Subgroups — C₄₁×#34976 #23811177

Order 10496.

2810 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₁	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2609	C₂	1	4	yes	maximal, complemented
3	C₄₁×#2582	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2538	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2537	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2485	C₂	1	4	yes	maximal, complemented
7	C₄₁×#2407	C₂	1	4	yes	maximal, complemented
8	C₄₁×#2392	C₂	1	4	yes	maximal, complemented
9	C₄×C₂²⋊Q₈×C₄₁	C₂	1	4	yes	maximal, complemented
10	C₄×#121×C₄₁	C₂	1	4	yes	maximal, complemented
11	C₄₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	2	yes	—
13	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	—
14	C₂×#121×C₄₁	C₂²	1	4	yes	—
15	C₄×#41×C₄₁	—	2	16	no	—
16	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
23	C₂×#117×C₄₁	C₂²	1	4	yes	—
24	C₂×#117×C₄₁	C₂²	1	2	yes	—
25	C₂×#117×C₄₁	C₂²	1	2	yes	—
26	C₂²×C₄²×C₄₁	C₂²	1	4	yes	—
27	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#398	C₂²	1	4	yes	—
29	C₄₁×#397	C₂²	1	4	yes	—
30	C₄₁×#396	C₂²	1	8	yes	—
31	C₄₁×#394	C₂²	1	4	yes	—
32	C₄₁×#394	C₂²	1	8	yes	—
33	C₄₁×#392	C₂²	1	4	yes	—
34	C₄₁×#391	C₂²	1	4	yes	—
35	C₄₁×#390	C₂²	1	4	yes	—
36	C₄₁×#389	C₂²	1	4	yes	—
37	C₄₁×#389	C₂²	1	4	yes	—
38	C₄₁×#388	C₂²	1	8	yes	—
39	C₄₁×#387	C₂²	1	8	yes	—
40	C₄₁×#386	C₂²	1	8	yes	—
41	C₄₁×#385	C₂²	1	8	yes	—
42	C₄₁×#384	C₂²	1	1	yes	characteristic
43	C₄₁×#384	C₂²	1	1	yes	characteristic
44	C₄₁×#382	C₂²	1	2	yes	—
45	C₄₁×#380	C₂²	1	4	yes	—
46	C₄₁×#380	C₂²	1	4	yes	—
47	C₄₁×#380	C₂²	1	4	yes	—
48	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
50	C₄×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	—
51	C₂×#41×C₄₁	—	2	8	no	—
52	C₂×#41×C₄₁	—	2	8	no	—
53	C₂×#41×C₄₁	—	2	8	no	—
54	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
55	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
56	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
57	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
59	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
60	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
61	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂²⋊Q₈×C₄₁	—	2	16	no	—
64	#121×C₄₁	—	2	16	no	—
65	C₄×Q₈×C₄₁	—	2	8	no	—
66	C₄×Q₈×C₄₁	—	2	8	no	—
67	C₄×D₄×C₄₁	—	2	16	no	—
68	C₄×D₄×C₄₁	—	2	16	no	—
69	C₄×D₄×C₄₁	—	2	8	no	—
70	C₄×D₄×C₄₁	—	2	8	no	—
71	C₄×D₄×C₄₁	—	4	8	no	—
72	#117×C₄₁	—	2	8	no	—
73	#117×C₄₁	—	2	16	no	—
74	#117×C₄₁	—	4	4	no	—
75	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
92	C₂×C₄²×C₄₁	—	2	16	no	—
93	C₂×C₄²×C₄₁	D₄	1	8	yes	complemented
94	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
95	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
96	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
97	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
98	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
101	#95×C₄₁	C₂³	1	8	yes	—
102	#95×C₄₁	C₂³	1	8	yes	—
103	#95×C₄₁	C₂³	1	4	yes	—
104	#95×C₄₁	C₂³	1	8	yes	—
105	#95×C₄₁	C₂³	1	4	yes	—
106	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
107	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
108	#41×C₄₁	—	2	64	no	—
109	C₂×Q₈×C₄₁	—	2	4	no	—
110	C₂×Q₈×C₄₁	—	2	4	no	—
111	C₂×Q₈×C₄₁	#41	1	8	yes	complemented
112	C₂×D₄×C₄₁	—	2	8	no	—
113	C₂×D₄×C₄₁	—	2	8	no	—
114	C₂×D₄×C₄₁	—	2	16	no	—
115	C₂×D₄×C₄₁	—	2	4	no	—
116	C₂×D₄×C₄₁	—	2	8	no	—
117	C₂×D₄×C₄₁	—	2	4	no	—
118	C₂×D₄×C₄₁	—	4	4	no	—
119	C₂×D₄×C₄₁	#41	1	8	yes	complemented
120	C₂²×C₄×C₄₁	—	2	8	no	—
121	C₂²×C₄×C₄₁	—	2	8	no	—
122	C₂²×C₄×C₄₁	—	2	8	no	—
123	C₂²×C₄×C₄₁	—	2	4	no	—
124	C₂²×C₄×C₄₁	—	2	4	no	—
125	C₂²×C₄×C₄₁	—	2	2	no	—
126	C₂²×C₄×C₄₁	—	2	2	no	—
127	C₂²×C₄×C₄₁	—	2	8	no	—
128	C₂²×C₄×C₄₁	—	2	8	no	—
129	C₂²×C₄×C₄₁	—	2	8	no	—
130	C₂²×C₄×C₄₁	—	2	8	no	—
131	C₂²×C₄×C₄₁	—	2	8	no	—
132	C₂²×C₄×C₄₁	—	2	8	no	—
133	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
134	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
144	C₄⋊C₄×C₄₁	—	2	8	no	—
145	C₄⋊C₄×C₄₁	—	2	8	no	—
146	C₄⋊C₄×C₄₁	—	2	4	no	—
147	C₄⋊C₄×C₄₁	—	2	4	no	—
148	C₄⋊C₄×C₄₁	—	2	8	no	—
149	C₄⋊C₄×C₄₁	—	2	8	no	—
150	C₄⋊C₄×C₄₁	—	2	16	no	—
151	C₄⋊C₄×C₄₁	—	4	2	no	—
152	C₄⋊C₄×C₄₁	—	4	2	no	—
153	C₄⋊C₄×C₄₁	—	4	4	no	—
154	C₂²⋊C₄×C₄₁	—	2	8	no	—
155	C₂²⋊C₄×C₄₁	—	2	16	no	—
156	C₂²⋊C₄×C₄₁	—	2	8	no	—
157	C₂²⋊C₄×C₄₁	—	2	8	no	—
158	C₂²⋊C₄×C₄₁	—	2	16	no	—
159	C₂²⋊C₄×C₄₁	—	4	4	no	—
160	C₂²⋊C₄×C₄₁	—	4	8	no	—
161	C₄²×C₄₁	—	2	8	no	—
162	C₄²×C₄₁	—	2	8	no	—
163	C₄²×C₄₁	—	2	8	no	—
164	C₄²×C₄₁	—	2	8	no	—
165	C₄²×C₄₁	C₂×D₄	1	8	yes	—
166	C₄²×C₄₁	C₂×D₄	1	4	yes	—
167	C₄²×C₄₁	C₂×D₄	1	4	yes	—
168	C₂³×C₄₁	—	2	4	no	—
169	C₂³×C₄₁	—	2	4	no	—
170	C₂³×C₄₁	—	2	2	no	—
171	C₂³×C₄₁	—	2	2	no	—
172	C₂³×C₄₁	—	2	4	no	—
173	C₂³×C₄₁	—	2	4	no	—
174	C₂³×C₄₁	—	2	1	no	—
175	C₂³×C₄₁	—	2	4	no	—
176	C₂³×C₄₁	—	2	1	no	—
177	C₂³×C₄₁	—	2	4	no	—
178	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
179	C₂³×C₄₁	C₂×#41	1	8	yes	—
180	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
181	Q₈×C₄₁	—	2	16	no	—
182	D₄×C₄₁	—	2	32	no	—
183	D₄×C₄₁	—	2	16	no	—
184	D₄×C₄₁	—	4	16	no	—
185	C₂×C₄×C₄₁	—	2	32	no	—
186	C₂×C₄×C₄₁	—	2	4	no	—
187	C₂×C₄×C₄₁	—	2	2	no	—
188	C₂×C₄×C₄₁	—	2	2	no	—
189	C₂×C₄×C₄₁	—	2	4	no	—
190	C₂×C₄×C₄₁	—	2	1	no	—
191	C₂×C₄×C₄₁	—	2	1	no	—
192	C₂×C₄×C₄₁	—	2	16	no	—
193	C₂×C₄×C₄₁	—	2	8	no	—
194	C₂×C₄×C₄₁	—	2	4	no	—
195	C₂×C₄×C₄₁	—	2	4	no	—
196	C₂×C₄×C₄₁	—	2	4	no	—
197	C₂×C₄×C₄₁	—	2	8	no	—
198	C₂×C₄×C₄₁	—	2	8	no	—
199	C₂×C₄×C₄₁	—	2	4	no	—
200	C₂×C₄×C₄₁	—	2	4	no	—
201	C₂×C₄×C₄₁	—	2	4	no	—
202	C₂×C₄×C₄₁	—	2	4	no	—
203	C₂×C₄×C₄₁	—	2	4	no	—
204	C₂×C₄×C₄₁	—	4	16	no	—
205	C₂×C₄×C₄₁	—	4	16	no	—
206	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
208	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₄₁	C₂×#41	1	8	yes	—
211	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
212	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
213	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
214	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
215	#34976	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₄₁	—	2	4	no	—
217	C₂²×C₄₁	—	2	8	no	—
218	C₂²×C₄₁	—	2	2	no	—
219	C₂²×C₄₁	—	2	8	no	—
220	C₂²×C₄₁	—	2	8	no	—
221	C₂²×C₄₁	—	4	4	no	—
222	C₂²×C₄₁	—	4	4	no	—
223	C₂²×C₄₁	—	4	1	no	—
224	C₂²×C₄₁	—	4	2	no	—
225	C₂²×C₄₁	—	4	4	no	—
226	C₂²×C₄₁	—	4	4	no	—
227	C₂²×C₄₁	—	4	1	no	—
228	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
229	C₂²×C₄₁	C₂²×#41	1	2	yes	—
230	C₂²×C₄₁	C₂²×#41	1	2	yes	—
231	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
232	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
233	C₄×C₄₁	—	2	4	no	—
234	C₄×C₄₁	—	2	8	no	—
235	C₄×C₄₁	—	2	2	no	—
236	C₄×C₄₁	—	4	4	no	—
237	C₄×C₄₁	—	4	4	no	—
238	C₄×C₄₁	—	4	4	no	—
239	C₄×C₄₁	—	4	4	no	—
240	C₄×C₄₁	#525	1	8	yes	—
241	C₄×C₄₁	#537	1	4	yes	—
242	C₂×C₄×#41	C₂×C₄₁	1	2	yes	complemented
243	#2609	C₂×C₄₁	1	4	yes	complemented
244	#2582	C₂×C₄₁	1	1	yes	characteristic, complemented
245	#2538	C₂×C₄₁	1	2	yes	complemented
246	#2537	C₂×C₄₁	1	1	yes	characteristic, complemented
247	#2485	C₂×C₄₁	1	4	yes	complemented
248	#2407	C₂×C₄₁	1	4	yes	complemented
249	#2392	C₂×C₄₁	1	4	yes	complemented
250	C₄×C₂²⋊Q₈	C₂×C₄₁	1	4	yes	complemented
251	C₄×#121	C₂×C₄₁	1	4	yes	complemented
252	#2285	C₂×C₄₁	1	1	yes	characteristic, complemented
253	C₂×C₄₁	—	4	2	no	—
254	C₂×C₄₁	—	4	8	no	—
255	C₂×C₄₁	C₂×#525	1	2	yes	—
256	C₂×C₄₁	C₂×#537	1	1	yes	characteristic
257	C₂×C₄₁	#3481	1	1	yes	characteristic
258	C₂×C₄₁	#3482	1	2	yes	—
259	C₂×C₄₁	#3483	1	1	yes	characteristic
260	C₂²×#41	C₂²×C₄₁	1	2	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	—
262	C₂×#121	C₂²×C₄₁	1	4	yes	—
263	C₄×#41	—	2	16	no	—
264	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
265	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
266	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
267	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
268	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
269	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
270	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
271	C₂×#117	C₂²×C₄₁	1	4	yes	—
272	C₂×#117	C₂²×C₄₁	1	2	yes	—
273	C₂×#117	C₂²×C₄₁	1	2	yes	—
274	C₂²×C₄²	C₂²×C₄₁	1	4	yes	—
275	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
276	#398	C₂²×C₄₁	1	4	yes	—
277	#397	C₂²×C₄₁	1	4	yes	—
278	#396	C₂²×C₄₁	1	8	yes	—
279	#394	C₂²×C₄₁	1	4	yes	—
280	#394	C₂²×C₄₁	1	8	yes	—
281	#392	C₂²×C₄₁	1	4	yes	—
282	#391	C₂²×C₄₁	1	4	yes	—
283	#390	C₂²×C₄₁	1	4	yes	—
284	#389	C₂²×C₄₁	1	4	yes	—
285	#389	C₂²×C₄₁	1	4	yes	—
286	#388	C₂²×C₄₁	1	8	yes	—
287	#387	C₂²×C₄₁	1	8	yes	—
288	#386	C₂²×C₄₁	1	8	yes	—
289	#385	C₂²×C₄₁	1	8	yes	—
290	#384	C₂²×C₄₁	1	1	yes	characteristic
291	#384	C₂²×C₄₁	1	1	yes	characteristic
292	#382	C₂²×C₄₁	1	2	yes	—
293	#380	C₂²×C₄₁	1	4	yes	—
294	#380	C₂²×C₄₁	1	4	yes	—
295	#380	C₂²×C₄₁	1	4	yes	—
296	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
297	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
298	C₄×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	—
299	C₄₁	#34976	1	1	yes	characteristic, direct product factor, Sylow
300	C₂×#41	—	2	8	no	—
301	C₂×#41	—	2	8	no	—
302	C₂×#41	—	2	8	no	—
303	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
304	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
305	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
306	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
307	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
308	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
309	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
310	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
312	C₂²⋊Q₈	—	2	16	no	—
313	#121	—	2	16	no	—
314	C₄×Q₈	—	2	8	no	—
315	C₄×Q₈	—	2	8	no	—
316	C₄×D₄	—	2	16	no	—
317	C₄×D₄	—	2	16	no	—
318	C₄×D₄	—	2	8	no	—
319	C₄×D₄	—	2	8	no	—
320	C₄×D₄	—	4	8	no	—
321	#117	—	2	8	no	—
322	#117	—	2	16	no	—
323	#117	—	4	4	no	—
324	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
329	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
330	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
331	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
341	C₂×C₄²	—	2	16	no	—
342	C₂×C₄²	D₄×C₄₁	1	8	yes	complemented
343	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
344	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
345	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
346	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
347	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
350	#95	C₂³×C₄₁	1	8	yes	—
351	#95	C₂³×C₄₁	1	8	yes	—
352	#95	C₂³×C₄₁	1	4	yes	—
353	#95	C₂³×C₄₁	1	8	yes	—
354	#95	C₂³×C₄₁	1	4	yes	—
355	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
356	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
357	#41	—	2	64	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	#41×C₄₁	1	8	yes	complemented
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	16	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	#41×C₄₁	1	8	yes	complemented
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
383	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
385	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
387	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
388	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	16	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	16	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	16	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	4	8	no	—
410	C₄²	—	2	8	no	—
411	C₄²	—	2	8	no	—
412	C₄²	—	2	8	no	—
413	C₄²	—	2	8	no	—
414	C₄²	C₂×D₄×C₄₁	1	8	yes	—
415	C₄²	C₂×D₄×C₄₁	1	4	yes	—
416	C₄²	C₂×D₄×C₄₁	1	4	yes	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	4	no	—
427	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
428	C₂³	C₂×#41×C₄₁	1	8	yes	—
429	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
430	Q₈	—	2	16	no	—
431	D₄	—	2	32	no	—
432	D₄	—	2	16	no	—
433	D₄	—	4	16	no	—
434	C₂×C₄	—	2	32	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	16	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	4	16	no	—
454	C₂×C₄	—	4	16	no	—
455	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
456	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
457	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
458	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
459	C₂×C₄	C₂×#41×C₄₁	1	8	yes	—
460	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
461	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
462	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
463	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	8	no	—
468	C₂²	—	2	8	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	1	no	—
476	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
477	C₂²	C₂²×#41×C₄₁	1	2	yes	—
478	C₂²	C₂²×#41×C₄₁	1	2	yes	—
479	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
480	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
481	C₄	—	2	4	no	—
482	C₄	—	2	8	no	—
483	C₄	—	2	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₄	C₄₁×#525	1	8	yes	—
489	C₄	C₄₁×#537	1	4	yes	—
490	C₂	—	4	2	no	—
491	C₂	—	4	8	no	—
492	C₂	C₂×C₄₁×#525	1	2	yes	—
493	C₂	C₂×C₄₁×#537	1	1	yes	characteristic
494	C₂	C₄₁×#3481	1	1	yes	characteristic
495	C₂	C₄₁×#3482	1	2	yes	—
496	C₂	C₄₁×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
socle	C₂³×C₄₁	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#41×C₄₁	C₂	semidirect
2. C₄₁×#2609	C₂	semidirect
3. C₄₁×#2582	C₂	semidirect
4. C₄₁×#2538	C₂	semidirect
5. C₄₁×#2537	C₂	semidirect
6. C₄₁×#2485	C₂	semidirect
7. C₄₁×#2407	C₂	semidirect
8. C₄₁×#2392	C₂	semidirect
9. C₄×C₂²⋊Q₈×C₄₁	C₂	semidirect
10. C₄×#121×C₄₁	C₂	semidirect
11. C₄₁×#2285	C₂	semidirect
93. C₂×C₄²×C₄₁	D₄	semidirect
111. C₂×Q₈×C₄₁	#41	semidirect
119. C₂×D₄×C₄₁	#41	semidirect
215. #34976	C₄₁	direct (N × H)
242. C₂×C₄×#41	C₂×C₄₁	semidirect
243. #2609	C₂×C₄₁	semidirect
244. #2582	C₂×C₄₁	semidirect
245. #2538	C₂×C₄₁	semidirect
246. #2537	C₂×C₄₁	semidirect
247. #2485	C₂×C₄₁	semidirect
248. #2407	C₂×C₄₁	semidirect
249. #2392	C₂×C₄₁	semidirect
250. C₄×C₂²⋊Q₈	C₂×C₄₁	semidirect
251. C₄×#121	C₂×C₄₁	semidirect
252. #2285	C₂×C₄₁	semidirect
299. C₄₁	#34976	direct (N × H)
342. C₂×C₄²	D₄×C₄₁	semidirect
360. C₂×Q₈	#41×C₄₁	semidirect
368. C₂×D₄	#41×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₄₁	2
C₄₁×#2609	2
C₄₁×#2582	2
C₄₁×#2538	2
C₄₁×#2537	2
C₄₁×#2485	2
C₄₁×#2407	2
C₄₁×#2392	2
C₄×C₂²⋊Q₈×C₄₁	2
C₄×#121×C₄₁	2
C₄₁×#2285	2
#34976	41

Subgroups — C41×#34976 #23811177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#34976 #23811177