Subgroups — C₁₃₁×#34720 #45720604

Order 33536.

2548 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2477×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2475×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2463×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2460×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2452×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2446×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2439×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#2432×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#2427×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#2421×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#2415×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#2407×C₁₃₁	C₂	1	1	yes	maximal, characteristic
15	#2398×C₁₃₁	C₂	1	2	yes	maximal, complemented
16	#2392×C₁₃₁	C₂	1	2	yes	maximal, complemented
17	C₄×#124×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂²⋊Q₈×C₁₃₁	C₂	1	2	yes	maximal, complemented
19	C₄×C₂²⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#121×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
21	#2295×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
22	#2290×C₁₃₁	C₂	1	2	yes	maximal, complemented
23	C₄²×D₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₁₃₁	C₂²	1	1	yes	characteristic
25	#533×C₁₃₁	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×#125×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₄×#41×C₁₃₁	—	2	8	no	—
37	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
39	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
49	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
50	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
51	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
54	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
55	#400×C₁₃₁	C₂²	1	2	yes	—
56	#400×C₁₃₁	C₂²	1	2	yes	—
57	#398×C₁₃₁	C₂²	1	2	yes	—
58	#397×C₁₃₁	C₂²	1	2	yes	—
59	#397×C₁₃₁	C₂²	1	2	yes	—
60	#397×C₁₃₁	C₂²	1	2	yes	—
61	#396×C₁₃₁	C₂²	1	2	yes	—
62	#396×C₁₃₁	C₂²	1	2	yes	—
63	#394×C₁₃₁	C₂²	1	2	yes	—
64	#394×C₁₃₁	C₂²	1	2	yes	—
65	#394×C₁₃₁	C₂²	1	2	yes	—
66	#394×C₁₃₁	C₂²	1	2	yes	—
67	#394×C₁₃₁	C₂²	1	2	yes	—
68	#393×C₁₃₁	C₂²	1	2	yes	—
69	#393×C₁₃₁	C₂²	1	2	yes	—
70	#392×C₁₃₁	C₂²	1	2	yes	—
71	#391×C₁₃₁	C₂²	1	2	yes	—
72	#391×C₁₃₁	C₂²	1	1	yes	characteristic
73	#391×C₁₃₁	C₂²	1	1	yes	characteristic
74	#391×C₁₃₁	C₂²	1	1	yes	characteristic
75	#391×C₁₃₁	C₂²	1	1	yes	characteristic
76	#390×C₁₃₁	C₂²	1	1	yes	characteristic
77	#390×C₁₃₁	C₂²	1	1	yes	characteristic
78	#389×C₁₃₁	C₂²	1	2	yes	—
79	#389×C₁₃₁	C₂²	1	1	yes	characteristic
80	#389×C₁₃₁	C₂²	1	1	yes	characteristic
81	#389×C₁₃₁	C₂²	1	1	yes	characteristic
82	#389×C₁₃₁	C₂²	1	1	yes	characteristic
83	#388×C₁₃₁	C₂²	1	2	yes	—
84	#388×C₁₃₁	C₂²	1	2	yes	—
85	#388×C₁₃₁	C₂²	1	2	yes	—
86	#388×C₁₃₁	C₂²	1	2	yes	—
87	#388×C₁₃₁	C₂²	1	2	yes	—
88	#387×C₁₃₁	C₂²	1	2	yes	—
89	#387×C₁₃₁	C₂²	1	2	yes	—
90	#387×C₁₃₁	C₂²	1	2	yes	—
91	#387×C₁₃₁	C₂²	1	2	yes	—
92	#387×C₁₃₁	C₂²	1	2	yes	—
93	#387×C₁₃₁	C₂²	1	2	yes	—
94	#387×C₁₃₁	C₂²	1	2	yes	—
95	#386×C₁₃₁	C₂²	1	2	yes	—
96	#386×C₁₃₁	C₂²	1	2	yes	—
97	#386×C₁₃₁	C₂²	1	2	yes	—
98	#385×C₁₃₁	C₂²	1	2	yes	—
99	#385×C₁₃₁	C₂²	1	2	yes	—
100	#385×C₁₃₁	C₂²	1	2	yes	—
101	#385×C₁₃₁	C₂²	1	2	yes	—
102	#385×C₁₃₁	C₂²	1	2	yes	—
103	#382×C₁₃₁	C₂²	1	1	yes	characteristic
104	#380×C₁₃₁	C₂²	1	1	yes	characteristic
105	#380×C₁₃₁	C₂²	1	1	yes	characteristic
106	#380×C₁₃₁	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
123	#376×C₁₃₁	C₂²	1	2	yes	—
124	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
125	C₂×#41×C₁₃₁	—	2	4	no	—
126	C₂×#41×C₁₃₁	—	2	4	no	—
127	C₂×#41×C₁₃₁	—	2	4	no	—
128	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
130	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
134	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
145	C₄⋊Q₈×C₁₃₁	—	2	4	no	—
146	#125×C₁₃₁	—	2	8	no	—
147	#124×C₁₃₁	—	2	4	no	—
148	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
149	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
150	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
151	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
152	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
153	#121×C₁₃₁	—	2	4	no	—
154	C₄×Q₈×C₁₃₁	—	2	4	no	—
155	C₄×Q₈×C₁₃₁	—	2	8	no	—
156	C₄×Q₈×C₁₃₁	—	2	4	no	—
157	C₄×Q₈×C₁₃₁	D₄	1	8	yes	complemented
158	C₄×D₄×C₁₃₁	—	2	4	no	—
159	C₄×D₄×C₁₃₁	—	2	4	no	—
160	C₄×D₄×C₁₃₁	—	2	8	no	—
161	C₄×D₄×C₁₃₁	—	2	8	no	—
162	C₄×D₄×C₁₃₁	—	2	4	no	—
163	C₄×D₄×C₁₃₁	—	2	4	no	—
164	C₄×D₄×C₁₃₁	—	2	4	no	—
165	C₄×D₄×C₁₃₁	—	2	8	no	—
166	#117×C₁₃₁	—	2	8	no	—
167	#117×C₁₃₁	—	2	4	no	—
168	#117×C₁₃₁	—	2	8	no	—
169	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₃₁	—	2	4	no	—
212	C₂×C₄²×C₁₃₁	—	2	8	no	—
213	C₂×C₄²×C₁₃₁	—	2	4	no	—
214	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
218	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
232	#95×C₁₃₁	C₂³	1	2	yes	—
233	#95×C₁₃₁	C₂³	1	2	yes	—
234	#95×C₁₃₁	C₂³	1	2	yes	—
235	#95×C₁₃₁	C₂³	1	2	yes	—
236	#95×C₁₃₁	C₂³	1	2	yes	—
237	#95×C₁₃₁	C₂³	1	2	yes	—
238	#95×C₁₃₁	C₂³	1	2	yes	—
239	#95×C₁₃₁	C₂³	1	2	yes	—
240	#95×C₁₃₁	C₂³	1	2	yes	—
241	#95×C₁₃₁	C₂³	1	2	yes	—
242	#95×C₁₃₁	C₂³	1	2	yes	—
243	#95×C₁₃₁	C₂³	1	1	yes	characteristic
244	#95×C₁₃₁	C₂³	1	2	yes	—
245	#95×C₁₃₁	C₂³	1	2	yes	—
246	#95×C₁₃₁	C₂³	1	2	yes	—
247	#95×C₁₃₁	C₂³	1	2	yes	—
248	#95×C₁₃₁	C₂³	1	2	yes	—
249	#95×C₁₃₁	C₂³	1	2	yes	—
250	#95×C₁₃₁	C₂³	1	1	yes	characteristic
251	#95×C₁₃₁	C₂³	1	1	yes	characteristic
252	#95×C₁₃₁	C₂³	1	1	yes	characteristic
253	#95×C₁₃₁	C₂³	1	1	yes	characteristic
254	#95×C₁₃₁	C₂³	1	1	yes	characteristic
255	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
256	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
257	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
258	#41×C₁₃₁	—	2	32	no	—
259	C₂×Q₈×C₁₃₁	—	2	4	no	—
260	C₂×Q₈×C₁₃₁	—	2	2	no	—
261	C₂×Q₈×C₁₃₁	—	2	2	no	—
262	C₂×Q₈×C₁₃₁	—	2	2	no	—
263	C₂×Q₈×C₁₃₁	—	2	4	no	—
264	C₂×Q₈×C₁₃₁	—	2	2	no	—
265	C₂×Q₈×C₁₃₁	—	2	2	no	—
266	C₂×Q₈×C₁₃₁	—	4	2	no	—
267	C₂×Q₈×C₁₃₁	C₂×D₄	1	4	yes	—
268	C₂×D₄×C₁₃₁	—	2	2	no	—
269	C₂×D₄×C₁₃₁	—	2	2	no	—
270	C₂×D₄×C₁₃₁	—	2	4	no	—
271	C₂×D₄×C₁₃₁	—	2	4	no	—
272	C₂×D₄×C₁₃₁	—	2	4	no	—
273	C₂×D₄×C₁₃₁	—	2	4	no	—
274	C₂×D₄×C₁₃₁	—	2	4	no	—
275	C₂×D₄×C₁₃₁	—	2	2	no	—
276	C₂×D₄×C₁₃₁	—	2	2	no	—
277	C₂×D₄×C₁₃₁	—	2	2	no	—
278	C₂×D₄×C₁₃₁	—	4	2	no	—
279	C₂×D₄×C₁₃₁	#41	1	4	yes	—
280	C₂²×C₄×C₁₃₁	—	2	4	no	—
281	C₂²×C₄×C₁₃₁	—	2	2	no	—
282	C₂²×C₄×C₁₃₁	—	2	4	no	—
283	C₂²×C₄×C₁₃₁	—	2	2	no	—
284	C₂²×C₄×C₁₃₁	—	2	4	no	—
285	C₂²×C₄×C₁₃₁	—	2	2	no	—
286	C₂²×C₄×C₁₃₁	—	2	2	no	—
287	C₂²×C₄×C₁₃₁	—	2	2	no	—
288	C₂²×C₄×C₁₃₁	—	2	4	no	—
289	C₂²×C₄×C₁₃₁	—	2	2	no	—
290	C₂²×C₄×C₁₃₁	—	2	4	no	—
291	C₂²×C₄×C₁₃₁	—	2	2	no	—
292	C₂²×C₄×C₁₃₁	—	2	2	no	—
293	C₂²×C₄×C₁₃₁	—	2	2	no	—
294	C₂²×C₄×C₁₃₁	—	2	2	no	—
295	C₂²×C₄×C₁₃₁	—	2	2	no	—
296	C₂²×C₄×C₁₃₁	—	2	2	no	—
297	C₂²×C₄×C₁₃₁	—	2	4	no	—
298	C₂²×C₄×C₁₃₁	—	2	2	no	—
299	C₂²×C₄×C₁₃₁	—	2	4	no	—
300	C₂²×C₄×C₁₃₁	—	2	2	no	—
301	C₂²×C₄×C₁₃₁	—	2	4	no	—
302	C₂²×C₄×C₁₃₁	—	4	1	no	—
303	C₂²×C₄×C₁₃₁	—	4	1	no	—
304	C₂²×C₄×C₁₃₁	—	4	2	no	—
305	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
306	C₂²×C₄×C₁₃₁	#41	1	4	yes	complemented
307	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₁₃₁	—	2	4	no	—
328	C₄⋊C₄×C₁₃₁	—	2	2	no	—
329	C₄⋊C₄×C₁₃₁	—	2	4	no	—
330	C₄⋊C₄×C₁₃₁	—	2	4	no	—
331	C₄⋊C₄×C₁₃₁	—	2	4	no	—
332	C₄⋊C₄×C₁₃₁	—	2	4	no	—
333	C₄⋊C₄×C₁₃₁	—	2	4	no	—
334	C₄⋊C₄×C₁₃₁	—	2	4	no	—
335	C₄⋊C₄×C₁₃₁	—	2	2	no	—
336	C₄⋊C₄×C₁₃₁	—	2	2	no	—
337	C₄⋊C₄×C₁₃₁	—	2	2	no	—
338	C₄⋊C₄×C₁₃₁	—	2	4	no	—
339	C₄⋊C₄×C₁₃₁	—	2	2	no	—
340	C₄⋊C₄×C₁₃₁	—	2	4	no	—
341	C₄⋊C₄×C₁₃₁	—	2	2	no	—
342	C₄⋊C₄×C₁₃₁	—	2	4	no	—
343	C₄⋊C₄×C₁₃₁	—	2	4	no	—
344	C₄⋊C₄×C₁₃₁	—	4	2	no	—
345	C₄⋊C₄×C₁₃₁	C₂×D₄	1	8	yes	—
346	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
347	C₄⋊C₄×C₁₃₁	#41	1	4	yes	complemented
348	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
350	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
352	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
353	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
354	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
355	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
356	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
357	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
358	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
359	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
360	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
361	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
362	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
365	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
366	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
367	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
368	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
369	C₄²×C₁₃₁	—	2	2	no	—
370	C₄²×C₁₃₁	—	2	2	no	—
371	C₄²×C₁₃₁	—	2	4	no	—
372	C₄²×C₁₃₁	—	2	4	no	—
373	C₄²×C₁₃₁	—	2	2	no	—
374	C₄²×C₁₃₁	—	2	2	no	—
375	C₄²×C₁₃₁	—	2	2	no	—
376	C₄²×C₁₃₁	—	2	2	no	—
377	C₄²×C₁₃₁	—	2	4	no	—
378	C₄²×C₁₃₁	—	2	2	no	—
379	C₄²×C₁₃₁	—	2	2	no	—
380	C₄²×C₁₃₁	—	2	2	no	—
381	C₄²×C₁₃₁	—	2	4	no	—
382	C₄²×C₁₃₁	—	2	2	no	—
383	C₄²×C₁₃₁	—	2	2	no	—
384	C₄²×C₁₃₁	—	4	1	no	—
385	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
386	C₄²×C₁₃₁	C₂×D₄	1	8	yes	—
387	C₂³×C₁₃₁	—	2	1	no	—
388	C₂³×C₁₃₁	—	2	2	no	—
389	C₂³×C₁₃₁	—	2	1	no	—
390	C₂³×C₁₃₁	—	2	2	no	—
391	C₂³×C₁₃₁	—	2	1	no	—
392	C₂³×C₁₃₁	—	2	1	no	—
393	C₂³×C₁₃₁	—	2	1	no	—
394	C₂³×C₁₃₁	—	2	1	no	—
395	C₂³×C₁₃₁	—	2	2	no	—
396	C₂³×C₁₃₁	—	2	2	no	—
397	C₂³×C₁₃₁	—	2	1	no	—
398	C₂³×C₁₃₁	—	2	1	no	—
399	C₂³×C₁₃₁	—	2	1	no	—
400	C₂³×C₁₃₁	—	2	1	no	—
401	C₂³×C₁₃₁	—	2	2	no	—
402	C₂³×C₁₃₁	—	2	1	no	—
403	C₂³×C₁₃₁	—	2	2	no	—
404	C₂³×C₁₃₁	—	2	1	no	—
405	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
406	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
407	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
408	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
409	Q₈×C₁₃₁	—	2	8	no	—
410	Q₈×C₁₃₁	—	4	8	no	—
411	Q₈×C₁₃₁	—	4	4	no	—
412	D₄×C₁₃₁	—	2	8	no	—
413	D₄×C₁₃₁	—	2	16	no	—
414	D₄×C₁₃₁	—	2	8	no	—
415	D₄×C₁₃₁	—	4	8	no	—
416	C₂×C₄×C₁₃₁	—	2	16	no	—
417	C₂×C₄×C₁₃₁	—	2	1	no	—
418	C₂×C₄×C₁₃₁	—	2	1	no	—
419	C₂×C₄×C₁₃₁	—	2	1	no	—
420	C₂×C₄×C₁₃₁	—	2	1	no	—
421	C₂×C₄×C₁₃₁	—	2	1	no	—
422	C₂×C₄×C₁₃₁	—	2	1	no	—
423	C₂×C₄×C₁₃₁	—	2	1	no	—
424	C₂×C₄×C₁₃₁	—	2	2	no	—
425	C₂×C₄×C₁₃₁	—	2	1	no	—
426	C₂×C₄×C₁₃₁	—	2	2	no	—
427	C₂×C₄×C₁₃₁	—	2	2	no	—
428	C₂×C₄×C₁₃₁	—	2	1	no	—
429	C₂×C₄×C₁₃₁	—	2	1	no	—
430	C₂×C₄×C₁₃₁	—	2	2	no	—
431	C₂×C₄×C₁₃₁	—	2	1	no	—
432	C₂×C₄×C₁₃₁	—	2	1	no	—
433	C₂×C₄×C₁₃₁	—	2	8	no	—
434	C₂×C₄×C₁₃₁	—	2	8	no	—
435	C₂×C₄×C₁₃₁	—	2	1	no	—
436	C₂×C₄×C₁₃₁	—	2	2	no	—
437	C₂×C₄×C₁₃₁	—	2	1	no	—
438	C₂×C₄×C₁₃₁	—	2	2	no	—
439	C₂×C₄×C₁₃₁	—	2	2	no	—
440	C₂×C₄×C₁₃₁	—	2	2	no	—
441	C₂×C₄×C₁₃₁	—	2	1	no	—
442	C₂×C₄×C₁₃₁	—	2	1	no	—
443	C₂×C₄×C₁₃₁	—	2	1	no	—
444	C₂×C₄×C₁₃₁	—	2	1	no	—
445	C₂×C₄×C₁₃₁	—	2	1	no	—
446	C₂×C₄×C₁₃₁	—	2	2	no	—
447	C₂×C₄×C₁₃₁	—	2	1	no	—
448	C₂×C₄×C₁₃₁	—	2	2	no	—
449	C₂×C₄×C₁₃₁	—	2	2	no	—
450	C₂×C₄×C₁₃₁	—	2	2	no	—
451	C₂×C₄×C₁₃₁	—	2	1	no	—
452	C₂×C₄×C₁₃₁	—	2	2	no	—
453	C₂×C₄×C₁₃₁	—	2	1	no	—
454	C₂×C₄×C₁₃₁	—	2	2	no	—
455	C₂×C₄×C₁₃₁	—	2	2	no	—
456	C₂×C₄×C₁₃₁	—	2	2	no	—
457	C₂×C₄×C₁₃₁	—	2	1	no	—
458	C₂×C₄×C₁₃₁	—	2	1	no	—
459	C₂×C₄×C₁₃₁	—	2	2	no	—
460	C₂×C₄×C₁₃₁	—	2	1	no	—
461	C₂×C₄×C₁₃₁	—	2	1	no	—
462	C₂×C₄×C₁₃₁	—	2	1	no	—
463	C₂×C₄×C₁₃₁	—	2	2	no	—
464	C₂×C₄×C₁₃₁	—	2	2	no	—
465	C₂×C₄×C₁₃₁	—	4	4	no	—
466	C₂×C₄×C₁₃₁	—	4	8	no	—
467	C₂×C₄×C₁₃₁	—	4	4	no	—
468	C₂×C₄×C₁₃₁	—	4	4	no	—
469	C₂×C₄×C₁₃₁	—	4	4	no	—
470	C₂×C₄×C₁₃₁	—	4	8	no	—
471	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
473	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
474	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
477	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
478	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
479	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
480	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
481	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
482	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
483	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
484	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
485	C₂²×C₁₃₁	—	2	4	no	—
486	C₂²×C₁₃₁	—	2	2	no	—
487	C₂²×C₁₃₁	—	2	2	no	—
488	C₂²×C₁₃₁	—	2	2	no	—
489	C₂²×C₁₃₁	—	2	2	no	—
490	C₂²×C₁₃₁	—	2	2	no	—
491	C₂²×C₁₃₁	—	2	2	no	—
492	C₂²×C₁₃₁	—	2	4	no	—
493	C₂²×C₁₃₁	—	2	4	no	—
494	C₂²×C₁₃₁	—	4	1	no	—
495	C₂²×C₁₃₁	—	4	2	no	—
496	C₂²×C₁₃₁	—	4	1	no	—
497	C₂²×C₁₃₁	—	4	2	no	—
498	C₂²×C₁₃₁	—	4	1	no	—
499	C₂²×C₁₃₁	—	4	2	no	—
500	C₂²×C₁₃₁	—	4	1	no	—
501	C₂²×C₁₃₁	—	4	2	no	—
502	C₂²×C₁₃₁	—	4	1	no	—
503	C₂²×C₁₃₁	—	4	1	no	—
504	C₂²×C₁₃₁	—	4	1	no	—
505	C₂²×C₁₃₁	—	4	1	no	—
506	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
507	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
508	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
509	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
510	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
511	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
512	C₂²×C₁₃₁	#585	1	1	yes	characteristic
513	C₄×C₁₃₁	—	2	2	no	—
514	C₄×C₁₃₁	—	2	4	no	—
515	C₄×C₁₃₁	—	2	2	no	—
516	C₄×C₁₃₁	—	2	2	no	—
517	C₄×C₁₃₁	—	2	2	no	—
518	C₄×C₁₃₁	—	2	2	no	—
519	C₄×C₁₃₁	—	2	4	no	—
520	C₄×C₁₃₁	—	2	2	no	—
521	C₄×C₁₃₁	—	4	1	no	—
522	C₄×C₁₃₁	—	4	2	no	—
523	C₄×C₁₃₁	—	4	2	no	—
524	C₄×C₁₃₁	—	4	1	no	—
525	C₄×C₁₃₁	—	4	1	no	—
526	C₄×C₁₃₁	—	4	2	no	—
527	C₄×C₁₃₁	—	4	2	no	—
528	C₄×C₁₃₁	—	4	1	no	—
529	C₄×C₁₃₁	—	4	2	no	—
530	C₄×C₁₃₁	—	4	1	no	—
531	C₄×C₁₃₁	#525	1	4	yes	—
532	C₄×C₁₃₁	#548	1	4	yes	—
533	C₂×C₁₃₁	—	4	2	no	—
534	C₂×C₁₃₁	—	4	4	no	—
535	C₂×C₁₃₁	—	4	2	no	—
536	C₂×C₁₃₁	C₂×#525	1	1	yes	characteristic
537	C₂×C₁₃₁	#3444	1	1	yes	characteristic
538	C₂×C₁₃₁	#3461	1	1	yes	characteristic
539	C₂×C₁₃₁	C₂×#548	1	1	yes	characteristic
540	C₂×C₁₃₁	D₄×#41	1	1	yes	characteristic
541	C₂×C₁₃₁	#3475	1	1	yes	characteristic
542	C₂×C₁₃₁	#3482	1	1	yes	characteristic
543	#34720	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
544	C₁₃₁	#34720	1	1	yes	characteristic, direct product factor, Sylow
545	C₂×#533	C₂×C₁₃₁	1	1	yes	characteristic, complemented
546	C₂×C₄×#41	C₂×C₁₃₁	1	1	yes	characteristic, complemented
547	#2477	C₂×C₁₃₁	1	2	yes	complemented
548	#2475	C₂×C₁₃₁	1	2	yes	complemented
549	#2463	C₂×C₁₃₁	1	2	yes	complemented
550	#2460	C₂×C₁₃₁	1	2	yes	complemented
551	#2452	C₂×C₁₃₁	1	1	yes	characteristic, complemented
552	#2446	C₂×C₁₃₁	1	1	yes	characteristic, complemented
553	#2439	C₂×C₁₃₁	1	1	yes	characteristic, complemented
554	#2432	C₂×C₁₃₁	1	1	yes	characteristic, complemented
555	#2427	C₂×C₁₃₁	1	1	yes	characteristic, complemented
556	#2421	C₂×C₁₃₁	1	1	yes	characteristic, complemented
557	#2415	C₂×C₁₃₁	1	1	yes	characteristic, complemented
558	#2407	C₂×C₁₃₁	1	1	yes	characteristic
559	#2398	C₂×C₁₃₁	1	2	yes	complemented
560	#2392	C₂×C₁₃₁	1	2	yes	complemented
561	C₄×#124	C₂×C₁₃₁	1	1	yes	characteristic, complemented
562	C₄×C₂²⋊Q₈	C₂×C₁₃₁	1	2	yes	complemented
563	C₄×C₂²⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
564	C₄×#121	C₂×C₁₃₁	1	1	yes	characteristic, complemented
565	#2295	C₂×C₁₃₁	1	1	yes	characteristic, complemented
566	#2290	C₂×C₁₃₁	1	2	yes	complemented
567	C₄²×D₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
568	C₂²×#41	C₂²×C₁₃₁	1	1	yes	characteristic
569	#533	—	2	8	no	—
570	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
571	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
572	C₂×#125	C₂²×C₁₃₁	1	2	yes	—
573	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
574	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
575	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
576	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
577	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
578	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
579	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
580	C₄×#41	—	2	8	no	—
581	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
582	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
583	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
584	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
585	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
586	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
587	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
588	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
589	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
590	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
591	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
592	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
593	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
594	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
595	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
596	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
597	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
598	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
599	#400	C₂²×C₁₃₁	1	2	yes	—
600	#400	C₂²×C₁₃₁	1	2	yes	—
601	#398	C₂²×C₁₃₁	1	2	yes	—
602	#397	C₂²×C₁₃₁	1	2	yes	—
603	#397	C₂²×C₁₃₁	1	2	yes	—
604	#397	C₂²×C₁₃₁	1	2	yes	—
605	#396	C₂²×C₁₃₁	1	2	yes	—
606	#396	C₂²×C₁₃₁	1	2	yes	—
607	#394	C₂²×C₁₃₁	1	2	yes	—
608	#394	C₂²×C₁₃₁	1	2	yes	—
609	#394	C₂²×C₁₃₁	1	2	yes	—
610	#394	C₂²×C₁₃₁	1	2	yes	—
611	#394	C₂²×C₁₃₁	1	2	yes	—
612	#393	C₂²×C₁₃₁	1	2	yes	—
613	#393	C₂²×C₁₃₁	1	2	yes	—
614	#392	C₂²×C₁₃₁	1	2	yes	—
615	#391	C₂²×C₁₃₁	1	1	yes	characteristic
616	#391	C₂²×C₁₃₁	1	1	yes	characteristic
617	#391	C₂²×C₁₃₁	1	1	yes	characteristic
618	#391	C₂²×C₁₃₁	1	1	yes	characteristic
619	#391	C₂²×C₁₃₁	1	2	yes	—
620	#390	C₂²×C₁₃₁	1	1	yes	characteristic
621	#390	C₂²×C₁₃₁	1	1	yes	characteristic
622	#389	C₂²×C₁₃₁	1	1	yes	characteristic
623	#389	C₂²×C₁₃₁	1	2	yes	—
624	#389	C₂²×C₁₃₁	1	1	yes	characteristic
625	#389	C₂²×C₁₃₁	1	1	yes	characteristic
626	#389	C₂²×C₁₃₁	1	1	yes	characteristic
627	#388	C₂²×C₁₃₁	1	2	yes	—
628	#388	C₂²×C₁₃₁	1	2	yes	—
629	#388	C₂²×C₁₃₁	1	2	yes	—
630	#388	C₂²×C₁₃₁	1	2	yes	—
631	#388	C₂²×C₁₃₁	1	2	yes	—
632	#387	C₂²×C₁₃₁	1	2	yes	—
633	#387	C₂²×C₁₃₁	1	2	yes	—
634	#387	C₂²×C₁₃₁	1	2	yes	—
635	#387	C₂²×C₁₃₁	1	2	yes	—
636	#387	C₂²×C₁₃₁	1	2	yes	—
637	#387	C₂²×C₁₃₁	1	2	yes	—
638	#387	C₂²×C₁₃₁	1	2	yes	—
639	#386	C₂²×C₁₃₁	1	2	yes	—
640	#386	C₂²×C₁₃₁	1	2	yes	—
641	#386	C₂²×C₁₃₁	1	2	yes	—
642	#385	C₂²×C₁₃₁	1	2	yes	—
643	#385	C₂²×C₁₃₁	1	2	yes	—
644	#385	C₂²×C₁₃₁	1	2	yes	—
645	#385	C₂²×C₁₃₁	1	2	yes	—
646	#385	C₂²×C₁₃₁	1	2	yes	—
647	#382	C₂²×C₁₃₁	1	1	yes	characteristic
648	#380	C₂²×C₁₃₁	1	1	yes	characteristic
649	#380	C₂²×C₁₃₁	1	1	yes	characteristic
650	#380	C₂²×C₁₃₁	1	2	yes	—
651	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
652	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
653	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
654	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
655	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
656	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
657	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
658	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
659	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
660	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
661	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
662	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
663	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
664	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
665	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
666	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
667	#376	C₂²×C₁₃₁	1	2	yes	—
668	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
669	C₂×#41	—	2	4	no	—
670	C₂×#41	—	2	4	no	—
671	C₂×#41	—	2	4	no	—
672	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
673	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
674	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
677	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
678	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
679	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
680	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
682	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
685	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
688	C₄⋊Q₈	—	2	4	no	—
689	C₄⋊Q₈	—	2	4	no	—
690	#125	—	2	8	no	—
691	#124	—	2	4	no	—
692	C₂²⋊Q₈	—	2	4	no	—
693	C₂²⋊Q₈	—	2	4	no	—
694	C₂²⋊Q₈	—	2	4	no	—
695	C₂²⋊Q₈	—	2	8	no	—
696	C₂²⋊Q₈	—	2	8	no	—
697	#121	—	2	4	no	—
698	C₄×Q₈	—	2	4	no	—
699	C₄×Q₈	—	2	8	no	—
700	C₄×Q₈	—	2	4	no	—
701	C₄×Q₈	D₄×C₁₃₁	1	8	yes	complemented
702	C₄×D₄	—	2	4	no	—
703	C₄×D₄	—	2	4	no	—
704	C₄×D₄	—	2	8	no	—
705	C₄×D₄	—	2	8	no	—
706	C₄×D₄	—	2	4	no	—
707	C₄×D₄	—	2	4	no	—
708	C₄×D₄	—	2	4	no	—
709	C₄×D₄	—	2	8	no	—
710	#117	—	2	8	no	—
711	#117	—	2	4	no	—
712	#117	—	2	8	no	—
713	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
734	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
755	C₂×C₄²	—	2	4	no	—
756	C₂×C₄²	—	2	8	no	—
757	C₂×C₄²	—	2	4	no	—
758	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
760	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
761	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
763	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
765	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
767	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
775	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
776	#95	C₂³×C₁₃₁	1	2	yes	—
777	#95	C₂³×C₁₃₁	1	2	yes	—
778	#95	C₂³×C₁₃₁	1	2	yes	—
779	#95	C₂³×C₁₃₁	1	2	yes	—
780	#95	C₂³×C₁₃₁	1	1	yes	characteristic
781	#95	C₂³×C₁₃₁	1	1	yes	characteristic
782	#95	C₂³×C₁₃₁	1	1	yes	characteristic
783	#95	C₂³×C₁₃₁	1	1	yes	characteristic
784	#95	C₂³×C₁₃₁	1	1	yes	characteristic
785	#95	C₂³×C₁₃₁	1	1	yes	characteristic
786	#95	C₂³×C₁₃₁	1	2	yes	—
787	#95	C₂³×C₁₃₁	1	2	yes	—
788	#95	C₂³×C₁₃₁	1	2	yes	—
789	#95	C₂³×C₁₃₁	1	2	yes	—
790	#95	C₂³×C₁₃₁	1	2	yes	—
791	#95	C₂³×C₁₃₁	1	2	yes	—
792	#95	C₂³×C₁₃₁	1	2	yes	—
793	#95	C₂³×C₁₃₁	1	2	yes	—
794	#95	C₂³×C₁₃₁	1	2	yes	—
795	#95	C₂³×C₁₃₁	1	2	yes	—
796	#95	C₂³×C₁₃₁	1	2	yes	—
797	#95	C₂³×C₁₃₁	1	2	yes	—
798	#95	C₂³×C₁₃₁	1	2	yes	—
799	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
800	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
801	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
802	#41	—	2	32	no	—
803	C₂×Q₈	—	2	4	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	2	2	no	—
807	C₂×Q₈	—	2	4	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	2	no	—
810	C₂×Q₈	—	4	2	no	—
811	C₂×Q₈	C₂×D₄×C₁₃₁	1	4	yes	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	#41×C₁₃₁	1	4	yes	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	4	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	4	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	4	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	4	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	4	1	no	—
847	C₂²×C₄	—	4	1	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
850	C₂²×C₄	#41×C₁₃₁	1	4	yes	complemented
851	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
871	C₄⋊C₄	—	2	4	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	4	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	2	4	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	2	4	no	—
878	C₄⋊C₄	—	2	4	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	4	2	no	—
889	C₄⋊C₄	C₂×D₄×C₁₃₁	1	8	yes	—
890	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
891	C₄⋊C₄	#41×C₁₃₁	1	4	yes	complemented
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	4	no	—
916	C₄²	—	2	4	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	2	no	—
921	C₄²	—	2	4	no	—
922	C₄²	—	2	2	no	—
923	C₄²	—	2	2	no	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	4	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	4	1	no	—
929	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
930	C₄²	C₂×D₄×C₁₃₁	1	8	yes	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	2	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	1	no	—
949	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
950	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
951	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
952	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
953	Q₈	—	2	8	no	—
954	Q₈	—	4	8	no	—
955	Q₈	—	4	4	no	—
956	D₄	—	2	16	no	—
957	D₄	—	2	8	no	—
958	D₄	—	2	8	no	—
959	D₄	—	4	8	no	—
960	C₂×C₄	—	2	16	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	8	no	—
978	C₂×C₄	—	2	8	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	4	4	no	—
1010	C₂×C₄	—	4	8	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	4	no	—
1013	C₂×C₄	—	4	4	no	—
1014	C₂×C₄	—	4	8	no	—
1015	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
1016	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
1017	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
1018	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
1020	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1021	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1022	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1023	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1024	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1025	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1026	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1027	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
1028	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
1029	C₂²	—	2	4	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	4	no	—
1037	C₂²	—	2	4	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
1051	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
1052	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
1053	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
1054	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
1055	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
1056	C₂²	#585×C₁₃₁	1	1	yes	characteristic
1057	C₄	—	2	2	no	—
1058	C₄	—	2	4	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	#525×C₁₃₁	1	4	yes	—
1076	C₄	#548×C₁₃₁	1	4	yes	—
1077	C₂	—	4	2	no	—
1078	C₂	—	4	4	no	—
1079	C₂	—	4	2	no	—
1080	C₂	C₂×#525×C₁₃₁	1	1	yes	characteristic
1081	C₂	#3444×C₁₃₁	1	1	yes	characteristic
1082	C₂	#3461×C₁₃₁	1	1	yes	characteristic
1083	C₂	C₂×#548×C₁₃₁	1	1	yes	characteristic
1084	C₂	D₄×#41×C₁₃₁	1	1	yes	characteristic
1085	C₂	#3475×C₁₃₁	1	1	yes	characteristic
1086	C₂	#3482×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
socle	C₂³×C₁₃₁	C₂⁵
prime radical	#2407×C₁₃₁	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₁₃₁	C₂	semidirect
2. C₂×C₄×#41×C₁₃₁	C₂	semidirect
3. #2477×C₁₃₁	C₂	semidirect
4. #2475×C₁₃₁	C₂	semidirect
5. #2463×C₁₃₁	C₂	semidirect
6. #2460×C₁₃₁	C₂	semidirect
7. #2452×C₁₃₁	C₂	semidirect
8. #2446×C₁₃₁	C₂	semidirect
9. #2439×C₁₃₁	C₂	semidirect
10. #2432×C₁₃₁	C₂	semidirect
11. #2427×C₁₃₁	C₂	semidirect
12. #2421×C₁₃₁	C₂	semidirect
13. #2415×C₁₃₁	C₂	semidirect
15. #2398×C₁₃₁	C₂	semidirect
16. #2392×C₁₃₁	C₂	semidirect
17. C₄×#124×C₁₃₁	C₂	semidirect
18. C₄×C₂²⋊Q₈×C₁₃₁	C₂	semidirect
19. C₄×C₂²⋊Q₈×C₁₃₁	C₂	semidirect
20. C₄×#121×C₁₃₁	C₂	semidirect
21. #2295×C₁₃₁	C₂	semidirect
22. #2290×C₁₃₁	C₂	semidirect
23. C₄²×D₄×C₁₃₁	C₂	semidirect
157. C₄×Q₈×C₁₃₁	D₄	semidirect
306. C₂²×C₄×C₁₃₁	#41	semidirect
347. C₄⋊C₄×C₁₃₁	#41	semidirect
543. #34720	C₁₃₁	direct (N × H)
544. C₁₃₁	#34720	direct (N × H)
545. C₂×#533	C₂×C₁₃₁	semidirect
546. C₂×C₄×#41	C₂×C₁₃₁	semidirect
547. #2477	C₂×C₁₃₁	semidirect
548. #2475	C₂×C₁₃₁	semidirect
549. #2463	C₂×C₁₃₁	semidirect
550. #2460	C₂×C₁₃₁	semidirect
551. #2452	C₂×C₁₃₁	semidirect
552. #2446	C₂×C₁₃₁	semidirect
553. #2439	C₂×C₁₃₁	semidirect
554. #2432	C₂×C₁₃₁	semidirect
555. #2427	C₂×C₁₃₁	semidirect
556. #2421	C₂×C₁₃₁	semidirect
557. #2415	C₂×C₁₃₁	semidirect
559. #2398	C₂×C₁₃₁	semidirect
560. #2392	C₂×C₁₃₁	semidirect
561. C₄×#124	C₂×C₁₃₁	semidirect
562. C₄×C₂²⋊Q₈	C₂×C₁₃₁	semidirect
563. C₄×C₂²⋊Q₈	C₂×C₁₃₁	semidirect
564. C₄×#121	C₂×C₁₃₁	semidirect
565. #2295	C₂×C₁₃₁	semidirect
566. #2290	C₂×C₁₃₁	semidirect
567. C₄²×D₄	C₂×C₁₃₁	semidirect
701. C₄×Q₈	D₄×C₁₃₁	semidirect
850. C₂²×C₄	#41×C₁₃₁	semidirect
891. C₄⋊C₄	#41×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₃₁	2
C₂×C₄×#41×C₁₃₁	2
#2477×C₁₃₁	2
#2475×C₁₃₁	2
#2463×C₁₃₁	2
#2460×C₁₃₁	2
#2452×C₁₃₁	2
#2446×C₁₃₁	2
#2439×C₁₃₁	2
#2432×C₁₃₁	2
#2427×C₁₃₁	2
#2421×C₁₃₁	2
#2415×C₁₃₁	2
#2407×C₁₃₁	2
#2398×C₁₃₁	2
#2392×C₁₃₁	2
C₄×#124×C₁₃₁	2
C₄×C₂²⋊Q₈×C₁₃₁	2
C₄×#121×C₁₃₁	2
#2295×C₁₃₁	2
#2290×C₁₃₁	2
C₄²×D₄×C₁₃₁	2
#34720	131

Subgroups — C131×#34720 #45720604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34720 #45720604