Subgroups — C₁₃×#34909 #15721248

Order 3328.

2726 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2600	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2599	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2598	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2580	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2536	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2535	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2485	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2407	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2395	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2388	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2290	C₂	1	4	yes	maximal, complemented
17	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×#121	C₂²	1	2	yes	—
22	C₄×C₁₃×#41	—	2	8	no	—
23	C₄×C₁₃×#41	—	2	8	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₁₃×#117	C₂²	1	2	yes	—
38	C₂×C₁₃×#117	C₂²	1	2	yes	—
39	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#400	C₂²	1	2	yes	—
45	C₁₃×#399	C₂²	1	2	yes	—
46	C₁₃×#398	C₂²	1	2	yes	—
47	C₁₃×#397	C₂²	1	2	yes	—
48	C₁₃×#397	C₂²	1	4	yes	—
49	C₁₃×#395	C₂²	1	2	yes	—
50	C₁₃×#394	C₂²	1	2	yes	—
51	C₁₃×#394	C₂²	1	4	yes	—
52	C₁₃×#394	C₂²	1	4	yes	—
53	C₁₃×#393	C₂²	1	2	yes	—
54	C₁₃×#392	C₂²	1	2	yes	—
55	C₁₃×#392	C₂²	1	4	yes	—
56	C₁₃×#391	C₂²	1	2	yes	—
57	C₁₃×#390	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#389	C₂²	1	2	yes	—
60	C₁₃×#388	C₂²	1	4	yes	—
61	C₁₃×#388	C₂²	1	4	yes	—
62	C₁₃×#388	C₂²	1	4	yes	—
63	C₁₃×#387	C₂²	1	4	yes	—
64	C₁₃×#387	C₂²	1	4	yes	—
65	C₁₃×#387	C₂²	1	4	yes	—
66	C₁₃×#386	C₂²	1	4	yes	—
67	C₁₃×#386	C₂²	1	4	yes	—
68	C₁₃×#386	C₂²	1	4	yes	—
69	C₁₃×#385	C₂²	1	4	yes	—
70	C₁₃×#385	C₂²	1	4	yes	—
71	C₁₃×#385	C₂²	1	4	yes	—
72	C₁₃×#383	C₂²	1	2	yes	—
73	C₁₃×#382	C₂²	1	1	yes	characteristic
74	C₁₃×#382	C₂²	1	1	yes	characteristic
75	C₁₃×#381	C₂²	1	2	yes	—
76	C₁₃×#380	C₂²	1	2	yes	—
77	C₁₃×#380	C₂²	1	2	yes	—
78	C₁₃×#380	C₂²	1	2	yes	—
79	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
80	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
84	C₁₃×#376	C₂²	1	2	yes	—
85	C₂×C₁₃×#41	—	2	4	no	—
86	C₂×C₁₃×#41	—	2	4	no	—
87	C₂×C₁₃×#41	—	2	4	no	—
88	C₂×C₁₃×#41	—	2	4	no	—
89	C₂×C₁₃×#41	—	2	8	no	—
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×C₂²⋊Q₈	—	2	8	no	—
107	C₁₃×#121	—	2	8	no	—
108	C₄×Q₈×C₁₃	—	2	4	no	—
109	C₄×Q₈×C₁₃	—	2	4	no	—
110	C₄×Q₈×C₁₃	—	2	4	no	—
111	C₄×Q₈×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	8	no	—
113	C₄×D₄×C₁₃	—	2	8	no	—
114	C₄×D₄×C₁₃	—	2	8	no	—
115	C₄×D₄×C₁₃	—	2	8	no	—
116	C₄×D₄×C₁₃	—	2	16	no	—
117	C₄×D₄×C₁₃	—	2	4	no	—
118	C₄×D₄×C₁₃	—	2	4	no	—
119	C₄×D₄×C₁₃	—	2	4	no	—
120	C₄×D₄×C₁₃	—	2	4	no	—
121	C₁₃×#117	—	2	4	no	—
122	C₁₃×#117	—	2	4	no	—
123	C₁₃×#117	—	2	8	no	—
124	C₁₃×#117	—	2	8	no	—
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	4	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	4	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	4	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₃	—	2	8	no	—
152	C₂×C₄²×C₁₃	—	2	8	no	—
153	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
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	4	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	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₁₃×#95	C₂³	1	4	yes	—
166	C₁₃×#95	C₂³	1	2	yes	—
167	C₁₃×#95	C₂³	1	2	yes	—
168	C₁₃×#95	C₂³	1	4	yes	—
169	C₁₃×#95	C₂³	1	4	yes	—
170	C₁₃×#95	C₂³	1	4	yes	—
171	C₁₃×#95	C₂³	1	4	yes	—
172	C₁₃×#95	C₂³	1	4	yes	—
173	C₁₃×#95	C₂³	1	4	yes	—
174	C₁₃×#95	C₂³	1	4	yes	—
175	C₁₃×#95	C₂³	1	2	yes	—
176	C₁₃×#95	C₂³	1	2	yes	—
177	#34909	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
180	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
181	C₁₃×#41	—	2	32	no	—
182	C₁₃×#41	—	2	32	no	—
183	C₂×Q₈×C₁₃	—	2	2	no	—
184	C₂×Q₈×C₁₃	—	2	2	no	—
185	C₂×Q₈×C₁₃	—	2	4	no	—
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	2	4	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	4	no	—
193	C₂×D₄×C₁₃	—	2	8	no	—
194	C₂×D₄×C₁₃	—	2	8	no	—
195	C₂×D₄×C₁₃	—	2	2	no	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	4	4	no	—
201	C₂×D₄×C₁₃	#41	1	4	yes	complemented
202	C₂²×C₄×C₁₃	—	2	4	no	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	2	4	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	4	no	—
209	C₂²×C₄×C₁₃	—	2	4	no	—
210	C₂²×C₄×C₁₃	—	2	4	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	2	8	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	4	2	no	—
218	C₂²×C₄×C₁₃	—	4	2	no	—
219	C₂²×C₄×C₁₃	—	4	4	no	—
220	C₂²×C₄×C₁₃	—	4	2	no	—
221	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
222	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
224	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
225	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
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	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	8	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	8	no	—
251	C₁₃×C₄⋊C₄	—	4	4	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	8	no	—
255	C₁₃×C₂²⋊C₄	—	2	8	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	8	no	—
261	C₁₃×C₂²⋊C₄	—	2	8	no	—
262	C₁₃×C₂²⋊C₄	—	4	4	no	—
263	C₁₃×C₂²⋊C₄	—	4	4	no	—
264	C₁₃×C₂²⋊C₄	—	4	4	no	—
265	C₄²×C₁₃	—	2	4	no	—
266	C₄²×C₁₃	—	2	4	no	—
267	C₄²×C₁₃	—	2	4	no	—
268	C₄²×C₁₃	—	2	4	no	—
269	C₄²×C₁₃	—	2	4	no	—
270	C₄²×C₁₃	—	2	4	no	—
271	C₄²×C₁₃	—	2	8	no	—
272	C₄²×C₁₃	C₂×D₄	1	4	yes	—
273	C₄²×C₁₃	C₂×D₄	1	4	yes	—
274	C₄²×C₁₃	C₂×D₄	1	4	yes	—
275	C₄²×C₁₃	C₂×D₄	1	4	yes	—
276	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2600	C₂×C₁₃	1	4	yes	complemented
279	#2599	C₂×C₁₃	1	2	yes	complemented
280	#2598	C₂×C₁₃	1	2	yes	complemented
281	#2581	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#2580	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#2536	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#2535	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#2485	C₂×C₁₃	1	2	yes	complemented
286	#2407	C₂×C₁₃	1	2	yes	complemented
287	#2395	C₂×C₁₃	1	2	yes	complemented
288	#2388	C₂×C₁₃	1	2	yes	complemented
289	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
290	C₄×#121	C₂×C₁₃	1	2	yes	complemented
291	#2290	C₂×C₁₃	1	4	yes	complemented
292	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	4	no	—
297	C₂³×C₁₃	—	2	1	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	1	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	2	4	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
308	C₂³×C₁₃	C₂×#41	1	4	yes	—
309	C₂³×C₁₃	C₂×#41	1	4	yes	—
310	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
311	Q₈×C₁₃	—	2	8	no	—
312	Q₈×C₁₃	—	2	8	no	—
313	D₄×C₁₃	—	2	8	no	—
314	D₄×C₁₃	—	2	16	no	—
315	D₄×C₁₃	—	2	16	no	—
316	D₄×C₁₃	—	2	8	no	—
317	D₄×C₁₃	—	4	16	no	—
318	C₂×C₄×C₁₃	—	2	16	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	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	8	no	—
329	C₂×C₄×C₁₃	—	2	8	no	—
330	C₂×C₄×C₁₃	—	2	16	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	4	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	2	4	no	—
340	C₂×C₄×C₁₃	—	2	4	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	4	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	2	4	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	4	4	no	—
348	C₂×C₄×C₁₃	—	4	8	no	—
349	C₂×C₄×C₁₃	—	4	8	no	—
350	C₂×C₄×C₁₃	—	4	8	no	—
351	C₂×C₄×C₁₃	—	4	8	no	—
352	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
359	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
360	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
361	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
362	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
363	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
364	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
366	C₂×#121	C₂²×C₁₃	1	2	yes	—
367	C₄×#41	—	2	8	no	—
368	C₄×#41	—	2	8	no	—
369	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
376	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
378	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
379	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
380	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#117	C₂²×C₁₃	1	2	yes	—
383	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#117	C₂²×C₁₃	1	2	yes	—
386	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
387	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
388	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
389	#400	C₂²×C₁₃	1	2	yes	—
390	#399	C₂²×C₁₃	1	2	yes	—
391	#398	C₂²×C₁₃	1	2	yes	—
392	#397	C₂²×C₁₃	1	2	yes	—
393	#397	C₂²×C₁₃	1	4	yes	—
394	#395	C₂²×C₁₃	1	2	yes	—
395	#394	C₂²×C₁₃	1	2	yes	—
396	#394	C₂²×C₁₃	1	4	yes	—
397	#394	C₂²×C₁₃	1	4	yes	—
398	#393	C₂²×C₁₃	1	2	yes	—
399	#392	C₂²×C₁₃	1	2	yes	—
400	#392	C₂²×C₁₃	1	4	yes	—
401	#391	C₂²×C₁₃	1	2	yes	—
402	#390	C₂²×C₁₃	1	2	yes	—
403	#389	C₂²×C₁₃	1	2	yes	—
404	#389	C₂²×C₁₃	1	2	yes	—
405	#388	C₂²×C₁₃	1	4	yes	—
406	#388	C₂²×C₁₃	1	4	yes	—
407	#388	C₂²×C₁₃	1	4	yes	—
408	#387	C₂²×C₁₃	1	4	yes	—
409	#387	C₂²×C₁₃	1	4	yes	—
410	#387	C₂²×C₁₃	1	4	yes	—
411	#386	C₂²×C₁₃	1	4	yes	—
412	#386	C₂²×C₁₃	1	4	yes	—
413	#386	C₂²×C₁₃	1	4	yes	—
414	#385	C₂²×C₁₃	1	4	yes	—
415	#385	C₂²×C₁₃	1	4	yes	—
416	#385	C₂²×C₁₃	1	4	yes	—
417	#383	C₂²×C₁₃	1	2	yes	—
418	#382	C₂²×C₁₃	1	1	yes	characteristic
419	#382	C₂²×C₁₃	1	1	yes	characteristic
420	#381	C₂²×C₁₃	1	2	yes	—
421	#380	C₂²×C₁₃	1	2	yes	—
422	#380	C₂²×C₁₃	1	2	yes	—
423	#380	C₂²×C₁₃	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
425	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
426	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
427	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
428	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
429	#376	C₂²×C₁₃	1	2	yes	—
430	C₂²×C₁₃	—	2	2	no	—
431	C₂²×C₁₃	—	2	2	no	—
432	C₂²×C₁₃	—	2	4	no	—
433	C₂²×C₁₃	—	2	4	no	—
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	2	4	no	—
436	C₂²×C₁₃	—	2	8	no	—
437	C₂²×C₁₃	—	2	4	no	—
438	C₂²×C₁₃	—	4	2	no	—
439	C₂²×C₁₃	—	4	2	no	—
440	C₂²×C₁₃	—	4	2	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	2	no	—
443	C₂²×C₁₃	—	4	2	no	—
444	C₂²×C₁₃	—	4	2	no	—
445	C₂²×C₁₃	—	4	4	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
448	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
449	C₂²×C₁₃	C₂²×#41	1	2	yes	—
450	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
451	C₂²×C₁₃	#585	1	2	yes	—
452	C₄×C₁₃	—	2	2	no	—
453	C₄×C₁₃	—	2	2	no	—
454	C₄×C₁₃	—	2	4	no	—
455	C₄×C₁₃	—	2	4	no	—
456	C₄×C₁₃	—	2	2	no	—
457	C₄×C₁₃	—	2	2	no	—
458	C₄×C₁₃	—	4	2	no	—
459	C₄×C₁₃	—	4	2	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	—	4	2	no	—
462	C₄×C₁₃	—	4	4	no	—
463	C₄×C₁₃	—	4	4	no	—
464	C₄×C₁₃	#525	1	4	yes	—
465	C₄×C₁₃	#525	1	4	yes	—
466	C₂×#41	—	2	4	no	—
467	C₂×#41	—	2	4	no	—
468	C₂×#41	—	2	4	no	—
469	C₂×#41	—	2	4	no	—
470	C₂×#41	—	2	8	no	—
471	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
475	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
476	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
477	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
479	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
480	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
481	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
484	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
485	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
486	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂²⋊Q₈	—	2	8	no	—
488	#121	—	2	8	no	—
489	C₄×Q₈	—	2	4	no	—
490	C₄×Q₈	—	2	4	no	—
491	C₄×Q₈	—	2	4	no	—
492	C₄×Q₈	—	2	4	no	—
493	C₄×D₄	—	2	8	no	—
494	C₄×D₄	—	2	8	no	—
495	C₄×D₄	—	2	8	no	—
496	C₄×D₄	—	2	8	no	—
497	C₄×D₄	—	2	16	no	—
498	C₄×D₄	—	2	4	no	—
499	C₄×D₄	—	2	4	no	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	2	4	no	—
502	#117	—	2	4	no	—
503	#117	—	2	4	no	—
504	#117	—	2	8	no	—
505	#117	—	2	8	no	—
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	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	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₂²⋊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	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
532	C₂×C₄²	—	2	8	no	—
533	C₂×C₄²	—	2	8	no	—
534	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
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	2	yes	—
540	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
541	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
542	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
546	#95	C₂³×C₁₃	1	4	yes	—
547	#95	C₂³×C₁₃	1	2	yes	—
548	#95	C₂³×C₁₃	1	2	yes	—
549	#95	C₂³×C₁₃	1	4	yes	—
550	#95	C₂³×C₁₃	1	2	yes	—
551	#95	C₂³×C₁₃	1	2	yes	—
552	#95	C₂³×C₁₃	1	4	yes	—
553	#95	C₂³×C₁₃	1	4	yes	—
554	#95	C₂³×C₁₃	1	4	yes	—
555	#95	C₂³×C₁₃	1	4	yes	—
556	#95	C₂³×C₁₃	1	4	yes	—
557	#95	C₂³×C₁₃	1	4	yes	—
558	C₂×C₁₃	—	4	2	no	—
559	C₂×C₁₃	—	4	4	no	—
560	C₂×C₁₃	—	4	4	no	—
561	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
562	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
563	C₂×C₁₃	#3449	1	1	yes	characteristic
564	C₂×C₁₃	#3475	1	2	yes	—
565	C₂×C₁₃	#3480	1	2	yes	—
566	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
567	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
568	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
569	#41	—	2	32	no	—
570	#41	—	2	32	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	8	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	C₁₃×#41	1	4	yes	complemented
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
610	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
611	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
612	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
613	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
614	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	8	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	8	no	—
639	C₄⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	8	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	8	no	—
649	C₂²⋊C₄	—	2	8	no	—
650	C₂²⋊C₄	—	4	4	no	—
651	C₂²⋊C₄	—	4	4	no	—
652	C₂²⋊C₄	—	4	4	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	8	no	—
660	C₄²	C₂×D₄×C₁₃	1	4	yes	—
661	C₄²	C₂×D₄×C₁₃	1	4	yes	—
662	C₄²	C₂×D₄×C₁₃	1	4	yes	—
663	C₄²	C₂×D₄×C₁₃	1	4	yes	—
664	C₁₃	#34909	1	1	yes	characteristic, direct product factor, Sylow
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	2	no	—
679	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
680	C₂³	C₂×C₁₃×#41	1	4	yes	—
681	C₂³	C₂×C₁₃×#41	1	4	yes	—
682	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
683	Q₈	—	2	8	no	—
684	Q₈	—	2	8	no	—
685	D₄	—	2	8	no	—
686	D₄	—	2	16	no	—
687	D₄	—	2	16	no	—
688	D₄	—	2	8	no	—
689	D₄	—	4	16	no	—
690	C₂×C₄	—	2	16	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	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	16	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	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	8	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
730	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
731	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
732	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
733	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
734	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	8	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	2	no	—
752	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
753	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
754	C₂²	C₂²×C₁₃×#41	1	2	yes	—
755	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
756	C₂²	C₁₃×#585	1	2	yes	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	4	no	—
769	C₄	C₁₃×#525	1	4	yes	—
770	C₄	C₁₃×#525	1	4	yes	—
771	C₂	—	4	2	no	—
772	C₂	—	4	4	no	—
773	C₂	—	4	4	no	—
774	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
775	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
776	C₂	C₁₃×#3449	1	1	yes	characteristic
777	C₂	C₁₃×#3475	1	2	yes	—
778	C₂	C₁₃×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
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. C₂×C₄×C₁₃×#41	C₂	semidirect
2. C₂×C₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#2600	C₂	semidirect
4. C₁₃×#2599	C₂	semidirect
5. C₁₃×#2598	C₂	semidirect
6. C₁₃×#2581	C₂	semidirect
7. C₁₃×#2580	C₂	semidirect
8. C₁₃×#2536	C₂	semidirect
9. C₁₃×#2535	C₂	semidirect
10. C₁₃×#2485	C₂	semidirect
11. C₁₃×#2407	C₂	semidirect
12. C₁₃×#2395	C₂	semidirect
13. C₁₃×#2388	C₂	semidirect
14. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₁₃×#121	C₂	semidirect
16. C₁₃×#2290	C₂	semidirect
17. C₁₃×#2283	C₂	semidirect
153. C₂×C₄²×C₁₃	D₄	semidirect
177. #34909	C₁₃	direct (N × H)
187. C₂×Q₈×C₁₃	#41	semidirect
201. C₂×D₄×C₁₃	#41	semidirect
224. C₂²×C₄×C₁₃	#41	semidirect
276. C₂×C₄×#41	C₂×C₁₃	semidirect
277. C₂×C₄×#41	C₂×C₁₃	semidirect
278. #2600	C₂×C₁₃	semidirect
279. #2599	C₂×C₁₃	semidirect
280. #2598	C₂×C₁₃	semidirect
281. #2581	C₂×C₁₃	semidirect
282. #2580	C₂×C₁₃	semidirect
283. #2536	C₂×C₁₃	semidirect
284. #2535	C₂×C₁₃	semidirect
285. #2485	C₂×C₁₃	semidirect
286. #2407	C₂×C₁₃	semidirect
287. #2395	C₂×C₁₃	semidirect
288. #2388	C₂×C₁₃	semidirect
289. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
290. C₄×#121	C₂×C₁₃	semidirect
291. #2290	C₂×C₁₃	semidirect
292. #2283	C₂×C₁₃	semidirect
534. C₂×C₄²	D₄×C₁₃	semidirect
575. C₂×Q₈	C₁₃×#41	semidirect
589. C₂×D₄	C₁₃×#41	semidirect
612. C₂²×C₄	C₁₃×#41	semidirect
664. C₁₃	#34909	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×#41	2
C₁₃×#2600	2
C₁₃×#2599	2
C₁₃×#2598	2
C₁₃×#2581	2
C₁₃×#2580	2
C₁₃×#2536	2
C₁₃×#2535	2
C₁₃×#2485	2
C₁₃×#2407	2
C₁₃×#2395	2
C₁₃×#2388	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2290	2
C₁₃×#2283	2
#34909	13

Subgroups — C13×#34909 #15721248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34909 #15721248