Subgroups — C₁₃×#34882 #15721221

Order 3328.

1750 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×#2586	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2585	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2574	C₂	1	2	yes	maximal
4	C₁₃×#2556	C₂	1	2	yes	maximal
5	C₁₃×#2522	C₂	1	2	yes	maximal
6	C₁₃×#2520	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2465	C₂	1	2	yes	maximal
8	C₁₃×#2462	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic
13	C₄×C₁₃×#125	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
15	C₁₃×#2298	C₂	1	2	yes	maximal
16	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2295	C₂	1	2	yes	maximal, complemented
18	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
20	C₂×C₁₃×#125	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×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#400	C₂²	1	1	yes	characteristic
30	C₁₃×#400	C₂²	1	1	yes	characteristic
31	C₁₃×#399	C₂²	1	1	yes	characteristic
32	C₁₃×#399	C₂²	1	1	yes	characteristic
33	C₁₃×#398	C₂²	1	2	yes	—
34	C₁₃×#398	C₂²	1	2	yes	—
35	C₁₃×#398	C₂²	1	2	yes	—
36	C₁₃×#398	C₂²	1	2	yes	—
37	C₁₃×#398	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	2	yes	—
39	C₁₃×#396	C₂²	1	2	yes	—
40	C₁₃×#396	C₂²	1	2	yes	—
41	C₁₃×#395	C₂²	1	2	yes	—
42	C₁₃×#395	C₂²	1	2	yes	—
43	C₁₃×#395	C₂²	1	2	yes	—
44	C₁₃×#395	C₂²	1	1	yes	characteristic
45	C₁₃×#395	C₂²	1	1	yes	characteristic
46	C₁₃×#395	C₂²	1	2	yes	—
47	C₁₃×#393	C₂²	1	1	yes	characteristic
48	C₁₃×#393	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	2	yes	—
50	C₁₃×#391	C₂²	1	2	yes	—
51	C₁₃×#391	C₂²	1	2	yes	—
52	C₁₃×#391	C₂²	1	2	yes	—
53	C₁₃×#389	C₂²	1	2	yes	—
54	C₁₃×#389	C₂²	1	2	yes	—
55	C₁₃×#389	C₂²	1	2	yes	—
56	C₁₃×#389	C₂²	1	2	yes	—
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#388	C₂²	1	2	yes	—
60	C₁₃×#388	C₂²	1	2	yes	—
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#387	C₂²	1	2	yes	—
64	C₁₃×#387	C₂²	1	2	yes	—
65	C₁₃×#387	C₂²	1	2	yes	—
66	C₁₃×#387	C₂²	1	2	yes	—
67	C₁₃×#387	C₂²	1	2	yes	—
68	C₁₃×#387	C₂²	1	2	yes	—
69	C₁₃×#387	C₂²	1	2	yes	—
70	C₁₃×#387	C₂²	1	2	yes	—
71	C₁₃×#387	C₂²	1	2	yes	—
72	C₁₃×#387	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×#385	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#382	C₂²	1	2	yes	—
82	C₁₃×#380	C₂²	1	2	yes	—
83	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
84	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
85	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
86	C₄×C₁₃×C₄⋊C₄	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	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊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	C₁₃×#376	C₂²	1	1	yes	characteristic
102	C₁₃×#376	C₂²	1	1	yes	characteristic
103	C₁₃×#376	C₂²	1	2	yes	—
104	C₄³×C₁₃	C₂²	1	1	yes	characteristic
105	C₄³×C₁₃	C₂²	1	1	yes	characteristic
106	C₄³×C₁₃	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#125	—	2	8	no	—
113	C₁₃×C₂²⋊Q₈	—	2	8	no	—
114	C₄×Q₈×C₁₃	—	2	8	no	—
115	C₄×Q₈×C₁₃	—	2	8	no	—
116	C₄×Q₈×C₁₃	—	2	4	no	—
117	C₄×Q₈×C₁₃	—	2	4	no	—
118	C₁₃×#117	—	2	4	no	—
119	C₁₃×#117	Q₈	1	8	yes	complemented
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	1	yes	characteristic
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	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	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×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	1	yes	characteristic
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃	—	2	4	no	—
154	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃	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	2	yes	—
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	2	yes	—
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
184	C₁₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	#34882	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂×Q₈×C₁₃	—	2	4	no	—
206	C₂×Q₈×C₁₃	—	2	2	no	—
207	C₂×Q₈×C₁₃	—	2	4	no	—
208	C₂×Q₈×C₁₃	—	2	2	no	—
209	C₂×Q₈×C₁₃	—	2	4	no	—
210	C₂×Q₈×C₁₃	—	4	2	no	—
211	C₂×Q₈×C₁₃	—	4	2	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	4	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	4	2	no	—
217	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	2	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	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	2	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
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	4	no	—
254	C₁₃×C₄⋊C₄	—	4	2	no	—
255	C₁₃×C₄⋊C₄	—	4	2	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	C₂×Q₈	1	8	yes	—
261	C₁₃×C₄⋊C₄	#41	1	8	yes	—
262	C₁₃×C₂²⋊C₄	—	2	2	no	—
263	C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	4	2	no	—
267	C₁₃×C₂²⋊C₄	—	4	2	no	—
268	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
269	C₄²×C₁₃	—	2	4	no	—
270	C₄²×C₁₃	—	2	2	no	—
271	C₄²×C₁₃	—	2	2	no	—
272	C₄²×C₁₃	—	2	4	no	—
273	C₄²×C₁₃	—	2	4	no	—
274	C₄²×C₁₃	—	2	4	no	—
275	C₄²×C₁₃	—	2	4	no	—
276	C₄²×C₁₃	—	2	4	no	—
277	C₄²×C₁₃	—	2	4	no	—
278	C₄²×C₁₃	—	2	4	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	—	4	2	no	—
281	C₄²×C₁₃	—	4	2	no	—
282	C₄²×C₁₃	—	4	2	no	—
283	C₄²×C₁₃	—	4	2	no	—
284	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
285	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
286	C₄²×C₁₃	#41	1	4	yes	—
287	C₄²×C₁₃	#41	1	4	yes	—
288	#2586	C₂×C₁₃	1	2	yes	complemented
289	#2585	C₂×C₁₃	1	2	yes	complemented
290	#2574	C₂×C₁₃	1	2	yes	—
291	#2556	C₂×C₁₃	1	2	yes	—
292	#2522	C₂×C₁₃	1	2	yes	—
293	#2520	C₂×C₁₃	1	2	yes	complemented
294	#2465	C₂×C₁₃	1	2	yes	—
295	#2462	C₂×C₁₃	1	2	yes	complemented
296	#2399	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2399	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2396	C₂×C₁₃	1	1	yes	characteristic
299	#2396	C₂×C₁₃	1	1	yes	characteristic
300	C₄×#125	C₂×C₁₃	1	2	yes	complemented
301	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	—
302	#2298	C₂×C₁₃	1	2	yes	—
303	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2295	C₂×C₁₃	1	2	yes	complemented
305	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
307	C₂³×C₁₃	—	2	1	no	—
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	1	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
312	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
313	Q₈×C₁₃	—	2	8	no	—
314	Q₈×C₁₃	—	4	8	no	—
315	Q₈×C₁₃	—	4	4	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	2	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	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	2	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	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	8	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	1	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	2	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	—	4	8	no	—
356	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
357	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
358	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
359	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
360	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
361	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
362	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
363	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
364	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
365	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
366	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
367	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
368	C₂×#125	C₂²×C₁₃	1	2	yes	—
369	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
370	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
373	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
374	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
377	#400	C₂²×C₁₃	1	1	yes	characteristic
378	#400	C₂²×C₁₃	1	1	yes	characteristic
379	#399	C₂²×C₁₃	1	1	yes	characteristic
380	#399	C₂²×C₁₃	1	1	yes	characteristic
381	#398	C₂²×C₁₃	1	2	yes	—
382	#398	C₂²×C₁₃	1	2	yes	—
383	#398	C₂²×C₁₃	1	2	yes	—
384	#398	C₂²×C₁₃	1	2	yes	—
385	#398	C₂²×C₁₃	1	2	yes	—
386	#398	C₂²×C₁₃	1	2	yes	—
387	#396	C₂²×C₁₃	1	2	yes	—
388	#396	C₂²×C₁₃	1	2	yes	—
389	#395	C₂²×C₁₃	1	2	yes	—
390	#395	C₂²×C₁₃	1	1	yes	characteristic
391	#395	C₂²×C₁₃	1	2	yes	—
392	#395	C₂²×C₁₃	1	1	yes	characteristic
393	#395	C₂²×C₁₃	1	2	yes	—
394	#395	C₂²×C₁₃	1	2	yes	—
395	#393	C₂²×C₁₃	1	1	yes	characteristic
396	#393	C₂²×C₁₃	1	1	yes	characteristic
397	#391	C₂²×C₁₃	1	2	yes	—
398	#391	C₂²×C₁₃	1	2	yes	—
399	#391	C₂²×C₁₃	1	2	yes	—
400	#391	C₂²×C₁₃	1	2	yes	—
401	#389	C₂²×C₁₃	1	2	yes	—
402	#389	C₂²×C₁₃	1	2	yes	—
403	#389	C₂²×C₁₃	1	2	yes	—
404	#389	C₂²×C₁₃	1	2	yes	—
405	#389	C₂²×C₁₃	1	2	yes	—
406	#389	C₂²×C₁₃	1	2	yes	—
407	#388	C₂²×C₁₃	1	2	yes	—
408	#388	C₂²×C₁₃	1	2	yes	—
409	#388	C₂²×C₁₃	1	2	yes	—
410	#388	C₂²×C₁₃	1	2	yes	—
411	#387	C₂²×C₁₃	1	2	yes	—
412	#387	C₂²×C₁₃	1	2	yes	—
413	#387	C₂²×C₁₃	1	2	yes	—
414	#387	C₂²×C₁₃	1	2	yes	—
415	#387	C₂²×C₁₃	1	2	yes	—
416	#387	C₂²×C₁₃	1	2	yes	—
417	#387	C₂²×C₁₃	1	2	yes	—
418	#387	C₂²×C₁₃	1	2	yes	—
419	#387	C₂²×C₁₃	1	2	yes	—
420	#387	C₂²×C₁₃	1	2	yes	—
421	#387	C₂²×C₁₃	1	2	yes	—
422	#387	C₂²×C₁₃	1	2	yes	—
423	#387	C₂²×C₁₃	1	2	yes	—
424	#387	C₂²×C₁₃	1	2	yes	—
425	#387	C₂²×C₁₃	1	2	yes	—
426	#387	C₂²×C₁₃	1	2	yes	—
427	#385	C₂²×C₁₃	1	2	yes	—
428	#385	C₂²×C₁₃	1	2	yes	—
429	#382	C₂²×C₁₃	1	2	yes	—
430	#380	C₂²×C₁₃	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
436	C₄×C₄⋊C₄	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	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
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	#376	C₂²×C₁₃	1	1	yes	characteristic
450	#376	C₂²×C₁₃	1	1	yes	characteristic
451	#376	C₂²×C₁₃	1	2	yes	—
452	C₄³	C₂²×C₁₃	1	1	yes	characteristic
453	C₄³	C₂²×C₁₃	1	1	yes	characteristic
454	C₄³	C₂²×C₁₃	1	2	yes	—
455	C₂²×C₁₃	—	2	2	no	—
456	C₂²×C₁₃	—	2	4	no	—
457	C₂²×C₁₃	—	4	1	no	—
458	C₂²×C₁₃	—	4	1	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
461	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
462	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
463	C₂²×C₁₃	C₂²×#41	1	2	yes	—
464	C₂²×C₁₃	#585	1	2	yes	—
465	C₄×C₁₃	—	2	2	no	—
466	C₄×C₁₃	—	2	4	no	—
467	C₄×C₁₃	—	2	2	no	—
468	C₄×C₁₃	—	2	2	no	—
469	C₄×C₁₃	—	2	4	no	—
470	C₄×C₁₃	—	2	4	no	—
471	C₄×C₁₃	—	2	4	no	—
472	C₄×C₁₃	—	2	4	no	—
473	C₄×C₁₃	—	2	4	no	—
474	C₄×C₁₃	—	4	1	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	—	4	1	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	—	4	2	no	—
479	C₄×C₁₃	—	4	2	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	—	4	2	no	—
482	C₄×C₁₃	#533	1	4	yes	—
483	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
485	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
487	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
488	#125	—	2	8	no	—
489	C₂²⋊Q₈	—	2	8	no	—
490	C₄×Q₈	—	2	8	no	—
491	C₄×Q₈	—	2	8	no	—
492	C₄×Q₈	—	2	4	no	—
493	C₄×Q₈	—	2	4	no	—
494	#117	—	2	4	no	—
495	#117	Q₈×C₁₃	1	8	yes	complemented
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
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×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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×C₄²	—	2	4	no	—
530	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄²	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	2	yes	—
537	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
538	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
539	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
544	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
545	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
549	#95	C₂³×C₁₃	1	2	yes	—
550	#95	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
564	#95	C₂³×C₁₃	1	1	yes	characteristic
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	#95	C₂³×C₁₃	1	1	yes	characteristic
578	#95	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×C₁₃	—	4	2	no	—
580	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
581	C₂×C₁₃	#3444	1	1	yes	characteristic
582	C₂×C₁₃	#3455	1	1	yes	characteristic
583	C₂×C₁₃	#3475	1	2	yes	—
584	C₂×C₁₃	Q₈×#41	1	2	yes	—
585	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
586	C₂×Q₈	—	2	4	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	2	2	no	—
590	C₂×Q₈	—	2	4	no	—
591	C₂×Q₈	—	4	2	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
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	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	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	C₄⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
642	C₄⋊C₄	C₁₃×#41	1	8	yes	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	4	2	no	—
662	C₄²	—	4	2	no	—
663	C₄²	—	4	2	no	—
664	C₄²	—	4	2	no	—
665	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
666	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
667	C₄²	C₁₃×#41	1	4	yes	—
668	C₄²	C₁₃×#41	1	4	yes	—
669	C₁₃	#34882	1	1	yes	characteristic, direct product factor, Sylow
670	C₂³	—	2	1	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	2	no	—
674	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
675	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
676	Q₈	—	2	8	no	—
677	Q₈	—	4	8	no	—
678	Q₈	—	4	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	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	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	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	2	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	—	4	8	no	—
719	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
720	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
721	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
722	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
723	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
724	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
725	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
726	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
727	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
728	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
729	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
730	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	2	no	—
736	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
737	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
738	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
739	C₂²	C₂²×C₁₃×#41	1	2	yes	—
740	C₂²	C₁₃×#585	1	2	yes	—
741	C₄	—	2	2	no	—
742	C₄	—	2	4	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	4	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	C₁₃×#533	1	4	yes	—
759	C₂	—	4	2	no	—
760	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
761	C₂	C₁₃×#3444	1	1	yes	characteristic
762	C₂	C₁₃×#3455	1	1	yes	characteristic
763	C₂	C₁₃×#3475	1	2	yes	—
764	C₂	Q₈×C₁₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁴×C₁₃	C₂⁴
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×#2586	C₂	semidirect
2. C₁₃×#2585	C₂	semidirect
6. C₁₃×#2520	C₂	semidirect
8. C₁₃×#2462	C₂	semidirect
9. C₁₃×#2399	C₂	semidirect
10. C₁₃×#2399	C₂	semidirect
13. C₄×C₁₃×#125	C₂	semidirect
16. C₁₃×#2295	C₂	semidirect
17. C₁₃×#2295	C₂	semidirect
18. C₄²×Q₈×C₁₃	C₂	semidirect
119. C₁₃×#117	Q₈	semidirect
203. #34882	C₁₃	direct (N × H)
288. #2586	C₂×C₁₃	semidirect
289. #2585	C₂×C₁₃	semidirect
293. #2520	C₂×C₁₃	semidirect
295. #2462	C₂×C₁₃	semidirect
296. #2399	C₂×C₁₃	semidirect
297. #2399	C₂×C₁₃	semidirect
300. C₄×#125	C₂×C₁₃	semidirect
303. #2295	C₂×C₁₃	semidirect
304. #2295	C₂×C₁₃	semidirect
305. C₄²×Q₈	C₂×C₁₃	semidirect
495. #117	Q₈×C₁₃	semidirect
669. C₁₃	#34882	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×#2586	2
C₁₃×#2585	2
C₁₃×#2574	2
C₁₃×#2556	2
C₁₃×#2522	2
C₁₃×#2520	2
C₁₃×#2465	2
C₁₃×#2462	2
C₁₃×#2399	2
C₁₃×#2396	2
C₄×C₁₃×#125	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2298	2
C₁₃×#2295	2
C₄²×Q₈×C₁₃	2
C₄×C₁₃×#117	2
#34882	13

Subgroups — C13×#34882 #15721221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34882 #15721221