Subgroups — C₁₃×#29156 #15715495

Order 3328.

912 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1920	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1893	C₂	1	2	yes	maximal
9	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1807	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₁₃×#391	—	2	1	no	—
24	C₁₃×#390	C₂²	1	1	yes	characteristic
25	C₁₃×#389	—	2	1	no	—
26	C₁₃×#389	C₂²	1	1	yes	characteristic
27	C₁₃×#389	C₂²	1	2	yes	—
28	C₁₃×#388	—	2	1	no	—
29	C₁₃×#386	—	2	1	no	—
30	C₁₃×#384	C₂²	1	1	yes	characteristic
31	C₁₃×#380	—	2	1	no	—
32	C₁₃×#380	C₂²	1	1	yes	characteristic
33	C₁₃×#380	C₂²	1	2	yes	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
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	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	—	2	4	no	—
51	C₂²×C₈×C₁₃	—	2	4	no	—
52	C₂²×C₈×C₁₃	—	4	2	no	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₁₃×C₄⋊Q₈	—	4	2	no	—
56	C₁₃×C₂²⋊Q₈	—	4	4	no	—
57	C₁₃×#121	—	2	2	no	—
58	C₁₃×#121	Q₈	1	4	yes	complemented
59	C₄×D₄×C₁₃	—	4	2	no	—
60	C₄×D₄×C₁₃	—	4	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	—	4	2	no	—
79	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#106	—	2	4	no	—
84	C₁₃×#106	—	4	2	no	—
85	C₁₃×#102	—	2	4	no	—
86	C₁₃×#102	—	4	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	#29156	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×Q₈×C₁₃	—	4	2	no	—
98	C₂×D₄×C₁₃	—	2	4	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	4	1	no	—
115	C₂²×C₄×C₁₃	—	4	1	no	—
116	C₂²×C₄×C₁₃	—	4	1	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	—	4	2	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
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	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₁₃	#41	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	4	8	no	—
135	C₂×C₈×C₁₃	#41	1	4	yes	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	4	2	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	—	4	4	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
149	C₁₃×C₂²⋊C₄	—	2	4	no	—
150	C₁₃×C₂²⋊C₄	—	4	2	no	—
151	C₁₃×C₂²⋊C₄	—	4	2	no	—
152	C₁₃×C₂²⋊C₄	—	4	4	no	—
153	C₁₃×C₂²⋊C₄	—	4	2	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	4	1	no	—
158	C₄²×C₁₃	—	4	1	no	—
159	C₄²×C₁₃	—	4	2	no	—
160	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₄×#121	C₂×C₁₃	1	1	yes	characteristic
162	#2100	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2094	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#2023	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1920	C₂×C₁₃	1	2	yes	complemented
167	#1893	C₂×C₁₃	1	2	yes	—
168	#1864	C₂×C₁₃	1	2	yes	complemented
169	#1807	C₂×C₁₃	1	2	yes	complemented
170	C₂×#336	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	2	1	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
183	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
184	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
185	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₃	—	8	4	no	—
187	D₄×C₁₃	—	2	4	no	—
188	D₄×C₁₃	—	4	8	no	—
189	D₄×C₁₃	—	4	2	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	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	4	4	no	—
205	C₂×C₄×C₁₃	—	4	4	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	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	8	4	no	—
221	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
222	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
223	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
224	C₂×C₄×C₁₃	#135	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
228	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
229	C₈×C₁₃	—	2	4	no	—
230	C₈×C₁₃	—	4	2	no	—
231	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
232	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₂²⋊Q₈	—	2	1	no	—
234	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₄×D₄	—	2	1	no	—
236	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×#106	C₂²×C₁₃	1	2	yes	—
239	C₂×#106	C₂²×C₁₃	1	2	yes	—
240	C₂×#102	C₂²×C₁₃	1	2	yes	—
241	C₂×#102	C₂²×C₁₃	1	2	yes	—
242	#391	—	2	1	no	—
243	#390	C₂²×C₁₃	1	1	yes	characteristic
244	#389	—	2	1	no	—
245	#389	C₂²×C₁₃	1	1	yes	characteristic
246	#389	C₂²×C₁₃	1	2	yes	—
247	#388	—	2	1	no	—
248	#386	—	2	1	no	—
249	#384	C₂²×C₁₃	1	1	yes	characteristic
250	#380	—	2	1	no	—
251	#380	C₂²×C₁₃	1	1	yes	characteristic
252	#380	C₂²×C₁₃	1	2	yes	—
253	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
254	C₄×C₂²⋊C₄	—	2	1	no	—
255	#340	C₂²×C₁₃	1	2	yes	—
256	#340	C₂²×C₁₃	1	2	yes	—
257	#340	C₂²×C₁₃	1	2	yes	—
258	#340	C₂²×C₁₃	1	2	yes	—
259	#336	C₂²×C₁₃	1	1	yes	characteristic
260	#336	C₂²×C₁₃	1	1	yes	characteristic
261	#336	C₂²×C₁₃	1	2	yes	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	2	2	no	—
265	C₂²×C₁₃	—	2	2	no	—
266	C₂²×C₁₃	—	2	2	no	—
267	C₂²×C₁₃	—	2	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	8	1	no	—
272	C₂²×C₁₃	—	8	1	no	—
273	C₂²×C₁₃	—	8	1	no	—
274	C₂²×C₁₃	—	8	1	no	—
275	C₂²×C₁₃	#476	1	4	yes	—
276	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
277	C₂²×C₁₃	#532	1	1	yes	characteristic
278	C₂²×C₁₃	#534	1	1	yes	characteristic
279	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
280	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
281	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₂²×C₁₃	#575	1	1	yes	characteristic
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	2	2	no	—
287	C₄×C₁₃	—	4	1	no	—
288	C₄×C₁₃	—	4	2	no	—
289	C₄×C₁₃	—	8	1	no	—
290	C₄×C₁₃	—	8	2	no	—
291	C₄×C₁₃	—	8	1	no	—
292	C₄×C₁₃	—	8	2	no	—
293	C₄×C₁₃	#551	1	2	yes	—
294	C₄×C₁₃	#554	1	2	yes	—
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
300	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×C₈	—	2	4	no	—
303	C₂²×C₈	—	2	4	no	—
304	C₂²×C₈	—	4	2	no	—
305	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
306	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
307	C₄⋊Q₈	—	4	2	no	—
308	C₂²⋊Q₈	—	4	4	no	—
309	#121	—	2	2	no	—
310	#121	Q₈×C₁₃	1	4	yes	complemented
311	C₄×D₄	—	4	2	no	—
312	C₄×D₄	—	4	4	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	4	2	no	—
331	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	#106	—	2	4	no	—
336	#106	—	4	2	no	—
337	#102	—	2	4	no	—
338	#102	—	4	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	—	2	1	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	C₂×C₁₃	—	2	4	no	—
345	C₂×C₁₃	—	8	2	no	—
346	C₂×C₁₃	#2564	1	1	yes	characteristic
347	C₂×C₁₃	C₂×#476	1	1	yes	characteristic
348	C₂×C₁₃	#3076	1	1	yes	characteristic
349	C₂×C₁₃	#3167	1	1	yes	characteristic
350	C₂×C₁₃	#3180	1	1	yes	characteristic
351	C₂×C₁₃	#3187	1	1	yes	characteristic
352	C₂×C₁₃	#3188	1	1	yes	characteristic
353	C₂⁴	—	2	1	no	—
354	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
386	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
387	C₂²×C₄	C₁₃×#41	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	4	8	no	—
395	C₂×C₈	C₁₃×#41	1	4	yes	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	4	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	—	4	4	no	—
413	C₂²⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	4	1	no	—
418	C₄²	—	4	1	no	—
419	C₄²	—	4	2	no	—
420	C₁₃	#29156	1	1	yes	characteristic, direct product factor, Sylow
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
433	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
434	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
435	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
436	Q₈	—	8	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	4	8	no	—
439	D₄	—	4	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	8	4	no	—
471	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
472	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
473	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
474	C₂×C₄	C₁₃×#135	1	2	yes	—
475	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
476	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
477	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
478	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
479	C₈	—	2	4	no	—
480	C₈	—	4	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	8	1	no	—
493	C₂²	—	8	1	no	—
494	C₂²	C₁₃×#476	1	4	yes	—
495	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
496	C₂²	C₁₃×#532	1	1	yes	characteristic
497	C₂²	C₁₃×#534	1	1	yes	characteristic
498	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
499	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
500	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
501	C₂²	C₁₃×#575	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	1	no	—
508	C₄	—	8	1	no	—
509	C₄	—	8	2	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	2	no	—
512	C₄	C₁₃×#551	1	2	yes	—
513	C₄	C₁₃×#554	1	2	yes	—
514	C₂	—	2	4	no	—
515	C₂	—	8	2	no	—
516	C₂	C₁₃×#2564	1	1	yes	characteristic
517	C₂	C₂×C₁₃×#476	1	1	yes	characteristic
518	C₂	C₁₃×#3076	1	1	yes	characteristic
519	C₂	C₁₃×#3167	1	1	yes	characteristic
520	C₂	C₁₃×#3180	1	1	yes	characteristic
521	C₂	C₁₃×#3187	1	1	yes	characteristic
522	C₂	C₁₃×#3188	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
1. C₁₃×#2857	C₂	semidirect
3. C₁₃×#2100	C₂	semidirect
4. C₁₃×#2094	C₂	semidirect
5. C₁₃×#2058	C₂	semidirect
6. C₁₃×#2023	C₂	semidirect
7. C₁₃×#1920	C₂	semidirect
9. C₁₃×#1864	C₂	semidirect
10. C₁₃×#1807	C₂	semidirect
11. C₂×C₁₃×#336	C₂	semidirect
58. C₁₃×#121	Q₈	semidirect
92. #29156	C₁₃	direct (N × H)
160. #2857	C₂×C₁₃	semidirect
162. #2100	C₂×C₁₃	semidirect
163. #2094	C₂×C₁₃	semidirect
164. #2058	C₂×C₁₃	semidirect
165. #2023	C₂×C₁₃	semidirect
166. #1920	C₂×C₁₃	semidirect
168. #1864	C₂×C₁₃	semidirect
169. #1807	C₂×C₁₃	semidirect
170. C₂×#336	C₂×C₁₃	semidirect
310. #121	Q₈×C₁₃	semidirect
420. C₁₃	#29156	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×#2857	2
C₄×C₁₃×#121	2
C₁₃×#2100	2
C₁₃×#2094	2
C₁₃×#2058	2
C₁₃×#2023	2
C₁₃×#1920	2
C₁₃×#1893	2
C₁₃×#1864	2
C₁₃×#1807	2
C₂×C₁₃×#336	2
#29156	13

Subgroups — C13×#29156 #15715495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29156 #15715495