Subgroups — C₁₃×#24429 #15710768

Order 3328.

1508 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2416	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₁₃	—	2	4	no	—
23	D₄×Q₈×C₁₃	—	2	4	no	—
24	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	—	2	1	no	—
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	—	2	1	no	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#465	—	2	4	no	—
38	C₁₃×#448	—	2	4	no	—
39	C₁₃×#448	—	2	4	no	—
40	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#103	—	2	4	no	—
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₁₃×#396	—	2	1	no	—
56	C₁₃×#394	—	2	1	no	—
57	C₁₃×#390	C₂²	1	1	yes	characteristic
58	C₁₃×#389	C₂²	1	1	yes	characteristic
59	C₁₃×#386	—	2	1	no	—
60	C₁₃×#380	C₂²	1	1	yes	characteristic
61	C₁₃×#340	C₂²	1	1	yes	characteristic
62	C₁₃×#340	C₂²	1	1	yes	characteristic
63	C₁₃×#336	C₂²	1	1	yes	characteristic
64	C₁₃×#336	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	—	2	2	no	—
66	C₂²×Q₈×C₁₃	—	2	2	no	—
67	C₂²×Q₈×C₁₃	—	2	1	no	—
68	C₂²×Q₈×C₁₃	—	2	1	no	—
69	C₂²×Q₈×C₁₃	—	2	2	no	—
70	C₂²×Q₈×C₁₃	—	2	2	no	—
71	C₂²×Q₈×C₁₃	—	2	2	no	—
72	C₂²×Q₈×C₁₃	—	2	2	no	—
73	C₂²×Q₈×C₁₃	—	2	2	no	—
74	C₂²×Q₈×C₁₃	—	4	1	no	—
75	C₂²×Q₈×C₁₃	—	4	1	no	—
76	C₂²×Q₈×C₁₃	—	4	1	no	—
77	C₂²×Q₈×C₁₃	—	4	1	no	—
78	C₂²×Q₈×C₁₃	D₄	1	4	yes	complemented
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	—	2	1	no	—
84	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	—	2	1	no	—
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	—	2	1	no	—
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×SD₁₆	—	2	2	no	—
92	C₂×C₁₃×SD₁₆	—	2	2	no	—
93	C₂×C₁₃×SD₁₆	—	2	2	no	—
94	C₂×C₁₃×SD₁₆	—	2	2	no	—
95	C₂×C₁₃×SD₁₆	—	2	2	no	—
96	C₂×C₁₃×SD₁₆	—	2	2	no	—
97	C₂×C₁₃×SD₁₆	—	4	1	no	—
98	C₂×C₁₃×SD₁₆	—	4	1	no	—
99	C₂×C₁₃×SD₁₆	—	4	1	no	—
100	C₂²×C₈×C₁₃	—	2	2	no	—
101	C₂²×C₈×C₁₃	—	2	2	no	—
102	C₂²×C₈×C₁₃	—	4	1	no	—
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊Q₈	—	2	8	no	—
108	C₁₃×C₄⋊Q₈	—	2	2	no	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₂²⋊Q₈	—	2	8	no	—
111	C₁₃×C₂²⋊Q₈	—	2	8	no	—
112	C₁₃×C₂²⋊Q₈	—	2	2	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	complemented
116	C₁₃×#121	—	2	2	no	—
117	C₁₃×#121	—	2	2	no	—
118	C₁₃×#121	—	2	2	no	—
119	C₁₃×#121	—	4	1	no	—
120	C₁₃×#121	—	4	4	no	—
121	C₄×Q₈×C₁₃	—	2	2	no	—
122	C₄×Q₈×C₁₃	—	2	2	no	—
123	C₄×D₄×C₁₃	—	2	8	no	—
124	C₄×D₄×C₁₃	—	2	2	no	—
125	C₄×D₄×C₁₃	—	2	2	no	—
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
147	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
148	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
149	C₂×C₄²×C₁₃	—	2	1	no	—
150	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	C₁₃×#106	—	2	2	no	—
152	C₁₃×#103	—	2	2	no	—
153	C₁₃×#103	—	2	2	no	—
154	C₁₃×#103	—	2	2	no	—
155	C₁₃×#103	—	2	2	no	—
156	C₁₃×#103	—	2	2	no	—
157	C₁₃×#103	—	2	2	no	—
158	C₁₃×#103	—	2	2	no	—
159	C₁₃×#103	—	4	1	no	—
160	C₁₃×#103	D₄	1	4	yes	complemented
161	C₁₃×#102	—	2	2	no	—
162	C₁₃×C₂²⋊C₈	—	2	2	no	—
163	C₁₃×C₂²⋊C₈	—	2	2	no	—
164	C₁₃×C₂²⋊C₈	—	4	1	no	—
165	C₁₃×#95	—	2	1	no	—
166	C₁₃×#95	—	2	1	no	—
167	#24429	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂⁴×C₁₃	—	2	1	no	—
169	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂×Q₈×C₁₃	—	2	4	no	—
172	C₂×Q₈×C₁₃	—	2	4	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	8	no	—
179	C₂×Q₈×C₁₃	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	4	2	no	—
188	C₂×Q₈×C₁₃	—	4	2	no	—
189	C₂×Q₈×C₁₃	—	4	2	no	—
190	C₂×Q₈×C₁₃	—	4	2	no	—
191	C₂×Q₈×C₁₃	—	4	4	no	—
192	C₂×Q₈×C₁₃	—	4	4	no	—
193	C₂×Q₈×C₁₃	—	4	4	no	—
194	C₂×Q₈×C₁₃	—	4	4	no	—
195	C₂×Q₈×C₁₃	—	4	4	no	—
196	C₂×Q₈×C₁₃	—	4	4	no	—
197	C₂×Q₈×C₁₃	—	4	4	no	—
198	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
199	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
200	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
201	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
202	C₂×Q₈×C₁₃	#41	1	2	yes	—
203	C₂×D₄×C₁₃	—	2	2	no	—
204	C₂×D₄×C₁₃	—	2	2	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	1	no	—
207	C₂×D₄×C₁₃	—	2	1	no	—
208	C₂×D₄×C₁₃	—	2	1	no	—
209	C₂×D₄×C₁₃	—	2	1	no	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	4	2	no	—
212	C₂×D₄×C₁₃	—	4	2	no	—
213	C₂×D₄×C₁₃	—	4	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂×D₄×C₁₃	—	8	1	no	—
217	C₂×D₄×C₁₃	SD₁₆	1	4	yes	complemented
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	1	no	—
235	C₂²×C₄×C₁₃	—	2	1	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	2	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	8	1	no	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₁₃×SD₁₆	—	4	4	no	—
252	C₁₃×SD₁₆	—	4	4	no	—
253	C₁₃×SD₁₆	—	4	4	no	—
254	C₂×C₈×C₁₃	—	2	1	no	—
255	C₂×C₈×C₁₃	—	2	1	no	—
256	C₂×C₈×C₁₃	—	2	1	no	—
257	C₂×C₈×C₁₃	—	2	1	no	—
258	C₂×C₈×C₁₃	—	2	1	no	—
259	C₂×C₈×C₁₃	—	2	1	no	—
260	C₂×C₈×C₁₃	—	2	1	no	—
261	C₂×C₈×C₁₃	—	2	1	no	—
262	C₂×C₈×C₁₃	—	2	1	no	—
263	C₂×C₈×C₁₃	—	2	1	no	—
264	C₂×C₈×C₁₃	—	2	1	no	—
265	C₂×C₈×C₁₃	—	4	4	no	—
266	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	4	2	no	—
280	C₁₃×C₄⋊C₄	—	4	2	no	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₁₃×C₂²⋊C₄	—	4	2	no	—
288	C₁₃×C₂²⋊C₄	—	4	2	no	—
289	C₁₃×C₂²⋊C₄	—	4	2	no	—
290	C₁₃×C₂²⋊C₄	—	4	2	no	—
291	C₁₃×C₂²⋊C₄	—	8	1	no	—
292	C₄²×C₁₃	—	2	4	no	—
293	C₄²×C₁₃	—	2	1	no	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2416	C₂×C₁₃	1	1	yes	characteristic
301	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2013	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#1869	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	2	1	no	—
312	C₂³×C₁₃	—	2	1	no	—
313	C₂³×C₁₃	—	2	1	no	—
314	C₂³×C₁₃	—	2	1	no	—
315	C₂³×C₁₃	—	2	1	no	—
316	C₂³×C₁₃	—	2	1	no	—
317	C₂³×C₁₃	—	2	1	no	—
318	C₂³×C₁₃	—	2	1	no	—
319	C₂³×C₁₃	—	2	1	no	—
320	C₂³×C₁₃	—	4	1	no	—
321	C₂³×C₁₃	—	4	1	no	—
322	C₂³×C₁₃	—	4	1	no	—
323	C₂³×C₁₃	—	4	1	no	—
324	C₂³×C₁₃	—	4	1	no	—
325	C₂³×C₁₃	—	4	1	no	—
326	C₂³×C₁₃	—	4	1	no	—
327	C₂³×C₁₃	#120	1	2	yes	—
328	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
329	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
330	C₂³×C₁₃	#137	1	2	yes	—
331	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
332	Q₈×C₁₃	—	2	2	no	—
333	Q₈×C₁₃	—	2	2	no	—
334	Q₈×C₁₃	—	2	2	no	—
335	Q₈×C₁₃	—	2	2	no	—
336	Q₈×C₁₃	—	2	2	no	—
337	Q₈×C₁₃	—	2	2	no	—
338	Q₈×C₁₃	—	2	2	no	—
339	Q₈×C₁₃	—	4	8	no	—
340	Q₈×C₁₃	—	4	8	no	—
341	Q₈×C₁₃	—	4	1	no	—
342	Q₈×C₁₃	—	4	1	no	—
343	Q₈×C₁₃	—	4	1	no	—
344	Q₈×C₁₃	—	4	1	no	—
345	Q₈×C₁₃	#121	1	4	yes	complemented
346	D₄×C₁₃	—	2	8	no	—
347	D₄×C₁₃	—	4	1	no	—
348	D₄×C₁₃	—	4	1	no	—
349	D₄×C₁₃	—	4	1	no	—
350	D₄×C₁₃	—	4	1	no	—
351	D₄×C₁₃	—	8	4	no	—
352	D₄×C₁₃	—	8	4	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	1	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	4	8	no	—
375	C₂×C₄×C₁₃	—	4	8	no	—
376	C₂×C₄×C₁₃	—	4	1	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	—	4	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	4	1	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	1	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	1	no	—
393	C₂×C₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	8	4	no	—
395	C₂×C₄×C₁₃	#120	1	2	yes	—
396	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
401	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
402	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
403	C₈×C₁₃	—	2	2	no	—
404	C₈×C₁₃	—	4	1	no	—
405	C₈×C₁₃	—	4	1	no	—
406	C₈×C₁₃	—	4	1	no	—
407	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
408	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
411	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
412	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
413	D₄×Q₈	—	2	4	no	—
414	D₄×Q₈	—	2	4	no	—
415	C₂×C₄⋊Q₈	—	2	1	no	—
416	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₂²⋊Q₈	—	2	1	no	—
418	C₂×C₂²⋊Q₈	—	2	1	no	—
419	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#121	—	2	1	no	—
422	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×C₄×D₄	—	2	1	no	—
426	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
427	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
428	#465	—	2	4	no	—
429	#448	—	2	4	no	—
430	#448	—	2	4	no	—
431	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#103	—	2	4	no	—
433	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
446	#396	—	2	1	no	—
447	#394	—	2	1	no	—
448	#390	C₂²×C₁₃	1	1	yes	characteristic
449	#389	C₂²×C₁₃	1	1	yes	characteristic
450	#386	—	2	1	no	—
451	#380	C₂²×C₁₃	1	1	yes	characteristic
452	#340	C₂²×C₁₃	1	1	yes	characteristic
453	#340	C₂²×C₁₃	1	1	yes	characteristic
454	#336	C₂²×C₁₃	1	1	yes	characteristic
455	#336	C₂²×C₁₃	1	1	yes	characteristic
456	C₂²×C₁₃	—	2	2	no	—
457	C₂²×C₁₃	—	2	2	no	—
458	C₂²×C₁₃	—	2	2	no	—
459	C₂²×C₁₃	—	2	2	no	—
460	C₂²×C₁₃	—	2	2	no	—
461	C₂²×C₁₃	—	2	2	no	—
462	C₂²×C₁₃	—	2	2	no	—
463	C₂²×C₁₃	—	2	2	no	—
464	C₂²×C₁₃	—	2	2	no	—
465	C₂²×C₁₃	—	4	1	no	—
466	C₂²×C₁₃	—	4	1	no	—
467	C₂²×C₁₃	—	4	1	no	—
468	C₂²×C₁₃	—	4	1	no	—
469	C₂²×C₁₃	—	8	1	no	—
470	C₂²×C₁₃	—	8	1	no	—
471	C₂²×C₁₃	—	8	1	no	—
472	C₂²×C₁₃	—	8	1	no	—
473	C₂²×C₁₃	—	8	1	no	—
474	C₂²×C₁₃	—	8	1	no	—
475	C₂²×C₁₃	—	8	1	no	—
476	C₂²×C₁₃	#448	1	4	yes	complemented
477	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
478	C₂²×C₁₃	D₄²	1	1	yes	characteristic
479	C₂²×C₁₃	#546	1	1	yes	characteristic
480	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
481	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
482	C₂²×C₁₃	#577	1	1	yes	characteristic
483	C₂²×C₁₃	#578	1	1	yes	characteristic
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	2	4	no	—
486	C₄×C₁₃	—	2	2	no	—
487	C₄×C₁₃	—	4	1	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	1	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	8	1	no	—
494	C₄×C₁₃	—	8	1	no	—
495	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
496	C₄×C₁₃	#534	1	1	yes	characteristic
497	C₄×C₁₃	D₄²	1	1	yes	characteristic
498	C₄×C₁₃	#546	1	1	yes	characteristic
499	C₂²×Q₈	—	2	2	no	—
500	C₂²×Q₈	—	2	2	no	—
501	C₂²×Q₈	—	2	1	no	—
502	C₂²×Q₈	—	2	1	no	—
503	C₂²×Q₈	—	2	2	no	—
504	C₂²×Q₈	—	2	2	no	—
505	C₂²×Q₈	—	2	2	no	—
506	C₂²×Q₈	—	2	2	no	—
507	C₂²×Q₈	—	2	2	no	—
508	C₂²×Q₈	—	4	1	no	—
509	C₂²×Q₈	—	4	1	no	—
510	C₂²×Q₈	—	4	1	no	—
511	C₂²×Q₈	—	4	1	no	—
512	C₂²×Q₈	D₄×C₁₃	1	4	yes	complemented
513	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
525	C₂×SD₁₆	—	2	2	no	—
526	C₂×SD₁₆	—	2	2	no	—
527	C₂×SD₁₆	—	2	2	no	—
528	C₂×SD₁₆	—	2	2	no	—
529	C₂×SD₁₆	—	2	2	no	—
530	C₂×SD₁₆	—	2	2	no	—
531	C₂×SD₁₆	—	4	1	no	—
532	C₂×SD₁₆	—	4	1	no	—
533	C₂×SD₁₆	—	4	1	no	—
534	C₂²×C₈	—	2	2	no	—
535	C₂²×C₈	—	2	2	no	—
536	C₂²×C₈	—	4	1	no	—
537	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
540	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
541	C₄⋊Q₈	—	2	8	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	8	no	—
545	C₂²⋊Q₈	—	2	8	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	complemented
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	4	1	no	—
554	#121	—	4	4	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×D₄	—	2	8	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	2	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	4	1	no	—
569	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₄²	—	2	1	no	—
584	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
585	#106	—	2	2	no	—
586	#103	—	2	2	no	—
587	#103	—	2	2	no	—
588	#103	—	2	2	no	—
589	#103	—	2	2	no	—
590	#103	—	2	2	no	—
591	#103	—	2	2	no	—
592	#103	—	2	2	no	—
593	#103	—	4	1	no	—
594	#103	D₄×C₁₃	1	4	yes	complemented
595	#102	—	2	2	no	—
596	C₂²⋊C₈	—	2	2	no	—
597	C₂²⋊C₈	—	2	2	no	—
598	C₂²⋊C₈	—	4	1	no	—
599	#95	—	2	1	no	—
600	#95	—	2	1	no	—
601	C₂×C₁₃	—	2	4	no	—
602	C₂×C₁₃	—	4	2	no	—
603	C₂×C₁₃	—	16	1	no	—
604	C₂×C₁₃	#2410	1	1	yes	characteristic
605	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
606	C₂×C₁₃	#3013	1	1	yes	characteristic
607	C₂×C₁₃	#3270	1	1	yes	characteristic
608	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
609	C₂×C₁₃	#3298	1	1	yes	characteristic
610	C₂×C₁₃	#3320	1	1	yes	characteristic
611	C₂⁴	—	2	1	no	—
612	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
614	C₂×Q₈	—	2	4	no	—
615	C₂×Q₈	—	2	4	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	8	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	4	2	no	—
631	C₂×Q₈	—	4	2	no	—
632	C₂×Q₈	—	4	2	no	—
633	C₂×Q₈	—	4	2	no	—
634	C₂×Q₈	—	4	4	no	—
635	C₂×Q₈	—	4	4	no	—
636	C₂×Q₈	—	4	4	no	—
637	C₂×Q₈	—	4	4	no	—
638	C₂×Q₈	—	4	4	no	—
639	C₂×Q₈	—	4	4	no	—
640	C₂×Q₈	—	4	4	no	—
641	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
642	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
643	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
644	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
645	C₂×Q₈	C₁₃×#41	1	2	yes	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	8	1	no	—
660	C₂×D₄	C₁₃×SD₁₆	1	4	yes	complemented
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	8	1	no	—
687	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
691	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
692	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	SD₁₆	—	4	4	no	—
695	SD₁₆	—	4	4	no	—
696	SD₁₆	—	4	4	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	—	2	1	no	—
701	C₂×C₈	—	2	1	no	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	2	1	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	4	4	no	—
709	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	8	1	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₁₃	#24429	1	1	yes	characteristic, direct product factor, Sylow
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	no	—
756	C₂³	C₁₃×#120	1	2	yes	—
757	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
758	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
759	C₂³	C₁₃×#137	1	2	yes	—
760	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
761	Q₈	—	2	2	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	2	no	—
768	Q₈	—	4	8	no	—
769	Q₈	—	4	8	no	—
770	Q₈	—	4	1	no	—
771	Q₈	—	4	1	no	—
772	Q₈	—	4	1	no	—
773	Q₈	—	4	1	no	—
774	Q₈	C₁₃×#121	1	4	yes	complemented
775	D₄	—	2	8	no	—
776	D₄	—	4	1	no	—
777	D₄	—	4	1	no	—
778	D₄	—	4	1	no	—
779	D₄	—	4	1	no	—
780	D₄	—	8	4	no	—
781	D₄	—	8	4	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	4	8	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	C₁₃×#120	1	2	yes	—
825	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
829	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
830	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	4	1	no	—
834	C₈	—	4	1	no	—
835	C₈	—	4	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	8	1	no	—
850	C₂²	—	8	1	no	—
851	C₂²	—	8	1	no	—
852	C₂²	—	8	1	no	—
853	C₂²	—	8	1	no	—
854	C₂²	—	8	1	no	—
855	C₂²	—	8	1	no	—
856	C₂²	C₁₃×#448	1	4	yes	complemented
857	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
858	C₂²	D₄²×C₁₃	1	1	yes	characteristic
859	C₂²	C₁₃×#546	1	1	yes	characteristic
860	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
861	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
862	C₂²	C₁₃×#577	1	1	yes	characteristic
863	C₂²	C₁₃×#578	1	1	yes	characteristic
864	C₄	—	2	2	no	—
865	C₄	—	2	4	no	—
866	C₄	—	2	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	8	1	no	—
874	C₄	—	8	1	no	—
875	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
876	C₄	C₁₃×#534	1	1	yes	characteristic
877	C₄	D₄²×C₁₃	1	1	yes	characteristic
878	C₄	C₁₃×#546	1	1	yes	characteristic
879	C₂	—	2	4	no	—
880	C₂	—	4	2	no	—
881	C₂	—	16	1	no	—
882	C₂	C₁₃×#2410	1	1	yes	characteristic
883	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
884	C₂	C₁₃×#3013	1	1	yes	characteristic
885	C₂	C₁₃×#3270	1	1	yes	characteristic
886	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
887	C₂	C₁₃×#3298	1	1	yes	characteristic
888	C₂	C₁₃×#3320	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×D₄×Q₈×C₁₃	C₂	semidirect
2. C₂×C₁₃×#465	C₂	semidirect
3. C₂×C₁₃×#448	C₂	semidirect
4. C₂×C₁₃×#448	C₂	semidirect
5. C₂²×C₁₃×#103	C₂	semidirect
7. C₁₃×#2043	C₂	semidirect
8. C₁₃×#2035	C₂	semidirect
9. C₁₃×#2013	C₂	semidirect
10. C₁₃×#2000	C₂	semidirect
11. C₁₃×#1880	C₂	semidirect
12. C₁₃×#1872	C₂	semidirect
13. C₁₃×#1869	C₂	semidirect
14. C₁₃×#1865	C₂	semidirect
15. C₁₃×#1787	C₂	semidirect
78. C₂²×Q₈×C₁₃	D₄	semidirect
115. C₁₃×C₂²⋊Q₈	D₄	semidirect
160. C₁₃×#103	D₄	semidirect
167. #24429	C₁₃	direct (N × H)
217. C₂×D₄×C₁₃	SD₁₆	semidirect
295. C₂×D₄×Q₈	C₂×C₁₃	semidirect
296. C₂×#465	C₂×C₁₃	semidirect
297. C₂×#448	C₂×C₁₃	semidirect
298. C₂×#448	C₂×C₁₃	semidirect
299. C₂²×#103	C₂×C₁₃	semidirect
301. #2043	C₂×C₁₃	semidirect
302. #2035	C₂×C₁₃	semidirect
303. #2013	C₂×C₁₃	semidirect
304. #2000	C₂×C₁₃	semidirect
305. #1880	C₂×C₁₃	semidirect
306. #1872	C₂×C₁₃	semidirect
307. #1869	C₂×C₁₃	semidirect
308. #1865	C₂×C₁₃	semidirect
309. #1787	C₂×C₁₃	semidirect
345. Q₈×C₁₃	#121	semidirect
476. C₂²×C₁₃	#448	semidirect
512. C₂²×Q₈	D₄×C₁₃	semidirect
549. C₂²⋊Q₈	D₄×C₁₃	semidirect
594. #103	D₄×C₁₃	semidirect
660. C₂×D₄	C₁₃×SD₁₆	semidirect
738. C₁₃	#24429	direct (N × H)
774. Q₈	C₁₃×#121	semidirect
856. C₂²	C₁₃×#448	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#465	2
C₂×C₁₃×#448	2
C₂²×C₁₃×#103	2
C₁₃×#2416	2
C₁₃×#2043	2
C₁₃×#2035	2
C₁₃×#2013	2
C₁₃×#2000	2
C₁₃×#1880	2
C₁₃×#1872	2
C₁₃×#1869	2
C₁₃×#1865	2
C₁₃×#1787	2
#24429	13

Subgroups — C13×#24429 #15710768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24429 #15710768