Subgroups — C₄₁×#23199 #23799400

Order 10496.

914 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#495	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2949	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2948	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1978	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#1977	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1888	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1885	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₁	C₂²	1	2	yes	—
16	C₄₁×#519	C₂²	1	2	yes	—
17	C₄₁×#518	C₂²	1	2	yes	—
18	C₄₁×#495	C₄	1	8	yes	complemented
19	C₄₁×#442	—	2	2	no	—
20	C₄₁×#441	—	2	2	no	—
21	C₄₁×#440	—	2	4	no	—
22	C₄×Q₁₆×C₄₁	—	2	2	no	—
23	C₄×SD₁₆×C₄₁	—	2	4	no	—
24	C₄×D₈×C₄₁	—	2	2	no	—
25	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#427	C₂²	1	1	yes	characteristic
28	C₄₁×#427	C₂²	1	1	yes	characteristic
29	C₄₁×#419	C₂²	1	2	yes	—
30	C₄₁×#419	C₂²	1	2	yes	—
31	C₄₁×#418	C₂²	1	2	yes	—
32	C₄₁×#418	C₂²	1	2	yes	—
33	C₂×#101×C₄₁	C₂²	1	2	yes	—
34	C₂×#100×C₄₁	C₂²	1	2	yes	—
35	C₄₁×#405	C₂²	1	1	yes	characteristic
36	C₄₁×#405	C₂²	1	2	yes	—
37	C₄₁×#405	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
39	C₄₁×#339	C₂²	1	1	yes	characteristic
40	C₄₁×#339	C₂²	1	2	yes	—
41	C₄₁×#339	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
44	C₂×Q₁₆×C₄₁	—	2	1	no	—
45	C₂×Q₁₆×C₄₁	—	2	1	no	—
46	C₂×Q₁₆×C₄₁	—	2	2	no	—
47	C₂×Q₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
48	C₂×SD₁₆×C₄₁	—	2	2	no	—
49	C₂×SD₁₆×C₄₁	—	2	2	no	—
50	C₂×SD₁₆×C₄₁	—	2	4	no	—
51	C₂×SD₁₆×C₄₁	C₂×C₄	1	8	yes	complemented
52	C₂×D₈×C₄₁	—	2	1	no	—
53	C₂×D₈×C₄₁	—	2	1	no	—
54	C₂×D₈×C₄₁	—	2	2	no	—
55	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	—
56	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
58	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
61	#124×C₄₁	—	4	2	no	—
62	#124×C₄₁	C₂×C₄	1	8	yes	complemented
63	C₄×Q₈×C₄₁	—	2	4	no	—
64	C₄×Q₈×C₄₁	—	2	4	no	—
65	C₄×D₄×C₄₁	—	2	4	no	—
66	C₄×D₄×C₄₁	—	2	4	no	—
67	#117×C₄₁	—	4	2	no	—
68	#117×C₄₁	C₂³	1	1	yes	characteristic
69	#117×C₄₁	C₂³	1	2	yes	—
70	#117×C₄₁	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
73	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
74	#108×C₄₁	—	2	2	no	—
75	#108×C₄₁	—	2	2	no	—
76	#107×C₄₁	D₄	1	2	yes	—
77	#107×C₄₁	D₄	1	2	yes	—
78	#106×C₄₁	D₄	1	2	yes	—
79	#106×C₄₁	D₄	1	2	yes	—
80	#103×C₄₁	—	2	4	no	—
81	#103×C₄₁	—	2	4	no	—
82	#102×C₄₁	—	2	4	no	—
83	#102×C₄₁	—	2	4	no	—
84	#101×C₄₁	—	4	2	no	—
85	#100×C₄₁	—	4	2	no	—
86	#97×C₄₁	—	2	2	no	—
87	#97×C₄₁	—	2	1	no	—
88	#97×C₄₁	—	2	1	no	—
89	C₄×C₈×C₄₁	—	2	1	no	—
90	C₄×C₈×C₄₁	—	2	2	no	—
91	C₄×C₈×C₄₁	—	2	1	no	—
92	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
93	C₂⁴×C₄₁	—	2	2	no	—
94	C₂×Q₈×C₄₁	—	2	2	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	2	no	—
98	C₂×Q₈×C₄₁	—	2	2	no	—
99	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
100	C₂×D₄×C₄₁	—	2	2	no	—
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂×D₄×C₄₁	—	2	2	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	4	4	no	—
109	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₄₁	—	2	4	no	—
111	Q₁₆×C₄₁	—	2	4	no	—
112	SD₁₆×C₄₁	—	2	8	no	—
113	SD₁₆×C₄₁	—	2	8	no	—
114	D₈×C₄₁	—	2	4	no	—
115	D₈×C₄₁	—	2	4	no	—
116	M₁₆×C₄₁	—	2	1	no	—
117	M₁₆×C₄₁	—	2	2	no	—
118	M₁₆×C₄₁	—	2	1	no	—
119	M₁₆×C₄₁	—	2	1	no	—
120	M₁₆×C₄₁	—	2	2	no	—
121	M₁₆×C₄₁	—	2	1	no	—
122	C₂×C₈×C₄₁	—	2	1	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	1	no	—
125	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₄₁	#41	1	2	yes	—
132	C₂×C₈×C₄₁	#41	1	2	yes	—
133	C₄⋊C₄×C₄₁	—	4	4	no	—
134	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
136	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₄₁	—	2	1	no	—
138	C₂²⋊C₄×C₄₁	—	2	2	no	—
139	C₂²⋊C₄×C₄₁	—	2	1	no	—
140	C₂²⋊C₄×C₄₁	—	4	8	no	—
141	C₂²⋊C₄×C₄₁	—	4	4	no	—
142	C₄²×C₄₁	—	2	1	no	—
143	C₄²×C₄₁	—	2	2	no	—
144	C₄²×C₄₁	—	2	1	no	—
145	C₄²×C₄₁	—	2	1	no	—
146	C₄²×C₄₁	—	4	4	no	—
147	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
148	C₂³×C₄₁	—	2	4	no	—
149	C₂³×C₄₁	—	4	2	no	—
150	C₂³×C₄₁	—	4	2	no	—
151	C₂³×C₄₁	—	8	4	no	—
152	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
153	Q₈×C₄₁	—	2	4	no	—
154	Q₈×C₄₁	—	2	4	no	—
155	Q₈×C₄₁	—	4	2	no	—
156	Q₈×C₄₁	—	4	2	no	—
157	D₄×C₄₁	—	2	4	no	—
158	D₄×C₄₁	—	2	4	no	—
159	D₄×C₄₁	—	4	2	no	—
160	D₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	4	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	4	no	—
165	C₂×C₄×C₄₁	—	2	2	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	4	2	no	—
169	C₂×C₄×C₄₁	—	16	4	no	—
170	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
176	C₈×C₄₁	—	4	1	no	—
177	C₈×C₄₁	—	4	2	no	—
178	C₈×C₄₁	—	4	1	no	—
179	C₈×C₄₁	C₄×D₄	1	2	yes	—
180	C₈×C₄₁	C₄×D₄	1	2	yes	—
181	C₈×C₄₁	C₄×D₄	1	2	yes	—
182	C₈×C₄₁	C₄×D₄	1	2	yes	—
183	#23199	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₁	—	2	2	no	—
185	C₂²×C₄₁	—	4	4	no	—
186	C₂²×C₄₁	—	8	4	no	—
187	C₂²×C₄₁	—	8	4	no	—
188	C₂²×C₄₁	—	16	2	no	—
189	C₂²×C₄₁	#518	1	1	yes	characteristic
190	C₂²×C₄₁	D₄²	1	1	yes	characteristic
191	C₂²×C₄₁	#559	1	1	yes	characteristic
192	C₄×C₄₁	—	4	2	no	—
193	C₄×C₄₁	—	4	4	no	—
194	C₄×C₄₁	—	4	2	no	—
195	C₄×C₄₁	—	4	4	no	—
196	C₄×C₄₁	—	4	2	no	—
197	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₄₁	#550	1	1	yes	characteristic
200	C₄×C₄₁	#550	1	1	yes	characteristic
201	C₂×#495	C₂×C₄₁	1	1	yes	characteristic
202	#2950	C₂×C₄₁	1	1	yes	characteristic, complemented
203	#2949	C₂×C₄₁	1	2	yes	complemented
204	#2948	C₂×C₄₁	1	1	yes	characteristic
205	#1979	C₂×C₄₁	1	1	yes	characteristic, complemented
206	#1978	C₂×C₄₁	1	1	yes	characteristic
207	#1977	C₂×C₄₁	1	2	yes	complemented
208	#1888	C₂×C₄₁	1	2	yes	complemented
209	#1885	C₂×C₄₁	1	2	yes	complemented
210	#1772	C₂×C₄₁	1	1	yes	characteristic, complemented
211	#1772	C₂×C₄₁	1	1	yes	characteristic, complemented
212	C₂×C₄₁	—	2	1	no	—
213	C₂×C₄₁	—	2	1	no	—
214	C₂×C₄₁	—	8	4	no	—
215	C₂×C₄₁	#2366	1	1	yes	characteristic
216	C₂×C₄₁	#3290	1	2	yes	—
217	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
218	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
219	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
220	C₂×#124	C₂²×C₄₁	1	2	yes	—
221	#519	C₂²×C₄₁	1	2	yes	—
222	#518	C₂²×C₄₁	1	2	yes	—
223	#495	C₄×C₄₁	1	8	yes	complemented
224	#442	—	2	2	no	—
225	#441	—	2	2	no	—
226	#440	—	2	4	no	—
227	C₄×Q₁₆	—	2	2	no	—
228	C₄×SD₁₆	—	2	4	no	—
229	C₄×D₈	—	2	2	no	—
230	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
231	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
232	#427	C₂²×C₄₁	1	1	yes	characteristic
233	#427	C₂²×C₄₁	1	1	yes	characteristic
234	#419	C₂²×C₄₁	1	2	yes	—
235	#419	C₂²×C₄₁	1	2	yes	—
236	#418	C₂²×C₄₁	1	2	yes	—
237	#418	C₂²×C₄₁	1	2	yes	—
238	C₂×#101	C₂²×C₄₁	1	2	yes	—
239	C₂×#100	C₂²×C₄₁	1	2	yes	—
240	#405	C₂²×C₄₁	1	1	yes	characteristic
241	#405	C₂²×C₄₁	1	2	yes	—
242	#405	C₂²×C₄₁	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
244	#339	C₂²×C₄₁	1	1	yes	characteristic
245	#339	C₂²×C₄₁	1	2	yes	—
246	#339	C₂²×C₄₁	1	1	yes	characteristic
247	C₄₁	#23199	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
249	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×Q₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×SD₁₆	C₂×C₄×C₄₁	1	8	yes	complemented
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	—	2	2	no	—
261	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	—
262	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
263	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
264	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
267	#124	—	4	2	no	—
268	#124	C₂×C₄×C₄₁	1	8	yes	complemented
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	#117	—	4	2	no	—
274	#117	C₂³×C₄₁	1	1	yes	characteristic
275	#117	C₂³×C₄₁	1	2	yes	—
276	#117	C₂³×C₄₁	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	4	2	no	—
278	C₂×C₂²⋊C₄	—	4	2	no	—
279	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
280	#108	—	2	2	no	—
281	#108	—	2	2	no	—
282	#107	D₄×C₄₁	1	2	yes	—
283	#107	D₄×C₄₁	1	2	yes	—
284	#106	D₄×C₄₁	1	2	yes	—
285	#106	D₄×C₄₁	1	2	yes	—
286	#103	—	2	4	no	—
287	#103	—	2	4	no	—
288	#102	—	2	4	no	—
289	#102	—	2	4	no	—
290	#101	—	4	2	no	—
291	#100	—	4	2	no	—
292	#97	—	2	2	no	—
293	#97	—	2	1	no	—
294	#97	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
299	C₂⁴	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
316	Q₁₆	—	2	4	no	—
317	Q₁₆	—	2	4	no	—
318	SD₁₆	—	2	8	no	—
319	SD₁₆	—	2	8	no	—
320	D₈	—	2	4	no	—
321	D₈	—	2	4	no	—
322	M₁₆	—	2	1	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	1	no	—
325	M₁₆	—	2	1	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
332	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
333	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
336	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
337	C₂×C₈	#41×C₄₁	1	2	yes	—
338	C₂×C₈	#41×C₄₁	1	2	yes	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
341	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
342	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	4	8	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	4	4	no	—
353	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
354	C₂³	—	2	4	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	8	4	no	—
358	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	2	4	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	16	4	no	—
376	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
381	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
382	C₈	—	4	1	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	1	no	—
385	C₈	C₄×D₄×C₄₁	1	2	yes	—
386	C₈	C₄×D₄×C₄₁	1	2	yes	—
387	C₈	C₄×D₄×C₄₁	1	2	yes	—
388	C₈	C₄×D₄×C₄₁	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	4	no	—
392	C₂²	—	8	4	no	—
393	C₂²	—	16	2	no	—
394	C₂²	C₄₁×#518	1	1	yes	characteristic
395	C₂²	D₄²×C₄₁	1	1	yes	characteristic
396	C₂²	C₄₁×#559	1	1	yes	characteristic
397	C₄	—	4	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	4	no	—
401	C₄	—	4	2	no	—
402	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
403	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
404	C₄	C₄₁×#550	1	1	yes	characteristic
405	C₄	C₄₁×#550	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	8	4	no	—
409	C₂	C₄₁×#2366	1	1	yes	characteristic
410	C₂	C₄₁×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₈×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2950	C₂	semidirect
3. C₄₁×#2949	C₂	semidirect
5. C₄₁×#1979	C₂	semidirect
7. C₄₁×#1977	C₂	semidirect
8. C₄₁×#1888	C₂	semidirect
9. C₄₁×#1885	C₂	semidirect
10. C₄₁×#1772	C₂	semidirect
11. C₄₁×#1772	C₂	semidirect
18. C₄₁×#495	C₄	semidirect
47. C₂×Q₁₆×C₄₁	C₂×C₄	semidirect
51. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
62. #124×C₄₁	C₂×C₄	semidirect
92. C₄×C₈×C₄₁	C₂×C₄	semidirect
183. #23199	C₄₁	direct (N × H)
202. #2950	C₂×C₄₁	semidirect
203. #2949	C₂×C₄₁	semidirect
205. #1979	C₂×C₄₁	semidirect
207. #1977	C₂×C₄₁	semidirect
208. #1888	C₂×C₄₁	semidirect
209. #1885	C₂×C₄₁	semidirect
210. #1772	C₂×C₄₁	semidirect
211. #1772	C₂×C₄₁	semidirect
223. #495	C₄×C₄₁	semidirect
247. C₄₁	#23199	direct (N × H)
253. C₂×Q₁₆	C₂×C₄×C₄₁	semidirect
257. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
268. #124	C₂×C₄×C₄₁	semidirect
298. C₄×C₈	C₂×C₄×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×#495	2
C₄₁×#2950	2
C₄₁×#2949	2
C₄₁×#2948	2
C₄₁×#1979	2
C₄₁×#1978	2
C₄₁×#1977	2
C₄₁×#1888	2
C₄₁×#1885	2
C₄₁×#1772	2
#23199	41

Subgroups — C41×#23199 #23799400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23199 #23799400