Subgroups — C₁₃×#17368 #15703707

Order 3328.

1210 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2973	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1467	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1465	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1464	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1463	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1459	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#324	C₂	1	2	yes	maximal, complemented
9	C₂²×C₁₃×#41	C₄	1	1	yes	characteristic
10	C₁₃×#520	—	2	8	no	—
11	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₁₃×#435	—	2	8	no	—
26	C₁₃×#432	C₂²	1	4	yes	—
27	C₁₃×#407	C₂²	1	4	yes	—
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
29	C₁₃×#324	C₂²	1	4	yes	—
30	C₁₃×#324	C₂²	1	4	yes	—
31	C₁₃×#324	C₂²	1	4	yes	—
32	C₁₃×#323	C₂²	1	4	yes	—
33	C₂×C₁₃×#41	—	2	4	no	—
34	C₂×C₁₃×#41	—	2	4	no	—
35	C₂×C₁₃×#41	—	2	4	no	—
36	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	—	2	4	no	—
50	C₂²×C₈×C₁₃	—	2	4	no	—
51	C₄×Q₈×C₁₃	—	2	4	no	—
52	C₄×Q₈×C₁₃	—	2	4	no	—
53	C₄×D₄×C₁₃	—	2	4	no	—
54	C₄×D₄×C₁₃	—	2	4	no	—
55	C₄×D₄×C₁₃	—	2	4	no	—
56	C₄×D₄×C₁₃	—	2	4	no	—
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	D₄	1	8	yes	—
59	C₁₃×#117	—	2	4	no	—
60	C₁₃×#117	—	2	4	no	—
61	C₁₃×#117	—	2	4	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	—	2	4	no	—
88	C₁₃×C₂²⋊C₈	—	2	4	no	—
89	C₁₃×C₂²⋊C₈	—	2	4	no	—
90	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
91	C₁₃×#97	—	2	4	no	—
92	#17368	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₁₃×#41	—	2	32	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	C₂²⋊C₄	1	4	yes	—
108	C₂×D₄×C₁₃	M₁₆	1	4	yes	complemented
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	8	1	no	—
122	C₂²×C₄×C₁₃	—	8	1	no	—
123	C₂²×C₄×C₁₃	—	8	1	no	—
124	C₂²×C₄×C₁₃	—	8	1	no	—
125	C₂²×C₄×C₁₃	—	8	1	no	—
126	C₂²×C₄×C₁₃	—	8	1	no	—
127	C₂²×C₄×C₁₃	M₁₆	1	4	yes	complemented
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₁₃×M₁₆	—	8	4	no	—
143	C₂×C₈×C₁₃	—	2	8	no	—
144	C₂×C₈×C₁₃	—	8	4	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
155	C₁₃×C₂²⋊C₄	—	2	2	no	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₁₃×C₂²⋊C₄	—	2	2	no	—
159	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
160	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	2	2	no	—
163	C₄²×C₁₃	—	2	2	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	C₂×D₄	1	4	yes	—
167	C₂×#520	C₂×C₁₃	1	1	yes	characteristic
168	#2973	C₂×C₁₃	1	2	yes	complemented
169	#1467	C₂×C₁₃	1	2	yes	complemented
170	#1465	C₂×C₁₃	1	2	yes	complemented
171	#1464	C₂×C₁₃	1	2	yes	complemented
172	#1463	C₂×C₁₃	1	2	yes	complemented
173	#1459	C₂×C₁₃	1	2	yes	complemented
174	C₂×#324	C₂×C₁₃	1	2	yes	complemented
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	—	2	1	no	—
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
188	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
189	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
190	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
191	Q₈×C₁₃	—	2	8	no	—
192	D₄×C₁₃	—	2	8	no	—
193	D₄×C₁₃	—	2	8	no	—
194	D₄×C₁₃	—	2	8	no	—
195	C₂×C₄×C₁₃	—	2	8	no	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	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	8	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	8	2	no	—
221	C₂×C₄×C₁₃	—	8	2	no	—
222	C₂×C₄×C₁₃	—	8	2	no	—
223	C₂×C₄×C₁₃	—	8	2	no	—
224	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
225	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₈×C₁₃	—	4	8	no	—
233	C₂²×#41	C₄×C₁₃	1	1	yes	characteristic
234	#520	—	2	8	no	—
235	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
238	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
239	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#117	C₄×C₁₃	1	1	yes	characteristic
244	C₂×#117	C₄×C₁₃	1	1	yes	characteristic
245	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
247	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
249	#435	—	2	8	no	—
250	#432	C₂²×C₁₃	1	4	yes	—
251	#407	C₂²×C₁₃	1	4	yes	—
252	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
253	#324	C₂²×C₁₃	1	4	yes	—
254	#324	C₂²×C₁₃	1	4	yes	—
255	#324	C₂²×C₁₃	1	4	yes	—
256	#323	C₂²×C₁₃	1	4	yes	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	2	no	—
259	C₂²×C₁₃	—	2	1	no	—
260	C₂²×C₁₃	—	2	2	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	2	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	4	1	no	—
272	C₂²×C₁₃	—	4	1	no	—
273	C₂²×C₁₃	#407	1	4	yes	—
274	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
276	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	4	1	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	4	1	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₂×#41	—	2	4	no	—
290	C₂×#41	—	2	4	no	—
291	C₂×#41	—	2	4	no	—
292	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
293	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
294	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
295	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
296	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
297	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
299	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
300	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
301	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
302	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×M₁₆	—	2	4	no	—
306	C₂²×C₈	—	2	4	no	—
307	C₄×Q₈	—	2	4	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	D₄×C₁₃	1	8	yes	—
315	#117	—	2	4	no	—
316	#117	—	2	4	no	—
317	#117	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
338	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
341	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
343	C₄⋊C₈	—	2	4	no	—
344	C₂²⋊C₈	—	2	4	no	—
345	C₂²⋊C₈	—	2	4	no	—
346	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
347	#97	—	2	4	no	—
348	C₂×C₁₃	—	2	1	no	—
349	C₂×C₁₃	—	2	1	no	—
350	C₂×C₁₃	—	2	4	no	—
351	C₂×C₁₃	—	4	2	no	—
352	C₂×C₁₃	—	4	2	no	—
353	C₂×C₁₃	C₂×#407	1	1	yes	characteristic
354	C₂×C₁₃	#2883	1	1	yes	characteristic
355	C₂×C₁₃	#2889	1	1	yes	characteristic
356	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
357	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
358	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
359	#41	—	2	32	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	C₁₃×C₂²⋊C₄	1	4	yes	—
371	C₂×D₄	C₁₃×M₁₆	1	4	yes	complemented
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	8	1	no	—
385	C₂²×C₄	—	8	1	no	—
386	C₂²×C₄	—	8	1	no	—
387	C₂²×C₄	—	8	1	no	—
388	C₂²×C₄	—	8	1	no	—
389	C₂²×C₄	—	8	1	no	—
390	C₂²×C₄	C₁₃×M₁₆	1	4	yes	complemented
391	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
405	M₁₆	—	8	4	no	—
406	C₂×C₈	—	2	8	no	—
407	C₂×C₈	—	8	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
423	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	C₂×D₄×C₁₃	1	4	yes	—
430	C₁₃	#17368	1	1	yes	characteristic, direct product factor, Sylow
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
442	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
443	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
444	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
445	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
446	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
447	Q₈	—	2	8	no	—
448	D₄	—	2	8	no	—
449	D₄	—	2	8	no	—
450	D₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	—	8	2	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
481	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
482	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
483	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
484	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
485	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
486	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
488	C₈	—	4	8	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	C₁₃×#407	1	4	yes	—
506	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
507	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
508	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	2	1	no	—
523	C₂	—	2	4	no	—
524	C₂	—	4	2	no	—
525	C₂	—	4	2	no	—
526	C₂	C₂×C₁₃×#407	1	1	yes	characteristic
527	C₂	C₁₃×#2883	1	1	yes	characteristic
528	C₂	C₁₃×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2973	C₂	semidirect
3. C₁₃×#1467	C₂	semidirect
4. C₁₃×#1465	C₂	semidirect
5. C₁₃×#1464	C₂	semidirect
6. C₁₃×#1463	C₂	semidirect
7. C₁₃×#1459	C₂	semidirect
8. C₂×C₁₃×#324	C₂	semidirect
92. #17368	C₁₃	direct (N × H)
108. C₂×D₄×C₁₃	M₁₆	semidirect
127. C₂²×C₄×C₁₃	M₁₆	semidirect
168. #2973	C₂×C₁₃	semidirect
169. #1467	C₂×C₁₃	semidirect
170. #1465	C₂×C₁₃	semidirect
171. #1464	C₂×C₁₃	semidirect
172. #1463	C₂×C₁₃	semidirect
173. #1459	C₂×C₁₃	semidirect
174. C₂×#324	C₂×C₁₃	semidirect
371. C₂×D₄	C₁₃×M₁₆	semidirect
390. C₂²×C₄	C₁₃×M₁₆	semidirect
430. C₁₃	#17368	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×#520	2
C₁₃×#2973	2
C₁₃×#1467	2
C₁₃×#1465	2
C₁₃×#1464	2
C₁₃×#1463	2
C₁₃×#1459	2
C₂×C₁₃×#324	2
#17368	13

Subgroups — C13×#17368 #15703707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17368 #15703707