Subgroups — C₄₁×#34284 #23810485

Order 10496.

2286 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#542	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2373	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2373	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2372	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2367	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2367	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#2363	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#2362	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#2361	C₂	1	1	yes	maximal, characteristic
13	C₄₁×#2360	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#2335	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2332	C₂	1	2	yes	maximal, complemented
16	C₄₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂²⋊Q₈×C₄₁	C₂	1	2	yes	maximal, complemented
18	C₄×#123×C₄₁	C₂	1	2	yes	maximal, complemented
19	C₄₁×#2298	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄₁×#2276	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄₁×#542	C₄	1	16	yes	complemented
25	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#126×C₄₁	C₂²	1	2	yes	—
27	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#124×C₄₁	C₂²	1	2	yes	—
29	C₂×#123×C₄₁	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
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	2	yes	—
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×C₄×D₄×C₄₁	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
45	C₄₁×#391	C₂²	1	1	yes	characteristic
46	C₄₁×#391	C₂²	1	1	yes	characteristic
47	C₄₁×#391	C₂²	1	2	yes	—
48	C₄₁×#391	C₂²	1	2	yes	—
49	C₄₁×#391	C₂²	1	2	yes	—
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×#389	C₂²	1	1	yes	characteristic
54	C₄₁×#389	C₂²	1	1	yes	characteristic
55	C₄₁×#389	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×#388	C₂²	1	1	yes	characteristic
60	C₄₁×#388	C₂²	1	1	yes	characteristic
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×#388	C₂²	1	2	yes	—
73	C₄₁×#387	C₂²	1	2	yes	—
74	C₄₁×#387	C₂²	1	2	yes	—
75	C₄₁×#387	C₂²	1	1	yes	characteristic
76	C₄₁×#387	C₂²	1	1	yes	characteristic
77	C₄₁×#387	C₂²	1	1	yes	characteristic
78	C₄₁×#387	C₂²	1	1	yes	characteristic
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×#386	C₂²	1	2	yes	—
84	C₄₁×#386	C₂²	1	2	yes	—
85	C₄₁×#385	C₂²	1	2	yes	—
86	C₄₁×#385	C₂²	1	2	yes	—
87	C₄₁×#385	C₂²	1	2	yes	—
88	C₄₁×#385	C₂²	1	2	yes	—
89	C₄₁×#381	C₂²	1	2	yes	—
90	C₄₁×#380	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
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	2	yes	—
109	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
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	C₄₁×#376	C₂²	1	1	yes	characteristic
121	C₄₁×#376	C₂²	1	2	yes	—
122	C₄₁×#376	C₂²	1	2	yes	—
123	C₄³×C₄₁	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×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	2	yes	—
129	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
130	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
134	#126×C₄₁	C₂×C₄	1	16	yes	complemented
135	#124×C₄₁	C₂×C₄	1	8	yes	complemented
136	#124×C₄₁	C₂×C₄	1	16	yes	complemented
137	#123×C₄₁	C₂×C₄	1	16	yes	complemented
138	C₂²⋊Q₈×C₄₁	C₂×C₄	1	16	yes	complemented
139	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
140	#121×C₄₁	C₂×C₄	1	8	yes	—
141	C₄×Q₈×C₄₁	—	2	4	no	—
142	C₄×Q₈×C₄₁	—	2	4	no	—
143	C₄×Q₈×C₄₁	—	4	4	no	—
144	C₄×Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
145	C₄×D₄×C₄₁	—	2	4	no	—
146	C₄×D₄×C₄₁	—	2	4	no	—
147	C₄×D₄×C₄₁	—	4	4	no	—
148	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
149	#117×C₄₁	—	2	4	no	—
150	#117×C₄₁	C₂×C₄	1	8	yes	complemented
151	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
152	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
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	2	yes	—
165	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
173	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
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	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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×C₄²×C₄₁	—	4	4	no	—
193	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
195	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
196	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
200	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
204	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
205	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
206	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
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	1	yes	characteristic
213	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
215	#95×C₄₁	C₂³	1	1	yes	characteristic
216	#95×C₄₁	C₂³	1	2	yes	—
217	#95×C₄₁	C₂³	1	2	yes	—
218	#95×C₄₁	C₂³	1	2	yes	—
219	#95×C₄₁	C₂³	1	1	yes	characteristic
220	#95×C₄₁	C₂³	1	1	yes	characteristic
221	#95×C₄₁	C₂³	1	2	yes	—
222	#95×C₄₁	C₂³	1	2	yes	—
223	#95×C₄₁	C₂³	1	1	yes	characteristic
224	#95×C₄₁	C₂³	1	2	yes	—
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	2	yes	—
230	#95×C₄₁	C₂³	1	1	yes	characteristic
231	#95×C₄₁	C₂³	1	2	yes	—
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	1	yes	characteristic
238	#95×C₄₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
243	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₄₁	—	2	2	no	—
246	C₂×Q₈×C₄₁	—	2	2	no	—
247	C₂×Q₈×C₄₁	—	4	2	no	—
248	C₂×Q₈×C₄₁	—	4	2	no	—
249	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
250	C₂×Q₈×C₄₁	C₂²×C₄	1	8	yes	—
251	C₂×D₄×C₄₁	—	2	2	no	—
252	C₂×D₄×C₄₁	—	2	2	no	—
253	C₂×D₄×C₄₁	—	4	2	no	—
254	C₂×D₄×C₄₁	—	4	2	no	—
255	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
256	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
257	C₂²×C₄×C₄₁	—	2	2	no	—
258	C₂²×C₄×C₄₁	—	2	2	no	—
259	C₂²×C₄×C₄₁	—	2	4	no	—
260	C₂²×C₄×C₄₁	—	2	4	no	—
261	C₂²×C₄×C₄₁	—	2	4	no	—
262	C₂²×C₄×C₄₁	—	2	4	no	—
263	C₂²×C₄×C₄₁	—	2	4	no	—
264	C₂²×C₄×C₄₁	—	4	2	no	—
265	C₂²×C₄×C₄₁	—	4	2	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	C₂²×C₄	1	4	yes	—
271	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
272	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
286	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
293	C₄⋊C₄×C₄₁	—	2	4	no	—
294	C₄⋊C₄×C₄₁	—	2	2	no	—
295	C₄⋊C₄×C₄₁	—	2	2	no	—
296	C₄⋊C₄×C₄₁	—	2	4	no	—
297	C₄⋊C₄×C₄₁	—	2	4	no	—
298	C₄⋊C₄×C₄₁	—	2	4	no	—
299	C₄⋊C₄×C₄₁	—	2	2	no	—
300	C₄⋊C₄×C₄₁	—	2	2	no	—
301	C₄⋊C₄×C₄₁	—	4	1	no	—
302	C₄⋊C₄×C₄₁	—	4	2	no	—
303	C₄⋊C₄×C₄₁	—	4	2	no	—
304	C₄⋊C₄×C₄₁	—	4	1	no	—
305	C₄⋊C₄×C₄₁	—	4	2	no	—
306	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
307	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
308	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
309	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
310	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
311	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
312	C₄⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
313	C₄⋊C₄×C₄₁	#41	1	4	yes	—
314	C₄⋊C₄×C₄₁	#41	1	4	yes	—
315	C₂²⋊C₄×C₄₁	—	2	4	no	—
316	C₂²⋊C₄×C₄₁	—	2	4	no	—
317	C₂²⋊C₄×C₄₁	—	2	4	no	—
318	C₂²⋊C₄×C₄₁	—	2	2	no	—
319	C₂²⋊C₄×C₄₁	—	2	2	no	—
320	C₂²⋊C₄×C₄₁	—	4	2	no	—
321	C₂²⋊C₄×C₄₁	—	4	1	no	—
322	C₂²⋊C₄×C₄₁	—	4	1	no	—
323	C₂²⋊C₄×C₄₁	—	4	2	no	—
324	C₂²⋊C₄×C₄₁	—	4	2	no	—
325	C₂²⋊C₄×C₄₁	—	4	2	no	—
326	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
327	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
328	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
329	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
330	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
331	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
332	C₂²⋊C₄×C₄₁	C₂²×C₄	1	8	yes	—
333	C₄²×C₄₁	—	2	4	no	—
334	C₄²×C₄₁	—	2	2	no	—
335	C₄²×C₄₁	—	2	2	no	—
336	C₄²×C₄₁	—	2	4	no	—
337	C₄²×C₄₁	—	2	4	no	—
338	C₄²×C₄₁	—	2	2	no	—
339	C₄²×C₄₁	—	2	2	no	—
340	C₄²×C₄₁	—	2	2	no	—
341	C₄²×C₄₁	—	2	4	no	—
342	C₄²×C₄₁	—	2	2	no	—
343	C₄²×C₄₁	—	4	2	no	—
344	C₄²×C₄₁	—	4	2	no	—
345	C₄²×C₄₁	—	4	1	no	—
346	C₄²×C₄₁	—	4	2	no	—
347	C₄²×C₄₁	—	4	2	no	—
348	C₄²×C₄₁	—	4	1	no	—
349	C₄²×C₄₁	—	4	2	no	—
350	C₄²×C₄₁	—	4	2	no	—
351	C₄²×C₄₁	—	4	2	no	—
352	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
353	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
354	C₄²×C₄₁	C₂²×C₄	1	8	yes	—
355	C₂³×C₄₁	—	2	1	no	—
356	C₂³×C₄₁	—	2	2	no	—
357	C₂³×C₄₁	—	2	2	no	—
358	C₂³×C₄₁	—	2	1	no	—
359	C₂³×C₄₁	—	2	1	no	—
360	C₂³×C₄₁	—	2	2	no	—
361	C₂³×C₄₁	—	2	1	no	—
362	C₂³×C₄₁	—	2	2	no	—
363	C₂³×C₄₁	—	2	2	no	—
364	C₂³×C₄₁	—	2	1	no	—
365	C₂³×C₄₁	—	2	2	no	—
366	C₂³×C₄₁	—	2	1	no	—
367	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
368	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
369	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
370	Q₈×C₄₁	—	2	8	no	—
371	Q₈×C₄₁	—	4	8	no	—
372	D₄×C₄₁	—	2	8	no	—
373	D₄×C₄₁	—	4	8	no	—
374	C₂×C₄×C₄₁	—	2	1	no	—
375	C₂×C₄×C₄₁	—	2	2	no	—
376	C₂×C₄×C₄₁	—	2	2	no	—
377	C₂×C₄×C₄₁	—	2	1	no	—
378	C₂×C₄×C₄₁	—	2	1	no	—
379	C₂×C₄×C₄₁	—	2	1	no	—
380	C₂×C₄×C₄₁	—	2	2	no	—
381	C₂×C₄×C₄₁	—	2	1	no	—
382	C₂×C₄×C₄₁	—	2	1	no	—
383	C₂×C₄×C₄₁	—	2	2	no	—
384	C₂×C₄×C₄₁	—	2	2	no	—
385	C₂×C₄×C₄₁	—	2	2	no	—
386	C₂×C₄×C₄₁	—	2	1	no	—
387	C₂×C₄×C₄₁	—	2	1	no	—
388	C₂×C₄×C₄₁	—	2	1	no	—
389	C₂×C₄×C₄₁	—	2	2	no	—
390	C₂×C₄×C₄₁	—	2	1	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	2	no	—
395	C₂×C₄×C₄₁	—	2	2	no	—
396	C₂×C₄×C₄₁	—	2	2	no	—
397	C₂×C₄×C₄₁	—	2	1	no	—
398	C₂×C₄×C₄₁	—	2	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	1	no	—
403	C₂×C₄×C₄₁	—	2	2	no	—
404	C₂×C₄×C₄₁	—	2	1	no	—
405	C₂×C₄×C₄₁	—	2	1	no	—
406	C₂×C₄×C₄₁	—	2	2	no	—
407	C₂×C₄×C₄₁	—	2	1	no	—
408	C₂×C₄×C₄₁	—	2	1	no	—
409	C₂×C₄×C₄₁	—	2	2	no	—
410	C₂×C₄×C₄₁	—	2	1	no	—
411	C₂×C₄×C₄₁	—	2	1	no	—
412	C₂×C₄×C₄₁	—	2	1	no	—
413	C₂×C₄×C₄₁	—	2	2	no	—
414	C₂×C₄×C₄₁	—	2	1	no	—
415	C₂×C₄×C₄₁	—	2	1	no	—
416	C₂×C₄×C₄₁	—	2	2	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	2	no	—
423	C₂×C₄×C₄₁	—	4	8	no	—
424	C₂×C₄×C₄₁	—	4	8	no	—
425	C₂×C₄×C₄₁	—	4	8	no	—
426	C₂×C₄×C₄₁	—	8	4	no	—
427	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
428	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
429	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
430	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
431	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
432	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
433	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
434	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
435	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
436	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
437	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
438	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
439	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
440	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
441	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
442	#34284	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
443	C₂²×C₄₁	—	2	2	no	—
444	C₂²×C₄₁	—	2	4	no	—
445	C₂²×C₄₁	—	2	4	no	—
446	C₂²×C₄₁	—	2	2	no	—
447	C₂²×C₄₁	—	2	2	no	—
448	C₂²×C₄₁	—	2	4	no	—
449	C₂²×C₄₁	—	4	2	no	—
450	C₂²×C₄₁	—	4	1	no	—
451	C₂²×C₄₁	—	4	2	no	—
452	C₂²×C₄₁	—	4	1	no	—
453	C₂²×C₄₁	—	4	2	no	—
454	C₂²×C₄₁	—	4	1	no	—
455	C₂²×C₄₁	—	4	1	no	—
456	C₂²×C₄₁	—	4	2	no	—
457	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
458	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
459	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
460	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
462	C₂²×C₄₁	#585	1	1	yes	characteristic
463	C₂²×C₄₁	#585	1	1	yes	characteristic
464	C₄×C₄₁	—	2	2	no	—
465	C₄×C₄₁	—	2	4	no	—
466	C₄×C₄₁	—	2	2	no	—
467	C₄×C₄₁	—	2	4	no	—
468	C₄×C₄₁	—	2	4	no	—
469	C₄×C₄₁	—	2	2	no	—
470	C₄×C₄₁	—	2	2	no	—
471	C₄×C₄₁	—	2	2	no	—
472	C₄×C₄₁	—	2	2	no	—
473	C₄×C₄₁	—	2	4	no	—
474	C₄×C₄₁	—	2	2	no	—
475	C₄×C₄₁	—	2	4	no	—
476	C₄×C₄₁	—	4	1	no	—
477	C₄×C₄₁	—	4	2	no	—
478	C₄×C₄₁	—	4	1	no	—
479	C₄×C₄₁	—	4	1	no	—
480	C₄×C₄₁	—	4	1	no	—
481	C₄×C₄₁	—	4	1	no	—
482	C₄×C₄₁	—	4	1	no	—
483	C₄×C₄₁	—	4	2	no	—
484	C₄×C₄₁	C₄×#41	1	4	yes	—
485	C₂×#542	C₂×C₄₁	1	1	yes	characteristic
486	#2373	C₂×C₄₁	1	2	yes	complemented
487	#2373	C₂×C₄₁	1	2	yes	complemented
488	#2372	C₂×C₄₁	1	2	yes	complemented
489	#2369	C₂×C₄₁	1	1	yes	characteristic, complemented
490	#2367	C₂×C₄₁	1	1	yes	characteristic, complemented
491	#2367	C₂×C₄₁	1	1	yes	characteristic, complemented
492	#2367	C₂×C₄₁	1	2	yes	complemented
493	#2365	C₂×C₄₁	1	1	yes	characteristic, complemented
494	#2363	C₂×C₄₁	1	1	yes	characteristic
495	#2362	C₂×C₄₁	1	1	yes	characteristic, complemented
496	#2361	C₂×C₄₁	1	1	yes	characteristic
497	#2360	C₂×C₄₁	1	1	yes	characteristic, complemented
498	#2335	C₂×C₄₁	1	2	yes	complemented
499	#2332	C₂×C₄₁	1	2	yes	complemented
500	#2319	C₂×C₄₁	1	1	yes	characteristic, complemented
501	C₄×C₂²⋊Q₈	C₂×C₄₁	1	2	yes	complemented
502	C₄×#123	C₂×C₄₁	1	2	yes	complemented
503	#2298	C₂×C₄₁	1	1	yes	characteristic, complemented
504	#2295	C₂×C₄₁	1	1	yes	characteristic, complemented
505	#2276	C₂×C₄₁	1	1	yes	characteristic, complemented
506	#2274	C₂×C₄₁	1	1	yes	characteristic, complemented
507	C₄²×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
508	C₂×C₄₁	—	4	2	no	—
509	C₂×C₄₁	—	4	4	no	—
510	C₂×C₄₁	C₂×C₄×#41	1	1	yes	characteristic
511	C₂×C₄₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
512	C₂×C₄₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
513	C₂×C₄₁	#3513	1	1	yes	characteristic
514	C₂×C₄₁	#3518	1	1	yes	characteristic
515	C₂×C₄₁	#3520	1	1	yes	characteristic
516	C₂×C₄₁	#3524	1	1	yes	characteristic
517	#542	C₄×C₄₁	1	16	yes	complemented
518	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
519	C₂×#126	C₂²×C₄₁	1	2	yes	—
520	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
521	C₂×#124	C₂²×C₄₁	1	2	yes	—
522	C₂×#123	C₂²×C₄₁	1	2	yes	—
523	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
524	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
525	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
526	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
527	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
528	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
529	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
530	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
531	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
532	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
533	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
534	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
535	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
536	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
537	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
538	#391	C₂²×C₄₁	1	2	yes	—
539	#391	C₂²×C₄₁	1	2	yes	—
540	#391	C₂²×C₄₁	1	1	yes	characteristic
541	#391	C₂²×C₄₁	1	1	yes	characteristic
542	#391	C₂²×C₄₁	1	2	yes	—
543	#390	C₂²×C₄₁	1	1	yes	characteristic
544	#390	C₂²×C₄₁	1	1	yes	characteristic
545	#390	C₂²×C₄₁	1	2	yes	—
546	#389	C₂²×C₄₁	1	1	yes	characteristic
547	#389	C₂²×C₄₁	1	1	yes	characteristic
548	#389	C₂²×C₄₁	1	2	yes	—
549	#389	C₂²×C₄₁	1	2	yes	—
550	#389	C₂²×C₄₁	1	1	yes	characteristic
551	#389	C₂²×C₄₁	1	1	yes	characteristic
552	#388	C₂²×C₄₁	1	2	yes	—
553	#388	C₂²×C₄₁	1	2	yes	—
554	#388	C₂²×C₄₁	1	2	yes	—
555	#388	C₂²×C₄₁	1	2	yes	—
556	#388	C₂²×C₄₁	1	2	yes	—
557	#388	C₂²×C₄₁	1	2	yes	—
558	#388	C₂²×C₄₁	1	1	yes	characteristic
559	#388	C₂²×C₄₁	1	2	yes	—
560	#388	C₂²×C₄₁	1	2	yes	—
561	#388	C₂²×C₄₁	1	2	yes	—
562	#388	C₂²×C₄₁	1	2	yes	—
563	#388	C₂²×C₄₁	1	1	yes	characteristic
564	#388	C₂²×C₄₁	1	1	yes	characteristic
565	#388	C₂²×C₄₁	1	1	yes	characteristic
566	#387	C₂²×C₄₁	1	1	yes	characteristic
567	#387	C₂²×C₄₁	1	2	yes	—
568	#387	C₂²×C₄₁	1	2	yes	—
569	#387	C₂²×C₄₁	1	2	yes	—
570	#387	C₂²×C₄₁	1	2	yes	—
571	#387	C₂²×C₄₁	1	2	yes	—
572	#387	C₂²×C₄₁	1	1	yes	characteristic
573	#387	C₂²×C₄₁	1	1	yes	characteristic
574	#387	C₂²×C₄₁	1	2	yes	—
575	#387	C₂²×C₄₁	1	1	yes	characteristic
576	#386	C₂²×C₄₁	1	2	yes	—
577	#386	C₂²×C₄₁	1	2	yes	—
578	#385	C₂²×C₄₁	1	2	yes	—
579	#385	C₂²×C₄₁	1	2	yes	—
580	#385	C₂²×C₄₁	1	2	yes	—
581	#385	C₂²×C₄₁	1	2	yes	—
582	#381	C₂²×C₄₁	1	2	yes	—
583	#380	C₂²×C₄₁	1	2	yes	—
584	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
585	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
586	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
587	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
588	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
590	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
592	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
594	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
595	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
596	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
598	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
599	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
600	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
601	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
602	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
603	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
604	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
605	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
606	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
607	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
608	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
609	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
611	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
612	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
613	#376	C₂²×C₄₁	1	1	yes	characteristic
614	#376	C₂²×C₄₁	1	2	yes	—
615	#376	C₂²×C₄₁	1	2	yes	—
616	C₄³	C₂²×C₄₁	1	1	yes	characteristic
617	C₄₁	#34284	1	1	yes	characteristic, direct product factor, Sylow
618	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
619	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
620	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
621	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
622	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
623	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
624	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
626	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
627	C₄⋊Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
628	#126	C₂×C₄×C₄₁	1	16	yes	complemented
629	#124	C₂×C₄×C₄₁	1	8	yes	complemented
630	#124	C₂×C₄×C₄₁	1	16	yes	complemented
631	#123	C₂×C₄×C₄₁	1	16	yes	complemented
632	C₂²⋊Q₈	C₂×C₄×C₄₁	1	16	yes	complemented
633	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
634	#121	C₂×C₄×C₄₁	1	8	yes	—
635	C₄×Q₈	—	2	4	no	—
636	C₄×Q₈	—	2	4	no	—
637	C₄×Q₈	—	4	4	no	—
638	C₄×Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
639	C₄×D₄	—	2	4	no	—
640	C₄×D₄	—	2	4	no	—
641	C₄×D₄	—	4	4	no	—
642	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
643	#117	—	2	4	no	—
644	#117	C₂×C₄×C₄₁	1	8	yes	complemented
645	C₂×C₄⋊C₄	—	2	4	no	—
646	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
686	C₂×C₄²	—	4	4	no	—
687	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
688	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
691	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
692	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
695	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
698	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
699	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
700	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
703	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
704	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
705	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
706	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
709	#95	C₂³×C₄₁	1	1	yes	characteristic
710	#95	C₂³×C₄₁	1	2	yes	—
711	#95	C₂³×C₄₁	1	2	yes	—
712	#95	C₂³×C₄₁	1	2	yes	—
713	#95	C₂³×C₄₁	1	1	yes	characteristic
714	#95	C₂³×C₄₁	1	1	yes	characteristic
715	#95	C₂³×C₄₁	1	2	yes	—
716	#95	C₂³×C₄₁	1	2	yes	—
717	#95	C₂³×C₄₁	1	1	yes	characteristic
718	#95	C₂³×C₄₁	1	2	yes	—
719	#95	C₂³×C₄₁	1	2	yes	—
720	#95	C₂³×C₄₁	1	1	yes	characteristic
721	#95	C₂³×C₄₁	1	2	yes	—
722	#95	C₂³×C₄₁	1	1	yes	characteristic
723	#95	C₂³×C₄₁	1	2	yes	—
724	#95	C₂³×C₄₁	1	1	yes	characteristic
725	#95	C₂³×C₄₁	1	2	yes	—
726	#95	C₂³×C₄₁	1	1	yes	characteristic
727	#95	C₂³×C₄₁	1	2	yes	—
728	#95	C₂³×C₄₁	1	2	yes	—
729	#95	C₂³×C₄₁	1	2	yes	—
730	#95	C₂³×C₄₁	1	2	yes	—
731	#95	C₂³×C₄₁	1	1	yes	characteristic
732	#95	C₂³×C₄₁	1	1	yes	characteristic
733	#95	C₂³×C₄₁	1	2	yes	—
734	#95	C₂³×C₄₁	1	2	yes	—
735	#95	C₂³×C₄₁	1	1	yes	characteristic
736	#95	C₂³×C₄₁	1	1	yes	characteristic
737	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
738	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	2	2	no	—
741	C₂×Q₈	—	4	2	no	—
742	C₂×Q₈	—	4	2	no	—
743	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
744	C₂×Q₈	C₂²×C₄×C₄₁	1	8	yes	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
750	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	—	4	2	no	—
762	C₂²×C₄	—	4	2	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
765	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
766	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	4	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	1	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	1	no	—
800	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
801	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
802	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
803	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
804	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
805	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
806	C₄⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
807	C₄⋊C₄	#41×C₄₁	1	4	yes	—
808	C₄⋊C₄	#41×C₄₁	1	4	yes	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	1	no	—
817	C₂²⋊C₄	—	4	1	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
821	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
822	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₄₁	1	8	yes	—
827	C₄²	—	2	4	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	4	no	—
831	C₄²	—	2	4	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	4	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	4	2	no	—
838	C₄²	—	4	2	no	—
839	C₄²	—	4	2	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	1	no	—
843	C₄²	—	4	2	no	—
844	C₄²	—	4	2	no	—
845	C₄²	—	4	1	no	—
846	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
847	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
848	C₄²	C₂²×C₄×C₄₁	1	8	yes	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	1	no	—
861	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
862	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
863	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
864	Q₈	—	2	8	no	—
865	Q₈	—	4	8	no	—
866	D₄	—	2	8	no	—
867	D₄	—	4	8	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	8	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	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	—	4	8	no	—
918	C₂×C₄	—	4	8	no	—
919	C₂×C₄	—	4	8	no	—
920	C₂×C₄	—	8	4	no	—
921	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
922	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
923	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
924	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
925	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
926	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
927	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
928	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
929	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
930	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
931	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
932	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
933	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
934	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
935	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
951	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
952	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
953	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
954	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
955	C₂²	C₄₁×#585	1	1	yes	characteristic
956	C₂²	C₄₁×#585	1	1	yes	characteristic
957	C₄	—	2	2	no	—
958	C₄	—	2	4	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	4	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	4	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	2	no	—
977	C₄	C₄×#41×C₄₁	1	4	yes	—
978	C₂	—	4	2	no	—
979	C₂	—	4	4	no	—
980	C₂	C₂×C₄×#41×C₄₁	1	1	yes	characteristic
981	C₂	C₄×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
982	C₂	C₄×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
983	C₂	C₄₁×#3513	1	1	yes	characteristic
984	C₂	C₄₁×#3518	1	1	yes	characteristic
985	C₂	C₄₁×#3520	1	1	yes	characteristic
986	C₂	C₄₁×#3524	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×#121×C₄₁	C₂²
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×#2373	C₂	semidirect
3. C₄₁×#2373	C₂	semidirect
4. C₄₁×#2372	C₂	semidirect
5. C₄₁×#2369	C₂	semidirect
6. C₄₁×#2367	C₂	semidirect
7. C₄₁×#2367	C₂	semidirect
8. C₄₁×#2367	C₂	semidirect
9. C₄₁×#2365	C₂	semidirect
11. C₄₁×#2362	C₂	semidirect
13. C₄₁×#2360	C₂	semidirect
14. C₄₁×#2335	C₂	semidirect
15. C₄₁×#2332	C₂	semidirect
16. C₄₁×#2319	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₄₁	C₂	semidirect
18. C₄×#123×C₄₁	C₂	semidirect
19. C₄₁×#2298	C₂	semidirect
20. C₄₁×#2295	C₂	semidirect
21. C₄₁×#2276	C₂	semidirect
22. C₄₁×#2274	C₂	semidirect
23. C₄²×D₄×C₄₁	C₂	semidirect
24. C₄₁×#542	C₄	semidirect
133. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
134. #126×C₄₁	C₂×C₄	semidirect
135. #124×C₄₁	C₂×C₄	semidirect
136. #124×C₄₁	C₂×C₄	semidirect
137. #123×C₄₁	C₂×C₄	semidirect
138. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
139. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
144. C₄×Q₈×C₄₁	C₂×C₄	semidirect
148. C₄×D₄×C₄₁	C₂×C₄	semidirect
150. #117×C₄₁	C₂×C₄	semidirect
442. #34284	C₄₁	direct (N × H)
486. #2373	C₂×C₄₁	semidirect
487. #2373	C₂×C₄₁	semidirect
488. #2372	C₂×C₄₁	semidirect
489. #2369	C₂×C₄₁	semidirect
490. #2367	C₂×C₄₁	semidirect
491. #2367	C₂×C₄₁	semidirect
492. #2367	C₂×C₄₁	semidirect
493. #2365	C₂×C₄₁	semidirect
495. #2362	C₂×C₄₁	semidirect
497. #2360	C₂×C₄₁	semidirect
498. #2335	C₂×C₄₁	semidirect
499. #2332	C₂×C₄₁	semidirect
500. #2319	C₂×C₄₁	semidirect
501. C₄×C₂²⋊Q₈	C₂×C₄₁	semidirect
502. C₄×#123	C₂×C₄₁	semidirect
503. #2298	C₂×C₄₁	semidirect
504. #2295	C₂×C₄₁	semidirect
505. #2276	C₂×C₄₁	semidirect
506. #2274	C₂×C₄₁	semidirect
507. C₄²×D₄	C₂×C₄₁	semidirect
517. #542	C₄×C₄₁	semidirect
617. C₄₁	#34284	direct (N × H)
627. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
628. #126	C₂×C₄×C₄₁	semidirect
629. #124	C₂×C₄×C₄₁	semidirect
630. #124	C₂×C₄×C₄₁	semidirect
631. #123	C₂×C₄×C₄₁	semidirect
632. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
633. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
638. C₄×Q₈	C₂×C₄×C₄₁	semidirect
642. C₄×D₄	C₂×C₄×C₄₁	semidirect
644. #117	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×#542	2
C₄₁×#2373	2
C₄₁×#2372	2
C₄₁×#2369	2
C₄₁×#2367	2
C₄₁×#2365	2
C₄₁×#2363	2
C₄₁×#2362	2
C₄₁×#2361	2
C₄₁×#2360	2
C₄₁×#2335	2
C₄₁×#2332	2
C₄₁×#2319	2
C₄×C₂²⋊Q₈×C₄₁	2
C₄×#123×C₄₁	2
C₄₁×#2298	2
C₄₁×#2295	2
C₄₁×#2276	2
C₄₁×#2274	2
C₄²×D₄×C₄₁	2
#34284	41

Subgroups — C41×#34284 #23810485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34284 #23810485