Subgroups — C₁₃×#34330 #15720669

Order 3328.

2772 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	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2366	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2364	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2363	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2357	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2339	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2333	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2328	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₁₃×#550	C₄	1	16	yes	complemented
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	2	yes	—
22	C₂×C₁₃×#121	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
37	C₁₃×#391	C₂²	1	1	yes	characteristic
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#390	C₂²	1	2	yes	—
41	C₁₃×#390	C₂²	1	2	yes	—
42	C₁₃×#390	C₂²	1	2	yes	—
43	C₁₃×#390	C₂²	1	2	yes	—
44	C₁₃×#390	C₂²	1	2	yes	—
45	C₁₃×#390	C₂²	1	2	yes	—
46	C₁₃×#390	C₂²	1	4	yes	—
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#388	C₂²	1	4	yes	—
50	C₁₃×#388	C₂²	1	4	yes	—
51	C₁₃×#388	C₂²	1	4	yes	—
52	C₁₃×#387	C₂²	1	2	yes	—
53	C₁₃×#387	C₂²	1	2	yes	—
54	C₁₃×#387	C₂²	1	4	yes	—
55	C₁₃×#386	C₂²	1	4	yes	—
56	C₁₃×#386	C₂²	1	4	yes	—
57	C₁₃×#386	C₂²	1	4	yes	—
58	C₁₃×#386	C₂²	1	4	yes	—
59	C₁₃×#386	C₂²	1	4	yes	—
60	C₁₃×#386	C₂²	1	4	yes	—
61	C₁₃×#386	C₂²	1	4	yes	—
62	C₁₃×#384	C₂²	1	1	yes	characteristic
63	C₁₃×#382	C₂²	1	2	yes	—
64	C₁₃×#381	C₂²	1	4	yes	—
65	C₁₃×#380	C₂²	1	2	yes	—
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₁₃×#376	C₂²	1	2	yes	—
82	C₂×C₁₃×#95	C₂²	1	4	yes	—
83	C₄³×C₁₃	C₂²	1	1	yes	characteristic
84	C₂×C₁₃×#41	—	4	4	no	—
85	C₂×C₁₃×#41	—	4	4	no	—
86	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
100	C₁₃×#127	C₂×C₄	1	8	yes	complemented
101	C₁₃×#127	C₂×C₄	1	16	yes	complemented
102	C₁₃×#121	C₂×C₄	1	16	yes	complemented
103	C₁₃×#121	C₂×C₄	1	32	yes	complemented
104	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
105	C₄×D₄×C₁₃	—	2	4	no	—
106	C₄×D₄×C₁₃	—	2	8	no	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	—	2	8	no	—
109	C₄×D₄×C₁₃	—	4	4	no	—
110	C₄×D₄×C₁₃	—	4	4	no	—
111	C₄×D₄×C₁₃	—	4	4	no	—
112	C₄×D₄×C₁₃	—	4	8	no	—
113	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
114	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
115	C₁₃×#117	—	4	4	no	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	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	1	yes	characteristic
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃	—	4	4	no	—
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
155	C₁₃×#95	C₂³	1	2	yes	—
156	C₁₃×#95	C₂³	1	2	yes	—
157	C₁₃×#95	C₂³	1	2	yes	—
158	C₁₃×#95	C₂³	1	2	yes	—
159	C₁₃×#95	C₂³	1	2	yes	—
160	C₁₃×#95	C₂³	1	2	yes	—
161	C₁₃×#95	C₂³	1	2	yes	—
162	C₁₃×#95	C₂³	1	4	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	C₁₃×#95	C₂³	1	4	yes	—
165	C₁₃×#95	C₂³	1	2	yes	—
166	C₁₃×#95	C₂³	1	4	yes	—
167	C₁₃×#95	C₂³	1	2	yes	—
168	C₁₃×#95	C₂³	1	2	yes	—
169	#34330	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
171	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
172	C₁₃×#41	—	4	32	no	—
173	C₂×Q₈×C₁₃	—	2	2	no	—
174	C₂×Q₈×C₁₃	—	2	2	no	—
175	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
176	C₂×D₄×C₁₃	—	2	2	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	2	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	4	2	no	—
183	C₂×D₄×C₁₃	—	4	4	no	—
184	C₂×D₄×C₁₃	—	4	2	no	—
185	C₂×D₄×C₁₃	—	4	4	no	—
186	C₂×D₄×C₁₃	—	4	4	no	—
187	C₂×D₄×C₁₃	—	4	4	no	—
188	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
189	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
190	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
191	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
192	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
193	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	8	no	—
200	C₂²×C₄×C₁₃	—	2	8	no	—
201	C₂²×C₄×C₁₃	—	4	2	no	—
202	C₂²×C₄×C₁₃	—	4	2	no	—
203	C₂²×C₄×C₁₃	—	4	2	no	—
204	C₂²×C₄×C₁₃	—	4	4	no	—
205	C₂²×C₄×C₁₃	—	4	4	no	—
206	C₂²×C₄×C₁₃	—	4	4	no	—
207	C₂²×C₄×C₁₃	—	4	4	no	—
208	C₂²×C₄×C₁₃	—	4	4	no	—
209	C₂²×C₄×C₁₃	—	4	4	no	—
210	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
211	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₁₃×C₄⋊C₄	—	4	2	no	—
234	C₁₃×C₄⋊C₄	—	4	2	no	—
235	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
236	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
237	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
238	C₁₃×C₄⋊C₄	#41	1	4	yes	complemented
239	C₁₃×C₂²⋊C₄	—	2	4	no	—
240	C₁₃×C₂²⋊C₄	—	2	8	no	—
241	C₁₃×C₂²⋊C₄	—	2	8	no	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	8	no	—
244	C₁₃×C₂²⋊C₄	—	4	4	no	—
245	C₁₃×C₂²⋊C₄	—	4	4	no	—
246	C₁₃×C₂²⋊C₄	—	4	4	no	—
247	C₁₃×C₂²⋊C₄	—	4	4	no	—
248	C₁₃×C₂²⋊C₄	—	4	4	no	—
249	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
250	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
251	C₄²×C₁₃	—	2	2	no	—
252	C₄²×C₁₃	—	2	4	no	—
253	C₄²×C₁₃	—	2	2	no	—
254	C₄²×C₁₃	—	2	4	no	—
255	C₄²×C₁₃	—	2	2	no	—
256	C₄²×C₁₃	—	2	2	no	—
257	C₄²×C₁₃	—	4	2	no	—
258	C₄²×C₁₃	—	4	2	no	—
259	C₄²×C₁₃	—	4	1	no	—
260	C₄²×C₁₃	—	4	4	no	—
261	C₄²×C₁₃	—	4	4	no	—
262	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
263	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
264	C₄²×C₁₃	#41	1	4	yes	complemented
265	C₂×#550	C₂×C₁₃	1	1	yes	characteristic
266	#2366	C₂×C₁₃	1	2	yes	complemented
267	#2366	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#2364	C₂×C₁₃	1	4	yes	complemented
269	#2363	C₂×C₁₃	1	2	yes	complemented
270	#2357	C₂×C₁₃	1	2	yes	complemented
271	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2339	C₂×C₁₃	1	2	yes	complemented
274	#2333	C₂×C₁₃	1	4	yes	complemented
275	#2328	C₂×C₁₃	1	2	yes	complemented
276	C₄×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₄×#121	C₂×C₁₃	1	2	yes	complemented
278	#2297	C₂×C₁₃	1	2	yes	complemented
279	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2275	C₂×C₁₃	1	2	yes	complemented
281	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂³×C₁₃	—	2	2	no	—
283	C₂³×C₁₃	—	2	4	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	4	no	—
286	C₂³×C₁₃	—	2	4	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	4	no	—
290	C₂³×C₁₃	—	2	4	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	4	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
295	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
296	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
297	Q₈×C₁₃	—	2	8	no	—
298	D₄×C₁₃	—	2	8	no	—
299	D₄×C₁₃	—	2	16	no	—
300	D₄×C₁₃	—	2	16	no	—
301	D₄×C₁₃	—	4	8	no	—
302	D₄×C₁₃	—	4	16	no	—
303	D₄×C₁₃	—	4	16	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	1	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	16	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	4	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	4	no	—
330	C₂×C₄×C₁₃	—	2	4	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	4	16	no	—
337	C₂×C₄×C₁₃	—	4	8	no	—
338	C₂×C₄×C₁₃	—	4	8	no	—
339	C₂×C₄×C₁₃	—	8	8	no	—
340	C₂×C₄×C₁₃	—	8	8	no	—
341	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
342	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
343	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
344	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
345	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
346	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
347	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
348	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
349	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
350	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
351	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
352	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
353	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
354	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
355	C₂²×#41	C₂²×C₁₃	1	2	yes	—
356	#550	C₄×C₁₃	1	16	yes	complemented
357	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#127	C₂²×C₁₃	1	2	yes	—
359	C₂×#121	C₂²×C₁₃	1	4	yes	—
360	C₂×#121	C₂²×C₁₃	1	2	yes	—
361	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
363	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
366	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
367	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
368	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
369	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
370	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
372	C₂×#117	C₂²×C₁₃	1	2	yes	—
373	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
374	#391	C₂²×C₁₃	1	1	yes	characteristic
375	#391	C₂²×C₁₃	1	2	yes	—
376	#391	C₂²×C₁₃	1	1	yes	characteristic
377	#390	C₂²×C₁₃	1	2	yes	—
378	#390	C₂²×C₁₃	1	2	yes	—
379	#390	C₂²×C₁₃	1	2	yes	—
380	#390	C₂²×C₁₃	1	2	yes	—
381	#390	C₂²×C₁₃	1	2	yes	—
382	#390	C₂²×C₁₃	1	4	yes	—
383	#390	C₂²×C₁₃	1	2	yes	—
384	#389	C₂²×C₁₃	1	1	yes	characteristic
385	#389	C₂²×C₁₃	1	1	yes	characteristic
386	#388	C₂²×C₁₃	1	4	yes	—
387	#388	C₂²×C₁₃	1	4	yes	—
388	#388	C₂²×C₁₃	1	4	yes	—
389	#387	C₂²×C₁₃	1	2	yes	—
390	#387	C₂²×C₁₃	1	4	yes	—
391	#387	C₂²×C₁₃	1	2	yes	—
392	#386	C₂²×C₁₃	1	4	yes	—
393	#386	C₂²×C₁₃	1	4	yes	—
394	#386	C₂²×C₁₃	1	4	yes	—
395	#386	C₂²×C₁₃	1	4	yes	—
396	#386	C₂²×C₁₃	1	4	yes	—
397	#386	C₂²×C₁₃	1	4	yes	—
398	#386	C₂²×C₁₃	1	4	yes	—
399	#384	C₂²×C₁₃	1	1	yes	characteristic
400	#382	C₂²×C₁₃	1	2	yes	—
401	#381	C₂²×C₁₃	1	4	yes	—
402	#380	C₂²×C₁₃	1	2	yes	—
403	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
404	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
407	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
411	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
415	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
416	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
417	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
418	#376	C₂²×C₁₃	1	2	yes	—
419	C₂×#95	C₂²×C₁₃	1	4	yes	—
420	C₄³	C₂²×C₁₃	1	1	yes	characteristic
421	C₂²×C₁₃	—	2	4	no	—
422	C₂²×C₁₃	—	2	8	no	—
423	C₂²×C₁₃	—	2	4	no	—
424	C₂²×C₁₃	—	2	8	no	—
425	C₂²×C₁₃	—	2	8	no	—
426	C₂²×C₁₃	—	2	4	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	4	no	—
429	C₂²×C₁₃	—	4	4	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	4	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	4	no	—
435	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
436	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂²×C₁₃	#585	1	1	yes	characteristic
442	C₄×C₁₃	—	2	4	no	—
443	C₄×C₁₃	—	2	4	no	—
444	C₄×C₁₃	—	2	2	no	—
445	C₄×C₁₃	—	2	4	no	—
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	2	4	no	—
450	C₄×C₁₃	—	4	2	no	—
451	C₄×C₁₃	—	4	4	no	—
452	C₄×C₁₃	—	4	1	no	—
453	C₄×C₁₃	—	4	2	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	C₄×#41	1	4	yes	—
456	C₄×C₁₃	#518	1	4	yes	—
457	C₂×#41	—	4	4	no	—
458	C₂×#41	—	4	4	no	—
459	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
460	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
462	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
464	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
465	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
466	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
467	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
468	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
469	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
470	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
471	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
472	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
473	#127	C₂×C₄×C₁₃	1	8	yes	complemented
474	#127	C₂×C₄×C₁₃	1	16	yes	complemented
475	#121	C₂×C₄×C₁₃	1	16	yes	complemented
476	#121	C₂×C₄×C₁₃	1	32	yes	complemented
477	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	8	no	—
480	C₄×D₄	—	2	4	no	—
481	C₄×D₄	—	2	8	no	—
482	C₄×D₄	—	4	4	no	—
483	C₄×D₄	—	4	4	no	—
484	C₄×D₄	—	4	4	no	—
485	C₄×D₄	—	4	8	no	—
486	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
487	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
488	#117	—	4	4	no	—
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
513	C₂×C₄²	—	4	4	no	—
514	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
519	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
521	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
522	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
528	#95	C₂³×C₁₃	1	2	yes	—
529	#95	C₂³×C₁₃	1	2	yes	—
530	#95	C₂³×C₁₃	1	4	yes	—
531	#95	C₂³×C₁₃	1	4	yes	—
532	#95	C₂³×C₁₃	1	2	yes	—
533	#95	C₂³×C₁₃	1	2	yes	—
534	#95	C₂³×C₁₃	1	2	yes	—
535	#95	C₂³×C₁₃	1	2	yes	—
536	#95	C₂³×C₁₃	1	2	yes	—
537	#95	C₂³×C₁₃	1	2	yes	—
538	#95	C₂³×C₁₃	1	4	yes	—
539	#95	C₂³×C₁₃	1	2	yes	—
540	#95	C₂³×C₁₃	1	4	yes	—
541	#95	C₂³×C₁₃	1	2	yes	—
542	C₂×C₁₃	—	4	4	no	—
543	C₂×C₁₃	—	4	8	no	—
544	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
545	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
546	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂×C₁₃	#3506	1	1	yes	characteristic
548	C₂×C₁₃	#3508	1	1	yes	characteristic
549	C₂×C₁₃	#3517	1	1	yes	characteristic
550	C₂×C₁₃	#3519	1	1	yes	characteristic
551	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
552	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
553	#41	—	4	32	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	4	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
570	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
571	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
572	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
573	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
574	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	8	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
592	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
593	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
617	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
618	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
619	C₄⋊C₄	C₁₃×#41	1	4	yes	complemented
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	8	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
631	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	4	2	no	—
639	C₄²	—	4	2	no	—
640	C₄²	—	4	4	no	—
641	C₄²	—	4	4	no	—
642	C₄²	—	4	1	no	—
643	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
644	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
645	C₄²	C₁₃×#41	1	4	yes	complemented
646	C₁₃	#34330	1	1	yes	characteristic, direct product factor, Sylow
647	C₂³	—	2	2	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	2	2	no	—
659	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
660	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
661	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
662	Q₈	—	2	8	no	—
663	D₄	—	2	8	no	—
664	D₄	—	2	16	no	—
665	D₄	—	2	16	no	—
666	D₄	—	4	8	no	—
667	D₄	—	4	16	no	—
668	D₄	—	4	16	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	16	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	4	16	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	—	8	8	no	—
705	C₂×C₄	—	8	8	no	—
706	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
707	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
708	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
709	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
710	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
711	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
712	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
713	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
714	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
715	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
716	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
717	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
718	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
719	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	8	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	8	no	—
724	C₂²	—	2	8	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	4	no	—
734	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
735	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
736	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
737	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
738	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
739	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂²	C₁₃×#585	1	1	yes	characteristic
741	C₄	—	2	2	no	—
742	C₄	—	2	4	no	—
743	C₄	—	2	4	no	—
744	C₄	—	2	4	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	C₄×C₁₃×#41	1	4	yes	—
755	C₄	C₁₃×#518	1	4	yes	—
756	C₂	—	4	4	no	—
757	C₂	—	4	8	no	—
758	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
759	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
760	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂	C₁₃×#3506	1	1	yes	characteristic
762	C₂	C₁₃×#3508	1	1	yes	characteristic
763	C₂	C₁₃×#3517	1	1	yes	characteristic
764	C₂	C₁₃×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#550	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2366	C₂	semidirect
3. C₁₃×#2366	C₂	semidirect
4. C₁₃×#2364	C₂	semidirect
5. C₁₃×#2363	C₂	semidirect
6. C₁₃×#2357	C₂	semidirect
7. C₁₃×#2355	C₂	semidirect
8. C₁₃×#2354	C₂	semidirect
9. C₁₃×#2339	C₂	semidirect
10. C₁₃×#2333	C₂	semidirect
11. C₁₃×#2328	C₂	semidirect
12. C₄×C₁₃×#127	C₂	semidirect
13. C₄×C₁₃×#121	C₂	semidirect
14. C₁₃×#2297	C₂	semidirect
15. C₁₃×#2295	C₂	semidirect
16. C₁₃×#2275	C₂	semidirect
17. C₄²×D₄×C₁₃	C₂	semidirect
19. C₁₃×#550	C₄	semidirect
86. C₂×C₁₃×#41	C₂×C₄	semidirect
100. C₁₃×#127	C₂×C₄	semidirect
101. C₁₃×#127	C₂×C₄	semidirect
102. C₁₃×#121	C₂×C₄	semidirect
103. C₁₃×#121	C₂×C₄	semidirect
104. C₄×Q₈×C₁₃	C₂×C₄	semidirect
113. C₄×D₄×C₁₃	C₂×C₄	semidirect
114. C₄×D₄×C₁₃	C₂×C₄	semidirect
169. #34330	C₁₃	direct (N × H)
238. C₁₃×C₄⋊C₄	#41	semidirect
264. C₄²×C₁₃	#41	semidirect
266. #2366	C₂×C₁₃	semidirect
267. #2366	C₂×C₁₃	semidirect
268. #2364	C₂×C₁₃	semidirect
269. #2363	C₂×C₁₃	semidirect
270. #2357	C₂×C₁₃	semidirect
271. #2355	C₂×C₁₃	semidirect
272. #2354	C₂×C₁₃	semidirect
273. #2339	C₂×C₁₃	semidirect
274. #2333	C₂×C₁₃	semidirect
275. #2328	C₂×C₁₃	semidirect
276. C₄×#127	C₂×C₁₃	semidirect
277. C₄×#121	C₂×C₁₃	semidirect
278. #2297	C₂×C₁₃	semidirect
279. #2295	C₂×C₁₃	semidirect
280. #2275	C₂×C₁₃	semidirect
281. C₄²×D₄	C₂×C₁₃	semidirect
356. #550	C₄×C₁₃	semidirect
459. C₂×#41	C₂×C₄×C₁₃	semidirect
473. #127	C₂×C₄×C₁₃	semidirect
474. #127	C₂×C₄×C₁₃	semidirect
475. #121	C₂×C₄×C₁₃	semidirect
476. #121	C₂×C₄×C₁₃	semidirect
477. C₄×Q₈	C₂×C₄×C₁₃	semidirect
486. C₄×D₄	C₂×C₄×C₁₃	semidirect
487. C₄×D₄	C₂×C₄×C₁₃	semidirect
619. C₄⋊C₄	C₁₃×#41	semidirect
645. C₄²	C₁₃×#41	semidirect
646. C₁₃	#34330	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×C₁₃×#550	2
C₁₃×#2366	2
C₁₃×#2364	2
C₁₃×#2363	2
C₁₃×#2357	2
C₁₃×#2355	2
C₁₃×#2354	2
C₁₃×#2339	2
C₁₃×#2333	2
C₁₃×#2328	2
C₄×C₁₃×#127	2
C₄×C₁₃×#121	2
C₁₃×#2297	2
C₁₃×#2295	2
C₁₃×#2275	2
C₄²×D₄×C₁₃	2
#34330	13

Subgroups — C13×#34330 #15720669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34330 #15720669