Subgroups — C₄₁×#34466 #23810667

Order 10496.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#553	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2377	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2376	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2373	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2363	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2352	C₂	1	2	yes	maximal, complemented
10	D₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#2346	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#2344	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#2334	C₂	1	2	yes	maximal, complemented
14	C₄₁×#2330	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#2324	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2322	C₂	1	2	yes	maximal, complemented
18	C₄₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2319	C₂	1	2	yes	maximal, complemented
20	C₄₁×#2316	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄₁×#553	C₄	1	16	yes	complemented
25	C₂×#126×C₄₁	C₂²	1	2	yes	—
26	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#123×C₄₁	C₂²	1	2	yes	—
28	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#121×C₄₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
37	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#117×C₄₁	C₂²	1	2	yes	—
41	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
45	C₄₁×#390	C₂²	1	1	yes	characteristic
46	C₄₁×#390	C₂²	1	2	yes	—
47	C₄₁×#390	C₂²	1	1	yes	characteristic
48	C₄₁×#390	C₂²	1	2	yes	—
49	C₄₁×#390	C₂²	1	2	yes	—
50	C₄₁×#390	C₂²	1	2	yes	—
51	C₄₁×#389	C₂²	1	1	yes	characteristic
52	C₄₁×#389	C₂²	1	1	yes	characteristic
53	C₄₁×#389	C₂²	1	1	yes	characteristic
54	C₄₁×#389	C₂²	1	1	yes	characteristic
55	C₄₁×#389	C₂²	1	1	yes	characteristic
56	C₄₁×#389	C₂²	1	2	yes	—
57	C₄₁×#389	C₂²	1	1	yes	characteristic
58	C₄₁×#389	C₂²	1	1	yes	characteristic
59	C₄₁×#389	C₂²	1	2	yes	—
60	C₄₁×#389	C₂²	1	2	yes	—
61	C₄₁×#389	C₂²	1	1	yes	characteristic
62	C₄₁×#389	C₂²	1	2	yes	—
63	C₄₁×#389	C₂²	1	2	yes	—
64	C₄₁×#388	C₂²	1	1	yes	characteristic
65	C₄₁×#388	C₂²	1	1	yes	characteristic
66	C₄₁×#388	C₂²	1	2	yes	—
67	C₄₁×#388	C₂²	1	2	yes	—
68	C₄₁×#388	C₂²	1	2	yes	—
69	C₄₁×#388	C₂²	1	2	yes	—
70	C₄₁×#388	C₂²	1	2	yes	—
71	C₄₁×#388	C₂²	1	2	yes	—
72	C₄₁×#388	C₂²	1	2	yes	—
73	C₄₁×#388	C₂²	1	2	yes	—
74	C₄₁×#388	C₂²	1	2	yes	—
75	C₄₁×#388	C₂²	1	2	yes	—
76	C₄₁×#387	C₂²	1	1	yes	characteristic
77	C₄₁×#387	C₂²	1	1	yes	characteristic
78	C₄₁×#387	C₂²	1	2	yes	—
79	C₄₁×#387	C₂²	1	2	yes	—
80	C₄₁×#387	C₂²	1	2	yes	—
81	C₄₁×#387	C₂²	1	2	yes	—
82	C₄₁×#387	C₂²	1	2	yes	—
83	C₄₁×#387	C₂²	1	2	yes	—
84	C₄₁×#386	C₂²	1	1	yes	characteristic
85	C₄₁×#386	C₂²	1	1	yes	characteristic
86	C₄₁×#386	C₂²	1	2	yes	—
87	C₄₁×#386	C₂²	1	2	yes	—
88	C₄₁×#386	C₂²	1	2	yes	—
89	C₄₁×#386	C₂²	1	2	yes	—
90	C₄₁×#385	C₂²	1	1	yes	characteristic
91	C₄₁×#385	C₂²	1	1	yes	characteristic
92	C₄₁×#385	C₂²	1	2	yes	—
93	C₄₁×#385	C₂²	1	2	yes	—
94	C₄₁×#385	C₂²	1	2	yes	—
95	C₄₁×#385	C₂²	1	2	yes	—
96	C₄₁×#385	C₂²	1	2	yes	—
97	C₄₁×#384	C₂²	1	1	yes	characteristic
98	C₄₁×#382	C₂²	1	2	yes	—
99	C₄₁×#381	C₂²	1	2	yes	—
100	C₄₁×#381	C₂²	1	2	yes	—
101	C₄₁×#380	C₂²	1	1	yes	characteristic
102	C₄₁×#380	C₂²	1	2	yes	—
103	C₄₁×#380	C₂²	1	2	yes	—
104	C₄₁×#380	C₂²	1	2	yes	—
105	C₄₁×#380	C₂²	1	2	yes	—
106	C₄₁×#380	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
122	C₄₁×#376	C₂²	1	1	yes	characteristic
123	C₄₁×#376	C₂²	1	2	yes	—
124	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
134	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
135	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
136	#126×C₄₁	C₂×C₄	1	16	yes	complemented
137	#125×C₄₁	C₂×C₄	1	8	yes	complemented
138	#123×C₄₁	C₂×C₄	1	16	yes	complemented
139	#121×C₄₁	C₂×C₄	1	8	yes	—
140	#121×C₄₁	C₂×C₄	1	16	yes	complemented
141	#121×C₄₁	C₂×C₄	1	8	yes	complemented
142	C₄×D₄×C₄₁	—	4	2	no	—
143	C₄×D₄×C₄₁	—	4	2	no	—
144	C₄×D₄×C₄₁	—	4	4	no	—
145	C₄×D₄×C₄₁	C₂×C₄	1	16	yes	complemented
146	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
147	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
148	#117×C₄₁	—	4	2	no	—
149	#117×C₄₁	—	4	4	no	—
150	#117×C₄₁	—	4	2	no	—
151	#117×C₄₁	—	4	2	no	—
152	#117×C₄₁	C₂×C₄	1	8	yes	complemented
153	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
154	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	8	yes	complemented
155	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₄₁	—	4	2	no	—
203	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
206	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
211	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
212	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
213	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
214	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
215	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
216	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
218	#95×C₄₁	C₂³	1	1	yes	characteristic
219	#95×C₄₁	C₂³	1	2	yes	—
220	#95×C₄₁	C₂³	1	1	yes	characteristic
221	#95×C₄₁	C₂³	1	2	yes	—
222	#95×C₄₁	C₂³	1	1	yes	characteristic
223	#95×C₄₁	C₂³	1	2	yes	—
224	#95×C₄₁	C₂³	1	1	yes	characteristic
225	#95×C₄₁	C₂³	1	1	yes	characteristic
226	#95×C₄₁	C₂³	1	1	yes	characteristic
227	#95×C₄₁	C₂³	1	1	yes	characteristic
228	#95×C₄₁	C₂³	1	2	yes	—
229	#95×C₄₁	C₂³	1	2	yes	—
230	#95×C₄₁	C₂³	1	2	yes	—
231	#95×C₄₁	C₂³	1	1	yes	characteristic
232	#95×C₄₁	C₂³	1	1	yes	characteristic
233	#95×C₄₁	C₂³	1	2	yes	—
234	#95×C₄₁	C₂³	1	2	yes	—
235	#95×C₄₁	C₂³	1	2	yes	—
236	#95×C₄₁	C₂³	1	2	yes	—
237	#95×C₄₁	C₂³	1	2	yes	—
238	#95×C₄₁	C₂³	1	2	yes	—
239	#95×C₄₁	C₂³	1	2	yes	—
240	#95×C₄₁	C₂³	1	2	yes	—
241	#95×C₄₁	C₂³	1	1	yes	characteristic
242	#95×C₄₁	C₂³	1	2	yes	—
243	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
246	C₂×D₄×C₄₁	—	2	2	no	—
247	C₂×D₄×C₄₁	—	2	2	no	—
248	C₂×D₄×C₄₁	—	4	2	no	—
249	C₂×D₄×C₄₁	—	4	1	no	—
250	C₂×D₄×C₄₁	—	4	2	no	—
251	C₂×D₄×C₄₁	—	4	2	no	—
252	C₂×D₄×C₄₁	—	4	1	no	—
253	C₂×D₄×C₄₁	—	4	2	no	—
254	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
255	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
256	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
257	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
258	C₂²×C₄×C₄₁	—	2	2	no	—
259	C₂²×C₄×C₄₁	—	2	2	no	—
260	C₂²×C₄×C₄₁	—	2	2	no	—
261	C₂²×C₄×C₄₁	—	2	2	no	—
262	C₂²×C₄×C₄₁	—	2	2	no	—
263	C₂²×C₄×C₄₁	—	2	4	no	—
264	C₂²×C₄×C₄₁	—	4	1	no	—
265	C₂²×C₄×C₄₁	—	4	1	no	—
266	C₂²×C₄×C₄₁	—	4	2	no	—
267	C₂²×C₄×C₄₁	—	4	2	no	—
268	C₂²×C₄×C₄₁	—	4	2	no	—
269	C₂²×C₄×C₄₁	—	4	2	no	—
270	C₂²×C₄×C₄₁	—	4	1	no	—
271	C₂²×C₄×C₄₁	—	4	1	no	—
272	C₂²×C₄×C₄₁	—	4	1	no	—
273	C₂²×C₄×C₄₁	—	4	2	no	—
274	C₂²×C₄×C₄₁	—	4	2	no	—
275	C₂²×C₄×C₄₁	—	4	2	no	—
276	C₂²×C₄×C₄₁	—	4	2	no	—
277	C₂²×C₄×C₄₁	—	4	2	no	—
278	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
279	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
280	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
281	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
282	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₄₁	—	2	2	no	—
303	C₄⋊C₄×C₄₁	—	2	4	no	—
304	C₄⋊C₄×C₄₁	—	2	2	no	—
305	C₄⋊C₄×C₄₁	—	2	2	no	—
306	C₄⋊C₄×C₄₁	—	2	2	no	—
307	C₄⋊C₄×C₄₁	—	2	2	no	—
308	C₄⋊C₄×C₄₁	—	4	2	no	—
309	C₄⋊C₄×C₄₁	—	4	2	no	—
310	C₄⋊C₄×C₄₁	—	4	2	no	—
311	C₄⋊C₄×C₄₁	—	4	2	no	—
312	C₄⋊C₄×C₄₁	—	4	2	no	—
313	C₄⋊C₄×C₄₁	—	4	2	no	—
314	C₄⋊C₄×C₄₁	—	4	1	no	—
315	C₄⋊C₄×C₄₁	—	4	2	no	—
316	C₄⋊C₄×C₄₁	—	4	1	no	—
317	C₄⋊C₄×C₄₁	—	4	1	no	—
318	C₄⋊C₄×C₄₁	—	4	2	no	—
319	C₄⋊C₄×C₄₁	—	4	2	no	—
320	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
321	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
322	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
323	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
324	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
325	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
326	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
327	C₂²⋊C₄×C₄₁	—	2	2	no	—
328	C₂²⋊C₄×C₄₁	—	4	1	no	—
329	C₂²⋊C₄×C₄₁	—	4	2	no	—
330	C₂²⋊C₄×C₄₁	—	4	1	no	—
331	C₂²⋊C₄×C₄₁	—	4	2	no	—
332	C₂²⋊C₄×C₄₁	—	4	2	no	—
333	C₂²⋊C₄×C₄₁	—	4	1	no	—
334	C₂²⋊C₄×C₄₁	—	4	1	no	—
335	C₂²⋊C₄×C₄₁	—	4	1	no	—
336	C₂²⋊C₄×C₄₁	—	4	2	no	—
337	C₂²⋊C₄×C₄₁	—	4	2	no	—
338	C₂²⋊C₄×C₄₁	—	4	2	no	—
339	C₂²⋊C₄×C₄₁	—	4	2	no	—
340	C₂²⋊C₄×C₄₁	—	4	2	no	—
341	C₂²⋊C₄×C₄₁	—	4	2	no	—
342	C₂²⋊C₄×C₄₁	—	4	2	no	—
343	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
344	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
345	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
346	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
347	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
348	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
349	C₄²×C₄₁	—	2	2	no	—
350	C₄²×C₄₁	—	2	2	no	—
351	C₄²×C₄₁	—	2	4	no	—
352	C₄²×C₄₁	—	2	2	no	—
353	C₄²×C₄₁	—	2	2	no	—
354	C₄²×C₄₁	—	4	1	no	—
355	C₄²×C₄₁	—	4	1	no	—
356	C₄²×C₄₁	—	4	2	no	—
357	C₄²×C₄₁	—	4	2	no	—
358	C₄²×C₄₁	—	4	2	no	—
359	C₄²×C₄₁	—	4	2	no	—
360	C₄²×C₄₁	—	4	2	no	—
361	C₄²×C₄₁	—	4	2	no	—
362	C₄²×C₄₁	C₂²×C₄	1	8	yes	—
363	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
364	C₂³×C₄₁	—	2	1	no	—
365	C₂³×C₄₁	—	2	1	no	—
366	C₂³×C₄₁	—	2	1	no	—
367	C₂³×C₄₁	—	2	1	no	—
368	C₂³×C₄₁	—	2	2	no	—
369	C₂³×C₄₁	—	2	2	no	—
370	C₂³×C₄₁	—	2	1	no	—
371	C₂³×C₄₁	—	2	1	no	—
372	C₂³×C₄₁	—	2	2	no	—
373	C₂³×C₄₁	—	2	2	no	—
374	C₂³×C₄₁	—	2	1	no	—
375	C₂³×C₄₁	—	2	1	no	—
376	C₂³×C₄₁	—	2	1	no	—
377	C₂³×C₄₁	—	2	2	no	—
378	C₂³×C₄₁	—	2	2	no	—
379	C₂³×C₄₁	—	2	1	no	—
380	C₂³×C₄₁	—	2	1	no	—
381	C₂³×C₄₁	—	2	1	no	—
382	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
383	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
384	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
385	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
386	D₄×C₄₁	—	2	8	no	—
387	D₄×C₄₁	—	4	4	no	—
388	D₄×C₄₁	—	4	8	no	—
389	D₄×C₄₁	—	4	8	no	—
390	C₂×C₄×C₄₁	—	2	2	no	—
391	C₂×C₄×C₄₁	—	2	1	no	—
392	C₂×C₄×C₄₁	—	2	1	no	—
393	C₂×C₄×C₄₁	—	2	1	no	—
394	C₂×C₄×C₄₁	—	2	1	no	—
395	C₂×C₄×C₄₁	—	2	2	no	—
396	C₂×C₄×C₄₁	—	2	1	no	—
397	C₂×C₄×C₄₁	—	2	1	no	—
398	C₂×C₄×C₄₁	—	2	1	no	—
399	C₂×C₄×C₄₁	—	2	2	no	—
400	C₂×C₄×C₄₁	—	2	2	no	—
401	C₂×C₄×C₄₁	—	2	1	no	—
402	C₂×C₄×C₄₁	—	2	2	no	—
403	C₂×C₄×C₄₁	—	2	1	no	—
404	C₂×C₄×C₄₁	—	2	2	no	—
405	C₂×C₄×C₄₁	—	2	1	no	—
406	C₂×C₄×C₄₁	—	2	8	no	—
407	C₂×C₄×C₄₁	—	2	8	no	—
408	C₂×C₄×C₄₁	—	2	1	no	—
409	C₂×C₄×C₄₁	—	2	1	no	—
410	C₂×C₄×C₄₁	—	2	1	no	—
411	C₂×C₄×C₄₁	—	2	1	no	—
412	C₂×C₄×C₄₁	—	2	2	no	—
413	C₂×C₄×C₄₁	—	2	1	no	—
414	C₂×C₄×C₄₁	—	2	1	no	—
415	C₂×C₄×C₄₁	—	2	2	no	—
416	C₂×C₄×C₄₁	—	2	2	no	—
417	C₂×C₄×C₄₁	—	2	2	no	—
418	C₂×C₄×C₄₁	—	2	2	no	—
419	C₂×C₄×C₄₁	—	2	1	no	—
420	C₂×C₄×C₄₁	—	2	2	no	—
421	C₂×C₄×C₄₁	—	2	1	no	—
422	C₂×C₄×C₄₁	—	2	1	no	—
423	C₂×C₄×C₄₁	—	2	1	no	—
424	C₂×C₄×C₄₁	—	2	2	no	—
425	C₂×C₄×C₄₁	—	2	1	no	—
426	C₂×C₄×C₄₁	—	2	2	no	—
427	C₂×C₄×C₄₁	—	2	1	no	—
428	C₂×C₄×C₄₁	—	2	2	no	—
429	C₂×C₄×C₄₁	—	2	2	no	—
430	C₂×C₄×C₄₁	—	2	1	no	—
431	C₂×C₄×C₄₁	—	2	1	no	—
432	C₂×C₄×C₄₁	—	2	1	no	—
433	C₂×C₄×C₄₁	—	2	2	no	—
434	C₂×C₄×C₄₁	—	2	1	no	—
435	C₂×C₄×C₄₁	—	2	1	no	—
436	C₂×C₄×C₄₁	—	2	1	no	—
437	C₂×C₄×C₄₁	—	2	1	no	—
438	C₂×C₄×C₄₁	—	2	1	no	—
439	C₂×C₄×C₄₁	—	2	1	no	—
440	C₂×C₄×C₄₁	—	2	2	no	—
441	C₂×C₄×C₄₁	—	4	8	no	—
442	C₂×C₄×C₄₁	—	4	8	no	—
443	C₂×C₄×C₄₁	—	4	4	no	—
444	C₂×C₄×C₄₁	—	4	4	no	—
445	C₂×C₄×C₄₁	—	8	4	no	—
446	C₂×C₄×C₄₁	—	8	4	no	—
447	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
448	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
449	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
450	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
451	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
452	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
453	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
454	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
455	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
456	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
457	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
458	#34466	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂²×C₄₁	—	2	2	no	—
460	C₂²×C₄₁	—	2	2	no	—
461	C₂²×C₄₁	—	2	4	no	—
462	C₂²×C₄₁	—	2	2	no	—
463	C₂²×C₄₁	—	2	4	no	—
464	C₂²×C₄₁	—	2	2	no	—
465	C₂²×C₄₁	—	2	2	no	—
466	C₂²×C₄₁	—	2	4	no	—
467	C₂²×C₄₁	—	2	2	no	—
468	C₂²×C₄₁	—	4	1	no	—
469	C₂²×C₄₁	—	4	1	no	—
470	C₂²×C₄₁	—	4	2	no	—
471	C₂²×C₄₁	—	4	1	no	—
472	C₂²×C₄₁	—	4	2	no	—
473	C₂²×C₄₁	—	4	1	no	—
474	C₂²×C₄₁	—	4	1	no	—
475	C₂²×C₄₁	—	4	1	no	—
476	C₂²×C₄₁	—	4	2	no	—
477	C₂²×C₄₁	—	4	1	no	—
478	C₂²×C₄₁	—	4	1	no	—
479	C₂²×C₄₁	—	4	2	no	—
480	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
481	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂²×C₄₁	#585	1	1	yes	characteristic
485	C₂²×C₄₁	#585	1	1	yes	characteristic
486	C₂²×C₄₁	#585	1	1	yes	characteristic
487	C₄×C₄₁	—	2	2	no	—
488	C₄×C₄₁	—	2	2	no	—
489	C₄×C₄₁	—	2	2	no	—
490	C₄×C₄₁	—	2	4	no	—
491	C₄×C₄₁	—	2	2	no	—
492	C₄×C₄₁	—	2	4	no	—
493	C₄×C₄₁	—	2	4	no	—
494	C₄×C₄₁	—	2	2	no	—
495	C₄×C₄₁	—	4	1	no	—
496	C₄×C₄₁	—	4	2	no	—
497	C₄×C₄₁	—	4	1	no	—
498	C₄×C₄₁	—	4	1	no	—
499	C₄×C₄₁	—	4	1	no	—
500	C₄×C₄₁	—	4	2	no	—
501	C₄×C₄₁	—	4	2	no	—
502	C₄×C₄₁	—	4	1	no	—
503	C₄×C₄₁	—	4	2	no	—
504	C₄×C₄₁	—	4	1	no	—
505	C₄×C₄₁	—	4	1	no	—
506	C₄×C₄₁	#520	1	4	yes	—
507	C₂×#553	C₂×C₄₁	1	1	yes	characteristic
508	#2377	C₂×C₄₁	1	2	yes	complemented
509	#2376	C₂×C₄₁	1	2	yes	complemented
510	#2373	C₂×C₄₁	1	2	yes	complemented
511	#2370	C₂×C₄₁	1	1	yes	characteristic, complemented
512	#2363	C₂×C₄₁	1	1	yes	characteristic, complemented
513	#2363	C₂×C₄₁	1	1	yes	characteristic, complemented
514	#2354	C₂×C₄₁	1	1	yes	characteristic, complemented
515	#2352	C₂×C₄₁	1	2	yes	complemented
516	D₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
517	#2346	C₂×C₄₁	1	1	yes	characteristic, complemented
518	#2344	C₂×C₄₁	1	1	yes	characteristic, complemented
519	#2334	C₂×C₄₁	1	2	yes	complemented
520	#2330	C₂×C₄₁	1	1	yes	characteristic, complemented
521	#2324	C₂×C₄₁	1	1	yes	characteristic, complemented
522	#2324	C₂×C₄₁	1	2	yes	complemented
523	#2322	C₂×C₄₁	1	2	yes	complemented
524	#2319	C₂×C₄₁	1	1	yes	characteristic, complemented
525	#2319	C₂×C₄₁	1	2	yes	complemented
526	#2316	C₂×C₄₁	1	1	yes	characteristic, complemented
527	C₄×#121	C₂×C₄₁	1	1	yes	characteristic, complemented
528	#2296	C₂×C₄₁	1	1	yes	characteristic, complemented
529	#2290	C₂×C₄₁	1	1	yes	characteristic, complemented
530	C₂×C₄₁	—	4	2	no	—
531	C₂×C₄₁	—	4	2	no	—
532	C₂×C₄₁	—	4	4	no	—
533	C₂×C₄₁	C₂×#520	1	1	yes	characteristic
534	C₂×C₄₁	#3428	1	1	yes	characteristic
535	C₂×C₄₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂×C₄₁	#3539	1	1	yes	characteristic
537	C₂×C₄₁	#3542	1	1	yes	characteristic
538	C₂×C₄₁	#3547	1	1	yes	characteristic
539	C₂×C₄₁	#3565	1	1	yes	characteristic
540	#553	C₄×C₄₁	1	16	yes	complemented
541	C₂×#126	C₂²×C₄₁	1	2	yes	—
542	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
543	C₂×#123	C₂²×C₄₁	1	2	yes	—
544	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
545	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
546	C₂×#121	C₂²×C₄₁	1	2	yes	—
547	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
548	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
549	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
550	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
552	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
553	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
554	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
555	C₂×#117	C₂²×C₄₁	1	2	yes	—
556	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
557	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
558	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
559	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
560	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
561	#390	C₂²×C₄₁	1	2	yes	—
562	#390	C₂²×C₄₁	1	1	yes	characteristic
563	#390	C₂²×C₄₁	1	1	yes	characteristic
564	#390	C₂²×C₄₁	1	2	yes	—
565	#390	C₂²×C₄₁	1	2	yes	—
566	#390	C₂²×C₄₁	1	2	yes	—
567	#389	C₂²×C₄₁	1	1	yes	characteristic
568	#389	C₂²×C₄₁	1	2	yes	—
569	#389	C₂²×C₄₁	1	1	yes	characteristic
570	#389	C₂²×C₄₁	1	1	yes	characteristic
571	#389	C₂²×C₄₁	1	1	yes	characteristic
572	#389	C₂²×C₄₁	1	2	yes	—
573	#389	C₂²×C₄₁	1	2	yes	—
574	#389	C₂²×C₄₁	1	1	yes	characteristic
575	#389	C₂²×C₄₁	1	2	yes	—
576	#389	C₂²×C₄₁	1	2	yes	—
577	#389	C₂²×C₄₁	1	1	yes	characteristic
578	#389	C₂²×C₄₁	1	1	yes	characteristic
579	#389	C₂²×C₄₁	1	1	yes	characteristic
580	#388	C₂²×C₄₁	1	1	yes	characteristic
581	#388	C₂²×C₄₁	1	2	yes	—
582	#388	C₂²×C₄₁	1	2	yes	—
583	#388	C₂²×C₄₁	1	2	yes	—
584	#388	C₂²×C₄₁	1	2	yes	—
585	#388	C₂²×C₄₁	1	2	yes	—
586	#388	C₂²×C₄₁	1	2	yes	—
587	#388	C₂²×C₄₁	1	2	yes	—
588	#388	C₂²×C₄₁	1	2	yes	—
589	#388	C₂²×C₄₁	1	2	yes	—
590	#388	C₂²×C₄₁	1	2	yes	—
591	#388	C₂²×C₄₁	1	1	yes	characteristic
592	#387	C₂²×C₄₁	1	2	yes	—
593	#387	C₂²×C₄₁	1	2	yes	—
594	#387	C₂²×C₄₁	1	2	yes	—
595	#387	C₂²×C₄₁	1	2	yes	—
596	#387	C₂²×C₄₁	1	1	yes	characteristic
597	#387	C₂²×C₄₁	1	2	yes	—
598	#387	C₂²×C₄₁	1	2	yes	—
599	#387	C₂²×C₄₁	1	1	yes	characteristic
600	#386	C₂²×C₄₁	1	2	yes	—
601	#386	C₂²×C₄₁	1	1	yes	characteristic
602	#386	C₂²×C₄₁	1	2	yes	—
603	#386	C₂²×C₄₁	1	2	yes	—
604	#386	C₂²×C₄₁	1	2	yes	—
605	#386	C₂²×C₄₁	1	1	yes	characteristic
606	#385	C₂²×C₄₁	1	1	yes	characteristic
607	#385	C₂²×C₄₁	1	2	yes	—
608	#385	C₂²×C₄₁	1	2	yes	—
609	#385	C₂²×C₄₁	1	2	yes	—
610	#385	C₂²×C₄₁	1	2	yes	—
611	#385	C₂²×C₄₁	1	1	yes	characteristic
612	#385	C₂²×C₄₁	1	2	yes	—
613	#384	C₂²×C₄₁	1	1	yes	characteristic
614	#382	C₂²×C₄₁	1	2	yes	—
615	#381	C₂²×C₄₁	1	2	yes	—
616	#381	C₂²×C₄₁	1	2	yes	—
617	#380	C₂²×C₄₁	1	2	yes	—
618	#380	C₂²×C₄₁	1	2	yes	—
619	#380	C₂²×C₄₁	1	2	yes	—
620	#380	C₂²×C₄₁	1	2	yes	—
621	#380	C₂²×C₄₁	1	1	yes	characteristic
622	#380	C₂²×C₄₁	1	1	yes	characteristic
623	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
624	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
625	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
626	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
627	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
628	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
629	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
630	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
631	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
632	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
633	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
634	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
635	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
636	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
637	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
638	#376	C₂²×C₄₁	1	1	yes	characteristic
639	#376	C₂²×C₄₁	1	2	yes	—
640	C₄₁	#34466	1	1	yes	characteristic, direct product factor, Sylow
641	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
642	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
643	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
644	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
646	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
647	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
648	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
649	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
650	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
652	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
653	#126	C₂×C₄×C₄₁	1	16	yes	complemented
654	#125	C₂×C₄×C₄₁	1	8	yes	complemented
655	#123	C₂×C₄×C₄₁	1	16	yes	complemented
656	#121	C₂×C₄×C₄₁	1	8	yes	—
657	#121	C₂×C₄×C₄₁	1	16	yes	complemented
658	#121	C₂×C₄×C₄₁	1	8	yes	complemented
659	C₄×D₄	—	4	2	no	—
660	C₄×D₄	—	4	2	no	—
661	C₄×D₄	—	4	4	no	—
662	C₄×D₄	C₂×C₄×C₄₁	1	16	yes	complemented
663	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
664	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
665	#117	—	4	2	no	—
666	#117	—	4	4	no	—
667	#117	—	4	2	no	—
668	#117	—	4	2	no	—
669	#117	C₂×C₄×C₄₁	1	8	yes	complemented
670	C₂×C₄⋊C₄	—	4	4	no	—
671	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	8	yes	complemented
672	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
713	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
715	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
718	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
719	C₂×C₄²	—	4	2	no	—
720	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
721	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
726	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
727	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
728	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
729	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
730	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
732	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
734	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
735	#95	C₂³×C₄₁	1	1	yes	characteristic
736	#95	C₂³×C₄₁	1	2	yes	—
737	#95	C₂³×C₄₁	1	1	yes	characteristic
738	#95	C₂³×C₄₁	1	2	yes	—
739	#95	C₂³×C₄₁	1	1	yes	characteristic
740	#95	C₂³×C₄₁	1	2	yes	—
741	#95	C₂³×C₄₁	1	1	yes	characteristic
742	#95	C₂³×C₄₁	1	1	yes	characteristic
743	#95	C₂³×C₄₁	1	1	yes	characteristic
744	#95	C₂³×C₄₁	1	1	yes	characteristic
745	#95	C₂³×C₄₁	1	2	yes	—
746	#95	C₂³×C₄₁	1	2	yes	—
747	#95	C₂³×C₄₁	1	2	yes	—
748	#95	C₂³×C₄₁	1	1	yes	characteristic
749	#95	C₂³×C₄₁	1	1	yes	characteristic
750	#95	C₂³×C₄₁	1	2	yes	—
751	#95	C₂³×C₄₁	1	2	yes	—
752	#95	C₂³×C₄₁	1	2	yes	—
753	#95	C₂³×C₄₁	1	2	yes	—
754	#95	C₂³×C₄₁	1	2	yes	—
755	#95	C₂³×C₄₁	1	2	yes	—
756	#95	C₂³×C₄₁	1	2	yes	—
757	#95	C₂³×C₄₁	1	2	yes	—
758	#95	C₂³×C₄₁	1	1	yes	characteristic
759	#95	C₂³×C₄₁	1	2	yes	—
760	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
761	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
762	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	1	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	1	no	—
770	C₂×D₄	—	4	2	no	—
771	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
772	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
773	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
774	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	4	1	no	—
782	C₂²×C₄	—	4	1	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	—	4	1	no	—
788	C₂²×C₄	—	4	1	no	—
789	C₂²×C₄	—	4	1	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	—	4	2	no	—
792	C₂²×C₄	—	4	2	no	—
793	C₂²×C₄	—	4	2	no	—
794	C₂²×C₄	—	4	2	no	—
795	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
796	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
797	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
798	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
799	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
809	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	4	2	no	—
826	C₄⋊C₄	—	4	2	no	—
827	C₄⋊C₄	—	4	1	no	—
828	C₄⋊C₄	—	4	1	no	—
829	C₄⋊C₄	—	4	2	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₄⋊C₄	—	4	2	no	—
833	C₄⋊C₄	—	4	2	no	—
834	C₄⋊C₄	—	4	2	no	—
835	C₄⋊C₄	—	4	1	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
838	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
839	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
840	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
841	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
842	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
843	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	4	1	no	—
846	C₂²⋊C₄	—	4	1	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	—	4	2	no	—
851	C₂²⋊C₄	—	4	2	no	—
852	C₂²⋊C₄	—	4	2	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₂²⋊C₄	—	4	1	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	1	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	1	no	—
860	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
861	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
862	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
863	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
864	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
865	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	4	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	4	1	no	—
872	C₄²	—	4	1	no	—
873	C₄²	—	4	2	no	—
874	C₄²	—	4	2	no	—
875	C₄²	—	4	2	no	—
876	C₄²	—	4	2	no	—
877	C₄²	—	4	2	no	—
878	C₄²	—	4	2	no	—
879	C₄²	C₂²×C₄×C₄₁	1	8	yes	—
880	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
900	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
901	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
902	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
903	D₄	—	2	8	no	—
904	D₄	—	4	4	no	—
905	D₄	—	4	8	no	—
906	D₄	—	4	8	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	8	no	—
924	C₂×C₄	—	2	8	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	4	8	no	—
959	C₂×C₄	—	4	8	no	—
960	C₂×C₄	—	4	4	no	—
961	C₂×C₄	—	4	4	no	—
962	C₂×C₄	—	8	4	no	—
963	C₂×C₄	—	8	4	no	—
964	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
965	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
966	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
967	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
968	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
969	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
970	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
971	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
972	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
973	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
974	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	4	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	2	4	no	—
980	C₂²	—	2	2	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	4	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	4	1	no	—
985	C₂²	—	4	1	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	2	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	2	no	—
996	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
997	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
998	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
999	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
1000	C₂²	C₄₁×#585	1	1	yes	characteristic
1001	C₂²	C₄₁×#585	1	1	yes	characteristic
1002	C₂²	C₄₁×#585	1	1	yes	characteristic
1003	C₄	—	2	2	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	4	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	4	no	—
1009	C₄	—	2	4	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	C₄₁×#520	1	4	yes	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	4	4	no	—
1026	C₂	C₂×C₄₁×#520	1	1	yes	characteristic
1027	C₂	C₄₁×#3428	1	1	yes	characteristic
1028	C₂	C₄×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1029	C₂	C₄₁×#3539	1	1	yes	characteristic
1030	C₂	C₄₁×#3542	1	1	yes	characteristic
1031	C₂	C₄₁×#3547	1	1	yes	characteristic
1032	C₂	C₄₁×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂×C₄₁×#553	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2377	C₂	semidirect
3. C₄₁×#2376	C₂	semidirect
4. C₄₁×#2373	C₂	semidirect
5. C₄₁×#2370	C₂	semidirect
6. C₄₁×#2363	C₂	semidirect
7. C₄₁×#2363	C₂	semidirect
8. C₄₁×#2354	C₂	semidirect
9. C₄₁×#2352	C₂	semidirect
10. D₄×C₄⋊C₄×C₄₁	C₂	semidirect
11. C₄₁×#2346	C₂	semidirect
12. C₄₁×#2344	C₂	semidirect
13. C₄₁×#2334	C₂	semidirect
14. C₄₁×#2330	C₂	semidirect
15. C₄₁×#2324	C₂	semidirect
16. C₄₁×#2324	C₂	semidirect
17. C₄₁×#2322	C₂	semidirect
18. C₄₁×#2319	C₂	semidirect
19. C₄₁×#2319	C₂	semidirect
20. C₄₁×#2316	C₂	semidirect
21. C₄×#121×C₄₁	C₂	semidirect
22. C₄₁×#2296	C₂	semidirect
23. C₄₁×#2290	C₂	semidirect
24. C₄₁×#553	C₄	semidirect
136. #126×C₄₁	C₂×C₄	semidirect
137. #125×C₄₁	C₂×C₄	semidirect
138. #123×C₄₁	C₂×C₄	semidirect
140. #121×C₄₁	C₂×C₄	semidirect
141. #121×C₄₁	C₂×C₄	semidirect
145. C₄×D₄×C₄₁	C₂×C₄	semidirect
146. C₄×D₄×C₄₁	C₂×C₄	semidirect
147. C₄×D₄×C₄₁	C₂×C₄	semidirect
152. #117×C₄₁	C₂×C₄	semidirect
154. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
458. #34466	C₄₁	direct (N × H)
508. #2377	C₂×C₄₁	semidirect
509. #2376	C₂×C₄₁	semidirect
510. #2373	C₂×C₄₁	semidirect
511. #2370	C₂×C₄₁	semidirect
512. #2363	C₂×C₄₁	semidirect
513. #2363	C₂×C₄₁	semidirect
514. #2354	C₂×C₄₁	semidirect
515. #2352	C₂×C₄₁	semidirect
516. D₄×C₄⋊C₄	C₂×C₄₁	semidirect
517. #2346	C₂×C₄₁	semidirect
518. #2344	C₂×C₄₁	semidirect
519. #2334	C₂×C₄₁	semidirect
520. #2330	C₂×C₄₁	semidirect
521. #2324	C₂×C₄₁	semidirect
522. #2324	C₂×C₄₁	semidirect
523. #2322	C₂×C₄₁	semidirect
524. #2319	C₂×C₄₁	semidirect
525. #2319	C₂×C₄₁	semidirect
526. #2316	C₂×C₄₁	semidirect
527. C₄×#121	C₂×C₄₁	semidirect
528. #2296	C₂×C₄₁	semidirect
529. #2290	C₂×C₄₁	semidirect
540. #553	C₄×C₄₁	semidirect
640. C₄₁	#34466	direct (N × H)
653. #126	C₂×C₄×C₄₁	semidirect
654. #125	C₂×C₄×C₄₁	semidirect
655. #123	C₂×C₄×C₄₁	semidirect
657. #121	C₂×C₄×C₄₁	semidirect
658. #121	C₂×C₄×C₄₁	semidirect
662. C₄×D₄	C₂×C₄×C₄₁	semidirect
663. C₄×D₄	C₂×C₄×C₄₁	semidirect
664. C₄×D₄	C₂×C₄×C₄₁	semidirect
669. #117	C₂×C₄×C₄₁	semidirect
671. C₂×C₄⋊C₄	C₂×C₄×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×#553	2
C₄₁×#2377	2
C₄₁×#2376	2
C₄₁×#2373	2
C₄₁×#2370	2
C₄₁×#2363	2
C₄₁×#2354	2
C₄₁×#2352	2
D₄×C₄⋊C₄×C₄₁	2
C₄₁×#2346	2
C₄₁×#2344	2
C₄₁×#2334	2
C₄₁×#2330	2
C₄₁×#2324	2
C₄₁×#2322	2
C₄₁×#2319	2
C₄₁×#2316	2
C₄×#121×C₄₁	2
C₄₁×#2296	2
C₄₁×#2290	2
#34466	41

Subgroups — C41×#34466 #23810667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34466 #23810667