Subgroups — C₁₃×#17650 #15703989

Order 3328.

1070 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1532	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1528	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1527	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1524	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×M₁₆	—	2	1	no	—
9	C₁₃×#529	—	2	1	no	—
10	C₁₃×#529	—	2	1	no	—
11	C₁₃×#529	—	2	1	no	—
12	C₁₃×#529	—	2	1	no	—
13	C₁₃×#529	C₄	1	2	yes	—
14	C₁₃×#529	C₄	1	2	yes	—
15	C₁₃×#529	C₂²	1	2	yes	—
16	C₁₃×#529	C₂²	1	2	yes	—
17	C₂×C₁₃×#126	—	2	1	no	—
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#123	—	2	1	no	—
21	C₂×C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₄	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	—	2	1	no	—
25	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
26	C₂×C₁₃×#117	—	2	1	no	—
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#432	—	2	1	no	—
29	C₁₃×#432	—	2	1	no	—
30	C₁₃×#432	C₂²	1	2	yes	—
31	C₁₃×#432	C₂²	1	2	yes	complemented
32	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
33	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
34	C₄×C₁₃×M₁₆	—	2	1	no	—
35	C₄×C₁₃×M₁₆	—	2	1	no	—
36	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
37	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
40	C₂×C₄×C₈×C₁₃	—	2	1	no	—
41	C₁₃×#330	C₂²	1	8	yes	complemented
42	C₁₃×#329	C₂²	1	8	yes	complemented
43	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	8	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂²×C₈×C₁₃	—	2	2	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₁₃×#126	—	2	2	no	—
56	C₁₃×#126	—	2	2	no	—
57	C₁₃×#126	—	2	2	no	—
58	C₁₃×#126	—	2	2	no	—
59	C₁₃×#125	—	2	1	no	—
60	C₁₃×#125	—	2	1	no	—
61	C₁₃×#125	C₂×C₄	1	2	yes	—
62	C₁₃×#125	C₂³	1	2	yes	—
63	C₁₃×#124	—	2	1	no	—
64	C₁₃×#124	—	2	1	no	—
65	C₁₃×#124	C₂×C₄	1	2	yes	—
66	C₁₃×#124	C₂³	1	2	yes	—
67	C₁₃×#123	—	2	2	no	—
68	C₁₃×#123	—	2	2	no	—
69	C₁₃×#123	—	2	2	no	—
70	C₁₃×#123	—	2	2	no	—
71	C₁₃×C₂²⋊Q₈	—	2	1	no	—
72	C₁₃×C₂²⋊Q₈	—	2	1	no	—
73	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
74	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
75	C₁₃×#121	—	2	1	no	—
76	C₁₃×#121	—	2	1	no	—
77	C₁₃×#121	C₂×C₄	1	2	yes	—
78	C₁₃×#121	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₁₃	—	2	1	no	—
80	C₄×Q₈×C₁₃	—	2	1	no	—
81	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
82	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	2	2	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
90	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
91	C₁₃×#117	—	2	2	no	—
92	C₁₃×#117	—	2	2	no	—
93	C₁₃×#117	—	2	2	no	—
94	C₁₃×#117	—	2	2	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₈	—	2	2	no	—
120	C₁₃×C₄⋊C₈	—	2	2	no	—
121	C₁₃×C₂²⋊C₈	—	2	2	no	—
122	C₁₃×C₂²⋊C₈	—	2	2	no	—
123	C₁₃×#97	—	2	2	no	—
124	C₁₃×#97	—	2	2	no	—
125	C₁₃×#97	C₂³	1	4	yes	—
126	C₁₃×#97	C₂³	1	4	yes	—
127	C₄×C₈×C₁₃	—	2	2	no	—
128	C₄×C₈×C₁₃	—	2	2	no	—
129	#17650	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	—	2	1	no	—
131	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	4	2	no	—
134	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	4	2	no	—
139	C₂×D₄×C₁₃	—	4	4	no	—
140	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₁₃×M₁₆	—	2	8	no	—
169	C₁₃×M₁₆	—	2	8	no	—
170	C₂×C₈×C₁₃	—	2	8	no	—
171	C₂×C₈×C₁₃	—	2	4	no	—
172	C₂×C₈×C₁₃	—	2	4	no	—
173	C₂×C₈×C₁₃	—	4	4	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
185	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₁₃×C₂²⋊C₄	—	2	2	no	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₁₃×C₂²⋊C₄	—	2	2	no	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	2	2	no	—
193	C₁₃×C₂²⋊C₄	—	2	2	no	—
194	C₁₃×C₂²⋊C₄	—	2	2	no	—
195	C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₄²×C₁₃	—	2	2	no	—
197	C₄²×C₁₃	—	2	2	no	—
198	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
199	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
200	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
201	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
215	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1532	C₂×C₁₃	1	4	yes	complemented
218	#1528	C₂×C₁₃	1	2	yes	complemented
219	#1527	C₂×C₁₃	1	2	yes	complemented
220	#1524	C₂×C₁₃	1	4	yes	complemented
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	4	1	no	—
223	C₂³×C₁₃	—	4	1	no	—
224	C₂³×C₁₃	—	4	2	no	—
225	C₂³×C₁₃	—	4	2	no	—
226	C₂³×C₁₃	—	4	2	no	—
227	C₂³×C₁₃	#104	1	4	yes	—
228	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	Q₈×C₁₃	—	4	2	no	—
232	Q₈×C₁₃	—	4	2	no	—
233	D₄×C₁₃	—	4	2	no	—
234	D₄×C₁₃	—	4	4	no	—
235	D₄×C₁₃	—	4	4	no	—
236	D₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	4	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	4	no	—
263	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₈×C₁₃	—	2	8	no	—
276	C₈×C₁₃	—	4	4	no	—
277	C₂²×M₁₆	—	2	1	no	—
278	#529	—	2	1	no	—
279	#529	—	2	1	no	—
280	#529	—	2	1	no	—
281	#529	—	2	1	no	—
282	#529	C₄×C₁₃	1	2	yes	—
283	#529	C₄×C₁₃	1	2	yes	—
284	#529	C₂²×C₁₃	1	2	yes	—
285	#529	C₂²×C₁₃	1	2	yes	—
286	C₂×#126	—	2	1	no	—
287	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#123	—	2	1	no	—
290	C₂×C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
291	C₂×#121	C₄×C₁₃	1	1	yes	characteristic
292	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
293	C₂×C₄×D₄	—	2	1	no	—
294	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
295	C₂×#117	—	2	1	no	—
296	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
297	#432	—	2	1	no	—
298	#432	—	2	1	no	—
299	#432	C₂²×C₁₃	1	2	yes	—
300	#432	C₂²×C₁₃	1	2	yes	complemented
301	C₂×C₄⋊C₈	—	2	1	no	—
302	C₂×C₂²⋊C₈	—	2	1	no	—
303	C₄×M₁₆	—	2	1	no	—
304	C₄×M₁₆	—	2	1	no	—
305	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
306	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
307	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
308	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
309	C₂×C₄×C₈	—	2	1	no	—
310	#330	C₂²×C₁₃	1	8	yes	complemented
311	#329	C₂²×C₁₃	1	8	yes	complemented
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	4	4	no	—
319	C₂²×C₁₃	—	4	2	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	4	2	no	—
322	C₂²×C₁₃	—	8	4	no	—
323	C₂²×C₁₃	C₂×#104	1	2	yes	—
324	C₂²×C₁₃	C₂×#104	1	2	yes	—
325	C₂²×C₁₃	C₂×#104	1	2	yes	—
326	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	4	2	no	—
338	C₄×C₁₃	—	4	2	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	#413	1	2	yes	—
341	C₄×C₁₃	#421	1	2	yes	—
342	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	—	2	1	no	—
346	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
347	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
348	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
349	C₂×M₁₆	—	2	8	no	—
350	C₂×M₁₆	—	2	2	no	—
351	C₂×M₁₆	—	2	2	no	—
352	C₂²×C₈	—	2	2	no	—
353	C₂²×C₈	—	2	2	no	—
354	#126	—	2	2	no	—
355	#126	—	2	2	no	—
356	#126	—	2	2	no	—
357	#126	—	2	2	no	—
358	#125	—	2	1	no	—
359	#125	—	2	1	no	—
360	#125	C₂×C₄×C₁₃	1	2	yes	—
361	#125	C₂³×C₁₃	1	2	yes	—
362	#124	—	2	1	no	—
363	#124	—	2	1	no	—
364	#124	C₂×C₄×C₁₃	1	2	yes	—
365	#124	C₂³×C₁₃	1	2	yes	—
366	#123	—	2	2	no	—
367	#123	—	2	2	no	—
368	#123	—	2	2	no	—
369	#123	—	2	2	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
373	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
374	#121	—	2	1	no	—
375	#121	—	2	1	no	—
376	#121	C₂×C₄×C₁₃	1	2	yes	—
377	#121	C₂×C₄×C₁₃	1	2	yes	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
381	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
389	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
390	#117	—	2	2	no	—
391	#117	—	2	2	no	—
392	#117	—	2	2	no	—
393	#117	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
407	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
408	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
418	C₄⋊C₈	—	2	2	no	—
419	C₄⋊C₈	—	2	2	no	—
420	C₂²⋊C₈	—	2	2	no	—
421	C₂²⋊C₈	—	2	2	no	—
422	#97	—	2	2	no	—
423	#97	—	2	2	no	—
424	#97	C₂³×C₁₃	1	4	yes	—
425	#97	C₂³×C₁₃	1	4	yes	—
426	C₄×C₈	—	2	2	no	—
427	C₄×C₈	—	2	2	no	—
428	C₂×C₁₃	—	2	2	no	—
429	C₂×C₁₃	—	2	2	no	—
430	C₂×C₁₃	—	2	2	no	—
431	C₂×C₁₃	—	8	2	no	—
432	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
433	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
434	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
435	C₂⁴	—	2	1	no	—
436	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	4	2	no	—
439	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	4	2	no	—
444	C₂×D₄	—	4	4	no	—
445	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	2	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
456	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
457	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
458	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
459	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
460	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
461	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
462	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
463	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	M₁₆	—	2	8	no	—
474	M₁₆	—	2	8	no	—
475	C₂×C₈	—	2	8	no	—
476	C₂×C₈	—	2	4	no	—
477	C₂×C₈	—	2	4	no	—
478	C₂×C₈	—	4	4	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
490	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
504	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
505	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
506	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
507	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
508	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
509	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
510	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
511	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
518	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
519	C₁₃	#17650	1	1	yes	characteristic, direct product factor, Sylow
520	C₂³	—	2	2	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	C₁₃×#104	1	4	yes	—
527	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
528	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
529	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
530	Q₈	—	4	2	no	—
531	Q₈	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
564	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
566	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
567	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
568	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
569	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
570	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
571	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
574	C₈	—	2	8	no	—
575	C₈	—	4	4	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	8	4	no	—
587	C₂²	C₂×C₁₃×#104	1	2	yes	—
588	C₂²	C₂×C₁₃×#104	1	2	yes	—
589	C₂²	C₂×C₁₃×#104	1	2	yes	—
590	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	C₁₃×#413	1	2	yes	—
605	C₄	C₁₃×#421	1	2	yes	—
606	C₂	—	2	2	no	—
607	C₂	—	2	2	no	—
608	C₂	—	2	2	no	—
609	C₂	—	8	2	no	—
610	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
611	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic
612	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂×C₁₃×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#432	C₂	semidirect
3. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
4. C₁₃×#1532	C₂	semidirect
5. C₁₃×#1528	C₂	semidirect
6. C₁₃×#1527	C₂	semidirect
7. C₁₃×#1524	C₂	semidirect
31. C₁₃×#432	C₂²	semidirect
37. C₄×C₁₃×M₁₆	C₂²	semidirect
38. C₂×C₁₃×#97	C₂²	semidirect
39. C₂×C₁₃×#97	C₂²	semidirect
41. C₁₃×#330	C₂²	semidirect
42. C₁₃×#329	C₂²	semidirect
129. #17650	C₁₃	direct (N × H)
215. C₂×#432	C₂×C₁₃	semidirect
216. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
217. #1532	C₂×C₁₃	semidirect
218. #1528	C₂×C₁₃	semidirect
219. #1527	C₂×C₁₃	semidirect
220. #1524	C₂×C₁₃	semidirect
300. #432	C₂²×C₁₃	semidirect
306. C₄×M₁₆	C₂²×C₁₃	semidirect
307. C₂×#97	C₂²×C₁₃	semidirect
308. C₂×#97	C₂²×C₁₃	semidirect
310. #330	C₂²×C₁₃	semidirect
311. #329	C₂²×C₁₃	semidirect
519. C₁₃	#17650	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×#529	2
C₂×C₁₃×#432	2
C₂×C₄×C₁₃×M₁₆	2
C₁₃×#1532	2
C₁₃×#1528	2
C₁₃×#1527	2
C₁₃×#1524	2
#17650	13

Subgroups — C13×#17650 #15703989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17650 #15703989