Subgroups — C₁₃×#35064 #15721403

Order 3328.

2822 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2854	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2663	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2661	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2602	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2591	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2583	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2498	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2430	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2412	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2410	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2322	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2321	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#525	—	2	8	no	—
22	C₂×C₁₃×#123	—	2	8	no	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×#123	C₂²	1	2	yes	—
26	C₂×C₁₃×#123	C₂²	1	2	yes	—
27	C₂×C₁₃×#123	C₂²	1	2	yes	—
28	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#121	C₂²	1	4	yes	—
33	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#120	C₂²	1	2	yes	—
35	C₂×C₁₃×#120	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
46	C₁₃×#400	C₂²	1	2	yes	complemented
47	C₁₃×#399	C₂²	1	2	yes	complemented
48	C₁₃×#398	C₂²	1	2	yes	complemented
49	C₁₃×#397	C₂²	1	2	yes	complemented
50	C₁₃×#397	C₂²	1	4	yes	complemented
51	C₁₃×#395	C₂²	1	2	yes	complemented
52	C₁₃×#394	C₂²	1	4	yes	—
53	C₁₃×#394	C₂²	1	2	yes	complemented
54	C₁₃×#394	C₂²	1	4	yes	complemented
55	C₁₃×#393	C₂²	1	2	yes	complemented
56	C₁₃×#392	C₂²	1	4	yes	—
57	C₁₃×#392	C₂²	1	2	yes	complemented
58	C₁₃×#390	C₂²	1	4	yes	complemented
59	C₁₃×#390	C₂²	1	4	yes	complemented
60	C₁₃×#389	C₂²	1	4	yes	complemented
61	C₁₃×#389	C₂²	1	4	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×#388	C₂²	1	4	yes	complemented
67	C₁₃×#387	C₂²	1	4	yes	complemented
68	C₁₃×#386	C₂²	1	4	yes	—
69	C₁₃×#386	C₂²	1	2	yes	—
70	C₁₃×#386	C₂²	1	2	yes	—
71	C₁₃×#386	C₂²	1	4	yes	complemented
72	C₁₃×#386	C₂²	1	4	yes	complemented
73	C₁₃×#385	C₂²	1	2	yes	—
74	C₁₃×#385	C₂²	1	2	yes	—
75	C₁₃×#385	C₂²	1	4	yes	complemented
76	C₁₃×#381	C₂²	1	2	yes	—
77	C₁₃×#380	C₂²	1	4	yes	complemented
78	C₁₃×#379	C₂²	1	2	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
83	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
84	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
86	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×#41	—	2	4	no	—
88	C₂×C₁₃×#41	—	4	4	no	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	—	2	4	no	—
91	C₂²×D₄×C₁₃	—	4	4	no	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
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	2	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	—	4	4	no	—
100	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
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	2	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#123	—	2	8	no	—
113	C₁₃×#123	—	2	8	no	—
114	C₁₃×#123	—	2	8	no	—
115	C₁₃×#123	—	2	8	no	—
116	C₁₃×#123	—	2	8	no	—
117	C₁₃×#123	—	2	8	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×#121	—	2	4	no	—
121	C₁₃×#121	—	2	4	no	—
122	C₁₃×#121	—	4	8	no	—
123	C₁₃×#120	—	2	8	no	—
124	C₁₃×#120	—	2	8	no	—
125	C₄×D₄×C₁₃	—	2	8	no	—
126	C₄×D₄×C₁₃	—	2	8	no	—
127	C₁₃×#117	—	2	4	no	—
128	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
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	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	—	4	4	no	—
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₁₃×#95	C₂³	1	4	yes	—
171	C₁₃×#95	C₂³	1	2	yes	—
172	C₁₃×#95	C₂³	1	2	yes	—
173	C₁₃×#95	C₂³	1	4	yes	—
174	C₁₃×#95	C₂³	1	4	yes	—
175	C₁₃×#95	C₂³	1	4	yes	—
176	C₁₃×#95	C₂³	1	4	yes	—
177	C₁₃×#95	C₂³	1	4	yes	—
178	C₁₃×#95	C₂³	1	4	yes	—
179	#35064	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	4	no	—
181	C₂⁴×C₁₃	—	2	4	no	—
182	C₂⁴×C₁₃	—	2	2	no	—
183	C₂⁴×C₁₃	—	2	4	no	—
184	C₂⁴×C₁₃	—	4	2	no	—
185	C₂⁴×C₁₃	—	4	2	no	—
186	C₂⁴×C₁₃	—	4	2	no	—
187	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
188	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
189	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
190	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₁₃×#41	—	4	16	no	—
194	C₂×Q₈×C₁₃	—	2	2	no	—
195	C₂×Q₈×C₁₃	—	4	2	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	4	no	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	2	8	no	—
204	C₂×D₄×C₁₃	—	2	8	no	—
205	C₂×D₄×C₁₃	—	2	2	no	—
206	C₂×D₄×C₁₃	—	2	8	no	—
207	C₂×D₄×C₁₃	—	4	4	no	—
208	C₂×D₄×C₁₃	—	4	4	no	—
209	C₂×D₄×C₁₃	—	4	2	no	—
210	C₂×D₄×C₁₃	—	4	4	no	—
211	C₂×D₄×C₁₃	—	4	4	no	—
212	C₂×D₄×C₁₃	—	4	16	no	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	2	4	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	4	no	—
219	C₂²×C₄×C₁₃	—	2	8	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	8	no	—
222	C₂²×C₄×C₁₃	—	4	16	no	—
223	C₂²×C₄×C₁₃	—	4	2	no	—
224	C₂²×C₄×C₁₃	—	4	2	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	4	2	no	—
227	C₂²×C₄×C₁₃	—	4	4	no	—
228	C₂²×C₄×C₁₃	—	4	2	no	—
229	C₂²×C₄×C₁₃	—	4	2	no	—
230	C₂²×C₄×C₁₃	—	4	4	no	—
231	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	4	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	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	8	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	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	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	—	2	8	no	—
273	C₁₃×C₂²⋊C₄	—	2	8	no	—
274	C₁₃×C₂²⋊C₄	—	2	8	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	#41	1	8	yes	complemented
280	C₄²×C₁₃	—	2	4	no	—
281	C₄²×C₁₃	—	4	2	no	—
282	C₄²×C₁₃	—	4	4	no	—
283	C₄²×C₁₃	—	4	2	no	—
284	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#2854	C₂×C₁₃	1	4	yes	complemented
287	#2663	C₂×C₁₃	1	2	yes	complemented
288	#2661	C₂×C₁₃	1	2	yes	complemented
289	#2602	C₂×C₁₃	1	4	yes	complemented
290	#2591	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#2583	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#2561	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#2539	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#2498	C₂×C₁₃	1	2	yes	complemented
295	#2430	C₂×C₁₃	1	2	yes	complemented
296	#2412	C₂×C₁₃	1	2	yes	complemented
297	#2410	C₂×C₁₃	1	2	yes	complemented
298	#2322	C₂×C₁₃	1	2	yes	complemented
299	#2321	C₂×C₁₃	1	2	yes	complemented
300	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	2	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	2	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	4	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	4	no	—
316	C₂³×C₁₃	—	2	4	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	4	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	4	4	no	—
321	C₂³×C₁₃	—	4	16	no	—
322	C₂³×C₁₃	—	4	4	no	—
323	C₂³×C₁₃	—	4	4	no	—
324	C₂³×C₁₃	—	4	4	no	—
325	C₂³×C₁₃	—	8	8	no	—
326	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
327	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
328	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
329	C₂³×C₁₃	C₂×#41	1	4	yes	—
330	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
331	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
332	Q₈×C₁₃	—	4	4	no	—
333	D₄×C₁₃	—	4	4	no	—
334	D₄×C₁₃	—	4	8	no	—
335	D₄×C₁₃	—	4	8	no	—
336	D₄×C₁₃	—	4	8	no	—
337	D₄×C₁₃	—	4	8	no	—
338	D₄×C₁₃	—	4	8	no	—
339	D₄×C₁₃	—	8	8	no	—
340	C₂×C₄×C₁₃	—	2	8	no	—
341	C₂×C₄×C₁₃	—	2	8	no	—
342	C₂×C₄×C₁₃	—	2	4	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	4	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	4	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	4	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	2	4	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	4	no	—
363	C₂×C₄×C₁₃	—	2	4	no	—
364	C₂×C₄×C₁₃	—	2	2	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	16	no	—
370	C₂×C₄×C₁₃	—	4	8	no	—
371	C₂×C₄×C₁₃	—	4	4	no	—
372	C₂×C₄×C₁₃	—	4	4	no	—
373	C₂×C₄×C₁₃	—	4	4	no	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
379	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
380	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
381	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
382	#525	—	2	8	no	—
383	C₂×#123	—	2	8	no	—
384	C₂×#123	C₂²×C₁₃	1	2	yes	—
385	C₂×#123	C₂²×C₁₃	1	2	yes	—
386	C₂×#123	C₂²×C₁₃	1	2	yes	—
387	C₂×#123	C₂²×C₁₃	1	2	yes	—
388	C₂×#123	C₂²×C₁₃	1	2	yes	—
389	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
390	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
392	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#121	C₂²×C₁₃	1	4	yes	—
394	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
395	C₂×#120	C₂²×C₁₃	1	2	yes	—
396	C₂×#120	C₂²×C₁₃	1	2	yes	—
397	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
399	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
400	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
405	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
406	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
407	#400	C₂²×C₁₃	1	2	yes	complemented
408	#399	C₂²×C₁₃	1	2	yes	complemented
409	#398	C₂²×C₁₃	1	2	yes	complemented
410	#397	C₂²×C₁₃	1	2	yes	complemented
411	#397	C₂²×C₁₃	1	4	yes	complemented
412	#395	C₂²×C₁₃	1	2	yes	complemented
413	#394	C₂²×C₁₃	1	4	yes	—
414	#394	C₂²×C₁₃	1	2	yes	complemented
415	#394	C₂²×C₁₃	1	4	yes	complemented
416	#393	C₂²×C₁₃	1	2	yes	complemented
417	#392	C₂²×C₁₃	1	4	yes	—
418	#392	C₂²×C₁₃	1	2	yes	complemented
419	#390	C₂²×C₁₃	1	4	yes	complemented
420	#390	C₂²×C₁₃	1	4	yes	complemented
421	#389	C₂²×C₁₃	1	4	yes	complemented
422	#389	C₂²×C₁₃	1	4	yes	complemented
423	#388	C₂²×C₁₃	1	4	yes	complemented
424	#388	C₂²×C₁₃	1	4	yes	complemented
425	#388	C₂²×C₁₃	1	4	yes	complemented
426	#388	C₂²×C₁₃	1	4	yes	complemented
427	#388	C₂²×C₁₃	1	4	yes	complemented
428	#387	C₂²×C₁₃	1	4	yes	complemented
429	#386	C₂²×C₁₃	1	2	yes	—
430	#386	C₂²×C₁₃	1	2	yes	—
431	#386	C₂²×C₁₃	1	4	yes	—
432	#386	C₂²×C₁₃	1	4	yes	complemented
433	#386	C₂²×C₁₃	1	4	yes	complemented
434	#385	C₂²×C₁₃	1	2	yes	—
435	#385	C₂²×C₁₃	1	2	yes	—
436	#385	C₂²×C₁₃	1	4	yes	complemented
437	#381	C₂²×C₁₃	1	2	yes	—
438	#380	C₂²×C₁₃	1	4	yes	complemented
439	#379	C₂²×C₁₃	1	2	yes	—
440	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
442	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
443	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
444	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
445	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
446	C₂²×C₁₃	—	2	2	no	—
447	C₂²×C₁₃	—	2	2	no	—
448	C₂²×C₁₃	—	2	2	no	—
449	C₂²×C₁₃	—	2	2	no	—
450	C₂²×C₁₃	—	2	8	no	—
451	C₂²×C₁₃	—	2	8	no	—
452	C₂²×C₁₃	—	2	2	no	—
453	C₂²×C₁₃	—	2	2	no	—
454	C₂²×C₁₃	—	2	2	no	—
455	C₂²×C₁₃	—	4	16	no	—
456	C₂²×C₁₃	—	4	4	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	2	no	—
463	C₂²×C₁₃	—	4	4	no	—
464	C₂²×C₁₃	—	4	4	no	—
465	C₂²×C₁₃	—	4	4	no	—
466	C₂²×C₁₃	—	4	4	no	—
467	C₂²×C₁₃	—	8	8	no	—
468	C₂²×C₁₃	#532	1	4	yes	—
469	C₂²×C₁₃	#534	1	4	yes	—
470	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
471	C₂²×C₁₃	C₂²×#41	1	2	yes	—
472	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
473	C₂²×C₁₃	#585	1	2	yes	—
474	C₄×C₁₃	—	2	2	no	—
475	C₄×C₁₃	—	2	2	no	—
476	C₄×C₁₃	—	2	2	no	—
477	C₄×C₁₃	—	2	2	no	—
478	C₄×C₁₃	—	2	8	no	—
479	C₄×C₁₃	—	4	2	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	—	4	2	no	—
482	C₄×C₁₃	—	4	2	no	—
483	C₄×C₁₃	—	4	2	no	—
484	C₄×C₁₃	—	4	2	no	—
485	C₄×C₁₃	—	4	4	no	—
486	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
487	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×#41	—	2	4	no	—
489	C₂×#41	—	4	4	no	—
490	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
491	C₂²×D₄	—	2	4	no	—
492	C₂²×D₄	—	4	4	no	—
493	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
494	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
495	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
496	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
497	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
498	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
500	C₂³×C₄	—	4	4	no	—
501	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
502	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
504	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
509	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
513	#123	—	2	8	no	—
514	#123	—	2	8	no	—
515	#123	—	2	8	no	—
516	#123	—	2	8	no	—
517	#123	—	2	8	no	—
518	#123	—	2	8	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	#121	—	2	4	no	—
522	#121	—	2	4	no	—
523	#121	—	4	8	no	—
524	#120	—	2	8	no	—
525	#120	—	2	8	no	—
526	C₄×D₄	—	2	8	no	—
527	C₄×D₄	—	2	8	no	—
528	#117	—	2	4	no	—
529	C₂×C₄⋊C₄	—	2	4	no	—
530	C₂×C₄⋊C₄	—	2	4	no	—
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₂²⋊C₄	—	2	4	no	—
544	C₂×C₂²⋊C₄	—	2	4	no	—
545	C₂×C₂²⋊C₄	—	2	8	no	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₄²	—	4	4	no	—
567	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
570	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
571	#95	C₂³×C₁₃	1	4	yes	—
572	#95	C₂³×C₁₃	1	2	yes	—
573	#95	C₂³×C₁₃	1	2	yes	—
574	#95	C₂³×C₁₃	1	4	yes	—
575	#95	C₂³×C₁₃	1	4	yes	—
576	#95	C₂³×C₁₃	1	4	yes	—
577	#95	C₂³×C₁₃	1	4	yes	—
578	#95	C₂³×C₁₃	1	4	yes	—
579	#95	C₂³×C₁₃	1	4	yes	—
580	C₂×C₁₃	—	2	4	no	—
581	C₂×C₁₃	—	2	4	no	—
582	C₂×C₁₃	—	4	2	no	—
583	C₂×C₁₃	—	8	2	no	—
584	C₂×C₁₃	—	8	2	no	—
585	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
586	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
587	C₂×C₁₃	#3449	1	1	yes	characteristic
588	C₂×C₁₃	#3513	1	4	yes	—
589	C₂⁴	—	2	4	no	—
590	C₂⁴	—	2	4	no	—
591	C₂⁴	—	2	2	no	—
592	C₂⁴	—	2	4	no	—
593	C₂⁴	—	4	2	no	—
594	C₂⁴	—	4	2	no	—
595	C₂⁴	—	4	2	no	—
596	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
597	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
598	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
599	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
600	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
601	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
602	#41	—	4	16	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	4	2	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	8	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	8	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	—	4	16	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	8	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	8	no	—
631	C₂²×C₄	—	4	16	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	—	4	4	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
641	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
642	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
643	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
644	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
645	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
646	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
647	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₁₃	1	2	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	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	8	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₄⋊C₄	—	4	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	2	8	no	—
683	C₂²⋊C₄	—	2	8	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	4	4	no	—
688	C₂²⋊C₄	C₁₃×#41	1	8	yes	complemented
689	C₄²	—	2	4	no	—
690	C₄²	—	4	2	no	—
691	C₄²	—	4	4	no	—
692	C₄²	—	4	2	no	—
693	C₁₃	#35064	1	1	yes	characteristic, direct product factor, Sylow
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	8	no	—
699	C₂³	—	2	8	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	4	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	4	4	no	—
714	C₂³	—	4	16	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	4	4	no	—
718	C₂³	—	8	8	no	—
719	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
720	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
721	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
722	C₂³	C₂×C₁₃×#41	1	4	yes	—
723	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
724	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
725	Q₈	—	4	4	no	—
726	D₄	—	4	4	no	—
727	D₄	—	4	8	no	—
728	D₄	—	4	8	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	8	no	—
732	D₄	—	8	8	no	—
733	C₂×C₄	—	2	8	no	—
734	C₂×C₄	—	2	8	no	—
735	C₂×C₄	—	2	4	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	4	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	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	4	4	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	16	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
769	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
771	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	8	no	—
777	C₂²	—	2	8	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	4	16	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	8	8	no	—
794	C₂²	C₁₃×#532	1	4	yes	—
795	C₂²	C₁₃×#534	1	4	yes	—
796	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
797	C₂²	C₂²×C₁₃×#41	1	2	yes	—
798	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
799	C₂²	C₁₃×#585	1	2	yes	—
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	8	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	4	no	—
812	C₂	—	2	4	no	—
813	C₂	—	2	4	no	—
814	C₂	—	4	2	no	—
815	C₂	—	8	2	no	—
816	C₂	—	8	2	no	—
817	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
818	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
819	C₂	C₁₃×#3449	1	1	yes	characteristic
820	C₂	C₁₃×#3513	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×#525	C₂	semidirect
2. C₂²×C₁₃×#123	C₂	semidirect
3. C₁₃×#2854	C₂	semidirect
4. C₁₃×#2663	C₂	semidirect
5. C₁₃×#2661	C₂	semidirect
6. C₁₃×#2602	C₂	semidirect
7. C₁₃×#2591	C₂	semidirect
8. C₁₃×#2583	C₂	semidirect
9. C₁₃×#2561	C₂	semidirect
10. C₁₃×#2539	C₂	semidirect
11. C₁₃×#2498	C₂	semidirect
12. C₁₃×#2430	C₂	semidirect
13. C₁₃×#2412	C₂	semidirect
14. C₁₃×#2410	C₂	semidirect
15. C₁₃×#2322	C₂	semidirect
16. C₁₃×#2321	C₂	semidirect
17. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
28. C₂×C₁₃×#123	C₂²	semidirect
30. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×#121	C₂²	semidirect
37. C₂×C₄×D₄×C₁₃	C₂²	semidirect
38. C₂×C₁₃×#117	C₂²	semidirect
45. C₂²×C₄²×C₁₃	C₂²	semidirect
46. C₁₃×#400	C₂²	semidirect
47. C₁₃×#399	C₂²	semidirect
48. C₁₃×#398	C₂²	semidirect
49. C₁₃×#397	C₂²	semidirect
50. C₁₃×#397	C₂²	semidirect
51. C₁₃×#395	C₂²	semidirect
53. C₁₃×#394	C₂²	semidirect
54. C₁₃×#394	C₂²	semidirect
55. C₁₃×#393	C₂²	semidirect
57. C₁₃×#392	C₂²	semidirect
58. C₁₃×#390	C₂²	semidirect
59. C₁₃×#390	C₂²	semidirect
60. C₁₃×#389	C₂²	semidirect
61. C₁₃×#389	C₂²	semidirect
62. C₁₃×#388	C₂²	semidirect
63. C₁₃×#388	C₂²	semidirect
64. C₁₃×#388	C₂²	semidirect
65. C₁₃×#388	C₂²	semidirect
66. C₁₃×#388	C₂²	semidirect
67. C₁₃×#387	C₂²	semidirect
71. C₁₃×#386	C₂²	semidirect
72. C₁₃×#386	C₂²	semidirect
75. C₁₃×#385	C₂²	semidirect
77. C₁₃×#380	C₂²	semidirect
82. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
83. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
84. C₂×C₁₃×#95	C₂²	semidirect
100. C₂³×C₄×C₁₃	D₄	semidirect
179. #35064	C₁₃	direct (N × H)
279. C₁₃×C₂²⋊C₄	#41	semidirect
284. C₂×#525	C₂×C₁₃	semidirect
285. C₂²×#123	C₂×C₁₃	semidirect
286. #2854	C₂×C₁₃	semidirect
287. #2663	C₂×C₁₃	semidirect
288. #2661	C₂×C₁₃	semidirect
289. #2602	C₂×C₁₃	semidirect
290. #2591	C₂×C₁₃	semidirect
291. #2583	C₂×C₁₃	semidirect
292. #2561	C₂×C₁₃	semidirect
293. #2539	C₂×C₁₃	semidirect
294. #2498	C₂×C₁₃	semidirect
295. #2430	C₂×C₁₃	semidirect
296. #2412	C₂×C₁₃	semidirect
297. #2410	C₂×C₁₃	semidirect
298. #2322	C₂×C₁₃	semidirect
299. #2321	C₂×C₁₃	semidirect
300. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
379. C₂²×#41	C₂²×C₁₃	semidirect
389. C₂×#123	C₂²×C₁₃	semidirect
391. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
394. C₂×#121	C₂²×C₁₃	semidirect
398. C₂×C₄×D₄	C₂²×C₁₃	semidirect
399. C₂×#117	C₂²×C₁₃	semidirect
406. C₂²×C₄²	C₂²×C₁₃	semidirect
407. #400	C₂²×C₁₃	semidirect
408. #399	C₂²×C₁₃	semidirect
409. #398	C₂²×C₁₃	semidirect
410. #397	C₂²×C₁₃	semidirect
411. #397	C₂²×C₁₃	semidirect
412. #395	C₂²×C₁₃	semidirect
414. #394	C₂²×C₁₃	semidirect
415. #394	C₂²×C₁₃	semidirect
416. #393	C₂²×C₁₃	semidirect
418. #392	C₂²×C₁₃	semidirect
419. #390	C₂²×C₁₃	semidirect
420. #390	C₂²×C₁₃	semidirect
421. #389	C₂²×C₁₃	semidirect
422. #389	C₂²×C₁₃	semidirect
423. #388	C₂²×C₁₃	semidirect
424. #388	C₂²×C₁₃	semidirect
425. #388	C₂²×C₁₃	semidirect
426. #388	C₂²×C₁₃	semidirect
427. #388	C₂²×C₁₃	semidirect
428. #387	C₂²×C₁₃	semidirect
432. #386	C₂²×C₁₃	semidirect
433. #386	C₂²×C₁₃	semidirect
436. #385	C₂²×C₁₃	semidirect
438. #380	C₂²×C₁₃	semidirect
443. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
444. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
445. C₂×#95	C₂²×C₁₃	semidirect
501. C₂³×C₄	D₄×C₁₃	semidirect
688. C₂²⋊C₄	C₁₃×#41	semidirect
693. C₁₃	#35064	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×#525	2
C₂²×C₁₃×#123	2
C₁₃×#2854	2
C₁₃×#2663	2
C₁₃×#2661	2
C₁₃×#2602	2
C₁₃×#2591	2
C₁₃×#2583	2
C₁₃×#2561	2
C₁₃×#2539	2
C₁₃×#2498	2
C₁₃×#2430	2
C₁₃×#2412	2
C₁₃×#2410	2
C₁₃×#2322	2
C₁₃×#2321	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#35064	13

Subgroups — C13×#35064 #15721403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35064 #15721403