Subgroups — C₄₁×#36738 #23812939

Order 10496.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#538	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2847	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2722	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2715	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2712	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2695	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2693	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2691	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2676	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#2672	C₂	1	2	yes	maximal, complemented
12	C₄₁×#2671	C₂	1	2	yes	maximal, complemented
13	C₄₁×#2617	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#2617	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#2564	C₂	1	2	yes	maximal, complemented
16	C₄₁×#2543	C₂	1	2	yes	maximal, complemented
17	C₄₁×#2417	C₂	1	2	yes	maximal, complemented
18	C₄₁×#2416	C₂	1	2	yes	maximal, complemented
19	C₂×C₄₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#538	—	2	16	no	—
22	C₂×#126×C₄₁	C₂²	1	2	yes	—
23	C₂×#126×C₄₁	C₂²	1	2	yes	—
24	C₂×#124×C₄₁	C₂²	1	2	yes	—
25	C₂×#124×C₄₁	C₂²	1	2	yes	—
26	C₂×#123×C₄₁	C₂²	1	2	yes	—
27	C₂×#123×C₄₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
30	C₂×#121×C₄₁	C₂²	1	2	yes	—
31	C₂×#121×C₄₁	C₂²	1	2	yes	—
32	C₂×#121×C₄₁	C₂²	1	2	yes	—
33	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×#121×C₄₁	C₂²	1	2	yes	—
35	C₂×#121×C₄₁	C₂²	1	2	yes	—
36	C₂×#121×C₄₁	C₂²	1	2	yes	—
37	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
39	C₂×#120×C₄₁	C₂²	1	2	yes	—
40	C₂×#120×C₄₁	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
46	C₄₁×#400	C₂²	1	2	yes	complemented
47	C₄₁×#399	C₂²	1	2	yes	complemented
48	C₄₁×#398	C₂²	1	2	yes	complemented
49	C₄₁×#398	C₂²	1	2	yes	complemented
50	C₄₁×#398	C₂²	1	2	yes	complemented
51	C₄₁×#397	C₂²	1	1	yes	characteristic
52	C₄₁×#397	C₂²	1	1	yes	characteristic
53	C₄₁×#397	C₂²	1	1	yes	characteristic
54	C₄₁×#397	C₂²	1	1	yes	characteristic
55	C₄₁×#397	C₂²	1	2	yes	complemented
56	C₄₁×#396	C₂²	1	2	yes	complemented
57	C₄₁×#396	C₂²	1	2	yes	complemented
58	C₄₁×#396	C₂²	1	2	yes	complemented
59	C₄₁×#396	C₂²	1	2	yes	complemented
60	C₄₁×#395	C₂²	1	2	yes	complemented
61	C₄₁×#394	C₂²	1	2	yes	—
62	C₄₁×#394	C₂²	1	2	yes	—
63	C₄₁×#394	C₂²	1	2	yes	—
64	C₄₁×#394	C₂²	1	2	yes	—
65	C₄₁×#394	C₂²	1	2	yes	complemented
66	C₄₁×#394	C₂²	1	2	yes	complemented
67	C₄₁×#394	C₂²	1	2	yes	complemented
68	C₄₁×#393	C₂²	1	2	yes	complemented
69	C₄₁×#392	C₂²	1	1	yes	characteristic
70	C₄₁×#392	C₂²	1	1	yes	characteristic
71	C₄₁×#392	C₂²	1	1	yes	characteristic
72	C₄₁×#392	C₂²	1	1	yes	characteristic
73	C₄₁×#392	C₂²	1	2	yes	complemented
74	C₄₁×#391	C₂²	1	2	yes	complemented
75	C₄₁×#390	C₂²	1	2	yes	complemented
76	C₄₁×#389	C₂²	1	2	yes	complemented
77	C₄₁×#389	C₂²	1	2	yes	complemented
78	C₄₁×#388	C₂²	1	2	yes	complemented
79	C₄₁×#388	C₂²	1	2	yes	complemented
80	C₄₁×#387	C₂²	1	2	yes	complemented
81	C₄₁×#387	C₂²	1	2	yes	complemented
82	C₄₁×#386	C₂²	1	2	yes	—
83	C₄₁×#386	C₂²	1	2	yes	—
84	C₄₁×#386	C₂²	1	2	yes	—
85	C₄₁×#386	C₂²	1	2	yes	—
86	C₄₁×#386	C₂²	1	2	yes	—
87	C₄₁×#386	C₂²	1	2	yes	—
88	C₄₁×#386	C₂²	1	2	yes	—
89	C₄₁×#386	C₂²	1	2	yes	—
90	C₄₁×#386	C₂²	1	2	yes	complemented
91	C₄₁×#386	C₂²	1	2	yes	complemented
92	C₄₁×#385	C₂²	1	2	yes	—
93	C₄₁×#385	C₂²	1	1	yes	characteristic
94	C₄₁×#385	C₂²	1	1	yes	characteristic
95	C₄₁×#385	C₂²	1	2	yes	—
96	C₄₁×#385	C₂²	1	1	yes	characteristic
97	C₄₁×#385	C₂²	1	1	yes	characteristic
98	C₄₁×#385	C₂²	1	2	yes	complemented
99	C₄₁×#385	C₂²	1	2	yes	complemented
100	C₄₁×#380	C₂²	1	1	yes	characteristic
101	C₄₁×#380	C₂²	1	2	yes	—
102	C₄₁×#380	C₂²	1	2	yes	—
103	C₄₁×#380	C₂²	1	2	yes	—
104	C₄₁×#380	C₂²	1	1	yes	characteristic
105	C₄₁×#380	C₂²	1	2	yes	complemented
106	C₄₁×#380	C₂²	1	2	yes	complemented
107	C₂×#95×C₄₁	C₂²	1	2	yes	—
108	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
114	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
116	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
117	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₄₁	—	4	4	no	—
121	C₂³×C₄×C₄₁	—	4	2	no	—
122	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
131	#126×C₄₁	—	2	8	no	—
132	#126×C₄₁	—	2	8	no	—
133	#124×C₄₁	—	2	8	no	—
134	#124×C₄₁	—	2	8	no	—
135	#123×C₄₁	—	2	8	no	—
136	#123×C₄₁	—	2	8	no	—
137	C₂²⋊Q₈×C₄₁	—	2	8	no	—
138	C₂²⋊Q₈×C₄₁	—	4	4	no	—
139	#121×C₄₁	—	2	8	no	—
140	#121×C₄₁	—	2	8	no	—
141	#121×C₄₁	—	2	8	no	—
142	#121×C₄₁	—	4	4	no	—
143	#121×C₄₁	—	4	4	no	—
144	#121×C₄₁	—	4	4	no	—
145	#121×C₄₁	—	4	4	no	—
146	#121×C₄₁	—	4	2	no	—
147	#121×C₄₁	—	4	2	no	—
148	#120×C₄₁	—	2	8	no	—
149	#120×C₄₁	—	2	8	no	—
150	C₄×D₄×C₄₁	—	2	8	no	—
151	C₄×D₄×C₄₁	—	2	8	no	—
152	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
153	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
171	C₂×C₂²⋊C₄×C₄₁	D₄	1	8	yes	complemented
172	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
203	#95×C₄₁	C₂³	1	2	yes	—
204	#95×C₄₁	C₂³	1	2	yes	—
205	#95×C₄₁	C₂³	1	2	yes	—
206	#95×C₄₁	C₂³	1	2	yes	—
207	#95×C₄₁	C₂³	1	1	yes	characteristic
208	#95×C₄₁	C₂³	1	2	yes	—
209	#95×C₄₁	C₂³	1	2	yes	—
210	#95×C₄₁	C₂³	1	1	yes	characteristic
211	#95×C₄₁	C₂³	1	2	yes	—
212	#95×C₄₁	C₂³	1	2	yes	—
213	#95×C₄₁	C₂³	1	2	yes	—
214	#95×C₄₁	C₂³	1	2	yes	—
215	#95×C₄₁	C₂³	1	1	yes	characteristic
216	#95×C₄₁	C₂³	1	1	yes	characteristic
217	#95×C₄₁	C₂³	1	2	yes	—
218	#95×C₄₁	C₂³	1	2	yes	—
219	#95×C₄₁	C₂³	1	2	yes	—
220	#95×C₄₁	C₂³	1	2	yes	—
221	C₂⁴×C₄₁	—	2	2	no	—
222	C₂⁴×C₄₁	—	2	2	no	—
223	C₂⁴×C₄₁	—	4	2	no	—
224	C₂⁴×C₄₁	—	4	2	no	—
225	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
226	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
227	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
228	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
229	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
230	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈×C₄₁	—	2	4	no	—
232	C₂×Q₈×C₄₁	—	4	2	no	—
233	C₂×Q₈×C₄₁	—	4	2	no	—
234	C₂×D₄×C₄₁	—	2	4	no	—
235	C₂×D₄×C₄₁	—	2	4	no	—
236	C₂×D₄×C₄₁	—	2	4	no	—
237	C₂×D₄×C₄₁	—	2	4	no	—
238	C₂×D₄×C₄₁	—	2	4	no	—
239	C₂×D₄×C₄₁	—	2	4	no	—
240	C₂×D₄×C₄₁	—	2	4	no	—
241	C₂×D₄×C₄₁	—	2	4	no	—
242	C₂×D₄×C₄₁	—	2	4	no	—
243	C₂×D₄×C₄₁	—	2	4	no	—
244	C₂×D₄×C₄₁	—	2	4	no	—
245	C₂×D₄×C₄₁	—	2	4	no	—
246	C₂×D₄×C₄₁	—	4	2	no	—
247	C₂×D₄×C₄₁	—	4	2	no	—
248	C₂×D₄×C₄₁	—	4	2	no	—
249	C₂×D₄×C₄₁	—	4	2	no	—
250	C₂×D₄×C₄₁	—	4	2	no	—
251	C₂×D₄×C₄₁	—	4	2	no	—
252	C₂×D₄×C₄₁	—	4	1	no	—
253	C₂×D₄×C₄₁	—	4	1	no	—
254	C₂×D₄×C₄₁	—	4	2	no	—
255	C₂×D₄×C₄₁	—	4	2	no	—
256	C₂×D₄×C₄₁	—	4	2	no	—
257	C₂×D₄×C₄₁	—	4	2	no	—
258	C₂×D₄×C₄₁	—	4	2	no	—
259	C₂×D₄×C₄₁	—	4	2	no	—
260	C₂×D₄×C₄₁	—	4	2	no	—
261	C₂×D₄×C₄₁	—	4	2	no	—
262	C₂²×C₄×C₄₁	—	2	4	no	—
263	C₂²×C₄×C₄₁	—	2	2	no	—
264	C₂²×C₄×C₄₁	—	2	2	no	—
265	C₂²×C₄×C₄₁	—	2	4	no	—
266	C₂²×C₄×C₄₁	—	2	4	no	—
267	C₂²×C₄×C₄₁	—	2	4	no	—
268	C₂²×C₄×C₄₁	—	2	4	no	—
269	C₂²×C₄×C₄₁	—	2	4	no	—
270	C₂²×C₄×C₄₁	—	4	2	no	—
271	C₂²×C₄×C₄₁	—	4	1	no	—
272	C₂²×C₄×C₄₁	—	4	2	no	—
273	C₂²×C₄×C₄₁	—	4	2	no	—
274	C₂²×C₄×C₄₁	—	4	2	no	—
275	C₂²×C₄×C₄₁	—	4	1	no	—
276	C₂²×C₄×C₄₁	—	4	2	no	—
277	C₂²×C₄×C₄₁	—	4	2	no	—
278	C₂²×C₄×C₄₁	—	4	2	no	—
279	C₂²×C₄×C₄₁	—	4	2	no	—
280	C₂²×C₄×C₄₁	—	4	2	no	—
281	C₂²×C₄×C₄₁	—	4	2	no	—
282	C₂²×C₄×C₄₁	—	4	2	no	—
283	C₂²×C₄×C₄₁	—	4	2	no	—
284	C₂²×C₄×C₄₁	—	4	16	no	—
285	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
286	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₄₁	—	2	4	no	—
301	C₄⋊C₄×C₄₁	—	2	4	no	—
302	C₄⋊C₄×C₄₁	—	2	4	no	—
303	C₄⋊C₄×C₄₁	—	2	4	no	—
304	C₄⋊C₄×C₄₁	—	2	4	no	—
305	C₄⋊C₄×C₄₁	—	2	4	no	—
306	C₄⋊C₄×C₄₁	—	2	4	no	—
307	C₄⋊C₄×C₄₁	—	2	4	no	—
308	C₄⋊C₄×C₄₁	—	2	4	no	—
309	C₄⋊C₄×C₄₁	—	4	2	no	—
310	C₄⋊C₄×C₄₁	—	4	2	no	—
311	C₄⋊C₄×C₄₁	—	4	2	no	—
312	C₄⋊C₄×C₄₁	—	4	2	no	—
313	C₄⋊C₄×C₄₁	—	4	2	no	—
314	C₄⋊C₄×C₄₁	—	4	1	no	—
315	C₄⋊C₄×C₄₁	—	4	1	no	—
316	C₄⋊C₄×C₄₁	—	4	2	no	—
317	C₂²⋊C₄×C₄₁	—	2	4	no	—
318	C₂²⋊C₄×C₄₁	—	2	4	no	—
319	C₂²⋊C₄×C₄₁	—	2	4	no	—
320	C₂²⋊C₄×C₄₁	—	2	4	no	—
321	C₂²⋊C₄×C₄₁	—	2	4	no	—
322	C₂²⋊C₄×C₄₁	—	2	4	no	—
323	C₂²⋊C₄×C₄₁	—	2	4	no	—
324	C₂²⋊C₄×C₄₁	—	2	4	no	—
325	C₂²⋊C₄×C₄₁	—	2	4	no	—
326	C₂²⋊C₄×C₄₁	—	2	4	no	—
327	C₂²⋊C₄×C₄₁	—	2	4	no	—
328	C₂²⋊C₄×C₄₁	—	2	4	no	—
329	C₂²⋊C₄×C₄₁	—	4	1	no	—
330	C₂²⋊C₄×C₄₁	—	4	1	no	—
331	C₂²⋊C₄×C₄₁	—	4	1	no	—
332	C₂²⋊C₄×C₄₁	—	4	1	no	—
333	C₂²⋊C₄×C₄₁	—	4	2	no	—
334	C₂²⋊C₄×C₄₁	—	4	2	no	—
335	C₂²⋊C₄×C₄₁	—	4	2	no	—
336	C₂²⋊C₄×C₄₁	—	4	2	no	—
337	C₂²⋊C₄×C₄₁	—	4	2	no	—
338	C₂²⋊C₄×C₄₁	—	4	2	no	—
339	C₂²⋊C₄×C₄₁	—	4	2	no	—
340	C₂²⋊C₄×C₄₁	—	4	2	no	—
341	C₂²⋊C₄×C₄₁	—	4	2	no	—
342	C₂²⋊C₄×C₄₁	—	4	2	no	—
343	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
344	C₂²⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
345	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
346	C₄²×C₄₁	—	2	4	no	—
347	C₄²×C₄₁	—	2	4	no	—
348	C₂³×C₄₁	—	2	2	no	—
349	C₂³×C₄₁	—	2	2	no	—
350	C₂³×C₄₁	—	2	8	no	—
351	C₂³×C₄₁	—	2	1	no	—
352	C₂³×C₄₁	—	2	1	no	—
353	C₂³×C₄₁	—	2	2	no	—
354	C₂³×C₄₁	—	2	2	no	—
355	C₂³×C₄₁	—	2	1	no	—
356	C₂³×C₄₁	—	2	1	no	—
357	C₂³×C₄₁	—	2	2	no	—
358	C₂³×C₄₁	—	2	2	no	—
359	C₂³×C₄₁	—	2	2	no	—
360	C₂³×C₄₁	—	2	2	no	—
361	C₂³×C₄₁	—	2	2	no	—
362	C₂³×C₄₁	—	2	2	no	—
363	C₂³×C₄₁	—	2	2	no	—
364	C₂³×C₄₁	—	2	2	no	—
365	C₂³×C₄₁	—	2	2	no	—
366	C₂³×C₄₁	—	2	2	no	—
367	C₂³×C₄₁	—	2	2	no	—
368	C₂³×C₄₁	—	2	2	no	—
369	C₂³×C₄₁	—	2	2	no	—
370	C₂³×C₄₁	—	2	2	no	—
371	C₂³×C₄₁	—	2	2	no	—
372	C₂³×C₄₁	—	2	2	no	—
373	C₂³×C₄₁	—	4	8	no	—
374	C₂³×C₄₁	—	4	4	no	—
375	C₂³×C₄₁	—	4	4	no	—
376	C₂³×C₄₁	—	4	8	no	—
377	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
378	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
379	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
380	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
381	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
382	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
383	Q₈×C₄₁	—	8	4	no	—
384	D₄×C₄₁	—	4	8	no	—
385	D₄×C₄₁	—	4	8	no	—
386	D₄×C₄₁	—	8	4	no	—
387	D₄×C₄₁	—	8	4	no	—
388	D₄×C₄₁	—	8	4	no	—
389	D₄×C₄₁	—	8	4	no	—
390	D₄×C₄₁	—	8	4	no	—
391	D₄×C₄₁	—	8	4	no	—
392	D₄×C₄₁	—	8	2	no	—
393	D₄×C₄₁	—	8	2	no	—
394	C₂×C₄×C₄₁	—	2	2	no	—
395	C₂×C₄×C₄₁	—	2	2	no	—
396	C₂×C₄×C₄₁	—	2	2	no	—
397	C₂×C₄×C₄₁	—	2	2	no	—
398	C₂×C₄×C₄₁	—	2	2	no	—
399	C₂×C₄×C₄₁	—	2	2	no	—
400	C₂×C₄×C₄₁	—	2	2	no	—
401	C₂×C₄×C₄₁	—	2	2	no	—
402	C₂×C₄×C₄₁	—	2	2	no	—
403	C₂×C₄×C₄₁	—	2	2	no	—
404	C₂×C₄×C₄₁	—	2	2	no	—
405	C₂×C₄×C₄₁	—	2	2	no	—
406	C₂×C₄×C₄₁	—	2	2	no	—
407	C₂×C₄×C₄₁	—	2	2	no	—
408	C₂×C₄×C₄₁	—	2	1	no	—
409	C₂×C₄×C₄₁	—	2	1	no	—
410	C₂×C₄×C₄₁	—	2	2	no	—
411	C₂×C₄×C₄₁	—	2	2	no	—
412	C₂×C₄×C₄₁	—	2	2	no	—
413	C₂×C₄×C₄₁	—	2	1	no	—
414	C₂×C₄×C₄₁	—	2	1	no	—
415	C₂×C₄×C₄₁	—	2	2	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	2	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	—	4	8	no	—
430	C₂×C₄×C₄₁	—	4	4	no	—
431	C₂×C₄×C₄₁	—	4	8	no	—
432	C₂×C₄×C₄₁	—	4	8	no	—
433	C₂×C₄×C₄₁	—	4	4	no	—
434	C₂×C₄×C₄₁	—	8	4	no	—
435	C₂×C₄×C₄₁	—	8	4	no	—
436	C₂×C₄×C₄₁	—	8	2	no	—
437	C₂×C₄×C₄₁	—	8	2	no	—
438	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
439	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
440	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
441	#36738	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂²×C₄₁	—	2	4	no	—
443	C₂²×C₄₁	—	2	2	no	—
444	C₂²×C₄₁	—	2	2	no	—
445	C₂²×C₄₁	—	2	4	no	—
446	C₂²×C₄₁	—	2	2	no	—
447	C₂²×C₄₁	—	2	2	no	—
448	C₂²×C₄₁	—	2	4	no	—
449	C₂²×C₄₁	—	2	4	no	—
450	C₂²×C₄₁	—	4	16	no	—
451	C₂²×C₄₁	—	4	1	no	—
452	C₂²×C₄₁	—	4	1	no	—
453	C₂²×C₄₁	—	4	1	no	—
454	C₂²×C₄₁	—	4	1	no	—
455	C₂²×C₄₁	—	4	2	no	—
456	C₂²×C₄₁	—	4	2	no	—
457	C₂²×C₄₁	—	4	2	no	—
458	C₂²×C₄₁	—	4	2	no	—
459	C₂²×C₄₁	—	4	2	no	—
460	C₂²×C₄₁	—	4	2	no	—
461	C₂²×C₄₁	—	4	2	no	—
462	C₂²×C₄₁	—	4	2	no	—
463	C₂²×C₄₁	—	4	2	no	—
464	C₂²×C₄₁	—	4	2	no	—
465	C₂²×C₄₁	—	4	2	no	—
466	C₂²×C₄₁	—	4	2	no	—
467	C₂²×C₄₁	—	4	2	no	—
468	C₂²×C₄₁	—	4	2	no	—
469	C₂²×C₄₁	—	4	2	no	—
470	C₂²×C₄₁	—	4	2	no	—
471	C₂²×C₄₁	#537	1	4	yes	—
472	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
473	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
475	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
476	C₂²×C₄₁	#585	1	2	yes	—
477	C₄×C₄₁	—	2	4	no	—
478	C₄×C₄₁	—	2	4	no	—
479	C₄×C₄₁	—	2	4	no	—
480	C₄×C₄₁	—	4	2	no	—
481	C₄×C₄₁	—	4	2	no	—
482	C₄×C₄₁	—	4	2	no	—
483	C₄×C₄₁	—	4	2	no	—
484	C₄×C₄₁	—	4	2	no	—
485	C₄×C₄₁	—	4	2	no	—
486	C₄×C₄₁	—	4	2	no	—
487	C₄×C₄₁	—	4	1	no	—
488	C₄×C₄₁	—	4	1	no	—
489	C₄×C₄₁	—	4	1	no	—
490	C₄×C₄₁	—	4	1	no	—
491	C₂×#538	C₂×C₄₁	1	2	yes	complemented
492	#2847	C₂×C₄₁	1	2	yes	complemented
493	#2722	C₂×C₄₁	1	1	yes	characteristic, complemented
494	#2715	C₂×C₄₁	1	2	yes	complemented
495	#2712	C₂×C₄₁	1	1	yes	characteristic, complemented
496	#2695	C₂×C₄₁	1	2	yes	complemented
497	#2693	C₂×C₄₁	1	1	yes	characteristic, complemented
498	#2691	C₂×C₄₁	1	2	yes	complemented
499	#2676	C₂×C₄₁	1	2	yes	complemented
500	#2675	C₂×C₄₁	1	1	yes	characteristic, complemented
501	#2672	C₂×C₄₁	1	2	yes	complemented
502	#2671	C₂×C₄₁	1	2	yes	complemented
503	#2617	C₂×C₄₁	1	1	yes	characteristic, complemented
504	#2617	C₂×C₄₁	1	1	yes	characteristic, complemented
505	#2564	C₂×C₄₁	1	2	yes	complemented
506	#2543	C₂×C₄₁	1	2	yes	complemented
507	#2417	C₂×C₄₁	1	2	yes	complemented
508	#2416	C₂×C₄₁	1	2	yes	complemented
509	C₂×#385	C₂×C₄₁	1	1	yes	characteristic, complemented
510	C₂×C₄₁	—	2	4	no	—
511	C₂×C₄₁	—	4	2	no	—
512	C₂×C₄₁	—	4	2	no	—
513	C₂×C₄₁	—	8	2	no	—
514	C₂×C₄₁	—	8	2	no	—
515	C₂×C₄₁	C₂×#537	1	1	yes	characteristic
516	C₂×C₄₁	#3496	1	2	yes	—
517	C₂×C₄₁	#3532	1	1	yes	characteristic
518	C₂×C₄₁	#3533	1	1	yes	characteristic
519	C₂×C₄₁	#3541	1	2	yes	—
520	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
521	#538	—	2	16	no	—
522	C₂×#126	C₂²×C₄₁	1	2	yes	—
523	C₂×#126	C₂²×C₄₁	1	2	yes	—
524	C₂×#124	C₂²×C₄₁	1	2	yes	—
525	C₂×#124	C₂²×C₄₁	1	2	yes	—
526	C₂×#123	C₂²×C₄₁	1	2	yes	—
527	C₂×#123	C₂²×C₄₁	1	2	yes	—
528	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
529	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
530	C₂×#121	C₂²×C₄₁	1	2	yes	—
531	C₂×#121	C₂²×C₄₁	1	2	yes	—
532	C₂×#121	C₂²×C₄₁	1	2	yes	—
533	C₂×#121	C₂²×C₄₁	1	2	yes	—
534	C₂×#121	C₂²×C₄₁	1	2	yes	—
535	C₂×#121	C₂²×C₄₁	1	2	yes	—
536	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
537	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
538	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
539	C₂×#120	C₂²×C₄₁	1	2	yes	—
540	C₂×#120	C₂²×C₄₁	1	2	yes	—
541	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
542	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
543	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
544	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
545	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
546	#400	C₂²×C₄₁	1	2	yes	complemented
547	#399	C₂²×C₄₁	1	2	yes	complemented
548	#398	C₂²×C₄₁	1	2	yes	complemented
549	#398	C₂²×C₄₁	1	2	yes	complemented
550	#398	C₂²×C₄₁	1	2	yes	complemented
551	#397	C₂²×C₄₁	1	1	yes	characteristic
552	#397	C₂²×C₄₁	1	1	yes	characteristic
553	#397	C₂²×C₄₁	1	1	yes	characteristic
554	#397	C₂²×C₄₁	1	1	yes	characteristic
555	#397	C₂²×C₄₁	1	2	yes	complemented
556	#396	C₂²×C₄₁	1	2	yes	complemented
557	#396	C₂²×C₄₁	1	2	yes	complemented
558	#396	C₂²×C₄₁	1	2	yes	complemented
559	#396	C₂²×C₄₁	1	2	yes	complemented
560	#395	C₂²×C₄₁	1	2	yes	complemented
561	#394	C₂²×C₄₁	1	2	yes	—
562	#394	C₂²×C₄₁	1	2	yes	—
563	#394	C₂²×C₄₁	1	2	yes	—
564	#394	C₂²×C₄₁	1	2	yes	—
565	#394	C₂²×C₄₁	1	2	yes	complemented
566	#394	C₂²×C₄₁	1	2	yes	complemented
567	#394	C₂²×C₄₁	1	2	yes	complemented
568	#393	C₂²×C₄₁	1	2	yes	complemented
569	#392	C₂²×C₄₁	1	1	yes	characteristic
570	#392	C₂²×C₄₁	1	1	yes	characteristic
571	#392	C₂²×C₄₁	1	1	yes	characteristic
572	#392	C₂²×C₄₁	1	1	yes	characteristic
573	#392	C₂²×C₄₁	1	2	yes	complemented
574	#391	C₂²×C₄₁	1	2	yes	complemented
575	#390	C₂²×C₄₁	1	2	yes	complemented
576	#389	C₂²×C₄₁	1	2	yes	complemented
577	#389	C₂²×C₄₁	1	2	yes	complemented
578	#388	C₂²×C₄₁	1	2	yes	complemented
579	#388	C₂²×C₄₁	1	2	yes	complemented
580	#387	C₂²×C₄₁	1	2	yes	complemented
581	#387	C₂²×C₄₁	1	2	yes	complemented
582	#386	C₂²×C₄₁	1	2	yes	—
583	#386	C₂²×C₄₁	1	2	yes	—
584	#386	C₂²×C₄₁	1	2	yes	—
585	#386	C₂²×C₄₁	1	2	yes	—
586	#386	C₂²×C₄₁	1	2	yes	—
587	#386	C₂²×C₄₁	1	2	yes	—
588	#386	C₂²×C₄₁	1	2	yes	—
589	#386	C₂²×C₄₁	1	2	yes	—
590	#386	C₂²×C₄₁	1	2	yes	complemented
591	#386	C₂²×C₄₁	1	2	yes	complemented
592	#385	C₂²×C₄₁	1	2	yes	—
593	#385	C₂²×C₄₁	1	1	yes	characteristic
594	#385	C₂²×C₄₁	1	1	yes	characteristic
595	#385	C₂²×C₄₁	1	2	yes	—
596	#385	C₂²×C₄₁	1	1	yes	characteristic
597	#385	C₂²×C₄₁	1	1	yes	characteristic
598	#385	C₂²×C₄₁	1	2	yes	complemented
599	#385	C₂²×C₄₁	1	2	yes	complemented
600	#380	C₂²×C₄₁	1	1	yes	characteristic
601	#380	C₂²×C₄₁	1	2	yes	—
602	#380	C₂²×C₄₁	1	2	yes	—
603	#380	C₂²×C₄₁	1	2	yes	—
604	#380	C₂²×C₄₁	1	1	yes	characteristic
605	#380	C₂²×C₄₁	1	2	yes	complemented
606	#380	C₂²×C₄₁	1	2	yes	complemented
607	C₂×#95	C₂²×C₄₁	1	2	yes	—
608	C₄₁	#36738	1	1	yes	characteristic, direct product factor, Sylow
609	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
610	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
611	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
612	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
613	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
614	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
615	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
616	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
617	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
618	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
619	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
621	C₂³×C₄	—	4	4	no	—
622	C₂³×C₄	—	4	2	no	—
623	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
624	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
628	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
629	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
630	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
632	#126	—	2	8	no	—
633	#126	—	2	8	no	—
634	#124	—	2	8	no	—
635	#124	—	2	8	no	—
636	#123	—	2	8	no	—
637	#123	—	2	8	no	—
638	C₂²⋊Q₈	—	2	8	no	—
639	C₂²⋊Q₈	—	4	4	no	—
640	#121	—	2	8	no	—
641	#121	—	2	8	no	—
642	#121	—	2	8	no	—
643	#121	—	4	4	no	—
644	#121	—	4	4	no	—
645	#121	—	4	4	no	—
646	#121	—	4	4	no	—
647	#121	—	4	2	no	—
648	#121	—	4	2	no	—
649	#120	—	2	8	no	—
650	#120	—	2	8	no	—
651	C₄×D₄	—	2	8	no	—
652	C₄×D₄	—	2	8	no	—
653	C₂×C₄⋊C₄	—	4	4	no	—
654	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
671	C₂×C₂²⋊C₄	—	4	2	no	—
672	C₂×C₂²⋊C₄	D₄×C₄₁	1	8	yes	complemented
673	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
703	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
704	#95	C₂³×C₄₁	1	2	yes	—
705	#95	C₂³×C₄₁	1	2	yes	—
706	#95	C₂³×C₄₁	1	2	yes	—
707	#95	C₂³×C₄₁	1	2	yes	—
708	#95	C₂³×C₄₁	1	1	yes	characteristic
709	#95	C₂³×C₄₁	1	2	yes	—
710	#95	C₂³×C₄₁	1	2	yes	—
711	#95	C₂³×C₄₁	1	1	yes	characteristic
712	#95	C₂³×C₄₁	1	2	yes	—
713	#95	C₂³×C₄₁	1	2	yes	—
714	#95	C₂³×C₄₁	1	2	yes	—
715	#95	C₂³×C₄₁	1	2	yes	—
716	#95	C₂³×C₄₁	1	1	yes	characteristic
717	#95	C₂³×C₄₁	1	1	yes	characteristic
718	#95	C₂³×C₄₁	1	2	yes	—
719	#95	C₂³×C₄₁	1	2	yes	—
720	#95	C₂³×C₄₁	1	2	yes	—
721	#95	C₂³×C₄₁	1	2	yes	—
722	C₂⁴	—	2	2	no	—
723	C₂⁴	—	2	2	no	—
724	C₂⁴	—	4	2	no	—
725	C₂⁴	—	4	2	no	—
726	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
727	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
728	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
729	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
730	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
731	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	4	2	no	—
734	C₂×Q₈	—	4	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	1	no	—
754	C₂×D₄	—	4	1	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	1	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	16	no	—
786	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
787	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	1	no	—
815	C₄⋊C₄	—	4	1	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	4	1	no	—
831	C₂²⋊C₄	—	4	1	no	—
832	C₂²⋊C₄	—	4	1	no	—
833	C₂²⋊C₄	—	4	1	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
845	C₂²⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
846	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
847	C₄²	—	2	4	no	—
848	C₄²	—	2	4	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	8	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	4	8	no	—
875	C₂³	—	4	4	no	—
876	C₂³	—	4	4	no	—
877	C₂³	—	4	8	no	—
878	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
879	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
880	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
881	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
882	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
883	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
884	Q₈	—	8	4	no	—
885	D₄	—	4	8	no	—
886	D₄	—	4	8	no	—
887	D₄	—	8	4	no	—
888	D₄	—	8	4	no	—
889	D₄	—	8	4	no	—
890	D₄	—	8	4	no	—
891	D₄	—	8	4	no	—
892	D₄	—	8	4	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	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	—	4	8	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	8	no	—
933	C₂×C₄	—	4	8	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	8	4	no	—
936	C₂×C₄	—	8	4	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
940	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
941	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
942	C₂²	—	2	4	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	4	no	—
950	C₂²	—	4	16	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	C₄₁×#537	1	4	yes	—
972	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
973	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
974	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
975	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
976	C₂²	C₄₁×#585	1	2	yes	—
977	C₄	—	2	4	no	—
978	C₄	—	2	4	no	—
979	C₄	—	2	4	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	1	no	—
991	C₂	—	2	4	no	—
992	C₂	—	4	2	no	—
993	C₂	—	4	2	no	—
994	C₂	—	8	2	no	—
995	C₂	—	8	2	no	—
996	C₂	C₂×C₄₁×#537	1	1	yes	characteristic
997	C₂	C₄₁×#3496	1	2	yes	—
998	C₂	C₄₁×#3532	1	1	yes	characteristic
999	C₂	C₄₁×#3533	1	1	yes	characteristic
1000	C₂	C₄₁×#3541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#538	C₂	semidirect
2. C₄₁×#2847	C₂	semidirect
3. C₄₁×#2722	C₂	semidirect
4. C₄₁×#2715	C₂	semidirect
5. C₄₁×#2712	C₂	semidirect
6. C₄₁×#2695	C₂	semidirect
7. C₄₁×#2693	C₂	semidirect
8. C₄₁×#2691	C₂	semidirect
9. C₄₁×#2676	C₂	semidirect
10. C₄₁×#2675	C₂	semidirect
11. C₄₁×#2672	C₂	semidirect
12. C₄₁×#2671	C₂	semidirect
13. C₄₁×#2617	C₂	semidirect
14. C₄₁×#2617	C₂	semidirect
15. C₄₁×#2564	C₂	semidirect
16. C₄₁×#2543	C₂	semidirect
17. C₄₁×#2417	C₂	semidirect
18. C₄₁×#2416	C₂	semidirect
19. C₂×C₄₁×#385	C₂	semidirect
29. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
38. C₂×#121×C₄₁	C₂²	semidirect
46. C₄₁×#400	C₂²	semidirect
47. C₄₁×#399	C₂²	semidirect
48. C₄₁×#398	C₂²	semidirect
49. C₄₁×#398	C₂²	semidirect
50. C₄₁×#398	C₂²	semidirect
55. C₄₁×#397	C₂²	semidirect
56. C₄₁×#396	C₂²	semidirect
57. C₄₁×#396	C₂²	semidirect
58. C₄₁×#396	C₂²	semidirect
59. C₄₁×#396	C₂²	semidirect
60. C₄₁×#395	C₂²	semidirect
65. C₄₁×#394	C₂²	semidirect
66. C₄₁×#394	C₂²	semidirect
67. C₄₁×#394	C₂²	semidirect
68. C₄₁×#393	C₂²	semidirect
73. C₄₁×#392	C₂²	semidirect
74. C₄₁×#391	C₂²	semidirect
75. C₄₁×#390	C₂²	semidirect
76. C₄₁×#389	C₂²	semidirect
77. C₄₁×#389	C₂²	semidirect
78. C₄₁×#388	C₂²	semidirect
79. C₄₁×#388	C₂²	semidirect
80. C₄₁×#387	C₂²	semidirect
81. C₄₁×#387	C₂²	semidirect
90. C₄₁×#386	C₂²	semidirect
91. C₄₁×#386	C₂²	semidirect
98. C₄₁×#385	C₂²	semidirect
99. C₄₁×#385	C₂²	semidirect
105. C₄₁×#380	C₂²	semidirect
106. C₄₁×#380	C₂²	semidirect
171. C₂×C₂²⋊C₄×C₄₁	D₄	semidirect
441. #36738	C₄₁	direct (N × H)
491. C₂×#538	C₂×C₄₁	semidirect
492. #2847	C₂×C₄₁	semidirect
493. #2722	C₂×C₄₁	semidirect
494. #2715	C₂×C₄₁	semidirect
495. #2712	C₂×C₄₁	semidirect
496. #2695	C₂×C₄₁	semidirect
497. #2693	C₂×C₄₁	semidirect
498. #2691	C₂×C₄₁	semidirect
499. #2676	C₂×C₄₁	semidirect
500. #2675	C₂×C₄₁	semidirect
501. #2672	C₂×C₄₁	semidirect
502. #2671	C₂×C₄₁	semidirect
503. #2617	C₂×C₄₁	semidirect
504. #2617	C₂×C₄₁	semidirect
505. #2564	C₂×C₄₁	semidirect
506. #2543	C₂×C₄₁	semidirect
507. #2417	C₂×C₄₁	semidirect
508. #2416	C₂×C₄₁	semidirect
509. C₂×#385	C₂×C₄₁	semidirect
529. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
538. C₂×#121	C₂²×C₄₁	semidirect
546. #400	C₂²×C₄₁	semidirect
547. #399	C₂²×C₄₁	semidirect
548. #398	C₂²×C₄₁	semidirect
549. #398	C₂²×C₄₁	semidirect
550. #398	C₂²×C₄₁	semidirect
555. #397	C₂²×C₄₁	semidirect
556. #396	C₂²×C₄₁	semidirect
557. #396	C₂²×C₄₁	semidirect
558. #396	C₂²×C₄₁	semidirect
559. #396	C₂²×C₄₁	semidirect
560. #395	C₂²×C₄₁	semidirect
565. #394	C₂²×C₄₁	semidirect
566. #394	C₂²×C₄₁	semidirect
567. #394	C₂²×C₄₁	semidirect
568. #393	C₂²×C₄₁	semidirect
573. #392	C₂²×C₄₁	semidirect
574. #391	C₂²×C₄₁	semidirect
575. #390	C₂²×C₄₁	semidirect
576. #389	C₂²×C₄₁	semidirect
577. #389	C₂²×C₄₁	semidirect
578. #388	C₂²×C₄₁	semidirect
579. #388	C₂²×C₄₁	semidirect
580. #387	C₂²×C₄₁	semidirect
581. #387	C₂²×C₄₁	semidirect
590. #386	C₂²×C₄₁	semidirect
591. #386	C₂²×C₄₁	semidirect
598. #385	C₂²×C₄₁	semidirect
599. #385	C₂²×C₄₁	semidirect
605. #380	C₂²×C₄₁	semidirect
606. #380	C₂²×C₄₁	semidirect
608. C₄₁	#36738	direct (N × H)
672. C₂×C₂²⋊C₄	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#538	2
C₄₁×#2847	2
C₄₁×#2722	2
C₄₁×#2715	2
C₄₁×#2712	2
C₄₁×#2695	2
C₄₁×#2693	2
C₄₁×#2691	2
C₄₁×#2676	2
C₄₁×#2675	2
C₄₁×#2672	2
C₄₁×#2671	2
C₄₁×#2617	2
C₄₁×#2564	2
C₄₁×#2543	2
C₄₁×#2417	2
C₄₁×#2416	2
C₂×C₄₁×#385	2
#36738	41

Subgroups — C41×#36738 #23812939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#36738 #23812939