Subgroups — C₁₃×#34871 #15721210

Order 3328.

2040 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2612	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2610	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2609	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2586	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2572	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2554	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2532	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2526	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2479	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2471	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2396	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2388	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₃×#126	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2293	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#117	C₂	1	2	yes	maximal, complemented
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#126	C₂²	1	2	yes	—
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#400	C₂²	1	2	yes	—
33	C₁₃×#400	C₂²	1	1	yes	characteristic
34	C₁₃×#399	C₂²	1	1	yes	characteristic
35	C₁₃×#399	C₂²	1	2	yes	—
36	C₁₃×#398	C₂²	1	2	yes	—
37	C₁₃×#398	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	1	yes	characteristic
39	C₁₃×#397	C₂²	1	1	yes	characteristic
40	C₁₃×#397	C₂²	1	2	yes	—
41	C₁₃×#396	C₂²	1	2	yes	—
42	C₁₃×#396	C₂²	1	2	yes	—
43	C₁₃×#395	C₂²	1	2	yes	—
44	C₁₃×#395	C₂²	1	1	yes	characteristic
45	C₁₃×#394	C₂²	1	2	yes	—
46	C₁₃×#394	C₂²	1	2	yes	—
47	C₁₃×#394	C₂²	1	1	yes	characteristic
48	C₁₃×#393	C₂²	1	1	yes	characteristic
49	C₁₃×#393	C₂²	1	2	yes	—
50	C₁₃×#392	C₂²	1	2	yes	—
51	C₁₃×#392	C₂²	1	1	yes	characteristic
52	C₁₃×#391	C₂²	1	2	yes	—
53	C₁₃×#391	C₂²	1	2	yes	—
54	C₁₃×#391	C₂²	1	1	yes	characteristic
55	C₁₃×#390	C₂²	1	2	yes	—
56	C₁₃×#390	C₂²	1	2	yes	—
57	C₁₃×#390	C₂²	1	2	yes	—
58	C₁₃×#390	C₂²	1	2	yes	—
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#389	C₂²	1	2	yes	—
61	C₁₃×#389	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	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×#386	C₂²	1	2	yes	—
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#386	C₂²	1	2	yes	—
81	C₁₃×#386	C₂²	1	2	yes	—
82	C₁₃×#386	C₂²	1	2	yes	—
83	C₁₃×#385	C₂²	1	2	yes	—
84	C₁₃×#383	C₂²	1	2	yes	—
85	C₁₃×#382	C₂²	1	1	yes	characteristic
86	C₁₃×#381	C₂²	1	2	yes	—
87	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
88	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
89	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₁₃×C₄⋊C₄	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×C₂²⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₂²⋊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	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	1	yes	characteristic
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₁₃×#376	C₂²	1	2	yes	—
104	C₁₃×#376	C₂²	1	2	yes	—
105	C₄³×C₁₃	C₂²	1	1	yes	characteristic
106	C₄³×C₁₃	C₂²	1	2	yes	—
107	C₂×C₁₃×#41	—	2	8	no	—
108	C₂×C₁₃×#41	—	4	2	no	—
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
120	C₁₃×#126	—	2	8	no	—
121	C₁₃×#124	—	2	4	no	—
122	C₁₃×#123	—	2	8	no	—
123	C₄×Q₈×C₁₃	—	4	2	no	—
124	C₄×D₄×C₁₃	—	2	8	no	—
125	C₄×D₄×C₁₃	—	4	2	no	—
126	C₁₃×#117	—	2	8	no	—
127	C₁₃×#117	—	2	8	no	—
128	C₁₃×#117	—	4	2	no	—
129	C₁₃×#117	—	4	4	no	—
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	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	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊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×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	—	2	8	no	—
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	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	#34871	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
211	C₁₃×#41	—	4	16	no	—
212	C₂×Q₈×C₁₃	—	2	2	no	—
213	C₂×Q₈×C₁₃	—	2	4	no	—
214	C₂×Q₈×C₁₃	—	4	1	no	—
215	C₂×Q₈×C₁₃	—	4	1	no	—
216	C₂×Q₈×C₁₃	—	4	1	no	—
217	C₂×D₄×C₁₃	—	2	4	no	—
218	C₂×D₄×C₁₃	—	2	4	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	4	no	—
221	C₂×D₄×C₁₃	—	2	2	no	—
222	C₂×D₄×C₁₃	—	2	4	no	—
223	C₂×D₄×C₁₃	—	4	1	no	—
224	C₂×D₄×C₁₃	—	4	2	no	—
225	C₂×D₄×C₁₃	—	4	1	no	—
226	C₂×D₄×C₁₃	—	4	2	no	—
227	C₂×D₄×C₁₃	—	4	1	no	—
228	C₂²×C₄×C₁₃	—	2	4	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	2	4	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	2	2	no	—
239	C₂²×C₄×C₁₃	—	4	2	no	—
240	C₂²×C₄×C₁₃	#41	1	8	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	4	2	no	—
265	C₁₃×C₄⋊C₄	—	4	2	no	—
266	C₁₃×C₄⋊C₄	—	4	2	no	—
267	C₁₃×C₄⋊C₄	—	4	1	no	—
268	C₁₃×C₄⋊C₄	—	4	1	no	—
269	C₁₃×C₄⋊C₄	—	4	1	no	—
270	C₁₃×C₄⋊C₄	—	4	1	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	#41	1	8	yes	complemented
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	4	2	no	—
288	C₁₃×C₂²⋊C₄	—	4	2	no	—
289	C₁₃×C₂²⋊C₄	—	4	2	no	—
290	C₁₃×C₂²⋊C₄	—	4	2	no	—
291	C₁₃×C₂²⋊C₄	—	4	2	no	—
292	C₁₃×C₂²⋊C₄	—	4	1	no	—
293	C₁₃×C₂²⋊C₄	—	4	1	no	—
294	C₄²×C₁₃	—	2	4	no	—
295	C₄²×C₁₃	—	2	4	no	—
296	C₄²×C₁₃	—	2	4	no	—
297	C₄²×C₁₃	—	2	4	no	—
298	C₄²×C₁₃	—	2	4	no	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	—	2	4	no	—
301	C₄²×C₁₃	—	2	4	no	—
302	C₄²×C₁₃	—	2	4	no	—
303	C₄²×C₁₃	—	2	4	no	—
304	C₄²×C₁₃	—	2	4	no	—
305	C₄²×C₁₃	—	2	2	no	—
306	C₄²×C₁₃	—	4	1	no	—
307	C₄²×C₁₃	—	4	2	no	—
308	C₄²×C₁₃	#41	1	4	yes	complemented
309	#2612	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#2610	C₂×C₁₃	1	2	yes	complemented
311	#2609	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#2586	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#2572	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#2554	C₂×C₁₃	1	2	yes	complemented
315	#2532	C₂×C₁₃	1	2	yes	complemented
316	#2526	C₂×C₁₃	1	2	yes	complemented
317	#2479	C₂×C₁₃	1	2	yes	complemented
318	#2471	C₂×C₁₃	1	2	yes	complemented
319	#2396	C₂×C₁₃	1	2	yes	complemented
320	#2395	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#2388	C₂×C₁₃	1	1	yes	characteristic
322	C₄×#126	C₂×C₁₃	1	2	yes	complemented
323	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
324	C₄×#123	C₂×C₁₃	1	2	yes	complemented
325	#2297	C₂×C₁₃	1	2	yes	complemented
326	#2293	C₂×C₁₃	1	2	yes	complemented
327	C₄×#117	C₂×C₁₃	1	2	yes	complemented
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	2	2	no	—
330	C₂³×C₁₃	—	2	2	no	—
331	C₂³×C₁₃	—	2	2	no	—
332	C₂³×C₁₃	—	2	2	no	—
333	C₂³×C₁₃	—	2	2	no	—
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	1	no	—
336	C₂³×C₁₃	—	2	1	no	—
337	C₂³×C₁₃	—	2	2	no	—
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	1	no	—
341	C₂³×C₁₃	—	2	1	no	—
342	C₂³×C₁₃	—	2	1	no	—
343	C₂³×C₁₃	—	2	1	no	—
344	C₂³×C₁₃	C₂×#41	1	4	yes	—
345	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
346	Q₈×C₁₃	—	4	4	no	—
347	Q₈×C₁₃	—	4	4	no	—
348	D₄×C₁₃	—	4	8	no	—
349	D₄×C₁₃	—	4	8	no	—
350	D₄×C₁₃	—	4	4	no	—
351	D₄×C₁₃	—	4	4	no	—
352	C₂×C₄×C₁₃	—	2	16	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	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	1	no	—
365	C₂×C₄×C₁₃	—	2	16	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	—	2	2	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	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	4	8	no	—
391	C₂×C₄×C₁₃	—	4	4	no	—
392	C₂×C₄×C₁₃	—	4	4	no	—
393	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
394	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
395	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
396	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
397	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
398	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
399	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
400	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
401	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#126	C₂²×C₁₃	1	2	yes	—
403	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#123	C₂²×C₁₃	1	2	yes	—
405	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#117	C₂²×C₁₃	1	2	yes	—
409	C₂×#117	C₂²×C₁₃	1	2	yes	—
410	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#117	C₂²×C₁₃	1	2	yes	—
412	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
413	#400	C₂²×C₁₃	1	1	yes	characteristic
414	#400	C₂²×C₁₃	1	2	yes	—
415	#399	C₂²×C₁₃	1	1	yes	characteristic
416	#399	C₂²×C₁₃	1	2	yes	—
417	#398	C₂²×C₁₃	1	1	yes	characteristic
418	#398	C₂²×C₁₃	1	2	yes	—
419	#398	C₂²×C₁₃	1	2	yes	—
420	#397	C₂²×C₁₃	1	2	yes	—
421	#397	C₂²×C₁₃	1	1	yes	characteristic
422	#396	C₂²×C₁₃	1	2	yes	—
423	#396	C₂²×C₁₃	1	2	yes	—
424	#395	C₂²×C₁₃	1	2	yes	—
425	#395	C₂²×C₁₃	1	1	yes	characteristic
426	#394	C₂²×C₁₃	1	1	yes	characteristic
427	#394	C₂²×C₁₃	1	2	yes	—
428	#394	C₂²×C₁₃	1	2	yes	—
429	#393	C₂²×C₁₃	1	2	yes	—
430	#393	C₂²×C₁₃	1	1	yes	characteristic
431	#392	C₂²×C₁₃	1	2	yes	—
432	#392	C₂²×C₁₃	1	1	yes	characteristic
433	#391	C₂²×C₁₃	1	1	yes	characteristic
434	#391	C₂²×C₁₃	1	2	yes	—
435	#391	C₂²×C₁₃	1	2	yes	—
436	#390	C₂²×C₁₃	1	2	yes	—
437	#390	C₂²×C₁₃	1	2	yes	—
438	#390	C₂²×C₁₃	1	2	yes	—
439	#390	C₂²×C₁₃	1	2	yes	—
440	#390	C₂²×C₁₃	1	1	yes	characteristic
441	#389	C₂²×C₁₃	1	2	yes	—
442	#389	C₂²×C₁₃	1	2	yes	—
443	#388	C₂²×C₁₃	1	2	yes	—
444	#388	C₂²×C₁₃	1	2	yes	—
445	#388	C₂²×C₁₃	1	2	yes	—
446	#388	C₂²×C₁₃	1	2	yes	—
447	#388	C₂²×C₁₃	1	2	yes	—
448	#388	C₂²×C₁₃	1	2	yes	—
449	#388	C₂²×C₁₃	1	2	yes	—
450	#388	C₂²×C₁₃	1	2	yes	—
451	#388	C₂²×C₁₃	1	2	yes	—
452	#388	C₂²×C₁₃	1	2	yes	—
453	#388	C₂²×C₁₃	1	2	yes	—
454	#387	C₂²×C₁₃	1	2	yes	—
455	#387	C₂²×C₁₃	1	2	yes	—
456	#387	C₂²×C₁₃	1	2	yes	—
457	#387	C₂²×C₁₃	1	2	yes	—
458	#387	C₂²×C₁₃	1	2	yes	—
459	#386	C₂²×C₁₃	1	2	yes	—
460	#386	C₂²×C₁₃	1	2	yes	—
461	#386	C₂²×C₁₃	1	2	yes	—
462	#386	C₂²×C₁₃	1	2	yes	—
463	#386	C₂²×C₁₃	1	2	yes	—
464	#385	C₂²×C₁₃	1	2	yes	—
465	#383	C₂²×C₁₃	1	2	yes	—
466	#382	C₂²×C₁₃	1	1	yes	characteristic
467	#381	C₂²×C₁₃	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
474	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
475	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
477	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
478	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
479	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
480	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
481	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
484	#376	C₂²×C₁₃	1	2	yes	—
485	#376	C₂²×C₁₃	1	2	yes	—
486	C₄³	C₂²×C₁₃	1	2	yes	—
487	C₄³	C₂²×C₁₃	1	1	yes	characteristic
488	C₂²×C₁₃	—	2	4	no	—
489	C₂²×C₁₃	—	2	4	no	—
490	C₂²×C₁₃	—	2	4	no	—
491	C₂²×C₁₃	—	4	2	no	—
492	C₂²×C₁₃	—	4	2	no	—
493	C₂²×C₁₃	—	4	2	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	2	no	—
496	C₂²×C₁₃	—	4	2	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	1	no	—
499	C₂²×C₁₃	—	4	1	no	—
500	C₂²×C₁₃	—	4	1	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	1	no	—
504	C₂²×C₁₃	—	4	1	no	—
505	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
506	C₂²×C₁₃	C₂²×#41	1	2	yes	—
507	C₂²×C₁₃	C₂²×#41	1	2	yes	—
508	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂²×C₁₃	#585	1	1	yes	characteristic
510	C₄×C₁₃	—	2	4	no	—
511	C₄×C₁₃	—	2	4	no	—
512	C₄×C₁₃	—	2	2	no	—
513	C₄×C₁₃	—	2	4	no	—
514	C₄×C₁₃	—	2	4	no	—
515	C₄×C₁₃	—	2	4	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	1	no	—
520	C₄×C₁₃	—	4	1	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	#551	1	4	yes	—
526	C₂×#41	—	2	8	no	—
527	C₂×#41	—	4	2	no	—
528	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
529	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
531	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
533	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
535	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
538	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
539	#126	—	2	8	no	—
540	#124	—	2	4	no	—
541	#123	—	2	8	no	—
542	C₄×Q₈	—	4	2	no	—
543	C₄×D₄	—	2	8	no	—
544	C₄×D₄	—	4	2	no	—
545	#117	—	2	8	no	—
546	#117	—	2	8	no	—
547	#117	—	4	2	no	—
548	#117	—	4	4	no	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄⋊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	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	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	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
586	C₂×C₄²	—	2	8	no	—
587	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
588	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
589	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
592	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
594	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
595	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
602	#95	C₂³×C₁₃	1	2	yes	—
603	#95	C₂³×C₁₃	1	2	yes	—
604	#95	C₂³×C₁₃	1	2	yes	—
605	#95	C₂³×C₁₃	1	2	yes	—
606	#95	C₂³×C₁₃	1	2	yes	—
607	#95	C₂³×C₁₃	1	2	yes	—
608	#95	C₂³×C₁₃	1	2	yes	—
609	#95	C₂³×C₁₃	1	2	yes	—
610	#95	C₂³×C₁₃	1	1	yes	characteristic
611	#95	C₂³×C₁₃	1	2	yes	—
612	#95	C₂³×C₁₃	1	2	yes	—
613	#95	C₂³×C₁₃	1	2	yes	—
614	#95	C₂³×C₁₃	1	1	yes	characteristic
615	#95	C₂³×C₁₃	1	2	yes	—
616	#95	C₂³×C₁₃	1	2	yes	—
617	#95	C₂³×C₁₃	1	1	yes	characteristic
618	#95	C₂³×C₁₃	1	2	yes	—
619	#95	C₂³×C₁₃	1	2	yes	—
620	#95	C₂³×C₁₃	1	2	yes	—
621	#95	C₂³×C₁₃	1	1	yes	characteristic
622	#95	C₂³×C₁₃	1	2	yes	—
623	#95	C₂³×C₁₃	1	2	yes	—
624	#95	C₂³×C₁₃	1	2	yes	—
625	#95	C₂³×C₁₃	1	2	yes	—
626	C₂×C₁₃	—	4	4	no	—
627	C₂×C₁₃	—	8	1	no	—
628	C₂×C₁₃	—	8	1	no	—
629	C₂×C₁₃	#3444	1	2	yes	—
630	C₂×C₁₃	#3460	1	1	yes	characteristic
631	C₂×C₁₃	C₂×#551	1	1	yes	characteristic
632	C₂×C₁₃	#3475	1	2	yes	—
633	C₂×C₁₃	#3483	1	1	yes	characteristic
634	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
636	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
637	#41	—	4	16	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	4	no	—
640	C₂×Q₈	—	4	1	no	—
641	C₂×Q₈	—	4	1	no	—
642	C₂×Q₈	—	4	1	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	4	1	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	1	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	C₁₃×#41	1	8	yes	—
667	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	4	1	no	—
694	C₄⋊C₄	—	4	1	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	C₁₃×#41	1	8	yes	complemented
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	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	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	1	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₄²	—	2	4	no	—
721	C₄²	—	2	4	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	4	no	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	4	no	—
730	C₄²	—	2	4	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	4	1	no	—
733	C₄²	—	4	2	no	—
734	C₄²	C₁₃×#41	1	4	yes	complemented
735	C₁₃	#34871	1	1	yes	characteristic, direct product factor, Sylow
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	2	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	C₂×C₁₃×#41	1	4	yes	—
753	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
754	Q₈	—	4	4	no	—
755	Q₈	—	4	4	no	—
756	D₄	—	4	8	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	4	no	—
759	D₄	—	4	4	no	—
760	C₂×C₄	—	2	16	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	16	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
802	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
803	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
804	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
805	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
806	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
807	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
808	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
827	C₂²	C₂²×C₁₃×#41	1	2	yes	—
828	C₂²	C₂²×C₁₃×#41	1	2	yes	—
829	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂²	C₁₃×#585	1	1	yes	characteristic
831	C₄	—	2	4	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	4	no	—
835	C₄	—	2	4	no	—
836	C₄	—	2	4	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₄	C₁₃×#551	1	4	yes	—
847	C₂	—	4	4	no	—
848	C₂	—	8	1	no	—
849	C₂	—	8	1	no	—
850	C₂	C₁₃×#3444	1	2	yes	—
851	C₂	C₁₃×#3460	1	1	yes	characteristic
852	C₂	C₂×C₁₃×#551	1	1	yes	characteristic
853	C₂	C₁₃×#3475	1	2	yes	—
854	C₂	C₁₃×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₁₃×#2388	C₂
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×#2612	C₂	semidirect
2. C₁₃×#2610	C₂	semidirect
3. C₁₃×#2609	C₂	semidirect
4. C₁₃×#2586	C₂	semidirect
5. C₁₃×#2572	C₂	semidirect
6. C₁₃×#2554	C₂	semidirect
7. C₁₃×#2532	C₂	semidirect
8. C₁₃×#2526	C₂	semidirect
9. C₁₃×#2479	C₂	semidirect
10. C₁₃×#2471	C₂	semidirect
11. C₁₃×#2396	C₂	semidirect
12. C₁₃×#2395	C₂	semidirect
14. C₄×C₁₃×#126	C₂	semidirect
15. C₄×C₁₃×#124	C₂	semidirect
16. C₄×C₁₃×#123	C₂	semidirect
17. C₁₃×#2297	C₂	semidirect
18. C₁₃×#2293	C₂	semidirect
19. C₄×C₁₃×#117	C₂	semidirect
207. #34871	C₁₃	direct (N × H)
272. C₁₃×C₄⋊C₄	#41	semidirect
308. C₄²×C₁₃	#41	semidirect
309. #2612	C₂×C₁₃	semidirect
310. #2610	C₂×C₁₃	semidirect
311. #2609	C₂×C₁₃	semidirect
312. #2586	C₂×C₁₃	semidirect
313. #2572	C₂×C₁₃	semidirect
314. #2554	C₂×C₁₃	semidirect
315. #2532	C₂×C₁₃	semidirect
316. #2526	C₂×C₁₃	semidirect
317. #2479	C₂×C₁₃	semidirect
318. #2471	C₂×C₁₃	semidirect
319. #2396	C₂×C₁₃	semidirect
320. #2395	C₂×C₁₃	semidirect
322. C₄×#126	C₂×C₁₃	semidirect
323. C₄×#124	C₂×C₁₃	semidirect
324. C₄×#123	C₂×C₁₃	semidirect
325. #2297	C₂×C₁₃	semidirect
326. #2293	C₂×C₁₃	semidirect
327. C₄×#117	C₂×C₁₃	semidirect
698. C₄⋊C₄	C₁₃×#41	semidirect
734. C₄²	C₁₃×#41	semidirect
735. C₁₃	#34871	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×#2612	2
C₁₃×#2610	2
C₁₃×#2609	2
C₁₃×#2586	2
C₁₃×#2572	2
C₁₃×#2554	2
C₁₃×#2532	2
C₁₃×#2526	2
C₁₃×#2479	2
C₁₃×#2471	2
C₁₃×#2396	2
C₁₃×#2395	2
C₁₃×#2388	2
C₄×C₁₃×#126	2
C₄×C₁₃×#124	2
C₄×C₁₃×#123	2
C₁₃×#2297	2
C₁₃×#2293	2
C₄×C₁₃×#117	2
#34871	13

Subgroups — C13×#34871 #15721210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34871 #15721210