Subgroups — C₁₃×#34332 #15720671

Order 3328.

2388 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2370	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2360	C₂	1	4	yes	maximal, complemented
6	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
8	D₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal
9	C₁₃×#2345	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2330	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2329	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#389	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2275	C₂	1	2	yes	maximal
17	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#554	C₄	1	16	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
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×C₄×D₄×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×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
35	C₁₃×#391	C₂²	1	1	yes	characteristic
36	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#391	C₂²	1	2	yes	—
38	C₁₃×#391	C₂²	1	4	yes	—
39	C₁₃×#389	C₂²	1	1	yes	characteristic
40	C₁₃×#389	C₂²	1	2	yes	—
41	C₁₃×#389	C₂²	1	4	yes	—
42	C₁₃×#389	C₂²	1	2	yes	—
43	C₁₃×#389	C₂²	1	2	yes	—
44	C₁₃×#389	C₂²	1	4	yes	—
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	2	yes	—
47	C₁₃×#389	C₂²	1	4	yes	—
48	C₁₃×#389	C₂²	1	2	yes	—
49	C₁₃×#389	C₂²	1	2	yes	—
50	C₁₃×#389	C₂²	1	4	yes	—
51	C₁₃×#387	C₂²	1	2	yes	—
52	C₁₃×#387	C₂²	1	2	yes	—
53	C₁₃×#387	C₂²	1	4	yes	—
54	C₁₃×#387	C₂²	1	4	yes	—
55	C₁₃×#387	C₂²	1	4	yes	—
56	C₁₃×#387	C₂²	1	4	yes	—
57	C₁₃×#385	C₂²	1	4	yes	—
58	C₁₃×#385	C₂²	1	4	yes	—
59	C₁₃×#385	C₂²	1	4	yes	—
60	C₁₃×#384	C₂²	1	1	yes	characteristic
61	C₁₃×#384	C₂²	1	2	yes	—
62	C₁₃×#380	C₂²	1	2	yes	—
63	C₁₃×#380	C₂²	1	4	yes	—
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
74	C₄×C₁₃×C₄⋊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	2	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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
92	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
93	C₁₃×#125	C₂×C₄	1	16	yes	complemented
94	C₁₃×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
95	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
96	C₄×Q₈×C₁₃	—	4	4	no	—
97	C₄×Q₈×C₁₃	—	4	4	no	—
98	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	—
102	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
103	C₄×D₄×C₁₃	Q₈	1	8	yes	complemented
104	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
105	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
106	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	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×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	—	4	4	no	—
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
143	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
149	C₁₃×#95	C₂³	1	2	yes	—
150	C₁₃×#95	C₂³	1	2	yes	—
151	C₁₃×#95	C₂³	1	2	yes	—
152	C₁₃×#95	C₂³	1	2	yes	—
153	C₁₃×#95	C₂³	1	2	yes	—
154	C₁₃×#95	C₂³	1	2	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	2	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	C₁₃×#95	C₂³	1	4	yes	—
162	C₁₃×#95	C₂³	1	2	yes	—
163	C₁₃×#95	C₂³	1	2	yes	—
164	C₁₃×#95	C₂³	1	2	yes	—
165	#34332	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
167	C₂×Q₈×C₁₃	—	2	2	no	—
168	C₂×Q₈×C₁₃	—	2	2	no	—
169	C₂×Q₈×C₁₃	—	4	2	no	—
170	C₂×Q₈×C₁₃	—	4	2	no	—
171	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
172	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
173	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
174	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
175	C₂×D₄×C₁₃	#41	1	4	yes	—
176	C₂²×C₄×C₁₃	—	2	4	no	—
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	—	2	8	no	—
180	C₂²×C₄×C₁₃	—	2	4	no	—
181	C₂²×C₄×C₁₃	—	4	2	no	—
182	C₂²×C₄×C₁₃	—	4	2	no	—
183	C₂²×C₄×C₁₃	—	4	4	no	—
184	C₂²×C₄×C₁₃	—	4	2	no	—
185	C₂²×C₄×C₁₃	—	4	4	no	—
186	C₂²×C₄×C₁₃	—	4	4	no	—
187	C₂²×C₄×C₁₃	—	4	4	no	—
188	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
189	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
190	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	2	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	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	2	no	—
211	C₁₃×C₄⋊C₄	—	2	8	no	—
212	C₁₃×C₄⋊C₄	—	2	4	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	4	4	no	—
215	C₁₃×C₄⋊C₄	—	4	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	4	no	—
220	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
221	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
222	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
223	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
224	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
225	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
226	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
227	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
228	C₁₃×C₂²⋊C₄	—	2	4	no	—
229	C₁₃×C₂²⋊C₄	—	2	8	no	—
230	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
231	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
232	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
233	C₄²×C₁₃	—	2	2	no	—
234	C₄²×C₁₃	—	2	4	no	—
235	C₄²×C₁₃	—	2	2	no	—
236	C₄²×C₁₃	—	2	4	no	—
237	C₄²×C₁₃	—	2	2	no	—
238	C₄²×C₁₃	—	2	2	no	—
239	C₄²×C₁₃	—	4	2	no	—
240	C₄²×C₁₃	—	4	2	no	—
241	C₄²×C₁₃	—	4	4	no	—
242	C₄²×C₁₃	—	4	1	no	—
243	C₄²×C₁₃	—	4	4	no	—
244	C₄²×C₁₃	—	4	4	no	—
245	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
246	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
247	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
248	C₂×#554	C₂×C₁₃	1	1	yes	characteristic
249	#2370	C₂×C₁₃	1	2	yes	complemented
250	#2369	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#2360	C₂×C₁₃	1	4	yes	complemented
252	#2360	C₂×C₁₃	1	2	yes	complemented
253	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
254	D₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	—
255	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
256	#2345	C₂×C₁₃	1	2	yes	complemented
257	#2330	C₂×C₁₃	1	2	yes	complemented
258	#2329	C₂×C₁₃	1	4	yes	complemented
259	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
261	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
262	C₂×#389	C₂×C₁₃	1	2	yes	complemented
263	#2275	C₂×C₁₃	1	2	yes	—
264	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
265	C₂³×C₁₃	—	2	2	no	—
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	2	2	no	—
269	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
270	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
271	C₂³×C₁₃	C₂×#41	1	4	yes	—
272	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
273	Q₈×C₁₃	—	2	8	no	—
274	Q₈×C₁₃	—	4	8	no	—
275	D₄×C₁₃	C₄×Q₈	1	16	yes	complemented
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	4	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	16	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	4	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	4	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	4	16	no	—
311	C₂×C₄×C₁₃	—	4	8	no	—
312	C₂×C₄×C₁₃	—	4	8	no	—
313	C₂×C₄×C₁₃	—	8	8	no	—
314	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
315	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
316	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
317	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
318	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
319	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
320	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
321	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
322	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
323	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
324	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
325	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
326	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
327	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
328	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
329	#554	C₄×C₁₃	1	16	yes	complemented
330	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#125	C₂²×C₁₃	1	2	yes	—
332	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
333	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
334	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
335	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
336	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
339	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
341	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
343	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
344	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
345	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
346	#391	C₂²×C₁₃	1	2	yes	—
347	#391	C₂²×C₁₃	1	4	yes	—
348	#391	C₂²×C₁₃	1	1	yes	characteristic
349	#391	C₂²×C₁₃	1	1	yes	characteristic
350	#389	C₂²×C₁₃	1	2	yes	—
351	#389	C₂²×C₁₃	1	2	yes	—
352	#389	C₂²×C₁₃	1	4	yes	—
353	#389	C₂²×C₁₃	1	4	yes	—
354	#389	C₂²×C₁₃	1	2	yes	—
355	#389	C₂²×C₁₃	1	2	yes	—
356	#389	C₂²×C₁₃	1	4	yes	—
357	#389	C₂²×C₁₃	1	1	yes	characteristic
358	#389	C₂²×C₁₃	1	2	yes	—
359	#389	C₂²×C₁₃	1	2	yes	—
360	#389	C₂²×C₁₃	1	4	yes	—
361	#389	C₂²×C₁₃	1	1	yes	characteristic
362	#387	C₂²×C₁₃	1	2	yes	—
363	#387	C₂²×C₁₃	1	4	yes	—
364	#387	C₂²×C₁₃	1	4	yes	—
365	#387	C₂²×C₁₃	1	4	yes	—
366	#387	C₂²×C₁₃	1	4	yes	—
367	#387	C₂²×C₁₃	1	2	yes	—
368	#385	C₂²×C₁₃	1	4	yes	—
369	#385	C₂²×C₁₃	1	4	yes	—
370	#385	C₂²×C₁₃	1	4	yes	—
371	#384	C₂²×C₁₃	1	1	yes	characteristic
372	#384	C₂²×C₁₃	1	2	yes	—
373	#380	C₂²×C₁₃	1	4	yes	—
374	#380	C₂²×C₁₃	1	2	yes	—
375	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
377	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
379	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
380	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
381	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
382	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
383	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
384	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
385	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
386	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
387	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
388	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
389	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
390	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
391	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
392	#376	C₂²×C₁₃	1	2	yes	—
393	C₂×#95	C₂²×C₁₃	1	4	yes	—
394	C₄³	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×C₁₃	—	2	4	no	—
396	C₂²×C₁₃	—	2	4	no	—
397	C₂²×C₁₃	—	2	4	no	—
398	C₂²×C₁₃	—	2	4	no	—
399	C₂²×C₁₃	—	2	4	no	—
400	C₂²×C₁₃	—	2	4	no	—
401	C₂²×C₁₃	C₂×C₄×Q₈	1	8	yes	—
402	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
403	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
404	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
405	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
406	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
408	C₂²×C₁₃	#585	1	1	yes	characteristic
409	C₄×C₁₃	—	2	4	no	—
410	C₄×C₁₃	—	2	4	no	—
411	C₄×C₁₃	—	2	4	no	—
412	C₄×C₁₃	—	2	8	no	—
413	C₄×C₁₃	—	2	2	no	—
414	C₄×C₁₃	—	2	2	no	—
415	C₄×C₁₃	—	2	4	no	—
416	C₄×C₁₃	—	2	2	no	—
417	C₄×C₁₃	—	2	2	no	—
418	C₄×C₁₃	—	4	1	no	—
419	C₄×C₁₃	—	4	2	no	—
420	C₄×C₁₃	—	4	2	no	—
421	C₄×C₁₃	—	4	4	no	—
422	C₄×C₁₃	—	4	2	no	—
423	C₄×C₁₃	C₂×C₄×Q₈	1	4	yes	—
424	C₄×C₁₃	#520	1	4	yes	—
425	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
427	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
429	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
430	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
431	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
432	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
433	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
434	#125	C₂×C₄×C₁₃	1	16	yes	complemented
435	C₂²⋊Q₈	C₂×C₄×C₁₃	1	32	yes	complemented
436	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
437	C₄×Q₈	—	4	4	no	—
438	C₄×Q₈	—	4	4	no	—
439	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
440	C₄×D₄	—	2	4	no	—
441	C₄×D₄	—	2	8	no	—
442	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	—
443	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
444	C₄×D₄	Q₈×C₁₃	1	8	yes	complemented
445	C₂×C₄⋊C₄	—	4	4	no	—
446	C₂×C₄⋊C₄	—	4	8	no	—
447	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
474	C₂×C₄²	—	4	4	no	—
475	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
477	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
479	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
482	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
483	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
485	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
486	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
487	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
488	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
490	#95	C₂³×C₁₃	1	2	yes	—
491	#95	C₂³×C₁₃	1	4	yes	—
492	#95	C₂³×C₁₃	1	4	yes	—
493	#95	C₂³×C₁₃	1	4	yes	—
494	#95	C₂³×C₁₃	1	2	yes	—
495	#95	C₂³×C₁₃	1	2	yes	—
496	#95	C₂³×C₁₃	1	2	yes	—
497	#95	C₂³×C₁₃	1	2	yes	—
498	#95	C₂³×C₁₃	1	2	yes	—
499	#95	C₂³×C₁₃	1	2	yes	—
500	#95	C₂³×C₁₃	1	2	yes	—
501	#95	C₂³×C₁₃	1	4	yes	—
502	#95	C₂³×C₁₃	1	4	yes	—
503	#95	C₂³×C₁₃	1	4	yes	—
504	#95	C₂³×C₁₃	1	2	yes	—
505	#95	C₂³×C₁₃	1	2	yes	—
506	C₂×C₁₃	—	2	8	no	—
507	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
508	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
509	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂×C₁₃	#3501	1	1	yes	characteristic
511	C₂×C₁₃	#3503	1	1	yes	characteristic
512	C₂×C₁₃	#3515	1	1	yes	characteristic
513	C₂×C₁₃	#3519	1	1	yes	characteristic
514	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	4	2	no	—
518	C₂×Q₈	—	4	2	no	—
519	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
520	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
521	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
522	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
523	C₂×D₄	C₁₃×#41	1	4	yes	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	8	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	—	4	4	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
537	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
538	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
539	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	8	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	4	4	no	—
563	C₄⋊C₄	—	4	4	no	—
564	C₄⋊C₄	—	4	4	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	—	4	4	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
569	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
570	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
571	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
573	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
574	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
575	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
580	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
581	C₄²	—	2	2	no	—
582	C₄²	—	2	4	no	—
583	C₄²	—	2	2	no	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	2	no	—
586	C₄²	—	2	2	no	—
587	C₄²	—	4	2	no	—
588	C₄²	—	4	2	no	—
589	C₄²	—	4	4	no	—
590	C₄²	—	4	4	no	—
591	C₄²	—	4	4	no	—
592	C₄²	—	4	1	no	—
593	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
594	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
595	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
596	C₁₃	#34332	1	1	yes	characteristic, direct product factor, Sylow
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
602	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
603	C₂³	C₂×C₁₃×#41	1	4	yes	—
604	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
605	Q₈	—	2	8	no	—
606	Q₈	—	4	8	no	—
607	D₄	C₄×Q₈×C₁₃	1	16	yes	complemented
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	16	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	4	16	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	8	8	no	—
646	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
647	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
648	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
649	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
650	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
651	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
652	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
653	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
654	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
655	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
656	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
657	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
658	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
659	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
660	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
661	C₂²	—	2	4	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	4	no	—
667	C₂²	C₂×C₄×Q₈×C₁₃	1	8	yes	—
668	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
669	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
670	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
671	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
674	C₂²	C₁₃×#585	1	1	yes	characteristic
675	C₄	—	2	2	no	—
676	C₄	—	2	4	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	4	no	—
679	C₄	—	2	8	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	2	no	—
689	C₄	C₂×C₄×Q₈×C₁₃	1	4	yes	—
690	C₄	C₁₃×#520	1	4	yes	—
691	C₂	—	2	8	no	—
692	C₂	C₂²×C₄×Q₈×C₁₃	1	1	yes	characteristic
693	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
694	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
695	C₂	C₁₃×#3501	1	1	yes	characteristic
696	C₂	C₁₃×#3503	1	1	yes	characteristic
697	C₂	C₁₃×#3515	1	1	yes	characteristic
698	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	C₂²×D₄×C₁₃	C₂³
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×#2370	C₂	semidirect
3. C₁₃×#2369	C₂	semidirect
4. C₁₃×#2360	C₂	semidirect
5. C₁₃×#2360	C₂	semidirect
6. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
9. C₁₃×#2345	C₂	semidirect
10. C₁₃×#2330	C₂	semidirect
11. C₁₃×#2329	C₂	semidirect
12. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
13. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₁₃×#2295	C₂	semidirect
15. C₂×C₁₃×#389	C₂	semidirect
18. C₁₃×#554	C₄	semidirect
92. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
93. C₁₃×#125	C₂×C₄	semidirect
94. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
95. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
98. C₄×Q₈×C₁₃	C₂×C₄	semidirect
103. C₄×D₄×C₁₃	Q₈	semidirect
106. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
165. #34332	C₁₃	direct (N × H)
249. #2370	C₂×C₁₃	semidirect
250. #2369	C₂×C₁₃	semidirect
251. #2360	C₂×C₁₃	semidirect
252. #2360	C₂×C₁₃	semidirect
253. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
256. #2345	C₂×C₁₃	semidirect
257. #2330	C₂×C₁₃	semidirect
258. #2329	C₂×C₁₃	semidirect
259. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
260. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
261. #2295	C₂×C₁₃	semidirect
262. C₂×#389	C₂×C₁₃	semidirect
275. D₄×C₁₃	C₄×Q₈	semidirect
329. #554	C₄×C₁₃	semidirect
433. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
434. #125	C₂×C₄×C₁₃	semidirect
435. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
436. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
439. C₄×Q₈	C₂×C₄×C₁₃	semidirect
444. C₄×D₄	Q₈×C₁₃	semidirect
447. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
596. C₁₃	#34332	direct (N × H)
607. D₄	C₄×Q₈×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#554	2
C₁₃×#2370	2
C₁₃×#2369	2
C₁₃×#2360	2
Q₈×C₁₃×C₄⋊C₄	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2345	2
C₁₃×#2330	2
C₁₃×#2329	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2295	2
C₂×C₁₃×#389	2
C₁₃×#2275	2
C₄²×D₄×C₁₃	2
#34332	13

Subgroups — C13×#34332 #15720671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34332 #15720671