Subgroups — C₁₃×#26102 #15712441

Order 3328.

708 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1921	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#125	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#106	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
32	C₁₃×#398	—	2	1	no	—
33	C₁₃×#398	—	2	1	no	—
34	C₁₃×#390	C₂²	1	1	yes	characteristic
35	C₁₃×#390	C₂²	1	1	yes	characteristic
36	C₁₃×#389	—	2	1	no	—
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#388	—	2	1	no	—
40	C₁₃×#388	—	2	1	no	—
41	C₁₃×#384	C₂²	1	1	yes	characteristic
42	C₁₃×#384	C₂²	1	1	yes	characteristic
43	C₁₃×#384	C₂²	1	1	yes	characteristic
44	C₁₃×#382	C₂²	1	1	yes	characteristic
45	C₁₃×#381	—	2	1	no	—
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
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×D₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#125	—	4	4	no	—
66	C₄×D₄×C₁₃	—	2	2	no	—
67	C₄×D₄×C₁₃	Q₈	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	—	2	1	no	—
92	C₂×C₄²×C₁₃	—	2	1	no	—
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#107	—	2	2	no	—
97	C₁₃×#107	—	4	1	no	—
98	C₁₃×#107	—	4	1	no	—
99	C₁₃×#106	—	2	2	no	—
100	C₁₃×#106	—	4	1	no	—
101	C₁₃×#106	—	4	1	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×C₄⋊C₈	—	2	2	no	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	4	1	no	—
108	C₁₃×#102	—	4	1	no	—
109	C₁₃×#97	—	2	2	no	—
110	C₁₃×#95	—	2	1	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	D₄	1	1	yes	characteristic
118	C₁₃×#95	D₄	1	1	yes	characteristic
119	#26102	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	8	1	no	—
136	C₂²×C₄×C₁₃	—	8	1	no	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	#41	1	2	yes	—
155	C₂×C₈×C₁₃	#41	1	2	yes	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	4	2	no	—
172	C₁₃×C₄⋊C₄	—	4	2	no	—
173	C₁₃×C₄⋊C₄	—	4	2	no	—
174	C₁₃×C₄⋊C₄	—	4	2	no	—
175	C₁₃×C₄⋊C₄	—	4	2	no	—
176	C₁₃×C₄⋊C₄	—	8	1	no	—
177	C₁₃×C₄⋊C₄	—	8	1	no	—
178	C₁₃×C₄⋊C₄	—	8	1	no	—
179	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₁₃×C₂²⋊C₄	—	4	2	no	—
182	C₁₃×C₂²⋊C₄	—	4	2	no	—
183	C₁₃×C₂²⋊C₄	—	8	1	no	—
184	C₁₃×C₂²⋊C₄	—	8	1	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	4	2	no	—
190	C₄²×C₁₃	—	8	1	no	—
191	C₄²×C₁₃	—	8	1	no	—
192	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
193	C₄²×C₁₃	#41	1	2	yes	—
194	#2552	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2357	C₂×C₁₃	1	1	yes	characteristic
196	#2094	C₂×C₁₃	1	1	yes	characteristic
197	#2093	C₂×C₁₃	1	1	yes	characteristic
198	#2067	C₂×C₁₃	1	1	yes	characteristic
199	#2065	C₂×C₁₃	1	1	yes	characteristic
200	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1921	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1847	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1802	C₂×C₁₃	1	1	yes	characteristic
208	#1762	C₂×C₁₃	1	1	yes	characteristic
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	4	1	no	—
211	C₂³×C₁₃	—	4	1	no	—
212	C₂³×C₁₃	—	4	1	no	—
213	C₂³×C₁₃	—	4	1	no	—
214	C₂³×C₁₃	—	4	1	no	—
215	C₂³×C₁₃	—	4	1	no	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	D₄×C₁₃	—	2	2	no	—
218	D₄×C₁₃	—	2	2	no	—
219	D₄×C₁₃	—	4	1	no	—
220	D₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	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	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
257	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
258	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
259	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
260	C₂×C₄×C₁₃	#137	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
267	C₈×C₁₃	—	2	2	no	—
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₂×#125	—	2	1	no	—
272	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
287	#398	—	2	1	no	—
288	#398	—	2	1	no	—
289	#390	C₂²×C₁₃	1	1	yes	characteristic
290	#390	C₂²×C₁₃	1	1	yes	characteristic
291	#389	—	2	1	no	—
292	#389	C₂²×C₁₃	1	1	yes	characteristic
293	#389	C₂²×C₁₃	1	1	yes	characteristic
294	#388	—	2	1	no	—
295	#388	—	2	1	no	—
296	#384	C₂²×C₁₃	1	1	yes	characteristic
297	#384	C₂²×C₁₃	1	1	yes	characteristic
298	#384	C₂²×C₁₃	1	1	yes	characteristic
299	#382	C₂²×C₁₃	1	1	yes	characteristic
300	#381	—	2	1	no	—
301	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
302	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
303	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
304	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
305	C₄×C₂²⋊C₄	—	2	1	no	—
306	#340	C₂²×C₁₃	1	1	yes	characteristic
307	#340	C₂²×C₁₃	1	1	yes	characteristic
308	#340	C₂²×C₁₃	1	1	yes	characteristic
309	#340	C₂²×C₁₃	1	1	yes	characteristic
310	#340	C₂²×C₁₃	1	1	yes	characteristic
311	#340	C₂²×C₁₃	1	1	yes	characteristic
312	#336	C₂²×C₁₃	1	1	yes	characteristic
313	#336	C₂²×C₁₃	1	1	yes	characteristic
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	8	1	no	—
318	C₂²×C₁₃	—	8	1	no	—
319	C₂²×C₁₃	—	8	1	no	—
320	C₂²×C₁₃	—	8	1	no	—
321	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
322	C₂²×C₁₃	#547	1	1	yes	characteristic
323	C₂²×C₁₃	#550	1	1	yes	characteristic
324	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
325	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
326	C₂²×C₁₃	#576	1	1	yes	characteristic
327	C₂²×C₁₃	#577	1	1	yes	characteristic
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	8	1	no	—
336	C₄×C₁₃	—	8	1	no	—
337	C₄×C₁₃	—	8	1	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	1	no	—
340	C₄×C₁₃	—	8	1	no	—
341	C₄×C₁₃	#533	1	1	yes	characteristic
342	C₄×C₁₃	#544	1	1	yes	characteristic
343	C₄×C₁₃	#552	1	1	yes	characteristic
344	C₄×C₁₃	#553	1	1	yes	characteristic
345	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
351	#125	—	4	4	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	Q₈×C₁₃	1	4	yes	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
382	#107	—	2	2	no	—
383	#107	—	4	1	no	—
384	#107	—	4	1	no	—
385	#106	—	2	2	no	—
386	#106	—	4	1	no	—
387	#106	—	4	1	no	—
388	C₄⋊C₈	—	2	2	no	—
389	C₄⋊C₈	—	2	2	no	—
390	C₄⋊C₈	—	2	2	no	—
391	#102	—	2	2	no	—
392	#102	—	2	2	no	—
393	#102	—	4	1	no	—
394	#102	—	4	1	no	—
395	#97	—	2	2	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	D₄×C₁₃	1	1	yes	characteristic
404	#95	D₄×C₁₃	1	1	yes	characteristic
405	C₂×C₁₃	—	8	2	no	—
406	C₂×C₁₃	#2441	1	1	yes	characteristic
407	C₂×C₁₃	#3079	1	1	yes	characteristic
408	C₂×C₁₃	#3081	1	1	yes	characteristic
409	C₂×C₁₃	#3345	1	1	yes	characteristic
410	C₂×C₁₃	#3346	1	1	yes	characteristic
411	C₂×C₁₃	#3399	1	1	yes	characteristic
412	C₂×C₁₃	#3400	1	1	yes	characteristic
413	C₂⁴	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	8	1	no	—
429	C₂²×C₄	—	8	1	no	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	C₁₃×#41	1	2	yes	—
448	C₂×C₈	C₁₃×#41	1	2	yes	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	8	1	no	—
470	C₄⋊C₄	—	8	1	no	—
471	C₄⋊C₄	—	8	1	no	—
472	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	8	1	no	—
477	C₂²⋊C₄	—	8	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	4	2	no	—
483	C₄²	—	8	1	no	—
484	C₄²	—	8	1	no	—
485	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
486	C₄²	C₁₃×#41	1	2	yes	—
487	C₁₃	#26102	1	1	yes	characteristic, direct product factor, Sylow
488	C₂³	—	2	2	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	8	4	no	—
536	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
537	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
538	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
539	C₂×C₄	C₁₃×#137	1	2	yes	—
540	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
541	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
542	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
543	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
544	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
545	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
546	C₈	—	2	2	no	—
547	C₈	—	2	2	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
558	C₂²	C₁₃×#547	1	1	yes	characteristic
559	C₂²	C₁₃×#550	1	1	yes	characteristic
560	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
561	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
562	C₂²	C₁₃×#576	1	1	yes	characteristic
563	C₂²	C₁₃×#577	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	C₁₃×#533	1	1	yes	characteristic
578	C₄	C₁₃×#544	1	1	yes	characteristic
579	C₄	C₁₃×#552	1	1	yes	characteristic
580	C₄	C₁₃×#553	1	1	yes	characteristic
581	C₂	—	8	2	no	—
582	C₂	C₁₃×#2441	1	1	yes	characteristic
583	C₂	C₁₃×#3079	1	1	yes	characteristic
584	C₂	C₁₃×#3081	1	1	yes	characteristic
585	C₂	C₁₃×#3345	1	1	yes	characteristic
586	C₂	C₁₃×#3346	1	1	yes	characteristic
587	C₂	C₁₃×#3399	1	1	yes	characteristic
588	C₂	C₁₃×#3400	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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
1. C₁₃×#2552	C₂	semidirect
7. C₁₃×#1949	C₂	semidirect
8. C₁₃×#1948	C₂	semidirect
9. C₁₃×#1947	C₂	semidirect
10. C₁₃×#1940	C₂	semidirect
11. C₁₃×#1921	C₂	semidirect
12. C₁₃×#1919	C₂	semidirect
13. C₁₃×#1847	C₂	semidirect
119. #26102	C₁₃	direct (N × H)
194. #2552	C₂×C₁₃	semidirect
200. #1949	C₂×C₁₃	semidirect
201. #1948	C₂×C₁₃	semidirect
202. #1947	C₂×C₁₃	semidirect
203. #1940	C₂×C₁₃	semidirect
204. #1921	C₂×C₁₃	semidirect
205. #1919	C₂×C₁₃	semidirect
206. #1847	C₂×C₁₃	semidirect
487. C₁₃	#26102	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×#2552	2
C₁₃×#2357	2
C₁₃×#2094	2
C₁₃×#2093	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#1949	2
C₁₃×#1948	2
C₁₃×#1947	2
C₁₃×#1940	2
C₁₃×#1921	2
C₁₃×#1919	2
C₁₃×#1847	2
C₁₃×#1802	2
C₁₃×#1762	2
#26102	13

Subgroups — C13×#26102 #15712441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26102 #15712441