Subgroups — C₄₁×#61960 #23838161

Order 10496.

1834 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3475	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3398	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3372	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3329	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3312	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3276	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3266	C₂	1	4	yes	maximal, complemented
9	C₄₁×#3252	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3218	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3116	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3039	C₂	1	2	yes	maximal, complemented
16	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₄₁	C₂²	1	4	yes	—
19	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
20	Q₈²×C₄₁	—	2	1	no	—
21	C₄₁×#557	C₂²	1	2	yes	complemented
22	C₄₁×#556	C₂²	1	1	yes	characteristic
23	C₄₁×#555	C₂²	1	1	yes	characteristic
24	C₄₁×#554	—	2	2	no	—
25	C₄₁×#554	—	2	1	no	—
26	C₄₁×#554	C₂²	1	1	yes	characteristic
27	C₄₁×#553	—	2	1	no	—
28	C₄₁×#552	—	2	1	no	—
29	C₄₁×#552	C₂²	1	2	yes	—
30	C₄₁×#551	—	2	2	no	—
31	D₄×Q₈×C₄₁	C₂²	1	4	yes	—
32	D₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
33	C₄₁×#547	C₂²	1	1	yes	characteristic
34	C₄₁×#546	C₂²	1	2	yes	—
35	C₄₁×#544	—	2	1	no	—
36	C₄₁×#544	—	2	2	no	—
37	C₄₁×#533	C₂²	1	1	yes	characteristic
38	C₄₁×#533	C₂²	1	1	yes	characteristic
39	C₄₁×#533	C₂²	1	2	yes	complemented
40	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
42	C₄₁×#529	—	2	2	no	—
43	C₄₁×#529	C₂²	1	2	yes	—
44	C₄₁×#525	—	2	1	no	—
45	C₄₁×#520	—	2	1	no	—
46	C₄×#41×C₄₁	C₂²	1	2	yes	—
47	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×#117×C₄₁	—	2	1	no	—
50	C₄₁×#497	C₂²	1	4	yes	—
51	C₄₁×#494	C₂²	1	2	yes	complemented
52	C₄₁×#491	C₂²	1	4	yes	complemented
53	C₄₁×#487	C₂²	1	2	yes	complemented
54	C₄₁×#485	C₂²	1	4	yes	complemented
55	C₄₁×#483	C₂²	1	2	yes	—
56	C₄₁×#479	C₂²	1	4	yes	complemented
57	C₄₁×#477	C₂²	1	2	yes	complemented
58	C₄₁×#477	C₂²	1	2	yes	complemented
59	C₄₁×#476	C₂²	1	1	yes	characteristic
60	C₄₁×#476	C₂²	1	1	yes	characteristic
61	C₄₁×#470	C₂²	1	4	yes	complemented
62	C₄₁×#468	C₂²	1	4	yes	—
63	C₄₁×#467	C₂²	1	4	yes	—
64	C₄₁×#464	C₂²	1	4	yes	—
65	C₄₁×#462	C₂²	1	4	yes	complemented
66	C₄₁×#462	C₂²	1	2	yes	complemented
67	C₄₁×#462	C₂²	1	2	yes	complemented
68	C₄₁×#462	C₂²	1	2	yes	complemented
69	C₄₁×#462	C₂²	1	2	yes	complemented
70	C₄₁×#461	C₂²	1	1	yes	characteristic
71	C₄₁×#461	C₂²	1	2	yes	—
72	C₄₁×#461	C₂²	1	4	yes	—
73	C₄₁×#461	C₂²	1	2	yes	—
74	C₄₁×#461	C₂²	1	1	yes	characteristic
75	C₄₁×#461	C₂²	1	2	yes	—
76	C₄₁×#461	C₂²	1	2	yes	—
77	C₄₁×#452	C₂²	1	4	yes	—
78	C₄₁×#451	C₂²	1	4	yes	—
79	C₄₁×#451	C₂²	1	4	yes	complemented
80	C₄₁×#450	C₂²	1	2	yes	—
81	C₄₁×#448	C₂²	1	4	yes	—
82	C₄₁×#446	C₂²	1	2	yes	complemented
83	C₄₁×#441	C₂²	1	4	yes	complemented
84	C₄₁×#440	C₂²	1	4	yes	—
85	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
86	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
87	C₄₁×#436	C₂²	1	2	yes	complemented
88	C₄₁×#435	C₂²	1	4	yes	—
89	C₄₁×#432	C₂²	1	2	yes	complemented
90	C₄₁×#431	C₂²	1	1	yes	characteristic
91	C₄₁×#423	C₂²	1	2	yes	complemented
92	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
93	C₄₁×#419	C₂²	1	4	yes	complemented
94	C₂×#103×C₄₁	C₂²	1	2	yes	—
95	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
96	C₂×#41×C₄₁	C₂³	1	2	yes	—
97	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
98	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
99	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₄₁	—	2	1	no	—
101	#137×C₄₁	—	4	8	no	—
102	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
103	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
104	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₄₁	—	4	4	no	—
106	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
110	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
111	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₄₁	—	2	4	no	—
113	C₄⋊Q₈×C₄₁	—	2	2	no	—
114	C₄⋊Q₈×C₄₁	—	2	1	no	—
115	C₄⋊Q₈×C₄₁	—	2	1	no	—
116	C₄⋊Q₈×C₄₁	—	2	2	no	—
117	C₄⋊Q₈×C₄₁	—	2	2	no	—
118	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
125	#126×C₄₁	—	2	2	no	—
126	#126×C₄₁	—	2	2	no	—
127	#126×C₄₁	—	2	2	no	—
128	#125×C₄₁	—	2	2	no	—
129	#125×C₄₁	—	2	2	no	—
130	#125×C₄₁	—	2	4	no	—
131	#125×C₄₁	—	2	1	no	—
132	#125×C₄₁	—	2	1	no	—
133	#125×C₄₁	—	2	2	no	—
134	#125×C₄₁	C₂³	1	2	yes	—
135	#124×C₄₁	—	2	2	no	—
136	#124×C₄₁	C₂³	1	2	yes	—
137	#123×C₄₁	—	2	2	no	—
138	#123×C₄₁	—	2	2	no	—
139	#123×C₄₁	—	2	2	no	—
140	#123×C₄₁	—	2	2	no	—
141	C₂²⋊Q₈×C₄₁	—	2	1	no	—
142	C₂²⋊Q₈×C₄₁	—	2	1	no	—
143	C₂²⋊Q₈×C₄₁	—	2	1	no	—
144	C₂²⋊Q₈×C₄₁	—	2	1	no	—
145	C₂²⋊Q₈×C₄₁	—	2	2	no	—
146	C₂²⋊Q₈×C₄₁	—	2	2	no	—
147	C₂²⋊Q₈×C₄₁	—	2	4	no	—
148	C₂²⋊Q₈×C₄₁	—	2	4	no	—
149	C₂²⋊Q₈×C₄₁	—	2	4	no	—
150	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
153	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
154	#121×C₄₁	—	2	1	no	—
155	#121×C₄₁	—	2	1	no	—
156	#121×C₄₁	—	2	2	no	—
157	#121×C₄₁	C₂³	1	2	yes	—
158	#120×C₄₁	—	2	2	no	—
159	C₄×Q₈×C₄₁	—	2	2	no	—
160	C₄×Q₈×C₄₁	—	2	1	no	—
161	C₄×Q₈×C₄₁	—	2	1	no	—
162	C₄×Q₈×C₄₁	—	2	2	no	—
163	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
165	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
168	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₄₁	—	2	4	no	—
170	C₄×D₄×C₄₁	—	2	2	no	—
171	C₄×D₄×C₄₁	—	2	2	no	—
172	C₄×D₄×C₄₁	—	2	2	no	—
173	C₄×D₄×C₄₁	—	2	2	no	—
174	C₄×D₄×C₄₁	—	2	1	no	—
175	C₄×D₄×C₄₁	—	2	1	no	—
176	C₄×D₄×C₄₁	D₄	1	2	yes	—
177	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
178	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₄₁	C₂³	1	2	yes	—
183	C₄×D₄×C₄₁	C₂³	1	2	yes	—
184	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
185	#117×C₄₁	—	2	1	no	—
186	#117×C₄₁	—	2	1	no	—
187	#117×C₄₁	—	2	2	no	—
188	#117×C₄₁	—	2	1	no	—
189	#117×C₄₁	—	2	1	no	—
190	#117×C₄₁	—	2	2	no	—
191	#117×C₄₁	—	2	2	no	—
192	#117×C₄₁	—	2	2	no	—
193	#117×C₄₁	D₄	1	1	yes	characteristic
194	#117×C₄₁	D₄	1	2	yes	—
195	#117×C₄₁	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
197	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
198	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
199	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
200	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
204	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
205	C₂×C₄²×C₄₁	—	2	2	no	—
206	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
208	#107×C₄₁	C₂³	1	4	yes	—
209	#106×C₄₁	C₂³	1	2	yes	—
210	#106×C₄₁	C₂³	1	2	yes	—
211	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
212	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
213	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
215	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
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	#103×C₄₁	C₂³	1	4	yes	—
223	#103×C₄₁	C₂³	1	4	yes	—
224	#102×C₄₁	C₂³	1	2	yes	—
225	#102×C₄₁	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
228	#97×C₄₁	C₂³	1	4	yes	—
229	C₄×C₈×C₄₁	C₂³	1	2	yes	—
230	C₂⁴×C₄₁	—	2	1	no	—
231	#41×C₄₁	—	2	4	no	—
232	#41×C₄₁	—	2	4	no	—
233	#41×C₄₁	—	4	2	no	—
234	C₂×Q₈×C₄₁	—	2	1	no	—
235	C₂×Q₈×C₄₁	—	2	1	no	—
236	C₂×Q₈×C₄₁	—	2	4	no	—
237	C₂×Q₈×C₄₁	—	2	2	no	—
238	C₂×Q₈×C₄₁	—	4	2	no	—
239	C₂×Q₈×C₄₁	—	4	4	no	—
240	C₂×Q₈×C₄₁	—	4	2	no	—
241	C₂×Q₈×C₄₁	—	4	4	no	—
242	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
244	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
246	C₂×D₄×C₄₁	—	2	2	no	—
247	C₂×D₄×C₄₁	—	2	2	no	—
248	C₂×D₄×C₄₁	—	2	2	no	—
249	C₂×D₄×C₄₁	—	2	1	no	—
250	C₂×D₄×C₄₁	—	4	1	no	—
251	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
254	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₄₁	—	2	1	no	—
256	C₂²×C₄×C₄₁	—	2	4	no	—
257	C₂²×C₄×C₄₁	—	2	2	no	—
258	C₂²×C₄×C₄₁	—	2	1	no	—
259	C₂²×C₄×C₄₁	—	2	2	no	—
260	C₂²×C₄×C₄₁	—	2	1	no	—
261	C₂²×C₄×C₄₁	—	2	1	no	—
262	C₂²×C₄×C₄₁	—	2	1	no	—
263	C₂²×C₄×C₄₁	—	2	2	no	—
264	C₂²×C₄×C₄₁	—	4	4	no	—
265	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
271	Q₁₆×C₄₁	—	4	4	no	—
272	Q₁₆×C₄₁	—	4	4	no	—
273	Q₁₆×C₄₁	—	4	4	no	—
274	SD₁₆×C₄₁	—	2	8	no	—
275	SD₁₆×C₄₁	—	2	4	no	—
276	SD₁₆×C₄₁	—	4	4	no	—
277	SD₁₆×C₄₁	—	4	2	no	—
278	M₁₆×C₄₁	—	4	4	no	—
279	C₂×C₈×C₄₁	—	4	2	no	—
280	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
281	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
282	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
283	C₄⋊C₄×C₄₁	—	2	2	no	—
284	C₄⋊C₄×C₄₁	—	2	1	no	—
285	C₄⋊C₄×C₄₁	—	2	2	no	—
286	C₄⋊C₄×C₄₁	—	2	1	no	—
287	C₄⋊C₄×C₄₁	—	2	1	no	—
288	C₄⋊C₄×C₄₁	—	2	1	no	—
289	C₄⋊C₄×C₄₁	—	2	2	no	—
290	C₄⋊C₄×C₄₁	—	2	2	no	—
291	C₄⋊C₄×C₄₁	—	2	4	no	—
292	C₄⋊C₄×C₄₁	—	2	2	no	—
293	C₄⋊C₄×C₄₁	—	2	4	no	—
294	C₄⋊C₄×C₄₁	—	2	2	no	—
295	C₄⋊C₄×C₄₁	—	2	1	no	—
296	C₄⋊C₄×C₄₁	—	2	1	no	—
297	C₄⋊C₄×C₄₁	—	2	2	no	—
298	C₄⋊C₄×C₄₁	—	2	2	no	—
299	C₄⋊C₄×C₄₁	—	2	2	no	—
300	C₄⋊C₄×C₄₁	—	2	2	no	—
301	C₄⋊C₄×C₄₁	—	2	4	no	—
302	C₄⋊C₄×C₄₁	—	2	2	no	—
303	C₄⋊C₄×C₄₁	—	2	1	no	—
304	C₄⋊C₄×C₄₁	—	2	4	no	—
305	C₄⋊C₄×C₄₁	—	2	2	no	—
306	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
310	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
314	C₂²⋊C₄×C₄₁	—	2	2	no	—
315	C₂²⋊C₄×C₄₁	—	2	4	no	—
316	C₂²⋊C₄×C₄₁	—	2	2	no	—
317	C₂²⋊C₄×C₄₁	—	2	2	no	—
318	C₂²⋊C₄×C₄₁	—	2	2	no	—
319	C₂²⋊C₄×C₄₁	—	2	1	no	—
320	C₂²⋊C₄×C₄₁	—	2	2	no	—
321	C₂²⋊C₄×C₄₁	—	2	2	no	—
322	C₂²⋊C₄×C₄₁	—	2	1	no	—
323	C₂²⋊C₄×C₄₁	—	2	1	no	—
324	C₂²⋊C₄×C₄₁	—	2	1	no	—
325	C₂²⋊C₄×C₄₁	—	2	2	no	—
326	C₂²⋊C₄×C₄₁	—	2	2	no	—
327	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
330	C₄²×C₄₁	—	2	2	no	—
331	C₄²×C₄₁	—	2	2	no	—
332	C₄²×C₄₁	—	2	2	no	—
333	C₄²×C₄₁	—	2	4	no	—
334	C₄²×C₄₁	—	2	2	no	—
335	C₄²×C₄₁	C₂×D₄	1	2	yes	—
336	C₄²×C₄₁	C₂×D₄	1	2	yes	—
337	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
340	C₄²×C₄₁	C₂⁴	1	2	yes	—
341	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
342	C₂³×C₄₁	—	2	1	no	—
343	C₂³×C₄₁	—	2	1	no	—
344	C₂³×C₄₁	—	4	2	no	—
345	C₂³×C₄₁	—	4	2	no	—
346	C₂³×C₄₁	—	8	1	no	—
347	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
348	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
349	Q₈×C₄₁	—	2	2	no	—
350	Q₈×C₄₁	—	2	4	no	—
351	Q₈×C₄₁	—	2	2	no	—
352	Q₈×C₄₁	—	2	2	no	—
353	Q₈×C₄₁	—	2	2	no	—
354	Q₈×C₄₁	—	2	2	no	—
355	Q₈×C₄₁	—	2	4	no	—
356	Q₈×C₄₁	—	4	2	no	—
357	Q₈×C₄₁	—	8	1	no	—
358	Q₈×C₄₁	—	8	4	no	—
359	Q₈×C₄₁	—	8	2	no	—
360	D₄×C₄₁	—	2	4	no	—
361	D₄×C₄₁	—	2	2	no	—
362	D₄×C₄₁	—	2	1	no	—
363	D₄×C₄₁	—	2	1	no	—
364	D₄×C₄₁	—	2	1	no	—
365	D₄×C₄₁	—	4	2	no	—
366	D₄×C₄₁	—	4	4	no	—
367	D₄×C₄₁	—	8	2	no	—
368	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
369	C₂×C₄×C₄₁	—	2	4	no	—
370	C₂×C₄×C₄₁	—	2	1	no	—
371	C₂×C₄×C₄₁	—	2	2	no	—
372	C₂×C₄×C₄₁	—	2	1	no	—
373	C₂×C₄×C₄₁	—	2	2	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	2	no	—
378	C₂×C₄×C₄₁	—	2	4	no	—
379	C₂×C₄×C₄₁	—	2	2	no	—
380	C₂×C₄×C₄₁	—	2	1	no	—
381	C₂×C₄×C₄₁	—	4	2	no	—
382	C₂×C₄×C₄₁	—	4	1	no	—
383	C₂×C₄×C₄₁	—	4	4	no	—
384	C₂×C₄×C₄₁	—	4	2	no	—
385	C₂×C₄×C₄₁	—	4	2	no	—
386	C₂×C₄×C₄₁	—	4	2	no	—
387	C₂×C₄×C₄₁	—	4	2	no	—
388	C₂×C₄×C₄₁	—	4	2	no	—
389	C₂×C₄×C₄₁	—	8	2	no	—
390	C₂×C₄×C₄₁	—	8	2	no	—
391	C₂×C₄×C₄₁	—	8	4	no	—
392	C₂×C₄×C₄₁	#137	1	4	yes	complemented
393	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
402	C₈×C₄₁	—	2	4	no	—
403	C₈×C₄₁	—	2	2	no	—
404	C₈×C₄₁	—	2	2	no	—
405	#61960	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂²×C₄₁	—	2	1	no	—
407	C₂²×C₄₁	—	2	1	no	—
408	C₂²×C₄₁	—	2	2	no	—
409	C₂²×C₄₁	—	2	2	no	—
410	C₂²×C₄₁	—	2	2	no	—
411	C₂²×C₄₁	—	2	2	no	—
412	C₂²×C₄₁	—	4	1	no	—
413	C₂²×C₄₁	—	4	1	no	—
414	C₂²×C₄₁	—	4	1	no	—
415	C₂²×C₄₁	—	4	1	no	—
416	C₂²×C₄₁	—	4	1	no	—
417	C₂²×C₄₁	—	8	4	no	—
418	C₂²×C₄₁	C₂×#137	1	2	yes	—
419	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
420	C₄×C₄₁	—	2	1	no	—
421	C₄×C₄₁	—	2	2	no	—
422	C₄×C₄₁	—	2	1	no	—
423	C₄×C₄₁	—	2	2	no	—
424	C₄×C₄₁	—	2	1	no	—
425	C₄×C₄₁	—	2	2	no	—
426	C₄×C₄₁	—	4	2	no	—
427	C₄×C₄₁	—	4	2	no	—
428	C₄×C₄₁	—	4	2	no	—
429	C₄×C₄₁	—	4	4	no	—
430	C₄×C₄₁	—	4	2	no	—
431	C₄×C₄₁	—	4	1	no	—
432	C₄×C₄₁	—	4	1	no	—
433	C₄×C₄₁	C₂×#137	1	2	yes	—
434	C₄×C₄₁	C₂×#137	1	2	yes	—
435	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	C₄×C₄₁	#585	1	1	yes	characteristic
437	#3503	C₂×C₄₁	1	1	yes	characteristic, complemented
438	#3475	C₂×C₄₁	1	1	yes	characteristic
439	#3398	C₂×C₄₁	1	2	yes	complemented
440	#3372	C₂×C₄₁	1	2	yes	complemented
441	#3329	C₂×C₄₁	1	2	yes	complemented
442	#3312	C₂×C₄₁	1	4	yes	complemented
443	#3276	C₂×C₄₁	1	2	yes	complemented
444	#3266	C₂×C₄₁	1	4	yes	complemented
445	#3252	C₂×C₄₁	1	2	yes	complemented
446	#3249	C₂×C₄₁	1	1	yes	characteristic, complemented
447	#3218	C₂×C₄₁	1	2	yes	complemented
448	#3209	C₂×C₄₁	1	1	yes	characteristic, complemented
449	#3116	C₂×C₄₁	1	2	yes	complemented
450	#3101	C₂×C₄₁	1	1	yes	characteristic, complemented
451	#3039	C₂×C₄₁	1	2	yes	complemented
452	C₂×#461	C₂×C₄₁	1	1	yes	characteristic, complemented
453	#2989	C₂×C₄₁	1	1	yes	characteristic, complemented
454	C₂×C₄₁	—	2	2	no	—
455	C₂×C₄₁	—	4	2	no	—
456	C₂×C₄₁	—	4	2	no	—
457	C₂×C₄₁	—	8	1	no	—
458	C₂×C₄₁	#3488	1	1	yes	characteristic
459	C₂×C₄₁	C₂²×#137	1	1	yes	characteristic
460	C₂×C₄₁	#3586	1	1	yes	characteristic
461	C₂×#137	C₂²×C₄₁	1	4	yes	—
462	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
463	Q₈²	—	2	1	no	—
464	#557	C₂²×C₄₁	1	2	yes	complemented
465	#556	C₂²×C₄₁	1	1	yes	characteristic
466	#555	C₂²×C₄₁	1	1	yes	characteristic
467	#554	—	2	2	no	—
468	#554	—	2	1	no	—
469	#554	C₂²×C₄₁	1	1	yes	characteristic
470	#553	—	2	1	no	—
471	#552	—	2	1	no	—
472	#552	C₂²×C₄₁	1	2	yes	—
473	#551	—	2	2	no	—
474	D₄×Q₈	C₂²×C₄₁	1	4	yes	—
475	D₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
476	#547	C₂²×C₄₁	1	1	yes	characteristic
477	#546	C₂²×C₄₁	1	2	yes	—
478	#544	—	2	1	no	—
479	#544	—	2	2	no	—
480	#533	C₂²×C₄₁	1	1	yes	characteristic
481	#533	C₂²×C₄₁	1	1	yes	characteristic
482	#533	C₂²×C₄₁	1	2	yes	complemented
483	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
484	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
485	#529	—	2	2	no	—
486	#529	C₂²×C₄₁	1	2	yes	—
487	#525	—	2	1	no	—
488	#520	—	2	1	no	—
489	C₄×#41	C₂²×C₄₁	1	2	yes	—
490	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
491	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
492	C₂×#117	—	2	1	no	—
493	#497	C₂²×C₄₁	1	4	yes	—
494	#494	C₂²×C₄₁	1	2	yes	complemented
495	#491	C₂²×C₄₁	1	4	yes	complemented
496	#487	C₂²×C₄₁	1	2	yes	complemented
497	#485	C₂²×C₄₁	1	4	yes	complemented
498	#483	C₂²×C₄₁	1	2	yes	—
499	#479	C₂²×C₄₁	1	4	yes	complemented
500	#477	C₂²×C₄₁	1	2	yes	complemented
501	#477	C₂²×C₄₁	1	2	yes	complemented
502	#476	C₂²×C₄₁	1	1	yes	characteristic
503	#476	C₂²×C₄₁	1	1	yes	characteristic
504	#470	C₂²×C₄₁	1	4	yes	complemented
505	#468	C₂²×C₄₁	1	4	yes	—
506	#467	C₂²×C₄₁	1	4	yes	—
507	#464	C₂²×C₄₁	1	4	yes	—
508	#462	C₂²×C₄₁	1	2	yes	complemented
509	#462	C₂²×C₄₁	1	2	yes	complemented
510	#462	C₂²×C₄₁	1	4	yes	complemented
511	#462	C₂²×C₄₁	1	2	yes	complemented
512	#462	C₂²×C₄₁	1	2	yes	complemented
513	#461	C₂²×C₄₁	1	2	yes	—
514	#461	C₂²×C₄₁	1	1	yes	characteristic
515	#461	C₂²×C₄₁	1	1	yes	characteristic
516	#461	C₂²×C₄₁	1	2	yes	—
517	#461	C₂²×C₄₁	1	4	yes	—
518	#461	C₂²×C₄₁	1	2	yes	—
519	#461	C₂²×C₄₁	1	2	yes	—
520	#452	C₂²×C₄₁	1	4	yes	—
521	#451	C₂²×C₄₁	1	4	yes	—
522	#451	C₂²×C₄₁	1	4	yes	complemented
523	#450	C₂²×C₄₁	1	2	yes	—
524	#448	C₂²×C₄₁	1	4	yes	—
525	#446	C₂²×C₄₁	1	2	yes	complemented
526	#441	C₂²×C₄₁	1	4	yes	complemented
527	#440	C₂²×C₄₁	1	4	yes	—
528	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
529	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
530	#436	C₂²×C₄₁	1	2	yes	complemented
531	#435	C₂²×C₄₁	1	4	yes	—
532	#432	C₂²×C₄₁	1	2	yes	complemented
533	#431	C₂²×C₄₁	1	1	yes	characteristic
534	#423	C₂²×C₄₁	1	2	yes	complemented
535	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
536	#419	C₂²×C₄₁	1	4	yes	complemented
537	C₂×#103	C₂²×C₄₁	1	2	yes	—
538	C₄₁	#61960	1	1	yes	characteristic, direct product factor, Sylow
539	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
540	C₂×#41	C₂³×C₄₁	1	2	yes	—
541	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
542	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
543	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
544	C₂³×C₄	—	2	1	no	—
545	#137	—	4	8	no	—
546	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
547	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
548	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
549	C₂×SD₁₆	—	4	4	no	—
550	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
551	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
552	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
553	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
554	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
555	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
556	C₄⋊Q₈	—	2	4	no	—
557	C₄⋊Q₈	—	2	2	no	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	—	2	2	no	—
561	C₄⋊Q₈	—	2	2	no	—
562	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
563	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
564	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
566	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
569	#126	—	2	2	no	—
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#125	—	2	2	no	—
573	#125	—	2	2	no	—
574	#125	—	2	4	no	—
575	#125	—	2	1	no	—
576	#125	—	2	1	no	—
577	#125	—	2	2	no	—
578	#125	C₂³×C₄₁	1	2	yes	—
579	#124	—	2	2	no	—
580	#124	C₂³×C₄₁	1	2	yes	—
581	#123	—	2	2	no	—
582	#123	—	2	2	no	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	4	no	—
592	C₂²⋊Q₈	—	2	4	no	—
593	C₂²⋊Q₈	—	2	4	no	—
594	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
595	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
596	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
597	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
598	#121	—	2	1	no	—
599	#121	—	2	1	no	—
600	#121	—	2	2	no	—
601	#121	C₂³×C₄₁	1	2	yes	—
602	#120	—	2	2	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
609	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
610	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
611	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
612	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
613	C₄×D₄	—	2	4	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	D₄×C₄₁	1	2	yes	—
621	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₄₁	1	2	yes	—
627	C₄×D₄	C₂³×C₄₁	1	2	yes	—
628	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
629	#117	—	2	1	no	—
630	#117	—	2	1	no	—
631	#117	—	2	2	no	—
632	#117	—	2	1	no	—
633	#117	—	2	1	no	—
634	#117	—	2	2	no	—
635	#117	—	2	2	no	—
636	#117	—	2	2	no	—
637	#117	D₄×C₄₁	1	1	yes	characteristic
638	#117	D₄×C₄₁	1	2	yes	—
639	#117	C₂³×C₄₁	1	2	yes	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	2	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	2	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	2	no	—
649	C₂×C₄²	—	2	2	no	—
650	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
652	#107	C₂³×C₄₁	1	4	yes	—
653	#106	C₂³×C₄₁	1	2	yes	—
654	#106	C₂³×C₄₁	1	2	yes	—
655	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
656	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
657	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
658	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
659	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
660	#103	C₂³×C₄₁	1	4	yes	—
661	#103	C₂³×C₄₁	1	4	yes	—
662	#103	C₂³×C₄₁	1	2	yes	—
663	#103	C₂³×C₄₁	1	4	yes	—
664	#103	C₂³×C₄₁	1	4	yes	—
665	#103	C₂³×C₄₁	1	2	yes	—
666	#103	C₂³×C₄₁	1	4	yes	—
667	#103	C₂³×C₄₁	1	4	yes	—
668	#102	C₂³×C₄₁	1	2	yes	—
669	#102	C₂³×C₄₁	1	2	yes	—
670	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
672	#97	C₂³×C₄₁	1	4	yes	—
673	C₄×C₈	C₂³×C₄₁	1	2	yes	—
674	C₂⁴	—	2	1	no	—
675	#41	—	2	4	no	—
676	#41	—	2	4	no	—
677	#41	—	4	2	no	—
678	C₂×Q₈	—	2	1	no	—
679	C₂×Q₈	—	2	1	no	—
680	C₂×Q₈	—	2	4	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	4	2	no	—
683	C₂×Q₈	—	4	4	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×Q₈	—	4	4	no	—
686	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
687	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
688	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
689	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	4	1	no	—
695	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
696	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
697	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
698	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	4	4	no	—
709	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
712	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
715	Q₁₆	—	4	4	no	—
716	Q₁₆	—	4	4	no	—
717	Q₁₆	—	4	4	no	—
718	SD₁₆	—	2	8	no	—
719	SD₁₆	—	2	4	no	—
720	SD₁₆	—	4	4	no	—
721	SD₁₆	—	4	2	no	—
722	M₁₆	—	4	4	no	—
723	C₂×C₈	—	4	2	no	—
724	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
725	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
726	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
751	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
752	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
753	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	2	no	—
779	C₄²	C₂×D₄×C₄₁	1	2	yes	—
780	C₄²	C₂×D₄×C₄₁	1	2	yes	—
781	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
782	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
783	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
784	C₄²	C₂⁴×C₄₁	1	2	yes	—
785	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	4	2	no	—
790	C₂³	—	8	1	no	—
791	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
792	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	4	no	—
795	Q₈	—	2	2	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	2	2	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	4	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	8	4	no	—
802	Q₈	—	8	2	no	—
803	Q₈	—	8	1	no	—
804	D₄	—	2	4	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	1	no	—
807	D₄	—	2	1	no	—
808	D₄	—	2	1	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	8	2	no	—
812	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	8	2	no	—
834	C₂×C₄	—	8	2	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	#137×C₄₁	1	4	yes	complemented
837	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
845	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
846	C₈	—	2	4	no	—
847	C₈	—	2	2	no	—
848	C₈	—	2	2	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	8	4	no	—
861	C₂²	C₂×#137×C₄₁	1	2	yes	—
862	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	4	no	—
875	C₄	—	4	2	no	—
876	C₄	C₂×#137×C₄₁	1	2	yes	—
877	C₄	C₂×#137×C₄₁	1	2	yes	—
878	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
879	C₄	C₄₁×#585	1	1	yes	characteristic
880	C₂	—	2	2	no	—
881	C₂	—	4	2	no	—
882	C₂	—	4	2	no	—
883	C₂	—	8	1	no	—
884	C₂	C₄₁×#3488	1	1	yes	characteristic
885	C₂	C₂²×#137×C₄₁	1	1	yes	characteristic
886	C₂	C₄₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3503	C₂	semidirect
3. C₄₁×#3398	C₂	semidirect
4. C₄₁×#3372	C₂	semidirect
5. C₄₁×#3329	C₂	semidirect
6. C₄₁×#3312	C₂	semidirect
7. C₄₁×#3276	C₂	semidirect
8. C₄₁×#3266	C₂	semidirect
9. C₄₁×#3252	C₂	semidirect
10. C₄₁×#3249	C₂	semidirect
11. C₄₁×#3218	C₂	semidirect
12. C₄₁×#3209	C₂	semidirect
13. C₄₁×#3116	C₂	semidirect
14. C₄₁×#3101	C₂	semidirect
15. C₄₁×#3039	C₂	semidirect
16. C₂×C₄₁×#461	C₂	semidirect
17. C₄₁×#2989	C₂	semidirect
21. C₄₁×#557	C₂²	semidirect
32. D₄×Q₈×C₄₁	C₂²	semidirect
39. C₄₁×#533	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
51. C₄₁×#494	C₂²	semidirect
52. C₄₁×#491	C₂²	semidirect
53. C₄₁×#487	C₂²	semidirect
54. C₄₁×#485	C₂²	semidirect
56. C₄₁×#479	C₂²	semidirect
57. C₄₁×#477	C₂²	semidirect
58. C₄₁×#477	C₂²	semidirect
61. C₄₁×#470	C₂²	semidirect
65. C₄₁×#462	C₂²	semidirect
66. C₄₁×#462	C₂²	semidirect
67. C₄₁×#462	C₂²	semidirect
68. C₄₁×#462	C₂²	semidirect
69. C₄₁×#462	C₂²	semidirect
79. C₄₁×#451	C₂²	semidirect
82. C₄₁×#446	C₂²	semidirect
83. C₄₁×#441	C₂²	semidirect
87. C₄₁×#436	C₂²	semidirect
89. C₄₁×#432	C₂²	semidirect
91. C₄₁×#423	C₂²	semidirect
93. C₄₁×#419	C₂²	semidirect
392. C₂×C₄×C₄₁	#137	semidirect
405. #61960	C₄₁	direct (N × H)
437. #3503	C₂×C₄₁	semidirect
439. #3398	C₂×C₄₁	semidirect
440. #3372	C₂×C₄₁	semidirect
441. #3329	C₂×C₄₁	semidirect
442. #3312	C₂×C₄₁	semidirect
443. #3276	C₂×C₄₁	semidirect
444. #3266	C₂×C₄₁	semidirect
445. #3252	C₂×C₄₁	semidirect
446. #3249	C₂×C₄₁	semidirect
447. #3218	C₂×C₄₁	semidirect
448. #3209	C₂×C₄₁	semidirect
449. #3116	C₂×C₄₁	semidirect
450. #3101	C₂×C₄₁	semidirect
451. #3039	C₂×C₄₁	semidirect
452. C₂×#461	C₂×C₄₁	semidirect
453. #2989	C₂×C₄₁	semidirect
464. #557	C₂²×C₄₁	semidirect
475. D₄×Q₈	C₂²×C₄₁	semidirect
482. #533	C₂²×C₄₁	semidirect
484. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
494. #494	C₂²×C₄₁	semidirect
495. #491	C₂²×C₄₁	semidirect
496. #487	C₂²×C₄₁	semidirect
497. #485	C₂²×C₄₁	semidirect
499. #479	C₂²×C₄₁	semidirect
500. #477	C₂²×C₄₁	semidirect
501. #477	C₂²×C₄₁	semidirect
504. #470	C₂²×C₄₁	semidirect
508. #462	C₂²×C₄₁	semidirect
509. #462	C₂²×C₄₁	semidirect
510. #462	C₂²×C₄₁	semidirect
511. #462	C₂²×C₄₁	semidirect
512. #462	C₂²×C₄₁	semidirect
522. #451	C₂²×C₄₁	semidirect
525. #446	C₂²×C₄₁	semidirect
526. #441	C₂²×C₄₁	semidirect
530. #436	C₂²×C₄₁	semidirect
532. #432	C₂²×C₄₁	semidirect
534. #423	C₂²×C₄₁	semidirect
536. #419	C₂²×C₄₁	semidirect
538. C₄₁	#61960	direct (N × H)
836. C₂×C₄	#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×#3503	2
C₄₁×#3475	2
C₄₁×#3398	2
C₄₁×#3372	2
C₄₁×#3329	2
C₄₁×#3312	2
C₄₁×#3276	2
C₄₁×#3266	2
C₄₁×#3252	2
C₄₁×#3249	2
C₄₁×#3218	2
C₄₁×#3209	2
C₄₁×#3116	2
C₄₁×#3101	2
C₄₁×#3039	2
C₂×C₄₁×#461	2
C₄₁×#2989	2
#61960	41

Subgroups — C41×#61960 #23838161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61960 #23838161