Subgroups — C₂×C₄₁×#1436 #23789959

Order 10496.

3550 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄²×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#95×C₄₁	C₂	1	2	yes	maximal
4	C₂²×#95×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#95×C₄₁	C₂	1	2	yes	maximal
6	C₄₁×#1436	C₂	1	8	yes	maximal, direct product factor
7	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₄₁	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₄₁	—	2	4	no	—
14	C₂²×C₄⋊C₄×C₄₁	C₄	1	8	yes	complemented
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
16	C₂²×C₄²×C₄₁	—	2	4	no	—
17	C₂²×C₄²×C₄₁	—	2	8	no	—
18	C₂²×C₄²×C₄₁	C₂²	1	4	yes	—
19	C₂×#95×C₄₁	—	2	4	no	—
20	C₂×#95×C₄₁	—	2	8	no	—
21	C₂×#95×C₄₁	C₄	1	16	yes	complemented
22	C₂×#95×C₄₁	C₂²	1	8	yes	—
23	C₂×#95×C₄₁	C₂²	1	4	yes	—
24	C₂×#95×C₄₁	C₂²	1	8	yes	—
25	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
26	C₂³×C₄×C₄₁	—	2	4	no	—
27	C₂³×C₄×C₄₁	—	2	4	no	—
28	C₂³×C₄×C₄₁	—	2	4	no	—
29	C₂³×C₄×C₄₁	—	2	2	no	—
30	C₂³×C₄×C₄₁	—	2	2	no	—
31	C₂³×C₄×C₄₁	—	2	4	no	—
32	C₂³×C₄×C₄₁	—	2	4	no	—
33	C₂³×C₄×C₄₁	—	2	4	no	—
34	C₂³×C₄×C₄₁	—	2	4	no	—
35	C₂³×C₄×C₄₁	—	2	2	no	—
36	C₂³×C₄×C₄₁	—	2	2	no	—
37	C₂³×C₄×C₄₁	—	2	4	no	—
38	C₂³×C₄×C₄₁	—	2	4	no	—
39	C₂³×C₄×C₄₁	—	2	4	no	—
40	C₂³×C₄×C₄₁	—	2	4	no	—
41	C₂³×C₄×C₄₁	—	2	4	no	—
42	C₂³×C₄×C₄₁	—	2	4	no	—
43	C₂³×C₄×C₄₁	—	2	4	no	—
44	C₂³×C₄×C₄₁	—	2	4	no	—
45	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
46	C₂³×C₄×C₄₁	C₂×C₄	1	8	yes	—
47	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
48	C₂³×C₄×C₄₁	C₂×C₄	1	8	yes	—
49	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
50	C₂³×C₄×C₄₁	C₂×C₄	1	8	yes	—
51	C₂³×C₄×C₄₁	D₄	1	4	yes	—
52	C₂³×C₄×C₄₁	D₄	1	4	yes	—
53	C₂³×C₄×C₄₁	D₄	1	8	yes	—
54	C₂³×C₄×C₄₁	Q₈	1	8	yes	—
55	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
57	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₁	—	2	32	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
63	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	16	yes	complemented
64	C₂×C₄²×C₄₁	—	2	32	no	—
65	C₂×C₄²×C₄₁	—	2	8	no	—
66	C₂×C₄²×C₄₁	—	2	16	no	—
67	#95×C₄₁	—	2	8	no	—
68	#95×C₄₁	—	2	16	no	—
69	#95×C₄₁	C₂×C₄	1	32	yes	complemented
70	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
71	C₂⁴×C₄₁	C₂²×C₄	1	4	yes	—
72	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
73	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
74	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
75	C₂⁴×C₄₁	C₂×Q₈	1	4	yes	—
76	C₂⁴×C₄₁	#41	1	4	yes	—
77	C₂⁴×C₄₁	#41	1	4	yes	—
78	C₂⁴×C₄₁	#41	1	4	yes	—
79	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
80	C₂²×C₄×C₄₁	—	2	8	no	—
81	C₂²×C₄×C₄₁	—	2	8	no	—
82	C₂²×C₄×C₄₁	—	2	16	no	—
83	C₂²×C₄×C₄₁	—	2	16	no	—
84	C₂²×C₄×C₄₁	—	2	16	no	—
85	C₂²×C₄×C₄₁	—	2	16	no	—
86	C₂²×C₄×C₄₁	—	2	16	no	—
87	C₂²×C₄×C₄₁	—	2	16	no	—
88	C₂²×C₄×C₄₁	—	2	8	no	—
89	C₂²×C₄×C₄₁	—	2	16	no	—
90	C₂²×C₄×C₄₁	—	2	16	no	—
91	C₂²×C₄×C₄₁	—	2	16	no	—
92	C₂²×C₄×C₄₁	—	2	16	no	—
93	C₂²×C₄×C₄₁	—	2	8	no	—
94	C₂²×C₄×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	2	4	no	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	4	no	—
101	C₂²×C₄×C₄₁	—	2	4	no	—
102	C₂²×C₄×C₄₁	—	2	4	no	—
103	C₂²×C₄×C₄₁	—	2	8	no	—
104	C₂²×C₄×C₄₁	—	2	16	no	—
105	C₂²×C₄×C₄₁	—	2	16	no	—
106	C₂²×C₄×C₄₁	—	2	16	no	—
107	C₂²×C₄×C₄₁	—	2	16	no	—
108	C₂²×C₄×C₄₁	—	2	4	no	—
109	C₂²×C₄×C₄₁	—	2	4	no	—
110	C₂²×C₄×C₄₁	—	2	4	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	2	4	no	—
114	C₂²×C₄×C₄₁	—	2	4	no	—
115	C₂²×C₄×C₄₁	—	2	4	no	—
116	C₂²×C₄×C₄₁	—	2	4	no	—
117	C₂²×C₄×C₄₁	—	2	4	no	—
118	C₂²×C₄×C₄₁	—	4	4	no	—
119	C₂²×C₄×C₄₁	—	4	8	no	—
120	C₂²×C₄×C₄₁	—	4	8	no	—
121	C₂²×C₄×C₄₁	—	4	4	no	—
122	C₂²×C₄×C₄₁	—	4	8	no	—
123	C₂²×C₄×C₄₁	—	4	8	no	—
124	C₂²×C₄×C₄₁	—	4	8	no	—
125	C₂²×C₄×C₄₁	C₄²	1	16	yes	complemented
126	C₂²×C₄×C₄₁	C₂²⋊C₄	1	16	yes	—
127	C₂²×C₄×C₄₁	C₄⋊C₄	1	32	yes	complemented
128	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
129	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
131	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
134	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
137	C₂²×C₄×C₄₁	C₂×Q₈	1	8	yes	—
138	C₄⋊C₄×C₄₁	—	2	32	no	—
139	C₄²×C₄₁	—	2	32	no	—
140	C₂³×C₄₁	C₂×C₄²	1	4	yes	—
141	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂³×C₄₁	C₂×C₄⋊C₄	1	8	yes	—
143	C₂³×C₄₁	#117	1	4	yes	—
144	C₂³×C₄₁	#117	1	8	yes	—
145	C₂³×C₄₁	C₄×D₄	1	8	yes	—
146	C₂³×C₄₁	C₄×D₄	1	8	yes	—
147	C₂³×C₄₁	C₄×D₄	1	8	yes	—
148	C₂³×C₄₁	C₄×D₄	1	8	yes	—
149	C₂³×C₄₁	C₄×Q₈	1	8	yes	—
150	C₂³×C₄₁	C₄×Q₈	1	8	yes	—
151	C₂³×C₄₁	#120	1	4	yes	—
152	C₂³×C₄₁	#121	1	8	yes	—
153	C₂³×C₄₁	C₂²⋊Q₈	1	8	yes	—
154	C₂³×C₄₁	C₂²⋊Q₈	1	8	yes	—
155	C₂³×C₄₁	#123	1	8	yes	—
156	C₂³×C₄₁	#123	1	4	yes	—
157	C₂³×C₄₁	#124	1	4	yes	—
158	C₂³×C₄₁	#125	1	8	yes	—
159	C₂³×C₄₁	#126	1	8	yes	—
160	C₂³×C₄₁	C₄⋊Q₈	1	4	yes	—
161	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
162	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
163	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
164	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
165	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
166	C₂³×C₄₁	C₂²×Q₈	1	2	yes	—
167	C₂³×C₄₁	C₂×#41	1	2	yes	—
168	C₂³×C₄₁	C₂×#41	1	2	yes	—
169	C₂³×C₄₁	C₂×#41	1	2	yes	—
170	C₂×C₄×C₄₁	—	2	4	no	—
171	C₂×C₄×C₄₁	—	2	4	no	—
172	C₂×C₄×C₄₁	—	2	8	no	—
173	C₂×C₄×C₄₁	—	2	8	no	—
174	C₂×C₄×C₄₁	—	2	8	no	—
175	C₂×C₄×C₄₁	—	2	8	no	—
176	C₂×C₄×C₄₁	—	2	8	no	—
177	C₂×C₄×C₄₁	—	2	8	no	—
178	C₂×C₄×C₄₁	—	2	4	no	—
179	C₂×C₄×C₄₁	—	2	8	no	—
180	C₂×C₄×C₄₁	—	2	8	no	—
181	C₂×C₄×C₄₁	—	2	8	no	—
182	C₂×C₄×C₄₁	—	2	8	no	—
183	C₂×C₄×C₄₁	—	2	4	no	—
184	C₂×C₄×C₄₁	—	2	32	no	—
185	C₂×C₄×C₄₁	—	2	64	no	—
186	C₂×C₄×C₄₁	—	2	32	no	—
187	C₂×C₄×C₄₁	—	2	4	no	—
188	C₂×C₄×C₄₁	—	2	8	no	—
189	C₂×C₄×C₄₁	—	2	8	no	—
190	C₂×C₄×C₄₁	—	2	8	no	—
191	C₂×C₄×C₄₁	—	2	8	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	—	4	4	no	—
194	C₂×C₄×C₄₁	—	4	4	no	—
195	C₂×C₄×C₄₁	—	4	2	no	—
196	C₂×C₄×C₄₁	—	4	4	no	—
197	C₂×C₄×C₄₁	—	4	4	no	—
198	C₂×C₄×C₄₁	—	4	4	no	—
199	C₂×C₄×C₄₁	—	4	16	no	—
200	C₂×C₄×C₄₁	—	4	32	no	—
201	C₂×C₄×C₄₁	C₂×C₄²	1	8	yes	complemented
202	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
203	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	16	yes	complemented
204	C₂×#1436	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₁	C₄×C₂²⋊C₄	1	8	yes	—
206	C₂²×C₄₁	C₄×C₄⋊C₄	1	16	yes	—
207	C₂²×C₄₁	#385	1	16	yes	—
208	C₂²×C₄₁	#386	1	8	yes	—
209	C₂²×C₄₁	#387	1	16	yes	—
210	C₂²×C₄₁	#387	1	16	yes	—
211	C₂²×C₄₁	#388	1	16	yes	—
212	C₂²×C₄₁	#389	1	16	yes	—
213	C₂²×C₄₁	#391	1	8	yes	—
214	C₂²×C₄₁	C₂²×C₄²	1	1	yes	characteristic
215	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₄₁	C₂²×C₄⋊C₄	1	2	yes	—
217	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
218	C₂²×C₄₁	C₂×#117	1	2	yes	—
219	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
220	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
221	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
222	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
223	C₂²×C₄₁	C₂×C₄×Q₈	1	2	yes	—
224	C₂²×C₄₁	C₂×C₄×Q₈	1	2	yes	—
225	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
226	C₂²×C₄₁	C₂×#121	1	2	yes	—
227	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
228	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
229	C₂²×C₄₁	C₂×#123	1	2	yes	—
230	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
231	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
232	C₂²×C₄₁	C₂×#125	1	2	yes	—
233	C₂²×C₄₁	C₂×#126	1	2	yes	—
234	C₂²×C₄₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
235	C₄×C₄₁	—	2	8	no	—
236	C₄×C₄₁	—	2	16	no	—
237	C₄×C₄₁	—	2	8	no	—
238	C₄×C₄₁	—	4	4	no	—
239	C₄×C₄₁	—	4	8	no	—
240	C₂³×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
241	C₂³×C₄²	C₂×C₄₁	1	1	yes	characteristic
242	C₂²×#95	C₂×C₄₁	1	2	yes	—
243	C₂²×#95	C₂×C₄₁	1	1	yes	characteristic
244	C₂²×#95	C₂×C₄₁	1	2	yes	—
245	#1436	C₂×C₄₁	1	8	yes	direct product factor
246	C₂×C₄₁	#1436	1	16	yes	direct product factor
247	C₂×C₄₁	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄₁	C₂×C₄×C₄⋊C₄	1	2	yes	—
249	C₂×C₄₁	C₂×#385	1	2	yes	—
250	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
251	C₂×C₄₁	C₂×#387	1	2	yes	—
252	C₂×C₄₁	C₂×#387	1	2	yes	—
253	C₂×C₄₁	C₂×#388	1	2	yes	—
254	C₂×C₄₁	C₂×#389	1	2	yes	—
255	C₂×C₄₁	C₂×#391	1	1	yes	characteristic
256	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
257	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
258	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
259	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
260	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
261	C₂²×C₄⋊C₄	—	2	4	no	—
262	C₂²×C₄⋊C₄	—	2	4	no	—
263	C₂²×C₄⋊C₄	C₄×C₄₁	1	8	yes	complemented
264	C₂²×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
265	C₂²×C₄²	—	2	4	no	—
266	C₂²×C₄²	—	2	8	no	—
267	C₂²×C₄²	C₂²×C₄₁	1	4	yes	—
268	C₂×#95	—	2	4	no	—
269	C₂×#95	—	2	8	no	—
270	C₂×#95	C₄×C₄₁	1	16	yes	complemented
271	C₂×#95	C₂²×C₄₁	1	8	yes	—
272	C₂×#95	C₂²×C₄₁	1	4	yes	—
273	C₂×#95	C₂²×C₄₁	1	8	yes	—
274	C₄₁	C₂×#1436	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	—	2	2	no	—
278	C₂³×C₄	—	2	4	no	—
279	C₂³×C₄	—	2	4	no	—
280	C₂³×C₄	—	2	4	no	—
281	C₂³×C₄	—	2	4	no	—
282	C₂³×C₄	—	2	4	no	—
283	C₂³×C₄	—	2	4	no	—
284	C₂³×C₄	—	2	4	no	—
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	—	2	4	no	—
288	C₂³×C₄	—	2	4	no	—
289	C₂³×C₄	—	2	4	no	—
290	C₂³×C₄	—	2	4	no	—
291	C₂³×C₄	—	2	4	no	—
292	C₂³×C₄	—	2	4	no	—
293	C₂³×C₄	—	2	4	no	—
294	C₂³×C₄	—	2	4	no	—
295	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
296	C₂³×C₄	C₂×C₄×C₄₁	1	8	yes	—
297	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
298	C₂³×C₄	C₂×C₄×C₄₁	1	8	yes	—
299	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
300	C₂³×C₄	C₂×C₄×C₄₁	1	8	yes	—
301	C₂³×C₄	D₄×C₄₁	1	4	yes	—
302	C₂³×C₄	D₄×C₄₁	1	4	yes	—
303	C₂³×C₄	D₄×C₄₁	1	8	yes	—
304	C₂³×C₄	Q₈×C₄₁	1	8	yes	—
305	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
306	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
307	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
308	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
309	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
310	C₂×C₄⋊C₄	—	2	32	no	—
311	C₂×C₄⋊C₄	—	2	8	no	—
312	C₂×C₄⋊C₄	—	2	8	no	—
313	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	16	yes	complemented
314	C₂×C₄²	—	2	32	no	—
315	C₂×C₄²	—	2	8	no	—
316	C₂×C₄²	—	2	16	no	—
317	#95	—	2	8	no	—
318	#95	—	2	16	no	—
319	#95	C₂×C₄×C₄₁	1	32	yes	complemented
320	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
321	C₂⁴	C₂²×C₄×C₄₁	1	4	yes	—
322	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
323	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
324	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
325	C₂⁴	C₂×Q₈×C₄₁	1	4	yes	—
326	C₂⁴	#41×C₄₁	1	4	yes	—
327	C₂⁴	#41×C₄₁	1	4	yes	—
328	C₂⁴	#41×C₄₁	1	4	yes	—
329	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	16	no	—
333	C₂²×C₄	—	2	16	no	—
334	C₂²×C₄	—	2	16	no	—
335	C₂²×C₄	—	2	16	no	—
336	C₂²×C₄	—	2	16	no	—
337	C₂²×C₄	—	2	16	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	2	16	no	—
341	C₂²×C₄	—	2	16	no	—
342	C₂²×C₄	—	2	16	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	2	16	no	—
355	C₂²×C₄	—	2	16	no	—
356	C₂²×C₄	—	2	16	no	—
357	C₂²×C₄	—	2	16	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	—	4	8	no	—
370	C₂²×C₄	—	4	8	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	8	no	—
374	C₂²×C₄	—	4	8	no	—
375	C₂²×C₄	C₄²×C₄₁	1	16	yes	complemented
376	C₂²×C₄	C₂²⋊C₄×C₄₁	1	16	yes	—
377	C₂²×C₄	C₄⋊C₄×C₄₁	1	32	yes	complemented
378	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
379	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
380	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
381	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
382	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
383	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
384	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
385	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
386	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
387	C₂²×C₄	C₂×Q₈×C₄₁	1	8	yes	—
388	C₄⋊C₄	—	2	32	no	—
389	C₄²	—	2	32	no	—
390	C₂³	C₂×C₄²×C₄₁	1	4	yes	—
391	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
392	C₂³	C₂×C₄⋊C₄×C₄₁	1	8	yes	—
393	C₂³	#117×C₄₁	1	4	yes	—
394	C₂³	#117×C₄₁	1	8	yes	—
395	C₂³	C₄×D₄×C₄₁	1	8	yes	—
396	C₂³	C₄×D₄×C₄₁	1	8	yes	—
397	C₂³	C₄×D₄×C₄₁	1	8	yes	—
398	C₂³	C₄×D₄×C₄₁	1	8	yes	—
399	C₂³	C₄×Q₈×C₄₁	1	8	yes	—
400	C₂³	C₄×Q₈×C₄₁	1	8	yes	—
401	C₂³	#120×C₄₁	1	4	yes	—
402	C₂³	#121×C₄₁	1	8	yes	—
403	C₂³	C₂²⋊Q₈×C₄₁	1	8	yes	—
404	C₂³	C₂²⋊Q₈×C₄₁	1	8	yes	—
405	C₂³	#123×C₄₁	1	8	yes	—
406	C₂³	#123×C₄₁	1	4	yes	—
407	C₂³	#124×C₄₁	1	4	yes	—
408	C₂³	#125×C₄₁	1	8	yes	—
409	C₂³	#126×C₄₁	1	8	yes	—
410	C₂³	C₄⋊Q₈×C₄₁	1	4	yes	—
411	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
412	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
413	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
414	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
415	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
416	C₂³	C₂²×Q₈×C₄₁	1	2	yes	—
417	C₂³	C₂×#41×C₄₁	1	2	yes	—
418	C₂³	C₂×#41×C₄₁	1	2	yes	—
419	C₂³	C₂×#41×C₄₁	1	2	yes	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	32	no	—
435	C₂×C₄	—	2	64	no	—
436	C₂×C₄	—	2	32	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	8	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	16	no	—
450	C₂×C₄	—	4	32	no	—
451	C₂×C₄	C₂×C₄²×C₄₁	1	8	yes	complemented
452	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
453	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	16	yes	complemented
454	C₂²	C₄×C₂²⋊C₄×C₄₁	1	8	yes	—
455	C₂²	C₄×C₄⋊C₄×C₄₁	1	16	yes	—
456	C₂²	C₄₁×#385	1	16	yes	—
457	C₂²	C₄₁×#386	1	8	yes	—
458	C₂²	C₄₁×#387	1	16	yes	—
459	C₂²	C₄₁×#387	1	16	yes	—
460	C₂²	C₄₁×#388	1	16	yes	—
461	C₂²	C₄₁×#389	1	16	yes	—
462	C₂²	C₄₁×#391	1	8	yes	—
463	C₂²	C₂²×C₄²×C₄₁	1	1	yes	characteristic
464	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
465	C₂²	C₂²×C₄⋊C₄×C₄₁	1	2	yes	—
466	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
467	C₂²	C₂×#117×C₄₁	1	2	yes	—
468	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
469	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
470	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
471	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
472	C₂²	C₂×C₄×Q₈×C₄₁	1	2	yes	—
473	C₂²	C₂×C₄×Q₈×C₄₁	1	2	yes	—
474	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
475	C₂²	C₂×#121×C₄₁	1	2	yes	—
476	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
477	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
478	C₂²	C₂×#123×C₄₁	1	2	yes	—
479	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
480	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
481	C₂²	C₂×#125×C₄₁	1	2	yes	—
482	C₂²	C₂×#126×C₄₁	1	2	yes	—
483	C₂²	C₂×C₄⋊Q₈×C₄₁	1	1	yes	characteristic
484	C₄	—	2	8	no	—
485	C₄	—	2	16	no	—
486	C₄	—	2	8	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	8	no	—
489	C₂	C₄₁×#1436	1	16	yes	direct product factor
490	C₂	C₂×C₄×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
491	C₂	C₂×C₄×C₄⋊C₄×C₄₁	1	2	yes	—
492	C₂	C₂×C₄₁×#385	1	2	yes	—
493	C₂	C₂×C₄₁×#386	1	1	yes	characteristic
494	C₂	C₂×C₄₁×#387	1	2	yes	—
495	C₂	C₂×C₄₁×#387	1	2	yes	—
496	C₂	C₂×C₄₁×#388	1	2	yes	—
497	C₂	C₂×C₄₁×#389	1	2	yes	—
498	C₂	C₂×C₄₁×#391	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁵×C₄₁	C₂³
commutator	C₂²	C₂²×C₄²×C₄₁
Frattini, cosocle	C₂⁴	C₂⁴×C₄₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄₁×#1436	C₂	direct (N × H)
14. C₂²×C₄⋊C₄×C₄₁	C₄	semidirect
21. C₂×#95×C₄₁	C₄	semidirect
63. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
69. #95×C₄₁	C₂×C₄	semidirect
125. C₂²×C₄×C₄₁	C₄²	semidirect
127. C₂²×C₄×C₄₁	C₄⋊C₄	semidirect
201. C₂×C₄×C₄₁	C₂×C₄²	semidirect
203. C₂×C₄×C₄₁	C₂×C₄⋊C₄	semidirect
204. C₂×#1436	C₄₁	direct (N × H)
245. #1436	C₂×C₄₁	direct (N × H)
246. C₂×C₄₁	#1436	direct (N × H)
263. C₂²×C₄⋊C₄	C₄×C₄₁	semidirect
270. C₂×#95	C₄×C₄₁	semidirect
274. C₄₁	C₂×#1436	direct (N × H)
313. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
319. #95	C₂×C₄×C₄₁	semidirect
375. C₂²×C₄	C₄²×C₄₁	semidirect
377. C₂²×C₄	C₄⋊C₄×C₄₁	semidirect
451. C₂×C₄	C₂×C₄²×C₄₁	semidirect
453. C₂×C₄	C₂×C₄⋊C₄×C₄₁	semidirect
489. C₂	C₄₁×#1436	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₄₁	2
C₂³×C₄²×C₄₁	2
C₂²×#95×C₄₁	2
C₄₁×#1436	2
C₂×#1436	41

Subgroups — C2×C41×#1436 #23789959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1436 #23789959