Subgroups — C₄₁×#13921 #23790122

Order 10496.

1282 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#383	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1443	C₂	1	4	yes	maximal
4	C₄₁×C₄⋊#95	C₂	1	2	yes	maximal
5	C₄₁×C₄⋊#95	C₂	1	2	yes	maximal
6	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#1434	C₂	1	2	yes	maximal
8	C₄×#95×C₄₁	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
13	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
14	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#383	—	2	8	no	—
16	C₄×C₄⋊C₄×C₄₁	C₄	1	8	yes	complemented
17	C₂×#95×C₄₁	C₂²	1	2	yes	—
18	C₂×#95×C₄₁	C₂²	1	4	yes	—
19	C₂×#95×C₄₁	C₂²	1	4	yes	—
20	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#95×C₄₁	C₂²	1	2	yes	—
22	C₂×#95×C₄₁	C₂²	1	4	yes	—
23	C₂×#95×C₄₁	C₂²	1	4	yes	—
24	C₂×#95×C₄₁	C₂²	1	2	yes	—
25	C₂×#95×C₄₁	C₂²	1	2	yes	—
26	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
27	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
28	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
29	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
30	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
32	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
37	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
40	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₄₁	—	2	4	no	—
44	C₂×C₄²×C₄₁	—	2	4	no	—
45	C₂×C₄²×C₄₁	—	2	4	no	—
46	C₂×C₄²×C₄₁	—	2	4	no	—
47	C₂×C₄²×C₄₁	—	2	4	no	—
48	C₂×C₄²×C₄₁	—	2	4	no	—
49	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₄₁	C₂×C₄	1	8	yes	—
51	#95×C₄₁	—	2	8	no	—
52	#95×C₄₁	—	2	8	no	—
53	#95×C₄₁	—	2	4	no	—
54	#95×C₄₁	—	2	4	no	—
55	#95×C₄₁	—	2	2	no	—
56	#95×C₄₁	—	2	8	no	—
57	#95×C₄₁	—	4	4	no	—
58	#95×C₄₁	—	4	2	no	—
59	#95×C₄₁	C₂×C₄	1	8	yes	—
60	#95×C₄₁	D₄	1	4	yes	—
61	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
62	C₂²×C₄×C₄₁	—	2	2	no	—
63	C₂²×C₄×C₄₁	—	2	2	no	—
64	C₂²×C₄×C₄₁	—	2	2	no	—
65	C₂²×C₄×C₄₁	—	2	2	no	—
66	C₂²×C₄×C₄₁	—	2	4	no	—
67	C₂²×C₄×C₄₁	—	2	2	no	—
68	C₂²×C₄×C₄₁	—	2	2	no	—
69	C₂²×C₄×C₄₁	—	2	2	no	—
70	C₂²×C₄×C₄₁	—	2	2	no	—
71	C₂²×C₄×C₄₁	—	2	2	no	—
72	C₂²×C₄×C₄₁	—	2	2	no	—
73	C₂²×C₄×C₄₁	—	2	2	no	—
74	C₂²×C₄×C₄₁	—	2	2	no	—
75	C₂²×C₄×C₄₁	—	2	2	no	—
76	C₂²×C₄×C₄₁	—	2	2	no	—
77	C₂²×C₄×C₄₁	—	2	2	no	—
78	C₂²×C₄×C₄₁	—	2	2	no	—
79	C₂²×C₄×C₄₁	—	2	4	no	—
80	C₂²×C₄×C₄₁	—	2	2	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	2	1	no	—
84	C₂²×C₄×C₄₁	—	2	2	no	—
85	C₂²×C₄×C₄₁	—	2	2	no	—
86	C₂²×C₄×C₄₁	—	2	1	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	4	no	—
91	C₂²×C₄×C₄₁	—	2	4	no	—
92	C₂²×C₄×C₄₁	—	2	4	no	—
93	C₂²×C₄×C₄₁	—	2	4	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	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₁	#41	1	4	yes	—
105	C₂²×C₄×C₄₁	#41	1	2	yes	—
106	C₂²×C₄×C₄₁	#41	1	4	yes	—
107	C₂²×C₄×C₄₁	#41	1	2	yes	—
108	C₂²×C₄×C₄₁	#41	1	4	yes	—
109	C₂²×C₄×C₄₁	#41	1	2	yes	—
110	C₄⋊C₄×C₄₁	—	2	8	no	—
111	C₄⋊C₄×C₄₁	—	2	8	no	—
112	C₄⋊C₄×C₄₁	—	4	8	no	—
113	C₄²×C₄₁	—	2	8	no	—
114	C₄²×C₄₁	—	2	16	no	—
115	C₄²×C₄₁	—	4	8	no	—
116	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
117	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
118	C₂³×C₄₁	C₂×#41	1	2	yes	—
119	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
120	C₂³×C₄₁	C₂×#41	1	2	yes	—
121	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
122	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
123	C₂³×C₄₁	C₂×#41	1	2	yes	—
124	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
125	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
126	C₂³×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
127	C₂×C₄×C₄₁	—	2	2	no	—
128	C₂×C₄×C₄₁	—	2	2	no	—
129	C₂×C₄×C₄₁	—	2	4	no	—
130	C₂×C₄×C₄₁	—	2	4	no	—
131	C₂×C₄×C₄₁	—	2	2	no	—
132	C₂×C₄×C₄₁	—	2	4	no	—
133	C₂×C₄×C₄₁	—	2	4	no	—
134	C₂×C₄×C₄₁	—	2	4	no	—
135	C₂×C₄×C₄₁	—	2	4	no	—
136	C₂×C₄×C₄₁	—	2	2	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	2	no	—
139	C₂×C₄×C₄₁	—	2	4	no	—
140	C₂×C₄×C₄₁	—	2	4	no	—
141	C₂×C₄×C₄₁	—	2	4	no	—
142	C₂×C₄×C₄₁	—	2	4	no	—
143	C₂×C₄×C₄₁	—	2	4	no	—
144	C₂×C₄×C₄₁	—	2	4	no	—
145	C₂×C₄×C₄₁	—	2	4	no	—
146	C₂×C₄×C₄₁	—	4	2	no	—
147	C₂×C₄×C₄₁	—	4	2	no	—
148	C₂×C₄×C₄₁	—	4	4	no	—
149	C₂×C₄×C₄₁	—	4	4	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	4	2	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	4	2	no	—
156	C₂×C₄×C₄₁	—	4	2	no	—
157	C₂×C₄×C₄₁	—	4	2	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	4	no	—
163	C₂×C₄×C₄₁	—	4	4	no	—
164	C₂×C₄×C₄₁	—	4	4	no	—
165	C₂×C₄×C₄₁	—	4	4	no	—
166	C₂×C₄×C₄₁	—	4	4	no	—
167	C₂×C₄×C₄₁	—	4	4	no	—
168	C₂×C₄×C₄₁	—	4	4	no	—
169	C₂×C₄×C₄₁	#117	1	4	yes	—
170	C₂×C₄×C₄₁	#117	1	4	yes	—
171	C₂×C₄×C₄₁	#117	1	4	yes	—
172	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
173	C₂×C₄×C₄₁	#126	1	8	yes	—
174	C₂×C₄×C₄₁	#126	1	8	yes	—
175	#13921	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
177	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
178	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
179	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
180	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
181	C₂²×C₄₁	#519	1	1	yes	characteristic
182	C₂²×C₄₁	#520	1	1	yes	characteristic
183	C₂²×C₄₁	C₂×#126	1	2	yes	—
184	C₂²×C₄₁	C₂×#126	1	2	yes	—
185	C₂²×C₄₁	#529	1	2	yes	—
186	C₂²×C₄₁	#532	1	2	yes	—
187	C₂²×C₄₁	#541	1	2	yes	—
188	C₂²×C₄₁	#542	1	2	yes	—
189	C₂²×C₄₁	#547	1	2	yes	—
190	C₂²×C₄₁	#547	1	1	yes	characteristic
191	C₂²×C₄₁	#550	1	1	yes	characteristic
192	C₂²×C₄₁	#552	1	2	yes	—
193	C₂²×C₄₁	#552	1	2	yes	—
194	C₂²×C₄₁	#553	1	2	yes	—
195	C₂²×C₄₁	#555	1	1	yes	characteristic
196	C₂²×C₄₁	#556	1	2	yes	—
197	C₂²×C₄₁	#556	1	1	yes	characteristic
198	C₂²×C₄₁	#556	1	2	yes	—
199	C₄×C₄₁	—	2	4	no	—
200	C₄×C₄₁	—	4	2	no	—
201	C₄×C₄₁	—	4	4	no	—
202	C₄×C₄₁	—	4	4	no	—
203	C₄×C₄₁	—	4	4	no	—
204	C₄×C₄₁	—	4	4	no	—
205	C₄×C₄₁	—	8	4	no	—
206	C₄×C₄₁	#383	1	8	yes	complemented
207	C₂×#383	C₂×C₄₁	1	2	yes	—
208	C₂×C₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
209	#1443	C₂×C₄₁	1	4	yes	—
210	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic
211	C₄⋊#95	C₂×C₄₁	1	2	yes	—
212	C₄⋊#95	C₂×C₄₁	1	2	yes	—
213	#1434	C₂×C₄₁	1	2	yes	—
214	C₄×#95	C₂×C₄₁	1	1	yes	characteristic
215	C₂×C₄₁	C₂×#383	1	1	yes	characteristic
216	C₂×C₄₁	#2293	1	1	yes	characteristic
217	C₂×C₄₁	#2320	1	1	yes	characteristic
218	C₂×C₄₁	#2344	1	1	yes	characteristic
219	C₂×C₄₁	#2347	1	1	yes	characteristic
220	C₂×C₄₁	#2354	1	1	yes	characteristic
221	C₂×C₄₁	#2356	1	1	yes	characteristic
222	C₂×C₄₁	#2495	1	2	yes	—
223	C₂×C₄₁	#2496	1	2	yes	—
224	C₂×C₄₁	#2512	1	2	yes	—
225	C₂×C₄₁	#2514	1	2	yes	—
226	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
227	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
229	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
230	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
231	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
232	#383	—	2	8	no	—
233	C₄×C₄⋊C₄	C₄×C₄₁	1	8	yes	complemented
234	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
235	C₂×#95	C₂²×C₄₁	1	2	yes	—
236	C₂×#95	C₂²×C₄₁	1	4	yes	—
237	C₂×#95	C₂²×C₄₁	1	2	yes	—
238	C₂×#95	C₂²×C₄₁	1	4	yes	—
239	C₂×#95	C₂²×C₄₁	1	4	yes	—
240	C₂×#95	C₂²×C₄₁	1	4	yes	—
241	C₂×#95	C₂²×C₄₁	1	2	yes	—
242	C₂×#95	C₂²×C₄₁	1	2	yes	—
243	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
244	C₄₁	#13921	1	1	yes	characteristic, direct product factor, Sylow
245	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
246	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
247	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
248	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
250	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
251	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
261	C₂×C₄²	—	2	4	no	—
262	C₂×C₄²	—	2	4	no	—
263	C₂×C₄²	—	2	4	no	—
264	C₂×C₄²	—	2	4	no	—
265	C₂×C₄²	—	2	4	no	—
266	C₂×C₄²	—	2	4	no	—
267	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
268	C₂×C₄²	C₂×C₄×C₄₁	1	8	yes	—
269	#95	—	2	8	no	—
270	#95	—	2	8	no	—
271	#95	—	2	4	no	—
272	#95	—	2	4	no	—
273	#95	—	2	2	no	—
274	#95	—	2	8	no	—
275	#95	—	4	4	no	—
276	#95	—	4	2	no	—
277	#95	C₂×C₄×C₄₁	1	8	yes	—
278	#95	D₄×C₄₁	1	4	yes	—
279	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
317	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
318	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
319	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
321	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
322	C₂²×C₄	#41×C₄₁	1	4	yes	—
323	C₂²×C₄	#41×C₄₁	1	2	yes	—
324	C₂²×C₄	#41×C₄₁	1	4	yes	—
325	C₂²×C₄	#41×C₄₁	1	2	yes	—
326	C₂²×C₄	#41×C₄₁	1	4	yes	—
327	C₂²×C₄	#41×C₄₁	1	2	yes	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	4	8	no	—
331	C₄²	—	2	8	no	—
332	C₄²	—	2	16	no	—
333	C₄²	—	4	8	no	—
334	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
335	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
336	C₂³	C₂×#41×C₄₁	1	2	yes	—
337	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
338	C₂³	C₂×#41×C₄₁	1	2	yes	—
339	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
340	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
341	C₂³	C₂×#41×C₄₁	1	2	yes	—
342	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
343	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
344	C₂³	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	#117×C₄₁	1	4	yes	—
388	C₂×C₄	#117×C₄₁	1	4	yes	—
389	C₂×C₄	#117×C₄₁	1	4	yes	—
390	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
391	C₂×C₄	#126×C₄₁	1	8	yes	—
392	C₂×C₄	#126×C₄₁	1	8	yes	—
393	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
394	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
395	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
396	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
397	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
398	C₂²	C₄₁×#519	1	1	yes	characteristic
399	C₂²	C₄₁×#520	1	1	yes	characteristic
400	C₂²	C₂×#126×C₄₁	1	2	yes	—
401	C₂²	C₂×#126×C₄₁	1	2	yes	—
402	C₂²	C₄₁×#529	1	2	yes	—
403	C₂²	C₄₁×#532	1	2	yes	—
404	C₂²	C₄₁×#541	1	2	yes	—
405	C₂²	C₄₁×#542	1	2	yes	—
406	C₂²	C₄₁×#547	1	2	yes	—
407	C₂²	C₄₁×#547	1	1	yes	characteristic
408	C₂²	C₄₁×#550	1	1	yes	characteristic
409	C₂²	C₄₁×#552	1	2	yes	—
410	C₂²	C₄₁×#552	1	2	yes	—
411	C₂²	C₄₁×#553	1	2	yes	—
412	C₂²	C₄₁×#555	1	1	yes	characteristic
413	C₂²	C₄₁×#556	1	2	yes	—
414	C₂²	C₄₁×#556	1	1	yes	characteristic
415	C₂²	C₄₁×#556	1	2	yes	—
416	C₄	—	2	4	no	—
417	C₄	—	4	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	4	no	—
422	C₄	—	8	4	no	—
423	C₄	C₄₁×#383	1	8	yes	complemented
424	C₂	C₂×C₄₁×#383	1	1	yes	characteristic
425	C₂	C₄₁×#2293	1	1	yes	characteristic
426	C₂	C₄₁×#2320	1	1	yes	characteristic
427	C₂	C₄₁×#2344	1	1	yes	characteristic
428	C₂	C₄₁×#2347	1	1	yes	characteristic
429	C₂	C₄₁×#2354	1	1	yes	characteristic
430	C₂	C₄₁×#2356	1	1	yes	characteristic
431	C₂	C₄₁×#2495	1	2	yes	—
432	C₂	C₄₁×#2496	1	2	yes	—
433	C₂	C₄₁×#2512	1	2	yes	—
434	C₂	C₄₁×#2514	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
16. C₄×C₄⋊C₄×C₄₁	C₄	semidirect
175. #13921	C₄₁	direct (N × H)
206. C₄×C₄₁	#383	semidirect
233. C₄×C₄⋊C₄	C₄×C₄₁	semidirect
244. C₄₁	#13921	direct (N × H)
423. C₄	C₄₁×#383	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#383	2
C₂×C₄×C₄⋊C₄×C₄₁	2
C₄₁×#1443	2
C₄₁×C₄⋊#95	2
C₄₁×#1434	2
C₄×#95×C₄₁	2
#13921	41

Subgroups — C41×#13921 #23790122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#13921 #23790122