Subgroups — C₁₃×#36697 #15723036

Order 3328.

1484 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2843	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2839	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2838	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2837	C₂	1	2	yes	maximal
5	C₁₃×#2836	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2833	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2832	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2831	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2823	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2821	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2402	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2401	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2398	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2396	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2396	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2395	C₂	1	2	yes	maximal
18	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₁₃×#126	C₂	1	2	yes	maximal, complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#126	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#117	C₂²	1	2	yes	—
27	C₁₃×#401	C₂²	1	2	yes	—
28	C₁₃×#400	C₂²	1	2	yes	—
29	C₁₃×#400	C₂²	1	2	yes	—
30	C₁₃×#400	C₂²	1	2	yes	—
31	C₁₃×#400	C₂²	1	2	yes	—
32	C₁₃×#400	C₂²	1	2	yes	—
33	C₁₃×#400	C₂²	1	2	yes	—
34	C₁₃×#400	C₂²	1	2	yes	—
35	C₁₃×#400	C₂²	1	2	yes	—
36	C₁₃×#400	C₂²	1	1	yes	characteristic
37	C₁₃×#400	C₂²	1	2	yes	—
38	C₁₃×#400	C₂²	1	2	yes	—
39	C₁₃×#400	C₂²	1	1	yes	characteristic
40	C₁₃×#399	C₂²	1	2	yes	—
41	C₁₃×#399	C₂²	1	2	yes	—
42	C₁₃×#399	C₂²	1	2	yes	—
43	C₁₃×#398	C₂²	1	2	yes	—
44	C₁₃×#398	C₂²	1	2	yes	—
45	C₁₃×#398	C₂²	1	1	yes	characteristic
46	C₁₃×#398	C₂²	1	2	yes	—
47	C₁₃×#398	C₂²	1	2	yes	—
48	C₁₃×#398	C₂²	1	2	yes	—
49	C₁₃×#398	C₂²	1	2	yes	—
50	C₁₃×#398	C₂²	1	1	yes	characteristic
51	C₁₃×#398	C₂²	1	2	yes	—
52	C₁₃×#398	C₂²	1	2	yes	—
53	C₁₃×#398	C₂²	1	2	yes	—
54	C₁₃×#398	C₂²	1	2	yes	—
55	C₁₃×#397	C₂²	1	2	yes	—
56	C₁₃×#397	C₂²	1	2	yes	—
57	C₁₃×#397	C₂²	1	2	yes	—
58	C₁₃×#397	C₂²	1	2	yes	—
59	C₁₃×#397	C₂²	1	2	yes	—
60	C₁₃×#397	C₂²	1	2	yes	—
61	C₁₃×#397	C₂²	1	2	yes	—
62	C₁₃×#396	C₂²	1	2	yes	—
63	C₁₃×#396	C₂²	1	2	yes	—
64	C₁₃×#396	C₂²	1	2	yes	—
65	C₁₃×#396	C₂²	1	2	yes	—
66	C₁₃×#396	C₂²	1	2	yes	—
67	C₁₃×#395	C₂²	1	2	yes	—
68	C₁₃×#395	C₂²	1	2	yes	—
69	C₁₃×#395	C₂²	1	1	yes	characteristic
70	C₁₃×#395	C₂²	1	1	yes	characteristic
71	C₁₃×#395	C₂²	1	2	yes	—
72	C₁₃×#394	C₂²	1	1	yes	characteristic
73	C₁₃×#394	C₂²	1	2	yes	—
74	C₁₃×#394	C₂²	1	2	yes	—
75	C₁₃×#394	C₂²	1	1	yes	characteristic
76	C₁₃×#393	C₂²	1	2	yes	—
77	C₁₃×#393	C₂²	1	2	yes	—
78	C₁₃×#393	C₂²	1	2	yes	—
79	C₁₃×#391	C₂²	1	1	yes	characteristic
80	C₁₃×#391	C₂²	1	1	yes	characteristic
81	C₁₃×#389	C₂²	1	2	yes	—
82	C₁₃×#389	C₂²	1	2	yes	—
83	C₁₃×#388	C₂²	1	2	yes	—
84	C₁₃×#388	C₂²	1	2	yes	—
85	C₁₃×#388	C₂²	1	2	yes	—
86	C₁₃×#387	C₂²	1	2	yes	—
87	C₁₃×#387	C₂²	1	2	yes	—
88	C₁₃×#387	C₂²	1	2	yes	—
89	C₁₃×#384	C₂²	1	1	yes	characteristic
90	C₁₃×#383	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₁₃×#376	C₂²	1	1	yes	characteristic
105	C₁₃×#376	C₂²	1	1	yes	characteristic
106	C₄³×C₁₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	—	2	4	no	—
113	C₁₃×#126	—	2	8	no	—
114	C₄×Q₈×C₁₃	—	4	2	no	—
115	C₄×Q₈×C₁₃	—	4	2	no	—
116	C₄×Q₈×C₁₃	—	4	2	no	—
117	C₄×D₄×C₁₃	—	4	2	no	—
118	C₁₃×#117	—	4	4	no	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	1	yes	characteristic
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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×C₄²×C₁₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₁₃×#95	C₂³	1	2	yes	—
170	C₁₃×#95	C₂³	1	2	yes	—
171	C₁₃×#95	C₂³	1	2	yes	—
172	C₁₃×#95	C₂³	1	2	yes	—
173	C₁₃×#95	C₂³	1	2	yes	—
174	C₁₃×#95	C₂³	1	2	yes	—
175	C₁₃×#95	C₂³	1	2	yes	—
176	C₁₃×#95	C₂³	1	2	yes	—
177	C₁₃×#95	C₂³	1	2	yes	—
178	C₁₃×#95	C₂³	1	2	yes	—
179	C₁₃×#95	C₂³	1	2	yes	—
180	C₁₃×#95	C₂³	1	2	yes	—
181	C₁₃×#95	C₂³	1	2	yes	—
182	C₁₃×#95	C₂³	1	2	yes	—
183	C₁₃×#95	C₂³	1	2	yes	—
184	C₁₃×#95	C₂³	1	2	yes	—
185	C₁₃×#95	C₂³	1	2	yes	—
186	C₁₃×#95	C₂³	1	2	yes	—
187	C₁₃×#95	C₂³	1	2	yes	—
188	C₁₃×#95	C₂³	1	2	yes	—
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	1	yes	characteristic
197	C₁₃×#95	C₂³	1	1	yes	characteristic
198	C₁₃×#95	C₂³	1	1	yes	characteristic
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	1	yes	characteristic
201	#36697	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	2	2	no	—
205	C₂×Q₈×C₁₃	—	4	1	no	—
206	C₂×Q₈×C₁₃	—	4	1	no	—
207	C₂×Q₈×C₁₃	—	4	1	no	—
208	C₂×Q₈×C₁₃	—	4	1	no	—
209	C₂×Q₈×C₁₃	—	4	1	no	—
210	C₂×Q₈×C₁₃	—	4	2	no	—
211	C₂×D₄×C₁₃	—	4	1	no	—
212	C₂×D₄×C₁₃	—	4	2	no	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	2	4	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	4	2	no	—
240	C₁₃×C₄⋊C₄	—	4	2	no	—
241	C₁₃×C₄⋊C₄	—	4	2	no	—
242	C₁₃×C₄⋊C₄	—	4	2	no	—
243	C₁₃×C₄⋊C₄	—	4	2	no	—
244	C₁₃×C₄⋊C₄	—	4	2	no	—
245	C₁₃×C₄⋊C₄	—	4	2	no	—
246	C₁₃×C₄⋊C₄	—	4	2	no	—
247	C₁₃×C₄⋊C₄	—	4	2	no	—
248	C₁₃×C₄⋊C₄	—	4	2	no	—
249	C₁₃×C₄⋊C₄	—	4	2	no	—
250	C₁₃×C₄⋊C₄	—	4	2	no	—
251	C₁₃×C₄⋊C₄	—	4	2	no	—
252	C₁₃×C₄⋊C₄	—	4	1	no	—
253	C₁₃×C₄⋊C₄	—	4	1	no	—
254	C₁₃×C₄⋊C₄	—	4	1	no	—
255	C₁₃×C₄⋊C₄	—	4	1	no	—
256	C₁₃×C₄⋊C₄	—	4	1	no	—
257	C₁₃×C₄⋊C₄	—	4	2	no	—
258	C₁₃×C₄⋊C₄	—	4	2	no	—
259	C₁₃×C₄⋊C₄	—	4	1	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	—	4	2	no	—
264	C₁₃×C₂²⋊C₄	—	4	2	no	—
265	C₁₃×C₂²⋊C₄	—	4	2	no	—
266	C₁₃×C₂²⋊C₄	—	4	2	no	—
267	C₁₃×C₂²⋊C₄	—	4	2	no	—
268	C₁₃×C₂²⋊C₄	—	4	2	no	—
269	C₁₃×C₂²⋊C₄	—	4	2	no	—
270	C₁₃×C₂²⋊C₄	—	4	2	no	—
271	C₁₃×C₂²⋊C₄	—	4	2	no	—
272	C₁₃×C₂²⋊C₄	—	4	2	no	—
273	C₄²×C₁₃	—	2	4	no	—
274	C₄²×C₁₃	—	2	4	no	—
275	C₄²×C₁₃	—	2	2	no	—
276	C₄²×C₁₃	—	2	2	no	—
277	C₄²×C₁₃	—	2	2	no	—
278	C₄²×C₁₃	—	2	4	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	—	2	4	no	—
281	C₄²×C₁₃	—	4	2	no	—
282	C₄²×C₁₃	—	4	1	no	—
283	C₄²×C₁₃	#41	1	4	yes	—
284	#2843	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#2839	C₂×C₁₃	1	2	yes	complemented
286	#2838	C₂×C₁₃	1	2	yes	complemented
287	#2837	C₂×C₁₃	1	2	yes	—
288	#2836	C₂×C₁₃	1	2	yes	complemented
289	#2833	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#2832	C₂×C₁₃	1	1	yes	characteristic
291	#2831	C₂×C₁₃	1	2	yes	complemented
292	#2823	C₂×C₁₃	1	1	yes	characteristic
293	#2821	C₂×C₁₃	1	2	yes	complemented
294	#2402	C₂×C₁₃	1	2	yes	complemented
295	#2401	C₂×C₁₃	1	2	yes	complemented
296	#2399	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2398	C₂×C₁₃	1	1	yes	characteristic
298	#2396	C₂×C₁₃	1	2	yes	complemented
299	#2396	C₂×C₁₃	1	2	yes	complemented
300	#2395	C₂×C₁₃	1	2	yes	—
301	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₄×#126	C₂×C₁₃	1	2	yes	complemented
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
311	Q₈×C₁₃	—	4	4	no	—
312	Q₈×C₁₃	—	4	4	no	—
313	Q₈×C₁₃	—	4	4	no	—
314	D₄×C₁₃	—	4	4	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	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	1	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	1	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	1	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	1	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	4	8	no	—
362	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
363	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
364	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
365	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
366	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#126	C₂²×C₁₃	1	2	yes	—
368	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#117	C₂²×C₁₃	1	2	yes	—
373	#401	C₂²×C₁₃	1	2	yes	—
374	#400	C₂²×C₁₃	1	2	yes	—
375	#400	C₂²×C₁₃	1	2	yes	—
376	#400	C₂²×C₁₃	1	2	yes	—
377	#400	C₂²×C₁₃	1	2	yes	—
378	#400	C₂²×C₁₃	1	2	yes	—
379	#400	C₂²×C₁₃	1	2	yes	—
380	#400	C₂²×C₁₃	1	2	yes	—
381	#400	C₂²×C₁₃	1	2	yes	—
382	#400	C₂²×C₁₃	1	1	yes	characteristic
383	#400	C₂²×C₁₃	1	2	yes	—
384	#400	C₂²×C₁₃	1	2	yes	—
385	#400	C₂²×C₁₃	1	1	yes	characteristic
386	#399	C₂²×C₁₃	1	2	yes	—
387	#399	C₂²×C₁₃	1	2	yes	—
388	#399	C₂²×C₁₃	1	2	yes	—
389	#398	C₂²×C₁₃	1	2	yes	—
390	#398	C₂²×C₁₃	1	2	yes	—
391	#398	C₂²×C₁₃	1	1	yes	characteristic
392	#398	C₂²×C₁₃	1	2	yes	—
393	#398	C₂²×C₁₃	1	2	yes	—
394	#398	C₂²×C₁₃	1	2	yes	—
395	#398	C₂²×C₁₃	1	2	yes	—
396	#398	C₂²×C₁₃	1	1	yes	characteristic
397	#398	C₂²×C₁₃	1	2	yes	—
398	#398	C₂²×C₁₃	1	2	yes	—
399	#398	C₂²×C₁₃	1	2	yes	—
400	#398	C₂²×C₁₃	1	2	yes	—
401	#397	C₂²×C₁₃	1	2	yes	—
402	#397	C₂²×C₁₃	1	2	yes	—
403	#397	C₂²×C₁₃	1	2	yes	—
404	#397	C₂²×C₁₃	1	2	yes	—
405	#397	C₂²×C₁₃	1	2	yes	—
406	#397	C₂²×C₁₃	1	2	yes	—
407	#397	C₂²×C₁₃	1	2	yes	—
408	#396	C₂²×C₁₃	1	2	yes	—
409	#396	C₂²×C₁₃	1	2	yes	—
410	#396	C₂²×C₁₃	1	2	yes	—
411	#396	C₂²×C₁₃	1	2	yes	—
412	#396	C₂²×C₁₃	1	2	yes	—
413	#395	C₂²×C₁₃	1	2	yes	—
414	#395	C₂²×C₁₃	1	2	yes	—
415	#395	C₂²×C₁₃	1	1	yes	characteristic
416	#395	C₂²×C₁₃	1	1	yes	characteristic
417	#395	C₂²×C₁₃	1	2	yes	—
418	#394	C₂²×C₁₃	1	1	yes	characteristic
419	#394	C₂²×C₁₃	1	2	yes	—
420	#394	C₂²×C₁₃	1	2	yes	—
421	#394	C₂²×C₁₃	1	1	yes	characteristic
422	#393	C₂²×C₁₃	1	2	yes	—
423	#393	C₂²×C₁₃	1	2	yes	—
424	#393	C₂²×C₁₃	1	2	yes	—
425	#391	C₂²×C₁₃	1	1	yes	characteristic
426	#391	C₂²×C₁₃	1	1	yes	characteristic
427	#389	C₂²×C₁₃	1	2	yes	—
428	#389	C₂²×C₁₃	1	2	yes	—
429	#388	C₂²×C₁₃	1	2	yes	—
430	#388	C₂²×C₁₃	1	2	yes	—
431	#388	C₂²×C₁₃	1	2	yes	—
432	#387	C₂²×C₁₃	1	2	yes	—
433	#387	C₂²×C₁₃	1	2	yes	—
434	#387	C₂²×C₁₃	1	2	yes	—
435	#384	C₂²×C₁₃	1	1	yes	characteristic
436	#383	C₂²×C₁₃	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
438	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
440	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
441	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
442	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
444	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
445	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
446	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
447	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
448	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
450	#376	C₂²×C₁₃	1	1	yes	characteristic
451	#376	C₂²×C₁₃	1	1	yes	characteristic
452	C₄³	C₂²×C₁₃	1	1	yes	characteristic
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
461	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
463	C₂²×C₁₃	#585	1	1	yes	characteristic
464	C₂²×C₁₃	#585	1	2	yes	—
465	C₄×C₁₃	—	2	2	no	—
466	C₄×C₁₃	—	2	4	no	—
467	C₄×C₁₃	—	4	2	no	—
468	C₄×C₁₃	—	4	1	no	—
469	C₄×C₁₃	—	4	2	no	—
470	C₄×C₁₃	—	4	1	no	—
471	C₄×C₁₃	—	4	2	no	—
472	C₄×C₁₃	—	4	2	no	—
473	C₄×C₁₃	—	4	2	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	1	no	—
476	C₄×C₁₃	—	4	1	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	—	4	1	no	—
479	C₄×C₁₃	—	4	2	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	—	4	2	no	—
482	C₄×C₁₃	#563	1	4	yes	—
483	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
488	C₄⋊Q₈	—	2	4	no	—
489	#126	—	2	8	no	—
490	C₄×Q₈	—	4	2	no	—
491	C₄×Q₈	—	4	2	no	—
492	C₄×Q₈	—	4	2	no	—
493	C₄×D₄	—	4	2	no	—
494	#117	—	4	4	no	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
534	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
536	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
540	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
541	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
542	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
543	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
545	#95	C₂³×C₁₃	1	2	yes	—
546	#95	C₂³×C₁₃	1	1	yes	characteristic
547	#95	C₂³×C₁₃	1	1	yes	characteristic
548	#95	C₂³×C₁₃	1	1	yes	characteristic
549	#95	C₂³×C₁₃	1	2	yes	—
550	#95	C₂³×C₁₃	1	1	yes	characteristic
551	#95	C₂³×C₁₃	1	2	yes	—
552	#95	C₂³×C₁₃	1	2	yes	—
553	#95	C₂³×C₁₃	1	2	yes	—
554	#95	C₂³×C₁₃	1	2	yes	—
555	#95	C₂³×C₁₃	1	2	yes	—
556	#95	C₂³×C₁₃	1	2	yes	—
557	#95	C₂³×C₁₃	1	2	yes	—
558	#95	C₂³×C₁₃	1	2	yes	—
559	#95	C₂³×C₁₃	1	2	yes	—
560	#95	C₂³×C₁₃	1	2	yes	—
561	#95	C₂³×C₁₃	1	2	yes	—
562	#95	C₂³×C₁₃	1	2	yes	—
563	#95	C₂³×C₁₃	1	2	yes	—
564	#95	C₂³×C₁₃	1	2	yes	—
565	#95	C₂³×C₁₃	1	2	yes	—
566	#95	C₂³×C₁₃	1	2	yes	—
567	#95	C₂³×C₁₃	1	2	yes	—
568	#95	C₂³×C₁₃	1	2	yes	—
569	#95	C₂³×C₁₃	1	2	yes	—
570	#95	C₂³×C₁₃	1	2	yes	—
571	#95	C₂³×C₁₃	1	2	yes	—
572	#95	C₂³×C₁₃	1	2	yes	—
573	#95	C₂³×C₁₃	1	2	yes	—
574	#95	C₂³×C₁₃	1	2	yes	—
575	#95	C₂³×C₁₃	1	2	yes	—
576	#95	C₂³×C₁₃	1	2	yes	—
577	C₂×C₁₃	—	8	2	no	—
578	C₂×C₁₃	#3460	1	1	yes	characteristic
579	C₂×C₁₃	#3461	1	2	yes	—
580	C₂×C₁₃	C₂×#563	1	1	yes	characteristic
581	C₂×C₁₃	#3529	1	1	yes	characteristic
582	C₂×C₁₃	#3531	1	2	yes	—
583	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	4	1	no	—
587	C₂×Q₈	—	4	1	no	—
588	C₂×Q₈	—	4	1	no	—
589	C₂×Q₈	—	4	1	no	—
590	C₂×Q₈	—	4	1	no	—
591	C₂×Q₈	—	4	2	no	—
592	C₂×D₄	—	4	1	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	1	no	—
623	C₄⋊C₄	—	4	1	no	—
624	C₄⋊C₄	—	4	1	no	—
625	C₄⋊C₄	—	4	1	no	—
626	C₄⋊C₄	—	4	1	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	1	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	4	2	no	—
663	C₄²	—	4	1	no	—
664	C₄²	C₁₃×#41	1	4	yes	—
665	C₁₃	#36697	1	1	yes	characteristic, direct product factor, Sylow
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
674	Q₈	—	4	4	no	—
675	Q₈	—	4	4	no	—
676	Q₈	—	4	4	no	—
677	D₄	—	4	4	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	4	8	no	—
725	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
726	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
727	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
728	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
737	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
738	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
739	C₂²	C₁₃×#585	1	2	yes	—
740	C₂²	C₁₃×#585	1	1	yes	characteristic
741	C₄	—	2	2	no	—
742	C₄	—	2	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	C₁₃×#563	1	4	yes	—
759	C₂	—	8	2	no	—
760	C₂	C₁₃×#3460	1	1	yes	characteristic
761	C₂	C₁₃×#3461	1	2	yes	—
762	C₂	C₂×C₁₃×#563	1	1	yes	characteristic
763	C₂	C₁₃×#3529	1	1	yes	characteristic
764	C₂	C₁₃×#3531	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2843	C₂	semidirect
2. C₁₃×#2839	C₂	semidirect
3. C₁₃×#2838	C₂	semidirect
5. C₁₃×#2836	C₂	semidirect
6. C₁₃×#2833	C₂	semidirect
8. C₁₃×#2831	C₂	semidirect
10. C₁₃×#2821	C₂	semidirect
11. C₁₃×#2402	C₂	semidirect
12. C₁₃×#2401	C₂	semidirect
13. C₁₃×#2399	C₂	semidirect
15. C₁₃×#2396	C₂	semidirect
16. C₁₃×#2396	C₂	semidirect
18. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
19. C₄×C₁₃×#126	C₂	semidirect
201. #36697	C₁₃	direct (N × H)
284. #2843	C₂×C₁₃	semidirect
285. #2839	C₂×C₁₃	semidirect
286. #2838	C₂×C₁₃	semidirect
288. #2836	C₂×C₁₃	semidirect
289. #2833	C₂×C₁₃	semidirect
291. #2831	C₂×C₁₃	semidirect
293. #2821	C₂×C₁₃	semidirect
294. #2402	C₂×C₁₃	semidirect
295. #2401	C₂×C₁₃	semidirect
296. #2399	C₂×C₁₃	semidirect
298. #2396	C₂×C₁₃	semidirect
299. #2396	C₂×C₁₃	semidirect
301. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
302. C₄×#126	C₂×C₁₃	semidirect
665. C₁₃	#36697	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2843	2
C₁₃×#2839	2
C₁₃×#2838	2
C₁₃×#2837	2
C₁₃×#2836	2
C₁₃×#2833	2
C₁₃×#2832	2
C₁₃×#2831	2
C₁₃×#2823	2
C₁₃×#2821	2
C₁₃×#2402	2
C₁₃×#2401	2
C₁₃×#2399	2
C₁₃×#2398	2
C₁₃×#2396	2
C₁₃×#2395	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#126	2
#36697	13

Subgroups — C13×#36697 #15723036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36697 #15723036