Subgroups — C₄₁×#3270 #19107050

Order 5248.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#137×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#548	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₄₁	C₂²	1	1	yes	characteristic
20	#137×C₄₁	—	2	4	no	—
21	C₂×Q₁₆×C₄₁	—	2	4	no	—
22	C₂×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
32	C₂²×C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄⋊Q₈×C₄₁	—	2	1	no	—
34	C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
35	#124×C₄₁	—	2	1	no	—
36	#124×C₄₁	C₂²	1	1	yes	characteristic
37	C₂²⋊Q₈×C₄₁	—	2	1	no	—
38	C₂²⋊Q₈×C₄₁	—	2	1	no	—
39	C₂²⋊Q₈×C₄₁	—	2	1	no	—
40	C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
42	C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
43	#121×C₄₁	—	2	1	no	—
44	#121×C₄₁	C₂²	1	1	yes	characteristic
45	C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
46	C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
47	C₄×D₄×C₄₁	—	2	1	no	—
48	C₄×D₄×C₄₁	—	2	1	no	—
49	C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
50	#106×C₄₁	C₂²	1	1	yes	characteristic
51	C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
52	#103×C₄₁	C₂²	1	1	yes	characteristic
53	#103×C₄₁	C₂²	1	1	yes	characteristic
54	#103×C₄₁	C₂²	1	1	yes	characteristic
55	#103×C₄₁	C₂²	1	1	yes	characteristic
56	#103×C₄₁	C₂²	1	1	yes	characteristic
57	#102×C₄₁	C₂²	1	1	yes	characteristic
58	C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
60	#97×C₄₁	C₂²	1	1	yes	characteristic
61	#41×C₄₁	—	2	2	no	—
62	#41×C₄₁	—	4	1	no	—
63	C₂×Q₈×C₄₁	—	2	1	no	—
64	C₂×Q₈×C₄₁	—	2	1	no	—
65	C₂×Q₈×C₄₁	—	2	1	no	—
66	C₂×Q₈×C₄₁	—	2	2	no	—
67	C₂×Q₈×C₄₁	—	2	2	no	—
68	C₂×Q₈×C₄₁	—	2	2	no	—
69	C₂×Q₈×C₄₁	—	4	1	no	—
70	C₂×Q₈×C₄₁	—	4	1	no	—
71	C₂×Q₈×C₄₁	—	4	1	no	—
72	C₂×Q₈×C₄₁	C₂³	1	1	yes	characteristic
73	C₂×Q₈×C₄₁	C₂³	1	1	yes	characteristic
74	C₂×Q₈×C₄₁	C₂³	1	1	yes	characteristic
75	C₂×Q₈×C₄₁	C₂³	1	1	yes	characteristic
76	C₂×Q₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₄₁	—	2	1	no	—
78	C₂×D₄×C₄₁	—	2	1	no	—
79	C₂×D₄×C₄₁	D₄	1	1	yes	characteristic
80	C₂×D₄×C₄₁	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₄₁	—	2	1	no	—
82	C₂²×C₄×C₄₁	—	2	1	no	—
83	C₂²×C₄×C₄₁	—	2	1	no	—
84	C₂²×C₄×C₄₁	—	2	1	no	—
85	C₂²×C₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₄₁	C₂³	1	1	yes	characteristic
87	Q₁₆×C₄₁	—	2	2	no	—
88	Q₁₆×C₄₁	—	2	2	no	—
89	Q₁₆×C₄₁	—	2	2	no	—
90	Q₁₆×C₄₁	—	2	2	no	—
91	Q₁₆×C₄₁	—	4	1	no	—
92	Q₁₆×C₄₁	D₄	1	4	yes	complemented
93	SD₁₆×C₄₁	—	2	2	no	—
94	SD₁₆×C₄₁	—	2	2	no	—
95	SD₁₆×C₄₁	—	4	1	no	—
96	M₁₆×C₄₁	—	2	2	no	—
97	C₂×C₈×C₄₁	—	2	2	no	—
98	C₂×C₈×C₄₁	C₂³	1	1	yes	characteristic
99	C₂×C₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₂×C₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₂×C₈×C₄₁	C₂³	1	1	yes	characteristic
102	C₄⋊C₄×C₄₁	—	2	1	no	—
103	C₄⋊C₄×C₄₁	—	2	1	no	—
104	C₄⋊C₄×C₄₁	—	2	1	no	—
105	C₄⋊C₄×C₄₁	—	2	1	no	—
106	C₄⋊C₄×C₄₁	—	2	1	no	—
107	C₄⋊C₄×C₄₁	—	2	1	no	—
108	C₄⋊C₄×C₄₁	—	2	1	no	—
109	C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
110	C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
112	C₂²⋊C₄×C₄₁	—	2	1	no	—
113	C₂²⋊C₄×C₄₁	—	2	1	no	—
114	C₂²⋊C₄×C₄₁	—	2	1	no	—
115	C₂²⋊C₄×C₄₁	—	2	1	no	—
116	C₂²⋊C₄×C₄₁	—	2	1	no	—
117	C₂²⋊C₄×C₄₁	—	2	1	no	—
118	C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
119	C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
120	C₄²×C₄₁	—	2	1	no	—
121	C₄²×C₄₁	—	2	1	no	—
122	C₄²×C₄₁	C₂³	1	1	yes	characteristic
123	C₂³×C₄₁	—	2	1	no	—
124	C₂³×C₄₁	C₂×D₄	1	1	yes	characteristic
125	C₂³×C₄₁	C₂×D₄	1	1	yes	characteristic
126	Q₈×C₄₁	—	2	1	no	—
127	Q₈×C₄₁	—	2	1	no	—
128	Q₈×C₄₁	—	2	1	no	—
129	Q₈×C₄₁	—	2	1	no	—
130	Q₈×C₄₁	—	2	1	no	—
131	Q₈×C₄₁	—	2	1	no	—
132	Q₈×C₄₁	—	2	1	no	—
133	Q₈×C₄₁	—	2	1	no	—
134	Q₈×C₄₁	—	4	2	no	—
135	Q₈×C₄₁	—	4	2	no	—
136	Q₈×C₄₁	—	4	2	no	—
137	Q₈×C₄₁	C₂×D₄	1	2	yes	—
138	Q₈×C₄₁	C₂×D₄	1	2	yes	—
139	D₄×C₄₁	—	2	2	no	—
140	D₄×C₄₁	—	2	1	no	—
141	D₄×C₄₁	—	2	1	no	—
142	D₄×C₄₁	—	4	2	no	—
143	D₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	2	1	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	2	1	no	—
148	C₂×C₄×C₄₁	—	2	1	no	—
149	C₂×C₄×C₄₁	—	2	1	no	—
150	C₂×C₄×C₄₁	—	2	1	no	—
151	C₂×C₄×C₄₁	—	2	1	no	—
152	C₂×C₄×C₄₁	—	2	1	no	—
153	C₂×C₄×C₄₁	—	2	1	no	—
154	C₂×C₄×C₄₁	—	2	1	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	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
164	C₈×C₄₁	—	2	1	no	—
165	C₈×C₄₁	—	2	1	no	—
166	C₈×C₄₁	—	2	1	no	—
167	C₈×C₄₁	C₂×D₄	1	2	yes	—
168	C₂²×C₄₁	—	2	1	no	—
169	C₂²×C₄₁	—	2	1	no	—
170	C₂²×C₄₁	—	2	1	no	—
171	C₂²×C₄₁	—	2	1	no	—
172	C₂²×C₄₁	—	2	1	no	—
173	C₂²×C₄₁	—	4	1	no	—
174	C₂²×C₄₁	—	4	1	no	—
175	C₂²×C₄₁	—	4	1	no	—
176	C₂²×C₄₁	#137	1	2	yes	complemented
177	C₂²×C₄₁	C₂²×D₄	1	1	yes	characteristic
178	C₄×C₄₁	—	2	1	no	—
179	C₄×C₄₁	—	2	1	no	—
180	C₄×C₄₁	—	2	2	no	—
181	C₄×C₄₁	—	2	2	no	—
182	C₄×C₄₁	—	2	1	no	—
183	C₄×C₄₁	—	2	1	no	—
184	C₄×C₄₁	—	4	1	no	—
185	C₄×C₄₁	—	4	1	no	—
186	C₄×C₄₁	—	4	1	no	—
187	C₄×C₄₁	—	4	1	no	—
188	C₄×C₄₁	—	4	1	no	—
189	C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
190	C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
191	#3270	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₄₁	—	2	2	no	—
193	C₂×C₄₁	—	4	1	no	—
194	C₂×C₄₁	—	8	1	no	—
195	C₂×C₄₁	D₄²	1	1	yes	characteristic
196	C₂×C₄₁	C₂×#137	1	1	yes	characteristic
197	C₂×C₄₁	#578	1	1	yes	characteristic
198	C₂×#137	C₂×C₄₁	1	1	yes	characteristic, complemented
199	C₂²×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
200	D₄×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
201	#548	C₂×C₄₁	1	1	yes	characteristic
202	#497	C₂×C₄₁	1	1	yes	characteristic, complemented
203	#470	C₂×C₄₁	1	1	yes	characteristic, complemented
204	#465	C₂×C₄₁	1	1	yes	characteristic, complemented
205	#464	C₂×C₄₁	1	1	yes	characteristic, complemented
206	#462	C₂×C₄₁	1	1	yes	characteristic, complemented
207	#452	C₂×C₄₁	1	1	yes	characteristic, complemented
208	#451	C₂×C₄₁	1	1	yes	characteristic, complemented
209	#451	C₂×C₄₁	1	1	yes	characteristic, complemented
210	#448	C₂×C₄₁	1	1	yes	characteristic, complemented
211	#441	C₂×C₄₁	1	1	yes	characteristic, complemented
212	#435	C₂×C₄₁	1	1	yes	characteristic, complemented
213	C₄₁	#3270	1	1	yes	characteristic, direct product factor, Sylow
214	C₂×#41	C₂²×C₄₁	1	1	yes	characteristic
215	C₂²×Q₈	C₂²×C₄₁	1	1	yes	characteristic
216	C₂²×Q₈	C₂²×C₄₁	1	1	yes	characteristic
217	C₂²×Q₈	C₂²×C₄₁	1	1	yes	characteristic
218	#137	—	2	4	no	—
219	C₂×Q₁₆	—	2	4	no	—
220	C₂×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
221	C₂×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
222	C₂×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
223	C₂×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
227	C₂×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
228	C₂×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
230	C₂²×C₈	C₂²×C₄₁	1	1	yes	characteristic
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
233	#124	—	2	1	no	—
234	#124	C₂²×C₄₁	1	1	yes	characteristic
235	C₂²⋊Q₈	—	2	1	no	—
236	C₂²⋊Q₈	—	2	1	no	—
237	C₂²⋊Q₈	—	2	1	no	—
238	C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
239	C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
240	C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
241	#121	—	2	1	no	—
242	#121	C₂²×C₄₁	1	1	yes	characteristic
243	C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
244	C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
248	#106	C₂²×C₄₁	1	1	yes	characteristic
249	C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
250	#103	C₂²×C₄₁	1	1	yes	characteristic
251	#103	C₂²×C₄₁	1	1	yes	characteristic
252	#103	C₂²×C₄₁	1	1	yes	characteristic
253	#103	C₂²×C₄₁	1	1	yes	characteristic
254	#103	C₂²×C₄₁	1	1	yes	characteristic
255	#102	C₂²×C₄₁	1	1	yes	characteristic
256	C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
257	C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
258	#97	C₂²×C₄₁	1	1	yes	characteristic
259	#41	—	2	2	no	—
260	#41	—	4	1	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	1	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	4	1	no	—
268	C₂×Q₈	—	4	1	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂×Q₈	C₂³×C₄₁	1	1	yes	characteristic
271	C₂×Q₈	C₂³×C₄₁	1	1	yes	characteristic
272	C₂×Q₈	C₂³×C₄₁	1	1	yes	characteristic
273	C₂×Q₈	C₂³×C₄₁	1	1	yes	characteristic
274	C₂×Q₈	C₂³×C₄₁	1	1	yes	characteristic
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	D₄×C₄₁	1	1	yes	characteristic
278	C₂×D₄	C₂³×C₄₁	1	1	yes	characteristic
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	C₂³×C₄₁	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₄₁	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	Q₁₆	—	2	2	no	—
287	Q₁₆	—	2	2	no	—
288	Q₁₆	—	2	2	no	—
289	Q₁₆	—	4	1	no	—
290	Q₁₆	D₄×C₄₁	1	4	yes	complemented
291	SD₁₆	—	2	2	no	—
292	SD₁₆	—	2	2	no	—
293	SD₁₆	—	4	1	no	—
294	M₁₆	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	C₂³×C₄₁	1	1	yes	characteristic
297	C₂×C₈	C₂³×C₄₁	1	1	yes	characteristic
298	C₂×C₈	C₂³×C₄₁	1	1	yes	characteristic
299	C₂×C₈	C₂³×C₄₁	1	1	yes	characteristic
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
308	C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
309	C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
310	C₂²⋊C₄	—	2	1	no	—
311	C₂²⋊C₄	—	2	1	no	—
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	2	1	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
317	C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	C₂³×C₄₁	1	1	yes	characteristic
321	C₂³	—	2	1	no	—
322	C₂³	C₂×D₄×C₄₁	1	1	yes	characteristic
323	C₂³	C₂×D₄×C₄₁	1	1	yes	characteristic
324	Q₈	—	2	1	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	2	1	no	—
330	Q₈	—	2	1	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	4	2	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	C₂×D₄×C₄₁	1	2	yes	—
336	Q₈	C₂×D₄×C₄₁	1	2	yes	—
337	D₄	—	2	2	no	—
338	D₄	—	2	1	no	—
339	D₄	—	2	1	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
358	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
360	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
361	C₂×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	C₂×D₄×C₄₁	1	2	yes	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	#137×C₄₁	1	2	yes	complemented
375	C₂²	C₂²×D₄×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	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	1	no	—
387	C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
388	C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	4	1	no	—
391	C₂	—	8	1	no	—
392	C₂	D₄²×C₄₁	1	1	yes	characteristic
393	C₂	C₂×#137×C₄₁	1	1	yes	characteristic
394	C₂	C₄₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#137×C₄₁	C₂	semidirect
2. C₂²×Q₁₆×C₄₁	C₂	semidirect
3. D₄×Q₈×C₄₁	C₂	semidirect
5. C₄₁×#497	C₂	semidirect
6. C₄₁×#470	C₂	semidirect
7. C₄₁×#465	C₂	semidirect
8. C₄₁×#464	C₂	semidirect
9. C₄₁×#462	C₂	semidirect
10. C₄₁×#452	C₂	semidirect
11. C₄₁×#451	C₂	semidirect
12. C₄₁×#451	C₂	semidirect
13. C₄₁×#448	C₂	semidirect
14. C₄₁×#441	C₂	semidirect
15. C₄₁×#435	C₂	semidirect
92. Q₁₆×C₄₁	D₄	semidirect
176. C₂²×C₄₁	#137	semidirect
191. #3270	C₄₁	direct (N × H)
198. C₂×#137	C₂×C₄₁	semidirect
199. C₂²×Q₁₆	C₂×C₄₁	semidirect
200. D₄×Q₈	C₂×C₄₁	semidirect
202. #497	C₂×C₄₁	semidirect
203. #470	C₂×C₄₁	semidirect
204. #465	C₂×C₄₁	semidirect
205. #464	C₂×C₄₁	semidirect
206. #462	C₂×C₄₁	semidirect
207. #452	C₂×C₄₁	semidirect
208. #451	C₂×C₄₁	semidirect
209. #451	C₂×C₄₁	semidirect
210. #448	C₂×C₄₁	semidirect
211. #441	C₂×C₄₁	semidirect
212. #435	C₂×C₄₁	semidirect
213. C₄₁	#3270	direct (N × H)
290. Q₁₆	D₄×C₄₁	semidirect
374. C₂²	#137×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#137×C₄₁	2
C₂²×Q₁₆×C₄₁	2
D₄×Q₈×C₄₁	2
C₄₁×#548	2
C₄₁×#497	2
C₄₁×#470	2
C₄₁×#465	2
C₄₁×#464	2
C₄₁×#462	2
C₄₁×#452	2
C₄₁×#451	2
C₄₁×#448	2
C₄₁×#441	2
C₄₁×#435	2
#3270	41

Subgroups — C41×#3270 #19107050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#3270 #19107050