Subgroups — C₁₃×#22444 #15708783

Order 3328.

1434 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#137	—	2	4	no	—
19	C₂×C₁₃×#137	—	2	4	no	—
20	C₂×C₁₃×#137	C₄	1	8	yes	complemented
21	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#440	—	2	4	no	—
31	C₄×C₁₃×SD₁₆	—	2	4	no	—
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#391	—	2	1	no	—
46	C₁₃×#391	—	2	1	no	—
47	C₁₃×#391	C₂²	1	1	yes	characteristic
48	C₁₃×#391	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#391	C₂²	1	1	yes	characteristic
51	C₁₃×#386	—	2	1	no	—
52	C₁₃×#386	—	2	1	no	—
53	C₁₃×#381	—	2	1	no	—
54	C₁₃×#380	—	2	1	no	—
55	C₁₃×#380	C₂²	1	1	yes	characteristic
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#95	—	2	1	no	—
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#340	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₁₃×#336	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	4	1	no	—
68	C₂×C₁₃×#41	—	4	1	no	—
69	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
70	C₂²×Q₈×C₁₃	—	2	1	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	C₂×C₄	1	4	yes	complemented
77	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	—	2	1	no	—
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#137	—	2	32	no	—
88	C₂×C₁₃×Q₁₆	—	2	2	no	—
89	C₂×C₁₃×Q₁₆	—	2	2	no	—
90	C₂×C₁₃×Q₁₆	—	2	2	no	—
91	C₂×C₁₃×Q₁₆	—	2	2	no	—
92	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	complemented
93	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	complemented
94	C₂×C₁₃×SD₁₆	—	2	2	no	—
95	C₂×C₁₃×SD₁₆	—	2	2	no	—
96	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
97	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
98	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
99	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
100	C₂×C₁₃×M₁₆	—	2	2	no	—
101	C₂×C₁₃×M₁₆	—	2	2	no	—
102	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	complemented
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	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	—	2	2	no	—
109	C₄×Q₈×C₁₃	—	4	1	no	—
110	C₄×Q₈×C₁₃	—	4	1	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	—	2	2	no	—
113	C₄×D₄×C₁₃	—	4	1	no	—
114	C₄×D₄×C₁₃	—	4	1	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
126	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	—	2	1	no	—
128	C₂×C₄²×C₁₃	—	2	1	no	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₁₃×#107	—	2	2	no	—
132	C₁₃×#106	—	2	2	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	4	1	no	—
136	C₁₃×#103	—	4	1	no	—
137	C₁₃×#103	—	4	1	no	—
138	C₁₃×#103	—	4	1	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×C₂²⋊C₈	—	2	2	no	—
142	C₁₃×#97	—	2	2	no	—
143	C₄×C₈×C₁₃	—	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	—	2	1	no	—
149	C₁₃×#95	—	2	1	no	—
150	C₁₃×#95	—	2	1	no	—
151	C₁₃×#95	—	2	1	no	—
152	C₁₃×#95	—	2	1	no	—
153	C₁₃×#95	—	2	1	no	—
154	C₁₃×#95	D₄	1	1	yes	characteristic
155	C₁₃×#95	D₄	1	1	yes	characteristic
156	#22444	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂⁴×C₁₃	—	2	1	no	—
158	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₁₃×#41	—	2	8	no	—
160	C₁₃×#41	—	4	4	no	—
161	C₁₃×#41	—	4	4	no	—
162	C₁₃×#41	—	4	4	no	—
163	C₂×Q₈×C₁₃	—	2	4	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	8	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	1	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	—	4	2	no	—
179	C₂×Q₈×C₁₃	—	4	2	no	—
180	C₂×Q₈×C₁₃	—	4	4	no	—
181	C₂×Q₈×C₁₃	—	4	4	no	—
182	C₂×Q₈×C₁₃	—	4	4	no	—
183	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
184	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
185	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
186	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
187	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	4	2	no	—
194	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
195	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
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	—	2	4	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	4	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	4	2	no	—
211	C₂²×C₄×C₁₃	—	4	2	no	—
212	C₂²×C₄×C₁₃	—	4	2	no	—
213	C₂²×C₄×C₁₃	—	4	2	no	—
214	C₂²×C₄×C₁₃	—	4	2	no	—
215	C₂²×C₄×C₁₃	—	4	2	no	—
216	C₂²×C₄×C₁₃	—	4	2	no	—
217	C₂²×C₄×C₁₃	—	4	2	no	—
218	C₂²×C₄×C₁₃	—	8	1	no	—
219	C₂²×C₄×C₁₃	—	8	1	no	—
220	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	#41	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₁₃×Q₁₆	—	2	8	no	—
229	C₁₃×Q₁₆	—	2	8	no	—
230	C₁₃×SD₁₆	—	2	8	no	—
231	C₁₃×SD₁₆	C₂²⋊C₄	1	16	yes	complemented
232	C₁₃×M₁₆	—	2	8	no	—
233	C₂×C₈×C₁₃	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	no	—
238	C₂×C₈×C₁₃	—	2	1	no	—
239	C₂×C₈×C₁₃	—	2	1	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
242	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
243	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
244	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
245	C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	4	2	no	—
254	C₁₃×C₄⋊C₄	—	4	2	no	—
255	C₁₃×C₂²⋊C₄	—	2	2	no	—
256	C₁₃×C₂²⋊C₄	—	4	1	no	—
257	C₁₃×C₂²⋊C₄	—	4	2	no	—
258	C₁₃×C₂²⋊C₄	—	4	2	no	—
259	C₁₃×C₂²⋊C₄	—	4	2	no	—
260	C₁₃×C₂²⋊C₄	—	8	1	no	—
261	C₄²×C₁₃	—	2	1	no	—
262	C₄²×C₁₃	—	2	1	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	—	4	2	no	—
266	C₄²×C₁₃	—	4	2	no	—
267	C₂²×#137	C₂×C₁₃	1	1	yes	characteristic
268	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
270	Q₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2339	C₂×C₁₃	1	1	yes	characteristic
272	#1971	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1788	C₂×C₁₃	1	1	yes	characteristic
280	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂³×C₁₃	—	2	2	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	1	no	—
286	C₂³×C₁₃	—	2	1	no	—
287	C₂³×C₁₃	—	2	1	no	—
288	C₂³×C₁₃	—	2	1	no	—
289	C₂³×C₁₃	—	2	1	no	—
290	C₂³×C₁₃	—	2	1	no	—
291	C₂³×C₁₃	—	4	1	no	—
292	C₂³×C₁₃	—	4	1	no	—
293	C₂³×C₁₃	—	4	1	no	—
294	C₂³×C₁₃	—	4	1	no	—
295	C₂³×C₁₃	C₄×D₄	1	2	yes	—
296	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₁₃	—	2	2	no	—
298	Q₈×C₁₃	—	2	2	no	—
299	Q₈×C₁₃	—	2	2	no	—
300	Q₈×C₁₃	—	2	2	no	—
301	Q₈×C₁₃	—	2	2	no	—
302	Q₈×C₁₃	—	2	2	no	—
303	Q₈×C₁₃	—	2	2	no	—
304	Q₈×C₁₃	—	4	8	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	C₂×C₂²⋊C₄	1	4	yes	—
310	D₄×C₁₃	—	2	2	no	—
311	D₄×C₁₃	—	2	2	no	—
312	D₄×C₁₃	—	2	2	no	—
313	D₄×C₁₃	—	4	8	no	—
314	D₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	1	no	—
321	C₂×C₄×C₁₃	—	2	1	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	2	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	1	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	—	4	8	no	—
338	C₂×C₄×C₁₃	—	4	8	no	—
339	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
356	C₂×C₄×C₁₃	—	8	4	no	—
357	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
358	C₂×C₄×C₁₃	#137	1	2	yes	complemented
359	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
363	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
365	C₈×C₁₃	—	2	2	no	—
366	C₈×C₁₃	—	4	1	no	—
367	C₈×C₁₃	—	4	1	no	—
368	C₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
369	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
370	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#137	—	2	4	no	—
372	C₂×#137	—	2	4	no	—
373	C₂×#137	C₄×C₁₃	1	8	yes	complemented
374	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
383	#440	—	2	4	no	—
384	C₄×SD₁₆	—	2	4	no	—
385	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
398	#391	—	2	1	no	—
399	#391	—	2	1	no	—
400	#391	C₂²×C₁₃	1	1	yes	characteristic
401	#391	C₂²×C₁₃	1	1	yes	characteristic
402	#391	C₂²×C₁₃	1	1	yes	characteristic
403	#391	C₂²×C₁₃	1	1	yes	characteristic
404	#386	—	2	1	no	—
405	#386	—	2	1	no	—
406	#381	—	2	1	no	—
407	#380	—	2	1	no	—
408	#380	C₂²×C₁₃	1	1	yes	characteristic
409	#380	C₂²×C₁₃	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	—	2	1	no	—
411	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#95	—	2	1	no	—
413	#340	C₂²×C₁₃	1	1	yes	characteristic
414	#340	C₂²×C₁₃	1	1	yes	characteristic
415	#336	C₂²×C₁₃	1	1	yes	characteristic
416	#336	C₂²×C₁₃	1	1	yes	characteristic
417	C₂²×C₁₃	—	2	2	no	—
418	C₂²×C₁₃	—	2	4	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	1	no	—
425	C₂²×C₁₃	—	4	1	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	1	no	—
429	C₂²×C₁₃	—	4	1	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
432	C₂²×C₁₃	D₄²	1	1	yes	characteristic
433	C₂²×C₁₃	D₄²	1	1	yes	characteristic
434	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
435	C₂²×C₁₃	#575	1	1	yes	characteristic
436	C₂²×C₁₃	#577	1	1	yes	characteristic
437	C₂²×C₁₃	#578	1	1	yes	characteristic
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	2	4	no	—
440	C₄×C₁₃	—	2	2	no	—
441	C₄×C₁₃	—	4	2	no	—
442	C₄×C₁₃	—	4	2	no	—
443	C₄×C₁₃	—	4	1	no	—
444	C₄×C₁₃	—	4	1	no	—
445	C₄×C₁₃	—	4	1	no	—
446	C₄×C₁₃	—	8	1	no	—
447	C₄×C₁₃	—	8	1	no	—
448	C₄×C₁₃	—	8	1	no	—
449	C₄×C₁₃	—	8	1	no	—
450	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
451	C₄×C₁₃	#518	1	1	yes	characteristic
452	C₄×C₁₃	#546	1	1	yes	characteristic
453	C₄×C₁₃	#546	1	1	yes	characteristic
454	C₂×#41	—	2	2	no	—
455	C₂×#41	—	2	2	no	—
456	C₂×#41	—	2	2	no	—
457	C₂×#41	—	4	1	no	—
458	C₂×#41	—	4	1	no	—
459	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
460	C₂²×Q₈	—	2	1	no	—
461	C₂²×Q₈	—	2	2	no	—
462	C₂²×Q₈	—	2	2	no	—
463	C₂²×Q₈	—	2	2	no	—
464	C₂²×Q₈	—	4	1	no	—
465	C₂²×Q₈	—	4	1	no	—
466	C₂²×Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
467	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	—	2	1	no	—
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
477	#137	—	2	32	no	—
478	C₂×Q₁₆	—	2	2	no	—
479	C₂×Q₁₆	—	2	2	no	—
480	C₂×Q₁₆	—	2	2	no	—
481	C₂×Q₁₆	—	2	2	no	—
482	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
483	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
484	C₂×SD₁₆	—	2	2	no	—
485	C₂×SD₁₆	—	2	2	no	—
486	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
487	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
488	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
489	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
490	C₂×M₁₆	—	2	2	no	—
491	C₂×M₁₆	—	2	2	no	—
492	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
493	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	4	1	no	—
500	C₄×Q₈	—	4	1	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	4	1	no	—
504	C₄×D₄	—	4	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	D₄×C₁₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
521	#107	—	2	2	no	—
522	#106	—	2	2	no	—
523	#103	—	2	2	no	—
524	#103	—	2	2	no	—
525	#103	—	4	1	no	—
526	#103	—	4	1	no	—
527	#103	—	4	1	no	—
528	#103	—	4	1	no	—
529	#102	—	2	2	no	—
530	#102	—	2	2	no	—
531	C₂²⋊C₈	—	2	2	no	—
532	#97	—	2	2	no	—
533	C₄×C₈	—	2	2	no	—
534	#95	—	2	1	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	#95	—	2	1	no	—
538	#95	—	2	1	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	D₄×C₁₃	1	1	yes	characteristic
545	#95	D₄×C₁₃	1	1	yes	characteristic
546	C₂×C₁₃	—	4	2	no	—
547	C₂×C₁₃	—	4	4	no	—
548	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
549	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
550	C₂×C₁₃	#2947	1	1	yes	characteristic
551	C₂×C₁₃	#3266	1	1	yes	characteristic
552	C₂×C₁₃	#3269	1	1	yes	characteristic
553	C₂×C₁₃	#3275	1	1	yes	characteristic
554	C₂×C₁₃	#3276	1	1	yes	characteristic
555	C₂⁴	—	2	1	no	—
556	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
557	#41	—	2	8	no	—
558	#41	—	4	4	no	—
559	#41	—	4	4	no	—
560	#41	—	4	4	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	8	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	—	2	1	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×Q₈	—	4	4	no	—
579	C₂×Q₈	—	4	4	no	—
580	C₂×Q₈	—	4	4	no	—
581	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
582	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
583	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
584	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
585	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	4	2	no	—
592	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
593	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
594	C₂×D₄	C₂×D₄×C₁₃	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	4	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	8	1	no	—
617	C₂²×C₄	—	8	1	no	—
618	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
619	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₁₃×#41	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
626	Q₁₆	—	2	8	no	—
627	Q₁₆	—	2	8	no	—
628	SD₁₆	—	2	8	no	—
629	SD₁₆	C₁₃×C₂²⋊C₄	1	16	yes	complemented
630	M₁₆	—	2	8	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
640	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
641	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
642	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	4	1	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	8	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	4	2	no	—
664	C₄²	—	4	2	no	—
665	C₁₃	#22444	1	1	yes	characteristic, direct product factor, Sylow
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	C₄×D₄×C₁₃	1	2	yes	—
680	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	2	no	—
688	Q₈	—	4	8	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	1	no	—
691	Q₈	—	4	1	no	—
692	Q₈	—	4	1	no	—
693	Q₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	4	8	no	—
698	D₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	8	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	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	—	8	4	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
742	C₂×C₄	C₁₃×#137	1	2	yes	complemented
743	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
746	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
747	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
748	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
749	C₈	—	2	2	no	—
750	C₈	—	4	1	no	—
751	C₈	—	4	1	no	—
752	C₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
768	C₂²	D₄²×C₁₃	1	1	yes	characteristic
769	C₂²	D₄²×C₁₃	1	1	yes	characteristic
770	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
771	C₂²	C₁₃×#575	1	1	yes	characteristic
772	C₂²	C₁₃×#577	1	1	yes	characteristic
773	C₂²	C₁₃×#578	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	4	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	8	1	no	—
783	C₄	—	8	1	no	—
784	C₄	—	8	1	no	—
785	C₄	—	8	1	no	—
786	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
787	C₄	C₁₃×#518	1	1	yes	characteristic
788	C₄	C₁₃×#546	1	1	yes	characteristic
789	C₄	C₁₃×#546	1	1	yes	characteristic
790	C₂	—	4	2	no	—
791	C₂	—	4	4	no	—
792	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
793	C₂	C₄×C₁₃×#137	1	1	yes	characteristic
794	C₂	C₁₃×#2947	1	1	yes	characteristic
795	C₂	C₁₃×#3266	1	1	yes	characteristic
796	C₂	C₁₃×#3269	1	1	yes	characteristic
797	C₂	C₁₃×#3275	1	1	yes	characteristic
798	C₂	C₁₃×#3276	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂×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
2. C₂×C₁₃×#440	C₂	semidirect
3. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
4. Q₈×C₁₃×C₂²⋊C₄	C₂	semidirect
6. C₁₃×#1971	C₂	semidirect
7. C₁₃×#1969	C₂	semidirect
8. C₁₃×#1878	C₂	semidirect
9. C₁₃×#1878	C₂	semidirect
10. C₁₃×#1877	C₂	semidirect
11. C₁₃×#1877	C₂	semidirect
12. C₁₃×#1809	C₂	semidirect
14. C₁₃×#1787	C₂	semidirect
15. C₁₃×#1753	C₂	semidirect
20. C₂×C₁₃×#137	C₄	semidirect
76. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
92. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
93. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
102. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
156. #22444	C₁₃	direct (N × H)
231. C₁₃×SD₁₆	C₂²⋊C₄	semidirect
268. C₂×#440	C₂×C₁₃	semidirect
269. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
270. Q₈×C₂²⋊C₄	C₂×C₁₃	semidirect
272. #1971	C₂×C₁₃	semidirect
273. #1969	C₂×C₁₃	semidirect
274. #1878	C₂×C₁₃	semidirect
275. #1878	C₂×C₁₃	semidirect
276. #1877	C₂×C₁₃	semidirect
277. #1877	C₂×C₁₃	semidirect
278. #1809	C₂×C₁₃	semidirect
280. #1787	C₂×C₁₃	semidirect
281. #1753	C₂×C₁₃	semidirect
358. C₂×C₄×C₁₃	#137	semidirect
373. C₂×#137	C₄×C₁₃	semidirect
466. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
482. C₂×Q₁₆	C₂×C₄×C₁₃	semidirect
483. C₂×Q₁₆	C₂×C₄×C₁₃	semidirect
492. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
629. SD₁₆	C₁₃×C₂²⋊C₄	semidirect
665. C₁₃	#22444	direct (N × H)
742. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#137	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×SD₁₆	2
Q₈×C₁₃×C₂²⋊C₄	2
C₁₃×#2339	2
C₁₃×#1971	2
C₁₃×#1969	2
C₁₃×#1878	2
C₁₃×#1877	2
C₁₃×#1809	2
C₁₃×#1788	2
C₁₃×#1787	2
C₁₃×#1753	2
#22444	13

Subgroups — C13×#22444 #15708783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22444 #15708783