Subgroups — C₁₃×#32826 #15719165

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2861	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2067	C₂	1	2	yes	maximal
8	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2042	C₂	1	2	yes	maximal
11	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#125	—	2	1	no	—
13	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₁₃×#391	C₂²	1	1	yes	characteristic
23	C₁₃×#391	C₂²	1	1	yes	characteristic
24	C₁₃×#390	C₂²	1	1	yes	characteristic
25	C₁₃×#390	C₂²	1	1	yes	characteristic
26	C₁₃×#389	—	2	1	no	—
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#388	—	2	1	no	—
31	C₁₃×#388	—	2	1	no	—
32	C₁₃×#388	—	2	1	no	—
33	C₁₃×#388	—	2	1	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₁₃×#384	C₂²	1	1	yes	characteristic
36	C₁₃×#382	—	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	2	yes	—
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₁₃×#125	—	4	2	no	—
48	C₁₃×#125	—	4	4	no	—
49	C₁₃×#124	—	4	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	4	2	no	—
76	C₁₃×#106	—	4	2	no	—
77	C₁₃×C₄⋊C₈	—	4	2	no	—
78	C₁₃×#103	—	4	2	no	—
79	C₁₃×#103	—	4	2	no	—
80	C₁₃×#102	—	4	2	no	—
81	C₁₃×#102	—	4	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	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	#32826	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	1	no	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	4	2	no	—
123	C₁₃×C₄⋊C₄	—	4	2	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	4	2	no	—
126	C₁₃×C₄⋊C₄	—	4	2	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	—	4	4	no	—
130	C₁₃×C₂²⋊C₄	—	4	2	no	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	4	1	no	—
144	#2861	C₂×C₁₃	1	1	yes	characteristic
145	#2859	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2095	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2094	C₂×C₁₃	1	1	yes	characteristic
148	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2071	C₂×C₁₃	1	1	yes	characteristic
150	#2067	C₂×C₁₃	1	2	yes	—
151	#2066	C₂×C₁₃	1	2	yes	complemented
152	#2059	C₂×C₁₃	1	2	yes	complemented
153	#2042	C₂×C₁₃	1	2	yes	—
154	#1831	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₁₃	—	4	2	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	#135	1	2	yes	—
198	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₁₃	#137	1	2	yes	—
200	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
202	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
203	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₁₃	—	4	2	no	—
205	C₈×C₁₃	—	4	2	no	—
206	C₂×#125	—	2	1	no	—
207	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#107	C₂²×C₁₃	1	2	yes	—
210	C₂×#106	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
212	C₂×#103	C₂²×C₁₃	1	2	yes	—
213	C₂×#103	C₂²×C₁₃	1	2	yes	—
214	C₂×#102	C₂²×C₁₃	1	2	yes	—
215	C₂×#102	C₂²×C₁₃	1	2	yes	—
216	#391	C₂²×C₁₃	1	1	yes	characteristic
217	#391	C₂²×C₁₃	1	1	yes	characteristic
218	#390	C₂²×C₁₃	1	1	yes	characteristic
219	#390	C₂²×C₁₃	1	1	yes	characteristic
220	#389	—	2	1	no	—
221	#389	—	2	1	no	—
222	#389	C₂²×C₁₃	1	2	yes	—
223	#389	C₂²×C₁₃	1	2	yes	—
224	#388	—	2	1	no	—
225	#388	—	2	1	no	—
226	#388	—	2	1	no	—
227	#388	—	2	1	no	—
228	#384	C₂²×C₁₃	1	1	yes	characteristic
229	#384	C₂²×C₁₃	1	1	yes	characteristic
230	#382	—	2	1	no	—
231	C₄³	C₂²×C₁₃	1	1	yes	characteristic
232	#340	C₂²×C₁₃	1	2	yes	—
233	#340	C₂²×C₁₃	1	2	yes	—
234	#336	C₂²×C₁₃	1	2	yes	—
235	#336	C₂²×C₁₃	1	1	yes	characteristic
236	#336	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×C₁₃	—	8	1	no	—
238	C₂²×C₁₃	—	8	1	no	—
239	C₂²×C₁₃	—	8	1	no	—
240	C₂²×C₁₃	—	8	1	no	—
241	C₂²×C₁₃	—	8	1	no	—
242	C₂²×C₁₃	—	8	1	no	—
243	C₂²×C₁₃	—	8	1	no	—
244	C₂²×C₁₃	#535	1	1	yes	characteristic
245	C₂²×C₁₃	#536	1	1	yes	characteristic
246	C₂²×C₁₃	#537	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
250	C₂²×C₁₃	#575	1	1	yes	characteristic
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	2	2	no	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	—	4	1	no	—
256	C₄×C₁₃	—	4	1	no	—
257	C₄×C₁₃	—	8	1	no	—
258	C₄×C₁₃	—	8	1	no	—
259	C₄×C₁₃	—	8	1	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	#562	1	2	yes	—
263	C₄×C₁₃	#563	1	2	yes	—
264	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
267	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
268	#125	—	4	2	no	—
269	#125	—	4	4	no	—
270	#124	—	4	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
290	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
291	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
292	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	#107	—	4	2	no	—
297	#106	—	4	2	no	—
298	C₄⋊C₈	—	4	2	no	—
299	#103	—	4	2	no	—
300	#103	—	4	2	no	—
301	#102	—	4	2	no	—
302	#102	—	4	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	1	no	—
306	#95	—	2	1	no	—
307	#95	—	2	1	no	—
308	#95	—	2	1	no	—
309	C₂×C₁₃	—	16	1	no	—
310	C₂×C₁₃	#2820	1	1	yes	characteristic
311	C₂×C₁₃	#3210	1	1	yes	characteristic
312	C₂×C₁₃	#3214	1	1	yes	characteristic
313	C₂×C₁₃	#3232	1	1	yes	characteristic
314	C₂×C₁₃	#3239	1	1	yes	characteristic
315	C₂×C₁₃	#3247	1	1	yes	characteristic
316	C₂×C₁₃	#3252	1	1	yes	characteristic
317	C₂⁴	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	4	1	no	—
372	C₁₃	#32826	1	1	yes	characteristic, direct product factor, Sylow
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	C₁₃×#135	1	2	yes	—
416	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
417	C₂×C₄	C₁₃×#137	1	2	yes	—
418	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
420	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
421	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	C₁₃×#535	1	1	yes	characteristic
432	C₂²	C₁₃×#536	1	1	yes	characteristic
433	C₂²	C₁₃×#537	1	1	yes	characteristic
434	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
435	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
436	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
437	C₂²	C₁₃×#575	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	2	no	—
449	C₄	C₁₃×#562	1	2	yes	—
450	C₄	C₁₃×#563	1	2	yes	—
451	C₂	—	16	1	no	—
452	C₂	C₁₃×#2820	1	1	yes	characteristic
453	C₂	C₁₃×#3210	1	1	yes	characteristic
454	C₂	C₁₃×#3214	1	1	yes	characteristic
455	C₂	C₁₃×#3232	1	1	yes	characteristic
456	C₂	C₁₃×#3239	1	1	yes	characteristic
457	C₂	C₁₃×#3247	1	1	yes	characteristic
458	C₂	C₁₃×#3252	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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
2. C₁₃×#2859	C₂	semidirect
3. C₁₃×#2095	C₂	semidirect
5. C₁₃×#2072	C₂	semidirect
8. C₁₃×#2066	C₂	semidirect
9. C₁₃×#2059	C₂	semidirect
11. C₁₃×#1831	C₂	semidirect
88. #32826	C₁₃	direct (N × H)
145. #2859	C₂×C₁₃	semidirect
146. #2095	C₂×C₁₃	semidirect
148. #2072	C₂×C₁₃	semidirect
151. #2066	C₂×C₁₃	semidirect
152. #2059	C₂×C₁₃	semidirect
154. #1831	C₂×C₁₃	semidirect
372. C₁₃	#32826	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×#2861	2
C₁₃×#2859	2
C₁₃×#2095	2
C₁₃×#2094	2
C₁₃×#2072	2
C₁₃×#2071	2
C₁₃×#2067	2
C₁₃×#2066	2
C₁₃×#2059	2
C₁₃×#2042	2
C₁₃×#1831	2
#32826	13

Subgroups — C13×#32826 #15719165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32826 #15719165