Subgroups — C₂×C₁₃×#1512 #15703892

Order 3328.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 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×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1512	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#328	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#327	C₂	1	2	yes	maximal
7	C₁₃×#529	—	2	2	no	—
8	C₁₃×#529	—	2	2	no	—
9	C₁₃×#529	C₄	1	4	yes	complemented
10	C₁₃×#529	C₂²	1	4	yes	—
11	C₂×C₁₃×#126	—	2	1	no	—
12	C₂×C₁₃×#125	C₄	1	1	yes	characteristic, complemented
13	C₂×C₁₃×#124	C₄	1	1	yes	characteristic, complemented
14	C₂×C₁₃×#123	—	2	1	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄×D₄×C₁₃	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic, complemented
20	C₂×C₁₃×#117	—	2	1	no	—
21	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#432	—	2	2	no	—
24	C₁₃×#432	C₂²	1	4	yes	complemented
25	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₃×#97	—	2	1	no	—
28	C₁₃×#382	—	2	2	no	—
29	C₁₃×#382	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#95	—	2	1	no	—
31	C₂×C₁₃×#95	C₂²	1	2	yes	—
32	C₁₃×#328	C₂²	1	8	yes	complemented
33	C₁₃×#327	C₂²	1	8	yes	—
34	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	—	2	1	no	—
38	C₂³×C₄×C₁₃	—	2	2	no	—
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	—	2	2	no	—
43	C₁₃×#126	—	2	4	no	—
44	C₁₃×#126	—	2	4	no	—
45	C₁₃×#125	—	2	2	no	—
46	C₁₃×#125	C₂×C₄	1	4	yes	complemented
47	C₁₃×#124	—	2	2	no	—
48	C₁₃×#124	C₂×C₄	1	4	yes	complemented
49	C₁₃×#123	—	2	4	no	—
50	C₁₃×#123	—	2	4	no	—
51	C₁₃×C₂²⋊Q₈	—	2	1	no	—
52	C₁₃×C₂²⋊Q₈	—	2	1	no	—
53	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
54	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
55	C₁₃×#121	—	2	1	no	—
56	C₁₃×#121	—	2	1	no	—
57	C₁₃×#121	C₂×C₄	1	2	yes	—
58	C₁₃×#121	C₂³	1	2	yes	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
61	C₄×D₄×C₁₃	—	2	4	no	—
62	C₄×D₄×C₁₃	—	2	4	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	complemented
65	C₁₃×#117	—	2	4	no	—
66	C₁₃×#117	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₁₃	D₄	1	2	yes	—
85	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	D₄	1	2	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
89	C₁₃×C₄⋊C₈	—	2	4	no	—
90	C₁₃×C₂²⋊C₈	—	2	2	no	—
91	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
92	C₁₃×#97	—	2	4	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₁₃×#95	—	2	4	no	—
95	C₁₃×#95	C₂³	1	4	yes	—
96	C₂×#1512	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	1	no	—
98	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₃	—	4	4	no	—
120	C₂²×C₄×C₁₃	—	4	4	no	—
121	C₂²×C₄×C₁₃	—	4	4	no	—
122	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₃	—	2	4	no	—
137	C₂×C₈×C₁₃	—	4	4	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	4	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	4	8	no	—
146	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
147	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
148	C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	2	2	no	—
150	C₁₃×C₂²⋊C₄	—	2	2	no	—
151	C₁₃×C₂²⋊C₄	—	2	4	no	—
152	C₁₃×C₂²⋊C₄	—	2	4	no	—
153	C₁₃×C₂²⋊C₄	—	2	4	no	—
154	C₁₃×C₂²⋊C₄	—	2	2	no	—
155	C₄²×C₁₃	—	2	4	no	—
156	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
157	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
158	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
159	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
160	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
161	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
162	C₄²×C₁₃	C₂×D₄	1	2	yes	—
163	C₄²×C₁₃	C₂×D₄	1	2	yes	—
164	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
165	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1512	C₂×C₁₃	1	8	yes	direct product factor
168	C₂×#328	C₂×C₁₃	1	2	yes	complemented
169	C₂×#327	C₂×C₁₃	1	2	yes	—
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
179	C₂³×C₁₃	#137	1	2	yes	—
180	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₁₃	—	4	2	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	4	2	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	2	no	—
187	D₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	8	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	4	no	—
213	C₂×C₄×C₁₃	—	8	8	no	—
214	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₈×C₁₃	—	4	4	no	—
223	#529	—	2	2	no	—
224	#529	—	2	2	no	—
225	#529	C₄×C₁₃	1	4	yes	complemented
226	#529	C₂²×C₁₃	1	4	yes	—
227	C₂×#126	—	2	1	no	—
228	C₂×#125	C₄×C₁₃	1	1	yes	characteristic, complemented
229	C₂×#124	C₄×C₁₃	1	1	yes	characteristic, complemented
230	C₂×#123	—	2	1	no	—
231	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
234	C₂×C₄×D₄	—	2	1	no	—
235	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic, complemented
236	C₂×#117	—	2	1	no	—
237	C₂²×C₄⋊C₄	—	2	1	no	—
238	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
239	#432	—	2	2	no	—
240	#432	C₂²×C₁₃	1	4	yes	complemented
241	C₂×C₄⋊C₈	—	2	1	no	—
242	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
243	C₂×#97	—	2	1	no	—
244	#382	—	2	2	no	—
245	#382	C₂²×C₁₃	1	4	yes	complemented
246	C₂×#95	—	2	1	no	—
247	C₂×#95	C₂²×C₁₃	1	2	yes	—
248	#328	C₂²×C₁₃	1	8	yes	complemented
249	#327	C₂²×C₁₃	1	8	yes	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	1	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	4	no	—
255	C₂²×C₁₃	—	2	4	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	8	4	no	—
260	C₂²×C₁₃	#410	1	2	yes	—
261	C₂²×C₁₃	#417	1	2	yes	—
262	C₂²×C₁₃	#417	1	2	yes	—
263	C₂²×C₁₃	#421	1	2	yes	—
264	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	2	2	no	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	4	2	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	4	2	no	—
278	C₄×C₁₃	—	8	4	no	—
279	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
285	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂²×C₈	—	2	2	no	—
288	#126	—	2	4	no	—
289	#126	—	2	4	no	—
290	#125	—	2	2	no	—
291	#125	C₂×C₄×C₁₃	1	4	yes	complemented
292	#124	—	2	2	no	—
293	#124	C₂×C₄×C₁₃	1	4	yes	complemented
294	#123	—	2	4	no	—
295	#123	—	2	4	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
299	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
300	#121	—	2	1	no	—
301	#121	—	2	1	no	—
302	#121	C₂×C₄×C₁₃	1	2	yes	—
303	#121	C₂³×C₁₃	1	2	yes	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	complemented
310	#117	—	2	4	no	—
311	#117	—	2	4	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	4	4	no	—
318	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
328	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
329	C₂×C₄²	D₄×C₁₃	1	2	yes	—
330	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₄²	D₄×C₁₃	1	2	yes	—
333	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
334	C₄⋊C₈	—	2	4	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
337	#97	—	2	4	no	—
338	#95	—	2	4	no	—
339	#95	—	2	2	no	—
340	#95	C₂³×C₁₃	1	4	yes	—
341	C₂×C₁₃	—	2	1	no	—
342	C₂×C₁₃	—	2	1	no	—
343	C₂×C₁₃	—	2	2	no	—
344	C₂×C₁₃	—	8	2	no	—
345	C₂×C₁₃	#1512	1	4	yes	direct product factor
346	C₂×C₁₃	C₂×#410	1	1	yes	characteristic
347	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
348	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
349	C₂⁴	—	2	1	no	—
350	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	4	2	no	—
353	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
375	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
376	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
377	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
378	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
379	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
380	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	4	4	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	4	8	no	—
398	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
399	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₄²	—	2	4	no	—
408	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
409	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
410	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
411	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
412	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
413	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
414	C₄²	C₂×D₄×C₁₃	1	2	yes	—
415	C₄²	C₂×D₄×C₁₃	1	2	yes	—
416	C₁₃	C₂×#1512	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
424	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
425	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
426	C₂³	C₁₃×#137	1	2	yes	—
427	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	4	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	8	8	no	—
461	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
462	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
465	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
466	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
467	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
469	C₈	—	4	4	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	8	4	no	—
480	C₂²	C₁₃×#410	1	2	yes	—
481	C₂²	C₁₃×#417	1	2	yes	—
482	C₂²	C₁₃×#417	1	2	yes	—
483	C₂²	C₁₃×#421	1	2	yes	—
484	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
485	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	4	no	—
499	C₂	—	2	1	no	—
500	C₂	—	2	2	no	—
501	C₂	—	2	1	no	—
502	C₂	—	8	2	no	—
503	C₂	C₁₃×#1512	1	4	yes	direct product factor
504	C₂	C₂×C₁₃×#410	1	1	yes	characteristic
505	C₂	C₂×C₁₃×#417	1	1	yes	characteristic
506	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×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×C₁₃×#382	C₂	semidirect
4. C₁₃×#1512	C₂	direct (N × H)
5. C₂×C₁₃×#328	C₂	semidirect
9. C₁₃×#529	C₄	semidirect
12. C₂×C₁₃×#125	C₄	semidirect
13. C₂×C₁₃×#124	C₄	semidirect
17. C₂×C₄×Q₈×C₁₃	C₄	semidirect
19. C₂×C₄×D₄×C₁₃	C₄	semidirect
24. C₁₃×#432	C₂²	semidirect
29. C₁₃×#382	C₂²	semidirect
32. C₁₃×#328	C₂²	semidirect
46. C₁₃×#125	C₂×C₄	semidirect
48. C₁₃×#124	C₂×C₄	semidirect
60. C₄×Q₈×C₁₃	C₂×C₄	semidirect
64. C₄×D₄×C₁₃	C₂×C₄	semidirect
96. C₂×#1512	C₁₃	direct (N × H)
165. C₂×#432	C₂×C₁₃	semidirect
166. C₂×#382	C₂×C₁₃	semidirect
167. #1512	C₂×C₁₃	direct (N × H)
168. C₂×#328	C₂×C₁₃	semidirect
225. #529	C₄×C₁₃	semidirect
228. C₂×#125	C₄×C₁₃	semidirect
229. C₂×#124	C₄×C₁₃	semidirect
233. C₂×C₄×Q₈	C₄×C₁₃	semidirect
235. C₂×C₄×D₄	C₄×C₁₃	semidirect
240. #432	C₂²×C₁₃	semidirect
245. #382	C₂²×C₁₃	semidirect
248. #328	C₂²×C₁₃	semidirect
291. #125	C₂×C₄×C₁₃	semidirect
293. #124	C₂×C₄×C₁₃	semidirect
305. C₄×Q₈	C₂×C₄×C₁₃	semidirect
309. C₄×D₄	C₂×C₄×C₁₃	semidirect
345. C₂×C₁₃	#1512	direct (N × H)
416. C₁₃	C₂×#1512	direct (N × H)
503. C₂	C₁₃×#1512	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×C₁₃×#382	2
C₁₃×#1512	2
C₂×C₁₃×#328	2
C₂×C₁₃×#327	2
C₂×#1512	13

Subgroups — C2×C13×#1512 #15703892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1512 #15703892