Subgroups — C₁₃×#22652 #15708991

Order 3328.

964 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#435	C₂	1	2	yes	maximal
2	C₂×C₁₃×#424	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1940	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1851	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1850	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1798	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	2	yes	—
14	C₁₃×#435	—	2	8	no	—
15	C₁₃×#424	—	2	8	no	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
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×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#97	C₂²	1	2	yes	—
27	C₁₃×#390	C₄	1	1	yes	characteristic
28	C₁₃×#390	C₄	1	1	yes	characteristic
29	C₁₃×#389	C₄	1	1	yes	characteristic
30	C₁₃×#389	C₄	1	1	yes	characteristic
31	C₁₃×#388	C₄	1	2	yes	—
32	C₁₃×#388	C₄	1	2	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₄³×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#336	C₂²	1	2	yes	—
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂×C₁₃×M₁₆	—	2	4	no	—
42	C₂×C₁₃×M₁₆	—	2	4	no	—
43	C₂×C₁₃×M₁₆	—	4	2	no	—
44	C₂²×C₈×C₁₃	—	2	4	no	—
45	C₂²×C₈×C₁₃	—	2	4	no	—
46	C₂²×C₈×C₁₃	—	4	2	no	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₄×D₄×C₁₃	D₄	1	4	yes	—
52	C₄×D₄×C₁₃	Q₈	1	4	yes	—
53	C₁₃×#117	—	2	4	no	—
54	C₁₃×#117	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊C₈	—	2	4	no	—
74	C₁₃×C₄⋊C₈	—	2	4	no	—
75	C₁₃×C₄⋊C₈	—	2	4	no	—
76	C₁₃×C₄⋊C₈	—	2	4	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	4	1	no	—
79	C₁₃×C₄⋊C₈	—	4	1	no	—
80	C₁₃×C₄⋊C₈	D₄	1	4	yes	complemented
81	C₁₃×C₂²⋊C₈	—	2	4	no	—
82	C₁₃×C₂²⋊C₈	—	2	4	no	—
83	C₁₃×#97	—	2	4	no	—
84	C₁₃×#95	C₂×C₄	1	2	yes	—
85	C₁₃×#95	C₂×C₄	1	2	yes	—
86	C₁₃×#95	C₂×C₄	1	2	yes	—
87	#22652	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	1	no	—
91	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₁₃×M₁₆	—	4	8	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	4	8	no	—
121	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
122	C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
127	C₁₃×C₂²⋊C₄	—	2	4	no	—
128	C₁₃×C₂²⋊C₄	—	2	4	no	—
129	C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₁₃×C₂²⋊C₄	—	4	2	no	—
131	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	4	1	no	—
138	C₄²×C₁₃	—	4	1	no	—
139	C₄²×C₁₃	—	4	1	no	—
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	C₂×D₄	1	2	yes	—
142	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
143	C₄²×C₁₃	#41	1	2	yes	—
144	C₂×#435	C₂×C₁₃	1	2	yes	—
145	C₂×#424	C₂×C₁₃	1	2	yes	complemented
146	#2293	C₂×C₁₃	1	1	yes	characteristic
147	#1940	C₂×C₁₃	1	2	yes	complemented
148	#1851	C₂×C₁₃	1	2	yes	complemented
149	#1850	C₂×C₁₃	1	2	yes	complemented
150	#1842	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1798	C₂×C₁₃	1	2	yes	complemented
152	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
160	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
161	D₄×C₁₃	—	4	4	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
190	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₁₃	#131	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
199	C₈×C₁₃	—	2	4	no	—
200	C₈×C₁₃	—	4	2	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₈×C₁₃	—	4	2	no	—
203	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
204	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
205	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#117	C₂²×C₁₃	1	2	yes	—
207	#435	—	2	8	no	—
208	#424	—	2	8	no	—
209	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
218	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
219	C₂×#97	C₂²×C₁₃	1	2	yes	—
220	#390	C₄×C₁₃	1	1	yes	characteristic
221	#390	C₄×C₁₃	1	1	yes	characteristic
222	#389	C₄×C₁₃	1	1	yes	characteristic
223	#389	C₄×C₁₃	1	1	yes	characteristic
224	#388	C₄×C₁₃	1	2	yes	—
225	#388	C₄×C₁₃	1	2	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
228	C₄³	C₂²×C₁₃	1	1	yes	characteristic
229	#336	C₂²×C₁₃	1	2	yes	—
230	#336	C₂²×C₁₃	1	2	yes	—
231	#336	C₂²×C₁₃	1	2	yes	—
232	C₂²×C₁₃	—	2	4	no	—
233	C₂²×C₁₃	—	2	4	no	—
234	C₂²×C₁₃	—	2	4	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
241	C₂²×C₁₃	#520	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
243	C₂²×C₁₃	#568	1	1	yes	characteristic
244	C₂²×C₁₃	#568	1	1	yes	characteristic
245	C₂²×C₁₃	#568	1	1	yes	characteristic
246	C₄×C₁₃	—	2	4	no	—
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	D₄²	1	1	yes	characteristic
256	C₄×C₁₃	#547	1	1	yes	characteristic
257	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
258	C₄×C₁₃	#554	1	1	yes	characteristic
259	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	2	4	no	—
263	C₂×M₁₆	—	4	2	no	—
264	C₂²×C₈	—	2	4	no	—
265	C₂²×C₈	—	2	4	no	—
266	C₂²×C₈	—	4	2	no	—
267	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
271	C₄×D₄	D₄×C₁₃	1	4	yes	—
272	C₄×D₄	Q₈×C₁₃	1	4	yes	—
273	#117	—	2	4	no	—
274	#117	—	2	4	no	—
275	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
285	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
286	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
288	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
293	C₄⋊C₈	—	2	4	no	—
294	C₄⋊C₈	—	2	4	no	—
295	C₄⋊C₈	—	2	4	no	—
296	C₄⋊C₈	—	2	4	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	4	1	no	—
299	C₄⋊C₈	—	4	1	no	—
300	C₄⋊C₈	D₄×C₁₃	1	4	yes	complemented
301	C₂²⋊C₈	—	2	4	no	—
302	C₂²⋊C₈	—	2	4	no	—
303	#97	—	2	4	no	—
304	#95	C₂×C₄×C₁₃	1	2	yes	—
305	#95	C₂×C₄×C₁₃	1	2	yes	—
306	#95	C₂×C₄×C₁₃	1	2	yes	—
307	C₂×C₁₃	—	4	4	no	—
308	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
309	C₂×C₁₃	#2905	1	1	yes	characteristic
310	C₂×C₁₃	#2906	1	1	yes	characteristic
311	C₂×C₁₃	#2932	1	1	yes	characteristic
312	C₂×C₁₃	#2935	1	1	yes	characteristic
313	C₂×C₁₃	#2992	1	1	yes	characteristic
314	C₂×C₁₃	#2995	1	1	yes	characteristic
315	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
325	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
326	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
333	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
335	M₁₆	—	4	8	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	8	no	—
348	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	1	no	—
367	C₄²	C₂×D₄×C₁₃	1	2	yes	—
368	C₄²	C₂×D₄×C₁₃	1	2	yes	—
369	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
370	C₄²	C₁₃×#41	1	2	yes	—
371	C₁₃	#22652	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
379	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
380	D₄	—	4	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
407	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
408	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
409	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
410	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
411	C₂×C₄	C₁₃×#131	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
416	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
430	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
431	C₂²	C₁₃×#520	1	1	yes	characteristic
432	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
433	C₂²	C₁₃×#568	1	1	yes	characteristic
434	C₂²	C₁₃×#568	1	1	yes	characteristic
435	C₂²	C₁₃×#568	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	1	no	—
445	C₄	D₄²×C₁₃	1	1	yes	characteristic
446	C₄	C₁₃×#547	1	1	yes	characteristic
447	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
448	C₄	C₁₃×#554	1	1	yes	characteristic
449	C₂	—	4	4	no	—
450	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
451	C₂	C₁₃×#2905	1	1	yes	characteristic
452	C₂	C₁₃×#2906	1	1	yes	characteristic
453	C₂	C₁₃×#2932	1	1	yes	characteristic
454	C₂	C₁₃×#2935	1	1	yes	characteristic
455	C₂	C₁₃×#2992	1	1	yes	characteristic
456	C₂	C₁₃×#2995	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#424	C₂	semidirect
4. C₁₃×#1940	C₂	semidirect
5. C₁₃×#1851	C₂	semidirect
6. C₁₃×#1850	C₂	semidirect
7. C₁₃×#1842	C₂	semidirect
8. C₁₃×#1798	C₂	semidirect
9. C₁₃×#1767	C₂	semidirect
80. C₁₃×C₄⋊C₈	D₄	semidirect
87. #22652	C₁₃	direct (N × H)
145. C₂×#424	C₂×C₁₃	semidirect
147. #1940	C₂×C₁₃	semidirect
148. #1851	C₂×C₁₃	semidirect
149. #1850	C₂×C₁₃	semidirect
150. #1842	C₂×C₁₃	semidirect
151. #1798	C₂×C₁₃	semidirect
152. #1767	C₂×C₁₃	semidirect
300. C₄⋊C₈	D₄×C₁₃	semidirect
371. C₁₃	#22652	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×#435	2
C₂×C₁₃×#424	2
C₁₃×#2293	2
C₁₃×#1940	2
C₁₃×#1851	2
C₁₃×#1850	2
C₁₃×#1842	2
C₁₃×#1798	2
C₁₃×#1767	2
#22652	13

Subgroups — C13×#22652 #15708991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22652 #15708991