Subgroups — C₁₃×#26235 #15712574

Order 3328.

998 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#482	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2034	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1875	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#127	—	2	1	no	—
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#121	C₂²	1	2	yes	—
15	C₂×C₁₃×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#117	C₂²	1	2	yes	—
18	C₁₃×#482	—	2	8	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#392	—	2	2	no	—
31	C₁₃×#390	—	2	1	no	—
32	C₁₃×#390	—	2	1	no	—
33	C₁₃×#388	—	2	2	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×#127	—	2	2	no	—
53	C₁₃×#127	—	2	2	no	—
54	C₁₃×#127	—	4	4	no	—
55	C₁₃×#121	—	2	4	no	—
56	C₁₃×#121	—	2	4	no	—
57	C₁₃×#121	—	4	2	no	—
58	C₁₃×#121	—	4	2	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₁₃×#117	—	2	4	no	—
62	C₁₃×#117	—	4	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
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	1	yes	characteristic
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	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	2	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#107	—	2	4	no	—
81	C₁₃×#106	—	2	2	no	—
82	C₁₃×#106	D₄	1	4	yes	complemented
83	C₁₃×C₄⋊C₈	—	2	2	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×#102	—	2	4	no	—
86	C₁₃×#102	—	4	2	no	—
87	C₁₃×#102	—	4	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	4	no	—
89	C₁₃×C₂²⋊C₈	—	4	2	no	—
90	C₄×C₈×C₁₃	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	1	no	—
94	#26235	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	2	no	—
96	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₃	—	2	2	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	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	4	4	no	—
107	C₂×D₄×C₁₃	—	4	4	no	—
108	C₂×D₄×C₁₃	—	4	4	no	—
109	C₂×D₄×C₁₃	—	4	4	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	—	8	1	no	—
115	C₂×D₄×C₁₃	—	8	1	no	—
116	C₂×D₄×C₁₃	—	8	2	no	—
117	C₂×D₄×C₁₃	—	8	2	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₄⋊C₄	—	8	1	no	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₁₃×C₄⋊C₄	#41	1	2	yes	—
155	C₁₃×C₂²⋊C₄	—	2	4	no	—
156	C₁₃×C₂²⋊C₄	—	4	4	no	—
157	C₁₃×C₂²⋊C₄	—	4	4	no	—
158	C₁₃×C₂²⋊C₄	—	4	4	no	—
159	C₁₃×C₂²⋊C₄	—	8	2	no	—
160	C₄²×C₁₃	—	4	4	no	—
161	C₄²×C₁₃	—	4	2	no	—
162	C₄²×C₁₃	—	4	2	no	—
163	C₄²×C₁₃	#41	1	2	yes	—
164	C₄²×C₁₃	#41	1	2	yes	—
165	C₂×#482	C₂×C₁₃	1	2	yes	complemented
166	#2541	C₂×C₁₃	1	1	yes	characteristic
167	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2034	C₂×C₁₃	1	2	yes	complemented
169	#2033	C₂×C₁₃	1	2	yes	complemented
170	#1982	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1875	C₂×C₁₃	1	2	yes	complemented
175	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	D₄×C₁₃	—	4	2	no	—
192	D₄×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	4	2	no	—
194	D₄×C₁₃	—	4	2	no	—
195	D₄×C₁₃	—	4	4	no	—
196	D₄×C₁₃	—	8	4	no	—
197	D₄×C₁₃	—	8	8	no	—
198	D₄×C₁₃	—	8	8	no	—
199	D₄×C₁₃	—	8	4	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	2	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	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	#123	1	2	yes	—
225	C₂×C₄×C₁₃	#123	1	2	yes	—
226	C₂×C₄×C₁₃	#135	1	2	yes	—
227	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	4	1	no	—
236	C₈×C₁₃	—	4	2	no	—
237	C₂×#127	—	2	1	no	—
238	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#121	C₂²×C₁₃	1	2	yes	—
240	C₂×#121	C₂²×C₁₃	1	2	yes	—
241	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#117	C₂²×C₁₃	1	2	yes	—
243	#482	—	2	8	no	—
244	C₂×#107	C₂²×C₁₃	1	2	yes	—
245	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#102	C₂²×C₁₃	1	2	yes	—
249	C₂×#102	C₂²×C₁₃	1	2	yes	—
250	C₂×#102	C₂²×C₁₃	1	2	yes	—
251	C₂×#102	C₂²×C₁₃	1	2	yes	—
252	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
253	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
255	#392	—	2	2	no	—
256	#390	—	2	1	no	—
257	#390	—	2	1	no	—
258	#388	—	2	2	no	—
259	#384	C₂²×C₁₃	1	1	yes	characteristic
260	#380	C₂²×C₁₃	1	2	yes	—
261	C₄×C₄⋊C₄	—	2	1	no	—
262	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
264	#340	C₂²×C₁₃	1	1	yes	characteristic
265	#340	C₂²×C₁₃	1	2	yes	—
266	#340	C₂²×C₁₃	1	1	yes	characteristic
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	4	2	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	8	2	no	—
275	C₂²×C₁₃	—	8	2	no	—
276	C₂²×C₁₃	—	8	2	no	—
277	C₂²×C₁₃	—	8	2	no	—
278	C₂²×C₁₃	—	8	2	no	—
279	C₂²×C₁₃	—	8	2	no	—
280	C₂²×C₁₃	—	8	2	no	—
281	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
282	C₂²×C₁₃	D₄²	1	1	yes	characteristic
283	C₂²×C₁₃	#546	1	1	yes	characteristic
284	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
285	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₂²×C₁₃	#576	1	1	yes	characteristic
287	C₂²×C₁₃	#577	1	1	yes	characteristic
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	4	2	no	—
290	C₄×C₁₃	—	4	2	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	2	no	—
293	C₄×C₁₃	—	8	2	no	—
294	C₄×C₁₃	—	8	1	no	—
295	C₄×C₁₃	#482	1	4	yes	complemented
296	C₄×C₁₃	#532	1	1	yes	characteristic
297	C₄×C₁₃	#540	1	1	yes	characteristic
298	C₄×C₁₃	#550	1	1	yes	characteristic
299	C₄×C₁₃	#559	1	1	yes	characteristic
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
305	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
306	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
307	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
309	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
310	#127	—	2	2	no	—
311	#127	—	2	2	no	—
312	#127	—	4	4	no	—
313	#121	—	2	4	no	—
314	#121	—	2	4	no	—
315	#121	—	4	2	no	—
316	#121	—	4	2	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	2	no	—
319	#117	—	2	4	no	—
320	#117	—	4	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
338	#107	—	2	4	no	—
339	#106	—	2	2	no	—
340	#106	D₄×C₁₃	1	4	yes	complemented
341	C₄⋊C₈	—	2	2	no	—
342	#102	—	2	4	no	—
343	#102	—	2	4	no	—
344	#102	—	4	2	no	—
345	#102	—	4	2	no	—
346	C₂²⋊C₈	—	2	4	no	—
347	C₂²⋊C₈	—	4	2	no	—
348	C₄×C₈	—	2	2	no	—
349	#95	—	2	2	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	C₂×C₁₃	—	8	2	no	—
353	C₂×C₁₃	—	16	2	no	—
354	C₂×C₁₃	#2445	1	1	yes	characteristic
355	C₂×C₁₃	C₂×#482	1	1	yes	characteristic
356	C₂×C₁₃	#3096	1	1	yes	characteristic
357	C₂×C₁₃	#3274	1	1	yes	characteristic
358	C₂×C₁₃	#3284	1	1	yes	characteristic
359	C₂×C₁₃	#3305	1	1	yes	characteristic
360	C₂×C₁₃	#3324	1	1	yes	characteristic
361	C₂⁴	—	2	2	no	—
362	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	8	1	no	—
381	C₂×D₄	—	8	1	no	—
382	C₂×D₄	—	8	2	no	—
383	C₂×D₄	—	8	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	8	1	no	—
418	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
419	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₄⋊C₄	C₁₃×#41	1	2	yes	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₂²⋊C₄	—	8	2	no	—
426	C₄²	—	4	4	no	—
427	C₄²	—	4	2	no	—
428	C₄²	—	4	2	no	—
429	C₄²	C₁₃×#41	1	2	yes	—
430	C₄²	C₁₃×#41	1	2	yes	—
431	C₁₃	#26235	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
447	D₄	—	4	4	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	8	4	no	—
453	D₄	—	8	8	no	—
454	D₄	—	8	8	no	—
455	D₄	—	8	4	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	C₁₃×#123	1	2	yes	—
481	C₂×C₄	C₁₃×#123	1	2	yes	—
482	C₂×C₄	C₁₃×#135	1	2	yes	—
483	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
486	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
487	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
488	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
490	C₈	—	2	2	no	—
491	C₈	—	4	1	no	—
492	C₈	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	2	no	—
507	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
508	C₂²	D₄²×C₁₃	1	1	yes	characteristic
509	C₂²	C₁₃×#546	1	1	yes	characteristic
510	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
511	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
512	C₂²	C₁₃×#576	1	1	yes	characteristic
513	C₂²	C₁₃×#577	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	8	2	no	—
520	C₄	—	8	1	no	—
521	C₄	C₁₃×#482	1	4	yes	complemented
522	C₄	C₁₃×#532	1	1	yes	characteristic
523	C₄	C₁₃×#540	1	1	yes	characteristic
524	C₄	C₁₃×#550	1	1	yes	characteristic
525	C₄	C₁₃×#559	1	1	yes	characteristic
526	C₂	—	8	2	no	—
527	C₂	—	16	2	no	—
528	C₂	C₁₃×#2445	1	1	yes	characteristic
529	C₂	C₂×C₁₃×#482	1	1	yes	characteristic
530	C₂	C₁₃×#3096	1	1	yes	characteristic
531	C₂	C₁₃×#3274	1	1	yes	characteristic
532	C₂	C₁₃×#3284	1	1	yes	characteristic
533	C₂	C₁₃×#3305	1	1	yes	characteristic
534	C₂	C₁₃×#3324	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2541	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#482	C₂	semidirect
3. C₁₃×#2354	C₂	semidirect
4. C₁₃×#2034	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#1982	C₂	semidirect
7. C₁₃×#1957	C₂	semidirect
8. C₁₃×#1954	C₂	semidirect
9. C₁₃×#1947	C₂	semidirect
10. C₁₃×#1875	C₂	semidirect
11. C₄×C₁₃×#106	C₂	semidirect
82. C₁₃×#106	D₄	semidirect
94. #26235	C₁₃	direct (N × H)
165. C₂×#482	C₂×C₁₃	semidirect
167. #2354	C₂×C₁₃	semidirect
168. #2034	C₂×C₁₃	semidirect
169. #2033	C₂×C₁₃	semidirect
170. #1982	C₂×C₁₃	semidirect
171. #1957	C₂×C₁₃	semidirect
172. #1954	C₂×C₁₃	semidirect
173. #1947	C₂×C₁₃	semidirect
174. #1875	C₂×C₁₃	semidirect
175. C₄×#106	C₂×C₁₃	semidirect
295. C₄×C₁₃	#482	semidirect
340. #106	D₄×C₁₃	semidirect
431. C₁₃	#26235	direct (N × H)
521. C₄	C₁₃×#482	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#482	2
C₁₃×#2541	2
C₁₃×#2354	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1954	2
C₁₃×#1947	2
C₁₃×#1875	2
C₄×C₁₃×#106	2
#26235	13

Subgroups — C13×#26235 #15712574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26235 #15712574