Subgroups — C₄₁×#61939 #23838140

Order 10496.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3400	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3397	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3377	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3375	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3370	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3368	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3224	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3222	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3219	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₄₁×#3120	C₂	1	2	yes	maximal, complemented
17	C₄₁×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₁×#563	—	2	2	no	—
21	C₄₁×#559	C₂²	1	2	yes	—
22	C₄₁×#559	C₂²	1	2	yes	—
23	Q₈²×C₄₁	C₂²	1	1	yes	characteristic, complemented
24	C₄₁×#557	C₂²	1	1	yes	characteristic, complemented
25	C₄₁×#557	C₂²	1	2	yes	complemented
26	C₄₁×#556	—	2	1	no	—
27	C₄₁×#556	C₂²	1	2	yes	—
28	C₄₁×#556	C₂²	1	2	yes	complemented
29	C₄₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#555	—	2	1	no	—
31	C₄₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₄₁×#553	—	2	2	no	—
33	C₄₁×#552	—	2	1	no	—
34	C₄₁×#550	C₂²	1	2	yes	—
35	C₄₁×#547	—	2	1	no	—
36	C₄₁×#544	—	2	1	no	—
37	C₄₁×#542	C₂²	1	2	yes	—
38	C₄₁×#541	—	2	1	no	—
39	C₄₁×#541	—	2	2	no	—
40	C₄₁×#541	C₂²	1	2	yes	—
41	C₄₁×#538	—	2	1	no	—
42	C₄₁×#538	—	2	1	no	—
43	C₄₁×#535	C₂²	1	2	yes	—
44	C₄₁×#533	C₂²	1	1	yes	characteristic
45	C₄₁×#533	C₂²	1	1	yes	characteristic
46	C₄₁×#532	C₂²	1	1	yes	characteristic
47	C₄₁×#529	C₂²	1	1	yes	characteristic
48	C₄₁×#525	—	2	2	no	—
49	C₄₁×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
51	C₄₁×#497	C₂²	1	2	yes	—
52	C₄₁×#497	C₂²	1	2	yes	complemented
53	C₄₁×#497	C₂²	1	1	yes	characteristic, complemented
54	C₄₁×#496	C₂²	1	2	yes	—
55	C₄₁×#496	C₂²	1	1	yes	characteristic, complemented
56	C₄₁×#495	C₂²	1	2	yes	—
57	C₄₁×#492	C₂²	1	2	yes	—
58	C₄₁×#491	C₂²	1	1	yes	characteristic, complemented
59	C₄₁×#490	C₂²	1	2	yes	—
60	C₄₁×#490	C₂²	1	1	yes	characteristic, complemented
61	C₄₁×#489	C₂²	1	2	yes	—
62	C₄₁×#489	C₂²	1	2	yes	complemented
63	C₄₁×#488	C₂²	1	2	yes	—
64	C₄₁×#486	C₂²	1	2	yes	—
65	C₄₁×#484	C₂²	1	2	yes	—
66	C₄₁×#483	C₂²	1	1	yes	characteristic
67	C₄₁×#480	C₂²	1	1	yes	characteristic
68	C₄₁×#479	C₂²	1	2	yes	complemented
69	C₄₁×#478	C₂²	1	2	yes	—
70	C₄₁×#478	C₂²	1	2	yes	complemented
71	C₄₁×#477	C₂²	1	2	yes	complemented
72	C₄₁×#474	C₂²	1	2	yes	—
73	C₄₁×#474	C₂²	1	2	yes	complemented
74	C₄₁×#464	C₂²	1	2	yes	—
75	C₄₁×#464	C₂²	1	2	yes	—
76	C₄₁×#464	C₂²	1	2	yes	—
77	C₄₁×#464	C₂²	1	2	yes	complemented
78	C₄₁×#464	C₂²	1	2	yes	complemented
79	C₄₁×#463	C₂²	1	2	yes	—
80	C₄₁×#463	C₂²	1	2	yes	—
81	C₄₁×#463	C₂²	1	2	yes	complemented
82	C₄₁×#463	C₂²	1	2	yes	complemented
83	C₄₁×#462	C₂²	1	2	yes	complemented
84	C₄₁×#462	C₂²	1	2	yes	complemented
85	C₄₁×#461	C₂²	1	2	yes	—
86	C₄₁×#461	C₂²	1	2	yes	complemented
87	C₄₁×#460	C₂²	1	2	yes	—
88	C₄₁×#460	C₂²	1	2	yes	—
89	C₄₁×#460	C₂²	1	2	yes	—
90	C₄₁×#460	C₂²	1	2	yes	complemented
91	C₄₁×#459	C₂²	1	2	yes	—
92	C₄₁×#452	C₂²	1	2	yes	—
93	C₄₁×#452	C₂²	1	2	yes	—
94	C₄₁×#452	C₂²	1	2	yes	—
95	C₄₁×#450	C₂²	1	2	yes	—
96	C₄₁×#450	C₂²	1	1	yes	characteristic
97	C₄₁×#449	C₂²	1	2	yes	—
98	C₄₁×#447	C₂²	1	1	yes	characteristic
99	C₄₁×#446	C₂²	1	2	yes	complemented
100	C₄₁×#446	C₂²	1	2	yes	complemented
101	C₄₁×#446	C₂²	1	2	yes	complemented
102	C₄₁×#446	C₂²	1	2	yes	complemented
103	C₄₁×#442	C₂²	1	2	yes	—
104	C₄₁×#441	C₂²	1	2	yes	complemented
105	C₄₁×#440	C₂²	1	2	yes	—
106	C₄₁×#440	C₂²	1	2	yes	—
107	C₄₁×#440	C₂²	1	2	yes	—
108	C₄₁×#440	C₂²	1	2	yes	complemented
109	C₄₁×#440	C₂²	1	2	yes	complemented
110	C₄₁×#440	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
112	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
114	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
115	C₄₁×#433	C₂²	1	2	yes	—
116	C₄₁×#433	C₂²	1	2	yes	—
117	C₄₁×#432	C₂²	1	1	yes	characteristic
118	C₄₁×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₄₁	—	2	2	no	—
120	C₂×#41×C₄₁	C₂³	1	2	yes	—
121	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₄₁	—	2	1	no	—
123	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
133	C₂×D₈×C₄₁	C₂³	1	2	yes	—
134	C₂×D₈×C₄₁	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₄₁	—	2	2	no	—
136	C₄⋊Q₈×C₄₁	—	2	2	no	—
137	C₄⋊Q₈×C₄₁	—	2	1	no	—
138	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
139	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
140	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
141	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
145	#127×C₄₁	C₂³	1	1	yes	characteristic
146	#127×C₄₁	C₂³	1	2	yes	—
147	#127×C₄₁	C₂³	1	2	yes	—
148	#126×C₄₁	—	2	2	no	—
149	#126×C₄₁	—	2	2	no	—
150	#126×C₄₁	—	2	2	no	—
151	#126×C₄₁	—	2	2	no	—
152	#126×C₄₁	—	2	2	no	—
153	#126×C₄₁	—	2	2	no	—
154	#126×C₄₁	—	2	2	no	—
155	#126×C₄₁	—	2	2	no	—
156	#126×C₄₁	—	2	1	no	—
157	#125×C₄₁	—	2	2	no	—
158	#125×C₄₁	—	2	2	no	—
159	#125×C₄₁	—	2	2	no	—
160	#125×C₄₁	—	2	2	no	—
161	#125×C₄₁	—	2	2	no	—
162	#125×C₄₁	—	2	1	no	—
163	#125×C₄₁	—	2	1	no	—
164	#125×C₄₁	D₄	1	2	yes	—
165	#125×C₄₁	C₂³	1	1	yes	characteristic
166	#125×C₄₁	C₂³	1	2	yes	—
167	#124×C₄₁	—	2	2	no	—
168	#124×C₄₁	—	2	2	no	—
169	#124×C₄₁	—	2	2	no	—
170	#124×C₄₁	C₂³	1	1	yes	characteristic
171	#124×C₄₁	C₂³	1	2	yes	—
172	#124×C₄₁	C₂³	1	2	yes	—
173	#124×C₄₁	C₂³	1	2	yes	—
174	#124×C₄₁	C₂³	1	2	yes	—
175	#123×C₄₁	—	2	1	no	—
176	#123×C₄₁	—	2	2	no	—
177	#123×C₄₁	—	2	2	no	—
178	#123×C₄₁	—	2	2	no	—
179	#123×C₄₁	—	2	2	no	—
180	#123×C₄₁	—	2	2	no	—
181	C₂²⋊Q₈×C₄₁	—	2	2	no	—
182	C₂²⋊Q₈×C₄₁	—	2	1	no	—
183	C₂²⋊Q₈×C₄₁	—	2	1	no	—
184	C₂²⋊Q₈×C₄₁	—	2	2	no	—
185	C₂²⋊Q₈×C₄₁	—	2	1	no	—
186	C₂²⋊Q₈×C₄₁	—	2	2	no	—
187	C₂²⋊Q₈×C₄₁	—	2	2	no	—
188	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
189	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
190	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
191	C₂²⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
192	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
193	#121×C₄₁	—	2	1	no	—
194	#121×C₄₁	—	2	1	no	—
195	#121×C₄₁	—	2	2	no	—
196	#121×C₄₁	—	2	2	no	—
197	#121×C₄₁	—	2	2	no	—
198	#121×C₄₁	—	2	2	no	—
199	#121×C₄₁	—	2	2	no	—
200	#121×C₄₁	C₂³	1	1	yes	characteristic
201	#120×C₄₁	—	2	2	no	—
202	#120×C₄₁	—	2	2	no	—
203	C₄×Q₈×C₄₁	—	2	1	no	—
204	C₄×Q₈×C₄₁	—	2	1	no	—
205	C₄×Q₈×C₄₁	—	2	2	no	—
206	C₄×Q₈×C₄₁	—	2	1	no	—
207	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
208	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₄₁	—	2	1	no	—
218	C₄×D₄×C₄₁	—	2	2	no	—
219	C₄×D₄×C₄₁	—	2	2	no	—
220	C₄×D₄×C₄₁	—	2	2	no	—
221	C₄×D₄×C₄₁	—	2	2	no	—
222	C₄×D₄×C₄₁	—	2	1	no	—
223	C₄×D₄×C₄₁	—	2	1	no	—
224	C₄×D₄×C₄₁	—	2	1	no	—
225	C₄×D₄×C₄₁	—	2	1	no	—
226	C₄×D₄×C₄₁	C₂³	1	2	yes	—
227	C₄×D₄×C₄₁	C₂³	1	2	yes	—
228	C₄×D₄×C₄₁	C₂³	1	2	yes	—
229	C₄×D₄×C₄₁	C₂³	1	2	yes	—
230	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₄₁	C₂³	1	2	yes	—
232	#117×C₄₁	—	2	1	no	—
233	#117×C₄₁	—	2	2	no	—
234	#117×C₄₁	—	2	2	no	—
235	#117×C₄₁	—	2	2	no	—
236	#117×C₄₁	—	2	1	no	—
237	#117×C₄₁	—	2	1	no	—
238	#117×C₄₁	C₂³	1	2	yes	—
239	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
240	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
241	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
243	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
244	#107×C₄₁	C₂³	1	2	yes	—
245	#107×C₄₁	C₂³	1	2	yes	—
246	#107×C₄₁	C₂³	1	2	yes	—
247	#106×C₄₁	C₂³	1	2	yes	—
248	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
249	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
250	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
251	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
252	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
253	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
254	#103×C₄₁	C₂³	1	2	yes	—
255	#103×C₄₁	C₂³	1	2	yes	—
256	#103×C₄₁	C₂³	1	2	yes	—
257	#103×C₄₁	C₂³	1	2	yes	—
258	#103×C₄₁	C₂³	1	2	yes	—
259	#103×C₄₁	C₂³	1	2	yes	—
260	#103×C₄₁	C₂³	1	2	yes	—
261	#102×C₄₁	C₂³	1	2	yes	—
262	#102×C₄₁	C₂³	1	2	yes	—
263	#102×C₄₁	C₂³	1	2	yes	—
264	#102×C₄₁	C₂³	1	2	yes	—
265	#102×C₄₁	C₂³	1	2	yes	—
266	#102×C₄₁	C₂³	1	2	yes	—
267	#102×C₄₁	C₂³	1	2	yes	—
268	#102×C₄₁	C₂³	1	2	yes	—
269	#102×C₄₁	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
273	#97×C₄₁	C₂³	1	1	yes	characteristic
274	#97×C₄₁	C₂³	1	1	yes	characteristic
275	#97×C₄₁	C₂³	1	2	yes	—
276	#97×C₄₁	C₂³	1	2	yes	—
277	#97×C₄₁	C₂³	1	2	yes	—
278	C₄×C₈×C₄₁	C₂³	1	2	yes	—
279	C₄×C₈×C₄₁	C₂³	1	2	yes	—
280	C₂⁴×C₄₁	—	2	1	no	—
281	#41×C₄₁	—	4	2	no	—
282	#41×C₄₁	—	4	2	no	—
283	#41×C₄₁	—	8	4	no	—
284	C₂×Q₈×C₄₁	—	2	1	no	—
285	C₂×Q₈×C₄₁	—	2	2	no	—
286	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
287	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
289	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
290	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
291	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
292	C₂×D₄×C₄₁	—	2	2	no	—
293	C₂×D₄×C₄₁	—	2	1	no	—
294	C₂×D₄×C₄₁	—	2	1	no	—
295	C₂×D₄×C₄₁	—	2	1	no	—
296	C₂×D₄×C₄₁	—	2	2	no	—
297	C₂×D₄×C₄₁	—	2	2	no	—
298	C₂×D₄×C₄₁	—	2	1	no	—
299	C₂×D₄×C₄₁	—	2	2	no	—
300	C₂×D₄×C₄₁	—	2	2	no	—
301	C₂×D₄×C₄₁	—	4	2	no	—
302	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
303	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
304	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₄₁	—	2	1	no	—
306	C₂²×C₄×C₄₁	—	2	1	no	—
307	C₂²×C₄×C₄₁	—	2	2	no	—
308	C₂²×C₄×C₄₁	—	2	2	no	—
309	C₂²×C₄×C₄₁	—	2	2	no	—
310	C₂²×C₄×C₄₁	—	2	2	no	—
311	C₂²×C₄×C₄₁	—	2	2	no	—
312	C₂²×C₄×C₄₁	—	2	2	no	—
313	C₂²×C₄×C₄₁	—	8	2	no	—
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	Q₁₆×C₄₁	—	4	2	no	—
318	Q₁₆×C₄₁	—	4	2	no	—
319	Q₁₆×C₄₁	—	4	2	no	—
320	SD₁₆×C₄₁	—	4	2	no	—
321	SD₁₆×C₄₁	—	4	2	no	—
322	SD₁₆×C₄₁	—	4	2	no	—
323	SD₁₆×C₄₁	—	4	2	no	—
324	SD₁₆×C₄₁	—	4	2	no	—
325	SD₁₆×C₄₁	—	4	2	no	—
326	SD₁₆×C₄₁	—	4	2	no	—
327	D₈×C₄₁	—	4	2	no	—
328	D₈×C₄₁	—	4	2	no	—
329	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
330	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
331	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
332	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₄₁	—	2	1	no	—
334	C₄⋊C₄×C₄₁	—	2	1	no	—
335	C₄⋊C₄×C₄₁	—	2	2	no	—
336	C₄⋊C₄×C₄₁	—	2	2	no	—
337	C₄⋊C₄×C₄₁	—	2	2	no	—
338	C₄⋊C₄×C₄₁	—	2	1	no	—
339	C₄⋊C₄×C₄₁	—	2	1	no	—
340	C₄⋊C₄×C₄₁	—	2	2	no	—
341	C₄⋊C₄×C₄₁	—	2	1	no	—
342	C₄⋊C₄×C₄₁	—	2	1	no	—
343	C₄⋊C₄×C₄₁	—	2	1	no	—
344	C₄⋊C₄×C₄₁	—	2	1	no	—
345	C₄⋊C₄×C₄₁	—	2	2	no	—
346	C₄⋊C₄×C₄₁	—	2	2	no	—
347	C₄⋊C₄×C₄₁	—	2	1	no	—
348	C₄⋊C₄×C₄₁	—	2	2	no	—
349	C₄⋊C₄×C₄₁	—	2	2	no	—
350	C₄⋊C₄×C₄₁	—	2	2	no	—
351	C₄⋊C₄×C₄₁	—	2	2	no	—
352	C₄⋊C₄×C₄₁	—	2	2	no	—
353	C₄⋊C₄×C₄₁	—	2	2	no	—
354	C₄⋊C₄×C₄₁	—	2	1	no	—
355	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
368	C₂²⋊C₄×C₄₁	—	2	2	no	—
369	C₂²⋊C₄×C₄₁	—	2	1	no	—
370	C₂²⋊C₄×C₄₁	—	2	2	no	—
371	C₂²⋊C₄×C₄₁	—	2	2	no	—
372	C₂²⋊C₄×C₄₁	—	2	1	no	—
373	C₂²⋊C₄×C₄₁	—	2	2	no	—
374	C₂²⋊C₄×C₄₁	—	2	2	no	—
375	C₂²⋊C₄×C₄₁	—	2	2	no	—
376	C₂²⋊C₄×C₄₁	—	2	2	no	—
377	C₂²⋊C₄×C₄₁	—	2	1	no	—
378	C₂²⋊C₄×C₄₁	—	2	1	no	—
379	C₂²⋊C₄×C₄₁	—	2	2	no	—
380	C₂²⋊C₄×C₄₁	—	2	2	no	—
381	C₂²⋊C₄×C₄₁	—	2	2	no	—
382	C₂²⋊C₄×C₄₁	—	2	2	no	—
383	C₂²⋊C₄×C₄₁	—	2	2	no	—
384	C₂²⋊C₄×C₄₁	—	2	2	no	—
385	C₂²⋊C₄×C₄₁	—	2	1	no	—
386	C₂²⋊C₄×C₄₁	—	2	2	no	—
387	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
389	C₄²×C₄₁	—	2	2	no	—
390	C₄²×C₄₁	—	2	2	no	—
391	C₄²×C₄₁	—	2	2	no	—
392	C₄²×C₄₁	—	2	1	no	—
393	C₄²×C₄₁	—	2	2	no	—
394	C₄²×C₄₁	—	2	2	no	—
395	C₄²×C₄₁	—	2	2	no	—
396	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₄₁	C₂⁴	1	2	yes	—
399	C₄²×C₄₁	C₂⁴	1	2	yes	—
400	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
401	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
402	C₂³×C₄₁	—	2	1	no	—
403	C₂³×C₄₁	—	2	2	no	—
404	C₂³×C₄₁	—	2	2	no	—
405	C₂³×C₄₁	—	4	2	no	—
406	C₂³×C₄₁	—	8	1	no	—
407	C₂³×C₄₁	—	8	1	no	—
408	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
409	Q₈×C₄₁	—	2	2	no	—
410	Q₈×C₄₁	—	2	2	no	—
411	Q₈×C₄₁	—	2	2	no	—
412	Q₈×C₄₁	—	2	2	no	—
413	Q₈×C₄₁	—	2	2	no	—
414	Q₈×C₄₁	—	4	1	no	—
415	Q₈×C₄₁	—	4	1	no	—
416	Q₈×C₄₁	—	4	2	no	—
417	Q₈×C₄₁	—	8	1	no	—
418	Q₈×C₄₁	—	8	2	no	—
419	D₄×C₄₁	—	2	2	no	—
420	D₄×C₄₁	—	2	2	no	—
421	D₄×C₄₁	—	2	2	no	—
422	D₄×C₄₁	—	2	2	no	—
423	D₄×C₄₁	—	2	2	no	—
424	D₄×C₄₁	—	4	2	no	—
425	D₄×C₄₁	—	4	2	no	—
426	D₄×C₄₁	—	4	4	no	—
427	D₄×C₄₁	—	8	1	no	—
428	D₄×C₄₁	—	8	2	no	—
429	D₄×C₄₁	—	8	2	no	—
430	D₄×C₄₁	—	8	2	no	—
431	D₄×C₄₁	—	8	2	no	—
432	D₄×C₄₁	—	8	1	no	—
433	C₂×C₄×C₄₁	—	2	2	no	—
434	C₂×C₄×C₄₁	—	2	2	no	—
435	C₂×C₄×C₄₁	—	2	1	no	—
436	C₂×C₄×C₄₁	—	2	1	no	—
437	C₂×C₄×C₄₁	—	2	2	no	—
438	C₂×C₄×C₄₁	—	2	2	no	—
439	C₂×C₄×C₄₁	—	2	1	no	—
440	C₂×C₄×C₄₁	—	2	2	no	—
441	C₂×C₄×C₄₁	—	4	1	no	—
442	C₂×C₄×C₄₁	—	4	1	no	—
443	C₂×C₄×C₄₁	—	4	2	no	—
444	C₂×C₄×C₄₁	—	4	4	no	—
445	C₂×C₄×C₄₁	—	4	4	no	—
446	C₂×C₄×C₄₁	—	8	2	no	—
447	C₂×C₄×C₄₁	—	8	2	no	—
448	C₂×C₄×C₄₁	—	8	2	no	—
449	C₂×C₄×C₄₁	—	8	2	no	—
450	C₂×C₄×C₄₁	—	8	1	no	—
451	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
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	2	yes	—
460	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
461	C₈×C₄₁	—	2	2	no	—
462	C₈×C₄₁	—	2	2	no	—
463	C₈×C₄₁	—	2	2	no	—
464	C₈×C₄₁	—	2	2	no	—
465	#61939	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
466	C₂²×C₄₁	—	2	1	no	—
467	C₂²×C₄₁	—	2	1	no	—
468	C₂²×C₄₁	—	2	1	no	—
469	C₂²×C₄₁	—	4	2	no	—
470	C₂²×C₄₁	—	4	2	no	—
471	C₂²×C₄₁	—	4	1	no	—
472	C₂²×C₄₁	—	4	1	no	—
473	C₂²×C₄₁	—	4	2	no	—
474	C₂²×C₄₁	—	4	2	no	—
475	C₂²×C₄₁	—	4	2	no	—
476	C₂²×C₄₁	—	4	2	no	—
477	C₂²×C₄₁	—	4	1	no	—
478	C₂²×C₄₁	—	8	4	no	—
479	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
480	C₄×C₄₁	—	2	1	no	—
481	C₄×C₄₁	—	2	1	no	—
482	C₄×C₄₁	—	2	2	no	—
483	C₄×C₄₁	—	2	2	no	—
484	C₄×C₄₁	—	2	1	no	—
485	C₄×C₄₁	—	2	1	no	—
486	C₄×C₄₁	—	2	2	no	—
487	C₄×C₄₁	—	2	2	no	—
488	C₄×C₄₁	—	2	1	no	—
489	C₄×C₄₁	—	4	2	no	—
490	C₄×C₄₁	—	4	2	no	—
491	C₄×C₄₁	—	4	1	no	—
492	C₄×C₄₁	—	4	1	no	—
493	C₄×C₄₁	—	4	2	no	—
494	C₄×C₄₁	—	4	2	no	—
495	C₄×C₄₁	—	4	1	no	—
496	C₄×C₄₁	#585	1	2	yes	—
497	#3555	C₂×C₄₁	1	1	yes	characteristic, complemented
498	#3506	C₂×C₄₁	1	1	yes	characteristic, complemented
499	#3402	C₂×C₄₁	1	2	yes	complemented
500	#3401	C₂×C₄₁	1	2	yes	complemented
501	#3400	C₂×C₄₁	1	2	yes	complemented
502	#3397	C₂×C₄₁	1	2	yes	complemented
503	#3377	C₂×C₄₁	1	2	yes	complemented
504	#3375	C₂×C₄₁	1	2	yes	complemented
505	#3370	C₂×C₄₁	1	2	yes	complemented
506	#3368	C₂×C₄₁	1	2	yes	complemented
507	#3224	C₂×C₄₁	1	2	yes	complemented
508	#3222	C₂×C₄₁	1	2	yes	complemented
509	#3219	C₂×C₄₁	1	1	yes	characteristic, complemented
510	#3216	C₂×C₄₁	1	1	yes	characteristic, complemented
511	#3124	C₂×C₄₁	1	2	yes	complemented
512	#3120	C₂×C₄₁	1	2	yes	complemented
513	#3114	C₂×C₄₁	1	1	yes	characteristic, complemented
514	#3110	C₂×C₄₁	1	1	yes	characteristic, complemented
515	#2987	C₂×C₄₁	1	1	yes	characteristic, complemented
516	C₂×C₄₁	—	4	1	no	—
517	C₂×C₄₁	—	8	2	no	—
518	C₂×C₄₁	—	8	1	no	—
519	C₂×C₄₁	—	8	2	no	—
520	C₂×C₄₁	#3487	1	1	yes	characteristic
521	C₂×C₄₁	#3585	1	1	yes	characteristic
522	C₂×C₄₁	#3586	1	1	yes	characteristic
523	#563	—	2	2	no	—
524	#559	C₂²×C₄₁	1	2	yes	—
525	#559	C₂²×C₄₁	1	2	yes	—
526	Q₈²	C₂²×C₄₁	1	1	yes	characteristic, complemented
527	#557	C₂²×C₄₁	1	1	yes	characteristic, complemented
528	#557	C₂²×C₄₁	1	2	yes	complemented
529	#556	—	2	1	no	—
530	#556	C₂²×C₄₁	1	2	yes	—
531	#556	C₂²×C₄₁	1	2	yes	complemented
532	#556	C₂²×C₄₁	1	1	yes	characteristic, complemented
533	#555	—	2	1	no	—
534	#554	C₂²×C₄₁	1	1	yes	characteristic, complemented
535	#553	—	2	2	no	—
536	#552	—	2	1	no	—
537	#550	C₂²×C₄₁	1	2	yes	—
538	#547	—	2	1	no	—
539	#544	—	2	1	no	—
540	#542	C₂²×C₄₁	1	2	yes	—
541	#541	—	2	1	no	—
542	#541	—	2	2	no	—
543	#541	C₂²×C₄₁	1	2	yes	—
544	#538	—	2	1	no	—
545	#538	—	2	1	no	—
546	#535	C₂²×C₄₁	1	2	yes	—
547	#533	C₂²×C₄₁	1	1	yes	characteristic
548	#533	C₂²×C₄₁	1	1	yes	characteristic
549	#532	C₂²×C₄₁	1	1	yes	characteristic
550	#529	C₂²×C₄₁	1	1	yes	characteristic
551	#525	—	2	2	no	—
552	#520	C₂²×C₄₁	1	2	yes	—
553	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
554	#497	C₂²×C₄₁	1	2	yes	—
555	#497	C₂²×C₄₁	1	2	yes	complemented
556	#497	C₂²×C₄₁	1	1	yes	characteristic, complemented
557	#496	C₂²×C₄₁	1	2	yes	—
558	#496	C₂²×C₄₁	1	1	yes	characteristic, complemented
559	#495	C₂²×C₄₁	1	2	yes	—
560	#492	C₂²×C₄₁	1	2	yes	—
561	#491	C₂²×C₄₁	1	1	yes	characteristic, complemented
562	#490	C₂²×C₄₁	1	2	yes	—
563	#490	C₂²×C₄₁	1	1	yes	characteristic, complemented
564	#489	C₂²×C₄₁	1	2	yes	—
565	#489	C₂²×C₄₁	1	2	yes	complemented
566	#488	C₂²×C₄₁	1	2	yes	—
567	#486	C₂²×C₄₁	1	2	yes	—
568	#484	C₂²×C₄₁	1	2	yes	—
569	#483	C₂²×C₄₁	1	1	yes	characteristic
570	#480	C₂²×C₄₁	1	1	yes	characteristic
571	#479	C₂²×C₄₁	1	2	yes	complemented
572	#478	C₂²×C₄₁	1	2	yes	—
573	#478	C₂²×C₄₁	1	2	yes	complemented
574	#477	C₂²×C₄₁	1	2	yes	complemented
575	#474	C₂²×C₄₁	1	2	yes	—
576	#474	C₂²×C₄₁	1	2	yes	complemented
577	#464	C₂²×C₄₁	1	2	yes	—
578	#464	C₂²×C₄₁	1	2	yes	—
579	#464	C₂²×C₄₁	1	2	yes	—
580	#464	C₂²×C₄₁	1	2	yes	complemented
581	#464	C₂²×C₄₁	1	2	yes	complemented
582	#463	C₂²×C₄₁	1	2	yes	—
583	#463	C₂²×C₄₁	1	2	yes	—
584	#463	C₂²×C₄₁	1	2	yes	complemented
585	#463	C₂²×C₄₁	1	2	yes	complemented
586	#462	C₂²×C₄₁	1	2	yes	complemented
587	#462	C₂²×C₄₁	1	2	yes	complemented
588	#461	C₂²×C₄₁	1	2	yes	—
589	#461	C₂²×C₄₁	1	2	yes	complemented
590	#460	C₂²×C₄₁	1	2	yes	—
591	#460	C₂²×C₄₁	1	2	yes	—
592	#460	C₂²×C₄₁	1	2	yes	—
593	#460	C₂²×C₄₁	1	2	yes	complemented
594	#459	C₂²×C₄₁	1	2	yes	—
595	#452	C₂²×C₄₁	1	2	yes	—
596	#452	C₂²×C₄₁	1	2	yes	—
597	#452	C₂²×C₄₁	1	2	yes	—
598	#450	C₂²×C₄₁	1	2	yes	—
599	#450	C₂²×C₄₁	1	1	yes	characteristic
600	#449	C₂²×C₄₁	1	2	yes	—
601	#447	C₂²×C₄₁	1	1	yes	characteristic
602	#446	C₂²×C₄₁	1	2	yes	complemented
603	#446	C₂²×C₄₁	1	2	yes	complemented
604	#446	C₂²×C₄₁	1	2	yes	complemented
605	#446	C₂²×C₄₁	1	2	yes	complemented
606	#442	C₂²×C₄₁	1	2	yes	—
607	#441	C₂²×C₄₁	1	2	yes	complemented
608	#440	C₂²×C₄₁	1	2	yes	—
609	#440	C₂²×C₄₁	1	2	yes	—
610	#440	C₂²×C₄₁	1	2	yes	—
611	#440	C₂²×C₄₁	1	2	yes	complemented
612	#440	C₂²×C₄₁	1	2	yes	complemented
613	#440	C₂²×C₄₁	1	2	yes	complemented
614	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
615	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
616	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
617	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
618	#433	C₂²×C₄₁	1	2	yes	—
619	#433	C₂²×C₄₁	1	2	yes	—
620	#432	C₂²×C₄₁	1	1	yes	characteristic
621	#432	C₂²×C₄₁	1	1	yes	characteristic
622	C₄₁	#61939	1	1	yes	characteristic, direct product factor, Sylow
623	C₂×#41	—	2	2	no	—
624	C₂×#41	C₂³×C₄₁	1	2	yes	—
625	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
626	C₂³×C₄	—	2	1	no	—
627	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
628	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
629	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
637	C₂×D₈	C₂³×C₄₁	1	2	yes	—
638	C₂×D₈	C₂³×C₄₁	1	2	yes	—
639	C₄⋊Q₈	—	2	2	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	1	no	—
642	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
643	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
644	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
647	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
648	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
649	#127	C₂³×C₄₁	1	1	yes	characteristic
650	#127	C₂³×C₄₁	1	2	yes	—
651	#127	C₂³×C₄₁	1	2	yes	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	1	no	—
661	#125	—	2	2	no	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	1	no	—
667	#125	—	2	1	no	—
668	#125	D₄×C₄₁	1	2	yes	—
669	#125	C₂³×C₄₁	1	1	yes	characteristic
670	#125	C₂³×C₄₁	1	2	yes	—
671	#124	—	2	2	no	—
672	#124	—	2	2	no	—
673	#124	—	2	2	no	—
674	#124	C₂³×C₄₁	1	1	yes	characteristic
675	#124	C₂³×C₄₁	1	2	yes	—
676	#124	C₂³×C₄₁	1	2	yes	—
677	#124	C₂³×C₄₁	1	2	yes	—
678	#124	C₂³×C₄₁	1	2	yes	—
679	#123	—	2	1	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	1	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
693	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
694	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
695	C₂²⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
697	#121	—	2	1	no	—
698	#121	—	2	1	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	C₂³×C₄₁	1	1	yes	characteristic
705	#120	—	2	2	no	—
706	#120	—	2	2	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	—	2	2	no	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
712	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
713	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
714	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
715	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
716	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
717	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
718	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
719	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
720	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	C₂³×C₄₁	1	2	yes	—
731	C₄×D₄	C₂³×C₄₁	1	2	yes	—
732	C₄×D₄	C₂³×C₄₁	1	2	yes	—
733	C₄×D₄	C₂³×C₄₁	1	2	yes	—
734	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
735	C₄×D₄	C₂³×C₄₁	1	2	yes	—
736	#117	—	2	1	no	—
737	#117	—	2	2	no	—
738	#117	—	2	2	no	—
739	#117	—	2	2	no	—
740	#117	—	2	1	no	—
741	#117	—	2	1	no	—
742	#117	C₂³×C₄₁	1	2	yes	—
743	C₂×C₄⋊C₄	—	2	2	no	—
744	C₂×C₄⋊C₄	—	2	1	no	—
745	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	—	2	1	no	—
747	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
748	#107	C₂³×C₄₁	1	2	yes	—
749	#107	C₂³×C₄₁	1	2	yes	—
750	#107	C₂³×C₄₁	1	2	yes	—
751	#106	C₂³×C₄₁	1	2	yes	—
752	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
753	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
754	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
755	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
756	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
757	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
758	#103	C₂³×C₄₁	1	2	yes	—
759	#103	C₂³×C₄₁	1	2	yes	—
760	#103	C₂³×C₄₁	1	2	yes	—
761	#103	C₂³×C₄₁	1	2	yes	—
762	#103	C₂³×C₄₁	1	2	yes	—
763	#103	C₂³×C₄₁	1	2	yes	—
764	#103	C₂³×C₄₁	1	2	yes	—
765	#102	C₂³×C₄₁	1	2	yes	—
766	#102	C₂³×C₄₁	1	2	yes	—
767	#102	C₂³×C₄₁	1	2	yes	—
768	#102	C₂³×C₄₁	1	2	yes	—
769	#102	C₂³×C₄₁	1	2	yes	—
770	#102	C₂³×C₄₁	1	2	yes	—
771	#102	C₂³×C₄₁	1	2	yes	—
772	#102	C₂³×C₄₁	1	2	yes	—
773	#102	C₂³×C₄₁	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
775	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
777	#97	C₂³×C₄₁	1	1	yes	characteristic
778	#97	C₂³×C₄₁	1	1	yes	characteristic
779	#97	C₂³×C₄₁	1	2	yes	—
780	#97	C₂³×C₄₁	1	2	yes	—
781	#97	C₂³×C₄₁	1	2	yes	—
782	C₄×C₈	C₂³×C₄₁	1	2	yes	—
783	C₄×C₈	C₂³×C₄₁	1	2	yes	—
784	C₂⁴	—	2	1	no	—
785	#41	—	4	2	no	—
786	#41	—	4	2	no	—
787	#41	—	8	4	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
791	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
792	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
793	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
794	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
795	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
807	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
808	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	8	2	no	—
818	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
821	Q₁₆	—	4	2	no	—
822	Q₁₆	—	4	2	no	—
823	Q₁₆	—	4	2	no	—
824	SD₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	SD₁₆	—	4	2	no	—
830	SD₁₆	—	4	2	no	—
831	D₈	—	4	2	no	—
832	D₈	—	4	2	no	—
833	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
834	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
835	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
836	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
860	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
861	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
862	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
863	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
864	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
865	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
869	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
870	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	1	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	1	no	—
882	C₂²⋊C₄	—	2	1	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
892	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	1	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	2	no	—
900	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
901	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
902	C₄²	C₂⁴×C₄₁	1	2	yes	—
903	C₄²	C₂⁴×C₄₁	1	2	yes	—
904	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
905	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
906	C₂³	—	2	1	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	4	2	no	—
910	C₂³	—	8	1	no	—
911	C₂³	—	8	1	no	—
912	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
913	Q₈	—	2	2	no	—
914	Q₈	—	2	2	no	—
915	Q₈	—	2	2	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	4	2	no	—
919	Q₈	—	4	1	no	—
920	Q₈	—	4	1	no	—
921	Q₈	—	8	1	no	—
922	Q₈	—	8	2	no	—
923	D₄	—	2	2	no	—
924	D₄	—	2	2	no	—
925	D₄	—	2	2	no	—
926	D₄	—	2	2	no	—
927	D₄	—	2	2	no	—
928	D₄	—	4	2	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	4	no	—
931	D₄	—	8	2	no	—
932	D₄	—	8	2	no	—
933	D₄	—	8	1	no	—
934	D₄	—	8	2	no	—
935	D₄	—	8	2	no	—
936	D₄	—	8	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	4	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	2	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	2	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	—	8	1	no	—
955	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
956	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
958	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
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	2	yes	—
964	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
965	C₈	—	2	2	no	—
966	C₈	—	2	2	no	—
967	C₈	—	2	2	no	—
968	C₈	—	2	2	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	8	4	no	—
982	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	2	no	—
991	C₄	—	2	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	1	no	—
999	C₄	C₄₁×#585	1	2	yes	—
1000	C₂	—	4	1	no	—
1001	C₂	—	8	2	no	—
1002	C₂	—	8	2	no	—
1003	C₂	—	8	1	no	—
1004	C₂	C₄₁×#3487	1	1	yes	characteristic
1005	C₂	C₄₁×#3585	1	1	yes	characteristic
1006	C₂	C₄₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3555	C₂	semidirect
2. C₄₁×#3506	C₂	semidirect
3. C₄₁×#3402	C₂	semidirect
4. C₄₁×#3401	C₂	semidirect
5. C₄₁×#3400	C₂	semidirect
6. C₄₁×#3397	C₂	semidirect
7. C₄₁×#3377	C₂	semidirect
8. C₄₁×#3375	C₂	semidirect
9. C₄₁×#3370	C₂	semidirect
10. C₄₁×#3368	C₂	semidirect
11. C₄₁×#3224	C₂	semidirect
12. C₄₁×#3222	C₂	semidirect
13. C₄₁×#3219	C₂	semidirect
14. C₄₁×#3216	C₂	semidirect
15. C₄₁×#3124	C₂	semidirect
16. C₄₁×#3120	C₂	semidirect
17. C₄₁×#3114	C₂	semidirect
18. C₄₁×#3110	C₂	semidirect
19. C₄₁×#2987	C₂	semidirect
23. Q₈²×C₄₁	C₂²	semidirect
24. C₄₁×#557	C₂²	semidirect
25. C₄₁×#557	C₂²	semidirect
28. C₄₁×#556	C₂²	semidirect
29. C₄₁×#556	C₂²	semidirect
31. C₄₁×#554	C₂²	semidirect
52. C₄₁×#497	C₂²	semidirect
53. C₄₁×#497	C₂²	semidirect
55. C₄₁×#496	C₂²	semidirect
58. C₄₁×#491	C₂²	semidirect
60. C₄₁×#490	C₂²	semidirect
62. C₄₁×#489	C₂²	semidirect
68. C₄₁×#479	C₂²	semidirect
70. C₄₁×#478	C₂²	semidirect
71. C₄₁×#477	C₂²	semidirect
73. C₄₁×#474	C₂²	semidirect
77. C₄₁×#464	C₂²	semidirect
78. C₄₁×#464	C₂²	semidirect
81. C₄₁×#463	C₂²	semidirect
82. C₄₁×#463	C₂²	semidirect
83. C₄₁×#462	C₂²	semidirect
84. C₄₁×#462	C₂²	semidirect
86. C₄₁×#461	C₂²	semidirect
90. C₄₁×#460	C₂²	semidirect
99. C₄₁×#446	C₂²	semidirect
100. C₄₁×#446	C₂²	semidirect
101. C₄₁×#446	C₂²	semidirect
102. C₄₁×#446	C₂²	semidirect
104. C₄₁×#441	C₂²	semidirect
108. C₄₁×#440	C₂²	semidirect
109. C₄₁×#440	C₂²	semidirect
110. C₄₁×#440	C₂²	semidirect
111. C₄×Q₁₆×C₄₁	C₂²	semidirect
112. C₄×Q₁₆×C₄₁	C₂²	semidirect
113. C₄×SD₁₆×C₄₁	C₂²	semidirect
114. C₄×D₈×C₄₁	C₂²	semidirect
465. #61939	C₄₁	direct (N × H)
497. #3555	C₂×C₄₁	semidirect
498. #3506	C₂×C₄₁	semidirect
499. #3402	C₂×C₄₁	semidirect
500. #3401	C₂×C₄₁	semidirect
501. #3400	C₂×C₄₁	semidirect
502. #3397	C₂×C₄₁	semidirect
503. #3377	C₂×C₄₁	semidirect
504. #3375	C₂×C₄₁	semidirect
505. #3370	C₂×C₄₁	semidirect
506. #3368	C₂×C₄₁	semidirect
507. #3224	C₂×C₄₁	semidirect
508. #3222	C₂×C₄₁	semidirect
509. #3219	C₂×C₄₁	semidirect
510. #3216	C₂×C₄₁	semidirect
511. #3124	C₂×C₄₁	semidirect
512. #3120	C₂×C₄₁	semidirect
513. #3114	C₂×C₄₁	semidirect
514. #3110	C₂×C₄₁	semidirect
515. #2987	C₂×C₄₁	semidirect
526. Q₈²	C₂²×C₄₁	semidirect
527. #557	C₂²×C₄₁	semidirect
528. #557	C₂²×C₄₁	semidirect
531. #556	C₂²×C₄₁	semidirect
532. #556	C₂²×C₄₁	semidirect
534. #554	C₂²×C₄₁	semidirect
555. #497	C₂²×C₄₁	semidirect
556. #497	C₂²×C₄₁	semidirect
558. #496	C₂²×C₄₁	semidirect
561. #491	C₂²×C₄₁	semidirect
563. #490	C₂²×C₄₁	semidirect
565. #489	C₂²×C₄₁	semidirect
571. #479	C₂²×C₄₁	semidirect
573. #478	C₂²×C₄₁	semidirect
574. #477	C₂²×C₄₁	semidirect
576. #474	C₂²×C₄₁	semidirect
580. #464	C₂²×C₄₁	semidirect
581. #464	C₂²×C₄₁	semidirect
584. #463	C₂²×C₄₁	semidirect
585. #463	C₂²×C₄₁	semidirect
586. #462	C₂²×C₄₁	semidirect
587. #462	C₂²×C₄₁	semidirect
589. #461	C₂²×C₄₁	semidirect
593. #460	C₂²×C₄₁	semidirect
602. #446	C₂²×C₄₁	semidirect
603. #446	C₂²×C₄₁	semidirect
604. #446	C₂²×C₄₁	semidirect
605. #446	C₂²×C₄₁	semidirect
607. #441	C₂²×C₄₁	semidirect
611. #440	C₂²×C₄₁	semidirect
612. #440	C₂²×C₄₁	semidirect
613. #440	C₂²×C₄₁	semidirect
614. C₄×Q₁₆	C₂²×C₄₁	semidirect
615. C₄×Q₁₆	C₂²×C₄₁	semidirect
616. C₄×SD₁₆	C₂²×C₄₁	semidirect
617. C₄×D₈	C₂²×C₄₁	semidirect
622. C₄₁	#61939	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3555	2
C₄₁×#3506	2
C₄₁×#3402	2
C₄₁×#3401	2
C₄₁×#3400	2
C₄₁×#3397	2
C₄₁×#3377	2
C₄₁×#3375	2
C₄₁×#3370	2
C₄₁×#3368	2
C₄₁×#3224	2
C₄₁×#3222	2
C₄₁×#3219	2
C₄₁×#3216	2
C₄₁×#3124	2
C₄₁×#3120	2
C₄₁×#3114	2
C₄₁×#3110	2
C₄₁×#2987	2
#61939	41

Subgroups — C41×#61939 #23838140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61939 #23838140