Subgroups — C₂×C₄₁×#3537 #23838925

Order 10496.

8890 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3537	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₄₁×#560	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₁×#553	C₂	1	4	yes	maximal, complemented
4	C₂×D₄²×C₄₁	C₂	1	4	yes	maximal, complemented
5	C₂×D₄²×C₄₁	C₂	1	4	yes	maximal, complemented
6	C₂×C₄₁×#540	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#538	C₂	1	4	yes	maximal, complemented
8	C₂×C₄₁×#535	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₁×#534	C₂	1	4	yes	maximal, complemented
10	C₂×C₄₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#121×C₄₁	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₄₁	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₄₁	C₂²	1	4	yes	complemented
15	C₂³×D₄×C₄₁	C₂²	1	8	yes	complemented
16	C₂³×D₄×C₄₁	C₂²	1	2	yes	complemented
17	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	C₄₁×#560	C₂²	1	64	yes	complemented
19	C₄₁×#553	C₂²	1	64	yes	complemented
20	D₄²×C₄₁	C₂²	1	64	yes	complemented
21	D₄²×C₄₁	C₂²	1	64	yes	complemented
22	C₄₁×#540	C₂²	1	32	yes	complemented
23	C₄₁×#538	C₂²	1	64	yes	complemented
24	C₄₁×#535	C₂²	1	32	yes	complemented
25	C₄₁×#534	C₂²	1	64	yes	complemented
26	C₂×#127×C₄₁	C₂²	1	4	yes	complemented
27	C₂×#127×C₄₁	C₂²	1	2	yes	complemented
28	C₂×#126×C₄₁	C₂²	1	8	yes	complemented
29	C₂×#125×C₄₁	C₂²	1	2	yes	complemented
30	C₂×#124×C₄₁	C₂²	1	4	yes	complemented
31	C₄₁×#525	C₂²	1	16	yes	complemented
32	C₂×#123×C₄₁	C₂²	1	2	yes	complemented
33	C₂×#123×C₄₁	C₂²	1	8	yes	complemented
34	C₂×#123×C₄₁	C₂²	1	8	yes	complemented
35	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	complemented
36	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
37	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
38	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
39	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
40	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
41	C₂×#121×C₄₁	C₂²	1	8	yes	complemented
42	C₂×#121×C₄₁	C₂²	1	4	yes	complemented
43	C₂×#121×C₄₁	C₂²	1	8	yes	complemented
44	C₂×#121×C₄₁	C₂²	1	8	yes	complemented
45	C₂×#121×C₄₁	C₂²	1	32	yes	complemented
46	C₂×#120×C₄₁	C₂²	1	2	yes	complemented
47	C₂×#120×C₄₁	C₂²	1	4	yes	complemented
48	C₂×#120×C₄₁	C₂²	1	8	yes	complemented
49	C₂×#120×C₄₁	C₂²	1	4	yes	complemented
50	C₂×#120×C₄₁	C₂²	1	8	yes	complemented
51	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	complemented
52	C₂×C₄×D₄×C₄₁	C₂²	1	8	yes	complemented
53	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	complemented
54	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic, complemented
55	C₂×#117×C₄₁	C₂²	1	2	yes	complemented
56	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
57	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	complemented
58	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
59	C₂⁵×C₄₁	C₂³	1	4	yes	—
60	C₂⁵×C₄₁	C₂³	1	4	yes	—
61	C₂×#41×C₄₁	—	4	4	no	—
62	C₂×#41×C₄₁	C₂³	1	8	yes	complemented
63	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₄₁	—	4	8	no	—
65	C₂²×D₄×C₄₁	—	4	8	no	—
66	C₂²×D₄×C₄₁	—	4	16	no	—
67	C₂²×D₄×C₄₁	—	4	32	no	—
68	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
69	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
70	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
71	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
73	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
74	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
75	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
76	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
77	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
78	C₂²×D₄×C₄₁	C₂³	1	16	yes	complemented
79	C₂²×D₄×C₄₁	C₂³	1	32	yes	complemented
80	C₂²×D₄×C₄₁	C₂³	1	64	yes	complemented
81	C₂²×D₄×C₄₁	C₂³	1	16	yes	complemented
82	C₂³×C₄×C₄₁	—	4	4	no	—
83	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
84	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
85	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
87	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
88	C₂³×C₄×C₄₁	C₂³	1	8	yes	—
89	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₁	C₂³	1	8	yes	complemented
91	#127×C₄₁	C₂³	1	32	yes	complemented
92	#127×C₄₁	C₂³	1	16	yes	complemented
93	#126×C₄₁	C₂³	1	64	yes	complemented
94	#125×C₄₁	C₂³	1	16	yes	complemented
95	#124×C₄₁	C₂³	1	32	yes	complemented
96	#123×C₄₁	C₂³	1	16	yes	complemented
97	#123×C₄₁	C₂³	1	64	yes	complemented
98	#123×C₄₁	C₂³	1	64	yes	complemented
99	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
100	#121×C₄₁	C₂³	1	32	yes	complemented
101	#121×C₄₁	C₂³	1	32	yes	complemented
102	#121×C₄₁	C₂³	1	32	yes	complemented
103	#121×C₄₁	C₂³	1	32	yes	complemented
104	#121×C₄₁	C₂³	1	16	yes	complemented
105	#121×C₄₁	C₂³	1	64	yes	complemented
106	#121×C₄₁	C₂³	1	32	yes	complemented
107	#121×C₄₁	C₂³	1	64	yes	complemented
108	#121×C₄₁	C₂³	1	64	yes	complemented
109	#120×C₄₁	C₂³	1	16	yes	complemented
110	#120×C₄₁	C₂³	1	32	yes	complemented
111	#120×C₄₁	C₂³	1	64	yes	complemented
112	#120×C₄₁	C₂³	1	32	yes	complemented
113	#120×C₄₁	C₂³	1	64	yes	complemented
114	C₄×D₄×C₄₁	C₂³	1	32	yes	complemented
115	C₄×D₄×C₄₁	C₂³	1	64	yes	complemented
116	C₄×D₄×C₄₁	C₂³	1	32	yes	complemented
117	#117×C₄₁	C₂³	1	8	yes	complemented
118	#117×C₄₁	C₂³	1	16	yes	complemented
119	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
124	C₂×C₄⋊C₄×C₄₁	C₂³	1	16	yes	complemented
125	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
127	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
131	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
132	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₄₁	C₂³	1	32	yes	complemented
134	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
136	C₂⁴×C₄₁	—	2	8	no	—
137	C₂⁴×C₄₁	—	2	16	no	—
138	C₂⁴×C₄₁	—	4	2	no	—
139	C₂⁴×C₄₁	—	4	8	no	—
140	C₂⁴×C₄₁	—	4	8	no	—
141	C₂⁴×C₄₁	—	4	8	no	—
142	C₂⁴×C₄₁	—	4	16	no	—
143	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
144	C₂⁴×C₄₁	C₂⁴	1	8	yes	—
145	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
147	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
148	C₂⁴×C₄₁	C₂⁴	1	16	yes	—
149	C₂⁴×C₄₁	C₂⁴	1	16	yes	—
150	#41×C₄₁	—	4	16	no	—
151	C₂×Q₈×C₄₁	—	4	2	no	—
152	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
153	C₂×D₄×C₄₁	—	2	32	no	—
154	C₂×D₄×C₄₁	—	2	16	no	—
155	C₂×D₄×C₄₁	—	2	16	no	—
156	C₂×D₄×C₄₁	—	4	32	no	—
157	C₂×D₄×C₄₁	—	4	32	no	—
158	C₂×D₄×C₄₁	—	4	8	no	—
159	C₂×D₄×C₄₁	—	4	8	no	—
160	C₂×D₄×C₄₁	—	4	16	no	—
161	C₂×D₄×C₄₁	—	4	16	no	—
162	C₂×D₄×C₄₁	—	4	16	no	—
163	C₂×D₄×C₄₁	—	4	2	no	—
164	C₂×D₄×C₄₁	—	4	4	no	—
165	C₂×D₄×C₄₁	—	4	64	no	—
166	C₂×D₄×C₄₁	—	4	128	no	—
167	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
168	C₂×D₄×C₄₁	C₂⁴	1	32	yes	—
169	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
170	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
171	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
172	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
173	C₂×D₄×C₄₁	C₂⁴	1	32	yes	—
174	C₂×D₄×C₄₁	C₂⁴	1	32	yes	—
175	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
176	C₂×D₄×C₄₁	C₂⁴	1	32	yes	—
177	C₂²×C₄×C₄₁	—	2	8	no	—
178	C₂²×C₄×C₄₁	—	2	4	no	—
179	C₂²×C₄×C₄₁	—	2	8	no	—
180	C₂²×C₄×C₄₁	—	4	16	no	—
181	C₂²×C₄×C₄₁	—	4	2	no	—
182	C₂²×C₄×C₄₁	—	4	4	no	—
183	C₂²×C₄×C₄₁	—	4	8	no	—
184	C₂²×C₄×C₄₁	—	4	16	no	—
185	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
186	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
187	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
191	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
194	C₂²×C₄×C₄₁	C₂⁴	1	16	yes	—
195	C₂²×C₄×C₄₁	C₂⁴	1	32	yes	—
196	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
198	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
199	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
200	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
201	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
202	C₄⋊C₄×C₄₁	C₂⁴	1	32	yes	—
203	C₂²⋊C₄×C₄₁	C₂⁴	1	32	yes	—
204	C₂²⋊C₄×C₄₁	C₂⁴	1	32	yes	—
205	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
206	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
207	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
208	C₂²⋊C₄×C₄₁	C₂⁴	1	32	yes	—
209	C₂²⋊C₄×C₄₁	C₂⁴	1	32	yes	—
210	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
211	C₄²×C₄₁	C₂⁴	1	8	yes	—
212	C₄²×C₄₁	C₂⁴	1	16	yes	—
213	C₂³×C₄₁	—	2	4	no	—
214	C₂³×C₄₁	—	2	4	no	—
215	C₂³×C₄₁	—	2	2	no	—
216	C₂³×C₄₁	—	2	4	no	—
217	C₂³×C₄₁	—	2	16	no	—
218	C₂³×C₄₁	—	2	8	no	—
219	C₂³×C₄₁	—	2	16	no	—
220	C₂³×C₄₁	—	2	16	no	—
221	C₂³×C₄₁	—	2	16	no	—
222	C₂³×C₄₁	—	2	4	no	—
223	C₂³×C₄₁	—	2	32	no	—
224	C₂³×C₄₁	—	4	4	no	—
225	C₂³×C₄₁	—	4	16	no	—
226	C₂³×C₄₁	—	4	16	no	—
227	C₂³×C₄₁	—	4	16	no	—
228	C₂³×C₄₁	—	4	32	no	—
229	C₂³×C₄₁	—	4	16	no	—
230	C₂³×C₄₁	—	8	32	no	—
231	C₂³×C₄₁	—	8	32	no	—
232	C₂³×C₄₁	H(5,𝔽₂)	1	8	yes	—
233	C₂³×C₄₁	C₂⁵	1	4	yes	—
234	C₂³×C₄₁	C₂⁵	1	16	yes	—
235	C₂³×C₄₁	C₂⁵	1	2	yes	—
236	C₂³×C₄₁	C₂⁵	1	4	yes	—
237	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
238	Q₈×C₄₁	—	4	4	no	—
239	D₄×C₄₁	—	2	64	no	—
240	D₄×C₄₁	—	2	32	no	—
241	D₄×C₄₁	—	2	32	no	—
242	D₄×C₄₁	—	4	16	no	—
243	D₄×C₄₁	—	4	16	no	—
244	D₄×C₄₁	—	4	32	no	—
245	D₄×C₄₁	—	4	32	no	—
246	D₄×C₄₁	—	4	32	no	—
247	D₄×C₄₁	—	4	4	no	—
248	D₄×C₄₁	—	4	8	no	—
249	C₂×C₄×C₄₁	—	2	4	no	—
250	C₂×C₄×C₄₁	—	2	2	no	—
251	C₂×C₄×C₄₁	—	2	4	no	—
252	C₂×C₄×C₄₁	—	2	16	no	—
253	C₂×C₄×C₄₁	—	2	8	no	—
254	C₂×C₄×C₄₁	—	2	16	no	—
255	C₂×C₄×C₄₁	—	2	8	no	—
256	C₂×C₄×C₄₁	—	2	16	no	—
257	C₂×C₄×C₄₁	—	4	4	no	—
258	C₂×C₄×C₄₁	—	4	8	no	—
259	C₂×C₄×C₄₁	—	4	16	no	—
260	C₂×C₄×C₄₁	—	4	32	no	—
261	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
262	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
263	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
264	C₂×C₄×C₄₁	C₂⁵	1	16	yes	—
265	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
266	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
267	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
268	C₂×#3537	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂²×C₄₁	—	2	4	no	—
270	C₂²×C₄₁	—	2	4	no	—
271	C₂²×C₄₁	—	2	16	no	—
272	C₂²×C₄₁	—	2	2	no	—
273	C₂²×C₄₁	—	2	4	no	—
274	C₂²×C₄₁	—	2	16	no	—
275	C₂²×C₄₁	—	2	8	no	—
276	C₂²×C₄₁	—	2	16	no	—
277	C₂²×C₄₁	—	2	16	no	—
278	C₂²×C₄₁	—	2	4	no	—
279	C₂²×C₄₁	—	4	16	no	—
280	C₂²×C₄₁	—	4	4	no	—
281	C₂²×C₄₁	—	4	8	no	—
282	C₂²×C₄₁	—	4	32	no	—
283	C₂²×C₄₁	—	8	32	no	—
284	C₂²×C₄₁	—	8	32	no	—
285	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	8	yes	—
286	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	4	yes	—
287	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
288	C₂²×C₄₁	C₂⁶	1	1	yes	characteristic
289	C₄×C₄₁	—	2	4	no	—
290	C₄×C₄₁	—	2	2	no	—
291	C₄×C₄₁	—	2	4	no	—
292	C₄×C₄₁	—	2	16	no	—
293	C₄×C₄₁	—	2	8	no	—
294	C₄×C₄₁	C₂×H(5,𝔽₂)	1	4	yes	—
295	#3537	C₂×C₄₁	1	32	yes	direct product factor
296	C₂×#560	C₂×C₄₁	1	4	yes	complemented
297	C₂×#553	C₂×C₄₁	1	4	yes	complemented
298	C₂×D₄²	C₂×C₄₁	1	4	yes	complemented
299	C₂×D₄²	C₂×C₄₁	1	4	yes	complemented
300	C₂×#540	C₂×C₄₁	1	2	yes	complemented
301	C₂×#538	C₂×C₄₁	1	4	yes	complemented
302	C₂×#535	C₂×C₄₁	1	2	yes	complemented
303	C₂×#534	C₂×C₄₁	1	4	yes	complemented
304	C₂×#525	C₂×C₄₁	1	1	yes	characteristic, complemented
305	C₂²×#121	C₂×C₄₁	1	2	yes	complemented
306	C₂×C₄₁	—	2	8	no	—
307	C₂×C₄₁	—	4	2	no	—
308	C₂×C₄₁	—	4	4	no	—
309	C₂×C₄₁	—	4	16	no	—
310	C₂×C₄₁	#3537	1	4	yes	direct product factor
311	C₂×C₄₁	C₂²×H(5,𝔽₂)	1	2	yes	—
312	C₂×C₄₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic, complemented
314	C₂³×D₄	C₂²×C₄₁	1	2	yes	complemented
315	C₂³×D₄	C₂²×C₄₁	1	4	yes	complemented
316	C₂³×D₄	C₂²×C₄₁	1	8	yes	complemented
317	C₂³×D₄	C₂²×C₄₁	1	2	yes	complemented
318	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
319	#560	C₂²×C₄₁	1	64	yes	complemented
320	#553	C₂²×C₄₁	1	64	yes	complemented
321	D₄²	C₂²×C₄₁	1	64	yes	complemented
322	D₄²	C₂²×C₄₁	1	64	yes	complemented
323	#540	C₂²×C₄₁	1	32	yes	complemented
324	#538	C₂²×C₄₁	1	64	yes	complemented
325	#535	C₂²×C₄₁	1	32	yes	complemented
326	#534	C₂²×C₄₁	1	64	yes	complemented
327	C₂×#127	C₂²×C₄₁	1	4	yes	complemented
328	C₂×#127	C₂²×C₄₁	1	2	yes	complemented
329	C₂×#126	C₂²×C₄₁	1	8	yes	complemented
330	C₂×#125	C₂²×C₄₁	1	2	yes	complemented
331	C₂×#124	C₂²×C₄₁	1	4	yes	complemented
332	#525	C₂²×C₄₁	1	16	yes	complemented
333	C₂×#123	C₂²×C₄₁	1	2	yes	complemented
334	C₂×#123	C₂²×C₄₁	1	8	yes	complemented
335	C₂×#123	C₂²×C₄₁	1	8	yes	complemented
336	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	complemented
337	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
338	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
339	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
340	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
341	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
342	C₂×#121	C₂²×C₄₁	1	8	yes	complemented
343	C₂×#121	C₂²×C₄₁	1	4	yes	complemented
344	C₂×#121	C₂²×C₄₁	1	8	yes	complemented
345	C₂×#121	C₂²×C₄₁	1	8	yes	complemented
346	C₂×#121	C₂²×C₄₁	1	32	yes	complemented
347	C₂×#120	C₂²×C₄₁	1	2	yes	complemented
348	C₂×#120	C₂²×C₄₁	1	4	yes	complemented
349	C₂×#120	C₂²×C₄₁	1	8	yes	complemented
350	C₂×#120	C₂²×C₄₁	1	4	yes	complemented
351	C₂×#120	C₂²×C₄₁	1	8	yes	complemented
352	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	complemented
353	C₂×C₄×D₄	C₂²×C₄₁	1	8	yes	complemented
354	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	complemented
355	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic, complemented
356	C₂×#117	C₂²×C₄₁	1	2	yes	complemented
357	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
358	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	complemented
359	C₄₁	C₂×#3537	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
361	C₂⁵	C₂³×C₄₁	1	4	yes	—
362	C₂⁵	C₂³×C₄₁	1	4	yes	—
363	C₂×#41	—	4	4	no	—
364	C₂×#41	C₂³×C₄₁	1	8	yes	complemented
365	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
366	C₂²×D₄	—	4	8	no	—
367	C₂²×D₄	—	4	8	no	—
368	C₂²×D₄	—	4	16	no	—
369	C₂²×D₄	—	4	32	no	—
370	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
371	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
372	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
373	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
374	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
375	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
376	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
377	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
378	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
379	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
380	C₂²×D₄	C₂³×C₄₁	1	16	yes	complemented
381	C₂²×D₄	C₂³×C₄₁	1	32	yes	complemented
382	C₂²×D₄	C₂³×C₄₁	1	64	yes	complemented
383	C₂²×D₄	C₂³×C₄₁	1	16	yes	complemented
384	C₂³×C₄	—	4	4	no	—
385	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
386	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
387	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
389	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
390	C₂³×C₄	C₂³×C₄₁	1	8	yes	—
391	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₄₁	1	8	yes	complemented
393	#127	C₂³×C₄₁	1	32	yes	complemented
394	#127	C₂³×C₄₁	1	16	yes	complemented
395	#126	C₂³×C₄₁	1	64	yes	complemented
396	#125	C₂³×C₄₁	1	16	yes	complemented
397	#124	C₂³×C₄₁	1	32	yes	complemented
398	#123	C₂³×C₄₁	1	16	yes	complemented
399	#123	C₂³×C₄₁	1	64	yes	complemented
400	#123	C₂³×C₄₁	1	64	yes	complemented
401	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
402	#121	C₂³×C₄₁	1	32	yes	complemented
403	#121	C₂³×C₄₁	1	32	yes	complemented
404	#121	C₂³×C₄₁	1	32	yes	complemented
405	#121	C₂³×C₄₁	1	32	yes	complemented
406	#121	C₂³×C₄₁	1	16	yes	complemented
407	#121	C₂³×C₄₁	1	64	yes	complemented
408	#121	C₂³×C₄₁	1	32	yes	complemented
409	#121	C₂³×C₄₁	1	64	yes	complemented
410	#121	C₂³×C₄₁	1	64	yes	complemented
411	#120	C₂³×C₄₁	1	16	yes	complemented
412	#120	C₂³×C₄₁	1	32	yes	complemented
413	#120	C₂³×C₄₁	1	64	yes	complemented
414	#120	C₂³×C₄₁	1	32	yes	complemented
415	#120	C₂³×C₄₁	1	64	yes	complemented
416	C₄×D₄	C₂³×C₄₁	1	32	yes	complemented
417	C₄×D₄	C₂³×C₄₁	1	64	yes	complemented
418	C₄×D₄	C₂³×C₄₁	1	32	yes	complemented
419	#117	C₂³×C₄₁	1	8	yes	complemented
420	#117	C₂³×C₄₁	1	16	yes	complemented
421	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
422	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
423	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
426	C₂×C₄⋊C₄	C₂³×C₄₁	1	16	yes	complemented
427	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₄₁	1	32	yes	complemented
436	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
437	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
438	C₂⁴	—	2	8	no	—
439	C₂⁴	—	2	16	no	—
440	C₂⁴	—	4	2	no	—
441	C₂⁴	—	4	8	no	—
442	C₂⁴	—	4	8	no	—
443	C₂⁴	—	4	8	no	—
444	C₂⁴	—	4	16	no	—
445	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
446	C₂⁴	C₂⁴×C₄₁	1	8	yes	—
447	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
448	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
449	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
450	C₂⁴	C₂⁴×C₄₁	1	16	yes	—
451	C₂⁴	C₂⁴×C₄₁	1	16	yes	—
452	#41	—	4	16	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
455	C₂×D₄	—	2	32	no	—
456	C₂×D₄	—	2	16	no	—
457	C₂×D₄	—	2	16	no	—
458	C₂×D₄	—	4	32	no	—
459	C₂×D₄	—	4	32	no	—
460	C₂×D₄	—	4	8	no	—
461	C₂×D₄	—	4	8	no	—
462	C₂×D₄	—	4	16	no	—
463	C₂×D₄	—	4	16	no	—
464	C₂×D₄	—	4	16	no	—
465	C₂×D₄	—	4	2	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	4	64	no	—
468	C₂×D₄	—	4	128	no	—
469	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
470	C₂×D₄	C₂⁴×C₄₁	1	32	yes	—
471	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
472	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
473	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
474	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
475	C₂×D₄	C₂⁴×C₄₁	1	32	yes	—
476	C₂×D₄	C₂⁴×C₄₁	1	32	yes	—
477	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
478	C₂×D₄	C₂⁴×C₄₁	1	32	yes	—
479	C₂²×C₄	—	2	8	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	4	16	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	4	no	—
485	C₂²×C₄	—	4	8	no	—
486	C₂²×C₄	—	4	16	no	—
487	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
490	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
493	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
494	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
496	C₂²×C₄	C₂⁴×C₄₁	1	16	yes	—
497	C₂²×C₄	C₂⁴×C₄₁	1	32	yes	—
498	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
500	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
501	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
502	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
503	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
504	C₄⋊C₄	C₂⁴×C₄₁	1	32	yes	—
505	C₂²⋊C₄	C₂⁴×C₄₁	1	32	yes	—
506	C₂²⋊C₄	C₂⁴×C₄₁	1	32	yes	—
507	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
508	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
509	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
510	C₂²⋊C₄	C₂⁴×C₄₁	1	32	yes	—
511	C₂²⋊C₄	C₂⁴×C₄₁	1	32	yes	—
512	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
513	C₄²	C₂⁴×C₄₁	1	8	yes	—
514	C₄²	C₂⁴×C₄₁	1	16	yes	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	16	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	16	no	—
522	C₂³	—	2	16	no	—
523	C₂³	—	2	16	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	32	no	—
526	C₂³	—	4	4	no	—
527	C₂³	—	4	16	no	—
528	C₂³	—	4	16	no	—
529	C₂³	—	4	16	no	—
530	C₂³	—	4	32	no	—
531	C₂³	—	4	16	no	—
532	C₂³	—	8	32	no	—
533	C₂³	—	8	32	no	—
534	C₂³	H(5,𝔽₂)×C₄₁	1	8	yes	—
535	C₂³	C₂⁵×C₄₁	1	4	yes	—
536	C₂³	C₂⁵×C₄₁	1	16	yes	—
537	C₂³	C₂⁵×C₄₁	1	2	yes	—
538	C₂³	C₂⁵×C₄₁	1	4	yes	—
539	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
540	Q₈	—	4	4	no	—
541	D₄	—	2	64	no	—
542	D₄	—	2	32	no	—
543	D₄	—	2	32	no	—
544	D₄	—	4	16	no	—
545	D₄	—	4	16	no	—
546	D₄	—	4	32	no	—
547	D₄	—	4	32	no	—
548	D₄	—	4	32	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	8	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	16	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	16	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	—	4	16	no	—
562	C₂×C₄	—	4	32	no	—
563	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
564	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
565	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
566	C₂×C₄	C₂⁵×C₄₁	1	16	yes	—
567	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
568	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
569	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
570	C₂²	—	2	4	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	16	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	16	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	16	no	—
578	C₂²	—	2	16	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	4	16	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	4	32	no	—
584	C₂²	—	8	32	no	—
585	C₂²	—	8	32	no	—
586	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	8	yes	—
587	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	4	yes	—
588	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
589	C₂²	C₂⁶×C₄₁	1	1	yes	characteristic
590	C₄	—	2	4	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	4	no	—
593	C₄	—	2	16	no	—
594	C₄	—	2	8	no	—
595	C₄	C₂×H(5,𝔽₂)×C₄₁	1	4	yes	—
596	C₂	—	2	8	no	—
597	C₂	—	4	2	no	—
598	C₂	—	4	4	no	—
599	C₂	—	4	16	no	—
600	C₂	C₄₁×#3537	1	4	yes	direct product factor
601	C₂	C₂²×H(5,𝔽₂)×C₄₁	1	2	yes	—
602	C₂	C₂²×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₄₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3537	C₂	direct (N × H)
2. C₂×C₄₁×#560	C₂	semidirect
3. C₂×C₄₁×#553	C₂	semidirect
4. C₂×D₄²×C₄₁	C₂	semidirect
5. C₂×D₄²×C₄₁	C₂	semidirect
6. C₂×C₄₁×#540	C₂	semidirect
7. C₂×C₄₁×#538	C₂	semidirect
8. C₂×C₄₁×#535	C₂	semidirect
9. C₂×C₄₁×#534	C₂	semidirect
10. C₂×C₄₁×#525	C₂	semidirect
11. C₂²×#121×C₄₁	C₂	semidirect
12. C₂²×#41×C₄₁	C₂²	semidirect
13. C₂³×D₄×C₄₁	C₂²	semidirect
14. C₂³×D₄×C₄₁	C₂²	semidirect
15. C₂³×D₄×C₄₁	C₂²	semidirect
16. C₂³×D₄×C₄₁	C₂²	semidirect
17. C₂⁴×C₄×C₄₁	C₂²	semidirect
18. C₄₁×#560	C₂²	semidirect
19. C₄₁×#553	C₂²	semidirect
20. D₄²×C₄₁	C₂²	semidirect
21. D₄²×C₄₁	C₂²	semidirect
22. C₄₁×#540	C₂²	semidirect
23. C₄₁×#538	C₂²	semidirect
24. C₄₁×#535	C₂²	semidirect
25. C₄₁×#534	C₂²	semidirect
26. C₂×#127×C₄₁	C₂²	semidirect
27. C₂×#127×C₄₁	C₂²	semidirect
28. C₂×#126×C₄₁	C₂²	semidirect
29. C₂×#125×C₄₁	C₂²	semidirect
30. C₂×#124×C₄₁	C₂²	semidirect
31. C₄₁×#525	C₂²	semidirect
32. C₂×#123×C₄₁	C₂²	semidirect
33. C₂×#123×C₄₁	C₂²	semidirect
34. C₂×#123×C₄₁	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
36. C₂×#121×C₄₁	C₂²	semidirect
37. C₂×#121×C₄₁	C₂²	semidirect
38. C₂×#121×C₄₁	C₂²	semidirect
39. C₂×#121×C₄₁	C₂²	semidirect
40. C₂×#121×C₄₁	C₂²	semidirect
41. C₂×#121×C₄₁	C₂²	semidirect
42. C₂×#121×C₄₁	C₂²	semidirect
43. C₂×#121×C₄₁	C₂²	semidirect
44. C₂×#121×C₄₁	C₂²	semidirect
45. C₂×#121×C₄₁	C₂²	semidirect
46. C₂×#120×C₄₁	C₂²	semidirect
47. C₂×#120×C₄₁	C₂²	semidirect
48. C₂×#120×C₄₁	C₂²	semidirect
49. C₂×#120×C₄₁	C₂²	semidirect
50. C₂×#120×C₄₁	C₂²	semidirect
51. C₂×C₄×D₄×C₄₁	C₂²	semidirect
52. C₂×C₄×D₄×C₄₁	C₂²	semidirect
53. C₂×C₄×D₄×C₄₁	C₂²	semidirect
54. C₂×#117×C₄₁	C₂²	semidirect
55. C₂×#117×C₄₁	C₂²	semidirect
56. C₂²×C₄⋊C₄×C₄₁	C₂²	semidirect
57. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
62. C₂×#41×C₄₁	C₂³	semidirect
78. C₂²×D₄×C₄₁	C₂³	semidirect
79. C₂²×D₄×C₄₁	C₂³	semidirect
80. C₂²×D₄×C₄₁	C₂³	semidirect
81. C₂²×D₄×C₄₁	C₂³	semidirect
90. C₂³×C₄×C₄₁	C₂³	semidirect
91. #127×C₄₁	C₂³	semidirect
92. #127×C₄₁	C₂³	semidirect
93. #126×C₄₁	C₂³	semidirect
94. #125×C₄₁	C₂³	semidirect
95. #124×C₄₁	C₂³	semidirect
96. #123×C₄₁	C₂³	semidirect
97. #123×C₄₁	C₂³	semidirect
98. #123×C₄₁	C₂³	semidirect
99. C₂²⋊Q₈×C₄₁	C₂³	semidirect
100. #121×C₄₁	C₂³	semidirect
101. #121×C₄₁	C₂³	semidirect
102. #121×C₄₁	C₂³	semidirect
103. #121×C₄₁	C₂³	semidirect
104. #121×C₄₁	C₂³	semidirect
105. #121×C₄₁	C₂³	semidirect
106. #121×C₄₁	C₂³	semidirect
107. #121×C₄₁	C₂³	semidirect
108. #121×C₄₁	C₂³	semidirect
109. #120×C₄₁	C₂³	semidirect
110. #120×C₄₁	C₂³	semidirect
111. #120×C₄₁	C₂³	semidirect
112. #120×C₄₁	C₂³	semidirect
113. #120×C₄₁	C₂³	semidirect
114. C₄×D₄×C₄₁	C₂³	semidirect
115. C₄×D₄×C₄₁	C₂³	semidirect
116. C₄×D₄×C₄₁	C₂³	semidirect
117. #117×C₄₁	C₂³	semidirect
118. #117×C₄₁	C₂³	semidirect
124. C₂×C₄⋊C₄×C₄₁	C₂³	semidirect
133. C₂×C₂²⋊C₄×C₄₁	C₂³	semidirect
268. C₂×#3537	C₄₁	direct (N × H)
295. #3537	C₂×C₄₁	direct (N × H)
296. C₂×#560	C₂×C₄₁	semidirect
297. C₂×#553	C₂×C₄₁	semidirect
298. C₂×D₄²	C₂×C₄₁	semidirect
299. C₂×D₄²	C₂×C₄₁	semidirect
300. C₂×#540	C₂×C₄₁	semidirect
301. C₂×#538	C₂×C₄₁	semidirect
302. C₂×#535	C₂×C₄₁	semidirect
303. C₂×#534	C₂×C₄₁	semidirect
304. C₂×#525	C₂×C₄₁	semidirect
305. C₂²×#121	C₂×C₄₁	semidirect
310. C₂×C₄₁	#3537	direct (N × H)
313. C₂²×#41	C₂²×C₄₁	semidirect
314. C₂³×D₄	C₂²×C₄₁	semidirect
315. C₂³×D₄	C₂²×C₄₁	semidirect
316. C₂³×D₄	C₂²×C₄₁	semidirect
317. C₂³×D₄	C₂²×C₄₁	semidirect
318. C₂⁴×C₄	C₂²×C₄₁	semidirect
319. #560	C₂²×C₄₁	semidirect
320. #553	C₂²×C₄₁	semidirect
321. D₄²	C₂²×C₄₁	semidirect
322. D₄²	C₂²×C₄₁	semidirect
323. #540	C₂²×C₄₁	semidirect
324. #538	C₂²×C₄₁	semidirect
325. #535	C₂²×C₄₁	semidirect
326. #534	C₂²×C₄₁	semidirect
327. C₂×#127	C₂²×C₄₁	semidirect
328. C₂×#127	C₂²×C₄₁	semidirect
329. C₂×#126	C₂²×C₄₁	semidirect
330. C₂×#125	C₂²×C₄₁	semidirect
331. C₂×#124	C₂²×C₄₁	semidirect
332. #525	C₂²×C₄₁	semidirect
333. C₂×#123	C₂²×C₄₁	semidirect
334. C₂×#123	C₂²×C₄₁	semidirect
335. C₂×#123	C₂²×C₄₁	semidirect
336. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
337. C₂×#121	C₂²×C₄₁	semidirect
338. C₂×#121	C₂²×C₄₁	semidirect
339. C₂×#121	C₂²×C₄₁	semidirect
340. C₂×#121	C₂²×C₄₁	semidirect
341. C₂×#121	C₂²×C₄₁	semidirect
342. C₂×#121	C₂²×C₄₁	semidirect
343. C₂×#121	C₂²×C₄₁	semidirect
344. C₂×#121	C₂²×C₄₁	semidirect
345. C₂×#121	C₂²×C₄₁	semidirect
346. C₂×#121	C₂²×C₄₁	semidirect
347. C₂×#120	C₂²×C₄₁	semidirect
348. C₂×#120	C₂²×C₄₁	semidirect
349. C₂×#120	C₂²×C₄₁	semidirect
350. C₂×#120	C₂²×C₄₁	semidirect
351. C₂×#120	C₂²×C₄₁	semidirect
352. C₂×C₄×D₄	C₂²×C₄₁	semidirect
353. C₂×C₄×D₄	C₂²×C₄₁	semidirect
354. C₂×C₄×D₄	C₂²×C₄₁	semidirect
355. C₂×#117	C₂²×C₄₁	semidirect
356. C₂×#117	C₂²×C₄₁	semidirect
357. C₂²×C₄⋊C₄	C₂²×C₄₁	semidirect
358. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
359. C₄₁	C₂×#3537	direct (N × H)
364. C₂×#41	C₂³×C₄₁	semidirect
380. C₂²×D₄	C₂³×C₄₁	semidirect
381. C₂²×D₄	C₂³×C₄₁	semidirect
382. C₂²×D₄	C₂³×C₄₁	semidirect
383. C₂²×D₄	C₂³×C₄₁	semidirect
392. C₂³×C₄	C₂³×C₄₁	semidirect
393. #127	C₂³×C₄₁	semidirect
394. #127	C₂³×C₄₁	semidirect
395. #126	C₂³×C₄₁	semidirect
396. #125	C₂³×C₄₁	semidirect
397. #124	C₂³×C₄₁	semidirect
398. #123	C₂³×C₄₁	semidirect
399. #123	C₂³×C₄₁	semidirect
400. #123	C₂³×C₄₁	semidirect
401. C₂²⋊Q₈	C₂³×C₄₁	semidirect
402. #121	C₂³×C₄₁	semidirect
403. #121	C₂³×C₄₁	semidirect
404. #121	C₂³×C₄₁	semidirect
405. #121	C₂³×C₄₁	semidirect
406. #121	C₂³×C₄₁	semidirect
407. #121	C₂³×C₄₁	semidirect
408. #121	C₂³×C₄₁	semidirect
409. #121	C₂³×C₄₁	semidirect
410. #121	C₂³×C₄₁	semidirect
411. #120	C₂³×C₄₁	semidirect
412. #120	C₂³×C₄₁	semidirect
413. #120	C₂³×C₄₁	semidirect
414. #120	C₂³×C₄₁	semidirect
415. #120	C₂³×C₄₁	semidirect
416. C₄×D₄	C₂³×C₄₁	semidirect
417. C₄×D₄	C₂³×C₄₁	semidirect
418. C₄×D₄	C₂³×C₄₁	semidirect
419. #117	C₂³×C₄₁	semidirect
420. #117	C₂³×C₄₁	semidirect
426. C₂×C₄⋊C₄	C₂³×C₄₁	semidirect
435. C₂×C₂²⋊C₄	C₂³×C₄₁	semidirect
600. C₂	C₄₁×#3537	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3537	2
C₂×C₄₁×#560	2
C₂×C₄₁×#553	2
C₂×D₄²×C₄₁	2
C₂×C₄₁×#540	2
C₂×C₄₁×#538	2
C₂×C₄₁×#535	2
C₂×C₄₁×#534	2
C₂×C₄₁×#525	2
C₂²×#121×C₄₁	2
C₂×#3537	41

Subgroups — C2×C41×#3537 #23838925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3537 #23838925