Subgroups — C₁₃×#24787 #15711126

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2416	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#121	—	2	1	no	—
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₁₃×#468	—	2	4	no	—
28	C₁₃×#465	—	2	4	no	—
29	C₁₃×#435	—	2	4	no	—
30	C₂×C₁₃×#107	—	2	4	no	—
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
46	C₁₃×#398	—	2	1	no	—
47	C₁₃×#396	—	2	1	no	—
48	C₁₃×#396	—	2	1	no	—
49	C₁₃×#394	—	2	1	no	—
50	C₁₃×#391	C₂²	1	1	yes	characteristic
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#386	—	2	1	no	—
55	C₁₃×#386	—	2	1	no	—
56	C₁₃×#380	—	2	1	no	—
57	C₁₃×#380	C₂²	1	1	yes	characteristic
58	C₁₃×#380	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#340	C₂²	1	1	yes	characteristic
62	C₁₃×#340	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	—	2	1	no	—
66	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×SD₁₆	—	2	2	no	—
73	C₂×C₁₃×SD₁₆	—	2	2	no	—
74	C₂×C₁₃×SD₁₆	—	2	2	no	—
75	C₂×C₁₃×M₁₆	—	2	2	no	—
76	C₂×C₁₃×M₁₆	—	2	2	no	—
77	C₂×C₁₃×M₁₆	—	2	2	no	—
78	C₂²×C₈×C₁₃	—	2	2	no	—
79	C₂²×C₈×C₁₃	—	2	2	no	—
80	C₂²×C₈×C₁₃	D₄	1	4	yes	complemented
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	—	4	1	no	—
89	C₁₃×#121	—	2	2	no	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	—	4	1	no	—
93	C₁₃×#121	—	4	4	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
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	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
122	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#107	—	2	2	no	—
125	C₁₃×#107	—	2	2	no	—
126	C₁₃×#107	—	2	2	no	—
127	C₁₃×#107	D₄	1	4	yes	complemented
128	C₁₃×#106	—	2	2	no	—
129	C₁₃×C₄⋊C₈	—	2	2	no	—
130	C₁₃×#103	—	2	2	no	—
131	C₁₃×#103	—	2	2	no	—
132	C₁₃×#103	—	4	1	no	—
133	C₁₃×#102	—	2	2	no	—
134	C₁₃×#102	—	2	2	no	—
135	C₁₃×#102	—	4	1	no	—
136	C₁₃×C₂²⋊C₈	—	2	2	no	—
137	C₁₃×C₂²⋊C₈	—	2	2	no	—
138	C₁₃×#97	—	2	2	no	—
139	C₁₃×#95	—	2	1	no	—
140	C₁₃×#95	—	2	1	no	—
141	C₁₃×#95	—	2	1	no	—
142	C₁₃×#95	—	2	1	no	—
143	C₁₃×#95	—	2	1	no	—
144	C₁₃×#95	—	2	1	no	—
145	#24787	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂⁴×C₁₃	—	2	1	no	—
147	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	4	2	no	—
165	C₂×D₄×C₁₃	—	4	2	no	—
166	C₂×D₄×C₁₃	—	4	2	no	—
167	C₂×D₄×C₁₃	—	4	2	no	—
168	C₂×D₄×C₁₃	—	4	2	no	—
169	C₂×D₄×C₁₃	—	8	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	4	2	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	—	4	2	no	—
190	C₂²×C₄×C₁₃	—	4	2	no	—
191	C₂²×C₄×C₁₃	—	8	1	no	—
192	C₂²×C₄×C₁₃	—	8	1	no	—
193	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₃	#41	1	2	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₁₃×SD₁₆	—	4	4	no	—
201	C₁₃×M₁₆	—	4	4	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	8	no	—
205	C₂×C₈×C₁₃	—	2	1	no	—
206	C₂×C₈×C₁₃	—	2	1	no	—
207	C₂×C₈×C₁₃	—	2	1	no	—
208	C₂×C₈×C₁₃	—	2	1	no	—
209	C₂×C₈×C₁₃	—	2	1	no	—
210	C₂×C₈×C₁₃	—	2	1	no	—
211	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
212	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
213	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
214	C₂×C₈×C₁₃	#41	1	2	yes	—
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	1	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	1	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	1	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	4	2	no	—
227	C₁₃×C₄⋊C₄	—	4	2	no	—
228	C₁₃×C₄⋊C₄	—	4	2	no	—
229	C₁₃×C₄⋊C₄	—	4	2	no	—
230	C₁₃×C₄⋊C₄	—	4	2	no	—
231	C₁₃×C₄⋊C₄	—	8	1	no	—
232	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
233	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
234	C₁₃×C₂²⋊C₄	—	2	2	no	—
235	C₁₃×C₂²⋊C₄	—	2	2	no	—
236	C₁₃×C₂²⋊C₄	—	4	2	no	—
237	C₁₃×C₂²⋊C₄	—	4	2	no	—
238	C₁₃×C₂²⋊C₄	—	4	2	no	—
239	C₁₃×C₂²⋊C₄	—	4	2	no	—
240	C₁₃×C₂²⋊C₄	—	4	2	no	—
241	C₁₃×C₂²⋊C₄	—	4	2	no	—
242	C₁₃×C₂²⋊C₄	—	8	1	no	—
243	C₁₃×C₂²⋊C₄	—	8	1	no	—
244	C₄²×C₁₃	—	2	1	no	—
245	C₄²×C₁₃	—	2	1	no	—
246	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
248	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
249	C₂²×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#2417	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#2416	C₂×C₁₃	1	1	yes	characteristic
252	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#1973	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#1943	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#1874	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	1	no	—
263	C₂³×C₁₃	—	2	1	no	—
264	C₂³×C₁₃	—	2	1	no	—
265	C₂³×C₁₃	—	2	1	no	—
266	C₂³×C₁₃	—	2	1	no	—
267	C₂³×C₁₃	—	2	1	no	—
268	C₂³×C₁₃	—	2	1	no	—
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	1	no	—
271	C₂³×C₁₃	—	2	1	no	—
272	C₂³×C₁₃	—	4	1	no	—
273	C₂³×C₁₃	—	4	1	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	4	1	no	—
276	C₂³×C₁₃	—	4	1	no	—
277	C₂³×C₁₃	—	4	1	no	—
278	C₂³×C₁₃	—	4	1	no	—
279	C₂³×C₁₃	#121	1	2	yes	—
280	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
281	C₂³×C₁₃	#137	1	2	yes	—
282	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	Q₈×C₁₃	—	4	1	no	—
284	Q₈×C₁₃	—	4	1	no	—
285	Q₈×C₁₃	—	4	1	no	—
286	Q₈×C₁₃	—	4	1	no	—
287	D₄×C₁₃	—	4	4	no	—
288	D₄×C₁₃	—	4	1	no	—
289	D₄×C₁₃	—	4	1	no	—
290	D₄×C₁₃	—	4	1	no	—
291	D₄×C₁₃	—	4	1	no	—
292	D₄×C₁₃	—	8	4	no	—
293	D₄×C₁₃	—	8	4	no	—
294	C₂×C₄×C₁₃	—	2	1	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	2	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	1	no	—
302	C₂×C₄×C₁₃	—	2	1	no	—
303	C₂×C₄×C₁₃	—	2	1	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	1	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	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	—	4	1	no	—
334	C₂×C₄×C₁₃	—	8	4	no	—
335	C₂×C₄×C₁₃	—	8	4	no	—
336	C₂×C₄×C₁₃	#121	1	2	yes	—
337	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
343	C₈×C₁₃	—	2	2	no	—
344	C₈×C₁₃	—	4	1	no	—
345	C₈×C₁₃	—	4	1	no	—
346	C₈×C₁₃	#121	1	4	yes	complemented
347	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
348	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
349	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#121	—	2	1	no	—
353	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
356	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
358	#468	—	2	4	no	—
359	#465	—	2	4	no	—
360	#435	—	2	4	no	—
361	C₂×#107	—	2	4	no	—
362	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
363	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
377	#398	—	2	1	no	—
378	#396	—	2	1	no	—
379	#396	—	2	1	no	—
380	#394	—	2	1	no	—
381	#391	C₂²×C₁₃	1	1	yes	characteristic
382	#390	C₂²×C₁₃	1	1	yes	characteristic
383	#389	C₂²×C₁₃	1	1	yes	characteristic
384	#389	C₂²×C₁₃	1	1	yes	characteristic
385	#386	—	2	1	no	—
386	#386	—	2	1	no	—
387	#380	—	2	1	no	—
388	#380	C₂²×C₁₃	1	1	yes	characteristic
389	#380	C₂²×C₁₃	1	1	yes	characteristic
390	#340	C₂²×C₁₃	1	1	yes	characteristic
391	#340	C₂²×C₁₃	1	1	yes	characteristic
392	#340	C₂²×C₁₃	1	1	yes	characteristic
393	#340	C₂²×C₁₃	1	1	yes	characteristic
394	C₂²×C₁₃	—	2	2	no	—
395	C₂²×C₁₃	—	2	2	no	—
396	C₂²×C₁₃	—	2	2	no	—
397	C₂²×C₁₃	—	2	2	no	—
398	C₂²×C₁₃	—	2	2	no	—
399	C₂²×C₁₃	—	2	2	no	—
400	C₂²×C₁₃	—	4	1	no	—
401	C₂²×C₁₃	—	4	1	no	—
402	C₂²×C₁₃	—	4	1	no	—
403	C₂²×C₁₃	—	4	1	no	—
404	C₂²×C₁₃	—	4	1	no	—
405	C₂²×C₁₃	—	4	1	no	—
406	C₂²×C₁₃	—	4	1	no	—
407	C₂²×C₁₃	—	8	1	no	—
408	C₂²×C₁₃	—	8	1	no	—
409	C₂²×C₁₃	—	8	1	no	—
410	C₂²×C₁₃	—	8	1	no	—
411	C₂²×C₁₃	—	8	1	no	—
412	C₂²×C₁₃	—	8	1	no	—
413	C₂²×C₁₃	—	8	1	no	—
414	C₂²×C₁₃	#468	1	4	yes	complemented
415	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
416	C₂²×C₁₃	D₄²	1	1	yes	characteristic
417	C₂²×C₁₃	#547	1	1	yes	characteristic
418	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
419	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
420	C₂²×C₁₃	#576	1	1	yes	characteristic
421	C₂²×C₁₃	#578	1	1	yes	characteristic
422	C₄×C₁₃	—	2	2	no	—
423	C₄×C₁₃	—	4	1	no	—
424	C₄×C₁₃	—	4	2	no	—
425	C₄×C₁₃	—	4	2	no	—
426	C₄×C₁₃	—	4	1	no	—
427	C₄×C₁₃	—	4	1	no	—
428	C₄×C₁₃	—	8	1	no	—
429	C₄×C₁₃	—	8	1	no	—
430	C₄×C₁₃	—	8	1	no	—
431	C₄×C₁₃	—	8	1	no	—
432	C₄×C₁₃	—	8	1	no	—
433	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
434	C₄×C₁₃	#537	1	1	yes	characteristic
435	C₄×C₁₃	#548	1	1	yes	characteristic
436	C₄×C₁₃	#553	1	1	yes	characteristic
437	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₂²×D₄	—	2	1	no	—
439	C₂²×D₄	—	2	1	no	—
440	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
446	C₂×SD₁₆	—	2	2	no	—
447	C₂×SD₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	2	2	no	—
449	C₂×M₁₆	—	2	2	no	—
450	C₂×M₁₆	—	2	2	no	—
451	C₂×M₁₆	—	2	2	no	—
452	C₂²×C₈	—	2	2	no	—
453	C₂²×C₈	—	2	2	no	—
454	C₂²×C₈	D₄×C₁₃	1	4	yes	complemented
455	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	2	no	—
462	C₂²⋊Q₈	—	4	1	no	—
463	#121	—	2	2	no	—
464	#121	—	2	2	no	—
465	#121	—	2	2	no	—
466	#121	—	4	1	no	—
467	#121	—	4	4	no	—
468	C₄×D₄	—	2	2	no	—
469	C₄×D₄	—	2	2	no	—
470	C₂×C₄⋊C₄	—	2	2	no	—
471	C₂×C₄⋊C₄	—	2	2	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	4	1	no	—
479	C₂×C₄⋊C₄	—	4	1	no	—
480	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
498	#107	—	2	2	no	—
499	#107	—	2	2	no	—
500	#107	—	2	2	no	—
501	#107	D₄×C₁₃	1	4	yes	complemented
502	#106	—	2	2	no	—
503	C₄⋊C₈	—	2	2	no	—
504	#103	—	2	2	no	—
505	#103	—	2	2	no	—
506	#103	—	4	1	no	—
507	#102	—	2	2	no	—
508	#102	—	2	2	no	—
509	#102	—	4	1	no	—
510	C₂²⋊C₈	—	2	2	no	—
511	C₂²⋊C₈	—	2	2	no	—
512	#97	—	2	2	no	—
513	#95	—	2	1	no	—
514	#95	—	2	1	no	—
515	#95	—	2	1	no	—
516	#95	—	2	1	no	—
517	#95	—	2	1	no	—
518	#95	—	2	1	no	—
519	C₂×C₁₃	—	2	4	no	—
520	C₂×C₁₃	—	8	1	no	—
521	C₂×C₁₃	—	16	1	no	—
522	C₂×C₁₃	#2416	1	1	yes	characteristic
523	C₂×C₁₃	C₂×#468	1	1	yes	characteristic
524	C₂×C₁₃	#3061	1	1	yes	characteristic
525	C₂×C₁₃	#3264	1	1	yes	characteristic
526	C₂×C₁₃	#3270	1	1	yes	characteristic
527	C₂×C₁₃	#3343	1	1	yes	characteristic
528	C₂×C₁₃	#3346	1	1	yes	characteristic
529	C₂⁴	—	2	1	no	—
530	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	4	2	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	—	4	2	no	—
550	C₂×D₄	—	4	2	no	—
551	C₂×D₄	—	4	2	no	—
552	C₂×D₄	—	8	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	8	1	no	—
575	C₂²×C₄	—	8	1	no	—
576	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
581	C₂²×C₄	C₁₃×#41	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
583	SD₁₆	—	4	4	no	—
584	M₁₆	—	4	4	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	8	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
595	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
596	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
597	C₂×C₈	C₁₃×#41	1	2	yes	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	8	1	no	—
615	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
616	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	4	2	no	—
625	C₂²⋊C₄	—	8	1	no	—
626	C₂²⋊C₄	—	8	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₁₃	#24787	1	1	yes	characteristic, direct product factor, Sylow
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	C₁₃×#121	1	2	yes	—
649	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
650	C₂³	C₁₃×#137	1	2	yes	—
651	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
652	Q₈	—	4	1	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	D₄	—	4	4	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	4	1	no	—
660	D₄	—	4	1	no	—
661	D₄	—	8	4	no	—
662	D₄	—	8	4	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	C₁₃×#121	1	2	yes	—
706	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
709	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
710	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
711	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
712	C₈	—	2	2	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	C₁₃×#121	1	4	yes	complemented
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	—	8	1	no	—
732	C₂²	—	8	1	no	—
733	C₂²	—	8	1	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	C₁₃×#468	1	4	yes	complemented
737	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
738	C₂²	D₄²×C₁₃	1	1	yes	characteristic
739	C₂²	C₁₃×#547	1	1	yes	characteristic
740	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
741	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
742	C₂²	C₁₃×#576	1	1	yes	characteristic
743	C₂²	C₁₃×#578	1	1	yes	characteristic
744	C₄	—	2	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	1	no	—
750	C₄	—	8	1	no	—
751	C₄	—	8	1	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	—	8	1	no	—
755	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
756	C₄	C₁₃×#537	1	1	yes	characteristic
757	C₄	C₁₃×#548	1	1	yes	characteristic
758	C₄	C₁₃×#553	1	1	yes	characteristic
759	C₂	—	2	4	no	—
760	C₂	—	8	1	no	—
761	C₂	—	16	1	no	—
762	C₂	C₁₃×#2416	1	1	yes	characteristic
763	C₂	C₂×C₁₃×#468	1	1	yes	characteristic
764	C₂	C₁₃×#3061	1	1	yes	characteristic
765	C₂	C₁₃×#3264	1	1	yes	characteristic
766	C₂	C₁₃×#3270	1	1	yes	characteristic
767	C₂	C₁₃×#3343	1	1	yes	characteristic
768	C₂	C₁₃×#3346	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2416	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#468	C₂	semidirect
2. C₂×C₁₃×#465	C₂	semidirect
3. C₂×C₁₃×#435	C₂	semidirect
4. C₂²×C₁₃×#107	C₂	semidirect
5. C₁₃×#2417	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2067	C₂	semidirect
9. C₁₃×#2036	C₂	semidirect
10. C₁₃×#2033	C₂	semidirect
11. C₁₃×#1973	C₂	semidirect
12. C₁₃×#1943	C₂	semidirect
13. C₁₃×#1874	C₂	semidirect
14. C₁₃×#1872	C₂	semidirect
15. C₁₃×#1809	C₂	semidirect
80. C₂²×C₈×C₁₃	D₄	semidirect
127. C₁₃×#107	D₄	semidirect
145. #24787	C₁₃	direct (N × H)
246. C₂×#468	C₂×C₁₃	semidirect
247. C₂×#465	C₂×C₁₃	semidirect
248. C₂×#435	C₂×C₁₃	semidirect
249. C₂²×#107	C₂×C₁₃	semidirect
250. #2417	C₂×C₁₃	semidirect
252. #2068	C₂×C₁₃	semidirect
253. #2067	C₂×C₁₃	semidirect
254. #2036	C₂×C₁₃	semidirect
255. #2033	C₂×C₁₃	semidirect
256. #1973	C₂×C₁₃	semidirect
257. #1943	C₂×C₁₃	semidirect
258. #1874	C₂×C₁₃	semidirect
259. #1872	C₂×C₁₃	semidirect
260. #1809	C₂×C₁₃	semidirect
346. C₈×C₁₃	#121	semidirect
414. C₂²×C₁₃	#468	semidirect
454. C₂²×C₈	D₄×C₁₃	semidirect
501. #107	D₄×C₁₃	semidirect
629. C₁₃	#24787	direct (N × H)
715. C₈	C₁₃×#121	semidirect
736. C₂²	C₁₃×#468	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#468	2
C₂×C₁₃×#465	2
C₂×C₁₃×#435	2
C₂²×C₁₃×#107	2
C₁₃×#2417	2
C₁₃×#2416	2
C₁₃×#2068	2
C₁₃×#2067	2
C₁₃×#2036	2
C₁₃×#2033	2
C₁₃×#1973	2
C₁₃×#1943	2
C₁₃×#1874	2
C₁₃×#1872	2
C₁₃×#1809	2
#24787	13

Subgroups — C13×#24787 #15711126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24787 #15711126