Subgroups — C₁₃×#26797 #15713136

Order 3328.

916 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	—	2	1	no	—
19	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₁₃×#482	—	2	4	no	—
24	C₁₃×#476	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#394	—	2	1	no	—
41	C₁₃×#393	—	2	1	no	—
42	C₁₃×#390	—	2	1	no	—
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#388	—	2	1	no	—
48	C₁₃×#388	—	2	1	no	—
49	C₁₃×#386	—	2	1	no	—
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	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	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×D₈	—	2	2	no	—
69	C₂×C₁₃×D₈	—	2	2	no	—
70	C₂×C₁₃×D₈	—	4	1	no	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	—	2	2	no	—
76	C₁₃×C₄⋊Q₈	—	4	1	no	—
77	C₁₃×#124	—	4	4	no	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	—	2	2	no	—
80	C₁₃×#121	—	2	2	no	—
81	C₁₃×#121	—	4	1	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	4	1	no	—
84	C₁₃×#117	—	2	2	no	—
85	C₁₃×#117	—	4	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	—	2	1	no	—
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#107	—	2	2	no	—
113	C₁₃×#107	—	4	1	no	—
114	C₁₃×#106	—	2	2	no	—
115	C₁₃×#106	—	2	2	no	—
116	C₁₃×#106	D₄	1	4	yes	complemented
117	C₁₃×C₄⋊C₈	—	2	2	no	—
118	C₁₃×#102	—	2	2	no	—
119	C₁₃×#102	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₁₃×C₂²⋊C₈	—	2	2	no	—
125	C₁₃×C₂²⋊C₈	—	2	2	no	—
126	C₄×C₈×C₁₃	—	2	2	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	D₄	1	1	yes	characteristic
132	C₁₃×#95	D₄	1	1	yes	characteristic
133	#26797	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	—	2	1	no	—
135	C₂⁴×C₁₃	—	2	1	no	—
136	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	—	4	2	no	—
138	C₂×Q₈×C₁₃	—	4	2	no	—
139	C₂×Q₈×C₁₃	—	8	1	no	—
140	C₂×D₄×C₁₃	—	2	4	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	4	2	no	—
153	C₂×D₄×C₁₃	—	4	2	no	—
154	C₂×D₄×C₁₃	—	8	1	no	—
155	C₂×D₄×C₁₃	—	8	1	no	—
156	C₂×D₄×C₁₃	—	8	1	no	—
157	C₂×D₄×C₁₃	#41	1	2	yes	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	4	2	no	—
171	C₂²×C₄×C₁₃	—	4	2	no	—
172	C₂²×C₄×C₁₃	—	8	1	no	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₁₃×D₈	—	4	4	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₁₃	#41	1	2	yes	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	4	2	no	—
202	C₁₃×C₄⋊C₄	—	8	1	no	—
203	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
204	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
205	C₁₃×C₄⋊C₄	#41	1	2	yes	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₁₃×C₂²⋊C₄	—	2	2	no	—
209	C₁₃×C₂²⋊C₄	—	4	2	no	—
210	C₁₃×C₂²⋊C₄	—	4	2	no	—
211	C₁₃×C₂²⋊C₄	—	4	2	no	—
212	C₁₃×C₂²⋊C₄	—	4	2	no	—
213	C₁₃×C₂²⋊C₄	—	4	2	no	—
214	C₁₃×C₂²⋊C₄	—	4	2	no	—
215	C₁₃×C₂²⋊C₄	—	4	2	no	—
216	C₁₃×C₂²⋊C₄	—	4	2	no	—
217	C₁₃×C₂²⋊C₄	—	8	1	no	—
218	C₁₃×C₂²⋊C₄	—	8	1	no	—
219	C₄²×C₁₃	—	2	1	no	—
220	C₄²×C₁₃	—	2	1	no	—
221	C₄²×C₁₃	—	2	1	no	—
222	C₄²×C₁₃	—	2	1	no	—
223	C₄²×C₁₃	—	4	2	no	—
224	C₄²×C₁₃	—	4	2	no	—
225	C₄²×C₁₃	—	8	1	no	—
226	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2491	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#2363	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2057	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1999	C₂×C₁₃	1	1	yes	characteristic
234	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#1923	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	1	no	—
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	2	1	no	—
248	C₂³×C₁₃	—	2	1	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	—	8	4	no	—
264	D₄×C₁₃	—	2	2	no	—
265	D₄×C₁₃	—	2	2	no	—
266	D₄×C₁₃	—	4	1	no	—
267	D₄×C₁₃	—	4	1	no	—
268	D₄×C₁₃	—	4	1	no	—
269	D₄×C₁₃	—	4	1	no	—
270	D₄×C₁₃	—	4	1	no	—
271	D₄×C₁₃	—	4	1	no	—
272	D₄×C₁₃	—	8	4	no	—
273	D₄×C₁₃	—	8	4	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
310	C₂×C₄×C₁₃	#135	1	2	yes	—
311	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
312	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
318	C₈×C₁₃	—	2	2	no	—
319	C₈×C₁₃	—	2	2	no	—
320	C₈×C₁₃	—	4	1	no	—
321	C₈×C₁₃	—	4	1	no	—
322	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#124	—	2	1	no	—
325	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
329	#482	—	2	4	no	—
330	#476	—	2	4	no	—
331	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
346	#394	—	2	1	no	—
347	#393	—	2	1	no	—
348	#390	—	2	1	no	—
349	#390	C₂²×C₁₃	1	1	yes	characteristic
350	#390	C₂²×C₁₃	1	1	yes	characteristic
351	#390	C₂²×C₁₃	1	1	yes	characteristic
352	#389	C₂²×C₁₃	1	1	yes	characteristic
353	#388	—	2	1	no	—
354	#388	—	2	1	no	—
355	#386	—	2	1	no	—
356	#380	C₂²×C₁₃	1	1	yes	characteristic
357	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
358	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
359	C₄×C₂²⋊C₄	—	2	1	no	—
360	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
361	#340	C₂²×C₁₃	1	1	yes	characteristic
362	#340	C₂²×C₁₃	1	1	yes	characteristic
363	#340	C₂²×C₁₃	1	1	yes	characteristic
364	#340	C₂²×C₁₃	1	1	yes	characteristic
365	#336	C₂²×C₁₃	1	1	yes	characteristic
366	#336	C₂²×C₁₃	1	1	yes	characteristic
367	C₂²×C₁₃	—	4	1	no	—
368	C₂²×C₁₃	—	4	1	no	—
369	C₂²×C₁₃	—	4	1	no	—
370	C₂²×C₁₃	—	4	2	no	—
371	C₂²×C₁₃	—	4	1	no	—
372	C₂²×C₁₃	—	4	2	no	—
373	C₂²×C₁₃	—	4	1	no	—
374	C₂²×C₁₃	—	4	2	no	—
375	C₂²×C₁₃	—	4	1	no	—
376	C₂²×C₁₃	—	4	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	—	8	1	no	—
388	C₂²×C₁₃	#525	1	1	yes	characteristic
389	C₂²×C₁₃	D₄²	1	1	yes	characteristic
390	C₂²×C₁₃	#547	1	1	yes	characteristic
391	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
392	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₂²×C₁₃	#576	1	1	yes	characteristic
394	C₂²×C₁₃	#577	1	1	yes	characteristic
395	C₄×C₁₃	—	2	2	no	—
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	4	1	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	—	4	1	no	—
400	C₄×C₁₃	—	4	1	no	—
401	C₄×C₁₃	—	4	2	no	—
402	C₄×C₁₃	—	4	2	no	—
403	C₄×C₁₃	—	8	1	no	—
404	C₄×C₁₃	—	8	1	no	—
405	C₄×C₁₃	—	8	1	no	—
406	C₄×C₁₃	#532	1	1	yes	characteristic
407	C₄×C₁₃	#542	1	1	yes	characteristic
408	C₄×C₁₃	#548	1	1	yes	characteristic
409	C₄×C₁₃	#551	1	1	yes	characteristic
410	C₂²×Q₈	—	2	1	no	—
411	C₂²×D₄	—	2	1	no	—
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂³×C₄	—	2	1	no	—
416	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×D₈	—	2	2	no	—
418	C₂×D₈	—	2	2	no	—
419	C₂×D₈	—	4	1	no	—
420	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄⋊Q₈	—	2	2	no	—
425	C₄⋊Q₈	—	4	1	no	—
426	#124	—	4	4	no	—
427	#121	—	2	2	no	—
428	#121	—	2	2	no	—
429	#121	—	2	2	no	—
430	#121	—	4	1	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	4	1	no	—
433	#117	—	2	2	no	—
434	#117	—	4	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	—	2	1	no	—
459	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
461	#107	—	2	2	no	—
462	#107	—	4	1	no	—
463	#106	—	2	2	no	—
464	#106	—	2	2	no	—
465	#106	D₄×C₁₃	1	4	yes	complemented
466	C₄⋊C₈	—	2	2	no	—
467	#102	—	2	2	no	—
468	#102	—	2	2	no	—
469	#102	—	2	2	no	—
470	#102	—	2	2	no	—
471	#102	—	2	2	no	—
472	#102	—	2	2	no	—
473	C₂²⋊C₈	—	2	2	no	—
474	C₂²⋊C₈	—	2	2	no	—
475	C₄×C₈	—	2	2	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	#95	D₄×C₁₃	1	1	yes	characteristic
481	#95	D₄×C₁₃	1	1	yes	characteristic
482	C₂×C₁₃	—	8	1	no	—
483	C₂×C₁₃	—	8	2	no	—
484	C₂×C₁₃	—	16	1	no	—
485	C₂×C₁₃	#2461	1	1	yes	characteristic
486	C₂×C₁₃	#3106	1	1	yes	characteristic
487	C₂×C₁₃	#3118	1	1	yes	characteristic
488	C₂×C₁₃	#3274	1	1	yes	characteristic
489	C₂×C₁₃	#3282	1	1	yes	characteristic
490	C₂×C₁₃	#3341	1	1	yes	characteristic
491	C₂×C₁₃	#3345	1	1	yes	characteristic
492	C₂⁴	—	2	1	no	—
493	C₂⁴	—	2	1	no	—
494	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂×Q₈	—	4	2	no	—
496	C₂×Q₈	—	4	2	no	—
497	C₂×Q₈	—	8	1	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	8	1	no	—
513	C₂×D₄	—	8	1	no	—
514	C₂×D₄	—	8	1	no	—
515	C₂×D₄	C₁₃×#41	1	2	yes	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	8	1	no	—
531	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
537	D₈	—	4	4	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
549	C₂×C₈	C₁₃×#41	1	2	yes	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	—	8	1	no	—
561	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
562	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
563	C₄⋊C₄	C₁₃×#41	1	2	yes	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	8	1	no	—
576	C₂²⋊C₄	—	8	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	4	2	no	—
582	C₄²	—	4	2	no	—
583	C₄²	—	8	1	no	—
584	C₁₃	#26797	1	1	yes	characteristic, direct product factor, Sylow
585	C₂³	—	2	2	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	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	—	4	1	no	—
606	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
607	Q₈	—	8	4	no	—
608	D₄	—	2	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	4	1	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	1	no	—
616	D₄	—	8	4	no	—
617	D₄	—	8	4	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	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	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	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	—	8	4	no	—
654	C₂×C₄	C₁₃×#135	1	2	yes	—
655	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
656	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
657	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
658	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
659	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
660	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
662	C₈	—	2	2	no	—
663	C₈	—	2	2	no	—
664	C₈	—	4	1	no	—
665	C₈	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	4	2	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	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	C₁₃×#525	1	1	yes	characteristic
688	C₂²	D₄²×C₁₃	1	1	yes	characteristic
689	C₂²	C₁₃×#547	1	1	yes	characteristic
690	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
691	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
692	C₂²	C₁₃×#576	1	1	yes	characteristic
693	C₂²	C₁₃×#577	1	1	yes	characteristic
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	1	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	C₁₃×#532	1	1	yes	characteristic
706	C₄	C₁₃×#542	1	1	yes	characteristic
707	C₄	C₁₃×#548	1	1	yes	characteristic
708	C₄	C₁₃×#551	1	1	yes	characteristic
709	C₂	—	8	1	no	—
710	C₂	—	8	2	no	—
711	C₂	—	16	1	no	—
712	C₂	C₁₃×#2461	1	1	yes	characteristic
713	C₂	C₁₃×#3106	1	1	yes	characteristic
714	C₂	C₁₃×#3118	1	1	yes	characteristic
715	C₂	C₁₃×#3274	1	1	yes	characteristic
716	C₂	C₁₃×#3282	1	1	yes	characteristic
717	C₂	C₁₃×#3341	1	1	yes	characteristic
718	C₂	C₁₃×#3345	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#1999	C₂
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×#482	C₂	semidirect
2. C₂×C₁₃×#476	C₂	semidirect
3. C₁₃×#2491	C₂	semidirect
4. C₁₃×#2363	C₂	semidirect
5. C₁₃×#2065	C₂	semidirect
6. C₁₃×#2057	C₂	semidirect
7. C₁₃×#2034	C₂	semidirect
9. C₁₃×#1970	C₂	semidirect
10. C₁₃×#1926	C₂	semidirect
11. C₁₃×#1925	C₂	semidirect
12. C₁₃×#1923	C₂	semidirect
13. C₁₃×#1879	C₂	semidirect
14. C₁₃×#1854	C₂	semidirect
15. C₄×C₁₃×#106	C₂	semidirect
116. C₁₃×#106	D₄	semidirect
133. #26797	C₁₃	direct (N × H)
226. C₂×#482	C₂×C₁₃	semidirect
227. C₂×#476	C₂×C₁₃	semidirect
228. #2491	C₂×C₁₃	semidirect
229. #2363	C₂×C₁₃	semidirect
230. #2065	C₂×C₁₃	semidirect
231. #2057	C₂×C₁₃	semidirect
232. #2034	C₂×C₁₃	semidirect
234. #1970	C₂×C₁₃	semidirect
235. #1926	C₂×C₁₃	semidirect
236. #1925	C₂×C₁₃	semidirect
237. #1923	C₂×C₁₃	semidirect
238. #1879	C₂×C₁₃	semidirect
239. #1854	C₂×C₁₃	semidirect
240. C₄×#106	C₂×C₁₃	semidirect
465. #106	D₄×C₁₃	semidirect
584. C₁₃	#26797	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×#482	2
C₂×C₁₃×#476	2
C₁₃×#2491	2
C₁₃×#2363	2
C₁₃×#2065	2
C₁₃×#2057	2
C₁₃×#2034	2
C₁₃×#1999	2
C₁₃×#1970	2
C₁₃×#1926	2
C₁₃×#1925	2
C₁₃×#1923	2
C₁₃×#1879	2
C₁₃×#1854	2
C₄×C₁₃×#106	2
#26797	13

Subgroups — C13×#26797 #15713136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26797 #15713136