Subgroups — C₄₁×#17738 #23793939

Order 10496.

1230 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2920	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1560	C₂	1	4	yes	maximal, complemented
4	C₄₁×#1558	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1555	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1543	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₄₁	C₄	1	2	yes	—
8	C₄₁×#532	—	2	2	no	—
9	C₄₁×#532	—	2	2	no	—
10	C₄₁×#532	C₄	1	2	yes	—
11	C₄₁×#532	C₄	1	2	yes	—
12	C₄₁×#532	C₂²	1	2	yes	—
13	C₄₁×#532	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₁	C₄	1	2	yes	—
17	C₂×#121×C₄₁	—	2	2	no	—
18	C₂×C₄×D₄×C₄₁	—	2	2	no	—
19	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#432	—	2	2	no	—
21	C₄₁×#432	C₂²	1	4	yes	—
22	C₄₁×#431	—	2	2	no	—
23	C₄₁×#431	C₂²	1	4	yes	complemented
24	C₄₁×#423	C₂²	1	4	yes	complemented
25	C₄₁×#407	—	2	2	no	—
26	C₄×M₁₆×C₄₁	—	2	2	no	—
27	C₄₁×#333	C₂²	1	8	yes	complemented
28	C₄₁×#331	C₂²	1	8	yes	complemented
29	C₂×#41×C₄₁	—	2	2	no	—
30	C₂×#41×C₄₁	—	2	2	no	—
31	C₂×#41×C₄₁	—	4	8	no	—
32	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
33	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
34	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₄₁	—	2	2	no	—
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₄₁	—	2	2	no	—
39	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₁	D₄	1	2	yes	—
41	C₂×M₁₆×C₄₁	—	2	4	no	—
42	C₄⋊Q₈×C₄₁	—	2	2	no	—
43	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
44	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
45	#127×C₄₁	—	2	2	no	—
46	#127×C₄₁	C₂×C₄	1	2	yes	—
47	#127×C₄₁	C₂³	1	2	yes	—
48	#124×C₄₁	—	2	4	no	—
49	#124×C₄₁	C₂×C₄	1	4	yes	—
50	#124×C₄₁	C₂×C₄	1	4	yes	—
51	#121×C₄₁	—	2	4	no	—
52	#121×C₄₁	—	2	4	no	—
53	#121×C₄₁	—	2	4	no	—
54	#121×C₄₁	—	2	4	no	—
55	C₄×D₄×C₄₁	—	2	4	no	—
56	C₄×D₄×C₄₁	—	2	4	no	—
57	C₄×D₄×C₄₁	—	2	4	no	—
58	C₄×D₄×C₄₁	—	2	4	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
61	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₁	D₄	1	2	yes	—
65	C₂×C₄²×C₄₁	D₄	1	2	yes	—
66	C₂×C₄²×C₄₁	D₄	1	2	yes	—
67	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₁	—	2	4	no	—
71	C₄⋊C₈×C₄₁	C₂³	1	8	yes	—
72	C₂²⋊C₈×C₄₁	—	2	4	no	—
73	C₂²⋊C₈×C₄₁	—	2	4	no	—
74	#97×C₄₁	—	2	4	no	—
75	C₄×C₈×C₄₁	—	2	4	no	—
76	C₂⁴×C₄₁	—	2	2	no	—
77	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
78	#41×C₄₁	—	4	8	no	—
79	#41×C₄₁	—	4	8	no	—
80	#41×C₄₁	—	4	8	no	—
81	#41×C₄₁	—	4	8	no	—
82	C₂×Q₈×C₄₁	—	2	2	no	—
83	C₂×Q₈×C₄₁	—	4	4	no	—
84	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
85	C₂×D₄×C₄₁	—	2	4	no	—
86	C₂×D₄×C₄₁	—	2	4	no	—
87	C₂×D₄×C₄₁	—	2	4	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	2	4	no	—
90	C₂×D₄×C₄₁	—	4	4	no	—
91	C₂×D₄×C₄₁	—	4	8	no	—
92	C₂×D₄×C₄₁	—	4	8	no	—
93	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	2	4	no	—
98	C₂²×C₄×C₄₁	—	4	4	no	—
99	C₂²×C₄×C₄₁	—	4	8	no	—
100	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
105	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
112	M₁₆×C₄₁	—	4	8	no	—
113	C₂×C₈×C₄₁	—	2	8	no	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	2	4	no	—
116	C₂²⋊C₄×C₄₁	—	2	8	no	—
117	C₂²⋊C₄×C₄₁	—	2	8	no	—
118	C₄²×C₄₁	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₄₁	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₄₁	C₂²⋊C₄	1	2	yes	—
121	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₄₁	C₂×D₄	1	2	yes	—
125	C₄²×C₄₁	C₂×D₄	1	2	yes	—
126	C₄²×C₄₁	C₂×D₄	1	2	yes	—
127	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
128	C₂³×C₄₁	—	2	2	no	—
129	C₂³×C₄₁	—	2	4	no	—
130	C₂³×C₄₁	—	4	2	no	—
131	C₂³×C₄₁	—	4	8	no	—
132	C₂³×C₄₁	—	4	4	no	—
133	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	Q₈×C₄₁	—	4	4	no	—
137	Q₈×C₄₁	—	4	4	no	—
138	D₄×C₄₁	—	4	4	no	—
139	D₄×C₄₁	—	4	8	no	—
140	D₄×C₄₁	—	4	4	no	—
141	D₄×C₄₁	—	4	8	no	—
142	D₄×C₄₁	—	4	8	no	—
143	D₄×C₄₁	—	4	8	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	4	no	—
146	C₂×C₄×C₄₁	—	2	4	no	—
147	C₂×C₄×C₄₁	—	2	4	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	4	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	4	no	—
157	C₂×C₄×C₄₁	—	4	8	no	—
158	C₂×C₄×C₄₁	—	4	8	no	—
159	C₂×C₄×C₄₁	#100	1	4	yes	—
160	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
168	C₈×C₄₁	—	4	8	no	—
169	#17738	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₄₁	—	2	2	no	—
171	C₂²×C₄₁	—	2	1	no	—
172	C₂²×C₄₁	—	2	1	no	—
173	C₂²×C₄₁	—	2	2	no	—
174	C₂²×C₄₁	—	2	2	no	—
175	C₂²×C₄₁	—	4	4	no	—
176	C₂²×C₄₁	—	4	4	no	—
177	C₂²×C₄₁	—	4	8	no	—
178	C₂²×C₄₁	—	8	8	no	—
179	C₂²×C₄₁	C₂×#100	1	2	yes	—
180	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
181	C₄×C₄₁	—	2	1	no	—
182	C₄×C₄₁	—	2	1	no	—
183	C₄×C₄₁	—	2	2	no	—
184	C₄×C₄₁	—	2	2	no	—
185	C₄×C₄₁	—	2	2	no	—
186	C₄×C₄₁	—	4	4	no	—
187	C₄×C₄₁	C₂×#100	1	2	yes	—
188	C₄×C₄₁	C₂×#100	1	2	yes	—
189	C₄×C₄₁	#575	1	4	yes	—
190	C₂×#532	C₂×C₄₁	1	1	yes	characteristic
191	#2920	C₂×C₄₁	1	2	yes	complemented
192	#1560	C₂×C₄₁	1	4	yes	complemented
193	#1558	C₂×C₄₁	1	2	yes	complemented
194	#1555	C₂×C₄₁	1	2	yes	complemented
195	#1543	C₂×C₄₁	1	4	yes	complemented
196	C₂×C₄₁	—	2	2	no	—
197	C₂×C₄₁	—	4	1	no	—
198	C₂×C₄₁	—	4	1	no	—
199	C₂×C₄₁	—	8	4	no	—
200	C₂×C₄₁	C₂²×#100	1	1	yes	characteristic
201	C₂×C₄₁	#2896	1	2	yes	—
202	C₂²×#41	C₄×C₄₁	1	2	yes	—
203	#532	—	2	2	no	—
204	#532	—	2	2	no	—
205	#532	C₄×C₄₁	1	2	yes	—
206	#532	C₄×C₄₁	1	2	yes	—
207	#532	C₂²×C₄₁	1	2	yes	—
208	#532	C₂²×C₄₁	1	2	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
210	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
211	C₂×#124	C₄×C₄₁	1	2	yes	—
212	C₂×#121	—	2	2	no	—
213	C₂×C₄×D₄	—	2	2	no	—
214	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
215	#432	—	2	2	no	—
216	#432	C₂²×C₄₁	1	4	yes	—
217	#431	—	2	2	no	—
218	#431	C₂²×C₄₁	1	4	yes	complemented
219	#423	C₂²×C₄₁	1	4	yes	complemented
220	#407	—	2	2	no	—
221	C₄×M₁₆	—	2	2	no	—
222	#333	C₂²×C₄₁	1	8	yes	complemented
223	#331	C₂²×C₄₁	1	8	yes	complemented
224	C₄₁	#17738	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	4	8	no	—
228	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
229	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
230	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
231	C₂²×D₄	—	2	2	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₄₁	1	2	yes	—
237	C₂×M₁₆	—	2	4	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
240	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
241	#127	—	2	2	no	—
242	#127	C₂×C₄×C₄₁	1	2	yes	—
243	#127	C₂³×C₄₁	1	2	yes	—
244	#124	—	2	4	no	—
245	#124	C₂×C₄×C₄₁	1	4	yes	—
246	#124	C₂×C₄×C₄₁	1	4	yes	—
247	#121	—	2	4	no	—
248	#121	—	2	4	no	—
249	#121	—	2	4	no	—
250	#121	—	2	4	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	—	2	4	no	—
253	C₄×D₄	—	2	4	no	—
254	C₄×D₄	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	4	no	—
257	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
258	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₄₁	1	2	yes	—
261	C₂×C₄²	D₄×C₄₁	1	2	yes	—
262	C₂×C₄²	D₄×C₄₁	1	2	yes	—
263	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
266	C₄⋊C₈	—	2	4	no	—
267	C₄⋊C₈	C₂³×C₄₁	1	8	yes	—
268	C₂²⋊C₈	—	2	4	no	—
269	C₂²⋊C₈	—	2	4	no	—
270	#97	—	2	4	no	—
271	C₄×C₈	—	2	4	no	—
272	C₂⁴	—	2	2	no	—
273	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
274	#41	—	4	8	no	—
275	#41	—	4	8	no	—
276	#41	—	4	8	no	—
277	#41	—	4	8	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	4	4	no	—
280	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	4	4	no	—
287	C₂×D₄	—	4	8	no	—
288	C₂×D₄	—	4	8	no	—
289	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	4	8	no	—
296	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
297	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
299	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
300	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
301	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
308	M₁₆	—	4	8	no	—
309	C₂×C₈	—	2	8	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	8	no	—
313	C₂²⋊C₄	—	2	8	no	—
314	C₄²	C₂²⋊C₄×C₄₁	1	2	yes	—
315	C₄²	C₂²⋊C₄×C₄₁	1	2	yes	—
316	C₄²	C₂²⋊C₄×C₄₁	1	2	yes	—
317	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
318	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
319	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₄₁	1	2	yes	—
321	C₄²	C₂×D₄×C₄₁	1	2	yes	—
322	C₄²	C₂×D₄×C₄₁	1	2	yes	—
323	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	4	4	no	—
329	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
330	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
331	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
332	Q₈	—	4	4	no	—
333	Q₈	—	4	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	4	no	—
336	D₄	—	4	8	no	—
337	D₄	—	4	8	no	—
338	D₄	—	4	8	no	—
339	D₄	—	4	8	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	#100×C₄₁	1	4	yes	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
357	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
360	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
362	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
363	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
364	C₈	—	4	8	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	8	8	no	—
374	C₂²	C₂×#100×C₄₁	1	2	yes	—
375	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	4	no	—
382	C₄	C₂×#100×C₄₁	1	2	yes	—
383	C₄	C₂×#100×C₄₁	1	2	yes	—
384	C₄	C₄₁×#575	1	4	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	4	1	no	—
387	C₂	—	4	1	no	—
388	C₂	—	8	4	no	—
389	C₂	C₂²×#100×C₄₁	1	1	yes	characteristic
390	C₂	C₄₁×#2896	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
prime radical	C₂×C₄₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2920	C₂	semidirect
3. C₄₁×#1560	C₂	semidirect
4. C₄₁×#1558	C₂	semidirect
5. C₄₁×#1555	C₂	semidirect
6. C₄₁×#1543	C₂	semidirect
23. C₄₁×#431	C₂²	semidirect
24. C₄₁×#423	C₂²	semidirect
27. C₄₁×#333	C₂²	semidirect
28. C₄₁×#331	C₂²	semidirect
169. #17738	C₄₁	direct (N × H)
191. #2920	C₂×C₄₁	semidirect
192. #1560	C₂×C₄₁	semidirect
193. #1558	C₂×C₄₁	semidirect
194. #1555	C₂×C₄₁	semidirect
195. #1543	C₂×C₄₁	semidirect
218. #431	C₂²×C₄₁	semidirect
219. #423	C₂²×C₄₁	semidirect
222. #333	C₂²×C₄₁	semidirect
223. #331	C₂²×C₄₁	semidirect
224. C₄₁	#17738	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×#532	2
C₄₁×#2920	2
C₄₁×#1560	2
C₄₁×#1558	2
C₄₁×#1555	2
C₄₁×#1543	2
#17738	41

Subgroups — C41×#17738 #23793939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17738 #23793939