Subgroups — C₄₁×#61593 #23837794

Order 10496.

2148 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3519	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3329	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3320	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3299	C₂	1	2	yes	maximal, complemented
6	D₄×SD₁₆×C₄₁	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3278	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3266	C₂	1	4	yes	maximal, complemented
9	C₄₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3193	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3190	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3004	C₂	1	2	yes	maximal, complemented
16	C₂×C₄₁×#448	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₄₁	C₂²	1	2	yes	complemented
19	C₂×#137×C₄₁	C₂²	1	4	yes	complemented
20	C₂²×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
21	C₄₁×#555	C₂²	1	1	yes	characteristic
22	C₄₁×#554	C₂²	1	1	yes	characteristic
23	C₄₁×#553	—	2	1	no	—
24	C₄₁×#553	C₂²	1	2	yes	—
25	C₄₁×#550	C₂²	1	1	yes	characteristic
26	D₄×Q₈×C₄₁	—	2	1	no	—
27	D₄×Q₈×C₄₁	—	2	2	no	—
28	D₄×Q₈×C₄₁	—	2	1	no	—
29	D₄×Q₈×C₄₁	C₂²	1	2	yes	—
30	D₄×Q₈×C₄₁	C₂²	1	4	yes	complemented
31	D₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
32	C₄₁×#546	—	2	2	no	—
33	C₄₁×#546	C₂²	1	2	yes	—
34	D₄²×C₄₁	—	2	1	no	—
35	D₄²×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#540	—	2	1	no	—
37	C₄₁×#538	—	2	2	no	—
38	C₄₁×#532	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₄₁	—	2	1	no	—
40	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
41	C₄₁×#529	C₂²	1	1	yes	characteristic
42	C₄₁×#525	C₂²	1	2	yes	—
43	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
44	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
45	C₂×#121×C₄₁	C₂²	1	2	yes	—
46	C₄₁×#518	—	2	1	no	—
47	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₄₁	—	2	1	no	—
49	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
50	C₄₁×#497	C₂²	1	2	yes	complemented
51	C₄₁×#492	C₂²	1	2	yes	complemented
52	C₄₁×#491	C₂²	1	2	yes	complemented
53	C₄₁×#487	C₂²	1	2	yes	complemented
54	C₄₁×#485	C₂²	1	4	yes	complemented
55	C₄₁×#484	C₂²	1	4	yes	complemented
56	C₄₁×#483	C₂²	1	1	yes	characteristic, complemented
57	C₄₁×#480	C₂²	1	1	yes	characteristic
58	C₄₁×#480	C₂²	1	2	yes	complemented
59	C₄₁×#479	C₂²	1	2	yes	complemented
60	C₄₁×#477	C₂²	1	2	yes	complemented
61	C₄₁×#468	C₂²	1	4	yes	complemented
62	C₄₁×#468	C₂²	1	4	yes	complemented
63	C₄₁×#467	C₂²	1	4	yes	complemented
64	C₄₁×#465	C₂²	1	4	yes	complemented
65	C₄₁×#464	C₂²	1	2	yes	complemented
66	C₄₁×#462	C₂²	1	2	yes	complemented
67	C₄₁×#461	C₂²	1	4	yes	complemented
68	C₄₁×#461	C₂²	1	2	yes	complemented
69	C₄₁×#460	C₂²	1	2	yes	complemented
70	C₄₁×#452	C₂²	1	4	yes	complemented
71	C₄₁×#451	C₂²	1	4	yes	complemented
72	C₄₁×#451	C₂²	1	1	yes	characteristic, complemented
73	C₄₁×#451	C₂²	1	2	yes	complemented
74	C₄₁×#450	C₂²	1	4	yes	complemented
75	C₄₁×#448	C₂²	1	1	yes	characteristic
76	C₄₁×#448	C₂²	1	2	yes	—
77	C₄₁×#448	C₂²	1	4	yes	complemented
78	C₄₁×#448	C₂²	1	4	yes	complemented
79	C₄₁×#448	C₂²	1	4	yes	complemented
80	C₄₁×#448	C₂²	1	2	yes	complemented
81	C₄₁×#448	C₂²	1	2	yes	complemented
82	C₄₁×#448	C₂²	1	2	yes	complemented
83	C₄₁×#440	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
86	C₄₁×#436	C₂²	1	2	yes	complemented
87	C₄₁×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₄₁	C₂²	1	2	yes	—
89	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
90	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₄₁×#419	C₂²	1	4	yes	complemented
92	C₂×#103×C₄₁	C₂²	1	4	yes	complemented
93	C₄₁×#407	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
95	C₂×#41×C₄₁	—	2	1	no	—
96	C₂×#41×C₄₁	C₂³	1	2	yes	—
97	C₂²×Q₈×C₄₁	—	2	2	no	—
98	C₂²×Q₈×C₄₁	—	2	2	no	—
99	C₂²×Q₈×C₄₁	—	2	2	no	—
100	C₂²×Q₈×C₄₁	—	4	8	no	—
101	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
103	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
104	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
105	C₂²×D₄×C₄₁	—	2	2	no	—
106	C₂²×D₄×C₄₁	—	2	1	no	—
107	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
108	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
109	C₂³×C₄×C₄₁	—	2	2	no	—
110	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
111	#137×C₄₁	—	4	8	no	—
112	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
113	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₄₁	—	4	8	no	—
115	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
120	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
121	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₄₁	—	2	2	no	—
123	C₄⋊Q₈×C₄₁	—	2	2	no	—
124	C₄⋊Q₈×C₄₁	—	2	4	no	—
125	C₄⋊Q₈×C₄₁	—	2	1	no	—
126	C₄⋊Q₈×C₄₁	—	2	1	no	—
127	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
130	#127×C₄₁	—	2	1	no	—
131	#127×C₄₁	C₂³	1	1	yes	characteristic
132	#126×C₄₁	—	2	2	no	—
133	#126×C₄₁	—	2	1	no	—
134	#125×C₄₁	—	2	1	no	—
135	#125×C₄₁	C₂³	1	1	yes	characteristic
136	#124×C₄₁	—	2	2	no	—
137	#124×C₄₁	—	2	1	no	—
138	#124×C₄₁	C₂³	1	1	yes	characteristic
139	#123×C₄₁	—	2	2	no	—
140	#123×C₄₁	—	2	1	no	—
141	#123×C₄₁	—	2	2	no	—
142	#123×C₄₁	—	2	2	no	—
143	C₂²⋊Q₈×C₄₁	—	2	2	no	—
144	C₂²⋊Q₈×C₄₁	—	2	2	no	—
145	C₂²⋊Q₈×C₄₁	—	2	4	no	—
146	C₂²⋊Q₈×C₄₁	—	2	4	no	—
147	C₂²⋊Q₈×C₄₁	—	2	4	no	—
148	C₂²⋊Q₈×C₄₁	—	2	4	no	—
149	C₂²⋊Q₈×C₄₁	—	2	2	no	—
150	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
152	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
153	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
154	#121×C₄₁	—	2	2	no	—
155	#121×C₄₁	—	2	1	no	—
156	#121×C₄₁	—	2	2	no	—
157	#121×C₄₁	—	2	2	no	—
158	#121×C₄₁	—	2	1	no	—
159	#121×C₄₁	—	2	1	no	—
160	#121×C₄₁	—	2	2	no	—
161	#121×C₄₁	—	2	2	no	—
162	#121×C₄₁	C₂³	1	1	yes	characteristic
163	#121×C₄₁	C₂³	1	2	yes	—
164	#121×C₄₁	C₂³	1	2	yes	—
165	#121×C₄₁	C₂³	1	2	yes	—
166	#121×C₄₁	C₂³	1	2	yes	—
167	#120×C₄₁	—	2	2	no	—
168	#120×C₄₁	—	2	2	no	—
169	#120×C₄₁	—	2	2	no	—
170	C₄×Q₈×C₄₁	—	2	1	no	—
171	C₄×Q₈×C₄₁	—	2	1	no	—
172	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
173	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
174	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₄₁	—	2	2	no	—
176	C₄×D₄×C₄₁	—	2	4	no	—
177	C₄×D₄×C₄₁	—	2	2	no	—
178	C₄×D₄×C₄₁	—	2	1	no	—
179	C₄×D₄×C₄₁	—	2	2	no	—
180	C₄×D₄×C₄₁	—	2	2	no	—
181	C₄×D₄×C₄₁	—	2	1	no	—
182	C₄×D₄×C₄₁	—	2	1	no	—
183	C₄×D₄×C₄₁	—	2	2	no	—
184	C₄×D₄×C₄₁	—	2	1	no	—
185	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
186	C₄×D₄×C₄₁	D₄	1	2	yes	—
187	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
188	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₄₁	C₂³	1	2	yes	—
190	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₄₁	C₂³	1	2	yes	—
192	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
193	#117×C₄₁	—	2	1	no	—
194	#117×C₄₁	—	2	1	no	—
195	#117×C₄₁	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
197	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
198	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
199	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
200	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
207	C₂×C₄²×C₄₁	—	2	1	no	—
208	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
209	#107×C₄₁	C₂³	1	2	yes	—
210	#107×C₄₁	C₂³	1	4	yes	—
211	#106×C₄₁	C₂³	1	2	yes	—
212	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
213	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
214	#103×C₄₁	C₂³	1	2	yes	—
215	#103×C₄₁	C₂³	1	4	yes	—
216	#103×C₄₁	C₂³	1	4	yes	—
217	#103×C₄₁	C₂³	1	4	yes	—
218	#103×C₄₁	C₂³	1	2	yes	—
219	#103×C₄₁	C₂³	1	4	yes	—
220	#103×C₄₁	C₂³	1	4	yes	—
221	#103×C₄₁	C₂³	1	2	yes	—
222	#102×C₄₁	C₂³	1	2	yes	—
223	#102×C₄₁	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
225	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
229	#97×C₄₁	C₂³	1	2	yes	—
230	C₄×C₈×C₄₁	C₂³	1	2	yes	—
231	C₂⁴×C₄₁	—	2	2	no	—
232	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
233	#41×C₄₁	—	4	4	no	—
234	#41×C₄₁	—	8	2	no	—
235	C₂×Q₈×C₄₁	—	2	4	no	—
236	C₂×Q₈×C₄₁	—	2	1	no	—
237	C₂×Q₈×C₄₁	—	2	4	no	—
238	C₂×Q₈×C₄₁	—	2	4	no	—
239	C₂×Q₈×C₄₁	—	2	2	no	—
240	C₂×Q₈×C₄₁	—	2	1	no	—
241	C₂×Q₈×C₄₁	—	2	8	no	—
242	C₂×Q₈×C₄₁	—	2	8	no	—
243	C₂×Q₈×C₄₁	—	4	4	no	—
244	C₂×Q₈×C₄₁	—	4	4	no	—
245	C₂×Q₈×C₄₁	—	4	4	no	—
246	C₂×Q₈×C₄₁	—	4	8	no	—
247	C₂×Q₈×C₄₁	—	4	8	no	—
248	C₂×Q₈×C₄₁	—	4	8	no	—
249	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
250	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
251	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
252	C₂×D₄×C₄₁	—	2	4	no	—
253	C₂×D₄×C₄₁	—	2	2	no	—
254	C₂×D₄×C₄₁	—	2	2	no	—
255	C₂×D₄×C₄₁	—	2	1	no	—
256	C₂×D₄×C₄₁	—	2	2	no	—
257	C₂×D₄×C₄₁	—	2	2	no	—
258	C₂×D₄×C₄₁	—	2	2	no	—
259	C₂×D₄×C₄₁	—	2	1	no	—
260	C₂×D₄×C₄₁	—	2	1	no	—
261	C₂×D₄×C₄₁	—	2	2	no	—
262	C₂×D₄×C₄₁	—	4	4	no	—
263	C₂×D₄×C₄₁	—	4	4	no	—
264	C₂×D₄×C₄₁	—	8	4	no	—
265	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
267	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
268	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₄₁	—	2	1	no	—
271	C₂²×C₄×C₄₁	—	2	1	no	—
272	C₂²×C₄×C₄₁	—	2	2	no	—
273	C₂²×C₄×C₄₁	—	2	4	no	—
274	C₂²×C₄×C₄₁	—	2	4	no	—
275	C₂²×C₄×C₄₁	—	2	2	no	—
276	C₂²×C₄×C₄₁	—	2	1	no	—
277	C₂²×C₄×C₄₁	—	2	2	no	—
278	C₂²×C₄×C₄₁	—	2	2	no	—
279	C₂²×C₄×C₄₁	—	4	4	no	—
280	C₂²×C₄×C₄₁	—	4	8	no	—
281	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₄₁	C₂×D₄	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	Q₁₆×C₄₁	—	2	4	no	—
290	Q₁₆×C₄₁	—	4	4	no	—
291	SD₁₆×C₄₁	—	2	4	no	—
292	SD₁₆×C₄₁	—	2	8	no	—
293	SD₁₆×C₄₁	—	4	4	no	—
294	SD₁₆×C₄₁	—	4	4	no	—
295	SD₁₆×C₄₁	—	4	4	no	—
296	M₁₆×C₄₁	—	4	4	no	—
297	C₂×C₈×C₄₁	—	4	4	no	—
298	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
299	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
300	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₄₁	—	2	2	no	—
302	C₄⋊C₄×C₄₁	—	2	2	no	—
303	C₄⋊C₄×C₄₁	—	2	2	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	4	no	—
308	C₄⋊C₄×C₄₁	—	2	4	no	—
309	C₄⋊C₄×C₄₁	—	2	1	no	—
310	C₄⋊C₄×C₄₁	—	2	2	no	—
311	C₄⋊C₄×C₄₁	—	2	1	no	—
312	C₄⋊C₄×C₄₁	—	2	1	no	—
313	C₄⋊C₄×C₄₁	—	2	1	no	—
314	C₄⋊C₄×C₄₁	—	2	1	no	—
315	C₄⋊C₄×C₄₁	—	2	2	no	—
316	C₄⋊C₄×C₄₁	—	2	1	no	—
317	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
318	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
320	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
324	C₂²⋊C₄×C₄₁	—	2	2	no	—
325	C₂²⋊C₄×C₄₁	—	2	4	no	—
326	C₂²⋊C₄×C₄₁	—	2	4	no	—
327	C₂²⋊C₄×C₄₁	—	2	2	no	—
328	C₂²⋊C₄×C₄₁	—	2	1	no	—
329	C₂²⋊C₄×C₄₁	—	2	1	no	—
330	C₂²⋊C₄×C₄₁	—	2	1	no	—
331	C₂²⋊C₄×C₄₁	—	2	2	no	—
332	C₂²⋊C₄×C₄₁	—	2	2	no	—
333	C₂²⋊C₄×C₄₁	—	2	2	no	—
334	C₂²⋊C₄×C₄₁	—	2	1	no	—
335	C₂²⋊C₄×C₄₁	—	2	2	no	—
336	C₂²⋊C₄×C₄₁	—	2	1	no	—
337	C₂²⋊C₄×C₄₁	—	2	2	no	—
338	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
339	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
342	C₄²×C₄₁	—	2	2	no	—
343	C₄²×C₄₁	—	2	2	no	—
344	C₄²×C₄₁	—	2	2	no	—
345	C₄²×C₄₁	—	2	1	no	—
346	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
349	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
350	C₂³×C₄₁	—	2	4	no	—
351	C₂³×C₄₁	—	2	4	no	—
352	C₂³×C₄₁	—	2	1	no	—
353	C₂³×C₄₁	—	2	2	no	—
354	C₂³×C₄₁	—	4	2	no	—
355	C₂³×C₄₁	—	4	4	no	—
356	C₂³×C₄₁	—	8	2	no	—
357	C₂³×C₄₁	—	8	2	no	—
358	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
359	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
360	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
361	Q₈×C₄₁	—	2	4	no	—
362	Q₈×C₄₁	—	2	2	no	—
363	Q₈×C₄₁	—	2	4	no	—
364	Q₈×C₄₁	—	2	4	no	—
365	Q₈×C₄₁	—	2	2	no	—
366	Q₈×C₄₁	—	4	8	no	—
367	Q₈×C₄₁	—	4	8	no	—
368	Q₈×C₄₁	—	4	4	no	—
369	Q₈×C₄₁	—	8	1	no	—
370	Q₈×C₄₁	H(5,𝔽₂)	1	4	yes	—
371	D₄×C₄₁	—	2	4	no	—
372	D₄×C₄₁	—	2	2	no	—
373	D₄×C₄₁	—	2	2	no	—
374	D₄×C₄₁	—	2	4	no	—
375	D₄×C₄₁	—	4	4	no	—
376	D₄×C₄₁	—	4	2	no	—
377	D₄×C₄₁	—	4	4	no	—
378	D₄×C₄₁	—	4	2	no	—
379	D₄×C₄₁	—	8	2	no	—
380	D₄×C₄₁	—	8	1	no	—
381	D₄×C₄₁	—	8	2	no	—
382	D₄×C₄₁	—	8	2	no	—
383	D₄×C₄₁	—	8	2	no	—
384	D₄×C₄₁	#137	1	4	yes	complemented
385	C₂×C₄×C₄₁	—	2	4	no	—
386	C₂×C₄×C₄₁	—	2	2	no	—
387	C₂×C₄×C₄₁	—	2	2	no	—
388	C₂×C₄×C₄₁	—	2	2	no	—
389	C₂×C₄×C₄₁	—	2	4	no	—
390	C₂×C₄×C₄₁	—	2	4	no	—
391	C₂×C₄×C₄₁	—	2	2	no	—
392	C₂×C₄×C₄₁	—	2	1	no	—
393	C₂×C₄×C₄₁	—	2	2	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	4	no	—
398	C₂×C₄×C₄₁	—	4	2	no	—
399	C₂×C₄×C₄₁	—	4	2	no	—
400	C₂×C₄×C₄₁	—	4	2	no	—
401	C₂×C₄×C₄₁	—	4	8	no	—
402	C₂×C₄×C₄₁	—	4	8	no	—
403	C₂×C₄×C₄₁	—	4	4	no	—
404	C₂×C₄×C₄₁	—	4	2	no	—
405	C₂×C₄×C₄₁	—	4	2	no	—
406	C₂×C₄×C₄₁	—	8	2	no	—
407	C₂×C₄×C₄₁	—	8	2	no	—
408	C₂×C₄×C₄₁	—	8	2	no	—
409	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
417	C₈×C₄₁	—	2	2	no	—
418	C₈×C₄₁	—	2	4	no	—
419	C₈×C₄₁	—	2	2	no	—
420	#61593	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
421	C₂²×C₄₁	—	2	1	no	—
422	C₂²×C₄₁	—	2	2	no	—
423	C₂²×C₄₁	—	2	1	no	—
424	C₂²×C₄₁	—	2	2	no	—
425	C₂²×C₄₁	—	2	2	no	—
426	C₂²×C₄₁	—	2	2	no	—
427	C₂²×C₄₁	—	2	2	no	—
428	C₂²×C₄₁	—	4	8	no	—
429	C₂²×C₄₁	—	4	2	no	—
430	C₂²×C₄₁	—	4	1	no	—
431	C₂²×C₄₁	—	4	1	no	—
432	C₂²×C₄₁	—	4	2	no	—
433	C₂²×C₄₁	—	4	2	no	—
434	C₂²×C₄₁	—	4	1	no	—
435	C₂²×C₄₁	—	16	4	no	—
436	C₂²×C₄₁	C₂×#137	1	4	yes	—
437	C₂²×C₄₁	#577	1	2	yes	—
438	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₄₁	—	2	4	no	—
440	C₄×C₄₁	—	2	1	no	—
441	C₄×C₄₁	—	2	2	no	—
442	C₄×C₄₁	—	2	2	no	—
443	C₄×C₄₁	—	2	1	no	—
444	C₄×C₄₁	—	2	1	no	—
445	C₄×C₄₁	—	2	1	no	—
446	C₄×C₄₁	—	4	4	no	—
447	C₄×C₄₁	—	4	1	no	—
448	C₄×C₄₁	—	4	1	no	—
449	C₄×C₄₁	—	4	2	no	—
450	C₄×C₄₁	—	4	1	no	—
451	C₄×C₄₁	—	4	2	no	—
452	C₄×C₄₁	C₂×#137	1	2	yes	—
453	C₄×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
454	#3519	C₂×C₄₁	1	1	yes	characteristic
455	C₂×D₄×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
456	#3329	C₂×C₄₁	1	2	yes	complemented
457	#3320	C₂×C₄₁	1	4	yes	complemented
458	#3299	C₂×C₄₁	1	2	yes	complemented
459	D₄×SD₁₆	C₂×C₄₁	1	2	yes	complemented
460	#3278	C₂×C₄₁	1	2	yes	complemented
461	#3266	C₂×C₄₁	1	4	yes	complemented
462	#3218	C₂×C₄₁	1	1	yes	characteristic, complemented
463	#3206	C₂×C₄₁	1	1	yes	characteristic, complemented
464	#3193	C₂×C₄₁	1	2	yes	complemented
465	#3190	C₂×C₄₁	1	2	yes	complemented
466	#3112	C₂×C₄₁	1	1	yes	characteristic, complemented
467	#3108	C₂×C₄₁	1	1	yes	characteristic, complemented
468	#3004	C₂×C₄₁	1	2	yes	complemented
469	C₂×#448	C₂×C₄₁	1	2	yes	complemented
470	#2974	C₂×C₄₁	1	1	yes	characteristic, complemented
471	C₂×C₄₁	—	2	2	no	—
472	C₂×C₄₁	—	2	4	no	—
473	C₂×C₄₁	—	4	2	no	—
474	C₂×C₄₁	—	8	2	no	—
475	C₂×C₄₁	—	8	1	no	—
476	C₂×C₄₁	#3484	1	1	yes	characteristic
477	C₂×C₄₁	C₂²×#137	1	1	yes	characteristic
478	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
479	C₂³×Q₈	C₂²×C₄₁	1	2	yes	complemented
480	C₂×#137	C₂²×C₄₁	1	4	yes	complemented
481	C₂²×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
482	#555	C₂²×C₄₁	1	1	yes	characteristic
483	#554	C₂²×C₄₁	1	1	yes	characteristic
484	#553	—	2	1	no	—
485	#553	C₂²×C₄₁	1	2	yes	—
486	#550	C₂²×C₄₁	1	1	yes	characteristic
487	D₄×Q₈	—	2	1	no	—
488	D₄×Q₈	—	2	2	no	—
489	D₄×Q₈	—	2	1	no	—
490	D₄×Q₈	C₂²×C₄₁	1	2	yes	—
491	D₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
492	D₄×Q₈	C₂²×C₄₁	1	4	yes	complemented
493	#546	—	2	2	no	—
494	#546	C₂²×C₄₁	1	2	yes	—
495	D₄²	—	2	1	no	—
496	D₄²	C₂²×C₄₁	1	1	yes	characteristic
497	#540	—	2	1	no	—
498	#538	—	2	2	no	—
499	#532	C₂²×C₄₁	1	1	yes	characteristic
500	C₂×C₄⋊Q₈	—	2	1	no	—
501	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
502	#529	C₂²×C₄₁	1	1	yes	characteristic
503	#525	C₂²×C₄₁	1	2	yes	—
504	C₂×C₂²⋊Q₈	—	2	2	no	—
505	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
506	C₂×#121	C₂²×C₄₁	1	2	yes	—
507	#518	—	2	1	no	—
508	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
509	C₂×C₄×D₄	—	2	1	no	—
510	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
511	#497	C₂²×C₄₁	1	2	yes	complemented
512	#492	C₂²×C₄₁	1	2	yes	complemented
513	#491	C₂²×C₄₁	1	2	yes	complemented
514	#487	C₂²×C₄₁	1	2	yes	complemented
515	#485	C₂²×C₄₁	1	4	yes	complemented
516	#484	C₂²×C₄₁	1	4	yes	complemented
517	#483	C₂²×C₄₁	1	1	yes	characteristic, complemented
518	#480	C₂²×C₄₁	1	1	yes	characteristic
519	#480	C₂²×C₄₁	1	2	yes	complemented
520	#479	C₂²×C₄₁	1	2	yes	complemented
521	#477	C₂²×C₄₁	1	2	yes	complemented
522	#468	C₂²×C₄₁	1	4	yes	complemented
523	#468	C₂²×C₄₁	1	4	yes	complemented
524	#467	C₂²×C₄₁	1	4	yes	complemented
525	#465	C₂²×C₄₁	1	4	yes	complemented
526	#464	C₂²×C₄₁	1	2	yes	complemented
527	#462	C₂²×C₄₁	1	2	yes	complemented
528	#461	C₂²×C₄₁	1	2	yes	complemented
529	#461	C₂²×C₄₁	1	4	yes	complemented
530	#460	C₂²×C₄₁	1	2	yes	complemented
531	#452	C₂²×C₄₁	1	4	yes	complemented
532	#451	C₂²×C₄₁	1	1	yes	characteristic, complemented
533	#451	C₂²×C₄₁	1	2	yes	complemented
534	#451	C₂²×C₄₁	1	4	yes	complemented
535	#450	C₂²×C₄₁	1	4	yes	complemented
536	#448	C₂²×C₄₁	1	1	yes	characteristic
537	#448	C₂²×C₄₁	1	2	yes	—
538	#448	C₂²×C₄₁	1	4	yes	complemented
539	#448	C₂²×C₄₁	1	2	yes	complemented
540	#448	C₂²×C₄₁	1	2	yes	complemented
541	#448	C₂²×C₄₁	1	2	yes	complemented
542	#448	C₂²×C₄₁	1	4	yes	complemented
543	#448	C₂²×C₄₁	1	4	yes	complemented
544	#440	C₂²×C₄₁	1	4	yes	complemented
545	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
546	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
547	#436	C₂²×C₄₁	1	2	yes	complemented
548	#435	C₂²×C₄₁	1	4	yes	complemented
549	C₈×D₄	C₂²×C₄₁	1	2	yes	—
550	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
551	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
552	#419	C₂²×C₄₁	1	4	yes	complemented
553	C₂×#103	C₂²×C₄₁	1	4	yes	complemented
554	#407	C₂²×C₄₁	1	2	yes	complemented
555	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
556	C₄₁	#61593	1	1	yes	characteristic, direct product factor, Sylow
557	C₂×#41	—	2	1	no	—
558	C₂×#41	C₂³×C₄₁	1	2	yes	—
559	C₂²×Q₈	—	2	2	no	—
560	C₂²×Q₈	—	2	2	no	—
561	C₂²×Q₈	—	2	2	no	—
562	C₂²×Q₈	—	4	8	no	—
563	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
564	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
565	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
566	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
567	C₂²×D₄	—	2	2	no	—
568	C₂²×D₄	—	2	1	no	—
569	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
571	C₂³×C₄	—	2	2	no	—
572	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
573	#137	—	4	8	no	—
574	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
575	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
576	C₂×SD₁₆	—	4	8	no	—
577	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
578	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
579	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
580	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
581	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
582	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
583	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
584	C₄⋊Q₈	—	2	2	no	—
585	C₄⋊Q₈	—	2	2	no	—
586	C₄⋊Q₈	—	2	4	no	—
587	C₄⋊Q₈	—	2	1	no	—
588	C₄⋊Q₈	—	2	1	no	—
589	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
591	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
592	#127	—	2	1	no	—
593	#127	C₂³×C₄₁	1	1	yes	characteristic
594	#126	—	2	2	no	—
595	#126	—	2	1	no	—
596	#125	—	2	1	no	—
597	#125	C₂³×C₄₁	1	1	yes	characteristic
598	#124	—	2	2	no	—
599	#124	—	2	1	no	—
600	#124	C₂³×C₄₁	1	1	yes	characteristic
601	#123	—	2	2	no	—
602	#123	—	2	1	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	C₂²⋊Q₈	—	2	2	no	—
606	C₂²⋊Q₈	—	2	2	no	—
607	C₂²⋊Q₈	—	2	4	no	—
608	C₂²⋊Q₈	—	2	4	no	—
609	C₂²⋊Q₈	—	2	4	no	—
610	C₂²⋊Q₈	—	2	4	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
613	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
614	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
615	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
616	#121	—	2	2	no	—
617	#121	—	2	1	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	—	2	1	no	—
621	#121	—	2	1	no	—
622	#121	—	2	2	no	—
623	#121	—	2	2	no	—
624	#121	C₂³×C₄₁	1	1	yes	characteristic
625	#121	C₂³×C₄₁	1	2	yes	—
626	#121	C₂³×C₄₁	1	2	yes	—
627	#121	C₂³×C₄₁	1	2	yes	—
628	#121	C₂³×C₄₁	1	2	yes	—
629	#120	—	2	2	no	—
630	#120	—	2	2	no	—
631	#120	—	2	2	no	—
632	C₄×Q₈	—	2	1	no	—
633	C₄×Q₈	—	2	1	no	—
634	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
635	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
636	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	4	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
648	C₄×D₄	D₄×C₄₁	1	2	yes	—
649	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₄₁	1	2	yes	—
652	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
653	C₄×D₄	C₂³×C₄₁	1	2	yes	—
654	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
655	#117	—	2	1	no	—
656	#117	—	2	1	no	—
657	#117	C₂³×C₄₁	1	2	yes	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	—	2	1	no	—
661	C₂×C₄⋊C₄	—	2	2	no	—
662	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₂²⋊C₄	—	2	2	no	—
668	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
671	#107	C₂³×C₄₁	1	2	yes	—
672	#107	C₂³×C₄₁	1	4	yes	—
673	#106	C₂³×C₄₁	1	2	yes	—
674	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
675	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
676	#103	C₂³×C₄₁	1	2	yes	—
677	#103	C₂³×C₄₁	1	4	yes	—
678	#103	C₂³×C₄₁	1	4	yes	—
679	#103	C₂³×C₄₁	1	4	yes	—
680	#103	C₂³×C₄₁	1	2	yes	—
681	#103	C₂³×C₄₁	1	4	yes	—
682	#103	C₂³×C₄₁	1	4	yes	—
683	#103	C₂³×C₄₁	1	2	yes	—
684	#102	C₂³×C₄₁	1	2	yes	—
685	#102	C₂³×C₄₁	1	4	yes	—
686	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
687	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
688	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
689	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
690	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
691	#97	C₂³×C₄₁	1	2	yes	—
692	C₄×C₈	C₂³×C₄₁	1	2	yes	—
693	C₂⁴	—	2	2	no	—
694	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
695	#41	—	4	4	no	—
696	#41	—	8	2	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	8	no	—
704	C₂×Q₈	—	2	8	no	—
705	C₂×Q₈	—	4	4	no	—
706	C₂×Q₈	—	4	4	no	—
707	C₂×Q₈	—	4	4	no	—
708	C₂×Q₈	—	4	8	no	—
709	C₂×Q₈	—	4	8	no	—
710	C₂×Q₈	—	4	8	no	—
711	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
712	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
713	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	8	4	no	—
727	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
728	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
729	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
730	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
731	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	4	4	no	—
742	C₂²×C₄	—	4	8	no	—
743	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
746	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
747	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
751	Q₁₆	—	2	4	no	—
752	Q₁₆	—	4	4	no	—
753	SD₁₆	—	2	4	no	—
754	SD₁₆	—	2	8	no	—
755	SD₁₆	—	4	4	no	—
756	SD₁₆	—	4	4	no	—
757	SD₁₆	—	4	4	no	—
758	M₁₆	—	4	4	no	—
759	C₂×C₈	—	4	4	no	—
760	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
761	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
762	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
780	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
781	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
782	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
783	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
784	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
785	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
801	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
803	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	1	no	—
808	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
809	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
810	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
811	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
812	C₂³	—	2	4	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	4	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
821	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
822	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
823	Q₈	—	2	4	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	4	no	—
826	Q₈	—	2	4	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	4	8	no	—
829	Q₈	—	4	8	no	—
830	Q₈	—	4	4	no	—
831	Q₈	—	8	1	no	—
832	Q₈	H(5,𝔽₂)×C₄₁	1	4	yes	—
833	D₄	—	2	4	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	2	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	1	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	2	no	—
846	D₄	#137×C₄₁	1	4	yes	complemented
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	8	no	—
864	C₂×C₄	—	4	8	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
878	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
879	C₈	—	2	2	no	—
880	C₈	—	2	4	no	—
881	C₈	—	2	2	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	8	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	16	4	no	—
897	C₂²	C₂×#137×C₄₁	1	4	yes	—
898	C₂²	C₄₁×#577	1	2	yes	—
899	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	4	no	—
912	C₄	—	4	1	no	—
913	C₄	C₂×#137×C₄₁	1	2	yes	—
914	C₄	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
915	C₂	—	2	2	no	—
916	C₂	—	2	4	no	—
917	C₂	—	4	2	no	—
918	C₂	—	8	1	no	—
919	C₂	—	8	2	no	—
920	C₂	C₄₁×#3484	1	1	yes	characteristic
921	C₂	C₂²×#137×C₄₁	1	1	yes	characteristic
922	C₂	C₂×C₄₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3519	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×Q₈×C₄₁	C₂	semidirect
3. C₄₁×#3329	C₂	semidirect
4. C₄₁×#3320	C₂	semidirect
5. C₄₁×#3299	C₂	semidirect
6. D₄×SD₁₆×C₄₁	C₂	semidirect
7. C₄₁×#3278	C₂	semidirect
8. C₄₁×#3266	C₂	semidirect
9. C₄₁×#3218	C₂	semidirect
10. C₄₁×#3206	C₂	semidirect
11. C₄₁×#3193	C₂	semidirect
12. C₄₁×#3190	C₂	semidirect
13. C₄₁×#3112	C₂	semidirect
14. C₄₁×#3108	C₂	semidirect
15. C₄₁×#3004	C₂	semidirect
16. C₂×C₄₁×#448	C₂	semidirect
17. C₄₁×#2974	C₂	semidirect
18. C₂³×Q₈×C₄₁	C₂²	semidirect
19. C₂×#137×C₄₁	C₂²	semidirect
20. C₂²×SD₁₆×C₄₁	C₂²	semidirect
30. D₄×Q₈×C₄₁	C₂²	semidirect
31. D₄×Q₈×C₄₁	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
44. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
47. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
50. C₄₁×#497	C₂²	semidirect
51. C₄₁×#492	C₂²	semidirect
52. C₄₁×#491	C₂²	semidirect
53. C₄₁×#487	C₂²	semidirect
54. C₄₁×#485	C₂²	semidirect
55. C₄₁×#484	C₂²	semidirect
56. C₄₁×#483	C₂²	semidirect
58. C₄₁×#480	C₂²	semidirect
59. C₄₁×#479	C₂²	semidirect
60. C₄₁×#477	C₂²	semidirect
61. C₄₁×#468	C₂²	semidirect
62. C₄₁×#468	C₂²	semidirect
63. C₄₁×#467	C₂²	semidirect
64. C₄₁×#465	C₂²	semidirect
65. C₄₁×#464	C₂²	semidirect
66. C₄₁×#462	C₂²	semidirect
67. C₄₁×#461	C₂²	semidirect
68. C₄₁×#461	C₂²	semidirect
69. C₄₁×#460	C₂²	semidirect
70. C₄₁×#452	C₂²	semidirect
71. C₄₁×#451	C₂²	semidirect
72. C₄₁×#451	C₂²	semidirect
73. C₄₁×#451	C₂²	semidirect
74. C₄₁×#450	C₂²	semidirect
77. C₄₁×#448	C₂²	semidirect
78. C₄₁×#448	C₂²	semidirect
79. C₄₁×#448	C₂²	semidirect
80. C₄₁×#448	C₂²	semidirect
81. C₄₁×#448	C₂²	semidirect
82. C₄₁×#448	C₂²	semidirect
83. C₄₁×#440	C₂²	semidirect
84. C₄×Q₁₆×C₄₁	C₂²	semidirect
85. C₄×SD₁₆×C₄₁	C₂²	semidirect
86. C₄₁×#436	C₂²	semidirect
87. C₄₁×#435	C₂²	semidirect
89. C₄₁×#432	C₂²	semidirect
90. C₄₁×#431	C₂²	semidirect
91. C₄₁×#419	C₂²	semidirect
92. C₂×#103×C₄₁	C₂²	semidirect
93. C₄₁×#407	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
384. D₄×C₄₁	#137	semidirect
420. #61593	C₄₁	direct (N × H)
455. C₂×D₄×Q₈	C₂×C₄₁	semidirect
456. #3329	C₂×C₄₁	semidirect
457. #3320	C₂×C₄₁	semidirect
458. #3299	C₂×C₄₁	semidirect
459. D₄×SD₁₆	C₂×C₄₁	semidirect
460. #3278	C₂×C₄₁	semidirect
461. #3266	C₂×C₄₁	semidirect
462. #3218	C₂×C₄₁	semidirect
463. #3206	C₂×C₄₁	semidirect
464. #3193	C₂×C₄₁	semidirect
465. #3190	C₂×C₄₁	semidirect
466. #3112	C₂×C₄₁	semidirect
467. #3108	C₂×C₄₁	semidirect
468. #3004	C₂×C₄₁	semidirect
469. C₂×#448	C₂×C₄₁	semidirect
470. #2974	C₂×C₄₁	semidirect
479. C₂³×Q₈	C₂²×C₄₁	semidirect
480. C₂×#137	C₂²×C₄₁	semidirect
481. C₂²×SD₁₆	C₂²×C₄₁	semidirect
491. D₄×Q₈	C₂²×C₄₁	semidirect
492. D₄×Q₈	C₂²×C₄₁	semidirect
501. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
505. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
508. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
511. #497	C₂²×C₄₁	semidirect
512. #492	C₂²×C₄₁	semidirect
513. #491	C₂²×C₄₁	semidirect
514. #487	C₂²×C₄₁	semidirect
515. #485	C₂²×C₄₁	semidirect
516. #484	C₂²×C₄₁	semidirect
517. #483	C₂²×C₄₁	semidirect
519. #480	C₂²×C₄₁	semidirect
520. #479	C₂²×C₄₁	semidirect
521. #477	C₂²×C₄₁	semidirect
522. #468	C₂²×C₄₁	semidirect
523. #468	C₂²×C₄₁	semidirect
524. #467	C₂²×C₄₁	semidirect
525. #465	C₂²×C₄₁	semidirect
526. #464	C₂²×C₄₁	semidirect
527. #462	C₂²×C₄₁	semidirect
528. #461	C₂²×C₄₁	semidirect
529. #461	C₂²×C₄₁	semidirect
530. #460	C₂²×C₄₁	semidirect
531. #452	C₂²×C₄₁	semidirect
532. #451	C₂²×C₄₁	semidirect
533. #451	C₂²×C₄₁	semidirect
534. #451	C₂²×C₄₁	semidirect
535. #450	C₂²×C₄₁	semidirect
538. #448	C₂²×C₄₁	semidirect
539. #448	C₂²×C₄₁	semidirect
540. #448	C₂²×C₄₁	semidirect
541. #448	C₂²×C₄₁	semidirect
542. #448	C₂²×C₄₁	semidirect
543. #448	C₂²×C₄₁	semidirect
544. #440	C₂²×C₄₁	semidirect
545. C₄×Q₁₆	C₂²×C₄₁	semidirect
546. C₄×SD₁₆	C₂²×C₄₁	semidirect
547. #436	C₂²×C₄₁	semidirect
548. #435	C₂²×C₄₁	semidirect
550. #432	C₂²×C₄₁	semidirect
551. #431	C₂²×C₄₁	semidirect
552. #419	C₂²×C₄₁	semidirect
553. C₂×#103	C₂²×C₄₁	semidirect
554. #407	C₂²×C₄₁	semidirect
555. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
556. C₄₁	#61593	direct (N × H)
846. D₄	#137×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3519	2
C₂×D₄×Q₈×C₄₁	2
C₄₁×#3329	2
C₄₁×#3320	2
C₄₁×#3299	2
D₄×SD₁₆×C₄₁	2
C₄₁×#3278	2
C₄₁×#3266	2
C₄₁×#3218	2
C₄₁×#3206	2
C₄₁×#3193	2
C₄₁×#3190	2
C₄₁×#3112	2
C₄₁×#3108	2
C₄₁×#3004	2
C₂×C₄₁×#448	2
C₄₁×#2974	2
#61593	41

Subgroups — C41×#61593 #23837794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61593 #23837794