Subgroups — C₁₃×#15139 #15701478

Order 3328.

1250 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#400	C₂	1	2	yes	maximal
2	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1443	C₂	1	2	yes	maximal
5	C₁₃×#1442	C₂	1	2	yes	maximal
6	C₁₃×#1442	C₂	1	2	yes	maximal
7	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#400	—	2	8	no	—
22	C₁₃×#389	—	2	4	no	—
23	C₁₃×#389	—	2	4	no	—
24	C₂×C₁₃×#95	C₂²	1	2	yes	—
25	C₂×C₁₃×#95	C₂²	1	2	yes	—
26	C₂×C₁₃×#95	C₂²	1	2	yes	—
27	C₂×C₁₃×#95	C₂²	1	2	yes	—
28	C₂×C₁₃×#95	C₂²	1	2	yes	—
29	C₂×C₁₃×#95	C₂²	1	2	yes	—
30	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	C₂²	1	2	yes	—
35	C₂×C₁₃×#95	C₂²	1	2	yes	—
36	C₂×C₁₃×#95	C₂²	1	2	yes	—
37	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	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×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
66	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
67	C₂×C₄²×C₁₃	—	2	2	no	—
68	C₂×C₄²×C₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	2	no	—
75	C₂×C₄²×C₁₃	—	2	2	no	—
76	C₁₃×#95	—	2	4	no	—
77	C₁₃×#95	—	2	4	no	—
78	C₁₃×#95	—	2	4	no	—
79	C₁₃×#95	—	2	4	no	—
80	C₁₃×#95	—	2	4	no	—
81	C₁₃×#95	—	2	4	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	4	no	—
86	C₁₃×#95	—	2	4	no	—
87	C₁₃×#95	—	2	4	no	—
88	C₁₃×#95	—	4	2	no	—
89	C₁₃×#95	D₄	1	4	yes	—
90	#15139	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	1	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	2	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
161	C₂²×C₄×C₁₃	#41	1	2	yes	—
162	C₂²×C₄×C₁₃	#41	1	2	yes	—
163	C₂²×C₄×C₁₃	#41	1	2	yes	—
164	C₂²×C₄×C₁₃	#41	1	2	yes	—
165	C₂²×C₄×C₁₃	#41	1	2	yes	—
166	C₂²×C₄×C₁₃	#41	1	2	yes	—
167	C₂²×C₄×C₁₃	#41	1	2	yes	—
168	C₂²×C₄×C₁₃	#41	1	2	yes	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	8	no	—
171	C₁₃×C₄⋊C₄	—	4	8	no	—
172	C₁₃×C₄⋊C₄	—	4	8	no	—
173	C₁₃×C₄⋊C₄	—	4	4	no	—
174	C₁₃×C₄⋊C₄	—	4	4	no	—
175	C₄²×C₁₃	—	4	4	no	—
176	C₄²×C₁₃	—	4	4	no	—
177	C₄²×C₁₃	—	4	4	no	—
178	C₂×#400	C₂×C₁₃	1	2	yes	—
179	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
180	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
181	#1443	C₂×C₁₃	1	2	yes	—
182	#1442	C₂×C₁₃	1	2	yes	—
183	#1442	C₂×C₁₃	1	2	yes	—
184	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
185	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
186	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
187	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
188	C₄×#95	C₂×C₁₃	1	1	yes	characteristic
189	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
192	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
193	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
195	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
198	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
202	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	4	1	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	2	no	—
235	C₂×C₄×C₁₃	—	4	2	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	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	2	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	2	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	2	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	2	no	—
274	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
275	C₂×C₄×C₁₃	#123	1	4	yes	—
276	C₂×C₄×C₁₃	#124	1	4	yes	—
277	C₂×C₄×C₁₃	#125	1	4	yes	—
278	C₂×C₄×C₁₃	#125	1	4	yes	—
279	C₂×C₄×C₁₃	#126	1	4	yes	—
280	C₂×C₄×C₁₃	#126	1	4	yes	—
281	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
284	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
285	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
287	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
288	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
289	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
290	#400	—	2	8	no	—
291	#389	—	2	4	no	—
292	#389	—	2	4	no	—
293	C₂×#95	C₂²×C₁₃	1	2	yes	—
294	C₂×#95	C₂²×C₁₃	1	2	yes	—
295	C₂×#95	C₂²×C₁₃	1	2	yes	—
296	C₂×#95	C₂²×C₁₃	1	2	yes	—
297	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#95	C₂²×C₁₃	1	2	yes	—
301	C₂×#95	C₂²×C₁₃	1	2	yes	—
302	C₂×#95	C₂²×C₁₃	1	2	yes	—
303	C₂×#95	C₂²×C₁₃	1	2	yes	—
304	C₂×#95	C₂²×C₁₃	1	2	yes	—
305	C₂×#95	C₂²×C₁₃	1	2	yes	—
306	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
307	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
308	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
309	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
310	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
311	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
312	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
314	C₂²×C₁₃	#529	1	1	yes	characteristic
315	C₂²×C₁₃	#529	1	1	yes	characteristic
316	C₂²×C₁₃	#529	1	1	yes	characteristic
317	C₂²×C₁₃	#532	1	1	yes	characteristic
318	C₂²×C₁₃	#532	1	1	yes	characteristic
319	C₂²×C₁₃	#532	1	1	yes	characteristic
320	C₂²×C₁₃	#541	1	1	yes	characteristic
321	C₂²×C₁₃	#541	1	1	yes	characteristic
322	C₂²×C₁₃	#541	1	1	yes	characteristic
323	C₂²×C₁₃	#542	1	1	yes	characteristic
324	C₂²×C₁₃	#542	1	1	yes	characteristic
325	C₂²×C₁₃	#542	1	1	yes	characteristic
326	C₂²×C₁₃	D₄²	1	1	yes	characteristic
327	C₂²×C₁₃	#547	1	1	yes	characteristic
328	C₂²×C₁₃	#547	1	1	yes	characteristic
329	C₂²×C₁₃	#547	1	1	yes	characteristic
330	C₂²×C₁₃	#548	1	1	yes	characteristic
331	C₂²×C₁₃	#548	1	1	yes	characteristic
332	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
333	C₂²×C₁₃	#552	1	1	yes	characteristic
334	C₂²×C₁₃	#552	1	1	yes	characteristic
335	C₂²×C₁₃	#552	1	1	yes	characteristic
336	C₂²×C₁₃	#553	1	1	yes	characteristic
337	C₂²×C₁₃	#554	1	1	yes	characteristic
338	C₂²×C₁₃	#555	1	1	yes	characteristic
339	C₂²×C₁₃	#556	1	1	yes	characteristic
340	C₂²×C₁₃	#557	1	1	yes	characteristic
341	C₂²×C₁₃	#557	1	1	yes	characteristic
342	C₄×C₁₃	—	4	2	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	—	4	2	no	—
345	C₄×C₁₃	—	4	4	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	4	2	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	—	4	2	no	—
350	C₄×C₁₃	—	8	2	no	—
351	C₄×C₁₃	—	8	2	no	—
352	C₄×C₁₃	#400	1	8	yes	complemented
353	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
354	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
356	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₁₃	1	2	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	1	yes	characteristic
363	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	4	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	4	no	—
372	C₂×C₄⋊C₄	—	2	4	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	4	2	no	—
379	C₂×C₄⋊C₄	—	4	2	no	—
380	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
381	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
382	C₂×C₄²	—	2	2	no	—
383	C₂×C₄²	—	2	2	no	—
384	C₂×C₄²	—	2	2	no	—
385	C₂×C₄²	—	2	2	no	—
386	C₂×C₄²	—	2	2	no	—
387	C₂×C₄²	—	2	2	no	—
388	C₂×C₄²	—	2	2	no	—
389	C₂×C₄²	—	2	2	no	—
390	C₂×C₄²	—	2	2	no	—
391	#95	—	2	4	no	—
392	#95	—	2	4	no	—
393	#95	—	2	4	no	—
394	#95	—	2	4	no	—
395	#95	—	2	4	no	—
396	#95	—	2	4	no	—
397	#95	—	2	2	no	—
398	#95	—	2	2	no	—
399	#95	—	2	2	no	—
400	#95	—	2	4	no	—
401	#95	—	2	4	no	—
402	#95	—	2	4	no	—
403	#95	—	4	2	no	—
404	#95	D₄×C₁₃	1	4	yes	—
405	C₂×C₁₃	C₂×#400	1	1	yes	characteristic
406	C₂×C₁₃	#2421	1	1	yes	characteristic
407	C₂×C₁₃	#2422	1	1	yes	characteristic
408	C₂×C₁₃	#2452	1	1	yes	characteristic
409	C₂×C₁₃	#2453	1	1	yes	characteristic
410	C₂×C₁₃	#2489	1	1	yes	characteristic
411	C₂×C₁₃	#2491	1	1	yes	characteristic
412	C₂×C₁₃	#2495	1	1	yes	characteristic
413	C₂×C₁₃	#2496	1	1	yes	characteristic
414	C₂×C₁₃	#2506	1	1	yes	characteristic
415	C₂×C₁₃	#2506	1	1	yes	characteristic
416	C₂×C₁₃	#2508	1	1	yes	characteristic
417	C₂×C₁₃	#2509	1	1	yes	characteristic
418	C₂×C₁₃	#2645	1	1	yes	characteristic
419	C₂×C₁₃	#2860	1	1	yes	characteristic
420	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
484	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
485	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
486	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
487	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
488	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
489	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
490	C₂²×C₄	C₁₃×#41	1	2	yes	—
491	C₂²×C₄	C₁₃×#41	1	2	yes	—
492	C₂²×C₄	C₁₃×#41	1	2	yes	—
493	C₂²×C₄	C₁₃×#41	1	2	yes	—
494	C₂²×C₄	C₁₃×#41	1	2	yes	—
495	C₂²×C₄	C₁₃×#41	1	2	yes	—
496	C₂²×C₄	C₁₃×#41	1	2	yes	—
497	C₂²×C₄	C₁₃×#41	1	2	yes	—
498	C₄⋊C₄	—	2	8	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	4	8	no	—
501	C₄⋊C₄	—	4	8	no	—
502	C₄⋊C₄	—	4	4	no	—
503	C₄⋊C₄	—	4	4	no	—
504	C₄²	—	4	4	no	—
505	C₄²	—	4	4	no	—
506	C₄²	—	4	4	no	—
507	C₁₃	#15139	1	1	yes	characteristic, direct product factor, Sylow
508	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
509	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
510	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
511	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
512	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
513	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
514	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
515	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
516	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
517	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
518	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
519	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
520	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
521	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
522	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	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	—	2	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
594	C₂×C₄	C₁₃×#123	1	4	yes	—
595	C₂×C₄	C₁₃×#124	1	4	yes	—
596	C₂×C₄	C₁₃×#125	1	4	yes	—
597	C₂×C₄	C₁₃×#125	1	4	yes	—
598	C₂×C₄	C₁₃×#126	1	4	yes	—
599	C₂×C₄	C₁₃×#126	1	4	yes	—
600	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
601	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
602	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
603	C₂²	C₂×C₁₃×#125	1	1	yes	characteristic
604	C₂²	C₂×C₁₃×#125	1	1	yes	characteristic
605	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
606	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
607	C₂²	C₁₃×#529	1	1	yes	characteristic
608	C₂²	C₁₃×#529	1	1	yes	characteristic
609	C₂²	C₁₃×#529	1	1	yes	characteristic
610	C₂²	C₁₃×#532	1	1	yes	characteristic
611	C₂²	C₁₃×#532	1	1	yes	characteristic
612	C₂²	C₁₃×#532	1	1	yes	characteristic
613	C₂²	C₁₃×#541	1	1	yes	characteristic
614	C₂²	C₁₃×#541	1	1	yes	characteristic
615	C₂²	C₁₃×#541	1	1	yes	characteristic
616	C₂²	C₁₃×#542	1	1	yes	characteristic
617	C₂²	C₁₃×#542	1	1	yes	characteristic
618	C₂²	C₁₃×#542	1	1	yes	characteristic
619	C₂²	D₄²×C₁₃	1	1	yes	characteristic
620	C₂²	C₁₃×#547	1	1	yes	characteristic
621	C₂²	C₁₃×#547	1	1	yes	characteristic
622	C₂²	C₁₃×#547	1	1	yes	characteristic
623	C₂²	C₁₃×#548	1	1	yes	characteristic
624	C₂²	C₁₃×#548	1	1	yes	characteristic
625	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
626	C₂²	C₁₃×#552	1	1	yes	characteristic
627	C₂²	C₁₃×#552	1	1	yes	characteristic
628	C₂²	C₁₃×#552	1	1	yes	characteristic
629	C₂²	C₁₃×#553	1	1	yes	characteristic
630	C₂²	C₁₃×#554	1	1	yes	characteristic
631	C₂²	C₁₃×#555	1	1	yes	characteristic
632	C₂²	C₁₃×#556	1	1	yes	characteristic
633	C₂²	C₁₃×#557	1	1	yes	characteristic
634	C₂²	C₁₃×#557	1	1	yes	characteristic
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	4	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	4	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	8	2	no	—
644	C₄	—	8	2	no	—
645	C₄	C₁₃×#400	1	8	yes	complemented
646	C₂	C₂×C₁₃×#400	1	1	yes	characteristic
647	C₂	C₁₃×#2421	1	1	yes	characteristic
648	C₂	C₁₃×#2422	1	1	yes	characteristic
649	C₂	C₁₃×#2452	1	1	yes	characteristic
650	C₂	C₁₃×#2453	1	1	yes	characteristic
651	C₂	C₁₃×#2489	1	1	yes	characteristic
652	C₂	C₁₃×#2491	1	1	yes	characteristic
653	C₂	C₁₃×#2495	1	1	yes	characteristic
654	C₂	C₁₃×#2496	1	1	yes	characteristic
655	C₂	C₁₃×#2506	1	1	yes	characteristic
656	C₂	C₁₃×#2506	1	1	yes	characteristic
657	C₂	C₁₃×#2508	1	1	yes	characteristic
658	C₂	C₁₃×#2509	1	1	yes	characteristic
659	C₂	C₁₃×#2645	1	1	yes	characteristic
660	C₂	C₁₃×#2860	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
90. #15139	C₁₃	direct (N × H)
352. C₄×C₁₃	#400	semidirect
507. C₁₃	#15139	direct (N × H)
645. C₄	C₁₃×#400	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#400	2
C₂×C₁₃×#389	2
C₁₃×#1443	2
C₁₃×#1442	2
C₁₃×C₄⋊#95	2
C₄×C₁₃×#95	2
#15139	13

Subgroups — C13×#15139 #15701478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#15139 #15701478