Subgroups — C₁₃×#34418 #15720757

Order 3328.

2390 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2377	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2370	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2366	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2361	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2357	C₂	1	2	yes	maximal, complemented
7	D₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2335	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2324	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2322	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#540	C₄	1	16	yes	complemented
15	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#123	C₂²	1	4	yes	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#390	C₂²	1	2	yes	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#390	C₂²	1	4	yes	—
32	C₁₃×#390	C₂²	1	4	yes	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#389	C₂²	1	2	yes	—
35	C₁₃×#389	C₂²	1	2	yes	—
36	C₁₃×#389	C₂²	1	4	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#388	C₂²	1	4	yes	—
39	C₁₃×#388	C₂²	1	4	yes	—
40	C₁₃×#388	C₂²	1	4	yes	—
41	C₁₃×#388	C₂²	1	4	yes	—
42	C₁₃×#388	C₂²	1	4	yes	—
43	C₁₃×#387	C₂²	1	4	yes	—
44	C₁₃×#387	C₂²	1	4	yes	—
45	C₁₃×#387	C₂²	1	4	yes	—
46	C₁₃×#386	C₂²	1	4	yes	—
47	C₁₃×#386	C₂²	1	4	yes	—
48	C₁₃×#386	C₂²	1	4	yes	—
49	C₁₃×#386	C₂²	1	4	yes	—
50	C₁₃×#385	C₂²	1	2	yes	—
51	C₁₃×#385	C₂²	1	2	yes	—
52	C₁₃×#385	C₂²	1	4	yes	—
53	C₁₃×#385	C₂²	1	4	yes	—
54	C₁₃×#385	C₂²	1	4	yes	—
55	C₁₃×#384	C₂²	1	1	yes	characteristic
56	C₁₃×#382	C₂²	1	1	yes	characteristic
57	C₁₃×#381	C₂²	1	4	yes	—
58	C₁₃×#380	C₂²	1	2	yes	—
59	C₁₃×#380	C₂²	1	4	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
67	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
77	C₁₃×#127	C₂×C₄	1	8	yes	complemented
78	C₁₃×#125	C₂×C₄	1	8	yes	complemented
79	C₁₃×#123	C₂×C₄	1	32	yes	complemented
80	C₁₃×#121	C₂×C₄	1	32	yes	complemented
81	C₁₃×#121	C₂×C₄	1	16	yes	complemented
82	C₄×D₄×C₁₃	—	4	4	no	—
83	C₄×D₄×C₁₃	—	4	4	no	—
84	C₄×D₄×C₁₃	—	4	8	no	—
85	C₄×D₄×C₁₃	—	4	8	no	—
86	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
87	C₁₃×#117	—	4	2	no	—
88	C₁₃×#117	C₂×C₄	1	8	yes	complemented
89	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₃	—	4	2	no	—
116	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#95	C₂³	1	2	yes	—
125	C₁₃×#95	C₂³	1	4	yes	—
126	C₁₃×#95	C₂³	1	4	yes	—
127	C₁₃×#95	C₂³	1	4	yes	—
128	C₁₃×#95	C₂³	1	2	yes	—
129	C₁₃×#95	C₂³	1	4	yes	—
130	C₁₃×#95	C₂³	1	2	yes	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	2	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	#34418	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
137	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	4	4	no	—
141	C₂×D₄×C₁₃	—	4	4	no	—
142	C₂×D₄×C₁₃	—	4	4	no	—
143	C₂×D₄×C₁₃	—	4	4	no	—
144	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
145	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
146	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	8	no	—
151	C₂²×C₄×C₁₃	—	4	1	no	—
152	C₂²×C₄×C₁₃	—	4	1	no	—
153	C₂²×C₄×C₁₃	—	4	4	no	—
154	C₂²×C₄×C₁₃	—	4	4	no	—
155	C₂²×C₄×C₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₃	—	4	4	no	—
157	C₂²×C₄×C₁₃	—	4	4	no	—
158	C₂²×C₄×C₁₃	—	4	4	no	—
159	C₂²×C₄×C₁₃	—	4	4	no	—
160	C₂²×C₄×C₁₃	—	4	4	no	—
161	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	8	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	4	4	no	—
180	C₁₃×C₄⋊C₄	—	4	4	no	—
181	C₁₃×C₄⋊C₄	—	4	2	no	—
182	C₁₃×C₄⋊C₄	—	4	2	no	—
183	C₁₃×C₄⋊C₄	—	4	1	no	—
184	C₁₃×C₄⋊C₄	—	4	1	no	—
185	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
186	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
187	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	4	4	no	—
190	C₁₃×C₂²⋊C₄	—	4	4	no	—
191	C₁₃×C₂²⋊C₄	—	4	2	no	—
192	C₁₃×C₂²⋊C₄	—	4	4	no	—
193	C₁₃×C₂²⋊C₄	—	4	4	no	—
194	C₁₃×C₂²⋊C₄	—	4	4	no	—
195	C₁₃×C₂²⋊C₄	—	4	4	no	—
196	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
197	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
198	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
199	C₄²×C₁₃	—	2	4	no	—
200	C₄²×C₁₃	—	2	4	no	—
201	C₄²×C₁₃	—	4	2	no	—
202	C₄²×C₁₃	—	4	4	no	—
203	C₄²×C₁₃	—	4	4	no	—
204	C₄²×C₁₃	—	4	4	no	—
205	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
206	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
207	C₂×#540	C₂×C₁₃	1	1	yes	characteristic
208	#2377	C₂×C₁₃	1	4	yes	complemented
209	#2370	C₂×C₁₃	1	2	yes	complemented
210	#2366	C₂×C₁₃	1	2	yes	complemented
211	#2361	C₂×C₁₃	1	4	yes	complemented
212	#2357	C₂×C₁₃	1	2	yes	complemented
213	D₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
214	#2335	C₂×C₁₃	1	4	yes	complemented
215	#2324	C₂×C₁₃	1	2	yes	complemented
216	#2322	C₂×C₁₃	1	4	yes	complemented
217	#2314	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₄×#121	C₂×C₁₃	1	2	yes	complemented
219	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂³×C₁₃	—	2	4	no	—
221	C₂³×C₁₃	—	2	1	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	—	2	4	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	2	4	no	—
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	2	no	—
230	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
231	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
232	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
233	D₄×C₁₃	—	2	16	no	—
234	D₄×C₁₃	—	4	16	no	—
235	D₄×C₁₃	—	4	16	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	4	16	no	—
263	C₂×C₄×C₁₃	—	4	4	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	—	8	8	no	—
266	C₂×C₄×C₁₃	—	8	8	no	—
267	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
268	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
269	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
271	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
272	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
273	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
274	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
275	#540	C₄×C₁₃	1	16	yes	complemented
276	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#123	C₂²×C₁₃	1	4	yes	—
279	C₂×#121	C₂²×C₁₃	1	2	yes	—
280	C₂×#121	C₂²×C₁₃	1	4	yes	—
281	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
282	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
283	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
284	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
285	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
286	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
289	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
290	#390	C₂²×C₁₃	1	2	yes	—
291	#390	C₂²×C₁₃	1	4	yes	—
292	#390	C₂²×C₁₃	1	4	yes	—
293	#390	C₂²×C₁₃	1	2	yes	—
294	#389	C₂²×C₁₃	1	2	yes	—
295	#389	C₂²×C₁₃	1	4	yes	—
296	#389	C₂²×C₁₃	1	2	yes	—
297	#389	C₂²×C₁₃	1	2	yes	—
298	#389	C₂²×C₁₃	1	2	yes	—
299	#388	C₂²×C₁₃	1	4	yes	—
300	#388	C₂²×C₁₃	1	4	yes	—
301	#388	C₂²×C₁₃	1	4	yes	—
302	#388	C₂²×C₁₃	1	4	yes	—
303	#388	C₂²×C₁₃	1	4	yes	—
304	#387	C₂²×C₁₃	1	4	yes	—
305	#387	C₂²×C₁₃	1	4	yes	—
306	#387	C₂²×C₁₃	1	4	yes	—
307	#386	C₂²×C₁₃	1	4	yes	—
308	#386	C₂²×C₁₃	1	4	yes	—
309	#386	C₂²×C₁₃	1	4	yes	—
310	#386	C₂²×C₁₃	1	4	yes	—
311	#385	C₂²×C₁₃	1	4	yes	—
312	#385	C₂²×C₁₃	1	4	yes	—
313	#385	C₂²×C₁₃	1	4	yes	—
314	#385	C₂²×C₁₃	1	2	yes	—
315	#385	C₂²×C₁₃	1	2	yes	—
316	#384	C₂²×C₁₃	1	1	yes	characteristic
317	#382	C₂²×C₁₃	1	1	yes	characteristic
318	#381	C₂²×C₁₃	1	4	yes	—
319	#380	C₂²×C₁₃	1	2	yes	—
320	#380	C₂²×C₁₃	1	4	yes	—
321	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
322	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
323	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
324	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
325	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
327	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
328	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	8	no	—
331	C₂²×C₁₃	—	2	8	no	—
332	C₂²×C₁₃	—	2	8	no	—
333	C₂²×C₁₃	—	2	4	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	4	no	—
338	C₂²×C₁₃	—	4	4	no	—
339	C₂²×C₁₃	—	4	2	no	—
340	C₂²×C₁₃	—	4	4	no	—
341	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
342	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
344	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
345	C₂²×C₁₃	#585	1	2	yes	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	2	4	no	—
348	C₄×C₁₃	—	2	8	no	—
349	C₄×C₁₃	—	2	4	no	—
350	C₄×C₁₃	—	2	4	no	—
351	C₄×C₁₃	—	4	2	no	—
352	C₄×C₁₃	—	4	4	no	—
353	C₄×C₁₃	—	4	2	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	—	4	4	no	—
356	C₄×C₁₃	#520	1	4	yes	—
357	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
358	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
359	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
360	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
363	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
366	#127	C₂×C₄×C₁₃	1	8	yes	complemented
367	#125	C₂×C₄×C₁₃	1	8	yes	complemented
368	#123	C₂×C₄×C₁₃	1	32	yes	complemented
369	#121	C₂×C₄×C₁₃	1	32	yes	complemented
370	#121	C₂×C₄×C₁₃	1	16	yes	complemented
371	C₄×D₄	—	4	4	no	—
372	C₄×D₄	—	4	4	no	—
373	C₄×D₄	—	4	8	no	—
374	C₄×D₄	—	4	8	no	—
375	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
376	#117	—	4	2	no	—
377	#117	C₂×C₄×C₁₃	1	8	yes	complemented
378	C₂×C₄⋊C₄	—	4	8	no	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
404	C₂×C₄²	—	4	2	no	—
405	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
407	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
408	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
409	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
410	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
411	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
413	#95	C₂³×C₁₃	1	2	yes	—
414	#95	C₂³×C₁₃	1	4	yes	—
415	#95	C₂³×C₁₃	1	4	yes	—
416	#95	C₂³×C₁₃	1	4	yes	—
417	#95	C₂³×C₁₃	1	2	yes	—
418	#95	C₂³×C₁₃	1	4	yes	—
419	#95	C₂³×C₁₃	1	2	yes	—
420	#95	C₂³×C₁₃	1	4	yes	—
421	#95	C₂³×C₁₃	1	4	yes	—
422	#95	C₂³×C₁₃	1	2	yes	—
423	#95	C₂³×C₁₃	1	4	yes	—
424	C₂×C₁₃	—	4	2	no	—
425	C₂×C₁₃	—	4	8	no	—
426	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
427	C₂×C₁₃	C₄×H(5,𝔽₂)	1	2	yes	—
428	C₂×C₁₃	#3537	1	1	yes	characteristic
429	C₂×C₁₃	#3539	1	1	yes	characteristic
430	C₂×C₁₃	#3554	1	2	yes	—
431	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
432	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
440	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
441	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
457	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
458	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	2	no	—
479	C₄⋊C₄	—	4	2	no	—
480	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
481	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
482	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₂²⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	—	4	4	no	—
489	C₂²⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	—	4	4	no	—
491	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
492	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
493	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	4	no	—
496	C₄²	—	4	2	no	—
497	C₄²	—	4	4	no	—
498	C₄²	—	4	4	no	—
499	C₄²	—	4	4	no	—
500	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
501	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
502	C₁₃	#34418	1	1	yes	characteristic, direct product factor, Sylow
503	C₂³	—	2	4	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	2	no	—
513	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
514	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
515	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
516	D₄	—	2	16	no	—
517	D₄	—	4	16	no	—
518	D₄	—	4	16	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	16	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	8	8	no	—
549	C₂×C₄	—	8	8	no	—
550	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
551	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
552	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
553	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
554	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
555	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
556	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
557	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	8	no	—
560	C₂²	—	2	8	no	—
561	C₂²	—	2	8	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	4	no	—
570	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
571	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
572	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
573	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
574	C₂²	C₁₃×#585	1	2	yes	—
575	C₄	—	2	4	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	4	no	—
578	C₄	—	2	8	no	—
579	C₄	—	2	4	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	4	no	—
585	C₄	C₁₃×#520	1	4	yes	—
586	C₂	—	4	2	no	—
587	C₂	—	4	8	no	—
588	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
589	C₂	C₄×C₁₃×H(5,𝔽₂)	1	2	yes	—
590	C₂	C₁₃×#3537	1	1	yes	characteristic
591	C₂	C₁₃×#3539	1	1	yes	characteristic
592	C₂	C₁₃×#3554	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#540	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2377	C₂	semidirect
3. C₁₃×#2370	C₂	semidirect
4. C₁₃×#2366	C₂	semidirect
5. C₁₃×#2361	C₂	semidirect
6. C₁₃×#2357	C₂	semidirect
7. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
8. C₁₃×#2335	C₂	semidirect
9. C₁₃×#2324	C₂	semidirect
10. C₁₃×#2322	C₂	semidirect
11. C₁₃×#2314	C₂	semidirect
12. C₄×C₁₃×#121	C₂	semidirect
13. C₁₃×#2296	C₂	semidirect
14. C₁₃×#540	C₄	semidirect
77. C₁₃×#127	C₂×C₄	semidirect
78. C₁₃×#125	C₂×C₄	semidirect
79. C₁₃×#123	C₂×C₄	semidirect
80. C₁₃×#121	C₂×C₄	semidirect
81. C₁₃×#121	C₂×C₄	semidirect
86. C₄×D₄×C₁₃	C₂×C₄	semidirect
88. C₁₃×#117	C₂×C₄	semidirect
135. #34418	C₁₃	direct (N × H)
208. #2377	C₂×C₁₃	semidirect
209. #2370	C₂×C₁₃	semidirect
210. #2366	C₂×C₁₃	semidirect
211. #2361	C₂×C₁₃	semidirect
212. #2357	C₂×C₁₃	semidirect
213. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
214. #2335	C₂×C₁₃	semidirect
215. #2324	C₂×C₁₃	semidirect
216. #2322	C₂×C₁₃	semidirect
217. #2314	C₂×C₁₃	semidirect
218. C₄×#121	C₂×C₁₃	semidirect
219. #2296	C₂×C₁₃	semidirect
275. #540	C₄×C₁₃	semidirect
366. #127	C₂×C₄×C₁₃	semidirect
367. #125	C₂×C₄×C₁₃	semidirect
368. #123	C₂×C₄×C₁₃	semidirect
369. #121	C₂×C₄×C₁₃	semidirect
370. #121	C₂×C₄×C₁₃	semidirect
375. C₄×D₄	C₂×C₄×C₁₃	semidirect
377. #117	C₂×C₄×C₁₃	semidirect
502. C₁₃	#34418	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×#540	2
C₁₃×#2377	2
C₁₃×#2370	2
C₁₃×#2366	2
C₁₃×#2361	2
C₁₃×#2357	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2335	2
C₁₃×#2324	2
C₁₃×#2322	2
C₁₃×#2314	2
C₄×C₁₃×#121	2
C₁₃×#2296	2
#34418	13

Subgroups — C13×#34418 #15720757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34418 #15720757