	1	1	yes	characteristic
788	C₄	C₄₁×#546	1	1	yes	characteristic
789	C₂	—	8	2	no	—
790	C₂	—	8	2	no	—
791	C₂	—	16	1	no	—
792	C₂	C₄₁×#2428	1	1	yes	characteristic
793	C₂	C₄₁×#3036	1	1	yes	characteristic
794	C₂	C₄₁×#3042	1	1	yes	characteristic
795	C₂	C₄₁×#3265	1	1	yes	characteristic
796	C₂	C₄₁×#3271	1	1	yes	characteristic
797	C₂	C₄₁×#3397	1	1	yes	characteristic
798	C₂	C₄₁×#3401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#496	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#460	C₂	semidirect
3. C₂×C₄₁×#463	C₂	semidirect
4. C₂×C₄₁×#461	C₂	semidirect
5. C₄₁×#2545	C₂	semidirect
6. C₄₁×#2366	C₂	semidirect
7. C₄₁×#2055	C₂	semidirect
8. C₄₁×#2054	C₂	semidirect
9. C₄₁×#2013	C₂	semidirect
10. C₄₁×#2012	C₂	semidirect
11. C₄₁×#1983	C₂	semidirect
12. C₄₁×#1940	C₂	semidirect
13. C₄₁×#1879	C₂	semidirect
14. C₄₁×#1877	C₂	semidirect
15. C₄₁×#1763	C₂	semidirect
140. #103×C₄₁	D₄	semidirect
346. #25378	C₄₁	direct (N × H)
391. C₂×#460	C₂×C₄₁	semidirect
392. C₂×#463	C₂×C₄₁	semidirect
393. C₂×#461	C₂×C₄₁	semidirect
394. #2545	C₂×C₄₁	semidirect
395. #2366	C₂×C₄₁	semidirect
396. #2055	C₂×C₄₁	semidirect
397. #2054	C₂×C₄₁	semidirect
398. #2013	C₂×C₄₁	semidirect
399. #2012	C₂×C₄₁	semidirect
400. #1983	C₂×C₄₁	semidirect
401. #1940	C₂×C₄₁	semidirect
402. #1879	C₂×C₄₁	semidirect
403. #1877	C₂×C₄₁	semidirect
404. #1763	C₂×C₄₁	semidirect
462. C₄₁	#25378	direct (N × H)
540. #103	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#496	2
C₂×C₄₁×#460	2
C₂×C₄₁×#463	2
C₂×C₄₁×#461	2
C₄₁×#2545	2
C₄₁×#2366	2
C₄₁×#2055	2
C₄₁×#2054	2
C₄₁×#2013	2
C₄₁×#2012	2
C₄₁×#1983	2
C₄₁×#1940	2
C₄₁×#1879	2
C₄₁×#1877	2
C₄₁×#1763	2
#25378	41

Subgroups — C41×#25378 #23801579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25378 #23801579