Subgroups — C₁₃×#20553 #15706892

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1752	C₂	1	1	yes	maximal, characteristic
15	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
19	C₁₃×#433	C₄	1	8	yes	complemented
20	C₁₃×#424	C₄	1	8	yes	complemented
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#388	C₄	1	2	yes	—
40	C₁₃×#388	C₄	1	2	yes	—
41	C₁₃×#387	C₄	1	2	yes	—
42	C₁₃×#387	C₄	1	2	yes	—
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#376	C₂²	1	1	yes	characteristic
48	C₄³×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#336	C₂²	1	1	yes	characteristic
50	C₁₃×#336	C₂²	1	1	yes	characteristic
51	C₁₃×#336	C₂²	1	1	yes	characteristic
52	C₁₃×#336	C₂²	1	1	yes	characteristic
53	C₁₃×#336	C₂²	1	1	yes	characteristic
54	C₁₃×#336	C₂²	1	1	yes	characteristic
55	C₁₃×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	—	4	1	no	—
59	C₂×C₁₃×M₁₆	—	4	1	no	—
60	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
61	C₂²×C₈×C₁₃	—	4	1	no	—
62	C₂²×C₈×C₁₃	—	4	1	no	—
63	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#117	C₂×C₄	1	4	yes	—
73	C₁₃×#117	C₂×C₄	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
91	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
92	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
93	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
94	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
95	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
96	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
97	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
98	C₁₃×#97	—	4	1	no	—
99	C₁₃×#97	—	4	1	no	—
100	C₁₃×#97	—	4	1	no	—
101	C₁₃×#97	—	4	1	no	—
102	C₁₃×#97	C₂×C₄	1	4	yes	—
103	C₄×C₈×C₁₃	—	4	1	no	—
104	C₄×C₈×C₁₃	—	4	1	no	—
105	C₄×C₈×C₁₃	—	4	1	no	—
106	C₄×C₈×C₁₃	—	4	1	no	—
107	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
108	C₁₃×#95	C₂×C₄	1	2	yes	—
109	C₁₃×#95	C₂×C₄	1	2	yes	—
110	C₁₃×#95	C₂×C₄	1	2	yes	—
111	C₁₃×#95	C₂×C₄	1	2	yes	—
112	C₁₃×#95	C₂×C₄	1	2	yes	—
113	C₁₃×#95	C₂×C₄	1	2	yes	—
114	#20553	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×M₁₆	—	4	4	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
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	—	4	4	no	—
150	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	4	2	no	—
160	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
161	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
162	C₁₃×C₂²⋊C₄	—	2	4	no	—
163	C₁₃×C₂²⋊C₄	—	4	2	no	—
164	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
165	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
166	C₄²×C₁₃	—	2	4	no	—
167	C₄²×C₁₃	—	2	1	no	—
168	C₄²×C₁₃	—	2	1	no	—
169	C₄²×C₁₃	—	2	1	no	—
170	C₄²×C₁₃	—	2	1	no	—
171	C₄²×C₁₃	—	2	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	—	2	1	no	—
175	C₄²×C₁₃	—	4	2	no	—
176	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
177	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
178	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
179	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
180	C₂×#433	C₂×C₁₃	1	1	yes	characteristic
181	C₂×#424	C₂×C₁₃	1	1	yes	characteristic
182	#2298	C₂×C₁₃	1	1	yes	characteristic
183	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#1770	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#1768	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1768	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1753	C₂×C₁₃	1	1	yes	characteristic
192	#1753	C₂×C₁₃	1	1	yes	characteristic
193	#1752	C₂×C₁₃	1	1	yes	characteristic
194	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
200	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	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	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	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	C₂×C₄²	1	2	yes	—
223	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
224	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
225	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
226	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
227	C₂×C₄×C₁₃	#131	1	4	yes	—
228	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	2	2	no	—
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	2	2	no	—
239	C₈×C₁₃	—	2	2	no	—
240	C₈×C₁₃	—	2	2	no	—
241	C₈×C₁₃	—	2	2	no	—
242	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
243	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
245	#433	C₄×C₁₃	1	8	yes	complemented
246	#424	C₄×C₁₃	1	8	yes	complemented
247	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
265	#388	C₄×C₁₃	1	2	yes	—
266	#388	C₄×C₁₃	1	2	yes	—
267	#387	C₄×C₁₃	1	2	yes	—
268	#387	C₄×C₁₃	1	2	yes	—
269	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
270	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
271	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
272	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
273	#376	C₂²×C₁₃	1	1	yes	characteristic
274	C₄³	C₂²×C₁₃	1	1	yes	characteristic
275	#336	C₂²×C₁₃	1	1	yes	characteristic
276	#336	C₂²×C₁₃	1	1	yes	characteristic
277	#336	C₂²×C₁₃	1	1	yes	characteristic
278	#336	C₂²×C₁₃	1	1	yes	characteristic
279	#336	C₂²×C₁₃	1	1	yes	characteristic
280	#336	C₂²×C₁₃	1	1	yes	characteristic
281	#336	C₂²×C₁₃	1	1	yes	characteristic
282	#336	C₂²×C₁₃	1	1	yes	characteristic
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
289	C₂²×C₁₃	#520	1	1	yes	characteristic
290	C₂²×C₁₃	#520	1	1	yes	characteristic
291	C₂²×C₁₃	C₂×#131	1	2	yes	—
292	C₂²×C₁₃	#568	1	2	yes	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	2	no	—
295	C₄×C₁₃	—	2	2	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	2	4	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	4	2	no	—
300	C₄×C₁₃	—	4	2	no	—
301	C₄×C₁₃	—	4	2	no	—
302	C₄×C₁₃	#518	1	1	yes	characteristic
303	C₄×C₁₃	#519	1	1	yes	characteristic
304	C₄×C₁₃	#520	1	1	yes	characteristic
305	C₄×C₁₃	#520	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×M₁₆	—	4	1	no	—
308	C₂×M₁₆	—	4	1	no	—
309	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
310	C₂²×C₈	—	4	1	no	—
311	C₂²×C₈	—	4	1	no	—
312	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
313	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
321	#117	C₂×C₄×C₁₃	1	4	yes	—
322	#117	C₂×C₄×C₁₃	1	4	yes	—
323	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
324	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
325	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
332	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
333	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
339	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
340	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
341	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
342	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
343	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
344	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
345	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
346	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
347	#97	—	4	1	no	—
348	#97	—	4	1	no	—
349	#97	—	4	1	no	—
350	#97	—	4	1	no	—
351	#97	C₂×C₄×C₁₃	1	4	yes	—
352	C₄×C₈	—	4	1	no	—
353	C₄×C₈	—	4	1	no	—
354	C₄×C₈	—	4	1	no	—
355	C₄×C₈	—	4	1	no	—
356	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
357	#95	C₂×C₄×C₁₃	1	2	yes	—
358	#95	C₂×C₄×C₁₃	1	2	yes	—
359	#95	C₂×C₄×C₁₃	1	2	yes	—
360	#95	C₂×C₄×C₁₃	1	2	yes	—
361	#95	C₂×C₄×C₁₃	1	2	yes	—
362	#95	C₂×C₄×C₁₃	1	2	yes	—
363	C₂×C₁₃	—	4	2	no	—
364	C₂×C₁₃	#2274	1	1	yes	characteristic
365	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
366	C₂×C₁₃	#2875	1	1	yes	characteristic
367	C₂×C₁₃	#2992	1	2	yes	—
368	C₂×C₁₃	#2993	1	2	yes	—
369	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
375	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
376	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
378	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
383	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
384	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
386	M₁₆	—	4	4	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	4	4	no	—
404	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
405	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
406	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
407	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
408	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
409	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
410	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
411	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
415	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
419	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
420	C₄²	—	2	4	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	4	2	no	—
430	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
431	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
432	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
433	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
434	C₁₃	#20553	1	1	yes	characteristic, direct product factor, Sylow
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
440	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
463	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
464	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
465	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
466	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
467	C₂×C₄	C₁₃×#131	1	4	yes	—
468	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
473	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
488	C₂²	C₁₃×#520	1	1	yes	characteristic
489	C₂²	C₁₃×#520	1	1	yes	characteristic
490	C₂²	C₂×C₁₃×#131	1	2	yes	—
491	C₂²	C₁₃×#568	1	2	yes	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	4	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	C₁₃×#518	1	1	yes	characteristic
502	C₄	C₁₃×#519	1	1	yes	characteristic
503	C₄	C₁₃×#520	1	1	yes	characteristic
504	C₄	C₁₃×#520	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	C₁₃×#2274	1	1	yes	characteristic
507	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
508	C₂	C₁₃×#2875	1	1	yes	characteristic
509	C₂	C₁₃×#2992	1	2	yes	—
510	C₂	C₁₃×#2993	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1771	C₂	semidirect
5. C₁₃×#1771	C₂	semidirect
6. C₁₃×#1770	C₂	semidirect
7. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
8. C₁₃×#1768	C₂	semidirect
9. C₁₃×#1768	C₂	semidirect
10. C₁₃×#1767	C₂	semidirect
11. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
19. C₁₃×#433	C₄	semidirect
20. C₁₃×#424	C₄	semidirect
114. #20553	C₁₃	direct (N × H)
183. #1771	C₂×C₁₃	semidirect
184. #1771	C₂×C₁₃	semidirect
185. #1770	C₂×C₁₃	semidirect
186. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
187. #1768	C₂×C₁₃	semidirect
188. #1768	C₂×C₁₃	semidirect
189. #1767	C₂×C₁₃	semidirect
190. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
245. #433	C₄×C₁₃	semidirect
246. #424	C₄×C₁₃	semidirect
434. C₁₃	#20553	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×#433	2
C₂×C₁₃×#424	2
C₁₃×#2298	2
C₁₃×#1771	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1768	2
C₁₃×#1767	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1753	2
C₁₃×#1752	2
C₈×C₁₃×C₂²⋊C₄	2
#20553	13

Subgroups — C13×#20553 #15706892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20553 #15706892