Subgroups — C₁₃×#17910 #15704249

Order 3328.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1586	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1585	C₂	1	2	yes	maximal, complemented
6	C₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1573	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1483	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	—	2	1	no	—
13	C₁₃×#529	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#484	C₄	1	1	yes	characteristic
16	C₁₃×#481	C₄	1	1	yes	characteristic
17	C₁₃×#478	C₄	1	2	yes	—
18	C₁₃×#463	C₄	1	2	yes	—
19	C₁₃×#450	C₄	1	1	yes	characteristic
20	C₁₃×#447	C₄	1	1	yes	characteristic
21	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
22	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
24	C₄×C₁₃×D₈	C₂²	1	2	yes	—
25	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#435	—	2	1	no	—
27	C₈×D₄×C₁₃	—	2	1	no	—
28	C₈×D₄×C₁₃	—	2	1	no	—
29	C₈×D₄×C₁₃	—	2	1	no	—
30	C₈×D₄×C₁₃	C₂²	1	2	yes	—
31	C₈×D₄×C₁₃	C₂²	1	2	yes	—
32	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#433	—	2	1	no	—
34	C₁₃×#432	C₂²	1	1	yes	characteristic
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
38	C₁₃×#405	—	2	1	no	—
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#335	C₂²	1	2	yes	complemented
42	C₁₃×#334	C₂²	1	2	yes	complemented
43	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
47	C₁₃×#322	C₂²	1	2	yes	complemented
48	C₈²×C₁₃	C₂²	1	2	yes	complemented
49	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂²×C₈×C₁₃	—	2	1	no	—
56	C₂²×C₈×C₁₃	—	2	2	no	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	—	4	4	no	—
60	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
62	C₁₃×#126	—	2	1	no	—
63	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
64	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
65	C₁₃×#123	—	2	1	no	—
66	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
67	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₃	—	2	1	no	—
70	C₄×D₄×C₁₃	—	2	1	no	—
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
73	C₄×D₄×C₁₃	C₂³	1	2	yes	—
74	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#117	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	C₂×C₄	1	2	yes	—
80	C₁₃×#106	C₂×C₄	1	2	yes	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	—	2	1	no	—
83	C₁₃×C₄⋊C₈	—	2	1	no	—
84	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
85	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
88	C₁₃×#103	C₂×C₄	1	2	yes	—
89	C₁₃×#102	C₂×C₄	1	2	yes	—
90	C₁₃×#102	C₂×C₄	1	2	yes	—
91	C₁₃×#102	C₂×C₄	1	2	yes	—
92	C₁₃×C₂²⋊C₈	—	2	1	no	—
93	C₁₃×C₂²⋊C₈	—	2	2	no	—
94	C₁₃×C₂²⋊C₈	—	2	2	no	—
95	C₁₃×C₂²⋊C₈	—	2	1	no	—
96	C₁₃×C₂²⋊C₈	—	2	1	no	—
97	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#97	—	2	1	no	—
100	C₁₃×#97	—	2	1	no	—
101	C₁₃×#97	—	2	1	no	—
102	C₄×C₈×C₁₃	—	2	1	no	—
103	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₁₃	C₂³	1	2	yes	—
106	C₄×C₈×C₁₃	C₂³	1	2	yes	—
107	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	#17910	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₃	—	2	4	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₁₃×SD₁₆	—	2	4	no	—
127	C₁₃×D₈	—	2	4	no	—
128	C₁₃×M₁₆	—	2	4	no	—
129	C₁₃×M₁₆	—	4	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	4	1	no	—
136	C₂×C₈×C₁₃	—	4	4	no	—
137	C₂×C₈×C₁₃	—	4	2	no	—
138	C₂×C₈×C₁₃	—	4	2	no	—
139	C₂×C₈×C₁₃	—	4	4	no	—
140	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	2	no	—
156	C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₃	#41	1	1	yes	characteristic
165	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
166	#3105	C₂×C₁₃	1	1	yes	characteristic
167	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1586	C₂×C₁₃	1	2	yes	complemented
170	#1585	C₂×C₁₃	1	2	yes	complemented
171	C₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
172	C₈×D₈	C₂×C₁₃	1	2	yes	complemented
173	#1573	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1490	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1483	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	4	2	no	—
181	C₂³×C₁₃	—	4	2	no	—
182	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
183	Q₈×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	2	4	no	—
185	D₄×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	#131	1	4	yes	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	4	4	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₈×C₁₃	—	2	4	no	—
210	C₈×C₁₃	—	2	2	no	—
211	C₈×C₁₃	—	2	2	no	—
212	C₈×C₁₃	—	2	1	no	—
213	C₈×C₁₃	—	2	1	no	—
214	C₈×C₁₃	—	2	1	no	—
215	C₈×C₁₃	—	4	1	no	—
216	C₈×C₁₃	—	4	2	no	—
217	C₈×C₁₃	—	4	1	no	—
218	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
219	C₂³×C₈	—	2	1	no	—
220	#529	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
222	#484	C₄×C₁₃	1	1	yes	characteristic
223	#481	C₄×C₁₃	1	1	yes	characteristic
224	#478	C₄×C₁₃	1	2	yes	—
225	#463	C₄×C₁₃	1	2	yes	—
226	#450	C₄×C₁₃	1	1	yes	characteristic
227	#447	C₄×C₁₃	1	1	yes	characteristic
228	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
229	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
230	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
231	C₄×D₈	C₂²×C₁₃	1	2	yes	—
232	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
233	#435	—	2	1	no	—
234	C₈×D₄	—	2	1	no	—
235	C₈×D₄	—	2	1	no	—
236	C₈×D₄	—	2	1	no	—
237	C₈×D₄	C₂²×C₁₃	1	2	yes	—
238	C₈×D₄	C₂²×C₁₃	1	2	yes	—
239	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
240	#433	—	2	1	no	—
241	#432	C₂²×C₁₃	1	1	yes	characteristic
242	#431	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₂²⋊C₈	—	2	1	no	—
245	#405	—	2	1	no	—
246	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
248	#335	C₂²×C₁₃	1	2	yes	complemented
249	#334	C₂²×C₁₃	1	2	yes	complemented
250	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
251	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
252	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
253	D₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
254	#322	C₂²×C₁₃	1	2	yes	complemented
255	C₈²	C₂²×C₁₃	1	2	yes	complemented
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	4	no	—
259	C₂²×C₁₃	—	4	8	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	1	no	—
263	C₂²×C₁₃	—	4	1	no	—
264	C₂²×C₁₃	—	4	1	no	—
265	C₂²×C₁₃	#443	1	2	yes	—
266	C₂²×C₁₃	C₂×C₄×D₄	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	—	4	1	no	—
272	C₄×C₁₃	—	4	1	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	C₂×#131	1	2	yes	—
276	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₄×C₁₃	#575	1	1	yes	characteristic
278	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
281	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	4	4	no	—
289	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
291	#126	—	2	1	no	—
292	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
293	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
294	#123	—	2	1	no	—
295	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
296	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
297	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
302	C₄×D₄	C₂³×C₁₃	1	2	yes	—
303	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
308	#107	C₂×C₄×C₁₃	1	2	yes	—
309	#106	C₂×C₄×C₁₃	1	2	yes	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
314	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
317	#103	C₂×C₄×C₁₃	1	2	yes	—
318	#102	C₂×C₄×C₁₃	1	2	yes	—
319	#102	C₂×C₄×C₁₃	1	2	yes	—
320	#102	C₂×C₄×C₁₃	1	2	yes	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
327	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
328	#97	—	2	1	no	—
329	#97	—	2	1	no	—
330	#97	—	2	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
333	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
334	C₄×C₈	C₂³×C₁₃	1	2	yes	—
335	C₄×C₈	C₂³×C₁₃	1	2	yes	—
336	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×C₁₃	—	2	2	no	—
339	C₂×C₁₃	—	4	4	no	—
340	C₂×C₁₃	—	8	1	no	—
341	C₂×C₁₃	#2929	1	1	yes	characteristic
342	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
343	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
344	C₂⁴	—	2	1	no	—
345	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
350	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
360	SD₁₆	—	2	4	no	—
361	D₈	—	2	4	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	4	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	4	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	—	4	4	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
375	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
376	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
386	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
387	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₄²	C₁₃×#41	1	1	yes	characteristic
399	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
400	C₁₃	#17910	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³	—	2	4	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	2	no	—
412	D₄	C₁₃×#131	1	4	yes	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
429	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₈	—	2	4	no	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	1	no	—
442	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	C₁₃×#443	1	2	yes	—
453	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	1	no	—
462	C₄	C₂×C₁₃×#131	1	2	yes	—
463	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
464	C₄	C₁₃×#575	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	4	4	no	—
467	C₂	—	8	1	no	—
468	C₂	C₁₃×#2929	1	1	yes	characteristic
469	C₂	C₄×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
470	C₂	C₂×C₁₃×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#447	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2966	C₂	semidirect
3. C₂×C₈×D₄×C₁₃	C₂	semidirect
4. C₁₃×#1586	C₂	semidirect
5. C₁₃×#1585	C₂	semidirect
6. C₈×C₁₃×SD₁₆	C₂	semidirect
7. C₈×C₁₃×D₈	C₂	semidirect
8. C₁₃×#1573	C₂	semidirect
9. C₁₃×#1490	C₂	semidirect
10. C₁₃×#1483	C₂	semidirect
11. C₈×C₁₃×M₁₆	C₂	semidirect
21. C₁₃×#446	C₂²	semidirect
22. C₈×Q₈×C₁₃	C₂²	semidirect
25. C₁₃×#436	C₂²	semidirect
32. C₈×D₄×C₁₃	C₂²	semidirect
41. C₁₃×#335	C₂²	semidirect
42. C₁₃×#334	C₂²	semidirect
43. C₁₃×Q₈⋊C₈	C₂²	semidirect
46. C₁₃×D₄⋊C₈	C₂²	semidirect
47. C₁₃×#322	C₂²	semidirect
48. C₈²×C₁₃	C₂²	semidirect
109. #17910	C₁₃	direct (N × H)
167. #2966	C₂×C₁₃	semidirect
168. C₂×C₈×D₄	C₂×C₁₃	semidirect
169. #1586	C₂×C₁₃	semidirect
170. #1585	C₂×C₁₃	semidirect
171. C₈×SD₁₆	C₂×C₁₃	semidirect
172. C₈×D₈	C₂×C₁₃	semidirect
173. #1573	C₂×C₁₃	semidirect
174. #1490	C₂×C₁₃	semidirect
175. #1483	C₂×C₁₃	semidirect
176. C₈×M₁₆	C₂×C₁₃	semidirect
228. #446	C₂²×C₁₃	semidirect
229. C₈×Q₈	C₂²×C₁₃	semidirect
232. #436	C₂²×C₁₃	semidirect
239. C₈×D₄	C₂²×C₁₃	semidirect
248. #335	C₂²×C₁₃	semidirect
249. #334	C₂²×C₁₃	semidirect
250. Q₈⋊C₈	C₂²×C₁₃	semidirect
253. D₄⋊C₈	C₂²×C₁₃	semidirect
254. #322	C₂²×C₁₃	semidirect
255. C₈²	C₂²×C₁₃	semidirect
400. C₁₃	#17910	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3105	2
C₁₃×#2966	2
C₂×C₈×D₄×C₁₃	2
C₁₃×#1586	2
C₁₃×#1585	2
C₈×C₁₃×SD₁₆	2
C₈×C₁₃×D₈	2
C₁₃×#1573	2
C₁₃×#1490	2
C₁₃×#1483	2
C₈×C₁₃×M₁₆	2
#17910	13

Subgroups — C13×#17910 #15704249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17910 #15704249