Subgroups — C₂×C₄₁×#3122 #23836752

Order 10496.

2338 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3122	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₁×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₁×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₁×#459	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#447	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#442	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₈×C₄₁	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
14	C₄₁×#540	—	2	4	no	—
15	C₄₁×#540	C₂²	1	8	yes	complemented
16	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic, complemented
17	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	C₂×#123×C₄₁	—	2	2	no	—
19	C₂×#121×C₄₁	—	2	2	no	—
20	C₂×#121×C₄₁	C₂²	1	2	yes	—
21	C₄₁×#518	—	2	4	no	—
22	C₄₁×#518	C₂²	1	8	yes	complemented
23	C₂×C₄×D₄×C₄₁	—	2	2	no	—
24	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	complemented
27	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₄₁	—	2	2	no	—
30	C₄₁×#482	C₂²	1	16	yes	complemented
31	C₄₁×#478	C₂²	1	16	yes	complemented
32	C₄₁×#459	C₂²	1	16	yes	complemented
33	C₄₁×#447	C₂²	1	16	yes	complemented
34	C₄₁×#442	C₂²	1	16	yes	complemented
35	C₄×D₈×C₄₁	C₂²	1	16	yes	complemented
36	C₄₁×#433	C₂²	1	8	yes	complemented
37	C₂×#107×C₄₁	C₂²	1	2	yes	complemented
38	C₂×#106×C₄₁	C₂²	1	2	yes	complemented
39	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
40	C₂×#102×C₄₁	C₂²	1	2	yes	—
41	C₂×#102×C₄₁	C₂²	1	2	yes	—
42	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
43	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
44	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
45	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
47	C₂⁵×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	8	no	—
49	C₂²×D₄×C₄₁	—	2	2	no	—
50	C₂²×D₄×C₄₁	—	2	1	no	—
51	C₂²×D₄×C₄₁	—	2	2	no	—
52	C₂²×D₄×C₄₁	—	2	2	no	—
53	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
54	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
55	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₁	—	2	2	no	—
57	C₂³×C₄×C₄₁	—	2	2	no	—
58	C₂³×C₄×C₄₁	—	2	2	no	—
59	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
60	C₂×D₈×C₄₁	—	2	8	no	—
61	C₂×D₈×C₄₁	—	2	8	no	—
62	C₂×D₈×C₄₁	C₂³	1	8	yes	—
63	C₂×D₈×C₄₁	C₂³	1	8	yes	—
64	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
66	#127×C₄₁	—	2	2	no	—
67	#127×C₄₁	C₂³	1	4	yes	complemented
68	#125×C₄₁	—	2	2	no	—
69	#125×C₄₁	C₂³	1	4	yes	complemented
70	#123×C₄₁	—	2	16	no	—
71	#121×C₄₁	—	2	4	no	—
72	#121×C₄₁	—	2	16	no	—
73	#121×C₄₁	C₂³	1	8	yes	—
74	C₄×D₄×C₄₁	—	2	16	no	—
75	C₄×D₄×C₄₁	—	2	4	no	—
76	C₄×D₄×C₄₁	—	2	4	no	—
77	C₄×D₄×C₄₁	—	2	4	no	—
78	C₄×D₄×C₄₁	C₂³	1	8	yes	—
79	C₄×D₄×C₄₁	C₂³	1	8	yes	—
80	C₄×D₄×C₄₁	C₂³	1	8	yes	complemented
81	#117×C₄₁	—	2	2	no	—
82	#117×C₄₁	D₄	1	4	yes	—
83	#117×C₄₁	C₂³	1	4	yes	—
84	#117×C₄₁	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	16	no	—
95	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
96	C₂×C₄²×C₄₁	—	2	1	no	—
97	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
99	#107×C₄₁	C₂³	1	8	yes	complemented
100	#106×C₄₁	C₂³	1	8	yes	complemented
101	C₄⋊C₈×C₄₁	C₂³	1	8	yes	complemented
102	#102×C₄₁	C₂³	1	8	yes	—
103	#102×C₄₁	C₂³	1	8	yes	—
104	#102×C₄₁	C₂³	1	8	yes	complemented
105	#102×C₄₁	C₂³	1	8	yes	complemented
106	C₂²⋊C₈×C₄₁	C₂³	1	8	yes	—
107	#97×C₄₁	C₂³	1	4	yes	complemented
108	C₄×C₈×C₄₁	C₂³	1	4	yes	complemented
109	C₂⁴×C₄₁	—	2	8	no	—
110	C₂⁴×C₄₁	—	2	2	no	—
111	C₂⁴×C₄₁	—	2	4	no	—
112	C₂⁴×C₄₁	—	2	2	no	—
113	C₂⁴×C₄₁	—	8	4	no	—
114	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₄₁	—	2	8	no	—
116	C₂×D₄×C₄₁	—	2	16	no	—
117	C₂×D₄×C₄₁	—	2	16	no	—
118	C₂×D₄×C₄₁	—	2	8	no	—
119	C₂×D₄×C₄₁	—	2	4	no	—
120	C₂×D₄×C₄₁	—	2	2	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	—	2	8	no	—
123	C₂×D₄×C₄₁	—	2	4	no	—
124	C₂×D₄×C₄₁	—	2	4	no	—
125	C₂×D₄×C₄₁	—	2	4	no	—
126	C₂×D₄×C₄₁	—	8	4	no	—
127	C₂×D₄×C₄₁	—	8	4	no	—
128	C₂×D₄×C₄₁	#41	1	8	yes	—
129	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
130	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₄₁	—	2	4	no	—
132	C₂²×C₄×C₄₁	—	2	2	no	—
133	C₂²×C₄×C₄₁	—	2	2	no	—
134	C₂²×C₄×C₄₁	—	2	8	no	—
135	C₂²×C₄×C₄₁	—	2	8	no	—
136	C₂²×C₄×C₄₁	—	2	8	no	—
137	C₂²×C₄×C₄₁	—	8	4	no	—
138	C₂²×C₄×C₄₁	—	8	4	no	—
139	C₂²×C₄×C₄₁	—	8	4	no	—
140	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
146	D₈×C₄₁	—	2	16	no	—
147	D₈×C₄₁	—	2	16	no	—
148	C₂×C₈×C₄₁	—	2	4	no	—
149	C₂×C₈×C₄₁	—	2	4	no	—
150	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
151	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₄₁	—	2	8	no	—
153	C₄⋊C₄×C₄₁	—	2	2	no	—
154	C₄⋊C₄×C₄₁	—	2	2	no	—
155	C₄⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
156	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
157	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
158	C₂²⋊C₄×C₄₁	—	2	4	no	—
159	C₂²⋊C₄×C₄₁	—	2	8	no	—
160	C₂²⋊C₄×C₄₁	—	2	8	no	—
161	C₂²⋊C₄×C₄₁	—	2	8	no	—
162	C₂²⋊C₄×C₄₁	—	2	8	no	—
163	C₂²⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
164	C₄²×C₄₁	—	2	4	no	—
165	C₄²×C₄₁	C₂×D₄	1	2	yes	—
166	C₄²×C₄₁	C₂×D₄	1	2	yes	—
167	C₄²×C₄₁	C₂⁴	1	2	yes	—
168	C₄²×C₄₁	C₂⁴	1	2	yes	—
169	C₂³×C₄₁	—	2	16	no	—
170	C₂³×C₄₁	—	2	2	no	—
171	C₂³×C₄₁	—	2	8	no	—
172	C₂³×C₄₁	—	2	4	no	—
173	C₂³×C₄₁	—	2	4	no	—
174	C₂³×C₄₁	—	2	4	no	—
175	C₂³×C₄₁	—	4	4	no	—
176	C₂³×C₄₁	—	4	4	no	—
177	C₂³×C₄₁	—	4	4	no	—
178	C₂³×C₄₁	—	4	4	no	—
179	C₂³×C₄₁	—	4	4	no	—
180	C₂³×C₄₁	—	8	8	no	—
181	C₂³×C₄₁	—	8	16	no	—
182	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
183	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
184	D₄×C₄₁	—	2	16	no	—
185	D₄×C₄₁	—	2	8	no	—
186	D₄×C₄₁	—	2	4	no	—
187	D₄×C₄₁	—	2	4	no	—
188	D₄×C₄₁	—	2	4	no	—
189	D₄×C₄₁	—	4	4	no	—
190	D₄×C₄₁	—	8	8	no	—
191	D₄×C₄₁	—	8	8	no	—
192	D₄×C₄₁	C₂×#41	1	8	yes	—
193	C₂×C₄×C₄₁	—	2	2	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	4	no	—
198	C₂×C₄×C₄₁	—	2	4	no	—
199	C₂×C₄×C₄₁	—	2	4	no	—
200	C₂×C₄×C₄₁	—	4	4	no	—
201	C₂×C₄×C₄₁	—	4	4	no	—
202	C₂×C₄×C₄₁	—	8	8	no	—
203	C₂×C₄×C₄₁	—	8	8	no	—
204	C₂×C₄×C₄₁	—	8	8	no	—
205	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
210	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
211	C₈×C₄₁	—	2	4	no	—
212	C₈×C₄₁	—	2	4	no	—
213	C₂×#3122	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂²×C₄₁	—	2	2	no	—
215	C₂²×C₄₁	—	2	8	no	—
216	C₂²×C₄₁	—	2	4	no	—
217	C₂²×C₄₁	—	4	4	no	—
218	C₂²×C₄₁	—	4	16	no	—
219	C₂²×C₄₁	—	4	4	no	—
220	C₂²×C₄₁	—	4	4	no	—
221	C₂²×C₄₁	—	4	4	no	—
222	C₂²×C₄₁	—	4	4	no	—
223	C₂²×C₄₁	—	4	4	no	—
224	C₂²×C₄₁	—	8	16	no	—
225	C₂²×C₄₁	—	8	8	no	—
226	C₂²×C₄₁	#525	1	2	yes	—
227	C₂²×C₄₁	#576	1	4	yes	—
228	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
229	C₄×C₄₁	—	2	2	no	—
230	C₄×C₄₁	—	2	4	no	—
231	C₄×C₄₁	—	2	4	no	—
232	C₄×C₄₁	—	4	4	no	—
233	C₄×C₄₁	—	4	4	no	—
234	C₄×C₄₁	#525	1	2	yes	—
235	C₄×C₄₁	C₂²×#41	1	2	yes	—
236	C₂×#540	C₂×C₄₁	1	1	yes	characteristic, complemented
237	C₂×#518	C₂×C₄₁	1	1	yes	characteristic, complemented
238	#3122	C₂×C₄₁	1	16	yes	direct product factor
239	C₂×#482	C₂×C₄₁	1	2	yes	complemented
240	C₂×#478	C₂×C₄₁	1	2	yes	complemented
241	C₂×#459	C₂×C₄₁	1	2	yes	complemented
242	C₂×#447	C₂×C₄₁	1	2	yes	complemented
243	C₂×#442	C₂×C₄₁	1	2	yes	complemented
244	C₂×C₄×D₈	C₂×C₄₁	1	2	yes	complemented
245	C₂×#433	C₂×C₄₁	1	1	yes	characteristic, complemented
246	C₂×C₄₁	—	4	2	no	—
247	C₂×C₄₁	—	4	8	no	—
248	C₂×C₄₁	—	8	4	no	—
249	C₂×C₄₁	#3122	1	4	yes	direct product factor
250	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
251	C₂×C₄₁	C₂×#576	1	2	yes	—
252	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
253	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
254	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
255	#540	—	2	4	no	—
256	#540	C₂²×C₄₁	1	8	yes	complemented
257	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic, complemented
258	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic, complemented
259	C₂×#123	—	2	2	no	—
260	C₂×#121	—	2	2	no	—
261	C₂×#121	C₂²×C₄₁	1	2	yes	—
262	#518	—	2	4	no	—
263	#518	C₂²×C₄₁	1	8	yes	complemented
264	C₂×C₄×D₄	—	2	2	no	—
265	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
266	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
267	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	complemented
268	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
269	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	—	2	2	no	—
271	#482	C₂²×C₄₁	1	16	yes	complemented
272	#478	C₂²×C₄₁	1	16	yes	complemented
273	#459	C₂²×C₄₁	1	16	yes	complemented
274	#447	C₂²×C₄₁	1	16	yes	complemented
275	#442	C₂²×C₄₁	1	16	yes	complemented
276	C₄×D₈	C₂²×C₄₁	1	16	yes	complemented
277	#433	C₂²×C₄₁	1	8	yes	complemented
278	C₂×#107	C₂²×C₄₁	1	2	yes	complemented
279	C₂×#106	C₂²×C₄₁	1	2	yes	complemented
280	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
281	C₂×#102	C₂²×C₄₁	1	2	yes	—
282	C₂×#102	C₂²×C₄₁	1	2	yes	—
283	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
284	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
285	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
286	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic, complemented
287	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
288	C₄₁	C₂×#3122	1	1	yes	characteristic, direct product factor, Sylow
289	C₂⁵	—	2	1	no	—
290	C₂²×D₄	—	2	8	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
296	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
297	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	—	2	2	no	—
300	C₂³×C₄	—	2	2	no	—
301	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
302	C₂×D₈	—	2	8	no	—
303	C₂×D₈	—	2	8	no	—
304	C₂×D₈	C₂³×C₄₁	1	8	yes	—
305	C₂×D₈	C₂³×C₄₁	1	8	yes	—
306	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
307	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
308	#127	—	2	2	no	—
309	#127	C₂³×C₄₁	1	4	yes	complemented
310	#125	—	2	2	no	—
311	#125	C₂³×C₄₁	1	4	yes	complemented
312	#123	—	2	16	no	—
313	#121	—	2	4	no	—
314	#121	—	2	16	no	—
315	#121	C₂³×C₄₁	1	8	yes	—
316	C₄×D₄	—	2	16	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	4	no	—
320	C₄×D₄	C₂³×C₄₁	1	8	yes	—
321	C₄×D₄	C₂³×C₄₁	1	8	yes	—
322	C₄×D₄	C₂³×C₄₁	1	8	yes	complemented
323	#117	—	2	2	no	—
324	#117	D₄×C₄₁	1	4	yes	—
325	#117	C₂³×C₄₁	1	4	yes	—
326	#117	C₂³×C₄₁	1	4	yes	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	16	no	—
337	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
341	#107	C₂³×C₄₁	1	8	yes	complemented
342	#106	C₂³×C₄₁	1	8	yes	complemented
343	C₄⋊C₈	C₂³×C₄₁	1	8	yes	complemented
344	#102	C₂³×C₄₁	1	8	yes	—
345	#102	C₂³×C₄₁	1	8	yes	—
346	#102	C₂³×C₄₁	1	8	yes	complemented
347	#102	C₂³×C₄₁	1	8	yes	complemented
348	C₂²⋊C₈	C₂³×C₄₁	1	8	yes	—
349	#97	C₂³×C₄₁	1	4	yes	complemented
350	C₄×C₈	C₂³×C₄₁	1	4	yes	complemented
351	C₂⁴	—	2	8	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	—	2	2	no	—
355	C₂⁴	—	8	4	no	—
356	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	16	no	—
359	C₂×D₄	—	2	16	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	8	4	no	—
369	C₂×D₄	—	8	4	no	—
370	C₂×D₄	#41×C₄₁	1	8	yes	—
371	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
372	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
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	—	8	4	no	—
380	C₂²×C₄	—	8	4	no	—
381	C₂²×C₄	—	8	4	no	—
382	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
388	D₈	—	2	16	no	—
389	D₈	—	2	16	no	—
390	C₂×C₈	—	2	4	no	—
391	C₂×C₈	—	2	4	no	—
392	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
393	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
398	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
399	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
406	C₄²	—	2	4	no	—
407	C₄²	C₂×D₄×C₄₁	1	2	yes	—
408	C₄²	C₂×D₄×C₄₁	1	2	yes	—
409	C₄²	C₂⁴×C₄₁	1	2	yes	—
410	C₄²	C₂⁴×C₄₁	1	2	yes	—
411	C₂³	—	2	16	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	8	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	8	8	no	—
423	C₂³	—	8	16	no	—
424	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
425	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
426	D₄	—	2	16	no	—
427	D₄	—	2	8	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	4	4	no	—
432	D₄	—	8	8	no	—
433	D₄	—	8	8	no	—
434	D₄	C₂×#41×C₄₁	1	8	yes	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	8	8	no	—
445	C₂×C₄	—	8	8	no	—
446	C₂×C₄	—	8	8	no	—
447	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
449	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
450	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
452	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
453	C₈	—	2	4	no	—
454	C₈	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	16	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	8	16	no	—
466	C₂²	—	8	8	no	—
467	C₂²	C₄₁×#525	1	2	yes	—
468	C₂²	C₄₁×#576	1	4	yes	—
469	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
470	C₄	—	2	4	no	—
471	C₄	—	2	4	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	4	no	—
475	C₄	C₄₁×#525	1	2	yes	—
476	C₄	C₂²×#41×C₄₁	1	2	yes	—
477	C₂	—	4	2	no	—
478	C₂	—	4	8	no	—
479	C₂	—	8	4	no	—
480	C₂	C₄₁×#3122	1	4	yes	direct product factor
481	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
482	C₂	C₂×C₄₁×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#540	C₂	semidirect
2. C₂×C₄₁×#518	C₂	semidirect
3. C₄₁×#3122	C₂	direct (N × H)
4. C₂×C₄₁×#482	C₂	semidirect
5. C₂×C₄₁×#478	C₂	semidirect
6. C₂×C₄₁×#459	C₂	semidirect
7. C₂×C₄₁×#447	C₂	semidirect
8. C₂×C₄₁×#442	C₂	semidirect
9. C₂×C₄×D₈×C₄₁	C₂	semidirect
10. C₂×C₄₁×#433	C₂	semidirect
15. C₄₁×#540	C₂²	semidirect
16. C₂×#127×C₄₁	C₂²	semidirect
17. C₂×#125×C₄₁	C₂²	semidirect
22. C₄₁×#518	C₂²	semidirect
26. C₂×C₄×D₄×C₄₁	C₂²	semidirect
30. C₄₁×#482	C₂²	semidirect
31. C₄₁×#478	C₂²	semidirect
32. C₄₁×#459	C₂²	semidirect
33. C₄₁×#447	C₂²	semidirect
34. C₄₁×#442	C₂²	semidirect
35. C₄×D₈×C₄₁	C₂²	semidirect
36. C₄₁×#433	C₂²	semidirect
37. C₂×#107×C₄₁	C₂²	semidirect
38. C₂×#106×C₄₁	C₂²	semidirect
39. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
42. C₂×#102×C₄₁	C₂²	semidirect
43. C₂×#102×C₄₁	C₂²	semidirect
45. C₂×#97×C₄₁	C₂²	semidirect
46. C₂×C₄×C₈×C₄₁	C₂²	semidirect
67. #127×C₄₁	C₂³	semidirect
69. #125×C₄₁	C₂³	semidirect
80. C₄×D₄×C₄₁	C₂³	semidirect
99. #107×C₄₁	C₂³	semidirect
100. #106×C₄₁	C₂³	semidirect
101. C₄⋊C₈×C₄₁	C₂³	semidirect
104. #102×C₄₁	C₂³	semidirect
105. #102×C₄₁	C₂³	semidirect
107. #97×C₄₁	C₂³	semidirect
108. C₄×C₈×C₄₁	C₂³	semidirect
213. C₂×#3122	C₄₁	direct (N × H)
236. C₂×#540	C₂×C₄₁	semidirect
237. C₂×#518	C₂×C₄₁	semidirect
238. #3122	C₂×C₄₁	direct (N × H)
239. C₂×#482	C₂×C₄₁	semidirect
240. C₂×#478	C₂×C₄₁	semidirect
241. C₂×#459	C₂×C₄₁	semidirect
242. C₂×#447	C₂×C₄₁	semidirect
243. C₂×#442	C₂×C₄₁	semidirect
244. C₂×C₄×D₈	C₂×C₄₁	semidirect
245. C₂×#433	C₂×C₄₁	semidirect
249. C₂×C₄₁	#3122	direct (N × H)
256. #540	C₂²×C₄₁	semidirect
257. C₂×#127	C₂²×C₄₁	semidirect
258. C₂×#125	C₂²×C₄₁	semidirect
263. #518	C₂²×C₄₁	semidirect
267. C₂×C₄×D₄	C₂²×C₄₁	semidirect
271. #482	C₂²×C₄₁	semidirect
272. #478	C₂²×C₄₁	semidirect
273. #459	C₂²×C₄₁	semidirect
274. #447	C₂²×C₄₁	semidirect
275. #442	C₂²×C₄₁	semidirect
276. C₄×D₈	C₂²×C₄₁	semidirect
277. #433	C₂²×C₄₁	semidirect
278. C₂×#107	C₂²×C₄₁	semidirect
279. C₂×#106	C₂²×C₄₁	semidirect
280. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
283. C₂×#102	C₂²×C₄₁	semidirect
284. C₂×#102	C₂²×C₄₁	semidirect
286. C₂×#97	C₂²×C₄₁	semidirect
287. C₂×C₄×C₈	C₂²×C₄₁	semidirect
288. C₄₁	C₂×#3122	direct (N × H)
309. #127	C₂³×C₄₁	semidirect
311. #125	C₂³×C₄₁	semidirect
322. C₄×D₄	C₂³×C₄₁	semidirect
341. #107	C₂³×C₄₁	semidirect
342. #106	C₂³×C₄₁	semidirect
343. C₄⋊C₈	C₂³×C₄₁	semidirect
346. #102	C₂³×C₄₁	semidirect
347. #102	C₂³×C₄₁	semidirect
349. #97	C₂³×C₄₁	semidirect
350. C₄×C₈	C₂³×C₄₁	semidirect
480. C₂	C₄₁×#3122	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#540	2
C₂×C₄₁×#518	2
C₄₁×#3122	2
C₂×C₄₁×#482	2
C₂×C₄₁×#478	2
C₂×C₄₁×#459	2
C₂×C₄₁×#447	2
C₂×C₄₁×#442	2
C₂×C₄×D₈×C₄₁	2
C₂×C₄₁×#433	2
C₂×#3122	41

Subgroups — C2×C41×#3122 #23836752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3122 #23836752