Subgroups — C₁₃×#17367 #15703706

Order 3328.

1350 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2973	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1466	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1465	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1464	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1462	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1459	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#323	C₂	1	2	yes	maximal, complemented
9	C₂³×D₄×C₁₃	C₄	1	1	yes	characteristic
10	C₁₃×#518	—	2	8	no	—
11	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
22	C₂²×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₁₃×#435	—	2	8	no	—
26	C₁₃×#432	C₂²	1	4	yes	complemented
27	C₁₃×#407	C₂²	1	4	yes	complemented
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
29	C₁₃×#324	C₂²	1	4	yes	complemented
30	C₁₃×#323	C₂²	1	4	yes	—
31	C₁₃×#323	C₂²	1	4	yes	complemented
32	C₁₃×#323	C₂²	1	4	yes	complemented
33	C₂⁵×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂⁵×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₃	—	2	4	no	—
36	C₂²×D₄×C₁₃	—	2	4	no	—
37	C₂²×D₄×C₁₃	—	2	4	no	—
38	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	—	2	4	no	—
52	C₂²×C₈×C₁₃	—	2	4	no	—
53	C₄×D₄×C₁₃	—	2	4	no	—
54	C₄×D₄×C₁₃	—	2	4	no	—
55	C₄×D₄×C₁₃	—	2	4	no	—
56	C₄×D₄×C₁₃	—	2	4	no	—
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	2	4	no	—
60	C₄×D₄×C₁₃	D₄	1	8	yes	—
61	C₁₃×#117	—	2	4	no	—
62	C₁₃×#117	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	—	2	4	no	—
88	C₁₃×C₂²⋊C₈	—	2	4	no	—
89	C₁₃×C₂²⋊C₈	—	2	4	no	—
90	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
91	C₁₃×#97	—	2	4	no	—
92	#17367	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	2	no	—
94	C₂⁴×C₁₃	—	2	2	no	—
95	C₂⁴×C₁₃	—	2	2	no	—
96	C₂⁴×C₁₃	—	2	2	no	—
97	C₂⁴×C₁₃	—	2	2	no	—
98	C₂⁴×C₁₃	—	8	1	no	—
99	C₂⁴×C₁₃	—	8	1	no	—
100	C₂⁴×C₁₃	—	8	1	no	—
101	C₂⁴×C₁₃	—	8	1	no	—
102	C₂⁴×C₁₃	M₁₆	1	4	yes	complemented
103	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×D₄×C₁₃	—	2	32	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	C₂²⋊C₄	1	4	yes	—
120	C₂×D₄×C₁₃	M₁₆	1	4	yes	complemented
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	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	8	1	no	—
131	C₂²×C₄×C₁₃	—	8	1	no	—
132	C₂²×C₄×C₁₃	—	8	1	no	—
133	C₂²×C₄×C₁₃	—	8	1	no	—
134	C₂²×C₄×C₁₃	—	8	1	no	—
135	C₂²×C₄×C₁₃	—	8	1	no	—
136	C₂²×C₄×C₁₃	—	8	1	no	—
137	C₂²×C₄×C₁₃	—	8	1	no	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₁₃×M₁₆	—	8	4	no	—
151	C₂×C₈×C₁₃	—	2	8	no	—
152	C₂×C₈×C₁₃	—	8	4	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
157	C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₁₃×C₂²⋊C₄	—	2	2	no	—
159	C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₁₃×C₂²⋊C₄	—	2	2	no	—
161	C₁₃×C₂²⋊C₄	—	2	2	no	—
162	C₁₃×C₂²⋊C₄	—	2	2	no	—
163	C₁₃×C₂²⋊C₄	—	2	2	no	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
168	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	2	2	no	—
172	C₄²×C₁₃	C₂×D₄	1	4	yes	—
173	C₂×#518	C₂×C₁₃	1	1	yes	characteristic
174	#2973	C₂×C₁₃	1	2	yes	complemented
175	#1466	C₂×C₁₃	1	2	yes	complemented
176	#1465	C₂×C₁₃	1	2	yes	complemented
177	#1464	C₂×C₁₃	1	2	yes	complemented
178	#1462	C₂×C₁₃	1	2	yes	complemented
179	#1459	C₂×C₁₃	1	2	yes	complemented
180	C₂×#323	C₂×C₁₃	1	2	yes	complemented
181	C₂³×C₁₃	—	2	8	no	—
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	—	2	1	no	—
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	—	2	8	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	—	4	1	no	—
193	C₂³×C₁₃	—	4	1	no	—
194	C₂³×C₁₃	—	4	1	no	—
195	C₂³×C₁₃	—	4	1	no	—
196	C₂³×C₁₃	—	4	1	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	—	4	1	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	8	2	no	—
202	C₂³×C₁₃	—	8	2	no	—
203	C₂³×C₁₃	—	8	2	no	—
204	C₂³×C₁₃	—	8	2	no	—
205	C₂³×C₁₃	—	8	4	no	—
206	C₂³×C₁₃	—	8	4	no	—
207	C₂³×C₁₃	—	8	4	no	—
208	C₂³×C₁₃	—	8	4	no	—
209	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
212	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
213	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
214	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
215	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
216	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
217	D₄×C₁₃	—	2	8	no	—
218	D₄×C₁₃	—	2	8	no	—
219	D₄×C₁₃	—	2	8	no	—
220	D₄×C₁₃	—	2	8	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	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	—	8	2	no	—
241	C₂×C₄×C₁₃	—	8	2	no	—
242	C₂×C₄×C₁₃	—	8	2	no	—
243	C₂×C₄×C₁₃	—	8	2	no	—
244	C₂×C₄×C₁₃	—	8	2	no	—
245	C₂×C₄×C₁₃	—	8	2	no	—
246	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
248	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
250	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
252	C₈×C₁₃	—	4	8	no	—
253	C₂³×D₄	C₄×C₁₃	1	1	yes	characteristic
254	#518	—	2	8	no	—
255	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
256	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
257	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
259	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#117	C₄×C₁₃	1	1	yes	characteristic
264	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	C₄×C₁₃	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	C₄×C₁₃	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
269	#435	—	2	8	no	—
270	#432	C₂²×C₁₃	1	4	yes	complemented
271	#407	C₂²×C₁₃	1	4	yes	complemented
272	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	complemented
273	#324	C₂²×C₁₃	1	4	yes	complemented
274	#323	C₂²×C₁₃	1	4	yes	—
275	#323	C₂²×C₁₃	1	4	yes	complemented
276	#323	C₂²×C₁₃	1	4	yes	complemented
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	2	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	—	4	2	no	—
289	C₂²×C₁₃	—	4	2	no	—
290	C₂²×C₁₃	—	4	2	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	4	1	no	—
298	C₂²×C₁₃	—	4	1	no	—
299	C₂²×C₁₃	—	4	1	no	—
300	C₂²×C₁₃	—	4	1	no	—
301	C₂²×C₁₃	—	4	1	no	—
302	C₂²×C₁₃	—	4	1	no	—
303	C₂²×C₁₃	—	8	8	no	—
304	C₂²×C₁₃	—	8	8	no	—
305	C₂²×C₁₃	#407	1	4	yes	—
306	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
307	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
308	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	2	no	—
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	2	2	no	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	4	1	no	—
316	C₄×C₁₃	—	4	1	no	—
317	C₄×C₁₃	—	4	1	no	—
318	C₄×C₁₃	—	4	1	no	—
319	C₂⁵	C₂×C₄×C₁₃	1	1	yes	characteristic
320	C₂⁵	C₂×C₄×C₁₃	1	1	yes	characteristic
321	C₂²×D₄	—	2	4	no	—
322	C₂²×D₄	—	2	4	no	—
323	C₂²×D₄	—	2	4	no	—
324	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
325	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
326	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
327	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
328	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
329	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
330	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
334	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×M₁₆	—	2	4	no	—
338	C₂²×C₈	—	2	4	no	—
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	—	2	4	no	—
344	C₄×D₄	—	2	4	no	—
345	C₄×D₄	—	2	4	no	—
346	C₄×D₄	D₄×C₁₃	1	8	yes	—
347	#117	—	2	4	no	—
348	#117	—	2	4	no	—
349	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	—	2	4	no	—
354	C₂×C₂²⋊C₄	—	2	4	no	—
355	C₂×C₂²⋊C₄	—	2	4	no	—
356	C₂×C₂²⋊C₄	—	2	4	no	—
357	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
373	C₄⋊C₈	—	2	4	no	—
374	C₂²⋊C₈	—	2	4	no	—
375	C₂²⋊C₈	—	2	4	no	—
376	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
377	#97	—	2	4	no	—
378	C₂×C₁₃	—	2	1	no	—
379	C₂×C₁₃	—	2	1	no	—
380	C₂×C₁₃	—	2	4	no	—
381	C₂×C₁₃	—	4	2	no	—
382	C₂×C₁₃	—	4	2	no	—
383	C₂×C₁₃	—	4	2	no	—
384	C₂×C₁₃	—	4	2	no	—
385	C₂×C₁₃	C₂×#407	1	1	yes	characteristic
386	C₂×C₁₃	#2883	1	1	yes	characteristic
387	C₂×C₁₃	#2888	1	1	yes	characteristic
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	—	8	1	no	—
394	C₂⁴	—	8	1	no	—
395	C₂⁴	—	8	1	no	—
396	C₂⁴	—	8	1	no	—
397	C₂⁴	C₁₃×M₁₆	1	4	yes	complemented
398	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
399	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
400	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
401	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
402	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
403	C₂×D₄	—	2	32	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	C₁₃×C₂²⋊C₄	1	4	yes	—
415	C₂×D₄	C₁₃×M₁₆	1	4	yes	complemented
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	8	1	no	—
426	C₂²×C₄	—	8	1	no	—
427	C₂²×C₄	—	8	1	no	—
428	C₂²×C₄	—	8	1	no	—
429	C₂²×C₄	—	8	1	no	—
430	C₂²×C₄	—	8	1	no	—
431	C₂²×C₄	—	8	1	no	—
432	C₂²×C₄	—	8	1	no	—
433	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	M₁₆	—	8	4	no	—
446	C₂×C₈	—	2	8	no	—
447	C₂×C₈	—	8	4	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
463	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	2	no	—
467	C₄²	C₂×D₄×C₁₃	1	4	yes	—
468	C₁₃	#17367	1	1	yes	characteristic, direct product factor, Sylow
469	C₂³	—	2	8	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	8	2	no	—
490	C₂³	—	8	2	no	—
491	C₂³	—	8	2	no	—
492	C₂³	—	8	2	no	—
493	C₂³	—	8	4	no	—
494	C₂³	—	8	4	no	—
495	C₂³	—	8	4	no	—
496	C₂³	—	8	4	no	—
497	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
498	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
499	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
500	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
501	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
502	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
503	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
504	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
505	D₄	—	2	8	no	—
506	D₄	—	2	8	no	—
507	D₄	—	2	8	no	—
508	D₄	—	2	8	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	—	8	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
535	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
536	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
537	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
538	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
540	C₈	—	4	8	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	8	8	no	—
568	C₂²	—	8	8	no	—
569	C₂²	C₁₃×#407	1	4	yes	—
570	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
571	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
572	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	4	no	—
586	C₂	—	4	2	no	—
587	C₂	—	4	2	no	—
588	C₂	—	4	2	no	—
589	C₂	—	4	2	no	—
590	C₂	C₂×C₁₃×#407	1	1	yes	characteristic
591	C₂	C₁₃×#2883	1	1	yes	characteristic
592	C₂	C₁₃×#2888	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2973	C₂	semidirect
3. C₁₃×#1466	C₂	semidirect
4. C₁₃×#1465	C₂	semidirect
5. C₁₃×#1464	C₂	semidirect
6. C₁₃×#1462	C₂	semidirect
7. C₁₃×#1459	C₂	semidirect
8. C₂×C₁₃×#323	C₂	semidirect
26. C₁₃×#432	C₂²	semidirect
27. C₁₃×#407	C₂²	semidirect
28. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
29. C₁₃×#324	C₂²	semidirect
31. C₁₃×#323	C₂²	semidirect
32. C₁₃×#323	C₂²	semidirect
92. #17367	C₁₃	direct (N × H)
102. C₂⁴×C₁₃	M₁₆	semidirect
120. C₂×D₄×C₁₃	M₁₆	semidirect
174. #2973	C₂×C₁₃	semidirect
175. #1466	C₂×C₁₃	semidirect
176. #1465	C₂×C₁₃	semidirect
177. #1464	C₂×C₁₃	semidirect
178. #1462	C₂×C₁₃	semidirect
179. #1459	C₂×C₁₃	semidirect
180. C₂×#323	C₂×C₁₃	semidirect
270. #432	C₂²×C₁₃	semidirect
271. #407	C₂²×C₁₃	semidirect
272. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
273. #324	C₂²×C₁₃	semidirect
275. #323	C₂²×C₁₃	semidirect
276. #323	C₂²×C₁₃	semidirect
397. C₂⁴	C₁₃×M₁₆	semidirect
415. C₂×D₄	C₁₃×M₁₆	semidirect
468. C₁₃	#17367	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×#518	2
C₁₃×#2973	2
C₁₃×#1466	2
C₁₃×#1465	2
C₁₃×#1464	2
C₁₃×#1462	2
C₁₃×#1459	2
C₂×C₁₃×#323	2
#17367	13

Subgroups — C13×#17367 #15703706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17367 #15703706