Subgroups — C₂×C₄₁×#3563 #23838934

Order 10496.

6458 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3563	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₄₁×#564	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#563	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#557	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₁×#554	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₁×#552	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₁×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#552	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₁×#544	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₁×#544	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₁×#541	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₁×#541	C₂	1	4	yes	maximal, complemented
13	C₂×C₄₁×#539	C₂	1	2	yes	maximal
14	C₂×C₄₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₁×#529	C₂	1	1	yes	maximal, characteristic
16	C₂²×#125×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₁×#564	C₂²	1	32	yes	complemented
18	C₄₁×#563	C₂²	1	32	yes	complemented
19	C₄₁×#557	C₂²	1	32	yes	complemented
20	C₄₁×#554	C₂²	1	32	yes	complemented
21	C₄₁×#552	C₂²	1	64	yes	complemented
22	C₄₁×#552	C₂²	1	32	yes	complemented
23	C₄₁×#552	C₂²	1	32	yes	complemented
24	C₄₁×#544	C₂²	1	32	yes	complemented
25	C₄₁×#544	C₂²	1	32	yes	complemented
26	C₄₁×#541	C₂²	1	32	yes	complemented
27	C₄₁×#541	C₂²	1	64	yes	complemented
28	C₄₁×#539	C₂²	1	32	yes	—
29	C₄₁×#533	C₂²	1	16	yes	complemented
30	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Q₈×C₄₁	C₂²	1	4	yes	—
33	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
34	C₂×C₄⋊Q₈×C₄₁	C₂²	1	4	yes	—
35	C₄₁×#529	C₂²	1	16	yes	—
36	C₂×#126×C₄₁	C₂²	1	2	yes	—
37	C₂×#126×C₄₁	C₂²	1	4	yes	—
38	C₂×#126×C₄₁	C₂²	1	4	yes	—
39	C₂×#126×C₄₁	C₂²	1	4	yes	—
40	C₂×#126×C₄₁	C₂²	1	4	yes	—
41	C₂×#125×C₄₁	C₂²	1	2	yes	—
42	C₂×#125×C₄₁	C₂²	1	2	yes	—
43	C₂×#125×C₄₁	C₂²	1	2	yes	—
44	C₂×#125×C₄₁	C₂²	1	2	yes	—
45	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×#125×C₄₁	C₂²	1	2	yes	—
47	C₂×#125×C₄₁	C₂²	1	4	yes	—
48	C₂×#125×C₄₁	C₂²	1	4	yes	—
49	C₂×#125×C₄₁	C₂²	1	4	yes	—
50	C₂×#125×C₄₁	C₂²	1	4	yes	—
51	C₂×#125×C₄₁	C₂²	1	4	yes	—
52	C₂×#125×C₄₁	C₂²	1	4	yes	—
53	C₂×#125×C₄₁	C₂²	1	2	yes	—
54	C₂×#125×C₄₁	C₂²	1	4	yes	—
55	C₂×#125×C₄₁	C₂²	1	4	yes	—
56	C₂×#125×C₄₁	C₂²	1	16	yes	complemented
57	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
58	C₂×#123×C₄₁	C₂²	1	2	yes	—
59	C₂×#123×C₄₁	C₂²	1	4	yes	—
60	C₂×#123×C₄₁	C₂²	1	4	yes	—
61	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
62	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
63	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
64	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	—
65	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
66	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
67	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	—
68	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	—
69	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	—
70	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
71	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
72	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
73	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
74	C₂×C₄×Q₈×C₄₁	C₂²	1	4	yes	—
75	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
76	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
77	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
78	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
80	C₂×#117×C₄₁	C₂²	1	2	yes	—
81	C₂×#117×C₄₁	C₂²	1	2	yes	—
82	C₂×#117×C₄₁	C₂²	1	4	yes	—
83	C₂×#117×C₄₁	C₂²	1	2	yes	—
84	C₂×#117×C₄₁	C₂²	1	4	yes	—
85	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
86	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
87	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
88	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
89	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
90	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
91	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
92	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
93	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
94	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
96	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
100	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
101	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
103	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
104	C₄⋊Q₈×C₄₁	C₂³	1	8	yes	—
105	C₄⋊Q₈×C₄₁	C₂³	1	8	yes	—
106	C₄⋊Q₈×C₄₁	C₂³	1	32	yes	—
107	C₄⋊Q₈×C₄₁	C₂³	1	16	yes	—
108	C₄⋊Q₈×C₄₁	C₂³	1	32	yes	—
109	#126×C₄₁	C₂³	1	16	yes	—
110	#126×C₄₁	C₂³	1	32	yes	—
111	#126×C₄₁	C₂³	1	32	yes	—
112	#126×C₄₁	C₂³	1	32	yes	—
113	#126×C₄₁	C₂³	1	32	yes	—
114	#125×C₄₁	C₂³	1	16	yes	—
115	#125×C₄₁	C₂³	1	16	yes	—
116	#125×C₄₁	C₂³	1	16	yes	—
117	#125×C₄₁	C₂³	1	16	yes	—
118	#125×C₄₁	C₂³	1	8	yes	—
119	#125×C₄₁	C₂³	1	16	yes	—
120	#125×C₄₁	C₂³	1	32	yes	—
121	#125×C₄₁	C₂³	1	32	yes	—
122	#125×C₄₁	C₂³	1	32	yes	—
123	#125×C₄₁	C₂³	1	32	yes	—
124	#125×C₄₁	C₂³	1	32	yes	—
125	#125×C₄₁	C₂³	1	32	yes	—
126	#125×C₄₁	C₂³	1	16	yes	—
127	#125×C₄₁	C₂³	1	32	yes	—
128	#125×C₄₁	C₂³	1	32	yes	—
129	#124×C₄₁	C₂³	1	8	yes	—
130	#123×C₄₁	C₂³	1	16	yes	—
131	#123×C₄₁	C₂³	1	32	yes	—
132	#123×C₄₁	C₂³	1	32	yes	—
133	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	—
134	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	—
135	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	—
136	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	—
137	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	—
138	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	—
139	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	—
140	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	—
141	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	—
142	#121×C₄₁	C₂³	1	8	yes	—
143	C₄×Q₈×C₄₁	C₂³	1	8	yes	—
144	C₄×Q₈×C₄₁	C₂³	1	16	yes	—
145	C₄×Q₈×C₄₁	C₂³	1	16	yes	—
146	C₄×Q₈×C₄₁	C₂³	1	32	yes	—
147	C₄×Q₈×C₄₁	C₂³	1	16	yes	—
148	C₄×Q₈×C₄₁	C₂³	1	16	yes	—
149	C₄×D₄×C₄₁	C₂³	1	8	yes	—
150	C₄×D₄×C₄₁	C₂³	1	16	yes	—
151	C₄×D₄×C₄₁	C₂³	1	32	yes	—
152	#117×C₄₁	C₂³	1	16	yes	—
153	#117×C₄₁	C₂³	1	16	yes	—
154	#117×C₄₁	C₂³	1	32	yes	—
155	#117×C₄₁	C₂³	1	16	yes	—
156	#117×C₄₁	C₂³	1	32	yes	—
157	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
161	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
166	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₄₁	C₂³	1	16	yes	—
168	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
169	C₂×C₄⋊C₄×C₄₁	C₂³	1	16	yes	—
170	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
171	C₂×C₄⋊C₄×C₄₁	C₂³	1	16	yes	—
172	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
175	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
177	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
181	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
186	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
190	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
191	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
195	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
197	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₄₁	C₂³	1	8	yes	—
204	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
205	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
206	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
208	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
209	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
210	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
211	C₂×Q₈×C₄₁	—	2	8	no	—
212	C₂×Q₈×C₄₁	—	4	8	no	—
213	C₂×Q₈×C₄₁	—	4	2	no	—
214	C₂×Q₈×C₄₁	—	4	4	no	—
215	C₂×Q₈×C₄₁	C₂⁴	1	8	yes	—
216	C₂×Q₈×C₄₁	C₂⁴	1	16	yes	—
217	C₂×Q₈×C₄₁	C₂⁴	1	8	yes	—
218	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
219	C₂×D₄×C₄₁	—	2	8	no	—
220	C₂×D₄×C₄₁	—	4	2	no	—
221	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
222	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₄₁	—	2	4	no	—
224	C₂²×C₄×C₄₁	—	2	8	no	—
225	C₂²×C₄×C₄₁	—	2	4	no	—
226	C₂²×C₄×C₄₁	—	2	8	no	—
227	C₂²×C₄×C₄₁	—	4	4	no	—
228	C₂²×C₄×C₄₁	—	4	8	no	—
229	C₂²×C₄×C₄₁	—	4	2	no	—
230	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
231	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
233	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
234	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
248	C₂²×C₄×C₄₁	C₂⁴	1	16	yes	—
249	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
250	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
251	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
252	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
253	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
254	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
255	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
256	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
257	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
258	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
259	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
260	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
261	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
262	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
263	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
264	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
265	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
266	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
267	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
268	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
269	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
270	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
271	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
273	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
274	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
275	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
276	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
277	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
278	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
279	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
280	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
281	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
282	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
283	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
284	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
285	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
286	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
287	C₄²×C₄₁	C₂⁴	1	4	yes	—
288	C₄²×C₄₁	C₂⁴	1	4	yes	—
289	C₄²×C₄₁	C₂⁴	1	4	yes	—
290	C₄²×C₄₁	C₂⁴	1	4	yes	—
291	C₄²×C₄₁	C₂⁴	1	16	yes	—
292	C₄²×C₄₁	C₂⁴	1	16	yes	—
293	C₄²×C₄₁	C₂⁴	1	8	yes	—
294	C₄²×C₄₁	C₂⁴	1	16	yes	—
295	C₄²×C₄₁	C₂⁴	1	16	yes	—
296	C₂³×C₄₁	—	2	2	no	—
297	C₂³×C₄₁	—	2	2	no	—
298	C₂³×C₄₁	—	2	4	no	—
299	C₂³×C₄₁	—	2	4	no	—
300	C₂³×C₄₁	—	2	4	no	—
301	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
302	C₂³×C₄₁	C₂⁵	1	4	yes	—
303	C₂³×C₄₁	C₂⁵	1	2	yes	—
304	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
305	Q₈×C₄₁	—	2	16	no	—
306	Q₈×C₄₁	—	4	16	no	—
307	Q₈×C₄₁	—	4	4	no	—
308	Q₈×C₄₁	—	4	8	no	—
309	D₄×C₄₁	—	2	16	no	—
310	D₄×C₄₁	—	4	4	no	—
311	C₂×C₄×C₄₁	—	2	8	no	—
312	C₂×C₄×C₄₁	—	2	16	no	—
313	C₂×C₄×C₄₁	—	2	2	no	—
314	C₂×C₄×C₄₁	—	2	2	no	—
315	C₂×C₄×C₄₁	—	2	8	no	—
316	C₂×C₄×C₄₁	—	2	2	no	—
317	C₂×C₄×C₄₁	—	2	4	no	—
318	C₂×C₄×C₄₁	—	2	4	no	—
319	C₂×C₄×C₄₁	—	2	8	no	—
320	C₂×C₄×C₄₁	—	2	8	no	—
321	C₂×C₄×C₄₁	—	2	2	no	—
322	C₂×C₄×C₄₁	—	2	8	no	—
323	C₂×C₄×C₄₁	—	2	2	no	—
324	C₂×C₄×C₄₁	—	2	4	no	—
325	C₂×C₄×C₄₁	—	2	8	no	—
326	C₂×C₄×C₄₁	—	2	16	no	—
327	C₂×C₄×C₄₁	—	4	8	no	—
328	C₂×C₄×C₄₁	—	4	16	no	—
329	C₂×C₄×C₄₁	—	4	4	no	—
330	C₂×C₄×C₄₁	2₋¹⁺⁴	1	4	yes	—
331	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
332	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
333	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
334	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
335	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
336	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
337	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
338	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
339	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
340	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
341	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
342	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
343	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
344	C₂×#3563	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂²×C₄₁	—	2	2	no	—
346	C₂²×C₄₁	—	2	2	no	—
347	C₂²×C₄₁	—	2	8	no	—
348	C₂²×C₄₁	—	2	4	no	—
349	C₂²×C₄₁	—	2	4	no	—
350	C₂²×C₄₁	—	2	4	no	—
351	C₂²×C₄₁	—	4	8	no	—
352	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	4	yes	—
353	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
354	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
355	C₂²×C₄₁	#585	1	2	yes	—
356	C₂²×C₄₁	C₂⁶	1	1	yes	characteristic
357	C₄×C₄₁	—	2	2	no	—
358	C₄×C₄₁	—	2	2	no	—
359	C₄×C₄₁	—	2	8	no	—
360	C₄×C₄₁	—	2	2	no	—
361	C₄×C₄₁	—	2	4	no	—
362	C₄×C₄₁	—	2	4	no	—
363	C₄×C₄₁	—	2	8	no	—
364	C₄×C₄₁	—	2	8	no	—
365	C₄×C₄₁	—	2	2	no	—
366	C₄×C₄₁	—	2	8	no	—
367	C₄×C₄₁	—	2	2	no	—
368	C₄×C₄₁	—	2	4	no	—
369	C₄×C₄₁	C₂×2₋¹⁺⁴	1	4	yes	—
370	#3563	C₂×C₄₁	1	32	yes	direct product factor
371	C₂×#564	C₂×C₄₁	1	2	yes	complemented
372	C₂×#563	C₂×C₄₁	1	2	yes	complemented
373	C₂×#557	C₂×C₄₁	1	2	yes	complemented
374	C₂×#554	C₂×C₄₁	1	2	yes	complemented
375	C₂×#552	C₂×C₄₁	1	4	yes	complemented
376	C₂×#552	C₂×C₄₁	1	2	yes	complemented
377	C₂×#552	C₂×C₄₁	1	2	yes	complemented
378	C₂×#544	C₂×C₄₁	1	2	yes	complemented
379	C₂×#544	C₂×C₄₁	1	2	yes	complemented
380	C₂×#541	C₂×C₄₁	1	2	yes	complemented
381	C₂×#541	C₂×C₄₁	1	4	yes	complemented
382	C₂×#539	C₂×C₄₁	1	2	yes	—
383	C₂×#533	C₂×C₄₁	1	1	yes	characteristic, complemented
384	C₂×#529	C₂×C₄₁	1	1	yes	characteristic
385	C₂²×#125	C₂×C₄₁	1	1	yes	characteristic, complemented
386	C₂×C₄₁	—	2	4	no	—
387	C₂×C₄₁	—	4	4	no	—
388	C₂×C₄₁	#3563	1	4	yes	direct product factor
389	C₂×C₄₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
390	C₂×C₄₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
391	C₂×C₄₁	C₂×#585	1	1	yes	characteristic
392	#564	C₂²×C₄₁	1	32	yes	complemented
393	#563	C₂²×C₄₁	1	32	yes	complemented
394	#557	C₂²×C₄₁	1	32	yes	complemented
395	#554	C₂²×C₄₁	1	32	yes	complemented
396	#552	C₂²×C₄₁	1	64	yes	complemented
397	#552	C₂²×C₄₁	1	32	yes	complemented
398	#552	C₂²×C₄₁	1	32	yes	complemented
399	#544	C₂²×C₄₁	1	32	yes	complemented
400	#544	C₂²×C₄₁	1	32	yes	complemented
401	#541	C₂²×C₄₁	1	32	yes	complemented
402	#541	C₂²×C₄₁	1	64	yes	complemented
403	#539	C₂²×C₄₁	1	32	yes	—
404	#533	C₂²×C₄₁	1	16	yes	complemented
405	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
406	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
407	C₂×C₄⋊Q₈	C₂²×C₄₁	1	4	yes	—
408	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
409	C₂×C₄⋊Q₈	C₂²×C₄₁	1	4	yes	—
410	#529	C₂²×C₄₁	1	16	yes	—
411	C₂×#126	C₂²×C₄₁	1	2	yes	—
412	C₂×#126	C₂²×C₄₁	1	4	yes	—
413	C₂×#126	C₂²×C₄₁	1	4	yes	—
414	C₂×#126	C₂²×C₄₁	1	4	yes	—
415	C₂×#126	C₂²×C₄₁	1	4	yes	—
416	C₂×#125	C₂²×C₄₁	1	2	yes	—
417	C₂×#125	C₂²×C₄₁	1	2	yes	—
418	C₂×#125	C₂²×C₄₁	1	2	yes	—
419	C₂×#125	C₂²×C₄₁	1	2	yes	—
420	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
421	C₂×#125	C₂²×C₄₁	1	2	yes	—
422	C₂×#125	C₂²×C₄₁	1	4	yes	—
423	C₂×#125	C₂²×C₄₁	1	4	yes	—
424	C₂×#125	C₂²×C₄₁	1	4	yes	—
425	C₂×#125	C₂²×C₄₁	1	4	yes	—
426	C₂×#125	C₂²×C₄₁	1	4	yes	—
427	C₂×#125	C₂²×C₄₁	1	4	yes	—
428	C₂×#125	C₂²×C₄₁	1	2	yes	—
429	C₂×#125	C₂²×C₄₁	1	4	yes	—
430	C₂×#125	C₂²×C₄₁	1	4	yes	—
431	C₂×#125	C₂²×C₄₁	1	16	yes	complemented
432	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
433	C₂×#123	C₂²×C₄₁	1	2	yes	—
434	C₂×#123	C₂²×C₄₁	1	4	yes	—
435	C₂×#123	C₂²×C₄₁	1	4	yes	—
436	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
437	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
438	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
439	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	—
440	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
441	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
442	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	—
443	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	—
444	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	—
445	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
447	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
448	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
449	C₂×C₄×Q₈	C₂²×C₄₁	1	4	yes	—
450	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
451	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
452	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
454	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
455	C₂×#117	C₂²×C₄₁	1	2	yes	—
456	C₂×#117	C₂²×C₄₁	1	2	yes	—
457	C₂×#117	C₂²×C₄₁	1	4	yes	—
458	C₂×#117	C₂²×C₄₁	1	2	yes	—
459	C₂×#117	C₂²×C₄₁	1	4	yes	—
460	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
461	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
462	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
463	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
464	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
465	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
466	C₄₁	C₂×#3563	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
468	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
469	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
470	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
472	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
474	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
477	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
478	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
480	C₄⋊Q₈	C₂³×C₄₁	1	8	yes	—
481	C₄⋊Q₈	C₂³×C₄₁	1	8	yes	—
482	C₄⋊Q₈	C₂³×C₄₁	1	32	yes	—
483	C₄⋊Q₈	C₂³×C₄₁	1	16	yes	—
484	C₄⋊Q₈	C₂³×C₄₁	1	32	yes	—
485	#126	C₂³×C₄₁	1	16	yes	—
486	#126	C₂³×C₄₁	1	32	yes	—
487	#126	C₂³×C₄₁	1	32	yes	—
488	#126	C₂³×C₄₁	1	32	yes	—
489	#126	C₂³×C₄₁	1	32	yes	—
490	#125	C₂³×C₄₁	1	16	yes	—
491	#125	C₂³×C₄₁	1	16	yes	—
492	#125	C₂³×C₄₁	1	16	yes	—
493	#125	C₂³×C₄₁	1	16	yes	—
494	#125	C₂³×C₄₁	1	8	yes	—
495	#125	C₂³×C₄₁	1	16	yes	—
496	#125	C₂³×C₄₁	1	32	yes	—
497	#125	C₂³×C₄₁	1	32	yes	—
498	#125	C₂³×C₄₁	1	32	yes	—
499	#125	C₂³×C₄₁	1	32	yes	—
500	#125	C₂³×C₄₁	1	32	yes	—
501	#125	C₂³×C₄₁	1	32	yes	—
502	#125	C₂³×C₄₁	1	16	yes	—
503	#125	C₂³×C₄₁	1	32	yes	—
504	#125	C₂³×C₄₁	1	32	yes	—
505	#124	C₂³×C₄₁	1	8	yes	—
506	#123	C₂³×C₄₁	1	16	yes	—
507	#123	C₂³×C₄₁	1	32	yes	—
508	#123	C₂³×C₄₁	1	32	yes	—
509	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	—
510	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	—
511	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	—
512	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	—
513	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	—
514	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	—
515	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	—
516	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	—
517	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	—
518	#121	C₂³×C₄₁	1	8	yes	—
519	C₄×Q₈	C₂³×C₄₁	1	8	yes	—
520	C₄×Q₈	C₂³×C₄₁	1	16	yes	—
521	C₄×Q₈	C₂³×C₄₁	1	16	yes	—
522	C₄×Q₈	C₂³×C₄₁	1	32	yes	—
523	C₄×Q₈	C₂³×C₄₁	1	16	yes	—
524	C₄×Q₈	C₂³×C₄₁	1	16	yes	—
525	C₄×D₄	C₂³×C₄₁	1	8	yes	—
526	C₄×D₄	C₂³×C₄₁	1	16	yes	—
527	C₄×D₄	C₂³×C₄₁	1	32	yes	—
528	#117	C₂³×C₄₁	1	16	yes	—
529	#117	C₂³×C₄₁	1	16	yes	—
530	#117	C₂³×C₄₁	1	32	yes	—
531	#117	C₂³×C₄₁	1	16	yes	—
532	#117	C₂³×C₄₁	1	32	yes	—
533	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
542	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₄₁	1	16	yes	—
544	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
545	C₂×C₄⋊C₄	C₂³×C₄₁	1	16	yes	—
546	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
547	C₂×C₄⋊C₄	C₂³×C₄₁	1	16	yes	—
548	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
549	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
563	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
564	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
575	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
576	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
577	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
579	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
580	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
582	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₄₁	1	8	yes	—
585	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
586	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
587	C₂×Q₈	—	2	8	no	—
588	C₂×Q₈	—	4	8	no	—
589	C₂×Q₈	—	4	2	no	—
590	C₂×Q₈	—	4	4	no	—
591	C₂×Q₈	C₂⁴×C₄₁	1	8	yes	—
592	C₂×Q₈	C₂⁴×C₄₁	1	16	yes	—
593	C₂×Q₈	C₂⁴×C₄₁	1	8	yes	—
594	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
595	C₂×D₄	—	2	8	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
598	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
599	C₂²×C₄	—	2	8	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	8	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
618	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
619	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
620	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
621	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
622	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
623	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
624	C₂²×C₄	C₂⁴×C₄₁	1	16	yes	—
625	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
626	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
627	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
628	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
629	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
630	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
631	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
632	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
633	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
634	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
635	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
636	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
637	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
638	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
639	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
640	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
641	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
642	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
643	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
644	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
645	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
646	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
647	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
648	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
649	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
650	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
651	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
652	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
653	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
654	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
655	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
656	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
657	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
658	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
659	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
660	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
661	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
662	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
663	C₄²	C₂⁴×C₄₁	1	4	yes	—
664	C₄²	C₂⁴×C₄₁	1	4	yes	—
665	C₄²	C₂⁴×C₄₁	1	4	yes	—
666	C₄²	C₂⁴×C₄₁	1	4	yes	—
667	C₄²	C₂⁴×C₄₁	1	16	yes	—
668	C₄²	C₂⁴×C₄₁	1	16	yes	—
669	C₄²	C₂⁴×C₄₁	1	8	yes	—
670	C₄²	C₂⁴×C₄₁	1	16	yes	—
671	C₄²	C₂⁴×C₄₁	1	16	yes	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	4	no	—
677	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
678	C₂³	C₂⁵×C₄₁	1	4	yes	—
679	C₂³	C₂⁵×C₄₁	1	2	yes	—
680	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
681	Q₈	—	2	16	no	—
682	Q₈	—	4	16	no	—
683	Q₈	—	4	4	no	—
684	Q₈	—	4	8	no	—
685	D₄	—	2	16	no	—
686	D₄	—	4	4	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	8	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	8	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	8	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	16	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	—	4	16	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	2₋¹⁺⁴×C₄₁	1	4	yes	—
707	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
708	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
709	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
710	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
711	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
712	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
713	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
714	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
715	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
716	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
717	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
718	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
719	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
720	C₂²	—	2	8	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	4	8	no	—
727	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	4	yes	—
728	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
729	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
730	C₂²	C₄₁×#585	1	2	yes	—
731	C₂²	C₂⁶×C₄₁	1	1	yes	characteristic
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	8	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	4	no	—
738	C₄	—	2	8	no	—
739	C₄	—	2	8	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	8	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	4	no	—
744	C₄	C₂×2₋¹⁺⁴×C₄₁	1	4	yes	—
745	C₂	—	2	4	no	—
746	C₂	—	4	4	no	—
747	C₂	C₄₁×#3563	1	4	yes	direct product factor
748	C₂	C₂²×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
749	C₂	C₂²×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
750	C₂	C₂×C₄₁×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
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×#3563	C₂	direct (N × H)
2. C₂×C₄₁×#564	C₂	semidirect
3. C₂×C₄₁×#563	C₂	semidirect
4. C₂×C₄₁×#557	C₂	semidirect
5. C₂×C₄₁×#554	C₂	semidirect
6. C₂×C₄₁×#552	C₂	semidirect
7. C₂×C₄₁×#552	C₂	semidirect
8. C₂×C₄₁×#552	C₂	semidirect
9. C₂×C₄₁×#544	C₂	semidirect
10. C₂×C₄₁×#544	C₂	semidirect
11. C₂×C₄₁×#541	C₂	semidirect
12. C₂×C₄₁×#541	C₂	semidirect
14. C₂×C₄₁×#533	C₂	semidirect
16. C₂²×#125×C₄₁	C₂	semidirect
17. C₄₁×#564	C₂²	semidirect
18. C₄₁×#563	C₂²	semidirect
19. C₄₁×#557	C₂²	semidirect
20. C₄₁×#554	C₂²	semidirect
21. C₄₁×#552	C₂²	semidirect
22. C₄₁×#552	C₂²	semidirect
23. C₄₁×#552	C₂²	semidirect
24. C₄₁×#544	C₂²	semidirect
25. C₄₁×#544	C₂²	semidirect
26. C₄₁×#541	C₂²	semidirect
27. C₄₁×#541	C₂²	semidirect
29. C₄₁×#533	C₂²	semidirect
56. C₂×#125×C₄₁	C₂²	semidirect
344. C₂×#3563	C₄₁	direct (N × H)
370. #3563	C₂×C₄₁	direct (N × H)
371. C₂×#564	C₂×C₄₁	semidirect
372. C₂×#563	C₂×C₄₁	semidirect
373. C₂×#557	C₂×C₄₁	semidirect
374. C₂×#554	C₂×C₄₁	semidirect
375. C₂×#552	C₂×C₄₁	semidirect
376. C₂×#552	C₂×C₄₁	semidirect
377. C₂×#552	C₂×C₄₁	semidirect
378. C₂×#544	C₂×C₄₁	semidirect
379. C₂×#544	C₂×C₄₁	semidirect
380. C₂×#541	C₂×C₄₁	semidirect
381. C₂×#541	C₂×C₄₁	semidirect
383. C₂×#533	C₂×C₄₁	semidirect
385. C₂²×#125	C₂×C₄₁	semidirect
388. C₂×C₄₁	#3563	direct (N × H)
392. #564	C₂²×C₄₁	semidirect
393. #563	C₂²×C₄₁	semidirect
394. #557	C₂²×C₄₁	semidirect
395. #554	C₂²×C₄₁	semidirect
396. #552	C₂²×C₄₁	semidirect
397. #552	C₂²×C₄₁	semidirect
398. #552	C₂²×C₄₁	semidirect
399. #544	C₂²×C₄₁	semidirect
400. #544	C₂²×C₄₁	semidirect
401. #541	C₂²×C₄₁	semidirect
402. #541	C₂²×C₄₁	semidirect
404. #533	C₂²×C₄₁	semidirect
431. C₂×#125	C₂²×C₄₁	semidirect
466. C₄₁	C₂×#3563	direct (N × H)
747. C₂	C₄₁×#3563	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×#3563	2
C₂×C₄₁×#564	2
C₂×C₄₁×#563	2
C₂×C₄₁×#557	2
C₂×C₄₁×#554	2
C₂×C₄₁×#552	2
C₂×C₄₁×#544	2
C₂×C₄₁×#541	2
C₂×C₄₁×#539	2
C₂×C₄₁×#533	2
C₂×C₄₁×#529	2
C₂²×#125×C₄₁	2
C₂×#3563	41

Subgroups — C2×C41×#3563 #23838934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3563 #23838934