Subgroups — C₁₃×#34383 #15720722

Order 3328.

2190 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2376	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2370	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2367	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2354	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
9	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2334	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2324	C₂	1	2	yes	maximal
13	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2317	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2314	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#529	C₄	1	16	yes	complemented
19	C₂×C₁₃×#126	C₂²	1	2	yes	—
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#123	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#390	C₂²	1	2	yes	—
38	C₁₃×#390	C₂²	1	4	yes	—
39	C₁₃×#389	C₂²	1	4	yes	—
40	C₁₃×#389	C₂²	1	4	yes	—
41	C₁₃×#389	C₂²	1	2	yes	—
42	C₁₃×#389	C₂²	1	2	yes	—
43	C₁₃×#389	C₂²	1	4	yes	—
44	C₁₃×#388	C₂²	1	4	yes	—
45	C₁₃×#388	C₂²	1	4	yes	—
46	C₁₃×#388	C₂²	1	4	yes	—
47	C₁₃×#388	C₂²	1	4	yes	—
48	C₁₃×#388	C₂²	1	4	yes	—
49	C₁₃×#388	C₂²	1	4	yes	—
50	C₁₃×#387	C₂²	1	4	yes	—
51	C₁₃×#387	C₂²	1	4	yes	—
52	C₁₃×#387	C₂²	1	4	yes	—
53	C₁₃×#387	C₂²	1	4	yes	—
54	C₁₃×#386	C₂²	1	4	yes	—
55	C₁₃×#385	C₂²	1	4	yes	—
56	C₁₃×#385	C₂²	1	4	yes	—
57	C₁₃×#385	C₂²	1	4	yes	—
58	C₁₃×#384	C₂²	1	1	yes	characteristic
59	C₁₃×#384	C₂²	1	1	yes	characteristic
60	C₁₃×#384	C₂²	1	1	yes	characteristic
61	C₁₃×#384	C₂²	1	1	yes	characteristic
62	C₁₃×#384	C₂²	1	2	yes	—
63	C₁₃×#382	C₂²	1	2	yes	—
64	C₁₃×#382	C₂²	1	2	yes	—
65	C₁₃×#382	C₂²	1	2	yes	—
66	C₁₃×#380	C₂²	1	2	yes	—
67	C₁₃×#380	C₂²	1	1	yes	characteristic
68	C₁₃×#380	C₂²	1	1	yes	characteristic
69	C₁₃×#380	C₂²	1	2	yes	—
70	C₁₃×#380	C₂²	1	2	yes	—
71	C₁₃×#380	C₂²	1	2	yes	—
72	C₁₃×#380	C₂²	1	2	yes	—
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
78	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
80	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
81	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
82	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
83	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
84	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#126	C₂×C₄	1	16	yes	complemented
93	C₁₃×#125	C₂×C₄	1	8	yes	complemented
94	C₁₃×#124	C₂×C₄	1	8	yes	—
95	C₁₃×#123	C₂×C₄	1	16	yes	complemented
96	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
97	C₁₃×#121	C₂×C₄	1	8	yes	—
98	C₄×Q₈×C₁₃	—	4	4	no	—
99	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
100	C₄×D₄×C₁₃	—	4	4	no	—
101	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
102	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
103	C₁₃×#117	—	4	4	no	—
104	C₁₃×#117	—	4	4	no	—
105	C₁₃×#117	—	4	4	no	—
106	C₁₃×#117	C₂×C₄	1	16	yes	complemented
107	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
143	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
147	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
154	C₁₃×#95	C₂³	1	2	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	2	yes	—
157	C₁₃×#95	C₂³	1	2	yes	—
158	C₁₃×#95	C₂³	1	4	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	2	yes	—
161	C₁₃×#95	C₂³	1	4	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	4	yes	—
166	#34383	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
169	C₂×Q₈×C₁₃	—	2	2	no	—
170	C₂×Q₈×C₁₃	—	2	2	no	—
171	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
172	C₂×D₄×C₁₃	—	2	2	no	—
173	C₂×D₄×C₁₃	—	2	2	no	—
174	C₂×D₄×C₁₃	—	4	2	no	—
175	C₂×D₄×C₁₃	—	4	2	no	—
176	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
177	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	—	2	2	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	2	no	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	4	1	no	—
185	C₂²×C₄×C₁₃	—	4	1	no	—
186	C₂²×C₄×C₁₃	—	4	4	no	—
187	C₂²×C₄×C₁₃	—	4	4	no	—
188	C₂²×C₄×C₁₃	—	4	4	no	—
189	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
192	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₁₃×C₄⋊C₄	—	2	2	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	2	2	no	—
212	C₁₃×C₄⋊C₄	—	2	4	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	4	no	—
216	C₁₃×C₄⋊C₄	—	4	4	no	—
217	C₁₃×C₄⋊C₄	—	4	2	no	—
218	C₁₃×C₄⋊C₄	—	4	2	no	—
219	C₁₃×C₄⋊C₄	—	4	2	no	—
220	C₁₃×C₄⋊C₄	—	4	2	no	—
221	C₁₃×C₄⋊C₄	—	4	4	no	—
222	C₁₃×C₄⋊C₄	—	4	2	no	—
223	C₁₃×C₄⋊C₄	—	4	2	no	—
224	C₁₃×C₄⋊C₄	—	4	4	no	—
225	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
226	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
227	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
228	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
229	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
230	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
231	C₁₃×C₂²⋊C₄	—	4	4	no	—
232	C₁₃×C₂²⋊C₄	—	4	2	no	—
233	C₁₃×C₂²⋊C₄	—	4	2	no	—
234	C₁₃×C₂²⋊C₄	—	4	4	no	—
235	C₁₃×C₂²⋊C₄	—	4	4	no	—
236	C₁₃×C₂²⋊C₄	—	4	4	no	—
237	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
238	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
239	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
240	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
241	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
242	C₄²×C₁₃	—	2	4	no	—
243	C₄²×C₁₃	—	2	4	no	—
244	C₄²×C₁₃	—	4	4	no	—
245	C₄²×C₁₃	—	4	4	no	—
246	C₄²×C₁₃	—	4	4	no	—
247	C₄²×C₁₃	—	4	4	no	—
248	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
249	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
250	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
251	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
252	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
253	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
254	#2376	C₂×C₁₃	1	4	yes	complemented
255	#2370	C₂×C₁₃	1	2	yes	complemented
256	#2367	C₂×C₁₃	1	2	yes	complemented
257	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#2354	C₂×C₁₃	1	2	yes	complemented
260	#2352	C₂×C₁₃	1	2	yes	complemented
261	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
262	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2334	C₂×C₁₃	1	4	yes	complemented
264	#2324	C₂×C₁₃	1	2	yes	—
265	#2323	C₂×C₁₃	1	2	yes	complemented
266	#2317	C₂×C₁₃	1	2	yes	complemented
267	#2314	C₂×C₁₃	1	2	yes	complemented
268	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
270	C₂³×C₁₃	—	2	1	no	—
271	C₂³×C₁₃	—	2	1	no	—
272	C₂³×C₁₃	—	2	2	no	—
273	C₂³×C₁₃	—	2	2	no	—
274	C₂³×C₁₃	—	2	1	no	—
275	C₂³×C₁₃	—	2	2	no	—
276	C₂³×C₁₃	—	2	1	no	—
277	C₂³×C₁₃	—	2	2	no	—
278	C₂³×C₁₃	—	2	2	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	1	no	—
281	C₂³×C₁₃	—	2	1	no	—
282	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
283	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
284	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
285	Q₈×C₁₃	—	2	8	no	—
286	D₄×C₁₃	—	2	8	no	—
287	D₄×C₁₃	—	4	8	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	1	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	16	no	—
303	C₂×C₄×C₁₃	—	2	8	no	—
304	C₂×C₄×C₁₃	—	2	8	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	4	no	—
311	C₂×C₄×C₁₃	—	2	4	no	—
312	C₂×C₄×C₁₃	—	2	4	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	4	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	4	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	4	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	4	4	no	—
324	C₂×C₄×C₁₃	—	8	8	no	—
325	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
326	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
327	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
328	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
329	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
330	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
331	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
332	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
333	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
334	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
335	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
336	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
337	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
338	#529	C₄×C₁₃	1	16	yes	complemented
339	C₂×#126	C₂²×C₁₃	1	2	yes	—
340	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#123	C₂²×C₁₃	1	2	yes	—
343	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
346	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
348	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
350	C₂×#117	C₂²×C₁₃	1	2	yes	—
351	C₂×#117	C₂²×C₁₃	1	2	yes	—
352	C₂×#117	C₂²×C₁₃	1	2	yes	—
353	C₂×#117	C₂²×C₁₃	1	2	yes	—
354	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
355	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
356	#391	C₂²×C₁₃	1	2	yes	—
357	#390	C₂²×C₁₃	1	2	yes	—
358	#390	C₂²×C₁₃	1	4	yes	—
359	#389	C₂²×C₁₃	1	4	yes	—
360	#389	C₂²×C₁₃	1	4	yes	—
361	#389	C₂²×C₁₃	1	2	yes	—
362	#389	C₂²×C₁₃	1	2	yes	—
363	#389	C₂²×C₁₃	1	4	yes	—
364	#388	C₂²×C₁₃	1	4	yes	—
365	#388	C₂²×C₁₃	1	4	yes	—
366	#388	C₂²×C₁₃	1	4	yes	—
367	#388	C₂²×C₁₃	1	4	yes	—
368	#388	C₂²×C₁₃	1	4	yes	—
369	#388	C₂²×C₁₃	1	4	yes	—
370	#387	C₂²×C₁₃	1	4	yes	—
371	#387	C₂²×C₁₃	1	4	yes	—
372	#387	C₂²×C₁₃	1	4	yes	—
373	#387	C₂²×C₁₃	1	4	yes	—
374	#386	C₂²×C₁₃	1	4	yes	—
375	#385	C₂²×C₁₃	1	4	yes	—
376	#385	C₂²×C₁₃	1	4	yes	—
377	#385	C₂²×C₁₃	1	4	yes	—
378	#384	C₂²×C₁₃	1	1	yes	characteristic
379	#384	C₂²×C₁₃	1	1	yes	characteristic
380	#384	C₂²×C₁₃	1	2	yes	—
381	#384	C₂²×C₁₃	1	1	yes	characteristic
382	#384	C₂²×C₁₃	1	1	yes	characteristic
383	#382	C₂²×C₁₃	1	2	yes	—
384	#382	C₂²×C₁₃	1	2	yes	—
385	#382	C₂²×C₁₃	1	2	yes	—
386	#380	C₂²×C₁₃	1	2	yes	—
387	#380	C₂²×C₁₃	1	2	yes	—
388	#380	C₂²×C₁₃	1	2	yes	—
389	#380	C₂²×C₁₃	1	1	yes	characteristic
390	#380	C₂²×C₁₃	1	1	yes	characteristic
391	#380	C₂²×C₁₃	1	2	yes	—
392	#380	C₂²×C₁₃	1	2	yes	—
393	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
394	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
395	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
396	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
397	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
398	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
399	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
400	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
402	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
403	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
404	C₂²×C₁₃	—	2	2	no	—
405	C₂²×C₁₃	—	2	2	no	—
406	C₂²×C₁₃	—	2	4	no	—
407	C₂²×C₁₃	—	2	4	no	—
408	C₂²×C₁₃	—	2	2	no	—
409	C₂²×C₁₃	—	2	4	no	—
410	C₂²×C₁₃	—	4	2	no	—
411	C₂²×C₁₃	—	4	1	no	—
412	C₂²×C₁₃	—	4	1	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	—	4	1	no	—
415	C₂²×C₁₃	—	4	2	no	—
416	C₂²×C₁₃	—	4	1	no	—
417	C₂²×C₁₃	—	4	2	no	—
418	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
419	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
422	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂²×C₁₃	#585	1	1	yes	characteristic
424	C₂²×C₁₃	#585	1	1	yes	characteristic
425	C₄×C₁₃	—	2	2	no	—
426	C₄×C₁₃	—	2	4	no	—
427	C₄×C₁₃	—	2	2	no	—
428	C₄×C₁₃	—	2	4	no	—
429	C₄×C₁₃	—	2	2	no	—
430	C₄×C₁₃	—	2	2	no	—
431	C₄×C₁₃	—	2	4	no	—
432	C₄×C₁₃	—	4	2	no	—
433	C₄×C₁₃	—	4	4	no	—
434	C₄×C₁₃	—	4	2	no	—
435	C₄×C₁₃	—	4	2	no	—
436	C₄×C₁₃	—	4	2	no	—
437	C₄×C₁₃	—	4	4	no	—
438	C₄×C₁₃	#520	1	4	yes	—
439	C₄×C₁₃	#520	1	4	yes	—
440	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
443	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
444	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
447	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
448	#126	C₂×C₄×C₁₃	1	16	yes	complemented
449	#125	C₂×C₄×C₁₃	1	8	yes	complemented
450	#124	C₂×C₄×C₁₃	1	8	yes	—
451	#123	C₂×C₄×C₁₃	1	16	yes	complemented
452	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
453	#121	C₂×C₄×C₁₃	1	8	yes	—
454	C₄×Q₈	—	4	4	no	—
455	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
456	C₄×D₄	—	4	4	no	—
457	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
458	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
459	#117	—	4	4	no	—
460	#117	—	4	4	no	—
461	#117	—	4	4	no	—
462	#117	C₂×C₄×C₁₃	1	16	yes	complemented
463	C₂×C₄⋊C₄	—	4	4	no	—
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
499	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
501	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
502	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
503	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
504	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
505	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
507	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
510	#95	C₂³×C₁₃	1	2	yes	—
511	#95	C₂³×C₁₃	1	4	yes	—
512	#95	C₂³×C₁₃	1	2	yes	—
513	#95	C₂³×C₁₃	1	2	yes	—
514	#95	C₂³×C₁₃	1	4	yes	—
515	#95	C₂³×C₁₃	1	4	yes	—
516	#95	C₂³×C₁₃	1	2	yes	—
517	#95	C₂³×C₁₃	1	4	yes	—
518	#95	C₂³×C₁₃	1	4	yes	—
519	#95	C₂³×C₁₃	1	4	yes	—
520	#95	C₂³×C₁₃	1	4	yes	—
521	#95	C₂³×C₁₃	1	4	yes	—
522	C₂×C₁₃	—	4	2	no	—
523	C₂×C₁₃	—	4	4	no	—
524	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
525	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
526	C₂×C₁₃	#3428	1	1	yes	characteristic
527	C₂×C₁₃	#3546	1	1	yes	characteristic
528	C₂×C₁₃	#3547	1	1	yes	characteristic
529	C₂×C₁₃	#3554	1	1	yes	characteristic
530	C₂×C₁₃	#3555	1	1	yes	characteristic
531	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
532	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	4	2	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
541	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	4	1	no	—
549	C₂²×C₄	—	4	1	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	—	4	4	no	—
552	C₂²×C₄	—	4	4	no	—
553	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
554	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
555	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
556	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	4	4	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₄⋊C₄	—	4	2	no	—
583	C₄⋊C₄	—	4	4	no	—
584	C₄⋊C₄	—	4	2	no	—
585	C₄⋊C₄	—	4	2	no	—
586	C₄⋊C₄	—	4	2	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	4	no	—
589	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
590	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
591	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
592	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
593	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
594	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
595	C₂²⋊C₄	—	4	2	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	4	4	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
602	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
603	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
604	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
605	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	4	4	no	—
609	C₄²	—	4	4	no	—
610	C₄²	—	4	4	no	—
611	C₄²	—	4	4	no	—
612	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
613	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
614	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
615	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
616	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
617	C₁₃	#34383	1	1	yes	characteristic, direct product factor, Sylow
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
631	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
632	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
633	Q₈	—	2	8	no	—
634	D₄	—	2	8	no	—
635	D₄	—	4	8	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	16	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	8	8	no	—
673	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
674	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
675	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
676	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
677	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
678	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
679	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
680	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
681	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
682	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
683	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
684	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
685	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	2	no	—
700	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
701	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
704	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
705	C₂²	C₁₃×#585	1	1	yes	characteristic
706	C₂²	C₁₃×#585	1	1	yes	characteristic
707	C₄	—	2	2	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	4	no	—
711	C₄	—	2	2	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	4	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	4	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	4	no	—
720	C₄	C₁₃×#520	1	4	yes	—
721	C₄	C₁₃×#520	1	4	yes	—
722	C₂	—	4	2	no	—
723	C₂	—	4	4	no	—
724	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
725	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
726	C₂	C₁₃×#3428	1	1	yes	characteristic
727	C₂	C₁₃×#3546	1	1	yes	characteristic
728	C₂	C₁₃×#3547	1	1	yes	characteristic
729	C₂	C₁₃×#3554	1	1	yes	characteristic
730	C₂	C₁₃×#3555	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×#121	C₂²
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×#2376	C₂	semidirect
3. C₁₃×#2370	C₂	semidirect
4. C₁₃×#2367	C₂	semidirect
5. C₁₃×#2355	C₂	semidirect
6. C₁₃×#2354	C₂	semidirect
7. C₁₃×#2354	C₂	semidirect
8. C₁₃×#2352	C₂	semidirect
9. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
10. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
11. C₁₃×#2334	C₂	semidirect
13. C₁₃×#2323	C₂	semidirect
14. C₁₃×#2317	C₂	semidirect
15. C₁₃×#2314	C₂	semidirect
16. C₁₃×#2285	C₂	semidirect
17. C₁₃×#2285	C₂	semidirect
18. C₁₃×#529	C₄	semidirect
92. C₁₃×#126	C₂×C₄	semidirect
93. C₁₃×#125	C₂×C₄	semidirect
95. C₁₃×#123	C₂×C₄	semidirect
96. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₄×Q₈×C₁₃	C₂×C₄	semidirect
102. C₄×D₄×C₁₃	C₂×C₄	semidirect
106. C₁₃×#117	C₂×C₄	semidirect
142. C₂×C₄²×C₁₃	C₂×C₄	semidirect
166. #34383	C₁₃	direct (N × H)
254. #2376	C₂×C₁₃	semidirect
255. #2370	C₂×C₁₃	semidirect
256. #2367	C₂×C₁₃	semidirect
257. #2355	C₂×C₁₃	semidirect
258. #2354	C₂×C₁₃	semidirect
259. #2354	C₂×C₁₃	semidirect
260. #2352	C₂×C₁₃	semidirect
261. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
262. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
263. #2334	C₂×C₁₃	semidirect
265. #2323	C₂×C₁₃	semidirect
266. #2317	C₂×C₁₃	semidirect
267. #2314	C₂×C₁₃	semidirect
268. #2285	C₂×C₁₃	semidirect
269. #2285	C₂×C₁₃	semidirect
338. #529	C₄×C₁₃	semidirect
448. #126	C₂×C₄×C₁₃	semidirect
449. #125	C₂×C₄×C₁₃	semidirect
451. #123	C₂×C₄×C₁₃	semidirect
452. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
455. C₄×Q₈	C₂×C₄×C₁₃	semidirect
458. C₄×D₄	C₂×C₄×C₁₃	semidirect
462. #117	C₂×C₄×C₁₃	semidirect
498. C₂×C₄²	C₂×C₄×C₁₃	semidirect
617. C₁₃	#34383	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×#529	2
C₁₃×#2376	2
C₁₃×#2370	2
C₁₃×#2367	2
C₁₃×#2355	2
C₁₃×#2354	2
C₁₃×#2352	2
Q₈×C₁₃×C₄⋊C₄	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2334	2
C₁₃×#2324	2
C₁₃×#2323	2
C₁₃×#2317	2
C₁₃×#2314	2
C₁₃×#2285	2
#34383	13

Subgroups — C13×#34383 #15720722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34383 #15720722