Subgroups — C₂×C₄₁×#1392 #23788779

Order 10496.

750 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#413	C₂	1	2	yes	maximal
2	C₂×C₄₁×#408	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1392	C₂	1	4	yes	maximal, direct product factor
4	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
5	C₂²×M₁₆×C₄₁	—	2	2	no	—
6	C₂²×M₁₆×C₄₁	C₄	1	1	yes	characteristic
7	C₂³×C₈×C₄₁	C₄	1	1	yes	characteristic
8	C₄₁×#413	—	2	2	no	—
9	C₄₁×#413	—	2	2	no	—
10	C₄₁×#413	C₄	1	4	yes	—
11	C₄₁×#413	C₂²	1	4	yes	—
12	C₂×#101×C₄₁	—	2	2	no	—
13	C₂×#100×C₄₁	C₄	1	4	yes	—
14	C₄₁×#408	—	2	2	no	—
15	C₄₁×#408	C₄	1	2	yes	—
16	C₄₁×#408	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₄₁	—	2	2	no	—
18	C₂×#41×C₄₁	—	4	1	no	—
19	C₂×#41×C₄₁	—	4	1	no	—
20	C₂×#41×C₄₁	—	4	1	no	—
21	C₂×#41×C₄₁	—	4	1	no	—
22	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
23	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
24	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
25	C₂×#41×C₄₁	D₄	1	2	yes	—
26	C₂×#41×C₄₁	Q₈	1	1	yes	characteristic
27	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
28	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₄₁	Q₈	1	1	yes	characteristic
31	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₄₁	D₄	1	2	yes	—
33	C₂×M₁₆×C₄₁	—	2	1	no	—
34	C₂×M₁₆×C₄₁	—	2	4	no	—
35	C₂×M₁₆×C₄₁	—	2	4	no	—
36	C₂×M₁₆×C₄₁	—	2	4	no	—
37	C₂×M₁₆×C₄₁	—	4	2	no	—
38	C₂×M₁₆×C₄₁	—	4	2	no	—
39	C₂×M₁₆×C₄₁	—	4	2	no	—
40	C₂×M₁₆×C₄₁	—	4	1	no	—
41	C₂×M₁₆×C₄₁	—	4	1	no	—
42	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₄₁	—	2	1	no	—
44	C₂²×C₈×C₄₁	—	2	1	no	—
45	C₂²×C₈×C₄₁	—	2	1	no	—
46	C₂²×C₈×C₄₁	—	4	2	no	—
47	C₂²×C₈×C₄₁	—	4	1	no	—
48	C₂²×C₈×C₄₁	—	4	1	no	—
49	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
50	#101×C₄₁	—	2	4	no	—
51	#101×C₄₁	—	2	4	no	—
52	#100×C₄₁	—	2	4	no	—
53	#100×C₄₁	C₂×C₄	1	8	yes	—
54	C₂²⋊C₈×C₄₁	—	2	4	no	—
55	C₂²⋊C₈×C₄₁	—	2	4	no	—
56	C₂⁴×C₄₁	C₄²	1	1	yes	characteristic
57	C₂⁴×C₄₁	C₄⋊C₄	1	2	yes	—
58	#41×C₄₁	—	4	2	no	—
59	#41×C₄₁	—	4	2	no	—
60	#41×C₄₁	—	4	1	no	—
61	#41×C₄₁	—	4	1	no	—
62	#41×C₄₁	—	4	1	no	—
63	#41×C₄₁	—	4	1	no	—
64	#41×C₄₁	—	4	2	no	—
65	#41×C₄₁	—	4	2	no	—
66	#41×C₄₁	—	4	1	no	—
67	#41×C₄₁	—	4	1	no	—
68	#41×C₄₁	—	4	1	no	—
69	#41×C₄₁	—	4	1	no	—
70	C₂×Q₈×C₄₁	—	4	1	no	—
71	C₂×Q₈×C₄₁	—	4	1	no	—
72	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
73	C₂×Q₈×C₄₁	C₄⋊C₄	1	1	yes	characteristic
74	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
75	C₂×D₄×C₄₁	—	4	2	no	—
76	C₂×D₄×C₄₁	—	4	2	no	—
77	C₂×D₄×C₄₁	—	4	1	no	—
78	C₂×D₄×C₄₁	—	4	1	no	—
79	C₂×D₄×C₄₁	C₄²	1	2	yes	—
80	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
81	C₂×D₄×C₄₁	C₄⋊C₄	1	2	yes	—
82	C₂×D₄×C₄₁	C₄⋊C₄	1	2	yes	—
83	C₂×D₄×C₄₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
85	C₂×D₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₄₁	—	2	1	no	—
87	C₂²×C₄×C₄₁	—	2	1	no	—
88	C₂²×C₄×C₄₁	—	2	1	no	—
89	C₂²×C₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	—	2	1	no	—
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₁	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
105	M₁₆×C₄₁	—	2	8	no	—
106	M₁₆×C₄₁	—	4	4	no	—
107	M₁₆×C₄₁	—	4	4	no	—
108	M₁₆×C₄₁	—	4	4	no	—
109	M₁₆×C₄₁	—	4	2	no	—
110	M₁₆×C₄₁	—	4	2	no	—
111	C₂×C₈×C₄₁	—	2	2	no	—
112	C₂×C₈×C₄₁	—	2	2	no	—
113	C₂×C₈×C₄₁	—	4	2	no	—
114	C₂×C₈×C₄₁	—	4	4	no	—
115	C₂×C₈×C₄₁	—	4	4	no	—
116	C₂×C₈×C₄₁	—	4	4	no	—
117	C₂×C₈×C₄₁	—	4	1	no	—
118	C₂×C₈×C₄₁	—	4	1	no	—
119	C₂×C₈×C₄₁	—	4	1	no	—
120	C₂×C₈×C₄₁	—	4	1	no	—
121	C₂×C₈×C₄₁	—	4	2	no	—
122	C₂³×C₄₁	—	2	1	no	—
123	C₂³×C₄₁	—	2	1	no	—
124	C₂³×C₄₁	—	2	2	no	—
125	C₂³×C₄₁	—	2	2	no	—
126	C₂³×C₄₁	—	4	2	no	—
127	C₂³×C₄₁	—	4	4	no	—
128	C₂³×C₄₁	#95	1	1	yes	characteristic
129	C₂³×C₄₁	#95	1	2	yes	—
130	C₂³×C₄₁	#95	1	1	yes	characteristic
131	C₂³×C₄₁	C₂×C₄²	1	1	yes	characteristic
132	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
133	Q₈×C₄₁	—	4	2	no	—
134	Q₈×C₄₁	—	4	1	no	—
135	Q₈×C₄₁	—	4	1	no	—
136	D₄×C₄₁	—	4	2	no	—
137	D₄×C₄₁	—	4	2	no	—
138	D₄×C₄₁	—	4	2	no	—
139	D₄×C₄₁	—	4	2	no	—
140	D₄×C₄₁	—	4	1	no	—
141	D₄×C₄₁	—	4	2	no	—
142	D₄×C₄₁	—	4	1	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	1	no	—
150	C₂×C₄×C₄₁	—	2	1	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	1	no	—
154	C₂×C₄×C₄₁	—	2	1	no	—
155	C₂×C₄×C₄₁	—	2	1	no	—
156	C₂×C₄×C₄₁	—	2	1	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	1	no	—
159	C₂×C₄×C₄₁	—	2	1	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	#95	1	1	yes	characteristic
164	C₂×C₄×C₄₁	#95	1	2	yes	—
165	C₂×C₄×C₄₁	#95	1	1	yes	characteristic
166	C₂×C₄×C₄₁	#99	1	1	yes	characteristic
167	C₂×C₄×C₄₁	#99	1	1	yes	characteristic
168	C₂×C₄×C₄₁	#99	1	1	yes	characteristic
169	C₂×C₄×C₄₁	#99	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₈×C₄₁	—	4	8	no	—
174	C₈×C₄₁	—	4	2	no	—
175	C₈×C₄₁	—	4	2	no	—
176	C₂×#1392	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	2	1	no	—
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	1	no	—
181	C₂²×C₄₁	—	2	2	no	—
182	C₂²×C₄₁	—	4	1	no	—
183	C₂²×C₄₁	—	4	2	no	—
184	C₂²×C₄₁	—	4	1	no	—
185	C₂²×C₄₁	—	4	2	no	—
186	C₂²×C₄₁	—	4	2	no	—
187	C₂²×C₄₁	—	4	2	no	—
188	C₂²×C₄₁	—	4	4	no	—
189	C₂²×C₄₁	—	8	2	no	—
190	C₂²×C₄₁	#342	1	1	yes	characteristic
191	C₂²×C₄₁	#342	1	1	yes	characteristic
192	C₂²×C₄₁	C₂×#95	1	1	yes	characteristic
193	C₄×C₄₁	—	2	2	no	—
194	C₄×C₄₁	—	2	2	no	—
195	C₄×C₄₁	—	2	1	no	—
196	C₄×C₄₁	—	2	1	no	—
197	C₄×C₄₁	#342	1	1	yes	characteristic
198	C₄×C₄₁	#342	1	1	yes	characteristic
199	C₄×C₄₁	C₂×#99	1	1	yes	characteristic
200	C₄×C₄₁	C₂×#99	1	1	yes	characteristic
201	C₂×#413	C₂×C₄₁	1	2	yes	—
202	C₂×#408	C₂×C₄₁	1	1	yes	characteristic
203	#1392	C₂×C₄₁	1	4	yes	direct product factor
204	C₂×C₄₁	—	2	1	no	—
205	C₂×C₄₁	—	2	1	no	—
206	C₂×C₄₁	—	4	1	no	—
207	C₂×C₄₁	—	4	1	no	—
208	C₂×C₄₁	—	4	2	no	—
209	C₂×C₄₁	—	4	2	no	—
210	C₂×C₄₁	#1392	1	2	yes	direct product factor
211	C₂×C₄₁	C₂×#342	1	1	yes	characteristic
212	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
213	C₂²×M₁₆	—	2	2	no	—
214	C₂²×M₁₆	C₄×C₄₁	1	1	yes	characteristic
215	C₂³×C₈	C₄×C₄₁	1	1	yes	characteristic
216	#413	—	2	2	no	—
217	#413	—	2	2	no	—
218	#413	C₄×C₄₁	1	4	yes	—
219	#413	C₂²×C₄₁	1	4	yes	—
220	C₂×#101	—	2	2	no	—
221	C₂×#100	C₄×C₄₁	1	4	yes	—
222	#408	—	2	2	no	—
223	#408	C₄×C₄₁	1	2	yes	—
224	#408	C₂²×C₄₁	1	2	yes	—
225	C₂×C₂²⋊C₈	—	2	2	no	—
226	C₄₁	C₂×#1392	1	1	yes	characteristic, direct product factor, Sylow
227	C₂×#41	—	4	1	no	—
228	C₂×#41	—	4	1	no	—
229	C₂×#41	—	4	1	no	—
230	C₂×#41	—	4	1	no	—
231	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
232	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
233	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
234	C₂×#41	D₄×C₄₁	1	2	yes	—
235	C₂×#41	Q₈×C₄₁	1	1	yes	characteristic
236	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
237	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
238	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
239	C₂²×D₄	Q₈×C₄₁	1	1	yes	characteristic
240	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
241	C₂³×C₄	D₄×C₄₁	1	2	yes	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	2	4	no	—
244	C₂×M₁₆	—	2	4	no	—
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	—	4	2	no	—
247	C₂×M₁₆	—	4	2	no	—
248	C₂×M₁₆	—	4	2	no	—
249	C₂×M₁₆	—	4	1	no	—
250	C₂×M₁₆	—	4	1	no	—
251	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	4	2	no	—
256	C₂²×C₈	—	4	1	no	—
257	C₂²×C₈	—	4	1	no	—
258	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
259	#101	—	2	4	no	—
260	#101	—	2	4	no	—
261	#100	—	2	4	no	—
262	#100	C₂×C₄×C₄₁	1	8	yes	—
263	C₂²⋊C₈	—	2	4	no	—
264	C₂²⋊C₈	—	2	4	no	—
265	C₂⁴	C₄²×C₄₁	1	1	yes	characteristic
266	C₂⁴	C₄⋊C₄×C₄₁	1	2	yes	—
267	#41	—	4	2	no	—
268	#41	—	4	2	no	—
269	#41	—	4	1	no	—
270	#41	—	4	1	no	—
271	#41	—	4	1	no	—
272	#41	—	4	1	no	—
273	#41	—	4	2	no	—
274	#41	—	4	2	no	—
275	#41	—	4	1	no	—
276	#41	—	4	1	no	—
277	#41	—	4	1	no	—
278	#41	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
282	C₂×Q₈	C₄⋊C₄×C₄₁	1	1	yes	characteristic
283	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	C₄²×C₄₁	1	2	yes	—
289	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
290	C₂×D₄	C₄⋊C₄×C₄₁	1	2	yes	—
291	C₂×D₄	C₄⋊C₄×C₄₁	1	2	yes	—
292	C₂×D₄	C₄⋊C₄×C₄₁	1	1	yes	characteristic
293	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
294	C₂×D₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	C₄²×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
305	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
306	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
307	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
308	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
309	C₂²×C₄	C₄⋊C₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₄⋊C₄×C₄₁	1	1	yes	characteristic
311	C₂²×C₄	C₄⋊C₄×C₄₁	1	1	yes	characteristic
312	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
314	M₁₆	—	2	8	no	—
315	M₁₆	—	4	4	no	—
316	M₁₆	—	4	4	no	—
317	M₁₆	—	4	4	no	—
318	M₁₆	—	4	2	no	—
319	M₁₆	—	4	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	4	no	—
324	C₂×C₈	—	4	4	no	—
325	C₂×C₈	—	4	4	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	2	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	#95×C₄₁	1	1	yes	characteristic
338	C₂³	#95×C₄₁	1	2	yes	—
339	C₂³	#95×C₄₁	1	1	yes	characteristic
340	C₂³	C₂×C₄²×C₄₁	1	1	yes	characteristic
341	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	1	no	—
344	Q₈	—	4	1	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	#95×C₄₁	1	1	yes	characteristic
373	C₂×C₄	#95×C₄₁	1	2	yes	—
374	C₂×C₄	#95×C₄₁	1	1	yes	characteristic
375	C₂×C₄	#99×C₄₁	1	1	yes	characteristic
376	C₂×C₄	#99×C₄₁	1	1	yes	characteristic
377	C₂×C₄	#99×C₄₁	1	1	yes	characteristic
378	C₂×C₄	#99×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
382	C₈	—	4	8	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	2	no	—
398	C₂²	C₄₁×#342	1	1	yes	characteristic
399	C₂²	C₄₁×#342	1	1	yes	characteristic
400	C₂²	C₂×#95×C₄₁	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	C₄₁×#342	1	1	yes	characteristic
406	C₄	C₄₁×#342	1	1	yes	characteristic
407	C₄	C₂×#99×C₄₁	1	1	yes	characteristic
408	C₄	C₂×#99×C₄₁	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	4	1	no	—
412	C₂	—	4	1	no	—
413	C₂	—	4	2	no	—
414	C₂	—	4	2	no	—
415	C₂	C₄₁×#1392	1	2	yes	direct product factor
416	C₂	C₂×C₄₁×#342	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	#99
commutator	C₂³	C₂×C₄²×C₄₁
Frattini, cosocle	C₂×#41	C₂³×C₄₁
socle	C₂²×C₄₁	#342
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1392	C₂	direct (N × H)
176. C₂×#1392	C₄₁	direct (N × H)
203. #1392	C₂×C₄₁	direct (N × H)
210. C₂×C₄₁	#1392	direct (N × H)
226. C₄₁	C₂×#1392	direct (N × H)
415. C₂	C₄₁×#1392	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×#413	2
C₂×C₄₁×#408	2
C₄₁×#1392	2
C₂×#1392	41

Subgroups — C2×C41×#1392 #23788779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1392 #23788779