Subgroups — C₁₃×#24305 #15710644

Order 3328.

1162 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2025	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1989	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1874	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1874	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#125	—	2	8	no	—
13	C₂×C₁₃×#125	—	2	1	no	—
14	C₂×C₁₃×#125	—	2	1	no	—
15	C₂×C₁₃×#125	C₂²	1	2	yes	—
16	C₂×C₁₃×#125	C₂²	1	2	yes	—
17	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
21	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#478	—	2	8	no	—
26	C₂×C₁₃×#107	C₂²	1	2	yes	—
27	C₂×C₁₃×#106	C₂²	1	2	yes	—
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₃×#390	C₂²	1	1	yes	characteristic
34	C₁₃×#389	C₂²	1	1	yes	characteristic
35	C₁₃×#388	—	2	1	no	—
36	C₁₃×#386	—	2	1	no	—
37	C₁₃×#380	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₁₃×#125	—	2	8	no	—
56	C₁₃×#125	—	2	8	no	—
57	C₁₃×#125	—	2	4	no	—
58	C₁₃×#125	—	2	4	no	—
59	C₁₃×#125	—	2	4	no	—
60	C₁₃×#125	D₄	1	8	yes	complemented
61	C₁₃×#121	—	2	2	no	—
62	C₁₃×#121	Q₈	1	4	yes	—
63	C₄×D₄×C₁₃	—	2	4	no	—
64	C₄×D₄×C₁₃	—	4	4	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₁₃	—	2	4	no	—
87	C₂×C₄²×C₁₃	—	2	1	no	—
88	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#107	—	2	4	no	—
93	C₁₃×#106	—	2	4	no	—
94	C₁₃×C₄⋊C₈	—	2	4	no	—
95	C₁₃×#102	—	2	4	no	—
96	C₁₃×#102	—	2	4	no	—
97	C₁₃×C₂²⋊C₈	—	2	2	no	—
98	C₁₃×C₂²⋊C₈	—	2	2	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	#24305	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₁₃	—	2	4	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	4	1	no	—
126	C₂²×C₄×C₁₃	—	4	1	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	4	2	no	—
129	C₂²×C₄×C₁₃	—	4	2	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	2	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	2	yes	—
140	C₂²×C₄×C₁₃	#41	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	8	no	—
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	4	2	no	—
160	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
162	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
163	C₁₃×C₂²⋊C₄	—	2	4	no	—
164	C₁₃×C₂²⋊C₄	—	4	2	no	—
165	C₁₃×C₂²⋊C₄	—	4	2	no	—
166	C₁₃×C₂²⋊C₄	—	4	2	no	—
167	C₁₃×C₂²⋊C₄	—	4	2	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	4	2	no	—
172	C₄²×C₁₃	C₂×D₄	1	4	yes	—
173	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂×#478	C₂×C₁₃	1	2	yes	complemented
175	C₄×#121	C₂×C₁₃	1	1	yes	characteristic
176	#2059	C₂×C₁₃	1	2	yes	complemented
177	#2025	C₂×C₁₃	1	2	yes	complemented
178	#1989	C₂×C₁₃	1	2	yes	complemented
179	#1874	C₂×C₁₃	1	1	yes	characteristic
180	#1874	C₂×C₁₃	1	1	yes	characteristic
181	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	4	1	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	—	4	1	no	—
193	C₂³×C₁₃	—	4	1	no	—
194	C₂³×C₁₃	—	4	1	no	—
195	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
196	C₂³×C₁₃	#135	1	2	yes	—
197	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
198	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	D₄×C₁₃	—	2	4	no	—
200	D₄×C₁₃	—	4	8	no	—
201	D₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	4	4	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	8	no	—
222	C₂×C₄×C₁₃	—	4	8	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	8	4	no	—
236	C₂×C₄×C₁₃	#120	1	2	yes	—
237	C₂×C₄×C₁₃	#120	1	2	yes	—
238	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
243	C₈×C₁₃	—	4	2	no	—
244	C₈×C₁₃	—	4	2	no	—
245	C₂×#125	—	2	8	no	—
246	C₂×#125	—	2	1	no	—
247	C₂×#125	—	2	1	no	—
248	C₂×#125	C₂²×C₁₃	1	2	yes	—
249	C₂×#125	C₂²×C₁₃	1	2	yes	—
250	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₄×D₄	—	2	1	no	—
252	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	—	2	1	no	—
254	C₂²×C₄⋊C₄	—	2	1	no	—
255	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
258	#478	—	2	8	no	—
259	C₂×#107	C₂²×C₁₃	1	2	yes	—
260	C₂×#106	C₂²×C₁₃	1	2	yes	—
261	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
262	C₂×#102	C₂²×C₁₃	1	2	yes	—
263	C₂×#102	C₂²×C₁₃	1	2	yes	—
264	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
266	#390	C₂²×C₁₃	1	1	yes	characteristic
267	#389	C₂²×C₁₃	1	1	yes	characteristic
268	#388	—	2	1	no	—
269	#386	—	2	1	no	—
270	#380	C₂²×C₁₃	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
272	C₄×C₂²⋊C₄	—	2	1	no	—
273	#340	C₂²×C₁₃	1	2	yes	—
274	#340	C₂²×C₁₃	1	2	yes	—
275	#340	C₂²×C₁₃	1	2	yes	—
276	#340	C₂²×C₁₃	1	2	yes	—
277	#336	C₂²×C₁₃	1	2	yes	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	8	1	no	—
288	C₂²×C₁₃	—	8	1	no	—
289	C₂²×C₁₃	—	8	1	no	—
290	C₂²×C₁₃	—	8	1	no	—
291	C₂²×C₁₃	#478	1	4	yes	complemented
292	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
293	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
294	C₂²×C₁₃	#536	1	1	yes	characteristic
295	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
296	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₂²×C₁₃	#575	1	1	yes	characteristic
298	C₂²×C₁₃	#575	1	1	yes	characteristic
299	C₄×C₁₃	—	2	2	no	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	4	1	no	—
304	C₄×C₁₃	—	4	4	no	—
305	C₄×C₁₃	—	4	1	no	—
306	C₄×C₁₃	—	4	4	no	—
307	C₄×C₁₃	—	8	1	no	—
308	C₄×C₁₃	—	8	1	no	—
309	C₄×C₁₃	#548	1	2	yes	—
310	C₄×C₁₃	D₄×Q₈	1	2	yes	—
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
317	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
320	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
321	#125	—	2	8	no	—
322	#125	—	2	8	no	—
323	#125	—	2	4	no	—
324	#125	—	2	4	no	—
325	#125	—	2	4	no	—
326	#125	D₄×C₁₃	1	8	yes	complemented
327	#121	—	2	2	no	—
328	#121	Q₈×C₁₃	1	4	yes	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	—	4	4	no	—
331	C₂×C₄⋊C₄	—	2	8	no	—
332	C₂×C₄⋊C₄	—	2	8	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	4	no	—
340	C₂×C₄⋊C₄	—	2	4	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₄²	—	2	4	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
358	#107	—	2	4	no	—
359	#106	—	2	4	no	—
360	C₄⋊C₈	—	2	4	no	—
361	#102	—	2	4	no	—
362	#102	—	2	4	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	C₂²⋊C₈	—	2	2	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	C₂×C₁₃	—	2	4	no	—
369	C₂×C₁₃	—	8	2	no	—
370	C₂×C₁₃	#2409	1	1	yes	characteristic
371	C₂×C₁₃	#3002	1	1	yes	characteristic
372	C₂×C₁₃	#3006	1	1	yes	characteristic
373	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
374	C₂×C₁₃	#3080	1	1	yes	characteristic
375	C₂×C₁₃	#3232	1	1	yes	characteristic
376	C₂×C₁₃	#3234	1	1	yes	characteristic
377	C₂⁴	—	2	1	no	—
378	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
414	C₂²×C₄	C₁₃×#41	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	—	2	8	no	—
427	C₄⋊C₄	—	2	8	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	4	2	no	—
434	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
435	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
436	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	4	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	4	2	no	—
446	C₄²	C₂×D₄×C₁₃	1	4	yes	—
447	C₁₃	#24305	1	1	yes	characteristic, direct product factor, Sylow
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
460	C₂³	C₁₃×#135	1	2	yes	—
461	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
462	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
463	D₄	—	2	4	no	—
464	D₄	—	4	8	no	—
465	D₄	—	4	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	8	4	no	—
500	C₂×C₄	C₁₃×#120	1	2	yes	—
501	C₂×C₄	C₁₃×#120	1	2	yes	—
502	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
504	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
505	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
506	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
507	C₈	—	4	2	no	—
508	C₈	—	4	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	—	8	1	no	—
521	C₂²	—	8	1	no	—
522	C₂²	C₁₃×#478	1	4	yes	complemented
523	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
524	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
525	C₂²	C₁₃×#536	1	1	yes	characteristic
526	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
527	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
528	C₂²	C₁₃×#575	1	1	yes	characteristic
529	C₂²	C₁₃×#575	1	1	yes	characteristic
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	4	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	C₁₃×#548	1	2	yes	—
541	C₄	D₄×Q₈×C₁₃	1	2	yes	—
542	C₂	—	2	4	no	—
543	C₂	—	8	2	no	—
544	C₂	C₁₃×#2409	1	1	yes	characteristic
545	C₂	C₁₃×#3002	1	1	yes	characteristic
546	C₂	C₁₃×#3006	1	1	yes	characteristic
547	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
548	C₂	C₁₃×#3080	1	1	yes	characteristic
549	C₂	C₁₃×#3232	1	1	yes	characteristic
550	C₂	C₁₃×#3234	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#125	C₂	semidirect
2. C₂×C₁₃×#478	C₂	semidirect
4. C₁₃×#2059	C₂	semidirect
5. C₁₃×#2025	C₂	semidirect
6. C₁₃×#1989	C₂	semidirect
9. C₁₃×#1853	C₂	semidirect
10. C₁₃×#1852	C₂	semidirect
11. C₁₃×#1797	C₂	semidirect
60. C₁₃×#125	D₄	semidirect
102. #24305	C₁₃	direct (N × H)
173. C₂²×#125	C₂×C₁₃	semidirect
174. C₂×#478	C₂×C₁₃	semidirect
176. #2059	C₂×C₁₃	semidirect
177. #2025	C₂×C₁₃	semidirect
178. #1989	C₂×C₁₃	semidirect
181. #1853	C₂×C₁₃	semidirect
182. #1852	C₂×C₁₃	semidirect
183. #1797	C₂×C₁₃	semidirect
291. C₂²×C₁₃	#478	semidirect
326. #125	D₄×C₁₃	semidirect
447. C₁₃	#24305	direct (N × H)
522. C₂²	C₁₃×#478	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#125	2
C₂×C₁₃×#478	2
C₄×C₁₃×#121	2
C₁₃×#2059	2
C₁₃×#2025	2
C₁₃×#1989	2
C₁₃×#1874	2
C₁₃×#1853	2
C₁₃×#1852	2
C₁₃×#1797	2
#24305	13

Subgroups — C13×#24305 #15710644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24305 #15710644