Subgroups — C₁₃×#20485 #15706824

Order 3328.

1150 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#405	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1753	C₂	1	2	yes	maximal, complemented
9	C₈×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1750	C₂	1	2	yes	maximal, complemented
11	C₄²×C₈×C₁₃	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	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	2	yes	—
16	C₁₃×#436	C₄	1	8	yes	complemented
17	C₈×D₄×C₁₃	C₄	1	8	yes	complemented
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₁₃×#405	—	2	8	no	—
23	C₂×C₁₃×#97	C₂²	1	2	yes	—
24	C₂×C₁₃×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#390	C₄	1	2	yes	—
33	C₁₃×#389	C₄	1	2	yes	—
34	C₁₃×#388	C₄	1	4	yes	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₄³×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
43	C₂×C₁₃×M₁₆	—	2	4	no	—
44	C₂×C₁₃×M₁₆	—	2	4	no	—
45	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
46	C₂²×C₈×C₁₃	—	2	4	no	—
47	C₂²×C₈×C₁₃	—	2	4	no	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
57	C₁₃×#117	—	2	4	no	—
58	C₁₃×#117	—	2	4	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
63	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
64	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
72	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
73	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
74	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
75	C₁₃×#97	—	2	4	no	—
76	C₁₃×#97	—	2	4	no	—
77	C₄×C₈×C₁₃	—	2	4	no	—
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
82	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
83	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
84	C₁₃×#95	C₂×C₄	1	4	yes	—
85	C₁₃×#95	C₂×C₄	1	2	yes	—
86	#20485	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₁₃	—	2	4	no	—
89	C₂×D₄×C₁₃	C₄²	1	4	yes	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₁₃×M₁₆	—	2	16	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	16	no	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
116	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₁₃	#41	1	2	yes	—
122	C₂×C₈×C₁₃	#41	1	2	yes	—
123	C₁₃×C₄⋊C₄	—	2	8	no	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
126	C₁₃×C₂²⋊C₄	—	2	8	no	—
127	C₁₃×C₂²⋊C₄	—	2	8	no	—
128	C₁₃×C₂²⋊C₄	C₄²	1	8	yes	—
129	C₄²×C₁₃	—	2	4	no	—
130	C₄²×C₁₃	—	2	4	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	2	1	no	—
133	C₄²×C₁₃	—	2	1	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	#41	1	2	yes	—
139	C₂×#436	C₂×C₁₃	1	1	yes	characteristic
140	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
141	C₂×#405	C₂×C₁₃	1	2	yes	complemented
142	#2293	C₂×C₁₃	1	1	yes	characteristic
143	#1770	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#1767	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	#1750	C₂×C₁₃	1	2	yes	complemented
149	C₄²×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	—	2	2	no	—
152	C₂³×C₁₃	—	2	4	no	—
153	C₂³×C₁₃	—	2	4	no	—
154	C₂³×C₁₃	C₂×C₄²	1	4	yes	—
155	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
156	D₄×C₁₃	—	2	8	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
173	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
174	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
175	C₂×C₄×C₁₃	#131	1	4	yes	—
176	C₂×C₄×C₁₃	#131	1	4	yes	—
177	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₈×C₁₃	—	2	4	no	—
184	C₈×C₁₃	—	2	4	no	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	2	2	no	—
187	C₈×C₁₃	C₄×D₄	1	4	yes	—
188	C₈×C₁₃	C₄×D₄	1	4	yes	—
189	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
190	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
191	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#117	C₂²×C₁₃	1	2	yes	—
193	#436	C₄×C₁₃	1	8	yes	complemented
194	C₈×D₄	C₄×C₁₃	1	8	yes	complemented
195	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
198	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
199	#405	—	2	8	no	—
200	C₂×#97	C₂²×C₁₃	1	2	yes	—
201	C₂×#97	C₂²×C₁₃	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
209	#390	C₄×C₁₃	1	2	yes	—
210	#389	C₄×C₁₃	1	2	yes	—
211	#388	C₄×C₁₃	1	4	yes	—
212	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
213	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
214	C₄³	C₂²×C₁₃	1	1	yes	characteristic
215	#336	C₂²×C₁₃	1	2	yes	—
216	#336	C₂²×C₁₃	1	2	yes	—
217	#336	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₁₃	—	2	4	no	—
219	C₂²×C₁₃	—	2	4	no	—
220	C₂²×C₁₃	—	2	4	no	—
221	C₂²×C₁₃	—	4	4	no	—
222	C₂²×C₁₃	—	4	4	no	—
223	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
224	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
226	C₂²×C₁₃	C₂×#131	1	2	yes	—
227	C₂²×C₁₃	C₂×#131	1	2	yes	—
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	2	4	no	—
230	C₄×C₁₃	—	2	4	no	—
231	C₄×C₁₃	—	2	4	no	—
232	C₄×C₁₃	—	4	4	no	—
233	C₄×C₁₃	#405	1	4	yes	complemented
234	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
235	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
237	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
238	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
240	C₂×M₁₆	—	2	4	no	—
241	C₂×M₁₆	—	2	4	no	—
242	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
243	C₂²×C₈	—	2	4	no	—
244	C₂²×C₈	—	2	4	no	—
245	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	—
246	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
253	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
254	#117	—	2	4	no	—
255	#117	—	2	4	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
262	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
263	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
264	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
268	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
269	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
270	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
271	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
272	#97	—	2	4	no	—
273	#97	—	2	4	no	—
274	C₄×C₈	—	2	4	no	—
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	—	2	2	no	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
279	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
280	C₄×C₈	D₄×C₁₃	1	4	yes	complemented
281	#95	C₂×C₄×C₁₃	1	4	yes	—
282	#95	C₂×C₄×C₁₃	1	2	yes	—
283	C₂×C₁₃	—	4	4	no	—
284	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
285	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
286	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
287	C₂×C₁₃	#2931	1	2	yes	—
288	C₂×C₁₃	#2966	1	2	yes	—
289	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	C₄²×C₁₃	1	4	yes	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
297	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
305	M₁₆	—	2	16	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	16	no	—
315	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
316	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
317	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
318	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
319	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
320	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
321	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
322	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
323	C₂×C₈	C₁₃×#41	1	2	yes	—
324	C₂×C₈	C₁₃×#41	1	2	yes	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
328	C₂²⋊C₄	—	2	8	no	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	C₄²×C₁₃	1	8	yes	—
331	C₄²	—	2	4	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	2	no	—
337	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
338	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
339	C₄²	C₂×D₄×C₁₃	1	2	yes	—
340	C₄²	C₁₃×#41	1	2	yes	—
341	C₁₃	#20485	1	1	yes	characteristic, direct product factor, Sylow
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	C₂×C₄²×C₁₃	1	4	yes	—
347	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
348	D₄	—	2	8	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
364	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
365	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
366	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
367	C₂×C₄	C₁₃×#131	1	4	yes	—
368	C₂×C₄	C₁₃×#131	1	4	yes	—
369	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
373	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
374	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	2	4	no	—
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	C₄×D₄×C₁₃	1	4	yes	—
380	C₈	C₄×D₄×C₁₃	1	4	yes	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
387	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
388	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
389	C₂²	C₂×C₁₃×#131	1	2	yes	—
390	C₂²	C₂×C₁₃×#131	1	2	yes	—
391	C₄	—	2	4	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	4	no	—
394	C₄	—	2	4	no	—
395	C₄	—	4	4	no	—
396	C₄	C₁₃×#405	1	4	yes	complemented
397	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
398	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
399	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
400	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
401	C₂	—	4	4	no	—
402	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
403	C₂	C₂×C₁₃×#405	1	1	yes	characteristic
404	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
405	C₂	C₁₃×#2931	1	2	yes	—
406	C₂	C₁₃×#2966	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
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×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#405	C₂	semidirect
5. C₁₃×#1770	C₂	semidirect
6. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
7. C₁₃×#1767	C₂	semidirect
8. C₁₃×#1753	C₂	semidirect
9. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
10. C₁₃×#1750	C₂	semidirect
11. C₄²×C₈×C₁₃	C₂	semidirect
16. C₁₃×#436	C₄	semidirect
17. C₈×D₄×C₁₃	C₄	semidirect
83. C₄×C₈×C₁₃	D₄	semidirect
86. #20485	C₁₃	direct (N × H)
141. C₂×#405	C₂×C₁₃	semidirect
143. #1770	C₂×C₁₃	semidirect
144. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
145. #1767	C₂×C₁₃	semidirect
146. #1753	C₂×C₁₃	semidirect
147. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
148. #1750	C₂×C₁₃	semidirect
149. C₄²×C₈	C₂×C₁₃	semidirect
193. #436	C₄×C₁₃	semidirect
194. C₈×D₄	C₄×C₁₃	semidirect
233. C₄×C₁₃	#405	semidirect
280. C₄×C₈	D₄×C₁₃	semidirect
341. C₁₃	#20485	direct (N × H)
396. C₄	C₁₃×#405	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#436	2
C₂×C₈×D₄×C₁₃	2
C₂×C₁₃×#405	2
C₁₃×#2293	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1767	2
C₁₃×#1753	2
C₈×C₁₃×C₂²⋊C₄	2
C₁₃×#1750	2
C₄²×C₈×C₁₃	2
#20485	13

Subgroups — C13×#20485 #15706824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20485 #15706824