Subgroups — C₄₁×#34473 #23810674

Order 10496.

2344 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#547	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×#2374	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2345	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#2335	C₂	1	2	yes	maximal, complemented
14	C₄₁×#2335	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2333	C₂	1	2	yes	maximal, complemented
16	C₄₁×#2327	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2313	C₂	1	2	yes	maximal, complemented
20	C₄₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₁×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#547	C₄	1	16	yes	complemented
27	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#123×C₄₁	C₂²	1	2	yes	—
29	C₂×#123×C₄₁	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#121×C₄₁	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
43	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
44	C₄₁×#391	C₂²	1	1	yes	characteristic
45	C₄₁×#391	C₂²	1	1	yes	characteristic
46	C₄₁×#391	C₂²	1	1	yes	characteristic
47	C₄₁×#391	C₂²	1	1	yes	characteristic
48	C₄₁×#390	C₂²	1	1	yes	characteristic
49	C₄₁×#390	C₂²	1	1	yes	characteristic
50	C₄₁×#390	C₂²	1	1	yes	characteristic
51	C₄₁×#390	C₂²	1	1	yes	characteristic
52	C₄₁×#390	C₂²	1	2	yes	—
53	C₄₁×#390	C₂²	1	2	yes	—
54	C₄₁×#390	C₂²	1	2	yes	—
55	C₄₁×#390	C₂²	1	2	yes	—
56	C₄₁×#389	C₂²	1	1	yes	characteristic
57	C₄₁×#389	C₂²	1	1	yes	characteristic
58	C₄₁×#389	C₂²	1	2	yes	—
59	C₄₁×#389	C₂²	1	2	yes	—
60	C₄₁×#389	C₂²	1	2	yes	—
61	C₄₁×#388	C₂²	1	1	yes	characteristic
62	C₄₁×#388	C₂²	1	1	yes	characteristic
63	C₄₁×#388	C₂²	1	2	yes	—
64	C₄₁×#388	C₂²	1	2	yes	—
65	C₄₁×#388	C₂²	1	2	yes	—
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×#387	C₂²	1	1	yes	characteristic
73	C₄₁×#387	C₂²	1	1	yes	characteristic
74	C₄₁×#387	C₂²	1	2	yes	—
75	C₄₁×#387	C₂²	1	2	yes	—
76	C₄₁×#387	C₂²	1	2	yes	—
77	C₄₁×#387	C₂²	1	2	yes	—
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×#387	C₂²	1	2	yes	—
85	C₄₁×#386	C₂²	1	1	yes	characteristic
86	C₄₁×#386	C₂²	1	1	yes	characteristic
87	C₄₁×#386	C₂²	1	2	yes	—
88	C₄₁×#386	C₂²	1	2	yes	—
89	C₄₁×#386	C₂²	1	2	yes	—
90	C₄₁×#386	C₂²	1	2	yes	—
91	C₄₁×#386	C₂²	1	2	yes	—
92	C₄₁×#385	C₂²	1	1	yes	characteristic
93	C₄₁×#385	C₂²	1	1	yes	characteristic
94	C₄₁×#385	C₂²	1	2	yes	—
95	C₄₁×#385	C₂²	1	2	yes	—
96	C₄₁×#382	C₂²	1	1	yes	characteristic
97	C₄₁×#381	C₂²	1	2	yes	—
98	C₄₁×#381	C₂²	1	2	yes	—
99	C₄₁×#380	C₂²	1	1	yes	characteristic
100	C₄₁×#380	C₂²	1	2	yes	—
101	C₄₁×#380	C₂²	1	2	yes	—
102	C₄₁×#380	C₂²	1	2	yes	—
103	C₄₁×#380	C₂²	1	2	yes	—
104	C₄₁×#380	C₂²	1	1	yes	characteristic
105	C₄₁×#380	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
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	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
123	C₄₁×#376	C₂²	1	1	yes	characteristic
124	C₂×#41×C₄₁	—	4	2	no	—
125	C₂×#41×C₄₁	—	4	2	no	—
126	C₂×#41×C₄₁	—	4	2	no	—
127	C₂×#41×C₄₁	—	4	2	no	—
128	C₂×#41×C₄₁	C₂×C₄	1	8	yes	complemented
129	C₂×#41×C₄₁	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
135	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
136	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
142	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
143	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
144	C₄⋊Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
145	#123×C₄₁	C₂×C₄	1	16	yes	complemented
146	#123×C₄₁	C₂×C₄	1	16	yes	complemented
147	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
148	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
149	#121×C₄₁	C₂×C₄	1	16	yes	—
150	C₄×Q₈×C₄₁	—	4	2	no	—
151	C₄×Q₈×C₄₁	—	4	2	no	—
152	C₄×Q₈×C₄₁	—	4	2	no	—
153	C₄×Q₈×C₄₁	—	4	2	no	—
154	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	—
155	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
156	#117×C₄₁	—	4	2	no	—
157	#117×C₄₁	—	4	2	no	—
158	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
159	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	16	yes	complemented
160	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
174	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
193	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₄₁	—	4	2	no	—
204	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
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	2	yes	—
218	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
219	#95×C₄₁	C₂³	1	1	yes	characteristic
220	#95×C₄₁	C₂³	1	1	yes	characteristic
221	#95×C₄₁	C₂³	1	1	yes	characteristic
222	#95×C₄₁	C₂³	1	1	yes	characteristic
223	#95×C₄₁	C₂³	1	1	yes	characteristic
224	#95×C₄₁	C₂³	1	1	yes	characteristic
225	#95×C₄₁	C₂³	1	2	yes	—
226	#95×C₄₁	C₂³	1	1	yes	characteristic
227	#95×C₄₁	C₂³	1	2	yes	—
228	#95×C₄₁	C₂³	1	1	yes	characteristic
229	#95×C₄₁	C₂³	1	1	yes	characteristic
230	#95×C₄₁	C₂³	1	2	yes	—
231	#95×C₄₁	C₂³	1	2	yes	—
232	#95×C₄₁	C₂³	1	2	yes	—
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	2	yes	—
242	#95×C₄₁	C₂³	1	2	yes	—
243	#95×C₄₁	C₂³	1	1	yes	characteristic
244	#95×C₄₁	C₂³	1	2	yes	—
245	#95×C₄₁	C₂³	1	2	yes	—
246	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
248	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
249	#41×C₄₁	—	4	16	no	—
250	#41×C₄₁	—	4	16	no	—
251	C₂×Q₈×C₄₁	—	2	2	no	—
252	C₂×Q₈×C₄₁	—	2	2	no	—
253	C₂×Q₈×C₄₁	—	2	2	no	—
254	C₂×Q₈×C₄₁	—	2	2	no	—
255	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
256	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
257	C₂×D₄×C₄₁	—	2	2	no	—
258	C₂×D₄×C₄₁	—	2	2	no	—
259	C₂×D₄×C₄₁	—	4	1	no	—
260	C₂×D₄×C₄₁	—	4	1	no	—
261	C₂×D₄×C₄₁	—	4	2	no	—
262	C₂×D₄×C₄₁	—	4	2	no	—
263	C₂×D₄×C₄₁	—	4	2	no	—
264	C₂×D₄×C₄₁	—	4	2	no	—
265	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
266	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
268	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
269	C₂²×C₄×C₄₁	—	2	2	no	—
270	C₂²×C₄×C₄₁	—	2	2	no	—
271	C₂²×C₄×C₄₁	—	2	2	no	—
272	C₂²×C₄×C₄₁	—	2	2	no	—
273	C₂²×C₄×C₄₁	—	2	2	no	—
274	C₂²×C₄×C₄₁	—	4	1	no	—
275	C₂²×C₄×C₄₁	—	4	1	no	—
276	C₂²×C₄×C₄₁	—	4	1	no	—
277	C₂²×C₄×C₄₁	—	4	2	no	—
278	C₂²×C₄×C₄₁	—	4	2	no	—
279	C₂²×C₄×C₄₁	—	4	1	no	—
280	C₂²×C₄×C₄₁	—	4	1	no	—
281	C₂²×C₄×C₄₁	—	4	2	no	—
282	C₂²×C₄×C₄₁	—	4	2	no	—
283	C₂²×C₄×C₄₁	—	4	2	no	—
284	C₂²×C₄×C₄₁	—	4	2	no	—
285	C₂²×C₄×C₄₁	—	4	2	no	—
286	C₂²×C₄×C₄₁	—	4	2	no	—
287	C₂²×C₄×C₄₁	—	4	2	no	—
288	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
289	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
290	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
291	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
292	C₂²×C₄×C₄₁	C₂²×C₄	1	8	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	1	yes	characteristic
296	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₄₁	—	2	2	no	—
314	C₄⋊C₄×C₄₁	—	2	2	no	—
315	C₄⋊C₄×C₄₁	—	2	2	no	—
316	C₄⋊C₄×C₄₁	—	2	2	no	—
317	C₄⋊C₄×C₄₁	—	2	2	no	—
318	C₄⋊C₄×C₄₁	—	4	2	no	—
319	C₄⋊C₄×C₄₁	—	4	1	no	—
320	C₄⋊C₄×C₄₁	—	4	2	no	—
321	C₄⋊C₄×C₄₁	—	4	2	no	—
322	C₄⋊C₄×C₄₁	—	4	1	no	—
323	C₄⋊C₄×C₄₁	—	4	1	no	—
324	C₄⋊C₄×C₄₁	—	4	2	no	—
325	C₄⋊C₄×C₄₁	—	4	2	no	—
326	C₄⋊C₄×C₄₁	—	4	2	no	—
327	C₄⋊C₄×C₄₁	—	4	2	no	—
328	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
329	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
330	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
331	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
332	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
333	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
334	C₂²⋊C₄×C₄₁	—	2	2	no	—
335	C₂²⋊C₄×C₄₁	—	2	4	no	—
336	C₂²⋊C₄×C₄₁	—	4	1	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	—	4	2	no	—
344	C₂²⋊C₄×C₄₁	—	4	1	no	—
345	C₂²⋊C₄×C₄₁	—	4	1	no	—
346	C₂²⋊C₄×C₄₁	—	4	2	no	—
347	C₂²⋊C₄×C₄₁	—	4	2	no	—
348	C₂²⋊C₄×C₄₁	—	4	1	no	—
349	C₂²⋊C₄×C₄₁	—	4	1	no	—
350	C₂²⋊C₄×C₄₁	—	4	2	no	—
351	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
352	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
353	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
354	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
355	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
356	C₄²×C₄₁	—	2	2	no	—
357	C₄²×C₄₁	—	2	2	no	—
358	C₄²×C₄₁	—	2	2	no	—
359	C₄²×C₄₁	—	2	2	no	—
360	C₄²×C₄₁	—	4	1	no	—
361	C₄²×C₄₁	—	4	1	no	—
362	C₄²×C₄₁	—	4	2	no	—
363	C₄²×C₄₁	—	4	2	no	—
364	C₄²×C₄₁	—	4	2	no	—
365	C₄²×C₄₁	—	4	2	no	—
366	C₄²×C₄₁	—	4	2	no	—
367	C₄²×C₄₁	—	4	2	no	—
368	C₄²×C₄₁	—	4	2	no	—
369	C₄²×C₄₁	—	4	2	no	—
370	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
371	C₂³×C₄₁	—	2	1	no	—
372	C₂³×C₄₁	—	2	1	no	—
373	C₂³×C₄₁	—	2	1	no	—
374	C₂³×C₄₁	—	2	1	no	—
375	C₂³×C₄₁	—	2	2	no	—
376	C₂³×C₄₁	—	2	2	no	—
377	C₂³×C₄₁	—	2	2	no	—
378	C₂³×C₄₁	—	2	1	no	—
379	C₂³×C₄₁	—	2	1	no	—
380	C₂³×C₄₁	—	2	2	no	—
381	C₂³×C₄₁	—	2	2	no	—
382	C₂³×C₄₁	—	2	2	no	—
383	C₂³×C₄₁	—	2	1	no	—
384	C₂³×C₄₁	—	2	1	no	—
385	C₂³×C₄₁	—	2	1	no	—
386	C₂³×C₄₁	—	2	1	no	—
387	C₂³×C₄₁	—	2	1	no	—
388	C₂³×C₄₁	—	2	1	no	—
389	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
390	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
391	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
392	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
393	Q₈×C₄₁	—	2	8	no	—
394	Q₈×C₄₁	—	2	8	no	—
395	D₄×C₄₁	—	2	8	no	—
396	D₄×C₄₁	—	4	4	no	—
397	D₄×C₄₁	—	4	8	no	—
398	D₄×C₄₁	—	4	8	no	—
399	C₂×C₄×C₄₁	—	2	1	no	—
400	C₂×C₄×C₄₁	—	2	1	no	—
401	C₂×C₄×C₄₁	—	2	1	no	—
402	C₂×C₄×C₄₁	—	2	2	no	—
403	C₂×C₄×C₄₁	—	2	2	no	—
404	C₂×C₄×C₄₁	—	2	2	no	—
405	C₂×C₄×C₄₁	—	2	2	no	—
406	C₂×C₄×C₄₁	—	2	1	no	—
407	C₂×C₄×C₄₁	—	2	1	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	2	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	8	no	—
416	C₂×C₄×C₄₁	—	2	8	no	—
417	C₂×C₄×C₄₁	—	2	1	no	—
418	C₂×C₄×C₄₁	—	2	1	no	—
419	C₂×C₄×C₄₁	—	2	1	no	—
420	C₂×C₄×C₄₁	—	2	1	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	2	no	—
426	C₂×C₄×C₄₁	—	2	2	no	—
427	C₂×C₄×C₄₁	—	2	2	no	—
428	C₂×C₄×C₄₁	—	2	1	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	2	no	—
435	C₂×C₄×C₄₁	—	2	2	no	—
436	C₂×C₄×C₄₁	—	2	2	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	—	2	1	no	—
442	C₂×C₄×C₄₁	—	2	1	no	—
443	C₂×C₄×C₄₁	—	2	1	no	—
444	C₂×C₄×C₄₁	—	2	1	no	—
445	C₂×C₄×C₄₁	—	2	2	no	—
446	C₂×C₄×C₄₁	—	2	1	no	—
447	C₂×C₄×C₄₁	—	2	1	no	—
448	C₂×C₄×C₄₁	—	2	2	no	—
449	C₂×C₄×C₄₁	—	2	1	no	—
450	C₂×C₄×C₄₁	—	4	8	no	—
451	C₂×C₄×C₄₁	—	4	8	no	—
452	C₂×C₄×C₄₁	—	4	8	no	—
453	C₂×C₄×C₄₁	—	4	4	no	—
454	C₂×C₄×C₄₁	—	4	4	no	—
455	C₂×C₄×C₄₁	—	8	4	no	—
456	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
459	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
460	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
461	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
462	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
463	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
465	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
466	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
467	#34473	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
468	C₂²×C₄₁	—	2	2	no	—
469	C₂²×C₄₁	—	2	2	no	—
470	C₂²×C₄₁	—	2	4	no	—
471	C₂²×C₄₁	—	2	4	no	—
472	C₂²×C₄₁	—	2	2	no	—
473	C₂²×C₄₁	—	2	2	no	—
474	C₂²×C₄₁	—	2	4	no	—
475	C₂²×C₄₁	—	2	2	no	—
476	C₂²×C₄₁	—	2	2	no	—
477	C₂²×C₄₁	—	4	1	no	—
478	C₂²×C₄₁	—	4	1	no	—
479	C₂²×C₄₁	—	4	2	no	—
480	C₂²×C₄₁	—	4	1	no	—
481	C₂²×C₄₁	—	4	1	no	—
482	C₂²×C₄₁	—	4	2	no	—
483	C₂²×C₄₁	—	4	1	no	—
484	C₂²×C₄₁	—	4	1	no	—
485	C₂²×C₄₁	—	4	2	no	—
486	C₂²×C₄₁	—	4	1	no	—
487	C₂²×C₄₁	—	4	1	no	—
488	C₂²×C₄₁	—	4	2	no	—
489	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
490	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
493	C₂²×C₄₁	#585	1	1	yes	characteristic
494	C₂²×C₄₁	#585	1	1	yes	characteristic
495	C₂²×C₄₁	#585	1	1	yes	characteristic
496	C₄×C₄₁	—	2	2	no	—
497	C₄×C₄₁	—	2	2	no	—
498	C₄×C₄₁	—	2	4	no	—
499	C₄×C₄₁	—	2	4	no	—
500	C₄×C₄₁	—	2	2	no	—
501	C₄×C₄₁	—	2	4	no	—
502	C₄×C₄₁	—	2	2	no	—
503	C₄×C₄₁	—	2	2	no	—
504	C₄×C₄₁	—	4	1	no	—
505	C₄×C₄₁	—	4	2	no	—
506	C₄×C₄₁	—	4	1	no	—
507	C₄×C₄₁	—	4	1	no	—
508	C₄×C₄₁	—	4	1	no	—
509	C₄×C₄₁	—	4	1	no	—
510	C₄×C₄₁	—	4	1	no	—
511	C₄×C₄₁	—	4	2	no	—
512	C₄×C₄₁	—	4	1	no	—
513	C₄×C₄₁	—	4	2	no	—
514	C₄×C₄₁	—	4	2	no	—
515	C₄×C₄₁	#518	1	4	yes	—
516	C₂×#547	C₂×C₄₁	1	1	yes	characteristic
517	#2377	C₂×C₄₁	1	2	yes	complemented
518	#2376	C₂×C₄₁	1	2	yes	complemented
519	#2374	C₂×C₄₁	1	2	yes	complemented
520	#2365	C₂×C₄₁	1	1	yes	characteristic, complemented
521	#2362	C₂×C₄₁	1	1	yes	characteristic, complemented
522	#2360	C₂×C₄₁	1	1	yes	characteristic, complemented
523	#2357	C₂×C₄₁	1	1	yes	characteristic, complemented
524	#2352	C₂×C₄₁	1	1	yes	characteristic, complemented
525	#2345	C₂×C₄₁	1	2	yes	complemented
526	#2341	C₂×C₄₁	1	1	yes	characteristic, complemented
527	#2341	C₂×C₄₁	1	1	yes	characteristic, complemented
528	#2335	C₂×C₄₁	1	2	yes	complemented
529	#2335	C₂×C₄₁	1	2	yes	complemented
530	#2333	C₂×C₄₁	1	2	yes	complemented
531	#2327	C₂×C₄₁	1	1	yes	characteristic, complemented
532	#2323	C₂×C₄₁	1	1	yes	characteristic, complemented
533	#2319	C₂×C₄₁	1	1	yes	characteristic, complemented
534	#2313	C₂×C₄₁	1	2	yes	complemented
535	#2311	C₂×C₄₁	1	1	yes	characteristic, complemented
536	C₄×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
537	#2297	C₂×C₄₁	1	1	yes	characteristic, complemented
538	#2290	C₂×C₄₁	1	1	yes	characteristic, complemented
539	C₂×C₄₁	—	4	2	no	—
540	C₂×C₄₁	—	4	2	no	—
541	C₂×C₄₁	—	4	4	no	—
542	C₂×C₄₁	C₂×#518	1	1	yes	characteristic
543	C₂×C₄₁	#3428	1	1	yes	characteristic
544	C₂×C₄₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
545	C₂×C₄₁	#3539	1	1	yes	characteristic
546	C₂×C₄₁	#3541	1	1	yes	characteristic
547	C₂×C₄₁	#3554	1	1	yes	characteristic
548	C₂×C₄₁	#3562	1	1	yes	characteristic
549	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
550	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
551	#547	C₄×C₄₁	1	16	yes	complemented
552	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
553	C₂×#123	C₂²×C₄₁	1	2	yes	—
554	C₂×#123	C₂²×C₄₁	1	2	yes	—
555	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
556	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
557	C₂×#121	C₂²×C₄₁	1	2	yes	—
558	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
559	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
560	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
561	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
562	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
563	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
564	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
565	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
566	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
567	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
568	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
569	#391	C₂²×C₄₁	1	1	yes	characteristic
570	#391	C₂²×C₄₁	1	1	yes	characteristic
571	#391	C₂²×C₄₁	1	1	yes	characteristic
572	#391	C₂²×C₄₁	1	1	yes	characteristic
573	#390	C₂²×C₄₁	1	1	yes	characteristic
574	#390	C₂²×C₄₁	1	1	yes	characteristic
575	#390	C₂²×C₄₁	1	1	yes	characteristic
576	#390	C₂²×C₄₁	1	2	yes	—
577	#390	C₂²×C₄₁	1	2	yes	—
578	#390	C₂²×C₄₁	1	2	yes	—
579	#390	C₂²×C₄₁	1	2	yes	—
580	#390	C₂²×C₄₁	1	1	yes	characteristic
581	#389	C₂²×C₄₁	1	1	yes	characteristic
582	#389	C₂²×C₄₁	1	1	yes	characteristic
583	#389	C₂²×C₄₁	1	2	yes	—
584	#389	C₂²×C₄₁	1	2	yes	—
585	#389	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	#388	C₂²×C₄₁	1	2	yes	—
593	#388	C₂²×C₄₁	1	2	yes	—
594	#388	C₂²×C₄₁	1	2	yes	—
595	#388	C₂²×C₄₁	1	2	yes	—
596	#388	C₂²×C₄₁	1	1	yes	characteristic
597	#387	C₂²×C₄₁	1	1	yes	characteristic
598	#387	C₂²×C₄₁	1	2	yes	—
599	#387	C₂²×C₄₁	1	2	yes	—
600	#387	C₂²×C₄₁	1	2	yes	—
601	#387	C₂²×C₄₁	1	2	yes	—
602	#387	C₂²×C₄₁	1	2	yes	—
603	#387	C₂²×C₄₁	1	2	yes	—
604	#387	C₂²×C₄₁	1	2	yes	—
605	#387	C₂²×C₄₁	1	2	yes	—
606	#387	C₂²×C₄₁	1	2	yes	—
607	#387	C₂²×C₄₁	1	2	yes	—
608	#387	C₂²×C₄₁	1	2	yes	—
609	#387	C₂²×C₄₁	1	1	yes	characteristic
610	#386	C₂²×C₄₁	1	2	yes	—
611	#386	C₂²×C₄₁	1	2	yes	—
612	#386	C₂²×C₄₁	1	1	yes	characteristic
613	#386	C₂²×C₄₁	1	2	yes	—
614	#386	C₂²×C₄₁	1	2	yes	—
615	#386	C₂²×C₄₁	1	2	yes	—
616	#386	C₂²×C₄₁	1	1	yes	characteristic
617	#385	C₂²×C₄₁	1	1	yes	characteristic
618	#385	C₂²×C₄₁	1	2	yes	—
619	#385	C₂²×C₄₁	1	1	yes	characteristic
620	#385	C₂²×C₄₁	1	2	yes	—
621	#382	C₂²×C₄₁	1	1	yes	characteristic
622	#381	C₂²×C₄₁	1	2	yes	—
623	#381	C₂²×C₄₁	1	2	yes	—
624	#380	C₂²×C₄₁	1	2	yes	—
625	#380	C₂²×C₄₁	1	2	yes	—
626	#380	C₂²×C₄₁	1	2	yes	—
627	#380	C₂²×C₄₁	1	2	yes	—
628	#380	C₂²×C₄₁	1	1	yes	characteristic
629	#380	C₂²×C₄₁	1	2	yes	—
630	#380	C₂²×C₄₁	1	1	yes	characteristic
631	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
632	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
633	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
634	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
635	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
636	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
637	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
638	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
639	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
640	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
641	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
642	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
643	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
644	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
645	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
646	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
647	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
648	#376	C₂²×C₄₁	1	1	yes	characteristic
649	C₄₁	#34473	1	1	yes	characteristic, direct product factor, Sylow
650	C₂×#41	—	4	2	no	—
651	C₂×#41	—	4	2	no	—
652	C₂×#41	—	4	2	no	—
653	C₂×#41	—	4	2	no	—
654	C₂×#41	C₂×C₄×C₄₁	1	8	yes	complemented
655	C₂×#41	C₂×C₄×C₄₁	1	8	yes	complemented
656	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
657	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
658	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
659	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
660	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
661	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
662	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
663	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
666	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
668	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
669	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
670	C₄⋊Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
671	#123	C₂×C₄×C₄₁	1	16	yes	complemented
672	#123	C₂×C₄×C₄₁	1	16	yes	complemented
673	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
674	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
675	#121	C₂×C₄×C₄₁	1	16	yes	—
676	C₄×Q₈	—	4	2	no	—
677	C₄×Q₈	—	4	2	no	—
678	C₄×Q₈	—	4	2	no	—
679	C₄×Q₈	—	4	2	no	—
680	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	—
681	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
682	#117	—	4	2	no	—
683	#117	—	4	2	no	—
684	C₂×C₄⋊C₄	—	4	2	no	—
685	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	16	yes	complemented
686	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
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	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
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	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
724	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
729	C₂×C₄²	—	4	2	no	—
730	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
735	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
736	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
737	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
738	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
739	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
740	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
743	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
744	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
745	#95	C₂³×C₄₁	1	1	yes	characteristic
746	#95	C₂³×C₄₁	1	1	yes	characteristic
747	#95	C₂³×C₄₁	1	1	yes	characteristic
748	#95	C₂³×C₄₁	1	1	yes	characteristic
749	#95	C₂³×C₄₁	1	1	yes	characteristic
750	#95	C₂³×C₄₁	1	1	yes	characteristic
751	#95	C₂³×C₄₁	1	2	yes	—
752	#95	C₂³×C₄₁	1	1	yes	characteristic
753	#95	C₂³×C₄₁	1	2	yes	—
754	#95	C₂³×C₄₁	1	1	yes	characteristic
755	#95	C₂³×C₄₁	1	1	yes	characteristic
756	#95	C₂³×C₄₁	1	2	yes	—
757	#95	C₂³×C₄₁	1	2	yes	—
758	#95	C₂³×C₄₁	1	2	yes	—
759	#95	C₂³×C₄₁	1	2	yes	—
760	#95	C₂³×C₄₁	1	2	yes	—
761	#95	C₂³×C₄₁	1	2	yes	—
762	#95	C₂³×C₄₁	1	2	yes	—
763	#95	C₂³×C₄₁	1	2	yes	—
764	#95	C₂³×C₄₁	1	2	yes	—
765	#95	C₂³×C₄₁	1	2	yes	—
766	#95	C₂³×C₄₁	1	2	yes	—
767	#95	C₂³×C₄₁	1	2	yes	—
768	#95	C₂³×C₄₁	1	2	yes	—
769	#95	C₂³×C₄₁	1	1	yes	characteristic
770	#95	C₂³×C₄₁	1	2	yes	—
771	#95	C₂³×C₄₁	1	2	yes	—
772	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
774	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
775	#41	—	4	16	no	—
776	#41	—	4	16	no	—
777	C₂×Q₈	—	2	2	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	2	no	—
781	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
782	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	4	2	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	1	no	—
790	C₂×D₄	—	4	1	no	—
791	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
792	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
793	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
794	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	4	1	no	—
801	C₂²×C₄	—	4	1	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	1	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	1	no	—
810	C₂²×C₄	—	4	1	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
815	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
816	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
817	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
818	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
819	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	4	2	no	—
845	C₄⋊C₄	—	4	1	no	—
846	C₄⋊C₄	—	4	1	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	1	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
855	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
856	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
857	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
858	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
859	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	4	1	no	—
863	C₂²⋊C₄	—	4	1	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	1	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	1	no	—
874	C₂²⋊C₄	—	4	1	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	4	1	no	—
887	C₄²	—	4	1	no	—
888	C₄²	—	4	2	no	—
889	C₄²	—	4	2	no	—
890	C₄²	—	4	2	no	—
891	C₄²	—	4	2	no	—
892	C₄²	—	4	2	no	—
893	C₄²	—	4	2	no	—
894	C₄²	—	4	2	no	—
895	C₄²	—	4	2	no	—
896	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	1	no	—
915	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
916	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
917	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
918	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
919	Q₈	—	2	8	no	—
920	Q₈	—	2	8	no	—
921	D₄	—	2	8	no	—
922	D₄	—	4	8	no	—
923	D₄	—	4	8	no	—
924	D₄	—	4	4	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	8	no	—
942	C₂×C₄	—	2	8	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	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	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	4	8	no	—
977	C₂×C₄	—	4	8	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	8	4	no	—
982	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
984	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
985	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
986	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
987	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
988	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
989	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
990	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
991	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
992	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	4	no	—
996	C₂²	—	2	4	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
1015	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1016	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
1017	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
1018	C₂²	C₄₁×#585	1	1	yes	characteristic
1019	C₂²	C₄₁×#585	1	1	yes	characteristic
1020	C₂²	C₄₁×#585	1	1	yes	characteristic
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	4	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	4	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	2	2	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	2	no	—
1031	C₄	—	4	2	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	C₄₁×#518	1	4	yes	—
1041	C₂	—	4	2	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	4	4	no	—
1044	C₂	C₂×C₄₁×#518	1	1	yes	characteristic
1045	C₂	C₄₁×#3428	1	1	yes	characteristic
1046	C₂	C₄×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
1047	C₂	C₄₁×#3539	1	1	yes	characteristic
1048	C₂	C₄₁×#3541	1	1	yes	characteristic
1049	C₂	C₄₁×#3554	1	1	yes	characteristic
1050	C₂	C₄₁×#3562	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×#547	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×#2374	C₂	semidirect
5. C₄₁×#2365	C₂	semidirect
6. C₄₁×#2362	C₂	semidirect
7. C₄₁×#2360	C₂	semidirect
8. C₄₁×#2357	C₂	semidirect
9. C₄₁×#2352	C₂	semidirect
10. C₄₁×#2345	C₂	semidirect
11. C₄₁×#2341	C₂	semidirect
12. C₄₁×#2341	C₂	semidirect
13. C₄₁×#2335	C₂	semidirect
14. C₄₁×#2335	C₂	semidirect
15. C₄₁×#2333	C₂	semidirect
16. C₄₁×#2327	C₂	semidirect
17. C₄₁×#2323	C₂	semidirect
18. C₄₁×#2319	C₂	semidirect
19. C₄₁×#2313	C₂	semidirect
20. C₄₁×#2311	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₄₁	C₂	semidirect
22. C₄₁×#2297	C₂	semidirect
23. C₄₁×#2290	C₂	semidirect
26. C₄₁×#547	C₄	semidirect
128. C₂×#41×C₄₁	C₂×C₄	semidirect
129. C₂×#41×C₄₁	C₂×C₄	semidirect
144. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
145. #123×C₄₁	C₂×C₄	semidirect
146. #123×C₄₁	C₂×C₄	semidirect
147. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
148. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
155. C₄×D₄×C₄₁	C₂×C₄	semidirect
159. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
467. #34473	C₄₁	direct (N × H)
517. #2377	C₂×C₄₁	semidirect
518. #2376	C₂×C₄₁	semidirect
519. #2374	C₂×C₄₁	semidirect
520. #2365	C₂×C₄₁	semidirect
521. #2362	C₂×C₄₁	semidirect
522. #2360	C₂×C₄₁	semidirect
523. #2357	C₂×C₄₁	semidirect
524. #2352	C₂×C₄₁	semidirect
525. #2345	C₂×C₄₁	semidirect
526. #2341	C₂×C₄₁	semidirect
527. #2341	C₂×C₄₁	semidirect
528. #2335	C₂×C₄₁	semidirect
529. #2335	C₂×C₄₁	semidirect
530. #2333	C₂×C₄₁	semidirect
531. #2327	C₂×C₄₁	semidirect
532. #2323	C₂×C₄₁	semidirect
533. #2319	C₂×C₄₁	semidirect
534. #2313	C₂×C₄₁	semidirect
535. #2311	C₂×C₄₁	semidirect
536. C₄×C₂²⋊Q₈	C₂×C₄₁	semidirect
537. #2297	C₂×C₄₁	semidirect
538. #2290	C₂×C₄₁	semidirect
551. #547	C₄×C₄₁	semidirect
649. C₄₁	#34473	direct (N × H)
654. C₂×#41	C₂×C₄×C₄₁	semidirect
655. C₂×#41	C₂×C₄×C₄₁	semidirect
670. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
671. #123	C₂×C₄×C₄₁	semidirect
672. #123	C₂×C₄×C₄₁	semidirect
673. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
674. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
681. C₄×D₄	C₂×C₄×C₄₁	semidirect
685. 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×#547	2
C₄₁×#2377	2
C₄₁×#2376	2
C₄₁×#2374	2
C₄₁×#2365	2
C₄₁×#2362	2
C₄₁×#2360	2
C₄₁×#2357	2
C₄₁×#2352	2
C₄₁×#2345	2
C₄₁×#2341	2
C₄₁×#2335	2
C₄₁×#2333	2
C₄₁×#2327	2
C₄₁×#2323	2
C₄₁×#2319	2
C₄₁×#2313	2
C₄₁×#2311	2
C₄×C₂²⋊Q₈×C₄₁	2
C₄₁×#2297	2
C₄₁×#2290	2
#34473	41

Subgroups — C41×#34473 #23810674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34473 #23810674