Subgroups — C₄₁×#60546 #23836747

Order 10496.

2172 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3117	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3116	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3115	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3114	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3111	C₂	1	4	yes	maximal, complemented
10	C₄₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3091	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3076	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3035	C₂	1	2	yes	maximal, complemented
15	C₄₁×#3002	C₂	1	2	yes	maximal, complemented
16	C₄₁×#2943	C₂	1	4	yes	maximal, complemented
17	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#135×C₄₁	C₂²	1	4	yes	—
20	C₄₁×#533	C₂²	1	1	yes	characteristic
21	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
22	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
23	C₄₁×#532	C₂²	1	1	yes	characteristic
24	C₄₁×#532	C₂²	1	1	yes	characteristic, complemented
25	C₄₁×#532	C₂²	1	1	yes	characteristic, complemented
26	C₄₁×#529	—	2	1	no	—
27	C₄₁×#529	—	2	1	no	—
28	C₄₁×#529	—	2	1	no	—
29	C₄₁×#529	—	2	1	no	—
30	C₄₁×#529	C₂²	1	2	yes	—
31	C₄₁×#529	C₂²	1	2	yes	complemented
32	C₄₁×#525	—	2	1	no	—
33	C₄₁×#525	—	2	1	no	—
34	C₄₁×#525	C₂²	1	2	yes	—
35	C₄×#41×C₄₁	—	2	1	no	—
36	C₄×#41×C₄₁	—	2	1	no	—
37	C₄×#41×C₄₁	—	2	1	no	—
38	C₄×#41×C₄₁	—	2	1	no	—
39	C₄×#41×C₄₁	—	2	1	no	—
40	C₄×#41×C₄₁	—	2	1	no	—
41	C₄×#41×C₄₁	C₂²	1	2	yes	—
42	C₄×#41×C₄₁	C₂²	1	2	yes	—
43	C₄×#41×C₄₁	C₂²	1	2	yes	—
44	C₄×#41×C₄₁	C₂²	1	2	yes	—
45	C₄×#41×C₄₁	C₂²	1	2	yes	complemented
46	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₄₁	—	2	1	no	—
49	C₂×C₄×D₄×C₄₁	—	2	1	no	—
50	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
52	C₂×#117×C₄₁	—	2	1	no	—
53	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
54	C₂²×C₄²×C₄₁	—	2	1	no	—
55	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
56	C₄₁×#485	C₂²	1	4	yes	complemented
57	C₄₁×#484	C₂²	1	2	yes	—
58	C₄₁×#483	C₂²	1	2	yes	—
59	C₄₁×#482	C₂²	1	4	yes	complemented
60	C₄₁×#481	C₂²	1	2	yes	—
61	C₄₁×#480	C₂²	1	2	yes	—
62	C₄₁×#479	C₂²	1	4	yes	complemented
63	C₄₁×#478	C₂²	1	4	yes	complemented
64	C₄₁×#477	C₂²	1	2	yes	complemented
65	C₄₁×#476	C₂²	1	2	yes	complemented
66	C₄₁×#475	C₂²	1	2	yes	complemented
67	C₄₁×#474	C₂²	1	2	yes	complemented
68	C₄₁×#464	C₂²	1	4	yes	complemented
69	C₄₁×#463	C₂²	1	4	yes	complemented
70	C₄₁×#462	C₂²	1	2	yes	complemented
71	C₄₁×#461	C₂²	1	2	yes	complemented
72	C₄₁×#460	C₂²	1	2	yes	complemented
73	C₄₁×#459	C₂²	1	2	yes	complemented
74	C₄₁×#452	C₂²	1	4	yes	—
75	C₄₁×#451	C₂²	1	2	yes	—
76	C₄₁×#450	C₂²	1	2	yes	—
77	C₄₁×#449	C₂²	1	4	yes	—
78	C₄₁×#448	C₂²	1	2	yes	—
79	C₄₁×#447	C₂²	1	2	yes	—
80	C₄₁×#442	C₂²	1	4	yes	complemented
81	C₄₁×#442	C₂²	1	4	yes	complemented
82	C₄₁×#441	C₂²	1	4	yes	complemented
83	C₄₁×#441	C₂²	1	4	yes	complemented
84	C₄₁×#440	C₂²	1	4	yes	complemented
85	C₄₁×#440	C₂²	1	4	yes	complemented
86	C₄₁×#440	C₂²	1	4	yes	complemented
87	C₄₁×#440	C₂²	1	4	yes	complemented
88	C₄₁×#432	C₂²	1	1	yes	characteristic
89	C₄₁×#432	C₂²	1	1	yes	characteristic
90	C₄₁×#432	C₂²	1	2	yes	—
91	C₄₁×#432	C₂²	1	2	yes	complemented
92	C₄₁×#432	C₂²	1	2	yes	complemented
93	C₄₁×#427	C₂²	1	4	yes	complemented
94	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
95	C₄₁×#416	C₂²	1	4	yes	—
96	C₄₁×#416	C₂²	1	4	yes	complemented
97	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
98	C₂×#97×C₄₁	C₂²	1	2	yes	complemented
99	C₂×#41×C₄₁	—	2	8	no	—
100	C₂×#41×C₄₁	—	2	1	no	—
101	C₂×#41×C₄₁	—	2	1	no	—
102	C₂×#41×C₄₁	—	2	1	no	—
103	C₂×#41×C₄₁	—	2	1	no	—
104	C₂×#41×C₄₁	C₂³	1	2	yes	—
105	C₂×#41×C₄₁	C₂³	1	2	yes	—
106	C₂×#41×C₄₁	C₂³	1	2	yes	—
107	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₄₁	—	2	1	no	—
109	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₄₁	—	2	1	no	—
111	C₂³×C₄×C₄₁	—	2	1	no	—
112	C₂³×C₄×C₄₁	—	2	1	no	—
113	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
114	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
115	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
116	#135×C₄₁	—	2	16	no	—
117	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
120	C₂×D₈×C₄₁	C₂³	1	4	yes	—
121	C₂²×C₈×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	#127×C₄₁	C₂³	1	1	yes	characteristic
126	#126×C₄₁	—	2	2	no	—
127	#126×C₄₁	—	2	2	no	—
128	#125×C₄₁	—	2	1	no	—
129	#125×C₄₁	—	2	1	no	—
130	#125×C₄₁	C₂³	1	2	yes	—
131	#124×C₄₁	—	2	1	no	—
132	#124×C₄₁	—	2	1	no	—
133	#124×C₄₁	C₂³	1	2	yes	—
134	#123×C₄₁	—	2	2	no	—
135	#123×C₄₁	—	2	2	no	—
136	#123×C₄₁	—	2	2	no	—
137	C₂²⋊Q₈×C₄₁	—	2	1	no	—
138	C₂²⋊Q₈×C₄₁	—	2	1	no	—
139	C₂²⋊Q₈×C₄₁	—	2	1	no	—
140	C₂²⋊Q₈×C₄₁	—	2	1	no	—
141	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
142	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
143	#121×C₄₁	—	2	1	no	—
144	#121×C₄₁	—	2	1	no	—
145	#121×C₄₁	—	2	1	no	—
146	#121×C₄₁	—	2	1	no	—
147	#121×C₄₁	C₂³	1	2	yes	—
148	#121×C₄₁	C₂³	1	2	yes	—
149	#120×C₄₁	—	2	2	no	—
150	C₄×Q₈×C₄₁	—	2	1	no	—
151	C₄×Q₈×C₄₁	—	2	1	no	—
152	C₄×Q₈×C₄₁	—	2	1	no	—
153	C₄×Q₈×C₄₁	—	2	1	no	—
154	C₄×Q₈×C₄₁	—	2	1	no	—
155	C₄×Q₈×C₄₁	—	2	1	no	—
156	C₄×Q₈×C₄₁	—	2	1	no	—
157	C₄×Q₈×C₄₁	—	2	1	no	—
158	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
160	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
161	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
162	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
163	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
164	C₄×D₄×C₄₁	—	2	2	no	—
165	C₄×D₄×C₄₁	—	2	2	no	—
166	C₄×D₄×C₄₁	—	2	2	no	—
167	C₄×D₄×C₄₁	—	2	2	no	—
168	C₄×D₄×C₄₁	—	2	2	no	—
169	C₄×D₄×C₄₁	—	2	2	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	2	no	—
175	C₄×D₄×C₄₁	—	2	2	no	—
176	C₄×D₄×C₄₁	—	2	2	no	—
177	C₄×D₄×C₄₁	—	2	2	no	—
178	C₄×D₄×C₄₁	—	2	1	no	—
179	C₄×D₄×C₄₁	—	2	1	no	—
180	C₄×D₄×C₄₁	—	2	1	no	—
181	C₄×D₄×C₄₁	—	2	1	no	—
182	C₄×D₄×C₄₁	—	2	1	no	—
183	C₄×D₄×C₄₁	—	2	1	no	—
184	C₄×D₄×C₄₁	—	2	1	no	—
185	C₄×D₄×C₄₁	—	2	1	no	—
186	C₄×D₄×C₄₁	C₂³	1	2	yes	—
187	C₄×D₄×C₄₁	C₂³	1	2	yes	—
188	C₄×D₄×C₄₁	C₂³	1	2	yes	—
189	C₄×D₄×C₄₁	C₂³	1	2	yes	—
190	C₄×D₄×C₄₁	C₂³	1	2	yes	—
191	C₄×D₄×C₄₁	C₂³	1	2	yes	—
192	#117×C₄₁	—	2	1	no	—
193	#117×C₄₁	—	2	1	no	—
194	#117×C₄₁	—	2	1	no	—
195	#117×C₄₁	—	2	1	no	—
196	#117×C₄₁	—	2	2	no	—
197	#117×C₄₁	—	2	2	no	—
198	#117×C₄₁	—	2	2	no	—
199	#117×C₄₁	—	2	2	no	—
200	#117×C₄₁	—	2	2	no	—
201	#117×C₄₁	—	2	2	no	—
202	#117×C₄₁	—	2	2	no	—
203	#117×C₄₁	C₂³	1	2	yes	—
204	#117×C₄₁	C₂³	1	2	yes	—
205	#117×C₄₁	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
207	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
208	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
211	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
212	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
213	C₂×C₄²×C₄₁	—	2	1	no	—
214	C₂×C₄²×C₄₁	—	2	1	no	—
215	C₂×C₄²×C₄₁	—	2	1	no	—
216	C₂×C₄²×C₄₁	—	2	2	no	—
217	C₂×C₄²×C₄₁	—	2	2	no	—
218	C₂×C₄²×C₄₁	—	2	2	no	—
219	C₂×C₄²×C₄₁	—	2	2	no	—
220	C₂×C₄²×C₄₁	—	2	2	no	—
221	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
224	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
233	#107×C₄₁	C₂³	1	4	yes	—
234	#107×C₄₁	C₂³	1	4	yes	—
235	#106×C₄₁	C₂³	1	4	yes	—
236	#106×C₄₁	C₂³	1	4	yes	—
237	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
238	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
239	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
240	#103×C₄₁	C₂³	1	4	yes	—
241	#103×C₄₁	C₂³	1	4	yes	—
242	#103×C₄₁	C₂³	1	4	yes	—
243	#103×C₄₁	C₂³	1	4	yes	—
244	#102×C₄₁	C₂³	1	4	yes	—
245	#102×C₄₁	C₂³	1	4	yes	—
246	#102×C₄₁	C₂³	1	4	yes	—
247	#102×C₄₁	C₂³	1	4	yes	—
248	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
249	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
250	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
251	#97×C₄₁	C₂³	1	2	yes	—
252	#97×C₄₁	C₂³	1	4	yes	—
253	#97×C₄₁	C₂³	1	2	yes	—
254	C₂⁴×C₄₁	—	2	1	no	—
255	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
256	#41×C₄₁	—	2	8	no	—
257	#41×C₄₁	—	2	8	no	—
258	#41×C₄₁	—	2	4	no	—
259	#41×C₄₁	—	2	4	no	—
260	#41×C₄₁	—	2	4	no	—
261	#41×C₄₁	—	2	8	no	—
262	#41×C₄₁	—	4	4	no	—
263	#41×C₄₁	—	4	4	no	—
264	#41×C₄₁	#41	1	8	yes	complemented
265	C₂×Q₈×C₄₁	—	2	4	no	—
266	C₂×Q₈×C₄₁	—	2	1	no	—
267	C₂×Q₈×C₄₁	—	2	1	no	—
268	C₂×Q₈×C₄₁	—	2	1	no	—
269	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
270	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
271	C₂×D₄×C₄₁	—	2	8	no	—
272	C₂×D₄×C₄₁	—	2	2	no	—
273	C₂×D₄×C₄₁	—	2	2	no	—
274	C₂×D₄×C₄₁	—	2	4	no	—
275	C₂×D₄×C₄₁	—	2	2	no	—
276	C₂×D₄×C₄₁	—	2	2	no	—
277	C₂×D₄×C₄₁	—	2	2	no	—
278	C₂×D₄×C₄₁	—	2	1	no	—
279	C₂×D₄×C₄₁	—	2	1	no	—
280	C₂×D₄×C₄₁	—	2	1	no	—
281	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
282	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₄₁	—	2	8	no	—
284	C₂²×C₄×C₄₁	—	2	1	no	—
285	C₂²×C₄×C₄₁	—	2	2	no	—
286	C₂²×C₄×C₄₁	—	2	2	no	—
287	C₂²×C₄×C₄₁	—	2	4	no	—
288	C₂²×C₄×C₄₁	—	2	1	no	—
289	C₂²×C₄×C₄₁	—	2	1	no	—
290	C₂²×C₄×C₄₁	—	2	2	no	—
291	C₂²×C₄×C₄₁	—	2	2	no	—
292	C₂²×C₄×C₄₁	—	2	2	no	—
293	C₂²×C₄×C₄₁	—	2	2	no	—
294	C₂²×C₄×C₄₁	—	2	2	no	—
295	C₂²×C₄×C₄₁	—	2	2	no	—
296	C₂²×C₄×C₄₁	—	2	2	no	—
297	C₂²×C₄×C₄₁	—	4	2	no	—
298	C₂²×C₄×C₄₁	—	4	2	no	—
299	C₂²×C₄×C₄₁	—	4	4	no	—
300	C₂²×C₄×C₄₁	—	4	4	no	—
301	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
319	Q₁₆×C₄₁	—	2	8	no	—
320	SD₁₆×C₄₁	—	2	8	no	—
321	SD₁₆×C₄₁	—	2	8	no	—
322	D₈×C₄₁	—	2	8	no	—
323	C₂×C₈×C₄₁	—	2	8	no	—
324	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
325	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₄₁	—	2	2	no	—
327	C₄⋊C₄×C₄₁	—	2	2	no	—
328	C₄⋊C₄×C₄₁	—	2	2	no	—
329	C₄⋊C₄×C₄₁	—	2	2	no	—
330	C₄⋊C₄×C₄₁	—	2	1	no	—
331	C₄⋊C₄×C₄₁	—	2	1	no	—
332	C₄⋊C₄×C₄₁	—	2	1	no	—
333	C₄⋊C₄×C₄₁	—	2	1	no	—
334	C₄⋊C₄×C₄₁	—	2	1	no	—
335	C₄⋊C₄×C₄₁	—	2	1	no	—
336	C₄⋊C₄×C₄₁	—	2	2	no	—
337	C₄⋊C₄×C₄₁	—	2	2	no	—
338	C₄⋊C₄×C₄₁	—	2	2	no	—
339	C₄⋊C₄×C₄₁	—	2	2	no	—
340	C₄⋊C₄×C₄₁	—	2	2	no	—
341	C₄⋊C₄×C₄₁	—	2	2	no	—
342	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
346	C₂²⋊C₄×C₄₁	—	2	2	no	—
347	C₂²⋊C₄×C₄₁	—	2	2	no	—
348	C₂²⋊C₄×C₄₁	—	2	2	no	—
349	C₂²⋊C₄×C₄₁	—	2	2	no	—
350	C₂²⋊C₄×C₄₁	—	2	2	no	—
351	C₂²⋊C₄×C₄₁	—	2	2	no	—
352	C₂²⋊C₄×C₄₁	—	2	2	no	—
353	C₂²⋊C₄×C₄₁	—	2	2	no	—
354	C₂²⋊C₄×C₄₁	—	2	2	no	—
355	C₂²⋊C₄×C₄₁	—	2	2	no	—
356	C₂²⋊C₄×C₄₁	—	2	2	no	—
357	C₂²⋊C₄×C₄₁	—	2	2	no	—
358	C₂²⋊C₄×C₄₁	—	2	2	no	—
359	C₂²⋊C₄×C₄₁	—	2	2	no	—
360	C₂²⋊C₄×C₄₁	—	2	2	no	—
361	C₄²×C₄₁	—	2	2	no	—
362	C₄²×C₄₁	—	2	2	no	—
363	C₄²×C₄₁	—	2	2	no	—
364	C₄²×C₄₁	—	2	2	no	—
365	C₄²×C₄₁	—	2	2	no	—
366	C₄²×C₄₁	—	2	2	no	—
367	C₄²×C₄₁	—	2	2	no	—
368	C₄²×C₄₁	—	2	2	no	—
369	C₄²×C₄₁	—	2	2	no	—
370	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
383	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
384	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
385	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
386	C₂³×C₄₁	—	2	4	no	—
387	C₂³×C₄₁	—	2	2	no	—
388	C₂³×C₄₁	—	2	2	no	—
389	C₂³×C₄₁	—	2	2	no	—
390	C₂³×C₄₁	—	2	2	no	—
391	C₂³×C₄₁	—	4	1	no	—
392	C₂³×C₄₁	—	4	2	no	—
393	C₂³×C₄₁	—	4	2	no	—
394	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
395	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
396	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
397	Q₈×C₄₁	—	2	4	no	—
398	Q₈×C₄₁	—	2	2	no	—
399	Q₈×C₄₁	—	2	4	no	—
400	Q₈×C₄₁	—	4	2	no	—
401	Q₈×C₄₁	—	4	2	no	—
402	Q₈×C₄₁	C₂×#41	1	4	yes	—
403	D₄×C₄₁	—	2	8	no	—
404	D₄×C₄₁	—	2	4	no	—
405	D₄×C₄₁	—	2	8	no	—
406	D₄×C₄₁	—	2	2	no	—
407	D₄×C₄₁	—	2	4	no	—
408	D₄×C₄₁	—	4	2	no	—
409	D₄×C₄₁	—	4	4	no	—
410	D₄×C₄₁	—	4	4	no	—
411	D₄×C₄₁	—	4	4	no	—
412	D₄×C₄₁	—	4	2	no	—
413	D₄×C₄₁	C₂×#41	1	4	yes	—
414	C₂×C₄×C₄₁	—	2	4	no	—
415	C₂×C₄×C₄₁	—	2	8	no	—
416	C₂×C₄×C₄₁	—	2	2	no	—
417	C₂×C₄×C₄₁	—	2	2	no	—
418	C₂×C₄×C₄₁	—	2	2	no	—
419	C₂×C₄×C₄₁	—	2	2	no	—
420	C₂×C₄×C₄₁	—	2	2	no	—
421	C₂×C₄×C₄₁	—	2	8	no	—
422	C₂×C₄×C₄₁	—	2	2	no	—
423	C₂×C₄×C₄₁	—	2	2	no	—
424	C₂×C₄×C₄₁	—	2	2	no	—
425	C₂×C₄×C₄₁	—	2	2	no	—
426	C₂×C₄×C₄₁	—	2	2	no	—
427	C₂×C₄×C₄₁	—	2	2	no	—
428	C₂×C₄×C₄₁	—	2	2	no	—
429	C₂×C₄×C₄₁	—	2	2	no	—
430	C₂×C₄×C₄₁	—	2	2	no	—
431	C₂×C₄×C₄₁	—	2	2	no	—
432	C₂×C₄×C₄₁	—	2	2	no	—
433	C₂×C₄×C₄₁	—	4	1	no	—
434	C₂×C₄×C₄₁	—	4	1	no	—
435	C₂×C₄×C₄₁	—	4	1	no	—
436	C₂×C₄×C₄₁	—	4	1	no	—
437	C₂×C₄×C₄₁	—	4	1	no	—
438	C₂×C₄×C₄₁	—	4	1	no	—
439	C₂×C₄×C₄₁	—	4	1	no	—
440	C₂×C₄×C₄₁	—	4	4	no	—
441	C₂×C₄×C₄₁	—	4	4	no	—
442	C₂×C₄×C₄₁	—	4	4	no	—
443	C₂×C₄×C₄₁	—	4	4	no	—
444	C₂×C₄×C₄₁	—	4	4	no	—
445	C₂×C₄×C₄₁	—	4	2	no	—
446	C₂×C₄×C₄₁	—	4	2	no	—
447	C₂×C₄×C₄₁	—	4	4	no	—
448	C₂×C₄×C₄₁	—	4	4	no	—
449	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
461	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
462	C₈×C₄₁	—	2	4	no	—
463	C₈×C₄₁	—	2	4	no	—
464	#60546	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
465	C₂²×C₄₁	—	2	1	no	—
466	C₂²×C₄₁	—	2	1	no	—
467	C₂²×C₄₁	—	2	1	no	—
468	C₂²×C₄₁	—	2	1	no	—
469	C₂²×C₄₁	—	2	1	no	—
470	C₂²×C₄₁	—	2	4	no	—
471	C₂²×C₄₁	—	2	1	no	—
472	C₂²×C₄₁	—	2	1	no	—
473	C₂²×C₄₁	—	4	4	no	—
474	C₂²×C₄₁	—	4	8	no	—
475	C₂²×C₄₁	—	4	2	no	—
476	C₂²×C₄₁	—	4	2	no	—
477	C₂²×C₄₁	—	4	2	no	—
478	C₂²×C₄₁	—	4	2	no	—
479	C₂²×C₄₁	—	4	2	no	—
480	C₂²×C₄₁	#525	1	2	yes	—
481	C₂²×C₄₁	#575	1	2	yes	—
482	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
483	C₄×C₄₁	—	2	1	no	—
484	C₄×C₄₁	—	2	4	no	—
485	C₄×C₄₁	—	2	1	no	—
486	C₄×C₄₁	—	2	1	no	—
487	C₄×C₄₁	—	2	1	no	—
488	C₄×C₄₁	—	2	1	no	—
489	C₄×C₄₁	—	2	1	no	—
490	C₄×C₄₁	—	2	1	no	—
491	C₄×C₄₁	—	2	1	no	—
492	C₄×C₄₁	—	2	1	no	—
493	C₄×C₄₁	—	4	2	no	—
494	C₄×C₄₁	—	4	2	no	—
495	C₄×C₄₁	—	4	2	no	—
496	C₄×C₄₁	—	4	2	no	—
497	C₄×C₄₁	—	4	2	no	—
498	C₄×C₄₁	#525	1	2	yes	—
499	C₄×C₄₁	#575	1	2	yes	—
500	C₄×C₄₁	C₂²×#41	1	2	yes	—
501	#3444	C₂×C₄₁	1	1	yes	characteristic, complemented
502	C₂×C₄×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
503	#3117	C₂×C₄₁	1	2	yes	complemented
504	#3116	C₂×C₄₁	1	2	yes	complemented
505	#3115	C₂×C₄₁	1	2	yes	complemented
506	#3114	C₂×C₄₁	1	2	yes	complemented
507	#3113	C₂×C₄₁	1	1	yes	characteristic, complemented
508	#3112	C₂×C₄₁	1	1	yes	characteristic, complemented
509	#3111	C₂×C₄₁	1	4	yes	complemented
510	#3110	C₂×C₄₁	1	1	yes	characteristic, complemented
511	#3109	C₂×C₄₁	1	1	yes	characteristic, complemented
512	#3091	C₂×C₄₁	1	2	yes	complemented
513	#3076	C₂×C₄₁	1	2	yes	complemented
514	#3035	C₂×C₄₁	1	2	yes	complemented
515	#3002	C₂×C₄₁	1	2	yes	complemented
516	#2943	C₂×C₄₁	1	4	yes	complemented
517	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
518	C₂×C₄₁	—	2	2	no	—
519	C₂×C₄₁	—	2	2	no	—
520	C₂×C₄₁	—	4	1	no	—
521	C₂×C₄₁	—	4	4	no	—
522	C₂×C₄₁	—	8	2	no	—
523	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
524	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
525	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
526	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
527	C₂×#135	C₂²×C₄₁	1	4	yes	—
528	#533	C₂²×C₄₁	1	1	yes	characteristic
529	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
530	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
531	#532	C₂²×C₄₁	1	1	yes	characteristic
532	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
533	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
534	#529	—	2	1	no	—
535	#529	—	2	1	no	—
536	#529	—	2	1	no	—
537	#529	—	2	1	no	—
538	#529	C₂²×C₄₁	1	2	yes	—
539	#529	C₂²×C₄₁	1	2	yes	complemented
540	#525	—	2	1	no	—
541	#525	—	2	1	no	—
542	#525	C₂²×C₄₁	1	2	yes	—
543	C₄×#41	—	2	1	no	—
544	C₄×#41	—	2	1	no	—
545	C₄×#41	—	2	1	no	—
546	C₄×#41	—	2	1	no	—
547	C₄×#41	—	2	1	no	—
548	C₄×#41	—	2	1	no	—
549	C₄×#41	C₂²×C₄₁	1	2	yes	—
550	C₄×#41	C₂²×C₄₁	1	2	yes	—
551	C₄×#41	C₂²×C₄₁	1	2	yes	—
552	C₄×#41	C₂²×C₄₁	1	2	yes	—
553	C₄×#41	C₂²×C₄₁	1	2	yes	complemented
554	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
555	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
556	C₂×C₄×D₄	—	2	1	no	—
557	C₂×C₄×D₄	—	2	1	no	—
558	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
559	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
560	C₂×#117	—	2	1	no	—
561	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
562	C₂²×C₄²	—	2	1	no	—
563	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
564	#485	C₂²×C₄₁	1	4	yes	complemented
565	#484	C₂²×C₄₁	1	2	yes	—
566	#483	C₂²×C₄₁	1	2	yes	—
567	#482	C₂²×C₄₁	1	4	yes	complemented
568	#481	C₂²×C₄₁	1	2	yes	—
569	#480	C₂²×C₄₁	1	2	yes	—
570	#479	C₂²×C₄₁	1	4	yes	complemented
571	#478	C₂²×C₄₁	1	4	yes	complemented
572	#477	C₂²×C₄₁	1	2	yes	complemented
573	#476	C₂²×C₄₁	1	2	yes	complemented
574	#475	C₂²×C₄₁	1	2	yes	complemented
575	#474	C₂²×C₄₁	1	2	yes	complemented
576	#464	C₂²×C₄₁	1	4	yes	complemented
577	#463	C₂²×C₄₁	1	4	yes	complemented
578	#462	C₂²×C₄₁	1	2	yes	complemented
579	#461	C₂²×C₄₁	1	2	yes	complemented
580	#460	C₂²×C₄₁	1	2	yes	complemented
581	#459	C₂²×C₄₁	1	2	yes	complemented
582	#452	C₂²×C₄₁	1	4	yes	—
583	#451	C₂²×C₄₁	1	2	yes	—
584	#450	C₂²×C₄₁	1	2	yes	—
585	#449	C₂²×C₄₁	1	4	yes	—
586	#448	C₂²×C₄₁	1	2	yes	—
587	#447	C₂²×C₄₁	1	2	yes	—
588	#442	C₂²×C₄₁	1	4	yes	complemented
589	#442	C₂²×C₄₁	1	4	yes	complemented
590	#441	C₂²×C₄₁	1	4	yes	complemented
591	#441	C₂²×C₄₁	1	4	yes	complemented
592	#440	C₂²×C₄₁	1	4	yes	complemented
593	#440	C₂²×C₄₁	1	4	yes	complemented
594	#440	C₂²×C₄₁	1	4	yes	complemented
595	#440	C₂²×C₄₁	1	4	yes	complemented
596	#432	C₂²×C₄₁	1	1	yes	characteristic
597	#432	C₂²×C₄₁	1	1	yes	characteristic
598	#432	C₂²×C₄₁	1	2	yes	—
599	#432	C₂²×C₄₁	1	2	yes	complemented
600	#432	C₂²×C₄₁	1	2	yes	complemented
601	#427	C₂²×C₄₁	1	4	yes	complemented
602	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
603	#416	C₂²×C₄₁	1	4	yes	—
604	#416	C₂²×C₄₁	1	4	yes	complemented
605	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
606	C₂×#97	C₂²×C₄₁	1	2	yes	complemented
607	C₄₁	#60546	1	1	yes	characteristic, direct product factor, Sylow
608	C₂×#41	—	2	8	no	—
609	C₂×#41	—	2	1	no	—
610	C₂×#41	—	2	1	no	—
611	C₂×#41	—	2	1	no	—
612	C₂×#41	—	2	1	no	—
613	C₂×#41	C₂³×C₄₁	1	2	yes	—
614	C₂×#41	C₂³×C₄₁	1	2	yes	—
615	C₂×#41	C₂³×C₄₁	1	2	yes	—
616	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
617	C₂²×D₄	—	2	1	no	—
618	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
619	C₂³×C₄	—	2	1	no	—
620	C₂³×C₄	—	2	1	no	—
621	C₂³×C₄	—	2	1	no	—
622	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
623	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
625	#135	—	2	16	no	—
626	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
627	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
628	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
629	C₂×D₈	C₂³×C₄₁	1	4	yes	—
630	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
631	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
633	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
634	#127	C₂³×C₄₁	1	1	yes	characteristic
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#125	—	2	1	no	—
638	#125	—	2	1	no	—
639	#125	C₂³×C₄₁	1	2	yes	—
640	#124	—	2	1	no	—
641	#124	—	2	1	no	—
642	#124	C₂³×C₄₁	1	2	yes	—
643	#123	—	2	2	no	—
644	#123	—	2	2	no	—
645	#123	—	2	2	no	—
646	C₂²⋊Q₈	—	2	1	no	—
647	C₂²⋊Q₈	—	2	1	no	—
648	C₂²⋊Q₈	—	2	1	no	—
649	C₂²⋊Q₈	—	2	1	no	—
650	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
651	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
652	#121	—	2	1	no	—
653	#121	—	2	1	no	—
654	#121	—	2	1	no	—
655	#121	—	2	1	no	—
656	#121	C₂³×C₄₁	1	2	yes	—
657	#121	C₂³×C₄₁	1	2	yes	—
658	#120	—	2	2	no	—
659	C₄×Q₈	—	2	1	no	—
660	C₄×Q₈	—	2	1	no	—
661	C₄×Q₈	—	2	1	no	—
662	C₄×Q₈	—	2	1	no	—
663	C₄×Q₈	—	2	1	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	—	2	1	no	—
667	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
668	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
669	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
670	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
671	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
672	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	1	no	—
688	C₄×D₄	—	2	1	no	—
689	C₄×D₄	—	2	1	no	—
690	C₄×D₄	—	2	1	no	—
691	C₄×D₄	—	2	1	no	—
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	1	no	—
694	C₄×D₄	—	2	1	no	—
695	C₄×D₄	C₂³×C₄₁	1	2	yes	—
696	C₄×D₄	C₂³×C₄₁	1	2	yes	—
697	C₄×D₄	C₂³×C₄₁	1	2	yes	—
698	C₄×D₄	C₂³×C₄₁	1	2	yes	—
699	C₄×D₄	C₂³×C₄₁	1	2	yes	—
700	C₄×D₄	C₂³×C₄₁	1	2	yes	—
701	#117	—	2	1	no	—
702	#117	—	2	1	no	—
703	#117	—	2	1	no	—
704	#117	—	2	1	no	—
705	#117	—	2	2	no	—
706	#117	—	2	2	no	—
707	#117	—	2	2	no	—
708	#117	—	2	2	no	—
709	#117	—	2	2	no	—
710	#117	—	2	2	no	—
711	#117	—	2	2	no	—
712	#117	C₂³×C₄₁	1	2	yes	—
713	#117	C₂³×C₄₁	1	2	yes	—
714	#117	C₂³×C₄₁	1	2	yes	—
715	C₂×C₄⋊C₄	—	2	1	no	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	—	2	1	no	—
720	C₂×C₂²⋊C₄	—	2	1	no	—
721	C₂×C₂²⋊C₄	—	2	1	no	—
722	C₂×C₄²	—	2	1	no	—
723	C₂×C₄²	—	2	1	no	—
724	C₂×C₄²	—	2	1	no	—
725	C₂×C₄²	—	2	2	no	—
726	C₂×C₄²	—	2	2	no	—
727	C₂×C₄²	—	2	2	no	—
728	C₂×C₄²	—	2	2	no	—
729	C₂×C₄²	—	2	2	no	—
730	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
731	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
732	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
733	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
734	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
735	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
742	#107	C₂³×C₄₁	1	4	yes	—
743	#107	C₂³×C₄₁	1	4	yes	—
744	#106	C₂³×C₄₁	1	4	yes	—
745	#106	C₂³×C₄₁	1	4	yes	—
746	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
747	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
748	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
749	#103	C₂³×C₄₁	1	4	yes	—
750	#103	C₂³×C₄₁	1	4	yes	—
751	#103	C₂³×C₄₁	1	4	yes	—
752	#103	C₂³×C₄₁	1	4	yes	—
753	#102	C₂³×C₄₁	1	4	yes	—
754	#102	C₂³×C₄₁	1	4	yes	—
755	#102	C₂³×C₄₁	1	4	yes	—
756	#102	C₂³×C₄₁	1	4	yes	—
757	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
758	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
759	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
760	#97	C₂³×C₄₁	1	2	yes	—
761	#97	C₂³×C₄₁	1	4	yes	—
762	#97	C₂³×C₄₁	1	2	yes	—
763	C₂⁴	—	2	1	no	—
764	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
765	#41	—	2	8	no	—
766	#41	—	2	8	no	—
767	#41	—	2	4	no	—
768	#41	—	2	4	no	—
769	#41	—	2	4	no	—
770	#41	—	2	8	no	—
771	#41	—	4	4	no	—
772	#41	—	4	4	no	—
773	#41	#41×C₄₁	1	8	yes	complemented
774	C₂×Q₈	—	2	4	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	2	1	no	—
778	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
779	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
780	C₂×D₄	—	2	8	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	4	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
791	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
792	C₂²×C₄	—	2	8	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	4	no	—
809	C₂²×C₄	—	4	4	no	—
810	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
811	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
812	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
813	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
814	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
815	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
816	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
817	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
818	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
821	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
822	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
823	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
824	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
828	Q₁₆	—	2	8	no	—
829	SD₁₆	—	2	8	no	—
830	SD₁₆	—	2	8	no	—
831	D₈	—	2	8	no	—
832	C₂×C₈	—	2	8	no	—
833	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
834	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
880	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
881	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
882	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
883	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
884	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
885	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
886	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
887	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
888	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
889	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
890	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
891	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
892	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
893	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
894	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
895	C₂³	—	2	4	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	4	1	no	—
901	C₂³	—	4	2	no	—
902	C₂³	—	4	2	no	—
903	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
904	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
905	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
906	Q₈	—	2	4	no	—
907	Q₈	—	2	2	no	—
908	Q₈	—	2	4	no	—
909	Q₈	—	4	2	no	—
910	Q₈	—	4	2	no	—
911	Q₈	C₂×#41×C₄₁	1	4	yes	—
912	D₄	—	2	8	no	—
913	D₄	—	2	4	no	—
914	D₄	—	2	8	no	—
915	D₄	—	2	2	no	—
916	D₄	—	2	4	no	—
917	D₄	—	4	2	no	—
918	D₄	—	4	4	no	—
919	D₄	—	4	4	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	2	no	—
922	D₄	C₂×#41×C₄₁	1	4	yes	—
923	C₂×C₄	—	2	4	no	—
924	C₂×C₄	—	2	8	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	8	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	4	1	no	—
944	C₂×C₄	—	4	1	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	1	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	4	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	4	no	—
954	C₂×C₄	—	4	2	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	4	no	—
957	C₂×C₄	—	4	4	no	—
958	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
962	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
968	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
969	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
970	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
971	C₈	—	2	4	no	—
972	C₈	—	2	4	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	4	no	—
981	C₂²	—	4	4	no	—
982	C₂²	—	4	8	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	C₄₁×#525	1	2	yes	—
989	C₂²	C₄₁×#575	1	2	yes	—
990	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
991	C₄	—	2	1	no	—
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	4	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	C₄₁×#525	1	2	yes	—
1007	C₄	C₄₁×#575	1	2	yes	—
1008	C₄	C₂²×#41×C₄₁	1	2	yes	—
1009	C₂	—	2	2	no	—
1010	C₂	—	2	2	no	—
1011	C₂	—	4	1	no	—
1012	C₂	—	4	4	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
1015	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
1016	C₂	C₂×C₄₁×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
socle	C₂²×C₄₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3444	C₂	semidirect
2. C₂×C₄×#41×C₄₁	C₂	semidirect
3. C₄₁×#3117	C₂	semidirect
4. C₄₁×#3116	C₂	semidirect
5. C₄₁×#3115	C₂	semidirect
6. C₄₁×#3114	C₂	semidirect
7. C₄₁×#3113	C₂	semidirect
8. C₄₁×#3112	C₂	semidirect
9. C₄₁×#3111	C₂	semidirect
10. C₄₁×#3110	C₂	semidirect
11. C₄₁×#3109	C₂	semidirect
12. C₄₁×#3091	C₂	semidirect
13. C₄₁×#3076	C₂	semidirect
14. C₄₁×#3035	C₂	semidirect
15. C₄₁×#3002	C₂	semidirect
16. C₄₁×#2943	C₂	semidirect
17. C₂×C₄₁×#432	C₂	semidirect
21. C₄₁×#533	C₂²	semidirect
22. C₄₁×#533	C₂²	semidirect
24. C₄₁×#532	C₂²	semidirect
25. C₄₁×#532	C₂²	semidirect
31. C₄₁×#529	C₂²	semidirect
45. C₄×#41×C₄₁	C₂²	semidirect
56. C₄₁×#485	C₂²	semidirect
59. C₄₁×#482	C₂²	semidirect
62. C₄₁×#479	C₂²	semidirect
63. C₄₁×#478	C₂²	semidirect
64. C₄₁×#477	C₂²	semidirect
65. C₄₁×#476	C₂²	semidirect
66. C₄₁×#475	C₂²	semidirect
67. C₄₁×#474	C₂²	semidirect
68. C₄₁×#464	C₂²	semidirect
69. C₄₁×#463	C₂²	semidirect
70. C₄₁×#462	C₂²	semidirect
71. C₄₁×#461	C₂²	semidirect
72. C₄₁×#460	C₂²	semidirect
73. C₄₁×#459	C₂²	semidirect
80. C₄₁×#442	C₂²	semidirect
81. C₄₁×#442	C₂²	semidirect
82. C₄₁×#441	C₂²	semidirect
83. C₄₁×#441	C₂²	semidirect
84. C₄₁×#440	C₂²	semidirect
85. C₄₁×#440	C₂²	semidirect
86. C₄₁×#440	C₂²	semidirect
87. C₄₁×#440	C₂²	semidirect
91. C₄₁×#432	C₂²	semidirect
92. C₄₁×#432	C₂²	semidirect
93. C₄₁×#427	C₂²	semidirect
94. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
96. C₄₁×#416	C₂²	semidirect
98. C₂×#97×C₄₁	C₂²	semidirect
264. #41×C₄₁	#41	semidirect
464. #60546	C₄₁	direct (N × H)
501. #3444	C₂×C₄₁	semidirect
502. C₂×C₄×#41	C₂×C₄₁	semidirect
503. #3117	C₂×C₄₁	semidirect
504. #3116	C₂×C₄₁	semidirect
505. #3115	C₂×C₄₁	semidirect
506. #3114	C₂×C₄₁	semidirect
507. #3113	C₂×C₄₁	semidirect
508. #3112	C₂×C₄₁	semidirect
509. #3111	C₂×C₄₁	semidirect
510. #3110	C₂×C₄₁	semidirect
511. #3109	C₂×C₄₁	semidirect
512. #3091	C₂×C₄₁	semidirect
513. #3076	C₂×C₄₁	semidirect
514. #3035	C₂×C₄₁	semidirect
515. #3002	C₂×C₄₁	semidirect
516. #2943	C₂×C₄₁	semidirect
517. C₂×#432	C₂×C₄₁	semidirect
529. #533	C₂²×C₄₁	semidirect
530. #533	C₂²×C₄₁	semidirect
532. #532	C₂²×C₄₁	semidirect
533. #532	C₂²×C₄₁	semidirect
539. #529	C₂²×C₄₁	semidirect
553. C₄×#41	C₂²×C₄₁	semidirect
564. #485	C₂²×C₄₁	semidirect
567. #482	C₂²×C₄₁	semidirect
570. #479	C₂²×C₄₁	semidirect
571. #478	C₂²×C₄₁	semidirect
572. #477	C₂²×C₄₁	semidirect
573. #476	C₂²×C₄₁	semidirect
574. #475	C₂²×C₄₁	semidirect
575. #474	C₂²×C₄₁	semidirect
576. #464	C₂²×C₄₁	semidirect
577. #463	C₂²×C₄₁	semidirect
578. #462	C₂²×C₄₁	semidirect
579. #461	C₂²×C₄₁	semidirect
580. #460	C₂²×C₄₁	semidirect
581. #459	C₂²×C₄₁	semidirect
588. #442	C₂²×C₄₁	semidirect
589. #442	C₂²×C₄₁	semidirect
590. #441	C₂²×C₄₁	semidirect
591. #441	C₂²×C₄₁	semidirect
592. #440	C₂²×C₄₁	semidirect
593. #440	C₂²×C₄₁	semidirect
594. #440	C₂²×C₄₁	semidirect
595. #440	C₂²×C₄₁	semidirect
599. #432	C₂²×C₄₁	semidirect
600. #432	C₂²×C₄₁	semidirect
601. #427	C₂²×C₄₁	semidirect
602. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
604. #416	C₂²×C₄₁	semidirect
606. C₂×#97	C₂²×C₄₁	semidirect
607. C₄₁	#60546	direct (N × H)
773. #41	#41×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3444	2
C₂×C₄×#41×C₄₁	2
C₄₁×#3117	2
C₄₁×#3116	2
C₄₁×#3115	2
C₄₁×#3114	2
C₄₁×#3113	2
C₄₁×#3112	2
C₄₁×#3111	2
C₄₁×#3110	2
C₄₁×#3109	2
C₄₁×#3091	2
C₄₁×#3076	2
C₄₁×#3035	2
C₄₁×#3002	2
C₄₁×#2943	2
C₂×C₄₁×#432	2
#60546	41

Subgroups — C41×#60546 #23836747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#60546 #23836747