Subgroups — C₁₃×#17647 #15703986

Order 3328.

1316 conjugacy classes of subgroups.

The subgroup lattice has 560 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×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1530	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1527	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1525	C₂	1	4	yes	maximal, complemented
7	C₂²×C₁₃×#41	C₄	1	2	yes	—
8	C₂²×C₁₃×M₁₆	—	2	1	no	—
9	C₁₃×#532	—	2	1	no	—
10	C₁₃×#532	—	2	1	no	—
11	C₁₃×#532	—	2	1	no	—
12	C₁₃×#532	—	2	1	no	—
13	C₁₃×#532	C₄	1	2	yes	—
14	C₁₃×#532	C₄	1	2	yes	—
15	C₁₃×#532	C₂²	1	2	yes	—
16	C₁₃×#532	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
18	C₂×C₁₃×#127	C₄	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	—	2	1	no	—
21	C₂×C₁₃×#121	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃	—	2	1	no	—
23	C₂×C₄×D₄×C₁₃	—	2	1	no	—
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#432	C₂²	1	2	yes	—
26	C₁₃×#432	C₂²	1	2	yes	complemented
27	C₁₃×#431	—	2	1	no	—
28	C₁₃×#431	—	2	1	no	—
29	C₁₃×#423	—	2	1	no	—
30	C₁₃×#407	—	2	1	no	—
31	C₄×C₁₃×M₁₆	—	2	1	no	—
32	C₄×C₁₃×M₁₆	—	2	1	no	—
33	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
34	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
35	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
37	C₂×C₄×C₈×C₁₃	—	2	1	no	—
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	8	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂²×C₈×C₁₃	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
61	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
62	C₁₃×#127	—	2	1	no	—
63	C₁₃×#127	—	2	1	no	—
64	C₁₃×#127	C₂×C₄	1	2	yes	—
65	C₁₃×#127	C₂×C₄	1	2	yes	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#124	—	2	2	no	—
68	C₁₃×#124	C₂×C₄	1	4	yes	—
69	C₁₃×#124	C₂³	1	4	yes	—
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	C₁₃×#121	—	2	2	no	—
76	C₁₃×#121	—	2	2	no	—
77	C₁₃×#121	—	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	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	2	2	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	C₂×C₄	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	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×C₄⋊C₈	—	2	2	no	—
104	C₁₃×C₂²⋊C₈	—	2	2	no	—
105	C₁₃×C₂²⋊C₈	—	2	2	no	—
106	C₁₃×#97	—	2	2	no	—
107	C₁₃×#97	C₂³	1	4	yes	—
108	C₁₃×#97	C₂³	1	4	yes	—
109	C₄×C₈×C₁₃	—	2	2	no	—
110	C₄×C₈×C₁₃	—	2	2	no	—
111	C₄×C₈×C₁₃	—	2	2	no	—
112	#17647	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₁₃×#41	—	4	8	no	—
116	C₁₃×#41	—	4	8	no	—
117	C₁₃×#41	—	4	8	no	—
118	C₁₃×#41	—	4	8	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	4	4	no	—
121	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	4	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	—	2	2	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	—	4	4	no	—
133	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	8	no	—
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	C₂²×C₄	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	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₁₃×M₁₆	—	2	8	no	—
160	C₁₃×M₁₆	—	2	8	no	—
161	C₁₃×M₁₆	—	4	4	no	—
162	C₂×C₈×C₁₃	—	2	8	no	—
163	C₂×C₈×C₁₃	—	2	4	no	—
164	C₂×C₈×C₁₃	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
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	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
190	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1530	C₂×C₁₃	1	4	yes	complemented
193	#1527	C₂×C₁₃	1	4	yes	complemented
194	#1525	C₂×C₁₃	1	4	yes	complemented
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	4	no	—
198	C₂³×C₁₃	—	4	1	no	—
199	C₂³×C₁₃	—	4	4	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	4	4	no	—
202	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	Q₈×C₁₃	—	4	4	no	—
206	Q₈×C₁₃	—	4	4	no	—
207	D₄×C₁₃	—	4	4	no	—
208	D₄×C₁₃	—	4	4	no	—
209	D₄×C₁₃	—	4	8	no	—
210	D₄×C₁₃	—	4	8	no	—
211	D₄×C₁₃	—	4	4	no	—
212	D₄×C₁₃	—	4	4	no	—
213	D₄×C₁₃	—	4	4	no	—
214	D₄×C₁₃	—	4	4	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	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	—	4	4	no	—
234	C₂×C₄×C₁₃	—	4	8	no	—
235	C₂×C₄×C₁₃	#100	1	4	yes	—
236	C₂×C₄×C₁₃	#104	1	4	yes	—
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₈×C₁₃	—	2	8	no	—
250	C₈×C₁₃	—	4	4	no	—
251	C₂²×#41	C₄×C₁₃	1	2	yes	—
252	C₂²×M₁₆	—	2	1	no	—
253	#532	—	2	1	no	—
254	#532	—	2	1	no	—
255	#532	—	2	1	no	—
256	#532	—	2	1	no	—
257	#532	C₄×C₁₃	1	2	yes	—
258	#532	C₄×C₁₃	1	2	yes	—
259	#532	C₂²×C₁₃	1	2	yes	—
260	#532	C₂²×C₁₃	1	2	yes	—
261	C₂×C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
262	C₂×#127	C₄×C₁₃	1	1	yes	characteristic
263	C₂×#124	C₂²×C₁₃	1	2	yes	—
264	C₂×#121	—	2	1	no	—
265	C₂×#121	—	2	1	no	—
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
269	#432	C₂²×C₁₃	1	2	yes	—
270	#432	C₂²×C₁₃	1	2	yes	complemented
271	#431	—	2	1	no	—
272	#431	—	2	1	no	—
273	#423	—	2	1	no	—
274	#407	—	2	1	no	—
275	C₄×M₁₆	—	2	1	no	—
276	C₄×M₁₆	—	2	1	no	—
277	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
278	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
279	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
280	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
281	C₂×C₄×C₈	—	2	1	no	—
282	#329	C₂²×C₁₃	1	16	yes	complemented
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	—	2	1	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	4	4	no	—
291	C₂²×C₁₃	—	4	4	no	—
292	C₂²×C₁₃	—	4	4	no	—
293	C₂²×C₁₃	—	4	4	no	—
294	C₂²×C₁₃	—	8	8	no	—
295	C₂²×C₁₃	C₂×#100	1	2	yes	—
296	C₂²×C₁₃	C₂×#104	1	2	yes	—
297	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	C₂×#100	1	2	yes	—
307	C₄×C₁₃	C₂×#100	1	2	yes	—
308	C₄×C₁₃	C₂×#104	1	2	yes	—
309	C₄×C₁₃	C₂×#104	1	2	yes	—
310	C₄×C₁₃	#421	1	2	yes	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	4	8	no	—
314	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
315	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
316	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
321	C₂³×C₄	—	2	2	no	—
322	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
323	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
324	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
325	C₂×M₁₆	—	2	8	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	—	2	2	no	—
328	C₂×M₁₆	—	2	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	1	no	—
331	C₄⋊Q₈	—	2	1	no	—
332	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
333	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
334	#127	—	2	1	no	—
335	#127	—	2	1	no	—
336	#127	C₂×C₄×C₁₃	1	2	yes	—
337	#127	C₂×C₄×C₁₃	1	2	yes	—
338	#124	—	2	2	no	—
339	#124	—	2	2	no	—
340	#124	C₂×C₄×C₁₃	1	4	yes	—
341	#124	C₂³×C₁₃	1	4	yes	—
342	#121	—	2	2	no	—
343	#121	—	2	2	no	—
344	#121	—	2	2	no	—
345	#121	—	2	2	no	—
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
363	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
364	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
365	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
366	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
374	C₄⋊C₈	—	2	2	no	—
375	C₄⋊C₈	—	2	2	no	—
376	C₂²⋊C₈	—	2	2	no	—
377	C₂²⋊C₈	—	2	2	no	—
378	#97	—	2	2	no	—
379	#97	C₂³×C₁₃	1	4	yes	—
380	#97	C₂³×C₁₃	1	4	yes	—
381	C₄×C₈	—	2	2	no	—
382	C₄×C₈	—	2	2	no	—
383	C₄×C₈	—	2	2	no	—
384	C₂×C₁₃	—	2	2	no	—
385	C₂×C₁₃	—	2	2	no	—
386	C₂×C₁₃	—	4	1	no	—
387	C₂×C₁₃	—	8	4	no	—
388	C₂×C₁₃	C₂²×#100	1	1	yes	characteristic
389	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
390	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
391	C₂⁴	—	2	2	no	—
392	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
393	#41	—	4	8	no	—
394	#41	—	4	8	no	—
395	#41	—	4	8	no	—
396	#41	—	4	8	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	4	4	no	—
399	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	8	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	8	no	—
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	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
425	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
426	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
427	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×C₄×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	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	M₁₆	—	2	8	no	—
438	M₁₆	—	2	8	no	—
439	M₁₆	—	4	4	no	—
440	C₂×C₈	—	2	8	no	—
441	C₂×C₈	—	2	4	no	—
442	C₂×C₈	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
452	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
453	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
454	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
455	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
456	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
457	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
458	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
459	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
467	C₁₃	#17647	1	1	yes	characteristic, direct product factor, Sylow
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	4	4	no	—
475	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
476	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
477	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
478	Q₈	—	4	4	no	—
479	Q₈	—	4	4	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	8	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	4	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	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	8	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	C₁₃×#100	1	4	yes	—
509	C₂×C₄	C₁₃×#104	1	4	yes	—
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	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
514	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
515	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
516	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
517	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
518	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
519	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
522	C₈	—	2	8	no	—
523	C₈	—	4	4	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	8	8	no	—
536	C₂²	C₂×C₁₃×#100	1	2	yes	—
537	C₂²	C₂×C₁₃×#104	1	2	yes	—
538	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	4	4	no	—
547	C₄	C₂×C₁₃×#100	1	2	yes	—
548	C₄	C₂×C₁₃×#100	1	2	yes	—
549	C₄	C₂×C₁₃×#104	1	2	yes	—
550	C₄	C₂×C₁₃×#104	1	2	yes	—
551	C₄	C₁₃×#421	1	2	yes	—
552	C₂	—	2	2	no	—
553	C₂	—	2	2	no	—
554	C₂	—	4	1	no	—
555	C₂	—	8	4	no	—
556	C₂	C₂²×C₁₃×#100	1	1	yes	characteristic
557	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic
558	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×#532	C₂
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. C₁₃×#2920	C₂	semidirect
3. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
4. C₁₃×#1530	C₂	semidirect
5. C₁₃×#1527	C₂	semidirect
6. C₁₃×#1525	C₂	semidirect
26. C₁₃×#432	C₂²	semidirect
34. C₄×C₁₃×M₁₆	C₂²	semidirect
35. C₄×C₁₃×M₁₆	C₂²	semidirect
36. C₂×C₁₃×#97	C₂²	semidirect
38. C₁₃×#329	C₂²	semidirect
112. #17647	C₁₃	direct (N × H)
190. #2920	C₂×C₁₃	semidirect
191. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
192. #1530	C₂×C₁₃	semidirect
193. #1527	C₂×C₁₃	semidirect
194. #1525	C₂×C₁₃	semidirect
270. #432	C₂²×C₁₃	semidirect
278. C₄×M₁₆	C₂²×C₁₃	semidirect
279. C₄×M₁₆	C₂²×C₁₃	semidirect
280. C₂×#97	C₂²×C₁₃	semidirect
282. #329	C₂²×C₁₃	semidirect
467. C₁₃	#17647	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×C₄×C₁₃×M₁₆	2
C₁₃×#1530	2
C₁₃×#1527	2
C₁₃×#1525	2
#17647	13

Subgroups — C13×#17647 #15703986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17647 #15703986