Subgroups — C₁₃×#20559 #15706898

Order 3328.

1118 conjugacy classes of subgroups.

The subgroup lattice has 444 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	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1771	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1753	C₂	1	2	yes	maximal, complemented
6	C₈×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1745	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#435	C₄	1	16	yes	complemented
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#97	C₂²	1	2	yes	—
23	C₂×C₁₃×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
26	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
29	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
30	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄³×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#336	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	1	yes	characteristic
35	C₁₃×#336	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	1	yes	characteristic
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	—	4	2	no	—
46	C₂×C₁₃×M₁₆	—	4	2	no	—
47	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	complemented
48	C₂²×C₈×C₁₃	—	4	2	no	—
49	C₂²×C₈×C₁₃	—	4	2	no	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₄×D₄×C₁₃	—	2	8	no	—
56	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₁₃	—	4	2	no	—
64	C₂×C₄²×C₁₃	—	4	2	no	—
65	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
75	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
76	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
77	C₁₃×#97	—	4	2	no	—
78	C₁₃×#97	C₂×C₄	1	8	yes	complemented
79	C₄×C₈×C₁₃	—	4	2	no	—
80	C₄×C₈×C₁₃	—	4	2	no	—
81	C₁₃×#95	C₂×C₄	1	2	yes	—
82	C₁₃×#95	C₂×C₄	1	2	yes	—
83	C₁₃×#95	C₂×C₄	1	2	yes	—
84	#20559	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂×D₄×C₁₃	—	2	4	no	—
88	C₂×D₄×C₁₃	C₄²	1	4	yes	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	4	2	no	—
100	C₂²×C₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₁₃×M₁₆	—	4	8	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	—	2	2	no	—
121	C₂×C₈×C₁₃	—	4	8	no	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
128	C₁₃×C₂²⋊C₄	—	2	4	no	—
129	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
130	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
131	C₁₃×C₂²⋊C₄	M₁₆	1	8	yes	complemented
132	C₄²×C₁₃	—	2	4	no	—
133	C₄²×C₁₃	—	2	4	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	—	4	2	no	—
140	C₄²×C₁₃	—	4	2	no	—
141	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
142	C₂×#435	C₂×C₁₃	1	2	yes	—
143	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
144	#1771	C₂×C₁₃	1	2	yes	complemented
145	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#1753	C₂×C₁₃	1	2	yes	complemented
147	C₈×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
148	#1749	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1745	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1728	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂×#336	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₁₃	—	2	1	no	—
154	C₂³×C₁₃	—	2	1	no	—
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	2	1	no	—
157	C₂³×C₁₃	—	2	1	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
161	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
162	C₂³×C₁₃	C₂×M₁₆	1	4	yes	—
163	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
164	D₄×C₁₃	—	2	8	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	4	8	no	—
185	C₂×C₄×C₁₃	—	4	8	no	—
186	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
188	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
191	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
192	C₂×C₄×C₁₃	#131	1	4	yes	—
193	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
194	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
197	C₈×C₁₃	—	2	4	no	—
198	C₈×C₁₃	—	2	4	no	—
199	C₈×C₁₃	—	2	4	no	—
200	C₈×C₁₃	—	2	4	no	—
201	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
202	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	—
204	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
205	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
207	#435	C₄×C₁₃	1	16	yes	complemented
208	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
209	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
211	C₂×#97	C₂²×C₁₃	1	2	yes	—
212	C₂×#97	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
215	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
216	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
217	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
218	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
219	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
220	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
221	C₄³	C₂²×C₁₃	1	1	yes	characteristic
222	#336	C₂²×C₁₃	1	1	yes	characteristic
223	#336	C₂²×C₁₃	1	1	yes	characteristic
224	#336	C₂²×C₁₃	1	2	yes	—
225	#336	C₂²×C₁₃	1	1	yes	characteristic
226	#336	C₂²×C₁₃	1	2	yes	—
227	#336	C₂²×C₁₃	1	1	yes	characteristic
228	#336	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	2	4	no	—
231	C₂²×C₁₃	—	2	4	no	—
232	C₂²×C₁₃	—	2	2	no	—
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	C₄×M₁₆	1	4	yes	—
239	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
240	C₂²×C₁₃	#518	1	1	yes	characteristic
241	C₂²×C₁₃	#520	1	1	yes	characteristic
242	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
243	C₂²×C₁₃	C₂×#131	1	2	yes	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	4	no	—
247	C₄×C₁₃	—	2	4	no	—
248	C₄×C₁₃	—	2	4	no	—
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	#518	1	2	yes	—
253	C₄×C₁₃	#520	1	2	yes	—
254	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
255	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
256	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×M₁₆	—	4	2	no	—
260	C₂×M₁₆	—	4	2	no	—
261	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
262	C₂²×C₈	—	4	2	no	—
263	C₂²×C₈	—	4	2	no	—
264	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	complemented
265	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
266	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
267	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
269	C₄×D₄	—	2	8	no	—
270	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
274	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
277	C₂×C₄²	—	4	2	no	—
278	C₂×C₄²	—	4	2	no	—
279	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
280	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
281	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
282	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
283	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
289	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
290	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
291	#97	—	4	2	no	—
292	#97	C₂×C₄×C₁₃	1	8	yes	complemented
293	C₄×C₈	—	4	2	no	—
294	C₄×C₈	—	4	2	no	—
295	#95	C₂×C₄×C₁₃	1	2	yes	—
296	#95	C₂×C₄×C₁₃	1	2	yes	—
297	#95	C₂×C₄×C₁₃	1	2	yes	—
298	C₂×C₁₃	—	2	4	no	—
299	C₂×C₁₃	—	4	2	no	—
300	C₂×C₁₃	#2275	1	1	yes	characteristic
301	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
302	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
303	C₂×C₁₃	#2974	1	2	yes	—
304	C₂×C₁₃	#2990	1	2	yes	—
305	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
306	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	C₄²×C₁₃	1	4	yes	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
322	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
327	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
329	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
332	M₁₆	—	4	8	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	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	—	4	8	no	—
342	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
343	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
344	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
345	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
350	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
351	C₂²⋊C₄	C₁₃×M₁₆	1	8	yes	complemented
352	C₄²	—	2	4	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	4	2	no	—
360	C₄²	—	4	2	no	—
361	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
362	C₁₃	#20559	1	1	yes	characteristic, direct product factor, Sylow
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
371	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
372	C₂³	C₂×C₁₃×M₁₆	1	4	yes	—
373	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
374	D₄	—	2	8	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
397	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
398	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
399	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
400	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
401	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
402	C₂×C₄	C₁₃×#131	1	4	yes	—
403	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
404	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
407	C₈	—	2	4	no	—
408	C₈	—	2	4	no	—
409	C₈	—	2	4	no	—
410	C₈	—	2	4	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	C₄×C₁₃×M₁₆	1	4	yes	—
421	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
422	C₂²	C₁₃×#518	1	1	yes	characteristic
423	C₂²	C₁₃×#520	1	1	yes	characteristic
424	C₂²	C₂²×C₁₃×M₁₆	1	2	yes	—
425	C₂²	C₂×C₁₃×#131	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	2	4	no	—
433	C₄	—	4	2	no	—
434	C₄	C₁₃×#518	1	2	yes	—
435	C₄	C₁₃×#520	1	2	yes	—
436	C₂	—	2	4	no	—
437	C₂	—	4	2	no	—
438	C₂	C₁₃×#2275	1	1	yes	characteristic
439	C₂	C₂×C₄×C₁₃×M₁₆	1	1	yes	characteristic
440	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
441	C₂	C₁₃×#2974	1	2	yes	—
442	C₂	C₁₃×#2990	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	C₂²×D₄×C₁₃	C₂×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
3. C₁₃×#1771	C₂	semidirect
4. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
5. C₁₃×#1753	C₂	semidirect
6. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
7. C₁₃×#1749	C₂	semidirect
8. C₄×C₁₃×C₂²⋊C₈	C₂	semidirect
9. C₁₃×#1745	C₂	semidirect
10. C₁₃×#1728	C₂	semidirect
11. C₂×C₁₃×#336	C₂	semidirect
18. C₁₃×#435	C₄	semidirect
47. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
50. C₂²×C₈×C₁₃	C₂×C₄	semidirect
74. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
75. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
76. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
78. C₁₃×#97	C₂×C₄	semidirect
84. #20559	C₁₃	direct (N × H)
131. C₁₃×C₂²⋊C₄	M₁₆	semidirect
144. #1771	C₂×C₁₃	semidirect
145. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
146. #1753	C₂×C₁₃	semidirect
147. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
148. #1749	C₂×C₁₃	semidirect
149. C₄×C₂²⋊C₈	C₂×C₁₃	semidirect
150. #1745	C₂×C₁₃	semidirect
151. #1728	C₂×C₁₃	semidirect
152. C₂×#336	C₂×C₁₃	semidirect
207. #435	C₄×C₁₃	semidirect
261. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
264. C₂²×C₈	C₂×C₄×C₁₃	semidirect
288. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
289. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
290. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
292. #97	C₂×C₄×C₁₃	semidirect
351. C₂²⋊C₄	C₁₃×M₁₆	semidirect
362. C₁₃	#20559	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
C₄²×D₄×C₁₃	2
C₁₃×#1771	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1753	2
C₈×C₁₃×C₂²⋊C₄	2
C₁₃×#1749	2
C₄×C₁₃×C₂²⋊C₈	2
C₁₃×#1745	2
C₁₃×#1728	2
C₂×C₁₃×#336	2
#20559	13

Subgroups — C13×#20559 #15706898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20559 #15706898