Subgroups — C₁₃×#26432 #15712771

Order 3328.

748 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2441	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2360	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₁₃×#399	—	2	1	no	—
32	C₁₃×#396	—	2	1	no	—
33	C₁₃×#391	C₂²	1	1	yes	characteristic
34	C₁₃×#389	—	2	1	no	—
35	C₁₃×#389	—	2	1	no	—
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#387	—	2	1	no	—
40	C₁₃×#387	—	2	1	no	—
41	C₁₃×#385	—	2	1	no	—
42	C₁₃×#384	C₂²	1	1	yes	characteristic
43	C₁₃×#380	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#340	C₂²	1	1	yes	characteristic
48	C₁₃×#340	C₂²	1	1	yes	characteristic
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×M₁₆	—	2	2	no	—
63	C₂×C₁₃×M₁₆	—	4	1	no	—
64	C₂×C₁₃×M₁₆	—	4	1	no	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	—	4	1	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	Q₈	1	4	yes	—
73	C₄×Q₈×C₁₃	—	2	2	no	—
74	C₄×Q₈×C₁₃	—	4	1	no	—
75	C₁₃×#117	—	2	2	no	—
76	C₁₃×#117	—	4	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	—	2	1	no	—
102	C₂×C₄²×C₁₃	—	2	1	no	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×#107	—	2	2	no	—
107	C₁₃×#107	—	4	1	no	—
108	C₁₃×C₄⋊C₈	—	4	1	no	—
109	C₁₃×C₄⋊C₈	—	4	1	no	—
110	C₁₃×#103	—	2	2	no	—
111	C₁₃×#103	—	4	1	no	—
112	C₁₃×#103	—	4	1	no	—
113	C₁₃×#103	—	4	1	no	—
114	C₁₃×C₂²⋊C₈	—	2	2	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	D₄	1	1	yes	characteristic
123	C₁₃×#95	D₄	1	1	yes	characteristic
124	#26432	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	4	2	no	—
145	C₂²×C₄×C₁₃	—	4	2	no	—
146	C₂²×C₄×C₁₃	—	8	1	no	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
153	C₂²×C₄×C₁₃	#41	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₁₃×M₁₆	—	4	4	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	4	2	no	—
181	C₁₃×C₄⋊C₄	—	4	2	no	—
182	C₁₃×C₄⋊C₄	—	4	2	no	—
183	C₁₃×C₄⋊C₄	—	4	2	no	—
184	C₁₃×C₄⋊C₄	—	4	2	no	—
185	C₁₃×C₄⋊C₄	—	4	2	no	—
186	C₁₃×C₄⋊C₄	—	8	1	no	—
187	C₁₃×C₄⋊C₄	—	8	1	no	—
188	C₁₃×C₄⋊C₄	—	8	1	no	—
189	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
190	C₁₃×C₄⋊C₄	#41	1	2	yes	—
191	C₁₃×C₄⋊C₄	#41	1	2	yes	—
192	C₁₃×C₂²⋊C₄	—	2	4	no	—
193	C₁₃×C₂²⋊C₄	—	2	2	no	—
194	C₁₃×C₂²⋊C₄	—	4	1	no	—
195	C₁₃×C₂²⋊C₄	—	4	2	no	—
196	C₁₃×C₂²⋊C₄	—	8	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	—	2	1	no	—
201	C₄²×C₁₃	—	4	2	no	—
202	C₄²×C₁₃	—	4	2	no	—
203	C₄²×C₁₃	—	8	1	no	—
204	#2441	C₂×C₁₃	1	1	yes	characteristic
205	#2360	C₂×C₁₃	1	1	yes	characteristic
206	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2087	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#2026	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1989	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1894	C₂×C₁₃	1	1	yes	characteristic
213	#1873	C₂×C₁₃	1	1	yes	characteristic
214	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1852	C₂×C₁₃	1	1	yes	characteristic
216	#1851	C₂×C₁₃	1	1	yes	characteristic
217	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1736	C₂×C₁₃	1	1	yes	characteristic
219	C₂³×C₁₃	—	2	1	no	—
220	C₂³×C₁₃	—	2	1	no	—
221	C₂³×C₁₃	—	2	1	no	—
222	C₂³×C₁₃	—	2	1	no	—
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	—	2	1	no	—
225	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
226	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	Q₈×C₁₃	—	2	2	no	—
228	Q₈×C₁₃	—	2	2	no	—
229	Q₈×C₁₃	—	4	1	no	—
230	Q₈×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	8	4	no	—
273	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
274	C₂×C₄×C₁₃	#137	1	2	yes	—
275	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
281	C₈×C₁₃	—	4	1	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	—	4	1	no	—
284	C₈×C₁₃	—	4	1	no	—
285	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
290	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
300	#399	—	2	1	no	—
301	#396	—	2	1	no	—
302	#391	C₂²×C₁₃	1	1	yes	characteristic
303	#389	—	2	1	no	—
304	#389	—	2	1	no	—
305	#389	C₂²×C₁₃	1	1	yes	characteristic
306	#389	C₂²×C₁₃	1	1	yes	characteristic
307	#389	C₂²×C₁₃	1	1	yes	characteristic
308	#387	—	2	1	no	—
309	#387	—	2	1	no	—
310	#385	—	2	1	no	—
311	#384	C₂²×C₁₃	1	1	yes	characteristic
312	#380	C₂²×C₁₃	1	1	yes	characteristic
313	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	—	2	1	no	—
315	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
316	#340	C₂²×C₁₃	1	1	yes	characteristic
317	#340	C₂²×C₁₃	1	1	yes	characteristic
318	#340	C₂²×C₁₃	1	1	yes	characteristic
319	#340	C₂²×C₁₃	1	1	yes	characteristic
320	#340	C₂²×C₁₃	1	1	yes	characteristic
321	#340	C₂²×C₁₃	1	1	yes	characteristic
322	#340	C₂²×C₁₃	1	1	yes	characteristic
323	#340	C₂²×C₁₃	1	1	yes	characteristic
324	#340	C₂²×C₁₃	1	1	yes	characteristic
325	#340	C₂²×C₁₃	1	1	yes	characteristic
326	#336	C₂²×C₁₃	1	1	yes	characteristic
327	#336	C₂²×C₁₃	1	1	yes	characteristic
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
336	C₂²×C₁₃	#546	1	1	yes	characteristic
337	C₂²×C₁₃	#546	1	1	yes	characteristic
338	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
339	C₂²×C₁₃	#575	1	1	yes	characteristic
340	C₂²×C₁₃	#576	1	1	yes	characteristic
341	C₂²×C₁₃	#578	1	1	yes	characteristic
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	4	1	no	—
345	C₄×C₁₃	—	4	2	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	2	no	—
351	C₄×C₁₃	—	8	1	no	—
352	C₄×C₁₃	—	8	1	no	—
353	C₄×C₁₃	—	8	1	no	—
354	C₄×C₁₃	—	8	1	no	—
355	C₄×C₁₃	#529	1	1	yes	characteristic
356	C₄×C₁₃	#538	1	1	yes	characteristic
357	C₄×C₁₃	#554	1	1	yes	characteristic
358	C₄×C₁₃	#554	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×M₁₆	—	2	2	no	—
363	C₂×M₁₆	—	4	1	no	—
364	C₂×M₁₆	—	4	1	no	—
365	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
369	#125	—	2	2	no	—
370	#125	—	4	1	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	Q₈×C₁₃	1	4	yes	—
373	C₄×Q₈	—	2	2	no	—
374	C₄×Q₈	—	4	1	no	—
375	#117	—	2	2	no	—
376	#117	—	4	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	4	1	no	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
406	#107	—	2	2	no	—
407	#107	—	4	1	no	—
408	C₄⋊C₈	—	4	1	no	—
409	C₄⋊C₈	—	4	1	no	—
410	#103	—	2	2	no	—
411	#103	—	4	1	no	—
412	#103	—	4	1	no	—
413	#103	—	4	1	no	—
414	C₂²⋊C₈	—	2	2	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	D₄×C₁₃	1	1	yes	characteristic
423	#95	D₄×C₁₃	1	1	yes	characteristic
424	C₂×C₁₃	—	4	2	no	—
425	C₂×C₁₃	#2450	1	1	yes	characteristic
426	C₂×C₁₃	#3078	1	1	yes	characteristic
427	C₂×C₁₃	#3083	1	1	yes	characteristic
428	C₂×C₁₃	#3312	1	1	yes	characteristic
429	C₂×C₁₃	#3315	1	1	yes	characteristic
430	C₂×C₁₃	#3322	1	1	yes	characteristic
431	C₂×C₁₃	#3333	1	1	yes	characteristic
432	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	8	1	no	—
454	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
460	C₂²×C₄	C₁₃×#41	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
462	M₁₆	—	4	4	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	8	1	no	—
494	C₄⋊C₄	—	8	1	no	—
495	C₄⋊C₄	—	8	1	no	—
496	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
497	C₄⋊C₄	C₁₃×#41	1	2	yes	—
498	C₄⋊C₄	C₁₃×#41	1	2	yes	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	2	no	—
503	C₂²⋊C₄	—	8	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	4	2	no	—
509	C₄²	—	4	2	no	—
510	C₄²	—	8	1	no	—
511	C₁₃	#26432	1	1	yes	characteristic, direct product factor, Sylow
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
519	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	8	4	no	—
566	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
567	C₂×C₄	C₁₃×#137	1	2	yes	—
568	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
569	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
570	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
571	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
572	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
573	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
586	C₂²	C₁₃×#546	1	1	yes	characteristic
587	C₂²	C₁₃×#546	1	1	yes	characteristic
588	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
589	C₂²	C₁₃×#575	1	1	yes	characteristic
590	C₂²	C₁₃×#576	1	1	yes	characteristic
591	C₂²	C₁₃×#578	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	C₁₃×#529	1	1	yes	characteristic
606	C₄	C₁₃×#538	1	1	yes	characteristic
607	C₄	C₁₃×#554	1	1	yes	characteristic
608	C₄	C₁₃×#554	1	1	yes	characteristic
609	C₂	—	4	2	no	—
610	C₂	C₁₃×#2450	1	1	yes	characteristic
611	C₂	C₁₃×#3078	1	1	yes	characteristic
612	C₂	C₁₃×#3083	1	1	yes	characteristic
613	C₂	C₁₃×#3312	1	1	yes	characteristic
614	C₂	C₁₃×#3315	1	1	yes	characteristic
615	C₂	C₁₃×#3322	1	1	yes	characteristic
616	C₂	C₁₃×#3333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
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
3. C₁₃×#2099	C₂	semidirect
4. C₁₃×#2087	C₂	semidirect
5. C₁₃×#2068	C₂	semidirect
6. C₁₃×#2026	C₂	semidirect
7. C₁₃×#1989	C₂	semidirect
8. C₁₃×#1918	C₂	semidirect
11. C₁₃×#1863	C₂	semidirect
14. C₁₃×#1803	C₂	semidirect
124. #26432	C₁₃	direct (N × H)
206. #2099	C₂×C₁₃	semidirect
207. #2087	C₂×C₁₃	semidirect
208. #2068	C₂×C₁₃	semidirect
209. #2026	C₂×C₁₃	semidirect
210. #1989	C₂×C₁₃	semidirect
211. #1918	C₂×C₁₃	semidirect
214. #1863	C₂×C₁₃	semidirect
217. #1803	C₂×C₁₃	semidirect
511. C₁₃	#26432	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2441	2
C₁₃×#2360	2
C₁₃×#2099	2
C₁₃×#2087	2
C₁₃×#2068	2
C₁₃×#2026	2
C₁₃×#1989	2
C₁₃×#1918	2
C₁₃×#1894	2
C₁₃×#1873	2
C₁₃×#1863	2
C₁₃×#1852	2
C₁₃×#1851	2
C₁₃×#1803	2
C₁₃×#1736	2
#26432	13

Subgroups — C13×#26432 #15712771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26432 #15712771