Subgroups — C₁₃×#17671 #15704010

Order 3328.

1232 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1536	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1530	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1527	C₂	1	4	yes	maximal, complemented
7	C₂²×C₁₃×#41	C₄	1	2	yes	—
8	C₁₃×#532	—	2	1	no	—
9	C₁₃×#532	—	2	1	no	—
10	C₁₃×#532	—	2	1	no	—
11	C₁₃×#532	—	2	1	no	—
12	C₁₃×#532	C₄	1	2	yes	—
13	C₁₃×#532	C₄	1	2	yes	—
14	C₁₃×#532	C₂²	1	2	yes	—
15	C₁₃×#532	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₁₃×#127	C₄	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	—	2	1	no	—
20	C₂×C₁₃×#121	—	2	1	no	—
21	C₂×C₄×D₄×C₁₃	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃	—	2	1	no	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#432	—	2	1	no	—
25	C₁₃×#432	—	2	1	no	—
26	C₁₃×#432	C₂²	1	2	yes	—
27	C₁₃×#432	C₂²	1	2	yes	complemented
28	C₁₃×#432	C₂²	1	2	yes	complemented
29	C₁₃×#432	C₂²	1	2	yes	complemented
30	C₁₃×#431	—	2	1	no	—
31	C₁₃×#431	—	2	1	no	—
32	C₁₃×#423	—	2	1	no	—
33	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
34	C₁₃×#407	—	2	1	no	—
35	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
36	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
37	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
38	C₁₃×#329	C₂²	1	16	yes	complemented
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	4	8	no	—
42	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
43	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
44	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₁₃	—	2	2	no	—
50	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	1	no	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
58	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
59	C₁₃×#127	—	2	1	no	—
60	C₁₃×#127	—	2	1	no	—
61	C₁₃×#127	C₂×C₄	1	2	yes	—
62	C₁₃×#127	C₂×C₄	1	2	yes	—
63	C₁₃×#124	—	2	2	no	—
64	C₁₃×#124	—	2	2	no	—
65	C₁₃×#124	C₂×C₄	1	4	yes	—
66	C₁₃×#124	C₂³	1	4	yes	—
67	C₁₃×#121	—	2	2	no	—
68	C₁₃×#121	—	2	2	no	—
69	C₁₃×#121	—	2	2	no	—
70	C₁₃×#121	—	2	2	no	—
71	C₁₃×#121	—	2	2	no	—
72	C₁₃×#121	—	2	2	no	—
73	C₁₃×#121	—	2	2	no	—
74	C₁₃×#121	—	2	2	no	—
75	C₄×D₄×C₁₃	—	2	2	no	—
76	C₄×D₄×C₁₃	—	2	2	no	—
77	C₄×D₄×C₁₃	—	2	2	no	—
78	C₄×D₄×C₁₃	—	2	2	no	—
79	C₄×D₄×C₁₃	—	2	2	no	—
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	—	2	2	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×C₄⋊C₈	—	2	2	no	—
100	C₁₃×C₄⋊C₈	—	2	2	no	—
101	C₁₃×C₄⋊C₈	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×C₂²⋊C₈	—	2	2	no	—
104	C₁₃×C₂²⋊C₈	—	2	2	no	—
105	C₁₃×C₂²⋊C₈	—	2	2	no	—
106	C₁₃×C₂²⋊C₈	—	2	2	no	—
107	C₁₃×#97	—	2	2	no	—
108	C₁₃×#97	C₂³	1	4	yes	—
109	C₁₃×#97	C₂³	1	4	yes	—
110	C₄×C₈×C₁₃	—	2	2	no	—
111	#17671	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₁₃×#41	—	4	8	no	—
115	C₁₃×#41	—	4	8	no	—
116	C₁₃×#41	—	4	8	no	—
117	C₁₃×#41	—	4	8	no	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	4	4	no	—
120	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	4	4	no	—
129	C₂×D₄×C₁₃	—	4	4	no	—
130	C₂×D₄×C₁₃	—	4	4	no	—
131	C₂×D₄×C₁₃	—	4	8	no	—
132	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	—	4	8	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₁₃×M₁₆	—	4	4	no	—
159	C₂×C₈×C₁₃	—	2	4	no	—
160	C₂×C₈×C₁₃	—	2	4	no	—
161	C₂×C₈×C₁₃	—	4	4	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	4	no	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
187	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1536	C₂×C₁₃	1	4	yes	complemented
190	#1530	C₂×C₁₃	1	4	yes	complemented
191	#1527	C₂×C₁₃	1	4	yes	complemented
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	2	4	no	—
195	C₂³×C₁₃	—	4	1	no	—
196	C₂³×C₁₃	—	4	4	no	—
197	C₂³×C₁₃	—	4	4	no	—
198	C₂³×C₁₃	—	4	4	no	—
199	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	Q₈×C₁₃	—	4	4	no	—
203	Q₈×C₁₃	—	4	4	no	—
204	D₄×C₁₃	—	4	4	no	—
205	D₄×C₁₃	—	4	4	no	—
206	D₄×C₁₃	—	4	4	no	—
207	D₄×C₁₃	—	4	4	no	—
208	D₄×C₁₃	—	4	8	no	—
209	D₄×C₁₃	—	4	8	no	—
210	D₄×C₁₃	—	4	4	no	—
211	D₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	8	no	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	#100	1	4	yes	—
234	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₈×C₁₃	—	4	4	no	—
247	C₈×C₁₃	—	4	4	no	—
248	C₂²×#41	C₄×C₁₃	1	2	yes	—
249	#532	—	2	1	no	—
250	#532	—	2	1	no	—
251	#532	—	2	1	no	—
252	#532	—	2	1	no	—
253	#532	C₄×C₁₃	1	2	yes	—
254	#532	C₄×C₁₃	1	2	yes	—
255	#532	C₂²×C₁₃	1	2	yes	—
256	#532	C₂²×C₁₃	1	2	yes	—
257	C₂×C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
258	C₂×#127	C₄×C₁₃	1	1	yes	characteristic
259	C₂×#124	C₂²×C₁₃	1	2	yes	—
260	C₂×#121	—	2	1	no	—
261	C₂×#121	—	2	1	no	—
262	C₂×C₄×D₄	—	2	1	no	—
263	C₂×C₄×D₄	—	2	1	no	—
264	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
265	#432	—	2	1	no	—
266	#432	—	2	1	no	—
267	#432	C₂²×C₁₃	1	2	yes	—
268	#432	C₂²×C₁₃	1	2	yes	complemented
269	#432	C₂²×C₁₃	1	2	yes	complemented
270	#432	C₂²×C₁₃	1	2	yes	complemented
271	#431	—	2	1	no	—
272	#431	—	2	1	no	—
273	#423	—	2	1	no	—
274	C₂×C₄⋊C₈	—	2	1	no	—
275	#407	—	2	1	no	—
276	C₂×C₂²⋊C₈	—	2	1	no	—
277	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
278	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
279	#329	C₂²×C₁₃	1	16	yes	complemented
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	—	2	1	no	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	2	1	no	—
284	C₂²×C₁₃	—	2	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	—	4	4	no	—
288	C₂²×C₁₃	—	4	4	no	—
289	C₂²×C₁₃	—	4	4	no	—
290	C₂²×C₁₃	—	4	4	no	—
291	C₂²×C₁₃	—	8	8	no	—
292	C₂²×C₁₃	C₂×#100	1	2	yes	—
293	C₂²×C₁₃	#421	1	2	yes	—
294	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	4	4	no	—
305	C₄×C₁₃	C₂×#100	1	2	yes	—
306	C₄×C₁₃	C₂×#100	1	2	yes	—
307	C₄×C₁₃	#421	1	2	yes	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	4	8	no	—
311	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
312	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
313	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
318	C₂³×C₄	—	2	2	no	—
319	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
320	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
321	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
322	C₂×M₁₆	—	2	2	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
327	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
328	#127	—	2	1	no	—
329	#127	—	2	1	no	—
330	#127	C₂×C₄×C₁₃	1	2	yes	—
331	#127	C₂×C₄×C₁₃	1	2	yes	—
332	#124	—	2	2	no	—
333	#124	—	2	2	no	—
334	#124	C₂×C₄×C₁₃	1	4	yes	—
335	#124	C₂³×C₁₃	1	4	yes	—
336	#121	—	2	2	no	—
337	#121	—	2	2	no	—
338	#121	—	2	2	no	—
339	#121	—	2	2	no	—
340	#121	—	2	2	no	—
341	#121	—	2	2	no	—
342	#121	—	2	2	no	—
343	#121	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
362	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
363	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	2	no	—
370	C₄⋊C₈	—	2	2	no	—
371	C₄⋊C₈	—	2	2	no	—
372	C₂²⋊C₈	—	2	2	no	—
373	C₂²⋊C₈	—	2	2	no	—
374	C₂²⋊C₈	—	2	2	no	—
375	C₂²⋊C₈	—	2	2	no	—
376	#97	—	2	2	no	—
377	#97	C₂³×C₁₃	1	4	yes	—
378	#97	C₂³×C₁₃	1	4	yes	—
379	C₄×C₈	—	2	2	no	—
380	C₂×C₁₃	—	2	2	no	—
381	C₂×C₁₃	—	2	2	no	—
382	C₂×C₁₃	—	4	1	no	—
383	C₂×C₁₃	—	8	4	no	—
384	C₂×C₁₃	C₂²×#100	1	1	yes	characteristic
385	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
386	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
387	C₂⁴	—	2	2	no	—
388	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
389	#41	—	4	8	no	—
390	#41	—	4	8	no	—
391	#41	—	4	8	no	—
392	#41	—	4	8	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	4	8	no	—
415	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
416	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
417	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
418	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
419	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
420	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
421	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
422	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
423	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	M₁₆	—	4	4	no	—
434	C₂×C₈	—	2	4	no	—
435	C₂×C₈	—	2	4	no	—
436	C₂×C₈	—	4	4	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
446	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
447	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
448	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
449	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
450	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
451	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
452	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
453	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
454	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
461	C₁₃	#17671	1	1	yes	characteristic, direct product factor, Sylow
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	4	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
470	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
471	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
472	Q₈	—	4	4	no	—
473	Q₈	—	4	4	no	—
474	D₄	—	4	4	no	—
475	D₄	—	4	4	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	4	no	—
478	D₄	—	4	8	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	C₁₃×#100	1	4	yes	—
504	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
505	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
506	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
507	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
508	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
509	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
510	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
511	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
512	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
513	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
516	C₈	—	4	4	no	—
517	C₈	—	4	4	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	8	8	no	—
530	C₂²	C₂×C₁₃×#100	1	2	yes	—
531	C₂²	C₁₃×#421	1	2	yes	—
532	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	4	4	no	—
543	C₄	C₂×C₁₃×#100	1	2	yes	—
544	C₄	C₂×C₁₃×#100	1	2	yes	—
545	C₄	C₁₃×#421	1	2	yes	—
546	C₂	—	2	2	no	—
547	C₂	—	2	2	no	—
548	C₂	—	4	1	no	—
549	C₂	—	8	4	no	—
550	C₂	C₂²×C₁₃×#100	1	1	yes	characteristic
551	C₂	C₂×C₁₃×#421	1	1	yes	characteristic
552	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2920	C₂	semidirect
3. C₂×C₁₃×#432	C₂	semidirect
4. C₁₃×#1536	C₂	semidirect
5. C₁₃×#1530	C₂	semidirect
6. C₁₃×#1527	C₂	semidirect
27. C₁₃×#432	C₂²	semidirect
28. C₁₃×#432	C₂²	semidirect
29. C₁₃×#432	C₂²	semidirect
37. C₂×C₁₃×#97	C₂²	semidirect
38. C₁₃×#329	C₂²	semidirect
111. #17671	C₁₃	direct (N × H)
187. #2920	C₂×C₁₃	semidirect
188. C₂×#432	C₂×C₁₃	semidirect
189. #1536	C₂×C₁₃	semidirect
190. #1530	C₂×C₁₃	semidirect
191. #1527	C₂×C₁₃	semidirect
268. #432	C₂²×C₁₃	semidirect
269. #432	C₂²×C₁₃	semidirect
270. #432	C₂²×C₁₃	semidirect
278. C₂×#97	C₂²×C₁₃	semidirect
279. #329	C₂²×C₁₃	semidirect
461. C₁₃	#17671	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×#532	2
C₁₃×#2920	2
C₂×C₁₃×#432	2
C₁₃×#1536	2
C₁₃×#1530	2
C₁₃×#1527	2
#17671	13

Subgroups — C13×#17671 #15704010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17671 #15704010