Subgroups — C₄₁×#61576 #23837777

Order 10496.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3319	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3311	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3268	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3267	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#3196	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3188	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#3003	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3002	C₂	1	2	yes	maximal, complemented
15	C₄₁×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	4	yes	complemented
19	C₂×#135×C₄₁	C₂²	1	4	yes	complemented
20	C₄₁×#559	—	2	2	no	—
21	C₄₁×#556	C₂²	1	2	yes	complemented
22	C₄₁×#555	C₂²	1	2	yes	complemented
23	C₄₁×#553	—	2	2	no	—
24	C₄₁×#550	C₂²	1	2	yes	complemented
25	C₄₁×#547	C₂²	1	2	yes	complemented
26	C₄₁×#546	—	2	2	no	—
27	C₄₁×#546	—	2	2	no	—
28	C₄₁×#546	C₂²	1	4	yes	—
29	C₄₁×#546	C₂²	1	4	yes	—
30	C₄₁×#538	—	2	1	no	—
31	C₄₁×#538	—	2	1	no	—
32	C₄₁×#535	—	2	1	no	—
33	C₄₁×#533	C₂²	1	1	yes	characteristic, complemented
34	C₄₁×#532	C₂²	1	1	yes	characteristic, complemented
35	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#525	C₂²	1	2	yes	—
37	C₄₁×#525	C₂²	1	2	yes	complemented
38	C₂×#123×C₄₁	—	2	1	no	—
39	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×#121×C₄₁	—	2	1	no	—
41	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#120×C₄₁	—	2	1	no	—
43	C₄₁×#520	—	2	1	no	—
44	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
47	C₄₁×#497	C₂²	1	2	yes	complemented
48	C₄₁×#496	C₂²	1	2	yes	complemented
49	C₄₁×#489	C₂²	1	2	yes	complemented
50	C₄₁×#489	C₂²	1	2	yes	complemented
51	C₄₁×#485	C₂²	1	4	yes	complemented
52	C₄₁×#484	C₂²	1	2	yes	complemented
53	C₄₁×#482	C₂²	1	4	yes	complemented
54	C₄₁×#481	C₂²	1	2	yes	complemented
55	C₄₁×#476	C₂²	1	2	yes	complemented
56	C₄₁×#474	C₂²	1	2	yes	complemented
57	C₄₁×#470	C₂²	1	4	yes	complemented
58	C₄₁×#468	C₂²	1	4	yes	complemented
59	C₄₁×#466	C₂²	1	4	yes	complemented
60	C₄₁×#465	C₂²	1	4	yes	complemented
61	C₄₁×#464	C₂²	1	4	yes	complemented
62	C₄₁×#463	C₂²	1	4	yes	complemented
63	C₄₁×#461	C₂²	1	2	yes	complemented
64	C₄₁×#459	C₂²	1	2	yes	complemented
65	C₄₁×#452	C₂²	1	4	yes	complemented
66	C₄₁×#452	C₂²	1	4	yes	complemented
67	C₄₁×#451	C₂²	1	2	yes	complemented
68	C₄₁×#450	C₂²	1	2	yes	—
69	C₄₁×#450	C₂²	1	2	yes	—
70	C₄₁×#450	C₂²	1	4	yes	complemented
71	C₄₁×#449	C₂²	1	4	yes	complemented
72	C₄₁×#449	C₂²	1	4	yes	complemented
73	C₄₁×#448	C₂²	1	2	yes	complemented
74	C₄₁×#447	C₂²	1	2	yes	—
75	C₄₁×#447	C₂²	1	2	yes	—
76	C₄₁×#447	C₂²	1	4	yes	complemented
77	C₄₁×#442	C₂²	1	4	yes	complemented
78	C₄₁×#440	C₂²	1	4	yes	complemented
79	C₄₁×#435	C₂²	1	4	yes	complemented
80	C₄₁×#435	C₂²	1	4	yes	complemented
81	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
82	C₄₁×#432	C₂²	1	1	yes	characteristic, complemented
83	C₄₁×#418	C₂²	1	4	yes	complemented
84	C₄₁×#416	C₂²	1	4	yes	complemented
85	C₄₁×#407	C₂²	1	2	yes	—
86	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
87	C₂⁵×C₄₁	—	2	1	no	—
88	C₂×#41×C₄₁	—	2	1	no	—
89	C₂×#41×C₄₁	—	2	2	no	—
90	C₂×#41×C₄₁	—	4	4	no	—
91	C₂×#41×C₄₁	C₂³	1	4	yes	—
92	C₂×#41×C₄₁	C₂³	1	2	yes	—
93	C₂×#41×C₄₁	C₂³	1	2	yes	complemented
94	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₄₁	—	2	1	no	—
96	C₂²×D₄×C₄₁	—	2	1	no	—
97	C₂²×D₄×C₄₁	—	2	1	no	—
98	C₂²×D₄×C₄₁	—	2	2	no	—
99	C₂²×D₄×C₄₁	—	4	4	no	—
100	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
101	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
103	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₄₁	—	2	1	no	—
105	C₂³×C₄×C₄₁	—	2	1	no	—
106	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
108	AGL(1,ℤ/8)×C₄₁	—	4	8	no	—
109	#135×C₄₁	—	4	8	no	—
110	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	complemented
111	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	complemented
114	C₂×D₈×C₄₁	C₂³	1	4	yes	—
115	C₂×D₈×C₄₁	C₂³	1	4	yes	—
116	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
117	C₂²×C₈×C₄₁	C₂³	1	4	yes	complemented
118	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic, complemented
119	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic, complemented
120	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic, complemented
121	#127×C₄₁	—	2	2	no	—
122	#127×C₄₁	C₂³	1	1	yes	characteristic, complemented
123	#126×C₄₁	—	2	2	no	—
124	#126×C₄₁	—	2	2	no	—
125	#125×C₄₁	—	2	1	no	—
126	#124×C₄₁	—	2	2	no	—
127	#124×C₄₁	—	2	2	no	—
128	#124×C₄₁	—	2	2	no	—
129	#124×C₄₁	—	2	1	no	—
130	#124×C₄₁	—	2	1	no	—
131	#124×C₄₁	—	2	1	no	—
132	#124×C₄₁	C₂³	1	2	yes	—
133	#124×C₄₁	C₂³	1	2	yes	—
134	#123×C₄₁	—	2	2	no	—
135	#123×C₄₁	—	2	2	no	—
136	#123×C₄₁	—	2	4	no	—
137	#123×C₄₁	—	2	4	no	—
138	#123×C₄₁	—	2	2	no	—
139	#123×C₄₁	—	2	2	no	—
140	C₂²⋊Q₈×C₄₁	—	2	2	no	—
141	C₂²⋊Q₈×C₄₁	—	2	1	no	—
142	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
143	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
144	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	complemented
146	#121×C₄₁	—	2	2	no	—
147	#121×C₄₁	—	2	2	no	—
148	#121×C₄₁	—	2	2	no	—
149	#121×C₄₁	—	2	1	no	—
150	#121×C₄₁	—	2	4	no	—
151	#121×C₄₁	—	2	4	no	—
152	#121×C₄₁	—	2	2	no	—
153	#121×C₄₁	—	2	2	no	—
154	#121×C₄₁	C₂³	1	4	yes	—
155	#121×C₄₁	C₂³	1	2	yes	—
156	#121×C₄₁	C₂³	1	2	yes	—
157	#121×C₄₁	C₂³	1	2	yes	complemented
158	#120×C₄₁	—	2	2	no	—
159	#120×C₄₁	—	2	2	no	—
160	#120×C₄₁	—	2	4	no	—
161	#120×C₄₁	—	2	4	no	—
162	C₄×Q₈×C₄₁	—	2	2	no	—
163	C₄×Q₈×C₄₁	—	2	1	no	—
164	C₄×Q₈×C₄₁	C₂³	1	2	yes	complemented
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	1	no	—
171	C₄×D₄×C₄₁	—	2	1	no	—
172	C₄×D₄×C₄₁	—	2	1	no	—
173	C₄×D₄×C₄₁	D₄	1	2	yes	—
174	C₄×D₄×C₄₁	D₄	1	2	yes	—
175	C₄×D₄×C₄₁	C₂³	1	2	yes	—
176	C₄×D₄×C₄₁	C₂³	1	2	yes	—
177	C₄×D₄×C₄₁	C₂³	1	2	yes	—
178	C₄×D₄×C₄₁	C₂³	1	2	yes	—
179	C₄×D₄×C₄₁	C₂³	1	2	yes	complemented
180	#117×C₄₁	—	2	1	no	—
181	#117×C₄₁	—	2	2	no	—
182	#117×C₄₁	C₂³	1	2	yes	—
183	#117×C₄₁	C₂³	1	2	yes	complemented
184	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
185	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
186	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
194	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
195	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
198	#107×C₄₁	C₂³	1	4	yes	complemented
199	#106×C₄₁	C₂³	1	4	yes	complemented
200	C₄⋊C₈×C₄₁	C₂³	1	2	yes	complemented
201	C₄⋊C₈×C₄₁	C₂³	1	2	yes	complemented
202	#103×C₄₁	C₂³	1	4	yes	complemented
203	#103×C₄₁	C₂³	1	4	yes	complemented
204	#103×C₄₁	C₂³	1	4	yes	complemented
205	#102×C₄₁	C₂³	1	4	yes	—
206	#102×C₄₁	C₂³	1	4	yes	—
207	#102×C₄₁	C₂³	1	4	yes	—
208	#102×C₄₁	C₂³	1	4	yes	—
209	#102×C₄₁	C₂³	1	4	yes	complemented
210	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
211	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
213	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	complemented
214	#97×C₄₁	C₂³	1	2	yes	complemented
215	#97×C₄₁	C₂³	1	2	yes	complemented
216	C₂⁴×C₄₁	—	2	1	no	—
217	C₂⁴×C₄₁	—	2	1	no	—
218	C₂⁴×C₄₁	—	2	4	no	—
219	C₂⁴×C₄₁	—	4	4	no	—
220	C₂⁴×C₄₁	—	4	4	no	—
221	C₂⁴×C₄₁	—	8	2	no	—
222	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
223	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
224	#41×C₄₁	—	2	8	no	—
225	#41×C₄₁	—	4	4	no	—
226	#41×C₄₁	—	4	4	no	—
227	#41×C₄₁	—	4	4	no	—
228	#41×C₄₁	—	4	4	no	—
229	#41×C₄₁	—	4	8	no	—
230	C₂×Q₈×C₄₁	—	2	1	no	—
231	C₂×Q₈×C₄₁	—	2	1	no	—
232	C₂×Q₈×C₄₁	—	2	1	no	—
233	C₂×Q₈×C₄₁	—	4	2	no	—
234	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
236	C₂×D₄×C₄₁	—	2	4	no	—
237	C₂×D₄×C₄₁	—	2	8	no	—
238	C₂×D₄×C₄₁	—	2	2	no	—
239	C₂×D₄×C₄₁	—	2	4	no	—
240	C₂×D₄×C₄₁	—	2	2	no	—
241	C₂×D₄×C₄₁	—	2	2	no	—
242	C₂×D₄×C₄₁	—	2	4	no	—
243	C₂×D₄×C₄₁	—	2	2	no	—
244	C₂×D₄×C₄₁	—	2	2	no	—
245	C₂×D₄×C₄₁	—	2	1	no	—
246	C₂×D₄×C₄₁	—	2	1	no	—
247	C₂×D₄×C₄₁	—	2	4	no	—
248	C₂×D₄×C₄₁	—	2	1	no	—
249	C₂×D₄×C₄₁	—	2	1	no	—
250	C₂×D₄×C₄₁	—	4	4	no	—
251	C₂×D₄×C₄₁	—	4	2	no	—
252	C₂×D₄×C₄₁	—	4	2	no	—
253	C₂×D₄×C₄₁	—	4	8	no	—
254	C₂×D₄×C₄₁	—	4	4	no	—
255	C₂×D₄×C₄₁	—	4	4	no	—
256	C₂×D₄×C₄₁	—	8	2	no	—
257	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
260	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
261	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₄₁	—	2	1	no	—
263	C₂²×C₄×C₄₁	—	2	1	no	—
264	C₂²×C₄×C₄₁	—	2	4	no	—
265	C₂²×C₄×C₄₁	—	2	2	no	—
266	C₂²×C₄×C₄₁	—	2	2	no	—
267	C₂²×C₄×C₄₁	—	2	2	no	—
268	C₂²×C₄×C₄₁	—	2	2	no	—
269	C₂²×C₄×C₄₁	—	2	2	no	—
270	C₂²×C₄×C₄₁	—	4	2	no	—
271	C₂²×C₄×C₄₁	—	4	2	no	—
272	C₂²×C₄×C₄₁	—	4	4	no	—
273	C₂²×C₄×C₄₁	—	8	2	no	—
274	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
283	Q₁₆×C₄₁	—	4	4	no	—
284	SD₁₆×C₄₁	—	2	8	no	—
285	SD₁₆×C₄₁	—	4	4	no	—
286	SD₁₆×C₄₁	—	4	4	no	—
287	D₈×C₄₁	—	2	8	no	—
288	D₈×C₄₁	—	4	4	no	—
289	M₁₆×C₄₁	—	4	4	no	—
290	C₂×C₈×C₄₁	—	4	4	no	—
291	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
292	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
293	C₄⋊C₄×C₄₁	—	2	1	no	—
294	C₄⋊C₄×C₄₁	—	2	2	no	—
295	C₄⋊C₄×C₄₁	—	2	2	no	—
296	C₄⋊C₄×C₄₁	—	2	4	no	—
297	C₄⋊C₄×C₄₁	—	2	1	no	—
298	C₄⋊C₄×C₄₁	—	2	1	no	—
299	C₄⋊C₄×C₄₁	—	2	2	no	—
300	C₄⋊C₄×C₄₁	—	2	1	no	—
301	C₄⋊C₄×C₄₁	—	2	1	no	—
302	C₄⋊C₄×C₄₁	—	2	2	no	—
303	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
308	C₂²⋊C₄×C₄₁	—	2	4	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	—	2	2	no	—
314	C₂²⋊C₄×C₄₁	—	2	2	no	—
315	C₂²⋊C₄×C₄₁	—	2	2	no	—
316	C₂²⋊C₄×C₄₁	—	2	4	no	—
317	C₂²⋊C₄×C₄₁	—	2	2	no	—
318	C₂²⋊C₄×C₄₁	—	2	2	no	—
319	C₂²⋊C₄×C₄₁	—	2	2	no	—
320	C₂²⋊C₄×C₄₁	—	2	2	no	—
321	C₂²⋊C₄×C₄₁	—	2	2	no	—
322	C₂²⋊C₄×C₄₁	—	2	2	no	—
323	C₂²⋊C₄×C₄₁	—	2	2	no	—
324	C₂²⋊C₄×C₄₁	—	2	2	no	—
325	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
329	C₄²×C₄₁	—	2	2	no	—
330	C₄²×C₄₁	—	2	2	no	—
331	C₄²×C₄₁	—	2	2	no	—
332	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
335	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
336	C₂³×C₄₁	—	2	4	no	—
337	C₂³×C₄₁	—	2	2	no	—
338	C₂³×C₄₁	—	2	2	no	—
339	C₂³×C₄₁	—	2	2	no	—
340	C₂³×C₄₁	—	2	2	no	—
341	C₂³×C₄₁	—	2	2	no	—
342	C₂³×C₄₁	—	4	1	no	—
343	C₂³×C₄₁	—	4	1	no	—
344	C₂³×C₄₁	—	4	1	no	—
345	C₂³×C₄₁	—	4	1	no	—
346	C₂³×C₄₁	—	4	8	no	—
347	C₂³×C₄₁	—	4	2	no	—
348	C₂³×C₄₁	—	4	2	no	—
349	C₂³×C₄₁	—	4	2	no	—
350	C₂³×C₄₁	—	4	8	no	—
351	C₂³×C₄₁	—	4	2	no	—
352	C₂³×C₄₁	—	4	2	no	—
353	C₂³×C₄₁	—	8	4	no	—
354	C₂³×C₄₁	—	8	16	no	—
355	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
356	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
357	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₄₁	—	2	4	no	—
359	Q₈×C₄₁	—	2	4	no	—
360	Q₈×C₄₁	—	4	2	no	—
361	Q₈×C₄₁	—	4	2	no	—
362	Q₈×C₄₁	—	8	1	no	—
363	D₄×C₄₁	—	2	4	no	—
364	D₄×C₄₁	—	2	2	no	—
365	D₄×C₄₁	—	2	4	no	—
366	D₄×C₄₁	—	2	4	no	—
367	D₄×C₄₁	—	4	2	no	—
368	D₄×C₄₁	—	4	2	no	—
369	D₄×C₄₁	—	4	8	no	—
370	D₄×C₄₁	—	4	2	no	—
371	D₄×C₄₁	—	4	2	no	—
372	D₄×C₄₁	—	4	8	no	—
373	D₄×C₄₁	—	4	4	no	—
374	D₄×C₄₁	—	8	1	no	—
375	D₄×C₄₁	—	8	2	no	—
376	D₄×C₄₁	—	8	2	no	—
377	D₄×C₄₁	—	8	4	no	—
378	D₄×C₄₁	—	8	2	no	—
379	D₄×C₄₁	—	8	2	no	—
380	D₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
381	C₂×C₄×C₄₁	—	2	2	no	—
382	C₂×C₄×C₄₁	—	2	4	no	—
383	C₂×C₄×C₄₁	—	2	4	no	—
384	C₂×C₄×C₄₁	—	2	2	no	—
385	C₂×C₄×C₄₁	—	2	2	no	—
386	C₂×C₄×C₄₁	—	2	2	no	—
387	C₂×C₄×C₄₁	—	2	2	no	—
388	C₂×C₄×C₄₁	—	2	2	no	—
389	C₂×C₄×C₄₁	—	2	2	no	—
390	C₂×C₄×C₄₁	—	4	1	no	—
391	C₂×C₄×C₄₁	—	4	2	no	—
392	C₂×C₄×C₄₁	—	4	1	no	—
393	C₂×C₄×C₄₁	—	4	2	no	—
394	C₂×C₄×C₄₁	—	4	1	no	—
395	C₂×C₄×C₄₁	—	4	8	no	—
396	C₂×C₄×C₄₁	—	4	4	no	—
397	C₂×C₄×C₄₁	—	4	2	no	—
398	C₂×C₄×C₄₁	—	4	2	no	—
399	C₂×C₄×C₄₁	—	8	2	no	—
400	C₂×C₄×C₄₁	—	8	2	no	—
401	C₂×C₄×C₄₁	—	8	2	no	—
402	C₂×C₄×C₄₁	—	8	2	no	—
403	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
411	C₈×C₄₁	—	2	4	no	—
412	C₈×C₄₁	—	2	4	no	—
413	#61576	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₂²×C₄₁	—	2	1	no	—
415	C₂²×C₄₁	—	2	1	no	—
416	C₂²×C₄₁	—	2	2	no	—
417	C₂²×C₄₁	—	2	2	no	—
418	C₂²×C₄₁	—	2	2	no	—
419	C₂²×C₄₁	—	2	2	no	—
420	C₂²×C₄₁	—	2	4	no	—
421	C₂²×C₄₁	—	2	2	no	—
422	C₂²×C₄₁	—	2	2	no	—
423	C₂²×C₄₁	—	4	8	no	—
424	C₂²×C₄₁	—	4	4	no	—
425	C₂²×C₄₁	—	4	2	no	—
426	C₂²×C₄₁	—	4	2	no	—
427	C₂²×C₄₁	—	4	2	no	—
428	C₂²×C₄₁	—	4	2	no	—
429	C₂²×C₄₁	—	4	2	no	—
430	C₂²×C₄₁	—	4	2	no	—
431	C₂²×C₄₁	—	4	2	no	—
432	C₂²×C₄₁	—	4	2	no	—
433	C₂²×C₄₁	—	8	2	no	—
434	C₂²×C₄₁	—	8	4	no	—
435	C₂²×C₄₁	—	8	16	no	—
436	C₂²×C₄₁	#575	1	2	yes	—
437	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
438	C₄×C₄₁	—	2	1	no	—
439	C₄×C₄₁	—	2	1	no	—
440	C₄×C₄₁	—	2	2	no	—
441	C₄×C₄₁	—	2	1	no	—
442	C₄×C₄₁	—	2	2	no	—
443	C₄×C₄₁	—	2	1	no	—
444	C₄×C₄₁	—	2	1	no	—
445	C₄×C₄₁	—	4	2	no	—
446	C₄×C₄₁	—	4	2	no	—
447	C₄×C₄₁	—	4	2	no	—
448	C₄×C₄₁	—	4	2	no	—
449	C₄×C₄₁	—	4	2	no	—
450	C₄×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
451	#3506	C₂×C₄₁	1	1	yes	characteristic, complemented
452	C₂×#546	C₂×C₄₁	1	1	yes	characteristic, complemented
453	#3319	C₂×C₄₁	1	4	yes	complemented
454	#3311	C₂×C₄₁	1	4	yes	complemented
455	#3268	C₂×C₄₁	1	4	yes	complemented
456	#3267	C₂×C₄₁	1	4	yes	complemented
457	#3215	C₂×C₄₁	1	1	yes	characteristic, complemented
458	#3213	C₂×C₄₁	1	1	yes	characteristic, complemented
459	#3196	C₂×C₄₁	1	2	yes	complemented
460	#3188	C₂×C₄₁	1	2	yes	complemented
461	#3110	C₂×C₄₁	1	1	yes	characteristic, complemented
462	#3109	C₂×C₄₁	1	1	yes	characteristic, complemented
463	#3003	C₂×C₄₁	1	2	yes	complemented
464	#3002	C₂×C₄₁	1	2	yes	complemented
465	#2973	C₂×C₄₁	1	1	yes	characteristic, complemented
466	C₂×C₄₁	—	2	2	no	—
467	C₂×C₄₁	—	4	2	no	—
468	C₂×C₄₁	—	4	2	no	—
469	C₂×C₄₁	—	4	4	no	—
470	C₂×C₄₁	—	8	2	no	—
471	C₂×C₄₁	—	8	2	no	—
472	C₂×C₄₁	#3484	1	1	yes	characteristic
473	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
474	C₂×C₄₁	#3585	1	1	yes	characteristic
475	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
476	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
477	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	4	yes	complemented
478	C₂×#135	C₂²×C₄₁	1	4	yes	complemented
479	#559	—	2	2	no	—
480	#556	C₂²×C₄₁	1	2	yes	complemented
481	#555	C₂²×C₄₁	1	2	yes	complemented
482	#553	—	2	2	no	—
483	#550	C₂²×C₄₁	1	2	yes	complemented
484	#547	C₂²×C₄₁	1	2	yes	complemented
485	#546	—	2	2	no	—
486	#546	—	2	2	no	—
487	#546	C₂²×C₄₁	1	4	yes	—
488	#546	C₂²×C₄₁	1	4	yes	—
489	#538	—	2	1	no	—
490	#538	—	2	1	no	—
491	#535	—	2	1	no	—
492	#533	C₂²×C₄₁	1	1	yes	characteristic, complemented
493	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
494	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
495	#525	C₂²×C₄₁	1	2	yes	—
496	#525	C₂²×C₄₁	1	2	yes	complemented
497	C₂×#123	—	2	1	no	—
498	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
499	C₂×#121	—	2	1	no	—
500	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
501	C₂×#120	—	2	1	no	—
502	#520	—	2	1	no	—
503	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
504	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
505	C₂²×C₂²⋊C₄	—	2	1	no	—
506	#497	C₂²×C₄₁	1	2	yes	complemented
507	#496	C₂²×C₄₁	1	2	yes	complemented
508	#489	C₂²×C₄₁	1	2	yes	complemented
509	#489	C₂²×C₄₁	1	2	yes	complemented
510	#485	C₂²×C₄₁	1	4	yes	complemented
511	#484	C₂²×C₄₁	1	2	yes	complemented
512	#482	C₂²×C₄₁	1	4	yes	complemented
513	#481	C₂²×C₄₁	1	2	yes	complemented
514	#476	C₂²×C₄₁	1	2	yes	complemented
515	#474	C₂²×C₄₁	1	2	yes	complemented
516	#470	C₂²×C₄₁	1	4	yes	complemented
517	#468	C₂²×C₄₁	1	4	yes	complemented
518	#466	C₂²×C₄₁	1	4	yes	complemented
519	#465	C₂²×C₄₁	1	4	yes	complemented
520	#464	C₂²×C₄₁	1	4	yes	complemented
521	#463	C₂²×C₄₁	1	4	yes	complemented
522	#461	C₂²×C₄₁	1	2	yes	complemented
523	#459	C₂²×C₄₁	1	2	yes	complemented
524	#452	C₂²×C₄₁	1	4	yes	complemented
525	#452	C₂²×C₄₁	1	4	yes	complemented
526	#451	C₂²×C₄₁	1	2	yes	complemented
527	#450	C₂²×C₄₁	1	2	yes	—
528	#450	C₂²×C₄₁	1	2	yes	—
529	#450	C₂²×C₄₁	1	4	yes	complemented
530	#449	C₂²×C₄₁	1	4	yes	complemented
531	#449	C₂²×C₄₁	1	4	yes	complemented
532	#448	C₂²×C₄₁	1	2	yes	complemented
533	#447	C₂²×C₄₁	1	2	yes	—
534	#447	C₂²×C₄₁	1	2	yes	—
535	#447	C₂²×C₄₁	1	4	yes	complemented
536	#442	C₂²×C₄₁	1	4	yes	complemented
537	#440	C₂²×C₄₁	1	4	yes	complemented
538	#435	C₂²×C₄₁	1	4	yes	complemented
539	#435	C₂²×C₄₁	1	4	yes	complemented
540	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
541	#432	C₂²×C₄₁	1	1	yes	characteristic, complemented
542	#418	C₂²×C₄₁	1	4	yes	complemented
543	#416	C₂²×C₄₁	1	4	yes	complemented
544	#407	C₂²×C₄₁	1	2	yes	—
545	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
546	C₄₁	#61576	1	1	yes	characteristic, direct product factor, Sylow
547	C₂⁵	—	2	1	no	—
548	C₂×#41	—	2	1	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	4	4	no	—
551	C₂×#41	C₂³×C₄₁	1	4	yes	—
552	C₂×#41	C₂³×C₄₁	1	2	yes	—
553	C₂×#41	C₂³×C₄₁	1	2	yes	complemented
554	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	2	no	—
559	C₂²×D₄	—	4	4	no	—
560	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
562	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
563	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
564	C₂³×C₄	—	2	1	no	—
565	C₂³×C₄	—	2	1	no	—
566	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
568	AGL(1,ℤ/8)	—	4	8	no	—
569	#135	—	4	8	no	—
570	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	complemented
571	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
573	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	complemented
574	C₂×D₈	C₂³×C₄₁	1	4	yes	—
575	C₂×D₈	C₂³×C₄₁	1	4	yes	—
576	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
577	C₂²×C₈	C₂³×C₄₁	1	4	yes	complemented
578	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic, complemented
579	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic, complemented
580	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic, complemented
581	#127	—	2	2	no	—
582	#127	C₂³×C₄₁	1	1	yes	characteristic, complemented
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#125	—	2	1	no	—
586	#124	—	2	2	no	—
587	#124	—	2	2	no	—
588	#124	—	2	2	no	—
589	#124	—	2	1	no	—
590	#124	—	2	1	no	—
591	#124	—	2	1	no	—
592	#124	C₂³×C₄₁	1	2	yes	—
593	#124	C₂³×C₄₁	1	2	yes	—
594	#123	—	2	2	no	—
595	#123	—	2	2	no	—
596	#123	—	2	4	no	—
597	#123	—	2	4	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	1	no	—
602	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
603	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
605	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	complemented
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	4	no	—
611	#121	—	2	4	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	C₂³×C₄₁	1	4	yes	—
615	#121	C₂³×C₄₁	1	2	yes	—
616	#121	C₂³×C₄₁	1	2	yes	—
617	#121	C₂³×C₄₁	1	2	yes	complemented
618	#120	—	2	2	no	—
619	#120	—	2	2	no	—
620	#120	—	2	4	no	—
621	#120	—	2	4	no	—
622	C₄×Q₈	—	2	2	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×Q₈	C₂³×C₄₁	1	2	yes	complemented
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	D₄×C₄₁	1	2	yes	—
634	C₄×D₄	D₄×C₄₁	1	2	yes	—
635	C₄×D₄	C₂³×C₄₁	1	2	yes	—
636	C₄×D₄	C₂³×C₄₁	1	2	yes	—
637	C₄×D₄	C₂³×C₄₁	1	2	yes	—
638	C₄×D₄	C₂³×C₄₁	1	2	yes	—
639	C₄×D₄	C₂³×C₄₁	1	2	yes	complemented
640	#117	—	2	1	no	—
641	#117	—	2	2	no	—
642	#117	C₂³×C₄₁	1	2	yes	—
643	#117	C₂³×C₄₁	1	2	yes	complemented
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	4	no	—
654	C₂×C₂²⋊C₄	—	2	4	no	—
655	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
658	#107	C₂³×C₄₁	1	4	yes	complemented
659	#106	C₂³×C₄₁	1	4	yes	complemented
660	C₄⋊C₈	C₂³×C₄₁	1	2	yes	complemented
661	C₄⋊C₈	C₂³×C₄₁	1	2	yes	complemented
662	#103	C₂³×C₄₁	1	4	yes	complemented
663	#103	C₂³×C₄₁	1	4	yes	complemented
664	#103	C₂³×C₄₁	1	4	yes	complemented
665	#102	C₂³×C₄₁	1	4	yes	—
666	#102	C₂³×C₄₁	1	4	yes	—
667	#102	C₂³×C₄₁	1	4	yes	—
668	#102	C₂³×C₄₁	1	4	yes	—
669	#102	C₂³×C₄₁	1	4	yes	complemented
670	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
673	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	complemented
674	#97	C₂³×C₄₁	1	2	yes	complemented
675	#97	C₂³×C₄₁	1	2	yes	complemented
676	C₂⁴	—	2	1	no	—
677	C₂⁴	—	2	1	no	—
678	C₂⁴	—	2	4	no	—
679	C₂⁴	—	4	4	no	—
680	C₂⁴	—	4	4	no	—
681	C₂⁴	—	8	2	no	—
682	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
683	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
684	#41	—	2	8	no	—
685	#41	—	4	4	no	—
686	#41	—	4	4	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	8	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
695	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	8	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	8	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	—	8	2	no	—
717	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
718	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
719	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
720	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
721	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	4	no	—
733	C₂²×C₄	—	8	2	no	—
734	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
739	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
743	Q₁₆	—	4	4	no	—
744	SD₁₆	—	2	8	no	—
745	SD₁₆	—	4	4	no	—
746	SD₁₆	—	4	4	no	—
747	D₈	—	2	8	no	—
748	D₈	—	4	4	no	—
749	M₁₆	—	4	4	no	—
750	C₂×C₈	—	4	4	no	—
751	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
752	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
764	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
765	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
787	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
788	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
793	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
794	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
795	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
796	C₂³	—	2	4	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	8	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	8	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	4	no	—
814	C₂³	—	8	16	no	—
815	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
816	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
817	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
818	Q₈	—	2	4	no	—
819	Q₈	—	2	4	no	—
820	Q₈	—	4	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	—	8	1	no	—
823	D₄	—	2	4	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	4	no	—
827	D₄	—	4	2	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	8	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	4	no	—
834	D₄	—	8	1	no	—
835	D₄	—	8	4	no	—
836	D₄	—	8	2	no	—
837	D₄	—	8	2	no	—
838	D₄	—	8	2	no	—
839	D₄	—	8	2	no	—
840	D₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	—	8	2	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
864	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
865	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
870	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
871	C₈	—	2	4	no	—
872	C₈	—	2	4	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	4	4	no	—
883	C₂²	—	4	8	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	8	2	no	—
893	C₂²	—	8	4	no	—
894	C₂²	—	8	16	no	—
895	C₂²	C₄₁×#575	1	2	yes	—
896	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
897	C₄	—	2	1	no	—
898	C₄	—	2	1	no	—
899	C₄	—	2	1	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
910	C₂	—	2	2	no	—
911	C₂	—	4	2	no	—
912	C₂	—	4	2	no	—
913	C₂	—	4	4	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	2	no	—
916	C₂	C₄₁×#3484	1	1	yes	characteristic
917	C₂	C₂×C₄₁×#575	1	1	yes	characteristic
918	C₂	C₄₁×#3585	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 ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3506	C₂	semidirect
2. C₂×C₄₁×#546	C₂	semidirect
3. C₄₁×#3319	C₂	semidirect
4. C₄₁×#3311	C₂	semidirect
5. C₄₁×#3268	C₂	semidirect
6. C₄₁×#3267	C₂	semidirect
7. C₄₁×#3215	C₂	semidirect
8. C₄₁×#3213	C₂	semidirect
9. C₄₁×#3196	C₂	semidirect
10. C₄₁×#3188	C₂	semidirect
11. C₄₁×#3110	C₂	semidirect
12. C₄₁×#3109	C₂	semidirect
13. C₄₁×#3003	C₂	semidirect
14. C₄₁×#3002	C₂	semidirect
15. C₄₁×#2973	C₂	semidirect
18. C₂×AGL(1,ℤ/8)×C₄₁	C₂²	semidirect
19. C₂×#135×C₄₁	C₂²	semidirect
21. C₄₁×#556	C₂²	semidirect
22. C₄₁×#555	C₂²	semidirect
24. C₄₁×#550	C₂²	semidirect
25. C₄₁×#547	C₂²	semidirect
33. C₄₁×#533	C₂²	semidirect
34. C₄₁×#532	C₂²	semidirect
37. C₄₁×#525	C₂²	semidirect
47. C₄₁×#497	C₂²	semidirect
48. C₄₁×#496	C₂²	semidirect
49. C₄₁×#489	C₂²	semidirect
50. C₄₁×#489	C₂²	semidirect
51. C₄₁×#485	C₂²	semidirect
52. C₄₁×#484	C₂²	semidirect
53. C₄₁×#482	C₂²	semidirect
54. C₄₁×#481	C₂²	semidirect
55. C₄₁×#476	C₂²	semidirect
56. C₄₁×#474	C₂²	semidirect
57. C₄₁×#470	C₂²	semidirect
58. C₄₁×#468	C₂²	semidirect
59. C₄₁×#466	C₂²	semidirect
60. C₄₁×#465	C₂²	semidirect
61. C₄₁×#464	C₂²	semidirect
62. C₄₁×#463	C₂²	semidirect
63. C₄₁×#461	C₂²	semidirect
64. C₄₁×#459	C₂²	semidirect
65. C₄₁×#452	C₂²	semidirect
66. C₄₁×#452	C₂²	semidirect
67. C₄₁×#451	C₂²	semidirect
70. C₄₁×#450	C₂²	semidirect
71. C₄₁×#449	C₂²	semidirect
72. C₄₁×#449	C₂²	semidirect
73. C₄₁×#448	C₂²	semidirect
76. C₄₁×#447	C₂²	semidirect
77. C₄₁×#442	C₂²	semidirect
78. C₄₁×#440	C₂²	semidirect
79. C₄₁×#435	C₂²	semidirect
80. C₄₁×#435	C₂²	semidirect
81. C₄₁×#432	C₂²	semidirect
82. C₄₁×#432	C₂²	semidirect
83. C₄₁×#418	C₂²	semidirect
84. C₄₁×#416	C₂²	semidirect
86. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
93. C₂×#41×C₄₁	C₂³	semidirect
110. C₂×Q₁₆×C₄₁	C₂³	semidirect
113. C₂×SD₁₆×C₄₁	C₂³	semidirect
117. C₂²×C₈×C₄₁	C₂³	semidirect
118. C₄⋊Q₈×C₄₁	C₂³	semidirect
119. C₄⋊Q₈×C₄₁	C₂³	semidirect
120. C₄⋊Q₈×C₄₁	C₂³	semidirect
122. #127×C₄₁	C₂³	semidirect
145. C₂²⋊Q₈×C₄₁	C₂³	semidirect
157. #121×C₄₁	C₂³	semidirect
164. C₄×Q₈×C₄₁	C₂³	semidirect
179. C₄×D₄×C₄₁	C₂³	semidirect
183. #117×C₄₁	C₂³	semidirect
198. #107×C₄₁	C₂³	semidirect
199. #106×C₄₁	C₂³	semidirect
200. C₄⋊C₈×C₄₁	C₂³	semidirect
201. C₄⋊C₈×C₄₁	C₂³	semidirect
202. #103×C₄₁	C₂³	semidirect
203. #103×C₄₁	C₂³	semidirect
204. #103×C₄₁	C₂³	semidirect
209. #102×C₄₁	C₂³	semidirect
213. C₂²⋊C₈×C₄₁	C₂³	semidirect
214. #97×C₄₁	C₂³	semidirect
215. #97×C₄₁	C₂³	semidirect
413. #61576	C₄₁	direct (N × H)
451. #3506	C₂×C₄₁	semidirect
452. C₂×#546	C₂×C₄₁	semidirect
453. #3319	C₂×C₄₁	semidirect
454. #3311	C₂×C₄₁	semidirect
455. #3268	C₂×C₄₁	semidirect
456. #3267	C₂×C₄₁	semidirect
457. #3215	C₂×C₄₁	semidirect
458. #3213	C₂×C₄₁	semidirect
459. #3196	C₂×C₄₁	semidirect
460. #3188	C₂×C₄₁	semidirect
461. #3110	C₂×C₄₁	semidirect
462. #3109	C₂×C₄₁	semidirect
463. #3003	C₂×C₄₁	semidirect
464. #3002	C₂×C₄₁	semidirect
465. #2973	C₂×C₄₁	semidirect
477. C₂×AGL(1,ℤ/8)	C₂²×C₄₁	semidirect
478. C₂×#135	C₂²×C₄₁	semidirect
480. #556	C₂²×C₄₁	semidirect
481. #555	C₂²×C₄₁	semidirect
483. #550	C₂²×C₄₁	semidirect
484. #547	C₂²×C₄₁	semidirect
492. #533	C₂²×C₄₁	semidirect
493. #532	C₂²×C₄₁	semidirect
496. #525	C₂²×C₄₁	semidirect
506. #497	C₂²×C₄₁	semidirect
507. #496	C₂²×C₄₁	semidirect
508. #489	C₂²×C₄₁	semidirect
509. #489	C₂²×C₄₁	semidirect
510. #485	C₂²×C₄₁	semidirect
511. #484	C₂²×C₄₁	semidirect
512. #482	C₂²×C₄₁	semidirect
513. #481	C₂²×C₄₁	semidirect
514. #476	C₂²×C₄₁	semidirect
515. #474	C₂²×C₄₁	semidirect
516. #470	C₂²×C₄₁	semidirect
517. #468	C₂²×C₄₁	semidirect
518. #466	C₂²×C₄₁	semidirect
519. #465	C₂²×C₄₁	semidirect
520. #464	C₂²×C₄₁	semidirect
521. #463	C₂²×C₄₁	semidirect
522. #461	C₂²×C₄₁	semidirect
523. #459	C₂²×C₄₁	semidirect
524. #452	C₂²×C₄₁	semidirect
525. #452	C₂²×C₄₁	semidirect
526. #451	C₂²×C₄₁	semidirect
529. #450	C₂²×C₄₁	semidirect
530. #449	C₂²×C₄₁	semidirect
531. #449	C₂²×C₄₁	semidirect
532. #448	C₂²×C₄₁	semidirect
535. #447	C₂²×C₄₁	semidirect
536. #442	C₂²×C₄₁	semidirect
537. #440	C₂²×C₄₁	semidirect
538. #435	C₂²×C₄₁	semidirect
539. #435	C₂²×C₄₁	semidirect
540. #432	C₂²×C₄₁	semidirect
541. #432	C₂²×C₄₁	semidirect
542. #418	C₂²×C₄₁	semidirect
543. #416	C₂²×C₄₁	semidirect
545. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
546. C₄₁	#61576	direct (N × H)
553. C₂×#41	C₂³×C₄₁	semidirect
570. C₂×Q₁₆	C₂³×C₄₁	semidirect
573. C₂×SD₁₆	C₂³×C₄₁	semidirect
577. C₂²×C₈	C₂³×C₄₁	semidirect
578. C₄⋊Q₈	C₂³×C₄₁	semidirect
579. C₄⋊Q₈	C₂³×C₄₁	semidirect
580. C₄⋊Q₈	C₂³×C₄₁	semidirect
582. #127	C₂³×C₄₁	semidirect
605. C₂²⋊Q₈	C₂³×C₄₁	semidirect
617. #121	C₂³×C₄₁	semidirect
624. C₄×Q₈	C₂³×C₄₁	semidirect
639. C₄×D₄	C₂³×C₄₁	semidirect
643. #117	C₂³×C₄₁	semidirect
658. #107	C₂³×C₄₁	semidirect
659. #106	C₂³×C₄₁	semidirect
660. C₄⋊C₈	C₂³×C₄₁	semidirect
661. C₄⋊C₈	C₂³×C₄₁	semidirect
662. #103	C₂³×C₄₁	semidirect
663. #103	C₂³×C₄₁	semidirect
664. #103	C₂³×C₄₁	semidirect
669. #102	C₂³×C₄₁	semidirect
673. C₂²⋊C₈	C₂³×C₄₁	semidirect
674. #97	C₂³×C₄₁	semidirect
675. #97	C₂³×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3506	2
C₂×C₄₁×#546	2
C₄₁×#3319	2
C₄₁×#3311	2
C₄₁×#3268	2
C₄₁×#3267	2
C₄₁×#3215	2
C₄₁×#3213	2
C₄₁×#3196	2
C₄₁×#3188	2
C₄₁×#3110	2
C₄₁×#3109	2
C₄₁×#3003	2
C₄₁×#3002	2
C₄₁×#2973	2
#61576	41

Subgroups — C41×#61576 #23837777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61576 #23837777