Subgroups — C₁₃×#29492 #15715831

Order 3328.

896 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1968	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1934	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1877	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	—	2	1	no	—
15	C₂×C₄×D₄×C₁₃	—	2	1	no	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#391	C₂²	1	1	yes	characteristic
24	C₁₃×#391	C₂²	1	1	yes	characteristic
25	C₁₃×#391	C₂²	1	1	yes	characteristic
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#390	—	2	1	no	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	1	yes	characteristic
30	C₁₃×#389	C₂²	1	1	yes	characteristic
31	C₁₃×#389	C₂²	1	1	yes	characteristic
32	C₁₃×#387	—	2	1	no	—
33	C₁₃×#387	—	2	1	no	—
34	C₁₃×#387	—	2	1	no	—
35	C₁₃×#384	C₂²	1	1	yes	characteristic
36	C₁₃×#383	—	2	1	no	—
37	C₄³×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	4	no	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	4	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×#127	—	2	4	no	—
54	C₄×D₄×C₁₃	—	4	2	no	—
55	C₄×D₄×C₁₃	—	4	2	no	—
56	C₄×D₄×C₁₃	—	4	4	no	—
57	C₄×D₄×C₁₃	—	4	4	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#106	—	4	2	no	—
78	C₁₃×#103	—	4	2	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×#102	—	4	2	no	—
82	C₄×C₈×C₁₃	—	2	4	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	1	no	—
92	#29492	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	4	no	—
99	C₂×D₄×C₁₃	—	2	4	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	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	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	#41	1	4	yes	—
110	C₂²×C₄×C₁₃	—	2	1	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	2	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	4	4	no	—
117	C₂²×C₄×C₁₃	—	4	4	no	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×SD₁₆	—	4	8	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	#41	1	4	yes	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₁₃×C₂²⋊C₄	—	4	4	no	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	4	1	no	—
153	C₄²×C₁₃	SD₁₆	1	4	yes	complemented
154	#2863	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
156	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2041	C₂×C₁₃	1	1	yes	characteristic
159	#2014	C₂×C₁₃	1	1	yes	characteristic
160	#1968	C₂×C₁₃	1	2	yes	complemented
161	#1934	C₂×C₁₃	1	2	yes	complemented
162	#1877	C₂×C₁₃	1	2	yes	complemented
163	#1864	C₂×C₁₃	1	2	yes	complemented
164	#1744	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	2	4	no	—
176	D₄×C₁₃	—	2	4	no	—
177	D₄×C₁₃	—	4	8	no	—
178	D₄×C₁₃	—	4	8	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	2	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	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	8	8	no	—
210	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
211	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
212	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
213	C₂×C₄×C₁₃	#135	1	2	yes	—
214	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
215	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
216	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
217	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
219	C₈×C₁₃	—	2	4	no	—
220	C₈×C₁₃	—	4	2	no	—
221	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
222	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄×D₄	—	2	1	no	—
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
226	C₂×#106	C₂²×C₁₃	1	2	yes	—
227	C₂×#103	C₂²×C₁₃	1	2	yes	—
228	C₂×#102	C₂²×C₁₃	1	2	yes	—
229	C₂×#102	C₂²×C₁₃	1	2	yes	—
230	C₂×#102	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
232	#391	C₂²×C₁₃	1	1	yes	characteristic
233	#391	C₂²×C₁₃	1	1	yes	characteristic
234	#391	C₂²×C₁₃	1	1	yes	characteristic
235	#390	—	2	1	no	—
236	#390	—	2	1	no	—
237	#390	C₂²×C₁₃	1	2	yes	—
238	#389	C₂²×C₁₃	1	1	yes	characteristic
239	#389	C₂²×C₁₃	1	1	yes	characteristic
240	#389	C₂²×C₁₃	1	1	yes	characteristic
241	#387	—	2	1	no	—
242	#387	—	2	1	no	—
243	#387	—	2	1	no	—
244	#384	C₂²×C₁₃	1	1	yes	characteristic
245	#383	—	2	1	no	—
246	C₄³	C₂²×C₁₃	1	1	yes	characteristic
247	#340	C₂²×C₁₃	1	2	yes	—
248	#340	C₂²×C₁₃	1	2	yes	—
249	#336	C₂²×C₁₃	1	1	yes	characteristic
250	#336	C₂²×C₁₃	1	1	yes	characteristic
251	#336	C₂²×C₁₃	1	2	yes	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	4	4	no	—
254	C₂²×C₁₃	—	4	4	no	—
255	C₂²×C₁₃	—	8	2	no	—
256	C₂²×C₁₃	—	8	2	no	—
257	C₂²×C₁₃	—	8	2	no	—
258	C₂²×C₁₃	—	8	2	no	—
259	C₂²×C₁₃	#525	1	1	yes	characteristic
260	C₂²×C₁₃	#532	1	1	yes	characteristic
261	C₂²×C₁₃	#535	1	1	yes	characteristic
262	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
263	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
264	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₂²×C₁₃	#575	1	1	yes	characteristic
266	C₄×C₁₃	—	2	2	no	—
267	C₄×C₁₃	—	2	2	no	—
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	2	2	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	4	1	no	—
272	C₄×C₁₃	—	8	1	no	—
273	C₄×C₁₃	—	8	1	no	—
274	C₄×C₁₃	—	8	1	no	—
275	C₄×C₁₃	—	8	2	no	—
276	C₄×C₁₃	—	8	1	no	—
277	C₄×C₁₃	#551	1	2	yes	—
278	C₄×C₁₃	#553	1	2	yes	—
279	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
283	C₂³×C₄	—	2	2	no	—
284	C₂×SD₁₆	—	2	4	no	—
285	C₂×SD₁₆	—	2	4	no	—
286	C₂×SD₁₆	—	4	2	no	—
287	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
289	#127	—	2	4	no	—
290	C₄×D₄	—	4	2	no	—
291	C₄×D₄	—	4	2	no	—
292	C₄×D₄	—	4	4	no	—
293	C₄×D₄	—	4	4	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
307	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
309	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
313	#106	—	4	2	no	—
314	#103	—	4	2	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	#102	—	4	2	no	—
318	C₄×C₈	—	2	4	no	—
319	#95	—	2	1	no	—
320	#95	—	2	1	no	—
321	#95	—	2	1	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	1	no	—
326	#95	—	2	1	no	—
327	#95	—	2	1	no	—
328	C₂×C₁₃	—	8	4	no	—
329	C₂×C₁₃	#2603	1	1	yes	characteristic
330	C₂×C₁₃	#3101	1	1	yes	characteristic
331	C₂×C₁₃	#3105	1	1	yes	characteristic
332	C₂×C₁₃	#3167	1	1	yes	characteristic
333	C₂×C₁₃	#3180	1	1	yes	characteristic
334	C₂×C₁₃	#3208	1	1	yes	characteristic
335	C₂×C₁₃	#3212	1	1	yes	characteristic
336	C₂⁴	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	C₁₃×#41	1	4	yes	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
368	SD₁₆	—	4	8	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	C₁₃×#41	1	4	yes	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	4	1	no	—
396	C₄²	C₁₃×SD₁₆	1	4	yes	complemented
397	C₁₃	#29492	1	1	yes	characteristic, direct product factor, Sylow
398	C₂³	—	2	4	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	4	8	no	—
411	D₄	—	4	8	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	C₂×C₄	—	2	1	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	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	8	8	no	—
443	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
444	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
445	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
446	C₂×C₄	C₁₃×#135	1	2	yes	—
447	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
448	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
449	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
450	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
452	C₈	—	2	4	no	—
453	C₈	—	4	2	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	C₁₃×#525	1	1	yes	characteristic
462	C₂²	C₁₃×#532	1	1	yes	characteristic
463	C₂²	C₁₃×#535	1	1	yes	characteristic
464	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
465	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
466	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
467	C₂²	C₁₃×#575	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	1	no	—
479	C₄	C₁₃×#551	1	2	yes	—
480	C₄	C₁₃×#553	1	2	yes	—
481	C₂	—	8	4	no	—
482	C₂	C₁₃×#2603	1	1	yes	characteristic
483	C₂	C₁₃×#3101	1	1	yes	characteristic
484	C₂	C₁₃×#3105	1	1	yes	characteristic
485	C₂	C₁₃×#3167	1	1	yes	characteristic
486	C₂	C₁₃×#3180	1	1	yes	characteristic
487	C₂	C₁₃×#3208	1	1	yes	characteristic
488	C₂	C₁₃×#3212	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2863	C₂	semidirect
3. C₁₃×#2084	C₂	semidirect
4. C₁₃×#2072	C₂	semidirect
7. C₁₃×#1968	C₂	semidirect
8. C₁₃×#1934	C₂	semidirect
9. C₁₃×#1877	C₂	semidirect
10. C₁₃×#1864	C₂	semidirect
11. C₁₃×#1744	C₂	semidirect
92. #29492	C₁₃	direct (N × H)
153. C₄²×C₁₃	SD₁₆	semidirect
154. #2863	C₂×C₁₃	semidirect
156. #2084	C₂×C₁₃	semidirect
157. #2072	C₂×C₁₃	semidirect
160. #1968	C₂×C₁₃	semidirect
161. #1934	C₂×C₁₃	semidirect
162. #1877	C₂×C₁₃	semidirect
163. #1864	C₂×C₁₃	semidirect
164. #1744	C₂×C₁₃	semidirect
396. C₄²	C₁₃×SD₁₆	semidirect
397. C₁₃	#29492	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×#2863	2
C₄×C₁₃×#127	2
C₁₃×#2084	2
C₁₃×#2072	2
C₁₃×#2041	2
C₁₃×#2014	2
C₁₃×#1968	2
C₁₃×#1934	2
C₁₃×#1877	2
C₁₃×#1864	2
C₁₃×#1744	2
#29492	13

Subgroups — C13×#29492 #15715831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29492 #15715831