Subgroups — C₂×C₁₃×#2450 #15721008

Order 3328.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2450	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
25	C₂×C₄×D₄×C₁₃	—	2	8	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#400	C₂²	1	8	yes	complemented
45	C₁₃×#398	C₂²	1	8	yes	complemented
46	C₁₃×#396	C₂²	1	8	yes	complemented
47	C₁₃×#393	C₂²	1	8	yes	complemented
48	C₁₃×#391	C₂²	1	8	yes	complemented
49	C₁₃×#387	C₂²	1	8	yes	complemented
50	C₁₃×#386	C₂²	1	8	yes	—
51	C₁₃×#386	C₂²	1	8	yes	—
52	C₁₃×#385	C₂²	1	8	yes	complemented
53	C₁₃×#385	C₂²	1	8	yes	complemented
54	C₁₃×#385	C₂²	1	8	yes	complemented
55	C₁₃×#380	C₂²	1	8	yes	complemented
56	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#95	C₂²	1	8	yes	complemented
69	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
70	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	—	2	4	no	—
72	C₂²×Q₈×C₁₃	—	2	4	no	—
73	C₂²×Q₈×C₁₃	—	4	2	no	—
74	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
75	C₂²×D₄×C₁₃	—	2	4	no	—
76	C₂²×D₄×C₁₃	—	2	4	no	—
77	C₂²×D₄×C₁₃	Q₈	1	8	yes	complemented
78	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃	—	2	4	no	—
80	C₂³×C₄×C₁₃	—	2	4	no	—
81	C₂³×C₄×C₁₃	—	2	4	no	—
82	C₂³×C₄×C₁₃	—	2	4	no	—
83	C₂³×C₄×C₁₃	—	2	4	no	—
84	C₂³×C₄×C₁₃	—	2	4	no	—
85	C₂³×C₄×C₁₃	—	2	4	no	—
86	C₂³×C₄×C₁₃	—	4	2	no	—
87	C₂³×C₄×C₁₃	—	4	2	no	—
88	C₂³×C₄×C₁₃	—	4	2	no	—
89	C₂³×C₄×C₁₃	—	4	2	no	—
90	C₂³×C₄×C₁₃	—	4	2	no	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
108	C₁₃×C₂²⋊Q₈	—	2	32	no	—
109	C₄×D₄×C₁₃	—	2	32	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
116	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
117	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₃	—	2	4	no	—
143	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	C₁₃×#95	C₂³	1	4	yes	—
150	C₁₃×#95	C₂³	1	4	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₂×#2450	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂⁴×C₁₃	—	2	2	no	—
158	C₂⁴×C₁₃	—	2	2	no	—
159	C₂⁴×C₁₃	—	2	2	no	—
160	C₂⁴×C₁₃	—	2	2	no	—
161	C₂⁴×C₁₃	—	2	2	no	—
162	C₂⁴×C₁₃	—	2	2	no	—
163	C₂⁴×C₁₃	—	2	2	no	—
164	C₂⁴×C₁₃	—	2	2	no	—
165	C₂⁴×C₁₃	—	2	2	no	—
166	C₂⁴×C₁₃	—	2	2	no	—
167	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
168	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
169	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
170	C₂⁴×C₁₃	#41	1	4	yes	—
171	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
172	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
173	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×Q₈×C₁₃	—	2	8	no	—
175	C₂×Q₈×C₁₃	—	2	8	no	—
176	C₂×Q₈×C₁₃	—	4	4	no	—
177	C₂×Q₈×C₁₃	—	4	16	no	—
178	C₂×D₄×C₁₃	—	2	32	no	—
179	C₂×D₄×C₁₃	—	2	8	no	—
180	C₂×D₄×C₁₃	—	2	8	no	—
181	C₂×D₄×C₁₃	C₂×Q₈	1	16	yes	complemented
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	2	2	no	—
185	C₂²×C₄×C₁₃	—	2	2	no	—
186	C₂²×C₄×C₁₃	—	2	2	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	2	no	—
189	C₂²×C₄×C₁₃	—	2	2	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	2	no	—
193	C₂²×C₄×C₁₃	—	2	2	no	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	8	no	—
197	C₂²×C₄×C₁₃	—	2	8	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	8	no	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	8	no	—
220	C₂²×C₄×C₁₃	—	2	8	no	—
221	C₂²×C₄×C₁₃	—	2	8	no	—
222	C₂²×C₄×C₁₃	—	2	8	no	—
223	C₂²×C₄×C₁₃	—	4	4	no	—
224	C₂²×C₄×C₁₃	—	4	4	no	—
225	C₂²×C₄×C₁₃	—	4	4	no	—
226	C₂²×C₄×C₁₃	—	4	4	no	—
227	C₂²×C₄×C₁₃	—	4	4	no	—
228	C₂²×C₄×C₁₃	—	4	16	no	—
229	C₂²×C₄×C₁₃	—	4	16	no	—
230	C₂²×C₄×C₁₃	—	4	16	no	—
231	C₂²×C₄×C₁₃	—	4	16	no	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
235	C₂²×C₄×C₁₃	#41	1	4	yes	—
236	C₂²×C₄×C₁₃	#41	1	4	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₁₃×C₄⋊C₄	—	2	8	no	—
251	C₁₃×C₄⋊C₄	—	2	8	no	—
252	C₁₃×C₄⋊C₄	—	2	8	no	—
253	C₁₃×C₄⋊C₄	—	2	8	no	—
254	C₁₃×C₄⋊C₄	—	2	8	no	—
255	C₁₃×C₄⋊C₄	—	4	4	no	—
256	C₁₃×C₄⋊C₄	—	4	4	no	—
257	C₁₃×C₄⋊C₄	—	4	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	8	no	—
259	C₁₃×C₂²⋊C₄	—	2	8	no	—
260	C₁₃×C₂²⋊C₄	—	2	8	no	—
261	C₁₃×C₂²⋊C₄	—	2	8	no	—
262	C₁₃×C₂²⋊C₄	—	4	4	no	—
263	C₁₃×C₂²⋊C₄	—	4	4	no	—
264	C₁₃×C₂²⋊C₄	—	4	4	no	—
265	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
266	C₄²×C₁₃	—	2	8	no	—
267	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
268	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
269	#2450	C₂×C₁₃	1	16	yes	direct product factor
270	C₂×#400	C₂×C₁₃	1	1	yes	characteristic, complemented
271	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
272	C₂×#396	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂×#393	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
275	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₂×#386	C₂×C₁₃	1	1	yes	characteristic
277	C₂×#386	C₂×C₁₃	1	1	yes	characteristic
278	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂³×C₁₃	—	2	8	no	—
284	C₂³×C₁₃	—	2	8	no	—
285	C₂³×C₁₃	—	2	8	no	—
286	C₂³×C₁₃	—	2	8	no	—
287	C₂³×C₁₃	—	2	8	no	—
288	C₂³×C₁₃	—	2	8	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	8	no	—
294	C₂³×C₁₃	—	2	8	no	—
295	C₂³×C₁₃	—	2	8	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	2	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	—	4	4	no	—
303	C₂³×C₁₃	—	4	4	no	—
304	C₂³×C₁₃	—	4	4	no	—
305	C₂³×C₁₃	—	4	4	no	—
306	C₂³×C₁₃	C₂²⋊Q₈	1	16	yes	—
307	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
308	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
309	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
310	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
311	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
312	C₂³×C₁₃	C₂×#41	1	4	yes	—
313	C₂³×C₁₃	C₂×#41	1	2	yes	—
314	C₂³×C₁₃	C₂×#41	1	2	yes	—
315	C₂³×C₁₃	C₂×#41	1	2	yes	—
316	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
317	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
318	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
319	Q₈×C₁₃	—	4	16	no	—
320	D₄×C₁₃	—	2	32	no	—
321	C₂×C₄×C₁₃	—	2	8	no	—
322	C₂×C₄×C₁₃	—	2	8	no	—
323	C₂×C₄×C₁₃	—	2	8	no	—
324	C₂×C₄×C₁₃	—	2	8	no	—
325	C₂×C₄×C₁₃	—	2	8	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	4	16	no	—
361	C₂×C₄×C₁₃	—	4	16	no	—
362	C₂×C₄×C₁₃	—	4	16	no	—
363	C₂×C₄×C₁₃	—	4	16	no	—
364	C₂×C₄×C₁₃	—	4	4	no	—
365	C₂×C₄×C₁₃	—	4	4	no	—
366	C₂×C₄×C₁₃	—	4	4	no	—
367	C₂×C₄×C₁₃	—	4	4	no	—
368	C₂×C₄×C₁₃	—	4	4	no	—
369	C₂×C₄×C₁₃	—	4	4	no	—
370	C₂×C₄×C₁₃	—	4	4	no	—
371	C₂×C₄×C₁₃	—	4	4	no	—
372	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
373	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
375	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
376	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
377	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
378	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
379	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
380	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
381	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
382	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×C₂²⋊Q₈	—	2	8	no	—
384	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
385	C₂×C₄×D₄	—	2	8	no	—
386	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
387	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
390	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
392	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
394	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
396	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
397	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
398	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
399	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
400	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
404	#400	C₂²×C₁₃	1	8	yes	complemented
405	#398	C₂²×C₁₃	1	8	yes	complemented
406	#396	C₂²×C₁₃	1	8	yes	complemented
407	#393	C₂²×C₁₃	1	8	yes	complemented
408	#391	C₂²×C₁₃	1	8	yes	complemented
409	#387	C₂²×C₁₃	1	8	yes	complemented
410	#386	C₂²×C₁₃	1	8	yes	—
411	#386	C₂²×C₁₃	1	8	yes	—
412	#385	C₂²×C₁₃	1	8	yes	complemented
413	#385	C₂²×C₁₃	1	8	yes	complemented
414	#385	C₂²×C₁₃	1	8	yes	complemented
415	#380	C₂²×C₁₃	1	8	yes	complemented
416	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
429	C₂²×C₁₃	—	2	4	no	—
430	C₂²×C₁₃	—	2	4	no	—
431	C₂²×C₁₃	—	2	4	no	—
432	C₂²×C₁₃	—	2	4	no	—
433	C₂²×C₁₃	—	2	4	no	—
434	C₂²×C₁₃	—	2	4	no	—
435	C₂²×C₁₃	—	2	32	no	—
436	C₂²×C₁₃	—	2	4	no	—
437	C₂²×C₁₃	—	2	4	no	—
438	C₂²×C₁₃	—	2	4	no	—
439	C₂²×C₁₃	—	4	2	no	—
440	C₂²×C₁₃	—	4	2	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	2	no	—
443	C₂²×C₁₃	—	4	16	no	—
444	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
445	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
446	C₂²×C₁₃	#529	1	4	yes	—
447	C₂²×C₁₃	#538	1	4	yes	—
448	C₂²×C₁₃	#546	1	4	yes	—
449	C₂²×C₁₃	#546	1	4	yes	—
450	C₂²×C₁₃	#554	1	4	yes	—
451	C₂²×C₁₃	#554	1	4	yes	—
452	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
453	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
454	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
455	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
456	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
457	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₄×C₁₃	—	2	4	no	—
460	C₄×C₁₃	—	2	4	no	—
461	C₄×C₁₃	—	2	4	no	—
462	C₄×C₁₃	—	2	4	no	—
463	C₄×C₁₃	—	2	4	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	—	4	2	no	—
468	C₄×C₁₃	—	4	2	no	—
469	C₄×C₁₃	—	4	2	no	—
470	C₄×C₁₃	—	4	2	no	—
471	C₄×C₁₃	—	4	2	no	—
472	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
473	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
474	C₂²×Q₈	—	2	4	no	—
475	C₂²×Q₈	—	2	4	no	—
476	C₂²×Q₈	—	4	2	no	—
477	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
478	C₂²×D₄	—	2	4	no	—
479	C₂²×D₄	—	2	4	no	—
480	C₂²×D₄	Q₈×C₁₃	1	8	yes	complemented
481	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
482	C₂³×C₄	—	2	4	no	—
483	C₂³×C₄	—	2	4	no	—
484	C₂³×C₄	—	2	4	no	—
485	C₂³×C₄	—	2	4	no	—
486	C₂³×C₄	—	2	4	no	—
487	C₂³×C₄	—	2	4	no	—
488	C₂³×C₄	—	2	4	no	—
489	C₂³×C₄	—	4	2	no	—
490	C₂³×C₄	—	4	2	no	—
491	C₂³×C₄	—	4	2	no	—
492	C₂³×C₄	—	4	2	no	—
493	C₂³×C₄	—	4	2	no	—
494	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
503	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
504	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
505	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
511	C₂²⋊Q₈	—	2	32	no	—
512	C₄×D₄	—	2	32	no	—
513	C₂×C₄⋊C₄	—	2	4	no	—
514	C₂×C₄⋊C₄	—	2	4	no	—
515	C₂×C₄⋊C₄	—	2	4	no	—
516	C₂×C₄⋊C₄	—	2	4	no	—
517	C₂×C₄⋊C₄	—	2	4	no	—
518	C₂×C₄⋊C₄	—	4	2	no	—
519	C₂×C₄⋊C₄	—	4	2	no	—
520	C₂×C₄⋊C₄	—	4	2	no	—
521	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
529	C₂×C₂²⋊C₄	—	2	4	no	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₂²⋊C₄	—	2	4	no	—
532	C₂×C₂²⋊C₄	—	2	4	no	—
533	C₂×C₂²⋊C₄	—	4	2	no	—
534	C₂×C₂²⋊C₄	—	4	2	no	—
535	C₂×C₂²⋊C₄	—	4	2	no	—
536	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
545	C₂×C₄²	—	2	4	no	—
546	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
547	#95	C₂³×C₁₃	1	4	yes	—
548	#95	C₂³×C₁₃	1	4	yes	—
549	#95	C₂³×C₁₃	1	4	yes	—
550	#95	C₂³×C₁₃	1	4	yes	—
551	#95	C₂³×C₁₃	1	4	yes	—
552	#95	C₂³×C₁₃	1	4	yes	—
553	#95	C₂³×C₁₃	1	4	yes	—
554	#95	C₂³×C₁₃	1	4	yes	—
555	#95	C₂³×C₁₃	1	4	yes	—
556	#95	C₂³×C₁₃	1	4	yes	—
557	#95	C₂³×C₁₃	1	4	yes	—
558	#95	C₂³×C₁₃	1	4	yes	—
559	C₂×C₁₃	—	2	8	no	—
560	C₂×C₁₃	—	4	4	no	—
561	C₂×C₁₃	#2450	1	8	yes	direct product factor
562	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
563	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
564	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
565	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
566	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
567	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
568	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
569	C₂⁴	—	2	2	no	—
570	C₂⁴	—	2	2	no	—
571	C₂⁴	—	2	2	no	—
572	C₂⁴	—	2	2	no	—
573	C₂⁴	—	2	2	no	—
574	C₂⁴	—	2	2	no	—
575	C₂⁴	—	2	2	no	—
576	C₂⁴	—	2	2	no	—
577	C₂⁴	—	2	2	no	—
578	C₂⁴	—	2	2	no	—
579	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
580	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
581	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
582	C₂⁴	C₁₃×#41	1	4	yes	—
583	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
584	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
585	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
586	C₂×Q₈	—	2	8	no	—
587	C₂×Q₈	—	2	8	no	—
588	C₂×Q₈	—	4	4	no	—
589	C₂×Q₈	—	4	16	no	—
590	C₂×D₄	—	2	32	no	—
591	C₂×D₄	—	2	8	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	C₂×Q₈×C₁₃	1	16	yes	complemented
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	8	no	—
609	C₂²×C₄	—	2	8	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	8	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	8	no	—
632	C₂²×C₄	—	2	8	no	—
633	C₂²×C₄	—	2	8	no	—
634	C₂²×C₄	—	2	8	no	—
635	C₂²×C₄	—	4	4	no	—
636	C₂²×C₄	—	4	4	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	—	4	4	no	—
639	C₂²×C₄	—	4	4	no	—
640	C₂²×C₄	—	4	16	no	—
641	C₂²×C₄	—	4	16	no	—
642	C₂²×C₄	—	4	16	no	—
643	C₂²×C₄	—	4	16	no	—
644	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
645	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
646	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
647	C₂²×C₄	C₁₃×#41	1	4	yes	—
648	C₂²×C₄	C₁₃×#41	1	4	yes	—
649	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
662	C₄⋊C₄	—	2	8	no	—
663	C₄⋊C₄	—	2	8	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	2	8	no	—
666	C₄⋊C₄	—	2	8	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₄⋊C₄	—	4	4	no	—
669	C₄⋊C₄	—	4	4	no	—
670	C₂²⋊C₄	—	2	8	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	2	8	no	—
673	C₂²⋊C₄	—	2	8	no	—
674	C₂²⋊C₄	—	4	4	no	—
675	C₂²⋊C₄	—	4	4	no	—
676	C₂²⋊C₄	—	4	4	no	—
677	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
678	C₄²	—	2	8	no	—
679	C₁₃	C₂×#2450	1	1	yes	characteristic, direct product factor, Sylow
680	C₂³	—	2	8	no	—
681	C₂³	—	2	8	no	—
682	C₂³	—	2	8	no	—
683	C₂³	—	2	8	no	—
684	C₂³	—	2	8	no	—
685	C₂³	—	2	8	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	8	no	—
691	C₂³	—	2	8	no	—
692	C₂³	—	2	8	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	4	4	no	—
701	C₂³	—	4	4	no	—
702	C₂³	—	4	4	no	—
703	C₂³	C₁₃×C₂²⋊Q₈	1	16	yes	—
704	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
705	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
706	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
707	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
708	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
709	C₂³	C₂×C₁₃×#41	1	4	yes	—
710	C₂³	C₂×C₁₃×#41	1	2	yes	—
711	C₂³	C₂×C₁₃×#41	1	2	yes	—
712	C₂³	C₂×C₁₃×#41	1	2	yes	—
713	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
714	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
715	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
716	Q₈	—	4	16	no	—
717	D₄	—	2	32	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	8	no	—
722	C₂×C₄	—	2	8	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	4	16	no	—
758	C₂×C₄	—	4	16	no	—
759	C₂×C₄	—	4	16	no	—
760	C₂×C₄	—	4	16	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
770	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
771	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
772	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
773	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	32	no	—
781	C₂²	—	2	4	no	—
782	C₂²	—	2	4	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	16	no	—
789	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
790	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
791	C₂²	C₁₃×#529	1	4	yes	—
792	C₂²	C₁₃×#538	1	4	yes	—
793	C₂²	C₁₃×#546	1	4	yes	—
794	C₂²	C₁₃×#546	1	4	yes	—
795	C₂²	C₁₃×#554	1	4	yes	—
796	C₂²	C₁₃×#554	1	4	yes	—
797	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
798	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
799	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
800	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
801	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
802	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
803	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
804	C₄	—	2	4	no	—
805	C₄	—	2	4	no	—
806	C₄	—	2	4	no	—
807	C₄	—	2	4	no	—
808	C₄	—	2	4	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₂	—	2	8	no	—
818	C₂	—	4	4	no	—
819	C₂	C₁₃×#2450	1	8	yes	direct product factor
820	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
821	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
822	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
823	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
824	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
825	C₂	C₂×C₁₃×#554	1	1	yes	characteristic
826	C₂	C₂×C₁₃×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2450	C₂	direct (N × H)
4. C₂×C₁₃×#400	C₂	semidirect
5. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#396	C₂	semidirect
7. C₂×C₁₃×#393	C₂	semidirect
8. C₂×C₁₃×#391	C₂	semidirect
9. C₂×C₁₃×#387	C₂	semidirect
12. C₂×C₁₃×#385	C₂	semidirect
13. C₂×C₁₃×#385	C₂	semidirect
14. C₂×C₁₃×#385	C₂	semidirect
15. C₂×C₁₃×#380	C₂	semidirect
16. C₂²×C₁₃×#95	C₂	semidirect
24. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
44. C₁₃×#400	C₂²	semidirect
45. C₁₃×#398	C₂²	semidirect
46. C₁₃×#396	C₂²	semidirect
47. C₁₃×#393	C₂²	semidirect
48. C₁₃×#391	C₂²	semidirect
49. C₁₃×#387	C₂²	semidirect
52. C₁₃×#385	C₂²	semidirect
53. C₁₃×#385	C₂²	semidirect
54. C₁₃×#385	C₂²	semidirect
55. C₁₃×#380	C₂²	semidirect
68. C₂×C₁₃×#95	C₂²	semidirect
77. C₂²×D₄×C₁₃	Q₈	semidirect
156. C₂×#2450	C₁₃	direct (N × H)
181. C₂×D₄×C₁₃	C₂×Q₈	semidirect
267. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
269. #2450	C₂×C₁₃	direct (N × H)
270. C₂×#400	C₂×C₁₃	semidirect
271. C₂×#398	C₂×C₁₃	semidirect
272. C₂×#396	C₂×C₁₃	semidirect
273. C₂×#393	C₂×C₁₃	semidirect
274. C₂×#391	C₂×C₁₃	semidirect
275. C₂×#387	C₂×C₁₃	semidirect
278. C₂×#385	C₂×C₁₃	semidirect
279. C₂×#385	C₂×C₁₃	semidirect
280. C₂×#385	C₂×C₁₃	semidirect
281. C₂×#380	C₂×C₁₃	semidirect
282. C₂²×#95	C₂×C₁₃	semidirect
384. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
404. #400	C₂²×C₁₃	semidirect
405. #398	C₂²×C₁₃	semidirect
406. #396	C₂²×C₁₃	semidirect
407. #393	C₂²×C₁₃	semidirect
408. #391	C₂²×C₁₃	semidirect
409. #387	C₂²×C₁₃	semidirect
412. #385	C₂²×C₁₃	semidirect
413. #385	C₂²×C₁₃	semidirect
414. #385	C₂²×C₁₃	semidirect
415. #380	C₂²×C₁₃	semidirect
428. C₂×#95	C₂²×C₁₃	semidirect
480. C₂²×D₄	Q₈×C₁₃	semidirect
561. C₂×C₁₃	#2450	direct (N × H)
593. C₂×D₄	C₂×Q₈×C₁₃	semidirect
679. C₁₃	C₂×#2450	direct (N × H)
819. C₂	C₁₃×#2450	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×C₁₃×C₂²⋊Q₈	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2450	2
C₂×C₁₃×#400	2
C₂×C₁₃×#398	2
C₂×C₁₃×#396	2
C₂×C₁₃×#393	2
C₂×C₁₃×#391	2
C₂×C₁₃×#387	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#380	2
C₂²×C₁₃×#95	2
C₂×#2450	13

Subgroups — C2×C13×#2450 #15721008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2450 #15721008