Subgroups — C₁₃×#34596 #15720935

Order 3328.

1760 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2665	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2663	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2655	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2653	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2652	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2650	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2638	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2630	C₂	1	2	yes	maximal
9	C₁₃×#2401	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2398	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2392	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#123	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#401	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	1	yes	characteristic
34	C₁₃×#400	C₂²	1	2	yes	—
35	C₁₃×#400	C₂²	1	2	yes	—
36	C₁₃×#400	C₂²	1	2	yes	—
37	C₁₃×#399	C₂²	1	1	yes	characteristic
38	C₁₃×#398	C₂²	1	2	yes	—
39	C₁₃×#398	C₂²	1	2	yes	—
40	C₁₃×#398	C₂²	1	1	yes	characteristic
41	C₁₃×#398	C₂²	1	2	yes	—
42	C₁₃×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	2	yes	—
44	C₁₃×#397	C₂²	1	2	yes	—
45	C₁₃×#397	C₂²	1	2	yes	—
46	C₁₃×#397	C₂²	1	1	yes	characteristic
47	C₁₃×#397	C₂²	1	2	yes	—
48	C₁₃×#397	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#396	C₂²	1	2	yes	—
51	C₁₃×#396	C₂²	1	2	yes	—
52	C₁₃×#395	C₂²	1	2	yes	—
53	C₁₃×#395	C₂²	1	1	yes	characteristic
54	C₁₃×#395	C₂²	1	2	yes	—
55	C₁₃×#394	C₂²	1	2	yes	—
56	C₁₃×#394	C₂²	1	2	yes	—
57	C₁₃×#394	C₂²	1	2	yes	—
58	C₁₃×#394	C₂²	1	1	yes	characteristic
59	C₁₃×#394	C₂²	1	2	yes	—
60	C₁₃×#393	C₂²	1	2	yes	—
61	C₁₃×#393	C₂²	1	2	yes	—
62	C₁₃×#393	C₂²	1	1	yes	characteristic
63	C₁₃×#393	C₂²	1	2	yes	—
64	C₁₃×#392	C₂²	1	1	yes	characteristic
65	C₁₃×#391	C₂²	1	2	yes	—
66	C₁₃×#391	C₂²	1	2	yes	—
67	C₁₃×#389	C₂²	1	2	yes	—
68	C₁₃×#389	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#386	C₂²	1	2	yes	—
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#385	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#381	C₂²	1	2	yes	—
86	C₁₃×#380	C₂²	1	2	yes	—
87	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
88	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
89	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₁₃×#123	—	2	8	no	—
116	C₁₃×C₂²⋊Q₈	—	2	8	no	—
117	C₄×Q₈×C₁₃	—	2	4	no	—
118	C₄×Q₈×C₁₃	—	4	4	no	—
119	C₄×D₄×C₁₃	—	2	8	no	—
120	C₄×D₄×C₁₃	—	2	4	no	—
121	C₄×D₄×C₁₃	—	4	4	no	—
122	C₁₃×#117	—	2	4	no	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	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	1	yes	characteristic
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃	—	4	4	no	—
160	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₁₃×#95	C₂³	1	1	yes	characteristic
174	C₁₃×#95	C₂³	1	2	yes	—
175	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
195	C₁₃×#95	C₂³	1	1	yes	characteristic
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	#34596	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₁₃	—	2	2	no	—
207	C₂×Q₈×C₁₃	—	2	4	no	—
208	C₂×Q₈×C₁₃	—	4	2	no	—
209	C₂×Q₈×C₁₃	—	4	2	no	—
210	C₂×Q₈×C₁₃	—	4	2	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	4	no	—
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	2	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	#41	1	8	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂⁴	1	2	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	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	2	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	4	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	4	2	no	—
257	C₁₃×C₄⋊C₄	—	4	2	no	—
258	C₁₃×C₄⋊C₄	—	4	2	no	—
259	C₁₃×C₄⋊C₄	—	4	2	no	—
260	C₁₃×C₄⋊C₄	—	4	2	no	—
261	C₁₃×C₄⋊C₄	—	4	2	no	—
262	C₁₃×C₄⋊C₄	—	4	2	no	—
263	C₁₃×C₄⋊C₄	—	4	2	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	2	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	4	2	no	—
275	C₁₃×C₂²⋊C₄	—	4	2	no	—
276	C₁₃×C₂²⋊C₄	—	4	2	no	—
277	C₁₃×C₂²⋊C₄	—	4	2	no	—
278	C₁₃×C₂²⋊C₄	—	4	2	no	—
279	C₁₃×C₂²⋊C₄	—	4	2	no	—
280	C₁₃×C₂²⋊C₄	—	4	2	no	—
281	C₄²×C₁₃	—	2	2	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	2	4	no	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	—	2	4	no	—
286	C₄²×C₁₃	—	2	4	no	—
287	C₄²×C₁₃	—	2	2	no	—
288	C₄²×C₁₃	—	2	2	no	—
289	C₄²×C₁₃	—	2	2	no	—
290	C₄²×C₁₃	—	4	2	no	—
291	C₄²×C₁₃	—	4	2	no	—
292	C₄²×C₁₃	—	4	2	no	—
293	C₄²×C₁₃	#41	1	4	yes	—
294	#2665	C₂×C₁₃	1	2	yes	complemented
295	#2663	C₂×C₁₃	1	2	yes	complemented
296	#2655	C₂×C₁₃	1	2	yes	complemented
297	#2653	C₂×C₁₃	1	2	yes	complemented
298	#2652	C₂×C₁₃	1	2	yes	complemented
299	#2650	C₂×C₁₃	1	2	yes	complemented
300	#2638	C₂×C₁₃	1	2	yes	complemented
301	#2630	C₂×C₁₃	1	2	yes	—
302	#2401	C₂×C₁₃	1	2	yes	complemented
303	#2399	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2398	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#2398	C₂×C₁₃	1	2	yes	complemented
306	#2396	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#2392	C₂×C₁₃	1	1	yes	characteristic
308	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
309	C₄×#123	C₂×C₁₃	1	2	yes	complemented
310	#2298	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	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	1	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	1	no	—
322	C₂³×C₁₃	—	2	1	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	C₂×#41	1	4	yes	—
325	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
326	Q₈×C₁₃	—	4	4	no	—
327	Q₈×C₁₃	—	4	8	no	—
328	D₄×C₁₃	—	2	8	no	—
329	D₄×C₁₃	—	4	8	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	1	no	—
338	C₂×C₄×C₁₃	—	2	1	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	1	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	1	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	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	4	8	no	—
371	C₂×C₄×C₁₃	—	4	8	no	—
372	C₂×C₄×C₁₃	—	4	8	no	—
373	C₂×C₄×C₁₃	—	4	4	no	—
374	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
375	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
376	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
377	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
378	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
379	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
380	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
381	C₂×#123	C₂²×C₁₃	1	2	yes	—
382	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
383	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
385	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
386	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
388	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
389	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
390	#401	C₂²×C₁₃	1	2	yes	—
391	#400	C₂²×C₁₃	1	2	yes	—
392	#400	C₂²×C₁₃	1	2	yes	—
393	#400	C₂²×C₁₃	1	2	yes	—
394	#400	C₂²×C₁₃	1	1	yes	characteristic
395	#400	C₂²×C₁₃	1	2	yes	—
396	#400	C₂²×C₁₃	1	2	yes	—
397	#400	C₂²×C₁₃	1	2	yes	—
398	#399	C₂²×C₁₃	1	1	yes	characteristic
399	#398	C₂²×C₁₃	1	2	yes	—
400	#398	C₂²×C₁₃	1	2	yes	—
401	#398	C₂²×C₁₃	1	1	yes	characteristic
402	#398	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	1	yes	characteristic
408	#397	C₂²×C₁₃	1	2	yes	—
409	#397	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	1	yes	characteristic
415	#395	C₂²×C₁₃	1	2	yes	—
416	#394	C₂²×C₁₃	1	2	yes	—
417	#394	C₂²×C₁₃	1	2	yes	—
418	#394	C₂²×C₁₃	1	2	yes	—
419	#394	C₂²×C₁₃	1	1	yes	characteristic
420	#394	C₂²×C₁₃	1	2	yes	—
421	#393	C₂²×C₁₃	1	2	yes	—
422	#393	C₂²×C₁₃	1	2	yes	—
423	#393	C₂²×C₁₃	1	1	yes	characteristic
424	#393	C₂²×C₁₃	1	2	yes	—
425	#392	C₂²×C₁₃	1	1	yes	characteristic
426	#391	C₂²×C₁₃	1	2	yes	—
427	#391	C₂²×C₁₃	1	2	yes	—
428	#389	C₂²×C₁₃	1	2	yes	—
429	#389	C₂²×C₁₃	1	2	yes	—
430	#388	C₂²×C₁₃	1	2	yes	—
431	#388	C₂²×C₁₃	1	2	yes	—
432	#388	C₂²×C₁₃	1	2	yes	—
433	#388	C₂²×C₁₃	1	2	yes	—
434	#387	C₂²×C₁₃	1	2	yes	—
435	#387	C₂²×C₁₃	1	2	yes	—
436	#387	C₂²×C₁₃	1	2	yes	—
437	#387	C₂²×C₁₃	1	2	yes	—
438	#387	C₂²×C₁₃	1	2	yes	—
439	#387	C₂²×C₁₃	1	2	yes	—
440	#387	C₂²×C₁₃	1	2	yes	—
441	#387	C₂²×C₁₃	1	2	yes	—
442	#386	C₂²×C₁₃	1	2	yes	—
443	#385	C₂²×C₁₃	1	2	yes	—
444	#385	C₂²×C₁₃	1	2	yes	—
445	#385	C₂²×C₁₃	1	2	yes	—
446	#381	C₂²×C₁₃	1	2	yes	—
447	#380	C₂²×C₁₃	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
456	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
460	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
462	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
465	#376	C₂²×C₁₃	1	1	yes	characteristic
466	#376	C₂²×C₁₃	1	2	yes	—
467	C₄³	C₂²×C₁₃	1	1	yes	characteristic
468	C₂²×C₁₃	—	2	4	no	—
469	C₂²×C₁₃	—	2	4	no	—
470	C₂²×C₁₃	—	2	4	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	1	no	—
476	C₂²×C₁₃	—	4	1	no	—
477	C₂²×C₁₃	—	4	1	no	—
478	C₂²×C₁₃	—	4	2	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
481	C₂²×C₁₃	C₂²×#41	1	2	yes	—
482	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂²×C₁₃	#585	1	2	yes	—
485	C₄×C₁₃	—	2	2	no	—
486	C₄×C₁₃	—	2	2	no	—
487	C₄×C₁₃	—	2	4	no	—
488	C₄×C₁₃	—	2	4	no	—
489	C₄×C₁₃	—	4	1	no	—
490	C₄×C₁₃	—	4	2	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	1	no	—
493	C₄×C₁₃	—	4	1	no	—
494	C₄×C₁₃	—	4	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	2	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	#542	1	4	yes	—
502	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
503	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
506	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
509	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
510	#123	—	2	8	no	—
511	C₂²⋊Q₈	—	2	8	no	—
512	C₄×Q₈	—	2	4	no	—
513	C₄×Q₈	—	4	4	no	—
514	C₄×D₄	—	2	8	no	—
515	C₄×D₄	—	2	4	no	—
516	C₄×D₄	—	4	4	no	—
517	#117	—	2	4	no	—
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
554	C₂×C₄²	—	4	4	no	—
555	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
560	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
566	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
575	#95	C₂³×C₁₃	1	2	yes	—
576	#95	C₂³×C₁₃	1	1	yes	characteristic
577	#95	C₂³×C₁₃	1	2	yes	—
578	#95	C₂³×C₁₃	1	2	yes	—
579	#95	C₂³×C₁₃	1	2	yes	—
580	#95	C₂³×C₁₃	1	2	yes	—
581	#95	C₂³×C₁₃	1	2	yes	—
582	#95	C₂³×C₁₃	1	2	yes	—
583	#95	C₂³×C₁₃	1	2	yes	—
584	#95	C₂³×C₁₃	1	2	yes	—
585	#95	C₂³×C₁₃	1	2	yes	—
586	#95	C₂³×C₁₃	1	2	yes	—
587	#95	C₂³×C₁₃	1	2	yes	—
588	#95	C₂³×C₁₃	1	2	yes	—
589	#95	C₂³×C₁₃	1	2	yes	—
590	#95	C₂³×C₁₃	1	2	yes	—
591	#95	C₂³×C₁₃	1	2	yes	—
592	#95	C₂³×C₁₃	1	2	yes	—
593	#95	C₂³×C₁₃	1	2	yes	—
594	#95	C₂³×C₁₃	1	2	yes	—
595	#95	C₂³×C₁₃	1	1	yes	characteristic
596	#95	C₂³×C₁₃	1	1	yes	characteristic
597	#95	C₂³×C₁₃	1	2	yes	—
598	C₂×C₁₃	—	4	4	no	—
599	C₂×C₁₃	—	8	1	no	—
600	C₂×C₁₃	#3444	1	1	yes	characteristic
601	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
602	C₂×C₁₃	#3455	1	1	yes	characteristic
603	C₂×C₁₃	#3459	1	2	yes	—
604	C₂×C₁₃	#3461	1	2	yes	—
605	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	4	2	no	—
610	C₂×Q₈	—	4	2	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	C₁₃×#41	1	8	yes	—
629	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	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	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	2	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	2	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	2	no	—
694	C₄²	C₁₃×#41	1	4	yes	—
695	C₁₃	#34596	1	1	yes	characteristic, direct product factor, Sylow
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	2	no	—
707	C₂³	C₂×C₁₃×#41	1	4	yes	—
708	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
709	Q₈	—	4	4	no	—
710	Q₈	—	4	8	no	—
711	D₄	—	2	8	no	—
712	D₄	—	4	8	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	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	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	1	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	1	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	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	—	4	8	no	—
754	C₂×C₄	—	4	8	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
758	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
759	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
760	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
761	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
762	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
763	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
777	C₂²	C₂²×C₁₃×#41	1	2	yes	—
778	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
779	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
780	C₂²	C₁₃×#585	1	2	yes	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	4	no	—
784	C₄	—	2	4	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	C₁₃×#542	1	4	yes	—
798	C₂	—	4	4	no	—
799	C₂	—	8	1	no	—
800	C₂	C₁₃×#3444	1	1	yes	characteristic
801	C₂	C₂×C₁₃×#542	1	1	yes	characteristic
802	C₂	C₁₃×#3455	1	1	yes	characteristic
803	C₂	C₁₃×#3459	1	2	yes	—
804	C₂	C₁₃×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₁₃×#392	C₂²
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×#2665	C₂	semidirect
2. C₁₃×#2663	C₂	semidirect
3. C₁₃×#2655	C₂	semidirect
4. C₁₃×#2653	C₂	semidirect
5. C₁₃×#2652	C₂	semidirect
6. C₁₃×#2650	C₂	semidirect
7. C₁₃×#2638	C₂	semidirect
9. C₁₃×#2401	C₂	semidirect
10. C₁₃×#2399	C₂	semidirect
11. C₁₃×#2398	C₂	semidirect
12. C₁₃×#2398	C₂	semidirect
13. C₁₃×#2396	C₂	semidirect
15. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
16. C₄×C₁₃×#123	C₂	semidirect
17. C₁₃×#2298	C₂	semidirect
18. C₁₃×#2295	C₂	semidirect
19. C₄²×D₄×C₁₃	C₂	semidirect
203. #34596	C₁₃	direct (N × H)
294. #2665	C₂×C₁₃	semidirect
295. #2663	C₂×C₁₃	semidirect
296. #2655	C₂×C₁₃	semidirect
297. #2653	C₂×C₁₃	semidirect
298. #2652	C₂×C₁₃	semidirect
299. #2650	C₂×C₁₃	semidirect
300. #2638	C₂×C₁₃	semidirect
302. #2401	C₂×C₁₃	semidirect
303. #2399	C₂×C₁₃	semidirect
304. #2398	C₂×C₁₃	semidirect
305. #2398	C₂×C₁₃	semidirect
306. #2396	C₂×C₁₃	semidirect
308. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
309. C₄×#123	C₂×C₁₃	semidirect
310. #2298	C₂×C₁₃	semidirect
311. #2295	C₂×C₁₃	semidirect
312. C₄²×D₄	C₂×C₁₃	semidirect
695. C₁₃	#34596	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×#2665	2
C₁₃×#2663	2
C₁₃×#2655	2
C₁₃×#2653	2
C₁₃×#2652	2
C₁₃×#2650	2
C₁₃×#2638	2
C₁₃×#2630	2
C₁₃×#2401	2
C₁₃×#2399	2
C₁₃×#2398	2
C₁₃×#2396	2
C₁₃×#2392	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#123	2
C₁₃×#2298	2
C₁₃×#2295	2
C₄²×D₄×C₁₃	2
#34596	13

Subgroups — C13×#34596 #15720935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34596 #15720935