Subgroups — C₁₃×#26250 #15712589

Order 3328.

932 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2445	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#123	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#492	—	2	4	no	—
26	C₄×C₁₃×SD₁₆	—	2	4	no	—
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#400	—	2	1	no	—
42	C₁₃×#398	—	2	1	no	—
43	C₁₃×#394	—	2	1	no	—
44	C₁₃×#394	—	2	1	no	—
45	C₁₃×#391	C₂²	1	1	yes	characteristic
46	C₁₃×#391	C₂²	1	1	yes	characteristic
47	C₁₃×#391	C₂²	1	1	yes	characteristic
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#389	C₂²	1	1	yes	characteristic
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#387	—	2	1	no	—
54	C₁₃×#387	—	2	1	no	—
55	C₁₃×#386	—	2	1	no	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×SD₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	—	2	2	no	—
71	C₂×C₁₃×SD₁₆	—	2	2	no	—
72	C₂×C₁₃×SD₁₆	—	2	2	no	—
73	C₂×C₁₃×SD₁₆	—	2	2	no	—
74	C₂×C₁₃×SD₁₆	—	2	2	no	—
75	C₂×C₁₃×SD₁₆	—	2	2	no	—
76	C₂×C₁₃×SD₁₆	—	2	2	no	—
77	C₂×C₁₃×SD₁₆	—	4	1	no	—
78	C₂×C₁₃×SD₁₆	—	4	1	no	—
79	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×C₄⋊Q₈	—	2	2	no	—
85	C₁₃×C₄⋊Q₈	—	4	1	no	—
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#127	—	4	1	no	—
88	C₁₃×#123	—	4	4	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	4	1	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	4	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₄²×C₁₃	—	2	1	no	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₁₃×#106	—	2	2	no	—
116	C₁₃×#106	—	2	2	no	—
117	C₁₃×C₄⋊C₈	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	4	1	no	—
120	C₁₃×#103	—	4	1	no	—
121	C₁₃×#103	—	4	1	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	4	1	no	—
124	C₁₃×#102	—	4	1	no	—
125	C₁₃×#102	—	4	1	no	—
126	C₄×C₈×C₁₃	—	2	2	no	—
127	C₄×C₈×C₁₃	—	2	2	no	—
128	C₄×C₈×C₁₃	—	2	2	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	D₄	1	1	yes	characteristic
138	C₁₃×#95	D₄	1	1	yes	characteristic
139	#26250	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂⁴×C₁₃	—	2	1	no	—
141	C₂⁴×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	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	—	2	1	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	C₂×D₄×C₁₃	—	8	1	no	—
171	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
179	C₂²×C₄×C₁₃	—	4	2	no	—
180	C₂²×C₄×C₁₃	—	8	1	no	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₁₃×SD₁₆	—	2	8	no	—
189	C₁₃×SD₁₆	—	4	4	no	—
190	C₁₃×SD₁₆	—	4	4	no	—
191	C₁₃×SD₁₆	—	4	4	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
201	C₂×C₈×C₁₃	#41	1	2	yes	—
202	C₂×C₈×C₁₃	#41	1	2	yes	—
203	C₂×C₈×C₁₃	#41	1	2	yes	—
204	C₁₃×C₄⋊C₄	—	2	2	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	4	2	no	—
214	C₁₃×C₄⋊C₄	—	4	2	no	—
215	C₁₃×C₄⋊C₄	—	4	2	no	—
216	C₁₃×C₄⋊C₄	—	4	2	no	—
217	C₁₃×C₄⋊C₄	—	4	2	no	—
218	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
219	C₁₃×C₂²⋊C₄	—	4	2	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	4	2	no	—
222	C₁₃×C₂²⋊C₄	—	4	2	no	—
223	C₁₃×C₂²⋊C₄	—	8	1	no	—
224	C₁₃×C₂²⋊C₄	—	8	1	no	—
225	C₁₃×C₂²⋊C₄	—	8	1	no	—
226	C₄²×C₁₃	—	2	1	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	2	1	no	—
229	C₄²×C₁₃	—	2	1	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	4	2	no	—
233	C₂×#492	C₂×C₁₃	1	1	yes	characteristic
234	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2446	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2445	C₂×C₁₃	1	1	yes	characteristic
237	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2041	C₂×C₁₃	1	1	yes	characteristic
241	#1968	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1968	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1968	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
248	C₂³×C₁₃	—	2	2	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	—	4	1	no	—
254	C₂³×C₁₃	—	4	1	no	—
255	C₂³×C₁₃	—	4	1	no	—
256	C₂³×C₁₃	—	4	1	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	Q₈×C₁₃	—	2	2	no	—
264	Q₈×C₁₃	—	2	2	no	—
265	Q₈×C₁₃	—	4	1	no	—
266	Q₈×C₁₃	—	4	1	no	—
267	Q₈×C₁₃	—	4	1	no	—
268	Q₈×C₁₃	—	4	1	no	—
269	Q₈×C₁₃	—	4	1	no	—
270	Q₈×C₁₃	—	4	1	no	—
271	D₄×C₁₃	—	2	2	no	—
272	D₄×C₁₃	—	2	2	no	—
273	D₄×C₁₃	—	4	1	no	—
274	D₄×C₁₃	—	4	1	no	—
275	D₄×C₁₃	—	4	1	no	—
276	D₄×C₁₃	—	4	1	no	—
277	D₄×C₁₃	—	4	1	no	—
278	D₄×C₁₃	—	4	1	no	—
279	D₄×C₁₃	—	8	4	no	—
280	D₄×C₁₃	—	8	4	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	8	4	no	—
314	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
315	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
316	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
317	C₂×C₄×C₁₃	#135	1	2	yes	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
324	C₈×C₁₃	—	2	2	no	—
325	C₈×C₁₃	—	4	1	no	—
326	C₈×C₁₃	—	4	1	no	—
327	C₈×C₁₃	#123	1	4	yes	complemented
328	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
329	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
330	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
331	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#123	—	2	1	no	—
335	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
337	#492	—	2	4	no	—
338	C₄×SD₁₆	—	2	4	no	—
339	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
353	#400	—	2	1	no	—
354	#398	—	2	1	no	—
355	#394	—	2	1	no	—
356	#394	—	2	1	no	—
357	#391	C₂²×C₁₃	1	1	yes	characteristic
358	#391	C₂²×C₁₃	1	1	yes	characteristic
359	#391	C₂²×C₁₃	1	1	yes	characteristic
360	#390	C₂²×C₁₃	1	1	yes	characteristic
361	#390	C₂²×C₁₃	1	1	yes	characteristic
362	#390	C₂²×C₁₃	1	1	yes	characteristic
363	#389	C₂²×C₁₃	1	1	yes	characteristic
364	#389	C₂²×C₁₃	1	1	yes	characteristic
365	#387	—	2	1	no	—
366	#387	—	2	1	no	—
367	#386	—	2	1	no	—
368	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
369	#340	C₂²×C₁₃	1	1	yes	characteristic
370	#340	C₂²×C₁₃	1	1	yes	characteristic
371	#336	C₂²×C₁₃	1	1	yes	characteristic
372	#336	C₂²×C₁₃	1	1	yes	characteristic
373	C₂²×C₁₃	—	4	2	no	—
374	C₂²×C₁₃	—	4	2	no	—
375	C₂²×C₁₃	—	4	2	no	—
376	C₂²×C₁₃	—	8	1	no	—
377	C₂²×C₁₃	—	8	1	no	—
378	C₂²×C₁₃	—	8	1	no	—
379	C₂²×C₁₃	—	8	1	no	—
380	C₂²×C₁₃	—	8	1	no	—
381	C₂²×C₁₃	—	8	1	no	—
382	C₂²×C₁₃	—	8	1	no	—
383	C₂²×C₁₃	—	8	1	no	—
384	C₂²×C₁₃	—	8	1	no	—
385	C₂²×C₁₃	—	8	1	no	—
386	C₂²×C₁₃	—	8	1	no	—
387	C₂²×C₁₃	#532	1	1	yes	characteristic
388	C₂²×C₁₃	D₄²	1	1	yes	characteristic
389	C₂²×C₁₃	#550	1	1	yes	characteristic
390	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
391	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
392	C₂²×C₁₃	#577	1	1	yes	characteristic
393	C₂²×C₁₃	#577	1	1	yes	characteristic
394	C₄×C₁₃	—	2	2	no	—
395	C₄×C₁₃	—	2	2	no	—
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	2	2	no	—
398	C₄×C₁₃	—	4	1	no	—
399	C₄×C₁₃	—	4	2	no	—
400	C₄×C₁₃	—	4	1	no	—
401	C₄×C₁₃	—	8	1	no	—
402	C₄×C₁₃	—	8	1	no	—
403	C₄×C₁₃	—	8	1	no	—
404	C₄×C₁₃	—	8	1	no	—
405	C₄×C₁₃	—	8	1	no	—
406	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
407	C₄×C₁₃	#540	1	1	yes	characteristic
408	C₄×C₁₃	#546	1	1	yes	characteristic
409	C₄×C₁₃	#559	1	1	yes	characteristic
410	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂³×C₄	—	2	1	no	—
417	C₂×SD₁₆	—	2	2	no	—
418	C₂×SD₁₆	—	2	2	no	—
419	C₂×SD₁₆	—	2	2	no	—
420	C₂×SD₁₆	—	2	2	no	—
421	C₂×SD₁₆	—	2	2	no	—
422	C₂×SD₁₆	—	2	2	no	—
423	C₂×SD₁₆	—	2	2	no	—
424	C₂×SD₁₆	—	2	2	no	—
425	C₂×SD₁₆	—	2	2	no	—
426	C₂×SD₁₆	—	4	1	no	—
427	C₂×SD₁₆	—	4	1	no	—
428	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
429	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₄⋊Q₈	—	2	2	no	—
434	C₄⋊Q₈	—	4	1	no	—
435	#127	—	2	2	no	—
436	#127	—	4	1	no	—
437	#123	—	4	4	no	—
438	C₄×Q₈	—	2	2	no	—
439	C₄×Q₈	—	4	1	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	4	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
464	#106	—	2	2	no	—
465	#106	—	2	2	no	—
466	C₄⋊C₈	—	2	2	no	—
467	#103	—	2	2	no	—
468	#103	—	4	1	no	—
469	#103	—	4	1	no	—
470	#103	—	4	1	no	—
471	#102	—	2	2	no	—
472	#102	—	4	1	no	—
473	#102	—	4	1	no	—
474	#102	—	4	1	no	—
475	C₄×C₈	—	2	2	no	—
476	C₄×C₈	—	2	2	no	—
477	C₄×C₈	—	2	2	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	D₄×C₁₃	1	1	yes	characteristic
487	#95	D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₁₃	—	8	2	no	—
489	C₂×C₁₃	—	16	1	no	—
490	C₂×C₁₃	#2445	1	1	yes	characteristic
491	C₂×C₁₃	#3167	1	1	yes	characteristic
492	C₂×C₁₃	#3174	1	1	yes	characteristic
493	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
494	C₂×C₁₃	#3282	1	1	yes	characteristic
495	C₂×C₁₃	#3392	1	1	yes	characteristic
496	C₂×C₁₃	#3394	1	1	yes	characteristic
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	4	2	no	—
525	C₂×D₄	—	4	2	no	—
526	C₂×D₄	—	8	1	no	—
527	C₂×D₄	—	8	1	no	—
528	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	8	1	no	—
538	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
542	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
545	SD₁₆	—	2	8	no	—
546	SD₁₆	—	4	4	no	—
547	SD₁₆	—	4	4	no	—
548	SD₁₆	—	4	4	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
558	C₂×C₈	C₁₃×#41	1	2	yes	—
559	C₂×C₈	C₁₃×#41	1	2	yes	—
560	C₂×C₈	C₁₃×#41	1	2	yes	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	4	2	no	—
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	—	4	2	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	8	1	no	—
581	C₂²⋊C₄	—	8	1	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	4	2	no	—
590	C₁₃	#26250	1	1	yes	characteristic, direct product factor, Sylow
591	C₂³	—	2	2	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
606	Q₈	—	2	2	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	4	1	no	—
609	Q₈	—	4	1	no	—
610	Q₈	—	4	1	no	—
611	Q₈	—	4	1	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	4	1	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	4	1	no	—
617	D₄	—	4	1	no	—
618	D₄	—	4	1	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	1	no	—
621	D₄	—	4	1	no	—
622	D₄	—	8	4	no	—
623	D₄	—	8	4	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	8	4	no	—
657	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
658	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
659	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
660	C₂×C₄	C₁₃×#135	1	2	yes	—
661	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
662	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
663	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
664	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
665	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
667	C₈	—	2	2	no	—
668	C₈	—	4	1	no	—
669	C₈	—	4	1	no	—
670	C₈	C₁₃×#123	1	4	yes	complemented
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	8	1	no	—
682	C₂²	—	8	1	no	—
683	C₂²	—	8	1	no	—
684	C₂²	—	8	1	no	—
685	C₂²	C₁₃×#532	1	1	yes	characteristic
686	C₂²	D₄²×C₁₃	1	1	yes	characteristic
687	C₂²	C₁₃×#550	1	1	yes	characteristic
688	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
689	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
690	C₂²	C₁₃×#577	1	1	yes	characteristic
691	C₂²	C₁₃×#577	1	1	yes	characteristic
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	2	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	—	8	1	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
705	C₄	C₁₃×#540	1	1	yes	characteristic
706	C₄	C₁₃×#546	1	1	yes	characteristic
707	C₄	C₁₃×#559	1	1	yes	characteristic
708	C₂	—	8	2	no	—
709	C₂	—	16	1	no	—
710	C₂	C₁₃×#2445	1	1	yes	characteristic
711	C₂	C₁₃×#3167	1	1	yes	characteristic
712	C₂	C₁₃×#3174	1	1	yes	characteristic
713	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
714	C₂	C₁₃×#3282	1	1	yes	characteristic
715	C₂	C₁₃×#3392	1	1	yes	characteristic
716	C₂	C₁₃×#3394	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
3. C₁₃×#2446	C₂	semidirect
5. C₁₃×#2055	C₂	semidirect
6. C₁₃×#2055	C₂	semidirect
7. C₁₃×#2043	C₂	semidirect
9. C₁₃×#1968	C₂	semidirect
10. C₁₃×#1968	C₂	semidirect
11. C₁₃×#1968	C₂	semidirect
12. C₁₃×#1941	C₂	semidirect
13. C₁₃×#1880	C₂	semidirect
14. C₁₃×#1877	C₂	semidirect
15. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
139. #26250	C₁₃	direct (N × H)
218. C₁₃×C₄⋊C₄	SD₁₆	semidirect
234. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
235. #2446	C₂×C₁₃	semidirect
237. #2055	C₂×C₁₃	semidirect
238. #2055	C₂×C₁₃	semidirect
239. #2043	C₂×C₁₃	semidirect
241. #1968	C₂×C₁₃	semidirect
242. #1968	C₂×C₁₃	semidirect
243. #1968	C₂×C₁₃	semidirect
244. #1941	C₂×C₁₃	semidirect
245. #1880	C₂×C₁₃	semidirect
246. #1877	C₂×C₁₃	semidirect
247. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
327. C₈×C₁₃	#123	semidirect
575. C₄⋊C₄	C₁₃×SD₁₆	semidirect
590. C₁₃	#26250	direct (N × H)
670. C₈	C₁₃×#123	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#492	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2446	2
C₁₃×#2445	2
C₁₃×#2055	2
C₁₃×#2043	2
C₁₃×#2041	2
C₁₃×#1968	2
C₁₃×#1941	2
C₁₃×#1880	2
C₁₃×#1877	2
C₈×C₁₃×C₄⋊C₄	2
#26250	13

Subgroups — C13×#26250 #15712589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26250 #15712589