Subgroups — C₁₃×#25105 #15711444

Order 3328.

1192 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2435	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₁₃×#470	—	2	4	no	—
28	C₁₃×#464	—	2	4	no	—
29	C₁₃×#450	—	2	4	no	—
30	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#418	—	2	4	no	—
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	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×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₃×#394	—	2	1	no	—
46	C₁₃×#394	—	2	1	no	—
47	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#388	—	2	1	no	—
52	C₁₃×#388	—	2	1	no	—
53	C₁₃×#387	—	2	1	no	—
54	C₁₃×#379	—	2	1	no	—
55	C₁₃×#379	—	2	1	no	—
56	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	—	2	2	no	—
68	C₂²×D₄×C₁₃	—	2	2	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	—	2	2	no	—
71	C₂²×D₄×C₁₃	—	4	1	no	—
72	C₂²×D₄×C₁₃	—	4	1	no	—
73	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×Q₁₆	—	2	2	no	—
77	C₂×C₁₃×Q₁₆	—	2	2	no	—
78	C₂×C₁₃×Q₁₆	—	4	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	2	no	—
80	C₂×C₁₃×SD₁₆	—	2	2	no	—
81	C₂×C₁₃×SD₁₆	—	2	2	no	—
82	C₂×C₁₃×SD₁₆	—	2	2	no	—
83	C₂×C₁₃×SD₁₆	—	4	1	no	—
84	C₂×C₁₃×SD₁₆	—	4	1	no	—
85	C₂×C₁₃×M₁₆	—	2	2	no	—
86	C₂×C₁₃×M₁₆	—	2	2	no	—
87	C₂×C₁₃×M₁₆	—	4	1	no	—
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#124	—	2	2	no	—
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	—	4	1	no	—
95	C₁₃×#124	—	4	1	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
100	C₄×Q₈×C₁₃	—	2	2	no	—
101	C₄×Q₈×C₁₃	—	4	1	no	—
102	C₁₃×#117	—	2	2	no	—
103	C₁₃×#117	—	4	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	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	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
124	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₂×C₄²×C₁₃	—	2	1	no	—
127	C₂×C₄²×C₁₃	—	2	1	no	—
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₁₃×#106	—	2	2	no	—
131	C₁₃×C₄⋊C₈	—	2	2	no	—
132	C₁₃×C₄⋊C₈	—	4	1	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	4	1	no	—
137	C₁₃×#102	—	2	2	no	—
138	C₁₃×#102	—	2	2	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×#102	D₄	1	4	yes	—
143	C₁₃×C₂²⋊C₈	—	2	2	no	—
144	C₁₃×#95	—	2	1	no	—
145	C₁₃×#95	—	2	1	no	—
146	C₁₃×#95	—	2	1	no	—
147	C₁₃×#95	—	2	1	no	—
148	C₁₃×#95	D₄	1	1	yes	characteristic
149	C₁₃×#95	D₄	1	1	yes	characteristic
150	#25105	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	—	2	1	no	—
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	—	4	2	no	—
154	C₂⁴×C₁₃	—	4	2	no	—
155	C₂⁴×C₁₃	—	4	2	no	—
156	C₂⁴×C₁₃	—	4	2	no	—
157	C₂⁴×C₁₃	—	4	2	no	—
158	C₂⁴×C₁₃	—	8	1	no	—
159	C₂⁴×C₁₃	—	8	1	no	—
160	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	—	2	1	no	—
166	C₂×Q₈×C₁₃	—	2	1	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
173	C₂×D₄×C₁₃	—	2	8	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	4	4	no	—
185	C₂×D₄×C₁₃	—	4	4	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	—	4	2	no	—
188	C₂×D₄×C₁₃	—	4	4	no	—
189	C₂×D₄×C₁₃	—	4	2	no	—
190	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×D₄×C₁₃	#41	1	2	yes	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₁₃	#41	1	2	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₁₃×Q₁₆	—	4	4	no	—
211	C₁₃×SD₁₆	—	4	4	no	—
212	C₁₃×SD₁₆	—	4	4	no	—
213	C₁₃×M₁₆	—	4	4	no	—
214	C₂×C₈×C₁₃	—	2	1	no	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	—	2	1	no	—
218	C₂×C₈×C₁₃	—	2	1	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
226	C₁₃×C₄⋊C₄	—	2	4	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	4	2	no	—
234	C₁₃×C₄⋊C₄	—	4	2	no	—
235	C₁₃×C₄⋊C₄	—	4	2	no	—
236	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
237	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	4	1	no	—
240	C₁₃×C₂²⋊C₄	—	4	1	no	—
241	C₁₃×C₂²⋊C₄	—	4	2	no	—
242	C₁₃×C₂²⋊C₄	—	4	2	no	—
243	C₁₃×C₂²⋊C₄	—	4	2	no	—
244	C₁₃×C₂²⋊C₄	—	4	2	no	—
245	C₁₃×C₂²⋊C₄	—	4	2	no	—
246	C₁₃×C₂²⋊C₄	—	4	2	no	—
247	C₁₃×C₂²⋊C₄	—	8	1	no	—
248	C₁₃×C₂²⋊C₄	—	8	1	no	—
249	C₁₃×C₂²⋊C₄	—	8	1	no	—
250	C₁₃×C₂²⋊C₄	—	8	1	no	—
251	C₄²×C₁₃	—	2	1	no	—
252	C₄²×C₁₃	—	2	1	no	—
253	C₄²×C₁₃	—	2	1	no	—
254	C₄²×C₁₃	—	2	1	no	—
255	C₄²×C₁₃	—	4	2	no	—
256	C₄²×C₁₃	—	4	2	no	—
257	C₄²×C₁₃	—	4	2	no	—
258	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
259	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂×#450	C₂×C₁₃	1	1	yes	characteristic
261	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
262	#2435	C₂×C₁₃	1	1	yes	characteristic
263	#2362	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#2015	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1983	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂³×C₁₃	—	2	1	no	—
274	C₂³×C₁₃	—	2	1	no	—
275	C₂³×C₁₃	—	2	1	no	—
276	C₂³×C₁₃	—	2	1	no	—
277	C₂³×C₁₃	—	2	1	no	—
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	4	8	no	—
282	C₂³×C₁₃	—	4	1	no	—
283	C₂³×C₁₃	—	4	1	no	—
284	C₂³×C₁₃	—	4	1	no	—
285	C₂³×C₁₃	—	4	1	no	—
286	C₂³×C₁₃	—	4	1	no	—
287	C₂³×C₁₃	—	4	1	no	—
288	C₂³×C₁₃	—	4	1	no	—
289	C₂³×C₁₃	—	4	1	no	—
290	C₂³×C₁₃	—	4	1	no	—
291	C₂³×C₁₃	—	4	1	no	—
292	C₂³×C₁₃	—	4	1	no	—
293	C₂³×C₁₃	—	4	1	no	—
294	C₂³×C₁₃	—	8	4	no	—
295	C₂³×C₁₃	—	8	4	no	—
296	C₂³×C₁₃	—	8	4	no	—
297	C₂³×C₁₃	—	8	4	no	—
298	C₂³×C₁₃	—	8	4	no	—
299	C₂³×C₁₃	—	8	4	no	—
300	C₂³×C₁₃	#121	1	2	yes	—
301	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₁₃	—	2	2	no	—
303	Q₈×C₁₃	—	2	2	no	—
304	Q₈×C₁₃	—	4	1	no	—
305	Q₈×C₁₃	—	4	1	no	—
306	Q₈×C₁₃	—	4	1	no	—
307	Q₈×C₁₃	—	4	1	no	—
308	Q₈×C₁₃	—	4	1	no	—
309	Q₈×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	2	2	no	—
311	D₄×C₁₃	—	2	2	no	—
312	D₄×C₁₃	—	2	2	no	—
313	D₄×C₁₃	—	2	2	no	—
314	D₄×C₁₃	—	4	8	no	—
315	D₄×C₁₃	—	4	1	no	—
316	D₄×C₁₃	—	4	1	no	—
317	D₄×C₁₃	—	4	1	no	—
318	D₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	1	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	1	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	4	1	no	—
341	C₂×C₄×C₁₃	—	4	1	no	—
342	C₂×C₄×C₁₃	—	4	1	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	1	no	—
345	C₂×C₄×C₁₃	—	4	1	no	—
346	C₂×C₄×C₁₃	—	4	1	no	—
347	C₂×C₄×C₁₃	—	4	1	no	—
348	C₂×C₄×C₁₃	—	4	1	no	—
349	C₂×C₄×C₁₃	—	4	1	no	—
350	C₂×C₄×C₁₃	—	4	1	no	—
351	C₂×C₄×C₁₃	—	4	1	no	—
352	C₂×C₄×C₁₃	—	4	1	no	—
353	C₂×C₄×C₁₃	—	4	1	no	—
354	C₂×C₄×C₁₃	—	4	1	no	—
355	C₂×C₄×C₁₃	#121	1	2	yes	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
362	C₈×C₁₃	—	2	2	no	—
363	C₈×C₁₃	—	4	1	no	—
364	C₈×C₁₃	—	4	1	no	—
365	C₈×C₁₃	—	4	1	no	—
366	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
367	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
368	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
370	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
376	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
377	#470	—	2	4	no	—
378	#464	—	2	4	no	—
379	#450	—	2	4	no	—
380	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
381	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
382	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
383	#418	—	2	4	no	—
384	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
395	#394	—	2	1	no	—
396	#394	—	2	1	no	—
397	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
398	#390	C₂²×C₁₃	1	1	yes	characteristic
399	#390	C₂²×C₁₃	1	1	yes	characteristic
400	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
401	#388	—	2	1	no	—
402	#388	—	2	1	no	—
403	#387	—	2	1	no	—
404	#379	—	2	1	no	—
405	#379	—	2	1	no	—
406	C₄×C₄⋊C₄	—	2	1	no	—
407	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
409	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	C₂²×C₁₃	—	2	2	no	—
414	C₂²×C₁₃	—	2	2	no	—
415	C₂²×C₁₃	—	2	2	no	—
416	C₂²×C₁₃	—	4	1	no	—
417	C₂²×C₁₃	—	4	1	no	—
418	C₂²×C₁₃	—	4	1	no	—
419	C₂²×C₁₃	—	4	1	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	2	no	—
426	C₂²×C₁₃	—	8	16	no	—
427	C₂²×C₁₃	—	8	1	no	—
428	C₂²×C₁₃	—	8	1	no	—
429	C₂²×C₁₃	—	8	1	no	—
430	C₂²×C₁₃	—	8	1	no	—
431	C₂²×C₁₃	—	8	1	no	—
432	C₂²×C₁₃	—	8	1	no	—
433	C₂²×C₁₃	—	8	1	no	—
434	C₂²×C₁₃	—	8	1	no	—
435	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
436	C₂²×C₁₃	D₄²	1	1	yes	characteristic
437	C₂²×C₁₃	#546	1	1	yes	characteristic
438	C₂²×C₁₃	#575	1	1	yes	characteristic
439	C₂²×C₁₃	#575	1	1	yes	characteristic
440	C₂²×C₁₃	#577	1	1	yes	characteristic
441	C₂²×C₁₃	#577	1	1	yes	characteristic
442	C₄×C₁₃	—	2	2	no	—
443	C₄×C₁₃	—	4	2	no	—
444	C₄×C₁₃	—	4	1	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	1	no	—
447	C₄×C₁₃	—	4	2	no	—
448	C₄×C₁₃	—	4	1	no	—
449	C₄×C₁₃	—	4	1	no	—
450	C₄×C₁₃	—	8	1	no	—
451	C₄×C₁₃	—	8	1	no	—
452	C₄×C₁₃	—	8	1	no	—
453	C₄×C₁₃	#525	1	1	yes	characteristic
454	C₄×C₁₃	#538	1	1	yes	characteristic
455	C₄×C₁₃	D₄²	1	1	yes	characteristic
456	C₄×C₁₃	#546	1	1	yes	characteristic
457	C₂⁵	—	2	1	no	—
458	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
460	C₂²×D₄	—	2	2	no	—
461	C₂²×D₄	—	2	2	no	—
462	C₂²×D₄	—	2	2	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	2	no	—
465	C₂²×D₄	—	4	1	no	—
466	C₂²×D₄	—	4	1	no	—
467	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×Q₁₆	—	2	2	no	—
471	C₂×Q₁₆	—	2	2	no	—
472	C₂×Q₁₆	—	4	1	no	—
473	C₂×SD₁₆	—	2	2	no	—
474	C₂×SD₁₆	—	2	2	no	—
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	2	2	no	—
477	C₂×SD₁₆	—	4	1	no	—
478	C₂×SD₁₆	—	4	1	no	—
479	C₂×M₁₆	—	2	2	no	—
480	C₂×M₁₆	—	2	2	no	—
481	C₂×M₁₆	—	4	1	no	—
482	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
486	#124	—	2	2	no	—
487	#124	—	2	2	no	—
488	#124	—	4	1	no	—
489	#124	—	4	1	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	4	1	no	—
496	#117	—	2	2	no	—
497	#117	—	4	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	—	2	1	no	—
521	C₂×C₄²	—	2	1	no	—
522	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
524	#106	—	2	2	no	—
525	C₄⋊C₈	—	2	2	no	—
526	C₄⋊C₈	—	4	1	no	—
527	#103	—	2	2	no	—
528	#103	—	2	2	no	—
529	#103	—	2	2	no	—
530	#103	—	4	1	no	—
531	#102	—	2	2	no	—
532	#102	—	2	2	no	—
533	#102	—	2	2	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	#102	D₄×C₁₃	1	4	yes	—
537	C₂²⋊C₈	—	2	2	no	—
538	#95	—	2	1	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	#95	D₄×C₁₃	1	1	yes	characteristic
543	#95	D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₁₃	—	4	2	no	—
545	C₂×C₁₃	—	8	2	no	—
546	C₂×C₁₃	—	8	2	no	—
547	C₂×C₁₃	#2424	1	1	yes	characteristic
548	C₂×C₁₃	#3040	1	1	yes	characteristic
549	C₂×C₁₃	#3043	1	1	yes	characteristic
550	C₂×C₁₃	#3267	1	1	yes	characteristic
551	C₂×C₁₃	#3275	1	1	yes	characteristic
552	C₂×C₁₃	#3311	1	1	yes	characteristic
553	C₂×C₁₃	#3323	1	1	yes	characteristic
554	C₂⁴	—	2	1	no	—
555	C₂⁴	—	2	1	no	—
556	C₂⁴	—	4	2	no	—
557	C₂⁴	—	4	2	no	—
558	C₂⁴	—	4	2	no	—
559	C₂⁴	—	4	2	no	—
560	C₂⁴	—	4	2	no	—
561	C₂⁴	—	8	1	no	—
562	C₂⁴	—	8	1	no	—
563	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	4	4	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
594	C₂×D₄	C₁₃×#41	1	2	yes	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
611	C₂²×C₄	C₁₃×#41	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
613	Q₁₆	—	4	4	no	—
614	SD₁₆	—	4	4	no	—
615	SD₁₆	—	4	4	no	—
616	M₁₆	—	4	4	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
640	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	4	1	no	—
643	C₂²⋊C₄	—	4	1	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	8	1	no	—
651	C₂²⋊C₄	—	8	1	no	—
652	C₂²⋊C₄	—	8	1	no	—
653	C₂²⋊C₄	—	8	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	4	2	no	—
659	C₄²	—	4	2	no	—
660	C₄²	—	4	2	no	—
661	C₁₃	#25105	1	1	yes	characteristic, direct product factor, Sylow
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	8	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	8	4	no	—
684	C₂³	—	8	4	no	—
685	C₂³	—	8	4	no	—
686	C₂³	—	8	4	no	—
687	C₂³	—	8	4	no	—
688	C₂³	—	8	4	no	—
689	C₂³	C₁₃×#121	1	2	yes	—
690	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	4	1	no	—
694	Q₈	—	4	1	no	—
695	Q₈	—	4	1	no	—
696	Q₈	—	4	1	no	—
697	Q₈	—	4	1	no	—
698	Q₈	—	4	1	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	2	no	—
702	D₄	—	2	2	no	—
703	D₄	—	4	8	no	—
704	D₄	—	4	1	no	—
705	D₄	—	4	1	no	—
706	D₄	—	4	1	no	—
707	D₄	—	4	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	C₁₃×#121	1	2	yes	—
745	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
747	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
748	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
749	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
750	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
751	C₈	—	2	2	no	—
752	C₈	—	4	1	no	—
753	C₈	—	4	1	no	—
754	C₈	—	4	1	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	16	no	—
769	C₂²	—	8	1	no	—
770	C₂²	—	8	1	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
778	C₂²	D₄²×C₁₃	1	1	yes	characteristic
779	C₂²	C₁₃×#546	1	1	yes	characteristic
780	C₂²	C₁₃×#575	1	1	yes	characteristic
781	C₂²	C₁₃×#575	1	1	yes	characteristic
782	C₂²	C₁₃×#577	1	1	yes	characteristic
783	C₂²	C₁₃×#577	1	1	yes	characteristic
784	C₄	—	2	2	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	2	no	—
792	C₄	—	8	1	no	—
793	C₄	—	8	1	no	—
794	C₄	—	8	1	no	—
795	C₄	C₁₃×#525	1	1	yes	characteristic
796	C₄	C₁₃×#538	1	1	yes	characteristic
797	C₄	D₄²×C₁₃	1	1	yes	characteristic
798	C₄	C₁₃×#546	1	1	yes	characteristic
799	C₂	—	4	2	no	—
800	C₂	—	8	2	no	—
801	C₂	—	8	2	no	—
802	C₂	C₁₃×#2424	1	1	yes	characteristic
803	C₂	C₁₃×#3040	1	1	yes	characteristic
804	C₂	C₁₃×#3043	1	1	yes	characteristic
805	C₂	C₁₃×#3267	1	1	yes	characteristic
806	C₂	C₁₃×#3275	1	1	yes	characteristic
807	C₂	C₁₃×#3311	1	1	yes	characteristic
808	C₂	C₁₃×#3323	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#470	C₂	semidirect
2. C₂×C₁₃×#464	C₂	semidirect
6. C₁₃×#2362	C₂	semidirect
7. C₁₃×#2065	C₂	semidirect
8. C₁₃×#2055	C₂	semidirect
9. C₁₃×#2042	C₂	semidirect
10. C₁₃×#2015	C₂	semidirect
11. C₁₃×#1983	C₂	semidirect
12. C₁₃×#1926	C₂	semidirect
13. C₁₃×#1880	C₂	semidirect
14. C₁₃×#1873	C₂	semidirect
15. C₁₃×#1851	C₂	semidirect
17. C₂²×C₁₃×Q₁₆	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
30. C₂×C₁₃×#106	C₂²	semidirect
31. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
32. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
34. C₂×C₁₃×#103	C₂²	semidirect
35. C₂×C₁₃×#103	C₂²	semidirect
36. C₂×C₁₃×#103	C₂²	semidirect
37. C₂×C₁₃×#103	C₂²	semidirect
47. C₁₃×#391	C₂²	semidirect
50. C₁₃×#389	C₂²	semidirect
57. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
59. C₁₃×#340	C₂²	semidirect
60. C₁₃×#340	C₂²	semidirect
61. C₁₃×#336	C₂²	semidirect
62. C₁₃×#336	C₂²	semidirect
150. #25105	C₁₃	direct (N × H)
258. C₂×#470	C₂×C₁₃	semidirect
259. C₂×#464	C₂×C₁₃	semidirect
263. #2362	C₂×C₁₃	semidirect
264. #2065	C₂×C₁₃	semidirect
265. #2055	C₂×C₁₃	semidirect
266. #2042	C₂×C₁₃	semidirect
267. #2015	C₂×C₁₃	semidirect
268. #1983	C₂×C₁₃	semidirect
269. #1926	C₂×C₁₃	semidirect
270. #1880	C₂×C₁₃	semidirect
271. #1873	C₂×C₁₃	semidirect
272. #1851	C₂×C₁₃	semidirect
367. C₂²×Q₁₆	C₂²×C₁₃	semidirect
375. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
380. C₂×#106	C₂²×C₁₃	semidirect
381. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
382. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
384. C₂×#103	C₂²×C₁₃	semidirect
385. C₂×#103	C₂²×C₁₃	semidirect
386. C₂×#103	C₂²×C₁₃	semidirect
387. C₂×#103	C₂²×C₁₃	semidirect
397. #391	C₂²×C₁₃	semidirect
400. #389	C₂²×C₁₃	semidirect
407. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
409. #340	C₂²×C₁₃	semidirect
410. #340	C₂²×C₁₃	semidirect
411. #336	C₂²×C₁₃	semidirect
412. #336	C₂²×C₁₃	semidirect
661. C₁₃	#25105	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×#470	2
C₂×C₁₃×#464	2
C₂×C₁₃×#450	2
C₂×C₁₃×#418	2
C₁₃×#2435	2
C₁₃×#2362	2
C₁₃×#2065	2
C₁₃×#2055	2
C₁₃×#2042	2
C₁₃×#2015	2
C₁₃×#1983	2
C₁₃×#1926	2
C₁₃×#1880	2
C₁₃×#1873	2
C₁₃×#1851	2
#25105	13

Subgroups — C13×#25105 #15711444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25105 #15711444