Subgroups — C₂×#1905×C₁₅₁ #50325922

Order 38656.

1678 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#519×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#421×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#419×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#410×C₁₅₁	C₂	1	1	yes	maximal, characteristic
6	#1905×C₁₅₁	C₂	1	8	yes	maximal, direct product factor
7	C₂×#344×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(3,ℤ/4)×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₅₁	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
11	C₂×#137×C₁₅₁	—	2	2	no	—
12	C₂×#137×C₁₅₁	—	2	2	no	—
13	C₂×#137×C₁₅₁	—	2	2	no	—
14	C₂×#137×C₁₅₁	—	2	2	no	—
15	C₂×#137×C₁₅₁	C₄	1	4	yes	complemented
16	C₂×#137×C₁₅₁	C₂²	1	4	yes	—
17	C₂²×Q₁₆×C₁₅₁	C₄	1	2	yes	complemented
18	C₂²×SD₁₆×C₁₅₁	C₄	1	2	yes	complemented
19	C₂²×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
21	#519×C₁₅₁	—	2	2	no	—
22	#519×C₁₅₁	—	2	2	no	—
23	#519×C₁₅₁	—	2	2	no	—
24	#519×C₁₅₁	C₂²	1	4	yes	complemented
25	C₂×C₄×Q₈×C₁₅₁	—	2	2	no	—
26	C₂×C₄×Q₈×C₁₅₁	—	2	2	no	—
27	C₂×#117×C₁₅₁	—	2	2	no	—
28	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
30	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
31	#421×C₁₅₁	—	2	2	no	—
32	#421×C₁₅₁	C₂²	1	4	yes	—
33	C₂×#104×C₁₅₁	—	2	2	no	—
34	#419×C₁₅₁	—	2	2	no	—
35	#419×C₁₅₁	C₂²	1	4	yes	complemented
36	C₂×#103×C₁₅₁	—	2	2	no	—
37	#410×C₁₅₁	—	2	2	no	—
38	#410×C₁₅₁	C₂²	1	4	yes	—
39	C₂×#99×C₁₅₁	—	2	2	no	—
40	#344×C₁₅₁	C₂²	1	4	yes	complemented
41	H(3,ℤ/4)×C₁₅₁	C₂²	1	4	yes	complemented
42	C₂×#41×C₁₅₁	—	2	1	no	—
43	C₂×#41×C₁₅₁	—	2	1	no	—
44	C₂×#41×C₁₅₁	—	2	1	no	—
45	C₂×#41×C₁₅₁	—	2	1	no	—
46	C₂×#41×C₁₅₁	—	2	1	no	—
47	C₂×#41×C₁₅₁	—	2	1	no	—
48	C₂×#41×C₁₅₁	—	2	1	no	—
49	C₂×#41×C₁₅₁	—	2	1	no	—
50	C₂×#41×C₁₅₁	—	2	1	no	—
51	C₂×#41×C₁₅₁	—	2	1	no	—
52	C₂×#41×C₁₅₁	C₂×C₄	1	2	yes	—
53	C₂×#41×C₁₅₁	C₂³	1	2	yes	—
54	C₂²×Q₈×C₁₅₁	—	2	1	no	—
55	C₂²×Q₈×C₁₅₁	—	2	1	no	—
56	C₂²×Q₈×C₁₅₁	—	2	1	no	—
57	C₂²×Q₈×C₁₅₁	—	2	1	no	—
58	C₂²×Q₈×C₁₅₁	—	2	1	no	—
59	C₂²×Q₈×C₁₅₁	—	2	1	no	—
60	C₂²×Q₈×C₁₅₁	—	2	1	no	—
61	C₂²×Q₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×Q₈×C₁₅₁	C₂×C₄	1	2	yes	—
63	C₂²×Q₈×C₁₅₁	C₂×C₄	1	2	yes	—
64	C₂²×Q₈×C₁₅₁	D₄	1	2	yes	—
65	C₂²×Q₈×C₁₅₁	D₄	1	2	yes	—
66	C₂²×Q₈×C₁₅₁	D₄	1	2	yes	—
67	C₂²×Q₈×C₁₅₁	D₄	1	2	yes	—
68	C₂²×Q₈×C₁₅₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₅₁	—	2	1	no	—
70	C₂²×D₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₁₅₁	—	2	1	no	—
72	C₂³×C₄×C₁₅₁	—	2	1	no	—
73	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
74	#137×C₁₅₁	—	2	8	no	—
75	#137×C₁₅₁	—	2	8	no	—
76	#137×C₁₅₁	—	2	8	no	—
77	#137×C₁₅₁	—	2	8	no	—
78	C₂×Q₁₆×C₁₅₁	—	2	4	no	—
79	C₂×Q₁₆×C₁₅₁	—	2	4	no	—
80	C₂×Q₁₆×C₁₅₁	C₂×C₄	1	8	yes	complemented
81	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
82	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
83	C₂×SD₁₆×C₁₅₁	C₂×C₄	1	8	yes	complemented
84	C₂×M₁₆×C₁₅₁	—	2	1	no	—
85	C₂×M₁₆×C₁₅₁	—	2	1	no	—
86	C₂×M₁₆×C₁₅₁	—	2	1	no	—
87	C₂×M₁₆×C₁₅₁	—	2	1	no	—
88	C₂×M₁₆×C₁₅₁	—	2	1	no	—
89	C₂×M₁₆×C₁₅₁	—	2	1	no	—
90	C₂×M₁₆×C₁₅₁	—	2	1	no	—
91	C₂×M₁₆×C₁₅₁	—	2	1	no	—
92	C₂×M₁₆×C₁₅₁	—	2	1	no	—
93	C₂×M₁₆×C₁₅₁	C₂×C₄	1	2	yes	—
94	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
95	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
96	C₂²×C₈×C₁₅₁	—	2	1	no	—
97	C₂²×C₈×C₁₅₁	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₁₅₁	—	2	8	no	—
99	C₄×Q₈×C₁₅₁	—	2	8	no	—
100	C₄×Q₈×C₁₅₁	—	2	8	no	—
101	C₄×Q₈×C₁₅₁	—	2	8	no	—
102	#117×C₁₅₁	—	2	8	no	—
103	#117×C₁₅₁	—	2	1	no	—
104	#117×C₁₅₁	—	2	1	no	—
105	#117×C₁₅₁	—	2	1	no	—
106	#117×C₁₅₁	—	2	1	no	—
107	#117×C₁₅₁	—	2	8	no	—
108	#117×C₁₅₁	—	2	1	no	—
109	#117×C₁₅₁	—	2	1	no	—
110	#117×C₁₅₁	—	2	1	no	—
111	#117×C₁₅₁	D₄	1	2	yes	—
112	#117×C₁₅₁	D₄	1	2	yes	—
113	#117×C₁₅₁	C₂³	1	2	yes	—
114	#117×C₁₅₁	C₂³	1	2	yes	—
115	#117×C₁₅₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₅₁	—	2	4	no	—
117	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
118	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
119	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₅₁	D₄	1	2	yes	—
123	C₂×C₄²×C₁₅₁	—	2	4	no	—
124	C₂×C₄²×C₁₅₁	—	2	1	no	—
125	C₂×C₄²×C₁₅₁	—	2	1	no	—
126	C₂×C₄²×C₁₅₁	D₄	1	2	yes	—
127	#104×C₁₅₁	—	2	8	no	—
128	#103×C₁₅₁	—	2	8	no	—
129	#99×C₁₅₁	—	2	8	no	—
130	C₂⁴×C₁₅₁	—	2	1	no	—
131	C₂⁴×C₁₅₁	C₂×D₄	1	1	yes	characteristic
132	#41×C₁₅₁	—	2	2	no	—
133	#41×C₁₅₁	—	2	2	no	—
134	#41×C₁₅₁	—	2	2	no	—
135	#41×C₁₅₁	—	2	2	no	—
136	#41×C₁₅₁	—	2	2	no	—
137	#41×C₁₅₁	—	2	2	no	—
138	#41×C₁₅₁	—	2	2	no	—
139	#41×C₁₅₁	—	2	2	no	—
140	#41×C₁₅₁	—	4	1	no	—
141	#41×C₁₅₁	—	4	1	no	—
142	#41×C₁₅₁	—	4	1	no	—
143	#41×C₁₅₁	—	4	1	no	—
144	#41×C₁₅₁	—	4	1	no	—
145	#41×C₁₅₁	—	4	1	no	—
146	#41×C₁₅₁	—	4	1	no	—
147	#41×C₁₅₁	—	4	1	no	—
148	C₂×Q₈×C₁₅₁	—	2	2	no	—
149	C₂×Q₈×C₁₅₁	—	2	2	no	—
150	C₂×Q₈×C₁₅₁	—	2	2	no	—
151	C₂×Q₈×C₁₅₁	—	2	2	no	—
152	C₂×Q₈×C₁₅₁	—	2	2	no	—
153	C₂×Q₈×C₁₅₁	—	2	2	no	—
154	C₂×Q₈×C₁₅₁	—	2	1	no	—
155	C₂×Q₈×C₁₅₁	—	2	2	no	—
156	C₂×Q₈×C₁₅₁	—	2	2	no	—
157	C₂×Q₈×C₁₅₁	—	2	2	no	—
158	C₂×Q₈×C₁₅₁	—	2	2	no	—
159	C₂×Q₈×C₁₅₁	—	2	2	no	—
160	C₂×Q₈×C₁₅₁	—	2	2	no	—
161	C₂×Q₈×C₁₅₁	—	2	2	no	—
162	C₂×Q₈×C₁₅₁	—	2	2	no	—
163	C₂×Q₈×C₁₅₁	—	2	2	no	—
164	C₂×Q₈×C₁₅₁	—	2	2	no	—
165	C₂×Q₈×C₁₅₁	—	2	2	no	—
166	C₂×Q₈×C₁₅₁	—	2	2	no	—
167	C₂×Q₈×C₁₅₁	—	2	2	no	—
168	C₂×Q₈×C₁₅₁	—	2	2	no	—
169	C₂×Q₈×C₁₅₁	—	2	2	no	—
170	C₂×Q₈×C₁₅₁	—	2	1	no	—
171	C₂×Q₈×C₁₅₁	—	2	1	no	—
172	C₂×Q₈×C₁₅₁	—	2	1	no	—
173	C₂×Q₈×C₁₅₁	—	2	1	no	—
174	C₂×Q₈×C₁₅₁	C₂²⋊C₄	1	4	yes	—
175	C₂×Q₈×C₁₅₁	C₂²⋊C₄	1	4	yes	—
176	C₂×Q₈×C₁₅₁	C₂²⋊C₄	1	4	yes	—
177	C₂×Q₈×C₁₅₁	C₂²⋊C₄	1	4	yes	—
178	C₂×Q₈×C₁₅₁	C₂²×C₄	1	2	yes	—
179	C₂×Q₈×C₁₅₁	C₂²×C₄	1	4	yes	—
180	C₂×Q₈×C₁₅₁	C₂×D₄	1	4	yes	—
181	C₂×Q₈×C₁₅₁	C₂×D₄	1	4	yes	—
182	C₂×D₄×C₁₅₁	—	2	2	no	—
183	C₂×D₄×C₁₅₁	—	2	2	no	—
184	C₂×D₄×C₁₅₁	—	2	1	no	—
185	C₂×D₄×C₁₅₁	—	2	1	no	—
186	C₂×D₄×C₁₅₁	—	2	1	no	—
187	C₂×D₄×C₁₅₁	—	2	1	no	—
188	C₂×D₄×C₁₅₁	—	2	1	no	—
189	C₂×D₄×C₁₅₁	—	4	1	no	—
190	C₂×D₄×C₁₅₁	—	4	1	no	—
191	C₂×D₄×C₁₅₁	—	4	1	no	—
192	C₂×D₄×C₁₅₁	—	4	1	no	—
193	C₂×D₄×C₁₅₁	C₂²×C₄	1	2	yes	—
194	C₂²×C₄×C₁₅₁	—	2	2	no	—
195	C₂²×C₄×C₁₅₁	—	2	2	no	—
196	C₂²×C₄×C₁₅₁	—	2	2	no	—
197	C₂²×C₄×C₁₅₁	—	2	2	no	—
198	C₂²×C₄×C₁₅₁	—	2	2	no	—
199	C₂²×C₄×C₁₅₁	—	2	2	no	—
200	C₂²×C₄×C₁₅₁	—	2	2	no	—
201	C₂²×C₄×C₁₅₁	—	2	1	no	—
202	C₂²×C₄×C₁₅₁	—	2	2	no	—
203	C₂²×C₄×C₁₅₁	—	2	2	no	—
204	C₂²×C₄×C₁₅₁	—	2	2	no	—
205	C₂²×C₄×C₁₅₁	—	2	2	no	—
206	C₂²×C₄×C₁₅₁	—	4	1	no	—
207	C₂²×C₄×C₁₅₁	—	4	1	no	—
208	C₂²×C₄×C₁₅₁	—	4	1	no	—
209	C₂²×C₄×C₁₅₁	—	4	1	no	—
210	C₂²×C₄×C₁₅₁	—	4	1	no	—
211	C₂²×C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
221	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
222	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
223	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
224	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
225	Q₁₆×C₁₅₁	—	2	16	no	—
226	SD₁₆×C₁₅₁	—	2	16	no	—
227	M₁₆×C₁₅₁	—	2	2	no	—
228	M₁₆×C₁₅₁	—	2	2	no	—
229	M₁₆×C₁₅₁	—	2	2	no	—
230	M₁₆×C₁₅₁	—	2	2	no	—
231	M₁₆×C₁₅₁	—	2	2	no	—
232	M₁₆×C₁₅₁	—	2	2	no	—
233	M₁₆×C₁₅₁	—	4	1	no	—
234	M₁₆×C₁₅₁	—	4	1	no	—
235	C₂×C₈×C₁₅₁	—	2	2	no	—
236	C₂×C₈×C₁₅₁	—	2	2	no	—
237	C₂×C₈×C₁₅₁	—	2	2	no	—
238	C₂×C₈×C₁₅₁	—	4	1	no	—
239	C₂×C₈×C₁₅₁	—	4	1	no	—
240	C₂×C₈×C₁₅₁	C₂²×C₄	1	4	yes	—
241	C₄⋊C₄×C₁₅₁	—	2	16	no	—
242	C₄⋊C₄×C₁₅₁	—	2	2	no	—
243	C₄⋊C₄×C₁₅₁	—	2	2	no	—
244	C₄⋊C₄×C₁₅₁	—	2	2	no	—
245	C₄⋊C₄×C₁₅₁	—	2	2	no	—
246	C₄⋊C₄×C₁₅₁	—	2	2	no	—
247	C₄⋊C₄×C₁₅₁	—	4	1	no	—
248	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
249	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
250	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
251	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
252	C₂²⋊C₄×C₁₅₁	—	4	1	no	—
253	C₂²⋊C₄×C₁₅₁	C₂×D₄	1	4	yes	—
254	C₄²×C₁₅₁	—	2	16	no	—
255	C₄²×C₁₅₁	—	2	2	no	—
256	C₄²×C₁₅₁	—	2	2	no	—
257	C₄²×C₁₅₁	—	2	2	no	—
258	C₄²×C₁₅₁	—	2	2	no	—
259	C₄²×C₁₅₁	—	4	1	no	—
260	C₄²×C₁₅₁	C₂×D₄	1	4	yes	—
261	C₂³×C₁₅₁	—	2	2	no	—
262	C₂³×C₁₅₁	—	4	2	no	—
263	C₂³×C₁₅₁	—	4	1	no	—
264	C₂³×C₁₅₁	—	4	1	no	—
265	C₂³×C₁₅₁	—	8	2	no	—
266	C₂³×C₁₅₁	C₄×D₄	1	1	yes	characteristic
267	C₂³×C₁₅₁	C₄×D₄	1	1	yes	characteristic
268	C₂³×C₁₅₁	#120	1	1	yes	characteristic
269	C₂³×C₁₅₁	#120	1	1	yes	characteristic
270	C₂³×C₁₅₁	#121	1	1	yes	characteristic
271	C₂³×C₁₅₁	#121	1	1	yes	characteristic
272	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
273	Q₈×C₁₅₁	—	2	4	no	—
274	Q₈×C₁₅₁	—	2	4	no	—
275	Q₈×C₁₅₁	—	2	4	no	—
276	Q₈×C₁₅₁	—	2	4	no	—
277	Q₈×C₁₅₁	—	2	4	no	—
278	Q₈×C₁₅₁	—	2	4	no	—
279	Q₈×C₁₅₁	—	2	4	no	—
280	Q₈×C₁₅₁	—	2	2	no	—
281	Q₈×C₁₅₁	—	2	2	no	—
282	Q₈×C₁₅₁	—	4	1	no	—
283	Q₈×C₁₅₁	—	4	1	no	—
284	Q₈×C₁₅₁	C₂×C₂²⋊C₄	1	8	yes	—
285	D₄×C₁₅₁	—	2	2	no	—
286	D₄×C₁₅₁	—	2	2	no	—
287	D₄×C₁₅₁	—	4	2	no	—
288	D₄×C₁₅₁	—	4	2	no	—
289	D₄×C₁₅₁	—	4	2	no	—
290	D₄×C₁₅₁	—	4	2	no	—
291	D₄×C₁₅₁	—	4	1	no	—
292	D₄×C₁₅₁	—	4	1	no	—
293	C₂×C₄×C₁₅₁	—	2	4	no	—
294	C₂×C₄×C₁₅₁	—	2	4	no	—
295	C₂×C₄×C₁₅₁	—	2	4	no	—
296	C₂×C₄×C₁₅₁	—	2	4	no	—
297	C₂×C₄×C₁₅₁	—	2	4	no	—
298	C₂×C₄×C₁₅₁	—	2	4	no	—
299	C₂×C₄×C₁₅₁	—	2	4	no	—
300	C₂×C₄×C₁₅₁	—	2	2	no	—
301	C₂×C₄×C₁₅₁	—	2	4	no	—
302	C₂×C₄×C₁₅₁	—	2	4	no	—
303	C₂×C₄×C₁₅₁	—	4	4	no	—
304	C₂×C₄×C₁₅₁	—	4	4	no	—
305	C₂×C₄×C₁₅₁	—	4	1	no	—
306	C₂×C₄×C₁₅₁	—	4	1	no	—
307	C₂×C₄×C₁₅₁	—	4	2	no	—
308	C₂×C₄×C₁₅₁	—	4	2	no	—
309	C₂×C₄×C₁₅₁	—	4	2	no	—
310	C₂×C₄×C₁₅₁	—	4	2	no	—
311	C₂×C₄×C₁₅₁	—	4	2	no	—
312	C₂×C₄×C₁₅₁	—	8	2	no	—
313	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₅₁	C₄×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₅₁	#120	1	1	yes	characteristic
324	C₂×C₄×C₁₅₁	#120	1	1	yes	characteristic
325	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
326	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
327	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
328	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
329	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
330	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
331	C₂×C₄×C₁₅₁	#123	1	1	yes	characteristic
332	C₂×C₄×C₁₅₁	#123	1	1	yes	characteristic
333	C₂×C₄×C₁₅₁	#123	1	1	yes	characteristic
334	C₂×C₄×C₁₅₁	#123	1	1	yes	characteristic
335	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
336	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
341	C₈×C₁₅₁	—	2	4	no	—
342	C₈×C₁₅₁	—	4	2	no	—
343	C₂²×C₁₅₁	—	2	2	no	—
344	C₂²×C₁₅₁	—	2	2	no	—
345	C₂²×C₁₅₁	—	2	2	no	—
346	C₂²×C₁₅₁	—	4	1	no	—
347	C₂²×C₁₅₁	—	4	1	no	—
348	C₂²×C₁₅₁	—	4	1	no	—
349	C₂²×C₁₅₁	—	4	1	no	—
350	C₂²×C₁₅₁	—	4	2	no	—
351	C₂²×C₁₅₁	—	8	2	no	—
352	C₂²×C₁₅₁	—	8	2	no	—
353	C₂²×C₁₅₁	—	8	2	no	—
354	C₂²×C₁₅₁	#386	1	1	yes	characteristic
355	C₂²×C₁₅₁	#386	1	1	yes	characteristic
356	C₂²×C₁₅₁	#386	1	1	yes	characteristic
357	C₂²×C₁₅₁	#386	1	1	yes	characteristic
358	C₂²×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
359	C₂²×C₁₅₁	C₂×#120	1	1	yes	characteristic
360	C₂²×C₁₅₁	C₂×#121	1	1	yes	characteristic
361	C₄×C₁₅₁	—	2	8	no	—
362	C₄×C₁₅₁	—	4	4	no	—
363	C₄×C₁₅₁	—	4	4	no	—
364	C₄×C₁₅₁	—	4	2	no	—
365	C₄×C₁₅₁	—	8	2	no	—
366	C₄×C₁₅₁	#386	1	1	yes	characteristic
367	C₄×C₁₅₁	#386	1	1	yes	characteristic
368	C₄×C₁₅₁	#386	1	1	yes	characteristic
369	C₄×C₁₅₁	#386	1	1	yes	characteristic
370	C₄×C₁₅₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
371	C₄×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
372	C₄×C₁₅₁	C₂×#121	1	1	yes	characteristic
373	C₄×C₁₅₁	C₂×#123	1	1	yes	characteristic
374	C₂×C₁₅₁	—	2	1	no	—
375	C₂×C₁₅₁	—	2	1	no	—
376	C₂×C₁₅₁	—	2	1	no	—
377	C₂×C₁₅₁	—	2	1	no	—
378	C₂×C₁₅₁	—	2	1	no	—
379	C₂×C₁₅₁	—	2	1	no	—
380	C₂×C₁₅₁	—	8	2	no	—
381	C₂×C₁₅₁	#1905	1	2	yes	direct product factor
382	C₂×C₁₅₁	C₂×#386	1	1	yes	characteristic
383	C₂×#1905	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₁₅₁	C₂×#1905	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²×#137	C₂×C₁₅₁	1	1	yes	characteristic
386	C₂×#519	C₂×C₁₅₁	1	1	yes	characteristic, complemented
387	C₂×#421	C₂×C₁₅₁	1	1	yes	characteristic
388	C₂×#419	C₂×C₁₅₁	1	1	yes	characteristic, complemented
389	C₂×#410	C₂×C₁₅₁	1	1	yes	characteristic
390	#1905	C₂×C₁₅₁	1	8	yes	direct product factor
391	C₂×#344	C₂×C₁₅₁	1	1	yes	characteristic, complemented
392	C₂×H(3,ℤ/4)	C₂×C₁₅₁	1	1	yes	characteristic, complemented
393	C₂²×#41	C₂²×C₁₅₁	1	1	yes	characteristic
394	C₂³×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
395	C₂×#137	—	2	2	no	—
396	C₂×#137	—	2	2	no	—
397	C₂×#137	—	2	2	no	—
398	C₂×#137	—	2	2	no	—
399	C₂×#137	C₄×C₁₅₁	1	4	yes	complemented
400	C₂×#137	C₂²×C₁₅₁	1	4	yes	—
401	C₂²×Q₁₆	C₄×C₁₅₁	1	2	yes	complemented
402	C₂²×SD₁₆	C₄×C₁₅₁	1	2	yes	complemented
403	C₂²×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
404	C₂²×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
405	#519	—	2	2	no	—
406	#519	—	2	2	no	—
407	#519	—	2	2	no	—
408	#519	C₂²×C₁₅₁	1	4	yes	complemented
409	C₂×C₄×Q₈	—	2	2	no	—
410	C₂×C₄×Q₈	—	2	2	no	—
411	C₂×#117	—	2	2	no	—
412	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
413	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
414	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
415	#421	—	2	2	no	—
416	#421	C₂²×C₁₅₁	1	4	yes	—
417	C₂×#104	—	2	2	no	—
418	#419	—	2	2	no	—
419	#419	C₂²×C₁₅₁	1	4	yes	complemented
420	C₂×#103	—	2	2	no	—
421	#410	—	2	2	no	—
422	#410	C₂²×C₁₅₁	1	4	yes	—
423	C₂×#99	—	2	2	no	—
424	#344	C₂²×C₁₅₁	1	4	yes	complemented
425	H(3,ℤ/4)	C₂²×C₁₅₁	1	4	yes	complemented
426	C₂×#41	—	2	1	no	—
427	C₂×#41	—	2	1	no	—
428	C₂×#41	—	2	1	no	—
429	C₂×#41	—	2	1	no	—
430	C₂×#41	—	2	1	no	—
431	C₂×#41	—	2	1	no	—
432	C₂×#41	—	2	1	no	—
433	C₂×#41	—	2	1	no	—
434	C₂×#41	—	2	1	no	—
435	C₂×#41	—	2	1	no	—
436	C₂×#41	C₂×C₄×C₁₅₁	1	2	yes	—
437	C₂×#41	C₂³×C₁₅₁	1	2	yes	—
438	C₂²×Q₈	—	2	1	no	—
439	C₂²×Q₈	—	2	1	no	—
440	C₂²×Q₈	—	2	1	no	—
441	C₂²×Q₈	—	2	1	no	—
442	C₂²×Q₈	—	2	1	no	—
443	C₂²×Q₈	—	2	1	no	—
444	C₂²×Q₈	—	2	1	no	—
445	C₂²×Q₈	C₂×C₄×C₁₅₁	1	1	yes	characteristic
446	C₂²×Q₈	C₂×C₄×C₁₅₁	1	2	yes	—
447	C₂²×Q₈	C₂×C₄×C₁₅₁	1	2	yes	—
448	C₂²×Q₈	D₄×C₁₅₁	1	2	yes	—
449	C₂²×Q₈	D₄×C₁₅₁	1	2	yes	—
450	C₂²×Q₈	D₄×C₁₅₁	1	2	yes	—
451	C₂²×Q₈	D₄×C₁₅₁	1	2	yes	—
452	C₂²×Q₈	C₂³×C₁₅₁	1	2	yes	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	C₂×C₄×C₁₅₁	1	1	yes	characteristic
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
458	#137	—	2	8	no	—
459	#137	—	2	8	no	—
460	#137	—	2	8	no	—
461	#137	—	2	8	no	—
462	C₂×Q₁₆	—	2	4	no	—
463	C₂×Q₁₆	—	2	4	no	—
464	C₂×Q₁₆	C₂×C₄×C₁₅₁	1	8	yes	complemented
465	C₂×SD₁₆	—	2	4	no	—
466	C₂×SD₁₆	—	2	4	no	—
467	C₂×SD₁₆	C₂×C₄×C₁₅₁	1	8	yes	complemented
468	C₂×M₁₆	—	2	1	no	—
469	C₂×M₁₆	—	2	1	no	—
470	C₂×M₁₆	—	2	1	no	—
471	C₂×M₁₆	—	2	1	no	—
472	C₂×M₁₆	—	2	1	no	—
473	C₂×M₁₆	—	2	1	no	—
474	C₂×M₁₆	—	2	1	no	—
475	C₂×M₁₆	—	2	1	no	—
476	C₂×M₁₆	—	2	1	no	—
477	C₂×M₁₆	C₂×C₄×C₁₅₁	1	2	yes	—
478	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
479	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
480	C₂²×C₈	—	2	1	no	—
481	C₂²×C₈	C₂×C₄×C₁₅₁	1	2	yes	—
482	C₄×Q₈	—	2	8	no	—
483	C₄×Q₈	—	2	8	no	—
484	C₄×Q₈	—	2	8	no	—
485	C₄×Q₈	—	2	8	no	—
486	#117	—	2	8	no	—
487	#117	—	2	1	no	—
488	#117	—	2	1	no	—
489	#117	—	2	1	no	—
490	#117	—	2	1	no	—
491	#117	—	2	8	no	—
492	#117	—	2	1	no	—
493	#117	—	2	1	no	—
494	#117	—	2	1	no	—
495	#117	D₄×C₁₅₁	1	2	yes	—
496	#117	D₄×C₁₅₁	1	2	yes	—
497	#117	C₂³×C₁₅₁	1	2	yes	—
498	#117	C₂³×C₁₅₁	1	2	yes	—
499	#117	C₂³×C₁₅₁	1	2	yes	—
500	C₂×C₄⋊C₄	—	2	4	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	D₄×C₁₅₁	1	2	yes	—
507	C₂×C₄²	—	2	4	no	—
508	C₂×C₄²	—	2	1	no	—
509	C₂×C₄²	—	2	1	no	—
510	C₂×C₄²	D₄×C₁₅₁	1	2	yes	—
511	#104	—	2	8	no	—
512	#103	—	2	8	no	—
513	#99	—	2	8	no	—
514	C₂⁴	—	2	1	no	—
515	C₂⁴	C₂×D₄×C₁₅₁	1	1	yes	characteristic
516	#41	—	2	2	no	—
517	#41	—	2	2	no	—
518	#41	—	2	2	no	—
519	#41	—	2	2	no	—
520	#41	—	2	2	no	—
521	#41	—	2	2	no	—
522	#41	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	4	1	no	—
525	#41	—	4	1	no	—
526	#41	—	4	1	no	—
527	#41	—	4	1	no	—
528	#41	—	4	1	no	—
529	#41	—	4	1	no	—
530	#41	—	4	1	no	—
531	#41	—	4	1	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	2	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	2	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	C₂²⋊C₄×C₁₅₁	1	4	yes	—
559	C₂×Q₈	C₂²⋊C₄×C₁₅₁	1	4	yes	—
560	C₂×Q₈	C₂²⋊C₄×C₁₅₁	1	4	yes	—
561	C₂×Q₈	C₂²⋊C₄×C₁₅₁	1	4	yes	—
562	C₂×Q₈	C₂²×C₄×C₁₅₁	1	2	yes	—
563	C₂×Q₈	C₂²×C₄×C₁₅₁	1	4	yes	—
564	C₂×Q₈	C₂×D₄×C₁₅₁	1	4	yes	—
565	C₂×Q₈	C₂×D₄×C₁₅₁	1	4	yes	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	4	1	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	C₂²×C₄×C₁₅₁	1	2	yes	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	1	no	—
592	C₂²×C₄	—	4	1	no	—
593	C₂²×C₄	—	4	1	no	—
594	C₂²×C₄	—	4	1	no	—
595	C₂²×C₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
596	C₂²×C₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
604	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
605	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
606	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
607	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
609	Q₁₆	—	2	16	no	—
610	SD₁₆	—	2	16	no	—
611	M₁₆	—	2	2	no	—
612	M₁₆	—	2	2	no	—
613	M₁₆	—	2	2	no	—
614	M₁₆	—	2	2	no	—
615	M₁₆	—	2	2	no	—
616	M₁₆	—	2	2	no	—
617	M₁₆	—	4	1	no	—
618	M₁₆	—	4	1	no	—
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	4	1	no	—
623	C₂×C₈	—	4	1	no	—
624	C₂×C₈	C₂²×C₄×C₁₅₁	1	4	yes	—
625	C₄⋊C₄	—	2	16	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	4	1	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	4	1	no	—
637	C₂²⋊C₄	C₂×D₄×C₁₅₁	1	4	yes	—
638	C₄²	—	2	16	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	4	1	no	—
644	C₄²	C₂×D₄×C₁₅₁	1	4	yes	—
645	C₂³	—	2	2	no	—
646	C₂³	—	4	2	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	8	2	no	—
650	C₂³	C₄×D₄×C₁₅₁	1	1	yes	characteristic
651	C₂³	C₄×D₄×C₁₅₁	1	1	yes	characteristic
652	C₂³	#120×C₁₅₁	1	1	yes	characteristic
653	C₂³	#120×C₁₅₁	1	1	yes	characteristic
654	C₂³	#121×C₁₅₁	1	1	yes	characteristic
655	C₂³	#121×C₁₅₁	1	1	yes	characteristic
656	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
657	Q₈	—	2	4	no	—
658	Q₈	—	2	4	no	—
659	Q₈	—	2	4	no	—
660	Q₈	—	2	4	no	—
661	Q₈	—	2	4	no	—
662	Q₈	—	2	4	no	—
663	Q₈	—	2	4	no	—
664	Q₈	—	2	2	no	—
665	Q₈	—	2	2	no	—
666	Q₈	—	4	1	no	—
667	Q₈	—	4	1	no	—
668	Q₈	C₂×C₂²⋊C₄×C₁₅₁	1	8	yes	—
669	D₄	—	2	2	no	—
670	D₄	—	2	2	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	2	no	—
673	D₄	—	4	2	no	—
674	D₄	—	4	2	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
698	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
699	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
700	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
701	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
702	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
703	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
704	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
705	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
706	C₂×C₄	C₄×D₄×C₁₅₁	1	1	yes	characteristic
707	C₂×C₄	#120×C₁₅₁	1	1	yes	characteristic
708	C₂×C₄	#120×C₁₅₁	1	1	yes	characteristic
709	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
710	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
711	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
712	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
713	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
714	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
715	C₂×C₄	#123×C₁₅₁	1	1	yes	characteristic
716	C₂×C₄	#123×C₁₅₁	1	1	yes	characteristic
717	C₂×C₄	#123×C₁₅₁	1	1	yes	characteristic
718	C₂×C₄	#123×C₁₅₁	1	1	yes	characteristic
719	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
722	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
723	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
724	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
725	C₈	—	2	4	no	—
726	C₈	—	4	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	8	2	no	—
736	C₂²	—	8	2	no	—
737	C₂²	—	8	2	no	—
738	C₂²	#386×C₁₅₁	1	1	yes	characteristic
739	C₂²	#386×C₁₅₁	1	1	yes	characteristic
740	C₂²	#386×C₁₅₁	1	1	yes	characteristic
741	C₂²	#386×C₁₅₁	1	1	yes	characteristic
742	C₂²	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
743	C₂²	C₂×#120×C₁₅₁	1	1	yes	characteristic
744	C₂²	C₂×#121×C₁₅₁	1	1	yes	characteristic
745	C₄	—	2	8	no	—
746	C₄	—	4	4	no	—
747	C₄	—	4	4	no	—
748	C₄	—	4	2	no	—
749	C₄	—	8	2	no	—
750	C₄	#386×C₁₅₁	1	1	yes	characteristic
751	C₄	#386×C₁₅₁	1	1	yes	characteristic
752	C₄	#386×C₁₅₁	1	1	yes	characteristic
753	C₄	#386×C₁₅₁	1	1	yes	characteristic
754	C₄	C₂²×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
755	C₄	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
756	C₄	C₂×#121×C₁₅₁	1	1	yes	characteristic
757	C₄	C₂×#123×C₁₅₁	1	1	yes	characteristic
758	C₂	—	2	1	no	—
759	C₂	—	2	1	no	—
760	C₂	—	2	1	no	—
761	C₂	—	2	1	no	—
762	C₂	—	2	1	no	—
763	C₂	—	2	1	no	—
764	C₂	—	8	2	no	—
765	C₂	#1905×C₁₅₁	1	2	yes	direct product factor
766	C₂	C₂×#386×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₅₁	#386
commutator	C₂×C₄	C₂³×C₄×C₁₅₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂²×#41×C₁₅₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₁ ◁ C₂³×C₄×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#519×C₁₅₁	C₂	semidirect
4. C₂×#419×C₁₅₁	C₂	semidirect
6. #1905×C₁₅₁	C₂	direct (N × H)
7. C₂×#344×C₁₅₁	C₂	semidirect
8. C₂×H(3,ℤ/4)×C₁₅₁	C₂	semidirect
15. C₂×#137×C₁₅₁	C₄	semidirect
17. C₂²×Q₁₆×C₁₅₁	C₄	semidirect
18. C₂²×SD₁₆×C₁₅₁	C₄	semidirect
24. #519×C₁₅₁	C₂²	semidirect
35. #419×C₁₅₁	C₂²	semidirect
40. #344×C₁₅₁	C₂²	semidirect
41. H(3,ℤ/4)×C₁₅₁	C₂²	semidirect
80. C₂×Q₁₆×C₁₅₁	C₂×C₄	semidirect
83. C₂×SD₁₆×C₁₅₁	C₂×C₄	semidirect
381. C₂×C₁₅₁	#1905	direct (N × H)
383. C₂×#1905	C₁₅₁	direct (N × H)
384. C₁₅₁	C₂×#1905	direct (N × H)
386. C₂×#519	C₂×C₁₅₁	semidirect
388. C₂×#419	C₂×C₁₅₁	semidirect
390. #1905	C₂×C₁₅₁	direct (N × H)
391. C₂×#344	C₂×C₁₅₁	semidirect
392. C₂×H(3,ℤ/4)	C₂×C₁₅₁	semidirect
399. C₂×#137	C₄×C₁₅₁	semidirect
401. C₂²×Q₁₆	C₄×C₁₅₁	semidirect
402. C₂²×SD₁₆	C₄×C₁₅₁	semidirect
408. #519	C₂²×C₁₅₁	semidirect
419. #419	C₂²×C₁₅₁	semidirect
424. #344	C₂²×C₁₅₁	semidirect
425. H(3,ℤ/4)	C₂²×C₁₅₁	semidirect
464. C₂×Q₁₆	C₂×C₄×C₁₅₁	semidirect
467. C₂×SD₁₆	C₂×C₄×C₁₅₁	semidirect
765. C₂	#1905×C₁₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₁₅₁	2
C₂×#519×C₁₅₁	2
C₂×#421×C₁₅₁	2
C₂×#419×C₁₅₁	2
C₂×#410×C₁₅₁	2
#1905×C₁₅₁	2
C₂×#344×C₁₅₁	2
C₂×H(3,ℤ/4)×C₁₅₁	2
C₂×#1905	151

Subgroups — C2×#1905×C151 #50325922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1905×C₁₅₁ #50325922