Subgroups — C₂×C₁₃×#1547 #15704042

Order 3328.

1354 conjugacy classes of subgroups.

The subgroup lattice has 466 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	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1547	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#332	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#331	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₃×#41	—	2	1	no	—
8	C₂²×C₁₃×M₁₆	—	2	1	no	—
9	C₂³×C₈×C₁₃	—	2	1	no	—
10	C₁₃×#532	—	2	2	no	—
11	C₁₃×#532	—	2	2	no	—
12	C₁₃×#532	C₄	1	4	yes	—
13	C₁₃×#532	C₂²	1	4	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#124	—	2	1	no	—
17	C₂×C₁₃×#121	—	2	1	no	—
18	C₂×C₁₃×#121	C₄	1	2	yes	—
19	C₂×C₄×D₄×C₁₃	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#423	—	2	2	no	—
23	C₁₃×#423	C₂²	1	4	yes	complemented
24	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
26	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	complemented
30	C₁₃×#332	C₂²	1	8	yes	complemented
31	C₁₃×#331	C₂²	1	8	yes	complemented
32	C₂×C₁₃×#41	—	2	4	no	—
33	C₂×C₁₃×#41	—	2	4	no	—
34	C₂×C₁₃×#41	—	4	4	no	—
35	C₂×C₁₃×#41	—	4	4	no	—
36	C₂²×Q₈×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	—	2	2	no	—
38	C₂²×D₄×C₁₃	—	2	1	no	—
39	C₂²×D₄×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₃	—	2	2	no	—
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	—	2	4	no	—
46	C₂×C₁₃×M₁₆	—	4	4	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	4	no	—
50	C₂²×C₈×C₁₃	—	4	4	no	—
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	—	2	1	no	—
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
54	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₁₃×#127	—	2	1	no	—
56	C₁₃×#127	—	2	1	no	—
57	C₁₃×#127	C₂×C₄	1	2	yes	—
58	C₁₃×#127	C₂³	1	2	yes	—
59	C₁₃×#124	—	2	4	no	—
60	C₁₃×#124	—	2	4	no	—
61	C₁₃×#121	—	2	4	no	—
62	C₁₃×#121	—	2	4	no	—
63	C₁₃×#121	—	2	4	no	—
64	C₁₃×#121	C₂×C₄	1	8	yes	—
65	C₄×D₄×C₁₃	—	2	4	no	—
66	C₄×D₄×C₁₃	—	2	4	no	—
67	C₄×D₄×C₁₃	—	2	4	no	—
68	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	D₄	1	2	yes	—
78	C₂×C₄²×C₁₃	D₄	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×C₄⋊C₈	—	2	4	no	—
83	C₁₃×C₄⋊C₈	—	2	4	no	—
84	C₁₃×C₄⋊C₈	—	2	2	no	—
85	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
86	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
87	C₂×#1547	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	2	no	—
89	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₁₃×#41	—	4	16	no	—
91	C₁₃×#41	—	4	8	no	—
92	C₁₃×#41	—	4	8	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	2	8	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	4	4	no	—
104	C₂×D₄×C₁₃	—	4	8	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	—	4	2	no	—
109	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	—	4	8	no	—
116	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	D₈	1	4	yes	—
123	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
124	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₁₃×M₁₆	—	4	8	no	—
131	C₂×C₈×C₁₃	—	2	4	no	—
132	C₂×C₈×C₁₃	—	2	4	no	—
133	C₂×C₈×C₁₃	—	4	8	no	—
134	C₂×C₈×C₁₃	—	4	4	no	—
135	C₂×C₈×C₁₃	—	4	4	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
140	C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₁₃×C₂²⋊C₄	—	2	8	no	—
142	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
143	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
144	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
145	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
146	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₃	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃	C₂×D₄	1	2	yes	—
149	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
153	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1547	C₂×C₁₃	1	8	yes	direct product factor
156	C₂×#332	C₂×C₁₃	1	2	yes	complemented
157	C₂×#331	C₂×C₁₃	1	2	yes	complemented
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	2	4	no	—
161	C₂³×C₁₃	—	4	4	no	—
162	C₂³×C₁₃	—	4	4	no	—
163	C₂³×C₁₃	—	4	4	no	—
164	C₂³×C₁₃	#102	1	4	yes	—
165	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	Q₈×C₁₃	—	4	4	no	—
170	D₄×C₁₃	—	4	4	no	—
171	D₄×C₁₃	—	4	4	no	—
172	D₄×C₁₃	—	4	16	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	4	no	—
178	D₄×C₁₃	—	4	4	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	4	no	—
189	C₂×C₄×C₁₃	—	4	16	no	—
190	C₂×C₄×C₁₃	#102	1	4	yes	—
191	C₂×C₄×C₁₃	#102	1	8	yes	—
192	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
200	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
202	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
203	C₂×C₄×C₁₃	#137	1	2	yes	—
204	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₈×C₁₃	—	4	4	no	—
208	C₈×C₁₃	—	4	4	no	—
209	C₂²×#41	—	2	1	no	—
210	C₂²×M₁₆	—	2	1	no	—
211	C₂³×C₈	—	2	1	no	—
212	#532	—	2	2	no	—
213	#532	—	2	2	no	—
214	#532	C₄×C₁₃	1	4	yes	—
215	#532	C₂²×C₁₃	1	4	yes	—
216	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#124	—	2	1	no	—
219	C₂×#121	—	2	1	no	—
220	C₂×#121	C₄×C₁₃	1	2	yes	—
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	—
223	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
224	#423	—	2	2	no	—
225	#423	C₂²×C₁₃	1	4	yes	complemented
226	C₂×C₄⋊C₈	—	2	2	no	—
227	C₂×C₄⋊C₈	—	2	1	no	—
228	C₂×C₄⋊C₈	—	2	1	no	—
229	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
232	#332	C₂²×C₁₃	1	8	yes	complemented
233	#331	C₂²×C₁₃	1	8	yes	complemented
234	C₂²×C₁₃	—	2	8	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	4	4	no	—
238	C₂²×C₁₃	—	4	4	no	—
239	C₂²×C₁₃	—	4	4	no	—
240	C₂²×C₁₃	—	8	8	no	—
241	C₂²×C₁₃	#413	1	2	yes	—
242	C₂²×C₁₃	C₂×#102	1	4	yes	—
243	C₂²×C₁₃	C₂×#102	1	2	yes	—
244	C₂²×C₁₃	#417	1	2	yes	—
245	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	4	4	no	—
251	C₄×C₁₃	C₂×#102	1	4	yes	—
252	C₄×C₁₃	C₂×#102	1	2	yes	—
253	C₄×C₁₃	#417	1	2	yes	—
254	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
255	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
256	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
257	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
258	C₂×#41	—	2	4	no	—
259	C₂×#41	—	2	4	no	—
260	C₂×#41	—	4	4	no	—
261	C₂×#41	—	4	4	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
267	C₂³×C₄	—	2	2	no	—
268	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
269	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
270	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
271	C₂×M₁₆	—	2	4	no	—
272	C₂×M₁₆	—	4	4	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	4	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	4	4	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
280	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
281	#127	—	2	1	no	—
282	#127	—	2	1	no	—
283	#127	C₂×C₄×C₁₃	1	2	yes	—
284	#127	C₂³×C₁₃	1	2	yes	—
285	#124	—	2	4	no	—
286	#124	—	2	4	no	—
287	#121	—	2	4	no	—
288	#121	—	2	4	no	—
289	#121	—	2	4	no	—
290	#121	C₂×C₄×C₁₃	1	8	yes	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	2	4	no	—
293	C₄×D₄	—	2	4	no	—
294	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
300	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
301	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
302	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₄²	D₄×C₁₃	1	2	yes	—
304	C₂×C₄²	D₄×C₁₃	1	2	yes	—
305	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	4	no	—
309	C₄⋊C₈	—	2	4	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
312	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
313	C₂×C₁₃	—	2	4	no	—
314	C₂×C₁₃	—	8	4	no	—
315	C₂×C₁₃	#1547	1	4	yes	direct product factor
316	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
317	C₂×C₁₃	C₂²×#102	1	1	yes	characteristic
318	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
319	C₂⁴	—	2	2	no	—
320	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
321	#41	—	4	16	no	—
322	#41	—	4	8	no	—
323	#41	—	4	8	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	—	4	8	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	8	no	—
347	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
348	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
349	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
350	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
351	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
352	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
353	C₂²×C₄	C₁₃×D₈	1	4	yes	—
354	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
355	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	M₁₆	—	4	8	no	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	4	8	no	—
365	C₂×C₈	—	4	4	no	—
366	C₂×C₈	—	4	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
371	C₂²⋊C₄	—	2	8	no	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
374	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
375	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
376	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
377	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₁₃	1	2	yes	—
379	C₄²	C₂×D₄×C₁₃	1	2	yes	—
380	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
383	C₁₃	C₂×#1547	1	1	yes	characteristic, direct product factor, Sylow
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	4	4	no	—
390	C₂³	C₁₃×#102	1	4	yes	—
391	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
392	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
393	Q₈	—	4	4	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	16	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	16	no	—
416	C₂×C₄	C₁₃×#102	1	4	yes	—
417	C₂×C₄	C₁₃×#102	1	8	yes	—
418	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
419	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
420	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
422	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
423	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
424	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
425	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
426	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
427	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
428	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
429	C₂×C₄	C₁₃×#137	1	2	yes	—
430	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	C₈	—	4	4	no	—
434	C₈	—	4	4	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	8	no	—
442	C₂²	C₁₃×#413	1	2	yes	—
443	C₂²	C₂×C₁₃×#102	1	4	yes	—
444	C₂²	C₂×C₁₃×#102	1	2	yes	—
445	C₂²	C₁₃×#417	1	2	yes	—
446	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	4	no	—
452	C₄	C₂×C₁₃×#102	1	4	yes	—
453	C₄	C₂×C₁₃×#102	1	2	yes	—
454	C₄	C₁₃×#417	1	2	yes	—
455	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
456	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
457	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
458	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
459	C₂	—	2	4	no	—
460	C₂	—	8	4	no	—
461	C₂	C₁₃×#1547	1	4	yes	direct product factor
462	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
463	C₂	C₂²×C₁₃×#102	1	1	yes	characteristic
464	C₂	C₂×C₁₃×#417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×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 ◁ 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×#423	C₂	semidirect
3. C₂²×C₁₃×C₄⋊C₈	C₂	semidirect
4. C₁₃×#1547	C₂	direct (N × H)
5. C₂×C₁₃×#332	C₂	semidirect
6. C₂×C₁₃×#331	C₂	semidirect
23. C₁₃×#423	C₂²	semidirect
29. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
30. C₁₃×#332	C₂²	semidirect
31. C₁₃×#331	C₂²	semidirect
87. C₂×#1547	C₁₃	direct (N × H)
153. C₂×#423	C₂×C₁₃	semidirect
154. C₂²×C₄⋊C₈	C₂×C₁₃	semidirect
155. #1547	C₂×C₁₃	direct (N × H)
156. C₂×#332	C₂×C₁₃	semidirect
157. C₂×#331	C₂×C₁₃	semidirect
225. #423	C₂²×C₁₃	semidirect
231. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
232. #332	C₂²×C₁₃	semidirect
233. #331	C₂²×C₁₃	semidirect
315. C₂×C₁₃	#1547	direct (N × H)
383. C₁₃	C₂×#1547	direct (N × H)
461. C₂	C₁₃×#1547	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
C₂×C₁₃×#423	2
C₂²×C₁₃×C₄⋊C₈	2
C₁₃×#1547	2
C₂×C₁₃×#332	2
C₂×C₁₃×#331	2
C₂×#1547	13

Subgroups — C2×C13×#1547 #15704042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1547 #15704042