Subgroups — C₁₃×#36703 #15723042

Order 3328.

4062 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2846	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2685	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2678	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2670	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2669	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2613	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2534	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2408	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#538	—	2	8	no	—
21	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#120	—	2	8	no	—
32	C₂×C₁₃×#120	C₂²	1	2	yes	—
33	C₂×C₁₃×#120	C₂²	1	4	yes	—
34	C₂×C₁₃×#120	C₂²	1	4	yes	—
35	C₂×C₁₃×#120	C₂²	1	2	yes	—
36	C₂×C₁₃×#120	C₂²	1	2	yes	—
37	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
38	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
39	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
40	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₁₃×#399	C₂²	1	2	yes	complemented
45	C₁₃×#397	C₂²	1	2	yes	complemented
46	C₁₃×#396	C₂²	1	4	yes	complemented
47	C₁₃×#394	C₂²	1	4	yes	complemented
48	C₁₃×#394	C₂²	1	4	yes	complemented
49	C₁₃×#394	C₂²	1	4	yes	complemented
50	C₁₃×#394	C₂²	1	4	yes	complemented
51	C₁₃×#394	C₂²	1	4	yes	complemented
52	C₁₃×#393	C₂²	1	2	yes	complemented
53	C₁₃×#392	C₂²	1	2	yes	complemented
54	C₁₃×#392	C₂²	1	4	yes	complemented
55	C₁₃×#392	C₂²	1	4	yes	complemented
56	C₁₃×#392	C₂²	1	4	yes	complemented
57	C₁₃×#392	C₂²	1	4	yes	complemented
58	C₁₃×#390	C₂²	1	4	yes	complemented
59	C₁₃×#390	C₂²	1	4	yes	complemented
60	C₁₃×#390	C₂²	1	2	yes	complemented
61	C₁₃×#390	C₂²	1	2	yes	complemented
62	C₁₃×#388	C₂²	1	4	yes	complemented
63	C₁₃×#388	C₂²	1	4	yes	complemented
64	C₁₃×#388	C₂²	1	4	yes	complemented
65	C₁₃×#388	C₂²	1	4	yes	complemented
66	C₁₃×#386	C₂²	1	4	yes	complemented
67	C₁₃×#381	C₂²	1	2	yes	complemented
68	C₁₃×#380	C₂²	1	2	yes	complemented
69	C₁₃×#379	C₂²	1	2	yes	—
70	C₁₃×#379	C₂²	1	2	yes	—
71	C₁₃×#379	C₂²	1	2	yes	—
72	C₁₃×#379	C₂²	1	4	yes	complemented
73	C₁₃×#379	C₂²	1	4	yes	complemented
74	C₁₃×#379	C₂²	1	2	yes	complemented
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₁₃	—	2	4	no	—
78	C₂⁵×C₁₃	—	4	4	no	—
79	C₂⁵×C₁₃	—	4	4	no	—
80	C₂⁵×C₁₃	—	4	4	no	—
81	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
82	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
83	C₂⁵×C₁₃	C₂³	1	4	yes	—
84	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
85	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
87	C₂²×D₄×C₁₃	—	2	4	no	—
88	C₂²×D₄×C₁₃	—	2	4	no	—
89	C₂²×D₄×C₁₃	—	2	4	no	—
90	C₂²×D₄×C₁₃	—	4	4	no	—
91	C₂²×D₄×C₁₃	—	4	4	no	—
92	C₂²×D₄×C₁₃	—	4	4	no	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
102	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
103	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
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	2	yes	complemented
108	C₁₃×#127	—	4	4	no	—
109	C₁₃×#126	—	2	8	no	—
110	C₁₃×#124	—	2	8	no	—
111	C₁₃×#124	—	4	4	no	—
112	C₁₃×#123	—	2	8	no	—
113	C₁₃×#123	—	4	4	no	—
114	C₁₃×C₂²⋊Q₈	—	2	4	no	—
115	C₁₃×#121	—	2	4	no	—
116	C₁₃×#121	—	2	8	no	—
117	C₁₃×#121	—	4	8	no	—
118	C₁₃×#120	—	2	8	no	—
119	C₁₃×#120	—	2	16	no	—
120	C₁₃×#120	—	2	16	no	—
121	C₁₃×#120	—	4	4	no	—
122	C₁₃×#120	—	4	4	no	—
123	C₁₃×#120	—	4	4	no	—
124	C₁₃×#120	—	4	8	no	—
125	C₁₃×#120	—	4	8	no	—
126	C₄×D₄×C₁₃	—	2	8	no	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
133	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
160	C₂×C₄²×C₁₃	C₂³	1	2	yes	complemented
161	C₂×C₄²×C₁₃	C₂³	1	2	yes	complemented
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	complemented
163	C₁₃×#95	C₂³	1	2	yes	complemented
164	C₁₃×#95	C₂³	1	2	yes	complemented
165	C₁₃×#95	C₂³	1	4	yes	complemented
166	C₁₃×#95	C₂³	1	4	yes	complemented
167	C₁₃×#95	C₂³	1	4	yes	complemented
168	#36703	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂⁴×C₁₃	—	2	2	no	—
170	C₂⁴×C₁₃	—	2	2	no	—
171	C₂⁴×C₁₃	—	2	4	no	—
172	C₂⁴×C₁₃	—	2	4	no	—
173	C₂⁴×C₁₃	—	2	4	no	—
174	C₂⁴×C₁₃	—	2	8	no	—
175	C₂⁴×C₁₃	—	2	2	no	—
176	C₂⁴×C₁₃	—	2	8	no	—
177	C₂⁴×C₁₃	—	2	8	no	—
178	C₂⁴×C₁₃	—	2	4	no	—
179	C₂⁴×C₁₃	—	2	4	no	—
180	C₂⁴×C₁₃	—	2	4	no	—
181	C₂⁴×C₁₃	—	4	2	no	—
182	C₂⁴×C₁₃	—	4	2	no	—
183	C₂⁴×C₁₃	—	4	2	no	—
184	C₂⁴×C₁₃	—	4	2	no	—
185	C₂⁴×C₁₃	—	4	4	no	—
186	C₂⁴×C₁₃	—	4	4	no	—
187	C₂⁴×C₁₃	—	4	4	no	—
188	C₂⁴×C₁₃	—	4	4	no	—
189	C₂⁴×C₁₃	—	4	2	no	—
190	C₂⁴×C₁₃	—	4	2	no	—
191	C₂⁴×C₁₃	—	4	16	no	—
192	C₂⁴×C₁₃	—	4	16	no	—
193	C₂⁴×C₁₃	—	4	16	no	—
194	C₂⁴×C₁₃	—	4	64	no	—
195	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
196	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
197	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
198	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
199	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
200	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
201	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₁₃	—	2	2	no	—
203	C₂×Q₈×C₁₃	—	4	2	no	—
204	C₂×D₄×C₁₃	—	2	4	no	—
205	C₂×D₄×C₁₃	—	2	8	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	8	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	8	no	—
214	C₂×D₄×C₁₃	—	2	8	no	—
215	C₂×D₄×C₁₃	—	2	8	no	—
216	C₂×D₄×C₁₃	—	2	4	no	—
217	C₂×D₄×C₁₃	—	2	4	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	4	2	no	—
220	C₂×D₄×C₁₃	—	4	2	no	—
221	C₂×D₄×C₁₃	—	4	4	no	—
222	C₂×D₄×C₁₃	—	4	4	no	—
223	C₂×D₄×C₁₃	—	4	4	no	—
224	C₂×D₄×C₁₃	—	4	4	no	—
225	C₂×D₄×C₁₃	—	4	4	no	—
226	C₂×D₄×C₁₃	—	4	4	no	—
227	C₂×D₄×C₁₃	—	4	4	no	—
228	C₂×D₄×C₁₃	—	4	4	no	—
229	C₂×D₄×C₁₃	—	4	4	no	—
230	C₂×D₄×C₁₃	—	4	4	no	—
231	C₂×D₄×C₁₃	—	4	4	no	—
232	C₂×D₄×C₁₃	—	4	2	no	—
233	C₂×D₄×C₁₃	—	4	4	no	—
234	C₂×D₄×C₁₃	—	4	16	no	—
235	C₂×D₄×C₁₃	—	4	16	no	—
236	C₂×D₄×C₁₃	—	4	16	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	2	4	no	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	4	no	—
243	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	2	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	4	4	no	—
259	C₁₃×C₄⋊C₄	—	4	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	8	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	8	no	—
267	C₁₃×C₂²⋊C₄	—	2	8	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	4	4	no	—
273	C₁₃×C₂²⋊C₄	—	4	4	no	—
274	C₁₃×C₂²⋊C₄	—	4	4	no	—
275	C₁₃×C₂²⋊C₄	—	4	4	no	—
276	C₁₃×C₂²⋊C₄	—	4	4	no	—
277	C₁₃×C₂²⋊C₄	—	4	4	no	—
278	C₁₃×C₂²⋊C₄	—	4	4	no	—
279	C₁₃×C₂²⋊C₄	—	4	4	no	—
280	C₁₃×C₂²⋊C₄	—	4	4	no	—
281	C₁₃×C₂²⋊C₄	—	4	4	no	—
282	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
283	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
284	C₄²×C₁₃	—	2	4	no	—
285	C₄²×C₁₃	—	4	2	no	—
286	C₄²×C₁₃	—	4	2	no	—
287	C₂×#538	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂²×#120	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#2846	C₂×C₁₃	1	2	yes	complemented
290	#2685	C₂×C₁₃	1	4	yes	complemented
291	#2678	C₂×C₁₃	1	4	yes	complemented
292	#2670	C₂×C₁₃	1	4	yes	complemented
293	#2669	C₂×C₁₃	1	4	yes	complemented
294	#2613	C₂×C₁₃	1	2	yes	complemented
295	#2561	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#2539	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2534	C₂×C₁₃	1	2	yes	complemented
298	#2435	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2433	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2408	C₂×C₁₃	1	2	yes	complemented
301	#2312	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	8	no	—
305	C₂³×C₁₃	—	2	8	no	—
306	C₂³×C₁₃	—	2	8	no	—
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	4	no	—
310	C₂³×C₁₃	—	2	4	no	—
311	C₂³×C₁₃	—	2	4	no	—
312	C₂³×C₁₃	—	2	4	no	—
313	C₂³×C₁₃	—	2	4	no	—
314	C₂³×C₁₃	—	2	4	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	4	no	—
324	C₂³×C₁₃	—	2	4	no	—
325	C₂³×C₁₃	—	2	4	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	2	4	no	—
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	4	4	no	—
330	C₂³×C₁₃	—	4	4	no	—
331	C₂³×C₁₃	—	4	16	no	—
332	C₂³×C₁₃	—	4	16	no	—
333	C₂³×C₁₃	—	4	16	no	—
334	C₂³×C₁₃	—	4	16	no	—
335	C₂³×C₁₃	—	4	16	no	—
336	C₂³×C₁₃	—	4	4	no	—
337	C₂³×C₁₃	—	4	4	no	—
338	C₂³×C₁₃	—	4	16	no	—
339	C₂³×C₁₃	—	4	16	no	—
340	C₂³×C₁₃	—	4	16	no	—
341	C₂³×C₁₃	—	4	16	no	—
342	C₂³×C₁₃	—	4	4	no	—
343	C₂³×C₁₃	—	4	4	no	—
344	C₂³×C₁₃	—	4	128	no	—
345	C₂³×C₁₃	—	4	16	no	—
346	C₂³×C₁₃	—	4	4	no	—
347	C₂³×C₁₃	—	4	4	no	—
348	C₂³×C₁₃	—	4	4	no	—
349	C₂³×C₁₃	—	8	8	no	—
350	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
351	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
352	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
353	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
354	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
355	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
356	Q₈×C₁₃	—	8	2	no	—
357	D₄×C₁₃	—	4	16	no	—
358	D₄×C₁₃	—	4	8	no	—
359	D₄×C₁₃	—	4	8	no	—
360	D₄×C₁₃	—	4	16	no	—
361	D₄×C₁₃	—	4	8	no	—
362	D₄×C₁₃	—	8	2	no	—
363	D₄×C₁₃	—	8	4	no	—
364	D₄×C₁₃	—	8	4	no	—
365	D₄×C₁₃	—	8	8	no	—
366	D₄×C₁₃	—	8	8	no	—
367	D₄×C₁₃	—	8	8	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	4	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	4	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	2	4	no	—
378	C₂×C₄×C₁₃	—	2	4	no	—
379	C₂×C₄×C₁₃	—	2	4	no	—
380	C₂×C₄×C₁₃	—	2	4	no	—
381	C₂×C₄×C₁₃	—	2	4	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	4	no	—
386	C₂×C₄×C₁₃	—	4	4	no	—
387	C₂×C₄×C₁₃	—	4	4	no	—
388	C₂×C₄×C₁₃	—	4	4	no	—
389	C₂×C₄×C₁₃	—	8	4	no	—
390	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
391	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
393	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
394	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
395	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
396	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
397	#538	—	2	8	no	—
398	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
399	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
400	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
401	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
402	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
403	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
404	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
406	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
407	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₂×#120	—	2	8	no	—
409	C₂×#120	C₂²×C₁₃	1	2	yes	—
410	C₂×#120	C₂²×C₁₃	1	4	yes	—
411	C₂×#120	C₂²×C₁₃	1	4	yes	—
412	C₂×#120	C₂²×C₁₃	1	2	yes	—
413	C₂×#120	C₂²×C₁₃	1	2	yes	—
414	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
415	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
416	C₂×#120	C₂²×C₁₃	1	2	yes	complemented
417	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
418	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
421	#399	C₂²×C₁₃	1	2	yes	complemented
422	#397	C₂²×C₁₃	1	2	yes	complemented
423	#396	C₂²×C₁₃	1	4	yes	complemented
424	#394	C₂²×C₁₃	1	4	yes	complemented
425	#394	C₂²×C₁₃	1	4	yes	complemented
426	#394	C₂²×C₁₃	1	4	yes	complemented
427	#394	C₂²×C₁₃	1	4	yes	complemented
428	#394	C₂²×C₁₃	1	4	yes	complemented
429	#393	C₂²×C₁₃	1	2	yes	complemented
430	#392	C₂²×C₁₃	1	4	yes	complemented
431	#392	C₂²×C₁₃	1	4	yes	complemented
432	#392	C₂²×C₁₃	1	4	yes	complemented
433	#392	C₂²×C₁₃	1	2	yes	complemented
434	#392	C₂²×C₁₃	1	4	yes	complemented
435	#390	C₂²×C₁₃	1	4	yes	complemented
436	#390	C₂²×C₁₃	1	4	yes	complemented
437	#390	C₂²×C₁₃	1	2	yes	complemented
438	#390	C₂²×C₁₃	1	2	yes	complemented
439	#388	C₂²×C₁₃	1	4	yes	complemented
440	#388	C₂²×C₁₃	1	4	yes	complemented
441	#388	C₂²×C₁₃	1	4	yes	complemented
442	#388	C₂²×C₁₃	1	4	yes	complemented
443	#386	C₂²×C₁₃	1	4	yes	complemented
444	#381	C₂²×C₁₃	1	2	yes	complemented
445	#380	C₂²×C₁₃	1	2	yes	complemented
446	#379	C₂²×C₁₃	1	2	yes	—
447	#379	C₂²×C₁₃	1	2	yes	—
448	#379	C₂²×C₁₃	1	2	yes	—
449	#379	C₂²×C₁₃	1	4	yes	complemented
450	#379	C₂²×C₁₃	1	4	yes	complemented
451	#379	C₂²×C₁₃	1	2	yes	complemented
452	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
454	C₂²×C₁₃	—	2	2	no	—
455	C₂²×C₁₃	—	2	2	no	—
456	C₂²×C₁₃	—	2	8	no	—
457	C₂²×C₁₃	—	2	4	no	—
458	C₂²×C₁₃	—	2	4	no	—
459	C₂²×C₁₃	—	2	4	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	2	4	no	—
462	C₂²×C₁₃	—	2	8	no	—
463	C₂²×C₁₃	—	2	8	no	—
464	C₂²×C₁₃	—	4	16	no	—
465	C₂²×C₁₃	—	4	16	no	—
466	C₂²×C₁₃	—	4	16	no	—
467	C₂²×C₁₃	—	4	64	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	4	no	—
473	C₂²×C₁₃	—	4	4	no	—
474	C₂²×C₁₃	—	4	4	no	—
475	C₂²×C₁₃	—	4	4	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	—	4	2	no	—
478	C₂²×C₁₃	—	4	2	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	2	no	—
481	C₂²×C₁₃	—	4	2	no	—
482	C₂²×C₁₃	—	4	4	no	—
483	C₂²×C₁₃	—	4	4	no	—
484	C₂²×C₁₃	—	4	4	no	—
485	C₂²×C₁₃	—	4	4	no	—
486	C₂²×C₁₃	—	8	8	no	—
487	C₂²×C₁₃	#535	1	4	yes	—
488	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
489	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
490	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
491	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
492	C₄×C₁₃	—	2	4	no	—
493	C₄×C₁₃	—	2	2	no	—
494	C₄×C₁₃	—	2	2	no	—
495	C₄×C₁₃	—	4	2	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	—	4	2	no	—
498	C₄×C₁₃	—	4	2	no	—
499	C₄×C₁₃	—	4	4	no	—
500	C₄×C₁₃	—	4	4	no	—
501	C₂⁵	—	2	4	no	—
502	C₂⁵	—	4	4	no	—
503	C₂⁵	—	4	4	no	—
504	C₂⁵	—	4	4	no	—
505	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
506	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
507	C₂⁵	C₂³×C₁₃	1	4	yes	—
508	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
509	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
510	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
511	C₂²×D₄	—	2	4	no	—
512	C₂²×D₄	—	2	4	no	—
513	C₂²×D₄	—	2	4	no	—
514	C₂²×D₄	—	4	4	no	—
515	C₂²×D₄	—	4	4	no	—
516	C₂²×D₄	—	4	4	no	—
517	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
518	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
519	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
520	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
521	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
522	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
523	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
524	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
525	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
526	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
527	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
528	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₁₃	1	2	yes	complemented
532	#127	—	4	4	no	—
533	#126	—	2	8	no	—
534	#124	—	2	8	no	—
535	#124	—	4	4	no	—
536	#123	—	2	8	no	—
537	#123	—	4	4	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	#121	—	2	4	no	—
540	#121	—	2	8	no	—
541	#121	—	4	8	no	—
542	#120	—	2	8	no	—
543	#120	—	2	16	no	—
544	#120	—	2	16	no	—
545	#120	—	4	4	no	—
546	#120	—	4	4	no	—
547	#120	—	4	4	no	—
548	#120	—	4	8	no	—
549	#120	—	4	8	no	—
550	C₄×D₄	—	2	8	no	—
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
557	C₂×C₂²⋊C₄	—	2	4	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
560	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	complemented
579	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	complemented
580	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
581	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
583	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
584	C₂×C₄²	C₂³×C₁₃	1	2	yes	complemented
585	C₂×C₄²	C₂³×C₁₃	1	2	yes	complemented
586	C₂×C₄²	C₂³×C₁₃	1	2	yes	complemented
587	#95	C₂³×C₁₃	1	2	yes	complemented
588	#95	C₂³×C₁₃	1	2	yes	complemented
589	#95	C₂³×C₁₃	1	4	yes	complemented
590	#95	C₂³×C₁₃	1	4	yes	complemented
591	#95	C₂³×C₁₃	1	4	yes	complemented
592	C₂×C₁₃	—	2	4	no	—
593	C₂×C₁₃	—	4	4	no	—
594	C₂×C₁₃	—	4	4	no	—
595	C₂×C₁₃	—	4	4	no	—
596	C₂×C₁₃	—	8	2	no	—
597	C₂×C₁₃	—	8	2	no	—
598	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
599	C₂×C₁₃	#3484	1	1	yes	characteristic
600	C₂×C₁₃	#3484	1	1	yes	characteristic
601	C₂×C₁₃	#3532	1	4	yes	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	4	no	—
605	C₂⁴	—	2	4	no	—
606	C₂⁴	—	2	4	no	—
607	C₂⁴	—	2	8	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	8	no	—
610	C₂⁴	—	2	8	no	—
611	C₂⁴	—	2	4	no	—
612	C₂⁴	—	2	4	no	—
613	C₂⁴	—	2	4	no	—
614	C₂⁴	—	4	2	no	—
615	C₂⁴	—	4	2	no	—
616	C₂⁴	—	4	2	no	—
617	C₂⁴	—	4	2	no	—
618	C₂⁴	—	4	4	no	—
619	C₂⁴	—	4	4	no	—
620	C₂⁴	—	4	4	no	—
621	C₂⁴	—	4	4	no	—
622	C₂⁴	—	4	2	no	—
623	C₂⁴	—	4	2	no	—
624	C₂⁴	—	4	16	no	—
625	C₂⁴	—	4	16	no	—
626	C₂⁴	—	4	16	no	—
627	C₂⁴	—	4	64	no	—
628	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
629	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
630	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
631	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
632	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
633	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
634	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	4	2	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	8	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	8	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	8	no	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	2	8	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	4	4	no	—
659	C₂×D₄	—	4	4	no	—
660	C₂×D₄	—	4	4	no	—
661	C₂×D₄	—	4	4	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	4	16	no	—
668	C₂×D₄	—	4	16	no	—
669	C₂×D₄	—	4	16	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	4	no	—
676	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
677	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
678	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	4	4	no	—
692	C₄⋊C₄	—	4	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	8	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	8	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	4	4	no	—
706	C₂²⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	4	4	no	—
709	C₂²⋊C₄	—	4	4	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	4	no	—
712	C₂²⋊C₄	—	4	4	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂²⋊C₄	—	4	4	no	—
715	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
716	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
717	C₄²	—	2	4	no	—
718	C₄²	—	4	2	no	—
719	C₄²	—	4	2	no	—
720	C₁₃	#36703	1	1	yes	characteristic, direct product factor, Sylow
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	8	no	—
724	C₂³	—	2	8	no	—
725	C₂³	—	2	8	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	4	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	4	no	—
743	C₂³	—	2	4	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	4	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	4	4	no	—
749	C₂³	—	4	4	no	—
750	C₂³	—	4	16	no	—
751	C₂³	—	4	16	no	—
752	C₂³	—	4	16	no	—
753	C₂³	—	4	16	no	—
754	C₂³	—	4	16	no	—
755	C₂³	—	4	16	no	—
756	C₂³	—	4	4	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	16	no	—
759	C₂³	—	4	16	no	—
760	C₂³	—	4	16	no	—
761	C₂³	—	4	4	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	4	128	no	—
764	C₂³	—	4	16	no	—
765	C₂³	—	4	4	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	8	8	no	—
769	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
770	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
771	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
772	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
773	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
774	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
775	Q₈	—	8	2	no	—
776	D₄	—	4	16	no	—
777	D₄	—	4	8	no	—
778	D₄	—	4	8	no	—
779	D₄	—	4	16	no	—
780	D₄	—	4	8	no	—
781	D₄	—	8	2	no	—
782	D₄	—	8	8	no	—
783	D₄	—	8	8	no	—
784	D₄	—	8	4	no	—
785	D₄	—	8	4	no	—
786	D₄	—	8	8	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
810	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
812	C₂²	—	2	8	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	8	no	—
816	C₂²	—	2	8	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	4	16	no	—
823	C₂²	—	4	16	no	—
824	C₂²	—	4	16	no	—
825	C₂²	—	4	64	no	—
826	C₂²	—	4	4	no	—
827	C₂²	—	4	4	no	—
828	C₂²	—	4	4	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	8	8	no	—
845	C₂²	C₁₃×#535	1	4	yes	—
846	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
847	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
848	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
849	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
850	C₄	—	2	4	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	4	no	—
854	C₄	—	4	4	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₂	—	2	4	no	—
860	C₂	—	4	4	no	—
861	C₂	—	4	4	no	—
862	C₂	—	4	4	no	—
863	C₂	—	8	2	no	—
864	C₂	—	8	2	no	—
865	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
866	C₂	C₁₃×#3484	1	1	yes	characteristic
867	C₂	C₁₃×#3484	1	1	yes	characteristic
868	C₂	C₁₃×#3532	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#538	C₂	semidirect
2. C₂²×C₁₃×#120	C₂	semidirect
3. C₁₃×#2846	C₂	semidirect
4. C₁₃×#2685	C₂	semidirect
5. C₁₃×#2678	C₂	semidirect
6. C₁₃×#2670	C₂	semidirect
7. C₁₃×#2669	C₂	semidirect
8. C₁₃×#2613	C₂	semidirect
9. C₁₃×#2561	C₂	semidirect
10. C₁₃×#2539	C₂	semidirect
11. C₁₃×#2534	C₂	semidirect
12. C₁₃×#2435	C₂	semidirect
13. C₁₃×#2433	C₂	semidirect
14. C₁₃×#2408	C₂	semidirect
15. C₁₃×#2312	C₂	semidirect
21. C₂×C₁₃×#127	C₂²	semidirect
22. C₂×C₁₃×#126	C₂²	semidirect
23. C₂×C₁₃×#124	C₂²	semidirect
24. C₂×C₁₃×#124	C₂²	semidirect
25. C₂×C₁₃×#123	C₂²	semidirect
26. C₂×C₁₃×#123	C₂²	semidirect
27. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₁₃×#121	C₂²	semidirect
29. C₂×C₁₃×#121	C₂²	semidirect
30. C₂×C₁₃×#121	C₂²	semidirect
37. C₂×C₁₃×#120	C₂²	semidirect
38. C₂×C₁₃×#120	C₂²	semidirect
39. C₂×C₁₃×#120	C₂²	semidirect
40. C₂×C₄×D₄×C₁₃	C₂²	semidirect
44. C₁₃×#399	C₂²	semidirect
45. C₁₃×#397	C₂²	semidirect
46. C₁₃×#396	C₂²	semidirect
47. C₁₃×#394	C₂²	semidirect
48. C₁₃×#394	C₂²	semidirect
49. C₁₃×#394	C₂²	semidirect
50. C₁₃×#394	C₂²	semidirect
51. C₁₃×#394	C₂²	semidirect
52. C₁₃×#393	C₂²	semidirect
53. C₁₃×#392	C₂²	semidirect
54. C₁₃×#392	C₂²	semidirect
55. C₁₃×#392	C₂²	semidirect
56. C₁₃×#392	C₂²	semidirect
57. C₁₃×#392	C₂²	semidirect
58. C₁₃×#390	C₂²	semidirect
59. C₁₃×#390	C₂²	semidirect
60. C₁₃×#390	C₂²	semidirect
61. C₁₃×#390	C₂²	semidirect
62. C₁₃×#388	C₂²	semidirect
63. C₁₃×#388	C₂²	semidirect
64. C₁₃×#388	C₂²	semidirect
65. C₁₃×#388	C₂²	semidirect
66. C₁₃×#386	C₂²	semidirect
67. C₁₃×#381	C₂²	semidirect
68. C₁₃×#380	C₂²	semidirect
72. C₁₃×#379	C₂²	semidirect
73. C₁₃×#379	C₂²	semidirect
74. C₁₃×#379	C₂²	semidirect
75. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
76. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
86. C₂²×Q₈×C₁₃	C₂³	semidirect
102. C₂²×D₄×C₁₃	C₂³	semidirect
103. C₂²×D₄×C₁₃	C₂³	semidirect
107. C₂³×C₄×C₁₃	C₂³	semidirect
127. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
128. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
129. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
130. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
131. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
132. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
135. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
154. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
155. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
156. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
157. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
158. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
159. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
160. C₂×C₄²×C₁₃	C₂³	semidirect
161. C₂×C₄²×C₁₃	C₂³	semidirect
162. C₂×C₄²×C₁₃	C₂³	semidirect
163. C₁₃×#95	C₂³	semidirect
164. C₁₃×#95	C₂³	semidirect
165. C₁₃×#95	C₂³	semidirect
166. C₁₃×#95	C₂³	semidirect
167. C₁₃×#95	C₂³	semidirect
168. #36703	C₁₃	direct (N × H)
287. C₂×#538	C₂×C₁₃	semidirect
288. C₂²×#120	C₂×C₁₃	semidirect
289. #2846	C₂×C₁₃	semidirect
290. #2685	C₂×C₁₃	semidirect
291. #2678	C₂×C₁₃	semidirect
292. #2670	C₂×C₁₃	semidirect
293. #2669	C₂×C₁₃	semidirect
294. #2613	C₂×C₁₃	semidirect
295. #2561	C₂×C₁₃	semidirect
296. #2539	C₂×C₁₃	semidirect
297. #2534	C₂×C₁₃	semidirect
298. #2435	C₂×C₁₃	semidirect
299. #2433	C₂×C₁₃	semidirect
300. #2408	C₂×C₁₃	semidirect
301. #2312	C₂×C₁₃	semidirect
398. C₂×#127	C₂²×C₁₃	semidirect
399. C₂×#126	C₂²×C₁₃	semidirect
400. C₂×#124	C₂²×C₁₃	semidirect
401. C₂×#124	C₂²×C₁₃	semidirect
402. C₂×#123	C₂²×C₁₃	semidirect
403. C₂×#123	C₂²×C₁₃	semidirect
404. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
405. C₂×#121	C₂²×C₁₃	semidirect
406. C₂×#121	C₂²×C₁₃	semidirect
407. C₂×#121	C₂²×C₁₃	semidirect
414. C₂×#120	C₂²×C₁₃	semidirect
415. C₂×#120	C₂²×C₁₃	semidirect
416. C₂×#120	C₂²×C₁₃	semidirect
417. C₂×C₄×D₄	C₂²×C₁₃	semidirect
421. #399	C₂²×C₁₃	semidirect
422. #397	C₂²×C₁₃	semidirect
423. #396	C₂²×C₁₃	semidirect
424. #394	C₂²×C₁₃	semidirect
425. #394	C₂²×C₁₃	semidirect
426. #394	C₂²×C₁₃	semidirect
427. #394	C₂²×C₁₃	semidirect
428. #394	C₂²×C₁₃	semidirect
429. #393	C₂²×C₁₃	semidirect
430. #392	C₂²×C₁₃	semidirect
431. #392	C₂²×C₁₃	semidirect
432. #392	C₂²×C₁₃	semidirect
433. #392	C₂²×C₁₃	semidirect
434. #392	C₂²×C₁₃	semidirect
435. #390	C₂²×C₁₃	semidirect
436. #390	C₂²×C₁₃	semidirect
437. #390	C₂²×C₁₃	semidirect
438. #390	C₂²×C₁₃	semidirect
439. #388	C₂²×C₁₃	semidirect
440. #388	C₂²×C₁₃	semidirect
441. #388	C₂²×C₁₃	semidirect
442. #388	C₂²×C₁₃	semidirect
443. #386	C₂²×C₁₃	semidirect
444. #381	C₂²×C₁₃	semidirect
445. #380	C₂²×C₁₃	semidirect
449. #379	C₂²×C₁₃	semidirect
450. #379	C₂²×C₁₃	semidirect
451. #379	C₂²×C₁₃	semidirect
452. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
453. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
510. C₂²×Q₈	C₂³×C₁₃	semidirect
526. C₂²×D₄	C₂³×C₁₃	semidirect
527. C₂²×D₄	C₂³×C₁₃	semidirect
531. C₂³×C₄	C₂³×C₁₃	semidirect
551. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
552. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
553. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
554. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
555. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
556. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
559. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
578. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
579. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
580. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
581. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
582. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
583. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
584. C₂×C₄²	C₂³×C₁₃	semidirect
585. C₂×C₄²	C₂³×C₁₃	semidirect
586. C₂×C₄²	C₂³×C₁₃	semidirect
587. #95	C₂³×C₁₃	semidirect
588. #95	C₂³×C₁₃	semidirect
589. #95	C₂³×C₁₃	semidirect
590. #95	C₂³×C₁₃	semidirect
591. #95	C₂³×C₁₃	semidirect
720. C₁₃	#36703	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#538	2
C₂²×C₁₃×#120	2
C₁₃×#2846	2
C₁₃×#2685	2
C₁₃×#2678	2
C₁₃×#2670	2
C₁₃×#2669	2
C₁₃×#2613	2
C₁₃×#2561	2
C₁₃×#2539	2
C₁₃×#2534	2
C₁₃×#2435	2
C₁₃×#2433	2
C₁₃×#2408	2
C₁₃×#2312	2
#36703	13

Subgroups — C13×#36703 #15723042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36703 #15723042